## 5 Conclusions  
The reference roof snow load for structural design is generally defined as the product of characteristic ground snow load, characterized by an annual probability of exceedance \(p=2\%\) and a nominal or notional roof conversion factor known as the shape factor. Consequently, roof snow loads do not necessarily have the same probability of exceedance of ground snow loads, since the uncertainty in the conversion factors from the ground to roof loads is not directly considered. In this context, it is important to develop stochastic models for roof snow loads which consider the roof's geometry and the wind exposure conditions based on the available results of experimental measurement campaigns. The development of such models is a necessary starting point for performing robust reliability analysis and it is also becoming crucial considering the current debate on the calibration of partial factors for climatic actions.  
In this paper, a methodology to evaluate design shape coefficient was illustrated in order to obtain values of roof snow loads characterized by a given annual probability of exceedance. In that way, it was possible to derive suitable design shape factors which allow to transform snow load on the ground having a given probability of exceedance, \(p\), in the snow load on the roof having the same probability of exceedance \(p\).  
Starting from experimental data, design values of shape coefficients for flat and pitched roofs were derived as a function of the coefficient of variation (\(COV_{g}\)) of the annual maxima of ground snow load expected at the site, considering different wind exposure conditions of the structure, i.e., sheltered, semi-sheltered (normal condition), and windswept (exposed condition).  
The results obtained for relevant weather stations were finally compared with the provisions given in the actual version of the Eurocode for snow loads EN1991-1-3:2003 [12] and in the new draft proposal prEN1991-1-3:2020 [17], while also discussing the actual probability of exceedance associated with these normative provisions.  
The outcomes of the study confirmed that the shape factors provided in EN1991-1-3 are somewhat unconservative, while those of the improved model adopted in prEN1991-1-3 are more consistent with the available measurements, especially for pitched roofs. In fact, the new model led to design values of roof loads for the different exposure conditions and roof slopes that, while slightly conservative, were much more in line with the expected probability of exceedance specified in the EN1990 [7].  
The proper evaluation of roof snow load together with the associated probability distribution allows for a refined structural reliability analysis for roof structures designed according to the Eurocode provisions for snow loads [27].  
Conceptualization, P.C., P.F., and F.L.; methodology, P.C., P.F., and F.L.; software, P.C., P.F., and F.L.; validation, P.C., P.F., and F.L.; writing--original draft preparation, P.C., P.F., and F.L.; writing--review and editing, P.C., P.F., and F.L.; resources, P.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available as they cannot be used for commercial purposes.  
The authors declare no conflict of interest.