Extreme snow loads in Austria

2021 ◽  
Author(s):  
Michael Winkler ◽  
Harald Schellander
Keyword(s):  
Structural Design ◽  
Snow Depth ◽  
Generalized Additive Models ◽  
Value Theory ◽  
Additive Models ◽  
Snow Load ◽  
Snow Loads ◽  
Snow Model ◽  
European Standards ◽  
Smooth Map

<p>In the framework of European standards for structural design, acceptable snow loads on constructions and buildings are based on maps for s<sub>k,</sub> the “characteristic snow load on the ground” with an average reoccurrence time of 50 years. The Austrian snow load standard is built on a very detailed zoning map from 2006, but underlying snow data is from the 1980s.</p><p>An updated snow load map for Austria is presented. It is based on 870 snow depth records with at least 30 years of regular daily observations between 1960 and 2019. ΔSNOW, a novel snow model, was used to simulate respective snow loads. Extreme value theory and generalized additive models led to a smooth map of extreme snow loads at 50x50m resolution. The methods are transparently published, reproducible and, thus, applicable in other regions as well.</p><p>The map can reasonably assign s<sub>k</sub> values up to 2000m altitude, a significant advantage compared to actual standards which are only valid up to 1500m. New insights in the spatial picture of extreme snow loads are provided and the quadratic altitude-s<sub>k</sub>-relation, which is widely used in snow load standards, is evaluated. Validation with station data reveals a higher accuracy for the presented map than for the currently used snow load map. The number of outliers, i.d. stations with significantly higher or lower s<sub>k</sub> values than the snow load maps would suggest, could be decreased in comparison with the actual standard. However, some problematic places remain, mostly in topographically and climatologically highly complex areas. In case the presented map will become a new base for future Austrian standards, those places will have to be treated in a special way.</p>

scholarly journals Snowpack Distribution Using Topographical, Climatological and Winter Season Index Inputs

Atmosphere ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 3
Author(s):  
Douglas M. Hultstrand ◽  
Steven R. Fassnacht ◽  
John D. Stednick ◽  
Christopher A. Hiemstra
Keyword(s):  
Snow Depth ◽  
Depth Distribution ◽  
Generalized Additive Models ◽  
Winter Season ◽  
Regression Tree ◽  
Distribution Patterns ◽  
Time Frame ◽  
Additive Models ◽  
Depth Measurement ◽  
Accumulation Index

A majority of the annual precipitation in many mountains falls as snow, and obtaining accurate estimates of the amount of water stored within the snowpack is important for water supply forecasting. Mountain topography can produce complex patterns of snow distribution, accumulation, and ablation, yet the interaction of topography and meteorological patterns tends to generate similar inter-annual snow depth distribution patterns. Here, we question whether snow depth patterns at or near peak accumulation are repeatable for a 10-year time frame and whether years with limited snow depth measurement can still be used to accurately represent snow depth and mean snow depth. We used snow depth measurements from the West Glacier Lake watershed, Wyoming, U.S.A., to investigate the distribution of snow depth. West Glacier Lake is a small (0.61 km2) windswept (mean of 8 m/s) watershed that ranges between 3277 m and 3493 m. Three interpolation methods were compared: (1) a binary regression tree, (2) multiple linear regression, and (3) generalized additive models. Generalized additive models using topographic parameters with measured snow depth presented the best estimates of the snow depth distribution and the basin mean amounts. The snow depth patterns near peak accumulation were found to be consistent inter-annually with an average annual correlation coefficient (r2) of 0.83, and scalable based on a winter season accumulation index (r2 = 0.75) based on the correlation between mean snow depth measurements to Brooklyn Lake snow telemetry (SNOTEL) snow depth data.

A scaling model for severity of operational losses using generalized additive models for location scale and shape (GAMLSS)

2012 ◽  
Vol 7 (1) ◽  
pp. 61-100 ◽  
Author(s):  
Amandha Ganegoda ◽  
John Evans
Keyword(s):  
Important Determinant ◽  
Generalized Additive Models ◽  
Value Theory ◽  
Tail Index ◽  
Additive Models ◽  
Scaling Properties ◽  
External Data ◽  
Industry Standards ◽  
Heavy Tailed ◽  
Loss Severity

AbstractIn this paper, we investigate the problem of how to combine operational losses collected from various banks of different sizes and loss reporting thresholds in order to estimate the distribution of operational loss severities for a bank of a given size. We model the severity of operational losses by using the extreme value theory to account for the reporting bias of the external data, and a regression analysis based on the GAMLSS framework to model the scaling properties of operational losses. In contrast to previous studies on the scaling problem, our analysis gives particular emphasis to the scaling properties of the tail of the loss distribution. Contrary to existing knowledge, we find that the size of a bank is an important determinant of the severity of operational losses and that the tail index of the distribution is negatively correlated with the size of the bank. The results indicate that for very large banks, distribution of the operational loss severity can be extremely heavy tailed (i.e. tail index less than 1), a finding which have significant implications for capital calculation as well as for risk management. Furthermore, we also demonstrate that the capital estimates provided by our model is consistent with the industry standards and the model can be used by individual banks to simulate data to complement their internal data.

Revised ground snow loads for the 1990 National Building Code of Canada

1989 ◽  
Vol 16 (3) ◽  
pp. 267-278 ◽  
Author(s):  
M. J. Newark ◽  
L. E. Welsh ◽  
R. J. Morris ◽  
W. V. Dnes
Keyword(s):  
Method Of Moments ◽  
Snow Depth ◽  
Extreme Value Distribution ◽  
Building Code ◽  
Snow Pack ◽  
Snow Density ◽  
Snow Load ◽  
The Mean ◽  
Snow Loads ◽  
Made In

The last systematic recalculation of ground snow loads in the Supplement to the National Building Code of Canada was made in 1977 and used data up to 1975. Data from three times as many stations are now available and there is also an additional 10 years of record. Using this expanded data base, ground snow loads have been recalculated for the 1990 Supplement.Several changes in methods have been utilized, the most significant of which is the use of an objective technique to estimate ground snow loads at Code (or other) locations. It explicitly incorporates an assumed dependence of the snow load on topographical elevation, and accounts for the magnitude of errors at snow depth observation sites. Other differences include (a) the use of the method of moments to fit the Gumbel extreme value distribution for the purpose of estimating the 30-year return period snow depth; (b) the use of geographically varying snow pack densities; and (c) using probabilistic rain components of the total snow load and estimating this component by use of a snow pack model.Results show an average national decrease of 6.6% in the 1990 loads compared with those in the 1985 Supplement. A regional exception is in the Northwest Territories where the use of a greater snow density has led to an average increase of about 16% in the loads. A reduction in the standard deviation about the mean load suggests a more spatially consistent set of values for the 1990 Supplement. Key words: snow, loads, building, code.

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

2021 ◽  
Author(s):  
Fabiana Castino ◽  
Bodo Wichura
Keyword(s):  
Time Series ◽  
Spatial Resolution ◽  
Snow Depth ◽  
Snow Water Equivalent ◽  
High Spatial Resolution ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Snow Load ◽  
Characteristic Values ◽  
Snow Loads

<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>

scholarly journals Towards a reproducible snow load map – an example for Austria

2021 ◽  
Vol 18 ◽  
pp. 135-144
Author(s):  
Harald Schellander ◽  
Michael Winkler ◽  
Tobias Hell
Keyword(s):  
Structural Design ◽  
Additive Model ◽  
Penalized Regression ◽  
Regression Splines ◽  
New Approach ◽  
Snow Load ◽  
Smooth Model ◽  
Validation Procedure ◽  
Snow Loads ◽  
Penalized Regression Splines

Abstract. 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.

scholarly journals Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models

2020 ◽  
Vol 17 (17) ◽  
pp. 6339
Author(s):  
François Freddy Ateba ◽  
Manuel Febrero-Bande ◽  
Issaka Sagara ◽  
Nafomon Sogoba ◽  
Mahamoudou Touré ◽  
...  
Keyword(s):  
Wind Speed ◽  
Malaria Incidence ◽  
Generalized Additive Models ◽  
Community Health Center ◽  
Additive Model ◽  
Additive Models ◽  
Functional Regression ◽  
Novel Approach ◽  
Malaria Incidence Rate ◽  
Mean Wind Speed

Mali aims to reach the pre-elimination stage of malaria by the next decade. This study used functional regression models to predict the incidence of malaria as a function of past meteorological patterns to better prevent and to act proactively against impending malaria outbreaks. All data were collected over a five-year period (2012–2017) from 1400 persons who sought treatment at Dangassa’s community health center. Rainfall, temperature, humidity, and wind speed variables were collected. Functional Generalized Spectral Additive Model (FGSAM), Functional Generalized Linear Model (FGLM), and Functional Generalized Kernel Additive Model (FGKAM) were used to predict malaria incidence as a function of the pattern of meteorological indicators over a continuum of the 18 weeks preceding the week of interest. Their respective outcomes were compared in terms of predictive abilities. The results showed that (1) the highest malaria incidence rate occurred in the village 10 to 12 weeks after we observed a pattern of air humidity levels >65%, combined with two or more consecutive rain episodes and a mean wind speed <1.8 m/s; (2) among the three models, the FGLM obtained the best results in terms of prediction; and (3) FGSAM was shown to be a good compromise between FGLM and FGKAM in terms of flexibility and simplicity. The models showed that some meteorological conditions may provide a basis for detection of future outbreaks of malaria. The models developed in this paper are useful for implementing preventive strategies using past meteorological and past malaria incidence.

The Relationship between Mobility and COVID-19 in Germany: Modeling Case Occurrence using Apple's Mobility Trends Data

2021 ◽  
Author(s):  
Mark David Walker ◽  
Mihály Sulyok
Keyword(s):  
Generalized Additive Models ◽  
Information Criterion ◽  
Additive Models ◽  
Online Data ◽  
German Government ◽  
Explanatory Variables ◽  
Mobility Data ◽  
Community Mobility ◽  
The Relationship ◽  
Potential Use

Abstract Background Restrictions on social interaction and movement were implemented by the German government in March 2020 to reduce the transmission of coronavirus disease 2019 (COVID-19). Apple's “Mobility Trends” (AMT) data details levels of community mobility; it is a novel resource of potential use to epidemiologists. Objective The aim of the study is to use AMT data to examine the relationship between mobility and COVID-19 case occurrence for Germany. Is a change in mobility apparent following COVID-19 and the implementation of social restrictions? Is there a relationship between mobility and COVID-19 occurrence in Germany? Methods AMT data illustrates mobility levels throughout the epidemic, allowing the relationship between mobility and disease to be examined. Generalized additive models (GAMs) were established for Germany, with mobility categories, and date, as explanatory variables, and case numbers as response. Results Clear reductions in mobility occurred following the implementation of movement restrictions. There was a negative correlation between mobility and confirmed case numbers. GAM using all three categories of mobility data accounted for case occurrence as well and was favorable (AIC or Akaike Information Criterion: 2504) to models using categories separately (AIC with “driving,” 2511. “transit,” 2513. “walking,” 2508). Conclusion These results suggest an association between mobility and case occurrence. Further examination of the relationship between movement restrictions and COVID-19 transmission may be pertinent. The study shows how new sources of online data can be used to investigate problems in epidemiology.

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