Modelling Solar Irradiation
With planetary movements, processes in the atmosphere and other effects, solar radiation on earth is an intermittent source of energy.
On the earth’s surface the peak solar intensity hovers around 1 kW/m² on a horizontal surface at sea level with the sun in its apex on a clear day. In general, the value will depend on the position of the sun, the clearness of the sky and the geometry of the surface.
Due to the complex nature of some of the processes, no theoretical calculations for irradiance is entirely accurate. Nevertheless, these models are helpful in understanding the main drivers as well as:
Mean intensity on horizontal surface on earth without atmosphere
Assuming the atmosphere has no impact on the incoming light, we can easily calculate a mean intensity on earth by dividing the total irradiance on the cross section of the earth by its surface area.
Given the diameter of the earth, D=12,800km, the cross section is C=¼pD2. The intensity on the cross section is the solar constant of 1,350W/m2. Hence, the mean intensity on the surface of the earth is I = I0 C / (pD^2). This value already takes into account that at any one time, the sun only shines on half of the surface of the earth.
Over a 24h period, this results in an average daily energy of 8.22 kWh/m2.
Eventhough this is a crude approximation it is very instructive. However, this simplistic model fails to describe the impact of: