## 1 Introduction  
The collapse of roof structures under extreme snow loads can have catastrophic consequences, as confirmed by the failures of large-span lightweight structures that have recently occurred in Europe [1, 2, 3]. In recent years, following the collapses of a considerable number of structures during the winter of 2005-2006, a debate on the structural reliability of roofs exposed to snow load has been initiated [4, 5], particularly with regard to whether the partial factors for climatic actions provided in modern structural codes are adequate or not. That criticism is based on the suspicion that the values of partial factors given in the Eurocodes as well as in most other international standards, like those issued by the International Organization for Standards (ISO), the American Society of Civil Engineers (ASCE), often underestimate the effects of climatic action uncertainties in lightweight structures. A proper evaluation of snow load is thus crucial for the structural design of such roofs, which are particularly sensitive to variable loads. In the evaluation of the snow loads on roofs, a major source of uncertainty is undoubtedly the limited availability of data regarding snow deposition patterns on roofs characterized by different shapes. Moreover, uncertainties are further emphasized if other relevant parameters influencing the snow deposition are considered, such as wind transportation, climatic conditions during and after snowfall, snow melting caused by heat transfer through the roof, exposure of the roof snow cover to solar radiation, accumulation processes due to snow precipitation during the winter season, and many other factors. For these reasons, the proper evaluation of the relationship between the ground snow load and the roof snow loads is a challenging task. In modern building codes for structural design, roof snow loads are usually derived from the ground snow loads at the site [6] by means of suitable conversion factors. In the Eurocodes, where the reference value of the ground snow load is characterized by a given probability of exceedance (e.g., \(p=0.02\) in one year [7]) the design value of the roof snow load is the product of the ground snow load multiplied by the so-called shape coefficient. The shape coefficient, which depends on the exposure, the slope, and the thermal conditions of the roof, usually varies in the interval of 0.4-1.1 [6]. This high variability should be duly considered in establishing design loads for roofs [8]. Until now, due to the limited number of the available direct in situ, the values of the shape coefficients provided in modern codes have usually been derived by supplementing that restricted statistical information with nominal safe-sided estimates, based on the physics of the phenomenon and engineering judgement. Of course, if the ground snow load is treated as a random variable and the conversion factors are assigned in terms of nominal safe-sided values, the obtained roof snow load will not have the same probability of exceedance of the ground snow loads, rather being a kind of notional value. Notwithstanding that this approach is specifically adopted in the Eurocodes, the introduction of more sophisticated methods for transforming ground snow loads into roof snow loads with the same probability of exceedance could be extremely helpful. A first attempt to derive design roof snow loads based on a probabilistic approach was proposed in [8; 9] for the United States, assuming a log-normal distribution for both ground snow loads and conversion factors. In that way, suitable design conversion factors were thus derived considering 128 sites in the United States [9]. To the authors' knowledge, no similar studies are available for Europe, where an extreme value distribution is commonly adopted for ground snow loads [10; 11].