Global Warming: Measuring Temperature vs Flux of Heat Energy vs Radiative Forcing

OLWR (right) as measured by CERES

The central concept in the prediction of global warming from human emissions of CO2 presented by IPCC, is that of radiative forcing as a warming effect of 3-4 W/m2 upon doubling of atmospheric CO2 from pre-industrial time with corresponding global warming of less than 1 C. From this non-alarming warming is obtained alarming warming by up to 4 C by various positive feed-backs. If the 1 C was instead 0.3 C corresponding radiative forcing of 1 W/m2 instead of 3-4 W/m2, there would be no reason for alarm. And of course not, if feed-backs are smaller (very likely) or even negative. 

Let us now check how IPCC comes up with a radiative forcing of 3-4 W/m2 as the central argument behind alarm.    

The radiative forcing of 3-4 W/m2 is obtained from a radiative perturbation computation starting from measured spectra of Outgoing LongWave Radiation OLWR or radiative flux from the Earth into space by bolometers in CERES satellites as shown above. The computation estimates the radiative forcing as the  change of OLWR from doubled CO2. See lecture by Will Happer.

The advantage of this approach is that knowledge of the complex physics of turbulent convective heat transfer and phase change behind the present measured OLWR is not needed. The radiative computation concerns the change of OLWR from a change of radiative properties of the atmosphere from doubled CO2 everything else being the same. The radiative forcing is thus obtained from a radiative heat transfer computation based on radiative properties.    

A bolometer measures temperature (in degrees Kelvin K) through a temperature dependent resistance which is translated to OLWR (in W/m2) through some form of Planck's Law. 

That primarily temperature is measured, is seen from the fact that CERES delivers the altitude from where OLWR is coming, because altitude directly connects to temperature, which would not be possible if OLWR was the prime measurement.

The translation from measured temperature in K to OLWR in W/m2 is tricky. To see the difficulty, let us consider heat conduction with heat flux corresponding to radiance and Planck's Law replaced by Fourier's Law taking the following form (in one space dimension): 

• $Q = C \frac{dT}{dx}$ 

where $T$ is temperature $Q$ heat flux, $x$ a spatial coordinate and $C$ is a coefficient of heat conductivity. Now, temperature can be directly measured by a thermometer corresponding to the bolometer in CERES, while to determine the heat flux Q the coefficient of heat conductivity must be known. Temperature is a primary measured quantity and heat flux is a secondary computed quantity requiring knowledge of a heat conduction coefficient and temperature derivative. 

To measure inside and outside temperature of a wall is direct and precise using a thermometer, while determining the heat flux through the wall requires (i) detailed data on the design of the wall or (ii) experiments with known heat source. 

Measurement of OLWR in CERES carries the same difficulty. What is directly measured by the satellite bolometer are temperatures of different spectral bands as seen from the bolometer, while the translation to OLWR requires detailed knowledge of atmospheric emittance corresponding to heat conductivity of a wall. Measured OLWR is thus subject to large uncertainties as well as the computation of radiative forcing. Experiments corresponding to (ii) cannot be made. 

Total OWLR is about 240 W/m2 and so a radiative forcing of 3-4 W/m2 is a small perturbation which is difficult to assess. It could as well be 2 or 0 or even negative. The central element of the IPCC global warming message to the World thus cannot be viewed to be scientifically settled. If the estimated radiative forcing was 1 W/m2  instead of 3-4 W/m2, then there would be no alarm.  

Radiative forcing of 3-4 W/m2 is by IPCC presented as the basic scientific argument behind the present march in the West into a fossil free society of pre-industrial standard and population.  The theory and observation supporting the argument is highly uncertain and cannot motivate continued march.   

Logarithmic Effect of More CO2 without Theoretical Basis

To serve as a basis for CO2 alarmism (together with back radiation), IPCC put together the following formula with inspiration from the Beer-Lambert law (exponential transport decrease in an absorbing medium):

• $\Delta RF = 5.35\ln (C/C_0)$ 

where $RF$ is Radiative Forcing from CO2 as a greenhouse gas, $\Delta RF$ is additional forcing caused by a change of concentration of atmospheric CO2 from $C_0$ (preindustrial) to a present $C$. Doubled concentration from preindustrial level would then cause an additional (warming) forcing of about $4$ Watts/m2, which is translated to 1C warming by Stefan-Boltzmann, which by feed back can become anything you like 1-5C with 5C utterly alarming! Note that without the 1C from the formula, feedback has nothing start from and so it is an absolutely crucial element of CO2 alarmism!

In CALCULATION OF ATMOSPHERIC RADIATIVE FORCING (WARMING EFFECT) OF CARBON DIOXIDE AT ANY CONCENTRATION by H. Douglas Lightfoot and Orval A. Mamer an effort is made to improve the formula from the starting point:

• Even though there is no theoretical basis for the Beer-Lambert formula, ∆RF = αln(C/Co), it has been accepted by the scientific community as a reasonable approximation.

but somewhat disappointingly ending up with:

• In this paper we propose an improved mathematical approximation that, like the Beer-Lambert law, has no theoretical basis.

Does a formula with no theoretical basis have a serious defect? Not always, since a formula may capture observations as some form of condensed experience. The validity of the formula can then be checked against observation/experience, and so be falsified. 

However, if there is no way to check the validity of the formula by observation, and this is the case with the above formula, then lack of theoretical basis is a serious defect because theory is what remains if you take away observation. 

So IPCC relies in its prediction of the warming effect of doubled CO2 on a formula which has neither theoretical basis nor observational support. You can say that this is shaky. How can you proclaim Net Zero with all its devastating consequences from nothing? It seems you must have some hidden agenda. You can learn about the agenda in new best seller The Truth about Energy, Global Warming, and Climate Change: Exposing Climate Lies in an Age of Disinformation by Jerome R. Corsi.

The Atmosphere Effect vs Climate Sensitivity

The global mean temperature on the Earth surface is about 15 C or 288 K. What would the temperature be if there was no atmosphere on Earth, that is what is the atmosphere effect? Klimatrealistene suggests 90 K after a comparison with an observed mean temperature of the Moon claimed to be 198 K. IPCC suggests 55 K.

But one can also argue that it is about 15 K  based on the attenuation effect of the radiation from the Sun surface at 5778 K spread over the Earth surface in a direct application of Stefan-Boltzmann's radiation law for a black/grey body, see earlier post, which gives Earth a temperature of about 273 K.

For Mars with a very thin atmosphere the same computation gives about 230 K in accordance with observation.

So we have a wide range for the atmosphere effect, from 15 K to 90 K, and one may say that the bigger the atmosphere effect is, the bigger can the effect be from changing properties of the atmosphere such as the amount of so called "green house gases". So which value for the estimated atmosphere effect is more relevant? 15 K or 90 K? Or the IPCC value in between?

The 90 K posted by Klimatrealsitene comes from an estimate of the mean temperature of the Moon (198 K) at the same distance to the Sun as Earth and without atmosphere, seemingly the perfect factual evidence. But the Moon-day is about 28 Earth days and so the temperature from day to night on the Moon varies from 100 K to 400 K (with then a mean of 250 K and not 198 K) and so a mean value may not be very meaningful.

With the evidence from Mars the value 15 K would seem to be a better estimate of the atmosphere effect, suggesting a climate sensitivity 0.15 C as the warming upon doubling of CO2 representing a 1% change of atmosphere properties, compare upcoming talk.

Talk at Climate Sense 2018

I have put up a preliminary version of my talk at Climate Sense 2018 for inspection.

Lukewarmers and Cooling

The climate debate can be divided as follows depending on estimated global warming upon doubled atmospheric CO2:

1. Warmers (IPCC): 1.5 - 4.5 C.
2. Lukewarmers (Lindzen, Spencer): 0.5 - 1 C.
3. Skeptics: 0 C. 

The observed "hiatus" of warming (slight cooling since 1998) presents a problem to both Warmers and Lukewarmers, since the absence of an expected steady warming under observed steadily increasing CO2, has to be explained as a cancellation effect from unknown natural variations.

The gap between Warmers and Lukewarmers is 0.5 C, which is within measurement error. 

A Skeptic has an easier job and does not have to explain anything different from expectation to rationalize the observations, and in this sense seems to be better off according to Ockham's razor.   

IPCC Follows Warming into the Deep Ocean

Swedish Minister of Climate Lena Ek assisting IPCC Co-chairman Thomas Stocker when presenting the Deep Ocean explanation of the non-existence of global warming.

Here is a summary the 2 hour IPCC webcast press conference presenting the Approved Summary for Policymakers concluding the yet unpublished IPCC 5th Asssessment Report Climate Change 2013: The Physical Science Basis:

The key role is played by Thomas Stocker, Co-Chair of IPCC Working Group 1, who reports that he has only slept 6 hours the last 4 days, which is less than 2 hours per night, and thus is very tired.

What has kept him awake is to come up with a convincing explanation why climate models predicting steady warming, while observations show no warming at all over the last 17 years, still can be used for reliable predictions over periods longer than 17 years.

No wonder that Stocker is tired, because his task has not been easy and lack of sleep is not the best precondition for good scientific work. Accordingly his explanation that the warming, which should have been observed on the Earth surface but was not observed, has been transferrred into the Deep Ocean where it cannot be observed, because it is so deep, was not convincing to media allowed to pose questions at the press conference. Nor the alternative of putting the blame on volcanic eruptions. In the Summary this was phrased as follows:

• The observed reduction in surface warming trend over the period 1998–2012 as compared to the period 1951–2012, is due in roughly equal measure to a reduced trend in radiative forcing and a cooling contribution from internal variability, which includes a possible redistribution of heat within the ocean (medium confidence). 
• The reduced trend in radiative forcing is primarily due to volcanic eruptions...

But Stocker did not mention during the press conference the third alternative presented in the Summary:

• There may also be a contribution from forcing inadequacies and, in some models, an overestimate of the response to increasing greenhouse gas forcing.

This was the reason he could not sleep, and why IPCC now will sink into the Deep Ocean.

PS The consensus message from IPCC to world policymakers is that any connection between the Deep Ocean of IPCC and the Deep Throat of Watergate, very likely (96%) is unprecedented, unequivocal and therefore very alarming.

The Funeral of IPCC: Too Strong Response to Greenhouse-Gas Forcing

The leaked IPCC AR5 Summary for Policymakers tells the world and its leaders that climate models tuned to the observed warming 1970 - 1998, do not fit with the observed lack of warming 1998 - 2013: 

• There is very high confidence that models reproduce the more rapid warming in the second half of the 20th century.
• Models do not generally reproduce the observed reduction in surface warming trend over the last 10–15 years. 
• There is medium confidence that this difference between models and observations is to a substantial degree caused by unpredictable climate variability, with possible contributions from inadequacies in the solar, volcanic, and aerosol forcings used by the models and, in some models, from too strong a response to increasing greenhouse-gas forcing. 

IPCC thus admits that climate models are constructed to have

• too strong a response to increasing greenhouse-gas forcing,

and are unable to capture

• unpredictable climate variability. 

This must be the end of IPCC since IPCC was formed on the sole doctrine of strong a response of green-house gas (CO2) forcing in climate model predictions. 

Since IPCC was born in Stockholm from the mind of the Swedish meteorologist Bert Bolin, it is fully logical that the funeral of IPCC now takes place in Stockholm along with the Bert Bolin Center for Climate Research.

PS Concerning climate predictions recall the prediction I made in 2009. 

Negative Climate Sensitivity: Global Cooling 2

Here is a remark connecting to the previous posts Negative Climate Sensitivity: Global Cooling 1 and  Leaked Climate Sensitivity of 0.3 C.

Climate sensitivity as the effect on the Earth surface temperature of doubled atmospheric CO2,  is by IPCC estimated to an alarming + 3 C. The idea is that CO2 by acting like a "greenhouse gas" blocks radiation from the Earth and thus causes warming. This is a very primitive idea and as such it may well be wrong.

Let us see what basic thermodynamics says:

1. The Earth surface is heated by incoming energy from the Sun, and the Earth-atmosphere system radiates an equal amount of energy from an outer boundary or top of the atmosphere TOA at the tropopause at a pressure of 0.2 - 0.3 bar.
2. The surface temperature is determined by the lapse rate from the temperature at TOA.  
3. In an atmosphere without thermodynamics of advection (still air) energy would be transported from the Earth surface to TOA by a combined process of conduction and radiation, which would require a linear temperature profile with constant lapse rate equal to the dry adiabatic lapse rate of 10 C/km as the maximal rate of a stable atmosphere without advective overturning (thus establishing the Loschmidt gravito-thermal effect).
4. The observed lapse rate in the real atmosphere with thermodynamics of advection is 6.5 C/km.
5. Increasing thermodynamics would thus tend to decrease the lapse rate and with a temperature of TOA unchanged, would thus cause global cooling.
6. The logic is that more vigorous thermodynamics would transport energy more efficiently from the Earth surface and thus cause cooling.

Doubled CO2 could increase the temperature of TOA, by decreasing the direct radiation to outer space from the Earth surface, but would also demand a more vigorous thermodynamics reducing the lapse rate.

The rationale is that conduction/radiation passively operates on a temperature gradient/lapse rate maintained by exterior forcing, while thermodynamics/advection actively works to decrease the gradient/lapse rate. To see the active part dominate the passive would not be surprising.

Climate sensitivity would thus come out by subtracting effects of radiation and thermodynamics, and not as suggested by IPCC by adding these effects. This may explain why the  +3 C by IPCC is not what is observed, and that what is observed is close to 0 or even negative.   

Global Warming Denial vs Hysteria Industry Database

I am listed on the Desmogblog Extensive Database of Individuals Involved in the Global Warming Denial Industry including many serious climate scientists. A corresponding list of Individuals Involved in the Global Warming Hysteria Industry would be much shorter.

Negative Climate Sensitivity: Global Cooling 1

The preceding posts lead to the conclusion that the Earth (and Venus) including atmosphere up to a pressure of 0.2 - 0.3 bar have a TOA temperature at the tropopause equal to the bolometric temperature determined by the distance to the Sun, as a minimal temperature.

The surface temperature would then be determined by a lapse rate observed to be 6.5 C/km resulting from atmospheric thermodynamics driven by radiative forcing of the Earth surface,  to be compared with the dry adiabatic lapse rate of g/c_p = 9.8 C/km with g gravitational acceleration and c_p the heat capacity of air at constant pressure.

The thermodynamics in the atmosphere would thus have the effect of reducing the dry adiabatic lapse representing a possible state without radiative forcing and thermodynamics, and thus an effect of reducing the surface temperature.

Doubling the atmospheric CO2 is by IPCC estimated to correspond to a radiative forcing of 2- 4 W/m2, to be added to the 180 - 40 = 140 W/m2 effectively absorbed by the Earth surface with 180 incoming and 40 directly outgoing through the atmospheric window.  The effect on the surface temperature would then be determined by the lapse rate with the bolometric temperature of TOA at the tropopause  unchanged because the distance to the Sun is unchanged.

The effect of additional effective radiative forcing of the Earth surface would be more active thermodynamics which would tend to further reduce the lapse rate and thus the Earth surface temperature.

Climate sensitivity as the increase of the Earth surface temperature upon doubling of CO2, would thus be negative: More CO2 would tend to be cooling rather than warming, but the effect would probably be so small that it could not be observed. Climate sensitivity would thus seem to be non-positive and the risk of global warming would (very likely) be small (with a most likely value of 0).

(This insight is now quickly eating its way into the minds of both people and politicians and global warming hysteria is already history).

Compare with the climate sensitivity of + 3 C by IPCC, which is obtained by a combination (i) radiative forcing increasing the bolometric temperature, as if the Earth was moved closer to the Sun and (ii) positive thermodynamics feedback, as if thermodynamics could slow down by additional forcing.

The IPCC view is presented by its Swedish representative Lennart Bengtsson with the following key argument:

• .... the Earth energy balance can temporarily be changed by reduced radiation to outer space by increased concentration of greenhouse gases. 

We see here the idea of heating (less outgoing radiation) with necessarily a warming effect by greenhouse gases, which is the key of global warming propaganda. But LB eliminates the warming effect by stating that it is only temporary, and thus seems to say that the effect in the end is zero.

PS Notice that in the IPCC and LB greenhouse gas argument, the TOA would be put at 5 km at a bolometric temperature of - 18 C corresponding to 240 W/m2 outgoing radiation, and would then be shifted upwards to cooler levels under increased concentration of greenhouse gases and then eventually cause surface warming.  But there is no TOA other than the tropopause (as concerns thermodynamics), and shifting an artificial TOA up or down would lack physical meaning.

Most Likely IPCC AR5 Very Likely Uncertain

The leaked IPCC AR5 states: 

• Despite considerable advances in climate models and in understanding and quantifying climate feedbacks, the assessed literature still supports the conclusion from AR4 that climate sensitivity is likely in the range 2–4.5°C, and very likely above 1.5°C. The most likely value remains near 3°C. 
• A few studies argued for low values of climate sensitivity, but almost all of them have received criticism in the literature.
• Equilibrium climate sensitivity, transient climate response and climate feedbacks are useful concepts to characterize the response of a model to an external forcing perturbation. However, there are limitations to the concept of radiative forcing. 
• Projections of climate change are uncertain, firstly because they are primarily dependent on scenarios of future anthropogenic and natural forcings, secondly because of incomplete understanding and inadequate models of the climate system and finally because of the existence of natural climate variability. 
• The term climate projection tacitly implies these uncertainties and dependencies. 
• Nevertheless, as greenhouse gas concentrations continue to rise, we expect to see future changes to the climate system that are greater than those already observed and attributed to human activities. 
• It is possible to understand future climate change using models and to use models to quantify likely outcomes and uncertainties dependent on assumptions about future forcing scenarios. 

We read contradictory statements expressing that the most likely value of climate sensitivity is 3 C, while projections of climate change are uncertain. In short, IPCC AR5 tells the world: 

• It is uncertain that climate sensitivity very likely is above 1.5 C and most likely is 3C.

One may ask if it is in fact very uncertain or most uncertain that the value is very likely above 1.5 C or most likely is  3 C? 

In any case, it seems to be very likely that the terminology developed by IPCC most likely does not represent considerable advances in climate models and in understanding. 

Recall that the IPCC climate sensitivity of 3 C is obtained from a starting guess of radiative sensitivity of 1 C from a guess of radiative forcing of 4 W/m2, combined with a freely invented thermodynamic feedback factor of 3, giving 3 C as an inventive guess work.

Leaked Climate Sensitivity of 0.3 C

The leaked Second Order Draft IPCC AR5 essentially repeats the AR4 estimate of a climate sensitivity of 3 C:

• Equilibrium climate sensitivity is likely in the range 2°C–4.5°C, and very likely above 1.5°C. The most likely value is near 3°C. Equilibrium climate sensitivity greater than about 6°C–7°C is very unlikely. 

Let me here  leak the following update of my previous 10 times smaller estimate of climate sensitivity coming down to 0.3 C, based on the following argument using the standard numbers of 

• Earth surface temperature: + 15 C
• top of the atmosphere TOA temperature: - 18 C at 5 km altitude
• lapse rate: 6.5 C/km 
• dry adiabatic lapse rate: 10 C/km
• transported from surface to TOA by thermodynamics: 120 W/m2 
• transported from surface to TOA by radiation: 60 W/m2.

Assuming that thermodynamics reduces the lapse rate from 10 to 6.5 C/km, thermodynamics would thus have the effect of decreasing the temperature increase from TOA to Earth surface by 5 x 3.5 = 18 C, thus with a relative decrease of 18/120 = 0.15 Cm^2/W. 

The corresponding number for radiation would be an increase of 33/60 = 0.5 Cm^2/W. 

The combined effect would thus be with a partition of 2/3 thermodynamics and 1/3 radiation:

• 1/3 x 0.5 - 2/3 x 0.15  = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15 Cm^2/W.

An assumed radiative forcing of 4 W/m2 would thus lead to a warming of  4/15 C, which is less than 0.3 C, thus a factor 10 smaller than IPCC's most likely value of 3 C. 

An alarm of 3 C would thus be replaced by a harmless 0.3 C, which could never be noticed.  

Do you say that the above argument is simplistic? Yes, it is, but it may well be more realistic than the IPCC argument  leading to a climate sensitivity probably inflated by a factor 10.

In business a value inflated by a factor 10, would be viewed as fraudulent.    

Why Do Skeptics Accept the Basic Dogma of Alarmism?

Leading skeptics including Lindzen, Singer, Spencer and Lord M, all adhere to the Basic Dogma of "radiative forcing" of 4 W/m2 from doubled CO2 which by Stefan-Boltzmann in the form dQ = 4 dT gives a global warming of 1 C.

Skeptics thus jump on the same band wagon as alarmists giving CO2 the alarming capacity of driving global climate. A doubled dose of a trace gas is thus attributed the amazing power of "forcing" global temperature to change by 1 C, and if 1 C why not 3 C?

Why are skeptics giving alarmists the advantage to set the agenda from the beginning with CO2 as the chosen evil to beat?

If we accept from the beginning a dogma that certain people are evil, what does it help then to argue that they are not so evil after all?

When I ask Lindzen, Singer and Spencer, why they are promoting alarmism in this way, by uncritically accepting the basic dogma of alarmism, I get silence or ridicule as response.

If leading skeptics used science to question the basic dogma of alarmism, then the debate would soon be over. Now it can continue for ever. Is this really the objective?

Radiative Forcing from Doubled CO2?

Water vapor and CO2 are referred to as "greenhouse gases" GHG because of their effect on the Outgoing Longwave Radiation OLR documented in the above energy spectrum for clear sky over Gulf of Mexico. The effect of CO2 is represented by the dip in the spectrum centered around a wave length of 15 microns. The "radiative forcing" from doubled CO2 of 4 W/m2 underlying the no-feedback sensitivity of IPCC of 1 C, is related to estimated changes of the dip area, with a larger dip area change connecting to larger sensitivity.

On the whole water vapor has a much bigger effect than CO2, and so may easily swamp the effect of CO2. Here is an argument showing that the estimated "radiative forcing" of 4 W/m2 from doubled CO2 may easily be too large.

Consider a a model of global climate with an equatorial region with wet air and a polar region with dry air of roughly the same area, assuming for the discussion that all OLR comes from the polar region.

Radiating 320 W/m2 from the polar region (= 2 x 160 W/m2 insolation) may require an effective temperature of about 0 C, which may be the mean surface temperature in the polar region. This means that the CO2 dip in spectrum will be counted from the lower level (0 C) than in the above figure (about 20 C), and thus have a smaller area.

In this model the effect of CO2 is totally swamped by water vapor in equatorial regions, and in polar regions the dip effect is reduced because the effective radiation temperature is lower.

This is yet another argument indicating that a no-feedback sensitivity of 1 C from "radiative forcing" of 4 W/m2, which is the basic postulate adopted by both alarmists and skeptics like Lindzen, Spencer and Monckton, may have little connection to reality.

It could very well be that the "radiative forcing" from doubled CO2 is rather 1 W/m2 than 4 W/m2, so small that it can never be identified.

Can The "Greenhouse Effect" Be Detected?

The recent exhange with Roy Spencer and Fred Singer concerning the "greenhouse effect" and "backradiation" identifies three groups in the climate debate with the following standpoints:

1. Alarmists: There is a greenhouse effect and it threatens to overheat the globe.
2. Skeptics: There is a greenhouse effect, but it is so small that it cannot be detected.
3. Deniers: As long as no greenhouse effect has been identified, one can act as if there is no greenhouse effect.

Roy and Fred belong to 2. and myself to 3. The discussion gets complicated by the fact that "the greenhouse effect" is not clearly described in the literature, but it is somehow connected to the radiative properties of the atmosphere:

Both alarmists and skeptics assume as a starting point that doubled CO2 will cause global warming by 1 C, which is referred to as no-feedback climate sensitivity. Alarmists then inflate it to 3 C with positive feedback and skeptics to about 0.5 C with negative feedback.

Both alarmists and skeptics thus firmly believe that science says that increasing the absorptivity of the atmosphere a little by doubling CO2, will cause warming.

Deniers are not so sure about that referring to the following argument:

• Earth surface temperature is determined by the lapse rate.
• Lapse rate is determined by thermodynamics with radiative forcing.
• Fully transparent atmosphere may be isothermal with zero lapse rate.
• Fully opaque atmosphere may be isothermal with zero lapse rate.
• Reality is somewhere in between with a certain lapse rate.
• It is not clear if more CO2 will increase or decrease the lapse rate.
• It is thus not clear if more CO2 will cause warming or cooling.
• There is no convincing evidence that any effect of doubled CO2 can be detected.

The dividing line goes between alarmists on one hand and skeptics/deniers on the other hand.

The quarrel between skeptics and deniers, about the existence of an effect which cannot be detected, seems to be of minor scientific importance compared to the main question of significant global warming or not.

The Empty Postulate of CO2 Alarmism

CO2 climate alarmism is based on two basic postulates concerning the effect of doubled concentration of atmospheric CO2 (compared to pre-industrial time):

1. Radiative forcing of 4 W/m2
2. Global heating of 1 C from radiative forcing of 4 W/m2.

Let us see how are these postulates motivated: 1. is supposed to follow from measurements of spectra like the above from "Atmospheric Radiation", Goody (1989) observed for clear skies over the Gulf of Mexico, April 23, 1969. After Conrath et al (1970).

The idea is that the dip in the spectrum between 14 - 16 microns reflects the absorption and emission of atmospheric CO2, and that doubled CO2 will cause a certain widening of the dip which is translated to so called "radiative forcing" of 4 W/m2 according to Planck-Stefan-Boltzmann's radiation law (SB).

The so obtained radiative forcing of 4 W/m2 is then translated to 1 C of global heating by another application of SB which is the rationale of 2.

We see that both 1. and 2. originate from a spectrum which its translated first to radiative forcing and then to global heating with both steps relying on SB.

Is this a correct scientific mathematical argument? Is it so clear how to go from measured spectrum to estimated spectrum for doubled CO2 to radiative forcing to global warming?

No it is not at all clear, because SB describes radiation from a body into a surrounding of 0 K.

The Earth plus atmosphere radiates into a surrounding of about 3 K, and so SB may be applicable to the whole system, but SB does not in the same way describe the exchange of heat energy between the Earth surface and the atmosphere and this is where the radiative forcing is supposed to change global climate.

The net result is that the climate sensitivity of 1 C global warming from doubled CO2, cannot be viewed to describe any scientific reality, but is instead used simply as a definition or agreement. This is evidenced by the fact that all scientists are supposed to agree on the 1 C, from skeptics to alarmists. An they all do agree on the 1 C.

If you say that you the 1 C is not valid, you will meet the response that this it is not possible to say so, because all scientists agree on the 1 C and you cannot question a scientific agreement which is a definition. Or if you do, then you are silly.

To question that there are 100 centimeters on a meter will meet the same laughs as questioning the 1 C from doubled CO2.

But a definition has no scientific content and says nothing about reality. In particular it cannot be taken as point of departure for feedbacks, which is nevertheless done by both alarmists and skeptics.

Alarmists start with 1 C and jack it up to 3 C by positive feedback.

Skeptics start with 1 C and take it down to 0.5 C by negative feedback.

But a real skeptic would not start with 1 C, because it is not science. A real skeptic would seek to directly assess climate sensitivity, by measurements. Doing so indicates a climate sensitivity smaller than 0.5 C, thus so small that it cannot be identified.

The net result is that the basic postulate of climate alarmism of a climate sensitivity of 1 C is a definition empty of scientific content and as such of no value. Both skeptics and alarmists should be able to agree on this.

Also Judy Curry has now understood the emptiness of IPCC:

• The IPCC might have outlived its usefulness. Let’s see what the next assessment report comes up with. But we are getting diminishing returns from these assessments, and they take up an enormous amount of scientists’ time.

Mathematics of Financial Crisis, and Climate Crisis

In Climate Crisis vs Financial Crisis I identified a common root of a (i) global financial crisis and (ii) global climate crisis as an instability from a two-way flow of (i) money between banks and loan takers and (ii) heat energy between atmosphere and Earth.

In the case (i) this is illustrated by an entrepreneur with an idea (e.g. solar panels) but no money (=0) who gets a loan X when signing a debt contract of X, according to the equation

• 0 = X - X

with the loan X exactly balanced by a corresponding debt X. This gives the entrepreneur the possibility to start a company for production of solar panels. If the interest rate is close to zero (as in Japan and the US) and there are no restrictions on the size of the loan, then the entrepreneur will be able to realize the idea on any scale.

But some ideas are not so good and the company will go bankrupt (e.g. Solyndra) leaving the contradictory equation 0 = - X , which will ask for new even bigger loans, et cet. This is how the financial crisis is now escalating with central banks feeding fresh X into the market without limit on X, and - X going to minus infinity, like in Greece right now.

In the case (ii) of climate crisis X is about 350 W/m2 according to the Kiel-Trenberth energy budget, about the same as the total insolation from the Sun.

The equation 0 = X - X has a special property, which underlies the instability, namely that X is arbitrary. If there is no interest are no restrictions the loan X can be take any size, and if X is large then instability results: If X is large then a loss of even a small portion of X may be large and a financial crisis will result.

The Kiehl-Trenberth energy budget has the same property: X = 350 W/m2 is supposedly being motivated by a Stefan-Boltzmann law, but the motivation is weak being based on a False-SB:

The exchange X in the Kiehl-Trenberth is fictitious and could be anything, and if it is chosen to be large (= total insolation), then climate crisis results: With X = 350 W/m2 an alarming climate sensitivity of 3 C is claimed by CO2 alarmists.

Conclusion: The financial crisis is real because the equation 0 = X - X with large X is real and unstable, while the climate crisis is fictitious because the equation 0 = X - X in climate science with X large is unreal, in fact only valid for X = 0 and then not unstable.

If you are unsure of the meaning of the equation 0 = X - X, assume that you have no money (=0)

and then as compensation you go to the bank and borrow X = $1 billion. Would you then say that you suddenly have become a billionaire?

Stability of True-SB vs False-SB

The different stability properties of the two versions discussed in recent posts of Stefan-Boltzmann's radiation law, True-SB and False-SB, can be exhibited by comparing the stability of the following simplified SBs:

1. $R = T_1 - T_2$
2. $R = T_3$ where $T_3 = T_1 - T_2$,

where $R$ is the heat flow between two bodies of temperature $T_1$ and $T_2$, expressed in two different forms: 1. as the difference of two-way gross flows and 2. as one-way net flow.

Stability concerns the effect on the output $R$ from perturbations of input ($T_1$, $T_2$ and $T_3$). Denoting the perturbation of $T_i$ by $dT_i$ for $i=1,2,3$, it is natural to assume a bound $E$ on relative perturbation of the form

• $\frac{\vert dT_i\vert}{T_i}\le E$ for $i=1,2,3$.

Estimating the effect $dR$ on the output $R$ from the $dT_i$, we have

$\vert dR\vert \le \vert dT_1\vert +\vert dT_2\vert = \frac{\vert dT_1\vert}{T_1} T_1 + \frac{\vert dT_2\vert}{T_2} T_2 \le ET_1 + ET_2=E(T_1+T_2)$,

which is to be compared with

$\vert dR\vert \le \frac{\vert dT_3\vert}{T_3}T_3 \le E T_3$.

If $T_3$ is much smaller than $T_1+ T_2$, then the second bound is much smaller which expresses that 2. is more stable than 1. or that 1. is more unstable than 2.

A particular case is given by $T_1=T_2$ with $T_3 =0$. This is the case of two blackbodies of equal temperature which according to 2. is very stable, but according to 1. much less stable.

The different stability gets expressed in different assessments of climate sensitivity, from 1. unstable with alarm to 2. stable without alarm.

Climate Alarmism Based on False Stefan-Boltzmann Law

The recent posts on Downwelling Longwave Radiation DLR give strong evidence, kindly supplied by Prof Grant W Petty, that climate alarmism of global warming is based on a false version of Stefan-Boltzmann's radiation law (SB), a version which lacks support in physics literature.

The original true-SB reads:

• R = sigma (T^4 - T_b^4)

where R is the radiance from a blackbody at temperature T into a background at temperature T_b < T and sigma is Stefan-Boltzmann's (positive) constant.

The false-SB reads:

• R =R_out - R_in,
• where R_out = sigma T^4 and R_in = sigma T_b^4.

Prof Petty claims that false-SB is obtained by formally applying true-SB with T_b = 0 and with T = 0, and then adding up the results. This is the same as formally rewriting true-SB in the form

• R = sigma T^4 - sigma T_b^4,

using formally the distributive law of algebra:

• sigma (T^4 - T_b^4) = sigma T^4 - sigma T_b^4.

According to Prof Petty, the false-SB is obtained by applying true-SB twice, or by using the distributive law. Prof Petty then expresses a consensus of (alarmist) climate scientists.

What Prof Petty is doing seems like a trivial operation, under the assumption that the trivial operation is permissible from physics point of view, or that it is permissible to use the distributive law from physics point of view. Prof Petty shows that he is firmly convinced that the trivial operation is permissible, because it is so trivial.

But triviality is not a sufficient condition for truth. The truth is that the operation, as trivial it may be, is not permissible:

It is not permissible to formally apply true-SB twice with T_b = 0 and with T = 0, because the assumption of true-SB is that T > T_b and this assumption is violated in the case T = 0.

It is not permissible to attribute to the distributive a physical meaning, unless this meaning is specified, and it is not.

The conclusion is that climate alarmists regularly, apparently without thinking, are using a false-SB.

Even worse, climate alarmists use the false-SB as the scientific evidence that the trace gas CO2 can cause dangerous global warming. The false-SB serves alarmism by offering the instability

required to make it credible that a small cause (trace gas) can have a big effect (dangerous global warming). It is like writing

• R = 10 = 100 - 90 = R_out - R_in

and then talking about perturbations, of say 1%. A 1% perturbation of net flow R (= 0.1) can then be turned into 1% perturbation of gross flow R_out (= 1), with an inflation factor of 10.

This is precisely the argument used to produce the climate sensitivity of 3 C upon doubling of CO2 of IPCC alarmism , which is 10 times too big. It is illustrated in the Kiel-Trenberth energy budget with its backradiation/DLR and

• R_out = 339/392 and R_in = 321 = DLR with R_out - R_in much smaller than R_out.

In short, climate alarmism is based on a false SB law, which allows a false 10-fold inflation of effects of doubled CO2.

For a more detailed presentation, take a look at my recent talk:

• CO2 Alarmism Debunked by Mathematics

and the upcoming book Mathematical Physics of Blackbody Radiation based on the article

Computational Blackbody Radiation in the book Slaying the Sky Dragon.

The use of false-SB is illustrated e.g. in

• Idealized Greenhouse Model
• The Global Energy Balance
• The Greenhouse Effect

and many other sources presenting the so-called greenhouse effect.

Of course, it is natural to pose the following questions:

• Is it really possible that a false-SB is used by so many climate scientists?
• What are physicists saying? After all, physicists are responsible for SB.
• If many scientists agree, then they must be correct?

I will report if some answers come in...

Climate Sensitivity from Basic Data < 0.4 C

Variation of monthly mean value temperature in Stockholm over the year.

The basic model of global climate, used by e.g. Spencer and Lindzen to determine climate sensitivity, takes the form

• C dT/dt = F(t) - lambda T(t),

where T(t) is some zonal temperature over some period of time t, F(t) is forcing, C is a constant heat capacity and lambda is a positive constant. Here climate sensitivity S = 1/lambda measures the change of temperature per unit change of forcing. The model underlies the recent Spencer-Braswell paper causing an uproar among climate alarmists.

The model can be used to determine S by fitting the model to measurements of T(t) and F(t) over time. If S is small then climate is not sensitive to changes in forcing e.g. from increased CO2.

To understand the dependence of S on characteristics of data (amplitudes and phase lag), assume F(t) = cos(t) with corresponding solution

• T(t) = A (lambda cos (t) + C sin(t)), where A = 1/(C^2 + lambda^2).

We see that the phase lag is determined by the quotient lambda/C:

• small lambda/C: phase lag 1/4 period = large phase lag
• large lambda/C: small phase lag
• lambda/C = 1: phase lag 1/8 period.

Let us now consider two specific cases: (i) diurnal and (ii) yearly variation of some zonal temperature T(t) under varying insolation F(t).

Diurnal:

• variation of F(t) = 200 W/m2 (from day to night)
• variation of T(t) = 10 C
• phase lag = 3 hours (max temp at 3 pm)
• C = lambda > 10

Yearly:

• variation of F(t) = 150 W/m2 (from Summer to Winther)
• variation of T(t) = 15 C
• phase lage = 1.5 month (max temp mid August)
• lambda > C > 10.

In both cases we find a climate sensitivity S < 0.1. We find that the value S =1 by IPCC is a factor 10 too big.

There is massive data duplicating the above and there is thus massive data indicating that:

• the global warming from doubled CO2 of 3-4 C by IPCC, is a factor 10 too big.

Note that climate has a natural variability over day and night and over the year under large variations of the insolation-forcing, which can be used to assess climate sensitivity with respect to small CO2 forcing.