MODTRAN

MODTRAN and Climate Sensitivity

Climate Sensitivity is one of the phrases used to indicate how much the temperature should increase for a doubling of CO2 in the atmosphere.

The truth is that no one knows what this value is - but speculations go from negative values up to about 8°C with the presumed most likely value being 3°C per doubling.

There are lots of references and models - you can basically support any value you like. This page tries to find a value using MODTRAN.

Archer's Post

While researching MODTRAN, I found this post at RealClimate by David Archer, professor in the Department of The Geophysical Sciences at the University of Chicago. In it, he criticizes David C. Archibald for a post claiming (archived version) that MODTRAN proves that global warming won't happen. According to Archibald

The projected increase of 40 ppm in atmospheric carbon dioxide to 2030 
is calculated to contribute a global atmospheric temperature increase of 0.04°C

Archer claims that this is because Archibald is using Idso's estimate of 0.4°C for doubling CO2 and that instead, he should have used the IPCC's "best-guess value" of 3°C.

Spoiler - I think they are both wrong.

Obvious Errors

In his post, Archer made the following incorrect statement.

the modtran model of atmospheric infrared radiation [is] an early example of a line-by-line code: No it is not. It uses 1 cm^-1 bins to compute the spectra. The MODTRAN documentation is very clear about this.

I am pretty sure that Archer knows that this is wrong, but it just sloppy to make a comment that is so easy to disprove .. especially when your intent is to attack someone else.

In his 2007 paper, Archibald claims that the current CO2 level is 380 ppm and that it is projected to rise to 420 ppm by 2030, and then implies that those are the values he used with MODTRANS.

In his rebuttal, Archer says

Run the model once with 375 ppm CO2 and another time with 415 ppm, and compare the Iout values in Watts / m2.

Really, at least use the same values !

Archibald says he used MODTRANS - I am not sure how that is different from MODTRAN 3.5. Archer did not comment on this and an internet search found nothing. Therefore, I am simply assuming that they both refer to the same basic application (model).

Archibald's Claim

In his paper, Archibald implies that he used MODTRANS to compute the "emission from the stratosphere to space" for CO2 at 380 ppm and 420 ppm.

The projected 40 ppm increase reduces emission from the stratosphere to space from 279.6 watts/m2 to 279.2 watts/m2.

Using the default MODTRAN 3.5 values and setting CO2 to 380 ppm and 420 ppm, the upward IR heat flux, and related change, are provided in the table.

CO2 ppm	IR heat flux looking down from 70 km W/m2
CO2 ppm	Archibald's	Tropical	US Standard
380	279.6	298.174	267.277
420	279.2	297.672	266.837
delta	0.40	0.50	0.44

Obviously, Archibald's values do not match the heat flux I obtained. Presumably, this is because he did not provided enough information for me to reproduce his experiment. So that I don't repeat the same mistake, these are the input parameters I used.

I used the model defaults
  CH4 (ppm)          1.7
  Trop Ozone (ppb)  28
  Strat Ozone scale  1
  Water Vapor Scale  1
  Freon Scale        1

  Temperature offset 0

  Locality Tropical Atmosphere & 1976 U.S. Standard Atmosphere
  No Clouds or Rain

  Altitude (km) 70  Looking down

To try and obtain his values, I also tried

All the Localities looking down from 70 km and 11 km
All the Localities looking up from 0 km
Setting water vapor to zero - significantly increased the outgoing heat
Setting all gases to zero except water vapor and CO2 - this was the closest when using the U.S. Standard Atmosphere

No match. Some were close, but I was not able to guess Archibald's configuration.

At this point, I have no confidence in Archibald's paper.

Simple Doubling

Archibald used values that are only 40 ppm apart, to obtain more accurate results, I normally want values further apart. Therefore, still using the default values for everything else

CO2 ppm	W/m2
400	297.923
800	294.595

When the 800 ppm surface temperature is increased by 0.76°C, then the output IR is 297.923 W/m2 - the same as it was with 400 ppm. This yields 0.76°C/doubling (no math required).

This is obviously different than the 3°C/doubling that Archer and the IPCC claim is most likely.

In all fairness, these computations do not include any "feedbacks" .. which is fine because the Archer response does not mention them. However, if the water vapor scale increases from 1.0 to 1.1 (and there is no documentation explaining what this value represents), then the 800 ppm temperature offset becomes 1.38°C, a bit higher, but still nowhere near 3°C.

The following analysis assumes the MODTRAN default configuration (detailed above). To return to the original upward IR heat flux after increasing the CO2, the ground temperature must be increased by some value which is entered via Temperature Offset, C. Using the tropical atmosphere and Archibald's CO2 values, the adjustment is 0.11°C which would yield an increase for doubling of 0.76°C.

dy/dx is what is needed
x is either CO2 or log(CO2) - the base does not matter
y is normally surface temperature

since dy/dx = slope
then  dy = slope * dx

0.11 / [ln(420) - ln(380)] = 0.11 / ln(420/380) = 1.099
1.099 * ln(2) = 0.76°C/doubling

0.76 / [ln(800) - ln(400)] = 0.76 / ln(800/400) = 1.096
1.096 * ln(2) = 0.76°C/doubling

Since the 2 slopes are nearly the same, it is obvious that the change in surface temperature with respect to a change in the CO2 mixing ratio is logarithmic.

(Reversing the calculation to get the same slope, the temperature increase would have to be 0.109691.. instead of 0.11.)

Just for fun, let's assume that the change is linear.

0.11 / (420 - 380) = 0.00275
0.00275 * (800 - 400) = 1.1°C for doubling

0.76 / (800 - 400) = 0.0019
0.0019 * (800 - 400) = 0.76°C for doubling

Since these numbers do not match, the relationship is not linear.

Thus, it is clear that the change in temperature with respect to changes in CO2 is logarithmic, not linear.

Since the model clearly indicates that the expected change in temperature for a doubling of CO2 is probably a little less than 1°C, it appears that both Archer and Archibald are wrong.

More Scenarios

Of course, science does not base a result on a single scenario and MODTRAN provides a number of different possibilities. This is just a sampling

CO2 ppm	Scenario Default surface temperature					Units
CO2 ppm	Tropical 299.7 K	US Standard 288.2 K w/ clouds		SubArtic Winter 257.2 K	Midlatitude Summer 294.2 K	Units
400	297.923	267.057	228.027	202.216	289.100	W/m2
800	294.595	264.105	226.206	200.489	286.117	W/m2
800	0.76	0.74	0.51	0.53	0.71	Δ°C to restore

I included one with clouds - US Standard with Altostratus (just marked *clouds* in the table).

This (very small) sample indicates that the true value for doubling CO2 is closer to 0.7°C than it is to 3°C.

But you be the judge.

Additional Data

The data in these tables was collected using the MODTRAN defaults with the noted exceptions. The purpose was to have enough data to make plots and, specifically, to test whether the relationship is logarithmic. You can just copy the data from the tables (actually, highlight and copy the entire table) and paste it into a spreadsheet. After that, plotting is fairly simple.

The data in this table was collected using the US Standard Atmosphere, no clouds or rain, 70 km looking down. delta-T is the change in surface temperature required to return the Upward IR Heat Flux to 267.057 W/m2, the 400 ppm value.

CO2 ppm	300	400	500	600	700	800
W/m2	268.282	267.057	266.115	265.33	264.671	264.105
delta T	-0.3	0	0.24	0.43	0.60	0.74

This data was collected using the US Standard Atmosphere, no clouds or rain, 1 km and 5 km looking down.

CO2 ppm	300	400	500	600	700	800
W/m2 @ 1km	371.148	371.148	370.834	370.834	370.834	370.834
W/m2 @ 5km	313.435	312.713	312.147	311.676	311.268	310.923

In my opinion, the data for looking down from 1km indicates a serious problem with the model. I have written my own line-by-line model and the results look nothing like that. Granted, my model uses only water vapor and CO2 and makes a lot of assumptions, but doubling CO2 has a much larger effect. The change in absorption for doubling is about 4 W/m2. Of course, MODTRAN is doing both absorption and emission, so perhaps that explains it. In addition, the relationship is not perfectly logarithmic - there is an obvious curve in the semi-log plot.

The other three data sets, when plotted in a spreadsheet, indicate that the relationship is almost exactly logarithmic.

This is an area where I need to do further research.

Summary

The MODTRAN model uses a band model to compute the expected spectral values and, as a result, provides lower precision than a true line-by-line method.

I do not know if the MODTRAN results are accurate or not, but they do not support the claims by either David Archer or David C. Archibald.

And obviously, whenever you post data from a model, be sure to include enough information so that others can replicate your work.

Author: Robert Clemenzi