Tuesday, 9 February 2016

Expressing sensitivity and feedback with dimensional values obfuscates the underlying requirements, Bode prescribes gain

A new comment on the post "Economist watch: Cruz denies climate change"
Author: co2isnotevil
Comment:and then ...

The 3.3 W/m^2 of feedback power comes from COE.  If 1 W/m^2 of forcing raises the average surface temperature of 287.5K up to 288.3 (0.8C rise), the average surface emissions must increase by 4.3 W/m^2 since in LTE, the surface must be receiving as much power as it's emitting.  If 1 W/m^2 comes from the initial forcing, the remaining 3.3 must come from the feedback.  You can redefine this in terms of an equivalent temperature change per W/m^2 since the Stefan-Boltzmann LAW trivially relates EQUIVALENT temperature to TOTAL power, but this doesn't change the required behavior in the power domain.

Expressing sensitivity and feedback with dimensional values obfuscates the underlying requirements,  Bode prescribes gain (where climate science calls the incremental gain the sensitivity) as ratios of quantities with common dimensions (volts per volt, W per W, W/m^2 per W/m^2), sensitivity as the ratios of a proportional change in gain per change in some parameter and feedback as the fraction of the output added to the input before being applied to the gain element, where the input and output have the same dimensions.

In Schlesinger's paper, he converts between temperature and power with an unspecified function and its inverse, which in fact is just the Stefan-Boltzmann LAW.

I should note that in Hansen's original feedback paper (which Schlesinger 'corrected'), Hansen had the units of feedback and gain properly ascribed.  He assumed unit open loop gain and mislabeled the closed look gain and feedback fraction, which Schlesinger 'corrected' by adding more errors.

The climate system can never experience run away feedback unless there's an implicit infinite source of power driving the modeled gain element.  Otherwise, the maximum gain is limited to only 2 W^2 of output emissions per W/m^2 of input forcing, which itself is less than the IPCC lower bound of 2.2 W/m^2 per W/m^2 of forcing (0.4C per W/m^2).

Venus is not a case of runaway GHG, but one of runaway clouds, where its the clouds that are in direct equilibrium with the Sun.,  The surface temperature follows as the lapse rate of its dense CO2 atmosphere dictates relative to the equilibrium temperature of the clouds.  Why do you think gas giants get hotter as you get deeper into their atmosphere?  Venus is just a much smaller scale version of a gas giant whose CO2 atmosphere weighs about as much as Earth's H2O oceans.

Comment:You said,
  "Water vapour is positive, clouds are probably positive, "

Water can only be considered by its end to end effect, which includes latent heat, GHG effects and clouds.  Weather is a heat engine whose source of heat is the surface.  The end to end effect of water is best illustrated by a Hurricane which leaves a path of cold water in its wake.    As the maximally efficient version of the heat engine driving weather, its clear that the end to end effect of water feedback is negative.  The Second Law has something to say about this as well, which is that a heat engine can not warm its source of heat.

I'm also well aware of the consensus terminology regarding sensitivity and feedback and the mis application of terms is part of the problem since consequences are presumed based on the  meanings of the terms per Bode.

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