Modeling Solar Radiation at the Earth’s Surface

Conclusions and Future Work

We would like to relate some of the main results of this work and to discuss the future research in the field of the modelling of the statistical properties of the in­stantaneous values of solar radiation.

The distribution of the solar radiation components at the Earth’s surface can be analysed based on the kt, kb y kd indices. This analysis is widely used. Most of the bibliography is related to the analysis of clearness index, while still scarce works have dealt with the direct and diffuse components of the solar radiation.

In most cases, the distributions are analysed conditionally by the optical air mass or based on time-averaged intervals. In this latter case, the distribution of the daily index kt for a given monthly-average value is the most widely used.

In many cases, although the bibliography shows a wide range of results, the dis­tributions show a marked bimodality. For daily distributions, this bimodality seems related to climatic features with relatively high cloudiness, while this bimodality is not observed for climates with relatively low cloudiness.

The hypothesis by Liu and Jordan (1960) of a universal character of the CDFs is not supported, as also deduced by works of Bendt et al. (1981), Reddy et al. (1985), Olseth and Skarveit (1984), Saunier et al. (1987) and Ronnelid (2000).

Additionally, the attempts of different authors to provide general models do not seem feasible. On the opposite, the bibliography is plenty of works proposing mod­els developed for specific regions, due to the non-adjust performance of these gen­eral models.

The instantaneous distribution shows a marked different behaviour from those of the hourly, daily and monthly distributions. Particularly, for the distributions condi­tioned by the optical air mass, an increment in the bimodal character is observed.

We have proposed a model for representing distributions of data collected in a wide range of climatic conditions. Particularly, the proposed distributions allow easily calibrate the parameter of these distributions based on the climatology of the study area. This makes the model, in some sense, general. Additionally, based on the proposed distribution functions it is easy to obtain the CDFs. and, also, the genera­tion of synthetic solar radiation time series. The CD attached to this book contains the programs and the code source used to fit the density distribution functions with the models proposed by the author.

We would like to highlight that, in our opinion, any attempt of solar radiation modelisation should take into account the climatic characteristics of the study area, since these characteristics strongly influence the solar radiation values and the asso­ciated statistics.

Some authors have used normalisation processes in their statistical analysis, try­ing to overcome the site dependences of the models. We think, on the opposite, that these dependences should be taken into account in the modelling process, through adequate parameter tuning.

We would also like to point out that there are still scarce works dealing with the statistical analysis of spectral solar radiation values. On the other hand, there are some preliminary works dealing with solar radiation instantaneous values collected at intervals less than 1-minute. Finally, in the last years, the wavelet spectral techniques have begun to be used in the analysis of solar radiation data. This tech­nique allows to identify the most important modes for the variability of the solar radiation time series and to allocate time flags when these modes take place.

Modeling Solar Radiation at the Earth’s Surface

Quality Assessment Based Upon Comparison with Models

Many models based on the physics of radiation transfer through the clear atmo­sphere have been developed (Lacis and Hansen 1974; Atwater and Ball 1978; Hoyt 1978; Bird and Hulstrom 1981a, …

Solar Horizontal Diffuse and Beam Irradiation on Clear Days

There exist a number of models to determine the solar horizontal diffuse irradia­tion on a clear day (Kondratyev 1969) but they are complex and have very stringent conditions. Similarly, there …


Reading the twenty chapters of this book caused me mixed reactions, though all were positive. My responses were shaped by several factors. Although I have main­tained a “watching brief’ on …

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