The definition of the effective radiative temperature tells exactly, what it is:

It’s the temperature of a blackbody that radiates as much as the Earth to the space.

That’s not exactly an average with any easily definable weights. Some weighted average may agree reasonably well with that, but not exactly. It’s better to stick with the definition. Trying to interpret it as a weighted average is probably more confusing than clarifying.

]]>Or something to this effect.

]]>Not necessarily at all. In SoD’s model it’s calculated as a separate “curiosity value”, that’s otherwise rather irrelevant.

]]>As far as I know no radiative transfer model calculates OLR flux using weighing based on Planck law calculated using the surface temperature and transmittance trough the whole atmosphere. Only some crude descriptions that have other than scientific purposes might do that. It’s possible that this error appears in some educational material for audience outside climate science.

Every serious radiative transfer model uses for emission the temperature at the point of emission, i.e. the lower temperature the higher in the troposphere, the emission takes place. This is also the approach in the model described in the series of posts on visualizing atmospheric radiation

https://scienceofdoom.com/roadmap/visualizing-atmospheric-radiation/

]]>It seems like the average net ‘T’ or net transmittance must be some sort of integral that’s weighted by the Planck Function of the surface temperature. That is, it is the fraction of surface radiative power that is considered to be transmitted through to space and the difference (i.e. 1-T) is the fraction of surface radiative power that is considered to be absorbed or attenuated by the atmosphere.

It does make sense to me that the net ‘T’ should be weighted by Planck Function of the surface since the radiating surface is the plane from which the opacity of the whole mass of the atmosphere through to the TOA is being measured.

]]>Zur Rechnung benutze ich lieber eine andere Form der Strahlungstransportgleichung

pa * dI / dp = I – B

Dabei ist pa ein Druckwert aus der vertikalen Säulenlänge, die gleich der Absorptionslänge ist. Die Absorptionslänge ist druckabhängig, weil die Dichte der Moleküle druckabhängig ist. Das fällt beim Absorptionsdruck weg, weil zu gleichen Druckdifferenzen gleiche Molekülmengen gehören.

The radiative transfer equation is a calculation only ostensible of the intensities as a function of the temperature. She is to calculate the fixed temperature profile because the sum of all changes in the intensities must yield zero – otherwise it would not stationary.

To account I use prefer a different form of the radiative transfer equation

pa * dI / dp = I – B

Here, pa is a pressure value from the vertical length of the column, equal to the absorption length. The absorption length is dependent on pressure because the density of the molecules depends on the pressure. The omitted away at the absorption pressure, because at the same pressure differences include same molecular quantities.

MfG

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