A. “However, in their article, L&C explicitly write “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4″ from which one gets, by a trivial summation, F = -DFlux/DT.”

In this case a “trivial summation” is not correct. If you read carefully, Lindzen starts the chapter by “When considering the LW and SW fluxes separately,….”. The whole notion refers to comparing the SW and LW radiations separately. In this case Lindzen’s notion is correct, but for a combined SW + LW comparison a different adjustment has to be made. This makes Lindzen’s definitions rational. But once again: This just my guess. Lindzen is not specific enough in his paper.

B. The other reason why you are threading on a slightly dangerous path with your dT = -Q/F notion is due to the question of causality. Lindzen clearly and correctly states the case of a feedback system (forget about his somewhat unusual definition of “feedback” by leaving the Stefan-Boltzmann out). If you define F = -DFlux/DT, then you should be specific over the direction of causality. In a feedback system both of these equations cannot be valid simultaneously. A feedback system is not linear system and thus you cannot make arithmetic operations freely. F has to be considered to be a transfer function. Now, depending on which of the two equations you pick to be correct F is either the feedback factor (with of without Stefan-Boltzmann) or the system transfer function. It is important to note that these two are different animals. (My understanding is that Lindzen picked the latter to be correct and for this reason your dT = -Q/F is incorrect in this context.)

I think this is Lindzen’s main contribution to the topic. Lindzen understands causality the way it should be understood.

But once again: This does not prove his mathematics is correct. For that we need more information.

]]>To Rob De Vos,

In case you didn’t realise, we are actually being quite sceptic right here in this post. Perhaps it’s hard to realize that, because we’re actually being sceptic towards a sceptic.

]]>To “Distant Observer”,

Thanks for your comments.

I’m well aware that writing “dT = -Q/F” would be a crucial error, IF L&C did use the common definition where, as you wrote, “feedback” is indeed all temperature dependent mechanisms except Stefan-Boltzmann radiation, i.e. F = –(DFlux/DT – 4). However, in their article, L&C explicitly write “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4” from which one gets, by a trivial summation, F = -DFlux/DT. From that, one gets to the dT = -Q/F. So while I agree with you that this equation would be a crucial error in the usual definition of what’s a feedback, it is correct IF one uses L&C’s definitions “FLW = –DOLR/DT + 4 and FSW = –DSWR/D? – 4” instead of the usual one. I’m sorry if I wasn’t clear enough about it earler.

Not having seen the codes, I cannot be a 100 % sure what L&C do when comparing their results with models – but I must say it seems to me, they’re not so sure themselves either. That’s the conclusion I draw from example from this part of the text:

“Indeed, Fig. 3c suggests that models should have a range of sensitivities extending from about 1.5°C to infinite sensitivity (rather than 5°C as commonly asserted), given the presence of spurious positive feedback. However, response time increases with increasing sensitivity [Lindzen and Giannitsis, 1998], and models were probably not run sufficiently long to realize their full sensitivity.”

So, from their funny way of analyzing AMIP model runs, they conclude that some models have an infinite sensitivity, and “probably” those others just have not run their models for long enough. Now let’s just think with some common sense, which is more likely, (1) the modelers just don’t know their models (or haven’t realised they haven’t run them long enough), or (2)this “infinite sensitivity” is a flaw in their analysis? You decide. Add to the common sense thinking the fact that if any model really had an infinite sensitivity, then “response time increases with increasing sensitivity” does not hold any more. Instead, as a model with infinite sensitivity would have the outward radiation flux decrease when temperature increases, you cannot even define a “response time” because the temperature would increase (or decrease) exponentially after being initiated.

]]>AJ, I think you have made a crucial error when you write dT = -Q/F.

I think Lindzen calls “feedback” all temperature dependent mechanism except Stefan-Boltzmann radiation. This co’ordidate transform sure is somewhat unusual, but I am sure he has his reasons. This becomes natural when one considers that one of his main goals is to evaluate the validity of feedback factors calcuted by the climate models. Please note that he compares the SW and LW radiations separately against models. All the models always have the 4 W/(m^2K) factor included and for this reason he must include it also in his data.

Now for the sum SW + LW this of course needs to be compensated, but Lindzen is not that specific. The paper is an abridged version.

But since Lindzen does not explicitly show the comparison method, we do not know for sure.

I would not get hooked on this point.

We all would like to see slightly more specific information over Lindzen’s mathematics.

]]>I mean, the use of AMIP results stuck out like two left feet to *me*, and I barely know anything about climate modeling.

It certainly did, thank you. 🙂

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