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BIG NEWS Part III: The notch means a delay

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

UPDATE: July 21 Thanks to Bernie Hutchins, David found a problem with the code, which means the notch no longer guarantees a delay. The delay still likely exists (see the other evidence in the references below) but this post, particularly figure 2 needs correction and updating. – Jo

Strap yourself in. The Notch in the Earth’s response to incoming solar energy means that every 11 years  (roughly) the solar energy peaks, and at the same time the climate’s response to the extra energy changes. What on Earth is going on?

The thing about notch filters that is hard for anyone who isn’t an electrical engineer to understand is that it appears to start working before “the event” it is filtering out. This is obvious in the step response graph. That’s Figure 2 – which shows what happens where there is a sudden step up in solar radiation (the brown line). The blue line shows the temperature response, which paradoxically starts to “rise” before the step up even occurs. This makes no sense, of course. Electronic engineers know that a [non-causal] notch filter always means a delay. Something triggers the filter before the event begins and the notch filter responds after a delay.

By mathematical inference David shows that there must be a delay. Later, by fitting the solar model to the measured temperatures, the delay is found to most likely be around 11 years (but is definitely between 10 and 20 years).

There is some empirical support for this from Lockwood and Froehlich’s paper, and also from Usokin, Archibald, Solheim, Soon, and Moffa-Sanchez.

The solar model also has a low pass filter, as well as the notch-delay combo. All the little flickering short rises and falls in solar radiation would not show up in Earth’s temperature. A low pass filter blends or smooths these short term cycles as the energy is absorbed by systems like the oceans. Only longer sustained changes in radiation make a difference, as heat either accumulates or dissipates over longer periods. The transfer function suggests (loosely) that changes lasting less than about 3 years make less and less impact on temperatures.  — Jo

Building the Model Part 1: Deducing the Delay

Dr David Evans, 16 June 2014, David Evans’ Notch-Delay Solar Theory and Model Home

We are building the solar model that would account for the recent global warming if it was associated almost entirely with solar radiation (notice that we didn’t say “caused”), and had no dependence on carbon dioxide. Here we assemble the first three parts of the model, a notch filter, a delay filter, and a low pass filter.

1          The Notch

In the previous post on exploring the data, we found that the most prominent feature in the empirical transfer function was the notch, which filters out the 11-year “hum” from the Sun.

The notch is a very curious fact. Solar radiation warms the Earth, providing nearly all the heat as incoming radiation—visible light, UV, infrared, and so on. So we’d expect the extra radiation from the Sun every 11 years to produce corresponding peaks in temperature here on Earth. Yet it doesn’t.

We have chosen to investigate what happens if the recent global warming was associated almost entirely with changes in solar radiation and has no dependence on carbon dioxide — the “solar assumption”. Obviously the solar assumption cannot be entirely true, and it is later discarded in the development of the solar model. It is only needed for finding the approximate parameters for the model, and it does not ultimately impact on whether the model is appropriate or not. This parallels the original development of the carbon dioxide theory, which temporarily assumed that carbon dioxide caused almost all of the global warming since 1800 — the “carbon dioxide assumption” — in order that the parameters of the carbon dioxide model could be found by curve-fitting it to the measured temperatures.

Using the solar assumption we curve-fitted a notch model to the measured temperatures, to find the approximate size and shape of the natural notch filter. It is more instructive to show the notch filter we eventually found by curve fitting the entire solar model (which contains a notch filter) to the measured temperatures, because that way we can build up the model’s transfer function piece by piece so that it matches the empirical transfer function. (The two notch filters are basically similar except for a different overall amplitude multiplier, that is, a vertical shift in the transfer function diagram.)

 

Figure 1: The transfer function of the notch filter in the solar model. Uses the P0 set of parameter values for the solar model, which are the rounded off versions of the parameters later determined to best fit the observed temperatures.

 

Ok, it’s notch shaped, and the notch is at 11 years, as we’d expect. (We are only concerned with the amplitudes, because we cannot adequately detect the phases of the sinusoids in the climate datasets.)

But what is much more interesting becomes apparent when the notch filter is portrayed in the time domain, as the step response. The step response of a system is what the output does when the input instantaneously steps up by one unit.

 

Figure 2: The step response of the notch filter in the solar model, corresponding to the transfer function in Figure 1. It is non-causal, that is, the response starts before the stimulus!

 

Notice that the step response starts several years before the step-up, which violates causality — it is impossible. In our universe, a response can only come after the corresponding stimulus. The non-causality of the step response of the notch filter in Figure 2 is not a fluke: in any electronic notch filter without an accompanying delay, the step response is blatantly non-causal. Notch filters by themselves are intrinsically non-causal.

2          The Delay

How we know there is a delay

When engineers design a filter whose transfer response has the desired shape of amplitude, but which is non-causal and therefore impossible, they simply include a delay with the filter. Adding a delay does not change the amplitude of the transfer function of the filter, it only changes the phase of the transfer function. The delay shifts the entire amplitude part of the step response  to the right in diagrams such as Figure 2, without changing its shape, as if the time axis were replaced with a new time axis.

For example, the step response of the combination of the notch filter in Figure 2 and a 7 year delay is the blue line in Figure 2 shifted 7 years to the right. Just imagine sliding the blue line 7 years to the right — the dagger of the notch would move from year 0 to year 7.  (Notice this would almost but not quite make the response causal, because the response would almost be zero before the stimulus begins. A delay of about 8 or 9 years would be sufficient to make it causal and therefore possible.)

The combined filter-delay combination can exist, so long as the response is shifted sufficiently that it is zero before the stimulus. For engineers designing filters, this means the combination is possible to build. (It is possible to use non-causal filters in simulations on a computer in the frequency domain, but they don’t exist in the real world!)

So given that we have detected a notch filter, and its step response is non-causal, one way that such a notch filter could possibly exist is that there is an accompanying delay sufficient to make it causal.

There do not appear to be any other possibilities. Adding any filter other than a delay filter would change the shape of the amplitude of the transfer function in Figure 2, which would change it from the notch filter we have detected into something else.

How much delay? Presumably as little as necessary, or at least this is what design engineers typically do. Given the notch filter portrayed in Figures 1 and 2, presumably the delay would be a bit larger than 8 years but presumably not a lot larger (like say 80 years).

To sum up, in the system whose input is TSI and whose output is temperature we have detected a notch filter whose transfer-function amplitude indicates that it cannot exist unless it is accompanied by a delay of several years.

Therefore we infer that there must be a delay of several years that is intrinsically part of the notch. The notch must be accompanied by a delay, because the notch on its own is physically impossible.

It is crucial to notice that this is a true delay, not due to a dissipative element like a store of ocean heat that declines at a rate governed by a time constant.

Deducing physical phenomena using mathematics is unusual but hardly new. Most famous were the deductions of quantum mechanics from a few physical facts, about a century ago. The results were logical, but many classical physicists of the time refused to believe them. Later experimentation has shown that the mathematical deductions by the quantum physicists were correct.

So let us add a delay filter into our solar model, in cascade with the notch filter. (“Cascade” means the output of one system is the input to the next system.)  The delay is intrinsically due to or associated with the notch, so the notch and delay filters must always go together with nothing between them.

There is some supporting evidence for a delay

Later, when we fit the notch-delay solar model being developed here to the measured temperatures, we find that the delay is mostly likely around 11 years (but definitely between 10 and 20 years).

Lockwood and Froehlich’s famous 2007 paper showed that four solar indicators, including TSI, rose until about 1986 then started falling slightly, yet temperature kept on rising until the mid to late ‘90s. They interpreted this as evidence that the Sun is not a major influence on temperature. However 1986 + 11 = 1997, which is about when global warming stopped.

A strong correlation between the length of a solar cycle and the temperature during the following solar cycle was discovered in 1991 by Friis-Christainsen & Lassen.  This correlation was verified and explored further in the last few years by David Archibald, and in 2012 Jan-Erik Solheim et al found that a lag of 11 years maximizes the correlation between solar cycle length and temperature. We will be doing a blog post on how this correlation fits in with the notch-delay solar model later in the series.

Willie Soon in 2009 found a ten year delay from TSI to sea surface temperature changes in the tropical Atlantic. Moffa-Sanchez et al in 2014 found a lag of around 12 years from TSI to North Atlantic surface temperatures over the last thousand years. Usoskin et al in 2004 found that the correlation coefficient between northern hemisphere temperature and reconstructed sunspot numbers from 850 AD was greatest when the temperature lagged the sunspot numbers by around 12 years. Greg Goodman finds a peak in the correlation between sea surface temperatures and sunspot numbers when the former lags by 10.1 years (though sunspot numbers would correlate a little like that with white noise).

 

3          The Low Pass Filter

The climate system is like a bucket of heat with a hole near the bottom of the bucket.

Unreflected TSI pours into the top of the bucket. About 30% of the TSI incident on the planet is reflected straight back to space by clouds, ice, snow, and so on, and does not heat the planet, but the other 70% warms the Earth. This figure of 30% is the “albedo” of the Earth.

The Earth emits energy to space as radiation across the electromagnetic frequencies, nearly all of it at infrared frequencies (that is, as “heat”). The amount of radiation is roughly proportional to the amount of heat in the climate system, or its temperature, just as the amount of water that spurts from a hole in a bucket is greater if there is a greater depth of water in the bucket.

The simply mechanics of the rates of heat input and output have the equation of a first order low pass filter, like an RC filter in electronics. This is a well-known observation in modeling the climate. We find from later fitting the notch-delay solar model to the measured temperatures that the time constant (or break frequency) is around 5 years, which agrees with what others have found.

 

Figure 3: The transfer function of the low pass filter that governs heat accumulation in our climate system. On a log-log graph it has a single 45° bend in the amplitude at the break frequency, sloping downward at higher frequencies. Parameter values from P0 (see Figure 1).

 

While it is exaggerating to say that a low pass filter is “evident” in the empirical transfer function, one can imagine the amplitude of the empirical transfer function being equal to a product of:

  • The amplitude of the transfer function of the notch filter in Figure 1.
  • The amplitude of the transfer function of the low pass filter in Figure 3.

( The transfer function of two systems in cascade is the product of their individual transfer functions. We are ignoring phases here, so just multiply the amplitudes to get the amplitude of the combined system. The vertical scales on these graphs are logarithmic, so add the red lines on the graphs.)

The notch filter is obscuring the low pass filter in the empirical transfer function, so it is difficult to “see” the low pass filter. But a simple basic approach to heat accumulation tells us there must be a low pass filter, and it is at least compatible with the empirical transfer function. So we will include a low pass filter in our solar model, in cascade with the notch-and-delay filters.

In the next post we look at mechanisms that might cause the mysterious delayed correlation.

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

————————————————-

REFERENCES:

Archibald, David, http://www.davidarchibald.info/papers/Past-and-Future-of-Climate.pdf, 2010

Archibald, David, “Solar Cycles 24 and 25 and Predicted Climate Response”, Energy and Environment, Volume 17 No. 1, 2006, pages 29–35

Friis-Christainsen, E.; Lassen, K. ,(1991) “Length of the Solar Cycle; An Indicator of Solar Activity Closely Associated with Climate”, Science, , pp. 698-700

Lockwood, Mike; Froehlich, Claus, “Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature”, Proceedings of the Royal Society, 2007

Moffa-Sanchez, Paola; Born, Andreas; Hall, Ian R.; Thornalley, David J.R.; Barker, Stehe, “Solar forcing of North Atlantic surface temperature and salinity over the past millennium”, Nature Geoscience, 2014, Supplementary Information

Solheim, Jan-Erik; Stordahl, Kjell; Humlum, Ole, “The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24″, Journal of Atmospheric and Solar-Terrestrial Physics, 2012

Soon, Willie W.H., “Solar Arctic-mediated Climate Variation on Multidecadel to Centennial Timescales: Empirical Evidence, Mechanistic Explanation, and Testable Consequences”, Physical Geography, 2009, pp. 144-184.

Usoskin, I. G.; Schuessler, M.; Solanki, S. K.; Mursula, K., “Solar activity over the last 1150 years: does it correlate with climate?”, Proc. The 13th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun, Hamburg, pp. 19 – 22, 2004

Usokin, I. G., M. Schuessler, S. K. Solanki, and K. Mursula 2005, Solar activity, cosmic rays, and the Earth’s temperature: A millennium-scale comparison, Journal of Geophysical Research, 110, A10102.

*July 21, I added the phrase [non-causal] in the intro which seemed overly complex on June 17, but is clearly important now. – Jo

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109 comments to BIG NEWS Part III: The notch means a delay

  • #
    EternalOptimist

    Is it possible that the step response is responding to the previous step up ? So its not two years ahead, but 9 years behind

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      David Evans

      No. The blue line in Figure 2 is the output of the notch filter shown in Figure 1 when the input is the step-up (brown line) in Figure 2.

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    • #

      “Is it possible that the step response is responding to the previous step up ? So its not two years ahead, but 9 years behind”
      “The blue line in Figure 2 is the output of the notch filter”…model.

      What happens after a long cycle compared to a short cycle may show the answer.

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    blackadderthe4th

    ‘The thing about notch filters that is hard for anyone who isn’t an electrical engineer to understand’ and no doubt electrical engineers do not understand the climate!

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      turnedoutnice

      Engineers are better suited to understand climate than virtually any other group except geologists. This is because they can think in terms of systems without getting hung up on the mechanism.

      The group which least understands climate is Climate Scientists taught at the schools which, because they were created for the purpose of Marxist Post-Normal Science, e.g. CRU, teach incorrect physics. The next group which has serious problems is Meteorology, which also teaches incorrect physics.

      The final group which has problems is Atmospheric Science, which also uses incorrect Sagan physics.

      We engineers have a head start on most!

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      • #

        turnedoutnice June 17, 2014 at 2:27 am

        “Engineers are better suited to understand climate than virtually any other group except geologists.”

        Naw! Engineers are willing to admit they do not know or understand! They have much fun poking at “it” to see what happens next! Never understanding “who” is paying for the beer needed for such fun! No need to understand, only to produce the useful. It is the distingusted professors that need to understand with “no skill at understanding”.

        “This is because they can think in terms of systems without getting hung up on the mechanism.”

        Naw This is because they can think!

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        • #
          turnedoutnice

          I’m an engineer and a PhD physicist so I can tell you from both sides that this Climate mess-up is the responsibility of 50 years of poor understanding by the academic physicists who defined Atmospheric Science 50 years ago..

          It all comes down to the ‘two-stream approximation’ essentially from Sagan via Schwarzschild, and a belief that a warm body continuously emits ‘photons’ at the S-B rate. Some even imagine that these bounce off filled sites on the cooler emitter in radiative equilibrium. Both Claes Johnson and i have come up with the bit of understanding beyond Planck, which shows how the energy transfer, which is effectively a travelling wave with the difference of the Poynting Vectors, superimposed on a standing wave of twice the colder amplitude, regulates the process.

          The ‘back radiation’ idea comes from poor physics’ knowledge and a failure to understand the difference between an Irradiance and the real energy transfer. Engineers, who have to get the sums right, know this intuitively. Sagan, who messed up the aerosol optical physics so believed much more SW energy entered the Venusian atmosphere, believed in his equations, assumptions and the numerical result, without checking it against reality. i call this the reality check: do it all the time!

          So, they imagine 3x real surface energy is offset to 1.6x by the false application of Kirchhoff’s Law of Radiation at ToA, another mistake – the grey body assumption. Then they offset the excess after this is used, with 3x real GHE, to give imaginary extra evaporation – ‘positive feedback’, by cheating in hind casting. This is compounded by the Meteorologists and their pyrgeometer, which converts temperature to irradiance.

          We now have people whose job as professors is to vary the fudge factors to make these models behave when they are fundamentally wrong. It takes engineers to teach the new generation of physicists to remember their job is to do experiments first then theory. Furthermore, engineers can take on the useless idiots who scream ”denier’ by telling them calmly and coldly: ‘I can prove my stuff from real experiments – all you can do is to scream and shout about mistaken physics which you dare not admit is wrong!’.

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    • #
      Backslider

      and no doubt electrical engineers do not understand the climate!

      And where exactly is your Youtube video to prove that?

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    • #
      Rereke Whakaaro

      … no doubt electrical engineers do not understand the climate!

      Possibly, but neither do climate scientists fully understand the climate system – they have admitted as much.

      What Electrical Engineers do understand, is the mathematics of cyclic phenomena. Are you suggesting that the climate is not cyclic?

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  • #

    Wow. While I work as a systems engineer on space programs, I did my BS in biology and I have seen this kind of response before in nature. Specifically neurons firing. If you apply a constant current the system builds up to a point where the nerve ‘fires’ and then resets back to ready to fire.

    Not exactly the same, but similar enough to see what you discovered. Solar cycles apply extra energy for a period of time then reduce input for a period of time. The Earth’s response lags into the next solar cycle, as if it was resetting the prior cycles energy first?

    It is interesting to realize how close we live to the edge of all ice or all water (and therefore a lot more clouds). Some years we (in Virginia, USA) see no ice, and other years we see a lot on ponds and rivers. So some years will build a reservoir of energy and never chill enough, others we lose a lot of energy (like this winter in the Eastern US) and we see a lot more ice and cold. Of course a lot of this is driven by the jet stream, but the local dynamics year to year show we could – with little change – be much colder or much hotter.

    Clearly energy dissipation time comes into play here. Energy dissipation occurs across the globe 24×7 – though attenuated by clouds and surface type (water vs land). But heating is only from one vector at any moment in time and covers a much smaller area with full energy flux. Even while the input on the hemisphere is also attenuated by clouds and where on the Earth the radiation is being deposited (land vs ocean, always through air). It would seem the energy input summed over years varies, creating a different dissipation signatures when the solar cycle adjusts the input.

    Of course, this all assumes I am reading this all correctly in the few minutes I have to scan it! Very “outside the box” thinking!

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    • #
      Peter C

      Some time ago Jo did a post. I don’t remember the title, but the subtext was “it is all about water

      I think you have summed that up.

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  • #
    crosspatch

    I have been a fan of Svensmark’s hypothesis and I wonder how that looks when blended into this. Basically, he says that a more active Sun (larger sunspot cycle) is the result of a stronger magnetic field and stronger solar wind. This sweeps the inner solar system clear of Galactic cosmic rays (GCR). When GCR impact earth’s atmosphere, they create nuclei for cloud formation. So — more active sun means fewer GCR and fewer clouds resulting in more solar radiation reaching Earth’s surface. This stronger magnetic field would likely be active before the sunspot numbers climb to maximum.

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  • #
    Sonny

    Hi David,

    I think you are on the right track in identifying this 11 year cycle.
    I think that in time it will be shown that this mysterious “notch and delay filter” occurring on earth coincides with electro magnetic forces within the earths core. If the sun goes through an 11 year cycle, the earth also goes through such a cycle. I.e the total irradiance could be only one output of this 11 year cycle. How is the earths inner core activated? What is the structure of the earths inner core? We don’t really know! Could it be that Svensmark was into something looking at the affect of cloud cover? Is there another variable and cyclical earth process that is also at play?

    60

  • #
    dimby

    “…and I’m saying it will probably take another year or two.”

    The last few minutes of the 50 to 1 interview with Topher takes on a whole new meaning with a little bit of hindsight.

    Congratulations on your research, it appears you finished ahead of schedule.

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    • #
      Yonniestone

      Yes well spotted dimby, I believe this type of “sensible thinking” would go down very well with the general public if only it could get the exposure and time to sink in.

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    • #
      David Evans

      Well spotted. I’d forgotten I’d said that. At that stage I expected to get this post to be out by Christmas. However the notch-delay theory grew and is stronger and bigger than I’d hoped for then. Stay tuned.

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  • #
    Sonny

    Hi David,

    Further to what I was previously saying. I don’t believe it is physically correct to say that the earth has a “notch or delay filter”. It seems to me that this is something you are artificially imposing in order to make the solar irradiance model fit. (Something you have admitted to but I think the terminology needs to be clarified). I.e the earth does not really have a non causal response to solar irradiance. Something deeper is going on!

    What your work is showing to me is that one of the major driver of changes on the sun and earth is tied into an 11 year solar cycle. I have come to be very taken by the “electric universe” theory, which poses that the sun is not a fusion reactor but is fundamentally an electric capacitor. I think that the 11-year solar cycles are electric resonance cycles in the heliosphere, the intensity of of which, affects the entire solar system including the earth. It is these changes on a solar system scale that drive our climate, solar irradiance being a part, but probably not the whole picture.

    The earth is also electric in nature which is aptly demonstrated by the strong magnetism of our poles! A molten rotating metal core does not adequately describe such phenomena as pole shifts and many other natural phenomena.

    I suggest further work is needed to determine what is the root cause of the 11 year solar cycle? Once we understand this we can extend the concept to theories about what is happening with the complete sun earth system.

    Electrically yours,

    Sonny

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    • #
      Rud Istvan

      Sonny, all models are just that. They are all ‘wrong’ somehow. None are ‘reality’ . Einstein supposedly said of his difficult general relativity math “God integrates empirically”.
      But some models are useful none-the-less.David and Jo think theirs is. Enjoy this intellectual adventure. I sure am.
      David has developed a new mathematical tool, not in the literature. I just got a second confirmation that it is both new and broadly useful from a knowledgable acquaintance in Colorado. (PS DE and JN, he says it has all kinds of uses in refining precision instrumentation by finding and eliminating more “hum”).
      In my experience, new tools that give new insights about existing data almost always lead to breakthroughs. For one of my businesses I developed a new calculation tool for estimating intrinsic capacitance from first principles. Solved all kinds of problems that the established approach could not. it led to new insights about EDCL energy storage materials since validated in the lab and on a pilot line. It may be leading to a business that makes a difference in energy conservation. About $10 billion per year of difference.
      What is happening here is the best of true scientific innovation in the Internet era. Bravo.

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  • #
    Brad

    Just staying in the loop so I can get comments emailed….:)

    30

  • #
    Aphan

    http://www.kidswincom.net/climate.pdf

    To the authors….can you read this amazing pdf and tell me if what is in it might answer the puzzle somehow? Or not?

    10

    • #
      Mark D.

      Aphan, interesting slides, I hope our resident CO2 mass-balance guru stops, reads it and comments.

      20

    • #
      michael hart

      I think he attempts too much at once, Aphan. Some bits seem more/less contentious than others, but not enough detail.

      00

  • #

    > the carbon dioxide theory, which temporarily assumed that carbon dioxide caused almost all of the global warming since 1800 — the “carbon dioxide assumption” — in order that the parameters of the carbon dioxide model could be found by curve-fitting it to the measured temperatures

    That’s completely wrong. But since its also irrelevant to your current concerns, its not a fatal flaw. If it teaches you to do curve-fitting, under the mistaken assumption that how the GCM’s work, then that would be a fatal error. Currently, you’re still looking like a no-physics model, and so uninteresting.

    (I notice that you bypassed 99.9999% of his post to defend your little gas relevance to anything significant) CTS

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    • #
      farmerbraun

      [SNIP - Sorry I'm removing chit chat about commenters however apt. Let's discuss the notch, not the commenters. I have deleted about 8 such comments entirely. Thanks for understanding. - Jo]

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    • #
      Mike Smith

      “uninteresting”

      Nevertheless, a great deal more interesting than your contribution to the discussion.

      161

    • #
      Kevin Lohse

      That’s the point Mr Connelly. GCM’s don’t work and have been empirically proven not to work – unless earning their proponents large sums of other people’s money to continue making GCM’s that don’t describe the climate is rated as success in your field. GCM’s are the quintessential no-physics model, of interest only in the way a Philosopher’s stone is interesting- as a failed artefact of an obsolescent whimsical fancy.

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      • #
        vic g gallus

        Off topic – The Philosopher’s Stone is thought to come from a poor understanding of the 9th century work of an Islamic philosopher who made aqua regia. The stone might be just saltpetre. He also wrote unrelated stuff on eternal life.

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    • #
      the Griss

      [SNIP]

      70

    • #
      bullocky

      william connelley:
      ‘ Currently, you’re still looking like a no-physics model, and so uninteresting’
      -
      http://en.wikipedia.org/wiki/Boredom
      “an unpleasant, transient affective state in which the individual feels a pervasive lack of interest and difficulty concentrating on the current activity.”

      70

    • #
      Yonniestone

      WC, if you are alluding to any type of curve fitting in the graphs in the above post I would be interested to see your explanation of how this has been applied, purely in the interests of science and the spirit of David Evans’ open dialogue.

      70

    • #
      Rereke Whakaaro

      Ah, we have reached a tipping point in social behaviour.

      The loquacious Mr Connolley has regressed into a drive-by troll. Who would have thought that would happen?

      80

    • #
      vic g gallus

      William, you need to change Wikipedia then.

      The Earth’s average surface temperature rose by 0.74±0.18 °C over the period 1906–2005. The rate of warming over the last half of that period was almost double that for the period as a whole (0.13±0.03 °C per decade, versus 0.07±0.02 °C per decade). The urban heat island effect is very small, estimated to account for less than 0.002 °C of warming per decade since 1900.[35] Temperatures in the lower troposphere have increased between 0.13 and 0.22 °C (0.22 and 0.4 °F) per decade since 1979, according to satellite temperature measurements. Climate proxies show the temperature to have been relatively stable over the one or two thousand years before 1850, with regionally varying fluctuations such as the Medieval Warm Period and the Little Ice Age.[36]

      Is it me or is it still implied that the warming is all due to CO2?

      30

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        • #
          vic g gallus

          It has been obvious for a long time ago that the warming from 1910-1940 was natural and was just as much as in the second part of the century. The admission that there was considerable natural warming is old but not that old.

          “Gore stated that the greenhouse gas levels and temperature changes over ice age signals had a complex relationship but that they ‘fit’. Both of these statements are true,” said Schmidt and Mann

          Do you remember this. It went with the “it is warmer since the Industrial Revolution than in the last 1000 years!”.

          00

  • #
    Michael Woods

    This is seriously the most fascinating thing I’ve read for a long time.

    For anyone struggling to understand the filter / delay mechanics, go and buy some noise cancelling headphones. Once you switch it on, it takes about 2 seconds to cancel the ambient noise after it samples the inputs looks for repeating noise patterns, then calculates the ‘notch filter’ and delay required to cancel it out. You’ll also enjoy much more pleasant and quiet in-flight experience going forward…

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    • #
      Rud Istvan

      Great post. Our gracious hostess JoAnne and her husband David Evans are mere designing, step by detailed step, Mother Nature’s CO2 canceling ‘headphones’. Perhaps that is a metaphor even the Australian, Holdren, and our dear leader OBummer here in the US might someday get.

      Jo, this post shows why I was strong as a high tech, med tech, and manufacturing consultant, but not so good at pure marketing issues. BTW, as predicted U.Q. Is radio silent on my horns of a dilemma challenge to them on Cook excuses. Perhaps you all there can dislodge something.

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      Rereke Whakaaro

      You’ll also enjoy much more pleasant and quiet in-flight experience going forward…

      Just don’t buy the Bose ones. Mine only lasted for one and a half overseas trips. And they were in the higher price-range.

      40

  • #
    farmerbraun

    What is becoming clearer is that the competition for laugh of the day is increasingly fierce. Any more entrants?

    30

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    R. Gates

    There are only two places a “delay” to a change in external forcing could exist in the system. Ocean heat content and the cryosphere. When looking at ocean heat content, the most important component is not SST’s. We know that for large volcanic eruptions, which reduce solar input to the ocean and the system, there is the immediate impact on tropospheric temperatures, but also a delayed impact via ocean and sea ice interactions. See:

    http://nldr.library.ucar.edu/repository/assets/osgc/OSGC-000-000-010-465.pdf

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      Mark D.

      Only two places eh Gates?

      At some point your naivety or ignorance starts to show doesn’t it Gates?

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      @R. Gates June 17, 2014 at 5:40 am
      The delay is caused by the Sun, not any part of the earth! What a wonderful planet! Perhaps musical. I wonder what Motzart would do with David’s findings. I am sure that the whales would love to hear it!

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    Aphan

    Mark D,
    I agree. It’s not my research, but it is impressive and it’s been around for a while. He found several cycles/patterns I’ve never heard anywhere else. And it’s all put together in such a logical way….

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    richo

    Hi David Evans

    Have you run some randomly generated data sets through analysis to verify that there is no underlying artifact of a “notch” built into your algorithms used in the analysis? Going back to Post II the labels for the UAH and RSS data sets appear not to be labeled on Figure 2.

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      David Evans

      The algorithms in the analysis just do Fourier analysis, and they reconstruct all the datasets form sinusoid very well (obvious just to the eye). There are no artifacts or anything in them that could give the notch. The same software and methods that found the peak at 11 years in Figure 2 of the last post failed to find a peak at 11 years in Figure 4.

      Figure 2 is for TSI. UAH and RSS are in Figure 4, the temperature graph.

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        David Evans June 17, 2014 at 6:03 pm

        More emphasis on “what is” less on “why it is”.
        There will be many suggestions of why, each eliminated until the only left “is” the why.

        Best wishes, or young witches, your choice! beware the Jo, if you err!

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    ColA

    David and Jo,
    It’s awesome – congratulations and can’t wait to see the rest and get to the bottom line!
    I remember Fourier series at the end of my 2nd year engineering maths course – I was so impressed I stuck those pages together and the book has now happily gathered 30 years of dust!! :-) :-)
    What is most impressive is that you are taking the time and making a significant effort to share this with everyone, more kudos to you both.

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    So we’d expect the extra radiation from the Sun every 11 years to produce corresponding peaks in temperature here on Earth.

    Why?

    Like CO2 itself as a small number of ppm in the atmosphere so is the amplitude of the 11 year cycle very small. A tiny bit more energy is being added every 11 years into a very complex system, energy that leads to the air temperature represents is only a fraction where that energy ends up AND there are all the inherent problems with measuring global energy without large error bars. So why “should” we see peaks when irradience varies by 0.001 of the total?

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      Rereke Whakaaro

      There is more to the sun than irradiance, as I think you already know?

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      vic g gallus

      He wrote in the first part that 0.8 W/m2 is the difference that corresponds to 0.5°C at the surface. What was downwelling again? 0.6 W/m2. He is also using a way to identifying individual frequencies in a signal that is a mixture of many.

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        vic… it was in part II and was not referenced. Do you know the reference? It also does not address the fact the difference between actual and measured.

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          vic g gallus

          It doesn’t have to be the full 0.5°C blip. That would show up without FT analysis. The mean temperature has only risen 0.8°C in 100 years.

          I do not have a reference but he did mention how it was estimated. He doesn’t argue that the big 0.5°C spikes should be seen, just that there should be a signal in all the noise.

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      Gee Aye, fair question and one I asked myself. The Earth gets about 1 W/m-2 extra solar radiation at the peak of the cycle. That peak lasts about 2-3 years. The dip at the opposite end of the cycle lasts the same time. It’s only 1W but it operates 24 hours a day on every square meter. There is a large cumulative effect there. The question is whether all those extra joules would show up in the temperature record.

      There is a low pass filter smoothing out the bumps, which makes it harder to see, but there should still be a regular difference, a wobble in the smoothed curve between the high half of the TSI cycle and the low half. There is nothing.

      As David has pointed out (@ #24.1 on a previous thread) if our temperature records can pick up a swing of 0.1C, accurate Fourier methods ought to find that regular beat, even if it is smaller than that. We are unable to find even a regular 0.05C bump during times the TSI peaks. The 11 year notch shows up especially strongly in UAH data for example, which I think is about the best we have. The Fourier method finds the sides of the notch. Many other researchers also find a correlation with a roughly 11 year delay between TSI and Temperatures. The solar model hindcasts better than the CO2 model — it finds a pause, and it predicts the rise from the LIA.

      It is hard to imagine a change of proportional magnitude of only 0.001 making a difference — but the Fourier method is analyzing the anomalies, not the proportional change, so “proportions” are irrelevant to the Fourier maths.

      But if it helps, consider the proportional change in temperature we are hunting for – it is proportionally smaller than the TSI change. Using the Kelvin scale — a 0.1C rise (in a system at 288K) is a change of 1 part in 2880 or 0.0003. If the irradiance rises by a factor of 0.001 — that’s proportionally three times larger.

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        HI Jo,

        I am not really convinced – nor do I think these posts have provided much convincing evidence that the cyclic fluctuations should transfer – that the cycle should be visible in the way you are anticipating. I do understand that Fourier is very good at finding the equivalent of residuals or even residuals of residuals but it will find nothing if there is nothing to find. Feel free to try to convince me as I’m sure, as your post above shows, it adds some useful clarity to the background. Thanks for that.

        For the moment though, just to move on to the other point I was trying to make is that the data itself might be masking the signal. I hear what you are saying about detecting changes of 0.1C (what did you mean buy this by the way – is this spot data, sliding window average?) but in such a noisy system measured as it is with noisy data, is the signal detectible. How is your method determining/testing if the input data is of sufficient quality for the analysis you are attempting?

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        Joanne Nova June 17, 2014 at 1:13 pm
        Jo,
        Get the raw temperatures from the one place in Ireland since 1600 something. I did not know that thermometers existed then. Anyhow the raw data on near surface temperature, for 500 years. No Global averaging, no 30 year Gaussian averaged of the Global average. that has no information left.

        David’s transform seems robust enough to filter all except the narrow frequency band of 11yr/cycle +- something. The crappy measurments With no smothing for your surface temperature response to your 11 year Solar cyclic is the best you will ever get. Your cycle should be detectable.

        “Donna change my numbers or I will eat your face off.”:Expect a huge delay. perhaps longer than your cycle.
        “Mommy I wish to be elsewhere or elsewhen” Bad is to happen here and now.

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      A tiny bit more energy is being added every 11 years

      A tiny bit more energy is being added continuously.

      Compare to this hypothetical – a drop of water in a bucket vs a continuous drip. The drops add up.

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    graphicconception

    I am a simple soul and have a simpler explanation for the delay caused by a filter.

    How could a real filter, that is one made of real components working in real time, know for sure that it was working on an 11 year(say) cycle? Well, it would have to wait for 11 years to be certain. If you only waited for 5.5 years and assumed the second half would complete the cycle then you could be wrong.

    There are other considerations that could increase the delay but that is the main one.

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      The solar cycles vary quite a bit, so to find a filter that runs on the same slightly irregular clock as the sun seems improbable on Earth, but inside the Sun, it’s credible. There appears to be some process which is tied to solar cycles that also affects the Earth. The delay is inside the Sun. See the next post we put up.

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        John M

        Hi Jo,

        Do the short term changes associated with volcanic forcings fit into your low pass filter model ?
        These changes are generally within a 5 year window (eg: Pinatubo).

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        Greg Goodman

        If it has to be a frequency filter that would seem unlikely.

        However, that explanation of a negative feedback to the signal does not require a mysterious coincidence of frequency.

        The apparent irregularity is because there are several frequencies present. 10,11,11.8 triplet in SSN ( probable1y with 136y modulation )

        The spectrum suggests a modulation is present, solar physicist Leif Svalgaard confirms there is a century scale modulation.
        http://wattsupwiththat.com/2014/05/24/its-the-evidence-stupid/#comment-1645190

        Since spectral analysis cannot represent modulated amplitudes directly, this comes out as a triplet in the spectrum.

        10,11 and 11,8 are the _same thing_ , a modulated 11y cycle.

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    If it is thes sun’s magnetic field that is the cause. The response will be seen in the Earth’s core which will slow or speed up due to the magnetic drag. Or will increase or reduce heat generation

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    Mikky

    A suggestion for determining the low pass filter:

    Imagine the sun suddenly switching off, the air would cool rapidly, but the oceans would retain heat for quite some time.
    A simple blackbody radiation model could be used to estimate the time constant of the heat decay.
    Probably been done many times before.

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    J Martin

    The red line in figure 1 looks to have the same shape as the cooling periods in the 42k world.

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    LightningCamel

    Either everyone else on here is smarter than me or nobody wants to ask so here goes. Basically I don’t understand how you get from Fig 1 to Fig 2. Can anyone explain or point me to a reference on how the time domain step response is inherent in or derived from the frequency domain notch filter?

    I’m trained in biological sciences and IT but the mathematics of notch filters is completely unknown territory so I’m prepared to concede this is an impossible ask in this forum. In that case feel free to bin this entire comment

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      David Evans

      Well asked :) I was wondering if anyone would ask. I didn’t include it in the main text because I didn’t want to scare people with details and it’s not germane — I wanted people to focus on the non-causality of the step response and the huge implication. The spreadsheet will be out soon to answer such questions in ultra-gory detail.

      1. Take the Fourier transform of the step function, the brown line in Fig. 2. Now you know the sinusoids “in” the step function, that is, a bunch of sinusoids, one at each frequency, whose sum is the step function (the “spectrum” of the step function).

      2. Apply the notch filter in Fig. 1 to that spectrum, to obtain a new spectrum. (For each sinusoid S in the spectrum, find the transfer function of the notch filter at the same frequency — red line for amplitude A, blue line in Fig. 1 for phase P. Modify the sinusoid S by multiplying its amplitude by A and increasing its phase by P, to obtain a new sinusoid at the same frequency. Put the new sinusoid in the new spectrum.)

      3. Add all the sinusoids in the new spectrum, which gives you the step response (the blue line in Figure 2). (That is, take the inverse Fourier transform of the new spectrum, when it is expressed as a Fourier transform.)

      That is, the Fourier transform of the response (blue line in Fig. 2) is the complex product of the Fourier transform of the step function (brown line n Fig. 1) and the transfer function of the notch filter (red and blue lines in Fig. 1)(which is itself a Fourier transform).

      (It takes everyone a while to get their head around this the first time they encounter this stuff. It’s complex and complicated.)

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      PhilJourdan

      No LC, you are not alone. You just were earlier. I can see I have a lot to learn about notch filters.

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    ControlPhD

    So where is the model output, i.e., TSI filtered by notch/delay/lp-filter? I do not expect a good fit!
    By the way, the step response is simply wrong, no matter how you shift it in time. If the real step response (causal of course) is h(t), the figure shows 0.5 – h(-t).
    I would expect better from an undergraduate student after a first introductory course in signal analysis …

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      David Evans

      Good joke. (The response in Figure 2 above is correct, but consider the response suggested by ControlPhD…)

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    DarrylC

    Great analysis.

    Obviously, the climate is a very complex system, and there are complexities that are missing in your model, but if the model adequately predicts some of the behaviour of the system it is useful, and we can build on it to refine the transfer function. If similar models could be developed to define some of the other relevant “black boxes” in the response function, we would be much better served than by the climatologists computer simulations that do NOT recognize the fundamental “system” nature of the climate.

    The key to understanding any complex system, is to understand its transfer function. The approach that climate scientists have been taking is akin to trying to predict the behaviour of a complex transistor circuit by modelling its physics and the statistical behaviour of electrons and how those electrons are affected by the myriad and complex (at statistical level) components of the circuit. It is VERY probable that such a model will miss something and will not yield useful results because it is difficult, if not impossible, to model ALL of the complexities of the system. On the other hand, the transfer functions of the components in a complex electronic system are predictable and repeatable. The transfer function is a high level representation of the EFFECT of the underlying physics and statistics on the output given an input. There is a good reason that you cannot write a control program for a complex system without first understanding the transfer functions of the components. Without factoring in the transfer functions, the system runs the risk of blowing up…..sometimes literally.

    Engineers have proven, beyond a shadow of a doubt that:

    1) Applying transfer function mathematics to very complex systems works very well in predicting the responses of those systems to different inputs. This applies to most systems, not just circuits.

    2) You can derive the transfer function empirically WITHOUT understanding all of the complexities in the system.

    All that climatologists have proven with their modelling is that they cannot accurately predict anything more than a couple of weeks into the future…..and even in that two week window, they are often wrong.

    Thank you for your efforts.

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    Willis Eschenbach

    The part of all of this that I love is that over at WUWT, I’ve had skeptics jumping all over me for saying that I can’t find the 11-year solar cycle in the temperature data.

    But here, folks cheer when David says:

    So we’d expect the extra radiation from the Sun every 11 years to produce corresponding peaks in temperature here on Earth. Yet it doesn’t.

    Make up your mind, folks …

    I see that despite my showing examples of a couple of kinds of systems where a notch does NOT mean that there is a notch filter, David is still pushing that claim. Deny reality much? However, if I had as little other evidence for a “notch filter” as he has … which is none, not one scrap … I might consider ignoring reality as well.

    His case would be helped greatly if he or anyone could produce just one example of a thermal “notch filter” … anyone? Because David certainly hasn’t presented one …

    Regards to all, and anyone who knows of a system containing such a thermal “notch filter”, now would be the time to bring it up. I don’t think such a system exists anywhere, even in the lab … so you have a choice—either prove me wrong, or you are proving David wrong.

    w.

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      In the domain David is working in what you see is “equivalent” to a notch filter.

      David calling it a “notch filter” is something EEs would immediately get. Unfortunately a lot of the audience is not so blessed.

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        Willis Eschenbach

        MSimon
        June 18, 2014 at 6:05 am · Reply

        In the domain David is working in what you see is “equivalent” to a notch filter.

        Your comment reminds me of the old riddle, viz:

        How many legs does a cow have, if you consider a tail as being exactly equivalent to a leg?

        The answer of course, is four … because considering a tail as being equivalent to a leg doesn’t make it a leg.

        In any case, in addition to his notch, his “notch filter” gives us a prominent peak at about 3 years … perhaps you might let us know what kind of filter that peak is “equivalent” to, and how do you (or he) explain that?

        w.

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          Willis,

          The purpose of looking at the “notch” which you also found is to figure out what causes it. OK. “Notch” offends you. You can call it “missing signal”. I’ll understand. As to the other wiggles – it would be good to find explanations for those as well. There is probably something to be learned about how the system operates.

          It might also be good to understand the connection between local electromagnetism and tectonic activity. I have some ideas of how to do that one.

          And BTW David is looking for causes for the “notch” Uh. missing signal. Wouldn’t it be more profitable for you to see if you can find a cause for that instead of arguing semantics?

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            Willis Eschenbach

            MSimon
            June 18, 2014 at 8:03 am

            And BTW David is looking for causes for the “notch” Uh. missing signal. Wouldn’t it be more profitable for you to see if you can find a cause for that instead of arguing semantics?

            I answered that in my very first comment on the subject in the previous thread. Wouldn’t it be more profitable for you to ask first before making a fool of yourself with unpleasant and untrue accusations?

            w.

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            • #

              Please explain how non-linearity disappears the signal? And only the 11 year signal.

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              Also explain the errors in the signal processing.

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                On second thought – don’t bother.

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                Willis Eschenbach

                MSimon
                June 18, 2014 at 9:51 am · Reply

                Please explain how non-linearity disappears the signal? And only the 11 year signal.

                Since I did not say that “non-linearity disappears the signal”, nor anything like that, I have no idea what you are referring to. And I’m not willing to guess. A quote or a link is required.

                Also, I don’t think that there are any “errors in the signal processing”, M, and I don’t ever recall saying there were such errors. Again, a quote or a link to what you are referring to would help greatly.

                In any case, the problem is not in the analysis. The problem is in the interpretation of the results. The existence of a notch does NOT mean the existence of a notch filter, as you and David both seem to assume.

                Regards,

                w.

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                1: I don’t think that there are any “errors in the signal processing”

                Fine. Then could you explain the absence of the 11 year signal?

                David claims he can. We shall see. What is your reasoning on that?

                David is an EE. So am I. His terminology seems perfectly reasonable to me. It offends you. That is irrelevant.

                What is the cause of the missing 11 year signal? Assuming you agree that signals exist at higher (3 year) and lower (22 year) frequencies. Why the notch (considered as a description of the graph and not implying any mechanism)?

                You are of course aware that electrical analogs of other types of systems are done all the time. Just consider this an electrical analog of the climate system. The fact that the climate system electronic analog is a “notch filter” says nothing about what is going on in the climate system. So what is going on in the climate system that has a notch filter electrical analog?

                David has made an electrical analog of the climate system for convenience. It says nothing about how the climate system does the “filtering”. I hope that clears up your confusion.

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                Mikky

                I’m familiar with determining the transfer function of systems using suitable signals:
                Impulses, pure sinewaves, swept-frequency sinewaves, white noise.
                The essence is the need to exercise (or at least sample) all frequencies.

                But here the input is DC plus a TINY 11-year oscillation, i.e. just 2 frequencies (actually just 1, DC does not count)
                I fear that fancy mathematics is being used here to reach conclusions that simply cannot be justified,
                given the MAJOR unsuitability of the input signal.

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                David Evans

                Mikky, The final model works well at hindcasting. The notch filter predicts has a delay, which has been corroborated half a dozen times in the last decade. If the solar model forecasts well too, which we’ll know in a few years, it is probably all ok.

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      David Evans

      Willis, I’ve replied to all that on the appropriate post, as replies to comment 62 at joannenova.com.au/2014/06/big-news-part-ii-for-the-first-time-a-mysterious-notch-filter-found-in-the-climate/

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    GDue

    Stepping right back to the initial facts (no response to 11 yr cyclic increase in solar output), is a possible explanation that other components associated with the increased radiation work against its interception at the surface of Earth? Very hypothetically, could something like increased proton flux density cause an increase in high level cloud and increased global albedo? I might be completely back to font with this particular example, but it serves to illustrate the idea. Alternatively, if there is an underlying influence in the solar system that causes the 11 year solar cycle (e.g. Jupiter’s orbit), might that also be affecting Earth?

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    Congratulations on the original research. Hope you have have a leap of imagination choosing a name for the phenomenom. Factor X is reminiscent of #42.

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    crosspatch

    Just to toss a little someting into the ForceX bucket

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  • #
    ControlPhD

    Well, the step response of the notch filter is not correct, and the estimated temperature (TSI filtered by notch/delay/low pass filter) has not been shown. Come on David, show the result, and your transfer function equation!

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      Willis Eschenbach

      As far as I know, David’s “transfer function equation” is simply the Fourier transform of the response (temperatures) divided by the Fourier transform of the impulse (sunspots), but I’m sure someone will correct me if I’m wrong.

      w.

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    Charles Davis

    I don’t know if the delay assumption is germaine to the central argument, but any delay would mainly have to do with the “Q” of the filter. The simplest filter would be a three point FIR, whose output would be the weighted sum of this year’s input, last year’s and the year before that. This can perfectly notch any single frequency, an 11 year one for instance.

    Your notch looks relatively broad, which would imply very little delay.

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    Willis Eschenbach

    MSimon
    June 18, 2014 at 1:58 pm

    [Willis]

    1: I don’t think that there are any “errors in the signal processing”

    Fine. Then could you explain the absence of the 11 year signal?

    I’ve been over this several times. It is the result of emergent phenomena. I’ve posted half a dozen links to further descriptions.

    David claims he can. We shall see. What is your reasoning on that?

    David claims he can what?

    David is an EE. So am I. His terminology seems perfectly reasonable to me. It offends you. That is irrelevant.

    I have no problem at all with his terminology, and I understand perfectly when he says “notch filter” … I disagree with his logic, not his terminology.

    What is the cause of the missing 11 year signal? Assuming you agree that signals exist at higher (3 year) and lower (22 year) frequencies. Why the notch (considered as a description of the graph and not implying any mechanism)?

    As I said above, I’ve written at length about how emergent phenomena regulate the temperature of the earth, and constrain it to a very narrow range (e.g. a variation in temperature of ± 0.1% over the entire 20th century. Is the regulation perfectly smooth across all frequencies? Of course not … but despite that, as David points out, the OFT of the temperature since 1600 is basically a straight line.

    And the “notch” exists because the temperature is NOT a function of the forcing. As I’ve said several times, if you use the sunspot data and compare it to white noise using David’s method, you’ll get a “notch” that’s basically identical to David’s.

    You are of course aware that electrical analogs of other types of systems are done all the time. Just consider this an electrical analog of the climate system. The fact that the climate system electronic analog is a “notch filter” says nothing about what is going on in the climate system. So what is going on in the climate system that has a notch filter electrical analog?

    David has made an electrical analog of the climate system for convenience. It says nothing about how the climate system does the “filtering”. I hope that clears up your confusion.

    No, he hasn’t. He’s made a claim that because there is a notch, there perforce must be a “notch filter”. He has provided no comparable “notch filter” circuit, nor even a clue as to what kind of notch filter he’s talking about.

    And you say that “It says nothing about how the climate system does the “filtering”.” Since neither you nor he have shown that there is “filtering” going on in the climate system, I suspect that’s true, but how would we know?

    Best regards,

    w.

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    Greg Goodman

    “There do not appear to be any other possibilities.”

    While I think this kind of engineering / systems analysis approach is what should have been done 30 years ago and is the way forward, I really don’t like all the talk of non causal filters and fudging with delays.

    I think the notch filter interpretation is flawed from the beginning.

    “We only care about the amplitudes here, because the phases of the sinusoids cannot be reliably determined from the climate datasets.”

    This I don’t like the sound of either, it sounds like an attempt to sideline a problem. If you do an FT you have both phase and frequency information. To suggest one is “reliable” and the other not seems inconsistent. If this means that phase information from the rag bag of different proxies was contradictory this needs to be stated clearly and dealt with, not brushed aside.

    Yes, I know engineers like to be pragmatic but there are limits.

    Frankly, I’m rather unimpressed with the idea of averaging the spectra that clearly don’t even agree that well in terms of frequency.

    Colours are frequencies too, and we all know from school what happens when you wash you brush while painting, you end up with muddy brown water.

    So you have a muddy brown 11y spike in what you assume to be the input and when you don’t find it in the output you conclude an 11y notch filter.

    Since you don’t have any other significant features in the input all you can conclude is that the system is not sensitive to this input signal. It does not tell you anything more general about frequency response.

    IMO you are making false assumption.

    So let’s re-examine “There do not appear to be any other possibilities.”

    I would suggest some:

    1) There are many other inputs and the one you are using is not having any visible impact on the system.

    2) There are strong negative feedbacks to this input which negate it, irrespective of frequency. There is nothing in what you show that suggests it is just the 11y component of solar that is being ‘filtered’.

    Both these seem more obvious and more credible than physically unreal non-causal notch filters.

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    Greg Goodman

    “You are of course aware that electrical analogs of other types of systems are done all the time. Just consider this an electrical analog of the climate system. ”

    I think that may be the heart of the problem. In an electrical circuit it is generally known what is “the” input and what is “the” output. The climate system is far more complex, with many inputs and internal variation.

    Analogies are risky. Applying general systems analysis approach should be valid whatever the system. However, taking specific methods from say EE, it is necessary to check whether they are general enough and can be applied to climate.

    Many will be, but care is needed.

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    Greg Goodman

    Delay between long term SSN and SST is about 10 years, from cross-correlation.

    http://climategrog.wordpress.com/?attachment_id=958

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