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Estimating winter balance and its uncertainty from direct measurements of snow depth and density on alpine glaciers



Accurately estimating winter surface mass balance on glaciers is central to assessing glacier health and predicting glacier run-off. However, measuring and modelling snow distribution is inherently difficult in mountainous terrain. Here, we explore rigorous statistical methods of estimating winter balance and its uncertainty from multiscale measurements of snow depth and density. In May 2016, we collected over 9000 manual measurements of snow depth across three glaciers in the St. Elias Mountains, Yukon, Canada. Linear regression, combined with cross-validation and Bayesian model averaging, as well as ordinary kriging are used to interpolate point-scale values to glacier-wide estimates of winter balance. Elevation and a wind-redistribution parameter exhibit the highest correlations with winter balance, but the relationship varies considerably between glaciers. A Monte Carlo analysis reveals that the interpolation itself introduces more uncertainty than the assignment of snow density or the representation of grid-scale variability. For our study glaciers, the winter balance uncertainty from all assessed sources ranges from 0.03 to 0.15 m w.e. (5–39%). Despite the challenges associated with estimating winter balance, our results are consistent with a regional-scale winter-balance gradient.

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Correspondence: Alexandra Pulwicki <>


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Anderton, SP, White, SM and Alvera, B (2004) Evaluation of spatial variability in snow water equivalent for a high mountain catchment. Hydrol. Process., 18(3), 435453
Arendt, AA and 5 others (2008) Validation of high-resolution GRACE mascon estimates of glacier mass changes in the St Elias Mountains, Alaska, USA, using aircraft laser altimetry. J. Glaciol., 54(188), 778787
Bagos, PG and Adam, M (2015) On the covariance of regression coefficients. Open J. Stat., 5, 680701
Balk, B and Elder, K (2000) Combining binary decision tree and geostatistical methods to estimate snow distribution in a mountain watershed. Water Resour. Res., 36(1), 1326
Barry, RG (1992) Mountain weather and climate, 3rd edn. Cambridge University Press
Beaumont, RT and Work, RA (1963) Snow sampling results from three samplers
Berthier, E, Schiefer, E, Clarke, GKC, Menounos, B and Rémy, F (2010) Contribution of Alaskan glaciers to sea-level rise derived from satellite imagery. Nat. Geosci., 3(2), 9295
Burgess, EW, Forster, RR and Larsen, CF (2013) Flow velocities of Alaskan glaciers. Nat. Commun., 4, 21462154
Burnham, KP and Anderson, DR (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociol. Method. Res., 33(2), 261304
Carroll, T (1977) A comparison of the CRREL 500 cm3 tube and the ILTS 200 and 100 cm3 box cutters used for determining snow densities. J. Glaciol., 18(79), 334337
Clark, MP and 8 others (2011) Representing spatial variability of snow water equivalent in hydrologic and land-surface models: a review. Water Resour. Res., 47(7)
Clarke, GKC (2014) A short and somewhat personal history of Yukon glacier studies in the Twentieth Century. Arctic, 37(1), 121
Clyde, GD (1932) Circular No. 99-Utah Snow Sampler and Scales for Measuring Water Content of Snow. UAES Circulars, Paper 90
Cogley, JG and 9 others (2011) Glossary of glacier mass balance and related terms. UNESCO-IHP, Paris
Conger, SM and DM, McClung (2009) Comparison of density cutters for snow profile observations. J. Glaciol., 55(189), 163169
Crochet, P and 6 others (2007) Estimating the spatial distribution of precipitation in iceland using a linear model of orographic precipitation. J. Hydrometeorol., 8(6), 12851306
Crompton, JW and Flowers, GE (2016) Correlations of suspended sediment size with bedrock lithology and glacier dynamics. Ann. Glaciol., 57(72), 19
Cullen, NJ and 10 others (2017) An 11-year record of mass balance of Brewster Glacier, New Zealand, determined using a geostatistical approach. J. Glaciol., 63(238), 199217
Dadić, R, Mott, R, Lehning, M and Burlando, P (2010) Parameterization for wind-induced preferential deposition of snow. J. Geophys. Res.-Earth, 24(14), 19942006
Danby, RK, Hik, DS, Slocombe, DS and Williams, A (2003) Science and the St. Elias: an evolving framework for sustainability in North America's highest mountains. Geogr. J., 169(3), 191204
Davis, JC and Sampson, RJ (1986) Statistics and data analysis in geology, 2nd edn. Wiley, New York
Deems, JS and Painter, TH (2006) Lidar measurement of snow depth: accuracy and error sources, ed. Proceedings of the International Snow Science Workshop, 1-6 October, 2006, Telluride, Colorado, Telluride, CO, International Snow Science Workshop, 30–38
Dixon, D and Boon, S (2012) Comparison of the SnowHydro snow sampler with existing snow tube designs. Hydrol. Process., 26(17), 25552562
Egli, L, Griessinger, N and Jonas, T (2011) Seasonal development of spatial snow-depth variability across different scales in the Swiss Alps. Ann. Glaciol., 52(58), 216222
Elder, K, Dozier, J and Michaelsen, J (1991) Snow accumulation and distribution in an alpine watershed. Water Resour. Res., 27(7), 15411552
Elder, K, Rosenthal, W and Davis, RE (1998) Estimating the spatial distribution of snow water equivalence in a montane watershed. Hydrol. Process., 12(1011), 17931808
Erxleben, J, Elder, K and Davis, R (2002) Comparison of spatial interpolation methods for estimating snow distribution in the Colorado Rocky Mountains. Hydrol. Process., 16(18), 36273649
Fames, PE, Peterson, NR, Goodison, BE and Richards, RP (1982) Metrication of Manual Snow Sampling Equipment, Proceedings of the 50th Western Snow Conference, 120–132
Fierz, CRLA and 8 others (2009) The international classification for seasonal snow on the ground, UNESCO/IHP, unesco/ihp paris ed
Garbrecht, J and Martz, L (1994) Grid size dependency of parameters extracted from digital elevation models. Comput. Geosci., 20(1), 8587
Grabiec, M, Puczko, D, Budzik, T and Gajek, G (2011) Snow distribution patterns on Svalbard glaciers derived from radio-echo soundings. Pol. Polar Res., 32(4), 393421
Gray, DM and Male, DH (1981) Handbook of snow: principles, processes, management & use, 1st edn. Pergamon Press
Grünewald, T, Bühler, Y and Lehning, M (2014) Elevation dependency of mountain snow depth. Cryosphere, 8(6), 23812394
Grünewald, T, Schirmer, M, Mott, R and Lehning, M (2010) Spatial and temporal variability of snow depth and ablation rates in a small mountain catchment. Cryosphere, 4(2), 215225
Grünewald, T and 9 others (2013) Statistical modelling of the snow depth distribution in open alpine terrain. Hydrol. Earth Syst. Sc., 17(8), 30053021
Guo-an, T, Yang-he, H, Strobl, J and Wang-qing, L (2001) The impact of resolution on the accuracy of hydrologic data derived from DEMs. J. Geogr. Sci., 11(4), 393401
Gusmeroli, A, Wolken, GJ and Arendt, AA (2014) Helicopter-borne radar imaging of snow cover on and around glaciers in Alaska. Ann. Glaciol., 55(67), 7888
Hagen, JO and Liestøl, O (1990) Long-term glacier mass-balance investigations in Svalbard, 1950–88. Ann. Glaciol., 14(1), 102106
Helbig, N and van Herwijnen, A (2017) Subgrid parameterization for snow depth over mountainous terrain from flat field snow depth. Water Resour. Res., 53(2), 14441456
Hock, R (2005) Glacier melt: a review of processes and their modelling. Prog. Phys. Geog., 29(3), 362391
Hock, R and Jensen, H (1999) Application of kriging interpolation for glacier mass balance computations. Geogr. Ann. A, 81(4), 611619
Kaser, G, Fountain, A and Jansson, P (2003) A manual for monitoring the mass balance of mountain glaciers. ICSI/UNESCO.
Kienzle, S (2004) The effect of DEM raster resolution on first order, second order and compound terrain derivatives. T. GIS, 8(1), 83111
Kinar, NJ and Pomeroy, JW (2015) Measurement of the physical properties of the snowpack. Rev. Geophys., 53(2), 481544
Kohavi, R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection, Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, 1137–1145
Korona, J, Berthier, E, Bernard, M, Rémy, F and Thouvenot, E (2009) SPIRIT SPOT 5 stereoscopic survey of Polar Ice: reference images and topographies during the fourth International Polar Year (2007–2009). J. Photogram. Rem. Sens., 64(2), 204212
Lehning, M and 5 others (2006) ALPINE3D: a detailed model of mountain surface processes and its application to snow hydrology. Hydrol. Process., 20(10), 21112128
Li, J and Heap, AD (2008) A review of spatial interpolation methods for environmental scientists
Liston, GE and Elder, K (2006) A distributed snow-evolution modeling system (SnowModel). J. Hydrometeorol., 7(6), 12591276
Liston, GE and Sturm, M (1998) A snow-transport model for complex terrain. J. Glaciol., 44(148), 498516
López-Moreno, JI and 7 others (2013) Small scale spatial variability of snow density and depth over complex alpine terrain: Implications for estimating snow water equivalent. Adv. Water Resour., 55, 4052
López-Moreno, JI, Latron, J and Lehmann, A (2010) Effects of sample and grid size on the accuracy and stability of regression-based snow interpolation methods. Hydrol. Process., 24(14), 19141928
López-Moreno, JI, Fassnacht, SR, Beguería, S and Latron, JBP (2011) Variability of snow depth at the plot scale: implications for mean depth estimation and sampling strategies. Cryosphere, 5(3), 617629
MacDougall, AH and Flowers, GE (2011) Spatial and temporal transferability of a distributed energy-balance glacier melt model. J. Climate, 24(5), 14801498
Machguth, H, Eisen, O, Paul, F and Hoelzle, M (2006) Strong spatial variability of snow accumulation observed with helicopter-borne GPR on two adjacent alpine glaciers. Geophys. Res. Lett., 33(13), 15
Madigan, D and Raftery, AE (1994) Model selection and accounting for model uncertainty in graphical models using occam's window. J. Am. Stat. Assoc., 89(428), 15351546
Marshall, HP and 7 others (2006) Spatial variability of the snowpack: Experiences with measurements at a wide range of length scales with several different high precision instruments, Proceedings International Snow Science Workshop, 359–364
McGrath, D and 7 others (2015) End-of-winter snow depth variability on glaciers in Alaska. J. Geophys. Res.-Earth, 120(8), 15301550
Metropolis, N and Ulam, S (1949) The Monte Carlo method. J. Am. Stat. Assoc., 44(247), 335341
Molotch, NP, Colee, MT, Bales, RC and Dozier, J (2005) 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. Hydrol. Process., 19(7), 14591479
Mott, R and 7 others (2008) Simulation of seasonal snow-cover distribution for glacierized sites on Sonnblick, Austria, with the Alpine3D model. Ann. Glaciol., 49(1), 155160
Musselman, KN, Pomeroy, JW, Essery, RLH and Leroux, N (2015) Impact of windflow calculations on simulations of alpine snow accumulation, redistribution and ablation. Hydrol. Process., 29(18), 39833999
Proksch, M, Rutter, N, Fierz, C and Schneebeli, M (2016) Intercomparison of snow density measurements: bias, precision, and vertical resolution. Cryosphere, 10(1), 371384
Pulwicki, A (2017) Multi-scale investigation of winter balance on alpine glaciers, (Master's thesis, Simon Fraser University)
Rasmussen, CE and Williams, CKI (2006) Gaussian processes for machine learning. MIT press Cambridge
Réveillet, M, Vincent, C, Six, D and Rabatel, A (2016) Which empirical model is best suited to simulate glacier mass balances?. J. Glaciol., 63(237), 116
Roustant, O, Ginsbourger, D and Deville, Y (2012) DiceKriging, DiceOptim: two R packages for the analysis of computer experiments by kriging-based metamodeling and optimization. J. Stat. Softw., 21, 155
Schneiderbauer, S and Prokop, A (2011) The atmospheric snow-transport model: SnowDrift3D. J. Glaciol., 57(203), 526542
Schuler, TV and 5 others (2008) Distribution of snow accumulation on the Svartisen ice cap, Norway, assessed by a model of orographic precipitation. Hydrol. Process., 22(19), 39984008
Scipión, DE, Mott, R, Lehning, M, Schneebeli, M and Berne, A (2013) Seasonal small-scale spatial variability in alpine snowfall and snow accumulation. Water Resour. Res., 49(3), 14461457
Shea, C and Jamieson, B (2010) Star: an efficient snow point-sampling method. Ann. Glaciol., 51(54), 6472
Sold, L and 5 others (2013) Methodological approaches to infer end-of-winter snow distribution on alpine glaciers. J. Glaciol., 59(218), 10471059
Stein, ML (1999) Interpolation of spatial data: some theory for kriging. Springer Science & Business Media
Tangborn, WV, Krimmel, RM and Meier, MF (1975) A comparison of glacier mass balance by glaciological, hydrological and mapping methods, South Cascade Glacier, Washington
Taylor-Barge, B (1969) The summer climate of the St. Elias Mountain region, Montreal: Arctic Institute of North America, Research Paper No. 53
Thibert, E, Blanc, R, Vincent, C and Eckert, N (2008) Glaciological and volumetric mass-balance measurements: error analysis over 51 years for Glacier de Sarennes, French Alps. J. Glaciol., 54(186), 522532
Trujillo, E and Lehning, M (2015) Theoretical analysis of errors when estimating snow distribution through point measurements. Cryosphere, 9(3), 12491264
Turcan, J and Loijens, HS (1975) Accuracy of snow survey data and errors in snow sampler measurements, 32nd Eastern Snow Conference
Tveit, J and Killingtveit, Å (1994) Snow surveys for studies of water budget on Svalbard 1991–1994, Proceedings of the 10th International Northern Research Basins Symposium and Workshop, Spitsbergen, Norway. SINTEF Report, vol. 22, A96415
Waechter, A, Copland, L and Herdes, E (2015) Modern glacier velocities across the Icefield Ranges, St Elias Mountains, and variability at selected glaciers from 1959 to 2012. J. Glaciol., 61(228), 624634
Walmsley, APU (2015) Long-term observations of snow spatial distributions at Hellstugubreen and Gråsubreen, Norway, (Master's thesis, University of Oslo)
Wetlaufer, K, Hendrikx, J and Marshall, L (2016) Spatial heterogeneity of snow density and its influence on snow water equivalence estimates in a large mountainous basin. Hydrology, 3(3), 117
Wilson, NJ and Flowers, GE (2013) Environmental controls on the thermal structure of alpine glaciers. Cryosphere, 7(1), 167182
Wilson, NJ, Flowers, GE and Mingo, L (2013) Comparison of thermal structure and evolution between neighboring subarctic glaciers. J. Geophys. Res.-Earth, 118(3), 14431459
Winstral, A, Elder, K and Davis, RE (2002) Spatial snow modeling of wind-redistributed snow using terrain-based parameters. J. Hydrometeorol., 3(5), 524538
Winther, JG, Bruland, O, Sand, K, Killingtveit, A and Marechal, D (1998) Snow accumulation distribution on Spitsbergen, Svalbard, in 1997. Polar Res., 17, 155164
Woo, M-K and Marsh, P (1978) Analysis of error in the determination of snow storage for small high arctic basins. J. Appl Meteorol., 17(10), 15371541
Wood, WA (1948) Project “Snow Cornice”: the establishment of the Seward Glacial research station. Arctic, 1(2), 107112
Work, RA, Stockwell, HJ, Freeman, TG and Beaumont, RT (1965) Accuracy of field snow surveys. Cold Regions Research & Engineering Laboratory
Zhang, W and Montgomery, DR (1994) Digital elevation model grid size, landscape representation, and hydrologic simulations. Water Resour. Res., 30(4), 10191028
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