Atmosphere as Air Conditioner Keeping Earth Temperature Constant

My journey into climate science started in 2010 with this analysis of black body radiation leading to an analysis of the atmosphere of the Earth as a form of air conditioner keeping the Earth surface mean temperature stable under varying mean heating from the Sun. My work was published as two chapters of the (ground-breaking) book Slaying the Sky Dragon - Death of the Greenhouse Gas Theory:

• Computational Blackbody Radiation
• Basic Thermodynamics of the Atmosphere.

The basic idea is that incoming energy to the Earth surface at 288 K of about 160 W/m2 from the Sun is transported to the mid troposphere at an altitude of 5 Km at 255 K by a combination of H20 thermodynamics with phase change (evaporation/condensation) with a minor contribution of radiation, for radiation to outer space at 0 K. The variation of incoming energy to the surface can depend on varying cloud cover. This is the scenario in tropical zones receiving most of the energy with sunny mornings followed by thunderstorms in the afternoon.

An increase of incoming energy to the surface is counterbalanced by more intense H2O thermodynamics keeping temperatures constant. Radiation then takes a passive role as constant under constant temperature. 

This is like an air conditioner keeping a stable room temperature of 15 C with constant outside temperature 0 C under variable interior heating of the room e g depending of number of people in the room. 

It also connects to boiling of water on a stove keeping a stable boiling temperature of 100 C under varying energy input from the stove, with more vigorous boiling with phase change responding to increasing input.  

The Sky Dragon analysis above from 2010 was written after a very quick introduction to the so called Greenhouse Effect, but I think it captures aspects valid also today. 

Tropical climate: Raising hot humid air in the morning releasing heat to the atmosphere by condensation effectively transporting  heat energy from surface to atmosphere as a cooling air conditioner.

Boiling water kept at 100 C under heating from stove by evaporation.

The simplest model consists of heat conduction through a wall of thickness 1 with heat conductivity $\kappa $ and temperature $T(x)$ varying linearly from $T_0=1$ at $x=0$ and $T_1=0$ at $x=1$ with heat flux $Q=\kappa \frac{dT}{dx}=\kappa$. Increasing $Q$ is balanced by increase of $\kappa$ without changing $T(x)$ an increase of more vigorous thermodynamics or boiling. 

Nobel Prize in Physics to Climate Models which Do Not Model Climate

The Nobel Committee in Physics has as an act of scientific political correctness today given half of the Nobel Prize in Physics in 2021 to Syukuro Manabe and Klaus Hasselmann for the physical modelling of Earth's climate quantifying variability and reliably predicting global warming.

In other words, the Prize has been given to Climate Models which Do Not Model the Climate, as is shown in the following graph of Global Warming over time comparing Climate Model predictions with Real World observations (second image from Roy Spencer Global Warming) : 

These graphs must have been unknown to the Committee. What is the meaning of "reliably predicting global warming" when the prediction has nothing to do with the actually observed absence of observable global warming (0.2 C over 40 years)? Is the "reliability" that all climate models show too much warming, or that the spread is so big that even virtually no warming is included in the predictions?

CO2: Warming or Cooling or Nothing?

Fred Singer has new post on the fundamental postulate of climate alarmism as a global temperature increase of 3 C upon doubled atmospheric CO2 as predicted by climate models.

Fred starts from the poor  correspondence between climate models predicting warming and observations of no warming, and asks the question if in fact more CO2 may have a cooling rather than warming effect.

Fred then brings in the customary elements of an Atmospheric Lapse Rate ALR and an "Effective" Altitude EA for emitting Outgoing Long Wave Radiation (OLR) from CO2, and notes a warming effect if EA lies in the troposphere and a cooling effect if EA lies in the stratosphere, assuming ALR stays the same.

Altogether, Fred's discussion shows a that it is not written in stone that CO2 has a warming effect:

• Such is the power of group-think that even experts, with some exception, find the idea that CO2 might cool the climate difficult to accept.

Here the exception may include myself, even if I may not count as an expert, with message that the effect on global temperature of a bit more CO2 as an atmospheric trace gas, is not measurable. 

It thus may well be impossible to experimentally determine warming or cooling and the whole question of CO2 warming will only be of concern interior to climate models, which tell nothing about real climate.

This connects to a discussion I had with Fred in 2011 on the question:

• Can the "Greenhouse Effect" be Detected?

SMHI:s Klimatmodeller: Extra Känsliga för Koldioxid med Förstärkt Växthuseffekt

SMHI:s klimatmodell som möjliggör (ganska) säker prediktion av snöfall 50 år framåt i tiden.

DN går idag ut med ett stort uppslag under rubriken Så blir den svenska vintern i framtiden:

• Hur kommer vädret att se ut om 50 år? Frågan är speciellt angelägen när kylan hugger tag i Sverige och våren känns långt borta. Enligt prognoser från SMHI:s Rossby Centre väntar stora förändringar i det svenska vinterklimatet.

Prognoserna bygger på s k klimatmodeller:

• Klimatmodellerna som forskningen på Rossby Centre utgår ifrån har utvecklats i över 20 år och inkluderar scenarier för Sverige, Europa och i viss mån klimatprognoser i ett globalt perspektiv. 
• En del av klimatmodellerna är extra känsliga för ändringar i atmosfärens koldioxidhalt, vilket kan påverka prognosernas resultat. Det kan alltså innebära olika utslag beroende på hur växthuseffekten artar sig.

En svårighet är att modellerna inte idag kan kalibreras mot framtida mätningar: 

• Vi har en ganska bra förståelse för växthuseffekten, men att den ändrar klimatet över tid innebär problem i vårt arbete med modellutvärdering. Det betyder att klimatet vi försöker säga något om 50 år i framtiden inte är detsamma och för det framtida varmare klimatet finns i dag inga mätningar som vi kan testa modellerna mot. Vi vet inte exakt hur mycket klimatsystemet kommer att svara på höjda halter av koldioxid, säger Erik Kjellström.

Vi förstår att klimatmodellerna är extra känsliga för koldioxidhalten, men inte kan kalibreras mot framtiden och att man därför inte vet hur klimatsystemet kommer att reagera. Men det hindrar inte att man kan göra ganska precisa förutsägelser:

• Trots osäkerheten kring hur den förstärkta växthuseffekten kommer att påverka klimatet regionalt säger Erik Kjellström att det mesta pekar på att svenska vintrar kommer att bli kortare i framtiden.
• Man kommer fortfarande kunna åka skidor i Norrland om 50 år, dock inte lika ofta som i dag.
• Det kommer innebära mer halka och fler krockar på grund av att man inte är van vid halt underlag, sådant som norrlänningar kan tycka att vi sörlänningar är dåliga på.
• Vintersäsongen blir kortare med färre snökanoner, men när de väl kommer kan inte jag utesluta att de blir kraftigare, avslutar han. 

Vad skall man säga om detta sammelsurium i sann Grönköpingsanda: Extra känsliga klimatmodeller med förstärkt växthuseffekt, som mycket väl medger att snöstormarna kan bli kraftigare och att även kommande generationer av sörlänningar måste se upp med halka. 

Ännu en triumf för den svenska klimatmodellen!

PS SMHI meddelar att i år är våren kraftigt försenad, och kommer så att förbli till den dag den äntligen inträder, då den kommer att meddelas att ha inträtt ca 10 dagar tidigare än normalt, allt enligt SMHI:s klimatmodell.

Update of Talk at Climate Sense 2018: Voodoo Physics

I have put up an new version of my upcoming talk at Climate Sense 2018 with the title:

• IPCC Voodoo Physics of the Greenhouse Effect

Of particular focus is the Fundamental Theorem of Calculus stating that if $F(x)$ is a primitive function of $f(x)$, that is $\frac{dF}{dx}=f$, then 

• $\int_a^bf(x)\, dx = F(b) - F(a)$.

For example, if $f(x)=1$, then $F(x)=x$, and so we can formally write

• $1  = \int_{100}^{101} f(x)\, dx = F(101)-F(100)=101 - 100$ 

expressing the positive quantity $\int_{100}^{101} f(x) dx = 1$ as the difference between the two (large) numbers 101 and 100. This is mathematics and not yet physics.

The radiative flux of heat energy $Q$ from a warm body of temperature $T_2$ to a colder body of temperature $T_1 < T_2$ is (essentially) given by the integral

• $Q = \int_{T_1}^{T_2}f(\nu )\,d\nu$  

where $f(\nu )$ is the Planck spectrum with $\nu$ frequency. Here the limits of the integral scale with temperature reflecting the cut-off in frequency expressed by Wien's displacement law giving the
warm body the "overkill" spectrum $f(\nu )$ above the cut-off $T_1$ for the cold body, with the overkill effectively causing the heating while the shared spectrum below cut-off has no heating effect, as explained in more detail here.

With $F(T)=\sigma T^4$ and $F$ acting as a primitive function of the Planck function $f$, the radiative flux $Q$ can now according to the Fundamental Theorem formally be expressed in the form of the Stefan-Boltzmann Law

• $Q =  \sigma T_2^4 - \sigma T_1^4$      

thus formally expressing the positive quantity $Q$ as the difference between two (large) numbers $\sigma T_2^4$ and $\sigma T_1^4$. 

The Voodoo Physics of the Greenhouse Effect is the result of giving the mathematical identity

• $\int_{T_1}^{T_2}f(\nu )\,d\nu =  \sigma T_2^4 - \sigma T_1^4$

a physical meaning with the physical one-way flux $Q=\int_{T_1}^{T_2}f(\nu )\,d\nu$ expressed as the difference between the entities $F(T_2)=\sigma T_2^4$ and $F(T_1)=\sigma T_1^4$, now freely invented to be forms of two-way "radiative fluxes" back-and-forth between the bodies. From one-way physical flux are thus created two-way fluxes from a mathematical identity without any proper physical correspondence. Note in particular that $F$ as primitive function of $f$ is undetermined up to a constant, thus allowing fictitious back-and-forth fluxes of any magnitude.

Note that $F(T)=\sigma T^4$ can be interpreted physically as the one-way radiative flux from a body of temperature $T$ into a background at 0 K.  But the physics is missing of viewing the one-way radiative flux between two bodies as a difference between two separate fluxes into a background at 0 K.   

A property (identity) of a mathematical model is thus freely interpreted to be real physics, in the same way as an operation of a voodoo doll is believed to be able to have a real effect on a real person. 

This is nothing but Voodoo Physics, and this is the nature of the Greenhouse Effect based on Back Radiation from cold to warm underlying the CO2-alarmism so forcefully preached by IPCC with now Macron as ardent follower.

Macron, despite (or maybe thanks to) his education in French elite schools with all its mathematics, thus appears to be overwhelmed by the Fundamental Theorem of Calculus and cannot separate model from reality.  

                       Voodoo = operation on model believed to have real effect on real person.

PS The Pyrgeometer is a perfect example of a voodoo doll, reporting (non-physical) back radiation $\sigma T_1^4$ from a cold atmosphere at $T_1$ to warmer Earth surface at $T_2$, by measuring $Q$ and (erroneously) viewing $\sigma T_2^4$ to be radiation from the Earth surface, as
if the Earth surface was radiating directly to surrounding space at 0 K and not to the atmosphere at $T_1$ K.

You can buy a pyrgeometer from Kipp and Zonen and play with it as a voodoo doll believing it reports real physics if you want to sell CO2-alarmism. From the above analysis you may understand that in fact it represents a symbiosis of science and commercial industry serving CO2-alarmism by supplying fictional physics.

Venus vs Earth: Atmospheric Mass, Pressure and Temperature

To help Lennart Bengtsson (as discussed in the previous post) to come up with his computation of the temperatures on Earth and Venus with switched atmospheric composition (with mass conserved), I suggest to take a look at the above picture comparing temperature and pressure through the atmospheres of Venus and Earth. We see that for pressure between 10 and 1000 bar the temperatures are pretty much the same (the difference can probably be explained from the fact that Venus is closer to the Sun), indicating that the composition of the atmosphere has little influence at the same pressure, and that it is the large mass and resulting high pressure that makes the surface of Venus about 450 C warmer than that of the Earth.

From the picture we can estimate an Earth-temperature of 15 C with Venus-atmosphere composition (2400 times as much CO2), and a Venus-temperature of 450 C with Earth-atmosphere composition. That is, no difference!

Prediction of Global Temperature May Well Be Possible

The recent "hiatus" of global warming, with slightly falling global temperature over now two decades under rising CO2 levels, in total contradiction to steadily rising temperature predicted by all of the complex climate models underlying the CO2 alarmism propagated by IPCC, has given support to a populistic view that "mathematical modeling of climate is impossible because the evolution of climate is chaotic". Both skeptics and alarmists have shown enthusiasm for such a scientific defaitism.

But it is not at all necessary to draw this conclusion, since chaos can sometimes be very predictable, for example as a null result of small stochastic perturbations.

For example, a simple climate model stating a balance between incoming radiation from the Sun, which is observed to be nearly constant, and outgoing radiation from the Earth system, which is observed to be nearly constant, can give the prediction that global temperature will stay nearly constant over forseeable time, say a couple of hundred years.

Such a model would be in excellent agreement with observations over the last two decades, and would also be within measurement accuracy since the start of recorded observations (with maybe half a degree Celsius nominal increase).

Climate as long-time-average of weather may thus be predictable, by the same mathematical reasons that mean-value aspects of turbulent flow like total drag and lift of an airplane are predictable (as shown in Computational Turbulent Incompressible Flow).

What may be impossible is a precise prediction of a very small effect of a small perturbation of atmospheric radiation from a change of concentration of a trace gas as CO2. But a precise prediction of something so small that it has no observable effect, is of course meaningless and thus the perceived impossibility is not real.

It is only if you like IPCC want to send an alarm of an effect of a vanishingly small cause, that you need a precise climate model supporting your case. The fact that such model is basically unthinkable is then something to hide, together with the fact that a prediction of no-change is certainly thinkable and may well be correct.

Lennart Bengtsson om Bränning av Böcker

Lennart Bengtsson kommenterar en debattartikel i dagens DN:

• Med det stora antalet akademiker bland undertecknarna kunde man kanske väntat sig lite mer kritiskt och öppet tänkande och inte bara detta sagolika flum. Att världen idag är beroende av fossil energi till mer än 80% och med 1.4 miljarder människor som saknar tillgång till el och där halva jordens befolkning är underförsörjda med energi verkar knappast bekymra denna ljusets riddarvakt det ringaste.
• Nästa steg blir väl att bannlysa det felaktiga tänkandet eller bannlysa eller rent av bränna olämpliga böcker som den framstående belgiske energiexperten Samuele Furfaris nyutkomna bok: ”Vive les énergies fossiles!” med undertiteln ”La contre-révolution énergétique” Det enda hoppfulla är väl att dessa untertecknare eller snarare deras klimatstridande studenter inte normalt läser böcker på franska. I slutstadiet får vi räkna med att även diverse olämpliga personer blir bannlysta i denna nysvenska omvända upplysningstid.

Mot detta står att LB deltog i det offentliga brännandet på KTH de 4e december 2010 (post with 4051 page views) av min matte-bok, eftersom matematiken hos enkla klimatmodeller ifrågasatte den då (och ännu) rådande dogmen av CO2-alarmism.  

Kan vi läsa LBs kommentar som ett uttryck för att LB inte skulle göra om samma sak idag?

Skulle man kunna säga att bokbränning inte är bra eftersom det leder till ökade CO2 utsläpp?

What Is Wrong with (IPCC) Climate Models?

CO2 alarmism is now falling apart because the global warming predicted by the IPCC ratified climate models show little similarity with observations of no warming the last 17 years. This is commonly viewed as evidence that mathematical modeling of global climate is impossible because weather and climate is "chaotic" and thus unpredictable.

It is true that weather is not predictable over more than a week, but climate as averaged weather may well be mathematically predicatble over long time. For example, the simple climate model of no change of global temperature, may well be a good model over centuries, until the next ice age.

The IPCC climate models predict global warming (at variance with observations) because they are so constructed, that is to show warming even if there is none, not because it is impossible to construct climate models which fit observations.

The defunding of mathematical climate modeling to be expected because of the failure of the IPCC models thus lacks rationale in a world in which prediction is needed and may be possible by clever use of computational mathematics.

In any case the question of the role of climate modeling is now on the table.  

Thomas Stocker's Defense of IPCC Climate Models at Variance with Observations

Global temperature increased according to observations in the periods 1920 - 40 and 1978 - 1996 with about 0.35 C, while the temperature was slightly decreasing in the periods 1880 - 1920, 1940 - 1978, 1997 - 2013.

The main argument used by IPCC co-chairman Thomas Stocker when defending the climate models of IPCC AR5 predicting steady warming, was that the 17 year period 1997 - 2013 with no warming was too short to allow any conclusion that CO2 forcing was too small to be observed, while the 18 year period 1978 - 1996 with warming was long enough be able to attribute with 95% likelihood the warming to CO2 forcing.  Stocker clarified the argument by adding that a period of 30 years would be required to be able to detect a trend in global cooling.

PS1 The temperature curves for the periods 1920 - 1950 and 1973 - 2013 are very similar with first warming and then slight cooling, only shifted with a steady rise of about 0.5 C/century after the Little Ice Age. The rise 1920 - 1940 is not attributed to CO2 by IPCC while the rise 1976 - 1996 is. The logic is missing.

PS2 The above graph produced by IPCC appears to present lower than actual temperatures before 1960 thus enhancing the warming thereafter.  

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. 

War Against Spencer-Braswell Low Climate Sensitivity

The recent article by Spencer and Braswell On the Misdiagnosis of Surface Temperature Feedbacks from Variations in Earth’s Radiant Energy Balance has caused an uproar by climate alarmists with an immediate rebuttal by Dessler and resignation of the chief editor in charge.

Climate science is fascinating: It concerns the complex system of global climate but it is studied using very simplistic mathematics. The Spencer-Braswell paper concerns fitting a very simplistic mathematical model of global climate of the form

• C dT/dt = F(t) - lambda T(t)

to measured data in order to determine the (positive) feedback coefficient lambda. Here T(t) can be sea surface temperature SST as function of time t, C is the heat capacity of the Earth-atmosphere system, F(t) is radiative forcing and S = 1/lambda measures climate sensitivity as change dT of T vs change dF of F in stationary state:

• dT = S dF

If lambda is small, then the sensitivity S is large and a small change of forcing dF can have a large effect dT on temperature T.

S is the holy grail of climate science: If S = 1 (large) then there may be reason for climate alarmism. If S = 0.1 (small) then there is no reason for alarm. The climate system is then so stable that an effect of doubled CO2 can never be measured or detected.

If S = 0.1 then a change of radiative forcing of 10 W/m2 (quite big out of a total of about 250 W/m2 with natural variability about 5 W/m2) could cause 1 C of warming. Nothing to worry about.

The radiative forcing from doubled CO2 can be estimated to be in the range 0f 1 - 4 W/m2, which with S = 0.1 gives a climate sensitivity of 0.1 - 0. 4 C, which is not at all alarming.

Now Spencer and Braswell determine the coefficients C and lambda in the above model from a best fit to measured time series of T(t) (from SST) and F(t) (from ERBE), and make the following observations:

• S < 0.3
• IPCC models give S > 1
• if F(t) is not properly measured then S cannot be reliably determined.

That this has caused an uproar is understandable: If S < 0.3, then climate alarmism collapses.

Now, there is a wealth of measurements of time series T(t) and F(t) which all indicate that S is smaller than 0.2, presented in work by Spencer, Lindzen and many others.

One can also use variations over time (diurnal, seasonal) and space (regional) of T and F to estimate S, see a summary of my posts on climate sensitivity on Basic Science: Climate Sensitivity < 0.3 C.

The Spencer-Braswell paper in all its innocence is thus a blockbuster to climate alarmism, and it is clear that it has to be eliminated, one way or the other no matter what the costs are.

Spencer is expecting the worst: More Thoughts an the War Being Waged Against Us.

The story is unfolding in real time with an IPCC in free fall...see What is IPPC Afraid Of? ...

IPCC Stops Scientific Debate ...Dessler launches a video presenting his trivialities ...

PS A simple model correctly illustrating some fundamental real aspect, is valuable because this helps understanding . The above model can serve this purpose in the stable case with lambda > 1, but the model is too simple to detect a small lambda and large sensitivity.

Simple Climate Model: Thermodynamics, Radiation and Observation

In the spirit of my article in Slaying the Sky Dragon, consider the following facts:

• The Earth with atmosphere absorbs 240 W/m2 sunlight and emits 240 W/m2 IR.
• The Earth surface temperature is 288 K.
• By Stefan Boltzmann 240 W/m2 corresponds to an effective blackbody temperature of 255 K (with an albedo of 0.3). The difference 288 - 255 = 33 C can be seen as the total warming effect of the atmosphere.
• 40 W/m2 is emitted directly from the Earth surface through an "atmospheric window".
• The climate system acts as an air conditioner in a combined thermodynamic-radiation cycle processing the remaining 200 W/m2.
• The effect of this process is to reduce the lapse from the base (dry adiabatic) value of 9.81 C/km to the observed 6.5 C/km, thus with a reduction of 3.5 C/km per 200 W/m2 or total cooling effect of 18 C, since the temperature is observed to be 255 K at a height of 5 km.
• The reduction of the lapse results mainly from the thermodynamics by evaporation/condensation, which has a cooling effect by lowering the temperature at low altitudes by evaporation and increasing the temperature by condensation at higher altitudes.
• Suppose now the atmospheric window is decreased by additional greenhouse gases by 4 W/m2, which are to be handled by the combined thermodynamic-radiation process.
• Suppose the 4 W/m2 are splitted equally between thermodynamics and radiation.
• Additional 2 W/m2 to be processed by thermodynamics means 1% reduction of the lapse rate with corresponding cooling effect of about 0.18 ~ 0.2 C.
• Additional 2 W/m2 to radiation gives a warming effect of about 0.5 C by Stefan-Boltzmann.
• The net is a warming effect of 0.3 C.
• In other words, with standard terminology, we find a climate sensitivity of 0.3 C, to be compared with IPCC´s value in the range 1.5 - 4.5 C, which is 5 - 15 times bigger.

I believe this argument is the simplest possible combining thermodynamics with radiation and observations. It is possible that it contains an element of truth.