Modtran Up and Down VI

This series is getting long, but there is one more avenue to explore before it can be finished. We left off with the kissing conundrum that was not completely resolved. That’s ok. We may not resolve this problem either. The kissing problem is that up and down looking Modtran intensity/blackbody values for CO2 spectra always kiss, even below the 1 km altitude where CO2 spectra are indistinguishable from blackbody in Modtran.

What we must explore to finish this series is what changes take place at a kilometer altitude to allow CO2 to begin radiating? To be clear, CO2 must radiate below a kilometer altitude to some extent, but it is absorbed so quickly that the Fourier Transform spectrometers used to gather the data for Modtran  see the atmosphere below one kilometer as a brick. A brick where individual molecular spectra are not apparent. A brick that radiates very close to the blackbody curve.

4Modtran up and down 1km

Above you can see the first hints of deviation from the blackbody spectrum looking down at one kilometer in the red curve, and the very strong deviation in the blue curve looking up.

3Modtran up and down 100m

This can be contrasted with the 100 meter or 1000 MB level where no deviation from the blackbody is seen in the CO2 bands looking down.

What has changed?



This is what has changed. A new source of energy from the release of enthalpy of vaporization becomes available at the condensation level at about 1 kilometer altitude. This is the typical altitude of the bottom of the cloud deck.

We can summarize this entire Modtran up and down exercise with the following image.


The background image credit to the Cloud Appreciation Society.

The principal greenhouse gasses do not absorb or radiate separately from the mass of the atmosphere below one kilometer. This is partly a pressure effect. All outgoing IR radiation is completely thermalized below this level and energy transport takes place by conduction and convection.

Above one kilometer we begin to see distinct outgoing radiation in the CO2 bands. Above two kilometers we begin to see distinct outgoing radiation in the water bands.

Outgoing radiation in CO2 bands increases continuously from one kilometer until it reaches a maximum about 17 kilometers. Outgoing radiation in water bands increases steadily from two kilometers and also reaches a maximum  about 17 kilometers.



That they both should reach maxima at the same altitude is very interesting. Who knows? We may have do do another post in this series some day.







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MODTRAN Up and Down V, The Kissing Conundrum


We left off the last post with the puzzlement that Modtran looking up and down from the same altitude sees CO2 deviation from the blackbody spectrum, evidence of CO2 absorption and radiance, that matches almost exactly in intensity.

4Modtran up and down 10km

This is illustrated well here from 10 kilometers.


When we zoom in a bit we can see that what is really kissing is the wavenumber 667.4 “spike”. The rotational “shoulders” of the fundamental bending spike are sloped to their respective Planck temperatures. The red upwelling (looking down) shoulders are at 237 K, the lapse temperature for 10 kilometers. This can be found in Modtran by “mouse over” in the lapse graph to the right. The mouse over gives you a pointer dot but no values in the main panel. Using my eyechrometer, I declare that the Planck temperature of the blue downwelling (looking up) shoulders is about 235 K. This corresponds to an altitude about 300 meters higher.

We can summarize that our theoretical spectrometer looking up and down in the CO2 bands at 10 kilometers sees radiation at the blackbody temperature for the altitude of the instrument for the rotational shoulders looking down, but sees the same radiation from a slightly lower temperature and higher altitude than the instrument looking up.The kissing spikes at 667.4 match nearly perfectly.

To get to the bottom of this we need to delve into the rotational shoulders.


This is a HITRAN plot of the absorption fraction in one meter for the CO2 molecule (credit Barret Bellamy). The Q branch, which is almost entirely absorbed within one meter of atmosphere with 380 ppm CO2, is vibrational only and corresponds to wavenumber 667.4. The P and R bands to the left and right represent situations where the 0 to 1  quantum vibrational transition is complicated by part of the energy being diverted to rotation. The P rotations decrease the overall energy of the molecule and the R rotations increase the overall energy. The rotational spectra largely cancel out with a slight net energy increase due to a slightly stronger R branch.

The important point here is this entire spectrum must be viewed as a unit entirely dependent on the fundamental 667.4 “bending” (vibration).


This is what our fundamental 667.4 unit looks like plotted against a bunch of stuff, notably various CO2 spectra seen from space and our 220 K Planck curve. It can be seen that the 667.4 unit defines a gap of zero transmission to the tropopause from the surface, and that this same 667.4 unit (and gap) corresponds to the inclined shoulders of the CO2 spectra the satellites see from space.

With this context, the conundrum we seek to explain is why this 667.4 unit when seen looking down, and inverted looking up, and inclined to the Planck curve; always shows the 667.4 Q branch kissing. This phenomenon is all the more amazing as the Q branch does not appear as a noticeable spike until 10 kilometers at Modtran detail, yet the up and down values for the 667.4 unit match even below 1 kilometer where the upwelling (looking down) CO2 spectra are no different than the Planck curve.

To summarize:

1Modtran up and down 1m

From 1 meter,

4Modtran up and down 30km

to 30 kilometers, the values are ALWAYS equal looking up and down at wavenumber 667.4 for CO2 only. This behavior is unique to CO2 among the main greenhouse gasses.

There is some fundamental limit to the total up and down radiation at 667.4 between the surface and 30 kilometers. My suspicion is this relates to the extraordinarily short (1 meter at surface pressure) extinction path for this wavelength in the 2 good greenhouse gas. Furthermore, since CO2 is a linear molecule with a dipole moment of zero, the zero to one quantum transition at 667.4 is the basis of ALL subsequent vibrational and rotational transitions.

Orders of CO2 Transitions

Not only are the rotational shoulders of 667.4 a “unit”, but the entire CO2 spectrum is essentially a unit. Whatever limits 667.4 limits everything else.

While this seems a good start, exactly how this would limit the total up and down radiation seen by Modtran at 667.4 is not clear to me. Perhaps this is a new level of meaning for “saturation”.

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MODTRAN Up and Down IV, Moving Higher

Time to make good on the promise to progress upwards. In the first post in this series we established that Modtran sees no significant deviation from the blackbody spectrum looking down in the CO2 bands until about one kilometer altitude. Looking up, Modtran sees classical deviation from the blackbody spectrum, indicating absorption and radiation by CO2 at every altitude.

In the second post in this series we established that essentially the same is true for water, except that the altitude of first radiation in water bands looking down is four or five kilometers altitude.

In the third post in this series, we surmise that the reason Modtran can see no radiation looking down in the CO2 and water bands below their respective first altitudes, yet can see strong signals all the way to the surface looking up; is that the higher energy quantized vibrational states of the molecules at lower altitudes are transparent to lower energy radiation from above.

Where we left off at one kilometer, CO2 was just beginning to show it’s stuff looking down for the first time above the surface.

4Modtran up and down 1kmHere it is. Let’s go to five kilometers.

4Modtran up and down 5kmBig difference. Ten kilometers.

4Modtran up and down 10kmThe upwelling signal now has greater intensity that the radiation from above.

4Modtran up and down 16kmAt sixteen kilometers we are at the tropical tropopause at the beginning of the little “vertical spot” that extends to 17 kilometers. Within this kilometer, the atmosphere basically does not change temperature as you climb. Above 17 kilometers the atmosphere begins to warm with increasing altitude.

4Modtran up and down 30km

The trend beginning at one kilometer has been increasing upwelling and decreasing downwelling radiation. The really remarkable thing is that even from one meter in the first post, the temperature/intensity of the down and up looking radiation have been the same. The down and up looking values “kiss”. This trend begins to break down at 30 kilometers above, with only the 667.4 band from above stretching mightily for the kiss.


At 50 kilometers the lovers are finally separated.

What does this mean? The down and up looking values for water never match.

Up and down Water only 5km

Above is water only up and down at its heyday altitude of 5 kilometers. No hanky panky here.

We will explore the remarkable equality of up and down CO2 values in the next post.


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Further delaying a repeated promise to progress upwards in prior posts in this series, it seems important to address an obvious question: why, when you look up and down from say 10 meters, can you see deviations from the blackbody spectrum indicating radiation from greenhouse gasses looking up? In other words, if we are going to say that no signal is seen looking down because such radiation is instantly and completely absorbed and thermalized, why doesn’t this happen to the radiation from above?

Always in the back of your mind there is the possibility that Modtran is just wrong, or somehow inadequately designed for this up and down exercise.

modtran-up-and-down-full-bore-10-meterHere is Modran full bore, as I call it, with all the greenhouse gasses; looking down with the red background run and up with the blue looking up at ten meters. At first glance one is inclined to say the signal from above is all water. We can check that.


What we have done here is leave the full bore signal looking up from ten meters in red as the background run compared to water only looking up from the same level in blue.

Interesting. In the CO2 bands from wave numbers 600-750, the water only signal comes from a much higher and colder altitude. This information is obscured in the full bore view because the virtual spectrometer registers the higher energy near surface thermalized radiation along the Planck curve to about WN 700 and then the “tops” of the water bands.

Through the atmospheric window the energy and altitude differences are much smaller and the blue water only signal barely “pokes out” below the full bore signal except in the ozone bands where the full bore lines “jump up”.


Using the same comparison between full bore and ozone you get the idea…ozone behaves peculiarly because there is significant surface ozone besides the better known stratospheric zone.


Just to complete the train of thought we compare full bore with CO2 only. CO2 agrees with water in the deviation from blackbody in the ozone bands.

After all this, how do we answer the initial question: why is radiation from above not absorbed and thermalized just as radiation from below? Why do we see a deviation from the blackbody temperature looking up but not down?


Getting back to the first graphic of full bore up and down from 10 meters, the answer is that the radiation from above is coming in at a lower energy than the radiation from below. The vibrations that dominate the molecular excitations in the infrared spectrum are quantized. The higher quanta/ higher energy molecules both below 10 meters and above are transparent to lower energy photons from above. They just sail right through.



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Tesla Carbon Footprint

According to the US Energy Information Administration (which heretofore I never knew existed) when you burn a typical E10 gallon of gasoline in your car, it produces about 18.95 pounds of CO2. Really? A gallon of gasoline only weighs 6 pounds. Part of the answer is that a lot of Oxygen with an atomic mass of 16 is drawn in during combustion. Yet a direct energy conversion using EIA figures of 157 pounds CO2 per million BTU yields only 18 pounds CO2 per gallon of ordinary (not 10% ethanol) gasoline which according to their figures produces 19.6 pounds CO2 when burned. We argue that this ~1.5 pound penalty represents CO2 produced in distribution of gasoline.

A Tesla will go about 90 miles on the equivalent amount of electrical energy to a gallon of gasoline. To assess the CO2 produced when the energy to create the 33.7 kWh of electricity that equals the gallon of gasoline, it is necessary to know where the electricity came from.

If that electricity came from solar panels on the house where the Tesla lives, it is a beautiful situation. That Tesla is driving on sunshine. Unfortunately, most Teslas do not live in houses with enough solar panels to feed them and their electricity comes from the grid.

The grid is not powered by sunshine. In California less than 2% of the grid comes from sunshine, less than biomass, which itself produces unaccounted (by international agreement) CO2. In California the grid is powered as follows:

California Energy.png

We want to be scrupulously fair, and whatever the “unspecified sources of power” may be, we will grant them to the renewable sources and just make it easy by saying 52% of California’s power comes from fossil fuels. We are saying that over half of the energy that drives Teslas from the grid comes from fossil fuels.

To create a weighted average Carbon footprint from the California grid we need to know the Co2 production from the 7.82% coal (purchased out of state of course) and the 44.31% natural gas. According to the US Energy Information Administration burning anthracite coal  produces 229 pounds of CO2 per million BTU, lignite 215, and bituminous (the highest grade) 206. Natural gas (mostly methane) is 117 pounds CO2 per million BTU.

In a further abundance of generosity we will say the out of state coal burned is all lignite. We get our weighted average CO2/ million BTU by multiplying .0782 x 206 + .4431 x 117=68 pounds of CO2 per million BTU from the California grid. We now need to know the kWh equivalent of a million BTU. We know that a gallon of gas=115000BTU=33.7kWh. Dividing 115000 by 33.7 gives us 3412 BTU/kWh as a raw energy conversion.

We know that a million BTU produces 68 pounds of CO2 so we cross multiply 3412 x 68=232016/1m=.23 pounds CO2 per kWh. Multiply by 33.7 yields 7.75 pounds of CO2 for the equivalent electricity to a gallon of gas that produces 18.95 pounds of CO2 when burned.

Sounds good, doesn’t it. Ah, we forget conversion efficiency. When you burn gasoline directly the pistons go back and forth and the wheels turn and this is built into miles per gallon. Not so electricity. First you must convert it from fossil fuel and all conversion comes with a penalty. The conversion efficiency of natural gas is about 41% and coal 33%. Other sources have similar conversion losses. We are just going to say that the efficiency is 40% across the grid. We must therefore divide the electric 7.75 pounds by .4 to yield 19.4 pounds. This somewhat more the 18.95 of a gallon of gas.

There is another problem. Line loss through the grid is about 30%. We will therefore say transmission efficiency is 70% and we must further divide the 19.4 pounds by .7 to yield 27.7 pounds of CO2 for the electric equivalent of a gallon of gas that produces 18.95, 32% more for the electricity.

What winds up saving the Tesla is the 90 miles it gets out of this. A typical gas/electric hybrid vehicle gets 50 miles per gallon. To make it really simple, we can say that while the electricity it uses produces 32% more CO2, the Tesla gets 44% better mileage.

The Tesla does have a smaller Carbon footprint than a hybrid, but not by very much.

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Modtran Up and Down II

Delaying a promise to progress upward in the first post in this series, further work has shown that we need to go sideways a bit. It turns out that according to MODTRAN, like CO2, water does not radiate in the lower troposphere either. We will step through the same sequence with water.

1Up and down Water only 1meter

Once again, the red “background run” is looking down and the blue looking up. Similar to CO2, no radiation signal looking down from 1 meter.

2Up and down Water only 10meter

Ditto 10 meters.

3Up and down Water only 100meter

Again at 100 meters.

Up and down Water only 1km

At 1 kilometer we began to see a signal in the CO2 bands but nothing equivalent in the water bands. We can note that the up looking signal is dropping to progressively lower temperature or intensity with the lapse rate, particularly in the atmospheric window.

Up and down Water only 5km

At 5 kilometers we finally get a good signal looking down, but looking up is still stronger.

Up and down Water only 10km.png

At 10 kilometers it is getting pretty dry, and except for the lower wave numbers not much is left of the up looking signal.

Up and down Water only 17km

At 17 kilometers where the atmosphere begins to warm with altitude, little up looking signal is left.

Up and down Water only 40km

At 40 kilometers the up signal is done. The down looking signal records the entire water spectrum radiating mightily to space at 329 watts per square meter. The solar radiation at the top of the atmosphere is measured at 340 watts per square meter. Without bothering to radiate significantly in the first 5 kilometers of the atmosphere, water still manages to radiate away 97% of the planet’s incoming energy.

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Modtran, Up and Down

We have explored up and down looking spectrometers in prior posts. In all cases the up looking instruments have been on the ground. A fun thing about the Modtran program is that you can look both up and down from any altitude you choose. Here we will begin at the surface and proceed up.

1Modtran up and down 1m Here we are looking at both up and down from 1 meter. The Modtran convention is that the “background run” is red and the “model” blue. In this series red will be looking down and seeing the radiation going up, and the blue will be looking up and seeing the radiation coming down.

It is interesting that looking down Modtran sees no signature of the CO2 bands, only a slight reduction in intensity and temperature from the surface blackbody over the range between WN’s 400-900. Looking up, there is a very strong signal from all the CO2 bands.

2Modtran up and down 10m

At ten meters there is very little difference.

3Modtran up and down 100m

Deja vu all over again at 100 meters except for the suggestion of a signal at WN 618 where CO2 picks up a vibrational quantum number. This is the strongest CO2 band besides 667.4, albeit two orders of magnitude weaker.

4Modtran up and down 1km

Finally, at one kilometer we begin to see a half baked signal in the CO2 bands looking down. How is this possible? How, in the first kilometer, where nearly all CO2 is introduced to the atmosphere, can there be no radiative signature?

The answer is simple and surprising. The atmosphere does not radiate in the CO2 bands in the first kilometer. At least not in the bands strong enough to generate a signal. In the first kilometer, all of the signal originates at higher altitudes.

CO2 is a fun kind of molecule. It likes to swim, and it likes to dance. Quantum vibration is the dominant form of excitation in the IR part of the spectrum and this “gitt’n jiggy wid it” is the reason CO2 absorption is thermalized rather that re radiated in the first kilometer of the earth’s atmosphere.

The concept here is very simple. We are talking about the percentage of light energy absorbed by CO2 that is kinetically dispersed (thermalized) rather than re emitted as a photon, and the observation that we are not seeing CO2 photons emitted in the first kilometer of the atmosphere.

The formal physics of this concept is very difficult. It engages the entire legal cannon of radiative transfer laws from Planck, Boltzmann, Kirchoff, Beer,, without being satisfyingly resolved by any of them. An important reason for this is that the atmosphere is never in equilibrium. This concept of a tendency for CO2 to thermalize rather than radiate in the first kilometer is probably better thought of as just a physical property of the atmosphere.

We will climb higher in the next post.

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