Solar Power » Radiation

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:

  • Assisting in sizing of systems
  • Aiding in choice of technology, as some technologies are more appropriate in certain locations than others.
  • Forecasting energy generation
  • Use before or in lieu of detailed site survey.
  • Optimizing the design of devices and operations - especially predicting short-term variations of irradiance in the 1 - 10 minutes forecasting timeframe.

 

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.

Calculation

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.

Result


  Calculated Mean Empirical Value
Intensity [W per m2] 342 187

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:

  • Variations over time due to planetary movements and activities in atmosphere.
  • Attenuation of light due to absorption in atmosphere.
  • Difference between diffuse and direct light.
  • Effect of latitude, tilting of surfaces and reflection off the ground.

On this site, we are presenting basic models for the effects of the solar orbit, tilting surfaces, earth's rotation as well as attenuation and absorption in the atmosphere.

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