Guest Post by Willis Eschenbach

There’s an online calculator called MODTRAN that calculates the absorption of longwave (“greenhouse”) radiation for various greenhouse gases (“GHGs”), and shows their resulting effect. It does this on a “line-by-line” basis, meaning it examines each interval of the longwave spectrum for each greenhouse gas at each altitude, and calculates the resulting absorption by each species given the concentration and the partial pressure of that species. Figure 1 shows the calculation results for the default values of CO2, ozone, and methane.

Figure 1. MODTRAN results. The jagged red line at the top right shows what is not absorbed by the atmosphere. Colored lines in the background are theoretical “no-absorption” curves for various temperatures. The big “bite” out of the middle section of the jagged red line is mainly water vapor absorption, although it overlaps with the CO2 absorption bands in parts of it. The graph at the lower right shows the pressure, temperature, and the concentration of H20, Ozone, CO2, and CH4 at various elevations. The number “Iout” is the total energy that is not absorbed, so as absorption increases, that number will decrease.

That all seems straightforward, it looks the same as in heaps of textbooks … so where’s the MODTRAN oddity?

The oddity arose as a result of my wanting to know more about the doubling of CO2, and the 3.7 watts per square metre of increased absorption that IPCC claims the aforesaid doubling of CO2 is supposed to cause. To find out what MODTRAN says, I put in 750 ppm of CO2 in the top cell, and I had MODTRAN recalculate the Iout. To my surprise, I found that it was 284.672 … which when subtracted from the starting Iout shown above of 287.844 gives us only 3.2 watts per square metre increased absorption (forcing change) for a doubling of CO2.

I had left the “No Clouds or Rain” choice selected, thinking that the biggest change in CO2 would be in clear-sky conditions. So I figured “well, perhaps clouds or rain increase the absorption when CO2 doubles” … but investigating various cloud results showed that was not the case, they all gave smaller absorption changes. My original intuition was correct, clear-sky conditions give the biggest change in absorption for a doubling of CO2.

So I thought, “well, perhaps I’m looking at the wrong region of the Earth”. The other latitude bands available in MODTRAN are Midlatitude Summer and Winter, and Subarctic Summer and Winter. I took nominal CO2 values to represent the CO2 concentration in 1850 (285 ppmv), default (375 ppmv), doubling of 1850 value (570 ppmv) and doubling of the present value (750 ppmv). I figured that would give me two doublings, and let me see if the increases were linear with the logarithm of the number of doublings. I used MODTRAN to calculate the absorption change in each latitude band. Figure 2 shows those results, with the X axis being the number of doublings, and the Y-axis showing the increase in longwave absorption.

Figure 2. MODTRAN and IPCC values for the increase in forcing due to increasing CO2. The forcing change in each region per doubling of CO2 in watts per square metre is shown after the name in the legend, followed by “T=” and the surface temperature.

First thing I noticed is that the lines are all straight. So MODTRAN does indeed show a linear relationship between logarithm of the CO2 increase and the calculated increase in absorption. So no surprise there.

What was a surprise is that none of the other latitude bands had larger changes in absorption than the tropics. I’d thought that since the IPCC says the global average change from doubling CO2 is 3.7 W/m2, that because the tropics were at 3.2 W/m2, somewhere else the absorption must be above 3.7 W/m2 to make the average correct. But that’s not the case. They’re all smaller.

I also thought that the difference in absorption might be due to the different surface temperatures … but Midlatitude Winter and Subarctic Summer have about the same calculated absorption, yet their surface temperatures are about 15 degrees apart.

Note that what I have shown, the change in absorption, is also called the “instantaneous” forcing, abbreviated Fi. There are various other forcings one can measure. Hansen discusses them here (PDF), and gives a value of 4.52 W/m2 for the instantaneous forcing from a doubling of CO2 according to his climate model (Table 1, p. 7). Presumably his model does a line-by-line calculation similar to MODTRAN to figure out the absorption changes.

The IPCC, on the other hand, says:

The simple formulae for RF [radiative forcing] of the LLGHG [long-lived greenhouse gases] quoted in Ramaswamy et al. (2001) are still valid. These formulae are based on global RF calculations where clouds, stratospheric adjustment and solar absorption are included, and give an RF of +3.7 W m–2 for a doubling in the CO2 mixing ratio. SOURCE: IPCC AR4 WG1 (PDF) page 140

So it appears the IPCC result is not based on a line by line calculation …

And that’s the MODTRAN oddity. Here’s the question:

1. Why does the MODTRAN calculated line-by-line change in absorption range from a low of 1.7 W/m2 to a high of 3.2 W/m2, while Hansen is saying the answer is really 4.5 W/m2 and the IPCC uses 3.7 W/m2?

Since according to MODTRAN (and logic) clouds reduce the effect of a doubling of CO2, and the IPCC (and presumably Hansen) are using all-sky conditions, that makes the IPCC/Hansen figures even farther from the MODTRAN figures.

Please note that (per Hansen) the instantaneous forcing Fi is greater than the adjusted forcing Fa by about 0.4 W/m2. The IPCC is saying that the 3.7 W/m2 is the adjusted forcing Fa, the forcing after the stratosphere adjusts to the change. So their value for instantaneous forcing would be larger, removing the stratospheric adjustment would put it at about 4.1 W/m2. So the IPCC is closer to Hansen’s value for the instantaneous forcing … but it means they’re further from the MODTRAN calculations.

I don’t know what I’m missing here, and I don’t understand these results, so any assistance gladly accepted.

w.

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