Spencer on Lindzen & Choi

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During the last three months, a paper by Lindzen and Choi (full text, PDF) has been repeatedly mentioned in the climate blogosphere.

Anthony Watts wrote about it July 2009. The key graphs were already announced in June, see Climate sensibilities and sensitivity on The Reference Frame.

This test of intelligence (which of the graphs depicting models doesn’t belong here? The red one – it’s reality) appeared in Climate feedbacks from measured energy flows, before I studied the paper more carefully.

The point of their paper is that in the reality, as measured by ERBE, the amount of outgoing radiation increases if the temperature increases. Lindzen and Choi claimed that all the 11 climate models had the opposite property: the outgoing radiation was shrinking if the Earth were getting warmer.

This conclusion of the models is paradoxical, contradicts the measurements, and Lord Monckton has elegantly promoted this disagreement on Glenn Beck’s show. Unfortunately, I am going to argue that the falsification is not quite correct.

Update: Dick is convinced that I am missing something important and that the genuine response of the energy flows in the tropics to changing temperatures substantially and qualitatively differs from the Stefan-Boltzmann intuition. So please be assured that your humble correspondent may still be wrong about the essence and the paper by Lindzen and Choi may be completely correct. However, let me continue with the previous text.

Criticism of the paper

A week ago, under one of the TRF articles, a reader named Rob claimed that Lindzen and Choi have made a mistake. Rob Dekker claimed that they confused radiative forcing with its effect, i.e. with the increase of the black body temperature.

Because I had previously written a similar observation to Richard, I had to agree with Rob’s point. They have essentially forgotten to subtract the “zero feedback” radiation from the total radiation when calculating the feedback; they have basically confused “f=0” and “f=1”.

Because the nature of the mistake may sound confusing, there is a simple way to clarify what we mean. The key question is what a “zero feedback” situation predicts for the energy flows. Some elementary thermodynamics is helpful to answer this question.

The average Earth’s surface brightness temperature is something like -15 °C: see the daily UAH data. Using the Stefan-Boltzmann constant and the “sigma T^4” law for the black body radiation, it is not hard to see that the radiation at this temperature, 258 Kelvin, is 251.22 W/m^2. Similarly, for 259 Kelvin, it is 255.14. For 1 °C of a temperature increase, we obtained the increase of the outgoing radiation by 4 W/m^2.

If the outgoing radiation depended on the temperature with this slope, 4 W/(m^2.K), then the feedback would be zero. You see that there is a lot of room for positive and negative feedbacks here. If the feedback were negative, the outgoing radiation would increase by more than 4 W/m^2 per 1 °C of warming. If the feedback were positive, the figure would be less than 4 W/m^2.

But it’s important that this figure remains positive.

Lindzen and Choi claim that the models predict a negative value of this slope. That would be pretty dramatic because the models would not only fail to be quantitatively realistic: they would be unstable and predict a qualitatively wrong behavior.