A Simple Method to Estimate Total Solar Radiation on a Slope Surface Considering Direct and Diffuse Components

Abstract

A simple climatological method to estimate the global radiation incident on a slope surface was developed. The direct, the sky diffuse and the ground-reflected diffuse radiations under actual weather conditions were considered in this model.The global radiation (Rs) incident on a slope surface may be expressed as follows;Rs=Rb+Rd+Rrwhere Rb, Rd and Rr are the direct, the sky diffuse (isotropically distributed diffuse component +circumsolar component) and the ground-reflected diffuse radiations incident on a slope surface, respectively.Each component was formulated as follows;Rb=[a+b(n/N)] [a′+b′(n/N)]RsdirRd=[a+b(n/N)] [Rsdif+{1-a′-b′(n/N)}Rsdir]Rr=[a+b(n/N)] Rsrefwhere Rsdjr, Rsdif and Rsref are the apparent direct, the isotropical sky diffuse and the ground-reflected radiations incident on the slope under “standard clear sky conditions”, respectively. n is the number of hours of bright sunshine, N the number of daylight hours, a, b, a′ and b′ are the empirical constants.Rsdir, Rsdif and Rsref are given as follows;Rsdir=(ro/r)2RoPm sinh′Rsdif=Rsdir(0)(1+cosβ)/2Rsref=ρ[Rsdir(0)+Rsdif (0)](1-cosβ)/2where r and r0 are the earth-sun distance and its mean, R0 the solar constant (=1382Wm-2); P the transmission coefficient, m the relative optical airmass, h′ the altitude of the sun for a slope surface, β the slope angle of the surface, ρ the mean albedo of the ground surface, Rsdir (0) the Rsdir for a horizontal surface and Rsdif (0) the sky diffuse radiation incident on a horizontal surface which was given by Berlage (1928).The values of empirical constants a, b, a′ and b′ are determined for several stations in Japan. Monthly mean values of these constants for the Pacific coastal zone in Japan, a=0.298, b=0.727, a′=0.119 and b′=1.116 were obtained (Table 2 and Table 3).The results obtained by this model are shown to compare favorably well with the observation data measured by Uchijima et al. (1981).The dependencies of Rs, Rd and Rb on the slope angles with each different slope orientation were evaluated. The results show that the values of Rs on the slope surface vary widely with the slope angle and with the orientation in winter season than that in summer as shown in Fig. 6.The annual changes of monthly mean values Rs/Rs, H; Rb/Rb, H and Rd/Rd, H are shown in Fig. 7 (A, B, C), where the suffix H indicates the radiation on a horizontal surface, respectively. The maximum annual variation of Rs/Rs, H is seen in the south-facing vertical slope (β=90°) surface with the values from 0.2 to 1.8. The change of direct radiation component (Rb) greatly contributes to the change of the total short-wave radiation (Rs) especially in winter. On the contrary, the diffuse radiation component (Rd) play an important role in summer season because the weather condition is generally abound with cloudy.The effect of the albedo on incoming shortwave radiation on the steep angle slope surface is greater than that on the gentle angle.