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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Hi Willis,
I question whether MODTRAN is simply buggy. Perhaps I don’t understand what it is supposed to be telling me, but I entered 990000ppm CO2 and it told me the ground T was exactly the same as with the actual ppm.
Did you change the “ground T offset” to account for the higher temperature that’s sure to come with the increase in CO2? Perhaps the expected higher temperature makes for more line spreading and hence more absorption.
This probably just confuses the issue even more, but IPCC AR4 shows a range of values for the forcing associated with a doubling of CO2.
The last page of the supplementary info for AR4 WG1 Chap 8 has a table of the apparent forcing for doubling of CO2 for the various models. More specifically, it is “Table S8.1 Parameter values used in a simple climate model (MAGICC) to approximately reproduce results from the AOGCM multi-model dataset at PCMDI.”
http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter8-supp-material.pdf
The estimated values range from 3.09 w m-2 K-1 for MIROC3.2(medres) up to 4.06 for GISS-ER and GISS-EH.
Ramaswamy et al. talks about LLGHG. Did they just assume methane and nitrous oxide would stay on the same trend and not mention it?
Ron House says:
August 18, 2011 at 6:37 pm
As I said, what I am measuring is the instantaneous forcing change. This is the change that occurs before the temperature rise … so indeed ground T will be the same.
w.
Ric Werme says:
August 18, 2011 at 6:43 pm
No, I’m looking at the instantaneous forcing change before any adjustment by the system. If there were no cloud throttle, the eventual effect of the forcing change would be that the surface temperature would rise until the initial radiation condition (amount of radiation Iout) is re-established.
But that’s not what I’m asking about, and there is a cloud throttle.
I’m looking at the instantaneous forcing “Fi”, the immediate change in absorption due to the higher levels of GHGs. I’m comparing it to the Fi from the IPCC, and the Fi from Hansen et al.
w.
Typo: There should be a “be” after “would” in:
“So their value for instantaneous forcing would larger, …”
Interesting.
I will need to reflect on this and perhaps have a little go on MODTRANS
Willis, setting the sensor altitude to 16 km or a top of troposphere value gives higher forcing and removes the slightly opposite stratospheric effect. Top of troposphere forcing is more appropriate to surface temperature as it is connected via the lapse rate. At other latitudes the troposphere is lower than in the tropics down to maybe 12 km.
Charlie A says:
August 18, 2011 at 6:44 pm
The existence of the MAGICC model probably deserves its own post, Charlie. Thanks for reminding me about it.
The MAGICC is a general purpose model that can “mimic” the output of the various models used by the IPCC. It does this by adjusting only four parameters—forcing per doubling (Fa), climate sensitivity, ocean thermal diffusivity, and land/ocean warming ratio. It determines the exact settings for a given model by comparing the input and the output of the model.
This “magic” model doesn’t get a lot of airtime in the IPCC reports … no good advertising that a linear model can replicate the entire model space of all of the IPCC models by just twisting four dials …
However, that’s just what the MAGICC uses to replicate the models, so it’s not quite correct to say the IPCC AR4 shows a range of values for doubling of CO2. The models are showing the range.
The IPCC AR4 (as far as I know, it’s huge) uses a canonical value of 3.7 W/m2. This may be related to the note in the referenced table, which says:
although the quotation in the head post suggests another source for the 3.7 W/m2 figure.
w.
Why bother with MODTRANS?
http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.doc.html
“Note This is an old model (1990’s), illustrative but not necessarily in strict quantitative agreement with current state of the art line-by-line models. ”
Try:
http://geoflop.uchicago.edu/forecast/docs/Projects/full_spectrum.html
The data for the AR5 scenarios is here: http://www.pik-potsdam.de/~mmalte/rcps/
“RCP 8.5” shows CO2 will double – from pre-industrial – in 2045 or so.
Pixel-counting of Potsdam’s “Global CO2 Radiative Forcing” graph shows about 3W/m^2 extra from the doubling. On page 60 of this: http://pik-potsdam.de/~mmalte/rcps/data/RCPs_FINAL_RELEASE_31May2010_OVERVIEW.pdf
Closer, but still more than modtran seems to show.
John W says:
Because I don’t understand how to get the result I want from your site. It automatically readjusts the surface temperature to re-establish the radiation balance … and I can’t find a way to turn that off. Is there one, and I’m missing it?
w.
According to “NCAR”
http://geoflop.uchicago.edu/forecast/docs/Projects/full_spectrum.html
Leaving all other values at default:
CO2 mixing ratio 375 ppm = Equilibrium near-surface air temperature is 16.0 degC (289.1 K)
CO2 mixing ratio 750 ppm = Equilibrium near-surface air temperature is 18.5 degC (291.7 K)
Sensitivity to 2XCO2 = 2.5 C from 375 to 750 @ur momisugly default conditions.
CO2 mixing ratio 200 ppm = Equilibrium near-surface air temperature is 13.9 degC (287.0 K)
CO2 mixing ratio 400 ppm = Equilibrium near-surface air temperature is 16.2 degC (289.3 K)
Sensitivity to 2XCO2 = 2.3 C from 200 to 400 @ur momisugly default conditions.
The more I think about it the more I agree with “the heretic”. The notion that the climate response to a forcing could be described by such a simple relationship as the form T=LQ seems counter intuitive. More research is needed, please send grant $.
RE Willis:
” Is there one, and I’m missing it?”
Well, if there is I’m missing it too.
I see what you’re trying to get at now.
Hmmm, I’ll keep looking.
Willis Eschenbach
“We calculate climate change and efficacy using measured
or estimated changes of forcing agents between 1880
and 2000, or, in some cases, the estimated changes between
1850 and 2000.”
What is the total change in forcing from 1880 – 2000 and the estimated change between 1850 and 2000 in w/m2?
MODTRAN is not an LBL (line by line), its a band model. It was when I used it, and still is today
http://en.wikipedia.org/wiki/Atmospheric_radiative_transfer_codes
I think a fairly rigorous treatment of this topic is in this series of blog posts on the scienceofdoom.com blog. Note the following is the twelfth in the series, the links to the others int the series are at the bottom in the conclusions section. Perhaps there is clue in here somewhere.
http://scienceofdoom.com/2011/04/30/understanding-atmospheric-radiation-and-the-%e2%80%9cgreenhouse%e2%80%9d-effect-%e2%80%93-part-twelve-curve-of-growth/
Willis, your first problem is that you are computing the data looking down from 70km.
Forcing should be computed looking up from the surface.
In the image above, the CO2 absorption near 666 cm-1 is actually the CO2 emission from the -53C tropopause. This is a common error in interpreting that particular image. To be clear, at those frequencies CO2 is totally opaque. More than 95% of the energy from the surface is absorbed in the first kilometer. What is measured from space is emitted from much higher in the atmosphere. The spike in the middle of the CO2 band is emitted from the stratopause, at 47 km. (Get it, the cold part is from 11 km and the warm spike is from 47 km.)
Willis, Modtran is band model. Myrhe 1998 uses LBL models.
here is an example lecture using modtran
http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBYQFjAA&url=http%3A%2F%2Fmensch.org%2F5223%2FRadForce_print.pdf&ei=wONNTq_nIo_RiALEuIF8&usg=AFQjCNFykz3SdwWLjD6wnStaJJmiA_dYHw&sig2=y11ZMUvjaj_Sk5E6P4aedg
http://www.barrettbellamyclimate.com/page24.htm
http://scienceofdoom.com/2010/02/05/co2-an-insignificant-trace-gas-part-four/
MODTRAN is a medium resolution spectroscopic simulator that calculates the IR spectrum at a resolution of about 0.5 to 5 cm-1, depending on how this is specified in the program. It is derived from the HITRAN database that contains the high resolution spectral data. I belive that Hansen’s original ‘forcing constants’ were derived from HITRAN. The main issue with MODTRAN is the approximation of the molecular linewidths. Each molecular line has a pressure and temperature dependent Lorentzian linewidth and all of the lines overlap. I did some line by line HITRAN claculations and I used 0.01 cm-1 resolution. I also used 100 m resolution on the altitude.
However, regardless of the differences in the total flux there are two important results that emerge from considerations of the linewidth .
First, the upward and downward LWIR fluxes are not equivalent. The LWIR emission to space does not magically emerge at the top of the atmosphere. It originates from the line narrowing with altitude, mainly from the rotational (lower wave number) water band. The upward LWIR emission from the wings of the lines in the middle troposphere are not reabsorbed at higher altitudes and escapes to space. The downward emission from line center at higher altitudes is reabsorbed and does not reach the surface. This negates the whole radiative forcing flux argument.
In addition, the over 90% of the downward LWIR flux reaching the surface originates in the first 2 km layer of the atmosphere. Similarly, over 90% of the molecular emission to space originates from above the first 2 km layer. The troposphere is really two independent thermal reserviors. The lower 2 km reservoir has a heat capacity of ~2MJ.K-1.m-2 (for a 2 km x 1 square meter air column). The upper reservoir has a heat capacity of ~6 MJ.K-1.m-2 (for a nominal 9 km x 1 square meter column). The both reservoirs are heated during the day by convection from the surface (and transport). The upper reservoir radiates to space all the time. The lower reservior stores the heat at night and cools quite slowly. The net upward LWIR emission at 2 km is ~50 W.m-2. This gives an approximate cooling rate of 0.1 K.hr-1 for the lower reservior. The night time downward LWIR emission at the surface balances the upward blackbody emission from the surface so that the net upward surface emission is between about 50 and 100 W.m-2 depending on humidity. The downward LWIR emission from any low cloud will close this LWIR window completely.
Full summer sun flux at the surface is ~25 MJ.m-2.day-1. Very roughly, about 20% goes to feed the LWIR transmission window and the rest ends up as moist convection. Once the dynamic properties of the surface energy transfer are understood, the whole CO2 induce global warming argument disappears. The observed increase of 100 ppm in atmospheric CO2 concentration has produced an increase of 0.15 MJ.m-2.day-1 in downward LWIR flux at the surface over 200 years. This has to be added to the total flux balance. Solar flux can from zero to 25 MJ.m-2.day-1. Net surface LWIR emission is from zero to ~ 5 MJ.m-2.day-1. These numbers are always changing each day with far larger fluctuations than the 0.17 MJ.m-2.day-1.
There is no such thing as climate equilibrium on any time scale and the equlibrium flux equations used in radiative forcing are a mathematical abstraction that has no basis in physical reality. One of the radiative forcing assumptions clearly stated by Manabe and Wetherald in their 1967 paper is that the surface heat capacity is assumed to be zero. The ‘equlibrium surface temperature’ calculated by the climate radiative forcing models is not even a measurable climate variable. The CO2 doubling argument is a problem that exists only in climate warming theoology. How does a doubling of the atmospheric CO2 concentration change the number of photonic angels that may reside on a climate pin?
More details at
http://hidethedecline.eu/pages/posts/what-surface-temperature-is-your-model-really-predicting-190.php
http://hidethedecline.eu/pages/posts/greenhouse-effect-vs.-gravity—guest-post-by-roy-clark-201.php
Brian W says:
August 18, 2011 at 9:00 pm
Not sure who you’re quoting there, but it’s not me …
w.
steven mosher says:
August 18, 2011 at 9:10 pm
Thank for the correction, Mosh. As a user of the program, do you understand why the absorption numbers it gives (1.7 to 3.2 W/m2 per doubling) are so much smaller than the corresponding Hansen (4.5 W/m2 per doubling) or the IPCC (4.1 W/m2 w/o stratospheric adjustment) numbers?
All the best,
w.
Willis Eschenbach
I’m quoting Hansen’s paper page 2 (9). Try reading your reference.
Ok here’s another question. By how much has the solar constant changed in the last 100 years?
I think the reason is that Modtran is not a climate modelling program – it just gives the absorption of a prescribed gas mixture. When you double CO2, warming evaporates more water. That’s the basis of the positive feedback. Modtran does not make that sort of calculation.