Mathematical model for predicting the magnitudes of total, diffuse, and direct-beam insolation

The simple mathematical model presented assumes that: 1. (i) the characteristic diurnal distribution of the fraction of the incident solar radiation available outside the atmosphere that is received on a horizontal surface under clear-sky conditions can be expressed as a curve of the form τgmr=Ae−cpαmr in which A is a scaling coefficient, mr is the relative air mass, and cρα is an attenuation factor which depends on the angle of incidence;2. (ii) the diffuse fraction can reasonably be described approximately as τdmr≈1−(Bmr+τgmr) in which B is the broad-band absorptivity. Measured values for the solar irradiance recorded at 1 min time intervals at a rural location near Cambridge, UK, were used to examine the relationship between the fraction of the solar radiation received on a horizontal surface and the diffuse fraction. The measurements corroborate the predictions from the mathematical model, whose validity is thus supported.