Modeling Solar Radiation at the Earth’s Surface
Hourly Distributions of Global Radiation
The number of studies about the hourly irradiance is less than for longer time scales. Some authors, as Engels et al. (1981) or Olseth and Skartveit (1987, 1993) emphasise that the hourly distributions are similar to the daily ones and they even use the same fitting procedures. Ettoumi et al. (2002) used Beta distributions to model the behaviour of the global solar irradiation in Algeria. Only few authors are pointing out an increase in the bimodality with regard to the daily distributions.
6.2 Instantaneous Distributions of Global Radiation
The distributions that can be considered as instantaneous (less than 10-minutes) show a different shape, since the transient effects caused by clouds are now evident and contribute to the increase of the bimodality. The first authors who proved the
strong bimodality of these clearness index distributions (with 1-minute basis data) were Suehrcke and McCormick (1988a). They analysed a year of irradiance data collected in Perth (Australia) for different values of optical air mass and proposed a fitting function. Tovar et al. (1998a) confirmed the hypothesis of Suehrcke and McCormick using 1-minute data collected during almost three years in Armilla, near Granada, (Southern Spain). They observed the strong bimodality of the distribution conditioned by the optical air mass, increasing as the air mass increases. These authors proposed a model based on the Boltzmann statistic. Later, they studied the variability of the probability density based on the daily irradiation (Tovar et al. 2001). These last distributions presented unimodal features, unlike the distributions conditioned by the optical air mass. Nevertheless, the same type of fitting function can be used (Tovar et al. 2001). The model of Tovar et al. (1998a) has been used by other authors, like Varo et al. (2006), who evaluated the model with data collected in Cordoba (Southern Spain). They achieved reasonable performance using different fitting parameters according to the local climatic conditions. Vijayakumar et al. (2006) analysed the instantaneous distributions, with the aim of exploring the differences between hourly and instantaneous distributions. They concluded that the variations in solar radiation within an hour cannot be considered negligible when conducting performance analyses of solar energy systems. Depending on the critical level, location and month, an analysis using hourly data rather than short-term data can underestimate the performance between 5% and 50%. Tomson and Tamm (2006) analysed the distribution functions of the increments of solar radiation mean values over a period of time, classifying the solar “climate” in stable and highly variable. They found that the distributions functions can be explained by the superposition of two exponential functions with different exponents. The study of Woyte et al. (2007) introduced the wavelet techniques to analyse the cumulative frequency distributions of the instantaneous clearness index for four datasets from three different locations. The analysis resulted in the known bimodal pattern of the distributions. The wavelet technique allows the identification of fluctuations of the instantaneous clearness index and their specific behaviour in the time dimension.
