Potential direct solar radiation

Potential direct solar radiation

Earlier in the unit we already mentioned some applications of visibility analyses like viewsheds, the watchtower problem, or maps of topographic shadows. In this section, we are setting sail for a more advanced topic that incorporates many of the terrain analysis operations discussed above. You will see that, with what you know about DTMs, you are ready to accomplish the complicated task of modelling potential direct solar radiation. Good resources for additional information on solar radiation modelling are Funk et al. (1992) and Corripio (2003).

Short problem description

The potential direct solar radiation is the energy of the solar radiation received by a particular surface point in one day under clear sky conditions. It depends on the components depicted in the figure below. Factors influencing the potential direct solar radiation received by the earth surface. The potential direct solar radiation $I_{\mathrm{p}}$ can be expressed mathematically as:

where $I_0$ is the incoming radiation of the sun, slope and aspect of the terrain surface are expressed by the surface normal N, S is the vector towards the sun, and tr and ts are the time of sunrise and sunset (Funk et al. 1992).

Incoming solar radiation

For the determination of the incoming solar radiation $I_0$, empirical models have been developed such as the one given in (Funk et al. 1992).

Surface normal

The surface normal N can be calculated as the vector product of the surface derivatives in x- and y-direction.

Vector towards the sun

The vector towards the sun S depends on latitude of the geographic position, the day of the year (i.e. the declination of the equatorial plane), and the time of the day. If all these parameters are given S can be calculated and indicated by means of two angles, the zenith angle and the azimuth angle (Funk et al. 1992).

Time of sunrise and sunset

Finally, the time of sunrise tr and sunset ts, are defined by the condition that the vector towards the sun S and the vector towards the horizon are identical. After determining tr and ts for each grid point and each azimuth angle of the sun the number of hours each grid point is in shadow (or sun, respectively) can be mapped.