Simulation of the sun's effect on temperature change on the ground surface

[hersh37]

Hi,

I am working on simulating the change in temperature over time for the ground, given different material types. For instance, I'm considering an asphalt patch of ground say 10 square meters in area. For now, I'm willing to ignore atmospheric effects like rain, wind, and varying sun angle. I assume for now that the sun is directly overhead.

If the ambient temperature of above the ground is 20 degrees Celsius, and I assume the asphalt is in thermal equilibrium with the environment at time t=0, then it is also at 20 degrees Celsius. How would I go about determining the aspalt's new temperature at time t=1?

I'm probably missing something, but I see that the radiant energy from the sun will act on the asphalt patch, and excite its molecules, which will cause it to rise in temperature, however is there a way to calculate how much (even approximate)?

According to sources the sun's radiant intensity at the Earth surface can be approximated to about 250 W/m^2. For the 10 square meter aspalt surface, this would be 2500 W then. If I use this is as the value of $$\Delta$$ Q in the equation $$\Delta$$ Q = c $$\Delta$$T, with c=0.93 for aspalt, this gives me an unbelievably high value for the change in temperature.

I know I'm doing something wrong here. Any help is greatly appreciated. Thanks :)

 

[Upisoft]

The asphalt is going to radiate the thermal energy. You will want to know how much its radiation differs than black body radiation.

 

[willem2]

Hi,

According to sources the sun's radiant intensity at the Earth surface can be approximated to about 250 W/m^2.

This is an average of the irradiaton over the whole globe, including the night side and places where the sun is far from the zenith.

With the sun directly overhead, it's 4 times as high. This is because the Earth only catches
the sunlight in a disk with an aria of $pi R^2$ where R is the radius of
the earth, but the surface of the Earth is $4 pi R^2$, so the average is only
(1/4) of the maximum