Modeling Solar Radiation at the Earth’s Surface
Distributions of Diffuse and Direct Components of Global Radiation
Research about the direct and diffuse components of the solar radiation is less prolific, mainly because of the scarce availability of such data. Moreover, most of the direct component analyses involve the use of data obtained from the differences between measured global and diffuse radiations. Lestienne’s works (1978, 1979) suggested the use of two different types of exponential functions for the daily behaviour: one for cloudy days and the other for clear days. Stuart and Hollands (1988) analysed the shape of the hourly direct component suggesting a polynomial fitting for the cumulative distribution function. Later, Callegari et al. (1992) developed a dynamical statistical analysis to reproduce daily direct solar component.
Skartveit and Olseth (1992) compared the global and direct instantaneous distributions, proposing some models for the PDFs of short-term (5-minutes) irradiances. These distributions are not unique functions of the hourly mean, but they depend on the averaging time and also on the inter-hourly variability among 3-hourly averages, namely, the hour of the study, the preceding and the following. Tovar et al. (1998b) continued their previous work and proposed some functions based on the Boltzmann statistic to explain the clearness index distributions. Regarding the diffuse component, the work is worthy of being mentioned by Suehrcke and McCormick (1988b). The results of this study have been used by Tovar et al. (1998b).
So far, the analyses of the solar radiation variability followed very different approaches. Nevertheless, one shared pitfall for most of them is that they were carried out using local data bases. This implies that the proposed models are site dependent and new evaluations must be performed when using data sets from other locations. Finally, it is worth to point out that the analysis devoted to the behaviour of the direct and diffuse components are still scarce. In the last years, these components are being investigated for some special spectral regions from the statistics point of view. For instance, among other works, the photosynthetically active region (PAR, 400-700 nm) have been studied by Ross et al. (1998) and Tovar-Pescador et al (2004), and the ultraviolet region (UV, 290-385 nm) was studied by Varo et al. (2005).
