**Appendix B**

Some useful formulas proposed in the absence of direct climatic data of irradiance.

To study the incidence of radiation on a vertical surface, we need to resort to formulas somewhat more complex. For the clear sky, vertical illuminance due to a half-hemisphere is, following Gillete and Pierpoint [18],

$$E\_v = 4000 \times \theta^{1.3} + 12000 \times \sin^{0.3} \theta \ge \cos^{1.3} \theta \times \left[\frac{2 + \cos \mathcal{Q}}{3 - \cos \mathcal{Q}}\right] \tag{A13}$$

where ∅ is the azimuth, and θ is the solar altitude.

The algorithm allows the daylight intensities to be obtained for the vertical and horizontal surfaces as a function of the location's latitude. In the situation of an overcast sky, typically defined by the CIE standards, the former expression simplifies as:

$$E\_v = 8500 \text{ xsin}\theta\_\prime \tag{A14}$$

The authors have also proposed a computer simulation program (not detailed here) that automatically gives the data required, following a few input parameters like solar altitude, the number of sun-hours per month, and the cloudiness index, if available.
