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  • Bob Armstrong

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    Understanding Planetary Temperature
    Show me your equations

    From  20140922Given such demonstrations of willful ignorance by an urban crowd ( which my observation of NYC events during my couple of decades there and the images I've seen , I judge to be significantly less than 300k )  as we just witnessed , I'm far from sure there is any way to inform the willfully stupid .

    #Need for an open online explication of the basic physics of planetary temperature
    I have been diverted into the whole AlGoreWarming ( blame Stanley Goldenberg ;)  )  statist stupidity only because I could not find a competent , quantitative analysis of the physics of planetary temperature anywhere on the openly accessible web . What I saw and continue to see is astoundingly mathematically and physically amateurish , and often just plain wrong .

    I come to the problem as someone who aced high-school physics thanks to the brilliant , but unforced , PSSC curriculum , but then followed other interests which eventually led to my living a life where array algebra was always at my fingertips .  It is far easier , and never conclusive , to wave around words or even indulge in computational clouds not grounded in the most basic observations and theory than to quantitatively explain observations from the most precisely understood theory and data .

    Planetary Temprature proportional to square-root of distance from sunI naturally started by implementing the most basic relationships . At Joe Bast's invitation , I initiated an Essential Physics page on Heartland's ClimateWiki . Even the inverse square-root law implied by Stefan-Boltzmann for the temperature of a planet given its distance from the sun and the fact that all the inner planets other than Venus are within a few percent of their calculated values is a high-school level fact I have never seen presented anywhere . It alone rules out fantasies of "terraforming" Mars to bring it up to a livable , ie , greater than 274k , temperature . ( As I noted in my presentation , the variation in our orbital distance from perihelion ( in January ) to aphelion implies a difference of about 4.7c . Yet I have never heard of a report finding this necessary effect , which is much larger than the total asserted warming , in the data . | 20150428 |: See Watts Up With That 2015/01/09 two-new-papers-suggest-solar-activity-is-a-climate-pacemaker/ )

    I encourage you to review Essential Physics for any errors , and to submit the algorithms in more common languages , and flesh out  the many stubs with the relevant explications and algorithms .

    Finding no basic college level introduction ( comparable to those in other branches of applied physics )  on the web , it took me a , in retrospect , ridiculous amount of time to reduce the essential equation for radiative balance given a source power spectrum and an object absorptionemission spectrum to finding T such that :

      dot[ solar ; objSpectrum ]  =  dot[ Planck[ T ] ; objSpectrum ]
       dot :  { +/ x * y }    . or most mimimally ,  dot : +/ *      in  K .

    This is the equation which , given the crude hypothesis that the earth absorbs 0.7 of incoming solar radiation , but emits as a black body , ie , 1.0 , produces the ubiquitous 33c atmospheric greenhouse effect .  I actually was surprised that when applied to Venus , it is quantitatively impossible by an order of magnitude to explain its surface temperature , 226% ( 2.26 times ) that of the gray body temperature in its orbit , as a greenhouse effect .

    This meme , that Venus is the greenhouse the Earth may turn into ,  promulgated unchallenged for years by James Hansen , is accepted without analysis by the general "climate science" community .  Recently in reply to a blog post I can't locate in which I  made the assertion above , Joe Bastardi expressed the common comment that the extreme Venusian surface pressure was the answer . In other words , that pressure , per se , was a parameter left out of the equation above . But it's not . Compressing a gas , of course increases its temperature , but static pressure does not simply make something have a higher equilibrium temperature . ff it did , we could solve our energy problems simply by filling up scuba tanks which would stay hot and we could stick a thermocouple in the middle of them and collect the current from an identical one outside . More formally , the divergence theorem says that the interior of an externally heated sphere will come to the same mean temperature as that calculated for its surface . That is , the center cannot be hotter than the surface without some internal source of heat . 

    Heartland Opening Screen ShotI remember a brief chat with Willie Soon at the 2009 WDC conference in which we disagreed on the value of experiment in addressing these planetary issues .  I think the above is an example where experiment can be  dispositive . Of course these laws were abstracted from experiments more than a century ago .  And it was largely the brilliantly simple experiments in the PSSC curriculum , despite my intense allergy to writing them up and turning them in , which contributed to my acing the College Board .   Now days small cryogenic vacuum chambers start around $1500 which is within the budget of affluent high-schools . ( BTW : Thanks to whoever chose that cover shot for my talk . Much more to the point than would have occurred to me . )

    Why APL
    My attack is as an APL programmer capable of expressing physics in executable notation as or more succinct than in any printed textbook . And that ability to casually compute and "play with" the computations was the subject of the first 2 slides of my Heartland presentation .  A half century after Ken Iverson's original work , APL remains as revolutionary as calculus was a half century after Newton and Leibniz  .  A friend of mine , Brooke Allen , recently connected on LinkedIn . His I owe EVERYTHING to some funny symbols provides another perspective on APL's impact . Yet another slice at APL is the videos of the winners of this year's Dyalog APL competition .

    I had an interesting brief chat with Roy Spencer the first evening of the Heartland  conference . After expressing my thumbs up for his justification of the use of the the  term climate nazis , I mentioned that my presentation would be on the most basic computations of radiative balance with all the algorithms used presented in APL in the slides . Roy mentioned they , like Gavin Schmidt , do everything in FORTRAN . He said he and his programmer had tried more "modern" languages , but always found limitations which drove them back to FORTRAN .  We did find that we both spoke the same language of dot products and the like tho .  ( I just tested that my nascent 4th.CoSy will do a dot product on a million floating points on my Intel 3470 based desktop in an imperceptible amount of time . )  I don't think the simple algorithms used to calculate the radiative balance for arbitrary spectra in my presentation get across the expressive power of APLs . A recent accounting example came up which better illustrates the abilities . This is in the legacy K from which I used in my presentation and still use for all my accounting .  I had a list of 8 expenses , call it Q .  I wanted to figure out what subset of the matched a check I received . So I executed the following lines :

      Q : -10 -28.18 -19.95 -28.79 -37.39 -35.58 -350 -29.67
      QW : &:' + 2 _vs ! _ 2 ^ 8       | make an array to select all the subsets
                                       | of the 8 items
      QW @ ,/ & -442.92 = +/' Q @ QW   | find the subset that adds up to 442.95
    2 4 5 6                            | The indices of the matching subset .

      Q @ 2 4 5 6
    -19.95 -37.39 -35.58 -350

    To explain a little : There are 2 ^ 8 , 256 , subsets of 8 items .  The  ! _ 2 ^ 8  returns the first 256 integers ( the first being 0  ) . The  2 _vs converts each one to its binary string of 0s and 1s .  The   &:'  converts each of them to the indices of all the 1s .  The second line selects selects all of those subsets of the expense items , Q , and adds each of them up . Then it tests which one equals -442.92 and returns the row corresponding list of indices from QW .  So , I know that the check was for items  2 4 5 6  of my list of expenses .

    Let me see that in FORTRAN , even with a lot of array features influenced by APL added over the decades . For that matter let me see that procedure expressed as succinctly in any traditional mathematical vocabulary , including Mathematica .

    I have Hollerith card boxes full of FORTRAN implementing a small sample statistic for my masters in the mid '70s .  Then the Vogelback Computing Center got APL and I never had time for legacy languages again . To me , their only use is implementing APL functionality .  And for that purpose , I see Forth , whose philosophical goal is the the minimal vocabulary capable of extending itself from the silicon up , as the only foundation of interest .

    Time out for a commercial :

    Of the 2 corporate systems I wrote after learning APL catalyzed my loss of tenure in grad school , the more significant was rewriting Xerox's long range world wide market forecasting system which I had been contracted to maintain . It took overnight to aggregate reports and cost a quarter-million a year in mainframe time .  It had been written in APL by COBOL programmers . It happens one of the last courses I had sat in on was introductory topology where I had learned the binary representation of a relation . One weekend , since I had access to the mainframe from my apartment , I took a cross section of data and implemented the essential relational selection functions in terms of a boolean image of the data .  I demonstrated that I could speed up retrievals and computations by a factor of about 3000 turning overnight requests into at worst a few minutes -- with concomitant savings in CPU costs  .

    That sold them on having me rewrite the whole system , essentially creating a numerical relational database language capable of doing rapid , for the time , computations on up to about 14 million entries .

    I would like to make a similar offer to anybody who has a planetary physics related computational task which would require a week or two in FORTRAN or whatever to program .  If I can't do it over night , I'll do it over a weekend . 

    My background gives me a pretty good understanding of spectra , but not conduction much less convection .  Convection doesn't come into long term averages .

    My overall goal , a planetary model in APL , specifically in , 4th.CoSy ,  requires personal collaboration with real physicists who know the essential algorithms and the data and how it is collected .  I don't even know how one accurately collects the ae spectrum of a planet . Does it change from day to night ?  Such a change could easily account for our 3% over our orbital gray body temperature . I actually implemented that sort of partition of the sphere for grayvalues  , ie ,  scalar ae , before taking on spectra .  That partition vocabulary is the foundation of any mapping of the sphere , eg , adding spectra and cosine functions to each patch .

    Beyond being my own tool of thought , my motivation for learning APL was to be able to read papers such as this :
     Astrophysical APL - Diamonds in the Sky , Schneider, Paluzzi, & Webb :
        Members of the Space Telescope group present the physics of carbon white
        dwarf stars in half a dozen short APL functions.

    presented at the APL89 conference in NYC . I felt a population understanding an APL level notation was the only way my own work could be communicated .

    In early September in a blog battle with a dedicated warmist , I was referred to a table of Venus's emission power spectrum David Crisp at JPL . I sent him messages thru JPL's website facility on Thursday , the 11th , and again on Wednesday , the 17 .  These are posted in the Disqus section of my Basic Basics page . I followed up leaving him a voice mail , Friday , the 19th . He has not gotten back to me even with a few relevant URLs .

    While this pursuit of a quantitative understanding of planetary temperature must , in the absence of support , fall back to being just a third order avocation , I have purchased a couple of old editions of books mentioned as classics on the Science of Doom warmist , but physics oriented , blog .  SoD is kind of like a warmist WUWT but oriented more towards understanding the physics rather than the data .

    Overall , they've confirmed my disinclination to gamble textbook prices on books which may or may not have a useful correlation with my particular path .

    Specifically , I've gotten

    • Introduction to Heat Transfer , 2006 , Incropera, Frank P. et al
      Has taught me more about the difference between engineering and physics . Slow on getting to the meat , but lots of interesting examples . Have learned one interesting observation :
      " because [density] and [mean free path] are directly and inversely proportional to the gas pressure, respectively, the thermal conductivity is interdependent of pressure except in extreme cases as, for example, when conditions approach that of a perfect vacuum."
      This implies that the temperature gradient across Venus's atmosphere should be fairly linear .

      Induced me to pull out an old Schaum's Outline of Theory and Problems of Heat Transfer , 1977 , Pitts & Sissom . to get straight to the formulae .

    • ATMOSPHERIC RADIATION , Theoretical Basis , 1964  Goody, R
      Suffers from age , eg , the prominence of byzantine British measures , eg , the Rankine temperature scale .

    Goody makes the interesting observation , quoted in the image on the right , that there are two approaches to understanding planetary temperatue , one starting from the measured phenomena and working to explain it . That appears to be the ubiquitous method . But without the other , the traditional analytical understanding of abstracted systems simple enough to be quantitatively confirmed by experiment , one never can be said to understand .


    I , obviously , am focused on the second approach . Indeed , my superior interest is the implementation of the executable computational notation itself . That's actually a significantly more difficult problem . This summer I failed to dissuade a guy out along Monterey Bay , CA  , even with the image of a piece of my path out to the Heartland Las Vegas conference , from attempting 4th.CoSy which spans the spectrum from Intel X86 language thru Chuck Moore's minimal Forth up to the ultimately abstracted notations inspired by Ken Iverson . He convincingly has never programmed in any language .

    So , I've been induced to upload a current version of here : 4th.CoSy  Download & Disqusion .

    Metaphor for both Understanding Planetary Temperature , or mastering & advancing 4th.CoSy
    Burr Trail UT , Wall

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