How close to detailed spectral calculations is the

Abstract

The k$k$-distribution method and the correlated-k$k$ approximation of Kato et al. (1999) is a smart approach originally designed for broadband calculations of the solar radiation at ground level by dividing the solar spectrum in 32 spectral bands. The approach is a priori not suited for calculation of spectral irradiance. Nevertheless, this paper evaluates its performance when compared to more detailed spectral calculations serving as references for the spectral intervals no. 3 [283, 307] nm to 26 [1613, 1965] nm for clear and cloudy situations. The evaluation is based on numerical simulations. The clearer the sky, the greater the root mean square error (RMSE) in all bands. In the spectral intervals no. 3 and 4 [307, 328] nm, the irradiance is underestimated by large – approximately −90 % and −17 % in relative value - because the wavelength interval is large with respect to the absorption by ozone and a single value of ozone cross section is not enough for each interval. For each spectral interval from no. 5 [328, 363] nm to no. 18 [743, 791] nm, and for both global and direct radiation, the bias and the RMSE are less than 1.5 % of the irradiance in the corresponding interval under clear skies and may amount to 3 % in cloudy conditions. For greater wavelength intervals no. 19 to no. 26, the relative bias and RMSE show a tendency to increase with wavelength and may reach 8 % and 7 % for global and direct under clear skies respectively, and 11 % and 15 % under cloudy skies.

Keywords

• absorption cross section
• clear sky atmosphere
• cloud
• correlated-
• spectral distribution of solar radiation