## 2 Previous Related Work  
Our previous work on solar modelling and mapping in a built environment ([PERSON] et al., 2010; [PERSON] et al., 2011; [PERSON] et al., 2011) was for the Solar Cadaster of the Canton of Geneva. To summarize, the implemented solar modelling process is structured into 3 main steps (Figure 1):  
1. Pre-processing: collection and preparation of input data (meteorological data based on Meteoromr(r) (Meteotest AG, Bern, Switzerland); DUSM--digital urban surface model based on LIDAR survey of 50 cm resolution; slope and orientation maps derived from DUSM; model of the facade of buildings as hyper-points). 2. Image processing: shadow casting and computation of hourly, monthly, yearly solar irradiation on each DUSM pixel. 3. Post-processing: integration of irradiation outputs on building roofs and calculation of energy, economic, and environmental indicators at different scales. Irradiation is the result of the image processing step. It has, as a physical property, 3 components. The first is the direct effect of sunlight in a straight line from the sun, the second is the effect of sunlight that is diffused by the atmosphere, the third is the reflected component of sunlight. Irradiation computation uses meteorological data from Meteoromr(r), which gives statistical and representative data on global, diffuse, and direct irradiation on horizontal surfaces for a given location like Geneva Airport in the context of the solar cadaster. In order to save computation time, hourly data were averaged by month and a representative day of each month (around the 15 th of the month) was chosen for the solar geometry as introduced by ([PERSON] et al., 2010). For the transposition of diffuse radiation on tilted surfaces, we opted for the Hay model [13], as it is the most suitable for using hourly irradiation data on horizontal surface averaged by month as demonstrated in [10] This model is structured into two parts: the circumsolar (anisotropic) that depends on the sun position and the isotropic that does not. In order to compute shadow casting on the direct and diffuse components of irradiation, we need to compute: (i) the Sky View Factor (SVF), which is not time-sensitive, (ii) the shadow maps (Direct Illumination, DI) corresponding to each month and hour of a representative day of the given month. Hourly shadow maps are applied to both direct and circumsolar components, whereas SVF is applied to the isotropic one. The SVF is a dimensionless parameter with values varying from 0 to 1, representing the fraction of the sky on a hemisphere that is visible from a given point (cf. [PERSON] et al. [14]). In the approach introduced by [10] used in this paper, the sky is subdivided into 580 equal solid angle light sources. In the SVF formula, sinus weighting factor is introduced in order to give more weight to light sources from the zenith (relative to the normal of the surface) than to those from the horizon, which is consistent with the purpose of solar potential analysis. Both shadow maps and SVF are based on the same shadow casting algorithm introduced by [PERSON] and [PERSON] [15; 16], which, given a point on the DUSM and a direction, will determine whether there is an obstruction across the straight line from that point in the given direction. The solar modelling process is also applied on building facades as introduced by [PERSON] et al. [10]. Points are generated along the facades (called hyper-points) and shadow casting and irradiation are computed on each facade point in the same way as for horizontal or roof surfaces. To integrate the solar modelling process into the solar cadaster, the Canton of Geneva (280 square kilometers in area) was split into about 55 square areas (called \"tiles\") of 3 by 3 km, with a padding zone of 200 m on each side, and a resolution of 50 cm, for an image size of \(6800\times 6800\) pixels. The reason for the subdivision is that computation time and memory usage would be prohibitive if the whole carton were to be processed as a single unit.