Modeling Solar Radiation at the Earth’s Surface

Parameter’s Dependence on the Local Climatology

As we have shown, the distributions and models proposed depend on the local cli­mate. In the case of the Tovar’s model the parameters A1, A2, kt01, kt02, X1, ^2 should be analysed for other locations. To this end, appropriate data bases for differ­ent latitudes are needed. However, based on the previous results, it can be concluded that:

• The A1 and A2 values depend on sky conditions (clear, completely overcast and partially-cloudy conditions). As observed inEq. (3.32), an increase in the number of clear-sky and overcast-sky events implies a decrease in the partially-cloudy conditions. Additionally, it should be taken in account that A1 and A2 are also influenced by the optical air mass and the latitude.

• The places, which exhibit climatology with predominance of clear-sky conditions experience an increase of A1 and, thus a decrease of A2. The opposite occurs in those places with a dominance of overcast conditions.

• The parameters kt01 and kt02 provide information about the position of the distri­bution’s maxima. Obviously, these positions fundamentally depend on the optical air mass in the case of clear skies, and also on the climatology for overcast con­ditions, the latter being more important.

• The parameters An and X2 are related to the width of the maxima. For clear skies, (An), and given the optical air mass, the width of the density distribution is as­sociated with the particles in suspension in the atmosphere, which modifies the transmittance of the atmosphere. For overcast conditions, (A,2), the main factors influencing the width are the amount and type of clouds, which can dramatically change the atmospheric transmitivity conditions.

In short, the affirmation supported by several authors that the distribution func­tions depend on local conditions and are not universal seems suitable. They could be adjusted for a certain region, but the local climatic conditions must be taken in account in order to get a proper fit of the statistic behaviour of the local clearness index. Certainly, all the parameters of the model depend on the optical air mass, the latitude, the climatology and even on the atmospheric turbidity conditions. Hence, the adjustment shown for the parameters A1, A2, kt01, kt02, An, X2 should be re­viewed in accordance to these conclusions.

We want to underline that this experimental features canbe applied to the analysis of the solar radiation components. Additionally, we think important to provide a function, which accurately describes all the local statistic behaviour.

Finally, we would like to highlight that the time interval considered strongly influences the distributions. The instantaneous values clearly provide bimodal dis­tributions, while data for a greater time average tend to make this bimodal character disappear. Figure 3.15 shows the adjustment with the Tovar’s model for the data of Armilla.