"Climate Scientists" like Al Gore invoke the phrase "radiative balance" and claim that without the "greenhouse effect" the Earth's temperature would be 33 Celsius  colder .  The classic computations here show the maximally biased useless nature of that assumption . We are 10c warmer than if there were literally no greenhouse effect .

When these computations are applied to the parameters of Venus , they show James Hansen's claim that its surface temperature is due to a "
runaway greenhouse effect" does not compute .
Calculation of
Earth's
Radiative Balance
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  • © Bob Armstrong
    Thu.Feb,20130207

    Below is a graph showing the calculation of Earth's radiative balance given a few different assumptions . If you have any questions or comments please post them below .

    The basics , how to calculate the equilibrium of a gray ball in our orbit , are at Category:Essential Physics - ClimateWiki which is a Heartland site . That provides the basis for How to Calculate the Temperature of a Radiantly Heated Colored Ball which culminates in the graph below :

    Spectra of Sun , Planet , and absorption-emission

    The blue and red curves are the Planck energy , black body , spectra of the sun , scaled to our distance from it , and of a black body in equilibrium with it .  The areas under the 2 curves are equal . The temperature generating the red curve is 278.7 kelvin .

    The absorptivity of the earth with respect to the sun's spectrum is about 0.7 . There is a line across the sun's spectrum at 7 on the graph . The simple flat , gray , spectrum line is extended in very light blue across the graph .

    Multiplying by 0.7 or any constant clearly won't change the radiative balance between the blue and red spectra . Thus a gray ball , no matter how dark or light , will come to the same equilibrium temperature . This is the fact ( Kirchhoff-Stewart ) that I learned as a grade school nerd during the Eisenhower administration which has driven my battling this global statist nonscience .
    The greenhouse effect can be defined as the difference from this temperature due to the color , ie , spectrum , of an object .

    The Stefan-Boltzmann law is simply that energy density* is proportional to the 4th power of temperature . Thus , In order to explain our 3% warmer than gray observed 288 or so temperature , we have to be about 15% less absorptive , more reflective , in the long wavelengths than our 0.7 with respect to the sun .  The green line continues at the ~ 0.6 that works out to .

    For the geeks , the essential relationship computed here it to find temperature T such that

    dot[ solar ; 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 .

    The black line jumping to 10 ( 1.0 ) in the long wavelengths manifests the ubiquitous assertion that without greenhouse gases , our planet would radiate as a black body . It produces a temperature of about 255.7 . This number and 33c greenhouse effect generated by this calculation has grossly retarded any progress in climate science . The field , both sides , just career around in their computational clouds somehow trying to make sense of a quantity which is 2%3 their own creation .

    I think it rather obvious that given any particular full spectrum , its radiative balance can be calculated . This balance depends on its spectrum as seen from the outside ,  not on how it gets there . Thus it is open to experimental verification as it has been for more than a century .

    It's when when applying these calculations to Venus came up in a blog exchange things really got interesting . But I'll leave that to my End of 2012 NewsLetter .

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