MATHEMATICAL-MODEL FOR PREDICTING THE MAGNITUDES OF TOTAL, DIFFUSE, AND DIRECT-BEAM INSOLATION

The simple mathematical model resented assumes that: (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 tau(gmr) = Ae(-c rho alpha mr) in which A is a scaling coefficient, m(r) is the relative air mass, and Cpa is an attenuation factor which depends on the angle of incidence; (ii) the diffuse fraction can reasonably be described approximately as tau(dmr) approximate to 1 - (Bm(r) + tau(gmr)) 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.