Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain

Terrain parameters derived from digital elevation models (DEMs), such as slope gradient, aspect and cell surface area, are represented as a vector normal to the surface and calculated using the minimum areal unit of the DEM, that is enclosed between four data points. The position of the Sun is calculated by applying rotational matrices to a unit vector defined at noon as a function of latitude and declination. The direct component of insolation intercepted by the cell surface is then calculated as a dot product between the unit vector in the direction of the Sun and the unit vector normal to surface, multiplied by direct normal irradiation. Hillshading is computed by scanning the projection of cells onto a solar illumination plane perpendicular to the Sun direction. Horizon angles and estimated sky view factor are calculated using a more economical algorithm than a rigorous evaluation of all the angles subtended by every grid cell to each other. The performance of the slope algorithm is evaluated using a synthetic surface and real world examples are given for the Mont Blanc Massif, in the French Alps.