Guest Post by Willis Eschenbach (@WEschenbach on X, my personal blog is here.)
Well, for my usual lack of reasons, I got to thinking about updating the subject of my three previous posts relating the input and the output of climate models. To my surprise, the most recent of these was a shocking fifteen years ago … tempus fuggit, as they say …
In that post, I discussed the idea of a “black box” analysis. This is where you have both the input and the output of some unknown process, and the challenge is to figure out what is happening functionally inside the black box. Here was my illustration showing the CCSM3 climate model as a black box, with the input being the “forcing” and the output representing the global annual surface temperature.
And what is “forcing” when it’s at home? Well, per the IPCC, it’s short for ‘radiative forcing’, which they define as
The change in the net, downward minus upward, radiative flux (expressed in W m−2) at the tropopause or top of atmosphere due to a change in an (external) driver of climate change, such as a change in the concentration of carbon dioxide (CO2), the concentration of volcanic aerosols or the output of the Sun.
Note that the result of a black box analysis may be totally different from what is actually happening inside the black box. The only requirement is that it takes the same input and produces the same output.
In the post linked to above, I showed that you can almost perfectly emulate the model output that represents the global annual surface temperature … and not only that, you can do it with a bozo-simple, one-line equation with only two tuned parameters. All that the equation does is to resize and lag the input forcing, and like some magic trick, it gives you the output temperature.
Now, there has been an intermittent series of climate model comparisons under the umbrella of something called the Climate Model Intercomparison Program. At that time, they were on the third comparison, called “CMIP3”. Since we’re now up to CMIP6, I thought I should take another look to see what changes have occurred.
I’m going to present the equation, and for those of you who are allergic to math, here is the trigger warning—avert your eyes …
With the trigger warning out of the way, here is the equation that rescales and lags the forcing to emulate the output temperature:
========================== Math Averse, skip this section ==========================
T(n+1) = T(n)+λ ∆F(n+1) * (1- exp( -1 / τ )) + ΔT(n) exp( -1 / τ )
OK, now lets render this equation in English. It looks complex, but it’s not.
T(n) is pronounced “T sub n”. It is the temperature “T” at time “n”. So T sub n plus one, written as T(n+1), is the temperature during the following time period. In this case we’re using years, so it would be the next year’s temperature.
F is the forcing, in watts per square metre. This is the total of all of the forcings under consideration. The same time convention is followed, so F(n) means the forcing “F” in time period “n”.
Delta, or “∆”, means “the change in”. So ∆T(n) is the change in temperature since the previous period, or T(n) minus the previous temperature T(n-1). ∆F(n), correspondingly, is the change in forcing since the previous time period F(n-1).
Lambda, or “λ”, is the scaling factor.
Tau, or “τ”, is the lag time constant. The time constant establishes the amount of the lag in the response of the system to forcing. And finally, “exp(-1/τ)” means the number 2.71828 to the power of -1/τ.
========================== End of the section to skip ==========================
So in English, this means that the temperature next year, or T(n+1), is equal to the temperature this year T(n), plus the immediate temperature increase due to the change in forcing, λ F(n+1) (1-exp( -1 / τ )), plus the lag term, ΔT(n) exp( -1 / τ ), which is the temperature increase from the previous forcing. This lag term is necessary because the effects of the changes in forcing are not instantaneous.
Now, regarding the choice of the computer model and the data. I used the GISS-E2.1 model for a simple reason. It’s one of the few where the modelers published the forcings that they used. Here are the forcing data and the model temperature output. The temperature output at that source (KNMI) shows five individual model runs and, as is the custom, I’ve used the average of the runs. There’s a discussion of the use of the GISS-E2.1 model in the study entitled “CMIP6 Historical Simulations (1850–2014) With GISS-E2.1“. The E2.1 model is described as “an updated and more skillful version of the GISS-E2 model used in CMIP5”.
The forcings that they used are divided into three groups: greenhouse gases (except water vapor), anthropogenic aerosols, and “natural” forcings. Here are those forcings, from the link above:
So without further ado, here is the result of my black box analysis.
As you can see, the simple one-line two-parameter equation above emulates the model results to a ludicrous degree of accuracy and precision. Even the smallest changes are captured by the black box emulation.
So … what can we conclude from this?
My conclusion is that despite the many hundreds of thousands of lines of code in the GISS E2.1 model, in reality, nothing makes a difference in the outcome except for the claimed forcings.
Modulation of the North Atlantic Oscillation; changes in the frequency and strength of the La Nina Pump; variations in the Gulf Stream; alterations in cloud type, cover, and time of emergence (except those due to aerosols); differences in where the forcing is occurring on the planetary surface; increasing or decreasing water vapor; variations in cloud albedo; the oft-predicted weakening of the Atlantic Meridional Overturning Circulation … none of that makes any difference in the model.
We know that because if any of them did make a difference, we couldn’t reproduce the output so exactly using just the input forcings.
And of course, the corollary of that conclusion is that the current generation and type of climate models is completely unfit for the purposes to which they are put. If their output is just a simple scaled and lagged version of their input, they cannot forecast the climate in the year 2100. They cannot tell us if a given drought is made more or less likely by “climate change”. In short, they are of little use for any serious purpose.
Here’s the thing. Climate models can only do what the modelers tell them to do. In this case, all of the models are running under the central paradigm of mainstream climate science, which says that changes in temperature are a linear function of changes in forcing. Expressed mathematically, that is
∆T = λ ∆F
So of course the models’ output is a scaled, lagged version of their input. It’s what the models have been told to tell us … so that’s what they tell us.
So that’s Part 1 of my look at the GISS E2.1 model. When the madness next strikes me, I’ll write up Part 2, which will be about the success of the model in hindcasting the past … or the lack thereof.
Late night here, a foggy evening after an overcast day. Must be climate change …
My very best to everyone,
w.
I know, I know, you’ve heard it before: When you comment, please QUOTE the exact words you are discussing. I choose my words carefully and can defend them. I can’t defend what you might think they mean.
