On Climate Sensitivity 1

Consider the following basic model for vertical heat transfer in an atmosphere (troposphere + stratosphere) represented by the interval [0 , 1]:

                    T_t + aT + bT_x - cT_xx = q,   

                    -c T_x(0,t)  =Q(t),   T(1,t)=0, 

where T(x,t) is temperature at position x at time t, the subindices t and  x indicate differentiation, a is coefficient of net outgoing radiation, b is convection velocity, c is coefficient of heat conduction/radiation, q internal forcing from evaporation/condensation, and Q(t) is incoming heat from the ocean (from insolation). 

The basic stationary case is Q(t)=1 constant, a =0, b=0, q=0 and c constant, which gives T=(1-x)/c with corresponding temperature sensitivity T(0)=1/c which is large if c is small. This is the right curve above with slope - 1/c reflecting that heat is transported by conduction with consistent negative temperature gradient: High temperature sensitivity to forcing Q.

Consider now the case q = -1 for x in [0, 0.5] (evaporation) , q = 1 for x in (0.5, 1] (condensation) and b =1 (upward convection), c small, with Q (t)= 1 as above, which in the stationary case gives T(x) ~ -x for x in [0,0.5] and T(x)= x - 1 for x in (0.5, 1], with T(0)=0: Low temperature sensitivity. The corresponding temperature is represented by the broken left curve, which mimics the real temperature decreasing in the tropsphere and increasing in the stratosphere. In this case heat is transported mainly by convection and the temperature gradient changes sign because of evaporation/condensation. 

We conclude that convection coupled with evaporation/condensation, like in the real atmosphere, can change temperature sensitivity drastically, and since climate sensitivity is related to temperature sensitivity,  also climate sensitivity can be drastically reduced as compared to that of the simplest radiative model underlying simple calculations of climate sensitivity based on conduction/radiation without convection.

In the boiling pot analogy increasing the forcing results in more vigorous boiling but the 

temperature stays the same, and the temperature sensitivity is zero.  It is likely that

Roy Spencer's upcoming report on climate sensitivity will have a similar message.

Compare with a common Green House GH, which has high temperature sensitivity because convection is prevented by the glass enclosure. The basic climate sensitivity of 1 degree Celscius upon doubling of CO2 in the atmosphere is computed with this model as basis, which thus may exaggerate sensitivity, which in IPCC AR4 is exaggerated even more by positive feed-back, from water in particular vapour, in contradiction to the above model with evaporation.  

To call CO2 a Green House Gas GHG, which is done by IPCC, thus appears questionable.

Nevertheless, the above analysis is supported by the following statement from IPCC 2007 Summary for Policymakers:

• Some aspects of climate have not been observed to change.
  

I will return to the dynamics of the model.

Läser Häggström Bara Expressen?

Olle Häggström  öser i dagens Expressen ur sig en massa invektiv över gruppen av "klimatskeptiker" som påstås representeras av "personer som till exempel Elisabet Höglund, Jonny Fagerström, Lars Bern, Maggie Thauersköld Crusell och Nils Lundgren – (som) för debatten på en så beklämmande låg nivå."

Häggtröm är lyckligen omedveten om att AGW-hypotesen och IPCCs klimatvetenskap kollapsat fullständigt i och med Climategate. Häggström vet inte att det finns tusentals synnerligen kompetenta  vetenskapsmän runt om i världen som påstår att AGW alarmismen saknar vetenskaplig grund, personer som Richard Lindzen, Roger Pielke Sr/Jr, Roy Spencer, Claude Allegre, m fl m fl. 

Läser Häggström bara Expressen? Varför inte prova Financial Post: The New Climate Game?

Eller Inhofe's Senatsrapport The CRU Controversy.

Glacial Cycles and Eccentricity

Lorraine Lisiecki reports in Nature Geoscience on the connection between glacial cycles and

the eccentricity of the Earth orbit around the Sun both showing 100.000 year periodicity. The main idea is that the intensity of the insolation during the Northern Hemisphere Summer influences the growths of ice caps: It seems that large eccentricity with short strong NH Summer insolation (coupled with long weak NH Winter insolation ) keeps the Ice Age away. In particular, the tilting of the Earth axis enhances the NH Summer heating. Moreover, one can expect more heat to flow North from the Equator during the long Winter of an eccentric orbit.

A simple argument based on Kepler's 2nd Law shows that the total insolation during a year is independent of the eccentricty, which indicates that the yearly dynamics determines glaciation rather than any varying total insolation.

Of course the heat exchange between the equatorial and pole regions is important; in particular during the long NH Winter. It thus seems that the yearly dynamics of the climate driven by the eccentricity is of importance, rather than a gross global mean value temperature. It may be possible Sweden gets covered by ice while the global temperature is increasing. Maybe this is what we have seen a sign of this long NH Winter?

Compare A New and Effective Climate Model by Stephen Wilde:

• ...virtually all climate variability is a result of internal system variability and additionally the system not only sets up a large amount of variability internally but also provides mechanisms to limit and then reduce that internal variability...The current models neither recognise the presence of that internal system variability nor the processes that ultimately stabilise it.
  

This connects nicely to the features of turbulent flow we have identified, namely large

local variability coupled with stable mean value outputs. The basic example is bluff body flow

in a slightly viscous fluid such as air and water, which is turbulent, highly variable and unpredictable locally (in the wake behind the body) while the drag as global mean-value is

highly predictable. This is a result of cancellation mechanisms in turbulent flow, which

comes down to saying that after up there will be down, or after rain there will be sunshine...

This gives hope of improved climate models on grids with millions of mesh points which is feasible today.

Compare with Con: Earth is never in equilibrium by Richard Lindzen.

Claude Allegre and Gravity

The claim by Claude Allegre that a light tennis ball and a heavy petanque (boule ball) will reach the ground at the same time if dropped from the top of the tower of Pisa, has caused some discussion and questioning. Can it be true? Yes, it can if the balls are scaled so that the quantity of radius times density, is the same for the two balls.  This is under the assumption the air drag scales like density times radius squared, while mass scales like the third power of the radius. 

This means that the heavy ball must have both a smaller radius, and smaller mass than the tennis balls (and not as would seem more natural that the radius or mass are equal). The quotient of the radii thus should be equal to the inverse of the quotient of densities, while if instead the mass is kept the same, the quotient of the radii would be equal to the third root of the inverse density quotient. A tennis ball and a small petanque could thus fall equally fast. If the density of the petanque is 10 times that of the tennis ball, then the petanque radius would be 10 times smaller, and its mass 100 times smaller: A small petanque.

WSJ: Science is Dying

WSJ expresses in Climategate: Science is Dying in WSJ  from Dec 3 2009:

• Science is on the credibility bubble. If it pops, centuries of what we understand to be the role of science go with it. 
• What is happening at East Anglia is an epochal event. 
• As the hard sciences—physics, biology, chemistry, electrical engineering—came to dominate intellectual life in the last century, some academics in the humanities devised the theory of postmodernism, which liberated them from their colleagues in the sciences. 
• Postmodernism, a self-consciously "unprovable" theory, replaced formal structures with subjectivity. 
• With the revelations of East Anglia, this slippery and variable intellectual world has crossed into the hard sciences.

But the credibility of  science was eroding long before Climategate and postmodernism,

in particular among young people entering education and chosing careers: Mathematics, physics, engineering and hard sciences was in decline and economy, politics and why not, postmodernism on the rise.

So, when did then the decline of  science start? Was it when

• the Cold War ended in 1989? 
• Einstein became four-dimensional in 1915 preparing the eleven dimensions of string theory?
• statistical mechanics and its offspring quantum mechanics coined coin-tossing as science?
• set theory became the basis of mathematics in Principia Mathematica in 1910?
• Cantor introduced his transfinite numbers in the late 1900s?
• the Lebesgue-integral replaced the Riemann-integral in the early 1900s? 
• Prandtl became the father of modern fluid mechanics in the early 1900s?
• set theory took over elementary school education in the 1960s?
• the pocket calculator made long division powerless? 
• Big Bang became the one and only cosmology starting in the 1960s. 
• chaos theory could be used as explanation of the unexplainable?
• Wikipedians took command of scientific truth? 
  
• the Royal Swedish Academy of Sciences endorsed IPCC?

Some of these questions are discussed in my My Book of Knols and previous blog posts. Or was

it not until IPCC showed that climate models were reliable? Compare Washington Post's Scientists' use of computer models to predict climate change is under attack.

Also compare James Lovelock on The Value of Skeptics and FT on Climate Science Needs to be More Objective and Thorough.

French Academy on Climate Science

Financial Post reports that at the suggestion of France’s science minister, Valérie Pécresse,

• France’s National Academy of Sciences will hold an official debate on climate change totry to defuse this newly explosive issue.
• The Academy of Sciences debate, expected to be held by October of this year, follows two months of heated debate on radio and television, during which France’s two most prominent sceptics, Claude Allegre and Vincent Courtillot, have sown great doubt in the minds of a once unskeptical French public.
• Allegre’s new book, L'imposture climatique (The Climate Fraud), has especially caused the French public to reconsider the conventional wisdom about global warming. In this runaway best-seller (110,000 copies sold to date), Allegre, France’s most celebrated scientist and a former Science Minister in a socialist government, calls the UN’s Intergovernmental Panel on Climate Change IPCC, a "mafia-like system" that promotes a "baseless myth" about climate change.

The French Academy of Sciences thus takes a different approach than the Royal Society of London and the Royal Swedish Academy, which under their wings keep IPCC from total collapse. It seems that an Academy without Royals can be more free to follow scientific principles...

Phil Jones Rentvådd enligt SvD

SvD meddelar idag svenska folket att

• Brittiske klimatprofessorn Phil Jones rentvås i en utredning i parlamentet.
• Enligt den finns inget i hans hackade e-mail som visar att han har fuskat.
• Panelen uttrycker också förståelse för att Jones sannolikt har känt sig frustrerad över att lämna ut data till klimatskeptiker vars syfte är att underminera hans forskning.
• Panelen konstaterar att det vetenskapliga anseendet är intakt, såväl för Phil Jones som för hans klimatforskningsavdelning,

Så kan man alltså rapportera 1 april. Jämför med Scientists Admit Global Warming is a Hoax,

House of Commons CRU Email Report samt Der Spiegel on Climate Science med tex A Superstorm for Golbal Warming Research och It Is Time to Rethink Public Policy in Climate Change och Richard Lindzen on The Peculiar Issue of Global Warming.

SMHI (och KVA) stödjer IPCC

SMHI uttalar i Om IPCC och Klimatvetenskapen:

• FNs klimatpanel, IPCC, har debatterats flitigt under de senaste månaderna. Upphovet har varit enstaka fel – och påstådda sådana – i IPCCs rapport från 2007. Även sättet på vilket panelen har reagerat på händelserna har väckt frågor.
• Att enstaka fel förekommer hindrar inte att kunskapsläget från den internationella forskningen står sig mycket väl. Befintlig kunskap har i huvudsak bekräftats av forskningen sedan den senaste rapporten, i takt med att nya mätningar tillkommit och modeller och analysmetoder förbättrats.

I likhet med Kungliga VetenskapsAkademien står SMHI oreserverat bakom IPCC, trots alla skandaler. Hur länge till skall detta hålla? Vad blir konsekvensen för svensk klimatpolitik när

SMHI och KVA tvingas revidera sin hållning?

Samtidigt meddelar SvD i Klimatpanelen Mitt i Stormen:

• FN:s klimatpanel IPCC sammanställer rapporter om tillståndet på jorden som världens ledare lutar sig mot. Men panelen har kritiserats hårt sedan flera fel upptäckts i klimatrapporterna. Hur ska IPCC återskapa förtroendet – för sig själv och forskningen?
  
• Phil Jones har löpt gatlopp efter mejlskandalen. Han övervägde självmord efter att ha blivit hotad till livet.

Hotad till livet, av vem/vilka? Att överväga självmord på grund av hot till livet? Klimatdebatten är motsägelsefylld.

Jämför med Monckton-Lambert Climate Debate och Mike Wallace on Warming Myopia.

Eller Freeing Energy Policy from Climate Change Debate och Gulf Stream Not Slowing Down.

Eller Global Warming Alarmism Dying a Slow Death.

Scepticism at the Science Museum

The Times reports that 

• 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 decision by the 100-year-old London museum reveals how deeply scientific institutions have been shaken by the public’s reaction to revelations of malpractice by climate scientists.
  

When will the Royal Swedish Academy of Sciences revise its statement on climate science to reflect the wave of scepticism in recent months?

Self Similarity of Temperature Graphs

The Reference Frame suggests that temperature graphs are self-similar e.g. in the sense of

red noise or Brownian motion with temperatures changes of size t^0.5 = squareroot of t,

over time intervals of length t.

In other words, temperature graphs are Hölder continuous with exponent 1/2, or something

of that size like 1/3.

This connects to a basic property of turbulent incompressible flow, namely that velocities are Hölder continuous with exponent 1/3, as we show computationally in Computational Turbulent Incompressible Flow, with support by analysis.

This gives hope that turbulent climate dynamics can be simulated computationally.