These authors contributed equally to this work.

The European Committee for Standardization defines zonings and calculation criteria for different European regions to assign snow loads for structural design. In the Alpine region these defaults are quite coarse; countries therefore use their own products, and inconsistencies at national borders are a common problem.

A new methodology to derive a snow load map for Austria is presented, which is reproducible and could be used across borders. It is based on (i) modeling snow loads with the specially developed

The new approach outperforms a standard smooth model and is much more accurate than the currently used Austrian snow load map when compared to the RMSE of the 50-year snow load return values through a cross-validation procedure. No zoning is necessary, and the new map's RMSE of station-wise estimated 50-year generalized extreme value (GEV) return levels gradually rises to 2.2 kN m

The current European standard for structural design – Eurocode EN 1991-1-3

Alpine region snow loads at sea level as provided by the Eurocode EN 1991-1-3

The aim of this default snow load definition by the European Committee for Standardization (CEN) is “to eliminate or reduce the inconsistencies of snow load values in CEN member states and at borderlines between countries”

Here we propose a novel methodology which will lead to an updated snow load map for Austria. It is based on updated snow data and on transparent and reproducible methods described in Sect.

Long-term snow depth data from 2740 stations in Austria and nearby (ca. 50 km) in Germany, Switzerland, Italy and Slovenia were collected. The data were corrected in many ways. Only a few tasks are shortly outlined here for a more comprehensive illustration the reader is referred to the report on the “Schneelast.Reform” project

at least 30 years of regular daily snow depths between 1960 and 2019;

latest year with data is 2009 or later;

no multiple stations within 0.1

The stations lie between 118 and 3109 m elevation (median: 655 m; Fig.

Relative number of stations in elevation classes, with the actual number on top of each bar (897 stations).

Values of 50-year snow load return from

The newly derived set of snow depth data series is the most comprehensive of its kind in Austria. No other snow dataset contains so many records with regular data at daily resolution for so many years – the most important prerequisites for deriving return levels of snow load. Individual single-day snow depth values are less important than completeness and capturing the yearly maxima as accurately as possible. Snow depth data still provide the base for snow load modeling rather than snow load or water equivalent observations, for which only too short, too sparse and too irregular series exist

Former developments of snow load standards used constant snow densities or parameterized elevation, snow type and/or age dependencies. An overview is given in

To simulate proper snow loads for the snow depth records described above,

The characteristic snow load on the ground (

Eurocode EN 1991-1-3

In this paper we try to overcome known problems with the smooth modeling approach, where responses are modeled with a linear combination of parametric terms, which results in difficulties; e.g., a linear elevation dependence of the location and scale parameters leads to too large return levels in the mountains

A simple methodology was used to find the best suitable GAM for the purpose of mapping snow load return values. The key idea was to incrementally add complexity to a null model and find the point where additional complexity turns into overfitting, which was checked by RMSE and the Akaike information criterion (AIC;

RMSE

Figure

As outlined in Sect.

Thereby

The best SSM for comparison was found via an AIC-based model selection procedure, which led to the following model for the three GEV parameters (see Appendix for details):

Table

Error measures for 50-year return levels of snow load for the generalized additive model (GAM), smooth spatial model (SSM) and Austrian standard (AS), calculated using all 897 stations. (687 stations within Austria and below 1500 m for AS.) The scores are shifted in favor of the GAM if only stations within the Austrian border and below 1500 m are used. The RMSE value of the GAM is only 0.85 kN m

While both models and also the Austrian standard mostly overestimate reference snow loads, the GAM has the smallest RMSE and a very small, slightly positive bias. This is also confirmed in Fig.

Values of 50-year snow load return for a region around Windischgarsten in the center of Austria, taken from the map of the current Austrian snow load standard (

The elevation class 1500 to 2000 m exhibits two severe negative outliers in the right panel of Fig.

A transparent way towards a reproducible snow load map, conformable to CEN standards

The presented methodology is proposed for the successor of the current Austrian snow load standard

A similar approach, combining the methods of snow load simulation and appropriate spatial extreme value modeling, could be applied in other countries as well since long-term snow records are the only prerequisite. This would minimize inconsistencies of snow load standards at national borders, a target expressed by the European Committee for Standardization

The R package mgcv

Secondly, the complexity of the GAM was incrementally increased for both terms by allowing more degrees of freedom, i.e., increasing

To find the best suitable GAM and to avoid overfitting, a 10-fold cross-validation for each model was performed. The dataset of 897 stations was randomly split into 10 subsets (Fig.

Figure

With increasing

Elevation histograms of the 10 randomly found subsets of all 897 stations. Respective number of members is given in brackets.

Lines show the RMSE based on a 10-fold cross-validation of all 897 stations for testing and training datasets for models with increasing degrees of freedom. The numbers refer to the largest AIC of the training datasets out of 10 passes for each degree of freedom.

To fit a smooth spatial model (SSM) to the snow load maxima we followed the approach of

R code used in this study is available from the authors upon reasonable request.

The observations used in this study are generally not freely available. However, in compliance with particular regulations they are available on request from ZAMG for research purposes.

HS and MW developed and designed the project together. HS did the coding and wrote the manuscript together with MW. MW raised the funding through his commitment at Austrian Standards International. TH helped with model development.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Applied Meteorology and Climatology Proceedings 2020: contributions in the pandemic year”.

The framework for this paper was provided by the “Schneelast.Reform” project, managed by Ulrich Hübner from the Association of the Austrian Wood Industries (FV Holzindustrie) and supported by the Austrian Research Promotion Agency (FFG; grant nos. 870909 and 879303) and the Austrian Economic Chamber (WKO). The authors are thankful for this support. We also thank Alexander Radlherr and Susanne Drechsel (ZAMG, Austria) as well as Gilbert Kotzbeck (LFRZ, Austria) for their help with data and mapping, respectively. The Swiss SLF and the Hydrographic Service of Tyrol, Austria, are thanked for providing the snow data.

This research has been supported by the Österreichische Forschungsförderungsgesellschaft (grant nos. 870909 and 879303).

This paper was edited by Tanja Cegnar and reviewed by three anonymous referees.