The IPCC defines radiative forcing at the tropopause. However, nowhere do they provide a diagram showing energy balances above the tropopause and below the tropopause – something that seems like one of the first things to do. Instead, they show the Kiehl and Trenberth cartoon which treats the atmosphere as a whole without distinguishing balances above and below the layer said to be critical to radiative forcing calculations Kiehl and Trenberth 1997 online here. (Kiehl and Trenberth 1997 is a very good and interesting article and deservedly is widely cited and relied on.) Willis Eschenbach has attempted to make these estimates and has produced a very interesting calculation and diagram, doing exactly this. His calculation also sheds some interesting light on the IPCC/Houghton explanation of the enhanced greenhouse effect as being due to higher effective radiation from the troposphere.
First here is the IPCC AR4 diagram (see FAQ and chapter 1) based on Kiehl and Trenberth. A similar diagram was used in TAR. This version varies from Kiehl and Trenberth by a few wm-2 here and there, but nothing material. As you see, there is no breakout of absorption above and below the tropopause.
FAQ 1.1, Figure 1. Estimate of the Earths annual and global mean energy balance. Over the long term, the amount of incoming solar radiation absorbed by the Earth and atmosphere is balanced by the Earth and atmosphere releasing the same amount of outgoing longwave radiation. About half of the incoming solar radiation is absorbed by the Earths surface. This energy is transferred to the atmosphere by warming the air in contact with the surface (thermals), by evapotranspiration and by longwave radiation that is absorbed by clouds and greenhouse gases. The atmosphere in turn radiates longwave energy back to Earth as well as out to space. Source: Kiehl and Trenberth (1997
Next here is Willis’ corresponding diagram first posted here distinguishing between the troposphere and the stratosphere, breaking out these energy balances (assumptions to be discussed below.)
Willis observes of this diagram:
1) The majority of the radiation emitted to space (147 w/m2 out of 237 w/m2) comes from the lower stratosphere, and not from the troposphere (50 w/m2) or the surface (40 w/m2).
2) The predicted temperature of the lower stratosphere (147 w/m2 and -48°C [226K] ) agrees well with the actual temperature of the lower stratosphere. This is the “cold, high” emission you [Steve] referred to in your head article.
3) All layers (surface, stratosphere, troposphere) are balanced in that they emit what they absorb. The atmospheric layers are balanced in that they emit the same amount both up and down.
4) The emission from the troposphere is at about 0°C (321 w/m2 = ~1°C). This makes sense to me, although I’m not sure I could explain why. It also puts the emission in the lower troposphere where we’d expect it to be.
6) The “temperature sensitivity” is highly dependent on how much of the increased downwelling radiation is turned into evapotranspiration/convection. If 3/4 of the increase comes back out as sensible/latent heat, it takes a whole lot more radiation to raise the global temperature than if only say 1/4 of the increase comes back as sensible/latent heat.
A few comments of my own on this. It is my understanding that, in the Pacific Warm Pool and hot tropical areas that, in a sense, are “heat engines” for the planet, incremental energy is nearly all used for evaporation and that it is hard to raise SST. So it’s not unreasonable to think that this is a very important effect in the tropics at least.
Secondly, let’s use this diagram to re-consider Houghton’s explanation of how enhanced AGW works, previously discussed here. Houghton said:
Absorbing gases in the atmosphere absorb some of the radiation emitted by the Earths surface and in turn emit radiation to space. Radiation is emitted out to space by these gases from levels somewhere near the top of the atmosphere – typically between 5 and 10 k high (See Fig. 2.3) … Let us imagine that the amount of CO2 in the atmosphere suddenly doubled, everything else remaining the same. What would happen to the numbers in the radiation budget? The solar radiation budget would not be affected. The greater amount of carbon dioxide in the atmosphere means that the thermal radiation emitted from it will originate on average from a higher and colder level than before (Fig 2.3).
Below is my re-plotting of Houghtons Figure 2.3:
As Willis observes below, if one takes a weighted average level for radiation-to-space, the average is in the troposphere. However substantially more (147 wm-2) radiation-to-space originates from the stratosphere as from the troposphere and surface combined (50 wm-2 + 40 wm-2). As we previously noted [see this image], in the stratosphere, temperatures are increasing with altitude. If Willis’ estimates are correct, then a larger proportion of radiation-to-space originates in a region with increasing temperatures with altitude (stratosphere) than in a region with decreasing temperatures with altitude (troposphere). This would make Houghton’s heuristic completely unusable. Note that Houghton’s heuristic was endorsed in TAR as follows (see ref in prior note):
Note that it is essential for the greenhouse effect that the temperature of the lower atmosphere is not constant (isothermal) but decreases with height.
Willis’ spreadsheet for calculating these results is here. When you open the spreadsheet, you’ll probably receive a diagnostic that there is a circular reference. As Willis states in his notes, you have to set the Options for iterative calculation. [I got wrongfooted on this my first try and thought there was a problem.] Here are Willis’ spreadsheet notes:
1 The model is currently coupled so that some of the change in downward radiation is offset by a change in sensible + latent heat loss. This coupling is adjusted by cell E4 (orange). The zero point (in total downwelling radiation at the surface) is set by cell E5 (yellow)
2 Stratospheric and tropospheric absorption are currently coupled, so that a change in tropospheric absorption (cell G25) causes a change in stratospheric absorption.
3 If an impossible value is entered, the model will go off the rails, and I know of no way to get it back on except to close it and re-open it.
4 For the model to work, set the “Calculation” (Mac menu item “Excel/Preferences/Calculation”, PC menu item “Tools/Options/Calculation) to “Iterative” with a limit of 100.
5 Only cells which are colored yellow or orange should be changed. Messing with the others is instant disaster.
6 Arrows /\ | indicate upwelling and downwelling energy flows
7 The calculation of the changes (∆) are made from a copied and pasted “comparison scenario”, located below the model and the “∆” change calculatations, starting at cell A71. If you wish to set up a scenario for comparison, adjust the variables, then do a copy and a “Paste Special/Values Only” in the comparison scenario area.
Again, I’m not saying that Willis’ calculations disproves Houghton’s argument. I’m just feeling our way through the data right now and trying to understand the provenance of various data. It’s quite possible that Willis has got something wrong in his calculations. However, at a minimum, Willis’ diagram showing the energy balances above and below the tropopause seems like a mandatory diagram for people who rely on radiative forcing at the tropopause as a mechanism for analyzing climate change and the apparent absence of such a diagram from peer reviewed literature seems astonishing. If Willis’ diagram is wrong in some respect, it would be instructive to see a Trenberth version and then see exactly how the differences arose.
Kiehl and Trenberth 1997 online here).