Guest Post by Willis Eschenbach
In my previous post, A Longer Look at Climate Sensitivity, I showed that the match between lagged net sunshine (the solar energy remaining after albedo reflections) and the observational temperature record is quite good. However, there was still a discrepancy between the trends, with the observational trends being slightly larger than the calculated results. For the NH, the difference was about 0.1°C per decade, and for the SH, it was about 0 05°C per decade.
I got to thinking about the “exponential decay” function that I had used to calculate the lag in warming and cooling. When the incoming radiation increases or decreases, it takes a while for the earth to warm up or to cool down. In my calculations shown in my previous post, this lag was represented by a gradual exponential decay.
But nature often doesn’t follow quite that kind of exponential decay. Instead, it quite often follows what is called a “fat-tailed”, “heavy-tailed”, or “long-tailed” exponential decay. Figure 1 shows the difference between two examples of a standard exponential decay, and a fat-tailed exponential decay (golden line).
Figure 1. Exponential and fat-tailed exponential decay, for values of “t” from 1 to 30 months. Lines show the fraction of the original amount that remains after time “t”. The “fatness” of the tail is controlled by the variable “c”. Line with circles shows the standard exponential decay, from t=1 to t=20. Golden line shows a fat-tailed exponential decay. Black line shows a standard exponential decay, with a longer time constant “tau”. The “fatness” of the tail is controlled by the variable “c”.
Note that at longer times “t”, a fat-tailed decay function gives the same result as a standard exponential decay function with a longer time constant. For example, in Figure 1 at “t” equal to 12 months, a standard exponential decay with a time constant “tau” of 6.2 months (black line) gives the same result as the fat-tailed decay (golden line).
So what difference does it make when I use a fat-tailed exponential decay function, rather than a standard exponential decay function, in my previous analysis? Figure 2 shows the results:
Figure 2. Observations and calculated values, Northern and Southern Hemisphere temperatures. Note that the observations are almost hidden by the calculation.
While this is quite similar to my previous result, there is one major difference. The trends fit better. The difference in the trends in my previous results is just barely visible. But when I use a fat-tailed exponential decay function, the difference in trend can no longer be seen. The trend in the NH is about three times as large as the trend in the SH (0.3°C vs 0.1°C per decade). Despite that, using solely the variations in net sunshine we are able to replicate each hemisphere exactly.
Now, before I go any further, I acknowledge that I am using three tuned parameters. The parameters are lambda, the climate sensitivity; tau, the time constant; and c, the variable that controls the fatness of the tail of the exponential decay.
Parameter fitting is a procedure that I’m usually chary of. However, in this case each of the parameters has a clear physical meaning, a meaning which is consistent with our understanding of how the system actually works. In addition, there are two findings that increase my confidence that these are accurate representations of physical reality.
The first is that when I went from a regular to a fat-tailed distribution, the climate sensitivity did not change for either the NH or the SH. If they had changed radically, I would have been suspicious of the introduction of the variable “c”.
The second is that, although the calculations for the NH and the SH are entirely separate, the fitting process produced the same “c” value for the “fatness” of the tail, c = 0.6. This indicates that this value is not varying just to match the situation, but that there is a real physical meaning for the value.
Here are the results using the regular exponential decay calculations
SH NH lambda 0.05 0.10°C per W/m2 tau 2.4 1.9 months RMS residual error 0.17 0.26 °C trend error 0.05 ± 0.04 0.11 ± 0.08, °C / decade (95% confidence interval)
As you can see, the error in the trends, although small, is statistically different from zero in both cases. However, when I use the fat-tailed exponential decay function, I get the following results.
SH NH lambda 0.04 0.09°C per W/m2 tau 2.2 1.5 months c 0.59 0.61 RMS residual error 0.16 0.26 °C trend error -0.03 ± 0.04 0.03 ± 0.08, °C / decade (95% confidence interval)
In this case, the error in the trends is not different from zero in either the SH or the NH. So my calculations show that the value of the net sun (solar radiation minus albedo reflections) is quite sufficient to explain both the annual and decadal temperature variations, in both the Northern and Southern Hemispheres, from 1984 to 1997. This is particularly significant because this is the period of the large recent warming that people claim is due to CO2.
Now, bear in mind that my calculations do not include any forcing from CO2. Could CO2 explain the 0.03°C per decade of error that remains in the NH trend? We can run the numbers to find out.
At the start of the analysis in 1984 the CO2 level was 344 ppmv, and at the end of 1997 it was 363 ppmv. If we take the IPCC value of 3.7 W/m2, this is a change in forcing of log(363/344,2) * 3.7 = 0.28 W/m2 per decade. If we assume the sensitivity determined in my analysis (0.08°C per W/m2 for the NH), that gives us a trend of 0.02°C per decade from CO2. This is smaller than the trend error for either the NH or the SH.
So it is clearly possible that CO2 is in the mix, which would not surprise me … but only if the climate sensitivity is as low as my calculations indicate. There’s just no room for CO2 if the sensitivity is as high as the IPCC claims, because almost every bit of the variation in temperature is already adequately explained by the net sun.
Best to all,
w.
PS: Let me request that if you disagree with something I’ve said, QUOTE MY WORDS. I’m happy to either defend, or to admit to the errors in, what I have said. But I can’t and won’t defend your interpretation of what I said. If you quote my words, it makes all of the communication much clearer.
MATH NOTES: The standard exponential decay after a time “t” is given by:
e^(-1 * t/tau) [ or as written in Excel notation, exp(-1 * t/tau) ]
where “tau” is the time constant and e is the base of the natural logarithms, ≈ 2.718. The time constant tau and the variable t are in whatever units you are using (months, years, etc). The time constant tau is a measure that is like a half-life. However, instead of being the time it takes for something to decay to half its starting value, tau is the time it takes for something to decay exponentially to 1/e ≈ 1/2.7 ≈ 37% of its starting value. This can be verified by noting that when t equals tau, the equation reduces to e^-1 = 1/e.
For the fat-tailed distribution, I used a very similar form by replacing t/tau with (t/tau)^c. This makes the full equation
e^(-1 * (t/tau)^c) [ or in Excel notation exp(-1 * (t/tau)^c) ].
The variable “c’ varies between zero and one to control how fat the tail is, with smaller values giving a fatter tail.
[UPDATE: My thanks to Paul_K, who pointed out in the previous thread that my formula was slightly wrong. In that thread I was using
∆T(k) = λ ∆F(k)/τ + ∆T(k-1) * exp(-1 / τ)
when I should have been using
∆T(k) = λ ∆F(k)(1 – exp(-1/ τ) + ∆T(k-1) * exp(-1 / τ)
The result of the error is that I have underestimated the sensitivity slightly, while everything else remains the same. Instead of the sensitivities for the SH and the NH being 0.04°C per W/m2 and 0.08°C per W/m2 respectively in the both the current calculations, the correct sensitivities for this fat-tailed analysis should have been 0.04°C per W/m2 and 0.09°C per W/m2. The error was slightly larger in the previous thread, increasing them to 0.05 and 0.10 respectively. I have updated the tables above accordingly.
w.]
[ERROR UPDATE: The headings (NH and SH) were switched in the two blocks of text in the center of the post. I have fixed them.
It is an oversimplification to resolve global temperature variability with only one independent and one internal feedback variable.
vukcevic says:
June 4, 2012 at 12:59 am (Edit)
Sorry it’s not complex enough for you, vukcevic. And yet it works … go figure.
w.
Willis:
This refinement of your model is an excellent response to those who have been attacking instead of assessing your model. Thankyou.
The principle of parsimony says your model is the best we have of recent global temperature rise.
However, I am writing to caution against overstatement of your findings.
I again remind of the warning I repeatedly stated on the previous thread; i.e.
Hence, I write to provide a caveat to your statement that says;
Although directly true, your statement suggests that ‘high’ vales of climate sensitivity are wrong. Please note that I think such ‘high’ values are wrong, but they may be possible despite your analysis being correct.
As I said in the previous thread:
Indeed, you later acknowledged that possibility in your later post to that thread at June 3, 2012 at 2:41 am where you wrote:
However, as you there point out, “increased clouds” would decrease temperature which would be a negative feedback providing a lower climate sensitivity than e.g. the IPCC proposes.
But that decrease is only one of several possible effects which may occur in the real climate system.
To avoid misunderstanding of what I am trying to say, I iterate that
• The principle of parsimony says your model is the best we have of recent global temperature rise.
And
• I find your model cogent.
However, we need to avoid jumping to undue certainty (which others did with the resulting creation of the IPCC). And, therefore, I again remind that an ability to attribute a cause(s) is NOT evidence that the cause is the true cause in part or in whole.
One of the reasons your model is so very important is that it suggests falsifiable hypotheses for mechanisms of global climate change (indeed, Stephen Wilde has provided one such falsifiable hypothesis on the previous thread). GCMs do not suggest such falsifiable hypotheses.
Hence, I am writing to caution against overstatement of your findings. Such overstatement provides ‘straw men’ which can be used to generate excuses for ignoring your important findings.
Richard
I went back thru the previous posts and couldn’t see the source of your temperature data.
Otherwise, its no surprise to me that albedo/solar insolation drives atmospheric temperatures. Nor does it surprise me that the effect of CO2 increases at current concentrations are minimal. What does surprise me is that your model seems to preclude ocean variability/cycles (ie variable heat release from the oceans) having a significant effect on atmospheric temperatures.
vukcevic says:
June 4, 2012 at 12:59 am
It is an oversimplification
=========
Complexity is no assurance that an answer is right. Simplicity is no assurance an answer is wrong. As a general rule, the simplest method that produces the correct answer is the preferred method.
So, the correlation implies that all non-solar forcings net out as albedo. You don’t need to account for them separately, as this would be double counting once you allow for changes in albedo. And it also implies that any theory of climate that assumes a constant albedo with changing temperature is wrong.
Willis, this is so simple and such a good fit it’s worrying.
If I follow you right, this albedo argument just works on incoming solar. However, albedo changes are presumably mostly cloud and cloud cover is well known to block out going IR. So I don’t see how your model can fit without taking outgoing IR into account.
Am I mis reading you hypothesis?
Mr. Eschenbach
Many of your previous posts I took very seriously, so I am still inclined to think that this is intended as a kind of a ‘summer season spoof’.
Either way good luck.
“It is an oversimplification to resolve global temperature variability with only one independent and one internal feedback variable”
Not if that one internal feedback variable serves as a proxy for the net outturn of all the many other internal system feedbacks.
I suggest that albedo / cloudiness is just such a proxy.
I have been aware of that principle in general terms for many years so my main interest is in the next step.
That step is to determine what feature of the system serves best as a means of determining HOW the system uses clouds to achieve such an effect as a means of producing the observed long term system stability.
Svensmark suggests simple changes in cloud quantities as driven by cosmic ray condensation nuclei but that suggests that changes in the system are DRIVEN by the cloudiness / albedo changes whereas I think the cloudiness / albedo changes are a RESPONSE which maintains system stability.
The feature we should be looking at is the way cloud quantities appear to decrease when the mid latitude jets shift poleward and become more zonal yet increase when the jets become more meridional and shift equatorward.
As Richard Courtney said in the previous thread the mechanism which I propose in support of Willis’s findings is plausible and should be falsifiable so I await such falsification – or not.
So the atmosphere moderates temperature changes imposed on the planet by the sun and its variations. The moon, zero atmosphere but receiving the same insolation as the Earth, has sunlit temperatures in excess of +150C whilst shadow temperatures are below -150C. Wonderful thing atmosphere.
Yup it is a travesty to use low number of parameters especially if none of them represents GHGs. Willis what were you thunking. You are smart but not Occam
Hi Willis,
As far as I can tell, it’s a good bit of work, congratulations. However I find it rich that you are content to curve fit and have ‘c’ as an as-yet unexplained variable, but dismiss others (often in quite childishly crass terms) when they do similar fitting. It’s not a case of “If the curve fits you must acquit”, but don’t be dismissive of great correlations just because science, as yet, has not come up with a suitable explanation.
As someone once said, k.i.s.s.
Let’s hear it for C-0.6!
OLR varies strictly with temperature, and all its forcings and factors work via albedo.
I like it!
I again remind that an ability to attribute a cause(s) is NOT evidence that the cause is the true cause in part or in whole.
What you say is correct, but begs the question what causes both decreased albedo and increased temperatures (the only other possible explanation).
All I can think of is black carbon, which certainly does both. However, I am sure, because BC scatters incoming solar radiation (warming the troposphere), it causes climate cooling after a fairly short lag. Because, had the BC not intercepted the incoming solar radiation, it would have reached the surface and the energy would be retained longer in the climate system.
I think it very unlikely BC is the cause of what Willis has found.
Stephen Wilde says: “Svensmark suggests simple changes in cloud quantities as driven by cosmic ray condensation nuclei but that suggests that changes in the system are DRIVEN by the cloudiness / albedo changes whereas I think the cloudiness / albedo changes are a RESPONSE which maintains system stability.”
Nothing to stop both being true.
If Svenmark style GCR infulences albedo that would not disrupt Willis’ findings. If that results in the GMT being a bit cooler than equilibrium , negative feedback reduces cloud . Again this would fit was Willis is suggesting.
Philip Bradley says ” I went back thru the previous posts and couldn’t see the source of your temperature data.”
I picked that up late in the last thead and Willis posted that is is HadCRUT. I think he ought to update the articles to show this (preferably with a precise version and a link to the data).
Figure 4 in this article shows the period used by W. was one of the few parts of the record that was not heavily “adjusted” by Hadley Centre , so perhaps it can be taken as reasonably accurate.
http://judithcurry.com/2012/03/15/on-the-adjustments-to-the-hadsst3-data-set-2/
Stephen Wilde says: June 4, 2012 at 2:27 am
…….
Hi Steven
Most of the temperature rise in the N. Hemisphere during the last 300+ years is due to change in the winter temperatures
http://www.vukcevic.talktalk.net/CETsw.htm
these changes are driven by the Arctic polar jet-stream, but since the Arctic gets very little if any insolation and has more or less stable winter albedo, I find the hypothesis proposed hardly plausible. I will look forward to further evaluation.
Philip Bradley asked:
“what causes both decreased albedo and increased temperatures (the only other possible explanation).”
Poleward shifting of the air circulation pattern which reduces global cloudiness and allows more energy into the oceans.
But the thermal effect is offset by the faster or larger water cycle implicit in a more poleward configuration.
So the question should be as to what shifts the air circulation poleward and the answer is more energy in the troposphere.
Whatever places that extra energy in the troposphere whether it be sun, oceans, GHGs or anything else the surface pressure configuration shifts so as to prevent it from affecting total system energy content.
Quite simply, anything that tries to make more energy accumulate in the troposphere just sees it negated by a faster throughput to space.
In the process, regions on the surface observe warmer air masses as the energy flows across them on its way out but total system energy content stays the same.
As regards human CO2 the effect is miniscule as compared to natural changes from sun and oceans.
From the abedo paper:
” The model is able to predict the seasonal and geographical vari-
ation of SW TOA fluxes. On a mean annual and global
basis, the model is in very good agreement with ERBE,
overestimating the outgoing SW radiation at TOA (OSR)
by 0.93 Wm−2 (or by 0.92%), within the ERBE uncertain-
ties. At pixel level, the OSR differences between model and
ERBE are mostly within ±10 Wm−2 , with ±5 Wm−2 over
extended regions, while there exist some geographic areas
with differences of up to 40 Wm−2 , associated with uncer-
tainties in cloud properties and surface albedo. ”
I know you share my dislike of pretending model output is “data”.
Have you checked to make sure that model is not using temps and the NASA isolation data to calculate the albedo !?
ferd berple says: June 4, 2012 at 1:47 am
…….
Ferd
I am always in favor of simplicity and elegance for a solution providing it is plausible, I am not certain this one is, see my post above addressed to Mr. Wild
http://wattsupwiththat.com/2012/06/04/sun-and-clouds-are-sufficient/#comment-1000844
DEEBEE and Harriet Harridan:
DEEBEE, I am assuming that your post at June 4, 2012 at 2:33 am is intended to be sarcasm and not a ‘true’ rejection of Willis’ analysis, but you do not indicate that. Perhaps it would be good if you were to clarify the matter.
Harriet Harridan at June 4, 2012 at 2:41 am you say to Willis:
But Willis has NOT merely conducted a “curve fit” and ‘c’ is not “an as-yet unexplained variable”
Willis showed by demonstration that solar input and albedo together are sufficient variables to describe change to mean global temperature over the observation period (i.e. 1984 to 1998). That is certainly not a mere curve fit.
However, the demonstration required a decay function which Willis chose as being exponential. His choice of exponential decay was arbitrary, and he explains
.
Willis’ ‘c’ is merely a determination of the decay rate obtained by best fit. Your point would have had more validity if it were an objection to Willis having originally chosen an exponential decay function because that choice was arbitrary.
This procedure is NOT the same as merely curve fitting to obtain a desired result. Willis original analysis determined the minimum number of variables required to match empirical observations, and his refinement (which adopts ‘c’) improves the already-determined match.
At issue now is
• if the determined two variables are coincidentally sufficient to match the empirical observations over the analysis period
or
• if there is an underlying mechanism(s) which induces the two variables to be sufficient for description of climate system behaviour which governs mean global temperature.
Hence, your criticism is without merit.
Richard
Philip Bradley:
Thankyou for your post at June 4, 2012 at 3:00 am. I agree all it says. However, I point out that it supports the argument in my post at June 4, 2012 at 1:35 am which it is answering.
As you say;
With respect, that demonstrates my point. It is yet another example of the logical fallacy of ‘argument from ignorance’ which got us into this AGW-scare.
“The only thing I can think of says X so Y must be correct” ignores everything one has failed to “think of”.
As I said in the post you are addressing
Or, to put that another way, I repeat what I said to Harriet Harriman
Richard
ferd berple says:
June 4, 2012 at 1:57 am
So, the correlation implies that all non-solar forcings net out as albedo. You don’t need to account for them separately, as this would be double counting once you allow for changes in albedo. And it also implies that any theory of climate that assumes a constant albedo with changing temperature is wrong.
Albedo – the reflectivity of clouds is an indication of the system response to increased internal heat content. The El Nino/La Nina variations can be due to the presence or lack of clouds inhibiting or allowing energy entering the Pacific. So the underlying homeostasis in the Earth system is driven by clouds forming as a response to the hydrological cycle speeding up or slowing down. Thus as Fred says, measuring the albedo of the clouds hides the complexity of what is causing the changes in cloudiness.
As Stephen Wilde reminds us larger scale variations, perhaps on longer timescales than this study, affect the albedo as the Hadley cells are compressed and the jet streams move equatorwards changing the distribution of clouds and the albedo.
As Svensmark (and others) have been showing albedo (cloudiness) could also be increased by increases in the rate of high energy galactic cosmic rays.
So we appear to be in a Goldilocks Earth system that over short timescales (two decades) exhibits homeostasis. But the homeostastic mechanism(s) although apparently unaffected by volcanic activity such as Pinatubo, may be subject to perturbations from longer large scale effects and/or from external GCR (and perhaps other unknown factors).
Well done Willis. The residuals are leaving very little wiggle room for the GCMs (pun intended).