Dr. Kiehl's Paradox

Guest Post by Willis Eschenbach

Back in 2007, in a paper published in GRL entitled “Twentieth century climate model response and climate sensitivity” Jeffrey Kiehl noted a curious paradox. All of the various different climate models operated by different groups were able to do a reasonable job of emulating the historical surface temperature record. In fact, much is made of this agreement by people like the IPCC. They claim it shows that the models are valid, physical based representations of reality.

Figure 1. Kiehl results, comparing climate sensitivity (ECS) and total forcing. 

The paradox is that the models all report greatly varying climate sensitivities but they all give approximately the same answer … what’s up with that? Here’s how Kiehl described it in his paper:

[4] One curious aspect of this result is that it is also well known [Houghton et al., 2001] that the same models that agree in simulating the anomaly in surface air temperature differ significantly in their predicted climate sensitivity. The cited range in climate sensitivity from a wide collection of models is usually 1.5 to 4.5C for a doubling of CO2, where most global climate models used for climate change studies vary by at least a factor of two in equilibrium sensitivity.

[5] The question is: if climate models differ by a factor of 2 to 3 in their climate sensitivity, how can they all simulate the global temperature record with a reasonable degree of accuracy?

How can that be? The models have widely varying sensitivities … but they all are able to replicate the historical temperatures? How is that possible?

Not to give away the answer, but here’s the answer that Kiehl gives (emphasis mine):

It is found that the total anthropogenic forcing for a wide range of climate models differs by a factor of two and that the total forcing is inversely correlated to climate sensitivity.

This kinda makes sense, because if the total forcing is larger, you’ll have to shrink it more (smaller sensitivity) to end up with a temperature result that fits the historical record. However, Kiehl was not quite correct.

My own research in June of this year, reported in the post Climate Sensitivity Deconstructed,  has shown that the critical factor is not the total forcing as Kiehl hypothesized. What I found was that the climate sensitivity of the models is emulated very accurately by a simple trend ratio—the trend of the forcing divided by the trend of the model output.

Figure 2. Lambda compared to the trend ratio. Red shows transient climate sensitivity (TCR) of four individual models plus one 19-model average. Dark blue shows the equilibrium climate sensitivity (ECS) of the same models. Light blue are the results of the forcing datasets applied to actual historical temperature datasets.

Note that Kiehl’s misidentification of the cause of the variations is understandable. First, the output of the models are all fairly similar to the historical temperature. This allowed Kiehl to ignore the model output, which simplifies the question, but it increases the inaccuracy. Second, the total forcing is an anomaly which starts at zero at the start of the historical reconstruction. As a result, the total forcing is somewhat proportional to the trend of the forcing. Again, however, this increases the inaccuracy. But as a first cut at solving the paradox, as well as being the first person to write about it, I give high marks to Dr. Kiehl.

Now, I probably shouldn’t have been surprised by the fact that the sensitivity as calculated by the models is nothing more than the trend ratio. After all, the canonical equation of the prevailing climate paradigm is that forcing is directly related to temperature by the climate sensitivity (lambda). In particular, they say:

Change In Temperature (∆T) = Climate Sensitivity (lambda) times Change In Forcing (∆F), or in short,

∆T = lambda ∆F

But of course, that implies that

lambda = ∆T / ∆F

And the right hand term, on average, is nothing but the ratio of the trends.

So we see that once we’ve decided what forcing dataset the model will use, and decided what historical dataset the output is supposed to match, at that point the climate sensitivity is baked in. We don’t even need the model to calculate it. It will be the trend ratio—the trend of the historical temperature dataset divided by the trend of the forcing dataset. It has to be, by definition.

This completely explains why, after years of better and better computer models, the models are able to hindcast the past in more detail and complexity … but they still don’t agree any better about the climate sensitivity.

The reason is that the climate sensitivity has nothing to do with the models, and everything to do with the trends of the inputs to the models (forcings) and outputs of the models (emulations of historical temperatures).

So to summarize, as Dr. Kiehl suspected, the variations in the climate sensitivity as reported by the models are due entirely to the differences in the trends of the forcings used by the various models as compared to the trends of their outputs.

Given all of that, I actually laughed out loud when I was perusing the latest United Nations Inter-Governmental Panel on Climate Change’s farrago of science, non-science, anti-science, and pseudo-science called the Fifth Assessment Report (AR5). Bear in mind that as the name implies, this is from a panel of governments, not a panel of scientists:

The model spread in equilibrium climate sensitivity ranges from 2.1°C to 4.7°C and is very similar to the assessment in the AR4. There is very high confidence that the primary factor contributing to the spread in equilibrium climate sensitivity continues to be the cloud feedback. This applies to both the modern climate and the last glacial maximum.

I laughed because crying is too depressing … they truly, truly don’t understand what they are doing. How can they have “very high confidence” (95%) that the cause is “cloud feedback”, when they admit they don’t even understand the effects of the clouds? Here’s what they say about the observations of clouds and their effects, much less the models of those observations:

• Substantial ambiguity and therefore low confidence remains in the observations of global-scale cloud variability and trends. {2.5.7}

• There is low confidence in an observed global-scale trend in drought or dryness (lack of rainfall), due to lack of direct observations, methodological uncertainties and choice and geographical inconsistencies in the trends. {2.6.2}

• There is low confidence that any reported long-term (centennial) changes in tropical cyclone characteristics are robust, after accounting for past changes in observing capabilities. {2.6.3}

I’ll tell you, I have “very low” confidence in their analysis of the confidence levels throughout the documents …

But in any case, no, dear Inter-Governmental folks, the spread in model sensitivity is not due to the admittedly poorly modeled effects of the clouds. In fact it has nothing to do with any of the inner workings of the models. Climate sensitivity is a function of the choice of forcings and desired output (historical temperature dataset), and not a lot else.

Given that level of lack of understanding on the part of the Inter-Governments, it’s gonna be a long uphill fight … but I got nothing better to do.

w.

PS—me, I think the whole concept of “climate sensitivity” is meaningless in the context of a naturally thermoregulated system such as the climate. In such a system, an increase in one area is counteracted by a decrease in another area or time frame.  See my posts It’s Not About Feedback and Emergent Climate Phenomena for a discussion of these issues.