Modeling Solar Radiation at the Earth’s Surface

Physical and Statistical Modelling of Solar Radiation

In order to understand and to model the behaviour of solar radiation, two approaches can be used (Festa and Ratto, 1993).

a) The first one is called “physical modelling”, and studies the physical processes occurring in the atmosphere and influencing solar radiation.

In the upper atmosphere, the incoming solar radiation is affected by atmospheric components, such as molecular gases, aerosols, water vapour or clouds. Part of this radiation is backscattered to space, another part is absorbed and the rest falls into the Earth’s surface. This latter component interacts with the surface, part is absorbed and the rest is reflected back to space. Therefore, the diffuse radiation is composed by the radiation backscattered by the atmosphere before reaching the ground and by the component reflected by the Earth’s surface. Finally, the radiation on the surface depends on the absorption and scattering processes in the atmosphere.

The physical method is exclusively based on physical considerations, allowing that the radiant energy exchanges take place within the Earth-atmosphere system. This approach dictates models that account for the estimated solar irradiation at the ground in terms of a certain number of physical parameters (water vapour content, dust, aerosols, clouds and cloud types, etc.).

b) The second approach, which could be called “statistical solar climatology”, arose mainly as a tool to reach immediate goals in solar energy conversion, rapidly becoming an autonomous field of solar energy research. This methodology can ide­ally be subdivided into the following topics:

• descriptive statistical analysis, for each place and period of the year, of the main quantities of interest (such as hourly or daily global, diffuse or beam solar irradi­ation) and statistical modelling of the observed empirical frequency distributions;

• investigation on the statistical relationship among the main solar radiation com­ponents on the one hand (for instance, diffuse versus global irradiation) and the spatial correlation between simultaneous solar data at different places on the other;

• research on the statistical interrelationship between the main solar irradiation components and other available meteorological parameters such as sunshine du­ration, cloudiness, temperature, etc;

• forecasting of solar radiation values at a given place or time based on historical data. The statistical forecasting models often constitute a method used in climate prediction. It is also an appropriate methodology to estimate the probabilistic future behaviour of a system based on its historical behaviour.

The application of the statistical methods to solar radiation research involves a wide range of studies:

• characterisation of numerical data to describe concisely the measurements and to aid to understand the behaviour of a system or process;

• to aid in the estimation of the uncertainties involved in observational data and those related to subsequent calculations based on observational data;

• characterisation of numerical outputs from physical models to understand the model behaviour and to assess the model ability to simulate important features of the natural system (model validation). Feeding this information back into the model enhances the performance;

• estimation of probabilistic future behaviour of a system based on historical information;

• spatial and temporal extrapolation or interpolation of data based on a mathemat­ical fitting method;

• estimation of input parameters for more complex physical models;

• estimation of the frequency spectra of observations and model outputs.

The main advantage offered by the physical methods, in comparison to the sta­tistical ones, is their spatial independence. In addition, they do not require solar radiation data measured at the Earth’s surface. However, the physical method needs complementary meteorological data to characterise the interactions of solar radia­tion with the atmosphere.

The physical and statistical methods are related to each other. On the one hand, the parameters which govern a physical model take values, which fluctuate accord­ing to the changes in the meteorological conditions. Thus, if we are interested in using a physical model in order to estimate data in a determined site, statistics must be introduced at the level of the model parameters. On the other hand, any statisti­cal analysis, which does not carefully choose the “right” quantities by taking into account their fundamental physical and meteorological relationships, is condemned to give trivial and/or useless results.