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## Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Eight

I thought some data provided in Grant Petty’s excellent book would be valuable as it helps explain some important points about the role of CO2 in the atmosphere.

Just recently I was kindly given access to the HITRAN database by Dr. Laurence S. Rothman but I’ve spent a bit too much time in the last few days trying to get MATLAB to read it (still a novice at MATLAB). I do plan to provide a followup article with some calculations of my own on the HITRAN data. Who knows how long that will take.

HITRAN is an acronym for high-resolution transmission molecular absorption database. It is a treasure trove of spectroscopic data.

First, here’s a couple of extracts from A First Course in Atmospheric Radiation by Grant Petty. (I briefly reviewed this book in Find Stuff Out and Book Reviews):

From "A First Course in Atmospheric Radiation", Grant Petty (2006)

What is “zenith transmittance”?

It is the proportion of radiation that is transmitted (not absorbed or scattered) through the atmosphere from the surface to the top of atmosphere. It doesn’t include any re-radiation by the atmosphere – an important element of atmospheric radiation (see, for example, Part Three).

What is “zenith transmittance of CO2”?

The above effect when only CO2 is taken into account.

This graph is therefore calculated not measured. The only way to measure it would be to take out all the water vapor while the satellite was taking the measurement, which is tricky. It would also be important to stop the atmosphere re-radiating which is even more challenging.

Of course, the calculations are based on the measured parameters of CO2.

Now, the value of this graph is in demonstrating that for much of the CO2 absorption band (e.g. around 600 cm-1 and 750 cm-1) the transmission through the entire atmosphere is not zero and not 1. Therefore, more CO2 will have an effect on the transmittance of the atmosphere.

Here’s the value through a 1m path around the better known peak absorption of CO2 at wavenumbers around 667cm-1 = wavelengths around 15μm:

From Grant Petty (2006)

Fascinating stuff. As you can see 95% of radiation at 15μm is absorbed in just 1 meter of atmosphere at the surface of the earth (1000 mb).

Amazing, considering that CO2 is only 370ppm or thereabouts.

You can see the effect of what is called “pressure broadening” of the individual lines with the 1000mb (surface pressure) vs the 100mb (about 16km altitude) value.

Many people write about the strong absorption of CO2 at 667 cm-1 / 15μm without commenting on the absorption at 600 cm-1 or 750 cm-1.

The less strong absorption around the “wings” of the band is the reason for this graph below of the wavelength dependent impact of a doubling of CO2 (from pre-industrial levels) on the “radiative forcing”:

Longwave radiative forcing from increases in various "greenhouse" gases

From Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the IPCC AR4, W.D. Collins et al, Journal of Geophysical Research (2006). Note that the vertical axis units are incorrect.

### Early comments on CO2 in the HITRAN database

There are almost 315,000 individual absorption lines for CO2 recorded in the database. The database has 2.7M absorption lines in total for 39 molecules.

Between 665 – 669 cm-1 there are over 2,000 lines.

Between 647 – 687 cm-1 there are over 16,000 lines.

Between 500 – 800 cm-1 (12.5 μm – 20μm) there are almost 63,000 lines.

Over 248,000 lines for CO2 are above 800 cm-1 , i.e., between 0-12.5 μm.

The main reference paper for HITRAN 2008 (see below) says:

The present atmospheric version of CDSD (Carbon Dioxide Spectroscopic Databank) consists of 419,610 lines .. covering a wavenumber range of 5–12784 cm-1.

– so I’m not sure whether not all of them made it into the HITRAN database, or whether I have missed something important.

Now that I’ve read the database into some Matlab arrays I will have a tinker around and see if I can come up with the same kind of calculations as people like Grant Petty.

If I can’t, I will immediately announce that climate science has made a huge mistake, write up my results and become the next internet-celebrated debunker of atmospheric physics.

Or, I’ll try and figure out why I got a different result from all the people who know so much more than me..

Other articles in the series:

Part One – a bit of a re-introduction to the subject.

Part Two – introducing a simple model, with molecules pH2O and pCO2 to demonstrate some basic effects in the atmosphere. This part – absorption only.

Part Three – the simple model extended to emission and absorption, showing what a difference an emitting atmosphere makes. Also very easy to see that the “IPCC logarithmic graph” is not at odds with the Beer-Lambert law.

Part Four – the effect of changing lapse rates (atmospheric temperature profile) and of overlapping the pH2O and pCO2 bands. Why surface radiation is not a mirror image of top of atmosphere radiation.

Part Five – a bit of a wrap up so far as well as an explanation of how the stratospheric temperature profile can affect “saturation”

Part Six – The Equations – the equations of radiative transfer including the plane parallel assumption and it’s nothing to do with blackbodies

Part Seven – changing the shape of the pCO2 band to see how it affects “saturation” – the wings of the band pick up the slack, in a manner of speaking

Part Eight – interesting actual absorption values of CO2 in the atmosphere from Grant Petty’s book

Part Nine – calculations of CO2 transmittance vs wavelength in the atmosphere using the 300,000 absorption lines from the HITRAN database

Part Ten – spectral measurements of radiation from the surface looking up, and from 20km up looking down, in a variety of locations, along with explanations of the characteristics

Part Eleven – Heating Rates – the heating and cooling effect of different “greenhouse” gases at different heights in the atmosphere

Part Twelve – The Curve of Growth – how absorptance increases as path length (or mass of molecules in the path) increases, and how much effect is from the “far wings” of the individual CO2 lines compared with the weaker CO2 lines

And Also –

Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.

### References

The reference describing the HITRAN database:

The HITRAN 2008 molecular spectroscopic database, L.S. Rothman et al, Journal of Quantitative Spectroscopy & Radiative Transfer 110 (2009) 533–572

### 21 Responses

1. While checking out your matlab skills, could I impose on you to see if octave will also work? Octave is supposed to be the open source, free, alternative to the somewhat pricey (for my home budget) matlab. Anyhow, I’ve also downloaded the HITRAN set and its Java codes. Haven’t taken the time away to actually get the Java working yet.

Still, the size of the database, as you describe, is impressive, and scary. Some things only look complex, but if you look at them differently, you can make a lot of the apparent complexity go away. In the case of the guts of radiative transfer, no such luck. The molecules do what they want, and if you want to pay attention to the details, it takes forever (i.e., the hundreds of thousands of lines for just CO2, add an equivalent number for H2O, and large numbers for O3, CH4, …)

I’ll also suggest that anybody interested in radiative transfer, but who isn’t already moderately expert in such things, get hold of Grant Petty’s A first course in atmospheric radiation (get it from sundog publishing — cheaper than Amazon or other routes). It looks like the most readable such book around.

2. on March 8, 2011 at 5:28 am | Reply DeWitt Payne

I hope you have a multi-core fast 64 bit CPU with as much RAM as you can cram into the motherboard and the 64 bit version of MATLAB. A solid state drive would probably help too. To calculate Petty’s Figure 9.12 at SpectralCalc, you can only do a range of 50 cm-1 for each calculation. The output file sizes for no instrument resolution function are greater that 20 MB each.

3. on March 8, 2011 at 5:47 am | Reply DeWitt Payne

This is the sort of thing you get:

4. on March 8, 2011 at 5:50 am | Reply intrepid_wanders

Also, I am curious as to 1/r^2 in this and many radiation theories. Transmittance (Inversion of Absorbance) does not indicate that non-transmitted energy is ‘reflected’ back. It requires a resonance (wings if you will). But the “wings” have to re-enforce the original signal for it to be of any notice, unless it is just a blanket, but the concentrations are not thick enough to warm anyone. HITRAN is not the answer of it all.

N2 and O2 are the only molecules of substance to “blanket” the LWR, and we know from the desert climates, this is not so.

So, the logical conclusion is water vapor is the “blanket”. I have listened to CO2 is “well mixed” for some time, so it should be “well mixed” in the desert.

Model something (ie, predict) and we shall determine the effects versus the theoretical causations. So done.

5. DeWitt Payne:

I like your graph (reproduced here):

• on March 8, 2011 at 5:52 pm | Reply DeWitt Payne

\$25/mo, less (per month) for longer subscriptions. You may still need something extra to handle the large data files, though. Excel tends to have problems. Maybe if they ever come out with a 64 bit version of Office that actually works…

It’s not worth it to me to write my own line-by-line program. It would be nice, though, if SpectralCalc would get around to implementing water vapor continuum absorption.

You also can’t do more than 6 molecules at a time for atmospheric paths.

The line display at the top of the graph is optional. I turned it off for the 750-800 cm-1 plot.

• It will be handy data to compare with my results.

I just got my first rough and ready “slab” model up and running – with the wrong results.
Right shape of graph, but wrong values. Tau=0.04 max at around 667cm-1 through 10m of air at stp.

Maybe got the wrong number of CO2 molecules per unit volume, or mixed up units..

Never works the first time.

6. In my last comment I said I was getting the wrong results in my first attempt – I had forgotten to multiply by path length. Not the first to make this rookie mistake, as some regular readers will understand..

So here is the first MATLAB line by line production. It is for 1m of atmosphere at 296K temperature and (surface) atmospheric pressure.

It looks the same as Grant Petty’s result in the article, which brings much joy.

In the next article I will clean up the code – it’s a bit thrown together at the moment – and provide some comparisons of different effects.

This was done with a spectral resolution of 0.001 cm-1 between 660 & 671 cm-1 and with 4534 lines contributing.

I neglected the isotopes of CO2 (which are also included in the database) because “standard” CO2 is 98.4% of the population.

This run takes 100 seconds, and probably could be quicker.

• on March 9, 2011 at 3:33 pm | Reply DeWitt Payne

Here’s the equivalent plot from SpectralCalc. You didn’t say what CO2 concentration you used. I used 380 ppmv.

I can send you the text file output for comparison if you want. It’s only 48 KB.

• I used 360 ppmv.
The text file would be great – please send to scienceofdoom – you know what goes here – gmail.com.

7. The attached publication has some information about the agreement between observed and calculated gas spectra. Discrepancies of 10-20% are seen. Figure 7 shows that peak shape can be fit perfectly by an optimum set of parameters (but doesn’t show how well we can predict peak shape under different conditions.)

Click to access Mihalcea%20AppPhysB1998.pdf

8. In earlier posts SOD has shown that radiative forcing from 2X CO2 comes mostly from the “wings” of the 15 um band. https://scienceofdoom.com/2010/11/01/theory-and-experiment-atmospheric-radiation/

If I think about a single strong isolated line, could radiative forcing originate from the “wings” of the line when the center is saturated? (Is this related to “self-absorption?) When line-by-line calculations are performed, is there one calculation for each line, or many calculations across the profile of each line?

• on March 10, 2011 at 5:48 pm | Reply DeWitt Payne

Line-by-line calculations are done by wavelength or frequency. At each step, the line table is searched for lines that might have significant absorption at that point. The contributions from each line are then summed and the absorptivity calculated. One of the larger uncertainties is from the far wings of intense lines. The Lorenz profile for pressure broadening is only an approximation and may not work all that well far from the line peak.

Self absorption is saturation to all intents and purposes. It means that the optical depth of the source is thick and emission isn’t linear with concentration any more.

That paper was published in 1998 and references the 1996 version of the HITRAN database. The current version of HITRAN is 2008. The problems in the paper you linked to have probably been addressed by now.

• DeWitt: Thanks for you reply. Could I (respectfully) clarify what meant when you said: “The contributions from each line are then summed and the absorptivity calculated.” If I look at the figure in SOD’s reply of 3/9 6:30 above, I see an isolated line at about 661.2 cm-1 that has a half width of about 0.2 cm-1. Are you telling me that line-by-line methods consider 10-100 wavelengths across this one peak (say from 660.5 to 661.9 cm-1) and calculate the absorbance and emission at each of these wavelengths as they pass through the atmosphere and as the peak narrows with decreasing pressure and temperature? Then the same thing is done with each of the overlapping lines at 667-670 cm-1 that aren’t resolved, but which have the parameters in the database needed to define each peak?

How does anyone get a good feeling for how well the whole process works? I saw in the paper I linked that a Voigt profile can fit the experimental data for a single line at a single pressure and temperature extremely well (until, as you point out, you get to the far wings which are only important for strong peaks). How well do the best-fit parameters from one pressure and temperature perform at a different temperature and pressure?

Are there any experiments that integrate energy transmitted through a range of wavelengths (say the 660-672 cm-1 range shown above) at a variety of temperature and pressure combinations? I suppose this is unnecessary; if I trust the ability of parameters and theory to reproduce the behavior of any one line, I should trust any ensemble of 30 or 30,000 lines. However, dealing with a range of wavelengths at once gives one an easy way to estimate the total error/uncertainty in the process.

• on March 14, 2011 at 2:37 pm DeWitt Payne

Frank,

The data files from SpectralCalc have a resolution of ~0.01 cm-1. So for a range of 1.4 cm-1 there are ~140 data points. For the range 660-672 cm-1 for a path length of 1m at surface pressure there were 1072 data points. The mean transmittance was 0.8205.

SoD is using something of a brute force approach. At each frequency, he calculates the data for every line in the database. But he’s doing one isotopologue of one molecule. For atmospheric calculations there are 39 (I think) molecules with many isotopologues. CO2 alone has nine. The chlorofluorocarbons, for example, have lots more.

9. on March 11, 2011 at 2:58 pm | Reply Harold Pierce Jr

SOD

How about doing some calculations for water vapor?

10. Frank & DeWitt,

In the calculations in Part Nine, as DeWitt says, I did the calculation with a “brute force” approach.

It was amazingly fast so I didn’t have to think about improving the code to only consider the impact of a line center x cm^-1 away – leading to sensitivity analyses for x.

I did also run all the isotopologues as well – all 315,000 lines each across 350 cm^-1 with a resolution of 0.001 cm^1.

11. If anyone in this thread wants to do accurate atmospheric emission/absorption calculations like the pros, the Line By Line Radiative Transfer Model (LBLRTM) is the tool of choice: http://rtweb.aer.com/lblrtm.html
It uses the HITRAN line database and does all the work of integrating over both wavenumber and altitude for various model atmospheres (including user-supplied). And the computational time isn’t bad as long as one is only interested in a few spectra over fairly narrow intervals.

Unfortunately, while the software can be freely downloaded and is easy to compile with a Fortran compiler, the documentation and the user interface are both archaic and arcane — very difficult for the average amateur to make heads or tails of unless they already have pretty good knowledge of what’s under the hood. In fact, I’m still working on it.

• the documentation and the user interface are both archaic and arcane

I’ll second that opinion. I’ve downloaded the program, but couldn’t get past the documentation to actually use it. It wasn’t at all clear to me how one constructed the multiple input files necessary to run the program. I suspect MODTRAN would be just as difficult if Archer hadn’t put together a graphical user interface for it.