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BIG NEWS Part II: For the first time – a mysterious notch filter found in the climate

The Solar Series: I Background   |  II: The notch filter (you are here)  |  III: The delay  |  IV: A new solar force?  |  V: Modeling the escaping heat.  |  VI: The solar climate model   |  VII — Hindcasting   | VIII — Predictions

This is the first of many posts. It is primarily about the entirely new discovery of a notch filter, which electrical engineers will immediately recognize, but few others will know. Notch filters are used in electronics to filter out a hum or noise. You will have some at home, but everyone seems to have missed the largest notch filter running on the planet.

This post is also about the broad outline of the new solar model. It’s a O-D (zero-dimensional) model. Its strength lies in its simplicity — it’s a top down approach. That solves a lot of problems the larger ambitious GCMs create — they are a bottom up approach, and effectively drown in the noise and uncertainty. This model does not even attempt to predict regional or seasonal effects at this stage. First things first — we need to figure out the main drivers of the global climate.

Here David explains why sinusoids are such powerful tools. Some of the most important graphs here are in frequencies — that’s where we non-EE’s (Electrical Engineers) will have to concentrate. Pay attention to the logarithmic scale on the bottom. 1,000 year cycles are on the left, and 1 year cycles are on the right.

There is a lot to cover. As you read, good skeptics will be thinking of criticisms and questioning assumptions. That’s all excellent, please bear in mind we have asked many of these at length already (like, is it fair to assume linearity?) and this is a short introductory article. There is a lot to discuss. We assume, but only temporarily, that the Sun’s radiation might be associated with all the warming (note I didn’t say “cause”). This assumption is used for the investigation and then dropped and tested. It parallels what CO2 driven models do — they assumed CO2 caused all the warming. They just got stuck on the “testing” step. Also, David used Fourier analysis to investigate the datasets and find the filters,  then used those filters he discovered to build a model. This two stage approach means skeptics may spot red flags that are relevant to one stage, but made irrelevant by the second stage. I’m flagging this at the start in the hope that we generate more constructive criticism.

No time? — skip to Figure 5 and 6 for the most important action! Look at the spike down at 11 years. See how it happens in all the datasets. (Figure 6 was the moment when Bob Carter sat up dead straight in his chair).

– Jo

——————————————————————————————————–

Discovering the Notch

Dr David Evans, 15 June 2014, David Evans’ Notch-Delay Solar Theory and Model Home

The carbon dioxide theory is clearly inadequate, as readers here know only all too well. So we wondered if the changes in the Sun might be causing some of the recent global warming. That is, the global warming over the last few decades, maybe back to 1800 or so.

Solar radiation and temperature

The best and most obvious solar datasets are those for total solar irradiance (TSI), or the total energy from the sun at all electromagnetic frequencies — mainly visible light, but also UV and some infrared. These datasets estimate the total energy from the Sun falling upon the plane that is at the average distance of the Earth from the Sun (1 AU, or astronomical unit). This TSI data is thus deseasonalized, so it cannot tell us anything about what is happening on time scales of less than a year or at frequencies greater than one cycle per year (this will become important later). TSI is measured in Watts per square meter (W/m2).

The temperature we are most interested in is the one for our immediate environment, the “global average surface air temperature”, namely air temperatures at or near the surface averaged across the entire planet. When we use “temperature” without qualification in these posts, we mean this temperature. “Global warming” is the rise in this temperature.

The initial aim of this project is to answer this question: If the recent global warming was associated almost entirely with solar radiation, and had no dependence on CO2, what solar model would account for it?

Let’s build that solar model

We are envisaging some sort of black box, whose input is TSI and whose output is temperature.

The climate system is approximately linear for small perturbations such as have occurred since the end of the last ice age. It is common in climate modeling to assume that the climate system is linear. The climate system is also “invariant”, which just means that its properties do not change significantly with time. So we assume that the climate system is linear and invariant, at least for the last few hundred years (and presumably as far back as the end of the last ice age).

The way to analyze a linear and invariant system is with sinusoids (aka sine waves). A sinusoid has a frequency, an amplitude, and a phase. Sinusoids are special for linear invariant systems, because:

  • If the input is a sinusoid, then the output is a sinusoid at the same frequency.
  • At each frequency, the ratio of output to input amplitudes and the difference between the output and input phases are always the same.
  • Behavior at one frequency is unaffected by what is occurring at other frequencies.

Lots of systems are linear and invariant, such as free space for electromagnetic fluctuations, which is why sinusoids and Fourier analysis are so ubiquitous in our analysis of the universe. While Fourier analysis can also be used for mere curve fitting, its true significance and power is that sinusoids are eigenfunctions of all linear invariant systems.

So let’s analyze the TSI and temperature datasets in the frequency domain. That is, we will recast them as sums of sinusoids.*

1          The Input Spectrum (TSI)

TSI has only been measured by satellites from late 1978. However the approximate numbers of sunspots have been recorded since 1610, and TSI has been reconstructed from the number of sunspots (Lean 2000). The main TSI datasets are the PMOD satellite observations from late 1978, Lean’s reconstruction from sunspots from 1610 to 2008, and the Steinhilber reconstructions from beryllium isotopes in ice cores going back 9,300 years.

The main TSI datasets are noisy and sometimes contradict one another. We did not attempt to pick a “best” empirical record, but instead tried to find the spectrum of TSI that best fits nearly all of the main TSI datasets. We only care about the amplitudes here, because the phases of the sinusoids cannot be reliably determined from the climate datasets.

Figure 1: The datasets used to estimate the TSI spectrum, from 1600.

 

The many disagreements of the TSI datasets make for a noisy combined amplitude spectrum.

 

Figure 2: The amplitude spectra of the various TSI datasets (the series of colored dots), and the smoothed curve of best fit (orange line). Larger dots have more weight in the smoothing. Note the peak around 11 years.

 

The TSI amplitude spectrum is the smooth curve in orange in Figure 2. It is basically straight over more than three orders of frequency magnitude, except for a pronounced spike around 11 years, the sharpness of which is understated by the smoothed curve.

The length of the sunspot cycle averages 11 years, though individual “cycles” vary between 8 and 14 years. So we’d expect to see stronger sinusoids around 11 years. This spectrum is about what we’d expect.

2          The Output Spectrum (Temperature)

The main temperature datasets are the satellite records since late 1978 (UAH and RSS), the surface thermometer records since 1850 or 1880 (HadCrut4, GISTEMP, and NCDC), the two comprehensive proxy time series of Christiansen and  Ljungqvist in 2012 going back to 1500 with 91 proxies and to 0 AD with 32 proxies, and the Dome C ice cores going back 9,300 years (to match the TSI data).

The main temperature datasets are noisy and sometimes contradict one another. Again we did not pick a “best” empirical record, but simply tried to find the spectrum that best fits all the main datasets.

Figure 3: The datasets used to estimate the temperature spectrum are more contradictory further back in time.

 

The temperature amplitude spectrum, the smooth orange curve in Figure 4, is essentially straight over more than three orders of frequency magnitude, with no other definite features.

 

Figure 4: The amplitude spectra of the various temperature datasets (the series of colored dots), and the smoothed curve of best fit (orange line). Larger dots have more weight in the smoothing.

 

Spot the big clue. There is no peak at 11 years!

This is unexpected, because TSI is the energy input that warms the Earth. The TSI peaks every 11 years or so, yet there is no detected corresponding peak in the temperature, even using our new low noise optimal Fourier transform!

(To put some numbers on it: TSI typically varies from the trough to the peak of a sunspot cycle by about 0.8 W/m2 out of 1361 W/m2. At the surface of the Earth, this is about 0.14 W/m2 of unreflected TSI.  If this was a long term change, the Stefan-Boltzmann equation would imply a change in radiating temperature of about 0.05°C, which would result in a change in surface temperature of about 0.1°C. The peaks only last for a year or two, so the low pass filter in the climate system would reduce the temperature peak to somewhat below 0.1°C. The error margin of the temperature records is generally about 0.1°C, but Fourier analysis will usually find repetitive bumps down to a small fraction of the error margin, maybe a tenth. However these bumps are not quite regularly spaced, so the threshold of detectability would be a bit higher. In any case, we’d expect the temperature peaks to be detectable using the data and methods we have employed, though not by a huge margin. Later in post IV of this series we propose a physical interpretation of the notch that implies a countering of the TSI warming, but of course such a countering would be very unlikely to completely cancel out the temperature effects of the TSI peak. But given that the margin for detection for the TSI peak alone is not great, it is credible that the mainly-countered TSI peaks are indeed not detectable.) This paragraph was corrected. **

This is an important clue. It’s the absence of something expected. (Like the “curious incident of the dog in the night-time”, in Silver Blaze, a Sherlock Holmes story. The clue was that the dog did nothing. The dog did not bark when the crime was being committed in the house, indicating that the dog was familiar with the criminal, which was a vital clue to their identity.)

In electronics, a filter in audio equipment that removes the hum due to mains power is called a notch filter. It removes a narrow range of frequencies, which looks like a notch on a frequency graph. Without a notch filter, the mains hum at 50 or 60 Hz would often be audible. It appears that something is removing the 11 year “solar hum” from the temperature, so we call this phenomenon “the notch”.

3          The Transfer Function

A transfer function tells how a sinusoid in the input is transferred through the system to the output. We are only concerned with amplitudes (that is, not phases), so its value at a given frequency is simply the output amplitude at that frequency divided by the input amplitude at that frequency. Dividing the orange line in Figure 4 by the orange line in Figure 2, we arrive at the empirical transfer function shown in Figure 5.

 

 

Figure 5: The amplitude of the empirical transfer function. The gray zone is a graphical device to make it easier to judge and compare locations on and between the graphs—because it is in exactly the same location in all the diagrams in this project.

 

The transfer function is fairly flat, except for the notch around 11 years, and hints of a fall off at the higher frequencies.

The notch is robust. We computed the empirical transfer function from subsets of the data, such as data before 1945 or data after 1945, and in each case the notch is clearly visible.

 

 

Figure 6: The amplitudes of the empirical transfer function when the data is restricted in the ways marked (that is, using a subset of the data used to find Figure 5). The black line and the gray zone are as in Figure 5.

 

The notch is such a prominent feature that we can verify it just by comparing the TSI to the temperature:

 

Figure 7: Solar radiation shows a strong heartbeat about every 11 years, but the temperature does not.

 

In the next post, we’ll build the solar model, starting with a notch filter.

Notch-delay solar project home page, including links to all the articles on this blog, with summaries.

 

*A technical side note: The traditional tool for estimating the spectrum of a time series (such as a climate dataset) is the discrete Fourier transform (DFT). The Fast Fourier Transform (FFT) is just a faster way of computing the DFT. Although the signals we are after are detectable using the DFT, and were initially detected using the DFT, they are not sufficiently clear and we wanted to gain more certainty in the analysis. So we developed the optimal Fourier transform (OFT) for this paper. The OFT is a new development in Fourier analysis, with greater sensitivity and frequency resolution than the DFT. It is described in the paper “The Optimal Fourier Transform (OFT)”. That paper contains examples in which the OFT does things that the DFT cannot. The OFT is used in all the analysis in this project.

The OFT is better than the DFT at estimating the exact frequencies of sinusoids in a time series, and it introduces less noise into the analysis. Like the DFT, the OFT is applied to a time series and produces an estimate of its spectrum, describing the sinusoids in the spectrum as a series of coefficients of cosines and sines. Unlike the DFT, it can analyze irregular time series (data points not equally spaced through time), it considers all frequencies when estimating the spectrum (rather than just a small pre-determined set of equally-spaced frequencies, like the DFT), it orders the spectral sinusoids by amplitude (so the lesser ones, which are probably just describing noise, can be easily discarded), it typically describes the spectrum in far fewer sinusoids than a DFT (because it stops once the sum of the spectral sinusoids is close enough to the original time series), but it is not invertible (the original time series cannot be exactly recovered from the OFT). The OFT takes much longer to compute than the DFT, because it uses multivariate function minimization to fit sums of sinusoids at variable frequencies to the time series.

 

** Original paragraph, before correction: (To put some numbers on it: TSI typically varies from the trough to the peak of a sunspot cycle by about 0.8 W/m2. If this was a long term change, the Stefan-Boltzmann equation would imply a change in radiating temperature of about 0.26°C, which would result in a change in surface temperature of about 0.5°C. Even allowing for some attenuation by a low pass filter, there ought to be a detectable temperature peaks.)

Comment: While the correction makes the margin for detection of any corresponding TSI peaks smaller, it increases the likelihood that what remains of  the peaks, after being mainly canceled by a countervailing cooling force, are undetectable.

Cite as Evans, David M.W.  “The Notch-Delay Solar Theory”, sciencespeak.com, 2014, http://sciencespeak.com/climate-nd-solar.html.

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418 comments to BIG NEWS Part II: For the first time – a mysterious notch filter found in the climate

  • #
    turnedoutnice

    This is a very important bit of work because it shows empirically that there is a mechanism in the Earth’s atmosphere which compensates for the effect of change of what the climate alchemists call ‘forcing’. By definition, that same mechanism must also reduce GHG-AGW to zero; extreme negative feedback. Yes, I am onto it, about a year now.

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    • #

      … it shows empirically that there is a mechanism in the Earth’s atmosphere …

      Why does the mechanism need to be in the atmosphere. Consider the orbit of jupiter. Over a very long time scale Inigo Jones found the average sunspot cycle length to be the same as the orbital period of Jupiter (11.862 vs 11.861 years).

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      • #
        turnedoutnice

        The mechanism has to be atmospheric because with no atmosphere, the diurnal temperature range would be far higher.

        The primary issue is how that mechanism compensates for ‘forcing’ change, e.g. to explain the ‘Faint Sun Paradox’, when insolation was 70% of today’s level.

        The secondary issue is how it copes with variation of [GHG], and the resultant diminution of ‘Climate Sensitivity’; I say it is reduced to near zero.

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        • #

          We are talking about an 11 or 11.862 year rate not a daily rate. So that is not proof.
          I would like to know if David used the TSI at 1AU(fixed average) or the the TSI at the variable earth distance.

          One mechanism could be the spectral shift from Ir to UV and back during the 11 year solar cycle which is again an external effect.

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          • #

            Siliggy TSI was at 1AU. All seasonal effects removed.

            These datasets estimate the total energy from the Sun falling upon the plane that is at the average distance of the Earth from the Sun (1 AU, or astronomical unit). This TSI data is thus deseasonalized, so it cannot tell us anything about what is happening on time scales of less than a year or at frequencies greater than one cycle per year (this will become important later).

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            • #

              Duh. I should have read that. Thanks Jo.
              This data is not very long but am getting curious about how the column 10 data would go instead of the column 5.
              http://lasp.colorado.edu/data/sorce/tsi_data/six_hourly/sorce_tsi_L3_c06h_latest.txt

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            • #
              John, who eats meat & never visits Paddington

              Jo,

              Would it be more accurate to describe the filter as a low pass filter, where temperature changes on timscales of less than ~20 years are filtered ?. A notch implies that smaller timescale changes (eg: 1 year) will pass through more easily than the the centre frequency.

              So, I’m now wondering what is the earth’s LP filter characteristic ?. It looks like > 20 years is the roll-off point looking at temperature and SSN trends.

              Last thought with a warmest hat on …
              Would CO2 changes (if real), also have a 20 year delay in the system caused by the filter ?

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              • #
                David Evans

                There is a low pass filter as well (with a break frequency or time constant around 5 years), which can be seen or perhaps imagined in the fall-off at the high frequency end. That comes in the next post:)
                The notch severely attenuates sinusoids near 11 years, but lets through unscathed those at say 1 or 2 years or 20 years.

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              • #

                Why not call it a band pass filter? Who started calling that a notch filter, and can we older scientists kick him for it?

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              • #

                Why not call it a band pass filter?

                Because it would be a band stop filter.
                A series band pass filter connected as a shunt becomes a band stop filter. The word notch indicates it is narrow bandwidth with high attenuatation at the centre frequency.

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              • #
                John, who eats meat & never visits Paddington

                Thanks David,

                I look forward to the additional posts, but I’m already curious what would cause an 11 year notch?. For a notch filter, you need a cancellation signal of the same amplitude and frequncy, but opposing phase. I’m guessing you already have ideas ? Another solar forcing, oceans currents, etc ?

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              • #
                David Evans

                Stumped us for months. Eventually figured it out, we think. Joanne eventually noticed the vital clue. Will be revealed soon…

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              • #
                Roy Hogue

                Why not call it a bandpass filter?

                Because a notch filter is a band stop filter.

                20

              • #
                the Griss

                But in electrical circuits all these filters allow the energy at particular frequencies to bypass back to ‘ground’, ie the other side of the driving potential.

                Not sure how that fits in with climate.

                That energy has to go somewhere, and my guess is it stored then gradually released into the system. Or maybe in surges like an ElNino effect.

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              • #
                John, who eats meat & never visits Paddington

                I notice that Willis E over at WUWT has spent much effort trying to find the elusive 11 year solar signal, all to no avail.

                If you guys have come up with something like a negative solar forcing at solar max which offsets the +ve TSI forcing it will annoy the pants off him:-)

                I’m guessing it’s related to the water cycle being modulated and offsetting TSI, but my guesses are generally wrong, so I’ll wait……..:-(

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              • #
                Konrad

                David,
                Through empirical experiment I have found it is possible for solar variation to be having a long term effect on climate, although it would not be great, it can account for 0.8C over 150 years, but it would not have an 11 year signal in available data sets.

                I am hoping you have an empirically provable mechanism for your hypothesis.

                I am very much hoping it does not rely on the following false assumptions -
                1. DWLWIR can slow the cooling rate of the oceans.
                2. The oceans can be treated as a “near blackbody” and their function as a selective surface ignored.
                3. The effective, not apparent, IR emissivity of water is near 1.

                I have the empirical experiments to disprove each of those climastrology claims.

                Here’s hoping ;-)

                PS. When you understand the science of selective surfaces, you can understand how UV variance below the thermocline can be cumulative. Which frequencies penetrate deepest into the oceans? Which frequencies vary the most between solar cycles?

                22

          • #
            turnedoutnice

            This is where it becomes very subtle. For example, the SW backscattered by a cloud varies as (droplet diameter)^6 and 1/(wavelength)^4, so as the UV balance changes it also affects albedo. Glider pilots get temporary blindness from this when circling convective cumulus clouds

            These aspects of the optical physics have been completely ignored, mainly because Sagan got it wrong, imagining there was just one optical process.

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            • #
              bananabender

              Sagan got it wrong because he assumed it was an optical physics problem. In fact it is mechanical engineering problem. The atmosphere acts as a piston compressing and heating the gas below it. Because the atmosphere is perfectly insulted by the vacuum of space the only heat loss is by radiation at the top of the atmosphere. The Sun merely provides enough energy to keeps the atmosphere at a more or less constant vapour pressure. The Earth would be approximately the same temperature regardless of the atmospheres composition or opacity.

              If you apply the Ideal Gas Law to any body in the solar system you will get a close approximation to the actual surface temperature. Planets with high atmospheric pressures (Venus, Jupiter, Saturn, Uranus) are hotter than expected. Planets with very low pressure atmospheres (Mercury and Mars) are cooler than expected. Earth is a special case because it is the only planet where water (the primary mechanism of heat transfer) exists in all three phases simultaneously.

              All planetary bodies in the solar system warm or cool simultaneously which shows that the actual gas composition of the atmosphere is essentially irrelevant.

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              • #
                turnedoutnice

                Agreed, but what he did, and it was unforgivable because it has poisoned the Well of Atmospheric Science for ~50 years, was to push his two-stream approximation in the direction of claiming that the surface Irradiance is a real energy flux**. He did this by overestimating SW energy input about 7x. having failed to realise most SW energy is backscattered at the top of the Venusian atmosphere. On Earth, it’s the first few 100 m of the thunder clouds.

                **Far too many otherwise competent physicists imagine that a warm body fires out ‘photons’ at the S-B rate when (1) the ‘photon’ only exists at the instant of energy conversion and (2) the warmer body in equilibrium with a cooler body emits the difference of irradiances.

                30

              • #
                NikFromNYC

                My best friend of 30 years worked for Sagan as a graduate student and was astonished at how unprofessional his vacuum apparatus was maintained so that all manner of highly toxic gases like ozone were leaking out, with air leaking in. When he simply brought it up to specification suddenly for the first time it afforded red “Mars dust,” but he didn’t get his Ph.D., not even a masters, since Carl died of brain cancer and his remaining gate keeping associates then snubbed him.

                20

          • #

            Some more theories about Jupiter and synchronisation with the sunspot cycle. In this one Timo Niroma claims the average sunspot cycle to be 11.08 years but to still synchronise even with a different period. Seems weird until read.
            At 2.2 here.
            http://personal.inet.fi/tiede/tilmari/sunspot2.html#artifact
            Also
            4.1 here.
            http://personal.inet.fi/tiede/tilmari/sunspot4.html#bascycle

            This Mexican one looks at the relationship between strength of the cycle and the also variable spot cycle period to estimate TSI during the Maunder minimum. This period is close to the synodic and sidereal periods of our moon.
            http://revistas.unam.mx/index.php/geofisica/article/viewFile/39597/36028

            00

    • #
      BillD

      If this is valid science, it needs to be published in a scientific journal, where it will be peer-reviewed and read by scientists. I know that it’s a lot of work to read the scientific literature and to write a paper (since that’s what I do as a scientist) but just posting on the internet is fairly useless.

      00

  • #
    the Griss

    hmmm.. a wide time-range lag might also have that effect.

    sort of like using a compressor/limiter/exciter combination to maintain an even level of sound.

    (I like this audio analogy…. but give me analog any day, vinyl and toobs ;-) )

    the peaks would then gradually build “volume” without taking out the eardrums.

    Then gradually ease of as inputs are reduced.

    Now I wonder what wet substance might do that?

    100

    • #
      turnedoutnice

      Yup: the water cycle is involved. More at a future date……..

      70

    • #
      David, UK

      @the Gross: Did you mean to say compressor/limiter/EXPANDER? An exciter would add beautiful but spurious distortions in the data. Great for audio engineering, not so great for data analysis!

      (Oh, and all these things existed decades before digital audio took off.) :)

      50

      • #
        the Griss

        Yep. expander.. (it was getting late for me last night)

        And I know they existed.. I’m old school audio.

        50

  • #

    …a wide time-range lag might also have that effect…
    Nope They took that into account.
    “Even allowing for some attenuation by a low pass filter, there ought to be a detectable temperature peaks.)”
    If you want an audio effect look here.
    http://www.esa.int/Our_Activities/Space_Science/Moving_to_the_rhythm_of_the_Sun/(print)

    60

    • #
      the Griss

      I’m more thinking of a storage device that gains energy, then releases it slowly.. A sort of capacitor.

      Somewhat different from a low pass filter.

      50

      • #

        You have described a classic RC low pass filter.

        40

        • #
          the Griss

          My electronics is rather rusty.. :-)

          I’m trying to think how it would function.

          A circuit where the buffering is enough to erase any peaks, but not actually lose the energy.

          40

        • #
          the Griss

          While I can see the standard RC filter as you suggest.. this seems to be a bit more complex.

          I guess we will see in part III :-)

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          • #

            True it is more complex in that there could be at least a different equivalent input and output resistance. More likely there are multiple paths, I suspect the effect is external because the atmosphere is unlikely to have a strong reactance to notch with due to the multiple damping paths.

            40

            • #
              the Griss

              Oceans ?

              60

            • #
              the Griss

              Either way, while electronic circuitry is a reasonable analogy, there are probably things going on that would be very difficult to describe using electronics only.

              Maybe a new type of “fuzzy” electronics :-)

              51

              • #

                I often get to see it after it has gone fuzzy. I once had a car radio that evolved by chance into a good lightening detector. It would quieten down suddenly if there was a nearby strike and come back very slowly. I left it like that and miss it now the van it was in has been replaced.

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              • #

                Siliggy just reminded me of an event where a bolt of lightening every few minutes, seen some km away over Roebuck Bay caused a fisheries research officer next to me to drop the stainless steel tool he was using to remove fish’ otoliths, due to a small electric shock. He was wearing rubber boots whilst I stood next to him barefeet on a wet floor and felt nothing. We were working on the same stainless steel bench. The tool dropped almost instantly each flash was seen. He gave up after a few zaps!
                Never been able to explain it.

                40

              • #

                Tom I suspect you narrowly escaped being hit by the big one. Also think he was building up a charge while being insulated. The shock would have been like the static zap you feel when touching a door knob after building a charge. Your bare feet stopped you from developing a charge. His discharge would have been simultaneous with the big one because he and the spanner were an antenna receiving it and conducting it through a narrow patch of skin to the spanner compared to your broad surface of two feet.

                A mate of mine was terminating coax in the radio hut on a hill when a cloud blew through the tower. The next coax inline for the job began to arc over from inner to sheild with loud bright cracks. He was white as a ghost for the rest of the day.

                50

              • #

                Siliggy,

                AGC overload/long time constant. i.e. a missing leak on the AGC capacitor.

                20

              • #

                MSimon. Yes that could well be it as a big pulse has all frequencies covered and strong. It could also have been a front end biasing dry joint leaving things in a precarious but working state. It came back with a little poppy squeel and the AGC seemed to work well otherwise.

                Speaking of AGC could Davids notch be an AGC style negative feedback on the front end? Like a synchronous decrease in refraction. Such that less light makes it in during the early morning and late afternoon when it is far from 90 degrees entry angle.
                See fig 4 here.
                http://www.philiplaven.com/p20.html

                Most people would assume that the refractive index of water is known to a high degree of accuracy.

                00

              • #
                TedM

                Maybe some inductance and hysteresis?

                00

      • #
        Konrad

        I have one in stock. The brand is “Ocean”. I believe it will suit your needs ;-)

        10

  • #
    King Geo

    This breakthrough research by Dr David (the electrical engineer) is great but a bit hard for us mathematically ignorant geos to grasp. I have faith because I know from my geological knowledge that “non-anthropogenic effects” e.g. solar activity are the main driver of climate on planet Earth, not CO2 emissions by Homo Sapiens – to myself it so “bleeding obvious”. This obsession with CAGW has to stop – it is causing “Economic Mayhem” globally e.g the EU & now the USA is following suit. The fast tracking to “hopelessly uneconomic Renewables” can only result in one outcome – a Global Recession of incalculable misery, especially as planet Earth is heading into the next “Grand Minimum” – and from what I gather we will be lucky to see another “Multi-decadel Warming Cycle” until the late 2000′s, yes another 80 years +. The “Warmists” will be vilified well before then, hopefully the sooner the better.

    390

    • #
      the Griss

      “The “Warmists” will be vilified well before then”

      Just send them to Siberia. ! :-)

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      • #
        King Geo

        Siberia? I think the UK will suffice – once the next Grand Minimum [GM] takes full hold, the “vilified Warmists” should be encouraged to pitch tents next to their beloved “giant wind turbines”. They should keep them warm during the next LIA shouldn’t they? But given the limitations of “wind power” in likely GM harsh arctic-type Winter weather conditions, the “vilified Warmists” will probably meet the same fate as Jack Torrance (played brilliantly by Jack Nicholson) who was found frozen solid in a snow bound maze outside a U.S. Mountain Resort – this happened at the end of Stanley Kubrick’s scary Stephen King horror movie “The Shining” (1980). The actual filming occurred at Timberline Lodge, Mt Hood, Oregon.

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        • #
          the Griss

          “I think the UK will suffice –”

          Hey.. skating on the Thames? too much fun to be had !!

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          John Of Cloverdale WA

          “Warmists” should be encouraged to pitch tents next to their beloved “giant wind turbines”.
          What and be covered with dead birds and bats. How cruel, you nasty fascist and Abbott lover.
          :-)

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            BruceC

            OT, but in response to John’s comment above, I think they would move due to Wind Turbine Noise before dead birds and bats start dropping on them. Australia’s STOP THESE THINGS blog has some great posts on the wind industry in Australia (and world-wide) and the shenanigans that goes on that you never read about in the MSM or hear on the ABC (or anywhere else for that matter).

            http://stopthesethings.com/

            Highly recommended for those that live near wind farms or know of friends or families that do. TonyfromOz may also find the site of interest.

            Regarding noise levels, see this post here with videos of turbines in action; http://stopthesethings.com/2014/05/17/wind-turbine-noise-a-psychopaths-symphony/

            It also seems as if the SA EPA has taken lessons from the worlds surface temp stations as far as positioning goes for recording data for studies. According to the SA EPA’s own guide-lines, recording devices (noise loggers)

            “should be located away from trees and “at least 5 metres from any reflecting surface (other than the ground)”.

            See below for locations of said noise loggers in the EPA’s latest study at Waterloo (SA);
            http://stopthesethings.com/2014/02/12/prof-colin-hansen-hammers-sa-epas-waterloo-noise-wash/

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      peter c

      King Geo, Your Highness,

      I also will follow this and try my hardest to understand.
      At the end of the day the Ordinary interested person has to follow the argument.

      The graphs are helpful.

      One interesting point is the graph of Total Solar Irradiance Data Sets (graph 1.). Before 1900 there was poor agreement between the data sets. After 1900 there is good agreement in phase (ie they all go up and down together) but poor agreement about the amplitude. That seems to me to be an important point. Do we actually know what the TOTAL SOLAR IRRADIANCE actually is?

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        David Evans

        Peter,

        The TSI data is a bit poor. Prior to the satellites from late 1978 it mainly comes from counts of sunspots. This is poor in two ways.

        First the standards of what “counts” as a sunspot have changed over the centuries in ways that cannot be undone.

        Second, the Lean 2000 dataset back to 1610 that we rely on mainly is a reconstruction — meaning she examined the way sunspots varied from 1979 to 2000 and the way measured TSI varied during the same period, then constructed a model, then applied that model to the sunspot numbers back to 1610 to estimate TSI. It’s probably roughly correct.

        The good news however is that the data analysis like above, and the solar model, both work pretty much the same on the sunspot numbers themselves, or the f10.7 data back to 1948 (a good proxy for TSI), or the Lean reconstruction of TSI. In broad terms, it is all pretty robust. However we really need better TSI data to make the model work better; as we shall see soon it shows hints of being *really* good, but sloppy data may be holding it back.

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          Peter C

          Thanks David,

          One small thing. In section 2. The Output Spectrum, paragraph two you mention that the TSi data sets are noisy. II think you meant that the Temperature data sets are noisy

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      blackadderthe4th

      @King Geo
      June 15, 2014

      ‘not CO2 emissions by Homo Sapiens’

      AGU, global warming and co2, with Richard Alley.

      ‘we should teach…the broad history of the globe’s climate…when we do that co2 keeps inserting itself everywhere we look, if you leave co2 out nothing makes sense, if you put co2 in a whole lot of it makes sense and then you can put the other pieces in the puzzle and make it work. So what we are going to do is wander through the history of the Earth’s climate and see how co2 is the only explanation for a lot of what happened…we are going to walk you through 4.6 billion years of history all the way to the present, we are going to start at the beginning and see where we end up’

      http://www.youtube.com/watch?v=RNPLjx5JSUI

      Edited from, under fair usage policy.

      http://www.agu.org/meetings/fm09/lectures/lecture_videos/A23A.shtml

      http://www.geosc.psu.edu/academic-faculty/alley-richard

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        Bob Cormack

        if you leave co2 out nothing makes sense

        Truly fascinating, Blackadder; Does Richard Alley happen to say how it is that CO2 is the controlling factor when it consistently lags temperature over the last 400K years? (Perhaps Alley invokes ‘magic’?)
        (Try to actually present an argument, rather than just Youtube links.)

        Having subjected myself to a couple of Alley’s videos, I don’t expect any actual logic or reason beyond what is required to promote his propaganda to an uncritical audience.

        Perhaps you have noticed how David’s model “makes sense” (i.e., fits the data) while “leaving CO2 out”. How do you explain that? (However you try, it directly contradicts Alley’s statement above, hence proving him wrong.)

        Does the fact that the “All CO2 all the time” models have shown no predictive skill give you pause? What does this say for the correctness of the models? When people who actually know how to do scientific forecasting (as opposed to “climate scientists”, who seem to be rank amateurs who can’t even research the subject) test climate models, they find that the usual “time series” models (i.e., “no physics” models) do significantly better than the GCMs, which are supposedly based on the physics.

        The AGW “crisis” is strictly a predicted crisis — there is no dangerous increase of temperature, sea level, storms, etc. happening now. The models used to claim this “future crisis” have been shown to have no significant predictive skill.

        When are you going to wake up and quit supporting this nonsense?

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          Heywood

          Bob, BA4 is just fishing for views on his YouTube channel. Don’t expect too much logic or sense.

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    vic g gallus

    In response to Philip’s continually denial of the pause, I graphed all the possible results of linear regression for the past 10 years and the past 15 years for HadCRUT3. The x axis shows the date of the final month. The purpose was to stop him from cherry picking dates but I noticed something unusual about the 10 year plot. It shows a period of about 8-9 years rather than 11, but only after 1940. While the sunspot cycles should be distinctive, you need to remember the quality of the data is a bit suspect.

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      the Griss

      “the quality of the data is a bit suspect”

      Gees, ya think ? :-)

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      the Griss

      “but only after 1940″

      You have to remember just how stuffed up the data is from 1940-1979.

      With all the cooling adjustments required to get rid of the 1930-40′s peak and create the trend, I reckon you would be lucky to find anything in that mess.

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    Manfred

    Am I right in thinking that the atmosphere is akin to a massive spongy energy transducer, attenuating the energy of the TSI?

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      Yonniestone

      Maybe a transducer in the form of atmospheric water vapour that combines or involves electromagnetic, acoustic and thermal energy conversions?

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        bobl

        The Spongy Transducer Of Radiant Motion , STORM

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          Yonniestone

          So we’re getting into acronyms already eh?

          STORM is good but I did wonder if David had a name in mind or maybe already has?

          I’m sure he’ll get plenty of good suggestions here. :)

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    mmxx

    As a five year tertiary qualified scientist with much subsequent experience, I broadly follow Dr Evans’ concepts and accept that his is not my specific field of expertise.

    I will follow with interest all future information he provides as well as critiques by others with more expertise than mine in this scientific subject area.

    Since this week-end’s launch of this fascinating initiative, I have gained much encouragement from David’s/Jo’s commitment to openly expose his work to the public via the internet and, especially, his declared willingness to acknowledge any failures of his hypotheses and model outputs if and when such may be demonstrated by empirical evidence or open/peer assessment.

    This last-mentioned approach alone is to be lauded. It is so refreshingly contrary to the self-serving peer review culture that now pervades contemporary climate science.

    It also challenges the attitudes of the myriad bands of camp followers who unquestionably adhere to para-religious and or political belief systems that human-made climate change imminently threatens to cause global catastrophic disaster.

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    A brief comment on the MFT: this is used in the preparation of tide tables which are based on a MFT of experimental data with frequencies at multiples of the underlying solar and lunar frequencies.

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    And the OFT looks a bit like SVD? These alternatives to the FFT are heavily used in modern NMR, where irregular sampling has become trendy again.

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      David Evans

      Not sure about SVD. However it wouldn’t surprise me if the MFT and OFT had been basically developed before. I looked around a bit but could not find anything like I wanted, so I developed it myself. Found a couple of methods for exactly finding a single frequency, but not tens at once. Have never seen the suprod functions either, but I expect someone has done those before — they are quite useful.

      Tim Channon at TallBloke’s climate blog has something along the same lines, but rolled it himself and hasn’t published it. It is aimed more at finding a few cycles in climate data, rather than computing transfer functions.

      The essential problem the OFT and MFT solve is moving off the predetermined set of orthogonal frequencies used by the DFT, which is necessary for the climate datasets where there are relatively few cycles of interest in the data. The irregular sampling then basically comes for free.

      Anyway I got the OFT to do exactly the task required here, and am pleased with how well it works. Wait ’til you see the spreadsheet, lovely graphs and curve fitting with the OFT :)

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    Jim Simpson

    Many thanks David for what has clearly been a huge, dedicated, albeit unfunded, effort on your part toward the progress and knowledge surrounding climate science.

    Whether you’re “Notch Filter” hypothesis is proven more accurate & reliable than the UN IPCC models (shouldn’t be hard!) remains to be seen. I certainly hope so for your sake but more importantly, for the benefit of climate science.

    Unlike others, you’re transparency is a credit to you, Joanne & others who have contributed. That you can expect no shortage of critical analysis is inevitable. After all that’s how real science should work!

    Those of us who lack to necessary maths & scientific background will watch with great interest. Thanks again!

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      Is the Notch filter useful to predict temperature on Earth? Seems to be. It gets tested… keep watching this space. ;-)

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        the Griss

        Careful.. Is there proof that the notch filter actually comes into action if there is no solar peak ?

        Or does it only act to dampen the major solar peaks.?

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        Rereke Whakaaro

        I think it is safe to assume that the answers to your two questions are, “Perhaps” and “Maybe”, but not necessarily in that order.

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        J Martin

        Excellent. Predictions / projections are what we want, otherwise such works are pointless. Too many people produce models that mimic past temperatures but these are essentially valueless unless they go on to project future temperatures. So I am glad to hear that David’s model is going to do that. The ultimate test.

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          David Evans

          Three things that make this theory stand out:

          1. It’s quantifiable, with a model that hindcasts and predicts. Not just a concept with handwaving or a rough one-off computation.

          2. It’s got physical interpretations for all the parts. Btw, Joanne found the interpretation for the notch filter, after months while we looked in all the wrong places. Obvious in retrospect, so you’ll wonder what took us so long when you hear what it is, but if you don’t know where to look it is hard… So this is a physical model, not just curve fitting or an unexplained correlation.

          3. It comes with a prediction and a falsifiability condition. If it fails, we chuck it away. (If it succeeds, kiss AGW goodbye.) As Bob Carter says, science is about testable hypotheses.

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        Annie

        Sorry Joanne …I accident knocked slightly to the side of the thumb up…I definitely did not mean a thumb down. A bit easy to make a mistake on a mobile ‘phone screen, darn it!

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        Roy Hogue

        Is the Notch filter useful to predict temperature on Earth? Seems to be. It gets tested… keep watching this space.

        Jo,

        I’ve been watching this “space” for years. You don’t really think I’d quit now with all this excitement going on, do you? ;-)

        You do know how to tease for sure though. I’d say not hype but dishing it out like the nightly news — even the best on the Fox News Channel do it these days. Only you don’t break for commercials — thankfully.

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          PhilJourdan

          I’ve been watching this “space” for years. You don’t really think I’d quit now with all this excitement going on, do you?

          Ditto! But thanks Jo for the heads up!

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    bananabender

    The Sun does not heat the atmosphere directly. It heats the ocean surface causing evaporation. This water vapour condenses in the upper atmosphere releasing latent heat. This latent heat warms the atmosphere primarily by conduction.

    The current atmospheric temperature actually measures historical (hundreds to thousands of years ago) solar activity. Ice core evidence suggest that the atmosphere CO2 levels represent the warming due to the MWP. [This is because the oceans and upper few metres of the crust combine to act as a massive heat sink (or capacitor) that stores energy and slowly releases it to the atmosphere (like a hot bath heats a cold bathroom for many hours after the water is poured).]

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      Bananabender, Seems like you are not engineer unless you made a typing mistake. It is convection not conduction. The latter occurs in solids and can be mimiced by electrical circuits (thermal conductivity is similar to electrical conductivity, temperature difference is similarities to electrical potential difference)
      I suggest you look up the Prandtl number or the Rayleigh number if you want to learn more.
      I hope that David will look at using some dimensionless numbers in his assessment.

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        bananabender

        Sorry I meant convection not conduction.

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          cohenite

          Nonetheless a good point about yesterday’s solar heating today. Trenberth of all people wrote a paper on ocean based lags on temperature in 2001:

          http://www.cgd.ucar.edu/cas/papers/2000JD000298.pdf

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          bananabender June 15, 2014 at 11:53 pm

          “Sorry I meant convection not conduction.”

          Sorry, Both. Convection,advection or forced, gets the aqueous vapour molecules to the colder atmosphere for condensation, Condensation releases 2500 J/gm as sensible heat via conduction to all air molecules (thermalisation). Both vapor and drizzle drops in clouds radiate that sensible heat/(cloud temperature) to cold space as entropy, never to return!

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    the Griss

    I think it is good to get this in bite size pieces.

    Lets each bit be munched upon by all and sundry for a while.

    Will be interesting to see if any knowledgeable alarmistas arrive.. ie. someone else apart from the regular trolls.

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      Roy Hogue

      So far there’s not much an alarmist could disagree with, Griss, unless they want to pick apart the math in David’s OFT. The next chapter should be meatier for them to contemplate. And I’m sure they won’t stay away any longer than it takes to find some criticism.

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    Rohan

    David, it’s been a while since I’ve used the maths involved, but I’m assuming you’ve used Fourier transforms.

    The reason I ask is that figure 5 looks a little like the damping response to a step change in a second order control loop. Especially at the 11 year mark, which makes sense with the sunspot activity being the step change.

    I would be interested to see that response after puting the data through a 2nd order feedback loop using Laplace transfers instead of Fourier. If that produces something resembling a true step change response in a second order feedback loop, then push that through a frequency analysis and plot it on a Bode diagram. If you get a distinct response at 11 years, you will see a shoulder to the plot. What this means in terms of climate change, I’ve no idea. But you may have already done this and will bring this up with part 2.

    Incidentally if Laplace transfers result in a true 2nd order system response, then it would be interesting to use root locus diagrams of that Laplace transfer. Mooving the transfer into the argand plane, might show that the environment is “in control” or “unstable”. If it’s in control, even if you don’t known what the control parameters are, it shows that the system is not catastrophically unstable. The earth is therefore not doomed.

    A good reference place to start is Process Dynamics and Control by Seborg, Edgar and Mellichamp published by John Wiley and Son.

    If I’ve put you in the right direction and you win the Nobel Prize for physics, remember the little people…

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      Rereke Whakaaro

      There is always somebody who has to introduce a “Plot Spoiler”. It ruins the suspense for the rest of us.

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      David Evans

      I used a complex frequency plane (argand diagram) to design and parametrize the notch filter in the model, with two poles and two zeroes. It’s in an Appendix in the main paper, ‘cos no one in climate world knows that stuff. It reproduces the notch filter and the empirical transfer function above (Fig 5) quite well, which is all that matters I suppose.

      Relax everybody, none of that stuff in the blog write up. There aren’t even any equations in the blog write up, just concepts and diagrams.

      The climate variables run basically forever forward and back in time at roughly the same levels, implying no exponential growth or decay in the longer term, so Fourier analysis is adequate. No need for Laplace transform as far as I can see.

      If you know DSP or filters, everything I am going to do is pretty simple. I am amazed that it hasn’t been done before, but I suppose it’s always easier in retrospect, and it took me a long while ad a lot of perserverance to find the notch.

      I was expecting to find just a low pass filter, and when I saw something messy like above (it was initially just a jumble of dots, no smooth orange or black lines in the frequency space, but those dots definitely didn’t make a low pass filter) I initially gave up because it wasn’t a low pass filter. No way. Thought the data was poor. David Stockwell and I looked a the frequency domain data, and it was fuzzy at that stage because we were using the DFT and no smoothed lines of best fit in the frequency domain except the straight ones expected for a low pass filter. But we definitely were not seeing a low pass filter.

      Then there was this massive aha moment when I realized that the best data points (low frequency, from satellite data) were the worst “outliers” from the expected low pass filter transfer function — and they were very low on the diagram, where the notch is now nicely identified by a black line. The data was trying to tell me there was a notch, and it was right at 11 years. Bingo! The project began.

      Btw, for a while we though the notching might arise from two second order control systems interacting in the atmosphere. But 11 years is a pretty big clue, and proved more fruitful…

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        Joe

        David, you say that the climate variables run basically forever back in time, but is the Fourier analysis based on a 400 year window in time, and that ‘window’ of course will add artifacts in the frequency spectrum would it not? The graphs show changes in TSI and Temp and this measurement of ‘change’ is by nature a ‘high pass’ filtering of the data itself. When the time window dates back to just 400 years, how valid is it to then refer to the low frequency spectral results of the transform below 1/400 cycles per year as being ‘fairly flat’, isn’t this end of the spectrum going to tend toward being flat as a consequence of the time ‘window’ of the data with any cycles beyond 400 years being filtered out? So the transform of that time window (pulse) that ‘colours’ the spectral result would be relevant too? Where you have the spectrum for the long and short term data sets on the same graph, would they not effectively have different spectral colourations (especially at the low frequencies) because they have different filters (windows) in the time domain?

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          David Evans

          That the climate variables run forever without becoming infinitely large or infinitesimal indicates that the Fourier transform is appropriate and sufficient (otherwise, the Laplace transform would be called for).

          There is no windowing or filtering of the data. That would only add noise to the signal. Moreover, because the OFT is free to fit any frequency, there is no inbuilt assumption of a repeating time series, as with the DFT. Thus, the treatment here with the OFT is “low noise”, carefully making no assumptions or adding any artifacts into the analysis.

          We are of course limited to the amount of data in the time series. The frequencies of interest only run for a few cycles in some datasets. For example, UAH started in Dec 1978, 35 years ago, so only has room for 3+ solar “cycles”. The longer datasets have more repetitions, but are of lower resolution or quality. The longest datasets in use were the ice cores, going back about 9,000 years.

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    graphicconception

    I must declare an interest here, I trained as an electrical engineer.

    When I first discovered the antipodean climate community and realising that we lived inside a large piece of rotating machinery I did wonder why Dr Evans was not pursuing the Fourier option. He was obviously well-qualified to do so. It seems that omission has now been rectified.

    I also think that the warmies ought to get a better grip on feedback. The touchie-feelies have now realised that positive feedback is not always a good thing – which is progress. When they work out that it can also be frequency dependent and that a body of work on the subject already exists then further progress will have been made. Electrical engineers could help with that.

    I am also a Sherlock Holmes fan and feel that I should point out that the dog that did not bark was in Silver Blaze.

    The introduction about linear time-invariant systems and about sine waves coming out just as they went in – apart from amplitude and phase changes – exactly mimics a short course I gave on time series analysis in 1985. It took me right back.

    I will follow your posts with interest.

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      de

      Silver Blaze! You are right, my mistake. http://en.wikipedia.org/wiki/Silver_Blaze.
      Thank you, will change that immediately.

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      Yonniestone

      Yes but the Hound of the Baskervilles sounded better and sometimes it’s ok to use a bit of hype. :)

      I’ll be watching with great interest as well.

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      David Evans

      I didn’t think the Fourier option applicable to climate. I noticed guys like Tim Channon at Tallbloke’s using it to find cycles, so they seemed to have that covered quite competently.

      Then David Stockwell talked me into looking for a low pass filter, in October 2012. He had done some initial analysis that showed there was a low pass filter in the solar signal, so I thought I would poke around and try to find the transfer function. Found the notch instead, and that turned out to be the key, as we shall see…

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        Roy Hogue

        I didn’t think the Fourier option applicable to climate.

        I’m not sure why you would think that. Fourier invented the thing because he thought his data was cyclic and needed a way to analyze it and see what was really going on. Maybe I’m missing something.

        ————————————————

        Fourier, by the way, was in the social sciences. So we owe at least one social science practitioner for this work in spite of how low some have sunk recently.

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          Yonniestone

          That would be wicked irony indeed if any facet of the social sciences helps to rectify the social and scientific injustice foisted upon the population by charlatans misrepresenting Fourier’s work in the first place.

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          Roy, I would not call Fourier a social scientist, see this http://www.britannica.com/EBchecked/topic/215097/Joseph-Baron-Fourier. He was a mathematician who carried out experiments. He developed the theory of heat transfer by conduction. He knew about radiation and Stefan (of S-B equation fame) used his experimental data (of heat transfer in a vacuum) to develop his equation. In fact Fourier probably knew more about heat transfer than any so-called climate scientist. He put in treatise “Baron Fourier: On the temperature of the Globe and the Planetary Spaces” the following “The heat of the earth is derived from three sources, which should first be distinctly mentioned.
          1. The earth is heated by the solar rays; the unequal distribution of which causes diversities of climate.” Maybe David Evans has read it.
          Look at this statement “The interposition of the air very much modifies the effects of the heat upon the surface of the globe.” (this refers to clouds)
          You can find Fourier’s treatise here http://tallbloke.wordpress.com/2012/01/20/baron-fourier-on-the-temperature-of-the-globeand-the-planetary-spaces/#more-4418

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            Roy Hogue

            Yes, he was a mathematician. But he was working in the social sciences according to research I did in 1997. I probably still have at least one of the books I bought on the subject of Fourier stashed away somewhere.

            In any case, I was much more interested in learning how to deploy the FFT at the time and not much interested in his bio.

            In the world of his day, without computers and without the fast version of the algorithm it must have been very frustratingly slow to get anywhere.

            Today with the FFT I can do 16,384 point transforms in a fraction of a second. It takes longer to collect the data.

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    R. Gates

    With the exception of large volcanic eruptions, the biggest driver of tropospheric temperatures on less than decadal average timescales is ENSO. That’s because sensible and latent heat flux from the ocean to the atmosphere accounts for more than half of the energy in the atmosphere. Failure to account for this key role of ocean to atmosphere energy flux will doom any climate model immediately.

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      David Evans

      The new solar model shows some skill in predicting ENSO. There is hope that with better TSI data it will do even better — there are signs of that, like when we drive it using PMOD satellite data only. Has to really, because ENSO predicts global surface air temp about 6 months in advance. See the post after next :)

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        R. Gates

        The irregularity of the ENSO cycle is indicative of a deterministic chaotic system with multiple variables. That solar is one of those, seems logical. But there are clouds, volcanic aerosols, sea ice, winds, ocean currents, ocean heat content, greenhouse gas concentrations, etc.

        I look forward to your further posts.

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          the Griss

          Just an inkling, but I just noticed that the last few ElNinos all look to have been somewhere on the upward arm of the sunspot count number.

          Relevant ?? ? or not ! ;-)

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      PhilJourdan

      Um, no R. Gates. ENSO does not heat the planet. It is the pot that holds the water – you still need the energy applied to boil the water.

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    When you apply your new solar model to the Earth’s climate, you need to fix the black body model for how solar energy really injects into Earth’s atmosphere, land and oceans and how energy radiates back out. See here.

    The problem with a black body Earth is the uniform surface assumption. Incoming radiation is not hitting the spherical surface equally as in the black body assumption. It is coming in as a point source on a single vector. Radiation out is on the entire sphere.

    And both incoming energy on the vector and outgoing energy on the sphere are also filtered by ever changing cloud cover.

    This is critical in modeling Earth’s response to TSI and radiative outflow

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      bananabender

      The Earth isn’t a theoretical black body that emits energy only at the surface. It is a solid sphere that radiates energy from all points within it’s mass.

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        The radiation method to space is at “surface”, but I do not disagree with your point. My point is the surface area through which it can lose and energy verses gains solar energy. And while it radiates across the entire sphere’s surface, it only warms on one hemisphere with only a small area getting 100% of solar energy given angle of incedence -(before we even deal with clouds)

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        BTW, the reason I agree with you is because no one seems to include the ginormous (engineering term) heat source under the thin crust of this planet.

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    BTW, in Section 2 you write the “TSI” data sets are noisy, I think you meant the “temperature data” sets.

    Can’t wait for the next installment!

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      J Knowles

      One instalment per week means I might just be able to assimilate this one as well as eat, sleep and earn a living.

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      • #

        No rush – I would rather see it done right.

        And great job here. I wish my math skills were still fresh. My hypothesis is the energy balance for the Earth is way out of wack, and there will be a missing heat energy that can explain why the Earth is not as cold as it should be. The Black Body model produces a Earth too warm (275° K). When adjusted by lower input I think it will drop this number way down. And then there will be a gap that GHG cannot explain (as is now the conventional wisdom (CW)). That’s step one of my theory – step two is identifying the source of the missing heat to get the temp back up to what we see.

        Anyway – good luck. The ‘Net is a tough and brutal place and by shaking the apple cart of CW you will get all types commenting here.

        Cheers, AJStrata

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    NikFromNYC

    Thinking out loud….

    You have two regular plots:

    (A) Temperature that rises throughout the last 350 years most conveniently embodied in the Central England thermometer record that serves as a near perfect proxy for the global average temperature, and there is some pseudo-cycles in it and lots of noise or chaos.

    (B) Total Solar Irradiance that varies regularly in 11 year spikes and varies also a bit in spike/valley height in a long term curving meander.

    So how is this model different from each spike merely bumping the temperature up a bit each time, as if the planet stores extra heat well?

    Or do you get the little bumps of the temperature record also correlated? But if so, how parametrized is it as mere wiggle matching “transfer function”?

    Can the same transfer function be used to correlate any regular plot to temperature, or only an 11 year one?

    What is the strongest argument, I wonder? So far I don’t see one. It looks like various snippets of the temperature records all spit out an 11 year result?

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      bananabender

      What is the strongest argument, I wonder? So far I don’t see one. It looks like various snippets of the temperature records all spit out an 11 year result?

      Sounds like the Pacific Decadal Oscillation has been rediscovered.

      http://jisao.washington.edu/pdo/

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      David Evans

      The CET has different spectral properties than some other datasets, so I am a little suspicious of how good a proxy it is. It is only one location. I used it as part of the composite temperature up to 1880.

      Yes the planet does store heat — that’s the low pass filter we will be visiting in the next blog post. But the low pass filter has a time constant of about 5 years, indicating that the planet doesn’t store that extra heat for more than a few years. Soon radiates off to space, mostly gone after a decade.

      I expected to see little bumps in the temperature record corresponding to the TSI peaks. If you are sloppy with your Fourier analysis you can sometimes think you see them, but if you get hard nosed about it and try to prove they exist they disappear. Hence the notch. Btw they no doubt do exist, they are just below the temperature record’s resolution, i.e. tiny.

      There is a lot more to come. This is the start of a long chain.

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        Andrew McRae

        That 5 year time constant was part of an approach which I tried but abandoned.
        I found the old paper on determining the heat capacity of the earth by Stephen Schwartz where he finds the earth’s temperature reacts to a heat spike according to a roughly 5 to 7 year e-folding decay curve. I thought I could use this for “cooling” the SSN integral to make a temperature indicator, in a similar manner to the way Dan Pangburn used 1/T^4 radiative cooling on the SSN integral. Well I tried it and with a bit of 63-year PDO mixed in the darn thing almost worked. However the way it predicted a major bump in 1965 that never happened, and predicted a downturn in the last 15 years that hasn’t actually happened, all led me to dump it.

        Perhaps the 5 year e-folding response is true of the earth, but I couldn’t personally see how it had predictive value.
        Will 5-year folding be yet another chapter in the Big News saga?

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        bobl

        Can’t wait David, just a little miffed you didn’t send me a copy after our exchanges about feedback last year. I have a couple of questions so far. Firstly you state the climate system is linear and invariate, last year in our discussion you refuted that, implying that feedback can’t be implied to work as in a linear system. My view is still that for small pertubations, the climate system can be considered to be linear (Ie climate sensitivity can be assumed to be constant) even though for large pertubations it is not. Has your view changed on that?

        Secondly I think you should better acknowledge, that in arriving at the transfer function you are implicity accepting that TSI and temperature are related. At this point that’s a key element of your hypothesis, you implied that in the early part of the text but I think it would help to emphasise it later.

        Eg.
        Spot the big clue. There is no peak at 11 years!
        This is unexpected, because TSI is the energy input that warms the Earth. The TSI peaks every 11 years or so, yet there is no detected corresponding peak in the temperature, even using our new low noise optimal Fourier

        This means that either the assumption that TSI drives temperature is wrong, that there is considerable negative feedback or that a secondary control system such as Willis E climate thermostat is acting. Mind you the climate thermostat would be an explanation for the notch, rather than refuting it, it would confirm it.

        Then move on to show why your interpretation is valid. – just an idea to avoid to much smoke and mirror refutation. Always good to acknowledge alternate interpretations. I think this is especially important since mainstream climate science would emphasise the TSI does not drive surface temperature explantion. They would say the black box is in the wrong place

        Other than those minor quibbles, so far, so good, I think the insight of looking for a transfer function is very. significant. Kinda Obvious now, makes you wonder doesn’t it why noone did this before, one of those doh! Moments for me.

        Another curious thought that emerges is what happens if you compute the transfer function between CO2 and temperature?

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          David Evans

          Several years ago I was indeed dubious that climate was linear and invariant enough to apply Fourier analysis and systems theory. Seemed like a huge mess of non-linear interactions. The mainstream climate modelers often assume linearity. David Stockwell talked me around in 2012, alerting me to the presence of a low pass filter. In this project I am assuming climate is linear for the small perturbations over the last few hundred years, and it seems to work fine. If the climate system is not sufficiently linear then the predictions here will probably be wrong and this theory will be falsified in a few years.

          Acknowledge that TSI and temperate might be related? Near the top of the post, most of it in bold: “The initial aim of this project is to answer this question: If the recent global warming was associated almost entirely with solar radiation, and had no dependence on CO2, what solar model would account for it?”

          Note that this does not assume that TSI “drives” temperature, only that is “associated with” temperature. It will become clearer soon.

          The rising curve of CO2 does not have a useful Fourier transform, because it is ever-increasing (or seems to be lately).

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            bobl

            Thanks for that, glad you have come around to the idea of a piecewise linear approach, though we should always bear in mind that there are distinct non linearities, for example at about 30 degrees over water the atmosphere becomes turbulent as the dew point rapidly falls below the ambient temperature. Even though climate sensitivity falls with increasing temperature (the system saturates) I think below these thresholds and for small pertubations a linear approximation is good enough. It follows too that we can use linear approximations for feedback, providing we assume small pertubations.

            I know you stated the assumption re TSI vs temperature early in the article, it was just a suggestion for clarity.

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        R. Gates

        Yes the planet does store heat — that’s the low pass filter we will be visiting in the next blog post. But the low pass filter has a time constant of about 5 years

        —–
        The primary storage for climate energy is the ocean, and certainly it can store it for far longer than five years. Energy in the atmosphere passes through quite quickly, with the majority of coming from latent and sensible heat flux from the ocean.

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          If the ocean near isotherm is less than +-0.4 degree Celsius and the surface/atmos is +-35 degree daily, what is that time constant, if the 11 year cyclic tsi, cannot be detected in the yearly average temperature.
          I am so interested someone attempting to descover “what is” without worry of “why it is”.
          All the alarmist present is a known solution, to a unknown problem, which is caused by what we “must” fix, while never even trying to figure out “what is”, that has this problem, caused by what must be fixed by our “known” solution. THE SOLUTION IS THE ONLY THING KNOWN, all else is fantasy!

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        bobl

        Yes, finally someone agrees with me on this.

        Another correlation, if you consider that 50 percent of excess CO2 is reabsorbed within a year and you assume that for each further year another 50% of the remainder is reabsorbed, it follows that CO2 too is reabsorbed in around 5 years. This might indicate that the biosphere adapts to CO2 and possible other parameters like temperature in a period of around 5 years.

        Correlation is not causation of course, just an interesting correlation.

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    Sonny

    David well done!

    How do you think the politicians will respond to this new science if your method is shown to be robust?

    Anybody following this debate has realised that its not really ever been about science, and rather science has been hijacked for political and economic agendas.

    Your paper and methods seem extremely complex. Do you think you will be able to simplify the approach so that the average person (currently brainwashed by the media). Can have the same “aha” moment?

    Otherwise, how do you see this new research helping in the fight against this oppressive global regime of false science and deliberate deception?

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      Rereke Whakaaro

      That is where Jo, and the other Science Communicators, come into the picture. It doesn’t just have to be scientifically robust, it has to be accessible.

      I reckon Jo is up to the task, and she will not be alone.

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      Ross

      Sonny I agree with RW’s answer to your question ( which I think is very important). I have always held the view that the despite little funding and little MSM support the skeptics have made so much progress because we have had extremely high calibre communicators on their side — Jo , Monckton , Morano , Watts, Montford, LaFromboise etc They all have different ways/strengths of communicating but are just far superior to the “other” side.

      I would not be surprised if the David’s work turns out to the be the “way out of the corner” for some key politicians and I hope that it will be what opens the flood gates for this issue world wide. By this I mean the warmists have hammered the politicians into a them where some if not many don’t believe what the warmists are saying but don’t know enough to fight back –hopefully this will help them get out of the corner.

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      David Evans

      Maybe. We are going to give it a go.

      The main document is rigorous, with equations.

      These blog posts explain the concepts in broad terms with diagrams but no equations.

      There is a sharply simplified version that seems to work well on the non-climate-heads we’ve tested it on so far.

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        Rightwinggit

        “There is a sharply simplified version that seems to work well on the non-climate-heads we’ve tested it on so far.”

        Want! :)

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    star comment
    The first step in solving any problem is to understand the problem. The perspective that should be used is that one is a total outsider, as an alien from a far away galaxy. The focus is to try to understand what is actually happening rather than why. Only after clearly understanding the what can you meaningfully ask why and expect to get a reliable answer.

    The proposed method and perspective is exactly such an approach. There is the simplest model of a black box being stimulated (forced?) by the sun. Time series measures of both the stimulus and response are more or less available and used. The question is asked: what are the properties of system stimulus/response with respect to time and these measures? If you don’t know this, what good is it to ask for the details of the impact of any partial internal whatever?

    The interesting thing about this approach, it does not matter what mechanisms are in operation within the black box. The only assumption that is made is that the mechanisms are what they are and do what they do which produces the response to the stimuli. There is no system in which this is not the case. Discovering the details is the ultimate challenge. The top down approach is the clean start.

    Why is this approach important? Any proposed contents of the black box can then be tested to the already known behavior of the black box system. Without the ability to do that, all you have is faith, hope, and wishes.

    It is understandable that a staggeringly huge number of yes-buts, ifs, and howevers can be brought up because we live INSIDE the black box. We are intimately familiar with and connect to our own limited short term piece of the action. We are as blind men exploring different parts of an elephant and coming up with more or less true but incomplete descriptions. I suggest that our task is to discover that there is an elephant first and then attempt to discover the significant parts, their behaviors, and their interconnections that make up the behavior of the whole elephant.

    The proposed eleven year notch filter is interesting in that it suggests that our climate system is remarkably and unexpectedly stable. This is in spite of the wild variation of all kinds of local things within the black box. That would mean, within the limits tested, there is no global catastrophe that is going to happen.

    Any catastrophes that do happen are and will be local in nature. That is except what we and our governments do in response to the much discussed global climate catastrophe that is supposed to happen unless we repent or sins and stop our evil ways. In that case, it likely we will be shooting ourselves in our feet with our feet firmly planted in our mouths.

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      Manfred

      …our climate system is remarkably and unexpectedly stable

      Lionell, remarkable perhaps, unexpected, I think not. Most things about the Earth, at least in the context of the HS time frame appear stunningly stable.

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        the Griss

        If it weren’t stable, we wouldn’t be here.

        Notice that even though CO2 rose after temperature in ice core data.. that raised CO2 level was not able to maintain the warm temperatures..

        … in fact the temperatures gradually dropped !

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        I expected some kind of response though not nearly enough to approach an end of the world scenario. I was genuinely surprised that an eleven year response was not found. However, given an additional three to four billions years, the sun is expected to explode and consume whatever is left of the earth. I doubt that neither you nor I need to worry about that.

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      David Evans

      Exactly Lionell. That’s the approach I took, and it takes us where it goes. I was surprised, then it all fitted in :)

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      Konrad

      Well, this is not planet Earth, we live on planet Ocean.

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      Lionell Griffith June 16, 2014 at 1:24 am
      “We are as blind men exploring different parts of an elephant and coming up with more or less true but incomplete descriptions. I suggest that our task is to discover that there is an elephant first and then attempt to discover the significant parts, their behaviors, and their interconnections that make up the behavior of the whole elephant.”

      Indeed Jo and David are indeed exploring the big elephant in the room! Can the rest of us assist in getting others to explore the lower extremities? Perhaps the original climate clowns? One mistouk there, and some other effilump will say, Look at what you just stepped on/into?

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    Martin Hall

    Um. So far the model seems to be saying, “There’s a 11-year signal at the input, which is missing nothing at the output. Therefore there must be a filter that attenuates the signal at that frequency.”

    That does make sense, though of course a low-pass filter would have worked too; I’m particularly interested in the expected amplitude at the output if there were no filter.

    But a notch filter has implications, particularly ‘specialness’. I’d be concerned if the upcoming physical explanation has a mechanism that is tuned to only attenuate at the 11-year point. That would be too much of a coincidence.

    What we need is a mechanism that would take any input frequency and provide a notch there. For example, if the solar output happened to have a peak at 17 years instead, I would expect the notch to be at that point instead.

    That in turn implies an adaptive system, one that evolves to match, and thereby exploit, the frequency of the incoming excitation.

    Ah! ‘evolves’. I think we’re going to hear about a mechanism based on living creatures.

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      Martin,

      I think we are going to find that any internal system forcing element is matched by an equal and opposite system response and I nominate a change in the global air circulation pattern which adjusts convective overturning to ensure that radiative balance with space remains stable.

      In global terms that means latitudinally shifting climate zones and jet stream tracks adjusting their degree of zonality or meridionality.

      The simplest description as far as greenhouse gases are concerned is as follows:

      i) More GHGs send more radiation out to space from within the atmosphere.

      ii) That energy leakage to space weakens the descent phase of convective overturning which then returns less gravitational potential energy (GPE) to the surface as kinetic energy (KE) and the surface potentially cools.

      iii) DWIR from the extra GHGs compensates for the weakening of convective overturning and leaves surface temperature as before.

      Or, in reverse:

      i) Less GHGs send less radiation out to space from within the atmosphere.

      ii) That reduced energy leakage to space strengthens the descent phase of convective overturning which then returns more GPE to the surface as KE and the surface potentially warms.

      iii) Reduced DWIR from less GHGs compensates for the strengthening of convective overturning and leaves the surface temperature as before.

      Relating that to the solar 11 year cycle and solar changes from MWP to LIA to date we would expect to see a similar shift in the jets and climate zones because the thermal changes on Earth are not so much caused by a change in the total energy delivery from the sun but rather by changes in the proportion of solar energy that gets into the oceans when solar wavelength and particle variations alter the thermal profile of the atmosphere both vertically and horizontally.

      Those circulation changes adjust the relative contributions to outgoing IR from atmosphere and surface so as to offset the effect of any internal system forcing element whether that be from volcanoes, GHGs, aerosols, cloudiness changes, ocean cycles such as ENSO and responses to changing solar wavelengths and particles which affect ozone in the stratosphere.

      The existence of the ‘notch’, if substantiated, would be the necessary evidence in support of such a negative system response.

      The role of the hydrological cycle would be to make the whole process far more efficient even to the extent of limiting the thermal effect from the gradually srengthening sun since the early faint sun days.

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      No, we are attempting to understand the residue of creation!
      What was created? The un-understandable, but wonderful Solar system by some very bored sub God, demanding the creation of Earth, critters, creachers, varments, and many others all with no ability to understand, but with much ability to wish to know. Not even the constructors of the earth systems know. Else they would have failed!

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    Ian Wilson

    David,

    Great stuff! I am looking forward to your ongoing posts.

    It would appear that I am “related” to you academically. You
    trained with Professor Ronald Bracewell (late of Stanford University).
    He was a post-grade student who worked with Prof. Frank H. Hibberd
    of the University of New England. For a short time before I started
    my Phd in Astronomy, I worked with Prof. Hibberd during my Honours
    year and for my Masters.

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      Rereke Whakaaro

      Six degrees of separation.

      Even this Maori boy has shaken hands with somebody who has spoken with the Queen.

      I can’t claim to be related, though, more to the pity.

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    Brad

    I am getting maybe 50% of what is being said here. As an engineer, I used to write technical reports as I had been taught, full of big words in complex sentences. Took me a lot of years to realize that most people who paid me couldn’t read them. Their eyes would glaze over by page 3. I now write reports at a high school level, keeping it as simple as possible while still getting the message across.
    I think this may be critical to reaching the masses on this project?

    Another thought: what would happen if it became known that some in the CAGW crowd already know this method of analysis but kept it quiet so their funding would continue? Like the Climategate emails indicate, bad news gets buried if it negatively affects your salary/ego.

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      Brad, you are right, this is hard. There is just a lot of content and some of it hurts ;-) . We have different versions to appeal to different levels. As well as this series of initial posts we have a 2 page, 15 page, 170 page version, plus a youtube coming and a spreadsheet. I’m expecting to discuss the implications of this, then people will probably really want to see these graphs again, and it will make more sense and gets more exciting. We need to run this version past digital signal analysts, climate scientists (more than we already have) and solar physicists.. plus general polymath smart skeptics.

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        Geoff Sherrington

        Jo,
        The versions you list, including the 170 page one, are quite readable. The barrier to comprehension is going to be the skill sets of the readers. There are many parts of the total story, like the detailed properties of notch filters, that are simply outside my past learning.
        Can I please do a small ask, for bloggers here to stick to their specialty when commenting? Specialist feedback is being sought and it might dilute the message if we post too many off the cuff general comments.

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          Rereke Whakaaro

          Geoff,

          I think that is a good suggestion, but I would like to add to it, in my speciality as a general oddball thinker.

          If specialists could take the time to explain the basic principles behind their specialists comments, in lay terms, then we could all come out of this richer and better informed. There is a military expression: “Nothing beats bullshit, like knowing the basics”.

          It would also provide a store of lay explanations, that can then be utilised in the general dissemination of the concepts on this blog and in other fora. Not everybody will bother to read Jo’s excellent documentation.

          Just an idea, of the top of my head.

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            the Griss

            “my speciality as a general oddball thinker..”

            nah, I don’t believe you. ;-)

            Done a whole heap of semi-relevant stuff myself. Highish level maths (20 years ago though).. I remember the terms Fourier, Laplace etc

            But also a lot of audio work and investigation of signal processing related to audio.. sort of as a hobby.

            I am actually grasping most of this so far. I think.

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          the Griss

          Geoff, when I was doing live audio work.. I was a feedback specialist :-)

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        Ross

        Jo
        I think it is great you are having all these different levels of presentation. That is certainly the way to allow everyone to be informed at “their own level” for a highly technical subject.
        A suggestion — could you publish the 2 page version on the blog sooner rather than later. I think this could allow even those with a great understanding of the maths and technical aspects to get an overview of the big picture and the rest of us with little technical background to see where the detail is heading when we read it.

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        Jo,

        I have notified my EE friends including Mosh. They will get it. Will they agree? Remains to be seen.

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    Scott Scarborough

    Couldn’t this transfer function “notch” just stem from a miscalculation of the effect of TSI on the temperature of earth? If TSI doesn’t have as great as effect as calculated then the 11 year sun spot cycle will produce a 11 year insensitivity of the earth to external forcing.

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      David Evans

      We’ve been over that a lot, wondering the same thing. Fourier methods can often see to fractions of the resolutions of the data, if the behavior is repetitive. The temperature records can generally get to with in about 0.1C, so I’d expect a quasi-periodic series of bumps of half or less than that size to be quite detectable. As shown above, the expected temperature peaks should be much larger.

      Also, the Fourier methods seem to be working well in all respects, and find the sides of the notch quite easily.

      Finally, the solar model based on the notch works — hindcasts well anyway!

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    Stephen Singer

    Section 2.

    Second paragraph starts with “The main tsi datasets…” shouldn’t that be “The main temperature datasets …”.

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    Willis Eschenbach

    The problem here is the underlying assumption. This is that the output of the of climate system is a linear function of the inputs.

    IF we assume that output is a linear function of the input, yes, there appears to be a “notch filter” in the system. But this is merely a result of our assumption that

    ∆T = lambda ∆F

    where delta (∆) means “the change in”, T is temperature, F is forcing, and lambda is the so-called “climate sensitivity”

    This is certainly the current climate paradigm. However, I see no reason, either theoretical or observational, to believe this paradigm. Theoretically, I don’t know of any complex flow systems whose outputs are a linear function of their inputs. Try to channelize a meandering river and you’ll see that right away.

    And observationally, we see no evidence that the increase in CO2 has led to a corresponding linear increase in temperature.

    Expecting the climate to show some sign of changing temperature in response to small changes in solar input is like expecting a house with a furnace and an air conditioner to show some sign of changing temperature in response to small changes in solar input.

    You see very little effect or evidence of any small variation of the solar input in the temperatures of either the house or the climate … but the explanation has nothing to do with a “notch filter”.

    Instead, the explanation is that like the house, the climate has various emergent phenomena that directly regulate the temperature and keep it in a narrow range, regardless of small changes in the forcing whether due to CO2, the sun, volcanoes, or any other source. By “narrow range”, I mean for example that over the 20th century the global average surface temperature only varied by ± 0.3°C. That kind of long-term thermal stability, in a system where global average temperature often swings several degrees in a single month, is direct evidence of strong thermostatic mechanisms at play.

    It is not a “notch filter”, however, because it has nothing to do with frequency—the climate control system operates only in the moment. It simply cools the hot spots and warms the cool spots without regards to how often they might happen. The climate system knows no more about the 11-year solar cycle than your thermometer knows about a 24-hour day. If a day were 36 hours long, your house temperature still wouldn’t show the effect, because it’s not a notch filter cutting out a 24-hour cycle. It’s a regulated system, which is indifferent to the length of the day. And similarly, the climate system is a regulated system, not a notch filter.

    Best regards, and as always, Jo, my thanks to you for your marvelous blog.

    w.

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      R. Gates

      The problem here is the underlying assumption. This is that the output of the of climate system is a linear function of the inputs.

      Indeed, we know the the output, or sum of all forcings is definitely not linear, and more likely varies by some modulated n-degree polynomial model. But most importantly, the different forcings on the system operate over different time frames and different intensities, and in the case of anthropogenic forcings, they can be both positive (warming) and negative (cooling).

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      David Evans is not saying the response to changes in solar output is linear.

      But he says the evidence for a pronounced notch at 11 years exists in all the datasets. This is a finding in Fourier analysis, not the preconception that Willis Eschenbach seems to be suggesting.

      It is self-evident from the geologic-timescale temperature reconstructions that the climate object is temperature-homeostatic. To be able to identify some of the relevant mechanisms, as David has done, is very valuable work. Best not to shoot it down until you have seen it all.

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        Hello, Christopher,

        Has David identified a relevant mechanism or has he just found numerical evidence that there is a mechanism ?

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        bobl

        I think we need to wait, both Willis and Dr Evans can both be right here, the transfer function of the climate black box, could be caused by the action of a regulating negative feedback or a large inertia holding the temperature constant for small pertubions of TSI, in fact in my opinion it’s the most likely explanation if we accept that TSI drives climate.

        It’s likely therefore that this will reduce to an argument about the mechanism by which the transfer function comes about – surely that’s the interesting bit and Dr Evans may yet agree with Willis.

        I think we are jumping ahead a bit.

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      At a fundamental systems analysis level, all systems having the same response to the same external stimuli set are equivalent systems. The analysis at this level says nothing and can say nothing about the mechanism that generates the response. It is the equivalence of behavior that counts.

      The challenge comes when one intends to replace the analyzed system with internal components and still maintain the same behavior. However, to do this before the behavior of the system is fully characterized leaves you unable to test your system of components. You can’t verify you have really captured the system behavior by your new system. Oh you can build it and it will have behavior of some kind but will it have the behavior of the target system? You have no way of knowing one way or the other. Why bother?

      A top down analysis and decomposition is always complete at the level of detail of the analysis and decomposition. It simply lacks lower level detail.

      A bottom up analysis has a lot of lower level detail but it can never be known to be complete. This is the primary problem of all the current climate system simulations used by the CAGW crowd. They were built bottom up so they contain a lot of detail. The detail they have might even be correct but they are not complete in every detail. Hence they fail to simulate the actual climate and will always fail to do so.

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      David Evans

      We are not using the concept of forcing, only TSI in and temperature out.

      Yes, linearity is an assumption. Obviously it is not true — the system is very non-linear. The assumption and hope is that the perturbations of the last few hundred and maybe thousand years are small enough that the system is roughly linear. All (but the most pathological and unreal) systems are linear for sufficiently small perturbations — we just don’t know what “sufficiently small” is here. If the system is not sufficiently linear then our analysis will be junk, our model will make faulty predictions, it will be falsified soon, and we will throw it away. Basically there is no other way to find out if it is sufficiently linear than to proceed as if it is linear and see if it works.

      We are going to model the climate with a notch filter, and the model hindcasts well. If it also predicts well, then perhaps there is a notch filter. We also found a physical interpretation for the notch — we think we know what causes it. Soon.

      The homeostatic principle or force you describe exists with respect to carbon dioxide, and we believe we found that too, sort of. Indeed, we use it in calculations later. However it is not part of the solar model. It will become clearer what I mean later, but that is towards the end of this series of blog posts. We don’t know the climate mechanisms that explain the homeostatic force, we just know what they end up doing (we think), and we need help there. Your thunderstorms mechanism is a top contender.

      Apologies for dribbling it out like this, but if I send people it all at once they get overwhelmed or put off, and anyway the conversation will be all over the place.

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        “We don’t know the climate mechanisms that explain the homeostatic force”

        That is the area that I have been focusing on for years past.

        I think it is changes in the rate or power of convective overturning leading to changes in climate zone sizes and positions plus changes in jet stream tracks.

        Due to there being no restraint on further atmospheric expansion towards space other than the gravitational field the system can increase the volume of the atmosphere as necessary to negate any rise of surface temperature from internal forcing elements by converting any ‘excess’ KE at the surface to additional gravitational potential energy within the atmosphere.

        THat process prevents radiative disequilibrium arising between energy in from and out to space.

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          Stephen Wilde June 16, 2014 at 4:54 pm
          “We don’t know the climate mechanisms that explain the homeostatic force”

          Indeed as there is no mechanism, nor force!
          Homeostatic is the spontanious result of a difference in potential. Homeostatic is always adabatic, isentropic, and passive. Static is the key. The entire atmospheric lapse rate is always homeostatic, the “natural” that is always a we bit disturbed by what is going on with your incessant earthling imaginary mechanisms.

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      Geoff Sherrington

      Willis
      Re the analogy “a house with a furnace and an air conditioner to show some sign of changing temperature in response to small changes in solar input”
      The Sun seems to be the primary provider of energy – energy that can be variable and so produce a variable climate.
      The man-made objects use energy that was earlier derived from the Sun. If your analogy is to hold, don’t you have to accept that the man-made things don’t produce spontaneous energy able to have an effect on climate? What do we derive? That in your analogy, there is an indefinable lag built into the air conditioner effect? Maybe the analogy is not so good in fine terms, though it is easy to see what you are driving at in general terms.

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      Willis,

      In the case of a house you could monitor the feedback signal to the temperature control apparatus to get the solar signal from the system. Monitoring the house internal temperature will do no good as you point out. At the very best the internal temperature will be a greatly attenuated version of the solar signal. If it is discernible at all.

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      Konrad

      “The problem here is the underlying assumption.”

      No Willis,
      The problem here is YOUR underlying assumptions. You assumed the math was right. You assumed that DWLWIR could slow the cooling rate of liquid water that was free to evaporatively cool. You assumed that the oceans were a “near blackbody”. You assumed that the effective IR emissivity of water was near 1.

      You assumed.

      You did not empirically check.

      I did.

      The time to stop digging that hole was way back in 2011.

      Hello?

      Hello down there?

      Willis, can you hear me? Remember the rule of holes? Willis?

      (Please no more of this) CTS

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        Willis Eschenbach

        Konrad, other than being unpleasant, you are just here beating your normal one-note drum—the bizarre claim that the heat loss of the ocean is not slowed by downwelling thermal infrared.

        I fear this is just more of your thread hijacking. This is not the place for a discussion of your bete noir of whether thermal infrared can slow the ocean cooling. This is a discussion of notch filters, and whether we expect SOLAR variations (not IR but solar) to be visible in the temperature record.

        So I’ll pass on the chance to once again demonstrate that your claims are wrong. It’s a funny coincidence, but me, I’m actually here to talk about the subject under discussion, notch filters. So I’ll have to take a rain check on your invitation to discuss your misunderstanding. This thread is about notch filters, I won’t get sidetracked by your single issue fanaticism.

        Best regards, and I am more than happy to discuss your monomania on an appropriate thread.

        w.

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          Willis Eschenbach June 17, 2014 at 3:18 am

          “Konrad, other than being unpleasant, you are just here beating your normal one-note drum—the bizarre claim that the heat loss of the ocean is not slowed by downwelling thermal infrared.”
          The heat loss of the ocean is not slowed by downwelling thermal infrared because there is no downwelling thermal infrared at all. Just Carl Sagan’s fantasy. It is your belief that you cannot demonstrate. You demonstrate irradiance then call that flux, same bold error as Carl!

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          Konrad

          “you are just here beating your normal one-note drum”

          Saying that does not make it so. Saying that in response to to a comment that referred to three not one principles I have empirical tested is just ludicrous.

          But this is not the first time you’ve tried your “one-note” ad hom attack. Lets review just some of the questions I have empirically tested with separate experiments -

          1. Does atmospheric pressure increase the ability of the surface to heat the atmosphere?
          2. Does DWLWIR slow the cooling rate of water that is free to evaporatively cool?
          3. Does the surface have equal ability to conductively heat and cool the atmosphere?
          4. Does relative height of energy entry and exit from a gas column effect average gas temperature?
          5. Does water act as a blackbody or selective surface.
          6. Does the depth of intermittent SW absorption effect the average and surface temperature of water?
          7. Is the effective emissivity of water lower than its apparent emissivity?

          Multiple questions. Multiple experiments.

          Your “one-note” accusation is utterly without foundation. You have been previously shown it is without foundation. Yet you repeat it. This speaks to character and motivation.

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    Willis said:

    “the climate has various emergent phenomena that directly regulate the temperature and keep it in a narrow range, regardless of small changes in the forcing whether due to CO2, the sun, volcanoes, or any other source”

    With which I absolutely agree and aver that changes in the rate or distribution of convective overturning within the atmosphere are the relevant variable.

    The question then is whether the operation of that adjustment mechanism can show up as a ‘notch’ in the analysis when David applies his methodology.

    As a separate issue I have tried to explain at WUWT why such changes in convective overturning must be due to the variable diversion of surface energy (KE-heat) to gravitational potential energy (GPE-not heat)but Willis has failed to appreciate that just such a mechanism is needed if his emergent phenomena are to have the consequences that he (and I) claim for them.

    Maybe discussions here can be helpful.

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    Roy Hogue

    For much of the past 17 years I’ve been involved with software using the DFT (FFT). Though I would never try to write the code for the FFT, preferring to buy it from experts at doing that job, I’m very well aware of its capabilities and limitations from long acquaintance. So when I read Dr. Evans description of what his OFT can do my jaw hit the floor.

    David, unless you intend this to become public domain (which you probably do) you better apply for patent and/or copyright protection. I know some people who might just like, at bare minimum, to evaluate it.

    I downloaded the pdf file and I’m going to be going through it just for my own interest since I’m now retired. And since my math is a bit rusty I suspect it will be hard going. But you’re never too old to learn.

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      Roy Hogue

      I’m in no way qualified to make any other judgment of this theory so far. But the discovery of the notch at ~11 year intervals that seems to stop the otherwise expected temperature increase also surprised me (knowing something about signal processing, I know what that notch means).

      I can hardly wait for the rest. :-) :-) :-) :-) :-) :-)

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      David Evans

      I wondered about legal protection, but unless you are a big enough player to use the law, it means little. Anyway, its not clear that one can “own” an idea, and there are many possible software implementations of the idea.

      When I was at Stanford I discovered something useful, in 1984, to do with permuting the data series that is required when doing an FFT. Took about 3 hours, neat bit of software, only 40 lines or so, an order of magnitude faster than the previous method. Ok. Then Stanford decided to patent it. I spend hours with a patent layer in San Francisco, inventing a hardware device that implemented the algorithm, because you had to patent a device — which then gave rights over any software implementation of same. The device was duly patented, and Stanford added it to their portfolio. As far as I know no one bought it, because they could just implement it in software anyhow. Then, a few years later, someone found essentially the same thing in a journal paper from 1973! Ha, there’s nothing new under the Sun.

      The OFT is probably not entirely new, is hard to protect for a big firm, and probably impossible to protect as an individual of modest means. However, it is very valuable, to some people, for some tasks.

      Anyway this is open science, so go for it. The code is in the spreadsheet, to be released soon. If you need help implementing or extending or using the OFT, consider hiring me — see http://sciencespeak.com

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        Roy Hogue

        Hi David,

        I can’t speak for Australia but here in the U.S. copyright of source code is very good protection. On the other hand I figured you’d want it to be public domain. So I may email it to someone and see if it offers them anything.

        I was involved once with patenting of “an idea” and the company got away with it because there was a circuit board with two processors on it that actually implemented the algorithm. I did hours of documenting exactly how it all worked. The whole product is now obsolete several times over, such is the pace of technology.

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        Full disclosure: I present the following from the perspective of an inventor who is skilled in the science and art of software engineering bs who has worked in the field of product R&D for his entire professional life.

        Patenting of software is possible. Protecting the IP is next to impossible. However, if the software is simply part of a “new and useful” hardware/software/process with a clear commercial objective then it not only can be patented but it can be protected. My name is on over ten such patents, they have been defended successfully, corporations known for “borrowing” technology respect them. However, you should also use copyright, trademark, and proprietary secrets to protect your IP.

        It is also important to improve the performance and capability of the technology as rapidly as possible. This actually is the best protection. That is if you can do it fast enough that the competition can’t keep up.

        If you could combine your OFT (as software) with hardware and process with a specific commercial objective, then I suspect that it could both be patented and protected. Then the challenge becomes making money for the contrivance before the end of the patent term.

        A hardware system and a software system having the same behavior are equivalent systems. The problem is that patent law precedence petrified before software became the primary means of producing novel behavior. Hence, even today, patent law does not know how to handle software. That is why there are many huge law suits raging over such things. I suspect, in a hundred years or so, enough precedent will have been built that software IP will be as respectable as hardware or process IP is today. Which means only that you can defend your rights in court and have a chance to win without losing the ranch.

        Fundamentally, this is why continuous product improvement is your strongest defense. A better product, that is easier to use, and at a lower cost of ownership has a better chance of selling.

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        I have attempted to read your PDF. It seemed familiar, I will study it further. When I was doing transforms. It was for determining the frequency response “of a step function” filtered by some low pass filter, an optical modulation transfer function at “any” frequency. Just what you filter out. I discovered that the transform for all of a step function “except” for your measured interval is calculable. Might be interesting for examining one time events as they happen, or the frequencies that are involved in a sampling group that has different begining and ending values, (the noise spectra from hooking up the battery”!

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    Rud Istvan

    WE and DE let me try to square this circle. I am a PhD level econometrician who also wrote one the first peer reviewed papers on applications oc chaos theory (non linear dynamics) to microeconomic systems. Even nonlinear dynamic systems have modes in which they behave well (linearly). One has to be careful near ‘tipping points’. We actually found one in North America’s largest truck assembly plant ( tipping between low rework and high rework) and were able to model the transition between the two ‘stable’ states quite nicely using continuous functions in the NLDM package STELLA from Dartmouth.
    So from first principles, the DE assumptions are a reasonable first order approximation on the climate attractor lobe which comprises the data set–since nothing has tipped. Even Ed Lorenz famous Navier Stokes simplification with two lobes in three dimensions was stable for many cycles on each lobe before bifurcating to the other lobe. And there are trustworthy signs of approaching such a tipping point or bifurcation, such as period doubling of ‘error’ or some modeled phenomenon whose frequency starts changing, that do not seem present in the climate data I have looked at (temps, ocean heat, cloud cover, UTsH, CONUS CEI and each of its components, ENSO, and so forth.
    All models have limitations, and all are ‘wrong’. Some are useful. I look forward to seeing where this goes, A very promising start. The MFT and OFT are a major advance, a tool solving the DFT problem and providing better S/N information for this (and other) porposes. I would by all means copyright the code. You can always release it ‘free’ for some purposes but not others. Probably too late to ‘patent’ or otherwise protect the math behind the algorithms, or the algorithms, since explained in the supplemental technical note attached above. That was a fascinating read, and well done.

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    Leigh

    David says:

    ’3. It comes with a prediction and a falsifiability condition. If it fails, we chuck it away. (If it succeeds, kiss AGW goodbye.) As Bob Carter says, science is about testable hypotheses.”

    I haven’t the time today to read both of Jo’s posts or all forum responses, so apologies if this is has been covered earlier, but all technicalities aside, how long until your theory is deemed successful? What is the process?

    [The final post will answer your question Leigh - Mod]

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    Greg Cavanagh

    I now understand why the sientists kept saying the sun wasn’t an influence on the temperature.

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      Roy Hogue

      I now understand why the sientists (sic) kept saying the sun wasn’t an influence on the temperature.

      And yet there are warming and cooling cycles as we all should know by now. So I think Dr. Evans has more to divulge in following chapters.

      The sun may yet be an influence in longer time frames. And 11 years seems far too short to account for the little ice age and the warming since.

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        Roy,

        Reading a Bode plot is second nature to me. This one says that any input at an 11 year frequency will be attenuated. Higher or lower frequencies WILL affect the Earth. So a Maunder or Dalton will “cool” the Earth because of their lower frequency component. The same for a series of high SSN cycles. So you need two or more high amplitude or low amplitude sun spot cycles to affect the climate.

        We will make EEs out of the rest of you yet. ;-)

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          Roy Hogue

          I started as an EE major but I changed to computer science as soon as I had a little exposure to programming. The bug bit me and that was that. No turning back now. ;-)

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            Roy,

            I’m self trained in EE (started at age 10). As soon as micros were reasonably affordable (1975) I got the bug. By 1978 I had designed the I/O board that went into the worlds first BBS.

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    I am not competent to grapple with all the complex mathematics in Dr Evans paper, since when I did physics at 1st year Uni the maths was what threw me and so I switched to Humanities, including History and Philosophy of Science (Melbourne). But I have done enough science to recognise good science when I see it, and this is very good science: data and evidence based, quantified, testable (and falsifiable), with published data and showing the processes of calculation etc., so that others can replicate it. Congratulations, Dr Evans!
    Significantly, the likes of Chester the jester, and BA the 4th are conspicuous by their absence when good science comes along. Against this appeals to authority, ad homs, credentialist put-downs, sneers, and appeals to numbers count for nothing, as is proper. Keep up the good work, Jo.

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      James Bradley

      MurrayA,

      I was hesitant to point out the obvious as described in your last paragraph for fear of tempting fate, but if nothing else it seems this may also serve as an affective pest repellant.

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    Mike Smith

    Fascinating work and I applaud the David’s efforts and Jo’s for having the courage to publish.

    But why the big tease with the drip-feed release? To me, this adds an aura of manipulation which really has no place in hard science. I don’t really see much of an upside — the mainstream media are not touching this and probably won’t even when it’s “settled science”.

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      Rud Istvan

      Mike, I am pretty remote. But given the attack above from WE, a fellow sceptic by all accounts, the drip feed is a very clever and proper communication strategy. Attacked before revealed and explained! My money is on Joanne and Dave. Plus, what I have seen so far breaks some new ground with respect to tools ( not that I am either current or a leading expert in those, merely a conversant practionioner these past 35 or so years…). So far, very good. very, very good.

      What they are doing is perfectly suited to the non-peer reviewed, but ultimately world reviewed, medium they have chosen. Beautiful. Patience, my person (see, even I can be PC albeit with great difficulty). Patience. You will obviously have your opportunity for your own shots on goal. They have already promised as much.

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      Rereke Whakaaro

      But why the big tease with the drip-feed release?

      Because people like me can only absorb complex issues at a certain rate. We need to have a means of presentation that says, “Now listen up, dummy. You take one of these, and you measure it, and then you take another and measure that too, and you keep on going until you run out of things to measure. When you have done that, go home and then come back tomorrow and we will explain what you do with those measurements, to figure out something you didn’t already know.

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      bobl

      I think you have to bear in mind too that this has to be written, and Jo/David have other things to do with their lives aside from entertaining us.

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      James Bradley

      Couldn’t agree more with Rud Istvan on the measured release of this material and it may well be the most transparent release of scientific work.

      The people that hold affective positions are in the silent majority, and to them go the tasks of assimilating, understanding, testing and questioning.

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      Mike, we have sent the full paper of 170 dense pages to several selected scientists and sometimes had simply had no response, or they would need ten days to read it to come back with feedback. Some were enthused about the idea, then silent on the details. It’s daunting in it’s size. Those who did reply had many different questions.

      Blog-world is brilliant for discussing one or two concepts at a time and getting feedback quickly. It’s impossible to discuss the full solar model without understanding the filters, assumptions and methods. By posting out the parts we hope to get rational detailed feedback.

      As it is, there is months of work in each blog post.

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        Mike Smith

        Thanks Jo. I certainly appreciate the issues involved in getting all of this work publication-ready with minimal resources. And also the point about effectively discussing individual parts/details.

        On the other hand, I personally find it a bit frustrating. When trying to absorb major works like this, I find it easier to skim the whole work a few times to build a broad outline before drilling down to examine the details.

        And perhaps I just don’t like feeling teased… at least in matters of climate :-)

        Anyway, I respect your decision, thank you for your explanation, and look forward to following the story as it unfolds. It really is very exciting indeed!

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    Ken Stewart

    Jo, David, congratulations. This is fascinating stuff, though way beyond my league. Looking for the reason for the absence of the 11 year TSI- temperature connection is brilliant. Of course there is strong correlation at less than one year, not just seasons and day/night but when a cloud moves across and blocks some of the sunlight, the temperature response is rapid, so that 11 year peak absence is a mystery. It appears we have been looking for love in all the wrong places…
    I look forward to hearing more about the ENSO connection, and hopefully warm periods/ little ice ages, and of course the big one- glacial periods. Because although the climate is stable in the short term, it does switch states, and that switch is now about due.
    Ken

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    Now that I’ve read BIG NEWS PART 2 I’m rather disappointed that there was no acknowledgement of Dr. Jeff Glassman’s previous work back in 2011, even though it was very highly germane:

    http://www.rocketscientistsjournal.com/2010/03/sgw.html

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  • #

    Quite different? Not thus far. But I’m very patient.

    (1) Why are other recent TSI datasets omitted from the figures? Svalgaard would be objecting already surely? However happy to wait and watch.

    (2) Glassman covered other related/parallel issues very competently IMHO. Presumably you acknowledge the depth/breadth of Glassman’s (2011) signal analyses. Lets see that aspect unfold too.

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    A Bode Plot of response vs frequency. I have seen those before. Heh.

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    Stupendus

    I studied Electrical/Electronic Engineering 30 years ago, spent 8 years as a research Tech (microwave filters) then moved on to electromenchanical servicing, computer systems, database development and data analysis and ending up in Federal government employment. I never could put my finger on why the Global warming alarmism was wrong, I just knew it, My background tends to show that my experience and knowledge equiped me to see the light, but I could never prove my “gut feeling” (I often see this in many skeptics), We know it is wrong but up until now no one ever articulated a possible theory that pulled everything together and still doesnt “smell off” This new theory smells right, sounds right and by golly may just be right. The struggle has turned a corner, I can now see light (sunlight) at the end of the tunnel and I anticipate some interesting backflips, conniptionsand downright dirty tactics from the other side in the near future, well done …but take care…

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      Popeye26

      farmer,

      I note NOT ONE OF THEM is game enough to show their ignorance over on this blog!!

      Gareth is a CLASSIC!!

      “Gareth June 16, 2014 at 2:25 pm
      You need to read a little about the Clausius-Clapeyron relation. it is basic physics, and describes how warmer atmospheres must contain more water vapour.

      Meanwhile, if wishes were ponies, Evans and Nova would be starting a stud. Interesting to note that Nova quotes Bob Carter and Monckton in support. In the real world, that’s as good a sign of nonsense as you are likely to find.”

      We all know why he won’t come over here spouting his BS – he can’t be SURE that he can go head to head with David and not look like the idiot he appears to be!!

      Cheers,

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        Rereke Whakaaro

        Gareth is a CLASSIC!!

        A classic … what? I wonder.

        He goes directly to ad hominem, does not pass Go, and does not collect 200 brownie points.

        Typically all mouth and no trousers, as they say in Britain.

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          farmerbraun

          Well I thought that it was only fair to give them the opportunity, and they seized it with both hands.

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        Good on you farmerbraun. The irony is sweet.

        Bill mocks our certainty:
        “all the faithfull stalwarts understand that just as soon as the promised super-weapon is deployed the tide of the war will turn permanently in their favour…”

        Bill (who hasn’t seen it) is certain it is wrong:
        “Do you really imagine this is going to amount to anything, Bio?”

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          the Griss

          “Bill (who hasn’t seen it) is certain it is wrong:
          “Do you really imagine this is going to amount to anything, Bio?””

          I’d say that Bill doesn’t amount to anything..

          A sort of drag on human society.

          A Greens or far-left voter, no doubt ;-)

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        Richard C (NZ)

        Re: Gareth June 16, 2014 at 2:25 pm (at Hot Topic):

        “You need to read a little about the Clausius-Clapeyron relation. it is basic physics, and describes how warmer atmospheres must contain more water vapour

        Basic physics huh. Note the plural “atmospheres” and the word “must”, then think of dry, arid, 50° C desert atmospheres. And then of the -57° C tropopause.

        Gareth trots this out from time to time. I suppose it projects the aura of climate authority to the unthinking he desperately needs for Hot Topic in lieu of say, an ability to foot it here at JoNova.

        But OK, let’s read (from Wiki will do – my emphasis):

        In practical terms, this equation [Magnus-Tetens approximation of Clausius-Clapeyron relation] determines that the water-holding capacity of the atmosphere increases by about 7% for every 1°C rise in temperature.

        http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation

        Wonderful, but it’s about capacity, not whether that capacity will be filled or not depending on the availability of evaporation.

        Except the strata of atmosphere we’re interested in, the troposphere, is tens of kilometres deep containing many of Gareth’s “atmospheres” but in an upwards temperature gradient of warm-to-cold opposite to the definition above in terms of what happens to warm air rising rather than the mass just getting warmer at a fixed altitude (my emphasis – abbreviated):

        High School Earth Science/Atmospheric Layers

        Air Temperature
        The atmosphere is divided into layers based on how the temperature in that layer changes with altitude, the layer’s temperature gradient (Figure 15.4). The temperature gradient of each layer is different. In some layers, temperature increases with altitude and in others it decreases. The temperature gradient in each layer is determined by the heat source of the layer. The different temperature gradients in each of the four main layers create the thermal structure of the atmosphere.

        Troposphere
        The temperature of the troposphere is highest near the surface of the Earth and declines with altitude. On average, the temperature gradient of the troposphere is 6.5°C per 1,000 m (3.6°F per 1,000 feet) of altitude.

        http://en.wikibooks.org/wiki/High_School_Earth_Science/Atmospheric_Layers

        Suddenly, “water-holding capacity of the atmosphere increases by about 7% for every 1°C rise in temperature” isn’t really the right perspective for the troposphere, 6.5°C per 1,000 m decreasing temperature gradient and decreasing water-holding capacity are the relevant and significant conditions in a troposphere 16 to 18 km thick at the Equator and where the warmest air is at the surface.

        Now let’s read about warm precipitation that Gareth omits to mention (my emphasis – abbreviated, cold precipitation follows warm):

        Warm Precipitation
        Saturation of air occurs when rising air currents cool adiabatically (that is, without loss of heat) by expansion. Because the saturation vapor pressure of water decreases exponentially with decreasing temperature (a property often summarized by the statement “cold air can hold less water vapor than warm air”), cooling of a moist air mass by lifting is an efficient mechanism for producing saturation and condensation.

        http://www.scholastic.com/teachers/article/precipitation-weather

        But in Gareth’s world (Warmer World), there’s no upwards warm-to-cold temperature gradient worth mentioning, or diverse states of humidity at the surface in hot climates, and warm moist air never rises, cools, and precipitates out. Apparently.

        Meanwhile, for the last week in NZ it’s been cold, bucketing down, and flooding — but that’s just weather I guess.

        [Lengthy, off topic really, and I apologize for that - but my fuse was lit unfortunately]

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    john robertson

    So far I comprehend only some bits and pieces, the rust in my math skills is frightening, however the use of a dictionary at my end and some patience from the communicators will win through in the end.
    The essence of good science, almost the proof of the scientists true grasp of a concept, is in their presentation,
    Being able to explain the idea , so an fairly bright 12 year old “gets it”.
    So far so good,
    I know we are blessed with some truly unique scientists and gifted communicators on this and other blog sites, I eagerly anticipate the full work and commentary to come.
    Like Rekeke says,11:58, the small parcelling gives blockheads like me a chance to get the general drift.
    Finally climate science that openly acknowledges cycles, I am so tired of govt grant modellers obsessing about linear trends.
    By their non logic by noon each day we are doomed to be toasted.
    Each tide is doom, every season a catastrophe.

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    Chuck Bradley

    Thanks for sharing this. If it works out or not, it is good to consider.
    Two nits so far, and I have not read the comments and am only up to the definitions in the paper. 1. In the paragraph after Introduction, is a word missing: “time series [is] a single sinusoid”? 2. For the pha function, do you mean the positive x axis instead of the origin?

    If I don’t report more problems, don’t get confident; most of my math is from 50 years ago,
    so I’m rusty at best, maybe decayed. But I hope you are right.

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    Steven Mosher

    “The temperature we are most interested in is the one for our immediate environment, the “global average surface air temperature”, namely air temperatures at or near the surface averaged across the entire planet. When we use “temperature” without qualification in these posts, we mean this temperature. “Global warming” is the rise in this temperature.”

    Nice, except the datasets you use are not air temperature.

    second, The TSI datasets/SSN datasets you use are all about to be OBE

    so back to square 1.

    Or supply the code and folks can put the correct data.

    link for the code would be cool.. just mail it to me

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      the Griss

      “Nice, except the datasets you use are not air temperature.”

      Ahh.. they were measured underground.. got ya. !!

      “second, The TSI datasets/SSN datasets you use are all about to be OBE”

      Liz approves of them… … sweet !!!

      “Or supply the code and folks can put the correct data.’

      You mean the “adjusted data”, I assume.

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      the Griss

      Mosh, you do know that you are now marked purely as an AGW tragic and alarmista mouthpiece, don’t you?

      On the climate trough, so to speak.

      That was your decision, though. :-)

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      Rereke Whakaaro

      If I was a suspicious sort of person, I might think your response was based on a preconceived conditional output, and not in a spirit of open inquiry.

      As I see it, David is building towards a model that is firmly based in first principle physics, in order to see where it goes. At this stage he is apparently unconcerned with where that leads.

      You on the other hand set yourself a boundary defined by the statement, “The temperature we are most interested in is the one for our immediate environment, the ‘global average surface air temperature’”. Why that should be important is unclear, but is not relevant to what David is attempting.

      However, what you present, is a very clear example of the difference between Climate Science, and the Physical Sciences. Thank you for that, it will be useful.

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        the Griss

        Yes, It is interesting.

        With that one post he has marked himself as NOT a scientist, because he shows he is not interested in alternative views or the science/physics behind them.

        The immediate attempt to downgrade what is at this stage only a brief introduction is totally true to form.

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    IS this the story so far? – TSI varies by about 1.5 w/msquared in an 11 year period or around 0.1% and this perturbation does not show up in global air temperature estimates. The graphs presented here are the notch (ie solar maxima TSI) and its inverse, the mysterious filter.

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    Yes – as Steve Mosher notes the TSI/SSN datasets are about to be ‘overcome by events’ because of the behavior of the just passed Solar Cycle 24 maximum (= weakest for over 100 years) and the unusually deep minimum that preceded it. It is now believed that Cycle 23 was anomalous for reasons just now being reviewed.

    In that sense; perhaps Glassman’s (2011) choice of the Wang et al (2005) estimated TSI record which was at least supported by a solar model might, in retrospect, be seen as wiser….?

    As I said; a lot of ‘watch this space’ yet to come.

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      the Griss

      Cycle 23 was a bit longer than usual, but its not as if the ‘notch’ is like a 48dB frequency band filter that one might get on a decent auto feedback exterminator.

      It has a certain range to it.

      In fact , if you look at Fig 6, there is a hint that the cycle length is increasing, with both the instrumental and post 1945 frequency notch being of slightly longer duration than the earlier series.

      As you say.. more to come. :-)

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        Looks like about 12db to me. Or roughly a factor of 4X to 5X. 48db is on the order of 64X.

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          48 db is on the order of 250X

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          the Griss

          Broad bottom, with around 9dB slopes, but I’m not going to measure it :-)

          Ever used on of those Sabine auto feedback things? they do 48dB slopes. an do a great job,

          except I had one go crazy on me once (old age I suspect) Good thing I had quality ear plugs in ! .

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            My audio work (radio stations – WTAO) ended around the mid 70s when those kinds of filters were just coming into use. We limited mostly. And not too aggressively – to prevent pumping. When I worked at WFMT (classical music except for the Midnight Special) the rule was FLAT and no limiting – maximum dynamic range.

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              the Griss

              Doubt this will get past the mods..

              but I always considered that a compressor/limiter was like a condom for the speakers.

              You only use one when you have to. :-)

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              the Griss

              Live gigs are a different kettle though.. Sometimes you have to use them.

              And apply them very firmly. !!! (compressor/limiters, that it)

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    Brad

    Joanne and David,
    Did some thinking regarding the July conference in Las Vegas. Decided to contribute to you what it would cost me to attend, $500.00.
    I am posting this to challenge all other reader/adherents to do the same, put your money where your position is.
    If you really care about your children’s future, you really have no choice in the matter.

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    I know I’m way down the long list of Comments here, and that’s not because I have no interest with this, because it is very interesting indeed, and while pitched over my head, I find a lot of things that I CAN actually understand, and there’s a good reason for that understanding.

    I’d like to add a comment here from an observational point of view, that of someone trained in the electrical field, and while I am at the bottom of the heap in that electrical field, what is happening here with Doctor Evans actually confirms my belief.

    Because all this CAGW thing this is basically about Science, quite a lot of people thought, (and probably somewhat correctly) and even told me in not so many words that electrically trained people had nothing to offer regarding the ….. Science!

    Right from when I started out doing what it is I do, I noticed something really odd. When I looked at some of the graphs and charts that were there for all to see, they seemed somewhat familiar to me, not in what they were about, but the actual shape of those graphs, especially when viewed in their longer form. (time related)

    They looked similar to Sine waves, and here I mean not kinda sorta roughly if you close one eye and imagine, but actually quite close to an actual sine wave. This led me to a thought that perhaps all these things were indeed cyclical, but try and explain a sine wave to someone who has a blind belief in CAGW, and all I got was blank looks.

    Over the years, the more graphs I looked at, the more this sine wave appearance came up.

    Coming from that electrical background, then, naturally, feedback came into the equation. This doesn’t affect the frequency, just the amplitude, be it positive, adding, or negative, subtracting.

    Now I see it in everything, and dare I say it, even in rooftop solar power generation, and allow me to explain that.

    People believe that while ever the Sun shines on the panels, they generate their full amount of power, and that’s incorrect. They only generate (close to, but never at the maximum) their full power when the Sun is shining directly square down onto the panels.

    To show you you this, I want you to look at two separate days of generation from rooftop arrays, in this case a large one, at UQ. Open each graph in a separate window and you can click from one back to the other.

    One is for a mid Summer day, here the 20th January 2014, shown at this link.

    The second is for a mid Winter date, here (last year) 21st July 2013, shown at this link.

    First thing on the first one you look at, note how the graph builds up and then falls away, with maximum generation when the Sun is at its peak, and before and after, shining on the panels at an angle, hence lesser generation. The same applies as the year moves on, with the Sun, even though rising to its peak, is still shining from an angle, directly overhead in Summer, and at a more Northerly aspect in Winter, hence a greater angle. hence lesser power generation.

    Now, note how both graphs have similar overall shapes, even approximately a half sine wave. Note the variation in time across the horizontal axis, Summer for approximately 12 hours and the Winter one for approximately 9 hours.

    Now, note the amplitude, the maximum generated power.

    The total Nameplate is just under 1600KW. (1.6MW)

    Even in Mid Summer, the maximum here is still only 1200KW, while in Winter, even though the graph is similar, it’s down to only around 750KW.

    The average generation is (approximate value of a sine wave) 0.707 of Peak value.

    All being well, if the Sun shone on clear bright cloud free days, and you calculated for each day, then the end result would be a sine wave for the whole 365 day year.

    The average point of that overall sine wave, the zero point is half way through (across) that sine wave.

    This gives the overall total generation of the panels, that half way point through the sine wave across the horizontal.

    Compare that to the Nameplate and you have the average generation of the whole array.

    Then, work out the overall time basis of generation, and average between the 9 and 12 hours calculating that then across the whole 24 hour period and you get the actual Capacity Factor of the array ….. IF THE SUN SHINES FULLY each day, so there are other factors in play, clouds etc.

    Now, why I went through all this, the same applies with daily temperatures, from the minimum though to the maximum and then back down again, basically sinusoidal, and then a sine wave on top of a sine wave as you calculate the average point across a whole year, and then that result across further cyclical changes, all basically sine waves in their nature.

    And the same applies with virtually every graph in this CAGW debate that you look at.

    So you see, electrically trained people do have a good insight into this debate, and in fact, better than most people do.

    I don’t claim to be the tiniest fraction as knowledgeable as Dr. Evans is on this, but I can understand in some small manner just what is happening here. It takes some work for me, but I can see the basics here.

    And hey, have you noticed how few trolls have come here to argue against this. So far over their heads that it leaves a vapour trail.

    Tony.

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      john robertson

      Bingo,
      Tony you describe how I fell into arguing against the CAGW madness.
      The denial of cyclic behaviour of nature, while the cycles dominate the data.
      The cycle of ice ages dominate this planets past
      Non-science from the political beasts.
      Once trained in control systems and electrical theory, I was amazed by the ignorance of the “World Experts”.
      Climategate helped confirm what I did not want to believe.

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    Willis Eschenbach

    Monckton of Brenchley
    June 16, 2014 at 7:38 am · Reply

    David Evans is not saying the response to changes in solar output is linear.

    David Evans clearly expects that if there is an 11-year cycle in the input energy, there will be an 11-year cycle in the temperature. How is this not the same as saying that the output is some approximately linear function of the input?

    But he says the evidence for a pronounced notch at 11 years exists in all the datasets. This is a finding in Fourier analysis, not the preconception that Willis Eschenbach seems to be suggesting.

    Lord Moncton, I encourage you to do the same experiment David has done (as a thought experiment) using a number of houses with thermostats. If you analyze the TSI hitting the houses, like David you will find that there is a strong solar cycle signal, in this case at 24 hours. And if you do the same kind of analysis David has done of the house temperatures, you will indeed find as David did that “a pronounced notch at 24 years exists in all the datasets”.

    So does the existence of this notch mean that there is a 24-hour “notch filter” operating somewhere within the house, as David claims for the corresponding climate situation?

    Of course not. The “notch” is real, as you point out, it is not a “preconception” … but the existence of the notch doesn’t mean that it is the result of a “notch filter”, in either the houses or the temperature datasets. All it means is that the system is temperature-homeostatic, to use your term.

    It is self-evident from the geologic-timescale temperature reconstructions that the climate object is temperature-homeostatic. To be able to identify some of the relevant mechanisms, as David has done, is very valuable work. Best not to shoot it down until you have seen it all.

    I fear that David has not “identified a mechanism”, or to be more accurate he has misidentified it. He claims that the mechanism is a natural “notch filter”.

    However, the example of the houses shows clearly that if the temperature is thermostatically controlled, as both you and I believe is the case with the climate, you’ll get the “notch” from that alone, without the necessity of any kind of “notch filter”.

    Always good to hear from you,

    w.

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      Willis,

      So why only a notch at 11 years? If the climate is homeostatic at all scales shouldn’t the Bode plot be flat? Why the notch? I look forward to an explanation in future posts.

      BTW you can see the solar input to the house by looking at the control signal in the feedback system. On a cold day solar will reduce the feedback. With the AC running the feedback will increase with solar input.

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      the Griss

      This is an introduction Willis, How do you know he hasn’t identified a mechanism. .

      I know its strange to say this to you….

      but open your mind and let it unfold. See where this leads.

      Its not time to diss it yet.

      ps..

      Are you suggesting the atmosphere is thermostatically controlled?

      A house is an enclosed system which can be heated or cooled from within…, is the atmosphere?

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        Rogueelement451

        I always think of two comments that I had from teachers as a child
        1 Keep your mouth shut and look a fool , or open it and prove it.
        2 You have 2 ears and 1 mouth , try to use accordingly.

        As this story unfolds and the rebuttals come in and I note that Willis Eschenbach, is in like Flint , we shall see how the cards fall.
        I note a huge amount of silence on every other blog and an absence of usual troll behavior on here, I guess this is one of those hold your breath moments and I am looking forward to how this pans out.
        My constant meme “its the troposphere stupid” may turn out to be as ludicrous as every other, but frankly I do not care,if acceptance can be gained as to an all encompassing theory then we slay the warmistas.
        Logic needs to be the winner , good luck David Evans and Jo .

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      Gee Aye

      Mates Willis

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      Willis Eschenbach June 16, 2014 at 5:49 pm

      “However, the example of the houses shows clearly that if the temperature is thermostatically controlled, as both you and I believe is the case with the climate, you’ll get the “notch” from that alone, without the necessity of any kind of “notch filter”.”

      Willis Please describe a thermostat as anything but a notch filter for anything cyclic? Why don’t you try to find thr thermostat, and describe its intended purpose?

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    Willis Eschenbach

    David Evans
    June 16, 2014 at 4:41 pm

    We are not using the concept of forcing, only TSI in and temperature out.

    David, first, my thanks for an interesting analysis.

    However, regarding “forcing”, TSI is one of what are generally called “forcings” in climate science. So you are indeed using the concept of forcing.

    Yes, linearity is an assumption. Obviously it is not true — the system is very non-linear. The assumption and hope is that the perturbations of the last few hundred and maybe thousand years are small enough that the system is roughly linear. All (but the most pathological and unreal) systems are linear for sufficiently small perturbations — we just don’t know what “sufficiently small” is here. If the system is not sufficiently linear then our analysis will be junk, our model will make faulty predictions, it will be falsified soon, and we will throw it away. Basically there is no other way to find out if it is sufficiently linear than to proceed as if it is linear and see if it works.

    Mmmm … I disagree strongly with your claim that:

    All (but the most pathological and unreal) systems are linear for sufficiently small perturbations …

    Actually, there are a whole class of systems for which that claim is not true. These are called “governed” or “regulated” or “temperature controlled” systems.

    A good example is the cruise control in your car. Normally, as you say, for small perturbations the car’s speed is some linear function of the amount of energy entering the engine.

    But when you turn on cruise control, all bets are off. When you turn on cruise control, you decouple the fuel use from the speed of the vehicle. The relation between fuel use and speed is not just no longer linear, it is totally disconnected. As you hit hills and such, fuel use goes up and down, but the speed barely wavers … and the same is true of your house. Your fuel use goes up and down, but the temperature hardly moves at all—not just no linear relation, but no relation of any kind.

    So no, your claim of linearity given small perturbations is not universally true as you claim.

    We are going to model the climate with a notch filter, and the model hindcasts well. If it also predicts well, then perhaps there is a notch filter. We also found a physical interpretation for the notch — we think we know what causes it. Soon.

    Model away, my friend. However, while you are doing it, consider my example of the houses. If you run your exact analysis on TSI and house temperatures, you will definitely get a notch at 24 hours … but if you think that means there is a notch-filter in the house set to filter out a 24-hour cycle, you’re not as smart as I think you are …

    The homeostatic principle or force you describe exists with respect to carbon dioxide, and we believe we found that too, sort of.

    Not true. The thermal regulation system of the climate operates in response to surface temperature. It has nothing at all to do with carbon dioxide. See my post called Emergent Climate Phenomena for a fuller discussion of this question.

    Indeed, we use it in calculations later. However it is not part of the solar model. It will become clearer what I mean later, but that is towards the end of this series of blog posts. We don’t know the climate mechanisms that explain the homeostatic force, we just know what they end up doing (we think), and we need help there. Your thunderstorms mechanism is a top contender.

    Apologies for dribbling it out like this, but if I send people it all at once they get overwhelmed or put off, and anyway the conversation will be all over the place.

    I have no problem with how you’ve expounded your idea, that’s your choice.

    Let me politely but strongly recommend that before you publish your next portion, you think long and hard about the example of the house. You’ve taken a wrong turn in your analysis. You are fortunate that you have time to correct it before it gets set in stone.

    The problem is that there is no more evidence for a “notch filter” in the climate filtering out the 11-year TSI cycle, than there is evidence for a “notch filter” in my house filtering out the 24-hour TSI cycle …

    w.

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      Willis,

      If you look at the right variable – the feedback signal – it will show the variation you are looking for. And “for small variations” is the basis of partial differential calculus.

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        Willis Eschenbach

        Willis,

        If you look at the right variable – the feedback signal – it will show the variation you are looking for.

        Since neither David nor I is looking at the feedback signal, I fear I don’t understand why this is relevant.

        And “for small variations” is the basis of partial differential calculus.

        That is true. However, when the input and output are decoupled, calculus is useless.

        w.

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      David Evans

      “Forcing” has a specific meaning in climate science. We are setting that aside here and only looking at a system whose input is TSI and whose output is temperature.

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      David Evans

      In your example of a car on cruise control, what is the input of the system?

      Presumably the output is the speed of the car?

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        David,

        I’m sure that you are aware that the input to the speed control system is the speed and the output is throttle position. If you look at throttle position or fuel flow it is possible to roughly determine if you are on a flat, or going uphill, or downhill. A PID algorithm is used (you can tell if you know what to look for) for control.

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          Tel

          Strictly speaking there are at least two inputs to the control system: the current speed, and the setpoint (your setting of the desired speed). I expect a real cruise control would take inputs from a lot of other stuff, manifold vacuum, engine revs, etc.

          However, let’s consider the whole car (including the engine, cruise control, and the setpoint) as one unit, the internal process of strong negative feedback will produce an output that is a constant speed. The inputs in this case are the driving conditions, slope of the hill, headwinds/tailwinds, etc. No linear control system can completely eliminate a sinusoidal input from getting through to the output, however it could attenuate that signal significantly.

          In order to properly eliminate the sinusoidal input you would need to do something like what the noise cancelling headphones do and systematically analyse the input to automatically tune the filter to cancel exactly that signal. If I found something operating like that in the Earth’s atmosphere I might be tempted to start believing in Intelligent Design (don’t tell Robert P Murphy I ever said that).

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            bobl

            Ok,
            In this example power (fuel) input to the engine becomes a function not of the speed of the vehixle but rather the load on the engine, which is friction, wind resistance, grade of the road etc. To keep the speed constant the system will adjust the power input to match the losses.

            The control system while it modulates power, actually works by comparing the actial speed to a setpoint, the power input is increased or decreased untill the output speed equals the input speed.

            The engine is a good analogy, it’s not particularly linear either, but for a given output, speed you could derive a transfer function relating throttle to load which would work for small pertubations of load that would keep speed constant in a range where the characteristic is close enough to being linear. This is essentailly what David has derived for the climate. Sure, if the speed was to change then the traansfer function from throttle to load may change a little, but within a defined range it will be close enough.

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            Tel,

            Automotive engineers try to make things as simple as possible. It lowers cost. So you only get set point (derived from speed when you do “set”) and speed. Output is throttle control.

            You might do all that other stuff if keeping the difference between set and actual very small is critical. It is not in the speed control case. Variations of a few mph for a short time don’t matter.

            Pay very careful attention to your speed the next time you use speed control. You will notice a proportional response (P). An integral response – the longer the error persists the smaller the error (I). A differential response – a limit to the rate of change of control (D). Thus PID.

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          MSimon I’m sure you are aware that op amps and comparitors have two inputs. Thus the input to the speed control system is not the speed it is the difference between desired speed and actual speed / the gain of the system.

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        dp

        Willis, a self-educated blogger who self-identifies as a climate scientist won’t be happy until your theory incorporates his pet emergent phenomena hypothesis. Ignore the buzzing and stay the course else your revelations, right or wrong, become indistinguishable from his.

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      David Evans

      Let’s consider your example of a system whose input is TSI and whose output is the temperature inside a climate-controlled house (that is, the house has a thermostat and heater/cooler to keep its temperature constant).

      Indeed, in this situation there would be a notch obtained by the methodology in the post above.

      However the system is not linear (except in the trivial sense that the temperature is independent of the TSI and therefore the proportionality constant is zero: delta-temp = 0 * delta-TSI = 0).

      To switch back to the system analyzed in the post, the changes in the Earth’s temperature might reasonably be expected to be dependent on changes in the TSI, and linearly dependent for sufficiently small perturbations of TSI. The temperature of the Earth, unlike the house, is not constant. So a notch is interesting, and there must be something or somethings that somehow create the appearance of a notch. Somehow the 11-year sinusoids from the Sun are not showing up nearly as strongly as we would expect.

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        Willis Eschenbach

        Thanks, David. You say:

        Let’s consider your example of a system whose input is TSI and whose output is the temperature inside a climate-controlled house (that is, the house has a thermostat and heater/cooler to keep its temperature constant).

        Indeed, in this situation there would be a notch obtained by the methodology in the post above.

        OK, folks, now we’re getting somewhere. We know that there is no “notch filter” of any kind in the house, and we agree that despite that, there would be a “notch” in the results if your analysis is done on the house data.

        As a result, we have agreement that when using your analysis method,the presence of a notch in your results does NOT imply the existence of a notch filter in the system.

        So let’s follow the implications of this agreement:

        1. Your argument that there is a notch filter is based on the existence of the notch in your results.

        2. As far as I can see, you have no other evidence for a “notch filter” other than the existence of that notch.

        3. We now agree, you and I, that the existence of such a notch DOESN’T imply the existence of a notch filter.

        Therefore … ?

        If you have any other evidence for the existence of said putative “notch filter”, now would be the time to pull it out …

        w.

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          But there is evidence of a notch. The 11 year cycle does not show up in the temperature record. Multi – 11 year cycles (which have a lower frequency component) do.

          Maunder and Dalton. And obviously the recent 20th century warming from multi 11 year cycles.

          Obviously without more information the case is not proved. But so far the results are “suggestive”. I look forward to future posts.

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            Willis Eschenbach

            MSimon
            June 17, 2014 at 5:09 am · Reply

            But there is evidence of a notch. The 11 year cycle does not show up in the temperature record.

            Thanks for the reply, M. Indeed it does not, and that causes the “notch” in the presumed transfer function. My point is that evidence of a notch is NOT evidence of a “notch filter”.

            Multi – 11 year cycles (which have a lower frequency component) do [show up].

            I’m sorry, but that’s simply not true. The author himself says:

            The temperature amplitude spectrum, the smooth orange curve in Figure 4, is essentially straight over more than three orders of frequency magnitude, with no other definite features.

            In other words, multi-11 year cycles do NOT show up, and the authors have commented on that fact.

            Maunder and Dalton.

            Good question. The Maunder and Dalton minima have no absolute defined time frames. One authority says 1645 to 1715 for the Maunder, and from 1790 to 1830 for the Dalton minimum, so let’s use that.

            Obviously, we have no thermometer data for the Maunder, so let’s set that aside for the moment. We do have a small number of stations for the Dalton, and Berkeley Earth has collated the stations that existed at that time. Those results are here. If you look at them, you’ll see that the temperature was low immediately before the start of the Dalton. But by the start of the Dalton in 1790, despite the reduction in solar energy, the earth is warmer, and it stays warm until about 1810. Then it drops, but only to the level it was at before the Dalton … and then, by the end of the Dalton in 1830, temperatures have risen again.

            So … obviously you have a belief about the Dalton, that there was some big dip in global temperature at that time. But according to the data we have, that’s simply not the case.

            And obviously the recent 20th century warming from multi 11 year cycles.

            I’m sorry, but what causes the variations in temperature is absolutely not established. And there is no “obviously” about the answer …

            Obviously without more information the case is not proved. But so far the results are “suggestive”. I look forward to future posts.

            Which case? The case for a notch filter? David Evans has not provided a single bit of evidence that such a mechanism exists.

            w.

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              Richard C (NZ)

              Willis (and David) #48.4.1.1.1

              Re your reply to MSimon:

              I’m asuming MSimon is not necessarily referring to the Figure 4 temperature spectra but David obviously is.

              However I think you misconstrue David. I’d like some clarification from either yourself Willis or from David by way of answers to the following question in respect to Figure 4:

              If the modern solar Grand Maximum (1950ish – 2009), the Dalton Minimum, and the Maunder Minimum were to show up in Figure 4, at what frequency or frequency range would we expect to look for each?

              I don’t see how a near 60 year timeframe can show up at a Figure 4 frequency for 1950 – 2009 for example because it is not as regular (if it is at all) as the 11 year cycle.

              The second to last Grand Maximum appears to have occurred about 2400 yrs prior to the Modern Grand Maximum but that frequency is out of Figure 4 range. Similarly for latest Grand Minimum (Maunder) and the preceding Grand Minimum.

              See:

              ‘A History of Solar Activity over Millennia’

              http://wattsupwiththat.com/2012/09/13/paper-demonstrates-solar-activity-was-at-a-grand-maxima-in-the-late-20th-century/

              If the frequencies mentioned are not covered by the Figure 4 analysis, how then can you state “multi-11 year cycles do NOT show up, and the authors have commented on that fact”?

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          David Evans

          Quote the whole relevant bit Willis: The presence of a notch obtained by the methodology above does NOT imply the existence of a notch filter in a system that has zero response, i.e. that is linear only in the trivial sense that the temperature is independent of the TSI and therefore the proportionality constant is zero: delta-temp = 0 * delta-TSI = 0).

          The Earth does not have a zero response to TSI — when there is more TSI the Earth heats up. So when the methodology shows a notch, there is a notch filter.

          Your house has a zero response to TSI — when there is more TSI your house does not heat up. So when the methodology shows a notch, it does not mean there is a notch filter.

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            Dave Reeve

            The Earth does not have a zero response to TSI — when there is more TSI the Earth heats up. So when the methodology shows a notch, there is a notch filter.

            The above is trivially true as evidenced by the thought experiment of removing the sun from the system. However, that doesn’t mean that there can’t be a ‘control range’ over which global temperature is largely uncoupled from TSI due to negative feedback. Willis’s point is that the failure to find an 11 year periodicity in global temperature is an indicator that the earth’s climate system is currently parked in such a ‘control range’.

            Your house has a zero response to TSI — when there is more TSI your house does not heat up. So when the methodology shows a notch, is does not mean there is a notch filter.

            This is exactly the same deal. If you remove the sun from the system, I reckon the house temperature is going to fall. That is, there is a control range within which the temperature is largely independent of TSI and once the system moves out of this stable range, temperature becomes dependent upon TSI.

            However, I have no problem with the thought experiment where we assume temperature is linearly coupled to TSI and then see what that means for the transfer function…. “ah ha, check out the notch!” This is all good as long as you state this assumption at every twist and turn of what follows. Let’s see if you do :-)

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              Dave,

              OK. There is a notch at 11 years. Nice to agree on that. There should be some mechanism tuned to that 11 years. As an example: Does plankton grow at a rate that exactly (well nearly anyway) counters the temperature rise expected from TSI variations? Is it something else.

              A general control mechanism (thermostat) should show equal (roughly) attenuation at all frequencies below the control system frequency response. How is the natural control mechanism tuned to the 11 year cycle?

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              Dave Reeve

              A general control mechanism (thermostat) should show equal (roughly) attenuation at all frequencies below the control system frequency response.

              Agreed!

              How is the natural control mechanism tuned to the 11 year cycle?

              Let’s not forget the predicate.

              Given our assumption that our black box is one where TSI input results in a Global Temp output, we need to scratch around for a natural mechanism tuned so as to provide an 11 year notch function.

              OK… let’s scratch around and see what we can come up with, but, in the process, let’s not forget Willis’s argument that an alternative approach would be to assume TSI and Global temp are not closely linked, quit looking for a notch-filter, and go scratch around looking for a mechanism providing homeostasis. Until one assumption set can be verified empirically, I don’t see a lot to choose between the two.

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            Andrew McRae

            I think David’s above point is the crucial argument in deciding whether David’s frequency analysis technique really implies a physical mechanism that functions like a notch filter.

            The main qualm I have with the Notch argument is that a suppressed response from a particular input frequency can be obtained physically by mechanisms other than a Notch Filter, with the heat capacity (“thermal inertia”) of the ocean being the most obvious candidate. If one wishes to continue looking at the problem through Fourier-coloured Electrical Engineering glasses, the thermal inertia manifests as a frequency remapping from HF to LF, as lots of small HF ripples in the input (11-year cycle) produce a slower warming and an even slower cooling. That is a transformation on the input that David’s basic filter analysis can’t represent.

            Furthermore, just by the definition of the transfer function, any frequency which appears in large amplitude in the input but is insignificant in the output must have an attenuation proportional to its size in the input. This means that everywhere in the frequency domain that the output has no significant component (but the input does) will make the transfer function look like the reciprocal (or mirror image) of the input – whatever the input. The question then also has to be asked, is this analysis technique creating a notch filter simply by definition and the particular input it was given, and not because of any physical relationship between input and output?
            Could that last statement be tested by substituting white noise for the temperature and then performing the same analytical procedure? If it still generates a notch surely that would show that the result was an artefact of the analysis technique and not a discovery of a real Notch Filter mechanism?

            I believe David has said on several occasions that he was never claiming a real notch filter exists, only that there is a notch in the effective end-to-end response. But the problem with that claim is that all the subsequent work after Part II assumes there is a real notch filter. I mean, if adding a delay in order to make the notch filter causal isn’t an attempt to locate an actual notch filter in reality then what was the point of adding the delay?

            It seems more likely that the notch is a result of the definition of the transfer function outputting the reciprocal of the input – an input which has an 11-year cycle as its most prominent component. The filter gain is above unity mainly for periods longer than 50 years, which is probably the quickest the oceans can respond to most of the insolation variance they receive. In other words there is no single 11-year notch filter mechanism because the Earth would filter any high frequency it was given, where “high” appears to mean “quicker than 50 years”.

            Then there is the issue of the strong gain in the 4-5 year component, which is probably a combination of two things: the ENSO event repeating every 4-5 years, plus annual variance downshifted to 5 years via the 5-year e-folding decay previously identified. ENSO is thought to be an internal variability of the ocean/atmosphere system, however we don’t have a spare Earth to use as a control in a constant TSI experiment, so we don’t know if Earth would have ENSO events even in the absence of TSI variance. IF it did, the 5 year gain would not represent a response to TSI variance and so would represent noise rather than climate response to TSI. We don’t have that spare Earth so we don’t know. That’s why I’m not sure the 5 year peak has much significance in deciding if the Notch is a real mechanism.

            My concerns are similar to what Willis has said, but this is not the same argument that Lubos made. It’s one thing to say there is no Notch Filter in reality. It’s quite another to say “the most obvious possible proof of the direct effect of the total solar irradiance doesn’t exist”, which is obviously nonsense because radiation heats objects and TSI is not the only solar-climate connection (as Svensmark+Shaviv have shown). Solar activity in both magnetic and shortwave dimensions drives Earth’s temperature, but the TSI spectral transfer function involves frequency shifting which a Notch Filter cannot represent.

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              Andrew McRae
              June 24, 2014 at 1:55 am

              Furthermore, just by the definition of the transfer function, any frequency which appears in large amplitude in the input but is insignificant in the output must have an attenuation proportional to its size in the input. This means that everywhere in the frequency domain that the output has no significant component (but the input does) will make the transfer function look like the reciprocal (or mirror image) of the input – whatever the input.

              Yup. Frequency input with no output is by definition a filter. Now what is doing the filtering is quite another question.

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      vic g gallus

      But when you turn on cruise control, all bets are off. When you turn on cruise control, you decouple the fuel use from the speed of the vehicle.

      No, using cruise control is the same as not changing speed without it on. If you keep the speed constant then the gain or drop in altitude shows up as changes in fuel use. Earth doesn’t tell the Sun what to do so that analogy is going nowhere.

      I’m still trying to decipher the house bit. Mine probably isn’t well insulated enough but there is a change in rate of cooling and rate of warming at sunrise and sunset. Nowhere near a linear response to intensity of the suns rays because of the rate of heat loss to the surroundings doesn’t reach a minimum till around 3pm, but still a period of 24 h. Only anecdotal but do I really need to get a pen, paper and thermometer out.

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      bobl

      Willis, you are missing the point, any control system has a time domain response, for example heating your house, the energy consumption increases as the temperature falls at night and then falls as the temperature rises during the day, this time response can be described by a filter. By taking the energy demand of the heater, and applying a fourier transform and dividing that into the output characteristic, a frequency domain transfer function for that system can be identified. This is all David has done so far. Any system can be analysed like this.

      In doing so David has made the assumption that in the absence of the control system (feedback) there would be a roughly linear relationship between TSI and temperature for small pertubations in TSI, hence there must be a system with the inverse transfer function operating in order to generate the flat output from the input. This control system for example could be your climate thermostat (early cloud emergence in the tropics). What David has shown is what the transfer function of the control system needs to be to generate the output from the input, all totally uncontraversial.

      What we need to see though, before we can really comment is the mechanism that David suggests is responsible for the transfer charateristic.

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        Willis Eschenbach

        bobl
        June 16, 2014 at 8:01 pm · Reply

        Willis, you are missing the point, any control system has a time domain response, for example heating your house, the energy consumption increases as the temperature falls at night and then falls as the temperature rises during the day, this time response can be described by a filter. By taking the energy demand of the heater, and applying a fourier transform and dividing that into the output characteristic, a frequency domain transfer function for that system can be identified. This is all David has done so far. Any system can be analysed like this.

        Great, bob. Since you claim this is true for “any control system”, here’s some theoretical data from a car running under cruise control at equally spaced times t0,t1,t2, etc, showing forcing in gallons of fuel per hour vs speed.

        Time : Forcing : Speed
        t0 2.0 gph 55 mph
        t1 2.3 gph 55 mph
        t2 1.9 gph 55 mph
        t3 1.8 gph 55 mph
        t4 2.2 gph 55 mph

        Please explain to me about the, what was it, oh, yeah, the “frequency domain response” of that system? Because as near as I can tell, it doesn’t have an inherent frequency domain response of any kind. The cruise control system is responding to changes in car speed, not changes in the frequency of hills.

        In the house example, you say that “the energy consumption increases as the temperature falls”. You are correct that there is a relationship between fuel burned and outside temperature, but you’ve missed the point.

        What there isn’t is a relationship between solar forcing and the house temperature … and that, in David’s case, is the relevant point of this example. Let me see if I can make it clearer.

        The lack of thermal response of a governed system to cyclically variable solar input does NOT mean that there is a notch filter as David claims. Instead, it is the expected response of such a system.

        For “governed system” read a house with a thermostat, or a climate with thermoregulation.

        Best regards,

        w.

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          t0 2.0 gph 55 mph
          t1 2.3 gph 55 mph
          t2 1.9 gph 55 mph
          t3 1.8 gph 55 mph
          t4 2.2 gph 55 mph

          t0 – flat terrain
          t1 – steep up hill
          t2 – down hill
          t3 – steeper down hill
          t4 – up hill

          That was not so hard was it? I of course assume t0 was on a flat. Modify accordingly if otherwise.

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            vic g gallus

            I think that the analogy of the car being in a train where all the cars responded to the fuel input differently would be the better analogy, since making a decision to put the foot down coming up a hill is not anything like the Earth’s response to TSI (or even cruise control response to a slowing speed). The shunting should still show up even if the car’s speed is close to constant.

            No response of the speedometer to throttle pressure suggests that its glued to the brake pedal.

            Either that or you bought a car from a dodgy second hand dealer and you can’t trust the speedo.

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              vic,

              That is a different question. I was merely trying to show Willis how you could discern system operation from some internal signal (in this case fuel flow – we could have used throttle position).

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          The lack of thermal response of a governed system to cyclically variable solar input does NOT mean that there is a notch filter as David claims. Instead, it is the expected response of such a system.

          But what does it tell you about the overall system? That the governor is short term and over the longer term the system is an integrator.

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          Willis,

          Please explain to me about the, what was it, oh, yeah, the “frequency domain response” of that system? Because as near as I can tell, it doesn’t have an inherent frequency domain response of any kind. The cruise control system is responding to changes in car speed, not changes in the frequency of hills.

          EVERY control system has a frequency domain response. I do control system engineering. It is inherent in the beast.

          David is not necessarily positing a control system. He is merely giving the frequency response of the system in the time domain. If the system was a tuning fork there would be a peak in the system. Tuning forks have no control. If David was looking at the energy input to a tuning fork for a given amplitude of response there would be a notch at the resonant frequency. The energy required for a given response goes down at resonance.

          David is merely working in a domain you are not familiar with. That does not make it wrong.

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            Willis Eschenbach

            MSimon
            June 18, 2014 at 2:27 am · Reply

            EVERY control system has a frequency domain response. I do control system engineering. It is inherent in the beast.

            Repeating a contested claim with one word in bold and claiming expertise is not a scientific argument.

            I gave an example of a car cruise control and asked for the frequency response. Your reply above made no sense. You said that the frequency response was:

            t0 – flat terrain
            t1 – steep up hill
            t2 – down hill
            t3 – steeper down hill
            t4 – up hill

            That was not so hard was it? I of course assume t0 was on a flat. Modify accordingly if otherwise.

            If that is a “frequency response” on your planet, I fear your terminology is totally unclear. Perhaps it would be clearer if you would show it in the usual way, as a graph of frequency vs response. Since you say you do control system engineering, this should be easy for you. Me, I don’t even understand what you are measuring as the “frequency” in terms of a car’s cruise control, so perhaps you could explain what you are measuring as well.

            w.

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      the Griss

      “you think long and hard about the example of the house”

      Why?

      A house, insulated and enclosed, little convection and reduced conduction, is nothing like the atmosphere.

      Furthermore, the heating or cooling happens within the enclosed system, not from outside (ie. the sun)

      A heated or cooled house is a REALLY BAD analog.

      It is almost totally decoupled.

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      the Griss

      Furthermore, a house with heating and cooling is an active system.

      If you turn off the active response you will definitely get a similar response to the inputs, delayed and attenuated a bit for sure, depending on construction, but it will definitely react pretty much in sync with the input.

      I know that, because its winter down here and I need to turn the active system on. brrrrrr.

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      the Griss

      Or are you saying that the Earth’s atmosphere is a active response system, that has its own internal heating and cooling systems that it turns on when needed. ????

      Which would really stuff up the CAGW myth !!!

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        Rogueelement451

        That would be a crazy idea! Who would have thought that life could have evolved on Earth in to an entirely Goldilocks situation?
        We are the product .not the freakin manufacturer.
        It is not entirely implausible that as a result of certain conditions that life might evolve and change over a period of Millennia to get where we are today and that we are the accidental result of evolution even if we might imagine we are something more important than that.
        We are but stardust ,even if we are not entirely golden.

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        Willis Eschenbach

        the Griss
        June 16, 2014 at 8:31 pm

        Or are you saying that the Earth’s atmosphere is a active response system, that has its own internal heating and cooling systems that it turns on when needed. ????

        Which would really stuff up the CAGW myth !!!

        That is exactly what I’m saying. And that is exactly what it would do to the CAGW myth. Which is why I fail to understand the hostility to the idea.

        See here for the control system, and here for the cooling system

        w.

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          farmerbraun

          Great Willis. Thanks for that. Plenty of convergence [ :-) ] happening now.
          It’s nearly 6.30 a.m. here in Godzone ; looking forward to a fruitful discussion today.
          Best regards
          Farmerbraun

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          I agree with you here Willis. The 11 year “notch” says exactly that. Active control. The fact of no notch at 22 years and lower frequency says the control system has limits.

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          the Griss

          I have to go to work now, unfortunately and don’t have time to read the links at the moment. :-(

          I do understand the emergent phenomena you are suggesting, but what drives them (sorry, only did a skim read)

          A link between your work and David’s would be very interesting..

          I’m going to adopt a wait and see attitude. :-)

          Notice that the 3 ElNino events in the satellite record all correspond with the upward leg of the TSI curve.

          Linkages to be found, I suspect.

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      NikFromNYC

      But the house stays at 78 degrees all year whereas the temperature outside varies a lot on various time scales that evidently spit out an eleven year long signal even when sampled variously. I may be misunderstanding the claim though. They don’t see no influence like the house and so seek to explain it through a matched feedback, but evidently have a correlation with real temperature variation as if the sun itself is the thermostat by complex mechanism. Besides, their math may be equivalent to your own homeostatic control in action. Now I’m way in over my head but its personally valuable for me as an outsider to signal analysis to at least record my confusion now to see how my intuition functioned, early on.

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    Jo, David,

    I can see now why you are dribbling this out. For someone not conversant with EE it is difficult to wrap your brains around. Very difficult. And you are dealing here mostly with folks on your side.

    I’d like to get it in one fell swoop. But that would be a disservice to most of your audience.

    I must say dealing with frequency analysis and then converting that to a Bode plot is brilliant. Not that it isn’t done every day in other realms. But for climate? That is brand new. Esp. the 11 year dip.

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      Yonniestone

      I agree it’s a very wise (and patient) move by David to release this new idea in everyday speak especially for laymen like myself, the greatest benefit of this will be not just for me but others in the same position when I can successfully relay this information to them also.
      And therein lies the greatest need for work like this to be publicly recognized not simply for it’s content but for it’s adherence to a method somehow lost in apparently modern times to the detriment of those who forgot or simply don’t realize.
      It may be quite poetic or sanctimonious of me to suggest the population needs another scientific age of enlightenment but considering the somewhat willing regression of people (who know better) to do so for little more than personal gain I believe it can’t come soon enough.

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        bobl

        Yonnie,

        You can be very insightful sometimes, I think we are on the cusp of a revolution, a revolution of citizen science fueled by the wealth of information available on the internet. I think perhaps some of the more insightful discoveries in the future won’t come from mainstream science but from lay scientists.

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          Science started before there were professional scientists. Clearly, you can’t be a master of a discipline before the discipline exists. It all has to start someplace. Hence, the foundation of ALL science was laid down by who were not scientists. (Gasp! The god of science has feet of clay. Woe is us. We are doomed. NOT!)

          A scientist is someone who was certified to be a scientist by a scientist who was certified to be … Its turtles all the way down and there is no bottom. Thus the absurdity of the claim that only a scientist certified in a particular branch of science can validly comment on that branch of science is established. The certification is not worth the paper it is printed on. What matters is what the person can do and prove.

          It has been my experience that people who are totally indoctrinated into their specialty can neither see the trees nor the forest of their specialty. Only their dogma exists for them. While skilled thinkers and doers from outside the specialty can see what is real far more clearly. The fact is, ALL interesting and meaningful problems to be solved are between multiple specialties. A specialist can only repeat his specialty endlessly and solve problems that have already been solved.

          This is why someone skilled in systems analysis, signal analysis, and electronics design has a better chance of coming up with a solid understanding of our climate system than a thousand so called climate scientists. This is largely because he doesn’t know what is true or false about our climate. He then simply attempts to discover the truth and knows how to do it.

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    Tel

    Very interesting. Agreed that you have brought up a valid observation that has no easy explanation… strong input signal at a period of 11.8 years, but no observation of this signal in the output. Yes, it’s worth having a look into, I’m sure it means something… however I’m uncomfortable with the “notch filter” idea.

    Here is my reason: a notch filter requires resonance. There is no such thing as thermal resonance, I’m completely confident that no one can demonstrate a working model of a thermodynamic resonator.

    Mechanical systems can have resonance (e.g. twanging a springy strip of metal, or making a metronome) and a mechanical device could indeed operate as a notch filter.

    Electromagnetic systems can have resonance, as has been demonstrated by plenty of electrical engineering.

    Electromechanical systems can have resonance (classic quartz crystal clock for example).

    Where is the resonator in our climate system? Why is it tuned to the same frequency as the Sun?

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      bobl

      Rubbish, any real feedback system takes time to act, when you combine a time lag with feedback you get reasonance in the feedback system.

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        any real feedback system takes time to act, when you combine a time lag with feedback you get reasonance in the feedback system.

        If the gain is high enough.

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      a working model of a thermodynamic resonator.

      Lava lamp.

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        If the lava lamp cycles at 11 minutes David Evans should be able to show this filtering frequency and Willis Eschenbach should be able to show how it works equally as well at 24 seconds.

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        Tel

        Lava lamp has a significant mechanical component, it depends on convection, driven by thermal expansion and contraction.

        I agree that convection in the troposphere is a bit similar, but that would imply we can directly see the moving parts of the resonator. With something like ESNO we can directly measure it, but ESNO does not appear to consistently lock with the Sun.

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      I suggest that it is important not to think of specific mechanism at this point in the analysis. It is the behavior that is important. Only when that is known, does investigation into mechanism have a chance to succeed.

      It has been found that the behavior of a system that has a notch filter is equivalent to the observed climate behavior. This does not mean that it IS a notch filter but that it BEHAVES like a notch filter. As a consequence, in any analog simulation of climate, this particular behavior can be correctly simulated by a notch filter.

      For example, an accelerating car is not F=MA but its behavior can be described by the equation and its derivatives.

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      Tel, you are onto something. The resonator you are looking for is not in Earths Climate — it is in the sun itself. See our newest post: http://joannenova.com.au/2014/06/big-news-part-iv-a-huge-leap-understanding-the-mysterious-11-year-solar-delay

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    Mikky

    Looking forward to reading more, but am puzzled by a few things so far:

    1. If TSI is essentially flat, but with an 11-year oscillation, then does the input not consist of just 2 frequencies:
    DC (direct current, i.e. 0 Hz) and 1/11 Hz (maybe with harmonics for a non-sinusoidal periodic variation)?
    Not sure how well you can deduce an entire transfer function from just 2 main input frequencies.

    2. The notch in all the temperature data-sets is just the absence of an 11-year oscillation.
    There would be a similar notch in the transfer function to my bank balance or to my weight.
    To me the data are saying “absence of peak in spectrum” rather than “notch” in transfer function.

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      David Evans

      Yep, grossly simplified, that’s it. So why doesn’t the 11 year sinusoid from the TSI cause a corresponding 11 year sinusoid in the temperature?

      In a more detailed view, frequencies near 11 years get attenuated too. Other frequencies (periods longer than about 5 years) of TSI seem to get through to heat the Earth just fine. Just the ones near 11 years and less than 5 years or so get clobbered.

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        Mikky

        This notch would be a great discovery, but many will be sceptical (certainly The Consensus advocates, but also some of the AGW sceptics).
        Can you provide positive evidence of responses at (say) 8 and 15 Hz?
        If so, where are those input frequencies coming from (non-regularity of the 11-year oscillation?)

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          David Evans

          Only proof I have is the transfer function, which is at a higher levels except for sinusoids with periods around 11 years and less than 3 years. When we get to the physical interpretation it will become clearer.

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            Mikky

            I am very worried that the notch frequency matches the peak frequency of the input data, suggesting a possible artifact of the processing algorithms.

            Have you tried estimating the transfer function to a set of random numbers (hoping here for no sign of a notch)?

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              David Evans

              The same software and procedures that found the peak in TSI (Fig. 2) failed to find a peak in the temperatures (Fig. 4). The software and procedures knows nothing about 11 years or climate data — its just generic Fourier analysis software that, by checking reconstruction of all types of climate datasets from the sinusoids it finds, obviously works well.

              As it happens I did run some random numbers through at some stage while I was fooling around with the effects of noise, but no notch emerged as I recall.

              I’m sure that the software has no artifacts that could produce a notch. You’ll be able to try it yourself soon :)

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                Mikky

                Sadly I think you are mistaken.

                Re-reading the post, you have derived the transfer function at a particular frequency as A/B,
                A = output amplitude, B = input amplitude.

                The “notch” simply arises from the peak in the input spectrum, as the output has no matching peak.
                The transfer function to my bank balance would also have a notch,
                i.e. the notch is an artifact not a genuine feature of the physics.

                Absence of signal may well be correct though.

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                David Evans

                Mikky, your bank balance has no connection to TSI (I assume). So any connection found by a transfer function from TSI to your bank balance developed over some time period would be random (the transfer function between independent variables is random). So finding the transfer function at another time period would likely give a different transfer function. And so on.

                However, see Figure 6. The transfer function from TSI to temperature is the roughly the same every time. (And anyway, we are implicitly assuming that more TSI leads to a warmer world, so they are not independent variables.)

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                Willis Eschenbach

                David, sadly, Mikky is right. Assuming that Mikky’s balance is like the temperature, without big cycles of any kind, the transfer function from TSI to Mikky’s bank balance will definitely have a notch at 11 years. And the notch, contrary to your claims, will be at eleven years every time. In fact, the transfer function for Mikky’s bank balance will look very much like your Figure 5.

                Truly, my friend, it appears that you need to try these things before opining on them. Try out your system using white noise, and you’ll get a transfer function that looks just like Figure 5.

                I’m totally serious, David. If you run your system against white noise instead of temperature datasets, you’ll get Figure 5 … are you going to claim that there is a “notch filter” in white noise?

                And all of you math-inclined folks out there that believe David’s claim that there is a “notch filter” in the climate … I encourage you to do the same. Get some plain vanilla white noise, and run a Fourier analysis on it … basically, you’ll get a straight line.

                And that straight line is exactly what you get from the temperature datasets, or as David put it,

                The temperature amplitude spectrum, the smooth orange curve in Figure 4, is essentially straight over more than three orders of frequency magnitude, with no other definite features.

                And if you subtract the solar Fourier results with the hump at 11 years from that straight line, YOU WILL GET A GRAPH WITH A NOTCH AT 11 YEARS THAT LOOKS JUST LIKE FIGURE 5.

                And after you do that and think about it for a while, if you still think that the notch in Fig. 5 means that both white noise and the climate system contains a mysterious “notch filter” specially tuned for 11 years … well, I fear at that point science can’t help you, and neither can I.

                w.

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                Willis says:

                If you run your system against white noise instead of temperature datasets, you’ll get Figure 5.

                If the OFT is correct you will not get a notch from white noise. The line will be “flat” all the way across (with some wiggles because it is noise).

                The notch is a clue.

                David is Sherlock against the average Yard Inspector. The Inspector is blinded by what he expects to see and what he thinks he knows. “The dog didn’t bark.”

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                And if you subtract the solar Fourier results with the hump at 11 years from that straight line, YOU WILL GET A GRAPH WITH A NOTCH AT 11 YEARS THAT LOOKS JUST LIKE FIGURE 5.

                True that. Now what does the subtraction?

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                Mikky

                Testing against white noise has the advantage of simplicity, but the disadvantage of fluctuations.

                Can I suggest testing against a simple low-order polynomial model of the temperature variation,
                or maybe against a temp time series that is a low pass filtered version of the TSI data.

                Pretty sure a notch will appear, even though the output was constructed without one.

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                Mikky

                To prove the presence of a special “notch” filter you really need to show that the low pass filter cannot provide adequate suppression.
                That will be very hard to do, for example a “flat” 11-year average of TSI data provides perfect nulling of 11-year cycles.
                A more realistic filter (e.g. over 20 years with tapered weights) can also provide such nulling, or at least severe suppression.

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    Paul Vaughan

    Observation:

    New SAM reconstruction (Figure 2) follows notch-filtered Sunspot Integral over the entire sunspot record.

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    janama

    Can I make a wild guess here? I bet the counter phase is related to the Moon’s cycles. :)

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    Mattb

    Forgetting climate for a second… surely the “smart” way to do this would be to have David and a couple of other genuine mainstream respected mathematicians simply work on having the Optimal Fourier Transform critiqued and accepted. I mean it would be a pretty decent (amazing) contribution to maths/engineering to have “invented” such a thing. Once this is achieved you would suddenly say “hey look what this means for climate science!”.

    To me your current approach is to say “HERE’S AMAZING* NEWS ON CLIMATE SCIENCE”

    *based upon a new and untested approach to fourier analysis that no one has had a chance to see if it works or not

    Linking it to climate of course means that when people question the OFT… well of course they would question/oppose they’re slaves to BIG SCIENCE. It’s an easy out for your opponents, and your supporters.

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      Backslider

      based upon a new and untested approach to fourier analysis that no one has had a chance to see if it works or not

      Problem Matt is that the above statement is false.

      Nice to see your grudging acceptance.

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        Mattb

        not a grudging acceptance of anything you say you miserable maggot. in a two sided debate there will always be prats on either side who get a smug grin in spite of their total lack of comprehension of pretty much anything.

        So anyway, I see no evidence that “the above statement is false”.

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          farmerbraun

          Fair enough. I have already read above that the approach has already likely been used /developed before by others.
          If you want to call it new and untested, that’s okay. Does it matter?

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          Backslider

          So anyway, I see no evidence that “the above statement is false”.

          That’s because you just dribble off at the mouth and do no read.

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          PhilJourdan

          miserable maggot

          Really matt? Is that what you have devolved into?

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        Mattb

        some genuine advice for you BS, and you could apply it in pretty much every situation in your life. When you are thinking of saying anything: take a deep breath, count to three, keep quiet.

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      Tel

      David has linked to an explanation of the algorithm along with worked examples. What else do you want? Anyone is welcome to test it.

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      David Evans

      Matt, the OFT is a straightforward refinement of the DFT, and the resulting discovery of a notch does not depend on it.

      The OFT, like all Fourier analysis, is hard to do but easy to check. Simply analyze a dataset using the OFT or whatever, then reconstruct the dataset. Compare the reconstructed dataset with the original dataset. The OFT obviously works, quickly approximating the typical climate dataset with a handful of sinusoids and progressively improving the as more of the sinusoids identified by the OFT are added to the reconstruction.

      I originally found the notch using the DFT. It was a bit hazy and indistinct, so I developed the OFT to be sure of it, and the picture came up a lot sharper. The notch can be seen by a causal inspection of the TSI and temperature, as in Figure 7.

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    A comment I left here: http://wattsupwiththat.com/2014/06/06/sunspots-and-sea-surface-temperature/#comment-1663381

    Willis,

    But you found the evidence of the “notch filter” yourself. The absence of the 11 year signal. And you know that the Maunder minimum shows up in the temperature record. So “low” frequency signals (in the case of Maunder several decades of low SSNs) get through. The question then is what causes the 11 year “notch” ?

    Jo and David claim to have found a mechanism to explain it. We shall see in due time if they have.

    In fact it was your analysis here [at WUWT link above] that got me excited about what David/Jo have claimed to have found.

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    I suggest that the 11 year solar variations are swamped by the seasonal adjustments in the global air circulation pattern as they move north or south annually.

    When one then moves on to multiple solar cycles trending towards warming or cooling the solar induced changes gradually become a larger proportion of the annual changes and become much more apparent over time as the distances that the climate zones and jet stream tracks migrate over decades or centuries starts to be noticed over and above the background annual shifting.

    If the sun alters the system so as to change global cloudiness then that will mimic a change in TSI because the proportion of TSI getting into the oceans will change and that will lead to overall warming or cooling subject only to the power and efficiency of a changed speed for the hydrological cycle which tends to neutralise even changes in the amount of TSI that gets into the oceans. Hence the early faint sun paradox.

    The notch, if substantiated, provides evidence of a powerful negative system response in the short term which causes the system to take decades or centuries to accumulate or dissipate the effects of solar induced changes.

    The single cycle effects disappear in the noise of the system but multiple cycles do have a cumulative effect. Hence nothing of note seen in the short term but eventually one gets times such as the MWP, LIA and current warm periods.

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      The notch, if substantiated, provides evidence of a powerful negative system response in the short term which causes the system to take decades or centuries to accumulate or dissipate the effects of solar induced changes.

      Yes.

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    Mark F

    I’m fascinated by two things:
    1. Knowing a bit about signal processing, I accept your simplified background explanation in total. I can’t wait for more shoes to drop.

    2. The pronounced overshoot and ringing from the usual gang of objectors simply reflects their inherently parasitic nature. IMO.
    Good work!

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    [...] BIG NEWS Part II: For the first time – a mysterious notch filter found in the climate [...]

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    Knowing a little bit about stochastic deconvolution/signal processing in catchment hydrology and water-related land climatology (rainfall, evapotranspiration) I also know that there is really no shortage of good signal processing experts around the world. I’ve already given a few the heads up on what is foreshadowed here (;-).

    But I am concerned that already we see here use of a selective set of TSI estimates at a time when both TSI as such, and even now related subtle effects such as the variation in upper atmosphere UV flux with variation in solar activity (with possible hitherto obscure teleconnections into global cycles such as ENSO) are being intensely studied and debated in the literature.

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      David Evans

      Selective? I used all the main TSI datasets and all the main proxies for TSI like sunspots (SIDC) and f10.7, except ACRIM before 1983 (when it flagrantly disagrees with PMOD and the others).

      It doesn’t matter which TSI datasets are used to look for a notch — they all show peaking every 11 years or so, obviously enough.

      The datasets of much more concern for the notch are the temperature datasets, none of which show the expected signal (satellite, land thermometer, or big mutli-proxy).

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    Rick H

    Looking at the graph showing both temp and tsi, you can actually see an obvious correlation of the curves after about 1945. Is there any chance that data prior to that time just isn’t accurate enough?

    —-
    The data is noisy (oh for satellites in 1880!) but figure 6 compares transfer functions before 1945 as well. – Jo

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    Willis,

    A thermostat is a notch filter for all frequencies less than the response frequency of the system. (not exactly correct but the farther [lower frequency] from the response frequency the more correct)

    So that leaves a question. Why 11 years? Why not 50 also? Or 500 in addition? You have not thought this through carefully. Very unlike you.

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    Willis Eschenbach

    David Evans
    June 17, 2014 at 6:24 pm · Reply

    The Earth does not have a zero response to TSI — when there is more TSI the Earth heats up. So when the methodology shows a notch, there is a notch filter.

    I thought that the whole thrust of your post is that in the ~11 year range, the earth does have a zero response to TSI, and you’re trying to explain that …

    Yes, the earth responds to variations TSI … but only large variations. But according to you and me and some other folks, it does have a zero response to minor TSI variations, that’s what you are trying to explain. (In passing, I note that over at WUWT people are yelling at me and abusing me loudly for saying what you are saying, that there is no 11-year solar cycle visible in the temperature records … but I digress.)

    So … when you are trying to explain why the earth doesn’t respond to minor TSI variations, claiming that “Earth does not have a zero response to TSI” makes no sense. That’s what you are trying to explain, you can’t use it as an explanation itself.

    My point remains. Originally, you claimed that if we had a signal and we didn’t see a response, it meant that there was a “notch filter” in the system.

    I have shown through several examples that this was simply untrue, because there are a number of systems out there where there is a signal, but there is no response and no notch filter, including things with a “governor”, like cars with cruise control and James Watt’s steam engine.

    Your response appears to be that if the signal overpowers the control system at times, this proves that there is a notch filter. You say above that because the changes in e.g. daily strength cause variations in the temperature, this shows that a notch filter exists.

    But that’s like watching a car with cruise control that hits a big hill … it will definitely slow down, but that doesn’t mean that for smaller variations you will see changes in the regulated speed of the car. It has a zero response to small variations, DESPITE having a response to large variations. The same is true of the house. On a really hot day, the air conditioner may not be able to keep up with the increasing heat … but it still has zero response to small variations, again DESPITE having a response to large variations.

    In other words, all you’ve shown is that for any control system (including the earth) a large enough input signal will be visible in the regulated output.

    But that means nothing at all about whether there is a “notch function” in the climate system, the house system, or the car system. It just means that every control system has a limit.

    In fact, your own graphic shows that there are other much smaller “notches” up at higher frequencies … and something I hadn’t noticed before, a peak at 3.5 years … is it also your claim that in addition to having a “notch filter” operating at ~11 years that there is an amplifier operating around the three year range?

    Look, David, you’ve lost already when you agreed with me that there are a variety of systems that have a notch without a notch filter. At that point, your “notch” ceases to be evidence in favor of your claim. But since the notch is the sum total of your evidence for your “notch filter”, your hypothesis is currently without a foundation.

    My other huge problem with your hypothesis is that I don’t know of any thermal system which contains a “notch filter”, and despite being a bear of little brain, I’m not sure I could figure out how to construct one. The problems is resonance. Filter circuits work by resonance. So … either you’ve developed some new and unseen type of filter, or you are asserting that the earth as a thermal system exhibits resonance.

    In either case, your claim would have much more chance of being both true and accepted if you could give us one, just one, example of a natural (or man-made, although it’s less relevant) thermally based notch filter circuit. You know, for example a piece of metal or a container of liquid that responds to daily changes in temperature and monthly changes in temperature, but shows no response at all to weekly changes in temperature. I can’t think of a single example of a “thermal notch filter” … which makes your claim very doubtful right out of the box, since it pre-supposes a “thermal notch filter” mechanism which is left as a “teaser”, but which as far as I know is totally novel and exists nowhere else in nature.

    So … if you know of such a thermal system which exhibits a “notch filter” behavior … now would be the time to point it out.

    Finally, my thanks to you for continuing the discussion, much appreciated.

    w.

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      http://joannenova.com.au/2014/06/big-news-part-ii-for-the-first-time-a-mysterious-notch-filter-found-in-the-climate/#comment-1487099

      Monckton of Brenchley
      June 16, 2014 at 7:38 am · Reply

      David Evans is not saying the response to changes in solar output is linear.

      But he says the evidence for a pronounced notch at 11 years exists in all the datasets. This is a finding in Fourier analysis, not the preconception that Willis Eschenbach seems to be suggesting.

      It is self-evident from the geologic-timescale temperature reconstructions that the climate object is temperature-homeostatic. To be able to identify some of the relevant mechanisms, as David has done, is very valuable work. Best not to shoot it down until you have seen it all.

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      Yes, the earth responds to variations TSI … but only large variations.

      We shall assume the signal processing is correct.

      There is signal at 3 years. There is signal at 22 years. There is a greatly attenuated signal at 11 years.

      Please explain the attenuation at that specific frequency.

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      David Evans

      Willis, “In passing, I note that over at WUWT people are yelling at me and abusing me loudly for saying what you are saying, that there is no 11-year solar cycle visible in the temperature records … but I digress.”

      Yes, I noticed you had found the notch by different means, and I reference your post in the big paper. The response concerned me because I knew I would be saying the same thing soon… Thanks for breaking the ice and “doing the hard yards”.

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        David,

        I had read that post and when this series came up I got real excited. Independent confirmation. And better yet you promised a mechanism which I’m beginning to see the outlines of. Excellent! I’m looking forward to the rest of the series.

        And really. It is a notch filter centered on 11 years and matches very well the variations in the cycles implicitly. Excellent.

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      David Evans

      Willis, “I have shown through several examples that this was simply untrue, ”

      Again I ask, what is the input and what is the output of your car-cruise-control system?

      Your example of the house is structurally different to the Earth system considered here (TSI in, temperature out), so is not relevant. The Earth system here was explicitly assumed to be linear and invariant (see post above), and implicitly assumed to have a non-zero response (that is, an increase in TSI will increases temperature somehow sometime).

      If your house is kept at exactly the same temperature by its heating/cooling/control system, then it has a zero response, so it is not like the Earth system considered here.

      If your house is a real temperature-controlled house then the heating/cooling/control system allows a bit of temperature variation before it kicks in and brings the temperature back into the desired range. In the period before acting, when it is allowing the temperature to drift, your house is linear, but when the heating or cooling kicks in it is very non-linear (the temperature change is not proportional to a corresponding move in the TSI). Overall the house is non-linear, that is, the system of (TSI in, house temperature out) is non-linear due to the cooling or heating that occasionally kicks in. So this house system is not like the Earth system considered here.

      What you are proposing as a control system on Earth is not a on-or-off control as in the house example, but its response comes in gradually, and might be more or less linear for small temperature perturbations. I assumed above that for small enough perturbation of TSI, the changes in temperature, even in the presence of such a control system, are linear in TSI.

      As remarked previously, I don’t know whether the Earth climate system really is linear enough to apply systems theory/Fourier analysis as above. There is no real way to find out in this case, AFAIK, except to apply it — if the resulting model works, it probably was sufficiently linear.

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      David Evans

      Willis, “Look, David, you’ve lost already when you agreed with me that there are a variety of systems that have a notch without a notch filter.”

      Read the qualifiers. That agreement was for a system with zero response to TSI, which is different from the Earth system under consideration here.

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      David Evans

      Willis, “My other huge problem with your hypothesis is that I don’t know of any thermal system which contains a “notch filter”, ”

      Illogical, IMHO (the state of the Universe is independent of your knowledge). Sorry, I know that sounds snarky, but argument from ignorance is weak.

      And I do the same myself in two posts on when I argue that an 11 year delay cannot be due to anything here on Earth because I can’t think of one, so it must be due to the Sun, which has an 11 year clock. (http://joannenova.com.au/2014/06/big-news-part-iv-a-huge-leap-understanding-the-mysterious-11-year-solar-delay/)

      Yep, I know that’s hypocritical. Even worse, we’ve been ragging on the warmists for years because their response to criticism of how poorly the CO2 theory fits real-world data is often to say “well what else could be causing global warming if not CO2?”. Ironies abound.

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        Willis Eschenbach

        Willis,

        “My other huge problem with your hypothesis is that I don’t know of any thermal system which contains a “notch filter”, ”

        Illogical, IMHO (the state of the Universe is independent of your knowledge). Sorry, I know that sounds snarky, but argument from ignorance is weak.

        And I do the same myself in two posts on when I argue that an 11 year delay cannot be due to anything here on Earth because I can’t think of one, so it must be due to the Sun, which has an 11 year clock. (http://joannenova.com.au/2014/06/big-news-part-iv-a-huge-leap-understanding-the-mysterious-11-year-solar-delay/)

        Yep, I know that’s hypocritical. Even worse, we’ve been ragging on the warmists for years because their response to criticism of how poorly the CO2 theory fits real-world data is often to say “well what else could be causing global warming if not CO2?”. Ironies abound.

        Thanks, David. While I agree in general with your description of the irony, I was actually speaking of something different. I’m not making the “argument from ignorance’.

        My problem is not “lack of an alternate explanation”, as in your example of “what else could be causing global warming”. That is indeed an argument from ignorance, saying that before you say that A is wrong you have to propose an alternative. That, as you say, is very weak … but lack of an explanation not my problem.

        My problem that you’ve proposed an explanation for which I know of no other real-world example. This explanation is that there is a “thermal notch filter”, a type of creature which I’m totally unaware of.

        Your case would be greatly strengthened by your providing a real-world example of such a beast. I can’t even begin to figure out how such a thing would work.

        My regards to you,

        w.

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      David Evans

      Willis, “Filter circuits work by resonance.”

      Not first order filters like low pass filters.

      But yes, to make a notch filter you basically make a resonant circuit and look at the voltage or whatever not taken by the resonant circuit (the transfer function of a notch and a resonant circuit are the same only flipped vertically). This had me stumped for months. To make a notch you need at least two 2nd order filters (2 poles and 2 zeroes), and while I could make vaguely plausible arguments for the existence of a pair of 2nd order control systems in the atmosphere, I couldn’t see why they would possibly interact to give a notch bang on 11 years. The explanation seems to lie in the Sun itself — see the fourth post in the series, on the physical interpretation of the cause of the notch: http://joannenova.com.au/2014/06/big-news-part-iv-a-huge-leap-understanding-the-mysterious-11-year-solar-delay/

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    Cees

    Joanne, you write “Dividing the orange line in Figure 4 by the orange line in Figure 2, we arrive at the empirical transfer function shown in Figure 5″.

    Well, you do not. You can only estimate a transfer function from the CROSS-spectrum of output and input, divided by the spectrum of the input (both properly averaged to suppress noise). Dividing the output spectrum by the input spectrum gives you nonsense. It is easy to see why: if what you did would work, then you could obtain valid nonzero estimates of transfer functions for pairs of totally unrelated variables. And obviously that is impossible.

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      David Evans

      A transfer function is the output divided by the input in the frequency domain, e.g. http://en.wikipedia.org/wiki/Transfer_function#Signal_processing (their variable s is the complex frequency, it simplifies to the frequency f as used here when it is brought appropriately into context).

      If you attempt to construct a transfer function from independent variables you get a random transfer function. So do it again, for data from another time period, and you will likely get another transfer function, and so on. In Figure 6 above we show you get the same transfer function over different periods.

      Basically, only use transfer functions when you know one variable depends on the other:) Note also the question we set out to answer in this project: If the recent global warming was associated almost entirely with solar radiation, and had no dependence on CO2, what solar model would account for it?

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    Cees

    Sorry, forgot something. What I wrote before does not even account properly for noise in the input. You can check by reversing input and output to estimate the inverse of the transfer function. If these estimates are inconsistent, then at least one of them is biased.

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    Richard C (NZ)

    David

    >”The TSI peaks every 11 years or so, yet there is no detected corresponding peak in the temperature, even using our new low noise optimal Fourier transform!”

    Maybe the peak isn’t an indicator, see:

    ‘Observed Tropospheric Temperature Response to 11-yr Solar Cycle and What It Reveals about Mechanisms’

    JIANSONG ZHOU AND KA-KIT TUNG
    Department of Applied Mathematics, University of Washington, Seattle, Washington
    (Manuscript received 27 July 2012, in final form 10 October 2012)

    ABSTRACT
    Using 54 yr of NCEP reanalysis global data from 1000 to 10 hPa, this study establishes the existence and the statistical significance of the zonal-mean temperature response to the 11-yr solar cycle throughout the troposphere and parts of the lower stratosphere. Two types of statistical analysis are used: the composite-mean difference projection method, which tests the existence of the solar cycle signal level by level, and the adaptive AR(p)-t test, which tells if a particular local feature is statistically significant at the 95% confidence level. A larger area of statistical significance than that in previous published work is obtained, due to the longer record and a better trend removal process. It reveals a spatial pattern consistent with a ‘‘bottom up’’ mechanism, involving evaporative feedback near the tropical ocean surface and tropical vertical convection, latent heating of the tropical upper troposphere, and poleward large-scale heat transport to the polar regions. It provides an
    alternative to the currently favored ‘‘top down’’ mechanism involving stratospheric ozone heating.

    http://depts.washington.edu/amath/old_website/research/articles/Tung/journals/Zhou_and_Tung_2013_solar.pdf

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    Curt

    David:

    A small suggestion on your linked OFT paper (from someone who also studied Fourier Transforms from Bracewell at Stanford):

    You invented the “pha” function to get a four-quadrant arctangent. There is a common standard function that already does this, called “atan2″, for two-argument arctangent.

    Both Excel and Matlab, and I’m sure most other math programs, provide this function standard. Just be a little careful if you are using multiple programs. Excel provides it as atan2(x,y), with the cosine argument first. Matlab provides it as atan2(y,x), with the sine argument first.

    I haven’t had time to go through your spreadsheet yet, but I think you could probably simplify it if you wanted.

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      David Evans

      Thanks Curt! I wasn’t aware of that, always rolled my own. Might be time to retire “pha” soon.

      I’ve added a note about atan2 to the OFT document.

      What a small world! Cannot be too many who studied FTs with Bracewell at Stanford who have drifted into climate world.

      The spreadsheet does all its computations in VBA. The sheets are just for entering and displaying data, and graphing. The pha function is about 15 lines of 15,000 lines. If people are interested in the model and so on, the spreadsheet code is pretty much ready to be ported to better computational environments. Will release it soon, but haven’t released it yet to keep the discussion focused on the blog posts as we roll out the topics and stop people jumping ahead.

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    Willis Eschenbach

    First, my thanks to David and Jo for a most interesting thread.

    Next, I note a most curious thing. Both David and I have independently been making the same claim, that there is no sign of an 11-year cycle in the temperature datasets. However, over at Watts Up With That I’ve been getting nothing but brickbats for saying that, with a host of people jumping up to tell me that I’m wrong and an idiot to boot, and proclaiming loudly that there IS such an 11-year cycle in some dataset or other.

    Over here, on the other hand, David is getting little but kudos for making the same claim, that there is no 11-year cycle in the temperature dataset.

    In addition to highlighting the ironic nature of this discrepancy in public reaction, I bring this up to point out that David and I are in agreement on the situation. We differ only in the explanation.

    Let me take as my departure point a review of the bidding:

    Willis:

    Look, David, you’ve lost already when you agreed with me that there are a variety of systems that have a notch without a notch filter. At that point, your “notch” ceases to be evidence in favor of your claim. But since the notch is the sum total of your evidence for your “notch filter”, your hypothesis is currently without a foundation.

    David:

    Read the qualifiers. That agreement was for a system with zero response to TSI, which is different form the Earth system under consideration here.

    And therein lies the problem. David believes the current paradigm, that changes in temperature are a linear function of changes in forcing. I find no evidence to support that view.

    Let me quote from my first post here on the subject:

    The problem here is the underlying assumption. This is that the output of the of climate system is a linear function of the inputs.

    IF we assume that output is a linear function of the input, yes, there appears to be a “notch filter” in the system.

    But this is merely a result of our assumption that

    ∆T = lambda ∆F

    where delta (∆) means “the change in”, T is temperature, F is forcing, and lambda is the so-called “climate sensitivity”

    This is certainly the current climate paradigm. However, I see no reason, either theoretical or observational, to believe this paradigm. Theoretically, I don’t know of any complex flow systems whose outputs are a linear function of their inputs. Try to channelize a meandering river and you’ll see that right away.

    And observationally, we see no evidence that the increase in CO2 has led to a corresponding linear increase in temperature.

    Expecting the climate to show some sign of changing temperature in response to small changes in solar input is like expecting a house with a furnace and an air conditioner to show some sign of changing temperature in response to small changes in solar input.

    In other words, as an average over time, not only does the climate have little response to changes in TSI, it has little response to changes in any forcing.

    Consider, for example, the 20th century. We had a number of large volcanic eruptions. We had very large changes in the aerosol content of the atmosphere. We had increases in GHGs, and changes in solar insolation.

    And with all of those changes, over the entire 20th century we only see a change of ±0.3°C, which is a variation of only 0.1%. All of those changes, tiny response … are we seeing a pattern here?

    Now, as I said above, David and I agree that there is no sign of the 11-year solar cycle in the temperature datasets. We only differ on the explanation.

    I say that this is a result of the existence of a range of emergent phenomena that materialize out of thin air to cool the earth when it gets hot. Chief among these are the tropical cumulus clouds and thunderstorms. Just like a car’s cruise control regulates the energy entering the engine, these tropical clouds regulate the solar energy entering the climate system.

    It’s a lovely mechanism. In the morning when it’s cool, there are no clouds. But when it hits a certain temperature threshold, typically around 10:30 AM, cumulus clouds form. The effect of this is so strong in some places that the average temperature actually drops despite increasing solar irradiance as the sun moves higher in the sky.

    So when the tropics are a bit warm, clouds form earlier, sunlight is cut off, and the earth cools down. When the tropics are a bit cool, the clouds form later, more solar energy enters the system, and the earth warms up. It’s a simple, fool-proof throttle-control system that has never failed. Consider that if this cloud regulation mechanism were to disappear and allow the full power of the sun to enter the climate system, it would fry the planet in very short order … but in millions of years, as far as we know this has never happened.

    In addition, there are a number of other emergent phenomena which cool the earth, ranging from dust devils to El Nino and the Pacific Decadal Oscillation. These all work in concert with the tropical clouds and thunderstorms that regulate the incoming energy. And like the thunderstorms, all of these only form when the temperature passes a certain threshold.

    And that is the main reason that the system is so stable—the thresholds for emergence of these phenomena are temperature based, not forcing based. Clouds don’t form because the sun is high in the sky and supplying lots of solar forcing. Clouds form because the temperature is high … and as a result, per your request, David, the climate system indeed has close to zero response to small or slow changes in TSI. Yes, we have responses on a daily and annual basis, so clearly the system can be forced up and down by large changes in forcing. This is the same thing that happens to a house with a cheap air-conditioner and furnace—on a really hot afternoon the house temperature goes up, on a really cold night the house temperature goes down, but on average over time, it keeps the temperature within a narrow range.

    To see the difference between my explanation and David’s explanation, consider that the sun, according to the accepted stellar evolution, is about 5% more luminous now than it was at the time of the Cambrian explosion. This represents an increase of about 16 watts per square metre (W/m2) over that time.

    Now, IF things were as David and the current IPCC climate paradigm claims, we should have seen a global warming of somewhere around 3° per doubling of CO2 = 0.8°C per W/m2 of warming. That works out to a predicted warming of about 13°C, or 24°F, in the half-billion years since the Cambrian explosion.

    But just like the rest of the alarmist predictions of warming due to increased forcing, obviously that one didn’t come true either. Nobody is claiming that the earth now is 24°F warmer than it was during the Cambrian, if anything, it’s a bit cooler … in other words, the climate system shows nearly a zero response to a slow change in TSI.

    I explain that by saying that the thermoregulatory system has acted (within the changing physical parameters of the locations of the continents) to minimize the temperature changes from that very large change in forcing.

    The same is true for the claimed effects of volcanoes. Their effect is much, much smaller than is predicted by the current paradigm or simulated by the models, and I explain that in the same way. When volcanoes cause the earth to cool a bit, in response clouds form say fifteen minutes later in the tropics, and that allows in a lot more solar energy … and the temperature changes very little. I hold that this is why the volcanoes don’t do what the current paradigm and the climate models say they should be doing.

    The alternate explanation is that there is a notch filter at 11 years, plus a long term filter at hundreds of thousands of years … plus a variable time filter for volcanoes … plus a filter for changes in albedo …

    Anyhow, that’s my take on all of this. Let me offer a few links to substantiate, further explain, and support my claims with evidence and observations.

    My first post on this subject was “The Thermostat Hypothesis“, which was an outgrowth of a similar peer-reviewed paper published in Energy & Environment, the journal alarmists love to hate.

    I referred above to an overview of how the regulation system called “Emergent Climate Phenomena“.

    There is evidence on the timing and strength of the cloud effects in my series on the TAO buoy dataset (Part 1, Part 2, Part 3)

    A discussion of the action of the El Nino pump is here.

    TO SUMMARIZE: David and I agree that there is no visible sign of any 11-year cycle in the temperature datasets. David says it’s the result of an 11-year notch filter.

    I say it’s the result of temperature regulation of the climate system by means of a number of emergent phenomena. These phenomena appear when and where the earth is too hot, cool it back down again, and then disappear. I also say that this temperature regulation is not limited to the 11-year solar cycles, but applies at all scales from a single volcano to half a billion year increase in solar luminosity. Finally, it also explains the lack of warming from the increases in CO2 and other greenhouse gases … CO2 makes no difference because the thresholds for emergence of the regulatory phenomena are temperature based, not forcing based.

    Those are the two competing explanations.

    Your choice …

    Best regards to all,

    w.

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      Willis,

      Then please explain the bump at 3 years. David’s method can explain (and I believe he has said something to that effect in passing) it as imperfect cancellation. I take it you would explain it as – the regulator has a delay. But of course I’m putting words in your mouth. I’d like to hear your view.

      BTW does your method have predictive power? David claims his does.

      If climate does follow David’s prediction (colder) how would your method account for that eventuality and predict how long the cold would last?

      Finally – what would you measure to show that you are correct? In the vehicle at constant speed (see way above) we could look at fuel flow or throttle position. What would you measure in the climate system that is equivalent to throttle position?

      Have you estimated the lag of your controller?

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        Willis Eschenbach

        MSimon
        June 19, 2014 at 7:31 pm

        Willis,

        Then please explain the bump at 3 years. David’s method can explain (and I believe he has said something to that effect in passing) it as imperfect cancellation. I take it you would explain it as – the regulator has a delay. But of course I’m putting words in your mouth. I’d like to hear your view.

        Good questions all, M.

        I have noticed that ~3 year anomaly in a number of temperature datasets. You can see it here, for example, in the Armagh and CET datasets, but not in the Berkeley Earth or the HadCRUT datasets. Go figure. I have no explanation for it, nor do I think it is all that important.

        BTW does your method have predictive power? David claims his does.

        My explanation has about the same predictive power as your house thermostat or your cruise control … it predicts that tomorrow will be much like today.

        If climate does follow David’s prediction (colder) how would your method account for that eventuality and predict how long the cold would last?

        The reasons for slow drift in a regulated system are not immediately apparent. However, since the regulatory system is cloud-based, anything that affects the rate of cloud formation is a candidate. I discuss that question in more detail here in the section called “Gradual Equilibrium Variation and Drift”.

        Finally – what would you measure to show that you are correct? In the vehicle at constant speed (see way above) we could look at fuel flow or throttle position. What would you measure in the climate system that is equivalent to throttle position?

        The equivalent of throttle position is the time of daily tropical cumulus cloud formation. The cloud timing and the action of the regulatory system are visible in the daily variations in tropical temperatures. See my posts on the TAO buoy set for details (Part 1, Part 2, Part 3)

        Have you estimated the lag of your controller?

        I’m not sure what this would mean in the climate system.

        Over a decade ago when I first started looking for the mechanism that has kept the earth’s climate to within a relatively narrow range over millions of years, I took a wrong turn. Because I wanted a long-term explanation, I started looking at long slow processes, like for example the rate of weathering of the earths crust and its relations to CO2.

        But one day I had a stunning insight, and I realized I was looking in the wrong place. The insight was that if there are processes that keep the daily tropical temperature within a certain range, those processes would also keep the weekly, monthly, annual, centennial, and millennial temperatures within that same range. I needed to look at daily processes.

        And what I found was that the major regulation of the system is done by the tropical clouds controlling the “throttle” of the system and regulating the amount of incoming splar energy. This regulation occurs in two ways—timing of the daily onset of the cumulus clouds, and the amount of clouds. If it is warm, tropical clouds form earlier and are denser. If it is cool, clouds form later or not at all and in reduced number. But in terms of the maximum effect, timing wins out because it is going from no clouds and ~900-1000 W/m2 solar input, to cloudy and ~400-600 W/m2 solar input, which is a huge jump. So a fifteen minute difference in cloud onset time makes a very large difference in the amount of energy that enters the system.

        And this, of course, happens moment to moment, and there is no lag between cloud formation and the change in incoming energy. So the maximum lag between warming and response in the form of a change in cloud onset time would be 24 hours, until the cloud formation time (on average about 10:30) of the following day. However, the changes in cloud density happen on a shorter term basis.

        As to how long it takes for the system to respond to that change in incoming energy, well, it depends on what your mean by “respond”. The local temperatures, of course, respond immediately—everyone knows what happens to the temperature when a cloud comes over the sun, and there is no time lag. However, the effects on the ocean ten metres down have a different response time, and so on.

        So I’m not clear on exactly how one would even measure the “lag” in the system. Any suggestions gladly accepted.

        Like I said, good questions all …

        My best to you,

        w.

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          As to how long it takes for the system to respond to that change in incoming energy, well, it depends on what your mean by “respond”.

          I should have been clearer. How long does it take your imputed control system to respond to temperature fluctuations. You say near instantaneous (which for purposes of this discussion is anywhere from seconds to days). David says longer.

          BTW you and David are not so far apart initially. You both say there is a control mechanism. And yes – to skip to one of your other points not mentioned immediately above – you do make a prediction –> low SSNs is not an indicator of any other control mechanism in the system and a lack of spots for an extended period will not alter climate.

          David OTOH predicts we are headed for cooling based on low SSNs and other associated phenomenon. And that cooling will last for as long as low SSNs continue. Above and beyond the PDO and other natural cycles.

          And to continue on responding to some of your other comments. Despite admitting that David’s OFT is not incorrect you say there is no notch because you know of no mechanism that could do that. David says there is a notch (looks like it to me) and that is “created” by the effect of the sun’s magnetic field on earth climate through some unspecified mechanism. I like charged particles and clouds myself but David has not (and may not) so specify.

          Now you say – no significant change in climate from low SSNs and associated mechanisms – and David says – colder.

          So we shall see in time – ten years for sure maybe less – who is correct. Being an old man I hope to live long enough to see it. My Dad lived to 82 and my Mother is still living at 94 (I was born when she was 25) so the odds are pretty good for me to see who has the best prediction.

          My bet is on David/Jo/Monckton and peripherally Corbyn as you know. But that is of course meaningless – Nature has its own agenda and will do what it does. And who ever is correct we will have a better theory than CO2/AGW drives climate. That is being disproved by the flatline despite rising CO2 as we speak.

          I look forward to David’s ENSO prediction – which will be an early indicator or so he says. I wish I had the whole story all at once. But waiting a few weeks is not too terrible a hardship. But as you point out it is a hardship for those of us who are relatively quick studies. I can see why David/Jo have decided on that method of release. But that is a whole ‘nother discourse.

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        Willis Eschenbach

        MSimon, one further point about the lag in the climate temperature control system.

        A huge problem with any consideration of lag is that the climate temperature control system is composed of a variety of complementary phenomena that exist at a variety of spatial and temporal scales. These range from small and short at one end of the scale, for example dust devils moving heat from the surface up into the atmosphere and changes in local cloud formation times, to the large and slow, for example the El Nino effect pumping warm water to the poles and the Pacific Decadal Oscillations at much larger and longer scales. (I describe the effect of the PDO in a post called “Decadal Oscillations of the Pacific Kind.)

        As a result … how would one calculate the “lag” in such a system?

        All the best,

        w.

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      Willis,

      For simple controllers (I’m thinking PID) you need to specify two things for reasonably good control. Lag and gain.

      What is the lag and gain of your controller?

      For more complex systems the lag and gain are varied according to the control level desired. That is referred to in the control industry as scheduling. It accounts for the non-linearity of the controlled system.

      Since you posit discernible non-linearity for small changes have you worked out the schedules?

      ===========

      And just so you know where I’m coming from – in my control work where the math gets heavy my employers bring in a mathematician such as David to assist my work. I am not real good at deriving such things. I then embody that math in my design. But I can read the math well enough to find egregious errors. (A mathematician and I went around and around for a couple of days until she saw that I HAD found an error in her derivation).

      I’m a circuits and software guy (real world). I do get the general principles.

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      In addition – you accept that David’s spectral notch is correct. Does your regulator have a notch in its spectrum as well? What in your regulator notches 11 years and allows 3years and 22years to pass?

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        Willis Eschenbach

        Yes, there is a “notch” in any system in which the response is disconnected from the input. For example, if you use David’s method and compare sunspots to white noise, you’ll also get a notch.

        As to whether “it allows 3 years and 22 years to pass”, it’s not at all clear why you think that there is a 22-year signal in the temperature data. I find no more evidence of that in David’s result than I do of an 11-year signal.

        w.

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          it’s not at all clear why you think that there is a 22-year signal in the temperature data.

          Because it shows up in the OFT – which you have assumed is correct (I make the same assumption).

          There is a notch between about 3 and 22 years. According to your hypothesis there should be no notch. We should see a flat line.

          What amazes me is that you can’t see the data which you agree to.

          You say the regulator “notches” all frequencies of interest (and that is correct if the regulator is predominate). David’s OFT clearly shows that is not so. David also says the “notch” shows up (not so distinctly) with the more common FT.

          The first principle is that you must not fool yourself — and you are the easiest person to fool. – Richard Feynman – This is particularly true if you are inventing something (a device or method). I’ve done it to myself more than once. Which is why I endeavor outside verification. Either experiment or input from others. It is one of the reasons my current effort is a team (small) effort.

          http://spacetimepro.blogspot.com/

          It prevents me from going off the rails quite so often.

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            I once had a customer who insisted that you can control the level in a tank with inflows and outflows by simply measuring the difference and integrating. I couldn’t convince him that you could not measure the flows accurately enough to do that.

            He did not remain my customer for long. I refused to even try what he wanted. I just couldn’t do it. Even for money.

            People – even highly trained/experienced people – have all kinds of ways of fooling themselves. I have done it to myself more than once. So I experiment or get outside opinions when I have any doubt.

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            I comment frequently on a board involved with Fusion. They discuss this:

            http://www.nbcnews.com/science/science-news/low-cost-fusion-project-steps-out-shadows-looks-money-n130661

            I made a mistake so stupid – well it was very stupid – and I was so convinced that I almost convinced people who knew better. That is the power of “fooling yourself”. It took almost two weeks of continuous discussion/argument for me to come to my senses.

            But I don’t mind making a fool of myself in public. Most people do mind. Which is why the ratio of lurkers to commenters is so high.

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          Please explain the 12 to 14dB drop between the 22 year/cy at 1 deg C per W/m^2 and the 11 yr/cy at .2 deg C per W/m^2. And then the rise at back to about 1 deg C per W/m^2 at .2 cy/yr ( that would be 5 years/cy).

          Did you notice that dip?

          Why is there a dip and not a flat line?

          Here is the graph in question: http://jonova.s3.amazonaws.com/evans/graphs/evans-fig-5-temp-amp-spectra-datasets-s.jpg

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      David Evans

      Ok, Willis, I’d agree with that. As we have each independently discovered, there is no 11 year signal in the temperature record.

      If the Earth does warm with more TSI then that absence of signal indicates a notch filter.

      If the Earth does not warm with TSI (due to internal control systems) then the apparent notch is a spurious artifact and of no consequence.

      In the later case the notch-delay model will turn out to be rubbish within a few years, and we will have learned something useful.

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        Willis Eschenbach

        David, my thanks for two things—your gracious reply, and your theory about the notch filter.

        I am greatly encouraged to see another theory out there for why the temperature is relatively insensitive to variations in forcing. Obviously I don’t agree with it, but it is a welcome development.

        I also like your excellent but these days mostly discarded method for determining if a theory works—compare it to the observations. A radical thought in the current climate science situation, I know, but a good one. I fear it will take more than the “few years” that you mention, but it is definitely the right path.

        My best to you,

        w.

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          the Griss

          My suggestion Willis , is to stick with it, keep an open mind..

          Dave says he has come up with a falsifiable hypothesis, which is more than any alarmista has managed to do (well, they did, but got falsified, and still hang onto their hypothesis….. doh !)

          Hang in , and see where this leads, without being too anti. :-)

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          David Evans

          Thanks Willis.

          By the way, I use some of your work in the main paper and spreadsheet.

          Been reading your stuff for years, and am quite sympathetic to some of your attitudes about the scientific process. This project is a bit of a different way to doing things.

          Anyway stay tuned, because there is a lot more to all this than the solar model.

          Best to you too. D.

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    A good book on PID controllers – good on theory. Light on math. I used it to design an autotuning PID controller:

    http://www.straightlinecontrol.com/

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      Table of contents:

      CHAPTER 1, GETTING STARTED: Science or Art, History, The Language of Control, Terminology for and Description of Controller Settings, Proportional Action, Integral Action, Reset Windup, Derivative Action, Filter Time, Filter Time and Derivative Action.

      CHAPTER 2, TUNING RULES AND PROCEDURES: Preparation, Closed-loop Tuning: What to Do, Closed-loop Tuning: How to Do It, Open-loop Tuning: What to Do, Open-loop Tuning: How to Do It, Comparison of Testing Methods, When to Not Tune by the Rules, Tuning Rules Overview.

      CHAPTER 3, TUNING OBJECTIVES AND EXPECTED LOOP PERFORMANCE: Response to Cyclic Upsets, Factors Affecting the Natural Period.

      CHAPTER 4, LAGS AND GAINS, BUT MOSTLY LAGS: Dead Time, Integrator, First Order Lag, Combining Building Blocks, Gains.

      CHAPTER 5, EXAMPLES OF ACTUAL LAGS: Dead Time, Controllers, Pneumatic Transmission Lags, Valves, Transmitters, Temperature Measurement, Tanks (Liquid Flow Lag), Tanks (Compositional Lag), Thermal Process Lags, Typical Natural Periods.

      CHAPTER 6, CASCADE CONTROL

      CHAPTER 7, DERIVATIVE ACTION

      CHAPTER 8, INTERACTIONS AND NONLINEARITIES: Interactions, Nonlinearities, Process, Hardware (Continuous Nonlinearities), Hardware (Discontinuous Nonlinearities), Velocity Limiting, Dead Band, Valves at Limits, Integral (Reset) Windup.

      CHAPTER 9, POTPOURRI: Digital Control Algorithms, Sampling Frequency and Loop Performance, Load Changes /Upsets / Disturbances, Dampening Noisy Measurements.

      IMPROVING CONTROL UNIFORMITY

      SUMMARY

      GLOSSARY

      APPENDIX: Pure Dead Time Process, Process with Dead Time and Integration, Derivative Frequency Response.

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      I might add that the late Bob Pease of National Semi was very fond of this book. He and I exchanged a few e-mails on it and how the LM628/9 related to it. Bob was not fond of the ’628 because the equations used were independent of each other. He liked the more physical notion of gains and lags. I’m of that opinion as well.

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        Curt

        MSimon: In the 1980s, I was working on the main competition to the LM628/9 control chip — the HP HCTL-1000. We had the type of control equations specialists like Bob Pease liked, but it was almost impossible to explain to people without a formal controls/filtering background. I tried to change it to be more like the National part, but I couldn’t get backing from management.

        Now that I make decisions like that for my company, I do it like the LM628/9.

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    Curt

    Some thoughts on this from someone whose academic concentration, technical professional specialization, and business for the last three decades has been feedback control systems.

    What David is attempting here at least starts out as a classic system identification problem. These are most commonly done in the engineering world in the frequency domain as David is doing. In the engineering world, we try where possible to put in a known input pattern that will excite all of the relevant modes of the system. One of the most popular is the “sine sweep” a series of sinusoidal inputs of a range of frequencies. Monitoring the output of the system, it is very easy, even without formal transforms, to see the frequency response of the system.

    Obviously, this is not possible for a large natural system such as the entire earth. But it often is not possible in engineered systems either, particularly if you want to identify changes in the system dynamics (transfer function) while the system is in operation, for purposes such as adaptive control.

    In this case we look at signals at two places in the system and use them to compute the transfer function of the system between them. This is fundamentally what David is trying here.

    The key issue here is whether the “input” signal is rich enough at the relative frequencies to reliably establish a relationship with the “output” signal of the system. It is very easy to fool yourself if it is not. In creating our algorithms for these purposes, one of the toughest issues is always to determine when and if the input signal is “rich” enough to yield valid conclusions about the system.

    It is also common practice to use “small signal linearization” on non-linear systems, as David as done here. This works well for many, but certainly not all, systems.

    In this case, if you have good data for both TSI and temperature response with the TSI signal having adequate power over the frequency range of interest, the frequency response of the temperature should be able to let us distinguish between Willis’ theory of integral restoring action (the governor hypothesis) and David’s “notch” theory. The two would have significantly different frequency response curves.

    As I understand it so far, David’s notch theory has an uncommon twist. He is apparently not arguing that the earth’s own dynamics have a notch in the frequency response, but that there is another input to the earth’s system (his Factor X) that is correlated to the TSI signal in a way that cancels its effect.

    I say this is an uncommon twist, because usually the starting assumption in these system analyses is that the various “disturbance” signals are uncorrelated with each other. It is wonderful when they are uncorrelated, because it makes it much easier to tease out the effects of each disturbance. But I have seen, in my field and others, horrible mistakes made when this assumption was wrong. (One of the reasons we are in the economic mess we are in was implicit assumptions of uncorrelated disturbances in bank and insurance economic models.)

    I’m still agnostic on this in the present case. Off to buy some popcorn!

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      In this case, if you have good data for both TSI and temperature response with the TSI signal having adequate power over the frequency range of interest, the frequency response of the temperature should be able to let us distinguish between Willis’ theory of integral restoring action (the governor hypothesis) and David’s “notch” theory. The two would have significantly different frequency response curves.

      That is my reason for preferring David over Willis at this time. Subject to change as my understanding improves. And of course new data.

      —-
      Email coming your way M. – Jo

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      David Evans

      Thanks Curt. Pretty similar to my thoughts at this stage in the project.

      At this stage we are just building an alternative to the CO2 theory, predicated on TSI somehow (maybe indirectly) driving temperature, to see if it can be done and what it would entail.

      Finding that the delay required to make the notch possible, and the best fit to the measured temperatures, was about 11 years opened a lot of doors for us. And it’s already been independently found to one degree or another half a dozen times. Once there is an indirect solar force operating after a delay, everything changes.

      A solar solution only becomes viable with an delay of at least 10 years (eg overcoming the argument of Froehlich and Lockwood 2007, 1986 + 11 = 1997, which is when gw stopped). Without a 10 – 20 year delay the solar case appears a non-starter.

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    Richard C (NZ)

    Tatiana Barlyaeva says she sees a temperature wavelet spectra corresponding to a solar cycle of “about” 11 years in some specific stations around the globe over the latter quarter of the 20th C (odd for a start). Personally I don’t quite see what she is seeing.

    ‘New paper finds solar cycle changes Earth temperature’

    http://hockeyschtick.blogspot.co.nz/2013/01/new-paper-finds-solar-cycle-changes.html

    ‘Solar, volcanic and geomagnetic forcing on air–surface temperature: Geographical distribution of sensitive climate zones’,

    Poster, Tatiana Barlyaeva

    http://www.spaceclimate.fi/presentations/posters/Barlyaeva_Forcings_poster.pdf

    ‘External forcing on air–surface temperature: Geographical distribution of sensitive climate zones’

    Tatiana V. Barlyaeva (2013) [Paper available as PDF via Google Scholar]

    I don’t expect to see an 11 year signal in globally averaged datasets at the surface, the sensitivity has been lost when all the stations are lumped together. If if was apparent it would show up in localized data as Barlyaeva has analysed and only where the locality allows (forget CET for example), but I don’t think she has proved anything conclusive. And SC 23 peak to SC 24 peak was 12 years 2 months (Dec 2001 to Feb 2014), not 11 years.

    I think Zhou and Tung’s look at the entire troposphere is the best approach. But to see any relationship between solar activity and the temperature of the surface (land), the best place to look is underground. See:

    LONG-TERM CLIMATE CHANGE AND SURFACE VERSUS UNDERGROUND TEMPERATURE MEASUREMENTS IN PARIS

    F. PERRIER, J.-L. LE MOUEL, J.-P. POIRIER and M. G. SHNIRMAN (2005)

    http://onlinelibrary.wiley.com/doi/10.1002/joc.1211/pdf

    See page 1629,

    Figure 12. Underground temperature records (diamonds) below the Paris Observatory (depth 28 m) compared with sunspot number: (a) data from Cassini. (b) data from Arago using the Lavoisier thermometer

    Annual subsoil temperature exhibits a similar profile, higher when energy input is higher (summer), lower when energy input is lower (winter). The “pulses” of energy at around 11 years are analogous to “pulses” of measured flux at the surface over a year or a month which monthly averaging smooths out but can be seen in monthly update graphs of solar activity i.e. the surface does not “see” a smooth flux curve but underground and subsoil does. See the period including the SC 24 peak (Feb 2014) for example of energy pulses seen by the surface:

    Solar Terrestrial Activity Report http://www.solen.info/solar/

    The other obvious solar “pulse” is diurnal. The temperature response at the surface is equally obvious but subsoil and underground doesn’t know about it.

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    Willis Eschenbach

    MSimon
    June 20, 2014 at 7:33 am

    Willis:

    it’s not at all clear why you think that there is a 22-year signal in the temperature data.

    Because it shows up in the OFT – which you have assumed is correct (I make the same assumption).

    There is a notch between about 3 and 22 years. According to your hypothesis there should be no notch. We should see a flat line.

    Thanks, M, but I still don’t see the “notch” you are talking about in the OFT of the temperature data. Neither does David Evans, who says:

    The temperature amplitude spectrum, the smooth orange curve in Figure 4, is essentially straight over more than three orders of frequency magnitude, with no other definite features.

    I agree with him that the OFT of the temperature data is “essentially straight”. You keep saying that there is a notch at 22 years … you’re going to have to point it out to me. Here’s the Fig. 4 graphic for reference:

    w.

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    Willis Eschenbach

    Ah, well, the Fig. 4 didn’t come up … it’s up at the top of this page, in any case.

    w.

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    Interested

    I suppose these are going to look like pretty stupid questions but here goes …

    Could someone spare a moment to put in simple words what Figures 2 and 4 actually represent?
    Figs. 1 and 3 seem fairly self-explanatory but I don’t get where 2 and 4 come from – in particular the abscissa (frequency) – and what they mean.
    I’m guessing my problem is I don’t get what ‘amplitude spectra’ really are.
    What is it that’s oscillating at a greater amplitude when its oscillation frequency is around 0.09/year?
    Is it suggested TSI is reasonably steady most of the time and then suddenly goes up and down more violently every 11 years? If so, is this peculiar behaviour happening at the solar maximum or solar minimum, or is that irrelevant, or don’t we know?

    There appear to be 5 main data sets in Figs. 1 and 3 but dozens of random points for each of those data sets in Figs. 2 and 4.
    What do these points actually represent?
    Who chose the frequencies?
    Frequency of what – is it these staccato up-and-down fluctuations in TSI?
    And why choose those specific frequencies out of what must be an infinite sea of options?
    Do you just pick random points on the curves in Figs. 1 and 3 and read off the rate of TSI oscillation there – and stop when you think you have enough points?

    I get the gist of where the broad logic of the notch filter is going but I feel sure I would understand the big picture much better if I could just get a firm handle on Figs. 2 and 4.
    Many thanks to anyone who can help.
    Cheers!
    [P.S. I haven't done any halfway serious mathematics for 40 years and most of that I've long forgotten. .... And worse than that(!) .. I have no knowledge at all of Fourier Transforms or Argand Diagrams, or how you would use either of them in this investigation.]

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      David Evans

      Take Figure 2. We expressed each TSI time series as a sum of sinusoids (or sine waves) that “best” adds up to the time series (thereby choosing the frequencies from among the real non-negative frequencies). Each sinusoid has an amplitude, a phase, and a frequency. The phases weren’t of much use to us, so ignore them. The amplitudes of the sinusoid thus found were plotted against the frequencies, to give us the dots in Figure 2. There were several TSI time series, so there are several sets of dots in Figure 2. These are several individual amplitude spectra.

      Then we smoothed all the dots in Figure 2 to produce the orange line. The orange line represents the combined amplitude spectrum, the amplitude of the sinusoid at the given frequency likely to be found in the TSI.

      The frequencies are marked on the x-axis in cycles per year, and just above that as periods — the period of a sinusoid is the reciprocal of its frequency, and is a more natural way of talking about the sinusoids in this context. We end up talking about a “frequency” of “11 years”, when what we mean it its frequency is 1/11 cycles per year.

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    Willis Eschenbach

    Let me say that I do think that there is an important finding in this study, but it’s in Figure 4, not Figure 5 or 6. Figure 4 shows what David calls the “temperature amplitude spectrum”, which is his type of periodogram or spectral power analysis of the temperature. Regarding Figure 4, David says:

    The temperature amplitude spectrum, the smooth orange curve in Figure 4, is essentially straight over more than three orders of frequency magnitude, with no other definite features.

    Note what this says. There is no sign of the 11-year solar sunspot cycle. There’s no sign of the long-discussed 20 year and 60 year temperature cycles advocated by Scafetta and many others. There’s no sign of the purported 80-year “Gleissberg” solar cycle. There’s no sign of the claimed 210-year “Seuss” solar cycle. In fact, David is saying that there are no periodic temperature fluctuations of any significance from any cause—the “temperature amplitude spectrum” is “essentially straight”, and has “no other definite features”.

    Now, to me, that’s a significant finding. Since he hasn’t published data and code, I don’t know if it will withstand close examination, but if it does, it is an important piece of evidence,.

    I say that it supports my hypothesis that any such cyclical temperature variation from any source at any frequency is negated by the opposing action of the emergent phenomena such as thunderstorms, dust devils, tropical cumulus clouds, the El Nino, and the PDO. These phenomena come into existence and cool the surface when and where it overheats. And when they are not in existence, the unimpeded strength of the sunlight quickly warms the surface. As a result, the global temperature is kept within tight bounds (e.g. ± 0.3°C over the entire 20th century).

    That is my explanation of why there are no significant regular cycles, solar or otherwise, in our global temperatures.

    I don’t see, however, how a finding that the sun’s 11-year sunspot and purported 80-year Gleissberg and 210-year Seuss cycles DON’T affect the temperature is evidence that the sun CONTROLS the temperature, as David claims. Nor do I see it as either evidence or support for the idea of a “notch filter”, as the existence of a “notch” does not imply the existence of a “notch filter”.

    w.

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      Richard C (NZ)

      Willis #74

      >”There is no sign of the 11-year solar sunspot cycle”

      Why bother looking for one in the first place?

      SC 22 9 yrs 8 months
      SC 23 12 yrs 6 months

      SC 23 peak to SC 24 peak 12 yrs 2 months.

      I think the long-term average is 11.2 yrs.

      The “cycle” is a recurring phenomenon conventionally described as an “11 yr cycle” because of the average length but that is not what it actually is (as with the other longer “cycles”).

      In other words, there is no such thing as an 11 year solar cycle to go looking for.

      Coughlan and Tung (2004) decided against Fourier analysis for this reason. See their criticism of Fourier analysis wrt solar vs temperature in the Part VI thread here:

      http://joannenova.com.au/2014/06/big-news-part-vi-building-a-new-solar-climate-model-with-the-notch-filter/#comment-1491912

      Paper linked above that at #33.3

      Using EMD they clearly identify SC peak warming from the surface right up through the troposphere in IMF 4.

      Similarly but with different methodology with Zhou and Tung (paper also linked at #33.3).

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    Interested

    Thanks for trying to explain but I still don’t know, in words, what Fig. 2 actually says.
    As far as I can tell, it says nothing of any interest except that the Sun’s energy output (TSI) oscillates up and down more noticeably when its oscillations have a period of 11 years.
    That says nothing about TSI itself and therefore I don’t see why it’s so surprising that there’s no corresponding rise in temperature every 11 years.
    Why should wilder up and down oscillations in TSI mean more energy arriving on Earth?
    I must be missing something fundamental here.

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    Dr. Evans:
    Your revision to the expected temperature effect due to TSI seems VERY important, i.e. it reduced the expected temperature effect by a factor of about 5 and made it difficult to separate from the noise. It would be interesting to know what prompted this change. (Also it would be helpful if date and time of changes were included.)

    With this change the argument that a notch filter is dictated by the transfer function is less convincing since the transfer seems essentially indistinguishable from noise.

    As a retired EE, I like your approach using black box analysis of the system – it makes the general flow of your theory easy to follow.

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      David Evans

      I was mulling it over and noticed the 0.8 was out of 1360, not out of 238 as in the original. This makes the overall case stronger IMHO, because the cancellation in Post IV does not have to be nearly as exact for the combined effect to slip beneath the threshold of notice. Yes, I am confident the Fourier analysis will pick up something repetitive around the noise level, or even half the noise level or less. Further, it appears the cosmic ray effect reinforces the TSI temperature influence–global cloud cover also dips wen TSI peaks–which would make the expected temperature peaks larger.

      Thanks. The EE’s are finding this easy, but many others are struggling, and overlooking the special nature of sinusoids.

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    [...] a recent interchange over at Joanne Nova’s always interesting blog, I’d said that the slow changes in the [...]

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    Interested

    Ummm. Oops!
    I just realised where and how I was misinterpreting what the graphs represent. Apologies for my last question! (Please ignore it.)

    I still don’t fully understand the mathematical mechanics of the graphical construction of Figs. 2 and 4 however, despite Dr. Evans’ great patience and kindness in taking the time to try and explain.
    But I can live with that.
    After all it is just ‘mechanics’ and needn’t detract from an appreciation of the main point.

    And the main point (the notch filter) is quite fascinating, and expressed in a remarkably accessible way given the complexity of the subject.
    Many thanks to both Jo and husband for this excellent work.
    I sincerely hope it rattles a few cages!

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    Richard Brown

    David,

    Something about the notch filter just doesn’t seem right to me, although I can see exactly where you’re coming from. It MIGHT be the correct solution, but here’s an alternative suggestion. The spectral peak in TSI is not too acute – looks like around 3:1 gain over “local” baseline, or +10 dB. It does not take much filtering effect to remove a 10 dB peak. Say the planet acts like a low-pass filter, kicking in at about 50 or 40 year period. The 11 year peak will be suppressed, and what you see at shorter periods is a noise signal arising from “other stuff” going on. So the net result is the product of an LPF and a noise source that increases with frequency, then eventually tails off. This removes the need for a highly specific notch. Would this be grossly inconsistent with your data?

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      So you are saying that the LPF has a notch in it.

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        Richard Brown

        MSimon – no, I’m saying the left edge of the apparent notch is caused by an LPF, and the right hand edge is not a filter effect as such but a rise in (temperature) noise…

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          But the noise is divided out by output/input.

          The spectrum I see is not what I’d expect from a LPF. I could see an “end effects of the FT” as an explanation. I can’t see how you get the spectrum of the response you see from about 20 years to 1 year from noise.

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      David Evans

      There is a low pass filter, but its time constant is about 5 years.

      Many others have found it, e.g. as Stephen Schwartz at Brookhaven said in “Determination of Earth’s transient and equilibrium climate sensitivities from observations over the twentieth century: Strong dependence on assumed forcing” in 2012, “The time constant characterizing the response of the upper ocean compartment of the climate system to perturbations is estimated as about 5 years, in broad agreement with other recent estimates, and much shorter than the time constant for thermal equilibration of the deep ocean, about 500 years.”

      The empirical transfer function above is consistent with a low pass filter at 5 years (starts falling off to high frequencies, hardly conclusive of course because it is mainly hidden by the notch). When we fit parameters to the model, it also finds a low pass filter at 5 years.

      On the other hand, frequencies in the TSI below about 1/20 years seem to make it through to the temperature just fine.

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        Richard C (NZ)

        Schwartz quote #79.2

        >“The time constant characterizing the response of the upper ocean compartment of the climate system to perturbations is estimated as about 5 years”

        Huh? 0 – 700m OHC (indicative):

        http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/heat_content55-07.png

        Lets say the solar Modern Grand Maximum began at SC 17 1933 and ended SC 23 2008.

        The oceanic heat sink response to the elevated level of solar activity 1933 – 2008 is only now just peaking in 2014.

        The ocean is the planet’s major heat sink so the thermal system is predominately sun => ocean => atmosphere. The atmosphere receives most of the solar heat signal from the ocean – not the sun. The upper ocean heat signal has been rising to a peak over at least the last 45 years or so and probably longer.

        The analogy is water-pot-on-stove-element. Alec Rawls (see WUWT) beat his head against the wall trying to get this concept through to about a dozen IPCC solar specialists but to no avail (or not much) from what I can gather.

        Now look at the residual trend (by EMD) in atmosphere (now out of data): Figure 2(a),(b),(c) bottom panel in each, Coughlan and Tung (2004):

        http://onlinelibrary.wiley.com/doi/10.1029/2004JD004873/full

        The residual trend in atmosphere is essentially a mirror of upper ocean heat accumulation and the heat signal of it.

        In the same Figure 2, C&T04 identify the atmospheric SC peak signal in IMF 4. Upper ocean heat content oscillation roughly corresponds to IMF 5.

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          Richard C (NZ)

          Should be:

          “(now out of [date])”

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          One minor problem with this:

          the thermal system is predominately sun => ocean => atmosphere

          It is contradicted by day/night, summer/winter temperature differences.

          Better might be: long term the thermal system is predominately sun => ocean => atmosphere

          Long term being > ~20 years. That given, there is something interesting happening at 11 years.

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            Richard C (NZ)

            >”It is contradicted by day/night, summer/winter temperature differences”

            That’s not the predominant (i.e. the overwhelming) solar heat signal in atmosphere of the oceanic heat sink.

            The signal is not necessarily a sinusoid. It is simply a rising trend. After it peaks, it will be followed by a falling trend of similar duration (if solar input continues to decline as predicted) as accumulated heat is released and until solar input stabilizes at a lower level for however long.

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              That’s not the predominant (i.e. the overwhelming) solar heat signal in atmosphere of the oceanic heat sink.

              True that. But that still leaves the signals from ~20 years to .01 second (and less) to deal with. And if you look at day/night temps or even summer/winter they seem to swamp all other signals.

              Time – it is the reason everything doesn’t happen all at once.

              =============

              “Not a sinusoid” can be made from a combination of sinusoids. Square waves are a combination of all of odd harmonics with amplitudes decreasing at 1/n (where n is the harmonic number). This is a significant factor in circuit design. Designers use this all the time as a rule of thumb = to reproduce a 1 KHz sq. wave you need a circuit whose 3 dB roll off begins at 10KHz or greater depending on fidelity rqmts. For very high fidelity you might want to go to 1Mhz. And if you are insane 10MHz. Of course there is wide band noise to worry about and aliasing from mixing and a whole host of other problems. (Mains hum).

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                Richard C (NZ)

                >”Not a sinusoid” can be made from a combination of sinusoids

                Understand. But I’m referring to the phenomenon. Given the Modern Grand Max appears to have been the highest level of solar activity for about 11,000 years, it cannot be described as or by a sinusoid

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                Richard C (NZ)

                >”But that still leaves the signals from ~20 years to .01 second (and less) to deal with”

                Not by David’s approach (My “wrong premise, wrong analysis tools, wrong datasets” argument.

                But see C&T04 above.

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                Given the Modern Grand Max appears to have been the highest level of solar activity for about 11,000 years, it cannot be described as or by a sinusoid

                True that. But a sum of sinusoids works nicely. And from that sum a model can be built. And it may be possible to learn something from the model.

                What you are saying in essence is that some signals are not Fourier Transformable. That is untrue. Now whether the particular windows, truncations, and assumptions can produce something useful is a different question.

                All signals can be represented as a sum of sine waves. –> This is an identity.

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                Richard C (NZ)

                >”What you are saying in essence is that some signals are not Fourier Transformable”

                I’m saying that in the case of temperature response to solar change, globally averaged datasets are not the place to look for the signal. And that other signal analysis techniques identify the signal in other datasets.

                I’ve taken exception to your reply in Part VI here:

                http://joannenova.com.au/2014/06/big-news-part-vi-building-a-new-solar-climate-model-with-the-notch-filter/#comment-1494828

                I’ve applied David’s rationale to the deVries cycle to try to demonstrate how the Modern Grand Max sits in temperature compared to recurring solar activity other than 11 yrs approx.

                There are two proxy datasets that detect a signal either side of 200 yrs in figure 4 of this post but that is all. My point here is that the paper I cite, Raspopov et al (2006), states “climate response to external long-term solar forcing, including the 200-year variation, differs in different regions of the Earth“.

                This comes back to my premise argument. Is it valid to look for a temperature response signal at different frequencies of globally averaged data when the signal differs in different regions of the Earth?

                Possibly is valid for the deVries cycle on the strength of two proxy sets but David’s approach says that a notch filter is required if the response signal is not detected.

                Basically, the signal does not necessarily manifest as David (and EE) wants it to but it does manifest and in the case of deVries and two datasets, even as he wants it to, too.

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                Richard C (NZ)

                >Raspopov et al (2008 [not 06]), states “climate response to external long-term solar forcing, including the 200-year variation, differs in different regions of the Earth“

                Page 9:

                Spatial non-uniformity in the temperature response to solar forcing has been modeled at a global scale by Waple et al. (2002). As can be seen from Fig. 5, the same solar irradiance variations lead to both positive and negative temperature responses in different regions.
                Moreover, there are border regions (e.g. the North Atlantic and the north of Scandinavia), where the response to long-term solar signal variations can be absent or change sign over time.”

                Here “long-term” is merely >40 years. In terms of the Modern solar Grand Max this is the timeframe of the rise in upper ocean heat. See fig 5 on page 9:

                Fig. 5. The map demonstrating results of simulation of the temperature response of the atmosphere-ocean system to the effect of long-term (>40 year) variations in solar irradiance (modified from Waple et al., 2002)….”

                Both warming AND cooling (mostly warming).

                According to Waple et al. (2002), there’s a solar-temperature response signal but not simply warming that one would “expect”.

                If this is the effect at >40 years should we expect anything different at <40 years?

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                I’m saying that in the case of temperature response to solar change, globally averaged datasets are not the place to look for the signal.

                Thanks for the clarification.

                The question is then: can I model with a few parameters a bipolar junction transistor (BJT) or do I need to follow every electron to get a working model?

                There is nothing wrong with the aggregate response – if it works.

                All models are wrong. Some are useful.

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              the Griss

              All signals can be represented as a sum of sine waves.

              Unfortunately the wiggles in the climate system are not like you would get from a Bach prelude….

              but more like from a bunch of learner rockstars playing in a garage. ! :-)

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            Richard C (NZ)

            >”there is something interesting happening at 11 years.”

            A minor oscillation identified in IMF 4 by C&T04.

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          David Evans

          Schwartz’s upper compartment is more like 100m deep (the only indication I can find in his paper). He doesn’t make it clear; I understand it is a functional division between upper and lower.

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            Richard C (NZ)

            >”Schwartz’s upper compartment is more like 100m deep”

            That would explain his 5 year time constant. Trenberth says 6 which is probably considering a similar depth. But he also says 10 – 100 years obviously in consideration of a deeper compartment.

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    [...] we now have a way of cross-checking the tree-ring based predictions.  A just-released climate model using a notch-delay filter has the promise of providing much higher resolution in climate [...]

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    Richard C (NZ)

    ‘Climate reveals periodic nature, thus no influence by CO2′

    Prof. H. Luedecke and C.O. Weiss

    http://notrickszone.com/2013/12/03/german-scientists-show-climate-driven-by-natural-cycles-global-temperature-to-drop-to-1870-levels-by-2100/

    We reported recently about our spectral analysis work of European temperatures [1] which shows that during the last centuries all climate changes were caused by periodic (i.e. natural) processes. Non-periodic processes like a warming through the monotonic increase of CO2 in the atmosphere could cause at most 0.1° to 0.2° warming for a doubling of the CO2 content, as it is expected for 2100.

    Fig. 1 (Fig. 6 of [1] ) shows the measured temperatures (blue) and the temperatures reconstructed using the 6 strongest frequency components (red) of the Fourier spectrum, indicating that the temperature history is determined by periodic processes only.

    On sees from Fig. 1 that two cycles of periods 200+ years and ~65 years dominate the climate changes, the 200+ year cycle causing the largest part of the temperature increase since 1870.

    The ~65 year cycle is the well-known, much studied, and well understood “Atlantic/Pacific oscillation” (AMO/PDO). It can be traced back for 1400 years. The AMO/PDO has no external forcing it is “intrinsic dynamics”, an “oscillator”.

    Although the spectral analysis of the historical instrumental temperature measurements [1] show a strong 200+ year period, it cannot be inferred with certainty from these measurements, since only 240 years of measurement data are available. However, the temperatures obtained from the Spannagel stalagmite show this periodicity as the strongest climate variation by far since about 1100 AD.

    The existence of this 200+ year periodicity has nonetheless been doubted. Even though temperatures from the Spannagel stalagmite agree well with temperatures derived from North Atlantic sedimentation; and even though the solar “de Vries cycle”, which has this period length, is known for a long time as an essential factor determining the global climate.

    A perfect confirmation for the existence and the dominant influence of the 200+ year cycle as found by us [1] is provided by a recent paper [2] which analyses solar activities for periodic processes.

    The spectrum Fig. 2 (Fig. 1d of [2]) shows clearly a 208-year period as the strongest variation of the solar activity. Fig. 3 (Fig. 4 of [2]) gives us the solar activity of the past until today as well as the prediction for the coming 500 years. This prediction is possible due to the multi-periodic character of the activity.

    The solar activity agrees well with the terrestrial climate. It clearly shows in particular all historic temperature minima. Thus the future temperatures can be predicted from the activities – as far as they are determined by the sun (the AMO/PDO is not determined by the sun).

    The 200+ year period found here [2], as it is found by us [1] is presently at its maximum. Through its influence the temperature will decrease until 2100 to a value like the one of the last “Little Ice Age” 1870.

    The wavelet analysis of the solar activity Fig. 4 (Fig. 1b of [2]) has interesting detail. In spite of its limited resolution it shows (as our analysis of the Spannagel stalagmite did) that the 200+ year period set in about 1000 years ago. This cycle appears, according to Fig. 4, regularly every 2500 years. (The causes for this 2500 year period are probably not understood.)

    [1] Multi-periodic climate dynamics: spectral analysis of long-term instrumental and proxy temperature records. H.Luedecke, A. Hempelmann, C.O.Weiss; Clim. Past. 9 (2013) p 447

    http://www.clim-past.net/9/447/2013/cp-9-447-2013.pdf

    [2] Prediction of solar activity for the next 500 years. F.Steinhilber, J.Beer; Journ. Geophys. Res.: Space Physics 118 (2013) p 1861

    http://www.eawag.ch/forschung/surf/publikationen/2013/2013_steinhilber.pdf

    ‘Claim: Solar, AMO, & PDO cycles combined reproduce the global climate of the past’

    Guest essay by H. Luedecke and C.O.Weiss

    http://wattsupwiththat.com/2013/12/17/solar-amo-pdo-cycles-combined-reproduce-the-global-climate-of-the-past/

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