# Can I estimate the long-term surface heat transfer coefficient based on a temperature difference between the air surface and ground surface?

I want to estimate the long-term or annual heat transfer coefficient for the earth's surface in a particular area where the mean annual air surface temperature is about 13$^\circ$C, and the mean ground surface temperature is about 15$^\circ$C. How can I do this?

The general expression is $h=\frac{Q}{A \cdot \Delta T}$. So I suppose the heat flux term $Q$ is some sort of sum of the earth's outward flux and the sun's inward flux (I have a good estimate of the former: ~70mW/m^2, but I don't know the latter for this latitude. The latitude is about 37 degrees south.)

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As Mark Rovetta notes in the answer below, this is not a convective heat transfer problem - you need to account for radiation. The simple linear heat transfer coefficient h is not the answer. Radiation is proportional to the 4th power of the absolute temperature. –  Mark Oct 2 '13 at 1:05
How is this not a convective problem, there is wind? –  user22620 Dec 18 at 5:18

## 1 Answer

Over a year or few, the net contribution due to solar needs to be zero - otherwise the temperature of the ground would be rising or falling.

See a Solar Radiation Data Manual for Buildings type of reference to get an idea of how incidence solar radiation actually varies at a particular locale.

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Not zero, surely?? There is always radiative energy coming in, how can it be zero? Over a year or so the net effect is a constant, but it must be greater than zero? I'm sorry if I misunderstand something here... not a physicist. –  a different ben Oct 9 '13 at 3:32
The earth radiates heat too. Much of the incident solar energy will be reflected and radiated back into space. –  Mark Rovetta Oct 9 '13 at 14:06
Of course at this time the net radiative heat transfer is slightly positive because of the higher CO2 concentration, and will continue to be positive until the earth warms enough to reach a new equilibrium. But that is small with regard to this question. –  Mark Oct 18 '13 at 1:00
Are you assuming that albedo is uniform globally? If albedo varies, and net radiative heat transfer is zero, then any given region is likely to have non-zero rad. heat transfer. –  user22620 Dec 18 at 5:16