On Wed, 15 Aug 2007 15:47:08 -0700, Phil. wrote:
>
> Phil. wrote:
>> Bill Ward wrote:
>> > On Wed, 15 Aug 2007 07:34:38 -0700, Phil. wrote:
>> >
>> >
>> > > ExterminateAllRepubliKKKans wrote:
>> > >> Arthur Brain wrote:
>> > >> >>Like 0 degrees Kelvin?
>> > >>
>> > >> Fool writes:
>> > >> > Nothing is zero degrees Kelvin, dummy.
>> > >>
>> > >> Ok. .004'K
>> > >>
>> > >> > Deserts are known to be quite cold on clear nights,
>> > >> > why you
>> > >> > would dispute that is beyond reason.
>> > >>
>> > >> Like .004 degrees Kelvin?
>> > >
>> > > In the 'paper' the authors made the assumption in equation 83 of a
>> > > Lambertian profile for the earth with a minimum temperature of 0K
>> > > which then produced mean temperatures of <-100ºC.
>> >
>> > I think you're reading assumptions that aren't there. The context is
>> > showing the difference between equation 81 (averaging the 4th powers
>> > and then taking the fourth root) and 83 (taking the 4th roots first,
>> > then averaging the results. That's already been discussed.
>>
>> Sorry Bill I forgot that you can't read math! In the first line of the
>> derivation of equation 83 the authors start with the surface integral of
>> T, so far so good. In the second line they assume T to be the 4th root
>> of T^4.cos( ) and integrate between the limits of cos( ) = 0 to 1, note
>> that as a result the minimum temperature on their model of earth will be
>> 0K (cos( )=0), hence the rather low mean temperature! The cos^0.25
>> profile that results from their analysis is characteristic of a
>> Lambertian profile and is in fact a good match to the temperature
>> profile of the moon:
>>
>> Brightness Temperatures of the Lunar Surface: The Clementine Long- wave
>> Infrared Global data set. S. L. Lawson and B. M. Jakosky,Lunar and
>> Planetary Science XXX
>>
>>
>>
>>
>> > Diffuse or specular reflection is not mentioned or particularly
>> > relevant at this level. You need to be more explicit if you mean
>> > something else.
>>
>> Just the math Bill very explicit!
>>
>>
>> > > They were apparently unaware
>> > > what they had done and attributed the low T to the averaging method
>> > > (Holder's inequality)! Holder's inequality is illustrated in their
>> > > table 13 where they correctly average T^4 and T for 6 values of T
>> > > where a difference of ~0.5K results.
>> > >
>> > > They then say: "According to the consensus among global
>> > > climatologists one takes the 18ºC computed from the T^ 4 average
>> > > and compares it to the fictitious Earth's average temperature of
>> > > +15ºC. The difference of 33ºC is attributed to the natural
>> > > greenhouse effect. As seen in Equation (83) a correct averaging
>> > > yields a temperature of
>> > > 129ºC. Evidently, something must be fundamentally wrong here."
>> > >
>> > > There is indeed something fundamentally wrong, two idiots made an
>> > > incorrect assumption and their equation produced an incorrect
>> > > answer, GIGO!
>> >
>> > You haven't made a case for that. Quote the part where they make the
>> > assumptions you claim.
>>
>> Done so, case made!
>>
>>
>> > They are simply pointing out the incorrect "global temperature
>> > averaging" claims, and the inconsistencies that result.
>>
>> They think they are I guess but in fact they've swamped it with the
>> gross error I've outlined above.
>> They were so carried away with their own agenda that they didn't pick up
>> on the clues that their own data was giving them (table 13) and bashed
>> on regardless!
>
> Sorry Bill the cos( ) should be cos(theta), the theta symbol on my
> computer apparently doesn't show uo.
No problem. It's obvious.
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