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Several approaches have been developed for the forecasting of solar radiation on various time scales. The approaches range from use of Artificial Neural Networks (ANN) using raw solar irradiance to several methods utlizing first some type of seasonal adjustment. This seasonal adjustment is either in the form of multiplicative deseasoning such as using clearness index or a clear sky model, or additive deseasoning using Fourier series or wavelets. This article focuses on comparison of various methods of seasonal adjustment, but first let us examine the range of forecasting tools subsequent to this process of the modelling. The tools range from ANN to Adaptive Autoregressive to Exponential Smoothing. As well as these single method approaches, several authors utilise what might be called hybrid models, like wavelets plus ANN , and the Coupled Autoregressive and Dynamical Systems (CARDS) model of the present author and colleagues. This is not an exhaustive list but it gives the idea of the wide range of possible methods used for short term forecasting of solar radiation. There are essentially two methods of dealing with the seasonalities inherent in climate variables. One can deal with it in a multiplicative or additive modelling framework. Interestingly, though The multiplicative approach is problematic, it is the approach most often used for solar forecasting models in particular. There are two versions of the multiplicative approach with respect to solar radiation, calculating the clearness index, and estimating the clear sky index. There is this distinction in terminology since to form the clearness index, one divides the global solar radiation by the extraterrestrial radiation, a quantity determined only via astronomical formulae. On the other hand the clear sky index involves dividing the global radiation by a clear sky model. Note that the wind resource is not as seasonally dependent as the solar radiation, and both multiplicative and additive versions of dealing with seasonality are used. Additive de-seasoning is enacted through subtracting a mean function from the solar radiation, that function formed usually through the addition of terms involving a basis of the function space. Arguments are presented to support the conjecture that the appropriate way to perform this operation is through the use of a Fourier set of basis functions. As well as specifically dealing with how appropriate this approach is for solar radiation, it will discussed with reference to modelling ambient temperature. There are occasions when the bivariate modelling of temperature and solar radiation is needed. For example, a solar photovoltaic cell loses efficiency as the temperature increases, and so for evaluating the expected performance of a PV cell, it would be useful to be able to model temperature and solar radiation together. It is not possible to deal with temperature seasonality via a multiplicative approach. It would be difficult to construct a bivariate time series model where one dealt with the seasonality with a multiplicative approach with one variable and an additive with the other. This is another compelling argument for dealing with the solar radiation seasonality using Fourier series.

Additive versus Multiplicative Seasonality in Solar Radiation Time Series