Correct Interpretation of Stefan-Boltzmann's Radiation Law

What is the physical meaning of my formula? I am not sure I know myself. And you?

Stefan-Boltzman's Radiation Law (SB) is commonly written

• Q = sigma T_h^4 - sigma T_c^4 ~ sigma 4 T_h^3(T_h - T_c),

where Q is radiative flow of heat energy from a hot body of temperture T_h to a cold body of lower temperature T_c, and sigma is a certain constant. We here express SB also in differentiated form.

There are two ways to interprete SB as written:

• (1) One-way flow of net heat energy Q ~ sigma 4 T_h^3(T_h - T_c) (differentiated form)
• (2) Two-way circulatory flow of heat energy with a certain net flow (non-differentiated).

Does it make a difference? The formula is the formula and so how can its interpretation be important?

Yes, it is important because CO2 climate alarmism results from a "greenhouse effect" based on (2) with "backradiation" from a cold atmosphere at T_c heating a warm Earth surface at T_h in a circulatory exchange of heat energy between atmosphere and Earth of magnitude ~ 360 W/m2 (with a net flow of 120 W/m2 with T_h - T_c ~ 30 C).

The alarm results from subjecting the 360 W/m2 to a small change, say a 1% change

~ 4 W/m2, which translates into a ~ 1 C change of T_h.

The result is a climate sensitivity of 1 C from a 1% change of the circulating flow. This

"no-feedback" climate sensitivity of 1 C is then augumented to 3 C by feedbacks: Alarm!

Now, 1% is a small perturbation of the circulating flow which thus results in considerable warming of 1 (or 3) C. Alarm from interpreting SB according to (2)!

However, if we instead interprete SB according to (1), then the 4 W/m2 corresponds to a 3% change of the net flow of 120 W/m2, and a 3% perturbation is a no longer a small perturbation.

A 1% perturbation of 120 W/m2 would give a climate sensitivity of 0.3 C = No Alarm!

We see that the interpretation of SB makes the difference between Alarm and No Alarm.

How can we judge which interpretation is the correct one from a physical point of view?

By looking at the derivation of the SB formula. Where do we find it? Well, SB is an integrated version (summing over frequencies) of Planck's radiation law (P) and Planck's derivation of P is based on statistics of quanta, which is difficult to dechiffer and interprete physically because statistics is not physics. Statistics concerns ensembles of physical events and physics does not play with ensembles of events, only with events. In the same way as there is no person identical to Meanvalue-Smith, who you can ask about reactions and opinions. Meanvalue-Smith is a non-physical person with no physical relation to anything and with nothing to say.

A derivation of P and thus SB without statistics, based on deterministic physical wave mechanics, is given in the chapter Computational Blackbody Radiation in our new book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory. This (new) derivation shows that the interpretation (1) is physically correct. There is no circulatory flow of heat energy, because such a flow is unstable.

Get the book and decide yourself between Alarm and No Alarm. You will find that it is necessary to understand the mathematical derivation of a mathematical formula, to properly understand the meaning of the formula. Read and then tell your friends and collegues about your findings.

Compare with the discussion on Science of Doom Understanding Atmospheric Radiation

and the Greenhouse Effect claiming the heat energy radiated from the Earth surface is measured experimentally to be ~ 360 W/m2 (or 390), while acknowledging that the flow of heat energy is calculated from SB: Q = sigma T^4 with a background temperature of 0 K by measuring the surface temperature T.

The instrument reading of 360 W/m2, is thus incorrectly interpreted as a reading of a real physical flow of heat energy of 360 W/m2, by letting the instrument calculate the flow of energy from measuring the temperature, using a physically incorrect interpretation of SB.

This shows that readings of experimental instruments must be interpreted with care, and that the mathematical theory/theorem behind an instrument design must be understood to allow a correct interpretation of instrument readings. Proper understanding of the proof of the theorem is then necessary to secure a correct interpretation of the meaning of the statement of the theorem.

IR detectors or sensors used in IR cameras are sensitive to the frequency of the incoming radiation, from which the emission temperature is calculated (using Wien's displacement law) and from the emission temperature the emitted radiation is calculated (by SB).

Thus frequency is measured and radiated energy is calculated by certain formulas.

Climate Feedbacks with Nothing Real to Feed On

Without anything real to feed on because of deep snow, deer are now starving to death...

IPCC climate alarmism is based on a climate sensitivity of 3 C from doubled CO2, presented as the result of feedbacks starting with an initial value of 1 C.

In a survey of IPCC climate science, (former) IPCC scientist Judith Curry has now come to the basic question of Climate Feedbacks:

• Everybody talks about climate feedbacks, but what are they, really? And where did the expression ΔTs = λRF actually come from?
• After two decades of wrestling with this issue, I’m not sure how useful the concept of “feedback” is in the context of the climate system.
• We already saw what kind of trouble we can get into on the thread on CO2 no feedback sensitivity, which is supposed to be the easy part of the problem.
• The problem flat out isn’t linear, and attempting to do a nonlinear control theory analysis is pretty hopeless, as illustrated by the Aires and Rossow paper.
• At best, it seems like the concept is useful as a conceptual aid in thinking about a complex system. Various metrics like ΔTs = λRF or the partial derivatives may have some use in comparing climate models with each other or with observations, but it may not say much about feedback.
• So is this concept useful? If not, can it be salvaged?
• Or are there better ways to try to understand the whole system, something from dynamical systems theory, entropy extremals, etc?

We read that Curry poses questions but we see nothing in the direction of answers.

Curry asks the logical question: If now both the sign and magnitude of feedbacks are

impossible to determine, why was the concept introduced at all?

Because it served IPCC climate alarmism, of course, but there is one important element to understand: Feedbacks need something to feed on, an initial perturbation which can be magnified by positive feedback. So what was then the initial perturbation and how could it be identified by IPCC if nothing else could?

The answer is given in my recent post Definition vs Axiom and Consensus in Climate Science

showing that the initial value to feed on by IPCC is stated to be 1 C, referred to as no-feedback climate sensitivity.

So how is then the initial value of 1 C as no-feedback climate sensitivity determined? By experiments? No, that is impossible. By a theory starting with some assumptions which can be verified? No, nobody knows such a theory.

What remains is to take 1 C as a definition of no-feedback sensitivity to be computed by a

direct application of Stefan-Boltzmann's Black-Body Radiation Law with certain data ("radiative forcing" of 4 W/m2), which invariably gives 1 C.

The advantage of a definition is that full consensus can be reached: It is pointless to question if there are 100 centimeters on a 1 meter. It is pointless to question a no-feedback climate sensitivity of 1 C computed from Stefan-Boltzmann's Law with certain data. That would be like questioning that there are 200 centimeters on 2 meters.

IPCC thus can safely state that there is full consensus about a no-feedback climate sensitivity of 1 C, because it is a definition.

So, a definition is wonderful in the sense that full consensus can be reached as concerns its validity. But the full consensus and absolute truth of a definition does not come without a serious drawback: A definition says nothing about reality.

If we understand this, we understand that the IPCC feedbacks have nothing real to feed on, and

thus cannot say anything about any reality. Curry has understood this, maybe. Anyone else?

For example, what about Lindzen and Spencer? Are they happy to twist, like IPCC, a definition into a potentially alarming physical fact of 1 C, and then have to argue that negative feedback can diminish it to a harmless 0.5 C, using an argument that can easily be questioned? Is this clever? Is it science?

It must be possible for a scientist to understand if a certain statement is a definition, which is true by its construction independent of any reality. Or if it is a statement about reality which may be true or false depending on the reality and therefore can be questioned, because perceptions of reality can differ and thus possibly prevent full consensus.

Why Students Fear the New

From the movie Hets (Torment) 1944, after a screenplay Ingmar Bergman.

KTH-gate concerns an undercover operation in the name of students to prevent BodyandSoul to be used in the new Bachelors program in Simulation Technology to start at KTH in the Fall 2011. Students were stimulated by the School of Engineering Sciences to approach the President of KTH and media with a protest against BodyandSoul in order to "save new students from the dangers of BodyandSoul".

The fact that BS contains some analysis of mathematical models used in climate science, was then used as a pretext, because in Sweden climate hysteria rules, to stop the reform of BS. Students never protested against the old trivial numerics course of little relevance, only against the new non-trivial course of high relevance.

How can we understand that students protest against the new and relevant and support conservation of the old and non-relevant, rather than the opposite as the natural expression of a youthful drive to reform?

How can we understand that older students suddenly become very concerned about the well-being of younger students? That older students want to protect younger students from new material, which the older students have not met and thus cannot judge?

My understanding is that this is a consequence of the fear transmitted to the students from the educational system:

• fear of failing in the studies,
• fear of not getting a job after the studies,
• fear that the younger students may learn new more useful material
• fear to miss something essential of the old when replacing it with the new.

The fear is enforced upon the students by the system with the motivation that it will help the students to perform well and succeed with the examinations.

The fist message by the math teacher is that students who fail in math will fail with everything else in life as well. The math teacher sends this message to inspire the students, knowing very well from experience that half will fail in the math exams, despite the inspiration.

A drawback of fear is that it produces adrenaline which blocks the mind. Another is that students are pushed into a conservative attitude viewing novelties as a threat to be met by resistance, rather than as a possibility to find a place in society to be met with enthusiasm.

I believe that the student engagement in KTH-gate can be understood from this perspective.

A good (non-scared) teacher can help students to open their minds to the new without fear. A bad (scared) teacher does the opposite.

The Ipad Effect and BodyandSoul

Having acquired an Ipad, and used it for a couple of days, I have become convinced that the Ipad Effect will have a huge impact on education on all levels.

This is good news for the BodyandSoul mathematics education reform program, since it is geared to become an Ipad App.

In this perspective the action at KTH to stop BodyandSoul, described as KTH-Gate, seems even more ridiculous than before. It would be the same as preventing new students at KTH to have access to the Ipad and its booming industry of Apps and Accessories.

KTH at the Fork

The Royal Institute of Technology KTH (in the service of humanity, for the society of tomorrow) is wrestling in agony under the pressure of the new age of the computer demanding changes in engineering education, in particular a reform of the basic mathematics education setting the frame for the entire education.

During this fall parts of the BodyandSoul reform program has been tried out in the 2nd year course Numerical Methods II as a test of functionality for the new Bachelors program in Simulation Technology planned to start in the Fall 2011.

The traditional system has met the demands of modernization in BodyandSoul with a relentless

oppression, which I have described as KTH-Gate in previous posts.

In short, the School of Engineering Sciences SCI (math, mechanics, physics) buying the course from the School of Computer Science and Communication CSC, has used the course

to kill the new program in Simulation Technology, using dirty techniques far outside rules of academic dispute, as told in KTH-Gate: The Story.

So is the deed completed? Has Simulation Technology and BodyandSoul and modernization of mathematics education been prevented to enter between the Cerberus dogs (hounds of Hell) protecting the impressive brick buildings of KTH from exterior influence?

Well, this is the question now pondered by the teachers of CSC behind Simulation Technology,

teachers which have been harassed by SCI all through the numerics course.

KTH has formally decided to start Simulation Technology in the Fall 2011, the brochures to attract students are out with applications to be submitted in April. What is missing is the formal decision of the CSC teachers to take on the responsibility to run the program.

But the teachers are hesitating: Is it worth risking physical and mental health to run the program under a continued subversive artillery from SCI?

Maybe not. But as an independent observer, you probably ask if there are no responsible persons at KTH, like the President and the Dean of the Faculty, with responsibility to both students, teachers and society, to guarantee that KTH functions properly.

Yes, the President and the Dean have this responsibility.

But the President says nothing, and the Dean says nothing. And saying nothing means doing nothing. They watch an auto-immun reaction with one part of KTH eating another, without lifting a finger. The President describes his inaction in Questions to the President from Media.

Whatever happens, and whatever decision the teachers of Simulation Technology will take, KTH-Gate is not over. During my entire academic career I have not seen anything worse, and I have seen quite a bit. Modernization of engineering education is necessary and not even Kerberos dogs can prevent it.

How to Kill a Sky Dragon by Mathematics

Our new book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory is topping Amazon eBook lists. The paperback version will appear after Christmas along with radio and TV presentations.

The message of the book is that the so-called atmospheric Greenhouse Gas Effect GGE, presented by IPCC as the scientific basis of CO2 alarmism, lacks sound mathematical and physical rationale.

My role in the team of authors is to shoot with the weapon of mathematics at the heart of climate science consisting of the two chambers

• blackbody radiation: transfer of heat energy by electromagnetic waves
• thermodynamics: interplay of heat energy and kinetic/potential energy under gravitation.

GGE is claimed to result from a small change of the atmospheric trace gas CO2 (from 0.028% to 0.056%) capable of changing the heat transfer between the Earth Surface ES and the Top Of the Atmosphere TOA and causing warming of ES of 2 - 4.5 C.

GGE thus concerns substantial change of ES temperature under a very small perturbation of the radiative transfer properties of the atmosphere connecting ES with TOA. GGE as

a mathematical/physical mechanism is thus unstable, in the sense that a small cause gives a big effect: a small change of an atmospheric trace gas can change global climate.

To change something small into something substantial, it is necessary to multiply the small with something big. To this end GGE has invented the concept of "backradiation" with ES emitting 390 W/m2 out of which 340 W/m2 is received from TOA as re-emitted radiation from ES, with 340 W/m2 = 100% of gross (total) incoming radiation from the Sun.

"Backradiation" thus gives GGE a major energy flow of 340 W/m2 to operate on, namely a circulating flow of energy (equal to gross incoming energy) transferring energy from ES to TOA and back again. GGE now says that a trace gas changing the radiative properties of the atmosphere by say 1% operating on the circulation of 340 W/m2 can give rise to a change of 3.4 W/m2 which by Stefan-Boltzmann's radiation law can be connected to about 1 C of global warming. This gives the basic axiom of IPCC CO2 alarmism of a climate sensitivity of 1 C upon doubling of atmospheric CO2, which then is inflated to 2 - 4.5 C by imagined feedbacks of factors 2 - 5.

The basic killer shot of my contribution to the book, is a mathematical analysis of blackbody radiation showing that "backradiation" is unphysical, because it corresponds to an unstable process which cannot be realized. The result is that the radiative transfer of heat energy between ES and TOA consists of a net transfer of about 120 W/m2, about 1/3 of the fictitious

circulating flow of 340 W/m2. This reduces the basic climate sensitivity to less than 0.3 C,

which cannot be used to create alarm, because feedback factors of size 10 lack any scientific rationale.

It thus appears to be possible to kill the Sky Dragon by one shot (my blackbody article). If that does not turn out to be enough, depending on the audience, another shot can be launched at an unprotected flank of the Dragon by recalling the fact that climate results from a combination of thermodynamics under gravitation and radiation, and that GGE is essentially based on radiation alone (my thermodynamics article). The second shot says that not only the magnitude of climate sensitivity is unclear but also its sign: It is conceivable that more CO2 can cause some (small) cooling.

I believe that the above shots can be effective in coming TV and radio presentations, because convincing mathematics is hard to deny, for both alarmists and skeptics.

But even if the Sky Dragon is afraid of mathematics, because alarmistic Dragons have limited intellectual capacity, what the Dragon fears the most is, yes cold weather, and the record lows now hitting Europe is turning the Dragon into a freezing lame duck which will not likely survive the winter. And what we have seen is only the beginning according to one of the slayers, Piers Corbyn.

An analogy in economics presents itself: Imagine a national economy with a large scale circulation of money from high taxes and large government subsidies of the order of trillions

of dollars, and imagine a broker charging the tiny percentage say 0.0o1%, with a net profit

of billions of dollars. Nice, right? But what about the stability of an economy with unlimited circulation of money, of fictitious money without any real value? Any clue?

Definition vs Axiom and Consensus in Climate Science

In mathematics and physics it is essential to understand the difference between a definition

and an axiom or assumption. The statement that 100 centimeters equals 1 meter, is a definition

which is true by its own inner logic, and which cannot be disputed. The statement that a certain stick is 100 cm may be true or not true, depending on the actual length of the stick in question.

An assumption may be true or false, while a definition always is true. Full consensus can only

be reached for definitions.

However, to confuse definition and axiom is a trick that is sometimes used to confuse opponents in a discussion. The more stupid your opponents are, the better it works if you decide to use this trick.

An example: No Feedback Climate Sensitivity, as the rise of global temperature upon doubling of atmospheric CO2, is claimed to be 0.25. This mean that the warming would be 1 C upon radiative forcing of 4 W/m2 associated with doubled CO2. This is well described by Judith Curry in threads on CO2 no-feedback sensitivity.

Is this a definition or a fact? Well, it is a definition because the number 0.25 comes from Stefan-Boltzmann's Law and it is assumed that this law is to be used and this gives 0.25.

This explains why also skeptics like Lindzen and Spencer agree on a No Feedback Climate Sensitivity of 0.25. In fact everybody agrees on this in complete consensus, because it is a definition. It is pointless to argue about a definition, but one should remember that a definition does not say anything about reality, about the length of specific stick for example. A definition

is always true, cannot be false by its construction, and thus is empty of content.

But now comes the trick: Since there is (complete) consensus about a Climate Sensitivity of 0.25, one can fool people to believe that this says something about real global climate, which can be taken as a starting point when adding various feedbacks to get an IPCC best estimate

of climate sensitivity of the size 1 sending an alarm of a global warming of up 4 C.

So by twisting a definition into a physical fact, one can obtain what seems to be a statement about physical reality, which cannot be denied. Clever, but it is a "trick", which you see through if you do not want to fool yourself.

The master of twisting a definition into a physical fact was Einstein, who based (special) relativity on the constancy of the speed of light (in vaccum), without ever telling if he meant it to be a definition or a statement about physics, something which physicists still don't know for sure, and which is still causing a lot of confusion.

So remember, if there is complete consensus about a statement expressed in physical terms, as IPCC claims to be the case as concerns a No Feedback Climate Sensitivity of 0.25, then the statement is a definition which says nothing about physics. It is not to be expected that IPCC will be able to understand this, but what about Lindzen and Spencer?

Recall:

• Penguin Logic of Greenhouse Gases.
• Is One Dollar = One Euro?

Cause-Effect vs Finite Precision Computation and Stability

In recent work I have explored the role of finite precision computation, in physics in analog form and in mathematics in digital form as models of physics, typically as differential equations of the form

• A(U) = F

where F is given forcing (input), A is a differential operator and U the corresponding system state (output).

In physics the input generates the output by some physical mechanism, viewed as some form of

analog computation, which is represented mathematically by digital computation with the output U being computed from the input F in computational solution of the differential equation.

The stability of the computational process, in analog physical or digital mathematical form, reflects how perturbations of input transform through the computational solution process to perturbations in output. If small perturbations of input transform to small perturbations of output, then the process is stable, while if small perturbations in input may result in large

perturbations in out, the problem is unstable.

As a basic example let us consider Newton's 2nd Law

• M dV/dt = F

where M is the mass of a particle moving with velocity V(t) under the action of the force F(t)

as functions of time t. With F(t) input and V(t) output this is a stable problem, since the solution process corresponds to integrating F(t), which is a stable summation process.

However, if we turn data around and view V(t) as input and F = M dV/dt as output, then the

process is unstable, since differentiation is unstable because it involves division by the small

quantity dt: Small perturbations in V(t) are magnified by the large factor 1/dt in the computation of dV/dt.

We now connect to the old question of cause-effect in a relation between two entities F and

U connected by an equation A(U) = F. The question is what is the cause and what is the effect,

F or U?

If the problem A(U) = F with F input and U output is a stable problem, then it is natural to view F as the cause and U the effect: The effect will then be essentially the same under small perturbations of the cause. On the other hand if it is an unstable problem, then it is not natural to view F as the cause and U as the effect, since small variations in F may give vastly different effects.

This argument has led us to identify cause-effect from stability point of view into a new analysis of the physics and mathematics of the 2nd law of thermodynamics and blackbody radiation, as developed in

• Computational Turbulent Incompressible Flow
• Computational Thermodynamics
• Computational Blackbody Radiation.

In the setting of Newton's 2nd law M dV/dt = F, we may thus view the force F as cause and

the velocity V as the effect, but not the other way around.

In climate science a basic problems concerns the relation between global temperature and

level of atmospheric CO2, which with temperature as input and CO2 as output may very well be stable, while CO2 as input and temperature as output may very well be unstable.

A diffusion process like heat conduction is stable with heat source and initial temperature as input and temperature at a later time as output. On the other hand, "backdiffusion" with

temperature input at a later time than output is unstable without cause-effect and thus unphysical. Softening a sharp image in Photoshop into a blurred image by diffusion is a stable

process, while sharpening by "backdiffusion" is unstable.

The same holds for "backradiation" proposed as a mechanism for global warming by "greenhouse" gases, as explained in Slaying the Sky Dragon: Death of the Greenhouse Gas Theory.

Why are Skeptics Skeptical to Other Skeptics?

Our new book Slaying the Sky Dragon: Death of the Greenhouse Gas Effect is topping Amazon

ebook lists, but its has (so far) received little attention from other climate skeptics.

This indicates that climate skeptics are not only skeptical to CO2 alarmism, but also to other

skeptics skeptical to CO2 climate alarmism. It seems as if each skeptic seeks to protect a special domain of skepticism, and that this separatism is more important that unity against the common target of CO2 alarmism. Is this a correct observation, and if so is it desirable to seek a correction?

Is it so that there are so many skeptics of different color, size, background and agenda, that unity among skeptics is impossible?

Skeptics do not even agree in their skepticism to the basic question of the physics of the greenhouse effect. Is it because the greenhouse effect is fiction and there are so many ways to be skeptical to a non-existing physical phenomena? Like skepticism to ghosts which can take a large variety of different forms?

In Sweden the book has been banned by Royal Institutions controling the minds of the loyal citizens of the Kingdom, and is invisible even on skeptical websites. The reason for the ban is that the book contains a mathematical analysis of Planck's model of blackbody radiation and the equations of thermodynamics, which raises questions concerning the so-called atmospheric greenhouse gas effect.

The control of mathematics taken by Institutions is similar to the control of physics by the same by declaring that the Earth will not be permitted to heat up more than 2 C, with UN negotiations under way setting the limit to 1.5 C. This is a firm action taken by in particular EU to control both climate energy budgets and state monetary budgets.

It seems that our free open democratic Swedish society can only exist under a very strict firm steady all encompassing control with uncompromising ban of anything unacceptable.

PS Lubos and The Reference Frame is representative of many skeptics: Instead of focussing on the real scientific issue, which is the nature of the so-called greenhouse gas effect and climate sensitivity, Lubos finds irrelevant aspects outside science to pick on. Why not follow Leibniz and ask if there is something of interest in our book, rather than just trying to find something of little interest to question?

In Search of a Lost Greenhouse Effect

Judith Curry is making a heroic effort to find the physics of the atmospheric "greenhouse effect", which is much talked about but nobody has really seen:

• We need to raise the level of our game in terms of explaining the planetary warming by infrared absorption of CO2 etc. The missing area of understanding seems to be the actual physical mechanism.

In the recent post CO2 No Feedback Sensitivity Curry questions even the very starting point of CO2 alarmism, namely a climate sensitivity of 1 C from a direct application of Stefan-Boltzmann's Law Q = sigma T^4, which in differentiated form with Q ~ 280 W/m2 and T ~ 280 K reads dQ ~ 4 dT and thus gives dT ~ 1 C upon input of "radiative forcing" of dQ ~ 4 W/m^2.

This is along the criticism I have expressed: To take 1 C as a starting point for various feedbacks is not science, because the formula Q = sigma T^4 as a model of global climate is so utterly simplistic: One can as well argue that one should take 0 C as starting point, and then enormous feedbacks would be required.

Curry admits that she does not know the physics ("the actual physical mechanism") of any atmospheric greenhouse effect, and she asks if there is anyone somewhere out there in cyberspace who does. Isn't this strange? Is the greenhouse effect dead? Was it never alive?

Compare with Slaying the Sky Dragon: Death of the Greenhouse Gas Theory (now #1 on Amazon ebook lists).