Guest Post by Willis Eschenbach
Now that my blood pressure has returned to normal after responding to Dr. Trenberth, I returned to thinking about my earlier somewhat unsatisfying attempt to make a very simple emulation of the GISS Model E (herinafter GISSE) climate model. I described that attempt here, please see that post for the sources of the datasets used in this exercise.
After some reflection and investigation, I realized that the GISSE model treats all of the forcings equally … except volcanoes. For whatever reason, the GISSE climate model only gives the volcanic forcings about 40% of the weight of the rest of the forcings.
So I took the total forcings, and reduced the volcanic forcing by 60%. Then it was easy, because nothing further was required. It turns out that the GISSE model temperature hindcast is that the temperature change in degrees C will be 30% of the adjusted forcing change in watts per square metre (W/m2). Figure 1 shows that result:
Figure 1. GISSE climate model hindcast temperatures, compared with temperatures hindcast using the formula ∆T = 0.3 ∆Q, where T is temperature and Q is the same forcings used by the GISSE model, with the volcanic forcing reduced by 60%.
What are the implications of this curious finding?
First, a necessary detour into black boxes. For the purpose of this exercise, I have treated the GISS-E model as a black box, for which I know only the inputs (forcings) and outputs (hindcast temperatures). It’s like a detective game, trying to emulate what’s happening inside the GISSE black box without being able to see inside.
The resulting emulation can’t tell us what actually is happening inside the black box. For example, the black box may take the input, divide it by four, and then multiply the result by eight and output that number.
Looking at this from the outside of the black box, what we see is that if we input the number 2, the black box outputs the number 4. We input 3 and get 6, we input 5 and we get 10, and so on. So we conclude that the black box multiplies the input by 2.
Of course, the black box is not actually multiplying the input by 2. It is dividing by 4 and multiplying by 8. But from outside the black box that doesn’t matter. It is effectively multiplying the input by 2. We cannot use the emulation to say what is actually happening inside the black box. But we can say that the black box is functionally equivalent to a black box that multiplies by two. The functional equivalence means that we can replace one black box with the other because they give the same result. It also allows us to discover and state what the first black box is effectively doing. Not what it is actually doing, but what it is effectively doing. I will return to this idea of functional equivalence shortly.
METHODS
Let me describe what I have done to get to the conclusions in Figure 1. First, I did a multiple linear regression using all the forcings, to see if the GISSE temperature hindcast could be expressed as a linear combination of the forcing inputs. It can, with an r^2 of 0.95. That’s a good fit.
However, that result is almost certainly subject to “overfitting”, because there are ten individual forcings that make up the total. With so many forcings, you end up with lots of parameters, so you can match most anything. This means that the good fit doesn’t mean a lot.
I looked further, and I saw that the total forcing versus temperature match was excellent except for one forcing — the volcanoes. Experimentation showed that the GISSE climate model is underweighting the volcanic forcings by about 60% from the original value, while the rest of the forcings are given full value.
Then I used the total GISS forcing with the appropriately reduced volcanic contribution, and we have the result shown in Figure 1. Temperature change is 30% of the change in the adjusted forcing. Simple as that. It’s a really, really short methods section because what the GISSE model is effectively doing is really, really simple.
DISCUSSION
Now, what are (and aren’t) the implications available within this interesting finding? What does it mean that regarding temperature, to within an accuracy of five hundredths of a degree (0.05°C RMS error) the GISSE model black box is functionally equivalent to a black box that simply multiplies the adjusted forcing times 0.3?
My first implication would have to be that the almost unbelievable complexity of the Model E, with thousands of gridcells and dozens of atmospheric and oceanic levels simulated, and ice and land and lakes and everything else, all of that complexity masks a correspondingly almost unbelievable simplicity. The modellers really weren’t kidding when they said everything else averages out and all that’s left is radiation and temperature. I don’t think the climate works that way … but their model certainly does.
The second implication is an odd one, and quite important. Consider the fact that their temperature change hindcast (in degrees) is simply 0.3 times the forcing change (in watts per meter squared). But that is also a statement of the climate sensitivity, 0.3 degrees per W/m2. Converting this to degrees of warming for a doubling of CO2 gives us (0.3°C per W/m2) times (3.7 W/m2 per doubling of CO2), which yields a climate sensitivity of 1.1°C for a doubling of CO2. This is far below the canonical value given by the GISSE modelers, which is about 0.8°C per W/m2 or about 3°C per doubling.
The third implication is that there appears to be surprisingly little lag in their system. I can improve the fit of the above model slightly by adding a lag term based on the change in forcing with time d(Q)/dt. But that only improves the r^2 to 0.95, mainly by clipping the peaks of the volcanic excursions (temperature drops in e.g. 1885, 1964). A more complex lag expression could probably improve that, but with the initial expression having an r^2 of 0.92, that only leaves 0.08 of room for improvement, and some of that is surely random noise.
The fourth implication is that the model slavishly follows the radiative forcings. The model results are a 5-run average, so it is not clear how far an individual model run might stray from the fold. But since the five runs’ temperatures average out so close to 0.3 times the forcings, no individual one of them can be very far from the forcings.
Anyhow, that’s what I get out of the exercise. Further inferences, questions, objections, influences and expansions welcomed, politeness roolz, and please, no speculation about motives. Motives don’t matter.
w.
Another conclusion which could be made is that if all the forcings cancel each other out leaving the simple outcome Willis noticed, then it might mean that we don’t really understand what drives climate in the first place, hence all the various forcing parameters are effectively random (does not explain weather) and thus cancel each other out and that the final outcome is simply verification of the model inbuilt assumption of “climate sensitivity”.
Mike Haseler:
At January 17, 2011 at 2:41 pm you say of Willis’ analysis;
“it’s the first time I’ve seen any kind of estimation of the effect of CO2 that actually is based on real world events rather than post-modernist scientific fantasy.”
Oh, really? Then I think you need to see Idso snr.’s work from long ago (published in Climate Research in 1998): 8 completely independent natural experiments to determine climate sensitivity that give a best estimate 0.10 C/W/m^2 which corresponds to a temperature increase of 0.37 Celsius for a doubling of CO2. You can read it at
http://www.warwickhughes.com/papers/Idso_CR_1998.pdf
A summary of the findings is at
http://www.friendsofscience.org/assets/documents/FOS%20Essay/Idso_CO2_induced_Global_Warming.htm
and that URL also has a link to the paper.
Several have attacked Idso’s work but nobody has faulted it.
Richard
Willis Eschenbach says:
I don’t really understand what you are asking. The point is that the climate gradually adjusts to the forcings over time. The transient response is defined as the change in temperature at the time when CO2 has doubled from pre-industrial levels, increasing at a rate of ~1% per year (I believe), which is about double what the actual rate of increase has been. I suggest reading the relevant parts of the IPCC report Chapter 8 that talk about the ECS and the TCR.
I think you are falling into the trap of thinking that because you can fit the data in one way, that is the only way in which the data can be fit. Also, note that when I mean a “lag”, I am not talking about simply offsetting by a certain amount of time. It would be something more like a term where at any time the climate is trying to exponentially-approach radiative equilibrium for the current levels of forcing at that time (rather than instantaneously responding to the current levels of forcing, as your picture assumes).
Brian Buerke says:
No…because the water vapor feedback changes the radiative balance. I.e., the total radiative effect of doubling of CO2 is, in essence, more than just the ~4 W/m^2. (It is a little more complex than this…What happens is that if you instantaneously doubled the CO2 levels, then the radiative imbalance would be about 4 W/m^2…As the temperature rose, this imbalance would decrease but not as fast as the Stefan-Boltzmann Equation would imply because the rise in temperature would cause an increase in water vapor in the atmosphere, which would reduce the effect of this heating up in restoring the radiative balance. So, the radiative balance is never more than 4 W/m^2, but if you could somehow factor out the effect on the radiative imbalance due to the temperature increase while not factoring out the increase in water vapor, it would be larger.)
Willis,
To put it another way, your fit of the GISS Model E would predict that if they hold the forcings constant starting today then the temperature would remain constant. However, we know that these sorts of experiments have been done on the models (although I am not sure about GISS Model E specifically) and the models predict that the temperature continues to climb, albeit at a decreasing rate and eventually leveling off.
So, your simple fit is clearly too simple to emulate this behavior that we know the models do actually exhibit.
10 forcings – “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk” (Attributed to von Neumann by Enrico Fermi).
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Willis,
This is truly a mind-blowing result – so much so that I think you need to do some careful verification work before crafting anything for publication. There is something seriously wrong here – and I don’t necessarily mean in your calculations.
At the very least, your statistical model should be showing heteroscedasticity in the residuals – with an increasing variance towards the later time-frame. Have you tested for this? Or at least eye-balled a graph of the residuals against time?
The GCMs should be generating/calculating a multi-decadal temperature perturbation from each year’s change in forcing. The model form you have adopted only recognises a weighted first year response. Given the overall increase in positive forcing over the timeframe, you should therefore be seeing an increasing separation between the GCM results and your statistical model as time goes on. If you DO see this, then the excellent quality of your match may be suggesting no more than that the “characteristic response” of the temperature response in the GCM is a big -step in the first year followed by a very shallow gradient extending out to the long-time equilibrium condition. You would then have to be suitably cautious about any claims about equilibrium climate sensitivity. If you DON’T see this, then the implications are staggering.
In this science, there are all kinds of tunable parametres that allow one to come up with any result one wants:
– you’ve got your forcing impact in Watts/m2 which is more calculated rather than measured;
– you’ve got your efficacy of forcing factors; like the need to change the volcanic forcing effectiveness as Willis demonstrated because the real climate does not respond the way the theory says it should;
– you’ve got your estimated negative adjustment like Aerosols which are techically three straight lines in GISS Model E; they completely offset all the GHG warming in Model E up to 1970; then they offset 50% of the increase that should have happened since 1970;
– then you have the infamous Temperature C response per forcing Watt/m2 which Willis is also pointing out here. This number has been quoted at everything from 0.1C to 1.5C per Watts/m2 – only a range of 15 times;
– Then one has this mysterious transient response. The energy hides in the ocean and melting ice sheets for a time and then impact starts to increase over time. One can play with this timeline any way one wants. It started out at 20 years in the first IPCC, moved to 30 by the third and the AR4 is really talking about 1000 years. Today’s CO2 will not have its full impact until 3010 AD.
Not too hard to come up with any number from 0.5C per doubling to 8.0C per doubling by just varying these assumptions.
In extremely complex systems like the climate, we have to measure what really happens. Forget the theory, there are a dozen hugely varying assumptions you have to use. They just changed the volcano assumptions because they did not work in the measured real climate. That is what they should be doing.
A thought experiment. Imagine the forcing suddenly went to zero in the last year. Willis’s model’s temperature perturbation would immediately go to zero, but obviously the earth’s (or the GISS model’s) temperature would not respond that quickly, maybe taking decades. What does this tell us? It says the temperature response is not just proportional to the current forcing, but to a weighting of the previous forcing that may be a decay function as you go back several decades.
Regarding:
Carl Chapman:
Since CO2 is going up, but temperatures haven’t gone up for 12 years, there must be a negative forcing cancelling CO2′s forcing.
Timisfree:
There is a fourth possibility: there is no CO2 forcing.
I was being sarcastic to show that the models are junk.
Is it me or does the hindcast model not reflect reality? I see no oceanic cycle whatsoever, some small solar forcing peaking in 1960, but made noticeable only by volcanic aerosols. No ENSO? I don’t see a grasp of (or an attempt really) the climatic system in this model…either really, just a keeling curve. Wonder what happens if you add this to the oceanic model, it would go way over reality. Guess you can’t add the oceanic cycles, or you would have to adjust the CO2 weighting…can’t have that!
The Lazy Teenager makes a good point. It’s essentially one that Willis made originally, but it is worthwhile to point out that it will likely be ignored or missed by anyone reading this or a similar article, which is what the Lazy Teenager did (though perhaps unclearly).
A well-considered and well-motivated model can give results which are matchable by a toy-model built for simplicity with no theoretical motivation or reasoning. After seeing those results, such a simple model can be built, but going in there is no way of knowing this would happen. The fact that such reconstruction is possible does not discredit the original model. It certainly raises the question of whether someone actually did the work that was claimed, but all it actually points out is an interesting cancellation or coincidence.
I use something similar in my work. I deal with a 124-parameter theory (minimal supersymmetry) in particle physics. There is an incomplete part of the theory (how the symmetry is broken) which people to work with different versions. Fortunately for computation, what I consider to be the best-motivated version (that gravity does it and that the breaking does not come from some new unknown realm of physics) predicts that the number reduces to primarily 4 free parameters and some others which are immeasurably close to zero. It doesn’t mean that I just ignore the other 120 or that the version was created just to be easy to handle. It just says they come out in a simple way which someone might guess without having studied the theory, and if it said something different I would be doing something different.
Mike D. said on January 17, 2011 at 1:05 pm:
The sheer size of the programming shows its value, larger is obviously worth more. The amount of computing resources consumed shows its worth in operation, if it takes more that it obviously does more.
This is the wisdom dispensed by Micro$oft. Everyone believed it up to Windoze Vista. Most still do. ☺
Willis – I admire your tenacity.
however I join the other sketics on this one.
I know nothing of modelling the climate.
I have some slight theoretical and practical exposure to econometric modelling.
They don’t do such a bad job over the next few quarters, after that, it’s “hello nurse time”.
But they have no predictive power when the unexpected occurs and being a chaotic system that happens very frequently.
The very idea of forecasting or projecting the future into the long term distance seems to me to be just boys playing with toys and pretending to be scientists.
We not only don’t know what we don’t know but we also don’t know what we can never do.
Do you disagree?
If so, what DO you know that I do not know or do not understand?
Please help.
Dennis Nikols, P. Geol. says:
January 17, 2011 at 8:00 am “I have worked with geophysical interments and geophysicists in mineral exploration for over 40 years. The black box is a standard joke. ”
Likewise. We used to say that the difference between a geophysicist and a […] was that the latter had a […] that worked.
[trimmed. Robt]
To Kadaka: Software bloat leads to morbid fatheadedness, the epidemic social disease of our day and age.
To Dan: Not my intention to speak for Willis, by my impression is that he was tweaking GISS’ nose, not attempting to build a better predictive model. As we all know, the GCMs can’t predict the future with any skill at all. Heck, they can’t post-dict the real past, just the homogenized-spliced-imaginary past. It’s all mental m************ — counting angels on pinheads.
“Jim D says:
January 17, 2011 at 8:10 pm
A thought experiment. Imagine the forcing suddenly went to zero in the last year. Willis’s model’s temperature perturbation would immediately go to zero, but obviously the earth’s (or the GISS model’s) temperature would not respond that quickly, maybe taking decades”
Weeks or months, not decades, or we wouldn’t have any winters on this planet.
Willis Eschenbach says: January 17, 2011 at 4:19 am “Because this is not a graph of the historical temperature. It is a graph of the GISSE climate model hindcast of the historical temperature. ”
Precisely. But if that is supposed to be a good hindcast, GISSE is not a good fit to land temperatures (with their attendant uncertainties).
Is the generation of the positive trend from 1940 to 1970 because the assumptions and numbers take it that way; or is it because the components are constrained to upwards trends, either singly or in aggregate? Seems to this non-specialist that there has to be an advertisement of temperature increase in each public picture, to ram home the message.
Should I still be alive, I’m going to be fascinated to learn how to calibrate proxies for temperature over the present period in which global temperature presents as T = const. It’s almost like Dr Trenberth’s call for reversal of the null hypothesis. Because T = const, does any proxy with equi-spaced response features have to be considered as a valid responder carrying a message?
Willis,
considering deciphering black boxes you might try using the brute force formula finder Eurequa to improve insights.
Mike_D
Thanks – fair enough.
It’s just that people take this long term forecasting so seriously that I sometimes get confused.
I KNOW they can’t do it.
But a little voice in me keeps saying “what if you are wrong?”
“What do they know that I don’t know or can’t understand?”
So I’m even skeptical of myself!
Thanks Mike_D
Maybe the answer to Life, the Universe and Everything really is 42. I guess the answer doesn’t matter if your not sure what the question really was.
Willis Eschenbach-
Thank you for your commentary and analysis. Very well done, except for the background on the chart.
I find that the chart background detracts more from the commentary than it adds to it.
Again, thank you for your most informative post.
kadaka (KD Knoebel) says:
The sheer size of the programming shows its value, larger is obviously worth more.
Do you remember the fad at one time for running part of the model as a screensaver on PCs? I even was tempted myself!
Now it appears, from Willis’ research that this added complexity was really adding nothing meaningful to the model in terms of science as output still equals 0.3 input when all the complexity is averaged.
But boy was that great publicity
There’s a psychological trick used to get people to “buy in” to things. You let them feel that it was partly their work, and they are far far far more likely to accept the result even if their work was pretty meaningless.
You could say that about US elections, where no-one’s vote is individually important but for some strange reason they all have some absurd nostalgia about the “president” even if they didn’t vote for him.
Likewise, I was gullible enough to buy a raingauge yesterday, just because it was made by a company I used to work for … and as I read their useless instructions I quickly remembered why I left them!
So, I don’t think that screensaver program had anything to do with real science. It was just a way of getting a lot of people to buy in to the idea of global warming. Basically those who ran the screensaver were being brainwashed in the best marketing tradition!
I agree with Warren of Minnesota. The shear fact that you are having to treat the model as a black box is surely unacceptable. When trillion dollar decisions, and laws that affect peoples’ fundamental freedoms are coming about as a result of these models, it is absolutely unacceptable that the codes are treated as commercial secrets.
The algorithms used should be published in full, so that they are open to peer review and scrutiny.