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New Science 12: How do we model the thermal inertia of the Earth?

Basic models take a top down approach, focusing on gross input and output rather than all the details within the system (which is mainly left to the feedbacks parameter). This makes them very different to the GCMs, which attempt to add up the climate from the bottom up and predict based on adding up grids and guesstimates of clouds, humidity, ice, etc.

The energy coming in to the Earth is called absorbed solar radiation (ASR). It varies significantly. The Earth will absorb the peaks and troughs of this to a certain extent. If we step back and look at the big picture, the question is how many years does it take for a step up in incoming energy to spread its way through the climate system, vanish into the top layer of the ocean, come back out and be released to space. To some extent that extra energy gets absorbed for a while before being released. David analyzed this system from the outside, graphing it like a low pass filter in electronics. (How much “noise” of spikes and troughs in ASR is being smoothed out by the Earth’s climate?)

Basic climate model, Absorbed Solar Radiation, Outgoing Longwave Radiation

In a low pass filter graph against frequency, the response of the filter is a flat line at lower frequencies, so all the bumps and wiggles in ASR at those low frequencies are faithfully reproduced in the outgoing longwave radiation (OLR). We know for sure that if the Sun gave off more energy (or somehow indirectly reduced our cloud-cover so that we absorbed more energy) that over a period of say, 200 years, the relationship is one to one. More energy in, equals more energy out. But the question is, how short a period does that apply too? Obviously not say 5 minutes. What kind of time-frame does the low pass filter work on?

The answer is a bit complicated because in every solar cycle (roughly every 11 years) there is a separate effect called the “notch” — the sun churns over it’s magnetic field, releases a little bit more solar radiation — and some effect we haven’t pinned down yet reduces Earth’s sensitivity to that extra bit of incoming radiation. (For those familiar with low pass filter graphs, that means the elbow or bend in the low pass filer graph gets obscured by a separate effect, which is the notch around 11 years.)

In the end, the best we can do is come up with a range, but it’s still useful. The low pass filter effect operates on a similar time-frame to the totally separate notch effect. Ultimately the outer edge of the Earth’s Climate system (including the atmosphere and the land we live on) absorbs, shares, and emits 90% of those spikes and troughs either within about 2 years, or maybe about 8 years, depending on which side of the notch the bend in the low pass filter graph is (the notch obscures the very range we are interested in).

The empirical transfer function and the notch are ahead of us in this series, and for now we are just concerned with modeling the thermal inertia, by describing it with an equation.
– Jo

12. Modeling the Thermal Inertia of the Earth

Dr David Evans, 16 October 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.

This post derives the relationship between absorbed solar radiation (ASR) and the radiating temperature, which is at the heart of the solar response in the sum-of-warmings model within the alternative model.

This relationship  is found to have the same structure as that of a simple low pass filter, so the thermal inertia of the Earth is mimicked by a low pass filter. The radiating temperature, which determines the outgoing longwave radiation (OLR), is a smoothed version of the ASR — slow changes in the ASR are faithfully reproduced in the radiating temperature and OLR, but faster changes are attenuated.

The result for transitions between steady states is straightforward and agrees with the conventional basic climate model; the main interest here is the time lag or thermal inertia when not merely modeling the changes between steady states, which is used later in the notch-delay solar model.

Functions of Time

Unlike the rest of the analyses in this series, in this section of this post we consider climate quantities at any time, rather than just in or between steady states. Let the ASR A, radiating temperature TR, and OLR R be considered as functions of time t, here only.

The only significant source of input energy to the climate system is ASR, because reflected TSI just bounces back out to space without heating the Earth — so the rate of heat input to the Earth, per unit area, is A. The only significant loss of energy is outgoing longwave radiation (OLR) — so the current rate of heat output, per unit area, is

by the Stefan-Boltzmann law (Eq. (2) of post 8). The variables we are concerned with here cannot characterize the total amount of heat in the Earth’s climate system, because they only describe the upper boundary of the climate system. However, for small perturbations, the rate of change in the accumulated heat of the climate system may be assumed to be proportional to the rate of change of TR because TR is a good proxy for the amount of heat at the outer boundary of the climate system. Thus the rate of change of TR is proportional to ASR less OLR, that is,

where k is a constant that converts between temperature and energy per unit area. Substituting for TR using Eq. (5) of post 8, which introduces λSB, *

Rearranging the constants,

where the “break frequency” is

Eq. (4) is the differential equation of a low pass filter of first order (like a simple RC filter in electronics). Its effect is simply to smooth out TR, as it mimics A. Because the rate of change of the radiating temperature TR is proportional to how different TR is from λSBA, it mimics the ASR but with a distorted lag — because the closer TR is to λSBA the less TR changes, and TR changes in the direction that minimizes its difference with λSBA. Thus Eq. (4) describes the thermal inertia of the Earth, or how the radiating temperature tracks the ASR. (Note that the amount of lag depends on frequency, but is not proportional to frequency (see Eq. (10) below), so in general the signal in the ASR is distorted and smoothed out by the time it gets to the OLR. It is only a simple lag if the ASR is a pure sinusoid.)

Consider a system whose input is the ASR, whose output is the radiating temperature, and where the relationship between them is as per Eq. (4). (The Earth from space would appear as such a system.) That equation is a linear differential equation, so the system is linear and invariant. Hence if the input to the system is a sinusoid then the output is a sinusoid at the same frequency. Letting the ASR input A be the sinusoid

the output  is therefore

for some amplitude change ρ and phase change φ. So, by Eq. (4),

Expanding the trigonometric functions then equating the coefficients of cos(2πft) and sin(2πft) gives

to which the solution is

pp

Figure 1: The low pass filter of Eq. (10), in the frequency domain. The red and blue lines are from the two parts of Eq. (10).

Eq. (10) shows that slow changes in the ASR are faithfully echoed by the radiating temperature, because for frequencies well below fB the ratio of the output amplitude to the input amplitude is a constant λSB. But quick changes in the ASR are weakly echoed in the radiating temperature, because for a frequency f well above fB the ratio of the output amplitude to the input sinusoid is a tiny

The switchover between copying the input sinusoid (low frequencies) and increasingly attenuating it (high frequencies) occurs around the break frequency fB. This is the behavior one would expect due to the thermal inertia of the Earth — the temperature of the Earth tracks slow changes in the ASR but increasingly isn’t quick enough to track faster changes.

Later in this series, when we observe the empirical transfer function from total solar irradiation (TSI) to surface temperature, we find that 1/fB is either about five years or about 20 years, depending on whether it is on the high-frequency or low-frequency side of the notch (the data generally fits slightly better on the high-frequency side). This corresponds to a step response whose time constant  is about 1/(2πfB), or about 0.8 years or 3.2 years. That is, after a step change in the ASR level it takes the surface temperature about 0.8 years or about 3.2 years to reach 63% (or 1- e-1) of its new corresponding level, and about  1.8 years or 7.4 years to reach 90% of its new corresponding level. Clearly this time lag reflects the thermal inertia of the atmosphere and land, and maybe some upper layer of the ocean (i.e. the outer boundary of the climate system), but not the remainder of the ocean.

Steady State

For short excursions around the Earth’s current position on the Stefan-Boltzmann curve, by Eq. (5) of post 8

For transitions between steady states ΔR is equal to ΔA. Hence for small transitions between steady states,

Obviously enough, the increase in radiating temperature is the product of the increase in ASR and the Stefan-Boltzmann sensitivity (SBS).

 

* 17 Oct 2015: Correction to post. Originally Eq. (3) omitted the factor of 4 (in the denominator of the last term). Correcting this error changed some scaling factors in equations, but not the character of the post or anything of consequence. The correction caused λSB to be replaced by 4λSB in Eq.s (4) through (10), and changed fB from (2πSB)-1 to (8πSB)-1. Because it comes from comparing  fB to the empirical transfer function, the estimated value of fB and the time constants estimated from fB were not affected by the correction. The logic of the “steady state” section, leading to Eq. (13), as initially posted was incorrect, and happened to give the correct result only because of the error in Eq. (3). Fixing Eq. (3) exposed this faulty logic. The “steady state” section has been rewritten using different reasoning, but the conclusion, namely Eq. (13), is the same as before the correction.

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152 comments to New Science 12: How do we model the thermal inertia of the Earth?

  • #
    Richard111

    Oh, my! This is way over my pay scale. For example, I can understand why CO2 is in the OLR side of the top graph but fail to see why it does not appear in the ASR side. When I attempt to calculate the energy of absorbed sunlight in the 2.7 and 4.3 micron bands this exceeds the ‘radiated energy’ from the whole 15 micron band of CO2, but then my math is very suspect.

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      Richard 111, the ASR can be treated more simply — we don’t need to specify where it heats the Earth, we only need to know how much there is in total. Yes, about a third of the incoming ASR is intercepted by CO2 and clouds in the atmosphere, and only about 2/3 hits the surface, but we do not need that info for the modelling that follows.

      The origins of the OLR on the other hand are very much tied up to the Earth’s response to increasing CO2 etc., so we are focusing on the changes in OLR emitted by the CO2, water vapor, etc. The small redistributive changes are the key to calculation the warming at the surface.

      “Everything should be as simple as possible, but no more so.” – A. Einstein

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      • #
        Richard111

        Thank you David, I think I’ve got that. Be interesting to see the details of effects of CO2 on the OLR. I have this fixation that CO2 must surely intercept some of the convective surface energy via molecular kinetic transfer.

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      Roy Hogue

      Oh, my! This is way over my pay scale.

      Even further over mine than yours, except that David’s explanations are straight forward and, so far at least, I can follow them. The math at places is beyond me.

      The concept of smoothing or filtering introducing a time delay between stimulus (TSI) and response (OLR) is something I know from long association with RF equipment so the example he cites is something I understand.

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    Rihard111 said:

    “I can understand why CO2 is in the OLR side of the top graph but fail to see why it does not appear in the ASR side”

    Subject to David’s comment I would suspect that would be because the effect of a change in ASR (Absorbed Solar Radiation) does result in a change of overall system temperature whereas a change in the amount of CO2 does not.

    I recall an earlier post saying that the solar effect should be treated differently to the CO2 effect and that one of the mistakes made by the models lay in treating them both the same way.

    The interesting question then is as to why the system response to CO2 is different to that of a change in ASR and my opinion is that the thermal effect of CO2 is neutralised by convective adjustments in a way that cannot apply if ASR is changed.

    If one increases ASR then the entire system is warmed because more energy becomes available but if ASR stays the same then there is only a redistribution of the same amount of available energy.

    I have a proposal as to how that difference comes about.

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  • #
    Robk

    Help. I’m missing something. Equation(6), “assume the input is a sinusoid”: Why?

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    • #
      Robk

      The graph makes it clearer but where is that data from?

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    • #

      Robk, the differential equation in Eq. (4) was solved using a piece of knowledge that isn’t widely known outside engineering maths: “That equation is a linear differential equation, so the system is linear and invariant. Hence if the input to the system is a sinusoid then the output is a sinusoid at the same frequency.” Or, to use the jargon, the eigenfunctions of the system implied by Eq. (4) are the sinusoids.

      I don’t expect most readers to necessarily understand all this: to see that it works, however, perhaps check that with A as in Eq. (6) and TR as in Eq.s (7) and (10) does indeed satisfy Eq. (4).

      This is part of the model coming later in the notch-delay section, and it has implications for even the alternative basic model we are building to replace the conventional basic model — i.e. Eq. (13). So logically it belongs here in the series, though I would much rather leap to the next few posts because they are much more interesting.

      This post is the only one left like this; less tricky maths from here on!

      Graph: The red and blue lines are from the two parts of Eq. (10). [Added to caption, thanks.]

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      • #
        Robk

        Thank you David. The penny’s dropped after reading your reply and some of the others. I am enjoying brushing the cob webs off the maths that I don’t use day to day.
        Great series.

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      • #
        Mark Fraser

        That phrase is still in my mind 50 years after enduring engineering math. Sinusoid in, sinusoid out. And I’m glad I was never faced with 2nd order DEs in my work life….

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  • #

    Jo

    If o?t censor


    Peter Miller

    October 16, 2015 at 1:26 am

    Unfortunately, in all fields of science there a few who deliberately alter data in order to prove their theories.

    Where climate science differs from all other fields of science is that this practice is so blatant and widespread it has become acceptable and even praised. From Mann’s Hockey Stick to GISS’ historic temperature statistics, everywhere you look in climate science, you find data manipulation/torturing tn an attempt to prove a false theory.

    As a geologist, I can tell you it is self-evident if there was the slightest bit of truth in CAGW theory it would be in the geological record and we would not be here. The truth is CAGW can only be found in computer climate models, which are either pre-programmed to find CAGW, or represent a very poor reflection of how our planet’s climate functions.

    The scary thing is the ‘science’ of climate alarmists is continually being exposed for the hoax it is, but this is largely ignored by the mainstream media. I guess being outspent by a factor of more than 1,000 to 1 also does not help.”

    A comment from

    http://wattsupwiththat.com/2015/10/16/how-a-liberal-vegan-environmentalist-made-the-switch-from-climate-proponent-to-climate-skeptic/#comment-2050259

    More there too.

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    • #
      KinkyKeith

      Good article.

      Another conversion

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    • #

      Another Ian October 16, 2015 at 7:45 pm

      AI,
      Timely post in this series, thank you!

      “Unfortunately, in all fields of science there a few who deliberately alter data in order to prove their theories.”

      Please think carefully of the concept “Being sold a Bill of Goods!”.

      “Where climate science differs from all other fields of science is that this practice is so blatant and widespread it has become acceptable and even praised. From Mann’s Hockey Stick to GISS’ historic temperature statistics, everywhere you look in climate science, you find data manipulation/torturing tn an attempt to prove a false theory.”

      Now think what must happen when us SERFS finally understand that we have “only been sold a Bill of Goods!” for the last 30 years. We have received no goods! There was never any intent to produce any goods. I do not mean what could happen, nor what may happen, but what must eventually happen! Earthlings are the current top predator for a very good reason.

      “The truth is CAGW can only be found in computer climate models, which are either pre-programmed to find CAGW, or represent a very poor reflection of how our planet’s climate functions.”

      That means “their truth” not “the truth”! How do we identify and isolate the individuals (they) that make up this “their truth”.

      “The scary thing is the ‘science’ of climate alarmists is continually being exposed for the hoax it is, but this is largely ignored by the mainstream media. I guess being outspent by a factor of more than 1,000 to 1 also does not help.”

      Ah! Is the trucking company that supposedly delivered the 3 tons of goods,“labeled as ‘corn’ on the Bill of Goods”, the same ‘they’ as those that claim to have produced only “3 tons of weightless ‘Bull crap’ labeled ‘corn’?.”
      ————————————————
      For David’s articles so far my criticism:
      Analogies are fraught with untended misunderstandings.

      Here “pipes” mean what to:
      Drainage ditch folk?
      Water supply folk?
      High pressure hydraulics folk?
      High pressure air tool folk?
      HVAC, fresh air folk?
      Ship handlers?
      Grain suppliers?
      Meteorologists?
      Some so called atmospheric physicists?
      Each different set of engineers?

      Analogies for this atmosphere must have the disclaimer: “this is but a different POV for a different subject than what you understand in your work”—- I.E. If the foe shits, wear it! Afterward discard it all, as such is an analogy ONLY, never what actually is, AFAIK! David’s analogies are fine for me. But still it remains, I do not know, humm, maybe! Beware of all that claim to know.
      All the best! -will-

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  • #

    This may be helpful.

    Newton’s Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).

    So cooling and warming will always occur with an exponential decreasing rate after a step change.
    http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

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    • #
      Mike Flynn

      I’m impressed with Newton’s thinking, and have been for a long time. A clever chap, one might say. Of course, Hansen, Mann and all the rest might not agree.

      The centre of the Earth is around 5500K. The temperature of Earths surroundings is, say, 3K.

      Warmists expect the Earth to increase in temperature – fat chance! No matter how they try, no amount of CO2 or unconcentrated sunlight can stop even boiling water from cooling, after you remove it from the stove.

      As Newton pointed out, it will cool to ambient – more quickly at first . . .

      Precisely as the Earth has, and will no doubt continue to do.

      Give it a try, if you believe Newton was a fool.

      Cheers.

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        Richard

        Makes you wonder if the ASR = OWLR is entirely appropriate when Earth’s core is radiating at a mind-boggling 53,000,000 W/sq.m and ASR is only 1368 W/sq.m. Apparently a signficant source of this heat from the Earth’s core comes from… you guessed it… gravitational pressure – which I think many would agree is likely the same source of heat that increases Venus’ surface temperature far above ASR. I haven’t done that much research into this area, I must admit, but the gravitational pressure argument as advocated by some scientists (and pushed a lot by sites like HockeySchtic) seems more intuitively reasonable to me than the ‘heat trapping’ effect from the 1% of gases in our atmosphere. I mean, CO2 makes up, what? One molecule in every 2,500 other non-greenhouse gas molecules spread evenly throughout the atmosphere. Imagine you have 1 grain of rice and attempted to heat up 2,000 grains of rice surrounding it, I can’t imagine you’d have much success at measurably increasing the mean temperature of the 2,500 grains with that single heated grain, but that’s essentially what climate scientists are saying is happening. In years to come I think people will look back at the ‘greenhouse’ model and gasp by how ridiculously inane it was and how easily so many people were fooled into thinking it had any relationship to reality.

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        • #
          Richard

          Rice sorry, not rise.

          Wish there was an edit button…

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        • #

          Richard You say “Apparently a signficant source of this heat from the Earth’s core comes from… you guessed it… gravitational pressure…”
          I like the term pressure as you will find all over the net I have for decades said that gravity is an external pushing repulsive force. Not a force of attraction. For gravitational pressure to provide a constant source of heat this energy MUST be refreshed. There is no such thing as free energy! So the elevated heat at the core of the planet is evidence of either an external source of energy that is NOT the sun or an internal source that needs to be accounted for.
          Where do you say the continuous flow of energy required for “gravitational pressure” to produce this heat flow comes from?

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            Siliggy October 17, 2015 at 4:38 am

            “Richard You say “Apparently a signficant source of this heat from the Earth’s core comes from… you guessed it… gravitational pressure…””

            Interesting! You seem to express all time accumulation (integral) of power as heat. Then Neavou physics now defines heat as only the shift of power accumulation to a different mass, in the form of energy.
            How frightfully bizarre thinking!
            Pressure of a compressible fluid is a distinct and different form of time accumulation (integral)of power.
            Your Neavou physics tries to schmush together all concept of sensible heat, gas pressure, and WORK, as the same (identical) thing. Always expressed as symbols in an algebraic expression. How absolutely absurd!! This could be done only by a group of academics that have never done any WORK.
            In most mathematics, there is seldom an identity symbol (three small stacked horizontal line segments). Two stacked segments (equality) is a symbol for similar scalar value of something expressed by whatever the symbols represent. Is such representation no longer taught to innocent children, now able to buy beer and reproduce?

            If this is now true, the least of all earthling worries is climate change! Stupidity has completely replaced earthling cleverness! :-(

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            • #

              Will you say “Interesting! You seem to express all time accumulation (integral) of power as heat.” Not sure if you are saying this to Richard or myself.
              The repulsive force I claim is a lossy ongoing force process, providing a flow of heat from massive quantities of subatomic particles that DO NOT COLLIDE but pass right on through the planet each leaving only an incredibly small magnetic interaction.
              These two effects could be related.

              Solar cycle variation of radioactive decay rates.
              https://www.youtube.com/watch?v=3RWX9XGCdm0

              Variable pendulum swings during lunar eclipse.
              https://www.youtube.com/watch?v=U_6B2QXQnUY

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            Richard

            The mainstream explanation for the source of the gravitational pressure heat at the core is the rotation of the planet as I understand. An increase in temperature can arise simply by compacting a gas generating more collisions per-second thereby increasing temperature and all that is required is gravity. It is the same mechanism by which suns are formed. The gases inside the sun are forced to the centre by gravity and as they compact thermal pressure works in the opposite direction forcing the gases outwards in proportion to the amount of compression exerted upon them. The gravity is doing the ‘work’ and the compacted super-heated molecules at the core are expanding and pushing outwards trying to escape the gravitational compression. This is what allows for the super-high temperatures necessary for nuclear fusion. The claim that earth’s atmospheric greenhouse (which let’s remember only composes 1% of our atmosphere) is responsible for raising the mean surface temperature by about 33°C above its blackbody temperature of about -18°C to its actual temperature of about 15°C ignores the fact that when air-molecules rise in the atmosphere they are rising in the earth’s gravitational field and so they lose kinetic energy, while air-molecules that are moving downwards in the atmosphere are effectively falling in the earth’s gravitational field and thus gain kinetic energy. Now according to physics, a molecule’s kinetic energy is equivalent to its temperature. So there is bound to be a temperature difference between molecules at the top of the atmosphere and those at the bottom anyway (with the warmest molecules at the surface and the coldest ones at the top), regardless of whether or not an atmospheric greenhouse is present to produce any extra warming. As the molecules at the surface increase in temperature they expand and rise but are also being compressed by the mass of atmosphere above and this compression is what decreases volume generating more collisions per-second thereby increasing temperature. Increase the atmospheric mass and you increase compression, increase collisions per-second, and so the temperature rises.

            The higher pressure at the surface caused by this gravitational compression and the mass of atmosphere above is (in my view) a more likely explanation as to why Venus can reach temperatures far in excess of solar isolation (it cannot be the conventional greenhouse model because according to physics an inert body cannot send back more radiation than it receives) and why there is a 33°K difference between earth’s predicted effective blackbody temperature and its actual temperature. Now according to physics, pressure is directly proportional to temperature. So if you increase pressure then temperature must also increase. This sort of pressure heat does not require an outside source of radiation for temperatures to increase and can operate under gravity alone. Suns, as already mentioned, generate their super-high temperatures through pressure alone as the force of gravity compresses hydrogen into an increasingly smaller space until temperatures reach 10 million Kelvin necessary for nuclear fusion. There is no reason to my mind why this gravitational pressure heat should not apply to any sufficiently large body with a gravitational field and not just to suns which means the temperature of any planet would not necessarily be constrained by ASR and gravitational pressure could act alongside ASR to increase the temperature to a higher level – and with a very high atmospheric pressure Venus is a good example of this additional ‘pressure heat’ increasing OLWR to a level much higher than ASR.

            In order to prove the greenhouse model that the 1% of gases in our atmosphere raises the surface temperature by 33°C and that changes in the 0.04% of CO2 in our atmosphere measurably affect OLWR and temperature I would need to see compelling evidence or at least a rational argument that this is so. But apart from the dubious method of pointing pyrometers at cloudy-skies and the questionable IR-computer models I have seen no such compelling evidence to date. Warmists could easily determine whether or not there is any real cause for worry by measuring the top-of-atmosphere (TOA) In-coming/Out-going radiation imbalance on CO2 absorption wavelengths, since this gives a direct measure of the absolute greenhouse effect from CO2. (Likewise for other greenhouse gases.) However when this was done by Harries 2001 they found no such radiation imbalance. The insignificant effect of CO2 in the atmosphere is further supported by the measurements of Hottel and Leckner, as Nasif Nahle points out: “Carbon dioxide has a total emissivity of almost zero below a temperature of 33°C (306 K) in combination with a partial pressure of the carbon dioxide of 0.6096 atm-cm. 17 year later, Leckner repeated Hottel’s experiment and corrected the graphs plotted by Hottel. However, the results of Hottel were verified and Leckner found the same extremely insignificant emissivity of the carbon dioxide below 33°C (306°K) of temperature and 0.6096 atm-cm of partial pressure. Hottel’s and Leckner’s graphs show a total emissivity of the carbon dioxide of zero under those conditions”.

            Anyone wanna guess what the radiative heating from CO2 would be with an emissivity of 0?

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              Richard

              Here is Stephen Hawking explaining the formation of stars: https://www.youtube.com/watch?v=9EnBBIx6XkM

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                Richard.
                Stated not just once but twice in that video at 1:26 and again at 3:04 is that his theory has NO heat energy at all being produced until 10 Million degrees of pre existing energy condensing has been achieved.

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              Joe Born

              when air-molecules rise in the atmosphere they are rising in the earth’s gravitational field and so they lose kinetic energy, while air-molecules that are moving downwards in the atmosphere are effectively falling in the earth’s gravitational field and thus gain kinetic energy. Now according to physics, a molecule’s kinetic energy is equivalent to its temperature. So there is bound to be a temperature difference between molecules at the top of the atmosphere and those at the bottom anyway (with the warmest molecules at the surface and the coldest ones at the top), regardless of whether or not an atmospheric greenhouse is present to produce any extra warming.

              That’s right. At equilibrium, mean molecular translational kinetic energy (temperature) does indeed decrease with altitude, as you can readily see by considering a single-molecule monatomic “gas” bouncing up and down in one dimension. If the total system energy E includes no potential energy at altitude z = 0, then the mean kinetic energy K at that altitude equals E, whereas it’s zero at altitude z = E/mg, where mg is the weight of a single molecule. So you’re right: there’s a temperature gradient, no greenhouse gas needed.

              The problem is that the gradient has the same relationship to total energy when the number of molecules equals what it is in our atmosphere. Again, the mean kinetic energy per molecule at equilibrium would fall linearly with altitude to zero at altitude z = E/mg if the acceleration g of gravity were uniform up to that altitude. Because the large number of molecules makes the total energy E so huge, though, that altitude would be astronomical, making the gravity-caused temperature gradient too small to measure as a practical matter. Even as a theoretical matter it would probably take something on the order of a lifetime to measure.

              So, no, they don’t ignore the exchange of kinetic energy for potential energy; it’s just that its effect is negligible for most purposes, including this one.

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              • #

                In line with what Joe Born said.
                Take two identical gas cylinders of a gas like oxygen, nitrogen or even CO2. Use two thirds of one but leave the other full. Put both of them in an air conditioned warmer than ambient room at a tight stable temperature for a month and log the wall temperature of the bottles. The difference between the two will tell you if “rotation of the planet” on either is more significant than the air conditioning stability. The air con electricity bill for the month will tell you how much free heat you got.

                “The mainstream explanation for the source of the gravitational pressure heat at the core is the rotation of the planet as I understand.”
                So what is the equal and opposite source of energy that stops this from decaying the planet orbit and plunging us into the sun?
                Photon repulsion?

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              • #

                Newton again. The Magnus efffect. Why would it not work with photons and or solar wind / cosmic radiation?
                https://www.youtube.com/watch?v=2OSrvzNW9FE

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      RB

      Newton’s Law isn’t for the situation where you have a pan on the stove and you swap lids on it. A lot more complex. Mind you, can you imagine doing all the maths and not checking with reality? And the Earth is another few orders of magnitude more complex.

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        Mike Flynn

        You might notice I said “after you remove it from the stove”. No amount of lids, insulators, or Warmist chants will stop it from cooling to ambient. And it will do so in accordance with Newton’s Law. Whether it cools more quickly or more slowly, it still obeys the law.

        An interesting application of Newton’s Law of cooling is to establish time of death where it can be reasonably be assumed that the ambient temperature was constant, or nearly so. Air conditioning, for example.

        Just thought you might be interested in a real world use of Newton’s Law of cooling. Not exact, but experimentally verifiable to a “satisfactory approximation”. Works for me!

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          Mike Flynn You say “The centre of the Earth is around 5500K.” While I might ask how you measured that it seems more important to compare the area. The area at the exact centre is zero. So what is that in Watts per M^2 compared to the infinately larger surface radiating area W/M^2?
          You also say “No amount of lids, insulators, or Warmist chants will stop it from cooling to ambient. And it will do so in accordance with Newton’s Law. Whether it cools more quickly or more slowly, it still obeys the law.”
          Yet when you stand on the cold ground at night your feet are not on fire. What did stop it(bearing in mind that I quoted Newton and do not think he was a fool)?

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          RB

          In the real world, the amount of heat energy (possibly grossly underestimated) that enters the atmosphere from the ground is about 0.1-0.2W/m2. Much of it not from the core cooling but heat generated by the crust moving. So as Sliggy mentioned kinetic energy becomes heat energy.

          Good luck in estimating when that core will cool. Its still irrelevant to what the surface temperature will be in 100 years.

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          Mike Flynn

          Silligy,

          Although neither I, nor anybody else, has measured the temperature of the Earths inner core, I am happy enough to accept the word of geophysicists and others, who apparently know about such things.

          Your query about the radiative intensity at the centre of the earth, is somewhat misleading. If the temperature at the centre is say 5500 K, then it will radiate at the wavelengths and intensity appropriate to its physical composition. The intensity is no more infinite than that that at the centre of a white hot cannonball.

          When you stand on cold ground at night, your feet are obviously not on fire. Stand on molten ground, white hot lava from deeper within the Earth, and you may well find your feet are on fire. While you live, you possess a distributed an internal heat source of course. Each cell, whilst it operates, generates waste heat. I’m not sure why you are surprised your feet are not on fire, though. It seems fairly straight forward to me.

          However, you raise an important matter. If you take a non living mass, such as a mountain, you will discover that the temperature within its interior increases as you move toward the centre of the Earth, and decreases as you proceed away from the centre.

          Maybe you believe that insulators can create warmth. Many people will say a blanket or jacket makes one “warmer”. Only subjectively. A corpse above ambient temperature increases its temperature not at all, regardless of how well insulated it may be, nor does a pot of boiling water if the heat source is withdrawn.

          I believe you may have misunderstood Newton’s Law of cooling. Obviously, if a body is insulated, the insulation itself becomes the environment, and as you say, the mathematics becomes complicated. Even determining the length of time required for a corpse to cool to certain core temperature, is subject to how well insulated the body is (or was). But cool it will. Faster at first, and slower as it approaches ambient. In accordance with Newton’s Law of cooling, as I said.

          I’m not sure what point you were trying to make. Please correct any factual error I may have inadvertently made, if you wouldn’t mind.

          Cheers.

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            “I’m not sure what point you were trying to make.”
            It was a point based upon extreme exaggeration. Extreme to the point of silliness (reductio ad absurdum). A little too absurd. Sorry about that.

            There are two variables in W/M^2 Watts is the one everyone remembers. Area is the one everyone forgets. A Watt is a Joule over second. At the surface the energy in Joules is greater than for the same temperature at great depth due to area at the depth being lower. So at the exact centre of the earth there is zero area and zero Joules per second despite a possible 5500 Degrees K. The difference between this zero Joules and the surface is the infinite value i was refering too.

            So I am saying that the total power that needs to be radiated from the surface is coming from a smaller surface area than your also absurdly exagerated argument presents (you mentioned the centre of the earth first).

            The question was in two parts to force you two think about the large volume and area of hot stuff below then deduce that this means the crust MUST be am effective insulator otherwise your feet would be onfire. I did not say the mathematics becomes complicated that was RB. To me it is pretty simple the thin crust is nearly as good an insulator as you paint to be impossible.

            The effectiveness of that insulator means that the further slowing down of heat escape by CO2 is well within the range of David Evans increasingly refined mathematics to eventually calculate.

            All that being said my comment to Richard above should tell you that I think the core of the earth is warmer than can be explained by RB’s “possibly grossly underestimated” value.

            Richard also faces the reality that the “gravitational pressure” at the centre of the earth is according to the conventional understanding of gravity ZERO. It is Zero because the forces in all directions cancel to nothing (There would be some pressure from the way people get crushed in crouds). The upside of this null gravity point is that it is more srongly subject to the moons tidal forces than the oceans above but not enough to make a magneto me thinks.

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      Roy Hogue

      This may be helpful.

      And it was. Thanks.

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        Roy a pleasure! I was simply pointing out that David’s

        Thus the rate of change of TR is proportional to ASR less OLR,…”

        Is in exact agreement with Newton’s

        The rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature

        Also that this is EXACTLY how capacitors charge and discharge through resistors, making the whole comparison to RC filters good.

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          Roy Hogue

          … Is in exact agreement with Newton’s…

          Which I did not recognize, familiarity with RC circuits to provide time delays notwithstanding. So yes, it was helpful.

          When you see something within one context for a long time you can get trapped into thinking about it only within that context and not recognize it elsewhere.

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    Roger

    This is probably directed to Jo: Could you please use Australian spelling everywhere! I am asking you to suppress all those ghastly Americanisms such as “modeling”, “center”, “fiber”, “traveling” “kilometer”and so on. (They really raise my blood pressure!)

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      Greg Goodman

      +1, I assumed that aussies had adopted american spelling.

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      bobl

      Jo has addressed this before and has made a conscious decision to use American spelling in order to internationalise the blog. While I would rather she stick with Australian English, I respect the decision she has taken.

      The rest of us do tend to stick to our own dialects

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        J Martin

        I wouldn’t have thought that exposing the Americans to UK / Australian English would hurt them and might add a little more autumnal colour to their otherwise colorless fall.

        International English and American English are usually regarded as different from each other.

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      Roy Hogue

      I’ve no trouble with either set of spelling rules so I have no ax to grind one way or the other. I assumed Jo made the decision because she has a rather large international audience, most of which will be more familiar with U.S. English than Aussie.

      Click the yellow button in the right sidebar and look at the whos.amung.us maps if you’ve never looked previously. More people are signed on right now in the U.S. than anywhere else, we’re coast to coast readers — accounted for, of course, by the fact that it’s daylight at 11:02 AM and David’s work is of intense interest.

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        gai

        Us Yanks out number you Aussies too, but we are still all on the same side.

        (I can’t spell worth beans so English vs Aussie doesn’t even register.)

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      Rereke Whakaaro

      When I type a word, continued Rereke, the spelling reflects the fact that I use eight fingers and one thumb, at a speed of approximately fifty words a minute, whilst trying to formulate a reasonable grammar, and not loose the intellectual intent of what I am typing. Spelling is sometimes a casualty in that process.

      The point of typing is the transfer of thought (intelligent or otherwise), and if it achieves that aim, the rest of the process is essentially irrelevant.

      If yer is more comfy loik, I culd type in lots of county dialekts wot is used arand the world by diffnt folks, an the meaning would still be plain.

      That is because it is a phonetic language, and the spelling reflects that. That is the joy of English. It constantly evolves.

      American English, uses spelling that is very close to that used by the Pilgrim Fathers. It uses some of the oldest spellings, and on that basis, can be argued to be superior.

      British English spelling changed, however, after the Napoleanic Wars, to adopt a more French style of spelling – an affectation, but one that stuck. Australian English is different, and newer, again. New Zealand English contains lots of Maori words, and so on …

      The spelling you use, depends upon where you bought the dictionary you possess. Buy a Websters, and what Jo writes will immediately become clear.

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        Roy Hogue

        Huh?

        I thought the subject was reading, not typing. And with but a little determination it’s easy to read either set of spelling rules. And even a lot of misspellings into the bargain. :-)

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          Roy Hogue

          Even your comments, Rereke. ;-)

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            gai

            Rereke is easier to understand then some of the comments I have seen around the web. What is humiliating is many of the worse cases are Americans whose spelling and grammar is horrible while some non-native speakers do a decent job even if the sentence structure is weird.

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      Roger, I am sorry about your blood pressure. Right from the start the word “sceptic” had US folk writing in to tell me they couldn’t read that without thinking of “septic”.

      I was trained in English spelling, but the American is simpler, and as Rereke says the Brits adopted the fancy Frenchification after they lost the War of Independence.

      FWIW, I mix it up, (somewhat inconsistently) choosing some English words and some US ones. Years of school…

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        Roy Hogue

        You do just fine, Jo. But I remember the first time I ran across one of your British spellings and it threw me until I realized it wasn’t misspelled but good “English” English.

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    Greg Goodman

    I’ve just discovered this series and have been ploughing through it.

    First reaction: very interesting but far,far, too long to get anywhere.

    It is very readable and presentation is deep, thorough and well-written. That is valuable to get everyone up to speed. However, a abridged version for those who already the a-b-c of physics and climate would be appreciated.

    Is there a short version that gets to the guts of what you are presenting ?

    BTW there is an error in the “NEXT” links that lead from one installment to the next. In article 8 “Next” brings me back to article 8. I’ve had to jump in here to try to work backwards. Maybe an index would be helpful.

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      StefanL

      Greg,
      The index you seek is at the “Project Home” link at the top of each of David Evans’ posts.

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      Thanks Greg. There’s no abridged version yet, but we’ll set about making some shorter versions when we are finished the series. We are learning from people’s reactions and comments, and have corrected a couple of minor errors so far.

      Link fixed, thanks.

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        mikerestin

        Can you get your concept down to an elevator speech?

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          Rereke Whakaaro

          Gravity Sucks, and all Physics depends on it.

          Is that “elevator” enough for you?

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          Yes. Here is the shortest one covering the whole series:

          Climate Scientists Misapplied Basic Physics
          The basic climate model, the application of “basic physics” to climate, is why alarmist climate scientists believe in the carbon dioxide theory, despite considerable contrary empirical evidence. Dating back to 1896, the model contains major architectural errors. Fixing the errors finds a much lower sensitivity to carbon dioxide — the UN’s Intergovernmental Panel on Climate Change (IPCC) overestimated future warming by a factor of five to ten. Less than 20% of the global warming of the last few decades was due to carbon dioxide.

          Notch-Delay Solar Theory Predicts Cooling from 2017
          Global temperatures will come off the current plateau into a sustained and significant cooling, beginning 2017 or maybe as late as 2021. The cooling will be about 0.3 °C in the 2020s, taking the planet back to the global temperature that prevailed in the 1980s. This was signaled (though not caused) by a fall in underlying solar radiation starting in 2004, one of the three largest falls since 1610 when records started. There is a delay of one sunspot cycle, currently 13 years (2004+13 = 2017).

          Dr David Evans
          Instrumental in building the carbon accounting system that Australia uses to estimate the carbon changes in its biosphere for the Kyoto Protocol, for the Australian Greenhouse Office. He earned six degrees related to modeling and applied mathematics over ten years, including a PhD from Stanford University. His wife’s blog at joannenova.com.au is the one of the biggest skeptic websites in the world.

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            Hang in there! Follow the script! You can actually ‘be’ the best-us fighter pilot! As soon as you believe that, in milliseconds you ‘will’ get your ass shot out of the sky!
            All the best! -will-

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              Unfortunately Will, nowadays if you don’t confidently toot your own horn sometimes people assume you don’t have anything worth looking at. Of course, some just confidently toot away with nothing to show, and others with lots to offer stay unnoticed. Crazy old world.

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      gai

      Greg,

      It may be long but it is introduced in bite size pieces and gives those of us with rusty to non-existent math skills a glimpse into the inner workings of the basic climate model. This is something few people have ever had a change to learn before this.

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    Greg Goodman

    This corresponds to a step response whose time constant is about 1/(2πfB), or about 0.8 years or 3.2 years. That is, after a step change in the ASR level it takes the surface temperature about 0.8 years or about 3.2 years to reach 63% (or 1- e-1) of its new corresponding level, and about 1.8 years or 7.4 years to reach 90% of its new corresponding level. Clearly this time lag reflects the thermal inertia of the atmosphere and land, and maybe some upper layer of the ocean (i.e. the outer boundary of the climate system), but not the remainder of the ocean.

    It will be interesting to see how you derive you result in later articles. It is close to the 8mo figure I derived from ERBE TOA satellite data around the Pinatubo eruption and also agrees with results published by Spencer & Baswell based on CERES data ( links in my article ):
    http://climategrog.files.wordpress.com/2014/04/tropical-feedback_resp-fcos.png?w=843
    https://climategrog.wordpress.com/2015/01/17/on-determination-of-tropical-feedbacks/

    it mimics the ASR but with a lag

    This is not an accurate description. The peak will occur later but the form is distorted by the non-linear phase response. The simple lag is only true for a pure sinusoid ( single frequency ). The lag is different for all frequencies hence the distortion of the form. It may somewhat similar but is not “mimicked”.

    This misconception has led to a lot uninformed lagged regression studies that end up with a significantly wrong regression coeff and false or inaccurate attributions. It is not a pendeantic detail. I’m sure David is aware of this distinction, but I’m just pointing out that it should be more carefully worded in the article.

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      Good point Greg — yes, the amount of lag depends on the frequency and is not proportional to the frequency (Eq. (10)), so in general the signal in the ASR is distorted and smoothed out by the time it gets to the OLR. Yes, know it well, but was thinking of a single sinusoid — correction added to the text, thanks.

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        Greg Goodman

        This is the behavior one would expect due to the thermal inertia of the Earth

        That is not accurate. The thermal inertia would simply integrate the incoming energy. The integral also displays low-pass filter characteristics ( 1/f ) but not the same as the RC filter or the reservoir with a negative feedback.

        I know EE usually present this as a log plot as a means of simplifying it into two straight lines. This may be helpful in EE where you are often dealing with many orders of magnitude in the signal. We are not dealing with many orders in SST , indeed all the linearisations depend on arguing small changes.

        You may like to avoid this contradiction.

        I suggest that presenting this as an impulse response so that the actual response to any input series by convolution is more applicable. You can readily get the *fully developed* ‘lag’ response to any input without making an more approximations than the linear model already has.

        The impulse response of RC is a decaying exponential, this fully characterises the response without the need for gross simplifications of being either side of Fb or whatever and not knowing what to say about the equally relevant transition band.

        If you have not read my article already I suggest you do. Sorry, it’s about as long-winded as your presentation here and for the same reasons. I think you will find the convolution approach more applicable than the RC Bode plot. This will hopefully be helpful in developing your model.

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    Greg Goodman

    Clearly this time lag reflects the thermal inertia of the atmosphere and land, and maybe some upper layer of the ocean (i.e. the outer boundary of the climate system), but not the remainder of the ocean.

    I don’t see this as being clear, nor do you say why you consider it to be so clear. My study of tropical TOA linked above gets a very similar result and the tropical climate is dominated geographically by ocean and energetically by deep convection thunder storms over oceans.

    My study is essentially a ‘single slab’ ocean model so the time constant is primarily due to the thermal inertia of the ocean mixed layer and the restoring feedbacks. ( of which the Planck feedback is the dominant one. )

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      The derivation above characterizes the heat contained in the climate system by the radiating temperature (essentially a proxy for the OLR), and is a composition of the temperatures of the layers that emit OLR (mainly the surface, cloud tops, water vapor and CO2 emission layers).

      The empirical transfer function used to estimate the time constant of 0.8 years (or maybe 3.2 years) is from the TSI to the surface temperature.

      The thermal inertia is therefore essentially that of the surface temperature, assuming the cloud tops, water vapor and CO2 emission layers can change temperature relatively fast compared to the surface. But that says nothing about how deep into the ocean the influence of this inertia goes — far enough to change with the surface temperature presumably, so it cannot be very deep at all.

      It’s more an empirical observation of how fast the surface temperature responds to changes in changes in ASR, in practice. Presumably this is why it matches your finding from the perturbation by the Pinatubo eruption.

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        Greg Goodman

        Thanks for the reply David,

        there is generally a simplification of the top layer of water which is well mixed by waves, eddy diffusion and wind: refered to as the mixed layer. This goes down to a level where there is much stronger change in temperature with depth. This zone is called the thermocline.

        The depth of the thermocline is anything from 30m to about 200m and varies greatly with latitude ( and who you listen to ).

        It’s all hand-waving generalities and gross approximation of course but there is a general structure of a sizable, finite depth that can be regarded as having a more or less uniform temp and be modelled as a single ocean slab. ie a uniform well mixed reservoir of water.

        This makes it pretty much the dominant heat reserve of climate system and thus relevant to you discussion of thermal inertia.

        The first improvement on that representation is diffusion of heat to the deeper ocean. This is usually regarded as primarily eddy diffusion ( not thermal conduction ) and is proportional to the square of the temp gradient between the surface and deep ocean temperature, regarded to be an infinite capacity sink.

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          Rud Istvan

          Greg, recheck your thermocline info. You are refering to its top, not the entire zone, and not its ‘bottom’. These do change with lattitude. This is discussed in essay Missing Heat about Trenberth’s speculative (and physically illogical) paper attempting to explain the pause.

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            Greg Goodman

            Thanks Rud. I was indeed referring to the top of the thermocline, I should have said depth *to* the TC not depth of which does not read as intended.

            I was discussing the single slab approximation as representing the mixed layer, ie depth *to* the TC. Thanks for pointing that out.

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            Rud Istvan

            Thought so. IMO single slab is more than good enough for ‘effective CS’ not just TCR. A distinction made in essay Sensitive Uncertainty. Sure looks like TCR is maybe 2/3 of effective CS. Hanson likes to overegg with 1000 year ECS some that TCR is 1/3 rather than 2/3. Which of course AMPLIFIES CAGW on timescales that are not meaningful for energy policy. See my ebook Gaia’s Limits for more on that.

            I very much enjoyed your posts at CE. We both look forward to what DE is bringing forth. As in a comment to TEL below, or my CE post critiquing Monckton’s Irreducibly Simple paper, I sense the beginning of an alternative model/observation convergence beyond the energy budget approach to sensitivity.
            If so, then really exciting because provides a new way of doing science outside the academic/peer reviewed paper tradition. Would provide the makings of a great book dependimg on outcomes, and whether I can muster the enthusiasm to spend a couple of future years on it. We shall see. Highest regards.

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    Greg Goodman

    In considering the question of thermal inertia of the world it needs to be noted that 70% of the surface is water. Water has a specific heat capacity about 4 times that of rock. Land is generally moist, ground up rock. Moist rock has a SHC about half that of water.

    The centennial scale heat sink of the planet is the deep ocean.

    Heat capacity of the atmosphere will be a very small contribution except perhaps on short times scales that are dominated by chaotic variability usually called weather.

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    Tel

    How do we model the thermal inertia of the Earth?

    Oh I know this one… something to do with mass, I think. It does get me wondering a bit, if the core of the Earth heats up by 0.5C per Century, am I bothered?

    Back in 2013 they recalculated the temperature of the core of the Earth and adjusted it by 1000 degrees! Strangely no one noticed any change to their lifestyle, I guess that means we don’t live in the core of the Earth. Fancy that! We don’t live in an average temperature either, each of us lives on a small patch of the surface. A very small patch.

    The switchover between copying the input sinusoid (low frequencies) and increasingly attenuating it (high frequencies) occurs around the break frequency fB. This is the behavior one would expect due to the thermal inertia of the Earth — the temperature of the Earth tracks slow changes in the ASR but increasingly isn’t quick enough to track faster changes.

    Yeah, if you use a first order model (measured at the surface) then you look at the summer / winter cycle you have a constant input frequency and you get a phase lag (as any low pass filter would do). It’s usually about two months (or 60 degrees), but the trick is that energy moves sideways so depends on where you measure. Thus, local surface features have a greater influence than some “whole Earth filter” concept, which makes me wonder… what does it mean?

    You care about the answer, because someone is trying to take away your money by using a tax on global temperature, but the same people would take your money with a tax on anything, or just a tax on nothing. We’ve all been down that particular rabit hole, what we found was dirt and a few rabit droppings. Recently I’ve been working through “The Failure of the New Economics” by Henry Hazlitt which is a systematic and ruthless evisceration of everything John Maynard Keynes ever did. The fact remains, the majority of economicsts still to this day think Keynes is a genius, and hardly anyone has even heard of Hazlitt. This bothers me deeply. I mean, it’s a clear empirical reflection on humanity, isn’t it?

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      gai

      “…The fact remains, the majority of economicsts still to this day think Keynes is a genius, and hardly anyone has even heard of Hazlitt. This bothers me deeply. I mean, it’s a clear empirical reflection on humanity, isn’t it?…

      Actually it has to do with what is taught in school and who is doing the funding of the economics departments.

      We can see how thinking and research on climate has been warped by $$$. The same thing happened with economics. Do not forget that Keynes had a lot of imput into the creation of the World Bank and IMF (the Bretton Woods system) and that he was also a Fabian Socialist. He was not an ‘official member’ of the Fabian Society but was a close friend of key members and lectured regularly at the Fabian Society meetings.

      The other principle in the creation of the Bretton Woods system was the soviet spy in the US treasury, Harry Dexter White.

      KEYNES AT HARVARD chapt 3 and KEYNES AT HARVARD chapt 10

      “By a continuous process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method, they not only confiscate, but they confiscate arbitrarily; and while the process impoverishes many, it actually enriches some….There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency. The process engages all the hidden forces of economic law on the side of destruction, and does it in a manner which not one man in a million is able to diagnose.” (John Maynard Keynes, The Economic Consequences of the Peace, 1919.)

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        Greg Goodman

        .. no surer means ..? Only because he had not thought of taxing “carbon”.

        Useful reference I’ll have to check that out.

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        Roy Hogue

        There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency.

        Convicted out of his own mouth. But of such a nature is the human race. Ego demands control and control demands power over others and this has been the way of it since the first two cavemen met by accident and each decided to control the other to his own advantage.

        Marx identified the problem as the competitiveness of humans. What he didn’t identify was the necessity that we be competitive for the very survival of the species. Some will rise to the top of society and some will sink to the bottom. Societies and whole civilizations will rise and fall. But the imperative is always survival of the species. And we can do nothing about that because it’s hard wired in.

        Isn’t it about time to acknowledge that fact? We might then have a basis from which to improve how we cope with it.

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          gai

          Roy,
          I figured that out at age 10 when big brother came home from university spouting Marxism. (Made for some very loud dinner conversation during the holidays.)

          Humans are aggressive and competitive, aka predators. Best to make use of it in organizing society. ‘Social justice’ and ‘affirmative action’ is promotion of the mediocre. Of course if you want to remain at the top of the heap and hamstring the competition it is a great idea. Use the law to make the new up and coming businesses hire lots of deadwood idiots under the banner of ‘equality’.

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      Rud Istvan

      Tel, there are comceptually two Earth thermal inertias. To simplify a bit, the ‘fast’ one includes the atmosphere and themocean mixed layer (to the depths churned by waves, roughly the euphotic zone (short wave radiation light penetratiing, the ocean photosynthetic zone. Think TCR. There are a few papers suggesting this netween 8 and 15 years. See, for example, Schwartz, Heat capacity, time constant, and sensitivity in J. Geophys Res. 2008. Discussed more extensively in the climate chapter of The Arts of Truth. The ‘slow’ includes ocean, ice and Henry’s law CO2 equilibration, think ECS. Since the thermohaline trsnsport is involved, the best present ‘guess’ is about 800 years. See essay Sensitive Uncertainty in Blowing Smoke for multiple references.
      From Dr. Evans maths, it appears he is modeling the ‘fast’ thermal intertia.

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        Rud Istvan October 17, 2015 at 2:52 am

        “Tel, there are comceptually two Earth thermal inertias. To simplify a bit, the ‘fast’ one includes the atmosphere and themocean mixed layer (to the depths churned by waves, roughly the euphotic zone (short wave radiation light penetratiing, the ocean photosynthetic zone. Think TCR. There are a few papers suggesting this netween 8 and 15 years…. The ‘slow’ includes ocean, ice and Henry’s law CO2 equilibration, think ECS. Since the thermohaline trsnsport is involved, the best present ‘guess’ is about 800 years.”

        Rud,
        These measurements, if left uncorrected give irreplaceable historic information! The conjecture of cycles provides little of that information. It appears that Earth has many interfering cycles, with a cyclic interval ranging from 12 hours to millions of years. Is it the interfering sidebands of these cycles that force this Earth’s response to appear chaotic?
        To me, much of what ‘is’ remains mostly cyclic, and mostly deterministic. I see no evidence, however, of “repetitive”, each and every cycle appears different.
        Do I have a clue? No! ;-) Is there a language for such?
        Is there proper mathematics for such observations? Is this like the digits of PI, or really just thermal noise?
        All the best! -will-

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    Joe Born

    As usual, I’m having a little difficulty in guessing which facts will ultimately prove important and which won’t. Just in case the Bode plot actually is important, though, I’ll mention Willis Eschenbach’s post about lags, which suggests a certain amount of diffusion relationship, at least over land. A purely diffusive response would result in only half as fast a magnitude roll-off (inversely proportional to the square root of the frequency rather than to the frequency itself) and a lower ceiling on the phase lag.

    Again, I can’t tell where you’re going with this, so that comment may be completely irrelevant.

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      Greg Goodman

      Thanks Joe, I recall that article from when he posted it. It is interesting that the profiles ( form land bores ) that he shows in fig 1 are quite similar to ocean depth temp profiles. This backs up the idea that heat loss to deep ocean can be characterised as a diffusion process too.

      Since you seem well versed in this sort of stuff, and if you are so inclined, can you comment my article which apparently gives an independent corroboration of one of David’s time constant values.

      https://climategrog.wordpress.com/2015/01/17/on-determination-of-tropical-feedbacks/

      You can get me via the About page ( I think comments are now closed where this was posted on Judith’s site ).

      Time constant is a key empirical parameter because it gives an indication of sensitivity. It is also something for which published values have been extracted from climate models. ( IIRC values in 30mo to 48mo are typical ). This is a direct indication of over-sensitivity in the models.

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        Joe Born

        Actually, I’m somewhat pressed for time at the moment, so I doubt that I’ll reach your post soon.

        As to time constants, the concept requires too much interpretation for my taste outside the context of first-order autonomous systems. Since such a “one-box” model does not yield relationships such as that between diurnal and annual lags that Mr. Eschenbach’s more-recent post “Leads and Lags” describes, I try to be circumspect about that concept’s use in the climate context.

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          Greg Goodman

          Thanks Joe. The whole linear approximated,forcings and sensitivity game is highly simplistic and of questionable value. However, we are racing ahead to redesign the world energy and political structure on that basis, so it merits full examination.

          I don’t get your point about Eschenbach’s post. He was effectively using a single slab model and also assuming sinusoidal forcing.

          Using an exponential convolution would have given a better result, especially for the asymmetric daily data. But his main result about sensitivity would have been consistent.

          Are you saying that you don’t think his result is valid?

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            Joe Born

            Diurnal and annual variations’ fundamental harmonics differ by more than two decades, so a “one-box” model would dictate that if the annual response has much phase lag at all, as Mr. Eschenbach found it does, the diurnal response’s phase lag would have to differ only negligibly from 90°, as he didn’t find.

            Unfortunately, Mr. Eschenbach adopted a hasty comment of mine giving the formula for a one-box-model phase lag, which I realize in retrospect was misleading in the context. And Mr. Watts spiked my proposed post explaining the difficulties that a one-box mode presents. (I’m persona non grata over there since Christopher Monckton took umbrage at my pointing out falsehoods in his recent “Irreducible Climate Model” paper. I believe that Mr. Watts was actually taken in by that paper.)

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    Svend Ferdinandsen

    Re time constants.
    To heat all the oceans 1K would need 4W/m2 ekstra going into the ocean in 100 year.
    The funny thing is that a 1K warmer ocean would radiate ~4W/m2 more out just as LWR. Some heat might also be lost by more evaporation.

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      Roy Hogue

      Wouldn’t heat lost through evaporation eventually end up radiated away anyway as the water vapor condenses again as it surely must do?

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    In equation 5 of Post 8:
    λ_SB = T_R / (4R)
    Is that factor of 4 missing in equation 3 above?

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      Well spotted nhill! Thank you, yes, the factor of 4 was indeed missing. Ouch.

      I’ve corrected eight equations and the figure, all of which had scaling errors.

      Correcting the error did not change the character of the post or anything of consequence. In particular, the estimates of f_B, which were from comparing f_B to the empirical transfer function, and the resulting time constants, did not change. Nor did Eq. (13), which we will be using in the alternative model. See the asterisked note at the bottom of the note.

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    Paul Vaughan

    Sometimes in the climate discussion it’s so obvious that due to our differing backgrounds we possess differing lucid awareness. Overcoming misunderstandings requires a lot of patience.

    I would say a key thing that goes wrong conceptually is people try to think in anomalies rather than absolutes and thereby mysteriously fail to recognize what’s obvious about insolation from annual & semi-annual variations.

    Analogy with Milankovitch:

    The solar cycle at earth’s poles isn’t the same as at the equator. (For example what is the solar cycle doing in a time series of the winter polar night? Zero…)

    Wind is proportional to the gradient.

    Mixing & evaporation (of ocean) are proportional to wind.

    Wind mixing is shaped by geography.

    Geography is asymmetric.

    Yes heat capacity of water is orders of magnitude greater than air …but kinetic energy of air is orders of magnitude greater than water ….and so this is about asymmetric spatial-insolation-gradient-derived wind evaporation & mixing.

    In-page search for “wind” turned up only one hit by Greg Goodman. Hence this note.

    The phase lag is spatially nonuniform …and it’s asymmetric.

    That should be obvious just by looking at geographic variations in the phase lag of the terrestrial year.

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      Greg Goodman

      “That should be obvious just by looking at geographic variations in the phase lag of the terrestrial year.”

      Could you elaborate bearing in mind that the terrestrial year in the tropics is not a 12mo cycle?

      Not saying that you’re wrong but that you’re not actually saying anything concrete, ie verifiable.

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        Greg Goodman

        PS climate sensitivity is less in the tropics so I would not expect the same phase relationship, but if you define your terms you may have an interesting and relevant point.

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        Paul Vaughan

        GG requested:
        “Could you elaborate bearing in mind that the terrestrial year in the tropics is not a 12mo cycle?”

        Yes. Please see link to illustration below (#16).

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      Roy Hogue

      Sometimes in the climate discussion it’s so obvious that due to our differing backgrounds we possess differing lucid awareness. Overcoming misunderstandings requires a lot of patience.

      A good reminder. Thank you. And a green thumb from me for that paragraph as well.

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    Paul Vaughan

    Elaboration…

    Poleward advection stream fire-hoses ice margin in North Atlantic introducing differential nonlinear spatial aberration from integral:

    http://s27.postimg.org/ab94dhsdf/Seasonal_Cycle_Map_ERA40_Phase_Amplitude.png

    https://tallbloke.wordpress.com/2015/08/11/niv-shaviv-nice-one-the-sun-still-is/comment-page-1/#comment-106030

    Equator-pole insolation-gradient-cycling shifts frequency. That defines the flow geometry.

    It’s analogous to what Jose Rial has shown at lower frequency (D-O 1470a & Milankovitch 100ka).

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      Paul Vaughan

      Supplementary:

      “Figure 12. Isolines of equal correlations which characterize a close connection between the mean annual ice cover extent to the Northern European Basin and mean annual air temperature north of 40° N” — p.30 (pdf p.36)

      Zakharov (2000) Sea ice Russian view …
      https://nsidc.org/pubs/special/16/NSIDC-special-report-16.pdf

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      Greg Goodman

      Thanks, the phase plot is quite surprising at first. In view of the grouping around the easterly side of the four oceans it must be stongly infulence by the correolis driven ocean gyres.

      Rather unfortunate that they dumped the tropical regions. There is an equally strong 6mo component it would have been informative to see the phase in those regions too.

      Someone obviously thought we should not know.

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        Paul Vaughan

        not surprising at all

        corresponds with wind

        (wind drives the gyres)

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        Greg Goodman October 17, 2015 at 11:47 am

        “PS climate sensitivity is less in the tropics so I would not expect the same phase relationship, but if you define your terms you may have an interesting and relevant point.”

        Tee Hee!

        In the United States today greater than 17,000,000 long rifles in the hands of SERFS, that only wish to get along! To count the sharpened pitchforks, takes a much larger computer. No were else of this planet are more weapons deployed than “they gots bullets!”

        Question:
        What/who need to come front and be the arbitrator of who/which is to be dispatched to the interior of the volcano FIRST? Can those that wish only to get along ever decide such?
        All the best! -will-

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        Greg Goodman

        I think you are mistaken Paul. The driving force is the correlis “force” in other word moment of inertia of the mass of the water interacting with the Earth’s rotation.

        That is why the gyres are in opposite directions in each hemisphere and confuent at the equator.

        Correolis also affects the atmosphere but since it is not constrained by the ocean basins it does not flow in the same pattern. There is not a similar gyre in the atmosphere that could be suggested to be driving the oceanic flow.

        You seem to have developed an idea that wind is causing everything. Like most single cause explanations it is ill-informed.

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          Paul Vaughan

          Misrepresentation, misunderstanding, &/or misinterpretation.

          10m & 850hpa winds have the same shape as the ocean gyres.

          Of course coriolis is a factor shaping that.

          Equator-pole gradients and land-ocean geometry are also factors.

          The point is this:

          Studying radiation while ignoring circulation is insufficient.

          Stuff moves around.

          The heat that moves to the North Atlantic ice margin nonlinearly obscures the global integral to geometry-ignorant eyes.

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          Paul Vaughan

          Fact:
          Surface wind drives the ocean gyres.

          There are 2 sources of wind:
          1. equator-pole heat engine
          2. interhemispheric heat engine

          It’s not enough to study just insolation. It’s necessary to also study insolation pattern because gradients drive geography-constrained flow (e.g. western boundary currents). The flow has non-negligible impact on global aggregate pattern. I’ve given a proof of this based on (a) geometric axioms and (b) the laws of large numbers & conservation of angular momentum.

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          Paul Vaughan

          It’s not sensible looking at radiation with blinders forcing ignorance of heat engine circulation as if Earth is uniform and no heat moves up the western boundary to nonlinearly erode the ice margin.

          https://i2.wp.com/s3.postimg.org/6skni7wj7/Rial_2012_Synchrony_Figure_01_07_11.png

          Rial, J.A. (2012). Synchronization of polar climate variability over the last ice age: in search of simple rules at the heart of climate’s complexity. American Journal of Science 312, 417-448.
          http://www.dynamicpaleoclimate.org/uploads/2/3/5/4/23543390/417.full.pdf

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          Paul Vaughan

          Annually-averaged (a) near-surface & (b) surface wind gyres:

          a) http://ds.data.jma.go.jp/gmd/jra/atlas/isobar-1/w850_ANN.png

          b) http://ds.data.jma.go.jp/gmd/jra/atlas/surface-1/w10m_ANN.png

          Annual cycle animation links from p.11 here.

          Watching all of the animations will take some time but the investment-in-basic-circulatory-awareness exercise will crush misconceptions that made the insolation-lag-map look “surprising” to GG.

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            Greg Goodman

            10m & 850hpa winds have the same shape as the ocean gyres.

            Oh yeah, wheres that? Certainly not in the the 1on and 850hPa maps you linked.

            There are 2 sources of wind:
            1. equator-pole heat engine
            2. interhemispheric heat engine

            There’s at least on other : correlis forces in the atmosphere.Because the air is free to move the resulting movement is NOTHING like the ocean gyres.

            You talk like you’ve just discovered that temp gradients drive wind that you have found the answer to life, the universe and everything.

            All data is useful and interesting and you’ve provided some good likes but it’s not the answer to the fumdamental question.

            What I found surprising was the near symmetry of the phase lag plots about the SE-NW axis in four major basins. There must be at least three causes combining to create those patterns.

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          Paul Vaughan

          visualizing & understanding coherence of terrestrial surface pressure, wind, waves, & currents (ocean gyres):

          http://imagizer.imageshack.us/a/img856/1999/01u6.gif

          http://old.ecmwf.int/research/era/ERA-40_Atlas/images/full/D04_LL_YEA.gif

          This isn’t just surface wind, it’s also water vapor flux:
          http://old.ecmwf.int/research/era/ERA-40_Atlas/images/full/C03_LL_YEA.gif

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          Paul Vaughan

          annual cycle mixed-layer-depth (MLD) animation:
          http://s1.postimg.org/f1qylntkv/Mixed_Layer_Depth.gif

          “Rial (2012) drew my attention to a fundamental correction that’s underway in oceanography” :

          https://tallbloke.wordpress.com/2015/03/14/paul-vaughan-wind-is-an-dominant-player-in-climate-variation/

          This is about understanding the spatial aberrations from the global integral.

          You may be able to understand the global integral from radiation considerations alone, but multidecadal regional variations will NOT be explained without attention to advection pacing.

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          Paul Vaughan

          This type of behavior is normal at wuwt, but it would be nice if it couldn’t be found here:

          Greg Goodman will not admit that insolation-gradient-driven wind spins ocean gyres.

          Therefore:
          Trust & sensible exchange are impossible.

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            gai

            Wind drives the surface currents:

            http://oceanmotion.org/html/background/wind-driven-surface.htm

            A tidbit of information:
            The strongest wind driven current is the Antarctic Circumpolar Current.

            The Drake Passage, the relatively narrow strait between Cape Horn (the southern tip of South America) and the Antarctic Peninsula, deflects some waters from the Antarctic Circumpolar Current to form a portion of the Peru Current that flows northward along the west coast of South America.

            This is one of the currents that controls ENSO and is dependent on the strength of the Antarctic Circumpolar Current and of the wind.

            Also note the Benguela current comes from the West Wind Drift and eventually ends up as part of the Gulf Stream.

            The South Atlantic current [SAC] as represented by the Mariano Global Surface Velocity Analysis (MGSVA). This current, with the Antarctic Circumpolar Current, is also known as the West Wind Drift. It feeds the Benguela Current… The eastward flowing SAC with the Antarctic Circumpolar Current is also known as the West Wind Drift. The SAC feeds the Benguela Current, the Agulhas Current, and the south Indian Current.
            http://oceancurrents.rsmas.miami.edu/atlantic/south-atlantic.html

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    Leonard Lane

    David. Thank you or an interesting and informative series that should (I hope) stir up and add leavening to the entire climate dialog (really a global warming dialog on the warmista side).
    One quick question. When you say “invariant system” do you mean time invariant system?

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      Thanks Leonard.

      Yes. “Invariant system” is the general term, but in climate contexts (and in electronics) it nearly always specifically means “time-invariant”.

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    BilB

    David,

    As I have mentioned, even though you move at this slow pace to your Poirot moment it is becoming ever clearer that your model is vastly incomplete, missing so many circuit essentials. I have been waiting for this expose to enter the real world with elements such as capacitors (with static leakage durations of thousands of years both variable and fixed), resistors (variable and fixed), batteries (with storage durations of hundreds of millions of years), flywheel dynamos (with spin down durations of decades to centuries), microcontrollers (with random factor generators), eproms, and the most important of all…loads (the most significant of which in the case of this planet is…..Life).

    I suspect that the last thing that you want to do is to examine with this degree of detail as it requires real effort on the one hand and it would require you to run your “calculation” in simulation model mode, not an attractive option for one who claims that all models are failures. So the next best option is to reduce the definition of the calculation. I include a visual so that others can get some grasp on what “definition” means in terms of orders of magnitude.

    https://youtu.be/0fKBhvDjuy0

    In simple terms the further away you are the less detail you see. Sometimes this is a good thing. However Global Warming and Climate Change affect us personally, from the perspective of 1^1 meters ie directly. The model you are building seems to me to be structured to see the energy passing through and around the earth from the highest perspective factor while still remaining in the Solar System, which would be you wanting people to see this from 10 ^ 12 meters which would be in the vicinity of Uranus.

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      Still throwing FUD Bilb. All those specific words, yet no content apart from saying that “simple” models must be wrong because they are not complex? David’s model is more complex than the IPCC core basic model he is criticizing. Point me to where you complained about the IPCC simplicity.

      Or are you just a mindless hypocrite?

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        “the IPCC core basic model”
        IPCC model? Reference?

        In fact, the AR4 does have a recognised “simple model”. They say:

        As in the TAR, a simple climate model is utilised in this report to emulate the projections of future climate change conducted with state-of-the-art AOGCMs, thus allowing the investigation of the temperature and sea level implications of all relevant emission scenarios (see Chapter 10). This model is an updated version of the Model for the Assessment of Greenhouse-Gas Induced Climate Change (MAGICC) model (Wigley and Raper, 1992, 2001; Raper et al., 1996). The calculation of the radiative forcings from emission scenarios closely follows that described in Chapter 2, and the feedback between climate and the carbon cycle is treated consistently with Chapter 7. The atmosphere-ocean module consists of an atmospheric energy balance model coupled to an upwelling-diffusion ocean model. The atmospheric energy balance model has land and ocean boxes in each hemisphere, and the upwelling-diffusion ocean model in each hemisphere has 40 layers with inter-hemispheric heat exchange in the mixed layer.

        40 layers? Upwelling? Doesn’t sound like what David has been talking about.

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      AndyG55

      Bilge, the only thing that is becoming increasing obvious is your complete lack of understanding of basically everything.

      “Global Warming and Climate Change affect us personally’

      What utter rubbish.

      No person under 18 years of age has experience any global warming and a period of decreased extreme weather such as hurricanes, droughts etc etc..
      People living from around 1979 onward experienced the small warming effect (a fraction of a degree) of a series of strong solar cycles.
      Those who lived from 1940 or so, experienced a cooling trend for 20-30 years then the 1979 to 2000 slight warming.

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        BilB

        G55 Andy,

        Try to sell that line in Pakistan, and Russia, and Europe’s Alps, and The Maldives, and Uganda, and Bangladesh, and China, and the Philippines, and India , and…..

        http://www.irinnews.org/pdf/convenient_solutions_to_an_inconvenient_truth.pdf

        There was one positive that stood out, Europes wine grapes are doing well appreciating climate change, so far. But is that enough of a gain to justify the trashing the ecologies of so many other nations?

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          AndyG55

          Show me one weather event that hasn’t happened in the past.

          Oh, and the past is at least 10,000 years of the Holocene.

          And seriously.. the World Bank???????

          .. they of course have absolutely nothing to gain from spreading climate fear and getting carbon taxes in, do they, you gullible twerp ! ;-)

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          AndyG55

          Let’s start at Box 1.1

          Please prove, without using adjusted data, that the climate is changing adversely in the area being referenced.

          Let’s look at a quote shall we…

          “Projected time frames for onset of significant impacts vary from 30 to 50 years…”

          sorry, but ROLMAO !!!!!!

          read what you link to before you post… bozo !!

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          markx

          Well, don’t worry about China, Bilb,
          I am sure their recent interest in the topic is simply political maneuvering:

          Global warming will benefit China by increasing rainfall in its dry northern regions while reducing flooding in the hotter southern areas, according to a new study by scientists in the country.

          The research team from the Chinese Academy of Sciences said that if the phenomenon continues, the planet’s thermal equator will move northward and push the rain belt associated with the monsoons in East Asia from the southern to northern part of the country.

          If such climatic change were to occur in China, bamboo forests would reappear along the banks of the Yellow River, which runs from Qinghai province in the far west and empties into the Bohai Sea in Shandong province on the eastern coast, pundits predict.

          http://m.scmp.com/tech/science-research/article/1867515/global-warming-may-help-alleviate-chinas-drought-and-flooding

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      Rereke Whakaaro

      The movie you reference was made in 1977, by IBM (or their advertising agency) to promote their new, water-cooled, CPU that was capable of twice the precision of previous machines.

      It was marginally effective. Unfortunately, Hewlett Packard had already produced a hand held calculator that could also handle numbers with that sort of precision, which sort of spoilt the impact.

      Engineers are used to dealing with very large and very small numbers, especially Electrical Engineers involved in designing integrated circuit transistor junctions. Those guys are moving individual electrons around, and sometimes even moving the lack of an electron around, and they also handle very large numbers in the region of 1015, or higher when they move to Anstroms.

      Nobody is impressed BilB

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        BilB

        When you are wrong Rereke you are really wrong. I saw that movie in 1973 at Randwick Design College. It was presented by someone who worked with Ray and Charles Eames (a famous Industrial Design husband and wife team) on its production. We saw the movie and a bunch of slides on the making of the movie which was done with a camera system that could have influenced the development of the famous Dyxtraflex camera used to make Star Wars so real. It may well have been financed by IBM, I don’t know, as Carles and Ray had done exhibition work for IBM in the 60′s. 1977 marked a “re-release” of the video, but it had to have been made prior to 1973. There is a possible coincidence that might make it 1971.

        But why would any Jonovian call something that is truly impressive, impressive. I notice that you didn’t say “I think it might be unimpressive”, that would be being skeptical about its impressiveness. Nope, you grab it by the throat and declare it to be unimpressive ,…to everyone “here”. Full on denial of the impressiveness of the movie, because that is what you guys do here,….isn’t it.

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    BilB

    Of course David’s “model” is complicated, that is because he is attempting to achieve a fractal outcome from a single computation. It doesn’t work. Just the same as creating a a compound interest formula to cope with various interest rates and changing time frames turns into a computational mess.

    The only way to achieve a real world solution to a changing environment is through iteration, and that means…… a model. The modular calculations are relatively simple, the complexity is in the completeness of the factors covered, in the iterated outcome, and then in the merged results of many models. You just cannot achieve this in a spread sheeted approach.

    Here are some real world outcomes for David to test his computation against.

    https://nsidc.org/cryosphere/sotc/ice_sheets.html

    http://www.antarctica.gov.au/about-antarctica/environment/climate-change/ice-sheets-and-sea-level-rise

    I’m not seeing an impending ice age yet, are you? and if so where is your proof (one which is not self referencing)?

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      AndyG55

      Wow.. look at that mass balance climbing up this year in Greenland.

      http://beta.dmi.dk/en/groenland/maalinger/greenland-ice-sheet-surface-mass-budget/

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        BilB

        G55Andy,

        From your link

        “Here you can follow the daily surface mass balance on the Greenland Ice Sheet. The snow and ice model from one of DMI’s climate models is driven every six hours with snowfall, sunlight and other parameters from a research weather model for Greenland, Hirlam-Newsnow…… Everything shown on this site, however, is calculated with this new model, so that all curves and values are comparable.

        Everything shown on this site, however, is calculated with this new model, so that all curves and values are comparable.”

        I take it that from now on you are accepting refined models and homogenised data as being an accurate assessment of the real world climate status.

        Good on you, you are moving forward with your climate experience.

        Apart from that it is early in the winter season, yet.

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      AndyG55

      “and then in the merged results of many models”

      roflmao..

      Averaging many things that are proven to be monumentally wrong, does not make a right.

      This is a fallacy that could only exist in the anti-science world of “climate change™”

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    Again a copy from Tallbloke

    “Guys! From our ability/inability to disagree/agree, it’s become apparent that the ‘weight’ of a ‘mass’ is difficult to determine with any accuracy. I propose a ‘standard’ for the ‘measurement’ of ‘weight’.”

    OK Good.

    “1). The ‘weight’ (force acting towards the major, and central’ mass) of a mass/massive object can only be determined when ‘weighed’ in a vacuum within a ‘zero reference frame’ for the relative gravity flux.”

    At what distance in a projective field such as ‘gravity’ Weight per steradian might be nice!

    “2). Because the ‘weight’ of a ‘massive object’ also possesses ‘inertia’, the ‘inertia value’ can also be taken as the ‘absolute weight’ of the mass under observation.”

    Yes indeed mass has an opposition to acceleration, adding the term weight only promotes confusion. I can buy 14.7 pounds of prime rib and “get” something to take home, and such belongs to me! What do I get to take home if I buy one square inch of atmosphere? Who does that belong to?
    Science is fine, so is mathematics. Neither feeds the kids. Both science and mathematics properly belong in the realm of fantasy.

    What are your thoughts? Best regards, Ray

    Thank you. The concept of weight, and what is wrong, was completely demonstrated by Archimedes, thus demonstrating the vast difference between atmosphere and compressible fluid or gas. A non-self buoyant mass of any volume within the atmosphere displaces atmosphere of that volume, without regard to density (rho, mass/volume) of either volume. Earth’s gravity replaces that concept with the displacement of space with no, mass, no specific heat, and no temperature. If that puppy floats in water (hydrostatic balance) it must displace the mass of water equal to the non self buoyant “weight” of just that puppy, at that location. Can there be any discussion that the volume of atmosphere displaced at any location has any (non zero) weight?

    Ray, This may sound pedantic, but is crucial to any possible understanding of this atmosphere. It is the isopotential nature of this atmosphere in every direction that allows/induces the convection/advection that earthlings try to measure with absolutely no understanding whatsoever!
    All the best! -will-

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    blouis79

    Sorry, there is a lot of math, but it doesn’t pass the sniff test to me. Earth at the surface can go from cold to hot in half a day in the sun and vice versa. There appears sufficient capacity in the IR heat absorbing/emitting system to find steady state relatively quickly of the timescale of days to weeks, not decades to centuries.

    How long does it take an astronaut to freeze by thermal radiation in space?

    Because of mixing phenomena and thermal mass, the oceans take longer too cool, but they are also absorbing geothermal energy from the hot core, which isn’t going to stop being hot anytime soon.

    Modelling of heat needs to account for the geothermal heat mass as well as radiative phenomena.

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    bloius79, the two years for a 90% accommodation (to the new global temperature corresponding to a new level of solar input) is empirical and takes into account the whole climate system and its feedbacks, including the oceans, clouds, atmospheric water vapor, etc, globally.

    Yes, an afternoon in the Sun warms a patch of land, but clouds come and go, night comes, winter comes, and the next day or next month or next year it is much the same temperature as it started at, and probably cooler in the meantime.

    Geothermal is insignificant, about 0.087 W/m2, or about 0.036% of the 239 W/m2 of average absorbed solar radiation.

    Btw, energy production from fossil fuels and nuclear is about 0.028 W/m2, and tidal might be as high as 0.01 W/m2 (about 5.8 TW).

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    KR

    The 1-box model (one time constant for climate response) you present here does a reasonable job of matching forcing data to temperatures. However, a two-box model (discussion here), with short and long time constants to deal with different thermal inertias for ocean and atmospheric temperatures, does considerably betterit demonstrates a better fit between forcings and temperature than a single box model.

    And if you add in ENSO variations (such as characterized by the southern oscillation index, the SOI), the two estimated time constants are 2 years and 26 years. The match between forcings and temperatures in that estimate is nothing short of amazing – a graph here. Note that the estimated climate sensitivity given this analysis is about 2.5°C per CO2 doubling.

    This brackets your 3.2 year time constant, and I would consider your estimate to be an approximation better refined with _two_ separate time constants. And probably better with three time constants, to reflect the atmosphere, the ocean mixed layer, and the deep ocean, though I suspect that reasonable uncertainty limits for a three time constant estimate would require more complex models including ocean circulation.

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      KR: Thanks, we are probably in the ballpark, but we’re not quite sure what game we’re playing. Yes, the 1-box model I used is simple. I don’t even know what is in the box — it is just an empirical result, and I have no way of knowing how deep in to the ocean it goes. Maybe the mixing zone? Maybe to the thermocline? The empirical transfer function method is only good enough to spot the distinctive low pass filter in the transfer function, so it can only detect one box.

      If I had more confidence in GCMs I might credit the GISS model, but it applies the solar response to the CO2 forcing (roughly) (posts 9 and 13), omits non-surface warming feedbacks (posts 5 and 7), and omits EDA input altogether (post 10). It didn’t see the pause coming and predicts a distinctive tropical hotspot that hasn’t really been found. A model tuned to the data but with the wrong architecture and inputs would also act something like the GISS model — sort of right, but also quite wrong some of the time.

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        “sort of right, but also quite wrong some of the time.”

        Any computer model is but a fantasy of numbers without a crude physical verification of some of those numbers. Aerodynamic computer models depend on wind tunnels. The Cal Tech Earth fluid dynamics atmospheric model was unintelligible until someone blew smoke at the rotational axis of a spinning sphere, to see where the smoke went! Without the gravitational effect no joy, except that the computer model is trash! The new one ‘can’ put the sphere in constant air pressure with repeatable result. How that stuff gets back to the poles is still much “Do I scratch my watch or wind my ass?” Peer reviewed by all that have ever done anything.
        All the best! -will-

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        KR

        The two-box model is descriptive of the GISS Model E, and of the observed relationship between forcings and temperatures, but that’s certainly not the basis of the GISS model – documentation links here. Rather, that’s a full GCM, including moist convection and ocean circulation. It does _not_ treat CO2 forcing identically to solar forcing, and atmospheric warming feedbacks _are_ included by the multi-layer radiative/convective code.

        The similarity in response between CO2 and solar forcing is due to the understood physics driving responses, not to any implicit or explicit assumptions in the GCMs. And that is fully demonstrated by the differences in response to those forcings, such as the stratospheric cooling that is a fingerprint of GHG forcing – and utterly absent from solar forcing.

        The two-box model describing the GISS GCM has the same relationship as Myhre 1998′s equation for direct forcing has to the radiative models it was derived from – descriptive of behavior, but not of how those answers were reached. I pointed it out as a still simple but more accurate and useful descriptive model than a 1-box variation.

        No, the GISS Model E variations don’t include what you describe as EDA inputs – primarily because there are insufficient observational data and for that matter physics to consider them as significant forcings. Cosmic ray influences as per Svensmarks research, for example, are trending the wrong direction to explain recent warming, not to mention the considerable counterexample of the Laschamp event and the notable lack of climate response to enormous changes in cosmic rays. There’s little reason to model hypothetical physics which lack evidence.

        If you’re going to criticize GCMs, rather than what you describe as the ‘basic model’ (is there an _actual_ IPCC model matching your description, and if so, could you reference it?), it would be IMO best to not project your ‘basic model’ onto how GCMs actually work.

        [ Side note, which I'm not going to spend more time on in these threads: As to the so-called 'pause, it's well within the range of previous variations around model means (both up and down), within the 2-sigma variability range of the models themselves, especially given actual historic rather than the simplified projected forcings that were used in the CMIP3/CMIP5 runs. There's no really statistical justification for claiming temperatures are outside what models project. ]

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          KR, I didn’t say GISS Model E “treat[ed] CO2 forcing identically to solar forcing” — I said “roughly” the same. As it happens, GISS Model E is the easiest GCM to show this behavior for.

          Yes, I agree that EDA is too nebulous to include in the GCMs at this stage — but as post 10 shows, EDA is also quite significant. Bit of a quandary, but hardly conducive to the confidence proclaimed by the IPCC.

          The “natural variation” is pretty much what GCMs cannot predict, even after being tuned to the data — and as the pause shows, there is a fair bit of it around at the moment. If the GCMs omitted an important factor, isn’t that pretty much how it would manifest itself in the GCMs?

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            KR

            Natural variation, in essence weather, is an initial value problem – the climate models are used for investigating the boundary condition problems of average behavior, of climate, and aren’t expected to exactly reproduce the weather in time with observations.

            I will note that many models do show ENSO style events, although generally not in sequence with the ‘single run’ of actual climate – and that models don’t include any projections of varying solar cycle heights (that would require a fusion model beyond our current data) nor projections of detailed volcanic eruptions (requiring some kind of magma model), but rather use stochastic projections in the range of what is expected.

            There is no expectation that GCMs will exactly duplicate short term variations, and there never has been – that’s not what they are intended for.

            “If the GCMs omitted an important factor, isn’t that pretty much how it would manifest itself in the GCMs?”

            No, it is not – variability within model ranges is in fact supportive of the models. If the GCMs omitted a significant factor, it would show as observations departing the range of modeled variability, and that has not happened. Let alone exceeding the 2-sigma (95%) variability ranges on a greater than 1 in 20 basis.

            You would see a difference in trajectories akin to that in IPCC AR5 Chapter 10, Fig 10.1.b, where modeled natural forcings show a diverging trajectory from the modeled natural and anthropogenic forcings which match observations.

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              KR: If GCMs have overestimated the warming effect of CO2 and omitted a factor that caused significant warming via EDA, then they would be tuned to show that the warming of the 1980s and 1990s was almost entirely due to increasing CO2. But if a large part of the 1980s-90s warming was in fact due to the omitted factor, which then faded after about 1998, then the GCMs would show good agreement for the 1980s and 1990s but would overestimate warming after 1998.

              That overestimate has occurred, and the data quoted in post 10 indicates EDA, which is omitted by the GCMs, has been a significant player.

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            KR

            I would have to disagree with this statement:

            Yes, I agree that EDA is too nebulous to include in the GCMs at this stage — but as post 10 shows, EDA is also quite significant.

            What you demonstrated in post 10 is that external albedo changes could be significant in scale, but you have not demonstrated that they actually exist.

            The ‘Earthshine’ data you reference, for example from Palle et al, are quite uncertain and for that matter multiply updated data – I would suggest looking at AR5 WG1 Ch. 7, Clouds and Aerosols, to see the current science regarding albedo trends.

            Before you argue that leprechauns are a significant influence, first demonstrate that there are indeed leprechauns.

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              KR, it’s always leprechauns when data disagrees with the conventional basic model :) As noted in post 1:

              The conventional basic climate model is superficially compelling. It is at the heart of the belief that carbon dioxide poses a dangerous threat. It must be compelling—otherwise why else would many sensible scientists still support the theory in the face of ample confounding evidence? They are convinced the basic physics is correct, so they know the something must be wrong with data that appears to contradict it.

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                Franktoo

                David: It imay always be unforced (internal) variability, not leprechauns, when observations disagree with models. That is what makes climate science so hard. How big must a discrepancy be before it invalidates a model? AOGCMs either predict too much warming or too little unforced variability.

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                Frank: “Unforced variability” is variability not accounted for by any forcing, and thus any known reason, isn’t it? Could be teams of leprechauns.

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                Franktoo (Frank)

                David: Your leprechauns control the mixing between several kilometers of deep ocean at 0-4 degC, roughly 1 kilometer of thermocline, and 50 m of mixed layer floating on top in near equilibrium with the atmosphere above.

                https://en.wikipedia.org/wiki/Thermocline#/media/File:THERMOCLINE.png

                Chaotic fluctuations in this exchange can easily change surface temperature in the absence of any external forcing – producing “unforced variability” aka “internal variability”.

                Among many other phenomena, the Eastern Equatorial Pacific is not cooled as much by upwelling of deep water off the coast of South America during El Nino. Due to the chaotic nature of the processes that occasionally allow warm water from the Western Pacific to flow east and suppress upwelling, no one is able to skillfully predict the state of ENSO a year in the future.

                Perhaps this passage from a Dick Lindzen op-ed will clarify the importance of unforced variability, which he calls “natural internal variability” herein. (To avoid confusion, I prefer the terms: “unforced variability”, “naturally-forced variability” and “anthropogenically-forced variability”, but many use natural variability (one or both of the first two) and “internal variability” (synonymous with unforced variability).

                “The main statement publicized after the last IPCC Scientific Assessment two years ago was that it was likely that most of the warming since 1957 (a point of anomalous cold) was due to man. This claim was based on the weak argument that the current models used by the IPCC couldn’t reproduce the warming from about 1978 to 1998 without some forcing, and that the only forcing that they could think of was man. Even this argument assumes that these models adequately deal with natural internal variability—that is, such naturally occurring cycles as El Nino, the Pacific Decadal Oscillation, the Atlantic Multidecadal Oscillation, etc.

                Yet articles from major modeling centers acknowledged that the failure of these models to anticipate the absence of warming for the past dozen years was due to the failure of these models to account for this natural internal variability. Thus even the basis for the weak IPCC argument for anthropogenic climate change was shown to be false.”

                http://www.wsj.com/articles/SB10001424052748703939404574567423917025400?alg=y

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                Frank, there exists a strong relationship between TSI fluctuations and ENSO, and in turn between ENSO and decadel (and shorter) movements in global surface temperature — so it is essentially the “well-known” correlation of TSI to surface temperature, but I reckon it might be lagged by one sunspot cycle.

                It’s hard to know whether some temperature fluctuation is forced by an influence as yet unaccounted for, or it is just “natural or internal variability” — the latter could just be an expression of ignorance for the former.

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    Franktoo (Frank)

    David: The large changes associated with seasonal warming and cooling provides some useful information about thermal inertia and the phase lag between forcing and response. Away from coasts, the warmest month is usually July and the coldest month is January, because the thermal inertia of the atmosphere and land surface is relatively low. In coastal area where I grew up, the hottest month was August, with September being warmer than June. I’ve never found data for how the maximum SST lags solar insolation. However, if you look at sea ice coverage in the Arctic, the minimum is always after September 1 (and often in the second half of September), showing a response that is 90 degrees out of phase with solar forcing. In the Arctic, we need to melt about 1 m of new sea ice every summer before the temperature of the ocean can begin warming. (Given that more than half of sea ice melts every year, if the earth traveled around the sun half as fast, all sea ice might melt and the response would not be 90% out of phase with solar forcing.)

    The simplest way to calculate something useful about thermal inertia is to consider the mixed layer of the ocean (which can be defined in terms of the depth to which average seasonal warming penetrates. It is easy to show that a instantaneous 1 W/m2 forcing is capable of warming an atmosphere and mixed layer 50 m deep (over 70% of the earth) at an INITIAL rate of 0.2 degC/yr. If we consider an instantaneous doubling of CO2, that would be 0.74 degC/yr. If climate sensitivity were 1.5 or 3.0 degC, a new equilibrium temperature could be reached in 2 or 4 years at that rate, and Planck (and other feedbacks) will have cut the warming rate in half within 1 or 2 years.

    FWIW, these hand-waving arguments give lagged responses similar to the ones you derive.

    At the Blackboard, Paul_K did a superb job re-analyzing the lagged response to Pinatubo (the largest documented forcing applied to our planet). He found a model with a single compartment (mixed layer) inadequate and previous published analyses also flawed:

    http://rankexploits.com/musings/2012/pinatubo-climate-sensitivity-and-two-dogs-that-didnt-bark-in-the-night/

    (Unfortunately, he chose to call the reciprocal of the climate feedback parameter operating during the response to Pinatubo “ECS” even though the surface albedo feedback can reach equilibrium in a few years.)

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      Very interesting post, thank you! The planetary time constants remain off the map for EEs. We love nanoseconds and pay big bucks to observe picoseconds. Time probably scales, but in a world where you likely die before lunch, multiple folk lifetimes is difficult to become comfortable and conversant with! ;-)

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        Franktoo (Frank)

        Will and David: Pinatubo is the biggest and best documented perturbation to our climate system: A 3 W/m2 reduction in ASR lasting nearly a year before tapering off. Anyone devising a new model for our climate should consider how that model applies to Pinatubo (rather than to electrical engineering or signal processing). The first problem one runs into is unforced (internal) variability, which obscures the cooling signal associated with this event.

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