(pdR/pdTs_GFDL)*(pdTs_GFDL/pdTs_model)

If you measure Planck feedback by raising the temperature 1 K in all grid cells, then lapse rate feedback corrects for the fact that rising absolute humidity reduces the lapse rate – meaning that 1 K of surface warming turns out to be more than 1 K in the upper troposphere. This seems straightforward to me. So I don’t expect the temperature feedback plot to include lapse rate feedback. However, those bright red areas at 300 mb (220? K) would have dW/dT of only 0.24 W/m2/K/100mb if they behaved like a blackbody.

]]>I have also been puzzling over Figure 2 in Soden & Held 2006. It does seem to show how different regions affect the response in that redder areas produce a larger change in emission to space for a given temperature change. But I don’t understand how to quantitatively interpret it since it must account for both emission at one height and absorption above that height. S&H 2000 does not look helpful after a quick glance.

On the bottom of page 2 they say: “We define feedbacks in terms of the change in global mean surface temperature (Ts) and the change in radiative flux at the top of the atmosphere (R).” So the Planck feedback is not for a uniform 1 K change.

Top of page 3 they say “The temperature feedback can be split further as … where 0 assumes that the temperature change is uniform throughout the troposphere and L (i.e., lapse rate feedback) is the modification due to nonuniformity of the temperature change”. Which seem to contradict the earlier statement. But I think this just refers to using the same T change at all altitudes (zero lapse rate feedback) rather than at all latitudes.

On page 4 under results they say “Intermodel differences in lambda_0 arise from different spatial patterns of warming; models with greater high-latitude warming, where the temperature is colder, have smaller values of lambda_0.” So they are computing the response per K for each location then multiplying by the T change at that location for a 1 K average T change. And using a model to get the distribution of T change.

So the larger T change in colder areas weights those areas more strongly and lowers the feedback. And they keep the stratosphere temperature unchanged, so that lowers the feedback in proportion to how much emission is from the stratosphere (a few percent).

]]>http://journals.ametsoc.org/doi/full/10.1175/JCLI3799.1

“Thus, we perturb [+1 K] only the tropospheric state in the feedback computation, but we examine the response of TOA fluxes, rather than the tropopause fluxes, to these perturbations. It can be shown that this is equivalent to assuming that the net dynamical heating of the stratosphere is unchanged, and that we can ignore the response of stratospheric temperatures to the change in tropospheric temperature, water, and clouds. In our experience, it is preferable to make these simplifications rather than attempt to define changes in GCM fluxes at the tropopause; the latter are sensitive to arbitrariness in the definition of the tropopause and to the movement of the tropopause as climate changes.”

To compute Kx, we first calculate the control top-of-the-atmosphere (TOA) radiative fluxes using 3-hourly values of temperature, water vapor, cloud properties, and surface albedo from a control simulation of the GFDL GCM. For each level k, the temperature is increased by 1 K and the resulting change in TOA fluxes determines(∂R/∂Tk). Similarly, (∂R/∂wk)is computed by perturbing the water vapor in each layer by holding relative humidity constant and increasing the temperature used to compute the saturation-mixing ratio by 1 K. For (∂R/∂α), a 1% decrease in surface albedo is used to compute the TOA flux perturbation. Figure 2 displays the zonal-mean, annual-mean distribution of Kx for temperature, water vapor, and surface albedo. The reader is referred to Held and Soden (2000) for further discussion of this method and interpretation of the spatial structure of the feedback kernels.

If I’m lucky, have have pasted Figure 2 below. Note the units are W/m2/K/100 mb or W/m2/K/tenth of the atmosphere.

A BB at 255 K model might be the brightest red -0.38 W/m2/K/100 mbar everywhere?

Or it might be -0.56 W/m2/K/100 mbar at the surface and drop to about -0.20 W/m2/K at the tropopause (210 K).

I don’t understand Figure 2 and S&H 2000 is behind a paywall.

]]>Again, I’m not quite sure what you’re getting at here. To me, the so-called ‘Planck feedback’ refers to the inherent negative feedback that exists because as anything warms it radiates more, i.e. its rate of cooling increases. The so-called ‘Planck response’ relates to the warming that would restore balance with ‘no-feedback’ and is something that would manifest itself at the TOA. For 1C of surface warming, the ‘Planck response’ is estimated to be around 3.3 W/m^2. All it is though is linear warming according the lapse rate, which itself is quantified by the ratio of emitted surface radiation to outgoing TOA radiation. That ratio is roughly 1.6 (385/239 = 1.61), and +1C from a baseline of 287K equals about +5.3 W/m^2 of surface radiation; and 5.3/1.6 = 3.3.

]]>The object here is not to reduce things to a simple model but to understand why the Planck feedback parameter is so small. Simple models are one way of trying to understand that. Saying “that’s what the models say” is not an explanation. A clear figure created from model output and showing what happens would be great, if that exists. I expect Frank would also be happy with that if someone could point us towards such a figure.

I think you are correct that the stratospheric cooling due to CO2 is probably not relevant, unlike what I supposed.

]]>If the S&H model calculation didn’t include CO2, which seems likely, you’re barking up the wrong tree anyway.

]]>Thanks. So that is about 4% from the stratosphere, which would not be enough if the stratospheric temperature stayed constant. But the temperature change is 2-3 times the tropospheric change and in the opposite direction. So that would seem to give a Planck response of 12-16%. About right if my mental math is right.

]]>If you use MODTRAN looking up from the tropopause, defined as where the temperature starts to increase, emission from the stratosphere is less than 10W/m². The decrease in the satellite lower stratosphere temperature anomaly from 1979 to the present is about 1.5°

]]>I’ve got an idea of what might be going on. The Planck feedback is for a uniform 1 K increase in temperature. But I think that applies only in the troposphere. If 15% of emission to space is from the stratosphere and stratospheric temperature does not change, then you get the calculated Planck feedback, which is 85% of that expected at 255 K. But increased CO2 causes stratospheric temperature to go down, since that is a purely radiative effect it may be included in the model calculation of Planck feedback. Then it would take less than 15% from the stratosphere to produce the smaller feedback.

There does some to be a fair bit emitted from the stratosphere. See figure 2 at https://scienceofdoom.com/2013/01/08/visualizing-atmospheric-radiation-part-three-average-height-of-emission/.

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