fredagen den 25:e juni 2010

AGW Myth of Back Radiation

AGW alarmism is  based on an idea of "back radiation" or "re-radiation" from an atmosphere with greenhouse gases, but the physics of this phenomenon remains unclear. 

To test if  "back radiation" is a real phenomenon, we suggest the following experiment: On a night with moon-light so feeble that you can cannot read a newspaper, place yourself in front of a mirror letting the moonlight reflect from the newspaper to the mirror and back again, and check if you can now read. You will probably find that the paper is still unreadable, as if "back radiation" does not give more light.

To give this experiment theoretical support we consider the mathematics of wave propagation from a source at x=0 (Earth surface)  to a receiver at x=1 (atmospheric layer) described by the wave equation (as a model of Maxwell's equations describing light as electromagnetic waves):

U_tt - U_xx = 0 for x in the interval (0,1)

with solution U(x,t) being a combination of waves traveling with velocity +1 and -1 along the x-axis, and with subindices indicating differentiation with respect to space x and time t. The boundary condition at the receiver may take the form

AU_t(1,t) + U_x(1,t) =0

with a positive coefficient A signifying:
  • A = 0: soft reflection with U_x(1,t) = 0
  • A large : hard reflection with U_t(1,t) = 0
  • A = 1: no reflection: transparent absorption of all incoming waves at x = 1.
The basic energy balance is obtained by multiplying the wave equation by U_t and integrating 
with respect to x to give:

E_t + AU_t(1,t)^2 = -U_x(0,t)U_t(0,t) = Input Energy.

where E(t) is the energy of the wave over the interval (0,1). Assuming that E(t) stays constant so that energy is no accumulating in the interval (0,1), we have that 

Output Energy = A U_t(1,t)^2 = Input Energy.

In particular, with soft reflection with A = 0, the Input Energy is also zero. We learn that  it is not possible to "pump the system" by reflection at x = 1: If you change from transparency with A = 1 to reflection with A = 0, the system reacts by refusing to accept Input Energy.

Ergo: Reflection/back radiation cannot increase the insolation to the Earth surface. 

(Back radiation seeks support in a description of light as a stream of particles proposed by Newton, which was replaced by Maxwell's wave theory in the late 19th century).

torsdagen den 24:e juni 2010

Climate Sensitivity of Pinatubo Eruption

Roy Spencer obtains, by fitting ERBE/SAGE observations of the effect of the Pinatuba Eruption to the most basic mathematical model
  • Cp T = F - lambda T
with T (change of) lower tropospheric temperature, F radiative forcing, lambda T radiative feedback and Cp heat capacity, the value lambda = 3.66 W/m2K.

This conforms with the relation dQ ~  4 dT which follows from differentiating Stefan-Boltzmann's Q = c T^4, as we have discussed in previous posts. 

Is this an indication that real climate sensitivity is about 1 C upon doubling of atmospheric CO2?

Maybe, maybe not: It requires that 
  • (i) doubled CO2 gives a forcing of about 4 W/m2 
  • (ii) the effect of the Pinatuba eruption with increasing aerosols in the stratosphere reducing incoming radiation, can be translated to a CO2 effect in the troposphere reducing outgoing radiation.  
As concerns (ii), Spencer observes that two years from the eruption, the stratospheric aerosol effect measured by SAGE is reduced to 50%, while the ERBE net flux anomaly is already zero,
  • there are other internally-generated radiative “forcings” in the climate system measured by ERBE, probably due to natural cloud variations. 
In other words, the Pinatuba effect is counterbalanced by "internal-generated radiative forcings", which indicates an even smaller climate sensitivity. In any case, the data and analysis by Spencer contradict the IPCC prediction of a climate sensitivity in the range 1.5 - 4.5 C. 

This is one of many indications of a climate sensitivity smaller than 1 C, maybe smaller than 
0.5 C.

ERBE measures incoming and outgoing radiation (net radiative forcing) which combined with measured temperatures gives input to determining climate sensitivity.  But as Spencer points out, and I have discussed in previous posts on climate sensitivity, it may be difficult to distinguish the effect of radiative forcing from a given source (say CO2) from unknown natural sources, if the latter dominate. 

tisdagen den 22:e juni 2010

Expert Credibility and Swedish Stupidity?

In the article Expert Credibility in Climate Science in PNAS AGW propgandists Schneider et al, argue that
  • Preliminary reviews of scientific literature and surveys of climate scientists indicate striking agreement with the primary conclusions of the Intergovernmental Panel on Climate Change (IPCC): 
  • anthropogenic greenhouse gases have been responsible for “most” of the “unequivocal” warming of the Earth’s average global temperature over the second half of the 20th century = ACC = Anthropogenic Climate Change. 
  • Nonetheless, substantial and growing public doubt remains about the anthropogenic cause and scientific agreement about the role of anthropogenic greenhouse gases in climate change.
  • A vocal minority of researchers and other critics contest the conclusions of the mainstream scientific assessment, frequently citing large numbers of scientists whom they believe support their claims. 
  • This group, often termed climate change skeptics, contrarians, or deniers, has received large amounts of media attention and wields significant influence in the societal debate about climate change impacts and policy.
The purpose of the article is to show that experts agree, but what is shown is the opposite: 
Experts don't agree.
On this basis the Swedish Alliance Government announces to lead  EU into  a new society without fossil fuels and CO2 ACC.

Reasonable? Rational? Clever? No.

Populistic stupidity? Yes. But people are not stupid, since it is their lives and wellfare which is at stake. Do we really as Swedes have to live up to the old idea of "Swedish Stupidity"?

fredagen den 18:e juni 2010

The Atmosphere as Refrigerator 2

The previous posts lead us into the following basic scenarios of global climate with top of the atmosphere TOA temperature always - 18 C:
  • isothermal opaque atmosphere: surface temp: - 18 C
  • isothermal transparent atmosphere: surface temp: - 18 C
  • isentropic opaque atmosphere: surface temp: + 32 C
  • thermodynamic semitransparent real atmosphere: surface temp:  + 15 C.
We understand that an isothermal atmosphere at - 18 C is possible both in the case of a fully transparent atmosphere without greenhouse gases GHG  and fully opaque atmosphere filled by GHG. The real case at 15 C is somewhere between these extremes with a semi-transparent atmosphere with thermodynamics including latent heat/evaporation/condensation. 

Isothermal (lapse rate = 0) and isentropic (lapse rate = 10 K/km) thermodynamic equilibrium states are possible without heat transport from the Earth surface to TOA. Convective heat transport tends to reduce the lapse rate. A reduced lapse rate connects to decreased radiative heat transport.

A simple calculation based on observed incoming = outgoing radiation = 240 W/m2 and a temperature drop dT of say 30 K from the Earth surface to TOA, gives heat transport by radiation = 4 x 30 = 120 Watts (by dQ = 4 dT), which fits with observed heat transport of 120 W by convection-evaporation/condensation (reducing the lapse rate by observed 3 K/km). This corresponds to a semi-opaque atmosphere absorbing 60 W and letting through 180 W to the Earth surface, and transporting back 120 W by convection and 120 W by radiation to TOA for radiation of 240 W to outer space at - 18 C.

We observe that in this model, increase of convective heat transport may reduce the lapse rate further and thus decrease the surface temperature. A balancing decrease of radiative heat transport fits with a smaller dT and a decrease of surface temperature. Less radiative heat transport may thus fit with increasing GHG. As noted in previous posts, the net result could be global cooling by more GHG!

Thus, not even the sign of climate sensitivity is clear, warming or cooling, not to speak of its magnitude: Whether increasing GHG will increase or decrease surface temperature will depend on the effect on incoming surface radiation and the thermodynamical heat transport including evaporation/condensation. In particular, the common belief that  doubled CO2 will cause a basic global warming of 1 C, may lack scientific rationale.

Compare with Basic Thermodynamics of the Atmosphere derived from basic properties of turbulent solutions of the Navier-Stokes equations.

Also compare with Roy Spencer's dicussion of the role of PDO in global temperature variations based on the simplest possible thermodynamic model. Spencer shows that even such a simplest model can be made to fit with observations quite well, and then indicates much smaller climate sensitivity that the simple radiative model used by IPCC to predict a basic climate sensitivity of 1 C upon doubling of atmospheric CO2 (augmented  to 1.5 - 4.5 C by various feedbacks).

The conclusion is that any climate model must include thermodynamics, and the natural model is then the Navier-Stokes equations with gravitation and radiation. 

torsdagen den 17:e juni 2010

The Atmosphere as Refrigerator

The previous posts lead us to view the thermodynamic action of the atmosphere to be similar to that of a refrigerator:
  • Evaporation at the ocean surface driven by incoming radiation generates cooling of the warm atmosphere above the surface.
  • Warm air rises by bouyancy under expansion and cooling to TOA where it releases heat by condensation for further radiation to outer space.
  • Cool air descends from TOA under compression and warming completing a thermodynamic refrigerating cyclic process.
In addition, some incoming heat is returned by radiation. If the radiation is blocked, more or less, by greenhouse gases, the refrigerator process must intensify to maintain heat balance. This requires more evaporation and thus more cooling of the atmosphere above the ocean surface. 

The atmosphere will thus act like a refrigerator giving additional cooling under increased energy input. More greenhouse gases will thus cause global cooling!

How much cooling? Assume that now 1/4 of incoming heat is returned by radiation and 3/4
by the  thermodynamic refrigerator process at a decrease of the lapse rate of 3 K/km from 10 to 7 K/km. Blocking the radiation fully would then require a further reduction of lapse by 1 K/km to 6K/km corresponding to a decrease of surface temperature by 5 K. 

If the radiation was blocked by 1% the decrease of global temperature would be 0.05 K. Climate sensitivity could thus be estimated to  - 0.05 K. To be compared with IPCC's + 1.5 to + 4.5 K.

onsdagen den 16:e juni 2010

Elementary Climate Mathematics: CO2 Cooling

We condense the previous post into:
  • The atmosphere of the Earth acts like a cooling system by transporting heat absorbed from the Sun to the top of the atmosphere TOA from where it is radiated to outer space.
  • 240 Watts/m2 is radiated from a TOA at 5 km altitude at a blackbody temperature of 255 K.
  • The heat absorbed by the Earth surface is transported to TOA mainly by thermodynamics (convection including evaporation/condensation) and partly by radiation.
  • The theoretical isentropic thermodynamical lapse rate is 10 K/km. 
  • The observed lapse rate is about 7 K/km.
  • The 3K reduction of lapse rate is a result of evaporation at the ocean surface (subtracting heat)  and condensation towards TOA (adding heat).
  • The effective lapse rate of 7 K/ km sets the Earth surface temperature to 288 ~  255 + 7 x 5 K.
  • Increasing evaporation decreases the lapse rate, and thus the surface temperature.
  • Increasing greenhouse gases GHG  = reduced heat transport by radiation = increased evaporation/condensation required to keep heat balance.
  • Ergo: Increasing GHG reduce surface temperature = global cooling.
  • More CO2 = Global Cooling!
Do you believe it?

To help reaching a conclusion, note that the above argument combines thermodynamics and radiation, while the claimed GHG global warming is based on radiation only. You may also recall that a refrigerator/air conditioner works by thermodynamics of expansion-evaporation-cooling + compression-condensation-warming just like in the above model of the atmosphere. 
A refrigerator working by radiation only would be wonderful, but nobody has been able to 
construct such a device.

måndagen den 14:e juni 2010

Elementary Climate Mathematics

Let us collect some basic facts about global climate:
  • temperature of stratopause: 273 K
  • temperature of tropopause: 218  K 
  • temperature at Earth surface: 288 K
  • observed lapse rate in troposphere: 7 K drop per km 
  • total temperature drop in troposphere: 288 - 218 = 70 K = 7 x 10 km 
  • isentropic thermodynamic theoretical lapse rate: 10 K/km 
  • 180 Watts/m2 absorbed by Earth surface
  • 120 Watts/m2 returned by convection/latent heat
  • 60 Watts/m2 returned by radiation 
  • Earth-atmosphere effective blackbody temperature: 273 K = temperature at stratopause.
We observe:
  • Convective heat transport in the troposphere decreases the theoretical isentropic lapse rate by 3 K/km (from 10 K to 7 K), by evaporation at the Earth surface removing heat and condensation a higher altitudes adding heat.
  • Stratopause temperature of 273 K fixed by blackbody radiation at given insolation.
  • Tropopause temperature determined by temperature distribution in the stratosphere.
  • Surface temperature is determined by troposphere lapse rate and tropopause temperature.
  • It is natural to compute temperatures outside in, starting at the stratopause at 273 K and ending at the Earth surface at 288 K.
  • 60 Watts of radiation dQ is consistent with the relation dQ ~ 4 dT (differentiated SB Stefan-Boltzmann radiation law) with a temperature drop dT of 15 K (from Earth surface to stratopause).
  • Observations indicate a climate sensitivity of dQ ~ 6 dT (negative feedback from dQ =4 dT).
Main question:
  • Suppose the heat transport in the troposphere changes so that less heat is radiated and more heat is transported by convection from the Earth surface, at a constant total, for example to 124 Watts by convection and 56 Watts by radiation.  Will then the Earth surface temperature increase or decrease? Warming or cooling?
Tentative answer:
  • The temperature will drop as the intensity of evaporation/condensation increases and the troposphere lapse rate is further decreased, assuming that the tropopause temperature stays constant (assuming the stratosphere temperature does not change). The change in temperature could come from a change of lapse rate of 4/120 x 3 = 0.3 K/km resulting in a 3 K drop of surface temperature.
  • A shift from radiative to convective heat transfer in the troposphere can be expected by by increasing the effect of GHG greenhouse gases (mainly water vapour). 
  • This could correspond to a decrease of surface temperature under increased cloud cover from increased GHG.
  • IPCC predicts an increase of surface temperature of 1.5 - 4. 5 C, from 1 C basic greenhouse effect/doubled CO2 based on SB plus assumed ad hoc positive feedbacks.
  • The above argument indicates instead a decrease of surface temperature from increased greenhouse effect, under constant insolation.
  • An increase of insolation by 4 Watts can by SB by expected to give an overall increase of 1 C.
The above argument uses more physics and more data than a direct application of SB argued by IPCC. Both arguments are simplistic. Which one is more realistic? Or none?

It is remarkable that not even the sign of climate sensitivity (warming or cooling by adding greenhouse gases) can be convincingly predicted by some form of mathematical analysis of the thermodynamics of an atmosphere. Or maybe it can, by a correct analysis based on computing turbulent solutions of the Navier-Stokes equations...stay tuned...

Compare with the canonized description of the greenhouse effect:
  • The greenhouse effect is a process by which radiative energy leaving a planetary surface is absorbed by some atmospheric gases, called greenhouse gases. They transfer this energy to other components of the atmosphere, and it is re-radiated in all directions, including back down towards the surface. This transfers energy to the surface and lower atmosphere, so the temperature there is higher than it would be if direct heating by
  • solar radiation were the only warming mechanism.
  • The Earth receives energy from the sun in the form of visible light. This light is absorbed at the Earth's surface, and re-radiated as thermal radiation. Some of this thermal radiation is absorbed by the atmosphere, and re-radiated both upwards and downwards; that radiated downwards is absorbed by the Earth's surface. Thus the presence of the atmosphere results in the surface receiving more radiation than it would were the atmosphere absent; and it is thus warmer than it would otherwise be.
  • This highly simplified picture of the basic mechanism needs to be qualified in a number of ways, none of which affect the fundamental process.
  • This mechanism is fundamentally different from that of an actual greenhouse, which works by isolating warm air inside the structure so that heat is not lost by convection.
We see that the lapse rate with an elevated surface temperature is viewed to come from radiation only, more precisely from atmospheric "re-radiation in all directions". We also see that the term "greenhouse gas" is admitted to be a (deliberately) misleading misnomer.  Like the Democratic People's Republic of North Korea.

Nevertheless, this is the essence of the scientific basis of climate alarmism: Re-radiation in all directions without any thermodynamics. Convincing science? Convincing to you?
What is the physics of 
  • the fundamental process, fundamentally different from that of a greenhouse, which results in the surface receiving more radiation? 

What physics books describe this fundamental process? I would like to learn about this phenomenon!

Note that the "fundamental process" referred to (probably) is "photons emitted by the Earth surface" which are "being trappedb y greenhouse gases in the atmosphere" and then "re-emitted back to the Earth". 

But is this the real physics of radiation as an electromagnetic wave phenomenon?
I don't think so. The idea of photons being trapped like fish in a net, is too simple. I would rather think of the situation as "dominance of the stronger over the weaker" as a flow of heat energy from higher to lower temperatures, instead of flows in both directions (at different strengths).

onsdagen den 9:e juni 2010

A Too Simplistic Climate Model

A simplistic climate model including effects of conduction, convection and radiation takes the form

R T + C T_x - RC T_xx = 0 for x in (0,1),  -  RC T_x(0) = Q, T(1) = small,

where T(x) is temperature at altitude x, T_x is the first and T_xx the second derivative with respect to x, R is a coefficient of net outgoing radiation, C is a convection velocity, RC is a
a combined conduction/radiation coefficient and Q (= 1 say) is a heat source. 

Depending on the size of the coefficients R, C and RC, the temperature profile T(x) takes the following main forms:
  • R = C = 0: T(x) = (1 - x)/RC : 
  • C = 0, A^2 = R/RC : T(x) = exp (-A x) 
  • RC = small: T(x) ~  exp(-R/C x).
We see a linearly decaying temperature profile with climate sensitivity T(0) = 1/RC,
or an exponentially decaying profile with T(0) = 1. 

In the case of substantial net outgoing radiation with R not small and R/RC and R/C large, the exponential decay is rapid. If R/RC and R/C is small, then T(x) is almost constant.

The linear profile observed in reality is realized only in the first case with RC dominating R and C, and then with a large climate sensitivity if RC is small. 

The above model is thus not easy to bend to fit with observation of a constant lapse rate which is not large, and thus seems too simplistic.

What the model is missing is the thermodynamics of an atmosphere under gravitation which 
has an equilibrium (isentropic) state with constant not large lapse rate, as shown in posts on

We thus find that radiation/conduction must be combined with thermodynamics to describe the action of the atmopshere as a global air conditioner maintaining a surface temperature of 15 C under permanent heating from the Sun, including the crucial aspect of climate sensitivity. 

The above argument gives yet another indication that a simplistic estimate of basic climate sensitivity of 1 C based on radiation only, may not be close to any reality.

New EBodyandSoul at KTH

A new e-version EBodyandSoul of the  BodyandSoul Applied Mathematics Reform Project will be used this fall at KTH in an engineering physics course, as a test of functionality as basis of the new program in Simulation Technology starting next fall. A draft of the new e-version is available for inspection. 

Different platforms for EBodyandSoul including iPad and iPhone are being investigated. 

In EBodyandSoul the synthesis of mathematics, computation and application is carried further, by guiding students to the tools of modern computational mathematics in construction of computer games from basic laws of physics. This helps the student to an active feedback interplay with different mathematical models and physics, with in particular direct experience of essential input-output aspects.   

söndagen den 6:e juni 2010

Basic Climate Sensitivity = 0.15 C

The Earth surface receives about 180 Watts/m2 out of which about 60 Watts are returned 
by radiation at a mean surface temperature of 15 C, and 120 Watts by convection coupled with evaporation/condensation.  By Stefan-Boltzmann's radiation law the 60 Watts radiated corresponds to a temperature drop of about 15 C, which is in accordance with a radiation temperature of 0 C of the stratopause.  

Suppose now the radiative properties of the atmosphere is changed by 1%, which is the estimated effect of doubled CO2. This could require an extra 0.6 Watts to be radiated,  which by Stefan-Boltzmann would correspond to an increase of surface temperature 0.15 C.  

This argument suggests a climate sensitivity 0.15 C. With an even more simplistic argument based on Stefan-Boltzmann, IPCC suggests instead 1 C, which is elevated by feedbacks 
to an alarming 3 C. Starting instead with 0.15 C gives no reason for alarm.

Which argument do you think is more correct? Both are simplistic and do not require more than  common sense to evaluate.

SMHI och Tällberg Foundation om Växthuseffekten?

SMHI fastställer inför svenska folket i en rapport om Växthuseffekten författad av Markku Rummukainen (ledande svensk klimatalarmist):
  • Att utsläpp förstärker växthuseffekten är lätt att förstå. En fördubbling av atmosfärens koldioxidhalt i sig höjer medeltemperaturen med en dryg grad, vilket är relativt enkelt att räkna fram. Klimatsystemet är dock mer komplext än så. Det finns ett antal indirekta effekter, s.k. återkopplingar som komplicerar. Dessa kan antingen förstärka eller motverka en ursprunglig påverkan i klimatsystemet.
Vi möter här klimatalarmismens grundpostulat om 1 C klimatkänslighet från koldioxidfördubbling, vilket är "enkelt att räkna fram", närmare bestämt från en simpel applikation av Stefan-Boltzmann's strålningslag. I en serie poster om climate sensitivity har jag visat att detta är en överförenkling som inte alls behöver ha något med verkligheten att göra, vilket också uttrycks av Rummukainen. SMHI signalerar alltså alarm utan vetenskaplig grund. Varför? Svenska folket vill ha en förklaring.

Ett annat enkelt sätt att räkna fram istället en klimatkänslighet på 0.15 C är följande: SMHI 
anger att strålning från jordytan avleder ca 60 Watt/m2 av ca 180 W/m2 inkommande, och 
resterande 120 tas om hand av konvektion med avdunstning/kondensering. Enligt Stefan-Boltzmann motsvarar 60 W/m2 en temperaturdifferens på ca 15 C, vilket stämmer med 
temperaturfallet från jordens yta till stratopausen. 

Antag nu att atmosfärens egenskaper förändras med 1%, vilket kan motsvara fördubbling av CO2 med "radiative forcing" på 1.8 W/m2. Motsvarande andel att tas om hand av strålning 
kan då vara 0.6 W/m2 vilket enligt SB motsvarar 0.15 C.  

Utgångsvärdet på klimatkänsligheten bör alltså vara 0.15 C snarare än 1 C, vilket inte är alarmerande. Eller hur SMHI?

Kanske är det detta argument som fått Tällberg Foundation att frångå sin tidigare klimatalarmism, som inte framförs i gårdagens debattinlägg i SvD.


lördagen den 5:e juni 2010

New Faculty Positions at Bolin Centre

Bert Bolin Centre for Climate Research opens 7 new tenured faculty positions in numerical modeling of the climate system

The Bolin Centre confesses to IPCC climate alarmism based on numerical modeling, for which the scientific foundation now is eroding, as evidenced in particular in a recent debate article by 9 professors at the Centre. In this perspective the announced expansion of the faculty is very remarkable. The centre conducts a 10-year research and research environment-building program, funded by FORMAS and VR embracing 
Bert Bolin (1925-2007 world leading scientist and science organizer played a central role in the formation and management of the Intergovernmental Panel on Climate Change (IPCC).

It is also very remarkable that the research is based on a preconcieved postulate of "man´s ever-increasing impact on the climate system through emission of greenhouse gases". Note the clever use of the term "ever-increasing" without quantitative information, which is meant to signal alarm without any need of providing scientific evidence, following the standard of IPCC. But what will happen to the Bolin Centre if the effect of CO2  shows to be neglible?

onsdagen den 2:e juni 2010

The Royal Swedish Academy Next?

Financial Post reports in And then there were three: Britain’s Royal Society rejects alarmism:
  • Britain’s Royal Society, the UK’s preeminent scientific body, has joined national science bodies in India and France in validating the views of global warming sceptics.
Will the Royal Swedish Academy be number 4 or 100?