# Extreme Ground Snow Loads in Europe from 1951 to 2100
## 2 Material and Methods  
### Snow Loads  
Snow load on structures \(s\), is usually determined from the snow load on ground, \(s_{k}\), using a suitable loading chain, like  
\[s=s_{k}\ C_{e}\ \mu_{i}\ C_{t}, \tag{1}\]where \(C_{e}\), the exposure coefficient, depending on the orographic conditions of the neighborhood of the construction, on the shelter effect of trees and other surrounding construction works, and on wind velocity, accounts for the removal or the accumulation of snow on roof exerted by wind; \(\mu_{i}\), the shape coefficient, which is a function of the shape and extension of the roof, and on the presence of taller adjacent constructions, is used to convert the ground into the roof snow load as well as to model possible non-uniform snow distributions on roof; finally \(C_{t}\), the thermal coefficient, accounts for changes in the snow cover caused by the heat flux through the roof. In the snow load model, the key information for structural design is snow load on ground [31]. In modern codes and standards, representative values of snow load on ground, characterized by a given annual probability of exceedance, are usually derived by extreme statistics, analyzing measurements of snow cover depth or of snow water equivalent (SWE) [32; 33]. In the past, the SWE was measured directly only in some weather stations of European countries such as Germany, Finland, Switzerland and partially UK, in the other cases, the height of snow cover was converted into snow load by means of analytical snow density laws depending on the climatic conditions and the snow lasting period [33]. In Europe, snow loads are defined in the Eurocode EN1991-1-3 [34], where an annual probability of exceedance equal to 0.02 of the time-varying part is considered. In the Eurocode, a loading chain format according to Equation (1) is adopted, but several ongoing studies are improving the formulation of design shape coefficients [35] and the main results are being introduced in the new revised version of the EN1991-1-3 standard. Maps of climatic actions are given in National Annexes to Eurocodes, since they are Nationally Determined Parameters (NDPs). A detailed discussion concerning the definition of snow load maps in Eurocodes, and the actual situation of European harmonization based on Eurocode recommendations and national provisions can be found in [31]. Despite the different methods adopted for the statistical treatment of extremes, the elaboration of climatic action maps in European countries, including ground snow load, is based on the extreme value statistics covering a time period of 40-50 years. In the statistical analysis, climate is hypothesized stationary over time, although that assumption potentially leads to an underestimation of possible consequences of climate change. The general methodology to elaborate snow load maps can be resumed as follows:  
* First, annual extremes are collected for the considered period in a proper set of weather stations adequately spread over the investigated area;
* Then, available data for each weather station are fitted to an appropriate extreme value probability distribution, in such a way that representative values can be derived. In Europe, a Gumbel (EVI) distribution is generally adopted for annual maxima [31; 33; 36], including also non-snowy winters, following a \"mixed distribution approach\" [31; 37];
* After that, homogenous climatic zones, which are characterized by a common load-altitude relationship, are identified;
* Finally, isopleths are drawn to show the variation of the load within the considered geographic area. The background study for definition of roof and ground snow loads in Europe was the European Snow Load Research Project (ESLRP) [33], led by the university, involving 18 CEN countries. In this project, snow data series from approximately 2600 weather stations were analyzed according to a common approach.