The True Energy Balance of the Earth+Atmosphere

Update 10 March, 2012: I have realized (on my own) that my blackbody understanding was wrong, and why my physical interpretation of the facts of my Venus/Earth comparison is nevertheless correct. I have posted on this at "My Own Blackbody Error". This post no longer reflects my scientific position, and should not be taken as such.

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UPDATE 03 March, 2012: I have obtained a better value for the mass mean temperature in the stratosphere [T(strat)] used in this article. From computerized numerical integration of the relevant stratosphere formulas (for T(h) and ρ(h)) in the 1976 US Standard Atmosphere, I found T(strat)=223.9K, not the 240K used in the article below. This does not change the analysis here or its conclusions substantially, as I will allow others to verify; it basically only means a slightly larger amount of solar absorption by the surface (from 50-52% of the incident solar, in the original article here, to perhaps as high as 54%). I also obtained a more precise mass mean temperature in the troposphere, through finer numerical integration on the computer, which merely confirms the 259.3K used here.
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When I posted the landmark article, "Venus: No Greenhouse Effect", which fundamentally corrects climate science, in November, 2010, I hoped that other competent scientists would quickly see the validity of my contribution and use it to re-establish climate science on a sound basis, stop the insanity of a politically promulgated, false consensus, and also establish my scientific worth to the world, thus allowing my far greater discoveries to gain serious attention and the worldwide recognition they deserve.

But that has not happened. I have seen NO positive advance in climate understanding since I proved, with the definitive facts, that there is no greenhouse effect, of increasing atmospheric temperature with increasing atmospheric carbon dioxide.

So here is yet another advance of my own, elementary but decisive.

In my recent post, "On the Fundamental Warming of the Atmosphere", I summarized the energy taken up, from the incident solar radiation, by the Earth-plus-atmosphere system, using widely used numbers (see, for example, the Kiehl-Trenberth energy budget). Based upon my simple Venus/Earth analysis, the relevant fractions are:

Incident solar energy = 100%

Solar energy reflected = 30%

Solar energy directly absorbed by surface = 50%

Solar energy directly absorbed by atmosphere = 20%

Of the 70% that goes to heating either the surface or the atmosphere, 2/7 directly heats the atmosphere, and 5/7 directly heats the surface. In the new understanding provided by my Venus/Earth comparison, the atmosphere and surface are separately and independently heated by incoming solar energy, and the governing hydrostatic temperature lapse rate structure of the troposphere moderates any inequality in their heating, with upward heat transport, "down" the temperature gradient, contributing to no further warming of the atmosphere, in my view.

The question should quickly have been taken up by any real climate experts, or competent scientists: Can the above energy balance be quantitatively validated (or invalidated)? The answer is yes, it can be validated.

The consensus claims that the radiating temperature of the system is 255K, based upon using "incident minus reflected" solar intensity in the Stefan-Boltzmann formula:

342 W/m^2 (mean incident) - 30% reflected = 239 W/m^2 (mean absorbed)

which gives a mean radiating temperature of 255K. (I am using whole numbers as much as possible throughout, reflecting the uncertainty I have seen in the numbers used by others.)

I know this 255K is wrong, and the radiating, or equivalent blackbody, temperature, is to be found from the incident radiation alone:

342 W/m^2, giving an equivalent blackbody temperature of 279K,

BUT THE CONSENSUS CALLS THIS RIDICULOUS, and everyone, from alarmists to the mildest skeptics, seems to accept the consensus radiation numbers, and believes 255K is the physical fact.

Here is what I find:

Incoming solar energy is absorbed in both the stratosphere and the troposphere, as well as by the surface. Because my Venus/Earth comparison looked at the Earth troposphere region, and got such definitive results, I first left out the stratosphere as being of minor importance, considered the troposphere the sole relevant atmosphere, and considered the following:

If we know the mean temperature of each of the two absorbing systems, atmosphere and surface, we can determine the mean temperature of the total surface-plus-atmosphere system, in the following way:

fraction of absorbed power given to atmosphere = f1 (= 2/7)

fraction of absorbed power given to surface = f2 (= 5/7)

mean temperature of atmosphere (troposphere) = T(trop)

mean temperature of surface =T(surf)

mean temperature of surface-plus-troposphere system = T(all)

where the consensus says T(all) is 255K, and I (and other critics of the consensus) say it should be 279K.

Then

f1 x T(trop) + f2 x T(surf) = T(all) (Equation 1)

Physically, this means that the fraction of the total power retained in the total system by a given subsystem, times that subsystem's mean temperature, gives that subsystem's contribution to the mean temperature of the whole.

For T(trop), I calculated the mass mean temperature of the troposphere, according to the formula:

T(trop) = Integral [T(h)dm] / Integral [dm] (Equation 2)

where h = altitude above the surface, and

dm = element of atmospheric mass,

with dm = ρ(h) dV, ρ = density and dV = element of volume,

and dV = volume of spherical shell of thickness dh, radius = Re + h
with Re, the radius of the Earth.

The following equations hold in the Standard Atmosphere troposphere:

T(h) = To x (1 - 6.5 h/To)

ln[ρ/ρ(o)] = 4.2559 x ln(1 - 6.5 h/To)

I plugged these into Equation 2 and solved it numerically, by dividing the troposphere between 0 and 11 km into spherical shells of thickness 0.2km, and found:

T(trop) = 259.3K (NOT 255K, note)

T(surf) = 288.15K, so Equation 1 becomes

(2/7)259.3K + (5/7)288.15K = 279.9K = 280K approximately.

Compare this to 279K obtained by using the Stefan-Boltzmann formula with INCIDENT mean solar intensity. I consider this a quantitative verification of my usage of the Stefan-Boltzmann formula, and a disproof of the consensus usage.

But WARNING:

If one uses 255K for T(trop)--as many do in their narratives, both consensus and skeptics--in the above equation, one gets

(2/7)255K + (5/7)288.15K = 278.7K,

an apparently more exact result for the true radiating temperature of the total system--by a mere 1.2K, however, which I suspect is well within the uncertainty of the calculation. And using 255K for the troposphere alone is inconsistent with making that the radiating temperature of the whole Earth-atmosphere system, and still makes the consensus wrong in its usage of the Stefan-Boltzmann formula, since 279K is still clearly the true effective radiating temperature of the total system, not 255K.

Even more importantly, from the use of Equation 1 it should be clear that the warming of the atmosphere must be independent of the warming of the surface, since the coefficients f1 and f2 on the left-hand side of the equation are independent of my Venus/Earth findings (they represent the actual solar power absorbed by the troposphere and the surface, as shown in the Kiehl-Trenberth Earth Energy Budget), and the above verification is thus an independent check upon my Venus/Earth conclusion (that is, it uses my conclusion, as expressed by Equation 1, with real-world numbers). So the atmosphere IS fundamentally warmed only by direct absorption of a fraction of the incident solar radiation (and the other upward heat transfers from the surface, in the K-T Energy budget, DO NOT CONTRIBUTE TO THE FUNDAMENTAL WARMING OF THE ATMOSPHERE--the incident 20% directly absorbed by the atmosphere does the job).

Now let's do the same budget calculation, but with the stratosphere properly included, so that we have an equation with three absorbing terms:

f1 T(strat) + f2 T(trop) + f3 T(surf) = T(all),

where f1 etc. are the fractions of the total absorbed radiation in each subsystem.

I do not have what I consider a definitive number for T(strat), the mean temperature in the stratosphere, so I estimated it from a graph of the TEMPERATURE PROFILE of the atmosphere, as a function of altitude (I leave it to the reader as an independent exercise, to check my work). I estimated T(strat) = 240K (+/- 5K, judging from what I could glean from a short internet search on the topic). The stratosphere absorbs ultraviolet (UV)--as much as 95% of the incident solar UV, internet sources say--and UV comprises between 8% and 8.5% of the incident solar energy, so I first took 8% to be the fraction of the incident solar absorbed by the stratosphere, leaving 12% to warm the troposphere and about 50% to warm the surface. The absorption equation becomes:

(8/70)x240K + (12/70)x259.3K + (50/70)x288.15K = 277.7K = 278K

I have provided this sample calculation to show that, given the uncertainties in the absorption numbers, one can still see that the true radiating temperature of the Earth-plus-atmosphere system MUST BE 279K, not 255K.

One can also play with the above equation (with 279K, on the right-hand side, as a physical constraint). Using numbers in the Kiehl-Trenberth energy budget, the reflected solar is 107 W/m^2, which is 31.3% of the incident 342 W/m^2. This makes the total absorption, spread over the stratosphere, troposphere, and surface, 68.7% of the total mean solar, rather than the 70% I used earlier. This gives us some idea of the uncertainties involved in the numbers used by different sources.

Using a reasonable variation in the absorbing fractions attributed to each of the three subsystems of stratosphere, troposphere, and surface, and using a total absorbed percentage between, say, 68.5% and 70% of the incident solar, I found 7-8% stratosphere, 10-12% troposphere, and 50-52% surface to be the most likely range for the solar fractions absorbed by each subsystem. For example, for a total of 68.7% of incident solar absorbed, as in the K-T Earth energy budget, I found 7.5% in the stratosphere, 10% in the troposphere, and 51.2% at the surface to give particularly good results:

(7.5/68.7) 240K + (10/68.7) 259.3K + (51.2/68.7) 288.15K = 278.7K

but I consider that just a good educated guess, and about as good as one can do with the numbers provided by climate science so far.

Summarizing: My evaluation of the fundamental warming of the atmosphere, separately from the warming of the surface, and both by direct absorption of entirely different fractions of the incident solar radiation, is quantitatively verified by a correct usage of the blackbody formula (to obtain 279K for the radiating temperature of the Earth-atmosphere system).

Incompetent Skeptics III: Roy Spencer, PhD

I have made the following comment on Roy Spencer's web site, concerning his defense of the greenhouse effect.

Roy Spencer wrote: "
...the cooler object (the atmosphere) keeps the warmer object (the ground) warmer than if the atmosphere was not there. That’s the (so-called) greenhouse effect."

Two points of simple fact, no three:

1) That is NOT the greenhouse effect that the IPCC and all of our suborned institutions are foisting upon the public. The greenhouse effect is an increase in atmospheric temperature with increasing atmospheric carbon dioxide. You are dissembling (intentionally or not) in refusing to admit that, and adhere to it. (And so is "steveta_uk", who commented above, "The absurd idea that GHE results in INCREASING surface temperatures is simply a misreading of the theory." That statement itself, in the face of the public debate over "global warming", is the height of absurdity, and in a sane intellectual atmosphere, could rightly be called a bald-faced lie. However, I understand that it is just the madness of those whose religiously-held belief in the greenhouse effect--and in the inerrancy of an overwhelming, albeit incompetent, consensus--is being strongly challenged by skeptics.)

2)I have DISPROVED the greenhouse effect, in my comparison of the temperatures in the atmospheres of Venus and Earth. YOU ARE INCOMPETENT as a physical scientist if you cannot see that simple fact.

3)You delude yourself by thinking the atmosphere keeps the surface warmer due to "backradiation", a.k.a. "downwelling longwave radiation". Since there is no greenhouse effect, I think it should be obvious that the atmosphere at night is keeping the surface from cooling faster, because upward heat transfer is not by radiation alone, with an atmosphere present, but also by convection and conduction, and these are SLOWER THAN RADIATION, and I would think can even reverse direction, against the temperature gradient, and even reverse it locally (downdrafts, precipitation, temperature inversions). That's what the radiative transfer theory does to you: It makes you forget there ARE even convection and conduction.

Your miseducation makes you part of the problem, Dr.--and of course you are not alone, climate scientists have been miseducated for, what, forty five years (I have read that 1967 or 1968 is when the current radiative transfer theory, applied to atmospheric warming, was brought out and accepted), and there has not been a competent climate scientist for at least the last 20 years, since the detailed temperature and pressure data of Venus, which should have signaled the death of the greenhouse effect as accepted science, was obtained by the Magellan spacecraft. Of course, the bottom line is, the very idea of "runaway climate", and thus of looking at climate as something balanced on the knife edge of "radiative forcings", only came into science through a mass turning away from, or forgetting of, the stability of the Standard Atmosphere (which of course my Venus/Earth comparison confirmed). Climate scientists' faith in radiative transfer theory is blind to the definitive facts, and has caused the failure--FAILURE, SIR--of their science. I am ashamed of all of you, and of what you continue to do, unseeing and undeterred by the strongest admonitions, to the integrity and natural authority of science.

Incompetent Skeptics II: Willis Eschenbach

In the interests of openness, which is one of my prime watchwords, the following is a submission I made today to Anthony Watt's site, wattsupwiththat.com (which takes a strong "lukewarm greenhouse believer" stance), and the quick result of that submission, which I made to correct ideas being promulgated on that site, according to the definitive facts I have uncovered, and to register my displeasure at the unbridled arrogance increasingly displayed by Willis Eschenbach on the WUWT site:

Submission:

In comments following a recent post by Willis Eschenbach, that author repeatedly and arrogantly dismissed those he called "Pressure-Heads", at one point with the following words:

" ... I have clearly shown, in 'A matter of some gravity' that if there are no GHGs and the atmosphere is transparent, then no pressure or gravity mechanism, or any other method, can raise the surface above the S-B blackbody temperature.... Duh."

The following is my response, for informational purposes only, to such naive hubris:

WARNING: The following does not come from a "Pressure-Head", so empty your mind of that prejudice. Of course pressure does not determine the temperature. But in a planetary gravitational field, with input solar energy, the atmosphere DOES take on a vertical pressure distribution, described by the elementary physics of the hydrostatic condition, which determines the vertical temperature distribution known as the lapse rate structure. The empirical Standard Atmosphere is defined by that structure, and the Standard Atmosphere is confirmed as the governing STABLE state of our atmosphere, by my Venus/Earth temperatures comparison (which also corrects current climate science on a whole handful of basic physical points).

Your assumptions, in your quoted words above, are irrelevant to the real situation in our atmosphere. The REAL atmosphere absorbs 15-20% of the incident solar energy. It is NOT "transparent" to IR radiation. Duh.

In fact, the atmosphere is fundamentally warmed, and the governing hydrostatic, vertical temperature lapse rate structure maintained, by that IR absorption (not by convection, and particularly not from the surface, which is independently heated by the Sun and does NOT fundamentally warm the atmosphere--does not change the governing lapse rate structure--but only contributes to the "weather"). Duh.

Atmospheric IR absorption does not mean there is a greenhouse effect, of increasing atmospheric temperature with increasing atmospheric carbon dioxide. Again, there is no such effect (that is the hard, definitive fact, from the comparison of two detailed atmospheres, having hugely different concentrations of atmospheric carbon dioxide). Duh.

But even without the definitive Venus/Earth comparison, there are no competent scientists defending the greenhouse effect (including, in particular, you), because such defenders fail to see that the atmospheric "backradiation", from the cooler atmosphere to the Earth's surface, is, in the theory, re-emitted by the surface at its own, higher temperature--which violates both energy conservation, as any first-year physics student SHOULD be able to see in the infamous Kiehl-Trenberth Earth Energy Budget diagram, and the second law of thermodynamics. Duh.

The reason you refuse to see the obvious is because you have been miseducated to believe in the radiative transfer theory, that falsely indicates the unphysical consensus greenhouse effect. Not only is that greenhouse effect nonexistent, but the radiation transfer theory that indicates that effect must also obviously be wrong--given my Venus/Earth findings--in its assumed thermodynamic effects, and misses the real thermodynamics of the atmosphere completely. The reason for that is also clear, to me: The radiation theory starts from the assumption of detailed thermodynamic equilibrium, that is, of a strict, set temperature distribution, because it ASSUMES not only that the surface is a blackbody--the 390 W/m^2 surface emission is just the power emitted by a blackbody at the 288K temperature of the Earth's surface--but also that every differential layer of the atmosphere emits as a "gray body", i.e., as local emissivity times the Planck distribution function. These assumptions are only valid, and only formally so, in the presence of a strict, set temperature distribution. It is therefore a formal theory only, whose apparent empirical confirmation is only the EFFECT of the lapse rate structure (which provides the set temperature distribution), not the CAUSE of it, or of any real thermodynamics. This point has also been made independently by Prof. Claes Johnson, who has written that so-called measurements of downwelling and upwelling longwave radiation are really only temperature measurements, (formally) converted to equivalent blackbody radiation levels.

Incompetent (duh) and angry (duh) arguments are damaging the credibility (duh) of WUWT (duh), and other sites critical of the consensus global warming scare. (DUH)

Anthony Watts e-mailed back:

"Sorry, not going to publish this, especially with all the 'duhs'. It will do nothing but create even bigger divides."

to which I replied:

"You are creating your own divides, that is now perfectly clear (you can't take your own medicine, as doled out by Eschenbach). Duh. Nevertheless, you--and Willis Eschenbach (duh)--have been informed of the facts, which is my intent. I will put this up on my own blog, for the sake of openness."

This is merely information for readers, and not intended to evoke arguments and vain debate over speculative theories. This is just how it is, between believers in the greenhouse effect--skeptic or otherwise--and those relative few of us who know better. I don't want to be part of vain arguments, and I don't think those who have become interested in my views would want me to indulge in them.

Sunshine and Fair Weather Skeptics

The Bishop Hill site today asks why persons in authority talk about healthy scientific skepticism, but deny its applicability to the climate science, a.k.a. global warming, debate. I submitted the following answer:

Nobody wants to hear it, but the reason is because DOGMA--received, rather than reasoned, belief--is ascendant in the world today. Science, it was once hoped, would counter the old dogmas, and so it did, but only so long as it didn't become addicted to dogma itself (and it never wiped out the endemic dogmas of established religions, superstitions, and ethnic traditions, whose dogmas continue to pound relentlessly upon the shores of reason and civil society). But with Darwin (yes, and denying it doesn't make it less true, in the final analysis), science made a fundamental error, cut off a whole line of valid reasoning about this strange and wonderful world--that it was in fact subjected to wholesale, intentional design, as my epochal research has uncovered for science--and has increasingly become mired in dogma, over sound (air-tight) logic, and sound experimental discovery and verification. A broad and deep, entrenched incompetence in science has been the result. Science has become just another part of the problem of Man on Earth, trying to learn how to treat, and how to live with, others of different beliefs.

As the discoverer of unprecedented new knowledge about the origin of the world as we find it today, I can only keep harping on the need to FOCUS, upon the DEFINITIVE FACTS that alone can correct current false theories. I have discovered, and verified, the definitive facts for correcting climate science (see my climate science posts, such as "Venus: No Greenhouse Effect"), but the world community of scientists needs to focus upon them, and accept them, in order to recover a competent climate science.

And the whole paradigm, of blind, undirected "evolution" of the Earth, and all the life on it, needs to be let go, because there is new knowledge, correcting both science and religion, waiting to be acknowledged, studied, and accepted by all. If you are not ready to hear that, you are part of the problem, that vexes us all.

On the Fundamental Warming of the Atmosphere

I have posted the following comment on the tallbloke web site, in response to a discussion there which involves both my Venus/Earth atmospheric temperatures comparisonand the "Unified Theory of Climate" of Nikolov and Zeller:

(Nikolov wrote:) "However, Huffman needs to correct his terminology."

No, Nikolov is obviously incapable of following what I consider a simple train of thought--because he thinks he already knows better, and refuses to follow the logic. And Tallbloke, who wrote on my site that "I don't feel ready to tackle your logic", indeed doesn't get it either. I don't know if it will do any good to try once again to spell it out, but here is the real logic:

1) The OBSERVED Venus/Earth atmospheric temperature ratio (over the range of Earth tropospheric pressures) is very precisely 1.176 (except within the Venus cloud layer). THAT IS A FACT.

2) That temperature ratio corresponds to an ABSORBED POWER RATIO (watts/sq. meter) of 1.91. THAT IS ANOTHER FACT. (i.e.: Two bodies, isolated in space, are subject to two different incident radiation intensities, with one intensity 1.91 times that of the other. What is the ratio of the equilibrium temperatures of the two bodies? By the Stefan-Boltzmann formula, it is 1.176.)

3) The actual (ACTUAL) INCIDENT POWER RATIO, from the ratio of the two planets' average distances from the Sun (i.e., calculated beyond the atmosphere), is also 1.91. Yet another FACT.

4) Ergo (and that means no fooling, this is just the unavoidable truth): a) the actual power per unit area absorbed by Venus's atmosphere is 1.91 times that absorbed by Earth's atmosphere--this is just factual statement (2) above; and b) that is also equal to the INCIDENT POWER RATIO (calculated beyond the atmosphere, BEFORE ANY REFLECTION of solar radiation)--this is just factual statement (3) above.

Statement (4a) above is the empirical fact, DESPITE THE FACT that Venus's albedo is much larger than Earth's. So you see I don't argue about the value of the albedo, there is no need to; instead I continue, logically and very simply in my professional opinion:

Thus, the portion of the solar radiation that goes to warm either planet's atmosphere DOES NOT INCLUDE the portion that is REFLECTED, by either planet--if it did, and Nikolov knew what he was talking about, then the observed Venus/Earth temperature ratio would NOT, could not, indicate statement (4a) above (that is, it would not BE 1.176, indicating an absorbed power ratio of 1.91)--but that temperature ratio DOES indicate statement (4a), and the two planets' difference in albedo OBVIOUSLY makes no difference in the amount of power absorbed by either atmosphere. Simply stated, their temperature ratio is completely and precisely explained by the ratio of their distances from the Sun, nothing else.

I gave David Socrates some numbers to indicate what is going on. Given that 30% of the solar radiation incident upon the Earth-plus-atmosphere system is reflected, and about 50% absorbed by the surface, then 20% is directly absorbed by the atmosphere, warming it. For Venus, given 70% is reflected, and the same 20% that warms Earth's atmosphere also warms Venus's atmosphere (only Venus is closer to the Sun, so that 20% contains 1.91 times the power that is in the same 20% hitting the Earth's atmosphere), then Venus's surface must absorb the remaining 10% (or, if the reflection is 75%, the surface absorbs about 5%). The approximate 20% of the incident solar power that warms BOTH planets is in the infrared, practically none is in the visible or in the ultraviolet (the latter, they tell us, is absorbed in the stratosphere).

So forget "albedo is a function of pressure and solar proximity", or "a function of the internal energy of the system" as Nikolov wrote at the top of this page. I am astounded that any physical scientist would make such a statement. The reflected radiation is simply not that radiation which can and does warm the atmosphere. All the above facts, plus the fact that the surfaces of Earth and Venus differ greatly (Earth being 70% ocean, while Venus is all solid crust) and would absorb different fractions of any radiation reaching them, also mean that THE ATMOSPHERES OF VENUS AND EARTH ARE BOTH WARMED BY DIRECT ABSORPTION OF INCIDENT SOLAR RADIATION (the approximate 20% of the total solar power just discussed), and NOT FROM THE SURFACE. The corollary to this is that, ANY UPWARD HEAT TRANSPORT, INCLUDING BY WAY OF THE ABSORPTION AND EMISSION OF UPWELLING LONGWAVE RADIATION, DOES NOT FUNDAMENTALLY WARM THE ATMOSPHERE (that is, has nothing to do with the tropospheric temperatures as established in the Standard Atmosphere, by its lapse rate structure and the incident solar intensity, but only has to do with the "weather"). ONLY DIRECT ABSORPTION OF INCIDENT SOLAR RADIATION FUNDAMENTALLY WARMS THE ATMOSPHERE. The only other person I know who independently came to this conclusion is William R. Pratt, but mine is the only factual demonstration of this revolutionary finding that I know of, and it is as important as the factual finding that there is no increase in global average atmospheric temperature with increasing carbon dioxide--no "greenhouse effect" as promulgated by the IPCC.

Some of you also need to stop saying "most of the Sun's radiation is in the visible". That is not correct, the PEAK of the Sun's spectrum is in the visible, but about half of the solar power is in the infrared (beyond the visible in wavelength).