## 2 Stochastic Modeling of Roof Snow Load
### Ground Snow Loads  
The ground snow load is the basic information needed to determine snow load for structural design [10; 11]. Characteristic load values are usually estimated under the assumption of a stationary climate [1; 2], starting with the statistical analysis of extreme values of snow water equivalent data, or snow depth measurements supplemented by an appropriate snow density model (generally depending on the climatic zone). The best-fitting extreme distribution of ground snow load data depends on the specific climate conditions as well. The most widely used extreme distribution in Europe is the Gumbel distribution, which was adopted for the development of the majority of maps presented in Annex C to EN1991-1-3-2003 [10; 11]. Considering specific local conditions, some countries consider alternative distributions: for example, the interactive snow map developed in Czech Republic [22] is based on the log-normal distribution. The climatic snow load maps provide a synoptic or interactive representation of the characteristic values of ground snow load (\(s_{g,k}\)) at any potential construction site within a given geographical region. In the Eurocode system, climatic maps for wind, snow, and temperature are included in the National Annexes, as prepared by the National Standard Body of each European country member of the European Committee for Standardization (CEN). Generally, maps of snow load on ground are plotted virtually in reference to the sea level; the specific value pertaining to the considered site is thus derived by means of suitable snow load-site altitude relationships, depending on the climatic zone. A critical review of the current definition of snow load maps in structural codes can be found in [11]. An example of modern map is summarized in Figure 2, where ground snow loads resulting from the assembly of all the National Annexes to EN1991-1-3_2003 [12] are plotted at the European scale. It must be stressed that the distribution of the annual maxima of the ground snow load is often characterized by a high coefficient of variation (\(COV_{g}\)), especially in temperate climates [10; 15]. This statement was also confirmed by the outcomes of European Snow Load Research Project (ESLRP) [10; 15], which was funded by the European Commission. In fact, in the 18 European countries involved in the project, the \(COV_{g}\) of the snow extremes varied in a range between 0.2 and 2, with values reaching 6.0 in the Iberian Peninsula. Generally, \(COV_{g}\) is a function of the altitude of the site. Of course, low-altitude regions, where snow events are more irregular, are characterized by higher \(COV_{g}\) values. A synthesis of the most relevant data characterizing the 10 European climatic regions defined in the ESLRP is reported in Table 1, but more exhaustive information can be found in Annex 3 of the final report of the ESLRP [15]. Figure 1: Stochastic distributions of snow action parameters assuming normal exposure condition (exposure coefficient \(C_{e}=1.0\)) and unheated building (thermal coefficient \(C_{t}=1.0\)). Figure 2: European ground snow load map resulting from European Committee for Standardization (CEN) National Annexes to EN1991-1-3:2003.