Non-linear models. modification of the Angstrom equation with two six-month seasons, namely, October-March and April-September periods leading to two different linear models as
^ = 0.18 + 0.60 S (37)
— = 0.24 + 0.53 — (38)
respectively. It is to be noticed that although the summations of (a + b) in these two models are the same, but a and b values have different distributions in two seasons. In some way use of these two linear models is dividing the overall linear variation domain between H/Hq and S/Sq into two nonparallel linear estimation models.
Gopinathan  has related the Angstrom parameters, a and b, to geographical elevation, h, and the ratio of sunshine duration as follows
a = 0.265 + 0.07h - 0.135 — (39)
b = 0.265 - 0.07h - 0.325— (40)
a = 0.395 - 1.247 + 2.680
b = 0.395 + 1.384 - 3.248
After the substitution of these parameters into the basic Eq. (36), the Zabara model for Greece appears as in Fig. 17.
Akinoglu and Ecevit  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 suggested in the following quadratic form
Given b this expression provides value of a and its substitution into Eq. (40) leads to a nonlinear model.