CRITICAL REVIEW OF PHYSICAL MODELLING OF SNOW ACCUMULATION ON ROOFS WITH ARBITRARY GEOMETRY

A review of the most significant domestic and, due to numerical superiority, foreign works on physical modelling of snow transport and snow accumulation processes, in particular, for the purpose of determining snow loads on roofs with arbitrary geometry, is presented. The existing practice of development of recommendations on assignment of snow loads in Russian laboratories is considered and critically evaluated. Comparison of do-mesticworks with scientific articles in the advanced world scientific journals and foreign regulatory documents leads to unfavorable conclusions. Recommendations on assigning snow loads, issued by Russian laboratories on the basisof extremely outdated and poorly substantiated methodology, bear a serious risk for evaluating mechan-ical safety of modern structures, for which such recommendations are developed. Recommendations are offered to remedy this current dangerous practice. The article also gives some suggestions on forming a basis for field observations of snow loads on existing roofs.

Towards a new ground snow-load map for structural design in Germany

<p>The current European standard for snow loads on structures relies on characteristic values (i.e., snow loads with an annual probability of exceedance of 0.02 and referred to as the 50-year mean return levels) derived for Germany in 2005 using about 350 snow water-equivalent (SWE) time series from ground stations operated by the German National Weather Service (DWD) [<em>DIN EN 1991-1-3/NA:2019-04</em>, 2019]. Here we present a methodology for generating a new ground snow-loads map for Germany, which aims at improving the relative coarse spatial resolution and reducing uncertainties and inconsistencies at national borders of the actual standard. Our methodology is based on (1) high-quality and homogeneous snow-cover time series, including both daily snow-depth (from about 6000 stations in Germany and in neighbouring countries) and three-weekly water-equivalent observation (from about 10<sup>3</sup> German stations) over the period from 1950 to 2020, (2) an integrated model combining an empirical regression model for snow bulk density and the semi-empirical multi-level ΔSNOW model for generating accurate daily SWE values from 6000 snow-depth time series [<em>Castino et al.</em>, 2022], (3) the spatial interpolation of both daily snow-depth and modelled-SWE time series using a universal-kriging method to generate high spatial-resolution (~1km<sup>2</sup>) rasterised daily snow loads over the period from 1950 to 2020, and (4) the extreme value analysis of the rasterized daily snow loads for estimating the characteristic values at high spatial resolution for the entire German territory. The uncertainties of the obtained characteristic snow-load values will be estimated using a leave-one-out cross validation based on a selection of observed-SWE time series representative of the diversity of the regional snow climatology in Germany. Finally, the characteristic values of the snow-load map generated with this methodology will be compared with the current German standard.   </p> <p> </p> <p><strong>References</strong></p> <p>Castino, F., H. Schellander, B. Wichura, and M. Winkler (2022), SWE modelling: comparison between different approaches applied to Germany, abstract submitted to D-A-CH MeteorologieTagung - 21-25.03.2022, Leipzig.</p> <p>DIN EN 1991-1-3/NA:2019-04 (2019), Nationaler Anhang - National festgelegte Parameter - Eurocode 1: Einwirkungen auf Tragwerke - Teil 1-3: Allgemeine Einwirkungen - Schneelasten, edited, p. 22, Deutsches Institut für Normung e.V., Beuth-Verlag, Berlin.</p>

Analysis of Roof Collapse Cases Caused by Snow Loads in Russia (2001–2021)

Cases of building decay and structural damage caused by the impact of snow loads are registered every year throughout the world. Such destruction not only results in property loss, but also leads to human losses. A database on 266 cases of roof collapse caused by snow loads in Russia for the period from 2001 to 2021 was collated for this study. The data were analyzed by date and place of collapse, building data, and number of victims. The analysis showed that civilian buildings are the most vulnerable, comprising 78% of the total number of collapses, followed by industrial buildings with 15% and agricultural buildings with only 7%. The relationships between roof shape, roofing material, number of floors, and type of collapsed building were determined. The data processing results showed that low-rise residential buildings (one to two floors) with a gable roof covered with fiber cement should be considered the most vulnerable. A linear relationship was revealed between a collapse area of more than 150 m2 and the cumulative number of collapse cases. The obtained results have practical application for rating building vulnerability to natural hazards and assessing the risk of emergencies associated with snow loads.

COMPARISON OF DETERMINATION OF SNOW LOADS FOR ROOFS IN BUILDING CODES OF VARIOUS COUNTRIES

The article compares the requirements for calculating the snow load on the coatings of buildings and structures in accordance with the regulations of technically developed countries and associations – Russia, the European Union, Canada and the United States. It was revealed that in these norms the general approaches, the subtleties of calculating the coefficients, the set of standard coatings and the schemes of the form coefficient proposed for them differ significantly. This situation reflects the general problem of determining snow loads – at the moment there is no recognized unified scientifically grounded approach to determining snow loads on coatings of even the simplest form. The difference in the normative schemes of snow loads is clearly demonstrated by the example of a three-level roof.

Extreme Ground Snow Loads in Europe from 1951 to 2100

Lightweight roofs are extremely sensitive to extreme snow loads, as confirmed by recently occurring failures all over Europe. Obviously, the problem is further emphasized in warmer climatic areas, where low design values are generally foreseen for snow loads. Like other climatic actions, representative values of snow loads provided in structural codes are usually derived by means of suitable elaborations of extreme statistics, assuming climate stationarity over time. As climate change impacts are becoming more and more evident over time, that hypothesis is becoming controversial, so that suitable adaptation strategies aiming to define climate resilient design loads need to be implemented. In the paper, past and future trends of ground snow load in Europe are assessed for the period 1950–2100, starting from high-resolution climate simulations, recently issued by the CORDEX program. Maps of representative values of snow loads adopted for structural design, associated with an annual probability of exceedance p = 2%, are elaborated for Europe. Referring to the historical period, the obtained maps are critically compared with the current European maps based on observations. Factors of change maps, referred to subsequent time windows are presented considering RCP4.5 and RCP8.5 emission trajectories, corresponding to medium and maximum greenhouse gas concentration scenarios. Factors of change are thus evaluated considering suitably selected weather stations in Switzerland and Germany, for which high quality point measurements, sufficiently extended over time are available. Focusing on the investigated weather stations, the study demonstrates that climate models can appropriately reproduce historical trends and that a decrease of characteristic values of the snow loads is expected over time. However, it must be remarked that, if on one hand the mean value of the annual maxima tends to reduce, on the other hand, its standard deviation tends to increase, locally leading to an increase of the extreme values, which should be duly considered in the evaluation of structural reliability over time.

Towards a reproducible snow load map – an example for Austria

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 Δsnow model at 897 sophistically quality controlled snow depth series in Austria and neighboring countries and (ii) a generalized additive model where covariates and their combinations are represented by penalized regression splines, fitted to series of yearly snow load maxima derived in the first step. This results in spatially modeled snow load extremes. 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−2 at an elevation of 2000 m. The bias is 0.18 kN m−2 and positive across all elevations. When restricting the range of validity of the new map to 2000 m elevation, negative bias values that significantly underestimate 50-year snow loads at a very small number of stations are the only objective problem that has to be solved before the new map can be proposed as a successor of the current Austrian snow load map.

Mapping the probability of forest snow disturbances in Finland

The changing forest disturbance regimes emphasize the need for improved damage risk information. Here, our aim was to (1) improve the current understanding of snow damage risks by assessing the importance of abiotic factors, particularly the modelled snow load on trees, versus forest properties in predicting the probability of snow damage, (2) produce a snow damage probability map for Finland. We also compared the results for winters with typical snow load conditions and a winter with exceptionally heavy snow loads. To do this, we used damage observations from the Finnish national forest inventory (NFI) to create a statistical snow damage occurrence model, spatial data layers from different sources to use the model to predict the damage probability for the whole country in 16 x 16 m resolution. Snow damage reports from forest owners were used for testing the final map. Our results showed that best results were obtained when both abiotic and forest variables were included in the model. However, in the case of the high snow load winter, the model with only abiotic predictors performed nearly as well as the full model and the ability of the models to identify the snow damaged stands was higher than in other years. The results showed patterns of forest adaptation to high snow loads, as spruce stands in the north were less susceptible to damage than in southern areas and long-term snow load reduced the damage probability. The model and the derived wall-to-wall map were able to discriminate damage from no-damage cases on a good level (AUC > 0.7). The damage probability mapping approach identifies the drivers of snow disturbances across forest landscapes and can be used to spatially estimate the current and future disturbance probabilities in forests, informing practical forestry and decision-making and supporting the adaptation to the changing disturbance regimes.

Snowiness as a factor for assessing the avalanche activity in poorly explored mountainous areas (on the example of the Baikal region)

The relevance of the study of snowiness in the Baikal region is due to the long-term existence of a stable snow cover, which determines the development of such dangerous natural phenomena as snow runup, snow loads, snow flows and avalanches, which can cause a serious damage to the infrastructure facil up, snow loads, snow flows and avalanches, which can cause a serious damage to the infrastructure facilities. The problem is aggravated by the lack of comprehensive studies of nival phenomena, which are not taken into account in the construction of such important industrial facilities as railway bridges, power lines, railways and highways. The purpose of the article is to assess the risks of unfavorable and dangerous phenomena of a nival nature in the Baikal region, as well as to develop methods of protection against them. The results of observations are presented. The total amount of precipitation was determined. The dynamics of snowfall indicators as indicators of the avalanche formation regime in the mountains of the Baikal region was carried out. The chronology of winters with different snowfall indicators was reconstructed. The amount of precipitation in the cold period was taken as a basic indicator. A scheme for assessing snowiness for poorly studied areas was developed. The calculation of values of the spatial correlation of snowfall indicators was carried out, which made it possible to identify areas with synchronous fluctuations in the amount of precipitation of the cold season for many years. It was established that dependences of the snow cover height and snow reserves on the terrain height remained unchanged. The dependences of snow cover indicators on different factors were identified.