Ahmet Duran §ahin and Zekai Sen
Solar irradiation is dependent on different causes including astronomical and meteorological factors. In practical studies it is not possible to consider all the factors, and therefore, so far simple but effective models for its prediction from a few numbers of factors are presented. The first of such models takes into consideration only the sunshine duration measurements for the solar irradiation estimation, and unfortunately, it is still under use without critical assessment of the underlying restrictive assumptions and simplifications in model parameter estimation methodology. In addition to these criticisms the classical models are in the form of linear mathematical expressions and the parameter estimation procedure is also a linear procedure, which leads to constant estimations based on all the data. The sunshine duration and solar irradiation data have seasonal and random effects especially for durations less than one year. The basic concern in this chapter is weather seasonal effects are also reflective in the parameter estimations? Classical approaches consider only the random errors and by using the least squares methodology tries to provide parameter estimations on the basis of the minimum squared error. Although some researchers proposed addition of a non-linear term into the basic Angstrom equation but again without consideration of the restrictive assumptions and finally they also obtained constant model parameter estimations. Unfortunately, all over the world the same estimation procedure is under current use, and therefore, in this chapter the attention is drawn on the pitfalls in the model parameter estimations and accordingly some innovative approaches are suggested without restrictive assumptions although the same simple solar estimation model is used. A dynamic model estimation procedure is proposed, which leads to a sequence of parameters and hence it is possible to
Ahmet Duran §ahin
Istanbul Technical University, Turkey, e-mail: sahind@itu. edu. tr Zekai Sen
Istanbul Technical University, Turkey, e-mail: zsen@itu. edu. tr
look at the frequency distribution function (probability distribution function, PDF) of the model parameters and decide whether the arithmetic average of the parameters or the mode (the most frequently occurring parameter value) should be used in further solar irradiation estimations. It is shown on the basis of some solar irradiation and sunshine duration data measurements on different locations in Turkey that the model parameter estimations abide by the Beta PDF. Besides, it is also possible to find the relationship between the model parameters at a single station, which shows temporal parameter variations. Apart from the dynamic model parameter estimation procedure, an unrestricted solar irradiation parameter estimation procedure is also presented which considers the conservation of the model input and output variables’ arithmetic mean and the standard deviations only, without the use of least squares technique. The quantitative comparisons of all the methodologies proposed in this chapter are presented with the classical model results on the basis of different error assessments.