Fig. 4.9 Parameter map for b'

Fig. 4.10 Parameter relation ship

Fig. 4.10 Parameter relation ship

Fig. 4.11 Distribution of a' and b' over Turkey

The beta distribution is checked to fit the empirical data with the chi-square criterion in the statistics literature at the 5% significance level. It is obvious even visually from Fig. 4.11 that the beta-type PDF is very convenient. The beta-type curves are helpful for any modeling studies in the future for areal radiation variations (see App. A).

4.6 Unrestricted Model (UM)

In practice, the estimation of model parameters is achieved most often by the least squares method and regression technique using procedural restrictive assumptions as already mentioned in Sect. 4.4.1. These are unnecessary procedural restrictions, which lead to unreliable biases in the parameter estimations. The averages and variances of the solar radiation and sunshine duration data play a predominant role in many calculations and the conservation of these parameters becomes more important than the cross-correlation coefficient. Gordon and Reddy (1988) stated that a simple functional form for the stationary relative frequency distribution for daily solar radiation requires knowledge of the mean and variance only. In almost any es timate of solar radiation by means of computer software, the parameter estimations are achieved without caring about the theoretical restrictions in Sect. 4.4.1. The application of the regression technique to Eq. 4.30 for estimating the model parameters from the available data (Bucciarelli 1986) leads to b = rh!

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