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Sci., 17, 3005–3021, 2013 Hydrology and Hydrology and www.hydrol-earth-syst-sci.net/17/3005/2013/ doi:10.5194/hess-17-3005-2013 Earth System Earth System © Author(s) 2013. CC Attribution 3.0 License. Sciences Sciences Discussions Open Access Open Access Ocean Science Ocean Science Discussions Statistical modelling of the snow depth distribution Open Access Open Access in open alpine terrain Solid Earth Solid Earth Discussions T. Grunewald¨ 1,2, J. Stotter¨ 3, J. W. Pomeroy4, R. Dadic5,6, I. Moreno Banos˜ 7, J. Marturia`7, M. Spross3, C. Hopkinson8, P. Burlando5, and M. Lehning1,2 1 WSL Institute for Snow and Avalanche Research SLF, Fluelastrasse¨ 35, 7260 Davos, Switzerland Open Access Open Access 2Cryos, School of Architecture, Civil and Environmental Engineering, Ecole´ Polytechnique Fed´ erale´ de Lausanne, GRAO 402 – Station 2, 1015 Lausanne, Switzerland The Cryosphere The Cryosphere 3Institute of Geography, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria Discussions 4Centre for Hydrology, University of Saskatchewan, 117 Science Place, Saskatoon, Saskatchewan, S7N 5C8, Canada 5Institute of Environmental Engineering, ETH Zurich, 8093 Zurich, Switzerland 6Antarctic Research Centre, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand 7Institut Geologic` de Catalunya, C/Balmes 209–211, 08006 Barcelona, Spain 8Department of Geography, University of Lethbridge, 4401 University Drive West, Lethbridge, Alberta, T1K 3M4, Canada Correspondence to: T. Grunewald¨ ([email protected]) Received: 28 February 2013 – Published in Hydrol. Earth Syst. Sci. Discuss.: 13 March 2013 Revised: 11 June 2013 – Accepted: 26 June 2013 – Published: 1 August 2013 Abstract. The spatial distribution of alpine snow covers is differed among the catchments. A “global” model, combin- characterised by large variability. Taking this variability into ing all the data from all areas investigated, could only explain account is important for many tasks including hydrology, 23 % of the variability. It appears that local statistical models glaciology, ecology or natural hazards. Statistical modelling cannot be transferred to different regions. However, models is frequently applied to assess the spatial variability of the developed on one peak snow season are good predictors for snow cover. For this study, we assembled seven data sets other peak snow seasons. 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 sea- sonal snow accumulation. Topographic parameters were used 1 Introduction to model the snow depth distribution on the catchment-scale by applying multiple linear regressions. We found that by av- One of the most apparent characteristics of mountain snow eraging out the substantial spatial heterogeneity at the metre cover is its spatial heterogeneity (e.g. Seligman, 1936; scales, i.e. individual drifts and aggregating snow accumula- McKay and Gray, 1981; Pomeroy and Gray, 1995). This spa- tion at the landscape or hydrological response unit scale (cell tial variability is present at a large range of scales, ranging size 400 m), that 30 to 91 % of the snow depth variability can from the sub-metre scale to hundreds of kilometres. The het- be explained by models that are calibrated to local conditions erogeneity of the mountain snow cover has a significant in- at the single study areas. As all sites were sparsely vegetated, fluence on avalanche formation (Schweizer et al., 2003), lo- only a few topographic variables were included as explana- cal ecology (Litaor et al., 2008) and especially on hydrol- tory variables, including elevation, slope, the deviation of the ogy (Balk and Elder, 2000; Lundquist and Dettinger, 2005; aspect from north (northing), and a wind sheltering parame- Bavay et al., 2013). The amount of water stored in the snow ter. In most cases, elevation, slope and northing are very good cover and its spatial distribution has an important impact on predictors of snow distribution. A comparison of the models the timing, magnitude and duration of run-off related to the showed that importance of parameters and their coefficients melt of snow (Pomeroy et al., 1998; Lundquist and Dettinger, 2005; Lehning et al., 2006) and ice (Dadic et al., 2008). Many Published by Copernicus Publications on behalf of the European Geosciences Union. 3006 T. Grunewald¨ et al.: Modelling of snow depth distribution human activities, including agriculture (e.g. irrigation), hy- et al., 2008), where the response data (e.g. snow depth) are dropower or water resources management, depend on in- repeatedly split along a predictor (e.g. terrain parameter) into formation on the spatio-temporal variability of snow cover sub-groups by minimising the sum of the residuals. Such re- and melt. In order to capture the temporally varying run-off gression tree models were capable of explaining 18 to 90 % caused by snowmelt, hydrological models need to account of the snow-cover variability. The performance of the models for the spatial distribution of snow. depends on both the complexity of the tree (number of ex- Recent years have seen advances in modelling snow dis- planatory parameters and number of splits), and on the qual- tributions by applying sophisticated physically based snow ity and complexity of the data that are analyzed. cover redistribution models (Pomeroy and Li, 2000; Liston A second very common statistical approach is multiple lin- and Elder, 2006; Lehning et al., 2008; Schneiderbauer and ear regression. As in the regression tree models, terrain pa- Prokop, 2011). Such models have been operated at grid res- rameters serve as explanatory variables. An early example olutions of a few metres (e.g. Essery et al., 1999; Liston is the multivariate regression model developed by Golding and Elder, 2006; Mott and Lehning, 2010; Mott et al., (1974) and applied to Marmot Creek Research Basin, Al- 2010; Schneiderbauer and Prokop, 2011) to hundreds of berta. Golding (1974) found that elevation, topographic po- meters (e.g. Bernhardt et al., 2009; Bavay et al., 2009, sition, aspect, slope, and forest density were the most impor- 2013; MacDonald et al., 2010; Magnusson et al., 2010). tant variables for predicting snow accumulation but together These models require high level input, including meteorolog- these could only explain 48 % of the variation of SWE. Based ical data, sometimes detailed flow fields (Raderschall et al., on 106 snow poles Lopez-Moreno and Nogues-Bravo (2006) 2008) and sometimes high-resolution digital elevation mod- were able to explain more than 50 % of the large scale snow els. They are therefore very expensive in terms of required depth variability over the Pyrenees with elevation, elevation information and calculation resources, and have not been ap- range, radiation and two location parameters. Chang and Li plied for larger areas or longer time frames. In general, there (2000) used monthly SWE data averaged from 13 to 36 snow is a trade-off between model complexity and generality on courses in Idaho to build regression models with a combina- the one hand and computation time on the other hand al- tion of elevation, slope, aspect and a relative position. The though reasonable compromises have been achieved using models could explain 60 to 90 % of the monthly SWE vari- the hydrological response unit concept (MacDonald et al., ability for different regions and large catchments. Marchand 2009; Fang and Pomeroy, 2009) which derives from that of and Killingtveit (2005) found that it was possible to model landscape units for stratified snow sampling (e.g. Steppuhn snow depth in open and forested areas of a large (849 km2) and Dyck, 1974). Norwegian catchment with different measures of elevation, Topography strongly influences snow distribution but is aspect, curvature and slope (R2 = 5–48 %). For their anal- not a causative factor in itself (e.g. McKay and Gray, 1981; ysis, they aggregated a very large number of snow depth Pomeroy and Gray, 1995). The spatial heterogeneity of the measurements, obtained by georadar and hand probing to snow cover is attributed to a number of different processes a grid of 1000 m. Pomeroy et al. (2002) used a paramet- which act on different scales: local precipitation amounts are ric model derived from a physically based snow intercep- strongly affected by the interaction of the terrain with the lo- tion model to explain snow accumulation in the boreal for- cal weather and climate (Choularton and Perry , 1986; Daly est of Saskatchewan