Monday, May 9, 2011

Radiation physics constraints on global warming

[Fig.1 from Trenberth et al. 2009 : reference-[1]]

[This article was first published on this Activist Teacher blog, on May 9, 2011. Reviews from peers are invited (e.g.). The University of Ottawa tried to stop this research: LINK. The article is available as a PDF file HERE.]





By Denis G. Rancourt

Abstract – I describe the basic physics of planetary radiation balance and surface temperature, in the simplest and most robust terms possible that capture the essential ingredients of planetary greenhouse warming. I show that the often repeated textbook and scientific report view that the Earth’s surface temperature would be –19C (degrees Celsius) in the absence of a planetary greenhouse effect (a 33C greenhouse effect difference) is wrong; and that an accepted calculation of the “longwave radiative forcing” by atmospheric greenhouse gases is also wrong. Our simple radiation-balance model – using only (i) the satellite-measured absolute longwave Earth emission, (ii) a present mean global surface temperature of 14C, (iii) the satellite-measured fraction of longwave absorbance due to CO2, (iv) a satellite-measured global mean surface albedo of 0.30, (v) the season-average solar constant and (vi) Kirchoff’s Law – predicts: (a) a total longwave emission atmospheric mean transmittance of {te} = 0.89, (b) a zero-greenhouse-effect Earth mean surface temperature of To = 5.5C, (c) a global mean surface emission intensity of 269 W/m2, (d) a post-industrial warming due only to CO2 increase of ΔTind = 0.56C, (e) a temperature increase from doubling the present CO2 concentration alone (without water vapour feedback) equal to ΔTdbl = 2.0C. Earth’s radiative balance determining its surface temperature is shown to be one order of magnitude more sensitive to solar irradiance and to planetary albedo/emissivity than to all atmospheric greenhouse effects combined. All the model predictions robustly follow from the starting assumptions without any need for elaborate global circulation models. A recent critique of the dominant climate change science narrative is evaluated in the light of our model.

Simplest model with essential features

The concepts of radiation physics are easy to explain but difficult to understand. Here we show that even the most fundamental concepts of albedo and emissivity have not been completely appreciated by most seasoned scientific writers addressing the phenomenon of a planetary greenhouse effect.

Let us start by building the simplest possible model of planetary radiation balance, realistic enough to capture the essential global average features.

We take the planet to be a perfect sphere with a smooth and homogeneous surface and to have a thin (compared to the planet radius) and homogeneous atmosphere. The planet is uniformly irradiated by a distant sun.

The incident intensity (in Watts per square-meter, W/m2) of “shortwave” radiation (largely visible light) from the sun at the planet is the so-called solar constant, Is, where for Earth Is = 1366 W/m2 (having a real seasonal variation in magnitude from 1412 to 1321 W/m2, or 6.7% of its average value).

Different parts of the planet’s surface receive different intensities of incident shortwave radiation. This is because the surfaces at different latitudes receive the incident rays at different angles and because half of the planet’s surface is shielded from all incident rays (only one hemisphere is exposed to the sun at any given time).

Rather than deal with the latter complexity of non-uniform irradiation, instead we take the entire planet’s surface to be uniformly irradiated with an intensity equal to the corresponding average solar constant. The correct average solar constant is {Is} = (1/4)Is = 341.5 W/m2, as is well known and easy to calculate. [Throughout the present article "{A}" means "the average of A", usually a global spacial and time average.]

In our model, therefore, every part of the planet’s surface is identical in terms of the radiation balance conditions. Each part of the planet’s surface represents what is happening on average, in terms of radiation balance, and of the planet properties which we will take to be the Earth’s average properties.

Of all the incident shortwave solar radiation that strikes the planet a fraction is reflected back into outer space without being absorbed by any part of the planet (surface or atmosphere). This fraction (from zero to one) of the incident shortwave solar radiation energy that is reflected out from the planet is called the planet’s albedo. Put simply: Albedo = Solar-Out/Solar-In.

The reflected outgoing shortwave radiation need not have the same spectral distribution (radiation intensity versus radiation frequency or wavelength) as the incoming incident solar shortwave radiation because the amount of absorption/reflection can be (and generally is) dependent on wavelength. The albedo is the net energy fraction that is reflected.

Modern satellite spectroscopic measurements can quantify the solar constant and the amount of out-reflected shortwave radiation, can resolve these radiations from longwave thermal radiation, and can measure continuously in orbit to obtain planet-wide averages.

Satellite measurements allow us to conclude that the average Earth albedo is {a} = 0.30 [1]. Arguably-more-direct and reliable Earth-based so-called “Earthshine observation” measurements give {a} = 0.297(5) where, using scientific error notation, the latter means 0.297 ± 0.005 [2]. There are daily changes in Earth’s albedo (from large scale weather changes) of ~5% and seasonal variations of ~15% (from snow and ice cover, vegetation, and weather and cloud cover) [2].

The source of heat on the planet is taken to be the planet’s surface that absorbs shortwave solar radiation. The physical absorption process transforms the electromagnetic energy of the incident solar radiation into heat energy (vibrational energy of the surface’s molecules).

Any opaque body at any temperature above 0 K (i.e., having vibrating rather than motionless molecules) in turn emits electromagnetic radiation. The latter so-called “thermal” or “black-body” radiation has characteristics that depend of the body’s (emitting) surface temperature. For the temperatures of interest the surface thermal radiation is shortwave (or infra-red) radiation.

The intensity Ie (in W/m2) of the emitted thermal (shortwave) electromagnetic radiation coming from the surface of an opaque body is given by the Stefan–Boltzmann law:

Ie = ε σ T^4 ... (eq.1)

where T is the temperature of the emitting surface in K, σ is the Stefan–Boltzmann constant σ = 5.6704 10^-8 W/m2K4, and ε is the “emissivity” of the emitting surface. "T^4" means T to the power 4 and “10^-8” means times 10 to the power minus-eight, giving 0.000000056704 W/m2K4 for σ.

The emissivity has a dimensionless value between zero and one. It is the fractional energy emission from the surface compared to the surface’s emission if it were an ideal black body emitter. ε = 1 for an ideal black body surface and ε = 0 for an ideally reflective surface (i.e., a surface having an albedo of exactly 1).

The global average emissivity, {ε}, of Earth’s surface is virtually impossible to measure. It can at best be reasonably estimated or deduced from relevant physical principles. This is a central difficulty in calculating Earth’s radiative behaviour.

Before we address the latter difficulty regarding {ε}, let us next describe how the planet’s mean surface temperature is established.

If the net radiant energy into the planet is larger than the net radiant energy escaping from the planet then the net received energy will heat the planet and increase its temperature. Likewise, if the net radiant energy out from the planet is larger than the net energy into the planet then the net loss of energy of the planet will cause the planet to loose heat and decrease its temperature.

Therefore, in a “steady state” situation, after a certain planetary response time following any change affecting radiation balance, the temperature of the planet’s surface will stabilize at some value corresponding to the rate of energy-in being equal to the rate of energy-out and there will be “radiation balance” at a stable surface temperature.

The net energy-in is the incident solar radiation minus the albedo loss. The net energy-out is the portion of all the shortwave emission energy that manages to escape the planet into outer space. By setting in = out we can solve for the resulting radiation-balancing planet surface temperature.

The corresponding radiation balance equation, therefore, is:

{Is}(1 – {a}) = {te} {ε} σ T^4 ... (eq.2)

where {te} is the fractional transmittance (having a dimensionless value between zero and one) of the total emitted shortwave radiation energy.

In other words, {te} is the planetary average transmission coefficient for escape of the emitted shortwave radiation through the atmosphere and into outer space. In the absence of all greenhouse effects {te} = 1. For a completely infrared-opaque atmosphere {te} = 0.

Solving for the planet surface temperature (in K), eq.2 gives:

T = [ (1 – {a}){Is} / {te}{ε}σ ]^(1/4) ... (eq.3)

Eq.3 is the central result for the steady state surface temperature in our simplest possible radiation balance model.

Evaluating needed parameter {te}{ε}

Note that {te}, like {ε}, is virtually impossible to measure. It is usually only (incorrectly, see below) estimated using model assumptions (e.g., [1]: Fig.1). Note also, that for infrared-opaque atmospheres, as {te} approaches a value of zero the resulting temperature tends to an infinite value (things get very hot).

On the other hand, the average net outgoing shortwave intensity, {te}{Ie}, is accurately measured by satellite [1]. It is {te}{Ie} = 238.5 W/m2 [1]. Since the global average surface temperature is accepted to be accurately known [3], it is therefore possible to calculate the value of the product quantity {te}{ε} for Earth as:

{te}{ε} = {te}{Ie} / σ T^4 ... (eq.4)

by using T = 287.15 K, since the reported mean surface temperature is 14.0C [3].

This, to our knowledge, gives the first accurate evaluation of {te}{ε} for the current Earth as {te}{ε} = 0.62.

[Note that all such products of average physical parameters assume statistical independence of the parameters, or that the inter-parameter correlations do not affect the averaging – that is, we assume {te ε}={te}{ε} and so on.]

As a self-consistency verification, using the latter value of {te}{ε} in eq.3 indeed gives a mean surface temperature of 14.0C, as expected since satellite measurements confirm the near equality (1 – {a}){Is} = {te}{Ie} relating energy-in and energy-out [1].

Having determined the Earth value of {te}{ε}, one might be tempted to use the determined value in eq.3 and explore the impact of variations in {a}. This would be a grave error however because {ε} and {a} are highly anti-correlated parameters. For all Earth surface materials, a low value of albedo corresponds to a high value of ε and vice versa (Kirchoff’s Law).

Earth temperature with zero greenhouse effect, To

Next, we calculate the Earth’s mean surface temperature in the absence of all greenhouse effects, when {te} = 1. We take “To” to be the symbol for the latter zero-greenhouse-effect surface temperature. In order to use eq.3 for this purpose it is necessary to know the Earth value of {ε} itself.

Possibly because {ε} cannot be measured and is not known, virtually all researchers and authors have incorrectly used {ε} = 1. That is, they have assumed that the Earth’s surface is an ideal black body emitter.

Using the latter assumption for {ε} and with {te} = 1 eq.3 gives To = 254.8 K or minus (–) 18.3C. Compared to the accepted actual mean global surface temperature of 14.0C this would imply a total global greenhouse effect warming on Earth of 32.3C – corresponding to the repeatedly stated textbook value of 33C of greenhouse effect warming [4]. I also taught this value in my university physics courses and repeated it in my 2007 critique of global warming [5]. Wikipedia is no exception [6]. American Geophysical Union (AGU) press releases typically announce [7]:

“Overall, the greenhouse effect warms the planet by about 33 °C, turning it from a frigid ice-covered ball with a global average temperature of about -17 °C, to the climate we have today. Heat-absorbing components contribute directly to that warmth by intercepting and absorbing energy passing through the atmosphere as electromagnetic waves.”

In describing the “physical science basis” the Intergovernmental Panel on Climate Change (IPCC) in its 2007 “Contribution of Working Group I to the Fourth Assessment Report” (incorrectly, see below) put it this way [8]:

“The energy that is not refl ected back to space is absorbed by the Earth’s surface and atmosphere. This amount is approximately 240 Watts per square metre (W m–2). To balance the incoming energy, the Earth itself must radiate, on average, the same amount of energy back to space. The Earth does this by emitting outgoing longwave radiation. Everything on Earth emits longwave radiation continuously. That is the heat energy one feels radiating out from a fi re; the warmer an object, the more heat energy it radiates. To emit 240 W m–2, a surface would have to have a temperature of around –19°C. This is much colder than the conditions that actually exist at the Earth’s surface (the global mean surface temperature is about 14°C). Instead, the necessary –19°C is found at an altitude about 5 km above the surface.

The reason the Earth’s surface is this warm is the presence of greenhouse gases, which act as a partial blanket for the longwave radiation coming from the surface. This blanketing is known as the natural greenhouse effect.”

The scientists at also use this 33C number in their interpretations [9]:

“Since we are looking at the whole of the present-day greenhouse effect (around 33 C), it is not surprising that the radiative forcings are very large compared to those calculated for the changes in the forcing. The factor of ~2 greater importance for water vapour compared to CO2 is consistent with the first calculation.”

Virtually all mainstream science and teaching has accepted and parrots this idea that the planetary greenhouse effect on Earth causes a warming of approximately 33C. In addition, research scientists use it ({ε} = 1) in their peer-reviewed published calculations about Earth global processes [1].

But in fact, the evaluation of a 33 degree warming is in serious error. It is not physically reasonable to assume the true value of Earth’s average emissivity {ε} to be equal to 1. Indeed, it is physically impossible from usual known radiative processes for any opaque body to have a surface albedo (reflectivity) as high as 0.30 yet have an emissivity of 1. An ideal black body has a reflectivity of zero.

This is not an elusive point in radiation physics. Emissivity has been studied since before the development of quantum mechanics and there exists a first-empirically-established relation between reflectivity (albedo) and emissivity. It is known as Kirchoff’s Law of radiation physics. Basically, it says that the larger the reflectivity the smaller the emissivity, in approximate linear relation to each other.

As an equation, in this context, Kirchoff’s Law is:

1 – {a} = {ε}. ... (eq.5)

It is a violation of Kirchoff’s Law to admit {a} = 0.30 yet use {ε} = 1 in calculating the Earth’s surface temperature, irrespective of the assumed amount of greenhouse effect.

Thus, this fiction which has become an ingrained part of the planetary greenhouse effect scientific folklore is wrong.

Instead, correctly using eq.5 with eq.3 and {te} = 1 gives the much higher Earth surface temperature of To = 278.6 K or 5.5C for an earth subjected to a complete absence of any planetary greenhouse effects. This was previously emphasized by Hertzberg and Stott in 1994 [10].

Therefore, the total warming from the entire greenhouse effect on Earth is realistically approximately 8 to 9C, not 33C. And even without a greenhouse effect the Earth does not become a solid ball of ice. Kirchoff’s Law implies that at relatively constant solar intensity, “ice ages” can only be transient states induced by sudden and large-magnitude changes in planetary properties but they are not stable.

Further consequences of Kirchoff’s Law

Recognizing Kirchoff’s Law also means that the proportion of long-term habitable planets must be re-evaluated up, for those scientific hobbyist interested in such questions.

Back on Earth, Kirchoff’s Law (eq.5) allows one to simplify eq.3 as:

T = [ {Is} / {te}σ ]^(1/4) ... (eq.6)

where, as above, “^(1/4)” means “to the power ¼”. Here, it becomes clear that the dominant long-term steady state parameters determining mean surface temperature are the average solar intensity at Earth (or average solar constant) {Is} and the net mean longwave atmospheric transmittance {te}, largely irrespective of surface property changes (i.e., changes in {a} and {ε}).

In other words, if the reflectance (albedo) is high then the emissivity is low in just such a way as to produce the same global mean surface temperature that produces a global radiation balance. That is, less incoming shortwave solar radiation is absorbed and less outgoing longwave surface emission radiation is produced, for the same mean surface temperature.

Evaluating longwave atmospheric transmission, {te}

Given the pivotal role of eq.6 in determining the steady-state mean surface temperature, it becomes important to properly evaluate {te}. This has not been done correctly in the past, again largely due to a lack of appreciation of Kirchoff’s Law. I show below that {te} has been vastly underestimated. As a result, 1 – {te}, the so-called
“longwave radiative forcing” (arising from all greenhouse effects on the planet), has been vastly overestimated.

Arguably the best way to determine {te} using constraints from measured quantities is as follows. Use eq.2 with Kirchoff’s Law (eq.5), the measured average surface temperature (14.0C [3]) and solve for {te}:

{te} = {Is} / σ T^4 . ... (eq.7)

This gives {te} = 0.89.

Alternatively (and equivalently), {te} can be calculated from its definition of longwave energy out (escaping the planet) divided by longwave emission energy from the surface. The longwave energy out is measured by satellite to be 239 W/m2 [1] whereas the longwave emission energy from the surface is calculated from eq.1 with the average emissivity from Kirchoff’s Law (eq.5 and measured {a}) and the measured average surface temperature (14.0C [3]). Given observed [1] global radiation balance (in = out), the same result is obtained: {te} = 0.89.

These considerations, to our knowledge, give the first accurate evaluation of {te} for the current Earth: {te} = 0.89. This value is significantly larger than the accepted value in the scientific literature (e.g., [1][11]). The accepted value arises as follows [1][11]: One uses {ε} = 1 (as an arbitrary choice and in violation of Kirchoff’s Law) and the measured mean surface temperature (14.0C [3]) with eq.1 to obtain a surface emission intensity of {Ie} = 396 W/m2 [1]. By comparison with the satellite-measured outgoing longwave radiation intensity (239 W/m2 [1]) one has {te} = 239/396 = 0.60, a vastly underestimated value.

The latter incorrect value of {te} = 0.60 in turn implies a value of the so-called “longwave radiative forcing” (1 – {te}) of 1 – 0.60 = 0.40 (40%) instead of the correct value of 1 – 0.89 = 0.11 (11%).

This means that the accepted magnitude of the longwave radiative forcing for Earth from all greenhouse effects in the atmosphere is an overestimate by a factor of ~4 (360%).

Corroboration of our value of {te} = 0.89 (rather than 0.60) is contained in the satellite data itself. For example, consider Fig.1 of reference [11] (reproduced below). This figure is for “global cloudy conditions” and shows both the satellite-measured spectrum of longwave radiation escaping to outer space (red curve) and the incorrect assumed model surface emission spectrum (using 14C and {ε} = 1) (smooth blue curve). The integrated fractional surface area between the two spectral curves (red and blue) is indeed ~0.4 but this is wrong. One sees that the blue curve is artificially uniformly much higher than the correct smooth envelope curve that would match the red curve in the non-scattering parts of the spectrum. The correct envelope curve would result from using {ε} = 1 – 0.3 = 0.7 (for global average conditions, cloudy and clear sky) and the corresponding integrated fractional surface area between the red spectral curve and the correct envelope (surface emission) curve would be ~0.1.

The psychological bias from the long-standing “33 degree” error and its underlying assumptions appears to be so strong that even the obvious satellite-measured emission spectra are systematically misinterpreted rather than taken at face value: There is a well defined spectral envelope curve in the measurement (red curve) which is disregarded in favour of an incorrect model curve (blue curve) that violates Kirchoff’s Law.

Here it is important to note one of several likely reasons that scientists have fooled themselves to this extent. One can measure the longwave scattering transmittance (or cross section) of a greenhouse effect gas (e.g., CO2, H2O) in the laboratory. However, virtually all such measurements evaluate the loss of transmitted intensity in the incident beam direction, thereby quantifying the amount of longwave radiation (incident on the gas sample) that is not scattered away from the incident beam direction. The error in using this measured total scattering cross section when reasoning with the atmosphere is that much (most) of the scattered (and multiply scattered) radiation will actually escape to outer space and therefore must be counted as part of the atmosphere’s net transmittance {te}.

In other words, one cannot, as has too often been done, calculate atmospheric scattering transmittance from collimated-beam laboratory measurements of scattering cross sections without calculating the escape probabilities for the atmosphere of all the scattered and multiply scattered radiation.

Refining the model

Having corrected longstanding and pervasive errors in the radiation balance physics for Earth, we now have a robust model (eq.6) that can be used predicatively. Here {te} directly arises from all contributions from greenhouse effect gases, clouds, etc., and any solar input variations (whether due to solar activity or Earth’s orbit) are modeled by {Is}. In particular, this allows robust sensitivity analyses.

The model (eq.6) can also be further refined by replacing {Is} with [(1 – {a}) / {ε}]{Is} (to reproduce eq.3) in order to consider possible deviations from Kirchoff’s Law, where the ratio [(1 – {a}) / {ε}] (let us call it the “Kirchoff ratio”) would not be exactly equal to 1.

The model could also be refined to include correlations between surface and atmosphere properties in doing the global time (day, season) and planet surface averages, as mentioned above.

The latter two improvements (Kirchoff-deviation and correlations) are expected to produce only small changes in the predictions from the model.

Given the straightforward nature of the model (eq.6) following directly from the most fundamental considerations of radiation physics, those who argue [12][13][14][15] that the more complex circumstances of a real (and thermodynamically active) atmosphere and a real non-uniform and non-smooth surface are such that no net global greenhouse effect warming of the planet surface can result have the burden of the proof in that they must explain in simple physical terms how no warming (whether measurable or not [5][16]) would occur despite the prediction of eq.6.

Further predictions from the model

Next, let us examine some immediate predictions of the model. In order to facilitate these calculations and also to make them more transparent we express {te} as 1 minus its deviation from 1. We denote the magnitude of the deviation as δ and write:

{te} ≡ 1 – δ ... (eq.8)

Eq.8 defines δ and δ = 0.11 for the present Earth atmosphere.

Since δ is small compared to 1, eq.8 allows eq.6 to be written (approximately) as:

T = To [ 1 + (δ/4) ] ... (eq.9)

where To, as defined above, is the correct Earth’s mean surface temperature in the absence of all greenhouse effects, To = 278.6 K.

In this way, any assumed changes in {te}, due to changes in concentrations of greenhouse effect gases for example, can be modelled as changes in the parameter δ which has a linear impact on (mean global) surface temperature T.

For example, let us use eq.9 to calculate the warming due to the total post-industrial increase in CO2 atmospheric concentration. In fact, for practical reasons (related to the polynomial expansion approximation used in deriving eq.9 from eq.6), it is more accurate to calculate the cooling that would result from turning the present CO2 atmospheric concentration (390 ppmv) back to the pre-industrial value (280 ppmv).

The corresponding change Δδ in the value of δ is given by:

Δδ = δp Fco2 Cpre ... (eq.10)

where δp is the present value of δ arising from all present Earth greenhouse effects, Fco2 is the present fraction (from 0 to 1) of all greenhouse effects that arise from CO2, and Cpre is the fractional change in CO2 concentration in going from the present value to the pre-industrial value.

As shown above, δp = 0.11. Also Cpre = [(280 ppmv – 390 ppmv) / 390 ppmv], corresponding to a 28% decrease. Finally, we need Fco2. It can most reliably be obtained from satellite spectral measurements. This was done in [11] but using the incorrect assumed surface emissivity {ε} = 1. This error systematically overestimates the surface emission spectrum, thereby producing a systematically overestimated “longwave radiative forcing” “spectrum”. But since the overestimate is at all wavelengths, we can expect that the fractional contributions for the different greenhouse effect gases, reported by [11], will be approximately correct. Therefore, Fco2 ~ 0.26 (for clear sky conditions).

This gives a net present to pre-industrial change in Earth surface temperature from changing the CO2 alone while leaving all other parameters constant as:

ΔTind = To Δδ/4 = To (δp Fco2 Cpre)/4 = – 0.56 K ... (eq.11)

Therefore, the predicted pre-industrial to present warming from the increase in CO2 alone is approximately 0.56C.

Similarly, we calculate the effect of doubling the present atmospheric concentration of CO2 (without changing anything else) using Δδ = δp Fco2 Cx2 where Cx2 is the fractional change in doubling the CO2, Cx2 = [(780 ppmv – 390 ppmv) / 390 ppmv] = 1. This gives a predicted warming ΔTdbl = 2.0 K (or 2.0C).

And so on. It is immediate to calculate the warming effect of positive or negative so-called water vapour feedback simply by applying the assumed multiplicative factor to the modelled change in CO2 concentration.

We note that our simple and correct model for global radiation balance gives all the same predictions as the state of the art global circulation models (GCMs). This suggests that the complexities of surface-wise inhomogeneities, altitude-wise atmospheric inhomogeneities, and atmospheric circulation are not relevant to the global mean radiation balance and resulting mean temperatures, as the above simple physics suggests.

One therefore should question the role of these models which are ill-suited to answering questions of global radiation balance. More could be gained from improving satellite data and interpretation and from studying radiation balance parameters on regional scales.

Sensitivity analysis of the model

Finally, let us consider the simple-model-calculated sensitivities regarding mean global surface temperature for different model parameters applied to the present Earth.

Since the solar constant itself varies by 6.7% of its mean value over the course of the seasons, let 6.7% variations be our standard of variation. The results are as follows:

• 6.7% change in {Is} causes ΔT = 4.7 K
• 6.7% change in the Kirchoff ratio ((1 – {a})/{ε}) causes ΔT = 4.7 K
• 6.7% change in ALL total greenhouse effects causes ΔT = 0.51 K

The radiation balance steady state temperature of Earth’s surface is an order of magnitude more sensitive to changes in solar constant and Kirchoff ratio than to changes in all sources of planetary greenhouse effects taken together.

It stands to reason, therefore, if reason matters and if we are concerned about the global mean surface temperature, that more research funding should go into studying solar variations and regional/planetary albedo/emissivity relations than trying to deduce the relatively subtle effects of “longwave radiative forcing”. After all, large scale human land use changes can have dramatic effects on both surface radiative properties and colloidal atmospheric particle pollution concentrations and depositions.

Likewise, land use practices should be subject to much more scrutiny, if radiation warming is our concern, than CO2 fluxes into and out of the atmosphere.

I have extensively argued from both the social science and climate science perspectives that global warming should not be our concern regarding environmental destruction and social injustice [5].

Relevance to the dominant climate science narrative

Recently, I critically reviewed the dominant narrative of climate science on several of its central points [17]: That the post-industrial atmospheric CO2 concentration increase is directly a result of fossil fuel burning production of CO2, that the post-industrial increase in atmospheric CO2 concentration causes a greenhouse warming, that a measurable global mean surface warming has occurred in the post-industrial period, and that anthropogenic global warming radiative forcing drives “climate chaos” and produces extreme weather events.

The considerations of the present model are not inconsistent with the critical review of reference [17].

The global inter-carbon-pool flux dynamics of exchanges with the atmosphere and the factors affecting these inter-compartment fluxes remain the dominant determinants of the resulting atmospheric CO2 concentration value [17] (and references therein).

There remains a vehement debate among atmospheric physicists on the question of whether or not a planetary greenhouse effect can occur on a real planet having a greenhouse effect gas bearing atmosphere [12][13][14][15][17]. However, as mentioned above, the simplicity and robustness of the model developed in the present paper imply that scientists claiming a complete absence of a planetary greenhouse effect mechanism should have the onus to provide a simple physical explanation regarding the strict absence of a planetary greenhouse effect in models of the radiation balance with a realistic atmosphere.

The physical-measurement and mathematical-statistics difficulties in obtaining a mean global surface temperature and in estimating the uncertainty error in this mean global surface temperature remain [5][16][17].

The reality of a post-industrial increase in extreme weather events remains undemonstrated and highly contested by climatologists and the physical mechanism whereby “climate chaos” would result from extra-CO2 “greenhouse radiative forcing” is at the level of a tenuous theoretical fantasy [17].

I hope that the present paper will help to clarify concepts regarding Earth’s planetary radiation balance in relation to global mean surface temperature.


[1] “Earth’s global energy budget” by K.E. Trenberth, J.T. Fasullo, and J. Kiehl. Bulletin of the American Meteorological Society, March 2009, 311-323, and references therein.

[2] “Earthshine observations of the Earth’s reflectance” by P.R. Goode et al. Geophysical Research Letters, 2001, v.28, 1671-1674.

[3] “Surface air temperature and its changes over the past 150 years” by P.D. Jones et al. Reviews of Geophysics, 1999, v.37, 173-199.

[4] “Physics: Concepts and connections” by A. Hobson, Prentice Hall, 1999.

[5] “Global Warming: Truth or dare?” by D.G. Rancourt, Activist Teacher blog, February 2007.

[6] “Greenhouse effect”, Wikipedia article, accessed on April 26, 2011.

[7] “Taking measure of the greenhouse effect” AGU Release No. 10–33. October 14, 2010.

[8] Le Treut, H., R. Somerville, U. Cubasch, Y. Ding, C. Mauritzen, A. Mokssit, T. Peterson and M. Prather (plus 26 other contributing authors and two review editors), 2007: “Historical Overview of Climate Change.” In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

[9] “Water vapour: feedback or forcing?” by G.A. Schmidt,, 2004. (And other articles on the site.)

[10] M. Hertzberg and J.B. Stott. "Greenhouse warming of the atmosphere: Constraints on its magnitude". Twenty-Fifth International Symposium on Combustion; Work-in-Progress Poster. 1994.

[11] “Earth’s annual global mean energy budget” by J.T. Kiehl and K.E. Trenberth. Bulletin of the American Meteorological Society, February 1997, v.78, 197-208, and references therein.

[12] "Falsification Of the atmospheric CO2 greenhouse effects within the frame Of Physics" by Gerhard Gerlich and Ralf D. Tscheuschner; International Journal of Modern Physics B, Vol. 23, No. 3 (2009) pages 275-364.

[13] "Proof of the atmospheric greenhouse effect" by Arthur P. Smith; arXiv:0802.4324v1 []

[14] "Comments on the "Proof of the atmospheric greenhouse effect" by Arthur P. Smith" by Gerhard Kramm, Ralph Dlugi, and Michael Zelger; arXiv:0904.2767v3 []

[15] "Reply to 'Comment on 'Falsification Of the atmospheric CO2 greenhouse effects within the frame Of Physics' by Joshua B. Halpern, Chistopher M. Colose, Chris Ho-Stuart, Joel D. Shore, Arthur P. Smith, Jorg Zimmermann" by Gerhard Gerlich and Ralf D. Tscheuschner, International Journal of Modern Physics B, Vol. 24, No. 10 (2010) pages 1333–1359.

[16] Christopher Essex, Ross McKitrick, Bjarne Andresen. “Does a Global Temperature Exist?” Journal of Non-Equilibrium Thermodynamics, Feb 2007, Vol.32, No.1, pages 1-27.

[17] “On the gargantuan lie of climate change science” by Denis G. Rancourt, March 2011, Activist Teacher blog.

Denis G. Rancourt is a former tenured and full professor of physics at the University of Ottawa in Canada. He practiced several areas of science (including physics and environmental science) which were funded by a national agency and ran an internationally recognized laboratory. He has published over 100 articles in leading scientific journals and several social commentary essays. He developed popular activism courses and was an outspoken critic of the university administration and a defender of student and Palestinian rights. He was fired for his dissidence in 2009. His dismissal case court hearings are presently on-going and will extend into 2012.


Hans Schreuder said...

Rather than deal with the latter complexity of non-uniform irradiation, instead we take the entire planet’s surface to be uniformly irradiated with an intensity equal to the corresponding average solar constant. UNQUOTE

To my way of reasoning, that kind of logic will inevitably have to lead to the presence of some sort of greenhouse effect to mathematically justify the satellite-recorded emission levels.

If we do take the trouble to deal with two separate half-earths - one hemisphere in sunshine, one hemisphere in darkness - we can arrive at a mathematically correct model that has no need at all for an atmospheric greenhouse effect making or keeping our earth warmer than it should be. No warming whatsoever is needed off so-called greenhouse gases, with water vapour acting only as a cooling retardant on the dark hemisphere yet as a strong coolant on the sunny hemisphere.

If the reality of two half-earths is taken full account of, it will be found that earth is in fact cooler than it should be, which makes sense when one considers that our atmosphere acts like the air around an air-cooled engine.

There will soon be a new paper that illustrates the above scenario, with no need at all for so-called greenhouse gases making earth warmer than it would be without those gases.

Anonymous said...

Noting (with interest)Schreuder's comment, I still believe that you have cleanly banished the nonsense propagated by the Luddites present in the Global Warming political movement.... their emperor (Algore) has no clothes (nor brains for that matter)

Anonymous said...

Please take this over to

If you'd like to see why I make this suggestion, take a look at "Story-telling angst" there. I realize there are many comments to get through, but they are well worth it.

K, teacher

Anonymous said...

You said:
"It is a violation of Kirchoff’s Law to admit {a} = 0.30 yet use {ε} = 1 in calculating the Earth’s surface temperature, irrespective of the assumed amount of greenhouse effect."

Why is this a problem? The value of a = 0.3 is a weighted average over shortwave radiation (less than ~ 3.5 um). The value of 1 is a weighted average over longwave radiation (more than ~ 3.5 um).

There is no reason to expect these values to be closely related. in fact, it is easy to find white paint with a ~ 0.9 and e ~ 0.9. This is in NO way a violation of Kirchhoff's law.

John O'Sullivan said...

Superb analysis. There is clearly a great deal of common ground between you and the Slayers. These are exciting times for advancing real climate science.
Many thanks,

Denis Rancourt said...

Yes, Anonymous is correct.

My use of Kirchoff's Law is wrong. Kirchoff's Law is for a given wavelength.

Raymond Pierrehumbert also pointed this out.

One has shortwave albedo versus longwave emissivity.

The longwave emissivity of surface water and vegetation is actually close to 1.

I will write a Revised article.

Bob Armstrong said...

A.teach ,

I , too , like your transformation to the case of a uniformly irradiated ball .

It reduces the problem to the essential 0th law of thermodynamics that the temperature of a point which is neither a source or a sink equals the temperature of its surrounding sphere . It reduces the problem to one of spectra . By Ritchie's  elegant experiment and Kirchhoff's law , the reflectance spectrum of a substance is the complement of its absorption spectrum which is identical to its emission spectrum .  A  uniform gray , that is , flat spectrum , ball has the little appreciated property that it's temperature is that associated with the unweighted sum ( integral ) of the energy flows impinging upon it . In this case , because absorptivity/emissivity is the same constant with respect to any spectrum , it does not matter how dark or light a gray the ball is ( except for a singularity at total reflectance ) .  Thus the graybody temperature of a ball like our earth is the appropriate null hypothesis against which to measure any spectral effects .

This is the approximately 279k temperature calculated independently by you , Marty Hertzberg , and myself . That leaves about 8 to 10 degrees
to be explained by spectra .  See my for an implementation of this essential physics for non-isotropically irradiated non-uniform gray balls in a handful of lines of array programming language . A few additional lines would unfold the spectral dimension allowing computation of an equilibrium temperature for any spectral map of the globe .

As your title states , such a computation on a sphere enclosing a planet and its atmosphere tightly constrains temperature within that shell just like the distribution of electric charge on a Gaussian surface tightly constrains the charge within . In that vein , since Pierrehumbert  is apparently involved in this discussion , I would ask him how the surface of Venus can have a temperature about twice as high as can be explained by irradiance from the sun - without an internal heat source . I found the explanation in a recent online manuscript of his  just non-quantitative word waving .

For me to understand something is to be able to implement  and play with it in succinct executable array notation such as I present on my website .

Denis Rancourt said...

Bob A.,

You need to read the revised article...

Denis Rancourt said...



Glenn Tamblyn said...


Having read your revised paper, there are some glaring problems with it.

A general observation. You began your first version with a copy of the energy budget diagram published by Trenberth & Kiehl. But you don't seem to have incorporated the insights from that into your analysis. You are treating the atmosphere as if it is simply a passive absorber of energy rather than being an active component of the model. Several points:

You refer to Albedo as if it is a single value when it is in fact made up of 3 separate parts. Reflection of SW from the atmosphere, mainly due to scattering, Reflection of SW from clouds, and reflection of SW from the surface. So in your arguments and equations, particularly discussing Kirchoffs Law you need to be referring only to the surface component of Albedo which from the T&K diagram is 23/184 = .125. Similarly when doing your 6.7% comparisons you need to be clear about this.

You make no allowance for the incoming SW that is absorbed by the atmosphere.

Next you work with transmissivity as if the atmosphere just passively absorbs the remainder. Apply Conservation of Energy. Where does this absorbed energy go? The atmosphere isn’t being turned into incandescent plasma so it’s not accumulating. It must be going somewhere. Some goes out to Space, and a lot is radiated back down to the Earth. So your treatment of the surface energy balance has to account for this – the back radiation on TK’s diagram. In addition, from TK, Thermals and Evapo-transpiration also convey energy into the atmosphere. The only pathway out of the atmosphere for this is via radiation again, up and down. So too the SR absorbed by the atmosphere

Now look at the figures from Trenberth. Surface Radiation of 396. Only 10% makes it through to space. That is a transmittance of 10%. Of radiation emitted from the upper atmosphere, 15% makes it too space. So most of the figure you are using for transmittance isn’t transmittance. It re-radiation. And more than half of this re-radiation is down.

Next this statement is wrong and simplistic “since the saturation band width, by definition, negatively and proportionally affects the relevant CO2 longwave transmission through the atmosphere (nothing at saturation escapes the planet)”

If you look at the actual spectrum for the planet in these saturated frequencies, radiation does escape the planet, just less of it. Why? At low altitude those frequencies are saturated – they are ‘optically thick’ However, as your altitude increases the atmosphere is thinner and eventually the amount of CO2 available in the air column above is no longer sufficient to block the path to space. It is no longer optically thick, it is no longer saturated. Therefore radiation being generated at that altitude at these frequencies can now reach space. However the air temperature here is lower than at the surface. So the total amount of radiation reaching space is still governed by the SB Eqn, even for a Gas. So the amount is less than for the surface.

The outgoing spectrum for the planet is thus the superposition of the temperature spectrum applicable at a range of altitudes, depending on the altitude at which the atmosphere to space is optically thick. The surface for those frequencies where the GH Effect does not aplly, high in the Troposphere or even the lower Stratosphere for those frequencies where the GH gases are most effective. And how does energy reach these altitudes to make it to space when saturation still has such a dominant effect. By Convection. What you aren’t including is that radiation absorption by GH gases has the principle effect of heating the surrounding molecules in the air. At several billion collisions per second, a molecules interactions with other molecules around it is a profoundly more powerful means of moving energy than re-radiation in situ. – Re-radiation comes to dominate when the frequency is no longer optically thick.

Glenn Tamblyn said...

To your 6.7% comparisons. I don’t know where you got your figure for 6.7% variation for Solar Insolation. It certainly isn’t as a result of variations of actual energy output from the Sun which only varies by about 0.1-0.2% over an 11 year solar cycle. So I can only assume you are referring to variations caused by the fact that the Earths orbit is elliptical rather than circular. In which the main source of the variability is down to geometry and trigonometry and most relevant ‘research’ into this began with Euclid. Since the variation is a regular trigonometric cycle, its average over 1 year is 0. Certainly it has an effect on an intra-annual time scale but most people on Earth are familiar with that. It’s called Summer & Winter.
Since the dominant factor in your te term is actually the GH effect * readiation, looking at this separately from CO2 is rather strange. And a 6.7% increase in SURFACE Albedo is called an Ice Age.

Back to the drawing board.

ps Since you have corresponded with Ray PierreHumbert, you might find this article by him in Physics Today interesting. Check out Fig 3, it is a work of Art!

Denis Rancourt said...


Regarding the revised version, you are correct. It does not admit a thermally active atmosphere.

It is a simple model for a non-thermalizing atmosphere. The real Earth atmosphere is not non-thermalizing.

I define a non-thermalizing atmosphere as an atmosphere that can resonantly absorb both shortwave and longwave radiations but where these radiations are immediately re-emitted (at the same frequencies and in random directions) by de-excitation of the molecular state without heating the gas atmosphere.

Physically, such a situation can occur with a dilute atmosphere such that the mean inter-molecular collision time is much longer than the molecular excited state lifetime, or simply when all molecular excited state lifetimes are much smaller than the mean molecular collision time.

This does not hold for most of the mass of the atmosphere on Earth but it is nonetheless instructive to examine the consequences of this type of atmosphere.

I'm now doing the thermalizing atmosphere case.

Version 3...

My implementation of CO2 saturation effects will be directly transposable.

I also like Pierrehumbert's Physics Today review.

Denis Rancourt said...


If physicists can't do these kinds of simple calculations to figure out what is going on without deferring to code-writing GCM hacks who won't spell out exactly what they are doing for all to see, then we are in big trouble...

Glenn Tamblyn said...

Small points to note Denis.

Ray PierreHumbolt is a physicist.

Radiative Transfer calculations such as ModTran aren't GCM's

If you want to know what the GCM's are doing, why not read the published literature from the modelling groups as to how they do it.

And if that isn't good enough, download the source code and have a look for yourself.