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  • Bob Armstrong
      20151223.1229 <

    ... ever since Kepler proved that the orbits of the planets are ellipses, relations expressible in quantitative form have carried greater weight than those which could be stated only qualitatively."
    F.K. Richtmyer , preface to 1st ed , 1928 , Introduction to Modern Physics , 1942 .

    I am splitting this discussion from  CoSy's  venerable Global Temperature page to start a ion focused on the actual quantitative audit trail ( h/t Lavoisier  who brought accounting to alchemy transmuting it into chemistry ) from the energy we receive almost totally from the Sun to our observed surface temperature .

     Physics is the mathematical abstraction of  ,
    as an old Hindu buddy would say : ? What is happening ?

    The discussion will be highly prejudiced for the presentation of equations , preferably executable algorithms in some freely available array capable language . This blog is a continuation of the educational effort started at ( archived ) ,  which works out the geometry of the portion of the celestial sphere subtended by the Sun and the Stefan-Boltzmann  T = sb * E ^ % 4  temperature of a gray body . Just this gray body temperature in our orbit , about 278.6 +- 2.3 degrees Kelvin from peri- to ap- helion , explains all but 3% of our estimated mean surface temperature .
    The magic %100
    Quantitatively reducing this 3% unexplained variance is the goal .

    The analysis begun in :Essential_Physics was continued with my Heartland presentation , The Basic Basics or How to Calculate the Equilibrium Temperature of a Radiantly Heated Uniformly colored ball , which boils down to

    The equilibrium temperature of a radiantly heated uniformly colored ball is the temperature T
     such that

    dot[ sourceSpectrum ; objSpectrum ]  =  dot[ Planck[ T ] ; objSpectrum ]

    where  objSpectrum  is the absorptivity(=emissivity) spectrum of a object , in this case treating the earth as a uniformly colored ball .  dot[ ; ] is the dot or inner product : the sum across the products of the two curves .

    This can be restated in terms of the Stefan-Boltzmann calculated temperature of a gray body as

    T = Tgray *
        ( dot[ sourceSpectrum ; objSpectrum ] % dot[ Planck[ T ] ; objSpectrum ] ) ^ % 4

    I'm establishing a fund for a prize for the best "YouTube" quantitative experimental test of one of the non-optional classical physical computations necessary to get from the Sun's output to our mean surface temperature . | 20170424.1405 |

    Donate to this prize . I'm starting it off with $25

    to CO2isNoEvil on WUWT :
    I'm sorry I don't have more time for this discussion because there is a lot which would be I think generally useful to get clearly communicated . I resonate to such details as "each pixel is 8 bits for most of the satellite channels" . I assume that is for each of some number of spectrally filtered channels ? Your second paragraph reflects any of the problems Roy Spencer describes at . I would be quite interested in what your "tools" are built in . APLs can express algorithms over data often orders of magnitude more succinctly and therefore more understandably to the math capable mind than traditional languages . Since in APLs A + B or in 4th.CoSy A B + because it is still at the Forth close to the chip level RPN , A and B
    ... un finished .

      Need to understand / implement  MODTRAN algorithms .

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