# Calculating temperature rise due to solar insolation

1. Feb 26, 2016

### Appledave

1. The problem statement, all variables and given/known data
(This is not a homework problem, just something I'm curious about.)

Assuming ideal conditions (clear skies, a flat landscape, no wind, anything else you can think of), is it possible to calculate how much the temperature (at 2 meters above the ground, as per meteorological standard) would increase during the day due to solar radiation?

2. The attempt at a solution
There are so many elements here that I know so little about that I don't really know where to start, but here are my thoughts on the problem:

As air is primarily heated by the ground, one would have to figure out how much the ground gets heated, and then how much the ground heats the air. I'm guessing this requires some sort combination of the Stefan-Boltzmann law, heat capacities, and possibly other things. I also think one would have to integrate over the day as the sun changes in strength. The answer would also depend on the ground albedo and the latitude and time of year.

I can probably find data on albedo, solar insolation by latitude etc. but the actual calculation has me beat. Any help is greatly appreciated :)

(It would be fun to take other things into account as well, like vegetation/buildings, different landscape topologies, inversion, wind, clouds, precipitation, morning dew etc. but now I'm probably entering the realm of computer simulations.)

2. Feb 26, 2016

### haruspex

Two key issues will be convection and moisture.
Strength of convection will depend on the temperature profile higher up.
Moisture in the ground will evaporate, aiding the transfer of heat from ground to air, but also boosting convection (moist air being less dense than dry air).

The discussion and diagram at http://www.skepticalscience.com/Tracking_Earths_Energy.html might help.