Model comparison for the calculation of linke's turbidity factor

Abstract

Pyrheliometric mesurements of direct solar radiation performed at Athens Observatory (NOA) from 1954 to 1992, were used to test the applicability of several models which compute the Link's turbidity factor, TL. The models used in this analysis belong to two categories: the direct, or the so-called pyrheliometric, formula and the indirect, or parameterized, method. The statistical indicators, mean bias (MBE) and root-mean-square (RMSE) error in combination with the t statistic are proposed for the evaluation and comparison of TL as produced by various models. The direct method is presented using three different parameterized algorithms for δR(λ), proposed by Louche et al., Granier et al. and Kasten; whereas the indirect schemes were Dogniaux's and Valko's parameterized models. Based on the comparison against the early pyrheliometric method, Grenier et al.'s model performed the best with respect to R2, MBE, and RMSE, whereas adjusted Louche et al.'s, Louche et al.'s, Valko's, and Dogniaux's II and I models follow in that order. It is significant that Valko's model performed the best with respect to the t statistic. Dogniaux's scheme was found to depend strongly on the acrosol's microphysics loading in the atmosphere, whereas Valko's scheme did not show such a dependence. Finally, the probable dependence on the water vapour content of the relationship linking TL to Ångstrom's turbidity coefficient β, is discussed. © 1997 by the Royal Moteorological Society