The LWIR Puzzle: Experiments with MODTRAN


Kevin Kilty

Determine 1. Variations in outgoing longwave radiation (OLR) on the best of a tropical setting between 260ppm and 420ppm CO2 focus. The one obvious variations are close to the atmospheric water vapor window.

A lot ink is spilled in this web site, each within the articles themselves and within the threads that apply, on CO2 and its have an effect on on lengthy wave infrared radiation (LWIR). As a web site visited through many skeptics of the CO2/international warming nexus, the majority of those arguments search to exonerate CO2 as a explanation for a warming local weather.

One commonplace theme is that the moderately small impact a doubling of CO2 has on LWIR on the best of setting (TOA) turns out too small to supply the a lot greater impact wanted for a 3K warming on the floor. A number of articles from final summer season referred to as into query the claims of the IPCC as opposed to the Stefan-Boltzmann regulation;[1][2] and lots of feedback mirror this sentiment additionally.  There seems to be a commonplace false impression that was once initiated and is perpetuated to the current time through the local weather analysis neighborhood themselves. Let’s read about the issue of infrared shipping within the setting via some easy modeling.  A few of these effects would possibly wonder other people.

Essence of a false impression

If the focus of CO2 is doubled in particular from its provide price of 400ppm to 800ppm, what effects is a discount in outgoing LWIR of about 3.7 W/m2 at TOA.[3] Nearly everybody refers to this decline as a “forcing”. The influence made through this unlucky word is that the three.7 W/m2 at TOA combines with sun radiation heading to the skin and at once drives floor temperature upper. It suggests one thing like a warmth go with the flow vector, if you’ll, pointing towards the skin.

This isn’t what occurs. The deficit of three.7 W/m2 doesn’t beam towards the skin from TOA in any respect. It represents a deficit of outgoing radiation led to through the upper focus of CO2 at each and every stage of the ambience which absorbs extra radiation and emits radiation extra successfully into all instructions. The determine of three.7 W/m2 at TOA depends upon the assumed temperature and composition of the ambience.

Close to the Earth’s floor one thing an identical happens. LWIR is absorbed and emitted otherwise on this setting on account of our new CO2 focus. For the reason that setting is moderately opaque to LWIR (no longer utterly opaque regardless that; quite a lot of fashions are 12% to 35% clear over the column from floor to TOA), what is going on at TOA has restricted impact on what occurs on the floor. What issues on the floor is principally absorption and emission of LWIR within the warmest and wettest a part of the ambience close to the bottom. Local weather forcing is the disturbance that CO2 reasons on native LWIR shipping; it’s not the three.7 W/m2 decline in LWIR that we would occur to look at at TOA on account of this disturbance.

Radiation Delivery

Radiation power switch is a fancy drawback. Other folks steadily use the Stefan-Boltzmann equation by myself as the foundation in their radiation computations. This works handiest when the radiation is exchanged between surfaces with out a IR energetic medium between them. In different phrases, relying at the Stefan-Boltzmann regulation by myself seriously restricts the issues one would possibly legitimately take on.

When a bodily scenario comes to limitations with mounted temperature, or mounted radiant flux, and a medium which will take part within the switch via emission, absorption or scattering, the issue turns into massively tougher and calls for an actual solver of radiation shipping. The one device at my disposal is MODTRAN which will calculate shipping between two issues in house so long as temperature and composition are specified. It is going to no longer resolve for unknown temperature as it isn’t a whole solver of the shipping equation.

What the radiation shipping drawback includes is that this: Radiation incident at any level inside of an area has traversed house on beams from different issues alongside which there was absorption, emission and scattering. In the meantime some quantity of emitted radiation originates at each and every level on account of its temperature and that is propagated away into all instructions. MODTRAN calculates the collected adjustments of radiant depth alongside any specified route of shuttle from some of these components.

This drawback is just about just like that of calculating the flux of neutrons in a nuclear reactor handing over warmth, transmuting parts, and emitting extra neutrons alongside the way in which.  With no shipping equation one would by no means perceive what is going on in a reactor and the similar is correct of radiant warmth shipping in an energetic setting.

Obstacles of MODTRAN

The model of MODTRAN to be had on the College of Chicago is composed of a legacy FORTRAN program written within the Eighties which an individual would possibly get right of entry to in a restricted manner via a “wrapper” written in every other language. The wrapper supplies a graphical interface (GUI) of edit bins the place one would possibly exchange boundary temperatures, choose between a restricted set of setting fashions and set ranges of greenhouse gasses or cloud quilt. It’s at hand however prevents the use of the total energy of the legacy FORTRAN code.

For something, one can not make a selection at any viewing perspective. Handiest vertical perspectives are allowed. With the intention to grow to be from radiant depth (I) alongside a vertical trail to a real irradiance (flux) on a floor (G), one typically assumes isotropic radiation which makes the conversion so simple as G= pI.[4] This isn’t particularly vital excluding to mention it is a part of a listing of problems [5] that save you accuracy of MODTRAN being higher than 5-10 W/m2. Then again, variations between fashions with just a parameter or two of difference between them are more than likely extra correct than this.

2d, when a scenario comes to an infrared (IR) energetic setting a temperature discontinuity happens at bounding surfaces.[6] This makes an idea like floor temperature ambiguous. It complicates blending convective warmth switch into an issue.

3rd, after working many fashions, I’ve spotted an error within the legacy FORTRAN code. The mistake manifests itself in separate runs with other parameters which lead to precisely the similar answers – and I imply precisely. That is an error. 40 years in the past I used to be paid to rewrite legacy FORTRAN codes, of the similar antique as MODTRAN, to port them between machines the use of other phrase lengths, other languages and ranging compilers. Identical to MODTRAN, those codes got here from Federal contracts or Federal companies. Maximum contained some selection of mistakes. Relating to MODTRAN the code turns out to make use of unmarried precision mathematics in puts it must use double precision.

Customers beware.

The have an effect on of CO2 focus adjustments

MODTRAN provides a number of fashions of the ambience.  Let’s take the tropical type for instance for no reason why rather than an enormous share of sun enter to the Earth takes position within the tropics. Moreover, let’s take a look at variations between 260ppm (preindustrial) to 420ppm (just about present) focus of CO2. As our best of setting (TOA) we will be able to suppose a peak of 18km above the 1013mb floor. Our reference type is 260ppm. There aren’t any clouds and we forget any results from convection. I focal point only on radiant shipping.

As Determine 2 displays, MODTRAN calculates radiant shipping variations led to through our selected build up in CO2 as resulting in a decline at TOA of three W/m2. The brand new setting absorbs extra LWIR. This decline in LWIR can be measured through satellites, excluding that it has taken position over 400 years and quantities to just a 10th watt in step with sq. meter in step with decade. It’s immeasurable, in different phrases, inside the resolving energy of any tool and noise contributed through the Earth.[7].

Determine 2. Reference type output and comparability to the type having upper (420ppm) CO2 focus. Notice that OLR has declined on account of new absorption within the setting.

The graph of OLR (Determine 3) in this contemporary WUWT essay displays that local weather disturbances provide a ways greater affects. For instance, two contemporary El Ninos and Mt. Pinatubo display up with a ways larger impact on this graph than our sluggish build up of CO2 ever may just. As a end result the graph doesn’t turn out the rest in regards to the provide affect of CO2.

Determine 3. Graph of satellite tv for pc measured outgoing longwave. Brief disturbances to local weather like El Ninos and Volcanic eruptions are roughly 1-2W/m2; while the affect of CO2 preindustrial to now can be handiest about 10%-20% as huge throughout all of the graph. This graph is from Dewitte and Clerbaux, 2018, Far off Sensing, 10(10), p.1539 and was once referenced in this contemporary WUWT essay.

In the meantime, close to the tropical floor this build up in CO2 boosts downward directed flux through 1W/m2. If we suppose that the tropical setting and floor had been in power steadiness in our reference type, then the adjustments in LWIR flux as calculated at 420ppm will build up temperature of the ambience and floor till the outgoing LWIR at TOA reaches the reference price of 301.6 W/m2 once more. To determine how a lot temperature upward thrust is had to repair steadiness, we will be able to use MODTRAN via a lot of iterations.

The use of first the Stefan-Boltzmann regulation we will be able to calculate {that a} 1 W/m2 build up in downward longwave on the floor would spice up floor boundary temperature through handiest 0.18K. That is a ways too small to steadiness power at TOA, however even this small adjustment of floor temperature will increase no longer handiest OLR however downward LWIR on the floor considerably. Repeated MODTRAN calculations with subtle guesses of floor temperature divulge that power steadiness at TOA is restored with a temperature upward thrust of 0.7K. Determine 4 displays this. Then again, a nil.7K build up on the floor which is just about black (e=0.97), isn’t imaginable to take care of with out an build up of emitted energy (calculated with the Stefan-Boltzmann regulation) of four.2 W/m2. A far greater price than we started with.

Determine 4. Expanding boundary temperature through 0.7K power steadiness is restored at TOA.

How does this occur? A small build up in irradiance on the flooring floor will increase its temperature. This, in flip, will increase emitted energy from the skin. The greater emitted energy is absorbed within the setting; close to the skin specifically as a result of that is the wet a part of the ambience. A few of this absorbed radiation is re-emitted to flooring. This, once more, raises the skin temperature fairly. The method repeats without end. It’s a limiteless sequence of re-radiation which ultimately converges when there’s a go back to power steadiness. Endless sequence like this are commonplace in issues of radiation change between surfaces without or with an energetic medium in between – the resonant hollow space of a laser is an excessive instance of the previous.


Our experiment displays that radiant shipping to the bounding surfaces of an IR energetic medium principally contain re-radiant exchanges between the surfaces and within sight medium. Exchanges happening in a single a part of the medium would possibly have minor affect on different portions. The extra that portions of the medium are remoted from one every other, the slower the go back to equilibrium via re-radiation and temperature changes.

In our check case, expanding CO2 focus from preindustrial estimated values to the current time manifests itself first as a lower of three W/m2 at TOA and an build up of one W/m2 on the floor. The disturbance from greater CO2 during the ambience passes via a sequence of occasions that leads to power steadiness restored at TOA and a temperature upward thrust on the floor showing to require an build up of four.2 W/m2.[8] To a couple other folks this appears to be like inconsistent with the Stefan-Boltzmann regulation. But, it’s not. Such obvious inconsistencies happen often when an energetic medium is interested in shipping.[9]


1.- A major query. On this case the three.7 W/m2  at TOA was once in comparison to power density required to take care of an build up in floor temperature of handiest 1K, calculated with the Stefan-Boltzmann equation which is 7 W/m2.  The plain contradiction is simple sufficient to look.

2.- Hayden quoted in the latest SEPP e-newsletter.

3.- This 3.7 W/m2 price of “local weather forcing” is quoted in lots of puts, however may also be demonstrated through the use of MODTRAN with any of its summer season atmospheric fashions through doubling CO2.

4.- Most commonly from radiation no longer being isotropic. For example, from a peak of 16km above the Earth’s floor a view of the decrease hemisphere can have 0.28 steradians full of a background of chilly house quite than the nice and cozy Earth floor of the remainder 6.00 steradians. That is it seems that visual out the porthole of an airliner. As a result of this alteration in background the flux price calculated through assuming G= pI will probably be biased too huge.

5.- This lengthy listing principally comes to issues of the isotropic assumption in quite a lot of contexts. Curiously the wrapper doesn’t use p however the consistent 3.14 as an alternative. There’s no time dependence in any of those calculations. MODTRAN calculations are on the spot, however the actual adjustments are behind schedule and take time.

6.- See as an example: Houghton, J.T., 1986, Physics of Atmospheres, second Ed., Cambridge. P. 13. Or, M. Necati Ozisik, 1973, Radiative Switch, Wiley-Interscience. p. 320.

7.- An individual may just nearly say that the Earth’s floor temperature reasons of a lot of its personal greenhouse impact.

8.-The go back to equilibrium can take a very long time to reach as it’s going to contain adjustments on the Earth’s floor like melting ice or converting crops.

9.- Different obvious inconsistencies come with {that a} emerging focus of CO2 can it sounds as if act to chill the Earth quite than heat it particularly when the IR energetic gasses within the setting are concentrated in a skinny layer close to the bottom and the remainder setting above is particularly clear, equivalent to within the Antarctic or winter-time Arctic, or on the flooring floor of increased areas.



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