Guest essay by Richard J. Petschauer, Senior Member IEEE
The physics of evaporation has complications related to what happens at the water / air interface such as wind speed and wave action. However if these factors remain constant, how evaporation changes with temperature and humidity can be estimated with well-known equations based on how water vapor pressure varies with temperature. For example, at a typical ocean temperature of 17 C, it should increase about 6.5% / C if the water vapor increases to maintain relative humidity, that the climate models indicate. If the surface air tracks the water within ± 2 C, the rate varies from 6.2% to 6.9% / C. Data over oceans by Wentz et, al (2007) report values of about 6% / C.
But the complex computer climate models show averages of only about 2.5% / C. There are no claims of reduced wind speeds or wave action or increased relative humidity to explain this. However many papers on the subject claim that the available energy is limiting evaporation in these models. But physics theory tells us that the latent energy for evaporation comes from the temperature of the water itself. The latent heat leaving the surface cools it and deposits heat in the atmosphere, part of which escapes to outer space. This combination causes negative feedback. The reduced net energy from increased CO2 still warms the surface, but this energy can’t be separated from what aids the final increased evaporation. A 6% / C increase applies to the water after the negative feedback is complete. Do the climate models ignore this cooling and feedback process?
A typical paper on this subject is one by O’Gorman and Schneider (2008) that defines this energy balance constraint that is supported by many other climate model references. Their equations (8) and (9) correctly show that an increase in latent heat transfer from evaporation must equal a reduction in the net surface radiation heat loss, assuming the loss from convection plus sensible heat and the net solar surface absorption all remain constant. However, this cannot provide a solution.
Let E = the latent heat loss from the surface due to evaporation, G the outward surface radiation and D the downwelling radiation from the atmosphere to the surface. Net surface radiation loss = G – D.
For a reduced radiation heat loss,
D E = D D – D G (1)
However, the developers of the climate models seem to be confusing independent and dependent variables. Evaporation is the driver or forcing agent controlled by the physics at the surface, and G and D must respond to a change in it. If the surface temperature rises, the additional latent heat lost at the surface will cause an offsetting decrease in the temperature and thus G. And the latent heat deposited in the atmosphere warms it and increases the downwelling radiation, D (and the outgoing radiation). We now have a feedback process at work. Equation (1) can only be used as a check after a correct solution is found to new values of E, D and G after the feedback process is complete. It appears there is a serious error in how climate models estimate evaporation as indicated in the rest of this paper.
We have developed a dynamic three level energy balance model (reference 1) with updates as described later that can be used for a number of forcings and feedbacks including the response to changes in evaporation and the cooling of the surface and the warming of the atmosphere.
The results are shown on the next page. No energy constraints of evaporations are seen.
As shown in Figure A1 in the appendix, we define S as the net incoming solar flux after albedo, A the absorption of the net solar flux by the atmosphere, G the surface radiation, W the surface radiation through the atmospheric window, H the convection from the surface, E the latent heat from surface evaporation (both H and E transfer heat to the atmosphere), U the atmosphere upward outgoing longwave radiation, and D the atmosphere downwelling longwave radiation to the surface. For this estimate the following values are fixed: S = 235; A = 67; H = 24. These and the baseline values shown in Table 1 are from Kiehl and Trenberth (1997) with average cloudy conditions of 60% coverage net considering overlaps.
From eqs (4 to 8) on the next page, Table 1 compares the baseline case with three having large forcings of 10 Wm-2 at the top of the atmosphere. One case has no evaporation changes, while two have rate changes of 6% and 10% / C. D T is calculated from the changes in G from the baseline.
The In minus Out fluxes are equal at all three levels for all the cases with each parameter used at least twice. No problem in finding the energy to support evaporation; the surface gave up some by cooling and the down radiation, D increased. Note that the increase in E is based on the final reduced temperature rise. In all cases D E = D D – D G, measured from the baseline.
Table 1 – With large TOA forcings no energy constraints on evaporation changes.
Increase in E follows that estimated from temperature change and the specified change %.
For example in case 3, E » Eo + r D T Eo = 78 + 0.06 x 1.57 x 78 = 85.34 » 85.40 shown.
Ignoring the drop in D T, from the value of 2.70 the increase in E to 85.40 is only 3.5% / C.
|
TOA forcing & evap change |
D T – C |
G |
W |
E |
U |
D |
| 1) 0 & 0 (Baseline) |
0 |
390 |
40 |
78 |
195 |
324 |
| 2) 10 Wm-2 & 0 % / C |
2.70 |
404.85 |
41.52 |
78 |
193.48 |
338.85 |
| 3) 10 Wm-2 & 6% / C |
1.57 |
398.57 |
40.88 |
85.40 |
194.12 |
339.97 |
| 4) 10 Wm-2 & 10% / C |
1.23 |
396.69 |
40.69 |
87.63 |
194.31 |
340.32 |
In – Out: Case 1
TOA = S – W + U = 235 – 40 – 195 = 0
Atmosphere = A + G – W + H + E – U – D = 67 + 390 – 40 + 24 + 78 – 195 – 324 = 0
Surface = S – A + D – G – H – E = 235 – 67 + 324 – 390 – 24 – 78 = 0
In – Out: Case 2
TOA = S – W + U = 235 – 41.52 – 193.48 = 0
Atm = A + G – W + H + E – U – = 67 + 404.85 – 41.52 + 24 + 78 – 193.48 – 338.85 = 0
Surface = S – A + D – G – H – E = 235 – 67 + 338.85 – 404.85 – 24 – 78 = 0
In – Out: Case 3
TOA = S – W + U = 235 – 40.88 – 194.12 = 0
Atm = A + G – W + H + E – U – D = 67 + 398.57 – 40.88 + 24 + 85.4 – 194.12 – 339.97 = 0
Surface = S – A + D – G – H – E = 235 – 67 + 339.97 – 398.57 – 24 – 85.4 = 0
In – Out: Case 4
TOA = S – W + U = 235 – 40.69 – 194.31 = 0
Atm = A + G – W + H + E – U – D = 67 + 396.69 – 40.69 + 24 + 87.63 – 194.31 – 340.32 = 0
Surface = S – A + D – G – H – E = 235 – 67 + 340.32 – 396.69 – 24 – 87.63 = 0
Note the increase in E follows that estimated from the temperature change and the specified change %. For example in case 4, E » Eo+ r D T Eo = 78 + 0.10 x 1.23 x 78 = 87.59 » 87.63.
No energy constraint is seen and all energy balances at the three levels are maintained.
The details of the calculations for the above table follow. The basic equations for energy balance at all three levels are from our paper, reference (1). For balance at the top of the atmosphere,
S = k (A + H + E) + k Ga + G (1 – a) (2)
Refer to Figure A1 in the appendix. S is the net incoming solar after albedo, k is the fraction of the total heat absorbed by the atmosphere that is radiated upward (here 0.3757), and a is the fraction of the surface longwave radiation absorbed by the atmosphere including clouds (here 0.8974).
Solving for G,
G = [S – k (A + H + E)] / (1 – a + ak) (3)
If we start with balance at the surface and again solve for G, we get the same result that also forces balance at the atmosphere.
To determine the feedback factor for E, add to it the increase caused by a 1 C surface temperature change and convert the change in G to a temperature change. For a 6% increase of 78, E becomes 82.68, the new value of G is 386.0014 Wm-2, down from 390, and provides a temperature change of –0.741 C which equals the feedback factor, the temperature change before additional feedback. With no other feedbacks, the feedback multiplier is M = 1 / (1 – F); here we get M = 0.5744. The temperature change of –0.741 would produce another change of -0.741 x –0.741 or +0.549, followed by (–0.741)3 or –0.406 then (–0.741)4 or +0.301, etc which sum converges to a final temperature drop –0.4256 C which also equals M x F or -0.741 x 0.5744.
As an alternate to using a feedback factor and a way to check it, the above equation for G can be modified to allow E, the evaporation rate, to vary with the change of surface temperature implied from the change in G, the surface radiation. Then the solution for the new surface radiation is,
G » [S – k (A + H) – k (E0 – r E G0 Tr)] / (1 – a + ak + k r E0Tr) (4)
Where r = the fractional rate of change / C of surface evaporation, E0 the initial evaporation, G0 the initial surface radiation, and Tr the temperature change rate factor at G0 which is T0 / (4 G0) with T0 the initial surface temperature. At 288 K or 15 C, Tr = 0.1846 C / W m-2. Here we get M = 0.581.
(Equation 3 is more accurate. The two values of M are very close for smaller forcings)
The final value of evaporation latent heat,
Ef = E0 + r TrE0 (G – G0) (5)
The temperature change uses the inverse of the Stefan-Boltzmann equation for G and G0.
The final value of W, Wf = G (1 – a) (6)
The final value of U, Uf = S – Wf (7)
The final value of D, Df = G + A + H + Ef – S (8)
The parameter a is the fraction of the surface longwave radiation absorbed by the atmosphere. Here it is 0.8974 or 1 – W0 / G0, whereW0 = 40, the amount through the atmospheric window and G0 = 390. The value k is the fraction of the total heat radiated from the atmosphere that is upward outgoing radiation. So k = U / (U + D). For our baseline k = 195 / (195 + 324) = 0.3757. To impose a forcing R at the TOA, k = (195 – R) / (195 – R + 324). Unless a or k is the value being perturbed, the equations above require the baseline values for a and k. For other values of a and k, partial derivatives are needed as described in the appendix.
It appears the climate models are grossly underestimating the negative feedback from latent heat transfer. For case 3 in the table above, the feedback multiplier of 1.57 / 2.70 = 0.581 implies a feedback factor for a change in evaporation of 6% / C of –0.720 C / C. This corresponds to the IPCC value for water vapor of 1.8 Wm-2 / C divided by their value of l of 3.2 to give a feedback factor of +0.562 C / C.
If we use the IPCC value of only 2.5% / C for evaporation changes, our feedback factor of –0.720 drops to –0.308. This compares fairly closely to the IPCC lapse rate feedback factor of –0.262 C / C, based on their value of –0.84 Wm-2 / C.
If one just wanted the feedback factor, equation (2) is more accurate. As described above, for a 6 % evaporation change rate, it gives a feedback factor of –0.741
The IPCC has a positive cloud feedback of 0.69 Wm-2 / C with a very large range. But it is not based on reduced clouds with warming, but as a residual of the amount of warming the models can not explain by the other feedbacks (Soden and Held (2006), p 3357, paragraph 2). So this is not a true estimate of cloud feedback. Eliminating it and replacing the lapse rate feedback with our evaporation feedback cuts the IPCC feedback multiplier from 2.48 down to 0.910.
The three level energy balance model used here is dynamic since it handles balance simultaneously at all three levels: the planet, the atmosphere and the surface. With atmospheric CO2 content increasing very slowly, only about 0.54% per year, there is more than enough time for the normal weather systems to move and distribute the small additional heat across the globe as it always has done in the past. So a simple improved global energy balance should be adequate. Another benefit of the three level model is that it can also handle changes in downwelling radiations. For both increased CO2 and water vapor, besides decreasing outgoing radiation, they will also increase downwelling radiation since these emission levels will move down to warmer temperatures. Present models that must refer everything to the outgoing radiation at the top of the atmosphere have a problem with this.
The use of spectral radiance tools for the atmosphere in both outward and downwelling directions under clear and cloudy conditions can handle the effects of CO2 and the significant water vapor feedback, including its negative feedback component of absorbing incoming solar radiation. These tools, available to all, can greatly improve accuracy and replace the present complicated unreliable computer models which, besides overestimating climate sensitivity, have large ranges of uncertainty of about ± 50%.
Richard J. Petschauer
Email: rjpetsch@aol.com
References
1) http://climateclash.com/improved-simple-climate-sensitivity-model/
2) Kiehl, J. T., and K. E. Trenberth (1997): Earth’s Annual Global Mean Energy Budget. Bull. Amer. Meteorol. Soc., 78: 197-208
3) Wentz, F. J., L. Ricciardulli, K. Hilburn and C. Mears (2007): How much more rain will global warming bring? Science, Vol 317, 13 July 2007, 233-235
4) Soden, B.J., and Held, I.M. (2006): An assessment of climate feedbacks in coupled ocean-atmosphere models. J. Clim.19: 3354–3360.
5) O’Gorman, P. A., and Schneider, T (2008): The Hydrological Cycle over a Wide Range of Climates Simulated with an Idealized GCM. Amer. Meteorol. Soc., 1 August 2008, 3815-2831
=============================================================
Appendix
From Figure A1, the present balanced conditions before any perturbation changes are (all in W m-2):
S = 342 – 77 – 30 = 235; A = 67; H = 24; E = 78; G = 390; W = 40; a = (390 – W) / 390 » 0.8974
where W is the amount through the atmospheric window, and k = 195 / (195 + 324) » 0.3757.
From Figure A1 it can be seen that for balance of heat flux in and out at the TOA,
S = k (A + H + E) + kGa + G (1 – a) (A1)
Solving for G,
G = [S – k (A + H + E)] / (1 – a + ak) (A2)
With the above base value in equation (A1), G = G0 = 390 Wm-2 corresponding to a surface at 14.9853 C. To perturb any value, change it and calculate a new G and from that a temperature change.
To impose a forcing R at the TOA, k = (195 – R) / (195 – R + 324). Unless a or k is the value being perturbed, the equations above require the baseline values for a and k. For other values of these, partial derivatives as shown below
At the lower part of the atmosphere,
∂G/∂ E = ∂G/∂ H = ∂G/∂A = –∂G/∂D = – k / (1 – a + ak) (A3)
At the top of the atmosphere for longwave radiation only,
∂G/∂ U= (k – 1) / (1 – a + ak) (A4)
For change in net solar, S, shortwave incoming radiation, the forcing is substantially larger than for longwave radiation:
From changes in the solar strength,
∂G/∂ S= (1 – kA / S) / (1 – a + ak ) (A5)
From changes in albedo,
∂G/∂ S » 1 / (1 – a + ak) (A6)
For changes in evaporation with the present value of k or a different one, equation (A3) is used to get a feedback factor. The present value of k assumes the division of changes in radiation leaving the atmosphere are in the same ratio as the present total values. This ends up with a smaller temperature change at the upward outgoing emission level than that of the downwelling level. Changing the ratio of U / D to (U / D) 0.75 results in equal temperature changes and increases k from 0.3757 to 0.4059. From forcing at the TOA from CO2 at a typical emission level of about 10 km, one would think that the upward emission level temperature would increase more than the lower level. This suggests a value of k greater than 0.4059 of about 0.42 to 0.43.
The value a is simply a function of the fraction of emission through the atmospheric window and the estimated net fractional cloud cover, Cc. For changes to be compatible with this baseline with 60% cloud cover for different cloud coverage,
a = 1 – 100 / 390 (1 – Cc) (A7)
This implies a clear sky atmospheric window of 100/390 or 25.6%. Based on spectral radiance runs with Hitran 2008, a closer value of 22.8% results. Then,
a = 1 – 0.228 (1 – Cc) (A8)
For 60% cloud coverage, a = 0.9086, up from 0.8974.
Changing k to 0.4059 and a to 0.9086, increases the evaporation feedback factor from = –0.741 to –0.765.
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Thanks, Richard J. Petschauer. That’s a lot of maths to go through, and I haven’t done it yet, but you appear to be on the right track:
“at a typical ocean temperature of 17 C, [evaporation] should increase about 6.5% / C “.
It seems reasonable to assume that precipitation would increase in line with evaporation:
Science 27 April 2012:Vol. 336 no. 6080 pp. 455-458 DOI: 10.1126/science.1212222
https://www.sciencemag.org/content/336/6080/455
“We show that ocean salinity patterns express an identifiable fingerprint of an intensifying water cycle. Our 50-year observed global surface salinity changes, combined with changes from global climate models, present robust evidence of an intensified global water cycle at a rate of 8 ± 5% per degree of surface warming. This rate is double the response projected by current-generation climate models and suggests that a substantial (16 to 24%) intensification of the global water cycle will occur in a future 2° to 3° warmer world.“.
Confirmation by Dr Susan Wijffels on ABC (Australian Broadcasting Corporation) “Catalyst” program ..
http://www.abc.net.au/catalyst/stories/3796205.htm
“We’re already starting to detect and see big changes in the extreme events. And we’ve only really warmed the Earth by 0.8 of a degree. If we were to warm the Earth by 3 or 4 degrees, the changes in the hydrological cycle could be near 30 percent. I mean, that’s just a huge change, and it’s very hard for us to imagine.“
It seems extraordinary unreasonable to assume that precipitation could increase like that without there being a similar increase in evaporation.
given
Alberto ARRIBAS HERRANZ Met Office, UK Ensemble Forecasting Research Group says in a paper “In terms of model formulation, there are two main sources of uncertainty: first of all, only imperfect models are available, and second, the resolution of these models is limited. The place where both factors more clearly come together is in what is known as physical parameterizations (i.e. the representation of the effects of processes occurring at unresolved scales using comparatively simple deterministic functions of the resolved variables). In any of them, the value of a large number of empirical-adjustable parameters and thresholds present is somewhat arbitrary, either because of being based on incomplete physical knowledge of the process or because of having been tuned to give optimal results for a test case that is not necessarily representative of more general applications (Yang and Arrit 2002). ”
from
‘Analysis of the impact of a stochastic physics parameterization on the seasonal
forecasting of the North Atlantic Oscillation’
Alberto ARRIBAS HERRANZ Met Office, UK Ensemble Forecasting Research Group
http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CEsQFjAD&url=http%3A%2F%2Frevistas.ucm.es%2Findex.php%2FFITE%2Farticle%2Fdownload%2FFITE0404110105A%2F11756&ei=09VMU_vcBKSa4wSenoGwAw&usg=AFQjCNHi-TE6Kazl7rdpI1eT_okZ2OcOQw&sig2=Zvn5e7978FFyQ1W1XAcGMQ&bvm=bv.64764171,d.bGE
then its open knowledge the problems with models but somehow all those caveats disappear when presenting science to the public or policy makers.
funnily enough oceanographers using a basic physics based model managed to recreate the effect of the sun in changing climate lol
” Using a physics-based climate model, the authors were able to test the response of the ocean to changes in the solar output and found similar results to the data. ”
http://www.reportingclimatescience.com/news-stories/article/sun-fingered-for-little-ice-age-say-researchers.html
Yeah, whatever.
Squealing little lukewarmers were given their chance. They blew it.
Evaporation rates wrong? This is news?
Evaporation is the primary way the atmosphere cools the oceans. How does the atmosphere cool? Radiative gases.
Just get over yourselves.
Sure, I am a nasty piece of work. That doesn’t stop me being right 😉
“There are no good and bad people in the world. There are only ever and always the bad people, it’s just that some of them are on different sides.” – T Pratchett
An unending sea of evil, shallow in most places, but deeper, oh so much deeper in others……
I may be a monster, by I am MY monster.
(Anthony, I can take out Monckton, Willis and Dr. Brown, yah got anything or anyone else?*)
*I am always the smartest guy in the room.**
** Dependant on room size. Serving suggestion only. Results may vary.
FWIW – Swimming pool engineering has a good body of knowledge on the topic of heat transfer from open water by evaporative losses.
Interesting, and the effect of convection on the calculations is ?
Is conductive loss so low that Equation (1) can ignore it?
“And the latent heat deposited in the atmosphere warms it and increases the downwelling radiation.” Is that correct? I had thought increased heat would increase radiation only after it became sensible.
I understand this blog to support negative feedback from phase change in H2O at the surface and radiation of the energy from the top of the atmosphere.
The author observes that models that support global warming incorrectly posit an energy constraint on evaporation.
I conclude that this is what forces them to introduce positive feedback to make their model work.
I think my conclusion follows from the data and discussion presented here. Any comment?
“But the complex computer climate models show averages of only about 2.5% / C. There are no claims of reduced wind speeds or wave action or increased relative humidity to explain this.”
I would have thought it would be decreased, rather than increased, relative humidity that would result from lower partial-pressure increase.
Mike writes “It seems reasonable to assume that precipitation would increase in line with evaporation: […]”
And yet they cant follow the logic through that the climate models underestimate the evaporation and hence surface energy lost through latent heat transfer to be deposited much higher in the atmosphere and subsequently radiated away…and hence overestimate the warming effect. No, instead they harp on about the 2C to 4C warming the models predict.
Very interesting post. LHV is such a powerful energy transfer when you appreciate that 1 kg water evaporated can cool about 2000 kg of air by 1 degree. Taken together with the huge energy absorbtion into the chemical binds of biomass ( via CO2 + H2O + whatever= biomass) and the CO2 GH effect looks like a popgun facing a minigun. It seems to me almost emblematic of those “scientists” inside the AGW bubble world that they would not bother to get the science and the maths right on these things as that really would reveal an inconvenient truth.
“6% / C” seems a great over simplification. The following is for fresh water:
E = 5([Tc+ 18]**2.5– r[Ta+ 18]**2.5)(V + 4) x 10**-6
where:
E = evaporation rate, kg/m2/h
r = relative humidity/100T
Ta= air temperature, °C
Tc= water surface temperature, °C
V = wind velocity, km/h.
This will be interesting to study in light of the “Decreasing Trend in Pan Evaporation.”
If the author is correct, then this is a pretty big deal. Infact, this could be one of the most significant events in the debate against AGW.
I assume the capital gammas in Eq’n A3 should be Gs?
This might be a little tangential, but it is also connected to precipitation, and specifically the resolution being too coarse to pick up rainstorms.
While discussing the Lovejoy 99% paper it struck me that a lot of the measurement accuracy is obtained by removing inhomogeneities by statistical techniques. However, if you consider that things that lower the surface temperature (rainstorms) are smaller scale than the rest of of the climate (i.e. there are more places, covering a larger area, where it is raining rather than not raining at any given time). What’s more, this evaporation problem will also occur over land, because you will have increased evaporation where it has recently rained.
In this context, what you get by doing that is just a high pass filter, and the more “accurate” result, the higher the skew to the positive side will be. If that is correct (and do correct me if I am wrong) it is not just in the models that suffer from this problem, but the measurements too.
Isn’t your approach based on the assumption that the vapor pressure immediately above the surface reflects that general humidity level? Have you double-checked the evaporation rate against the rate of rainfall?
From my stream-of-consciousness question barrage above, you may justifiably infer that I haven’t yet completely comprehended the post. I nonetheless persist:
“From forcing at the TOA from CO2 at a typical emission level of about 10 km, one would think that the upward emission level temperature would increase more than the lower level. ”
I would have thought that CO2-caused forcing would be represented by a decrease in k matched by such an increase in G as to keep U + W equal to (a constant) S. That sounds like a constant emission-level temperature to me.
The CMIP3 models all underestimate precipitation by a factor of 2. There is a direct connection.
The CMIP3 and 5 models all produce a tropical upper troposphere hotspot when none is observed. Again, there is a direct connection.
If surface evaporation is misstated, yet relative humidity is maintained at all altitudes AR4 black box 8.1, then the water vapor feedback is overestimated by about half and mismodeled precipitation is direct evidence. The mismodeling is greatest in the tropics where more precipitation occurs (ITCZ), which is why models have a tropical hotspot while the world doesn’t. In the world, upper humidity is lowered by washout, and the latent heat left in the atmosphere is freer to radiate away.
None of this got corrected in CMIP5. Perhaps this post offers a specific fundamental reason why.
One last question before I turn to my taxes:
For someone who is good with the data sets, it should be relatively easy to apply your function of evaporation versus temperature to the gridded temperature data set,area-weight the results, and compare that with global average rainfall. Wouldn’t that be a good sanity check?
This doesn’t pass a smell test, if evaporation increases 6% then precipitation must increase a similar amount. Taking into account that average rainfall across the surface is a meter per annum and the specific heat of evaporation and change in potential energy between the surface and 3 km a forcing of at least 5.5W per meter squared would be required to break even on the energy budget to do this. Since the total forcing is only 3.7 Watts per square meter, and the imbalance only 0.6W per square meter, there is clearly insufficient energy in CO2 related reflected IR to sustain the 6% increase in the hydrological cycle, even at 5.5W per square meter, if there was a 6 % increase in evaporation then the cooling effect would completely cancel the warming, so it seems to me that a driving energy of considerably more than 5.5W per square meter would be required to sustain such an increased evaporation AND warm the atmosphere at the same time. (Of course then we should add in the other losses, such a heating gigatonnes of liquid water, melting a few gigatonnes of ice, sustaining increased photosysthesis, greater storm energies and all the other magical effects that are supposed to happen – apparently without expending any of that magical 0.6W of heating that’s supposed to be causing these effects
I need to understand where you think the energy is coming from to sustain this warming in the presence of such a huge increase in evaporation.
“Konrad says:
April 15, 2014 at 12:55 am
*I am always the smartest guy in the room.**”
He says, as he posts from a phone booth.
He, he…
“It seems to me almost emblematic of those “scientists” inside the AGW bubble world that they would not bother to get the science and the maths right on these things as that really would reveal an inconvenient truth.”
I have oten wondered if that is the sad and sorry case. They are certainly quite capable of correcting their errors to make sure those laughable models be much more accurate, but they resist, why?
Why do they continually demonstrate their complete ineptitude and bias by not fixing those models to reflect true current results, instead of their own biased, fantasy driven ever higher temperatures. It is just beyond comprehension. Does it refer to that old saying “better to let them think you’re stupid than to open your mouth and remove all doubt?’. I am perplexed by this entire scenario. Even when faced with the obvious facts like the examples above they will still continue on their ignorant and deliberate of scientific principles, theories and conduct.
I believe IEEE stands for Institute of Electrical and Electronics Engineers. Electrical engineers normally have a good grasp of mathematics but I am not so sure of their grasp of chemical engineering science. I have come across electrical engineers who have no idea of process control because they do not understand engineering science such as reaction kinetics, fluid dynamics or heat & mass transfer. Mention of physics instead of engineering science makes me suspicious. Instead of humidity you should be using partial pressures-just think of the lower pressures in a cyclone which helps evaporation at the warm ocean surface to feed in energy. For forced convection and evaporation I did not see any mention of the Nusselt number or Prandtl number. Engineers normally take great care with units and dimensions. Working with dimensionless numbers helps to get sensible answers. Every part of an equation has to be in the same units- you can not add or multiply apples and oranges.. By the way CO2 can not do any of forcing -check the units.
Fancy quoting Kiehl & Trenberth that paper would never be published in an engineering journal.
When the missing heat is found, might it be due to this very miscalculation?
From upstream in this thread, I too think this mathematical model as a number of checkpoints that can be possibly varified with observation. What additional checks have you made besides the one mentioned in the paper? Precip, humidty, temperature, pressure, etc are all sources of potential checks for this model besides observed evaporation rate.
Thank you for your efforts.
But – and you knew a “but” was coming didn’t you? 8<)
If we start with balance at the surface and again solve for G, we get the same result that also forces balance at the atmosphere.
Does that not "require" the usual assumption of a single flat-earth, flat-plate, one-sided, "average' earth at a single constant distance from the sun in a "perfect" equilibrium" with space?
Rather, how does your work change if you require the use of a "spotlight" solar heating on a rotating 24 hour sphere? Solar heating is NOT an uniform average of 324 watts over 24 hours, but is a constantly-changing value between 200 watts (at 07:00) to over 1150 watts (noon) to 0 (after dark, before sunrise.)
Today, for example, day-of-year 105 (15 April) the amount of solar energy on each square meter of the earth's surface at the equator each hour of the day on a clear day is NOT 324 watts, but the following:
So, your “equilibrium model” must evaporate, radiate (long wave), convect, and conduct (from the upper 2 millimeters of water to the depths), not 342, but 1131 watts (at the equator, at noon.) But, over night, an adequate model must change to evaporate, long wave radiate, convect, and conduct 0.0 SW solar radiation, and cool the ocean using the available stored energy from the previous day.
But the earth at any latitude is not radiated evenly either, and the north-south distribution invalidates a simplified flat-plate radiated evenly at equilibrium mode as well. Same day-of-year as above, same one square meter flat surface at noon as above, same clear skies in direct sunlight as above, but at each latitude.