After exploring the relevant pieces finally has come the time to put them all together. I have dealt with a number of mistakes, all having pivotal impacts on ECS estimates. Oddly enough, all these mistakes produce biases in the same direction, that is overheating the planet due to CO2 emissions. To provide an oversight let me recapitulate the main points.
The Lambda Mistake
Lambda, as a conversion factor of radiative forcing or feedback to temperature, is assumed to be 0.3. The figure is derived from the assumption a surface at 288K would emit 240W/m2 into space, as 1 / (((289/288)^4 - 1) * 240) = 0.3. In reality it is a much colder emission temperature of 255K, higher up the atmosphere on average, emitting these 240W/m2, so that lambda = 1 / (((256/255)^4 – 1) * 240) = 0.264. With orthodox parameters for 2xCO2 (3.7W/m2) and WV radiative feedback (1.8W/m2), this will introduce an error overstating ECS by 30%.
3.7 * 0.3 / (1 – 1.8 x 0.3) = 2.41K
3.7 * 0.264 / (1 – 1.8 x 0.264) = 1.86K
Moreover including further suggested feedbacks (albedo, clouds..), the lambda issue will produce ever bigger errors, the larger the sum of primary feedbacks is.
Surface Emissivity Denial
“The surface emissivity is 1, or so close to 1 that we do not need to know the real figure, and it should not matter anyhow” summarizes the position of both the orthodoxy and the “critical” side. Just about everything is wrong with it. The GHE is per definition the difference between emissions at surface and TOA. In order to even know the magnitude of the GHE, it is indispensable to know surface emissions. And since they can not be measured on a global and spectral range, they have to be inferred based on surface temperatures and surface emissivity.
For every surface emissivity < 1, the GHE will be accordingly smaller. With every percentage point in less emissivity, surface emissions decrease by 3.9W/m2, and so does the GHE. Though, since the GHE is 240W/m2 smaller than surface emissions, it is highly sensitive to any deviation. As I have shown, the spectral hemispheric emissivity of water which dominates the surface emissivity all over, is only 0.91. It may be a little known fact, but not a new one.
Accordingly the surface emissivity = 1 postulate introduces not just a large error with the size of the GHE (~115W/m2 for real), but also with the individual forcings of GHGs, most severely affecting vapor.
Denial of Overlaps and Clouds
The way “climate science” deals with clouds in simply appalling. Even though they get exploited to argue a positive cloud feedback in the end, their existence gets otherwise ignored from the get go. Forcings, as well as feedbacks, of individual GHGs are all based on clear sky scenarios. The extensive overlaps between clouds and GHGs provide a large redundant GHE component of about 45W/m2, which is caused by clouds AND GHGs simultaneously. In a ludicrous logical blunder this component is attributed to GHGs alone. Of course modelling with clear sky scenarios may cause blindness to the underlying problem.
As a consequence the “single factor removal”, or net GHE of well mixed GHGs, is only about 40W/m2 (35W/m2 in my earlier estimates). The largest part of this net GHGE (greenhouse gas effect) is due to CO2 and vapor, with roughly equal shares. The radiative effects (be it forcing or feedbacks) of changing, or specifically increasing GHG concentrations, must necessarily be derived from their net GHGEs, as increases in overlaps can not produce any radiative effects.
Absurdly not just pivotal overlaps between clouds and GHGs, but even intra-GHG overlaps, like these between CO2 and vapor, are usually denied and ignored. As Wijngaarden, Happer (2021)1 rightfully pointed out, even this small overlap would reduce a 2xCO2 forcing from circumstantial 3.7W/m2 to only 3W/m2. However this is just an awkwardly small step towards realizing the real severity of the issue.
Lapse Rate Feedback (LRF)
Lapse Rate Feedback remains a subject of uncertainty for a couple of reasons. Obviously it can not be derived from modtran or hitran, which both have other scopes. Apart from LRF being negative by nature, it is not at all a feedback in a strict sense. Mixing LRF with true feedbacks essentially kills off the feedback loop, thereby producing a much larger effect than actually intended. LRF should always be considered separately from real feedbacks, and eventually be applied as a “discount” on surface temperatures.
This causes severe issues with the way the orthodoxy accounts for it, thereby unintendedly vastly overstating its magnitude. Implicitly AR4 suggests a -59%, and AR6 a -39% LRF, mitigating otherwise unrealistically high feedbacks by vapor, surface albedo and clouds. Even though it might look appealing to use such figures to lower a corrected ECS estimate, it would be a cheap shot and science driven by intent, rather than evidence. Realistically LRF should be in the -25% to -32% range, that is in the context of a CO2 driven forcing.
Spoiler alert: there could be forcings which affect the lapse rate more directly, making theoretical considerations obsolete.
Surface Albedo Feedback (SAF)
This is one of the subjects I otherwise omit by intent. The idea is simple and comprehensible. Ice and snow reflect a lot of sun light, and as the Earth warms, the loss of ice should result in additional uptake of solar energy, warming the planet even more. As logical as it may seem, there are some issues with it.
- clouds cover a good part of snowy surface anyhow
- it is cold where the sun is weak, meaning not much light to be reflected
- at low angles water reflects a lot of sun light, mitigating the effective difference in albedo between open water and ice
- in the near IR just beyond the visible spectrum, and that accounts for a large share or the solar spectrum, snow is a poor reflector. If we could see it with our eyes, it would appear very dark
Maybe “climate science” accurately accounted for all of it, resulting in 0.26W/m2 (AR4) and 0.35W/m2 (AR6) surface albedo feedback. I would doubt it, but who knows. However, there is a way more severe problem just around the corner. This coin has two sides, and we need to consider both shortwave AND longwave reflectivity. And there are two things we know for certain; a) short- and longwave reflectivity tend to cancel each other out, and b) “climate science” does not care about longwave reflectivity, or emissivity respectively, as I have thoroughly discussed.
The latter point is knock-out criterion to any orthodox claim on SAF
Cloud Feedback (CF)
The AR6 gives a “very likely range” of -0.1 to 0.94 for CF. So it should be a significant positive feedback, though it could be negative as well. Uncertainty over the magnitude of a feedback is one thing, not really knowing which way it even goes, is another, way more concerning problem. Then these estimates are mainly derived from models, of which we know they are based on totally wrong assumptions.
The bitter irony lies in calculating forcings and feedbacks with clear sky scenarios, thereby denying even the sheer existence of clouds. Such an undue “simplification” produces huge errors vastly overstating ECS, that can not possibly be compensated by speculative cloud feedbacks in the end. Modelling with clear skies only and then arguing a tendentially positive CAF is just off limit. In no way such an impudent rape of scientific principles can be tolerated. The orthodox position on CAF is far too unsubstantiated to even be considered.
Water Vapor and Lapse Rate Feedback (WVF + LRF)
“The net feedback from water vapour and lapse rate changes together is extremely likely positive and approximately doubles the black body response”2. Well, it better should be, because if not, “climate change” is going nowhere. It is a funny statement on its own right. Vapor primary feedback is assumed to be around 1.8W/m2, and that figure is pretty consistent throughout the orthodoxy. Although this estimate is certainly at the high end of spectroscopic models, it is arguable within the given assumptions.
In reality the emission level elevating effect, or radiative effect of WV respectively, is hugely overstated. Surface emissivity underneath the main absorption band of WV, within the far-IR is, specifically low (~0.875). Almost half of the emissions vapor allegedly suppresses as a GHG do not exist in the first place. On the other side WV is extensively overlapped with other GHGs and clouds, so that its net radiative effect AND feedback potential is indeed very restricted. Consequently the actual radiative feedback by WV is only about 0.65W/m2.
LRF on the other side is not subject to any overlaps, as WV is the only relevant condensing GHG. Despite the wrong terminology, since it is technically not a feedback, and the IPCC putting it in the wrong envelope, LRF should provide some -25 to -32% negative “feedback” all over (other than the much higher figures the IPCC unintendedly names). Although there is some uncertainty, it more than suffices to turn combined WVF and LRF negative over all.
Eventually CO2 forcing itself is severely affected by the net vs. gross issue as well. Introducing clouds, accurate surface emissivity parameters, allowing for intra-GHG overlaps and implicitly avoiding the lambda mistake, 2xCO2 forcing will yield 2W/m2, or 0.53K respectively. Notably this essential correction alone halves ECS.
Putting raw modtran output into perspective
As pointed out in the introduction to the series of articles on ECS, modtran suggests very low climate sensitivity, despite otherwise being perfectly in line with the orthodoxy on single radiative effects by the respective GHGs. That is about 3.7W/m2 in 2xCO2 forcing and arguably 1.8W/m2 WV feedback. The reason for this dissent is in the simple fact that GHGs do not stack. Other than the erroneous “logic” of conventional radiative climate sensitivity estimates, which add gross effects and thereby count and partial GHEs multiple times, modtran has no such “fudge logic” included.
These net effects are the smaller, the more overlaps there are. It is easy to show what happens if we add even more clouds. The above “Stratus/Strato CU Base .66 Top 2.0km” represents a net CRElw of 25W/m2, while “Cumulus Cloud Base .66 Top 2.7km” adds 39W/m2 of CRElw. In this instance a difference of 14W/m2 in additional overlaps drops climate sensitivity from 0.78 to 0.64K. Given the orthodoxy is not considering overlaps at all, it is an impressive example of their significance on its own.
With the orthodoxy CO2 forcing plus WV feedback should amount to 3.7 * 0.3 / ( 1 - 1.8 * 0.3 ) = 2.41K. Modtran however is immune to the lambda issue and necessarily uses net effects. Implicitly it calculates 2.292 * 0.262 / ( 1 - 0.88 * 0.262 ) = 0.78, and 1.853 * 0.276 / ( 1 - 0.72 * 0.276 ) = 0.64 in the two instances above. The figures for CO2 forcing here can be read directly from modtran, Lambda and WV feedback can be inferred from the context.
Note: even without clouds modtran will only produce 1.06K (= 2.983 * 0.246 / ( 1 - 1.25 * 0.246 ) with US std, and 1.21K (= 3.329 * 0.227 / ( 1 - 1.65 * 0.227 ) with the inner tropic scenario. Logically Lambda turns ever smaller, the higher emissions TOA are in absolute terms and this produces a trade off. The less greenhouse agents you have in the model, the higher the sensitivity in W/m2 to the few agents, or the single agent (f.e. CO2), remaining. On the other hand, with less greenhouse agents, emissions TOA are ever higher and so Lambda shrinks. In any way climate sensitivity has to be very restricted, as the chart below shows. It features the four modtran derived scenarios (one could add a lot more without changing the basic shape) vs. the impossible “consensus” claim colored in red.
It is this innate immunity by modtran vs. two of the fundamental mistakes of “climate science” which reduces climate sensitivity by already 70%. It is right there in the most basic climate tool there is, subtle as a sledge hammer, and yet no one takes notice. Just unbelievable! So I made a little inquiry, as there should be some reflection on the issue. For instance I searched WUWT (wattsupwiththat). Indeed there are some articles and comments touching the issue (apart from mine), though remain stuck early on. People look more on the “back radiation” part than on emissions TOA, or they would only consider thus impaired CO2 forcing, rather than the more severely affected WV feedback. Also there is little reflection on why modtran behaves like it, which would otherwise lead to that eureka moment. The spark just won’t ignite..
So I thought why not ask Professor David Archer from the University of Chicago, as he provides the here heavily exploited uchicago modtran3 installation. Also he runs the alarmist site “realclimate dot org”4. I explained the problem, why modtran behaves like it does and provided the screenshots. And although I do not like to publish private conversation, let me give this part: “You're absolutely right, this is a known thing”, followed by some ill fated lamentations why it was irrelevant. Of course it is not “a thing” with modtran, but with the science. It is the “emperor’s now clothes” on steroids, if you neglect what your own model, so to say, rightfully points out, because it does not fit your beliefs.
Of course this “thing” with modtran is nothing else but the incarnation of a principle well described in the literature, like in Schmidt et al (2010)5. There is a “Single Factor Removal” (SFR) and a “Single Factor Addition” (SFA), or rather net and gross GHE attributable to any GHG. The difference is defined by overlaps. If such a distinction is due with the given magnitude of the GHE, is it so hard to understand it will equally apply to any growth of it?
In fact it is likely the easiest way to send any climate scientist into embarrassment. Is, for example, a CO2 forcing of 3.7W/m2 SFR or SFA? He would not know, because he will not be aware of the distinction. “Climate science” has its eyes wide shot on this issue.
Modtran is simplified and so it does not account for real surface emissivity, lapse rate “feedback” or further, enhancing speculative cloud and surface albedo feedbacks. As discussed, the ignorant assumption of a perfectly emitting surface overestimates the GHE all over, the partial GHEs of the single agents (both “Single Factor Removal” and “Single Factor Addition”) and of course forcings or feedbacks by these GHGs. Allowing for this bias, the best estimate is 2W/m2 of 2xCO2 forcing and 0.65W/m2 in WV feedback. With a lambda of 0.264 we get 0.64K climate sensitivity and WV feedback.
2 x 0.264 / ( 1 – 0.65 x 0.264) = 0.64K
With an arguable lambda of 0.27 it would be 0.65K. Also I should note I revised WV feedback sharply up from 0.5W/m2 to now 0.65, but this increased the result only by 0.03K, from 0.61K to 0.64K. More importantly we need to consider lapse rate “feedback”. Although it may be a bit uncertain, there will be a substantial difference in the warming at emission- and at surface level. Since the all the calculations implicitly model ECS at emission level, we need to apply a discount of 25% to 32% on this figure get to surface ECS. Of course this would not be necessary if we followed the orthodoxy and mixed LRF with other feedbacks, but that is logically wrong. Even with a conservative -25% combined WV-LR feedback will be negative btw.
0.64K x (1 – 0.25) = 0.48K
With a likely stronger LRF, results as low as 0.43K seem anything but unreasonable. Either way, the effect of WV in total reduces climate sensitivity. This counters the assumption of the IPCC of WV and LR feedback combined were “extremely likely positive”. Dueful consideration of the net radiative WV feedback necessarily produces this outcome, and the margins are large enough to let lapse rate “feedback” dominate it under all circumstances.
Eventually even if we considered cloud and surface albedo feedbacks with their central estimates as given in the AR66, and again there is no scientific foundation to these claims, it would only add a total 0.77W/m2 (0.35 + 0.42) primary feedback. This again would not suffice to pull off any significant, let alone alarmist warming.
2 x 0.264 / ( 1 – (0.65 + 0.35 + 0.42) x 0.264) x (1 – 0.25) = 0.63K
Within the CO2 plus WV response envelope it is impossible to produce an ECS beyond 0.5K. The main drivers of “consensus science” (sic!) estimates on ECS are the lambda mistake, the ignorance or surface emissivity, the denial of overlaps and unsubstantiated claims on further feedbacks. Without these errors, or fudge factors, CO2 has a certain role to play, but it is a small one. In fact this is so small, that it is negligible in the context of paleoclimate. Any research on the subject, allegedly trying to support the CO2 hypothesis is henceforth pointless, next to being recursive by nature.
Moreover the current almost 5 decadal warming trend can not be explained by CO2. Whatever causes it, despite a tiny contribution, CO2 and feedbacks to it are not to blame. This is very important, given there have been numerous attempts to discredit the CO2 theory by comparing model based predictions to the actual warming trend. It is odd since a theory either makes or breaks. The claim a theory would be “too extreme” is no valid argument in science.
In fact we have a surreal situation, where “climate science” claims to have high confidence to name precise emission budgets to keep global warming within certain limits, be it 1.5K or 2K, while at the same time naming extremely wide ECS ranges. It is an anti-scientific dogma to claim whatever warming occurs, it must be due to CO2. Because of such loose estimates, the theory gets shielded from falsification. And it is a dogma the critical side buys into, rather than considering the alternative. If the evidence rejects the theory, ask what might be wrong with the theory itself, and do not ask for modifications to it.
The scope of this article is to outline how consensus assumptions violate logical restrictions and produce impossible outcomes. Whether an ECS of about 0.45K could somehow fit an extended “consensus range”, if something like it even exists, is not the question. Rather this estimate is based on the very same foundations the orthodoxy uses. The only difference is in the elimination of logical mistakes. And these mistakes are undeniable.