Size of Backradiation?

In Computational Blackbody Radiation I present and analyze a wave-equation model for blackbody radiation with statistical mechanics replaced by finite precision computation.

The radiative interaction of two blackbodies Body 1 and 2, can in a simplified version of this model be described as a system of the form 

                        dT1/dt = R T2 - R T1 = R (T2 - T1),   dT2/dt = R T1 - R T2 = - R (T2 - T1)

with T1 and T2 the temperatures of the two bodies (or with R T1 replaced by R T1^4 and  R T2 by  R T2^4 to connect to Stefan-Boltzmann's Radiation Law), and R is a radiation constant. Here the term  R T2 in the equation for T1 represents heat absorbed from Body 2 while emitting R T1, and vice versa. 

Adding the equations, we find the balance d(T1 + T2)/dt = 0 and conclude that T1 + T2 stays constant,  irrespective  of the strength R of the interaction. 

This connects to the discussion in the comments to the previous post Thermodynamics of Global Climate 2  about the size of the  "backradiation" from the atmosphere, which connects to the size of R in the model. Clearly, in the model you can assign any value to R, strong or weak  interaction, without affecting the mean value T1 + T2.  

As indicated in the above formulas, one can also view the net exchange R (T1 - T2 ) to work on the difference T1 - T2 rather the absolute values T1 and T2, which may be closer to a reality

of radiation.

The above argument is intended to support to the idea that "circulating radiation" and "backradiation"  is fictional rather than real.

The Royals are Losing Faith

The Royal Society will revise its public statement on climate change, because 

• communications did not properly distinguish between what was widely agreed on climate science and what is not fully understood.

The society's ruling council has responded by setting up a panel to produce a consensus document. Members express:

• ....in any society like this there will inevitably be people who disagree about anything - and my fear is that the society may become paralysed on this issue
• The sceptics have been very strident and well-organised. It's not clear to me how we are going to get precise agreement on the wording 
• some of the previous communications of the organisation in the past were poorly judged.

Will also the Royal Swedish of Academy of Sciences revise its climate statement, or is the Academy already paralysed? Evidence in this direction is given by the lack of answer to my

question concerning the physical basis of the socalled greenhouse effect. Is there no basis?

Listen to the story on BBC 54 minutes into the 3 hour program.

Rubbat Förtroende för Bolincentret för Klimatforskning

Nio professorer verksamma vid Bolincentret för klimatforskning vid Stockholms universitet

skriver i en debattartikeln Rubbat Förtroende för Forskarna i SvD under rubriken Det Vetenskapliga Kunskapsläget:

• Jordens medeltemperatur har ökat med cirka 0,8 grader under de senaste 150 åren. De senaste årtiondenas uppvärmning på cirka 0,5 grader beror med stor sannolikhet på den ökande halten av växthusgaser. Denna slutsats stöds såväl av beräkningar baserade på grundläggande fysikaliska lagar som på avsaknaden av andra rimliga naturliga förklaringsmodeller.

Forskarna sammanfattar här den vetenskapliga grunden för den alarmism beträffande växthusgasers inverkan på klimatet som Bolincentret representerar, i linje med FNs klimatpanel IPCC.

Låt oss granska dessa klimatalarmismens huvudargument:

1. Med "grundläggande fysikaliska lagar" menas Newton's lagar samt Stefan-Boltzmann's strålningslag, och med "beräkningar" menas klimatmodeller. Men klimatet är en komplex

kombination av många fysikaliska mekanismer och ingen forskare hävdar att de klimatmodeller som används kan förutsäga något om framtiden. Det är tvärtom så att ju mer

grundläggande modellen är, desto mindre kan den beskriva av ett komplext fenomen. I en serie

poster om klimatsensitivitet har jag visat att detta gäller inte minst för Stefan-Boltzmann's grundläggande strålningslag.

2. Med "avsaknaden av andra rimliga naturliga förklaringsmodeller" menas att man bortser från andra möjliga förklaringar, utan närmare granskning. Detta kallas tunnelseende och tillhör inte den vetenskapliga metoden.

När nu Bolincentrets professorer känner sig manade att yttra sig i egen sak, är det anmärkningsvärt att den framförda vetenskapen är så skakig. Detta är väl själva grunden till "Rubbat Förtroende för Forskarna". Men vad händer med Bolincentret om/när förtroendet är rubbat?

Samtidigt meddelas jag att

• Svenska Mekanisters Riksförbund har den tråkiga nyheten att orientera er om att vi blir så illa tvungna att ställa in seminariet den 27 maj avseende Validering av väder- och klimatprognoser.
• Detta orsakat av de få anmälda till detta seminarium.
• Märkligt, då vårt föregående seminarium i närliggande ärende/ämne var mycket uppskattat och välbesökt.

Vid detta seminarium skulle jag granska klimatmodelleringens vetenskapliga grund. Övriga talare var Per Undén, Chef för forskningsenheten Analys och Prognos, SMHIs Forskningsavdelning och Patrick Samuelsson, fil. dr. SMHI, Rossby Centre.

SMHI och Bolincentret är helt koordinerade i sin klimatalarmism enligt IPCC.

Om nu klimatet är mänsklighetens ödesfråga nummer ett, så är "förklaringsmodellen" att det var för få anmälda, inte övertygande, åtminstone inte med vetenskapliga mått mätt, speciellt som en spännande konfrontation mellan synsätt kunde utlovas. Det bör finnas en annan "naturlig förklaring".

För en klimatdebatt som inte ställdes in se Oxford Union Debate on Climate Catastrophe.

Jämför med dagens NYT klimartikel Climat Fears Turn to Doubts...

Eftersom KVA ansluter sig till IPCCs klimatalarmism och därmed ger backup till SMHI och Bolincentret, är det naturligt att fråga sig om förtroendet även för KVA är rubbat? Det är nu hög tid för KVA att revidera sitt klimatuttalande. Eller hur KVA?

Thermodynamics of Global Climate 2

We recall the 2nd Law of Thermodynamics for an atmosphere from the previous post:

                                  dK + dP = W - D,          dE = - W + D + Q,

where dK, dP and dE is the rate of change of kinetic energy K, potential energy P and internal (heat) energy E, W is rate of work, D is the rate of turbulent dissipation and we added a heat source Q. 

Let's put in some numbers from observations:

• Q ~ 250 Watts (per m2) from insolation
• dP ~ 0.01 x 0.65 x 10000 x g = 650 Watts
• average vertical velocity = 0.01 m/s
• average density = 0.65 kg/m3
• average thickness of troposphere = 10000 m 
• dE ~ 0.01 x 0.65 x 10000 x 6 = 400 Watts
• lapse rate 6 C/km

These numbers are compatible with dP = W - D = 650 ,  dE = - W+D+Q = - 400 Watts.

With an isentropic lapse rate of 10 C/km we would have dE = -650 Watts,  and we can thus 

view the input of 250 Watts as being spent on turbulent dissipation, effectively reducing the temperature drop with increasing height.

We sum up: We have formulated a basic thermodynamic model of an atmosphere acting in a cyclic thermodynamic convective process of an ascending/expanding/cooling and descending/compressing/warming flow of air, which is driven by insolation spent on 

maintaining the convection under turbulent dissipation. This model is compatible with observation without any presence of socalled greenhouse gases, and thus suggests that global climate is  is mainly determined by thermodynamics and not by greenhouse gases.

For more details see the article in progress Basic Thermodynamics of the Atmosphere.

Thermodynamics of Global Climate

The atmosphere of the Earth transports the heat energy absorbed by the Earth surface (and lower levels of the atmosphere) from insolation, to higher levels where it is radiated back into space.

The 2nd Law of Thermodynamics  for a gas subject to gravitation but without external heat sources, as formulated in Computational Thermodynamics, takes the form 

                                  dK + dP = W - D,          dE = - W + D,

where dK, dP and dE is the rate of change of kinetic energy K, potential energy P and internal (heat) energy E, W is rate of work and D is the rate of turbulent dissipation. See The Atmosphere as Air Conditioner.

We identify two extreme cases:

• D = 0: isentropic expansion/contraction: dK + dP = W, dE= - W: lapse rate = -10 C/km
• D=W: maximal turbulent dissipation: dK + dP =0, dE =0: lapse rate = 0,

where lapse rate is vertical temperature gradient. The case D = 0 represents a lossless cyclic motion of ascending/expanding/cooling and descending/contracting/warming flow. The case D = W represents a motionless isothermal state maintained by maximal turbulent dissipation. 

The observed lapse rate - 6 C/km rate lies between these extreme cases, connecting 15 C at the Earth surface with - 57 C at the tropopause over a height of 12 km.

In this analysis there is no external heat source and the non-zero lapse rate results from internal  thermodynamics of bouyancy-driven light hot air at the Earth surface which rises under expansion and cooling, combined with cold denser air which descends under compression and heating.  

In particular this analysis shows that a vertical temperature gradient can be maintained without both incoming and outgoing radiation, in particular without any effect of socalled greenhouse gases. 

The above model is compatible with radiative heat transfer with the Earth surface radiating

all incoming radiation into space without interaction with the atmosphere, in particular without interaction with socalled greenhouse gases. 

The model may also be combined with partial heat transfer by evaporation/condensation.

Note that conduction as well as radiation is compatible with a constant lapse rate, without however determining the magnitude of the lapse rate, which can be anything from zero to 

minus inifinity. This is because both conduction and radiation in a layered atmosphere satisfies a heat flow balance law of the form (in a basic case):  

                                         E(z-h) - 2 E(z) + E(z+h) =0,

with  E(z) heat energy  at height z and h is a layer thickness. The effective lapse rate is then determined  by a boundary condition of the form    - c (E(h) - E(0))= Q with c a coefficient of 

conduction/radiation and Q a heat source. Typically  c  would be small, which would define

much more negative lapse rate than observed. 

We learn from this analysis that the 15 C at the Earth surface is not necessarily related to the presence of any socalled greenhouse gases in the atmosphere. Similar conclusions have been drawn in The Thermodynamic Atmosphere Effect, by Heinz Thieme.

Note that scientific evidence (experimental or theoretical) of major effects of greenhouse gases on the Earth surface temperature, seems to be lacking. The evidence put forward consists of differentiating Stefan-Boltzmann's Radiation Law which connects  socalled "radiative forcing" dQ to surface temperature change dT by the simple relation dQ = 4 dT.

However, this evidence is not convincing, to me at least, because  Stefan-Boltzmann's Radiation Law concerns a simple system (one black-body) and not a coupled system of planet + atmosphere with internal temperature gradient.

It is surprising to see large parts of the scientific community including academies of sciences embracing a hypothesis of global warming from atmospheric CO2, without any convincing scientific support. It appears that the mere mentioning of Stefan-Boltzmann's Radiation Law has been enough to annihilate any further demands of scientific evidence. 

This may be a result a 2oth century physics education with both the Radiation Law and  the 2nd Law of Thermodynamics being based on statistical mechanics not understood by anybody. In any case, the acceptance by the scientific community of CO2 climate alarmism without physical basis, needs to be understood and corrected.

I agree with Roy Spencer in The Missing Climate Projections:

• It is time to return to the scientific method before those who pay us to do science — the public — lose all trust of scientists.
  

Compare with IPCC's description of the "greenhouse effect" in FAQ 1.3:

• 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. 
  

The different physical process is thus described as reradiation back to Earth.

But what is the physics of this reradiation, and how big is it? Physics books do not seem to 

give any clue, so where is then the evidence?

The Atmosphere as Air Conditioner

In Atmosphere as Air Conditioner we argue than a planetary atmosphere partly acts like an air conditioner or refrigerator, transporting heat from the  planet surface to the top of the atmosphere in a cyclic thermodynamic process of air rising-expanding-cooling  and descending-compressing-warming. The "engine" driving this process is gravitational bouyancy forcing hot light air to rise and cool dense air to descend. Ocean circulation is driven similarly.

We identify two extreme hydrostatic base solutions depending on height, one isentropic with 

zero turbulent dissipation and with constant maximal temperature gradient/lapse rate, and one with maximal turbulent dissipation and with constant temperature/zero lapse rate. 

We observe that the real lapse rate of - 6 C/km lies between these extremes of -10 (dry adiabatic lapse rate) and 0.

This analysis indicates that the main aspect of global climate of a temperate Earth surface

of 15 C connected to a tropopause at  - 55 C, results from thermodynamics and 

not radiation. 

The lapse rate in the troposhere is - 6 C/km, and changes sign in the stratosphere to reach 

0 C at the stratopause thus with a climb of 55 C, with the stratosphere being heated by ozon absorbing radiation from the Sun. Without this effect the Earth surface temperature might have been 55 + 15 = 70 C. The ozon in the stratosphere thus may have a cooling effect on the Earth surface.

The 0 C in the stratopause fits with blackbody radiation, which is also the effective blackbody temperature of  an Earth without an atmosphere. 

An Earth with atmosphere without radiation can thus be expected to be at 70 C. The absorption in the stratosphere by the ozon appears to have a major cooling effect, while the warming effect of a small amount of CO2 in the troposphere may be small.

We make a connection to the Joule experiment of a gas expanding-cooling under warming from turbulent dissipation, which we analyze in Mathematical Simulation Technology, Chap 166 The Secret of Thermodynamics. 

 

Computation of Atmospheric Lapse Rate

To compute the lapse rate (temperature drop with height z) of an atmosphere, we start from the  2nd Law of Thermodynamics in the form presented in Computational Thermodynamics:

                                                c_v dT + P dV     non-negative

where c_v is specific heat under constant volume, which combined with the differentiated form PdV + V dP = R dT of the gas law PV =RT gives 

                                                                   (c_v+R) dT - V dP    non-negative.

Vertical hydrostatic balance is expressed by dP =  - g Rho dz with Rho = 1/V density, from which follows that 

                                                                     dT/dz + g/C_p   non-negative,

where C_p = (c_v+R)/V Rho = (c_v+R)/mass.  The lapse rate is thus bounded below by - g/C_p, which for a dry Earth atmosphere equals  - 10 C/km. 

The observed lapse rate is dT/dz = - 6 C/km, which is partly (because there is also

evaporation/condensation) an effect of turbulent dissipation with c_v dT + P dV  strictly positive: Rising hot air expands under temperature drop which  is counterbalanced by turbulent dissipation reducing the drop. 

The Joule experiment discussed in the previous post, concerns precisely this effect. We have shown that we can simulate this effect by computing turbulent soutions of the Navier-Stokes equations, and thus it should be possible to similarly compute the effective lapse rate in the 

Earth Atmosphere.

In the ideal case of isentropic expansion the 2nd Law is satisfied with equality, from which follows 

                                             c_v dT + R T dV/V = 0.

This gives 

                             T V^a = constant

where   a = R/c_v, which determines P and V (or Rho) as functions of z through T(z).

Your Second Climate Model

The thermodynamics of global climate is described by the Navier-Stokes equations, for compressible flow of air in the atmosphere, and incompressible variable-density flow of water in the oceans.

For the atmosphere there are two possible basic hydrostatic equilibrium states depending on a vertical coordinate, which can be taken as a starting points for climate dynamics:

• (i) constant temperature (T = 261 K, zero lapse rate)
• (ii) isentropic with linear temperature profile (T = 302 K, constant lapse rate 10 C/km),

as shown in On Atmospheric Circulation. Fitting these solutions to data as in On Maximum Entropy Profiles by Verley and Gerkema, Journal of the Atmospheric Sciences, Vol 41, 2004,

pp 931-937, one obtains the ground temperatures given above, with (i) too low with too small lapse rate and (ii) too high with too large lapse rate, as compared to the observed T = 288 with lapse rate 6 C/km.

Real atmosphere dynamics involves turbulent vertical convection, which can be viewed as increasing (i) and decreasing (ii): Rising hot air cools by expansion, and turbulent dissipation heats. This directly connects to the computational simulation of the Joule experiment in The Secret of Thermodynamics in BodyandSoul Mathematical Simulation Technology, chapter 166.

We learn that the observed ground temperature of 288 K and the observed lapse rate

of about 6 C/km, are compatible with a flow model without "heat-trapping greenhouse gases".

The same argument explains the high temperature on the surface of Venus as a primary effect of high pressure thermodynamics and not greenhouse gases. Compare The Reference Frame: Venus with the crucial observation:

• The cause of most of the temperature gradients is mechanical (lapse rate) rather than infrared-radiative.

This gives perspective on the role of greenhouse gases in an atmosphere. You may compare

the above model with the climate alarmism basic model: Stefan-Boltzmann's Radiation Law.

Which model do you think best describes the physics?

Svenska Mekanisters Riksförening om Klimatsimulering

Nästa vecka håller jag ett föredrag med titel "Är klimatsimulering möjlig" vid Svenska Mekanisters Riksförenings seminarium om "Validering av väder- och klimatprognoser".

Övriga föredraghållare är Per Unden som talar om "Vetenskaplig uppbyggnad av väderprognosmodeller" samt Patrick Samuelssson  om "Modellutveckling av regionala och globala klimatmodeller", båda från SMHI.

Förmodligen står Unden och Samuelsson bakom IPCCs klimatalarmism, som högt prisas på SMHIs hemsida,  där vi också läser:

• Atmosfärens sammansättning påverkas av utsläpp av växthusgaser. Att detta i sin tur har effekter på klimatet är grundläggande fysik. I enlighet med teori visar mätningar och modellering att den långsiktiga temperaturhöjningen under det senaste seklet är nära kopplat till ökningen av växthusgaser i atmosfären. Sammantaget ger forskningen en konsistent bild av människans effekt på klimatet.
  

Vi ser att SMHI hänvisar till "grundläggande fysik" vilket närmare bestämt är Stefan-Boltzmann's strålningslag, vars tillämplighet i sammanhanget jag just nu på denna blogg diskuterar med en expert på grundläggande fysik, Ulf Danielsson. Svar från Ulf förväntas inkomma inom kort.

Som motpol till IPCC, SMHI och KVA, pågår just nu  Climategate 2010, 4th International Conference on Climate Change med live sändingar av bla McIntyre, Lindzen, Spencer och Monckton. Jag antar att SMHI följer detta med största intresse.

Lindzen påminner om att man inte kan bygga klimatpolitik på simplistisk fysik eller på trivialiteter  som att CO2 ökar och temperaturen ibland stiger något och därför CO2 styr temperaturen.

Är då klimatsimulering möjlig? Kanske om simulering av turbulent strömning är möjlig, vilket

jag tillsammans med Johan Hoffman visar i Computational Turbulent Incompressible Flow.

Som en inledning till mitt föredrag kan man läsa Your First Climate Model, där jag motiverar

varför IPCCs uppskattade klimatkänslighet om 1.5 - 4.5 C saknar fysikalisk grund, samt 

FEniCS as Climate Simulator inkl diverse bloggposter om climate sensitivity.

Det är stor skillnad mellan simplistisk fysik och grundläggande fysik. Om de blandas ihop

blir det konstig vetenskap, vilket inte är ens KTHs devis.

Man kan också läsa om klimatmötet i Chicago: The Inconvenient Facts about Global Warming.

Vad Säger en Fysiker om Klimatvetenskap?

Strängfysiker Ulf Danielsson, som vi ofta hör i medierna, meddelar oss vid Det Stora Klimatgrälet på Engelsbergs Bruk via Axess TV att vi skall lita på klimatvetenskap och 

vetenskapliga akademier som KVA i synnerhet. Så gör Ulf Danielsson själv och har ingen egen 

uppfattning i frågan, eftersom han inte kan ha det eftersom han inte är klimatvetenskapsman

och därför inte alls kan greppa frågan, trots att titeln på Ulfs föredrag är

• Det räcker inte att lyssna på klimatvetenskapen - man måste förstå också.

Men hur går detta ihop? Är det verkligen omöjligt för en fysiker att förstå något av jordens värmebalans och det vetenskapligt tveksamma i att dra långtgående slutsatser från Stefan-Boltzmann's strålningslag angående ett komplext klimatsystem som inte bara innehåller strålning? Berör inte detta själva kärnan av en fysikers kompetensområde?

Och hur skall vi kunna lita på ett KVA som inte motiverar sitt ställningstagande angående klimatpåverkan av CO2 med annat än tystnad? 

Ulf säger sig vara medlem av KVA och stå bakom KVAs uttalande, dock utan att själv kunna bedöma om det är riktigt. Är det så vetenskap skall bedrivas? Genom auktoritet?

Skulle vara intressant att höra någon reaktion från Ulf, annat än tystnad.

Ulf svarar i kommentar nedan: Ulf säger sig ha redovisat en uppfattning, att det finns ett stort problem med förbränning av fossila bränslen, dvs Ulf verkar instämma  i IPCCs klimatalarmism. Ulf påstår sig vara fullt kapabel till generella bedömningar av forskningsläget (vad gäller klimatvetenskap antar jag),  men säger sig inte veta så mycket om klimatmodeller och måste därför luta sig mot andras forskning. 

Frågan är väl då varför Ulf känner sig manad att säga någonting om klimatvetenskap i sin roll som fysiker. Skall bli inressant att höra hans svar på min vetenskapliga följdfråga.

Svaret kopplar till den vidare frågan om varför samhället betalar vetenskapsmän med skattemedel? Är det för att vetenskapsmän förväntas veta något som är viktigt för samhället, på samma sätt som olika yrkesmän förväntas kunna utföra olika för samhället viktiga sysslor? Eller har vetenskapsmän en annan funktion? Vad säger en strängfysiker?

Jo, Ulf hänvisar till IPCCs AR4  utan att själv ta ställning till huruvida vad som där påstås kan vara riktigt. Jag försöker i mitt svar få Ulf att betrakta frågan om klimatkänslighet som en fråga om fundamental fysik som ligger inom en fysikers kompetensområde och som en fysiker bör kunna uttala sig om.

Jämför gärna med analysen på Reference Frame av fördelen med att som akademiker hålla på AGW, för tillfället...

Your First Climate Model

What would be the first climate model to consider? If you take an engineering approach 

to global climate? Well, one idea is to start from an observation of the (global mean) temperature distribution through the  atmosphere, starting at 15 C at the Earth surface, dropping to -55 C at the tropopause and climbing back to 0 C at the stratopause, as displayed in the above figure. 

To this we add the insight that without any atmosphere the effective temperature of the Earth surface can be estimated to be 0 C, as a consequence of Stefan-Boltzmann's Radiation Law assuming that emissivity equals absorbitivity. 

This leads to describing the total effect of the atmosphere, as a result of a complex interaction of convection-evaporation/condensation-radiation-conduction, as a change of temperature profile from a flat constant zero profile to the observed V-profile of 15 to - 55 to 0 C.

Suppose now that the combined properties of the atmosphere change by 1%. How much would the temperature profile change? The first guess would be a change of profile by 0.15 to -0.55 to 0 C. In particular, Earth surface temperature could be expected to change by 0.15 C. 

A 1% change (of "radiative forcing") is what is commonly attributed to doubling the CO2 in the atmosphere, and the associated climate sensitivity could thus in a first basic approximation be a global warming of 0.15 C, which is  not alarming. 

We may compare with a simple application of Stefan-Boltzmann's Radiation Law with a fully opaque atmospheric layer at the assumed reference temperature 255 K with corresponding ground temperature of 2^(1/4) x 255 = 303 K = 30 C.  This is too high and adjusting the absorbitivity of the atmosphere we can get any ground temperature between 255 and 303 K, in particular the observed 288 K. Changing then the absorbitivity by 1%, the temperature would change 1% of 303 -255 ~ 0.3 C. SB would thus indicate a climate sensitivity of 0.3 C. 

Compare with ERBE observation indicating a climate sensitivity of less than 0.5 C.

In order to reach the alarming IPCC climate sensitivity prediction of 1.5 - 4.5 C, positive feedback with a  factor 5 - 30 is required, which seems way beyond rationale. To get around this alarming threat to climate alarmism, IPCC claims that the basic approximation is not 0.15 C, but instead 1 C as a result of an even more simplistic application of Stefan-Boltzmann's Radiation Law different from the above. With that starting point, feedback factors of size 2-3 would suffice and alarmism is no longer unthinkable, even if not probable.

We have thus two approaches: One approach based on observation combined with what could be referred to as sound down-to-earth engineering.  Another approach without observation based on applying a simple physical law to a complex situation not at all described by the physical law.

Which approach would you prefer as a starting point for a more detailed study, to form the the climate politics of tomorrow? What is the science of feedback factors 0f size 5 - 30?

Compare with increasing the heating in your house by 1% a day with outside temperature 0 C by turning on an extra 40 W lamp, and observing how much the inside temperature in Celsius will rise: 1% or 30%?

Altogether we understand that the entire flow of heat received from the Sun from the Earth 

operates on a temperature drop of 15 C from the Earth surface to the stratopause in a complex combination of convection-evaporation/condensation-radiation/conduction. A first mathematical model would connect heat flow linearly to temperature drop according to Fourier's Law.   An engineer predicting the heating cost for a house under different outside temperatures, would use Fourier's Law as a first approximation of the complex flow of  heat through a wall or window. An engineer relying only an incorrect application of Stefan-Boltzmann's Radiation Law, would not have a job.

Compare also with

• A Few Questions to Climate Alarmists by Paul Driessen
  
• Crisis in New Zealand's Climatology by Barry Brill.

FEniCS as Global Climate Simulator?!

                                           Radiation Budget according to NASA IPCC

This is an outline of my talk at FEniCS 10 May 10-12 at KTH based on

• On Atmospheric Circulation
• Variable Density Turbulent Incompressible Flow
• Temperature Sensitivity of a Basic Climate Model
• Greenhouse Gases without Greenhouse Effect

Question:

• Can FEniCS save humanity from Global Warming?
  

Global Circulation Models = GCM = NAVIER-STOKES eqns for Ocean-Atmosphere:

• convection
• evaporation-condensation: phase change
• turbulence: diffusion, dissipation
• radiation (black-body: absorb SW emit LW)
• conduction
• atmosphere: compressible
• ocean: incompressible variable density salinity
• full 3d (vertical convection)
• insolation
• rotation.

IDEAL for FEniCS!! IDEAL for UNICORN!!

Variable Density Turbulent Circulation: Movie 1   Movie 2

 (Johan Jansson/Hoffman)

                             CASE STUDY of SCIENCE in OUR TIME

Postulate of Climate Alarmism: (rock solid undeniable basic physics)

• dQ = 4 dT
  

Stefan-Boltzmann's Radiation Law: 

•    Q= c T^4                Q = 288 Watts/m2      T= 288 K

Differentiation: 

• dQ = 4c T^3 dT = Q/T 4dT = 288/288 4 dT = 4 dT
  

Basic Climate  Sensitivity: 

• Doubled CO2: dQ = 4 Watts/m2: dT = 1 C Basic
  

• "Radiative Forcing" 2 - 4 W (estimated)
• 5.35 log(C/C_0) ad hoc
• CO2 280 - 380 (1900 -2000): 0.7 C : 2.8 W

IPCC Prediction Global Warming: 

• 1 C gives 3 C by positive feed back: Alarm! 
  

Alarm: 

• 1% of Q (4 W)  gives 1% of T (3 C) from SB + feedback
  

Reality Check:

• without atmosphere T = 273 or T = 255 K
• with atmosphere T = 288 K 
• effect of full atmosphere  + 15/45 C
• effect of 1% atmosphere = 0.15/0.45 C

IPCC 3 C = 10-20 times too big!   3 C instead of 0.15 C!

Observation ERBE: dQ = 8 dT      dT = 0.5 C  instead of 3 C!

Is SB incorrect? 

• No, but too simplistic as climate model: Convection...missing.

Conclusion:

• No CO2 Alarm ?! 
  
• FEniCS?! 
• Real Climate Sensitivity?! 
• FEniCS Mission!
• Obama Cap and Trade EPA Global Emision Control? 

Ref: Lord Monckton Apocalypse? NO   

Conventional Greenhouse: 

• Absorb SW Radiation
• Block Convection

"Greenhouse" Gases: (rock solid undeniable basic physics)

• Absorb SW Radiation
• Absorb-Emit LW Radiation = "Blanket"

Atmospheric Blanket Layer Effect:

• Absorb  f x Earth Re-emit  f/2 x Earth Down   +  f/2 x Earth Up-Out

• Total Out (1- f + f/2) x Earth = (1 - f/2) x Earth

• T_Earth = 2^(1/4) T_Atmos = 1.2 x T_Atmos

• T_Atmos 255 K     T_Earth = 30 C Wrong!

• Radiation Blanket Model Too Simplistic

• Gerlich: Falsification of CO2 Atmospheric Greenhouse Effect 2009

Model of Radiation: Radiation Budget of Layer at height z:

                                  E(z+h) - 2 E(z) + E(z-h)

Radiation ~ Conduction: From Hot to Cold 

Constant lapse rate:

• Temperature  ~ (1 - z)    observed
• Pressure ~ (1 - z)^3         observed
• Density ~ (1 - z)^2           observed

PS1 BodyandSoul Mathematical Simulation Technology EBook

PS2 My question to the Royal Swedish Academy of Sciences concerning its statement that 

• "the effect of greenhouse gases is well established"

has not been answered. Conclusion? 

Once it was "well established" that the Earth is flat, but the scientific evidence was lacking...

To say that something is "well established" is not a scientific argument, even if a Scientific Academy so believes...

What does FEniCS say? Are we allowed to continue to breath?

Science Museum vs Academy of Science

The Science Museum is revising the contents of its new climate science gallery to 

• reflect the wave of scepticism that has engulfed the issue in recent months,
• the Science Museum will not state a position on whether or not climate change is real, driven by humans or threatening.

When will the Royal Academy of Sciences revise its own statement on threatening climate change driven by humans? 

My previous questions to the Academy concerning this statement are not answered, yet.