Statistical modelling of the snow depth distribution in open alpine terrain

The spatial distribution of alpine snow covers is characterised by large variability. Taking this variability into account is important for many tasks including hydrology, glaciology, ecology or natural hazards. Statistical modelling is frequently applied to assess the spatial variability of the snow cover. For this study, we assembled seven data sets of high-resolution snow-depth measurements from different mountain regions around the world. All data were obtained from airborne laser scanning near the time of maximum seasonal snow accumulation. Topographic parameters were used to model the snow depth distribution on the catchment-scale by applying multiple linear regressions. We found that by averaging out the substantial spatial heterogeneity at the metre scales, i.e. individual drifts and aggregating snow accumulation at the landscape or hydrological response unit scale (cell size 400 m), that 30 to 91% of the snow depth variability can be explained by models that are calibrated to local conditions at the single study areas. As all sites were sparsely vegetated, only a few topographic variables were included as explanatory variables, including elevation, slope, the deviation of the aspect from north (northing), and a wind sheltering parameter. In most cases, elevation, slope and northing are very good predictors of snow distribution. A comparison of the models showed that importance of parameters and their coefficients differed among the catchments. A "global" model, combining all the data from all areas investigated, could only explain 23% of the variability. It appears that local statistical models cannot be transferred to different regions. However, models developed on one peak snow season are good predictors for other peak snow seasons.

[1]  M. Goodchild,et al.  The Fractal Nature of Geographic Phenomena , 1987 .

[2]  J. Parrot,et al.  Measurement of DEM roughness using the local fractal dimension , 2005 .

[3]  Kelly Elder,et al.  Spatial Snow Modeling of Wind-Redistributed Snow Using Terrain-Based Parameters , 2002 .

[4]  Michael Lehning,et al.  Spatial and temporal variability of snow depth and ablation rates in a small mountain catchment , 2010 .

[5]  Norbert Pfeifer,et al.  Laser scanning - a paradigm change in topographic data acquisition for natural hazard management , 2009 .

[6]  Michael Lehning,et al.  Response of snow cover and runoff to climate change in high Alpine catchments of Eastern Switzerland , 2013 .

[7]  J. Pomeroy,et al.  Simulation of the snowmelt runoff contributing area in a small alpine basin , 2010 .

[8]  L. H.,et al.  Snow Structure and Ski Fields , 1936, Nature.

[9]  M. Seyfried,et al.  Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling , 1995 .

[10]  Kelly Elder,et al.  Estimating the spatial distribution of snow water equivalence in a montane watershed , 1998 .

[11]  Michael Lehning,et al.  Altitudinal dependency of snow amounts in two small alpine catchments: can catchment-wide snow amounts be estimated via single snow or precipitation stations? , 2011, Annals of Glaciology.

[12]  C. Schär,et al.  A PRECIPITATION CLIMATOLOGY OF THE ALPS FROM HIGH-RESOLUTION RAIN-GAUGE OBSERVATIONS , 1998 .

[13]  Murugesu Sivapalan,et al.  ON THE REPRESENTATIVE ELEMENTARY AREA (REA) CONCEPT AND ITS UTILITY FOR DISTRIBUTED RAINFALL-RUNOFF MODELLING , 1995 .

[14]  Kelly Elder,et al.  Scaling properties and spatial organization of snow depth fields in sub‐alpine forest and alpine tundra , 2009 .

[15]  S. Gruber,et al.  A mass‐conserving fast algorithm to parameterize gravitational transport and deposition using digital elevation models , 2007 .

[16]  Douglas L. Golding,et al.  The Correlation of Snowpack with Topography and Snowmelt Runoff on Marmot Creek Basin, Alberta , 1974 .

[17]  K. Elder,et al.  Interannual Consistency in Fractal Snow Depth Patterns at Two Colorado Mountain Sites , 2005 .

[18]  K. Elder,et al.  Scale effects in a distributed snow water equivalence and snowmelt model for mountain basins , 1998 .

[19]  M. Beniston,et al.  Snow pack in the Swiss Alps under changing climatic conditions: an empirical approach for climate impacts studies , 2003 .

[20]  J. Dozier,et al.  Estimating the spatial distribution of snow water equivalent in an alpine basin using binary regression tree models: the impact of digital elevation data and independent variable selection , 2005 .

[21]  J. Pomeroy,et al.  Prairie and arctic areal snow cover mass balance using a blowing snow model , 2000 .

[22]  D. H. Gray,et al.  An evaluation of snow accumulation and ablation processes for land surface modelling , 1998 .

[23]  Robert Kirnbauer,et al.  An analysis of snow cover patterns in a small alpine catchment , 1992 .

[24]  Raymond J. Spiteri,et al.  Implications of mountain shading on calculating energy for snowmelt using unstructured triangular meshes , 2012 .

[25]  T. Choularton,et al.  A model of the orographic enhancement of snowfall by the seeder‐feeder mechanism , 1986 .

[26]  C. Hopkinson,et al.  Spatial Snow Depth Assessment Using LiDAR Transect Samples and Public GIS Data Layers in the Elbow River Watershed, Alberta , 2012 .

[27]  Dmitri Kavetski,et al.  Representing spatial variability of snow water equivalent in hydrologic and land‐surface models: A review , 2011 .

[28]  T. Farr,et al.  The roughness of natural terrain: A planetary and remote sensing perspective , 2001 .

[29]  M. Lehning,et al.  Inhomogeneous precipitation distribution and snow transport in steep terrain , 2008 .

[30]  Alain Pietroniro,et al.  On the importance of sublimation to an alpine snow mass balance in the Canadian Rocky Mountains , 2010 .

[31]  Michael D. Dettinger,et al.  How snowpack heterogeneity affects diurnal streamflow timing , 2005 .

[32]  Brian Klinkenberg,et al.  Fractals and morphometric measures: is there a relationship? , 1992 .

[33]  D. Gray,et al.  Small-Scale Spatial Structure of Shallow Snowcovers , 1996 .

[34]  Aloysius Wehr,et al.  Airborne laser scanning—an introduction and overview , 1999 .

[35]  John W. Pomeroy,et al.  Prediction of seasonal snow accumulation in cold climate forests , 2002 .

[36]  Michael Lehning,et al.  A comparison of measurement methods: terrestrial laser scanning, tachymetry and snow probing for the determination of the spatial snow-depth distribution on slopes , 2008, Annals of Glaciology.

[37]  John W. Pomeroy,et al.  Snowcover Accumulation, Relocation, and Management , 1995 .

[38]  Kelly Elder,et al.  A Distributed Snow-Evolution Modeling System (SnowModel) , 2004 .

[39]  Kelly Elder,et al.  Comparison of spatial interpolation methods for estimating snow distribution in the Colorado Rocky Mountains , 2002 .

[40]  John W. Pomeroy,et al.  Modelling blowing snow redistribution to prairie wetlands , 2009 .

[41]  T. Seastedt,et al.  Topographic controls on snow distribution, soil moisture, and species diversity of herbaceous alpine vegetation, Niwot Ridge, Colorado , 2008 .

[42]  J. Skaloud,et al.  An Eye for Landscapes - Rapid Aerial Mapping with Handheld Sensors , 2006 .

[43]  M. Bavay,et al.  Understanding snow-transport processes shaping the mountain snow-cover , 2010 .

[44]  A. Pietroniro,et al.  Parameterizing redistribution and sublimation of blowing snow for hydrological models: tests in a mountainous subarctic catchment , 2009 .

[45]  Danny Marks,et al.  Simulating wind fields and snow redistribution using terrain‐based parameters to model snow accumulation and melt over a semi‐arid mountain catchment , 2002 .

[46]  M. Goodchild,et al.  The fractal properties of topography: A comparison of methods , 1992 .

[47]  Michael Lehning,et al.  Parameterization for wind–induced preferential deposition of snow , 2010 .

[48]  J. Pomeroy,et al.  Sensitivity of snowmelt hydrology in Marmot Creek, Alberta, to forest cover disturbance , 2012 .

[49]  G. Bloschl.  AN ANALYSIS OF SNOW COVER PATTERNS IN A SMALL ALPINE CATCHMENT , 2006 .

[50]  Karsten Schulz,et al.  SnowSlide: A simple routine for calculating gravitational snow transport , 2010 .

[51]  Nicholas Kouwen,et al.  Watershed modeling using land classifications , 1992 .

[52]  Laura Chasmer,et al.  Mapping Snowpack Depth Beneath Forest Canopies Using Airborne Lidar , 2004 .

[53]  Kelly Elder,et al.  Topographic, meteorologic, and canopy controls on the scaling characteristics of the spatial distribution of snow depth fields , 2007 .

[54]  Younes Alila,et al.  The influence of forest and topography on snow accumulation and melt at the watershed-scale , 2007 .

[55]  Snowpack depth modelling and water availability from LIDAR measurements in eastern Pyrenees , 2009 .

[56]  Jürg Hosang,et al.  Evaluation of a water equivalent of snow cover map in a small catchment area using a geostatistical approach , 1991 .

[57]  Terry E. Tullis,et al.  Euclidean and fractal models for the description of rock surface roughness , 1991 .

[58]  H. Douville,et al.  A comparison of four snow models using observations from an alpine site , 1999 .

[59]  William L. Quinton,et al.  The cold regions hydrological model: a platform for basing process representation and model structure on physical evidence , 2007 .

[60]  Keith Beven,et al.  Effects of spatial variability and scale with implications to hydrologic modeling , 1988 .

[61]  J. Vallet,et al.  Variation of deposition depth with slope angle in snow avalanches: Measurements from Vallée de la Sionne , 2010 .

[62]  Kang-Tsung Chang,et al.  Modelling snow accumulation with a geographic information system , 2000, Int. J. Geogr. Inf. Sci..

[63]  Emmanuel P. Baltsavias,et al.  Airborne laser scanning: basic relations and formulas , 1999 .

[64]  Michael Lehning,et al.  Persistence in intra‐annual snow depth distribution: 1. Measurements and topographic control , 2011 .

[65]  Michael Lehning,et al.  Fine‐scale modeling of the boundary layer wind field over steep topography , 2008 .

[66]  S. E. Alexander,et al.  Optimal sampling schemes for estimating mean snow water equivalents in stratified heterogeneous landscapes , 2006 .

[67]  Juan I. López-Moreno,et al.  Interpolating local snow depth data: an evaluation of methods , 2006 .

[68]  Michael Lehning,et al.  Spatio-temporal measurements and analysis of snow depth in a rock face , 2011 .

[69]  I. Moore,et al.  Fractals, fractal dimensions and landscapes — a review , 1993 .

[70]  Å. Killingtveit,et al.  Statistical properties of spatial snowcover in mountainous catchments in Norway , 2004 .

[71]  Thomas Grünewald,et al.  Dynamics of snow ablation in a small Alpine catchment observed by repeated terrestrial laser scans , 2012 .

[72]  Michael Lehning,et al.  Meteorological Modeling of Very High-Resolution Wind Fields and Snow Deposition for Mountains , 2010 .

[73]  Shunlin Liang,et al.  Fractal analysis of remotely sensed images: A review of methods and applications , 2006 .

[74]  Michael Lehning,et al.  Wind influence on snow depth distribution and accumulation over glaciers , 2010 .

[75]  A. Prokop,et al.  The atmospheric snow-transport model: SnowDrift3D , 2011, Journal of Glaciology.

[76]  H. Löwe,et al.  Simulations of future snow cover and discharge in Alpine headwater catchments , 2009 .

[77]  P. Burlando,et al.  Mass-balance estimates for Haut Glacier d’Arolla, Switzerland, from 2000 to 2006 using DEMs and distributed mass-balance modeling , 2008, Annals of Glaciology.

[78]  Kelly Elder,et al.  Combining binary decision tree and geostatistical methods to estimate snow distribution in a mountain watershed , 2000 .

[79]  G. Liston,et al.  Spatial-Temporal Variability in Turbulent Fluxes during Spring Snowmelt , 2006 .

[80]  Michael Lehning,et al.  Mountain snow distribution governed by an altitudinal gradient and terrain roughness , 2011 .

[81]  T. Erickson,et al.  Persistence of topographic controls on the spatial distribution of snow in rugged mountain terrain, Colorado, United States , 2005 .

[82]  M. Bavay,et al.  Micrometeorological processes driving snow ablation in an Alpine catchment , 2011 .

[83]  Kelly Elder,et al.  Snow accumulation and distribution in an Alpine Watershed , 1991 .

[84]  Wolfram Mauser,et al.  Using wind fields from a high‐resolution atmospheric model for simulating snow dynamics in mountainous terrain , 2008 .

[85]  Enrico Bertuzzo,et al.  Transport at basin scales: 1. Theoretical framework , 2005 .

[86]  Kelly Elder,et al.  Fractal Distribution of Snow Depth from Lidar Data , 2006 .

[87]  H. Ahlmann,et al.  Snow Structure and Ski Fields , 1937 .

[88]  R. Essery,et al.  Implications of spatial distributions of snow mass and melt rate for snow-cover depletion: observations in a subarctic mountain catchment , 2004, Annals of Glaciology.

[89]  Christian Briese,et al.  Potential of airborne laser scanning for geomorphologic feature and process detection and quantifications in high alpine mountains , 2011 .

[90]  M. Lehning,et al.  Persistence in intra‐annual snow depth distribution: 2. Fractal analysis of snow depth development , 2011 .

[91]  H. Marchant.  Snow Ecology: An Interdisciplinary Examination of Snow-Covered Ecosystems , 2001 .

[92]  J. Schweizer,et al.  Snow avalanche formation , 2003 .

[93]  M. Zappa,et al.  ALPINE3D: a detailed model of mountain surface processes and its application to snow hydrology , 2006 .

[94]  C. Hopkinson,et al.  Relationships between snowpack depth and primary LiDAR point cloud derivatives in a mountainous environment , 2012 .

[95]  B. Alvera,et al.  Evaluation of spatial variability in snow water equivalent for a high mountain catchment , 2004 .

[96]  C. Daly,et al.  A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain , 1994 .

[97]  M. Lehning,et al.  Snow cover response to climate change in a high alpine and half-glacierized basin in Switzerland , 2010 .