Much ink is spilled on this site, both in the articles themselves and in the threads that follow, on CO2 and its impact on long wave infrared radiation (LWIR). As a site visited by many skeptics of the CO2/global warming nexus, the bulk of these arguments seek to exonerate CO2 as a cause of a warming climate.
One common theme is that the relatively small effect a doubling of CO2 has on LWIR at the top of atmosphere (TOA) seems too small to produce the much larger effect needed for a 3K warming at the surface. Several articles from last summer called into question the claims of the IPCC versus the Stefan-Boltzmann law; and many comments reflect this sentiment also. There appears to be a common misconception that was initiated and is perpetuated to the present time by the climate research community themselves. Let’s examine the problem of infrared transport in the atmosphere through some simple modeling. Some of these results may surprise folks.
Essence of a misconception
If the concentration of CO2 is doubled specifically from its present value of 400ppm to 800ppm, what results is a reduction in outgoing LWIR of about 3.7 W/m2 at TOA. Almost everyone refers to this decline as a “forcing”. The impression made by this unfortunate phrase is that the 3.7 W/m2 at TOA combines with solar radiation heading to the surface and directly drives surface temperature higher. It suggests something like a heat flow vector, if you will, pointing toward the surface.
This is not what happens. The deficit of 3.7 W/m2 doesn’t beam toward the surface from TOA at all. It represents a deficit of outgoing radiation caused by the higher concentration of CO2 at every level of the atmosphere which absorbs more radiation and emits radiation more effectively into all directions. The figure of 3.7 W/m2 at TOA depends on the assumed temperature and composition of the atmosphere.
Near the Earth’s surface something similar occurs. LWIR is absorbed and emitted differently in this atmosphere because of our new CO2 concentration. Because the atmosphere is relatively opaque to LWIR (not completely opaque though; various models are 12% to 35% transparent over the column from surface to TOA), what goes on at TOA has limited effect on what happens at the surface. What matters at the surface is mainly absorption and emission of LWIR in the warmest and wettest part of the atmosphere near the ground. Climate forcing is the disturbance that CO2 causes on local LWIR transport; it is not the 3.7 W/m2 decline in LWIR that we might happen to observe at TOA because of this disturbance.
Radiation energy transfer is a complex problem. People often use the Stefan-Boltzmann equation alone as the basis of their radiation computations. This works only when the radiation is exchanged between surfaces with no IR active medium between them. In other words, depending on the Stefan-Boltzmann law alone severely restricts the problems one may legitimately tackle.
When a physical situation involves boundaries with fixed temperature, or fixed radiant flux, and a medium which can participate in the transfer through emission, absorption or scattering, the problem becomes hugely more difficult and requires a real solver of radiation transport. The only tool at my disposal is MODTRAN which can calculate transport between two points in space as long as temperature and composition are specified. It will not solve for unknown temperature because it isn’t a complete solver of the transport equation.
What the radiation transport problem entails is this: Radiation incident at any point within a space has traversed space on beams from other points along which there has been absorption, emission and scattering. Meanwhile some amount of emitted radiation originates at every point because of its temperature and this is propagated away into all directions. MODTRAN calculates the accumulated changes of radiant intensity along any specified direction of travel from all these factors.
This problem is nearly identical to that of calculating the flux of neutrons in a nuclear reactor delivering heat, transmuting elements, and emitting more neutrons along the way. Without a transport equation one would never understand what goes on in a reactor and the same is true of radiant heat transport in an active atmosphere.
Limitations of MODTRAN
The version of MODTRAN available at the University of Chicago consists of a legacy FORTRAN program written in the 1980s which a person may access in a limited way through a “wrapper” written in some other language. The wrapper provides a graphical interface (GUI) of edit boxes where one may change boundary temperatures, choose from a limited set of atmosphere models and set levels of greenhouse gasses or cloud cover. It is handy but prevents using the full power of the legacy FORTRAN code.
For one thing, one cannot choose at any viewing angle. Only vertical views are allowed. In order to transform from radiant intensity (I) along a vertical path to a true irradiance (flux) on a surface (G), one usually assumes isotropic radiation which makes the conversion as simple as G= pI. This isn’t especially important except to say it is part of a list of issues  that prevent accuracy of MODTRAN being better than 5-10 W/m2. However, differences between models with only a parameter or two of distinction between them are probably more accurate than this.
Second, when a situation involves an infrared (IR) active atmosphere a temperature discontinuity occurs at bounding surfaces. This makes a concept like surface temperature ambiguous. It complicates mixing convective heat transfer into a problem.
Third, after running many models, I have noticed an error in the legacy FORTRAN code. The error manifests itself in separate runs with different parameters which result in exactly the same solutions – and I mean exactly. This is an error. Forty years ago I was paid to rewrite legacy FORTRAN codes, of the same vintage as MODTRAN, to port them between machines using different word lengths, different languages and varying compilers. Just like MODTRAN, these codes came from Federal contracts or Federal agencies. Most contained some number of errors. In the case of MODTRAN the code seems to use single precision arithmetic in places it should use double precision.
The impact of CO2 concentration changes
MODTRAN offers several models of the atmosphere. Let’s take the tropical model as an example for no reason other than a huge proportion of solar input to the Earth takes place in the tropics. Furthermore, let’s look at differences between 260ppm (preindustrial) to 420ppm (nearly current) concentration of CO2. As our top of atmosphere (TOA) we will assume a height of 18km above the 1013mb surface. Our reference model is 260ppm. There are no clouds and we neglect any effects from convection. I focus solely on radiant transport.
As Figure 2 shows, MODTRAN calculates radiant transport differences caused by our chosen increase in CO2 as leading to a decline at TOA of 3 W/m2. The new atmosphere absorbs more LWIR. This decline in LWIR would be measured by satellites, except that it has taken place over 400 years and amounts to only a tenth watt per square meter per decade. It is immeasurable, in other words, within the resolving power of any instrument and noise contributed by the Earth..
The graph of OLR (Figure 3) in this recent WUWT essay shows that climate disturbances present far larger impacts. For example, two recent El Ninos and Mt. Pinatubo show up with far greater effect in this graph than our slow increase of CO2 ever could. As a consequence the graph doesn’t prove anything about the present influence of CO2.
Meanwhile, near the tropical surface this increase in CO2 boosts downward directed flux by 1W/m2. If we assume that the tropical atmosphere and surface were in energy balance in our reference model, then the changes in LWIR flux as calculated at 420ppm will increase temperature of the atmosphere and surface until the outgoing LWIR at TOA reaches the reference value of 301.6 W/m2 again. To figure out how much temperature rise is needed to restore balance, we can use MODTRAN through a number of iterations.
Using first the Stefan-Boltzmann law we can calculate that a 1 W/m2 increase in downward longwave at the surface would boost surface boundary temperature by only 0.18K. This is far too small to balance energy at TOA, but even this small adjustment of surface temperature increases not only OLR but downward LWIR at the surface significantly. Repeated MODTRAN calculations with refined guesses of surface temperature reveal that energy balance at TOA is restored with a temperature rise of 0.7K. Figure 4 shows this. However, a 0.7K increase at the surface which is nearly black (e=0.97), is not possible to maintain without an increase of emitted power (calculated with the Stefan-Boltzmann law) of 4.2 W/m2. A much larger value than we began with.
How does this happen? A small increase in irradiance at the ground surface increases its temperature. This, in turn, increases emitted power from the surface. The increased emitted power is absorbed in the atmosphere; near the surface particularly because this is the moist part of the atmosphere. Some of this absorbed radiation is re-emitted to ground. This, again, raises the surface temperature slightly. The process repeats ad infinitum. It’s an infinite series of re-radiation which eventually converges when there is a return to energy balance. Infinite series like this are common in problems of radiation exchange between surfaces with or without an active medium in between – the resonant cavity of a laser is an extreme example of the former.
Our experiment shows that radiant transport to the bounding surfaces of an IR active medium mainly involve re-radiant exchanges between the surfaces and nearby medium. Exchanges taking place in one part of the medium might have minor influence on other parts. The more that parts of the medium are isolated from one another, the slower the return to equilibrium through re-radiation and temperature adjustments.
In our test case, increasing CO2 concentration from preindustrial estimated values to the present time manifests itself first as a decrease of 3 W/m2 at TOA and an increase of 1 W/m2 at the surface. The disturbance from increased CO2 throughout the atmosphere passes through a chain of events that ends in energy balance restored at TOA and a temperature rise at the surface appearing to require an increase of 4.2 W/m2. To some people this looks inconsistent with the Stefan-Boltzmann law. Yet, it is not. Such apparent inconsistencies occur commonly when an active medium is involved in transport.
1.- A serious question. In this case the 3.7 W/m2 at TOA was compared to energy density required to maintain an increase in surface temperature of only 1K, calculated with the Stefan-Boltzmann equation which is 7 W/m2. The apparent contradiction is easy enough to see.
2.- Hayden quoted in the most recent SEPP newsletter.
3.- This 3.7 W/m2 value of “climate forcing” is quoted in many places, but can be demonstrated by using MODTRAN with any of its summer atmospheric models by doubling CO2.
4.- Mostly from radiation not being isotropic. As an example, from a height of 16km above the Earth’s surface a view of the lower hemisphere will have 0.28 steradians filled with a background of cold space rather than the warm Earth surface of the remaining 6.00 steradians. This is plainly visible out the porthole of an airliner. Because of this change in background the flux value calculated by assuming G= pI will be biased too large.
5.- This long list mainly involves problems with the isotropic assumption in various contexts. Interestingly the wrapper doesn’t use p but the constant 3.14 instead. There is no time dependence in any of these calculations. MODTRAN calculations are instantaneous, but the true changes are delayed and take time.
6.- See for instance: Houghton, J.T., 1986, Physics of Atmospheres, 2nd Ed., Cambridge. P. 13. Or, M. Necati Ozisik, 1973, Radiative Transfer, Wiley-Interscience. p. 320.
7.- A person could almost say that the Earth’s surface temperature causes of much of its own greenhouse effect.
8.-The return to equilibrium can take a long time to achieve as it may involve changes at the Earth’s surface like melting ice or changing vegetation.
9.- Other apparent inconsistencies include that a rising concentration of CO2 can apparently act to cool the Earth rather than warm it especially when the IR active gasses in the atmosphere are concentrated in a thin layer near the ground and the remaining atmosphere above is especially transparent, such as in the Antarctic or winter-time Arctic, or at the ground surface of elevated regions.
Why is it possible to look directly at the disk of the setting Sun at dusk without being blinded?
If the thermal radiance of the Earth measured from Space is a black body (ε = 1) and the solid surface is a gray-body (ε <1) what has happened to the insolation energy of reflectance (ρ =1-ε).
Given that all of the post-albedo insolation flux must be quenched by the atmosphere, otherwise the planetary black body status could not be achieved, it follows therefore that it is the presence of atmospheric dust and not greenhouse gases that absorbs the post-albedo insolation component of the surface reflectance. It is dust opacity that allows us the view the setting sun and not greenhouse gas opacity.
The radiance measured from space is not a black body. Within the atmospheric water vapor window is, as Figure 1 shows, atmosphere is almost transparent from surface to space. At other frequencies the atmosphere is nearly opaque, as Figure 1 also shows. A composite radiance that appears to come from different temperatures over different parts of the spectrum is neither black nor gray.
MODTRAN calculations assume that what solar insolation is absorbed at surface or in the atmosphere is what maintains system temperature.
The only solar incoming radiation (insolation) that is truly absorbed is converted into atmospheric potential energy and is held in place indefinitely by ongoing convective overturning.
The Dynamic Atmosphere Energy Transport model (DAET) shows that that is all that is needed to account for observations on multiple planets and moons with atmospheres.
All radiative imbalances however caused are neutralised by convective adjustments that use changes in total atmospheric potential energy as a variable buffer against radiative changes that are internal to the system.
Unlike the radiative model the DAET model fully accounts for all real world observations.
Kevin K & others simply ignore the graphs on incoming SW, or otherwise they do not exist?
I have done a study taking both LW and SW into account. I would surely be much obliged if you could tell me what you think of it?
An evaluation of the greenhouse effect by carbon dioxide | Bread on the water
Atmosphere | Free Full-Text | Radiative Energy Flux Variation from 2001–2020 (mdpi.com)
Take some time to look at the conclusion…
I have an interesting thought experiment that you might want to comment on. Given the atmosphere we have today with 420 ppm CO2 what would the OLR look like in the band 14-16 microns if there was no radiation from the surface in that band? The same energy would be radiated from the surface just none in the CO2 band.
Keep in mind that the well-separated CO2 molecules are in a sea of molecules and are having collisions millions if not billions of times a second. Each collision has the potential to excite a kinetic energy level similar to that created by absorbing a IR photon. All molecules are radiating energy the sum of which equals the Planck (BB) spectrum for the local temperature.
So is the outgoing radiated spectrum in the band just the BB spectrum? Do the CO2 molecules filter out or enhance the outgoing 14 to 16 micron portion of the energy? How would the OLR differ from what is predicted with surface radiation in the band as is currently modelled?
I don’t know what the answer is but I would like to know.
A discussion of insolation takes us far afield of the topic here, which is LWIR. However, light from the setting sun takes a long path through the atmosphere. Dust may weaken it along this journey at times, but the effect that is always present is scattering from oxygen, nitrogen, and density fluctuations. I fail to see how opacity at solar wavelengths has a bearing on the topic at hand.
In your essay you state the following:
Indeed so, and by focusing on the narrow issue of CO2 and LWIR you stray dangerously into the circular argument of “we cannot think of anything else.”
In a problem as enormous as climate to focus on one specific aspect speaks more to agenda rather than to enquiry.
It would greatly help my understanding of your work if you explained what this 3 degrees increase actually is. What is the base line for this calculation?
This is a terrible analogy for the following reason -In neutron flux enhancement the extra neutrons result from the physical destruction of atomic nuclei in the irradiated material. This cannot be a valid analogy because in atmospheric radiation flux no new energy is created. I encourage you to present a better analogy, for example the retention of heat in the circulation water of a gas-fired home central heating system.
You are now in the territory of “We get the right answer even though the sums are wrong.”
Huge? It would be nice if here you used real number relationships it’s a way of showing competence in this complex subject. For example, half of the surface area of the planet lies in the Tropics between the 30 degrees north and south parallels. However, 61% of the insolation disk energy intercept takes place within this zone.
In reply to your responses to me:
So, what is the grey-body emittance being used here and why? The Vacuum Planet Equation is specifically formulated to account for all the post-albedo intercepted solar irradiance. If you accept that the surface is a grey body then the rejected energy of reflectance must all be absorbed by the atmosphere else intercepted energy is being neglected in the budget calculation. Because greenhouse gas opacity cannot absorb insolation it necessarily follows that atmospheric dust and aerosol opacity must do the job.
I disagree this is relevant because energy cannot be created or destroyed and all processes must be accounted for in climate analysis.
As Clyde indicated, visible direct sunlight (especially wavelengths shorter than 600nm) are greatly attenuated by scattering in the atmosphere. The eye cannot focus infrared sunlight so there is no damage.
The scattered sunlight is either back-scattered or forward scattered, the later results in sky radiation (i.e. a blue sky). Due to particle sizes, very little scattering happens at solar wavelengths longer than 2000nm (2 um).
For wavelengths longer than 4 um there is very little direct solar irradiance, just a handful of W/m2. Beyond 10 um there is essentially zero direct solar (13-17 um is the primary CO2 absorption band).
You ask a lot of questions.
I am OK with the surface being a gray body. MODTRAN uses an emissivity of 0.97, and I couldn’t change it if I wanted to. But the atmosphere has line spectra throughout and is not gray. Have a look at Figure 1. Over some parts of the spectrum the OLR has a very different spectrum than over other parts and only over very short intervals does it parallel one of the temperature curves. MODTRAN handles the line by line calculation from 4.5 to 4000 micrometers.
MODTRAN does not take insolation into account except indirectly. The temperature stucture of a model atmosphere and a typical surface temperature depend on insolation as it is the only energy addition source. The atmosphere loses energy through LWIR and couldn’t maintain these temperatures without implied insolation.
No its not. The same terms are involved and only the mechanisms change. The absorption of particles delivers, of neutrons transmutes elements and the fragments deliver heat, and the transmutation releases more neutrons — looks pretty similar to me. People who operate reactors have large equation solvers based on their equation of transport to keep track of changes occuring during the fuel cycle.
The 3K surface temperature increase is what the climate modeler think will happen with a doubling of CO2 after a return to equilibrium. A decline in OLR is what the modelers calculate will occur immediately following a doubling. But this involves a whole list of feedbacks.
OK, I’ll take that under advisement.
It isn’t just absorption by dust that attenuates the intensity of sunlight. Mie and Rayleigh scattering (what makes the sky appear blue) reduce sunlight intensity. When the sun appears near the horizon, its light has a much longer path length than when it is high overhead. Thus, more light gets scattered out of a beam.
Clyde, That is true, however beam attenuation by scattering does not result in energy absorption.
I was responding to your comment that only mentioned the ability to observe the setting sun directly.
However, scattering does effect the energy balance because a beam of light arriving at a specular surface (71% of the Earth) at a particular angle will have the blue light scattered more strongly than the red light, with the scattered light having different angles of incidence than the original beam, and some of it will be directed to outer space. These are second-order effects, but then climatologists are worrying about 1 Watt per m2 after subtractions.
OKAY then …
Stand outside at night in a desert, in the summer, and feel the depths of space sucking the infrared energy from your body.
In a more humid climate, in the summer, the atmosphere feels like a warm comfy blanket.
You can directly experience the fact that water vapor is, by far, the most important greenhouse gas.
Good point, though up in the Rockies during the summer, you don’t even have to wait for evening. Just having the sun go behind some mare’s tails in the sky is enough.
Here in Arizona when the sun sets it cools fast. I also consider the 60 cold unless we do have some moisture in the air. Moisture it is nice no moisture it is cold. Yet the temperature measurement is the same. How it feels are worlds apart.
You just perfectly described enthalpy, the correct measure of heat. Temperature is a poor, poor proxy for heat content.
Radiation models do not model the atmosphere. They don’t model convection. They don’t model evaporation/latent heat. They don’t model kinetic energy transfers. Since energy is moving between all these transport mechanisms in the real atmosphere, using radiation models will always provide the wrong answer.
As energy is radiated upward from the surface, it is absorbed very quickly and incorporated in the bulk atmosphere. It is then part of the bulk atmosphere. The next emission from the molecule that absorbed the energy will have nothing to do with the energy that was absorbed. It is some other energy extracted from the bulk atmosphere. Radiation models don’t “see” this difference.
The energy that was absorbed could have move upward/downward due to convection/conduction/radiation. Without knowing this movement of the energy it is impossible to determine what is going to happen next. From what I can tell, radiation models just assume that movement is irrelevant. I don’t think anyone really knows.
In addition, it is often assumed that any radiation back to the surface produces warming. Once again, this appears to be a questionable assumption. Most of the photons will strike a liquid or solid H2O molecule and often participate in evapotranspiration events. This creates a water vapor molecule and usually ends up cooling the surface as more energy than just the weak CO2 photon is available.
From a pure energy perspective about half the energy striking the surface goes into evaporation in the tropics. It is probably even higher for CO2 generated photons given they are weak and absorbed immediately in the surface skin.
The bottom line is you can get a wide range to answers depending on the exact assumptions you use. I haven’t seen these problems detailed in any paper that looks at radiation models. It seems like the problem is too difficult and hence ignored. Instead, it is assumed all the energy goes into warming the surface with iterative increases in IR assumed.
Hence, radiation model results are always wrong.
How much LWIR is absorbed, surface to TOA, ranges from 85 to 65 percent depending mainly on how much water vapor the air contains. The term very quickly is not true if you mean within a very short distance above the surface.
I do not understand the insistance that radiation models are a priori wrong simply because they do not contain every detail of energy transport. Just because there are components of energy carried by latent heat and air motion does not mean that one cannot abstract a different portion of the problem and gain some insight by considering it alone — i.e. just LWIR. In fact MODTRAN does not explicitly account for radiation at wavelengths below 4.5 micrometers; that is, it does not account for solar radiation. We cannot input a value for insolation. Solar radiation is accounted for, implicitly, by boundary temperature and the total OLR. So is convection similarly.
Yes, there is some variance for water vapor and how much it intrudes into the atmospheric window. I should have been more specific. For CO2 all the available surface energy is absorbed within a few meters of the surface.
Radiation models have many valid uses. Trying to infer a complete picture of energy transport just isn’t one of them. However, that is exactly what climate science does. Probably the worst mistake is holding water vapor constant.
I always enjoy people who can think in three dimensions, it adds perspective.
I would even go one further: All calculations I have seen, operate on the assumption of homogeneity. “Consider this cube, it contains X water, Y CO2 and Z wishful thinking. Plug it into your equation, and find some answer that relates to homogenous blocks of gas.” I won’t even start in on their choice of 100-mile blocks…
I admit to not having done the calculations myself, or even so much as intently studying the infra-dead sky demons visiting ultraviolence upon our collective corpuses, for frankly, I think it navel-gazing of the most retentive kind. For the simple basic fact that even inside a cloud, there is texture, and the multiplicity of constantly-moving interfaces between moist/ dry, high/low pressure inside a swirling mass of decidedly non-homogenous plasma has not even been modeled on meter-scale, never mind the millimeter-scale we would need.
Gimme a can of beans, and I will blow away the effects of LWIR downradiation for an entire acre…
IOW: The transfer effect between two swirls of air inside a cloud causes enough temperature noise to confuse any satellite measurement sensitive enough to be useful. Its like looking down at a crowd of people, and deciding they all are thirsty, or tired, or they want an apple…
But in a world where we “treat” existential disenchantment by “correcting the brains chemical imbalance”, climastrology is Truth.
“IOW: The transfer effect between two swirls of air inside a cloud causes enough temperature noise to confuse any satellite measurement sensitive enough to be useful. Its like looking down at a crowd of people, and deciding they all are thirsty, or tired, or they want an apple…”
Maybe another way to look at it is that the radiation models provide merely a ceiling on the potential, hypothetical “effect” of CO2 on the Earth’s temperature because it simply looks at it in isolation.
By the time feedbacks and other atmospheric processes are factored in there is no CO2 “effect” distinguishable from zero. THAT is what OBSERVATIONS support.
There ARE NO observations that support an effect of rising CO2 on the Earth’s temperature. Assuming it has an effect because of a pet hypothesis is not a valid scientific conclusion.
Since a large percent of the earth is covered in H2O, water vapor is a large player. That latent heat has to hide radiation at the surface.
Yes, latent heat is a significant factor in over-all transport, but what do you mean by “hide radiation at the surface”? If a satellite detects a certain temperature of cloud tops or Earth’s surface it can only do that by measurments of radiance. How would that be possible if radiation were hidden?
As long as the H2O remains in a vapor state, i.e., has not radiated the latent heat away and turned back to liquid, what started as radiation is “hidden”. That is why it is latent. If H2O can absorb the “back radiation” from CO2, then it can also absorb the original radiation from the source, again removing it from further interaction with CO2.
I do have a problem with an analysis system that can not properly allocate radiation between the various phenomena that removes it from the immediate CO2 emissions for later radiation.
I also never see a plot of how the radiation from CO2 has changed over the years. That CO2 dip that is shown must have changed as the CO2 concentration has increased. It is a flux, as more material is added one should expect an increase in the flux. I would also like to see an hourly or half hourly depiction of what the radiation curve actually does. Using daily or longer average is probably misleading as to what is actually occurring.
It is interesting that the energy transmitted in the CO2 band is not zero and does not change as the concentration changes. I choose for simplicity a single spectrum line at 15 microns which is heavily attenuated by CO2 and then ask why isn’t that energy not completely absorbed?
My answer would be, all of the surface radiated energy at 15 microns is absorbed by CO2 molecules and the energy is distributed into the atmosphere. The energy transmitted at 15 microns is then blackbody radiation from the atmosphere. In fact practically all of the upwelling and downwelling radiation other than the surface radiation is blackbody radiation., primarily from water vapor. Since total absorption of the radiated energy occurs at both concentrations the blackbody radiation remains the same so the residual energy radiated at 15 microns is unchanged.
You might look at David Dibbell’s comment below, but CO2 doesn’t absorb all radiation at 13 or 15 micrometers no matter how strong the absorption line. In effect the cross section is large but not infinite.
If less than total absorption occurs why then would changing the concentration show no difference?
If one makes reasonable estimates of the photon flux over the 15 micron bandwidth (10^9 photons/m2/sec) and the number of CO2 molecules (10^21 molecules/m3) even without knowing the MFP and cross section it is hard to image any % is not absorbed by thousands of meters.
If you are including reradiation by CO2 molecules then I would question that also.
PS Davi8d Dibbell’s comment shows zero energy radiated at 15 microns.
My additional plots of overall transmittance for CO2 at 280 ppm and 560 ppm mean that none of the LWIR energy radiated from the surface at 15 microns makes it to space directly without being absorbed. There is still energy at 15 microns being emitted to space from the atmosphere itself in both cases. You can see this in the graphic output of Modtran, looking down.
Yes. I like Pat Frank’s comment (and conclusions) on the process from a post not too long ago:
“The radiant energy is absorbed (by CO₂) and then lost by collisional decay. Right up to the stratosphere, 15 μ vibrationally excited CO₂ decays by collision, not re-radiation.
The energy lost to collision is then dispersed into the KE of the atmospheric gases and thereby becomes one with the overall black body radiation field. Then, it gets radiated away into space, but across all the TOA BB wavelengths.
There isn’t any evidence at all that our CO₂ emissions have contributed diddly to warm the climate. Supposing otherwise is just that: supposition. Observationally unsupported. Theoretically invisible. Presently indistinguishable from zero.”
What you say makes sense. Good job.
What Pat Frank said makes sense.
Nobody I know of claims it was CO2 emissions that warmed the climate, it has always been CO2 absorption.
You still have to add to your summary for completeness what causes the BB radiation to flow down toward the warmer body more than up toward deep space and why all this kinetic energy transfer doesn’t heat the atmosphere.
But I am happy to see that it is now standard thinking that all radiation from the surface is absorbed by the atmosphere.
‘But I am happy to see that it is now standard thinking that all radiation from the surface is absorbed by the atmosphere.’
Except for the LW atmospheric window that allows the passage of some IR from the surface to radiate directly out to space. I assume it’s the part of the spectrum to the ‘right’ of the CO2 ‘notch’ corresponding to 288.15K (or whatever), on the MODTRAN output.
I thought about including that exception but then I thought it was likely there might be some slight water vapor interaction. I should check the satellite data to see it energy in that area deviates from the Planck Spectrum.
Just played a bit with Modtran. Very low CO2 concentrations (I used 1,3,10 ppm) depress the overall transmittance very strongly at 15 micrometers or wavenumber 666.
I hoped I had explained this. The dip from CO2 over the years would be nearly a flat line if it were shown separately on Figure 3. A total of over a 400 year increase in CO2 can’t be resolved in the presence of the much larger planetary factors like El Nino.
To demonstrate credible time dependence is not possible using MODTRAN because it is not a full solver of the transport equation. It can’t solve for unknown temperatures. It uses fixed models of the atmosphere. All I can say is that it takes some amount of surface temperature increase to return the OLR back to balance after fussing with CO2 by some amount.
Thanks for this article! I feel guilty in saying this, but I still think there is some merit in Dr. Hayden’s reasoning that the modelers need to demonstrate how CO2 doubling, which they say results in an atmospheric imbalance of 3.7 W/m^2 (the ‘forcing’) causes a 3K increase in surface temperature (the ‘response), which is equivalent to about 16.5 W/m^2 based on S-B.
You’re absolutely correct in that there is an interactive process in which radiative balance is restored, but I’m not getting any comfort from a radiative model like MODTRAN as to how the 3.7 vs 16.5 gap is closed:
Specifically, I setup the ‘background’ scenario using 280 ppm CO2 (the so-called pre-industrial level), US standard atmosphere (because I’m provincial) and allow constant relative humidity (the IPCC’s assumption), which gives 270.511 W/m^2 and a surface temperature of 288.15K. I then compare this to a scenario with a 3C offset where I adjust the CO2 concentration until we again get 270.511 W/m^2, which turns out to be about 1,420 ppm CO2. Note that without the temperature offset, the second scenario would have given 262.000 W/m^2, which is an atmospheric imbalance of about 8.5 W/m^2.
A couple of observations: First, the required change in CO2 to achieve a 3C increase at surface goes way beyond the IPCC’s ubiquitous 2xCO2 bogey man. And second, the 8.5 W/m^2 change in ‘forcing’ looks a lot like the alarmist number for CO2 doubling (3.7), plus water vapor feedback (3.7), plus other feedbacks, but I’m assuming this is just a coincidence.
Obviously there is a lot more to modeling Earth’s climate than radiative heat transfer and, as you noted above, MODTRAN itself is inadequate to tell us much about the latter.
So while you’ve convinced me that Dr. Hayden’s analysis shouldn’t be considered stand alone proof that the alarmists are full of it, I think that what he, you and many others say about the lack of evidence for CAGW are powerful reasons for us to demand at least some compelling evidence from the alarmists before proceeding to with their ‘mitigation’ schemes.
That is an interesting way of looking at it. Latent heat being “hidden” radiation.
It is not directly measurable by using temperature. It is radiation that is absorbed and no longer can participate in “back radiation” until it precipitates. It is different from N2/O2 since those have a temp increase and can be measured.
I’m sorry but using a static, one instant in time, ignores the insolation change as the sun moves across the sky among other things. It ignores heat storage for later release. Averages just don’t work for gradients of heat movement. If I may so bold, it is like using DC circuit analysis with averaged values for an instant in time for a circuit processing an AC signal. You can’t even do an integration to get an answer because you don’t have the gradient equations.
My big problem is that a cold atmosphere simply can not heat further, a hotter surface warmed by the sun. It can’t happen because no one can then explain how equilibrium would ever be achieved. Continued, infinite, heating is the only option as both bodies warm from the ever increasing reflected radiation. If back radiation adds to the heat (temperature) in the hot body, S-B is totally invalid.
Now, can heat storage “add” to the heat as the hot body cools due to reduced insolation. Sure! But, notice that REDUCED temperature are involved, not increased temperatures
There is no infinite heating. First because the atmosphere is not heated by radiation from the surface both bodies don’t warm (neglecting the minor much delayed heating from the increased evaporation convection and conduction). In fact all of the radiation from the surface entering the atmosphere leaves the atmosphere either at the ToA or at the surface.
The GHE returns about 2/3 of the energy radiated from the surface and transported from the surface. So increasing the surface temperature will increase heat energy leaving the surface but only 2/3 of it will return allowing effective equilibrium to be obtained rapidly.
‘The GHE returns about 2/3 of the energy radiated from the surface and transported from the surface.’
Is that 2/3 analogous to the ratios in the following link?
It is not the same two thirds. Mine includes the effect of water vapor.
If you can’t measure it then it is hidden. How do you use a ruler to measure a buried box you can’t see?
“Radiation models do not model the atmosphere. They don’t model convection. They don’t model evaporation/latent heat. They don’t model kinetic energy transfers. Since energy is moving between all these transport mechanisms in the real atmosphere, using radiation models will always provide the wrong answer.” +10
And that is the real problem with all the CO2 Climate Models.
Those “Rivers of water that flooded California last week moved Mega-Quadrillions of BTUs of energy as it transported water vapor that sucked up BTUs to make that water vapor river and then release those BTUs when that water vapor transitions to water drops.
Home work: Calculate how much energy was released from the conversion of water vapor to water drops in CA last week.
Extra Credit: Find a Climate Change report or model that incorporates this obvious phenomenon.
“Latent heat of condensation is energy released when water vapor condenses to form liquid droplets. An identical amount of calories (about 600 cal/g) is released in this process as was needed in the evaporation process.
Latent heat of evaporation is the energy used to change liquid to vapor.
IMPORTANT: The temperature does not change during this process, so heat added goes directly into changing the state of the substance.”
This happens as a result of the liquid absorbing the energy from the sun in the process of evaporating. A walk in the early morning along a river or lake shore will allow you to see this happen.
I note that the translation to this version on WordPress replaced with ‘p’.
In other words, assuming isotropic radiation the relationship between radiant intensity (I) and irradiance on a surface (G) is
Kevin, I’m going to whine at you. G? Really ? We already have B, I, L, M, and who-knows-what other radiances, irradiances, emittances…Planck’s equation is wall-papered with conflicting nomenclature depending on whether you are reading physics, astrophysics, spectrometry, or engineering textbooks. Where in F did you get a friggin’ G from?
Just kidding, but I feel much better now…
For Earthly purposes, just use P=I x A , P is Watts, I is Intensity in Watts/sq.M, A is area in square meters.
I= (2 Pi H C^2 / wavelength^5) / [ EXP( H C /(wavelength k T) -1]
You can also numerically integrate it on a spreadsheet over a wavelength range pretty accurately as done folowing. I’ve had to dona spreadsheet a couple of times as a result of computer glitches…no prob, works good….use meters everywhere but if you want your Y-axis to be in watts/sq.M/micron, you gotta multiply your answer by e-6
It is a pain to make conversions all over, I agree, but MODTRAN uses cm and we are stuck with it. It also calculates radiant intensity in units of Watts per unit area, per steradian per unit of spectral wavenumber. At least it calculates the integral over wavenumber, but it still arrives at an intensity that has steradians in it. Thus, to reach an irradiance in power per unit area, which can be compared to emitted power as in the Stefan-Boltzmann law, we have to integrate over a hemisphere above a surface. Here we run into troubles because the UofChicago version of MODTRAN wont let us view at all angles to integrate, so we just assume isotropic radiation and the integral results in a factor of Pi.
G is what the last textbook I taught from used…
BTW, I think Modtran UChicago cases used to find ground level warming should be run with fixed relative humidity, ground temp offset changed until TOA flux is same as previous case, with latitude and cloud cover changed until you are at a realistic TOA flux under 250 watts/sq.m. and altitude of over 70 km looking downward. This stops doubters from saying you didn’t allow for water vapour feedback. IIRC you’ll get about .8 degrees for 2xCO2….
My wife translates it into pie every pie day, as a minimum. She says pie are round, pie are not square.
I read this but I don’t understand it. Can someone help out with a plain and simple explanation of what Kevin’s concerns are, whether he answered them and whether his answers enhance the skeptic view or the alarmist view.
My take on it was- Modtran has its uses but don’t bet your family jewels on accurate numbers coming out of it.
It isn’t a compelling argument to admit that there is a known bug that produces the exact same output with different inputs, and then claim that because there is very little difference between two runs with different inputs it is ‘proof’ that CO2 has little effect. To be compelling, I think that the known bugs need to be fixed and then redo the runs.
I resorted to running multiple models to span the troublesome areas in parameter space; then see how an interpolation among the results where I wanted an answer would work.
One more point. When I find something surprising (but not unexpected) I like to report it even if it might undermine something else. In this case I had hoped by speaking of this error to set off some discussion about topics like 1. does climate modeling use this code in any way? Like verification, or was part of it extracted to form the basis of some other code? 2. What other uses has this code been put to? Calibration?
It did. Note the conversation below by “dk_” and Steve Richards.
My recollection is that Modtran was developed as an approach to do radiance corrections for nadir-viewing, multispectral imaging satellites, and was optimized for that geometry.
Wikipedia and Spectral Science’s descriptions validate our recollections, Clyde. Spectral seems to be providing a web enabled interface for version 6. With only a superficial look, I’ve found no interface for bug reporting, revision control, change history, or software source code, or any version warnings or technical limitations documentation.
Kevin said it was the tool available to him, and stated why the known errors do not affect his conclusion.
The tool is suitable for this use, but in such cases, I will always look for dependencies where the software is not the best choice for the job — it may lead to inadvertent errors (perhaps several of the errors referenced by Kevin in this piece) or to enable deliberate fraud.
Thanks Kevin, can I ask what your view is? Is there a climate crisis?
Thanks, go Griz!
Are you a U of Montana fan?
Then I should tease you with the nickname “Bob cat”.
I have been called worse.
Some years ago, I was driving through Missoula on vacation and saw a car ahead of me with this bumper sticker:
“Follow the Grizzlies or have a bear behind”
The other interesting local feature in the area is the remnant shoreline from Glacial Lake Missoula seen high up on the hills which surround the valley.
Here is a climate crisis mitigation question looking ahead fifteen thousand years in to the depths of the next ice age.
If a huge ice sheet threatens to block the Clark Fork River in the year 17000 AD, will the Army Corps of Engineers use nuclear explosives to keep another ice dam from forming?
Yes the Lake Missoula story is fascinating as for your question about future Lake Missoulas, no there is no need to blow up the dam we will move conservatives to higher ground and let nature take it’s course. I had a better bumper sticker but the moderators disallowed it.
Nut Zero does not have the potential to become a crisis?
If so, it could be called a climate crisis.
As you know, it’s like COVID19. It does have the potential to become a crisis depending upon how we respond to it.
This is a point that alarmists who cite Arrhenius fail to recognize. They confuse the qualitative ability of CO2 to absorb IR with being proof that that is how the system is controlled, and ignore all the other parameters of the system.
Here I was referring to the lab model of Seim and Olson. Their apparatus atmosphere was so transparent to CO2 that most of what they measured came from the apparatus structure itself. But the lesson from this work shows that transport is largely a function of the temperature and composition of the atmosphere which changes substantially over the troposphere on Earth, but not at all in the lab apparatus.
Nor does the lab apparatus replicate the exponential increases in volume with height and reduction of density with height.
Fatal flaws preventing a realistic outcome.
Thanks for the article. I intend to try and understand it a bit better when I have more time.
Slightly off subject.
I’ve been trying to understand how the no feedback warming to CO2x2 is calculated.
The results/approximations I’ve seen range from 1.05C (Happer) to 1.2C (Lacis et al).
The formular that I believe is used is (with assumptions),
T = 1.66 x ln(CO2 current concentration/CO2 original concentration)
T = 1.66 x ln2 = 1.15C
My guess is the 1.66 figure is derived by dividing the radiated energy from a black body at the surface temp. of about 15C (390 w/m2) by the radiated energy at the emission height temp. at about -18C. (240 w/m2).
i.e. 390/240 = 1.625. The difference explained by the earth not being a perfect black body.etc.
The logic being that if there are no feedback then the surface would be close to a black body.
I’d appreciate any help you can give me.
Thanks in advance.
My take on this is that the formula involving a logarithm is a “rule of thumb” that is a good approximation to the impact of CO2 over the entire thermal spectrum. You could be correct about how they found the 1.66 factor. Although one could also make a gang of detailed calculations and then fit a log function to a reasonable portion of the results.
However, what is actually done in a more complete analysis is to calculate for each narrow wavenumber band a solution to the full transport equation over some path in space. At each differential element of path in the atmosphere it takes into account attenuation of intensity from absorption and scattering and then augmented intensity of new emission because of local temperature. Then the entire spectrum is integrated over all relevant wavenumbers. It is a data and calculation intensive process. And I might add, possibly prone to round-off which is my thought about the apparent error in MODTRAN.
MODTRAN and probably all similar transport equation solvers/caculators make use of a detailed library of absorption line intensities and assume a particular shape of these lines after they are Doppler and pressure broadened — the Voigt profile. Happer and Wijngaarten have recognized through observations that this model of broadening produces aborption lines that are too broad and have too much effect as a result. They have imposed some empirical trimming of the wings of the broadened lines which compare better with measurements. The result may seem small, but this entire debate has many small signals that only become significant because of long times scales.
By the way, Bob. You wrote an essay here some months ago about the measured change in RH as opposed to what modellers of the alarmists believe. I had a suggestion about why the trend in RH falls short of their expectations. But when I wrote about it in the comments, I had a senior moment and addressed it to Kip Hansen for some reason. I figured you never saw it. Go have a look at that comment. I have been doing some additional thinking about it.
How can an “influence” be an influence if it/they are “truly unknown”? Sounds very “Rumsfeldian” to me, but then again climate science and “Intelligence” appear , to me at least, to have similar opacity quotients.
Kevin is confused, he does not understand, and he communicates his confusion in this article.
Can you demonstrate that you understand him well enough to communicate just how and in what manner he is “confused?” If not, then I guess we can all assume that you don’t know what you are talking about and are just providing an unsupported personal attack. Saying that you don’t know where to start is a cop out. However, it reflects poorly on you to say you disagree with someone but can’t explain why or even how.
There is so much confusion that I really don’t know where to start. I suggest you just hold on to the real stuff here..
I didn’t read your entire paper carefully. After seeing a couple of obvious malaprops, I began to doubt that you pay attention to detail and started to skim. If you want to be taken seriously, you should probably ask someone to edit your paper.
This and “recent WUWT essay[s]” tend to oversimplify what happens at the surface in the tropics. In the natural environment there will be considerable variation. Inhabited locations will be the same,eg in high density closed back yards, and “bluff body” locations (buildings on the ground) you do not need gas or fuel under a plate to cook an egg, and you don’t pick up steel tools without gloves. There will still be great turbulence taking place where there is no convection or advection. It is not easy to render the turbulence visible, and modelling it has so far not been successful. Mosquitos don’t like advection, but will accumulate in “bluff body” locations. This is one reason why houses spaced 25m apart on 2m stumps were once common, as it placed head height much closer to the stratified boundary layer. Ground cover and dust level makes a difference, AH and RH can vary considerably. I don’t recall that the same degree of turbulence occurring in cold climates.
Turbulence is convection and advection.
No convection. No turbulence.
This is a common refrain and I’d like to make a response. When Newton and Huygens were starting to formulate mechanics they faced the prospect of trying to account for all sorts of complicating factors like friction. What they did was to oversimplify — they imagined the isolated mass that would continue to “remain at rest or continue its constant motion unless acted upon by a force.”
Without this simplification the law of inertia could never have arisen. Once on figures out the ramifications of the oversimplified model the complication can be put back in.
Having had a few classes in reactor design, I’ve also noticed some of the parallels between neutron transport and radiative transport. #1 is the concept of energy self shielding where neutron loss in the resonance absorption energy levels is limited by the fact that there is a depletion of neutrons at that energy level due to the resonance absorption. Thus the concept of saturation in the CO2 absorption bands was almost immediately obvious.
As far as MODTRAN possibly having problems with use of single precision, that led me to wonder if MODTRAN was originally written on a CDC machine with 60 bit single precision.
Energy self shielding — that’s an excellent observation. Without a transport equation to guide thinking a person would never understand how the composition of the core would change during a cycle, and how to shuffle fuel to get the most from it; or how burnable absorbers help with the issue of loss of reactivity.
That’s a good thought about the precision issue, too. I am unsure what machine was originally involved, but I may have a resource to find out. A lot of nuance sort of got lost in the translation from some very specialized machine architectures to the PC. Common area alignment always presented trouble for instance.
All of these models assume a well mixed gas … which globally neither water vapor nor CO2 are … garbage in garbage out … alot of mathematical navel gazing … must be a fun hobby …
Amazing.Devastating.Worthy of separate, detailed documentationI’m not in the software testing and fixing business anymore, either, but hardly anyone realizes how really common this sort of software error is, or how much it affects policy and the tools that we use to manage daily life. This is huge.
Although Spectral Sciences and AFRL still claim ownership of MODTRAN, at a glance it looks like a maintenance and upgrade orphan. While there is apparently some newish interface development, I’m unable to find bug reporting for it.
It appears that MODTRAN was written with government funding, is the software etc available to be ported to a new language. Making it more accurate, verifiable and testable?
It was coded by Spectral Sciences Inc. for the Air Force Research Lab. http://www.modtran.com. I am disappointed by the state of both orgs web presence. Not having any interest in personally engaging with either organization again, I haven’t tried contacting Spectral’s MODTRAN support. If you do, please post how it goes.
Many such FORTRAN programs were written for and by the Federal Government, most of these are orphaned. Many were originally written by Gov’t scientists and engineers. Years ago, there were some funds to modernize some of these and the rights were then assigned to companies like those listed above. But computer scientist and modern programmers appear have a bias against using FORTRAN. Yes, it was originally written for punch cards in mind but its an easy language to write numerical code that is compiles and runs faster and more accurately than other languages. Double precision rocks! The Gov’t still runs a lot of FORTRAN code on their supercomputers. This minimizes computer run time. Yes, they still keep track of how much time you use on these computers and are charged accordingly.
One of my favorite statements, for example :
GO TO ( 10, 20, 30, 40 ), N (I believe this FORTRAN 77 code)
I used it to get a reactions from programmers. It makes me smile.
Almost like the assigned GOTO statement.
I was not surprised to find this, but one can only wonder the various ways this code itself is being used, or perhaps how parts of it have become parts of other codes and so forth. Legacy codes are commonly the parents of other codes and they sometimes grant their offsping a “genetic” flaw.
Note Erik Magnuson’s comment above about one possible source for this error — i.e. word length differences machine to machine.
Vintage of MODTRAN is about right to have been one of the examples motivating the aborted attempt to create and promulgate ADA.
One would hope that subsequent efforts realized the code limitation and implemented something with more precision; and or validated results as you have. I know of no certain way to audit all related software systems to find out about dependencies — one of my nascent objections/rants regarding the results of software or modeling used as if it was a measured and verified observation.
I’m hoping that DOD, NASA and NOAA aren’t using un-modified MODTRAN for anything critical.
Again, my recollection is that it was being used in the early era of the Landsat program. Since then, numerous other multispectral imaging satellites have been launched, and at least a couple of other atmospheric correction programs have been written, often with the intention of being used in conjunction with specific remote sensing, image processing package or as a pre-processing step to derive true radiance after sunlight has made two passes through the atmosphere.
This is an unusually thorough article, and spends enough time discussing the likely quality of the data used.
The problems with modern climate science differ among people, based on their politics. The science says CO2 is a weak greenhouse gas above 400ppm
The leftists, however, see the claim of CO2 being very dangerous as a great propaganda tool to gain more control over the private sector of economies. To reach their ultimate goal of totalitarian governments run by leftist “experts”
Most conservatives understand that CO2 is a weak greenhouse gas. Some understand that more CO2 benefits the colder nations and especially benefits most plants,
There is a group of conservatives who reject 100% of consensus climate science They reject the 99.9% consensus (my conservative estimate) that there is a greenhouse effect and CO2 is part of it.
They also reject the 59% consensus (2022 poll) that CAGW is real.
It’s good that they reject the 59% CAGW consensus, which is 59 percentage points too high.
But when they reject AGW (the greenhouse effect, and that CO2 as a greenhouse gas) they become ineffective in refuting CAGW.
These AGW deniers are trying to convince 999 out of 1,000 scientists they are wrong. A hopeless cause. An impossible dream.
The right debate is trying to convince 59 of 100 scientists that CAGW is not real — it’s just a prediction that has been wrong since the 1979 Charney Report.
When you observe the “climate war” from above, modern climate science is mainly politics, not real science like this article.
Modern climate science consists of over 50 years of scary, and wrong, climate predictions, with no one ever admitting they were wrong.
Predictions of a coming global cooling crisis from about 1970 to 1975
Predictions of a coming global warming crisis from 1979 to 2023
The predicted (imaginary) climate crisis is always coming, but never arrives
The obvious conclusion is humans can’t predict the climate…. except for me, and my prediction came after only my first hour reading about climate science in 1997: “The climate will get warmer, unless it gets colder”.
I am 100% sure of that, with 102% confidence.
Honest Climate Science and Energy Blog
Good points, Richard.
Richard, public policy decision makers have a habit of asking for predictions of what is likely to be happening in the future if one course of action is being followed versus some other course of action.
If a public policy decision maker asked me for my opinion concerning where global mean temperature (GMT) is headed over the next eighty years, this is what I would say.
Based on my one-page graphical analysis of past and current trends in global mean temperature, the earth will see another 1C to 1.5C rise in GMT between now and the year 2100, from some combination of natural and anthropogenic causes.
Further, the rise in GMT between now and the year 2100 is more likely to be closer to +1C than it is to be +1.5C, as indicated by the pattern of warming and cooling trends over the past 170 years.
For purposes of public policy decision making, this is my position. It must be assumed that a measurable rise in global mean temperature is now baked in to the earth’s climate system. Nothing anyone does between 2023 and the year 2100 will make much, if any, difference to the outcome.
Any problems this relatively minor but unstoppable rise in global mean temperature will cause are easily handled by climate adaptation policies — as opposed to imposing aggressive climate mitigation policies which destroy our legacy energy production and delivery systems for no measurable reduction in the rate of future increase of GMT.
If the climate activists who who pushing hard for the Net Zero transition want to disagree with my analysis, that’s fine, let them do so.
But in making their arguments for destroying our legacy energy supply system in the name of fighting climate change, we should expect the climate activists to offer a credible plan and strategy for convincing China and India to do the same; and we should demand that these activists produce a science-based prediction for just how much the rise in GMT will be slowed if their anti-carbon policy agenda is adopted.
Just my opinion – The US and Western Europe are headed down the same path the Roman Empire went down. The politicians are more interested in getting and maintaining power than in getting things done and the citizenry is degenerate and lives for the bread and circuses put on by government.
I predict the AGW deniers will go berserk after reading this article.
Don’t bother responding to each negative comment, Mr. Kilty, because you will not change one mind of one AGW denier. They are 100% sure of themselves.
Reading the article I did wonder why with all the 100s of millions of $ going into climate research a 1980s piece of legacy software is still being used. Even with a fancy frontend it’s like an old banger with sawdust in the gearbox and filler and newspaper in the sills
Surely these days you could develop a better solution for an iPhone 14 or Android 12 phone so everyone could play to their heart’s content ? Or Or something open source for Windows?
Good article, Kevin Kilty.
“Interestingly the wrapper doesn’t use p [pi] but the constant 3.14 instead.”
Yes. I discovered this a few months ago as I was trying to sum the model output by wavenumber to match the overall W/m^2 in the graphic output box. Using exactly 3.14 worked.
I would like to make one more point and “connect the dots” to the NOAA GOES East band 16 images I have been linking to frequently here at WUWT for over a year now. Band 16 is centered at a wavelength of 13.3 microns.
The image attached here to this comment is a plot of the Modtran-derived (i.e. instantaneous, static) difference in overall transmittance by wavelength, for a doubling of CO2 from 280 ppm to 560 ppm, everything else held fixed, using the 1976 U.S. standard atmosphere, no clouds or rain. (In other words, the plotted values show how much reduction in transmittance is computed for a doubling from 280 ppm to 560 ppm.) Notice the peak difference at about 13 microns. Interesting.
And here again is a link to the NOAA GOES East Band 16 (13.3 micron) images. NOAA calls this the CO2 Longwave IR band. The radiance at 30C (yellow) on the brightness temperature color scale is 10 times the radiance at -90C (white.) This is how the motion of the real atmosphere, including the influence on the formation and dissipation of clouds, changes everything about where to expect the energy from the incremental static surface warming effect to end up.
Thanks again for helping to shed light on the Modtran model and its peculiarities and limitations.
With regard to the 3.14 factor, I find it gratifying that two people working independently can find the same small issues in a complex topic. I dig a bit at things until I am satisfied that I understand a topic and then dig further to see if everything is consistent. You must be the same.
Good comment. That graphic you present is interesting and the GOES image is fascinating. I have seen that GOES image before, but as you must know, there is so much science to look at NOAA sites that a person has a tendency to be overwhelmed and then forgets about it quickly. I should go back and look at your writings on this topic.
Thank you for this reply. I enjoy your posts and comments.
I’m replying to add the plots of overall transmittance for the 560 ppm case and the 280 ppm case separately. Here is the 560 ppm plot.
And here is the 280 ppm plot.
In the 8 to 13.5 IR micron band, the atmosphere is just about transparent regardless of the amount of CO2 or H2O vapor. This corresponds to Weins law temp of ALL Earthly surface temperatures, and thus (by the shape of the Planck curve) over 30% of all IR radiated from the surface would go directly to outer space…except for that which strikes clouds as it tries to escape…..and clouds cover about 65% of the Earth’s surface at any given time. With about half of the planet’s Albedo due to clouds as well, it is actually cloud cover that controls the planet’s temperature.
Radiation enthusiasts don’t like it, but the greenhouse gas effect cannot be separated from the convection. They come as a bundle.
With an adequate concentration of IR active gases the convecting troposphere must develop.
This includes the transport of moist air by fluid dynamic motions, and the associated phases changes of water.
Conceptually, more IR active gases, more convection. Power is delivered where and when it is needed to maximize radiative emission to space.
And so, a radiative-convective equilibrium.
And we have a thermodynamic system on Earth which has already achieved radiative convective balance. The optical depth has been optimized already by a limitless supply of H2O in all its phases.
Any addition or removal of trace gas will be compensated in the system to maintain its optimal optical depth and associated convective equilibrium.
The optimization state set by the density and gravitational properties of the system.
“And we have a thermodynamic system on Earth which has already achieved radiative convective balance.” Yes. And if the atmosphere’s radiative coupling to the surface improves a bit, its performance as the compressible working fluid of its own heat engine operation to drive overturning circulation at local to global scale is incrementally enhanced, not diminished. The “forcing + feedback” framing of the GHG question has been a misdirection from the beginning of the “climate” opposition to fossil fuels.
Yes, the virtual increase in tropospheric depth by addition of trace gas in reality increases the entropy budget in the fluid dynamic system.
Energy is a conserved quantity, while entropy increases.
For the empiricists:
It is not a coincidence that the ratio of the environmental lapse rate and the adiabatic one is the same as the ratio of surface radiative flux equivalent and clear sky OLR
This is because they are bundled in thermodynamic harmony. They are one, and the same.
The degree of atmospheric instability is equal to the radiative equivalent flux ratio:
Environmental lapse rate 6.5 K/km
Adiabatic lapse rate 9.8 K/km
ratio 0.66 or 2/3
Radiative equivalent factor:
Clear sky OLR 265 Wm-2
Surface radiative flux equivalent 400 Wm-2
ratio 0.66 or 2/3
Clear sky greenhouse factor = 1 – instability factor.
And the lapse rates are dependent on the Cp of dry air.
Once again, enthalpy and not temperature.
I would never disagree that enthalpy is what is being missed. I was only addressing JCM’s comment about the lapse rate.
‘ratio 0.66 or 2/3’
Thank goodness this ratio isn’t 0.62 (i.e., 0.618) or you’d have to deal with the Fibonacci / Golden Ratio crowd. Kidding aside, your comments are always interesting.
I’m still missing a piece of this. As the surface temperature rises so does its LWIR. Let’s look at the moment that the sun goes below the horizon. From this point till sunrise the radiation from the surface is approximately exponential or, even more closely, a polynomial of order 3. If the temperature has gone up that decay will start from a higher value than it was before. If you integrate that decay curve, say over the first hour, the area beneath the curve will be greater for the first hour than if it started at a lower value. Attached is a graph of nighttime temps from Aug 2, 2022 and Mar 2, 2022. Significantly different integrals for the first hour, About 15,500 for Aug and 7500 for Mar. While these are vastly different months it shows that the radiation is different for different starting points. Even a 3K difference in temp will show a different integral.
I did this over an hour in order to allow “back radiation” effects to be propagated through the atmosphere back to the surface. I don’t expect this to be anything other than a first attempt and therefore needing to be refined a lot.
“ It’s an infinite series of re-radiation which eventually converges when there is a return to energy balance.”
The curves look to be asymptotic. Does this infinite series converge slowly enough over a 10-12 hour nighttime period to result in a higher minimum temperature when you start out with a higher initial value?
Very interesting looking data. There is very little information to go on, but I note that the August curve goes flat for a long time. In august around here we often get a “katabatic wind” well after sunset that comes down river valleys. Sometimes very windy. This really disturbs local temperature near the ground. Isolated places on the surface can become significantly colder than places exposed to nearby vegetation, buildings, and the wind, etc. Also, ponder the difference in surface cover between March and August.
While I hoped to isolate the effects of LWIR in this essay, it’s obvious there are many factors involved in heat transport and the evolution of temperatures.
It’s more likely my random picking of start points! At some point during the day the sun’s insolation and the LWIR from the earth begin to balance. That balance can last for some time. I just did this quickly and didn’t label anything or try to pick exactly the same times. The x-xaxis is 5-min temp data so that plateau is less than an hour in length.
It’s only after that balance “breaks over” that you truly see the decay kick in.
But you are right, there are all kinds of factors that affect the curve, especially clouds. I just wanted to show the impact on the temperature, not what was actually causing the temperature. There is a bump between about 50 and 80 and I have no idea what that was. Could have been a pressure front with clouds moving through.
The pedigree of MODTRAN:
The name stands for MODerate TRANsmittance, originally there was only LOWTRAN and later HITRAN. I don’t recall exactly what the distinction between low, moderate, and high resolution was/is.
It is a product of the U.S. Air Force Geophysical Research Laboratory at Hanscom Air Force Base (Bedford MA) in the 1970s (it may have even started earlier), and yes it is very much card deck-oriented batch-mode FORTRAN. The guys who wrote it were spectroscopists so they did everything in inverse-cm (conversion um = 10000/(1/cm).
I remember getting a copy of LOWTRAN off a mag tape in the 1980s and yes, it was written with little or no regard for software engineering. Using “3.14” for pi is but one example of bad practice.
I needed to calculate atmospheric transmittance (from vacuum to ground) but could not employ the atmospheric layer models that LOWTRAN/MODTRAN uses. I ended up converting the molecular absorption calculations into Pascal, then C, and finally LabVIEW. This was done by cutting the absorption coefficients out of the DATA statements and interpolating them to the wavelengths I needed. The absorption coefficients have only 2-3 digits precision, IIRC.
One odd point I never understood about the differences between the models: LOWTRAN and MODTRAN had the exact same DATA statements for the absorption coefficients. And because they are in constant inverse-cm steps (either 5 or 10 1/cm), the resolution degrades toward shorter wavelengths.
This penchant for using FORTRAN continues to the present in atmospheric calculations; there is a solar irradiance model called SMARTS written in card deck FORTRAN (originated in the 1990s), as are the UAH satellite temperature anomalies of today. The UAH documentation tells how to read the data files with FORTRAN statements, and from what I understand the IPCC monster models are also FORTRAN. If you look at the UAH data files month-to-month, they apparently calculate the 30-year anomaly baseline data each month, even though the baseline period does not change. As a result the five-digit baseline temperatures can change by one digit (0.01 K). This tells me they rerun the entire 1979-present calculations in batch mode every month.
One more point—as this was weapons-related research, my understanding is the primary use of LOWTRAN/MODTRAN was calculating laser line attenuation between two points in the atmosphere. In the 70s-80s high-power gas lasers were primarily CO2 lasers.
I’m guessing that the LOWTRAN/MODTRAN work was based on research done in the early 60’s on reducing the IR signature of the B-70. The idea was having a coating having high emissivity for the wavelengths with high atmospheric IR attenuation and low emissivity in the atmosphere’s IR windows. The IR sensors on the YF-12A were capable of detecting an airplane from well over 100 miles away.
FWIW, I don’t think there is anything wrong with doing numerically intensive work in FORTRAN.
True—it is possible to write bad code in any programming language.
This was weapons research. It was done to improve the Sidewinder Missile. I don’t know about the laser research.
My work wasn’t weapons so all I know was offhand—the 1980s was the SDI era.
Thanks for this background. FYI, the current website interface to MODTRAN by the University of Chicago gives the model output for radiance by wavenumber (1/cm) from 2 to 2200 in steps of 2. This is viewed by clicking on the “show raw model output” button.
Kevin Kilty’s, “The LWIR Puzzle: Experiments with MODTRAN”, is just another glib
paper, out of many frequently appearing in Watts Up With That, preaching the catechism
according to the Global Warming Climatistas, in their never-ending demonization of
CO2. No, Mr. Kilty, I am no more an “exonerator” of CO2 with respect to its causing
global warming than I am an exonerator of Astrology in its causing global warming.
The simple fact is that a stable, simple gas in the atmosphere present at 420 ppm can
no more be responsible for warming the Earth than the position of Scorpio in the sky
on the date of your birth. Neither “cause” needs exoneration … nor serious thought.
And no experiment has ever shown that doubling the amount of CO2 in our atmosphere
will have any effect whatsoever on decreasing the intensity of the long wave infrared
radiation escaping the upper atmosphere going into outer space or on increasing the
temperature of the surface of the Earth presumably 25 miles below. All this is part
of the catechism, not the science. And that figure which starts this paper is a
mind-boggler, purporting to show “differences in outgoing longwave radiation (OLR) at
the top of a tropical atmosphere between 260ppm and 420ppm CO2 concentration” without
any unit in the figure indicating anything to do with ppm of CO2 in the atmosphere!
What warms the Earth, of course, is the Sun — the Sun’s energy reaching the
surface of the Earth and being absorbed thereat. (The absorption of the Sun’s
insolation on the way down hardly affects the temperature of the surface of the Earth
at all and produces weather or climate effects only secondarily, like (maybe)
affecting liquid or solid water in the upper atmosphere as it passes by). Barring the
obvious consideration of how much of the Sun’s energy actually makes it to the
surface, and barring the corollary consideration of how much of that energy gets
instantaneously reflected right back to outer space at the surface (reflected
radiation will have the same frequency and so will have little additional absorption
by the atmosphere on its return trip to outer space), and barring the other corollary
consideration of scattering (very much like absorption — see below), once it makes it
to the surface, whether this incoming energy warms the Earth more or less is really
dependent on only ONE major factor: namely, does that heat from the Sun reaching the
surface and being absorbed there stay at or under that surface for any significant
period of time thereafter as opposed to very quickly entering the gaseous atmosphere
above that surface, and then, through convective processes, quickly going up to the
upper atmosphere via mass transport of heat, and then quickly being converted to
radiation there and then going into outer space. Little of the heat radiated from the
surface of the Earth makes it directly into outer space. Infrared radiation detected
in the atmosphere at night comes slightly from the surface but much more so from the
atmosphere itself radiating that heat — compare the temperature of the Moon’s
“atmosphere” during its nighttime. Mr. Kilty states the opposite (the “atmosphere is
almost [infrared] transparent from surface to space”) and I say he is mistaken.
It is true that the pressure of the atmosphere, along with its height and
turbulence, have the potential to, over time, slow down or speed up that convection
process somewhat, but obviously not if that pressure and height and turbulence remain
pretty much the same with time, as is the case for the Earth over millennial time
frames of reference, and, as is certainly the case for burning fossil fuels adding
trivial amounts (relative to the total mass of the atmosphere) of new CO2 gas into the
atmosphere, having no appreciable effect on convective processes. The fact that the
CO2 molecule, and overwhelmingly more so, the H2O molecule (along with the molecules
of all the other make-believe “greenhouse gases”), absorbs certain frequencies of heat
energy, when that energy reaches the atmosphere from the surface of the Earth, is
essentially irrelevant to the crucial (and rapid) heat convection processes occurring
under these gaseous conditions of this open atmospheric system bordering the cold,
black, emptiness of outer space. The catechism of the Climatistas, incessantly
talking about this infrared radiation absorption (and, worse yet, “infrared
reflection”, which Mr. Kilty states he does NOT subscribe to) as if it had any effect
on anything directly relating to weather or temperature or climate, is obsessive,
unbalanced word-slinging. I think this is also what Richard M was saying in
his comments above. Any gas absorbing electromagnetic energy in the atmosphere will,
within microseconds, have that electronic energy transduced into heat in its
surroundings. No scientific evidence (as opposed to “theoretical” modeling) has ever
shown any of these obsessions relevant to anything relating to weather or temperature
or climate in any direct way.
It’s surface heating and convection which tell most of the story, not radiation.
You are a prime example of why Willis Eschenbach asks that a person quote exactly what he wrote. What Mr. Kilty actually said was this.
It is exactly the opposite of what you claim and I ask “how can a person be so wrong?”
Interesting article, Kevin, and there sure does seem to be a lot of confusion on this topic. My analysis indicates that the confusion is centered on a failure to properly grasp the concepts of “energy”, “power”, “work”, “temperature”, “entropy”, and “radiation”, and how these relate to each other.
It is not clear from your article whether you have grasped these concepts properly yourself, but let’s try a simple (ish) stab at the issue.
You wrote “near the tropical surface this increase in CO2 boosts downward directed flux by 1W/m2”. Now you didn’t write a value for the “unboosted” downward directed flux (as power, in Watts), but others have. Usually this is around 300 to 400 W/m^2 (for example, as reported by NOAA’s SURFRAD stations). So I wondered whether MODTRAN is part of the problem, and I asked it what its default value (with default input parameters) for downward (i.e. looking up) LWIR power is, at the surface, aggregated over all the LW wavelengths it is concerned with.
It reports about 369 W/m^2, similar to NOAA’s values, but it also says the surface temperature at altitude 0 km is 0 K. Interesting. I don’t see any way to tell it what the actual surface temperature is, but this downward power at that fictional surface temperature is in the ballpark that I would expect, based on S-B and average atmospheric temperatures. From this I would conclude that MODTRAN is not part of the problem, but perhaps folks failed to notice that “0 K” condition, or thought it was irrelevant.
So my question to you is: what would you propose as the approximate average downward LWIR power at the actual surface of Earth, at night, at ambient temperature (which would typically be around 288 K, give or take)?