Teknikdelegationens Slutbetänkande

Teknikdelegationen har lämnat sitt slutbetänkande som inleds med följande dystra analys:

• Många ungdomar söker relevans för samhället och den egna identiteten när de väljer utbildning och karriär, men har svårt att finna detta i matematik, naturvetenskap, teknik och IKT. Problematiken förvärras av att skolväsendet inte har förmåga att fånga upp det grundläggande intresse som de flesta barn och ungdomar har, och inte heller i tillräcklig utsträckning förmedla den kunskap alla behöver. I dag ser vi konsekvenserna i form av sjunkande kunskapsresultat.
  

Eller annorlunda uttryckt: Dagens ungdomar hindras från att utveckla sitt naturliga intresse för matematik-naturvetenskap-teknik av att utbildningen inom dessa ämnen är gammalmodig, träig, tråkig och dysfunktionell, och inte utnyttjar datorsamhällets alla möjligheter. 

Om detta har dock Delegationen ingenting att säga: En sökning visar att "dator" förkommer i två meningar i betänkandet:

• Dessutom är ungdomar förstås utomordentligt aktiva datoranvändare.
• ...att det inte bara handlar om att skolan införskaffar datorer...
  

Mina försök att komma till tals med Delegationen har varit helt fruktlösa. Leif Johansson svarar naturligtvis inte på brev från den ende av landets matematikprofessorer som bryr sig om svensk utbildning och konkurrenskraft. Självklart inte.

Delegationen har ingenting förstått, och kan därför inte komma med annat än tomma 

fraser, och begäran om en massa pengar (1235 Mkr).

Vad som behövs är förståelse att utbildningen måste moderniseras för att motsvara

datorsamhällets nya möjligheter och krav. Är nu detta så svårt att förstå, Leif?

Denna post är publicerad på Newsmill.

Proof of the Atmospheric Greenhouse Effect?

Even if according to the Royal Swedish Academy of Sciences "the effect of greenhouse gases is well established", the American Physical Society through Arthur P Smith feels an urge to demonstrate the effect mathematically in the article Proof of the Atmospheric Greenhouse Effect, as if the effect was not already proven to be real.

The proof consists of using Stefan-Boltzmann's Radiation Law Q = cT^4 as a model of the Earth in radiative equilbrium with an atmospheric layer absorbing a factor f of the radiation E from the Earth surface and re-emitting f/2 E back again and f/2 E to outer space together with the non-absorbed  (1-f) E, to give the total outgoing 

                                                        (1 - f/2) E

suggesting a global warming with the factor (1 - f/2)^1/4 (fourth root of (1 - f/2)) by Stefan-Boltzmann.  (If you iterate with n layers transmitting a factor (1-f/2n), then the outgoing radiation decrease to approximately exp(-f/2)E with global warming factor exp(-f/8)).

This supposedly generic (trivial) model of the greenhouse effect is presented also by Richard Lindzen in Greenhouse Effect: A Scientific Analysis, with the result that with f = 1 the Earth surface temperature comes out to be 303 K, about 15 K too high.  Definitely a major greenhouse effect, much more than asked for, but not convincing scientifically since it does not fit at all with observation. Of course, adjusting  f can give any desired result with less warming:

For example, if you say that the Earth temperature would be 255 K without atmosphere, then

you would get the observed 288 K if you arbitrarily choose  f = 0.68. Any model with a free parameter at your disposal can be made to fit this data, but any model is not a correct model.

A scientist has two ways to handle a theory which does not fit with observation: (i) Dismiss the theory as incorrect and start anew with some different theory. (ii) Or simply add an ad hoc assumption, for example that you can divide your model results by 2, or fiddle with f,  and you have it! Perfect match, but the trouble is that the corresponding physical model is missing, and without a physical model it is not science. What physics divides by 2?

The evidence is overwhelming that you cannot prove any greenhouse effect simply by waving at the Stefan-Boltzmann's Radiation Law. Science does not work that way. Either your model gives results consistent with observations, and then the model may be correct, or the model results do not agree at all with observations, and then the model is useless.

The above argument is developed in some more detail in the new article Greenhouse Gases without Greenhouse Effect.

A climate model only based on radiation cannot explain the observed temperture profile starting at 15 C at the Earth surface, dropping linearly to -55 C at the top of troposphere (tropopause) and climbing back to 0 C at the top of the stratosphere (stratopause). 

Why? Because black body radiation from the tropopause as compared to that from the Earth surface is reduced with a factor (218/288)^4 = o.33, and compared to 0 C the drop is a factor 0.4. The  cold tropopause would then act as a barrier to radiation and in order to reach radiation balance the Earth surface temperature would have to increase to 15 + 55 = 70 C. You could then speak about a terrible greenhouse effect as a result of a cold tropopause! (without any greenhouse gas effect at all). Fortunately there is also convection-evaporation/condensation, which changes the model.

In any case, a model without convection-evaporation/condensation only based on radiation

does not describe physics correctly, and is useless for prediction.  Nevertheless such a model

is the starting point for IPCC global warming alarmism.

Question to the Royal Swedish Academy of Sciences

I try the debate strategy from the previous post in a new letter to

The Royal Swedish Academy of Sciences

Secretary Gunnar Öquist

The Royal Academy states in The Scientific Basis for Climate Change that

• The effect of greenhouse gases is well established.
  

Since this statement is critical as concerns a possibly alarming global warming from CO2 threatening humanity, I would like the Royal Academy to answer the following scientific questions related to the scientific statement:

• What effect of greenhouse gases is well established?
• Which are the original scientific sources demonstrating the effect?
  

Sincerely

Claes Johnson

Summary: Incorrect Postulate of Climate Science

In a series of posts on climate sensitivity I have been searching for the scientific basis of 

alarmism of global warming from atmospheric CO2.  If there is a rational scientific basis, it is well hidden without any references. 

What I have found is an irrational non-scientific basis, which can be summarized in the relation dQ = 4 dT connecting "radiative forcing" dQ to "global warming" dT, which is the Basic Postulate of global warming alarmism.

The Basic Postulate comes trivially from differentiating Stefan-Boltzmann's Black Body Radiation Law Q= c T^4 at T = 273 K with Q = 273 W/m^2, as shown in previous posts.

That this is the derivation of the Basic Postulate is evidenced in the basic document of climate alarmism  Carbon Dioxide and Climate A Scientific Assessment by the National Academy of Sciences:

• For the simplest case in which only the temperature change is considered (no feed back), and the Earth is assumed effectively to be a black body the value of dQ/dT = 4 cT^3 is readily computed to be about 4 W/m^2. For such a case doubled CO2 produces a temperature increase of 1 C.
  

Climate alarmism was then presented as a direct corollary to the Basic Postulate, with a bit of ad hoc feed back:

• Our best estimate is that changes in global temperature of the order of 3 C will occur and that these will accompanied by significant changes in regional climate patterns.

The relation dQ = 4 dT can be used to compute "radiative forcing" dQ= 2.8 W/m^2  attributed

to increased CO2 during the 20th century from an observed dT = 0.7 K.  A projection into 

this century can then give dT = 1.4 K from a double dose of "radiative forcing" from doubled CO2, which with a dose of feed back can give the desired alarming 3 C. Clever or stupid?

The scientific basis of IPCC global warming alarmism is thus Stefan-Boltzmann's Radiation Law as a model of global climate, coupled with an attribution of some warming during the 20th century entirely to CO2. 

But Stefan-Boltzmann's Radiation Law is not a model of global climate, because the Earth with atmosphere dynamics does not function like a black body.  The relation dQ = 4 dT cannot be used to draw any conclusions about neither dQ nor dT. Nor can temperature variations arbitrarily be attributed to CO2. 

The Basic Postulate dQ = 4 dT of IPCC global warming alarmism thus lacks scientific basis. 

How is it possible that Royal Academies of Sciences continue to support a global warming alarmism which does not have any scientific basis?

The comments below lead to the following strategy to come to grips with a climate alarmism

without any scientific basis:

• In any debate, just repeat  one question: WHY is dQ = 4 dT?
• When repeated 10-100 times without any answer, the debate is over. Try it!

PS The documents lead back to the 1981 Science article Climate Impact of Increasing Atmospheric Carbon Dioxide, by James Hansen, et al, where it is claimed that:

• The estimated black body Earth surface temperature without atmosphere is 255 K.
• The 33 K increase  to the observed 288 K is the greenhouse effect of gases and clouds. 
• The surface greenhouse effect is analogous to the depth of water in a leaky bucket with constant inflow rate. If the holes in the bucket are reduced in size the water depth and pressure will increase until the flow rate of of the holes again equals the inflow rate.

This is the scientific basis of global warming alarmism, basically the same as dQ = 4 dT, resting on Stefan-Boltzmann's Radiation Law and the obviously incorrect assumption that the Earth surface temperature is determined by radiation only, without major influence from convection evaporation/condensation. Is it reasonable to base far-reaching regulations on this form of black magic science? From a very leaky bucket of science? DS

PS 2 There is something correct about the leaky bucket analogy, which has been forgotten by followers of Hansen, namely that the inflow rate is constant, that is that there is no "radiative forcing" from greenhouse gases.

Climate Sensitivity 7: Radiation Only

Suppose as a thought experiment we remove the troposphere with its convection-evaporation/condensation from the atmosphere and consider a system consisting of the Earth together with a stratosphere only governed by radiation. 

The radiation from the Sun would be absorbed partly by the stratosphere and partly by the Earth, all of which would eventually be re-emitted as infrared radiation from the stratopause, the outer surface of the Earth-stratosphere system. The Earth  and the stratosphere would then be in radiative equilibrium at the same temperature, which we can assume to be the 0 C of the present stratopause, which is the Earth black-body temperature balancing that of the Sun. 

The Earth with stratosphere would then act as one black body of temperature 0 C, independent of the transparency of the stratosphere, emitting as infrared radiation whatever was absorbed.

This would be an inhabitable Earth different from the real case at 15 C, and so a model only based on radiation is incompatible with observation.

Nevertheless, let us ask what the climate sensitivity of this system would be, that is the change of temperature dT upon a change of (i) transparency of stratosphere or (ii) insolation dQ?

We have just concluded that (i) gives dT = 0, and in previous posts on climate sensitivity we have shown that (ii) gives  dT = 0.25 dQ.

(i) gives a very small climate sensitivity, while (ii) with  dT = 0.25 dQ by IPCC  is presented as alarming.

Now IPCC with support in e.g.  Radiative Forcing of Climate Change: Expanding the Concept and Addressing Uncertainties (2005) Board on Atmospheric Sciences and Climate argues as follows:

• dQ is estimated to 2.8 W/m2 by using dT = 0.25 dQ with an observed dT = 0.7 C during the 20th century.
• doubled dQ during the 21st century gives dT = 1.5 C: Alarm!

To see if this is Penguin Logic or scientific logic, we must ask from where does the dQ come?

From change of insolation? No because that is not human induced AGW. OK so the change

comes from change of transparency of the stratosphere. But we just noticed that in this case dT = 0, which is not alarming. So we have a clear case of Penguin Logic.

We have seen that in an Earth-atmosphere model with radiation only, there can be no AGW from greenhouse gasses. 

OK, so we have to include the troposphere with convection..., but then the dT = 0.25 dQ no longer can be assumed, so even if we accept some dQ from AGW, its effect on temperature

cannot be estimated by dT = 0.25 dQ, and IPCC does not present any other relation.

The basic question of climate sensitivity needs a complete restart. In IPCC AR5? By some 

Royal Academy? 

 

Experimental Non-Support of CO2 Global Warming Effect

Click on image to see experiment.

If you are a responsible parent, you are supposed to tell your kids that the Earth is kept warm partly by the presence of CO2 in the atmosphere absorbing and emitting/backradiating heat which otherwise would get lost into outer space.

Since kids are not convinced easily by theoretical arguments based on Stefan-Boltzmann's Law of Radiation usually presented as the scientific basis of this "greenhouse effect", you are supposed to point to an experiment with a bottle of water being warmed more by a lamp if a tiny bit of CO2 is added to the water, as shown above.

So you say to your kids: See, CO2 absorbs radiation and heats the water in the bottle and similarly the Earth is kept warm by a small fraction of CO2 in the atmosphere. The same argument has convinced scientific academies about the threat of global warming from CO2.

But if you are a really responsible parent, you could ask if the experiment is relevant. You might say to yourself: What really matters is the insulating effect of the atmosphere, which is what keeps the Earth surface at 15 C and not the 0 C without atmosphere.

You might say to yourself: Insulation cannot come from radiative absorption/emission, and the experiment has nothing to do with insulation, only radiative absorption, and so it is irrelevant Penguin Logic.

If anything, increasing radiative absorption/emission would decrease insulation, and thus more CO2 would rather cause global cooling than global warming!

So you may say to your kids: The CO2 bottle experiment does not show what it is supposed to show, namely global warming.

Are there other experiments you could point to? Not, as far as I know. And science without empirical basis is not science. For more critique of greenhouse theory, see the Hockey Schtick list.

We recall that R. W. Wood showed already in 1909 that a conventional greenhouse is not heated by trapping infrared radiation, but by blocking convection.

Accordingly IPCC very cleverly claims that the atmosphere greenhouse effect results from a "different physical process", because the atmosphere obviously does not block convection.

But IPCC gives no clue to what the "different physical process" could be, other than trapping infrared radiation, disproved in 1909.

Notice the clever Penguin Logic: Since a conventional greenhouse works by blocking convection and not radiation, IPCC states that the atmosphere greenhouse effect comes from "a different physical process", that is different from convection (because the atmosphere does not block convection). The Penguin Logic is then completed by stating that the atmosphere greenhouse effect is precisely the effect not used by a conventional greenhouse, that is trapping radiation. Undeniably, trapping radiation is is different from blocking convection, and the loop of Penguin Logic is closed!

Here is another rough estimate of climate sensitivity as a variant to those discussed in previous posts: A fully transparent atmosphere without convection-conduction would according to Stefan-Boltzmann give an Earth surface temperature of 0 C (which is Arctic Summer temperature). A non-transparent atmosphere (like in the tropics) with convection-evaporation-condensation, gives an observed tropical temperaure of 27 C. Note that without convection..., the tropical temperature would be o C, and so convection... is very important.

The real case is somewhere in between the above extremes, thus with a temperature span of 27 C. A 1% change of the atmosphere properties (radiation-convection...) can be estimated to give a 1% change of 27 C, that is 0.27 C. This argument thus gives a climate sensitivity of less than 0.3 C, one tenth of the IPCC alarm of 3 C.

PS Climate scientist Michael Mann reveals that

• The attacks against climate science represent the most highly coordinated, heavily financed, attack against science that we have ever witnessed.

Fascinating; I am just waiting to see the bucks rolling in...

Climate Science Without Physical Basis

Global climate is governed by physical laws and physical laws are expressed mathematically.

A physical law without a mathematical expression is not a physical law. Global climate is 

a coupled ocean-atmosphere thermodynamical process powered by radiation from the Sun and 

rotation of the Earth, which is described by mathematical equations for

• convection-diffusion-conduction of  (in)compressible flow (Navier-Stokes equations) 
• phase-change: ice-water-vapour
• radiation

based on in particular the following physics of heat transfer with heat represented as atomic

vibrations: 

• conduction in a material medium by successive excitation of atomic vibrations
  
• convection by transfer of the material medium carrying the heat as atomic vibrations
• radiation without medium by electromagnetic waves.

The basic law for heat conduction is Fourier's Law: 

                                                  q = - c  gradT

where q is heat flow, gradT is temperature gradient and c a positive constant. Fourier's Law states that heat flows from hot to cold with a magnitude proportional to the difference or gradient hot-cold.

Convective heat transfer has a very simple mathematical expression as material motion.

The heat exchange between phases of ice-water-vapour can also be described mathematically.

The basic law of heat transfer by radiation from a hot body of temperature Thot to a colder body of temperature Tcold, is Stefan-Boltzmann's Radiation Law

                                     q = c (Thot^4 -Tcold^4)

where c is a positive constant. 

We understand that basic physics tells that conduction-radiation is not by itself capable of transferring heat from a cold body to a hotter body (2nd Law of Thermodynamics if you like). Only convection (or phase change) can do that.

We now apply our knowledge to the coupled system Earth-atmosphere with the Earth

absorbing heat radiated from a hot Sun, which is somehow transferred through the atmosphere consisting of the troposphere connecting to the Earth and the stratosphere on top, and then 

radiated out into space.

We start from the observation that the (mean) temperature drops from 15 C  at the Earth surface through the troposhere to about - 55 C at its top (the tropopause), and then in the 

stratosphere increases to 0 C at its top (the stratopause). 

The heat accumulated from the Sun is thus first transferred from hot (15 C) to cold (-55 C) 

and then from cold (-55 C) to hot (0 C).  

We conclude that convection is necessary; radiation alone cannot transfer heat through the 

atmosphere with the observed temperature profile.

The basic postulate of IPCC climate alarmism is the relation dQ = 4 dT connecting 

global warming dT to change of heat forcing dQ. This relation is a consequence of using

Stefan-Boltzmann's Radiation Law as a model for global climate, as shown in previous posts.  

But we just realized that a model including only radiation is incompatible with observation. It is necessary to include convection in the model. But then the derivation of the relation dQ = 4 dT is no longer valid, and no other derivation is available.

The net result is that the basic postulate of climate alarmism of dQ = 4 dT lacks physical/mathematical basis. It is derived from a mathematical model which is not compatible with observation, and thus it is not scientific. 

Let us take an analogous example. Suppose someone (a climate scientist e.g.) explains why a bird can fly as follows: We start from a model saying that on birds there is an upward force balancing the downward gravitational force, because there is a physical law that states that all bodies (thus also birds) are acted upon by an upward force which balances gravitation. 

Do you buy this argument? Probably not: Such a law would be contradicted by observing an apple fall. The conclusion is that the law is false in the case of an apple and also for a bird without a further explanation. It doesn't matter that it is valid in some other case, namely the case of zero gravitation, or a mass-less apple/bird.

We repeat: If we make the observation that the Radiation Law as a model of global climate, is (completelly) incompatible with observation, then we must (if we are scientists) draw the conclusion that the Radiation Law as a model for global climate is (completely) useless. Climate alarmism on this basis is not scientific.

Note that it is the Radition Law as model of global climate which is incorrect, not the 

Radition Law per se,  possibly being valid for something else (like the radiation from the Sun).

Or a combination of the Radiation Law with e.g. convection.

To claim that the Radiation Law as a model of global climate is correct, because it is correct when applied to the Sun (or when augmented by convection), is nothing but Penguin Logic, which is not the logic of science even if practiced by climate scientists.

And with Penguin Logic you can do wonders: For example, you can argue that an estimated 

d T = 0.7 C during the 20th century, from and increase of CO2 from 280 to 380 ppm, corresponds to dQ = 2.8 W/m2, and then make the prediction that further increase of CO2 will double dQ and thus dT to 1.5 C, the lower IPCC prediction. You can then feed your climate models with both dT and dQ and boost to at least 4.5 C. Penguin Logic at its best, used by IPCC.

For a simple mathematical model of global climate including conduction-convection-evaporation-condensation-radiation, see Temperature Sensitivity of a Basic Climate Model.

Also compare what the English factory worker Derek Alker comes up with in Do IR Budgets Make Sense?? Better than any Royal Academy...

But the Royal Academy is not alone: According to Huffington Post:

• Ninety seven percent of climatologists agreed that climate change is real and largely man-made in a poll released last year. At least 60 major scientific organizations across the globe also concur, while not one of any repute holds an opposing opinion. 
  

All major scientific organizations give their praise to a climate science without physical basis. 

How is this possible?

PS Maybe an alarmist would argue as follows: Let's skip the kink in the temperature profile

and just concentrate on an Earth at 15 C radiating infrared through a infrared transparent

atmosphere to a cold outer space. That is possible, but in this case the Earth surface temperature would have to drop to its black body temperature 0 C, in contradiction to observation.  The temperature profile of a non-transparent radiative atmosphere cannot have a kink.

 

The Myth of an Atmosphere Greenhouse Effect

There are at least two scientists denying the basic postulate of climate alarmism dQ = 4 dT: Gerhard Gerlach and Ralf Tscheuschner, who in Falsification of the Atmospheric CO2 Greenhouse Effect, give massive evidence that this postulate is incorrect:

• There is no atmospheric greenhouse effect, in particular CO2-greenhouse effect, in theoretical physics and engineering thermodynamics.
  

I agree completely, based on my experience as applied and computational mathematician. So we are three. See Temperature Sensitivity of a Basic Climate Model.

RealClimate presents a few weak "rebuttals" of Gerlach/Tscheuschner, very weak, just words. 

But Royal Societies and Academies of Sciences keep quiet, and in doing so support a postulate of climate alarmism,  which cannot be motivated by any known form of physics and thermodynamics.

How is this possible? Is it a consequence of the collapse of rational science from the crisis

of classical physics in the late 19th and early 20th century, out of which emerged relativity

theory and quantum mechanics? 

Probably. The result today is a physics of 11 dimensions in parallel universes totally beyond any rationale and human understanding in which anything is possible, even an Atmospheric Greenhouse Effect without verifiable physics basis. But is it so clever to build society on non-physical non-rational myths presented as rational physics, even if supported by scientific academies?

Where Are All Climate Scientists?

                                  Everybody seems to be facing the same direction, but one...

In previous posts on climate sensitivity I have shown that the basic postulate of climate alarmism is the relation dQ = 4 dT connecting "radiative forcing" dQ = 4 Watts/m^2 from doubling CO2 (1% of total) to "global warming" of  dT = 1 C. The relation dQ = 4 dT is claimed to be an undeniable basic rock solid consequence of Stefan-Boltzmann's Radiation Law, which cannot be disputed.

Myself I can only find that to apply the Radiation Law to compute changes of the Earth surface temperature from increased CO2, is as incorrect as applying it to compute the change of the inside temperature of a house (or conventional greenhouse) from some change of interior heating. An engineer doing so would not have a job: Nobody would believe that a 1% radiator change from 1000 W to 1050 W can elevate an inhabitable inside temperature of 15 C to a cosy 20 C.

 

That climate alarmists like IPCC claim rock solid undeniable truth of the basic postulate is understandable, since it is alarming by indicating high climate sensitivity.

What I cannot understand is that  all scientists skeptic to IPPC alarmism, including Lindzen, Spencer, Pielke,..., and all sceptic blogs including the Reference Frame and WUWT,....also seem to consider the basic postulate of dQ = 4 dT to be correct. How is that possible? Is this an expression of the Dark Age of the Uncertainty Principle?

Oh, there is one, and one is enough: Compare with the very interesting 2009 article Falsification of the Atmospheric CO2 Greenhouse Effect within the Frame of Physics by the physicist Gerhard Gerlich: By showing that 

• (a) there are no common physical laws between the warming phenomenon in glass houses and the ctitious atmospheric green- house eects, 
• (b) there are no calculations to determine an average surface temperature of a planet,
• (c) the frequently mentioned dierence of 33 C is a meaningless number calculated wrongly, 
• (d) the formulas of cavity radiation are used inappropriately, 
• (e) the assumption of a radiative balance is unphysical, 
• (f) thermal conductivity and friction must not be set to zero, 

the atmospheric greenhouse conjecture is falsied.

I agree. But how can it be that no climate scientist understands? In fact, Gerlich already in 1995 

expressed:

• the CO2-greenhouse effect of the earth atmosphere is pure fiction of people who like to use big computers, without physical fundamentals. 
  

Climate scientists did not listen then and do not listen today. Why?

What is of particular interest, from a scientific point of view, is that according to Gerlich: The "atmospheric greenhouse effect" does not appear 

•  in any fundamental work of thermodynamics, 
•  in any fundamental work of physical kinetics, 
•  in any fundamental work of radiation theory.

What we have is thus a form of folklore carried by climate scientists and Royal Academies, a folklore without any scientific basis and scientific source, as if  we are living in a Dark Age of Science covered up by a Dark Age of Information... Are we?

Maximal Green House Effect Without Effect

If the atmosphere had a maximal Green House Effect GHE by blocking all outgoing infrared radiation, what would then be the surface temperaturebe on Earth? Let's first collect the data describing the present situation from the top picture of the previous post:

• Out of incoming 100% from the Sun, 51% is absorbed by the surface of the Earth,
• 30% is delivered back by conduction-convection/evaporation-condensation and 21% as infrared radiation.
• The temperature at the Earth surface is 15 C, and at the top of the stratosphere 0 C.

Suppose now all of 21% outgoing infrared radiation would be blocked by a maximal GHE, so that all of the incoming 51% would have to be delivered back by convection-evaporation-condensation. What would the temperature increase be? Well, if we assume proportionality we get 21/30 x 15 = 10 C.   The maximal GHE thus may be 10 C.

What is then the present GHE? We did an estimate in the previous post and obtained about

50%.  So the present GHE may be 5 C. Without the present GHE the temperature would be about 15 - 5 = 10 C. The temperature gradient would then be maintained by convection-evaporation/condensation-conduction, not by any radiation.

Out of the total present GHE, 10-20% comes from CO2 , 70-80% from water vapour/clouds. 

With 10% the present GHE of CO2 would thus be 0.5 C. Doubling the CO2 could thus be expected to give at most 0.5 C. This conforms with Lindzens more elaborate analysis.

This argument includes feed back since it is part of the convection-evaporation/condensation. 

We thus have another (simple, but maybe relevant) argument indicating a small climate sensitivity of less than 0.5 C, based on observations of the present Earth surface temperature from the present radiative forcing.

The climate sensitivity estimate of 0.15 C in previous post, based on an even simpler argument using less data, may be a minimal climate sensitivity. It is easy argue that it should be doubled. By simple arguments we thus estimate the climate sensitivity to 0.3 - 0.5 C, about 10 times smaller than the IPCC value of  1.5 - 4.5 C based on even simpler (probably irrelevant) arguments.

It is natural to also make the following thought experiment: Suppose the effect of conduction-convection-evaporation/condensation was eliminated and only the GHE was left. What would then be the surface temperature? Right: 0 C, the same as at the top of the stratopshere.  Any temperature gradient in the atmosphere would be eliminated by radiation and the temperature would become constant through the atmosphere. From this one can argue that the GHE has no effect, right? An effect without effect? 

What Is the Greenhouse Effect, Really?

This post connects to previous posts on Climate Sensitivity and the Incorrect Postulate of Climate Alarmism.

Above is the Wikipedia pictorial explanation of the Green House Effect GHE (from IPCC): Of the incoming radiation from the Sun of 235 W/m2, the surface of the Earth absorbs 168 W/m2, and then by the GHE recirculates 324 W/m2. The recirculation is believed to be driven by reradiation (absorption and emission) by the atmosphere of infrared radiation from the surface of the Earth with the following key motivation:

• The ability of the atmosphere to capture and recycle energy emitted by the Earth surface is the defining characteristic of the greenhouse effect. 
  

OK, we learn that GHE amounts to "recycling of energy". We understand that recycled energy is not new input energy, just recirculation of whatever comes in from the Sun (235 W/m2) and eventually gets radiated away from the top of the atmosphere (235 Watts/m2). 

It is like the cash flow in a company with cash-in = cash-out, and a certain amount of recirculation between different branches of the company. 

How is the size of the GHE effect, the recirculating radiation, computed, that is the 324 W/m2? (And what drives the recirculation?)

Well, let's see what else of interest is presented in the above figure: Yes, the surface temperature T_S of the Earth is indicated to be 14 C. Is there a connection between 324 W/m2 and  T_S=14 C? There should be, since the whole idea is that GHE is responsible for T_S = 14 C, instead of the surface temperature without any atmosphere, which is  estimated to T_B = -18 C. Thus the GHE is viewed to increase the surface temperature by 32 C.

The idea could be that if by recycling the input to the Earth surface is not 168, but instead 168 + x, then  to get rid of that extra input x the surface temperature would have to increase by 32 C. By Stefan-Boltzmann's Radiation Law we would then get

             (168 + x)/235 =  (288/255)^4 = 1.64, that is   x = 230  W/m2.

OK, not so bad, but not quite the same:  230 vs 324. 

We make a new try: Suppose that the atmosphere reradiates the fraction c of the radiation from the Earth. Then trivial radiation balance gives 

                       (168 + x) c = x, that is x = 168/(1-c)  

and so x = 324 corresponds to  c = 0.48. Yes, why not assuming that the reradiation coefficient

is about 0.5. With x = 230 we get c = 0.27, also conceivable. 

In either case, the GHE does not include the real physics of heat transfer in the atmosphere (convection coupled with condensation-evaporation), just some very simplistic radiation assumptions. The whole concept of the GHE with its recycled radiation seems to have very 

simplistic basis.

IPCC now uses this very simplistic basis to compute climate sensitivity (without feed back) according to the rule dQ = 4 dT on the same simplistic (discussed in previous posts), and comes up with a global warming of 1 C upon doubling of CO2, as the starting point of climate alarmism. The physical basis of this results seems to be too simplistic to be able to have any scientific significance. 

The whole idea of GHE as an explanation of the temperature distribution through the atmosphere from 15 C at the Earth surface to -50 C at the tropopause to 0 C at the stratopause, seems utterly strange. How is possible that the GHE is not seriously challenged by serious scientists?

Note that the top picture by NASA does not include any "recycled energy" but instead  23% "carried (by convection) to clouds and atmosphere by latent heat in water vapour".

Black Body Temperatures of the Planets

Let us test Stefan-Boltzmann's Black Body Radiation Law  Q = c T^4 = cTTTT on the planets in the Solar system assuming similar absorption and emission. The radius of the Sun is about 2.3 light seconds. The radiation from the Sun is diluted at a distance of R (light seconds) with the factor (r)^2 where r = R/2.3. Taking into account that the area of a disc is 1/4 of a that of a sphere with the same radius, the radiation from the Sun reaching a planet at distance R is diluted  by the factor 4 r^2, which determines the effective temperature T_P of the planet  by the relation

                                  4r^2 = (T_S/T_P)^4

where T_S = 5778 K is the effective temperature of the Sun. We get

1. Earth: distance D = 500 light seconds = 1 AU, r =220, T_P= 5778/21 = 275 K (288 K)
2. Mars: D =1.5, r = 330,  T_P = 275 / 1.22 = 229 K (232 K)
3. Jupiter: D = 5.2, T_P = 275/2.28 = 120 K ( 134 K)
4. Saturn: D = 9.5, T_P = 275/3.08 = 90 K (103 K)
5. Uranus: D = 19.2, T_P = 63 K ( 73 K)
6. Neptune: D = 30.1, T_P = 48 K ( 63 K)
7. Venus: D = 0.72, T_P = 312 K (465 K)
8. Mercury: D = 0.39, T_P = 443 K ( 400 K)

where in parenthesis we give observed mean surface temperatures. We see a close fit for Mars, which has a thin atmosphere of 95% CO2. The atmospheres of the Earth and Venus increase surface temperatures substantially above the black body temperature. The very cold Saturn, Uranus and Neptune give off more heat than receieved, from some internal source of heat. Jupiter is estimated to give off about 2 times what is received from the Sun. The day and night temperatures of Mercury vary between -100 K and 700 K and a mean temperature is difficult to define.

For the Earth, the 275 K fits well with the temperature of the stratopause, while the surface temperature of an Earth without an atmosphere is commonly estimated to the lower value -18 C (instead of 2 C) as a result of certain assumptions on albedo and emissivity modifiying the black body aspects. So the -18 C is speculation and not observation.

The most interesting feature is the close fit for Mars, with seemingly small heating from 

its CO2 atmosphere. 

The Incorrect Postulate of Climate Alarmism 2

Svante Arrhenius 1896: If the quantity of carbonic acid (CO2) increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression.

Climate sensitivity or global warming of 1.5 - 4.5 C from doubled CO2, is by IPCC presented as a consequence of Stefan-Boltzmann's Black Body Radiation Law. This argument was used by the Swedish scientist Svante Arrhenius (1859-1927) in On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, Philosophical Magazine 41, 237 (1896), to predict a climate sensitivity of 5 - 6 C:

• For this radiation we will suppose that Stefan's law of radiation, which is now generally accepted, holds good, or in other words that the quantity of heat (W) that radiates from a body of the albedo (1-n) and temperature T (absolute) to another body of the absorption-coefficient b and absolute temperature q is W = nbg(T^4-q^4),where g is the so-called radiation constant (1.21x10-12 per sec. and cm.2) Empty space may be regarded as having the absolute temperature 0[11].
  

Alan Thorpe in Climate Change Prediction on behalf of the Institute of Physics, repeats the argument 110 years later: 

• The existence of an atmosphere that is capable of absorbing and retransmitting certain wavelengths in the electromagnetic spectrum means that there must be a socalled greenhouse effect whereby the atmosphere traps outgoing infrared radiation, thereby increasing the atmospheric temperature (see box insert and Andrews 2000). This was first postulated by Jean- Baptiste Fourier in 1827 and further elaborated upon by John Tyndall in 1860 and Svante Arrhenius in 1896. It was Arrhenius who first noted that, say, a doubling of the carbon dioxide concentration in the atmosphere could lead to an increase in surface temperature of some 5 to 6ºC.
  

IPCC AR4 follows up in 2007:

• The Sun powers Earth’s climate, radiating energy at very short wavelengths, predominately in the visible or near-visible (e.g., ultraviolet) part of the spectrum. Roughly one-third of the solar energy that reaches the top of Earth’s atmosphere is reflected directly back to space. The remaining two-thirds is absorbed by the surface and, to a lesser extent, by the atmosphere. To balance the absorbed incoming energy, the Earth must, on average, radiate the same amount of energy back to space. Because the Earth is much colder than the Sun, it radiates at much longer wavelengths, primarily in the infrared part of the spectrum. Much of this thermal radiation emitted by the land and ocean is absorbed by the atmosphere, including clouds, and reradiated back to Earth. This is called the greenhouse effect. 

• The glass walls in a greenhouse reduce airflow and increase the temperature of the air inside. Analogously, but through a different physical process, the Earth’s greenhouse effect warms the surface of the planet. Without the natural greenhouse effect, the average temperature at Earth’s surface would be below the freezing point of water. Thus, Earth’s natural greenhouse effect makes life as we know it possible. However, human activities, primarily the burning of fossil fuels and clearing of forests, have greatly intensified the natural greenhouse effect, causing global warming.
  

IPCC suggests that the atmosphere with its GreenHouse Gasses GHG, mainly water vapour and CO2, acts like the window of a conventional Green House GH, "but through a different physical process".

IPCC concludes that since a  GH gets very hot inside (because the window prevents convective heat transfer), the Earth will warm from a marginal increase of GHG ("through a different physical process"). 

But that is Penguin Logic disguised by the clever use of the terminology of GH and GHG, suggesting that it is the same thing, while in effect it is "through a different physical process".

So what is then this "different physical process"? Right: it is convection (combined with evaporation/condensation). So what heats a GH (absence of convection) is precisely what

is present in the atmosphere = Penguin Logic.

In previous posts a model for the "different physical process" is discussed, suggesting that climate sensitivity may very well be much smaller than what IPCC alarmism suggests.  This is accordance with Roy Spencer's new book: The Great Global Warming Blunder: How Mother Nature Fooled the World’s Top Climate Scientists. And also to Roger Pielke's criticism of Kevin Trenberth's analysis of the Global Energy Budget with 0.9 Watts/m^2 (0.26% of total insolation) seemingly mysteriously disappearing. 

The following different aspect of Penguin Logic is also employed by IPCC alarmists: Since Stefan-Boltzmann's Black Body Radiation Law is a mystery based on statistics of quanta, as much a mystery as entropy based on statistics of molecular chaos, it can be used very effectively  in any argument, because nobody wants to question it and thereby risk giving the impression of not understanding the mystery...It is smarter to pretend to understand black-body radiation and its alarming message...but misunderstanding may be costly... 

• No one knows what entropy is, so if you in a debate use this concept, you will always have an advantage. (von Neumann to Shannon)
  

You can here trade "entropy" for "black body radiation". Compare with the knol Black Body Radiation.

Also compare with the recent article The Greenhouse Gas Theory Under a Cloud  by Jeffrey A. Glassmann concluding: 

• The IPCC willfully ignored the importance of the interaction between the sun and clouds probably to suit a pre-conceived agenda supportive of the man-made greenhouse gas theory.
  

PS Svante Arrhenius not only initiated AGW alarmism, but was also

• actively engaged in the process leading to the creation in 1922 of The State Institute for Racial Biology in Uppsala, Sweden, which had originally been proposed as a Nobel Institute. Arrhenius was a member of the institute's board, as he had been in The Swedish Society for Racial Hygiene (Eugenics), founded in 1909. Swedish racial biology was world-leading at this time, and the results formed the scientific basis for the Compulsory sterilization program in Sweden.
  

The Incorrect Postulate of Climate Alarmism

The basic postulate of IPCC climate alarmism is the relation dQ = 4 dT connecting radiative forcing dQ to global warming dT, with dQ = 4 Watts/m^2 from doubling of CO2 giving a climate sensitivity or global warming of dT = 1 C, which is inflated to 1.5 - 4.5 C by feed back. 

See Climate System Modeling by Kevin Trenberth.

The relation dQ = 4 dT comes from Stefan-Boltzmann's Radiation Law, which cannot be disputed as such.

However, the application of the Radiation Law by IPCC to motivate that dQ = 4 dT with dT the warming of the surface of the Earth, can be disputed. This is what I do in the previous posts on Climate Sensitivity and in the related article A New Approach to Climate Sensitivity with a model study indicating instead a basic climate sensitivity of  0.15 C without feed backs. 

The resaon the Radiation Law does not determine the temperature of the surface of the Earth to its value of 15 C, is that the Earth is one part of the coupled Earth-atmosphere system with radiation exchange between the parts.  The Radiation Law determines the temperature of the surface of the system, the stratopause, to 0 C, but not the Earth surface temperature. 

Comments are wellcome.

Climate Sensitivity 6: The SuperFerry

Global Climate is like a SuperFerry powered by radiative forcing  Q = 273 Watts/m^2 from the Sun, and radiating back the same to outer space from the top of the stratosphere at T = 273 K = 0 C, according to Stefan-Boltzmann's Radiation Law

                                                     Q = c TTTT .

You don't easily change the trajectory of a SuperFerry, but is it easy to change Global Climate?

Is Global Climate sensitive to changes in radiative forcing? If we remember a tiny bit of Calculus, we may get the idea to differentiate Stefan-Boltzmann's Law to get 

                             dQ = 4 c TTT dT = 4 Q/T dT = 4 dT .

Beautiful! You can now say that if you change radiative forcing by 4 Watts/m^2 , roughly 1% of

the incoming/outgoing 273 Watts/m^2, then dT = 1 Kelvin K (or 1 Celsius C). See Climate System Modeling by Kevin Trenberth.

You have just derived the basis of IPCC climate alarmism: 1% change of forcing is small, but 

a corresponding 1 C of global warming is alarming, in particular if you combine it with various positive feed backs to inflate it up to 4.5 C. The alarm clock sounds because the radiative forcing from doubling CO2 in the atmosphere is, guess, about 4 Watts/m^2. 

Voila: A small extra radiative forcing dQ = 4 Watts/m^2 from CO2 threatens to destroy human civilization by global warming with dT = 1.5 - 4.5 C.

As further support, the formula dQ = 4 dT is fed into a Climate Model in two ways: The Sea Surface Temperature SST is increased by 1 C, and the radiative forcing by dQ = 4 Watts/m^2, and the Climate Model then with the help of a supercomputer and a bit of positive feed back,

delivers global warming of 1.5 - 4.5 C. 

The formula dQ = 4 dT is presented by IPCC as rock solid undeniable fundamental physics which cannot be disputed by any sane person. Even skeptics like Richard Lindzen (and the Reference Frame) buys this formula but then seeks to compensate by negative feed back to bring down 1 C to the less alarming 0.5 C. 

But wait! We applied Stefan-Boltzmann to the top of the stratosphere, and did not have a chance to use a very important piece of information: 

                                                 SST = 15 C.

And global warming concerns change of SST, the temperature at the surface of the Earth,

which is very different from the temperature at the top of the stratosphere. 

If we think of it, we understand that the atmosphere acts like an insulating medium connecting

surface temperature to outer atmosphere temperature, in a similar way as an isolating window connects the inside of  a room (at say 15 C) to the outside (at say 0 C). 

Now, no sane engineer would seek to determine the inside temperature of a building by using only Stefan-Bolzmann's Radiation Law. A sane engineer would instead use Fourier's Law stating that the heat flow through a window is proportional to the temperature difference inside-outside. 

Using Fourier's Law we understand that 1% change of forcing corresponds to 1% of the temperature difference, that is 0.15 C. 

The sane engineer would thus conclude that, modulo positive/negative feed backs) the climate

sensitivity is 0.15 C, almost a factor 10 smaller than the 1 C of IPCC climate alarmism.

So what do you say?  Or the Royal Academy?

On Climate Sensitivity 5

The basis of IPCC climate alarmism is presented in IPCC AR4 The Physical Science Basis as follows:

• An albedo decrease of only 1%, bringing the Earth’s albedo from 30% to 29%, would cause an increase in the black-body radiative equilibrium temperature of about 1°C, a highly significant value, roughly equivalent to the direct radiative effect of a doubling of the atmospheric CO2 concentration.
  

We have seen in the previous posts 1-4 on the topic that this comes from the formula

                                                 dQ = 4 dT

where dQ is change in radiative forcing and dT corresponding global warming. We have seen that the simple ("undeniable, undisputed")  formula dQ = 4 dT comes out from Stefan-Boltmann's Black Body Radiation Law Q = cTTTT, by inserting Q = 273 Watts/m^2 and T = 273 Kelvin, which fixes the constant c = Q/TTTT.  The formula then follows by differentiation:

                                 dQ= 4 cTTT dT = 4 Q/T dT = 4 dT.

Now 1% change of albedo changes the total radiative forcing of 273 Watts/m^2  by 2.73 Watts,

say 4 Watts/m^2, which gives the alarming global warming of dT = 1 K = 1 C, then elevated to 

1.5 - 4.5 C by feed backs.

So IPCC alarmism claims that we live in a highly unstable surface climate in which human civilization can get destroyed by a 1% change of albedo, or doubling of CO2. 

But the climate does not seem that unstable, certainly the albedo has changed 1% by human activities without any climate catastrophy. 

What is wrong is not Stefan-Boltzmann's Law or differentiation per se. What is wrong is to apply it to the coupled Earth-atmosphere system, where the atmopshere acts like an insulating window connecting the Earth surface temperature of 15 C to the top of the stratosphere at 0 C, just like an ordinary window connects the inside of a room to the outside.

The connection is a combined process of convection-diffusion-radiation-evaporation-condensation, which is not at all described by Stefan Boltzmann's Radiation Law.  No engineer

would model the inside temperature of a house relying only of Stefan-Boltzmann's Law.

So the entire basis of IPCC alarmism appears to rest on a fundamenatlly incorrect application

of Stefan-Boltmann's Radiation Law. If this is true, it is remarkable. And so?

The posts on Climate Sensitivity 1-5 are summarized in the new report A Simple Climate Model.

  

Times Online Climate Debate

Follow the live debate on Times Online: Can We Trust the Outcome of the Climategate Inquiry?

4 pm April 15. Interesting? See also Climategate Whitewash.

What is a Metaphor, in Mathematics?

According to About.com a methaphor 

• is a figure of speech in which an implied comparison is made between two unlike things that actually have something important in common. The word metaphor itself is a metaphor, coming from a Greek word meaning to "transfer" or "carry across." Metaphors "carry" meaning from one word, image, or idea to another, 
• expresses the unfamiliar (the tenor) in terms of the familiar (the vehicle). When Neil Young sings, "Love is a rose," "rose" is the vehicle for "love," the tenor. 

Fine: metaphors are very useful and effective in communication, and poetry of course.

Are there metaphors in mathematics? Figures of speech? Yes, mathematics is full of metaphors:

An equation in mathematics has the form A = B, where B is not identical to A, because the equation A = A is not interesting. Thus an equation A = B rather expresses something like CA = CB where C is a shared aspect while A and B represent something which is different. The basic example is 

                                            2 = 1 + 1

or 

                                         whole = sum of parts (integral of parts per unit step)

like in  

                                      position = sum of increments of position = integral of velocity

                                       velocity = sum of increments of velocity = integral of accelleration.

It is clear that "the whole" as a non-subdivided unity (like 2) is something different than 

"the sum of the parts" (like 1 + 1) because the parts and the summation are visible/present 

in "the sum of the parts" but not in "the whole". One can decompose 2 also as 2 = 0.5 + 1.5.

So "the whole" and "the sum of the parts" share something without being identical. So what

do they share? Yes, they share the number associated with "the whole" (that is 2) and the 

number associated with "the sum of the parts" (that is also 2). Thus 1 + 1 is exactly "as big as"

2, but 1 + 1 carries an additional structure (parts and summation), which is not visible when looking merely on the size of 1 + 1.

So mathematical equations are metaphors, and is it then so,  like in ordinary language, that an interesting equation (metaphor) tells us something of interest? Probably.  About the tenor 

or the vehicle? It can probably go both ways, so that something unfamiliar in something familiar gets exposed, or that something unfamilar is made more familiar.

A Fourier expansion of a function is interesting because it reveals "a construction" or maybe

rather "deconstruction" of the given function in terms of elementary functions. Familiar, simple, trivial functions can be deconstructed by Fourier analysis showing that they are not so simple trivial (make the familiar unfamiliar):   

In the other direction,  seemingly complex functions can be constructed from simple Fourier

expansions, like Weierstrass functions (from unfamiliar to familiar):

Brev till Högskoleverket

Jag skickade idag nedanstående brev till Högskoleverket och Univkansler Anders Flodström.

Till Högskoleverket, Universitetskansler Anders Flodström

Härmed anmodar jag Högskolverket att utvärdera matematikutbildningen vid svensk högskola och universitet.

Ingen påstår idag att utbildningen fungerar tillfredställande och att den motsvarar IT-samhällets krav. Effekten är en omfattande förstörelse av resurser. Men ingen är ansvarig, varken matematikprofessorer, didaktiker eller rektorer. Studenterna och svenska samhället får betala priset.

Högskoleverket har ett övergripande ansvar för att upprätthålla en tillfredställande utbildningskvalitet och måste enligt min mening nu träda in och bära detta ansvar, samt efter utredning föreslå åtgärder till förbättring.

Jag har länge arbetat med reform av matematikutbildning och mina ansträngningar finns redovisade på min hemsida inkl kursböcker, studiematerial, debattartiklar, knols, blogg mm.

Jag önskar klart svar huruvida min anmodan kommer att tas upp till behandling.
Naturligtvis är jag tillgänglig för ytterligare information.

Jag har försökt få TeknikDelegationen att förstå frågans allvar, men inte lyckats.

Hälsningar,

Claes Johnson

Prof i Tillämpad Matematik
KTH

Här kommer svaret, prompt:

Hej Claes Johnson,

Du har ställt en fråga till universitetskanslern om behovet att utvärdera matematik vid svenska universitet och högskolor. En sådan utvärdering är planerad att genomföras 2012 enligt den fyra års plan för utvärdering av samtliga universitet och högskoleutbildningar som nu föreligger. 

Med vänlig hälsning

Joakim Palestro
Bitr. Avdelningschef/Deputy Head of Department

Jaja, ingen ko på isen alltså, enligt HSV. Vi kan lugnt låta resursförstörelsen fortgå ett par år till...Enligt HSV med huvudansvar för utbildningskvalitet. Men när gjorde då senast HSV en utvärdering av matematikutbildning och vad sade denna? 

Jo, den senaste utvärderingen gjordes 2005 där utbildningen vid Chalmers/GU sågas med:

• Studentgruppen hävdade att undervisningen i många fall är gammaldags.
• Bedömargruppen fick också intryck av att pedagogiskt förnyelsearbete förekommer i liten utsträckning ...
• Lärarna ger intryck av viss konservatism och institutionen av tungroddhet i detta avseende. 
  

Bedömargruppen rekommenderar att

• institutionen verkar för en öppnare attityd gentemot pedagogiskt förnyelsearbete 
• det pedagogiska utvecklingsprojekt i matematik som rönt internationell uppmärksamhet ges möjlighet att utvecklas samt att projektet utvärderas av externa bedömare.
• Närmare bestämt: Vid Chalmers pågår ett omfattande reformprojekt med syfte att ge en helt ny introduktion till grundläggande matematik. Projektet har väckt internationell uppmärksamhet och ett omfattande läromedel som kombinerar matematik, beräkningar och tillämpningar har utvecklats. Den nya undervisningen bygger i stor utsträckning på konstruktiv matematik och innebär därmed en god grund för ett intensivt bruk av numeriska beräkningar med datorer. Genom att också introducera tillämpningar tidigt i studierna hoppas man kunna motivera studenterna bättre än vid traditionell undervisning där studenterna möter tillämpningar sent. Den nya utbildningen lägger stor vikt vid genomförandet av projekt och integrerar datorer i undervisningen på ett naturligt sätt. Bedömargruppen anser att det är för tidigt att dra slutsatser om modellens användbarhet men anser att Chalmers bör utvärdera projektet och skapa förutsättningar för att det skall kunna vidareutvecklas.

Det pedagogiska utvecklingsprojektet var BodyandSoul!  När jag lämnade Chalmers 2007 lades det ner i brist på kompetenta lärare, och sedan dess har utvecklingen varit = 0. Samma sak på andra tekniska högskolor inkl KTH.

HSVs utvärdering 2005 krävde förnyelse, men ingen sådan har gjorts 2010. HSV har inte gjort någon uppföljning. Är det så HSV bär sitt ansvar för kvalitet?

On Climate Sensitivity 4

IPCC climate alarmism with a climate sensitivity/global warming of 1.5 - 4.5 degrees Celcius upon doubling of CO2 in the atmosphere, is based on the following argument:

Stefan-Boltzmann's Radiation Law states that a black body radiates heat Q which scales like the fourth power of its temperature T in degrees Kelvin K, that is 

                                   Q = c TTTT ,

where c is a constant. Differentiation gives 

                                   dQ = 4 c TTT = 4 Q/T .

It is known that the Earth radiates about 273 Watts per squaremeter at a temperature of about 273 K or 0 Celcius C, which gives the crucial relation

                                  dQ = 4 dT  

connecting change of radiation dQ to change of temperature. 

 

IPCC now argues that dQ from doubling of CO2 is about 4 Watts per squaremeter, and thus 

the corresponding global warming dT = 1 C (the same as 1 K). By positive feed back this is then

elevated to 1.5 - 4.5 C. 

The global warming of dT = 1 C is presented as rock solid basic physics which cannot be questioned, because that would amount to violate Stefan-Boltzmann.

To get perspective, let us compare with an even simpler argument: Changing Q=273 with 

say dQ = 2.73 (instead of 4 to make it simple) corresponds to 1% and a corresponding 1% change of T=273 would amount to a global warming of dT of about 3 C. 

This seems too big even to IPCC, but corrected by the marvellous factor 4 from differentiation, it becomes the starting point of global warming with climate sensitivity dT of about 1 C.

But is it scientifically correct to use Stefan-Boltzmann's Law to compute dT =1 C? Or

is it Penguin Logic?

Let's see: The atmosphere acts like an window insulating the Earth surface at a temperature of 15 C from the radiating upper atmosphere at 0 C.  It acts like a window separating the inside of a room at say 15 C from the outside at 0 C. 

But this situation is not described by Stefan-Bolzmann's Law, but rather by the even more fundamental Fourier's Law stating that heat transfer is proportional to temperature difference with a certain heat transfer coefficient.  

Now according to IPCC, doubled CO2 corresponds to 1% increase of radiative forcing, which 

can be translated to a 1% decrease of heat transfer coefficient, that is 1% better insulation, which would require a 1% increase of temperature difference inside-outside to maintain heat balance. But 1% of 15 C is 0.15 C.

The basic climate sensitivity thus appears to be 0.15 C (by Fourier's Law), rather than the commonly presented rock solid 1 C (by Stefan-Boltzmann's Law).

To reach a climate sensitivity of 4.5 C starting from 0.15 C requires a positive feed back factor of 30. What can be the science behind a so large positive feed back factor? IPCC does not give any clue, and nobody else... Maybe  climate sensitivity is about 0.15 C? Barely noticable?

This post is also put up as the knol Climate Sensitivity.

Penguin Logic of Oxburgh

The International Panel set up by the University of East Anglia to examine the research of the Climatic Research Unit lead by Lord Oxburgh of Liverpool did not find anything wrong motivated by the following excuse:

• CRU accepts with hindsight that they should have devoted more attention in the past to archiving data and algorithms and recording exactly what they did. At the time the work was done, they had no idea that these data would assume the importance they have today and that the Unit would have to answer detailed inquiries on earlier work. 
  

Lord Oxburgh and his Panel does not understand that this argument uses Penguin Logic, which is surprisingly popular in particular among scientists, but still is not correct logic of science. 

A result which is not documented cannot be an important scientific result. To say that a result without documentation can be an important scientific result requires Penguin Logic, and that 

is not correct logic of science. Scientists using Penguin Logic are often unaware of doing so and are seldom willing to understand that it is incorrect scientific logic.  

No wonder that the credibility of science and scientists is suffering; Penguin logic is not

logic of science, even if it is used by Lords and Royal Societies.

On Climate Sensitivity 3

Summarizing the previous Climate Sensitivity posts 1 and  2, we have

• The Earth seen as a black body without atmosphere would according to Stefan-Boltzmann's radiation law have a surface temperature 21 times smaller than that of the Sun.
• Assuming the surface temperature of the Sun to be 5700 K (or 5250 K) we obtain a black body Earth surface temperature of 273 K (250 K). Without atmosphere the temperature would be 0 Celcius (-23 C). Not pleasant. Like during a cloudfree dry air night in Sahara.
• With atmosphere (with clouds and water vapour) the Earth surface temperature is 288 K. 
• The upper atmosphere must act like a blackbody and radiate whatever comes in at 273 K (250 K).
• The net insolation to the Earth-atmosphere is 69% of a total incoming radiation of 380 W/m^2 = 262 W / m^2.
• The temperature effect of the atmosphere per unit net insolation, is 15/262 (38/262)
• A radiative forcing of 1 W/m^2 thus can be estimated to give a temperature rise of 0.06 (0.14) C.
• The radiative forcing from doubling CO2 in the atmopshere is estimated to be 2-4 W/m^2, which would give a climate sensitivity of 0.12-0.24 (0.28-0.56) C. 
• IPCC AR claims the climate sensitivity to be in the interval 1.5 - 4.5 C. The IPPC upper bound is about 40 times the above lower bound. The IPPC lower bound is about 3 times the above upper bound. 
• The estimated feed back factor changing the above simple radiation estimate is thus a factor 3 - 40.  

I don´t see IPCC (or anyone) presenting physical mechanisms capable of producing so large feed-back factors (can it be some dark energy popping up?). Concerning the origin of 

the 1.5 - 4.5 interval, note what Wikipedia controled by IPCC writes:

• The standard modern estimate of climate sensitivity - 3°C, plus or minus 1.5°C - originates with a committee on anthropogenic global warming convened in 1979 by the National Academy of Sciences and chaired by Jule Charney. Only two sets of models were available; one, due to Syukuro Manabe, exhibited a climate sensitivity of 2°C, the other, due to James E. Hansen, exhibited a climate sensitivity of 4°C. "According to Manabe, Charney chose 0.5°C as a not-unreasonable margin of error, subtracted it from Manabe’s number, and added it to Hansen’s. Thus was born the 1.5°C-to-4.5°C range of likely climate sensitivity that has appeared in every greenhouse assessment since..."^[7]
  

On the contrary, the fact that the early Earth with a weaker Sun  was not deep frozen indicates that the global mean temperature really is quite insensitive to varying insolation. In particular, global mean temperature (whatever that means) does not vary much over glacial and interglacial periods.  See the recent WUWT post Lies, Damned Lies, Statistics and Graphs..

Compare also A Complete List of Things Caused by Global Warming (if there are any...)

This conforms with the position of Lindzen and Spencer that climate sensitivity is small.

Spencer also gives an argument that you can fool yourself to believing in high climate sensitivity if you notice from measurements only a small energy imbalance between hot and cold years, because the system is never in equilibrium because the insolation varies with changing cloud cover. 

To sum up: We have seen that global mean temperatures can vary under constant radiative forcing, as an expression of the internal dynamics of the coupled ocean-atmosphere system. 

From this observation you can fool yourself (and the World) that a small change in the radiative forcing will have a large effect on global temperatures.  This is what IPCC seems to be doing. 

Mathematically this is is an illposed problem: You are trying to compute a derivative Df(x),

of a function f(x), namely climate sensitivity, with f(x) the temperature as function of forcing x.

But you only know the value of f(x) (+ perturbations) for one value of  x (or values very close to x). Now Df = df/dx where df is change in f and dx is change in x, and if dx = 0 (or very small) then Df is not well defined,  that is Df is illposed. 

Accordingly IPCC puts climate sensitivity in the interval 1.5 - 4.5 (or bigger) ,which is so large that it carries no information of value, except that 4.5 (or bigger) looks scary. It could as well be 0 - ∞ . And the true value seems to be close to 0. While the value ∞ is used in IPCC alarmism.

Note that the usual way of estimating climate sensitivity is to differentiate

Stefan-Boltzmann's Radiation Law Q = c T^4 to get dQ=4cT^3dT, which with dQ = 3 gives 

the commonly  predicted value of dT = 1, that is a climate sensitivity of 1 C, which is the further inflated by positive feed back to 1.5 - 4.5 C.  

But this argument lacks logic because it only focusses on black body radiation, and does not 

take into account that the atmosphere acts as an insulating layer, for which case the above

(simple) computation shows a climate sensitivity of at most 0.3 C. 

On Climate Sensitivity 2

On the Importance of of Black Bodies remind us that according to Stefan-Boltzmann's Radiation Law (heat radiated by a black body is proportional to the fourth power of temperature):

• The ideal black body temperature of the Earth surface is 21 times smaller than that of the Sun, say 5700/21 = 273 K = 0 Celcius.
• Taking variations from albedo and Sun radiation into account, the Radiation Law gives an estimated Earth surface of temperature of  273 - 33 = 240K = -33 C.
• Taking an estimated reduction of emissivity, from "total radiative forcing"  from water vapour and CO2, into account in the Radiation Law, the temperature increases to 288 K = 15 C, which is surprisingly close to the real global mean temperature. 
• Changing the emissivity 1% changes the temperature 0.25%.

But how is now "total radiative forcing" determined? So that the corresponding Radiation Law gives the expected 288K? Probably. 

Is this the way to compute the "radiative forcing" from doubling CO2 to be about 4 Watts/K m^2? Probably. 

Is this the way the corresponding climate sensitivity of 1 C (upon doubling of CO2) is computed? (4 Watts is about 1% of total insolation which gives 0.25% of 273 about 0.7 C temperature increase). Probably.

But in Climate Sensitivity 1 we showed that the Earth with atmosphere does not radiate from the Earth's surface like a black body, because convection coupled with evaporation/condensation changes the heat flux and temperature profile.  

Instead it seems to be the top of the stratosphere which radiates according the original Radiation Law at a temperature of 273 K, which seems close to reality. 

The computation of radiative forcing from CO2 with corresponding climate sensitivity 

0f 1 C, seems to be based on applying the Radiation Law to the surface of the Earth, which 

does not seem to reflect correct physics.  

From where does then the crucial CO2 radiative forcing of 4 Watts/m^2 with its associated

climate sensitivity of about 1 K upon doubling of C02? Climate Audit traces its origins

to the following formula expressing the "radiative forcing" F in Watts/m^2 

upon changing the CO2 concentration to C from a reference value C_0:

                                            F= 5.35 ln C/C_0 ~ 4  if   C/C_0 = 2.

From where does this formula come? Nobody seems to know.  Does the logarithm reflect 

some deep law of physics? And the constant 5.35? In IPCC AR4 2007 a reference 

is made to IPCC 1990 with a reference to Hansen et al  1988 with the following reference to Lacis et al GRL 1981: 

• Radiative forcing of the climate system can be specified by the global surface air temperature change ΔT0 that would be required to maintain energy balance with space if no climate feedbacks occurred (paper 2). Radiative forcings for a variety of changes of climate boundary conditions are compared in Figure B1, based on calculations with a one-dimensional radiative-convective model (Lacis et al, 1981). 

But Lacis does not contain the logarithmic formula, only a sketchy derivation of a 1-d model.

This was so far Climate Audit came in Jan 2007. Any progress since then in the search for a derivation of the formula? The formula that underlies the whole of AGW. 

The very concept of radiative forcing from CO2 is dubious if the Earth surface insolation is 

supposed to be kept constant, since it is this heat which eventually will have to be radiated from the top of the atmosphere,  at about 273 K.  

The Earth surface temperature depends on the convection-evaporation/condensation and radiation through the atmosphere as shown in Climate Sensitivity 1 with vastly different temperature profiles with vastly different sensitivity to varying forcing (e.g. varying insolation). The broken temperature profile with small sensitivity seems to be closer to reality.

The most direct way of estimating climate sensitivity is to consider the 280 W/m^2 

being absorbed by the Earth surface, which is eventually re-emitted from the top of the atmosphere at 273 K while the surface temperature is 288 K.  The temperature sensitivity

total insolation would thus be 15/280.

A radiative forcing perturbation of say 2.8 W/m^2 would then give rise to an increase of surface temperature of 0.15 K. To be compared with the above 0.7 K inflated by feedback to 1.5 - 4.5 K or more by IPCC.