The basis of IPCC predictions is that any moderate warming caused by increased CO2 levels is enhanced by more evaporation from the oceans. Water vapour is itself a strong greenhouse gas and this increase results in a large “positive feedback” boosting climate sensitivity to a doubling of CO2 as high as 6C.
This is all just theory however, so it is important to observe whether water vapour in the atmosphere has actually increased or not in response to increasing CO2. The data shown below are from the NASA NVAP [1] project based on radiosonde, TIROS,TOVS & SSM/I satellite based data. This data was kindly brought to my attention by Ken Gregory [2].
Fig 1: total Precipitative water vapour in 3 levels in the atmosphere im mm. The 3 curves are Northern Hemisphere, Southern Hemisphere and the “Global average” – see 2) below.
The data from NVAP shows little change in water vapour from 1988 until 2001 at all levels in the atmosphere. If anything a small decrease in the important upper atmospheric layers in the detail shown below Fig1b.
Fig 1b: detail of TWP for upper layers in atmosphere.
If we now integrate all layers to get the total water vapour column we then get figure 2:
Figure 2 total water vapour content global averaged for all levels.
There is no evidence whatsoever in NVAP of any increase in water vapour in the atmosphere during the period 1988 – 2001 during which time CO2 levels increased by ~30 ppm (10%) and temperature anomalies by ~0.3C. The data show some reduction in water vapour in the radiative crucial upper layers of the atmosphere. Based on this data water vapour feedback looks to be small or even negative.
This result is evidence against significant positive feedback from water vapour to CO2 radiative forcing. Small changes in water vapour can completely offset (or enhance) any change in CO2 radiation flux to space. The evidence does not support any trend increase in water vapour with either surface temperature or CO2.
References
1. http://eosweb.larc.nasa.gov/project/nvap/table_nvap.html see also http://www.leif.org/EOS/2012GL052094-pip.pdf
2. Ken Gregory points out that our water vapour values calculated by the Fortran program supplied give slightly higher values than that quoted in the new paper: Weather and Climate Analyses Using Improved Global Water Vapor Observations. The reason for this is currently unknown. However that paper also shows no increase in water vapour from 19880 until 2010.
Globally averaged monthly water vapour (from ref. 1)
Water vapour lowers the absolute value of the thermal gradient, leading to a lower surface temperature.
The fundamental assumption of the greenhouse effect is that back radiation has warmed the surface from 255K to 288K. But this assumption is itself based on a false assumption.
Roy Spencer (in his post about Greenhouse misunderstandings) claims in his point (6) that the atmosphere would have been isothermal at 255K in the absence of any GHG.
An isothermal atmosphere in a gravitational field would violate the Second Law of Thermodynamics, which reads: “An isolated system, if not already in its state of thermodynamic equilibrium, spontaneously evolves towards it. Thermodynamic equilibrium has the greatest entropy amongst the states accessible to the system”
In isothermal conditions there would be more potential energy (PE) in eash molecule at the top, and, because kinetic energy (KE) is homogeneous, molecules could “fall” downwards and do work in the process. hence it was not an equilibrium state, let alone one of maximum entropy, as is required by the Second Law of Thermodynamics.
The Second Law of Thermodynamics has to be obeyed. So (PE+KE) has to be homogeneous, because otherwise work could be done, and so the system would not be at an equilibrium with greatest entropy, as the Second Law requires. In the process of reaching such equilibrium it is inevitable that molecules at the bottom have more kinetic energy, and there are more of them in any given volume, and so that does give a measure of higher pressure, yes. But the whole column could still cool down, maintaining the same gradient and pressure.
So pressure does not maintain temperature. The relationship in the ideal gas law only applies in adiabatic conditions, but the atmosphere can radiate heat away. If you “turned off” the Sun, Venus atmosphere and surface would eventually cool down.
We need to consider how the thermal energy actually gets into the Venus surface, especially at the poles. The facts are ..
(1) the poles receive less than 1W/m^2 of direct insolation.
(2) the atmosphere 1Km above the poles is at least 9 degrees cooler, and not absorbing much insolation either. It could have at most 1W/m^2 coming back out of the surface, which (at 0.5 absorptivity) would raise it to a mere 7K.
(3) Rather than being 7K, the lowest Km of the Venus atmosphere is around 720K, just a few degrees less hot than the surface.
If all convection (resulting from absorbed incident insolation at various altitudes) only went down the thermal gradient (ie towards space) how would enough energy get into the surface, especially if it were even just 1 degree hotter than the base of the atmosphere?
My answer is that the sloping playing field (the thermal profile) becomes a level playing field due to gravity, so all energy absorbed in the atmosphere (mostly incident insolation) spreads out in all directions, creating convection both up and down, and also diffusion and convection right around the globe producing equal temperatures at equal altitudes, but higher temperatures at lower altitudes. Then intra-atmospheric radiation reduces the magnitude of the net gradient by about 10% to 15% on Venus, (as best I can work out) but by about a third on Earth. Some of the extra reduction on Earth. though, is probably due to release of latent heat.
Here’s a thought experiment. Construct a perfectly insulated sealed cylinder filled with pure nitrogen gas. Suppose there are two insulating dividers which you can now slide into place one third and two thirds up the cylinder, thus making three equal zones. Warm the middle zone with a heating element, which you then turn off. Allow equilibrium to establish with the warmer nitrogen in the central zone. Then remove the dividers. Those molecules which move to the top zone will lose some KE as they gain extra PE, whereas those which fall to the lowest zone will gain KE as they lose PE. Hence, when the new equilibrium is established, the highest zone measures a lower temperature than the middle zone, and the lowest zone measures a higher temperature than the middle zone. Hence the highest zone measures a lower temperature than the lowest zone. QED.
So there is no need for any greenhouse effect to raise the surface temperature, simply because gravity cannot help but do so, because the atmosphere must obey the Second Law of Thermodynamics.
Much of what you write is correct. Your argument is very similar to that of Stephen Wilde – see for example long discussions here and here.
At exactly the Dry Adiabatic Lapse Rate (DALR) a packet of air moving upwards gains potential energy and loses kinetic energy exactly as you say. The atmosphere is stable and no external work is needed to move air in a vertical column. The atmosphere is stable against convection.
With water vapour present then as air rises it reaches the dew point and water condenses warming the surrounding air by releasing latent heat. This warming reduces the environmental lapse rate towards the moist adiabatic lapse rate. This is the case in the tropics where the lapse rate is much less and the tropopause much higher.
When solar energy heats the surface during the day this tends to steepen the lapse rate making the atmosphere unstable and convection starts. Rising air and evaporated water transport heat from the surface to the atmosphere to restore the stable lapse rate. When the temperature profile is very unstable thunderstorms ensue and moist air continues rising up to the tropopause. Convection and evaporation move about 2/3 of surface heat to the atmosphere, another 1/3 radiates out the IR window. The atmosphere can only lose heat through radiation to space – roughly 80% from H2O molecules and 20% by CO2, ozone, methane etc.
You are right that the lapse rate and the surface pressure determines the temperature gradient through the atmosphere and that is why Venus surface temperatures are so high. It is not due to CO2 really at all. However you still need convection to drive the lapse rate to its equilibrium value. On Venus there are violent convection winds and whirlpools at the poles. Solar heating is mainly in the atmosphere itself and only a small amount reaches the surface.
Now we take a 100% N2 atmosphere. Would there be a lapse rate and if so what would the surface temperature be ? There would still be considerable solar differential heating differences both in latitude and in night/day so convection cells would still exist. However now there is no direct way for the atmosphere itself to lose heat to space – although some radiation would still escape due to N2 collisions. I have thought long and hard about this – and my current opinion is that there would still be a lapse rate but it would now shift so that the Teff height (255K) was now practically touching the surface. I think the tropopause would be lower and colder. 99% of radiation loss to space would be from the surface.
Therefore there is an effect from “IR active gases” which has been mis-named the greenhouse effect. It turns out that for CO2 the central 15 micron line is currently saturated and only high up in the stratosphere does the air thin enough so photons escape to space. The temperature there is HIGHER than that below the tropopause. Increasing CO2 levels perversely moves that level up to higher temperatures – so more radiation escapes to space – not LESS. However for all the side lines this is not the case and the average emission heights for these are from 2-5km above the surface. So increasing CO2 slightly reduces the IR energy to space – the so-called greenhouse effect.
Of course this small decrease due to more CO2 can simply be offset by water vapour levels decreasing in the high atmosphere and this seems to be what has happened. The lapse rate is fundamental to the greenhouse effect. It depends on lower temperatures higher up where the mean free path for photons increases such that they can eventually escape to space carrying away heat energy. The heat energy transported is proportional to sigmaT^4 where the photons originate.
In a complete nitrogen atmosphere the atmosphere would be heated directly by the earth by conduction of heat and consequently by conduction. During day time atmospheric temperatures would rise because of this heat transfer. The atmosphere can’t lose energy, no infrared active gases present. However during the night the atmosphere start loses heat to the earth, but the cooled air near the bottom will stay there and form an insulation layer which resists further cooling of the atmosphere: formation of a large temperature gradient near the bottom. The average temperature of this atmosphere (at 1.5 meter for instance) would be well above any calculated average radiation bottom temperature? ! This is a real greenhouse. Heat can’t be lost by the atmosphere, just as in a real greenhouse.
second time conduction must be convection.
Typos: about in “The data support abut a 10%”; and 1988 and increase in Reference 2.
The global average should be the same as (NH + SH)/2. This is exactly true for the years 1993 – 1997. In figure 1, the global average curve should be the midpoint of the NH and the SH curves. There must be some problem with the Fortran routine that causes the global average to be different from the simple average of the two hemispheres for some years.
Clive found a error in the NASA supplied Fortran code.
I now calculate the 1988 total precipitable water vapour to be 25.01 mm. This compares well to the Heritage and NVAP-M values of 25.12 and 25.06 mm, respectively, reported in the Vonder Haar et al 2012 NVAP paper at Ref 1.
Clive, you wrote, “The data shown below are from the NASA NVAP-M [1] project …”. The data is from the Heritage NVAP project. The NVAP-M refers to the extension of the Heritage NVAP to 2009, and includes a reanalysis of the Heritage NVAP data 1988 to 2001. Only the Heritage NVAP 1988 to 2001 data is publicly available. The reference 1 paper gives the preliminary results of the NVAP-M project, but the gridded data is not publicly available. That data is expected to be made available in March 2013.
I plotted the global and hemispheric annual average precipitable water vapour by atmospheric layer on a logarithmic scale here:
The data is in Excel format at:
http://members.shaw.ca/sch25/Ken/NVAP.xls
The graph is presented on a logarithmic scale so the vertical change of the curves approximately represents the forcing effect of the change. The water content of the L1 layer, surface to 700 mb, is about 20 times greater than in the L3 layer, 500 to 300 mb, whereas the forcing effect of a change in the L3 is approximately 20 times the same change in the L1. From 1990 to 2001, the water vapour changed by: L3 -0.55 mm, L2 -0.57 mm, L1 +1.73 mm. The decrease in L3 is equivalent to an 11 mm reduction in L1. The water vapor decline in the L2 and L3 layers overwhelms the forcing effect of the water vapor increase in the L1 layer, so the water vapor feedback is negative. The upper atmosphere (L2 and L3) water vapor content of the southern hemisphere is less than, and has declined more than the water vapor content of the northern hemisphere.
The graph and discussion is presented at:
http://friendsofscience.org/assets/documents/FOS%20Essay/Climate_Change_Science.html#Water_vapour
Ken, Thanks for the correction – yes it really should be labelled “Heritage NVAP”. I was thinking that the 2000 and 2001 data was from NVAP-M, but now I understand that they haven’t made any data available yet from NVAP-M. The new data will be interesting because they coincide with the standstill in surface temperatures.
I agree that the upper layers in the atmosphere dominate the greenhouse effect. It is changes in water vapour in L2 and L3 which controls the heat radiation losses to space from the broad water absorption bands. Any decline there will increases IR losses thereby offsetting a reduction caused by increasing CO2 higher up.
I made two graphs, for 1988 and 1991, of precipitable water vapor by layer versus latitude by 1 degree bands. See:
Interesting that in the Arctic, going to higher latitudes, the water vapor in the 500 to 300 mb layer 3 goes to a minimum at 58.5 degrees North, then increases to the North Pole. In 1991 layer 3 minimum is 0.53 mm, increasing to 0.94 mm at the North Pole.
I wonder if the cause of the drop in humidity at 58 deg. is not perhaps the polar jet stream? The altitude is about right and the latitude is not far off. I don’t know why they should dry out the level 3 but in winter low pressure systems track the jet stream bringing rain to those below.
Nice graphs Ken. For the northern hemisphere it might be worthwhile to add land mass to the equation. Iain Inglis at climateprediction.net has a useful Excel workbook of land mass by 5 degree latitude bands.
Water vapor is something that confuses the heck out of noobs to climate science, especially when like me they have a limited background in physics.
Water vapor is about 10 times as abundant in the atmosphere as CO2. Its optical thickness is three times higher. A one percent change in water vapor abundance should have three times the effect of a one per cent change in CO2 abundance. (I think.)
According to my primitive calculations, a one per cent change in albedo should have ten times the effect of a one per cent change in CO2 abundance. I would be interested to learn what percentage of albedo is due to cloud. The wiki article on albedo is typical of those I googled and gives an unsatisfactory answer:
Cloud albedo has substantial influence over atmospheric temperatures. Different types of clouds exhibit different reflectivity, theoretically ranging in albedo from a minimum of near 0 to a maximum approaching 0.8. On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water.
My total thumb-suck says that cloud cover is responsible for a third of albedo, therefore a one per cent change in cloud cover will have three times the effect of a one per cent change in CO2.
Against all predictions of the models, water vapor has stayed more or less constant since the late1980’s. Apparently cloud cover has also stayed constant.
This leads me to a half-baked dilettante kind of idea that I want to bounce off you guys:
Due to the supposed lack of nucleation points, theoretically there should be no cloud over the oceans. James Lovelock in his work on the sulfur cycle discovered that the nucleation points were supplied by methane sulfonic acid (MSA) evaporating from the ocean.
Lovelock also learned from ice cores that during Ice Ages, MSA was from 3 to 5 times more abundant than at the present. That would have resulted in more cloud, higher albedo, and a lower climate flux.
Gaia theory (as I read it) says that the increased MSA output from the oceans will be cause, not effect, as the planet switches to its “normal” stable state of glaciation. Naturally it could be the other way round, and colder oceans may release more MSA.
My laboriously-arrived-at point is, nobody is tracking MSA, not that I can see. This trace constituent of the atmosphere seems to have the same potential or more, to affect planetary temperatures as do the better-known greenhouse gases.
Good points oldfossil.
Roy Spencer has been arguing that a reduction in global cloud cover may be the primary cause of recent warming. A recent paper (see here) found that cloud cover over all regions has decreased slightly over the last 40 years.
Less cloud = lower albedo
The net effect of clouds (and ice) are to cool the Earth.
The net effect of water vapour is to warm the Earth though the greenhouse effect
Such is the importance of phase transitions of water on the Earth’s climate. I made a mickey mouse model of how water could act as the Earth’s thermostat –Water World.
The DMS story is also fascinating. DMS is produced by phytoplankton. Phytoplankton thrive in cold water rich in nutrients. That is why whales go to feed in Antarctica and the Arctic. I didn’t know that DMS was 3 to 5 times higher during the ice ages !
Note also that Lovelock has recently become a climate sceptic ! He now admits that he too readily accepted IPCC predictions and that consequently he was wrong in his book -The Revenge of Gaia. That proves he is a great scientist who recognizes that any theory whatsoever must agree with the experimental data. The data show no warming for 16 years whereas the theory predicted a 0.4 C rise. Therefore the theory must either be modified to agree with data or else replaced.
I’ve been having fun creating Water World in NetLogo. Still needs lots of work but the negative feedback is there. I appreciate all the formulas you supply on the Water World page. Checking them against my own primitive Excel model I see I’m on the right track.
Re Lovelock, you have to admit that back in 1998-99 when the anomaly was shooting skyward, it would have taken a very brave man to reject AGW. Practically nobody who understood GH theory would have predicted a negative water vapour feedback.
Apologies, I mistakenly attempted to format the para “Cloud albedo has substantial…” with blockcode instead of blockquote. Duh.
oldfossil says:
The radiative spectrum of water vapor overlaps with CO2, so you need a line-by-line radiative code that can calculate the effect on out-going longwave radiation of a change in water vapor or CO2.
A 10% increase in CO2 concentration has the same effect as a uniform 1.80% increase in water vapor. This is shown in the following graph:
A uniform 1% change in H20 causes a -0.077% change in OLR.
A 1% change in CO2 causes a -0.014% change in OLR.
Therefore, a 1% change in water vapor has 5.38 times the effect on OLR of a 1% change in CO2.
Thanks Ken, some very valuable data points to check my calcs against. Sooner or later I’m going to come after you for your mathematical algorithm, but I’ll understand it better if I have to work it out for myself. What value are you using for epsilon (emissivity)? I was told to assume 0.95 for all surfaces for all temperatures.
Some radiative code (HARTCODE) results are here:
http://members.shaw.ca/sch25/Ken/rr_s.xlsx
Note that the fluxes assume clear sky, no clouds.
The graph of the previous comment is at cell AW17.
Row 1 of column A represents the base conditions.
The red rows show the fluxes when the surface temperature is changed, keeping CO2 and H2O constant. The blue rows change the water vapour amount uniformly by a fractor in column R. The black rows change the CO2 concentrations, keeping surface temperatures and H2O constant.
I have compared the precipitable water vapour calculated from the NOAA ESRL radiosonde reconstruction to the NVAP precipitable water data. See graph:
The NVAP 500 to 300 mbar data declines much more than the NOAA data after 1995! Does that suggest the specific humidity after 1995 in the upper atmosphere declined more over oceans than over the land? Radiosonde data is only over land.
For comparison, I converted the NOAA specific humidity to precipitable water. I assumed the average specific humidity in the 300 to 400 mb layer is the average of the specific humidities at 300 mb and at 400 mb levels.
I converted specific humidity (SH) in each NOAA layer to precipitable water (PW) using PW = SH X Air Density X Layer thickness.
You point out that there is no change in the NVAP data for total globally averaged precipitable water vapour between 1988-2001. But there is a discernible rise in the graph for the lower layer ( surface-700mb in your Fig 1 ) starting in about 1997.
Also in 1997 there is a change in gradient in the albedo measurements reported by Goode and Palle from decreasing until 1997, to slightly increasing after 1997. See fig 4 in: http://bbso.njit.edu/Research/EarthShine/literature/Goode_Palle_2007_JASTP.pdf
According to Goode and Palle “ low clouds cool (reflection dominates) “ – so could this be evidence of the global thermostat in operation ?
Bob – Yes you’re right there is a rise in humidity for the lowest level from 1997. I was really referring to the total NVAP (integrated over all levels- Fig 2) as not really changing. The data suggest that NVAP increased slightly near the surface but decreased in the upper atmosphere. The upper atmosphere determines greenhouse forcing. A reduction high up reduces the greenhouse effect of water. – negative feedback to increasing CO2 forcing
However, it is very interesting that albedo (clouds) seems also to change around 1997. More water vapour at low level levels should produce more clouds – increasing albedo. The net effect of low level clouds is to cool the planet. So yes this is more evidence of the global thermostat at work !
Hello,
I was tediously searching the scientific literature to find information on atmosphere moisture content for a report I am working on. One google search brought up your information. Thank you very much for your work and you will be referenced.
You also might me interested in this post https://clivebest.com/blog/?p=4871 which analyses the latest NVAP-M data.
Clive, there is a linked in conversation going on about cities in Texas running dry of water. Several people have mentioned harvesting of atmospheric moisture for some drinking water needs. I was curious at what level we should or would need to get concerned about harvesting the atmospheric water before it had a direct effect on local and global climate? There was also mention of a rather large project to provide water to the interior reaches of South America by pulling water vapor through pipes built into the Andes. Thoughts on that?
Although these ideas are feasible they would need vast amounts of energy to implement. As far as I can see the only way to take water out of the atmosphere would be through a refrigeration plant to condense out water vapor. I think that desalination of sea water may actually cost less.
Here in California the wind energy farms show up on radar as precipitation.Somehow they condense water vapor .Not sure if it precipitates or just creates clouds.
I think that is because wind energy farms are basically a damp squid. Any minimal amount of energy they produce is extracted from natural weather cycles resulting in reduced winds which allow clouds to form.
So in effect, the ‘pause’ has been caused by the reduction in water vapour. The pause is now some 18 + years long which is roughly when atmosdpheric water vaspour started to decline. From the comments and graphs above, AWV has declined by a sufficient percentage ~ 6% or more which when multiplied by 5.4 comes to over 30% equivalent increase in co2.
So it is entirely possible that “the pause” is entirely due to the decrease in atmospheric water vapour cancelling out the effect of the increase in atmospheric co2 over the same period.
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Where is the most recent data? Looks like most of your graphs end around 2001–wherer did the last 15 years go and what does it look like?
See https://clivebest.com/blog/?p=4871 for the updated NVAP data There is no more recent data as the measurements ended in 2009. see: https://eosweb.larc.nasa.gov/project/nvap/nvap-m_table
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I see an AMO signal there from the mid 1990’s. The water vapour increase from 0-700m will raise the lower troposphere greenhouse effect to the surface, and the decrease from 700m and above will allow greater penetration of solar near infrared to the lower troposphere and surface.
And the warm AMO mode is driven by increased negative North Atlantic Oscillation, due to declining solar wind wind pressure since the mid 1990’s. So its all functioning as a negative feedback and nothing to do with increased forcing of the climate in any form.
https://www.linkedin.com/pulse/association-between-sunspot-cycles-amo-ulric-lyons?trk=pulse_spock-articles
typo.. 700mb
Not a reply but a question.
When studying the outgoing infrared spectra measured by the Nimbus-4 satellite, I noticed that in many cases H2O radiates at about the same temperature. The attached illustration has been compiled from measurements above the Sahara and above the Pacific Ocean. Surface temperatures and moisture levels are completely different. Despite this, the spectra in the water vapor range are practically identical. Do you have an explanation?
Sorry, but I can’t insert the Illustration. Could you contact me at rob@geophenture.com for it?
Hi Robbert,
You can insert the illustration if it has a URL. You just need to put the URL on a line by itself. Like this (“earthzine.org/wp-content/uploads/2013/12/6.1.jpg”).
Clive
Here is the figure. Note the similarity in the H2O range!
Yes H20 spectra shape look similar. There is very little water vapour or clouds over the Sahara so IR from can escapes almost directly from the surface to space. The effective temperature there looks like ~ 325K or 50C in the window and 315K or 42C in the second peak which overlaps with H2O. I think the real difference is the extensive cloud cover over the Tropical Western Pacific. so IR is emitted from cloud tops at a much lower temperature.
It may be true that the humidity in the Sahara is very low, but then the radiation into space would take place at a low altitude. Within the H2O range, however, the emission takes place at an altitude with a temperature between 260 and 270K (2km). Above the Pacific Ocean with a surface temperature of 295K (22°C) the water content must be very high and the radiance should occur at even higher altitudes. It can hardly be a coincidence that in both cases the radiation takes place at exact same temperatures. An explanation may be that, in both cases condensation occurs at a temperature of < 270K while the overlying air, becomes transparent. There are not many H2Omixing profiles to find, but here is an illustration showing a dramatic reduction of H2O above ~2.3km.
Clive, I really appreciate your response, but I don’t have an explanation yet for the great similarity of the spectra within the H2O range. This is an important matter with respect to water vapour feedback. If water vapour EEH depends mainly on temperature (~270K) and not on density, then part of the positive feedback assertion is void. Remains of course the feedback from clouds, but the EEH is often not far above top clouds due to the drop in mixing ratio. Again, here the (positive feedback is not proportional to the H2O density. Further, I noticed that most spectra from satellite measurements show the EEH to be at around 270K. Also, the spectra you posted show little difference below 400cm-1 and above 1200cm-1, summer or winter, midlatitude or tropical.
One problem with that plot is that it cuts off at a wavenumber 400, so we don’t see the full S-B spectrum. However you are right that the H2O regions for Sahara and N-Pacific do look almost identical, although the surface temperatures and humidity are totally different. It almost seems that the H2O EEH adjusts itself to maximise heat loss – higher in the Sahara (low humidity) and lower in the tropics (high humidity). Both climates give effectively the same IR profile.
I can’t explain why !
Can instrument problems be ruled out?
This paper ( https://arxiv.org/pdf/2006.03098.pdf ) shows some calculated spectra and compares them with observed spectra for Sahara, Mediterranean and Antarctica. The agreement between calculated and observed seems very good, but what surprised me was that the satellite measurements came from 1970 !
Also very surprising is the last sentence before the conclusions: “We conclude that our modeled spectral fluxes would also be close to observed fluxes, if a reliable way to measure spectral fluxes were invented”. So they seem to be saying there is not yet a reliable way to measure spectral fluxes – in a paper written in 2020.
It looks like a very thorough job of calculating radiative forcing based on all IR lines in HITRAN. The detailed agreement with observations is vey impressive. The satellite comparisons almost look too good to be true.
However I don’t understand this parametrisation of water vapour with altitude
C*exp(-z/zw) , with Zw = 5 km
where
C= 31, 000 ppm for the Sahara, C= 12, 000 ppm for the Mediterranean, and C= 2, 000 ppm for Antarctica.
I would have thought the values of C should be inverted for Sahara and Mediterranean !
The second author is Will Happer
https://youtu.be/CA1zUW4uOSw