Feed-Back on Climate Sensitivity by Lindzen and Spencer

Spencer comments on the recent article by Lindzen and Choi about climate feed-backs computed from ERBE data. Let me add some comments: A simple mathematical climate model takes the form

dT/dt = Q + A T - B T,

where T is temperature, e.g. global ocean surface temperature, t is time, Q is radiative heat forcing, A T is feed-back heat forcing from e.g. water vapour and clouds and B T is feed-back into outgoing LW radiation, with B a positive constant and A positive for positive feed-back.

ERBE data gives information on time-variations of T and outgoing radiation B T, indicating that B is in the range 4-6 W/m2K. The time-variation of Q + A T thus is given by measured data, which may allow determination the coefficient A under some assumption on Q as an unknown source. This would allow computation of climate sensitivity

S = Q/C with C = B - A

with Q = 3.7 W/m2K the known radiative forcing from doubling of CO2.

Lindzen claims to obtain from measurement that S is less than 1 degree Celcius, while IPCC from climate models gets S in the range 2 - 5 degrees Celcius, which is the scientific climate debate in a nutshell. I don't see how to retrace Lindzen's estimate of S in the data, which is also the concern of Spencer.

It seems that Lindzen from outgoing radiation computes A to be negative thus indicating negative feedback. But outgoing radiation is modeled by B T and not A T and in principle B - A can be small corresponding to large climate sensitivity, even if B = 4 - 6 as measured. It seems that true climate sensitivity is still to be determined, although Lindzen in his lecture Deconstructing Global Warming makes the rather bold statement: the very issue of global warming is wrong, since climate sensitivity is about 0.5 degrees Celcius upon doubling of CO2. I have written to Lindzen to get some clarification and am expecting some feed-back.

Nevertheless, Lindzen observed that current climate models driven by surface temperature predict much less outgoing LW radiation than measured by ERBE, which is an indication that current climate models overestimate S, by underestimating C.

More precisly, it seems that Lindzen claims that current climate models predict that less radiation escapes to space as the surface temperature rises. In the model this would seem to mean that B, or B - A is negative, which Lindzen interpretes as cloud cover thickening with increasing temperature and compares with measurements indicating instead a thinning cloud cover. Lindzen calls this thermostatic behavior the Iris-effect. But can it really be true that current climate models are so completely off track that they indicate less outgoing radiation under surface temperature increase, which seems exponentially unstable?

As a more domestic interpretation of the above model we may think of heating a room with a window with a curtain through a heat source Q, where B T represents the heat going out through the window and A T represents shielding from the curtain, with B the heat transfer coefficient of the window and A a shielding coefficient of the curtain. With positive feed-back A is positive, which means that increasing temperature comes with increasing curtain cover, obviously a case of concern. Measurements are made of T and B T under an unknown heat source Q, and what is sought is the temperature rise T under a given heat source Q, which directly relates to the shielding coefficient A through T = Q/C with C = B - A. The response of the system to changes in T is thus measured, under an unknown heat source, and what is sought is the response of the system under a known heat source. Depending on the data the requested feedback coefficient A can be more or less well determined. The time-dynamics is determined by the exponential damping factor exp(- C t) and slow damping indicates small C and thus large positive feedback, while quick damping indicates small feedback.

The above equation is a very simple climate model, and Lindzen uses an even simpler model in his estimation of climate sensitivity. It cannot be reasonable to let the fate of humanity depend on such simple models. It must be possible to do better...I thus agree with the statements of Spencer:

• In any event, I don’t think the question of exactly what feedbacks are exhibited by the ERBE satellite is anywhere close to being settled.
• I predict that Lindzen and Choi will eventually be challenged by other researchers who will do their own analysis of the ERBE data ... and then publish conclusions that are quite divergent from the authors’ conclusions.