Watts Up With That?

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.

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