Most of the sunshine based non-linear solar irradiation estimation models are defined as the modifications of the Angstrom expression in Eq. (6.10). Some authors have suggested changes in the model parameters, a and b, seasonally, for arriving at better estimations. On the other hand, Ogelman et al. (1984) added a non-linear term, which appears as a quadratic expression,
Akinoglu and Ecevit (1990) have observed that this model is superior to others in terms of global applicability. They have applied it to some Turkish data, and finally, obtained a suitable model as,
After these preliminary non-linear methods, higher order polynomial type of nonlinear models are also proposed into the solar energy literature, and especially, Zabara (1986) correlated the Angstrom parameters to third power of the sunshine duration ratio.
Akinoglu and Ecevit (1990) found a global relationship between the Angstrom parameters by using the published a and b values for 100 locations from all over the world and the relationship is expressed in quadratic form as
a = 0.783 – 1.509b + 0.89b2 (6.15)
Details of these proposals and models are given in Chapter 5 of this book.