Model Climate Sensitivity Calculated Directly From Model Results

Guest Post by Willis Eschenbach

[UPDATE: Steven Mosher pointed out that I have calculated the transient climate response (TCR) rather than the equilibrium climate sensitivity (ECS). For the last half century, the ECS has been about 1.3 times the TCR (see my comment below for the derivation of this value). I have changed the values in the text, with strikeouts indicating the changes, and updated the graphic. My thanks to Steven for the heads up. Additionally, several people pointed out a math error, which I’ve also corrected, and which led to the results being about 20% lower than they should have been. Kudos to them as well for their attention to the details.]

In a couple of previous posts, Zero Point Three Times the Forcing and Life is Like a Black Box of Chocolates, I’ve shown that regarding global temperature projections, two of the climate models used by the IPCC (the CCSM3 and GISS models) are functionally equivalent to the same simple equation, with slightly different parameters. The kind of analysis I did treats the climate model as a “black box”, where all we know are the inputs (forcings) and the outputs (global mean surface temperatures), and we try to infer what the black box is doing. “Functionally equivalent” in this context means that the contents of the black box representing the model could be replaced by an equation which gives the same results as the climate model itself. In other words, they perform the same function (converting forcings to temperatures) in a different way but they get the same answers, so they are functionally equivalent.

The equation I used has only two parameters. One is the time constant “tau”, which allows for the fact that the world heats and cools slowly rather than instantaneously. The other parameter is the climate sensitivity itself, lambda.

However, although I’ve shown that two of the climate models are functionally equivalent to the same simple equation, until now I’ve not been able to show that is true of the climate models in general. I stumbled across the data necessary to do that while researching the recent Otto et al paper, “Energy budget constraints on climate response”, available here (registration required). Anthony has a discussion of the Otto paper here,  and I’ll return to some curious findings about the Otto paper in a future post.

Figure 1. A figure from Forster 2013 showing the forcings and the resulting global mean surface air temperatures from nineteen climate models used by the IPCC. ORIGINAL CAPTION. The globally averaged surface temperature change since preindustrial times (top) and computed net forcing (bottom). Thin lines are individual model results averaged over their available ensemble members and thick lines represent the multi-model mean. The historical-nonGHG scenario is computed as a residual and approximates the role of aerosols (see Section 2).

In the Otto paper they say they got their forcings from the 2013 paper Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models by Forster et al. (CMIP5 is the latest Coupled Model Intercomparison Project.) Figure 1 shows the Forster 2013 representation of the historical forcings used by the nineteen models studied in Forster 2013, along with the models’ hindcast temperatures. which at least notionally resemble the historical global temperature record.

Ah, sez I when I saw that graph, just what I’ve been looking for to complete my analysis of the models.

So I digitized the data, because trying to get the results from someone’s scientific paper is a long and troublesome process, and may not be successful for valid reasons. The digitization these days can be amazingly accurate if you take your time. Figure 2 shows a screen shot of part of the process:

Figure 2. Digitizing the Forster data from their graphic. The red dots are placed by hand, and they are the annual values. As you can see, the process is more accurate than the width of the line … see the upper part of Figure 1 for the actual line width. I use “GraphClick” software on my Mac, assuredly there is a PC equivalent.

Once I had the data, it was a simple process to determine the coefficients of the equation. Figure 3 shows the result:

Figure 3. The blue line shows the average hindcast temperature from 19 models in the  the Forster data. The red line is the result of running the equation shown in the graph, using the Forster average forcing as the input.

As you can see, there is an excellent fit between the results of the simple equation and the average temperature hindcast by the nineteen models. The results of this analysis are very similar to my results from the individual models, CCSM3 and GISS. For CCSM3, the time constant was 3.1 years, with a sensitivity of 1.2 2.0°C per doubling. The GISS model gave a time constant of 2.6 years, with the same sensitivity, 1.2 2.0°C per doubling. So the model average results show about the same lag (2.6 to 3.1 years), and the sensitivities are in the same range (1.2 2.0°C/doubling vs 1.6 2.4°C/doubling) as the results for the individual models. I note that these low climate sensitivities are similar to the results of the Otto study, which as I said above I’ll discuss in a subsequent post.

So what can we conclude from all of this?

1. The models themselves show a  lower climate sensitivity (1.2 2.0°C to 1.6 2.4°C per doubling of CO2) than the canonical values given by the IPCC (2°C to 4.5°C/doubling).

2. The time constant tau, representing the lag time in the models, is fairly short, on the order of three years or so.

3. Despite the models’ unbelievable complexity, with hundreds of thousands of lines of code, the global temperature outputs of the models are functionally equivalent to a simple lagged linear transformation of the inputs.

4. This analysis does NOT include the heat which is going into the ocean. In part this is because we only have information for the last 50 years or so, so anything earlier would just be a guess. More importantly, the amount of energy going into the ocean has averaged only about 0.25 W/m2 over the last fifty years. It is fairly constant on a decadal basis, slowly rising from zero in 1950 to about half a watt/m2 today. So leaving it out makes little practical difference, and putting it in would require us to make up data for the pre-1950 period. Finally, the analysis does very, very well without it …

5. These results are the sensitivity of the models with respect to their own outputs, not the sensitivity of the real earth. It is their internal sensitivity.

Does this mean the models are useless? No. But it does indicate that they are pretty worthless for calculating the global average temperature. Since all the millions of calculations that they are doing are functionally equivalent to a simple lagged linear transformation of the inputs, it is very difficult to believe that they will ever show any skill in either hindcasting or forecasting the global climate.

Finally, let me reiterate that I think that this current climate paradigm, that the global temperature is a linear function of the forcings and they are related by the climate sensitivity, is completely incorrect. See my posts It’s Not About Feedback and Emergent Climate Phenomena for a discussion of this issue.

Regards to everyone, more to come,

w.

DATA AND CALCULATIONS: The digitized Forster data and calculations are available here as an Excel spreadsheet.