References

The Cryosphere

1994-0424

Copernicus Publications

Göttingen, Germany

10.5194/tc-8-257-2014

Solving Richards Equation for snow improves snowpack meltwater runoff estimations in detailed multi-layer snowpack model

Wever

¹ Fierz

https://orcid.org/0000-0001-9490-6732

¹ Mitterer

¹ Hirashima

² Lehning

https://orcid.org/0000-0002-8442-0875

¹ ³

WSL Institute for Snow and Avalanche Research SLF, Flüelastrasse 11, 7260 Davos Dorf, Switzerland

Snow and Ice Research Center, NIED, Japan

CRYOS, School of Architecture, Civil and Environmental Engineering, EPFL, Lausanne, Switzerland

20 02 2014

8 1 257 274

2014

This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/

This article is available from https://tc.copernicus.org/articles/8/257/2014/tc-8-257-2014.html

The full text article is available as a PDF file from https://tc.copernicus.org/articles/8/257/2014/tc-8-257-2014.pdf

The runoff from a snow cover during spring snowmelt or rain-on-snow events is an important factor in the hydrological cycle. In this study, three water balance schemes for the 1 dimensional physically-based snowpack model SNOWPACK are compared to lysimeter measurements at two alpine sites with a seasonal snow cover, but with different climatological conditions: Weissfluhjoch (WFJ) and Col de Porte (CDP). The studied period consists of 14 and 17 yr, respectively. The schemes include a simple bucket-type approach, an approximation of Richards Equation (RE), and the full RE. The results show that daily sums of snowpack runoff are strongly related to a positive energy balance of the snow cover and therefore, all water balance schemes show very similar performance in terms of Nash-Sutcliffe efficiency (NSE) coefficients (around 0.63 and 0.72 for WFJ and CDP, respectively) and <i>r</i><sup>2</sup> values (around 0.83 and 0.72 for WFJ and CDP, respectively). An analysis of the runoff dynamics over the season showed that the bucket-type and approximated RE scheme release meltwater slower than in the measurements, whereas RE provides a better agreement. Overall, solving RE for the snow cover yields the best agreement between modelled and measured snowpack runoff, but differences between the schemes are small. On sub-daily time scales, the water balance schemes behave very differently. In that case, solving RE provides the highest agreement between modelled and measured snowpack runoff in terms of NSE coefficient (around 0.48 at both sites). At WFJ, the other water balance schemes loose most predictive power, whereas at CDP, the bucket-type scheme has an NSE coefficient of 0.39. The shallower and less stratified snowpack at CDP likely reduces the differences between the water balance schemes. Accordingly, it can be concluded that solving RE for the snow cover improves several aspects of modelling snow cover runoff, especially for deep, sub-freezing snow covers and in particular on the sub-daily time scales. The additional computational cost was found to be in the order of a factor of 1.5–2.

References 1

Bartelt, P. and Lehning, M.: A physical SNOWPACK model for the Swiss avalanche warning Part I: Numerical model, Cold Reg. Sci. Technol., 35, 123–145, <a href="http://dx.doi.org/10.1016/S0165-232X(02)00074-5">https://doi.org/10.1016/S0165-232X(02)00074-5</a>, 2002.

Baunach, T., Fierz, C., Satyawali, P. K., and Schneebeli, M.: A model for kinetic grain growth, Ann. Glaciol., 32, 1–6, <a href="http://dx.doi.org/10.3189/172756401781819427">https://doi.org/10.3189/172756401781819427</a>, 2001.

Boone, A. and Etchevers, P.: An Intercomparison of Three Snow Schemes of Varying Complexity Coupled to the Same Land Surface Model: Local-Scale Evaluation at an Alpine Site, J. Hydrometeorol., 2, 374–394, <a href="http://dx.doi.org/10.1175/1525-7541(2001)002<0374:AIOTSS>2.0.CO;2">https://doi.org/10.1175/1525-7541(2001)002<0374:AIOTSS>2.0.CO;2</a>, 2001.

Brun, E., Martin, E., Simon, V., Gendre, C., and Coléou, C.: An energy and mass model of snow cover suitable for operational avalanche forecasting, J. Glaciol., 35, 333–342, 1989.

Calonne, N., Geindreau, C., Flin, F., Morin, S., Lesaffre, B., Rolland du Roscoat, S., and Charrier, P.: 3-D image-based numerical computations of snow permeability: links to specific surface area, density, and microstructural anisotropy, The Cryosphere, 6, 939–951, <a href="http://dx.doi.org/10.5194/tc-6-939-2012">https://doi.org/10.5194/tc-6-939-2012</a>, 2012.

Carmagnola, C. M., Morin, S., Lafaysse, M., Domine, F., Lesaffre, B., Lejeune, Y., Picard, G., and Arnaud, L.: Implementation and evaluation of prognostic representations of the optical diameter of snow in the detailed snowpack model SURFEX/ISBA-Crocus, The Cryosphere Discuss., 7, 4443–4500, <a href="http://dx.doi.org/10.5194/tcd-7-4443-2013">https://doi.org/10.5194/tcd-7-4443-2013</a>, 2013.

Celia, M. A., Bouloutas, E. T., and Zarba, R. L.: A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26, 1483–1496, <a href="http://dx.doi.org/10.1029/WR026i007p01483">https://doi.org/10.1029/WR026i007p01483</a>, 1990.

Colbeck, S. C.: A theory of water percolation in snow, J. Glaciol., 11, 369–385, 1972.

Colbeck, S. C.: The capillary effects on water percolation in homogeneous snow, J. Glaciol., 13, 85–97, 1974.

Coléou, C. and Lesaffre, B.: Irreducible water saturation in snow: experimental results in a cold laboratory, Ann. Glaciol., 26, 64–68, 1998.

Conway, H. and Benedict, R.: Infiltration of water into snow, Water Resour. Res., 30, 641–649, <a href="http://dx.doi.org/10.1029/93WR03247">https://doi.org/10.1029/93WR03247</a>, 1994.

Conway, H. and Raymond, C. F.: Snow stability during rain, J. Glaciol., 39, 635–642, 1993.

Daanen, R. and Nieber, J.: Model for Coupled Liquid Water Flow and Heat Transport with Phase Change in a Snowpack, J. Cold Reg. Eng., 23, 43–68, <a href="http://dx.doi.org/10.1061/(ASCE)0887-381X(2009)23:2(43)">https://doi.org/10.1061/(ASCE)0887-381X(2009)23:2(43)</a>, 2009.

Davis, R. E., Jordan, R., Daly, S., and Koenig, G. G.: Model Validation: Perspectives in Hydrological Science, John Wiley & Sons Ltd, 2001.

Domine, F., Morin, S., Brun, E., Lafaysse, M., and Carmagnola, C. M.: Seasonal evolution of snow permeability under equi-temperature and temperature-gradient conditions, The Cryosphere, 7, 1915–1929, <a href="http://dx.doi.org/10.5194/tc-7-1915-2013">https://doi.org/10.5194/tc-7-1915-2013</a>, 2013.

Essery, R., Morin, S., Lejeune, Y., and Ménard, C. B.: A comparison of 1701 snow models using observations from an alpine site, Adv. Water Resour., 55, 131–148, <a href="http://dx.doi.org/10.1016/j.advwatres.2012.07.013">https://doi.org/10.1016/j.advwatres.2012.07.013</a>, 2013.

Fierz, C., Armstrong, R., Durand, Y., Etchevers, P., Greene, E., McClung, D., Nishimura, K., Satyawali, P., and Sokratov, S.: The International Classification for Seasonal Snow on the Ground (ICSSG), Tech. Rep., IHP-VII Technical Documents in Hydrology No. 83, IACS Contribution No. 1, UNESCO-IHP, 2009.

Flerchinger, G. N. and Saxton, K. E.: Simultaneous heat and water model of a freezing snow-residue-soil system: I. Theory and development., Trans. Am. Soc. Agric. Eng., 32, 565–571, 1989.

Førland, E., Allerup, P., Dahlström, B., Elomaa, E., Jónsson, T., Madsen, H., Perälä, Rissanen, P., Vedin, H., and Vejen, F.: Manual for operational correction of Nordic precipitation data, Tech. Rep. 24/96, Norske Meteorologiske Institutt, 1996.

Goodison, B., Louie, P., and Yang, D.: WMO Solid precipitation measurement intercomparison, Final Report, Tech. Rep., World Meteorological Organization (WMO), 1998.

Hirashima, H., Kamiishi, I., Yamaguchi, S., Sato, A., and Lehning, M.: Application of a numerical snowpack model to estimate full-depth avalanche danger, in: Proceedings of the 2010 International Snow Science Workshop, 2010a.

Hirashima, H., Yamaguchi, S., Sato, A., and Lehning, M.: Numerical modeling of liquid water movement through layered snow based on new measurements of the water retention curve, Cold Reg. Sci. Technol., 64, 94–103, <a href="http://dx.doi.org/10.1016/j.coldregions.2010.09.003">https://doi.org/10.1016/j.coldregions.2010.09.003</a>, 2010b.

Huang, K., Mohanty, B., and van Genuchten, M.: A new convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation, J. Hydrol., 178, 69–91, <a href="http://dx.doi.org/10.1016/0022-1694(95)02799-8">https://doi.org/10.1016/0022-1694(95)02799-8</a>, 1996.

Illangasekare, T. H., Walter Jr., R. J., Meier, M. F., and Pfeffer, W. T.: Modeling of meltwater infiltration in subfreezing snow, Water Resour. Res., 26, 1001–1012, <a href="http://dx.doi.org/10.1029/WR026i005p01001">https://doi.org/10.1029/WR026i005p01001</a>, 1990.

Ippisch, O., Vogel, H.-J., and Bastian, P.: Validity limits for the van Genuchten-Mualem model and implications for parameter estimation and numerical simulation, Adv. Water Resour., 29, 1780–1789, <a href="http://dx.doi.org/10.1016/j.advwatres.2005.12.011">https://doi.org/10.1016/j.advwatres.2005.12.011</a>, 2006.

Jin, J., Gao, X., Yang, Z.-L., Bales, R. C., Sorooshian, S., Dickinson, R. E., Sun, S. F., and Wu, G. X.: Comparative Analyses of Physically Based Snowmelt Models for Climate Simulations, J. Climate, 12, 2643–2657, <a href="http://dx.doi.org/10.1175/1520-0442(1999)012<2643:CAOPBS>2.0.CO;2">https://doi.org/10.1175/1520-0442(1999)012<2643:CAOPBS>2.0.CO;2</a>, 1999.

Jordan, P.: Meltwater movement in a deep snowpack: 2. Simulation model, Water Resour. Res., 19, 979–985, <a href="http://dx.doi.org/10.1029/WR019i004p00979">https://doi.org/10.1029/WR019i004p00979</a>, 1983.

Jordan, R.: A one-dimensional temperature model for a snow cover: Technical documentation {SNTHERM.89, Tech. Rep. Spec. Rep. 657, U.S. Army Cold Reg. Res. Eng. Lab., Hanover, NH, 1991.

Jordan, R.: Effects of capillary discontinuities on water flow and water retention in layered snowcovers., in: Proceedings of the International Symposium on Snow and Related Manifestations, edited by: Agrawal, K. C., Vol. 94, 157–170, Snow and Avalanche Study Establishment, Manali, India, 1996.

Katsushima, T., Yamaguchi, S., Kumakura, T., and Sato, A.: Experimental analysis of preferential flow in dry snowpack, Cold Reg. Sci. Technol., 85, 206–216, <a href="http://dx.doi.org/10.1016/j.coldregions.2012.09.012">https://doi.org/10.1016/j.coldregions.2012.09.012</a>, 2013.

Kattelmann, R.: Macropores in snowpacks of Sierra Nevada, Ann. Glaciol., 6, 272–273, 1985.

Kattelmann, R.: Snowmelt lysimeters in the evaluation of snowmelt models, Ann. Glaciol., 31, 406–410, <a href="http://dx.doi.org/10.3189/172756400781820048">https://doi.org/10.3189/172756400781820048</a>, 2000.

Koster, R. D., Mahanama, S. P. P., Livneh, B., Lettenmaier, D. P., and Reichle, R. H.: Skill in streamflow forecasts derived from large-scale estimates of soil moisture and snow, Nat. Geosci., 3, 613–616, <a href="http://dx.doi.org/10.1038/ngeo944">https://doi.org/10.1038/ngeo944</a>, 2010.

Lehning, M., Bartelt, P., Brown, B., and Fierz, C.: A physical SNOWPACK model for the Swiss avalanche warning Part III: Meteorological forcing, thin layer formation and evaluation, Cold Reg. Sci. Technol., 35, 169–184, <a href="http://dx.doi.org/10.1016/S0165-232X(02)00072-1">https://doi.org/10.1016/S0165-232X(02)00072-1</a>, 2002a.

Lehning, M., Bartelt, P., Brown, B., Fierz, C., and Satyawali, P.: A physical SNOWPACK model for the Swiss avalanche warning Part II. Snow microstructure, Cold Reg. Sci. Technol., 35, 147–167, <a href="http://dx.doi.org/10.1016/S0165-232X(02)00073-3">https://doi.org/10.1016/S0165-232X(02)00073-3</a>, 2002b.

Mahanama, S. P., Livneh, B., Koster, R., Lettenmaier, D., and Reichle, R.: Soil Moisture, Snow, and Seasonal Streamflow Forecasts in the United States, J. Hydrometeorol., 13, 189/203, <a href="http://dx.doi.org/10.1175/JHM-D-11-046.1">https://doi.org/{10.1175/JHM-D-11-046.1</a>, 2012.

Marks, D., Domingo, J., Susong, D., Link, T., and Garen, D.: A spatially distributed energy balance snowmelt model for application in mountain basins, Hydrol. Process., 13, 1935–1959, <a href="http://dx.doi.org/10.1002/(SICI)1099-1085(199909)13:12/13<1935::AID-HYP868>3.0.CO;2-C">https://doi.org/10.1002/(SICI)1099-1085(199909)13:12/13<1935::AID-HYP868>3.0.CO;2-C</a>, 1999.

Marks, D., Link, T., Winstral, A., and Garen, D.: Simulating snowmelt processes during rain-on-snow over a semi-arid mountain basin, Ann. Glaciol., 32, 195–202, <a href="http://dx.doi.org/10.3189/172756401781819751">https://doi.org/10.3189/172756401781819751</a>, 2001.

Marsh, P.: Water flux in melting snow covers, Vol. 1, Advances in Porous Media, 61–124, Elsevier, Amsterdam, 1991.

Marsh, P.: Snowcover formation and melt: recent advances and future prospects, Hydrol. Process., 13, 2117–2134, <a href="http://dx.doi.org/10.1002/(SICI)1099-1085(199910)13:14/15<2117::AID-HYP869>3.0.CO;2-9">https://doi.org/10.1002/(SICI)1099-1085(199910)13:14/15<2117::AID-HYP869>3.0.CO;2-9</a>, 1999.

Marsh, P.: Encyclopedia of Hydrological Sciences., chap. 161: Water Flow Through Snow and Firn, John Wiley & Sons, Ltd, <a href="http://dx.doi.org/10.1002/0470848944.hsa167">https://doi.org/10.1002/0470848944.hsa167</a>, 2006.

Mazurkiewicz, A. B., Callery, D. G., and McDonnell, J. J.: Assessing the controls of the snow energy balance and water available for runoff in a rain-on-snow environment, J. Hydrol., 354, 1–14, <a href="http://dx.doi.org/10.1016/j.jhydrol.2007.12.027">https://doi.org/10.1016/j.jhydrol.2007.12.027</a>, 2008.

McCord, J. T.: Application of Second-Type Boundaries in Unsaturated Flow Modeling, Water Resour. Res., 27, 3257–3260, <a href="http://dx.doi.org/10.1029/91WR02158">https://doi.org/10.1029/91WR02158</a>, 1991.

McCuen, R., Knight, Z., and Cutter, A.: Evaluation of the Nash-Sutcliffe Efficiency Index, J. Hydrol. Eng., 11, 597–602, <a href="http://dx.doi.org/10.1061/(ASCE)1084-0699(2006)11:6(597)">https://doi.org/10.1061/(ASCE)1084-0699(2006)11:6(597)</a>, 2006.

Mitterer, C., Hirashima, H., and Schweizer, J.: Wet-snow instabilities: comparison of measured and modelled liquid water content and snow stratigraphy, Ann. Glaciol., 52, 201–208, <a href="http://dx.doi.org/10.3189/172756411797252077">https://doi.org/10.3189/172756411797252077</a>, 2011.

Morin, S., Lejeune, Y., Lesaffre, B., Panel, J.-M., Poncet, D., David, P., and Sudul, M.: An 18-yr long (1993–2011) snow and meteorological dataset from a mid-altitude mountain site (Col de Porte, France, 1325 m alt.) for driving and evaluating snowpack models, Earth Syst. Sci. Data, 4, 13–21, <a href="http://dx.doi.org/10.5194/essd-4-13-2012">https://doi.org/10.5194/essd-4-13-2012</a>, 2012.

Mott, R., Schirmer, M., Bavay, M., Grünewald, T., and Lehning, M.: Understanding snow-transport processes shaping the mountain snow-cover, The Cryosphere, 4, 545–559, <a href="http://dx.doi.org/10.5194/tc-4-545-2010">https://doi.org/10.5194/tc-4-545-2010</a>, 2010.

Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12, 513–522, <a href="http://dx.doi.org/10.1029/WR012i003p00513">https://doi.org/10.1029/WR012i003p00513</a>, 1976.

Nash, J. and Sutcliffe, J.: River flow forecasting through conceptual models part I – A discussion of principles, J. Hydrol., 10, 282–290, <a href="http://dx.doi.org/10.1016/0022-1694(70)90255-6">https://doi.org/10.1016/0022-1694(70)90255-6</a>, 1970.

Paniconi, C. and Putti, M.: A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems, Water Resour. Res., 30, 3357–3374, <a href="http://dx.doi.org/10.1029/94WR02046">https://doi.org/10.1029/94WR02046</a>, 1994.

Peitzsch, E., Karl, B., and Kathy, H.: Water movement and capillary barriers in a stratified and inclined snowpack, in: Proceedings Whistler 2008 International Snow Science Workshop September 21–27, 2008, 179–187, 2008.

Rathfelder, K. and Abriola, L. M.: Mass conservative numerical solutions of the head-based Richards equation, Water Resour. Res., 30, 2579–2586, <a href="http://dx.doi.org/10.1029/94WR01302">https://doi.org/10.1029/94WR01302</a>, 1994.

Richards, L.: Capillary conduction of liquids through porous mediums, J. Appl. Phys., 1, 318–333, <a href="http://dx.doi.org/10.1063/1.1745010">https://doi.org/10.1063/1.1745010</a>, 1931.

Schmucki, E., Marty, C., Fierz, C., and Lehning, M.: Evaluation of modelled snow depth and snow water equivalent at three contrasting sites in Switzerland using SNOWPACK simulations driven by different meteorological data input, Cold Reg. Sci. Technol., 99, 27–37, <a href="http://dx.doi.org/10.1016/j.coldregions.2013.12.004">https://doi.org/10.1016/j.coldregions.2013.12.004</a>, 2014.

Schneebeli, M.: Development and stability of preferential flow paths in a layered snowpack, in: Biogeochemistry of Seasonally Snow-Covered Catchments (Proceedings of a Boulder Symposium July 1995), edited by: Tonnessen, K., Williams, M., and Tranter, M., 89–95, AHS Publ. no. 228, 1995.

Seyfried, M. S., Grant, L. E., Marks, D., Winstral, A., and McNamara, J.: Simulated soil water storage effects on streamflow generation in a mountainous snowmelt environment, Idaho, USA, Hydrol. Process., 23, 858–873, <a href="http://dx.doi.org/10.1002/hyp.7211">https://doi.org/10.1002/hyp.7211</a>, 2009.

Shimizu, H.: Air permeability of deposited snow, Institute of Low Temperature Science, Sapporo, Japan, 1970.

Stössel, F., Guala, M., Fierz, C., Manes, C., and Lehning, M.: Micrometeorological and morphological observations of surface hoar dynamics on a mountain snow cover, Water Resour. Res., 46, W04511, <a href="http://dx.doi.org/10.1029/2009WR008198">https://doi.org/10.1029/2009WR008198</a>, 2010.

Szymkiewicz, A. and Helmig, R.: Comparison of conductivity averaging methods for one-dimensional unsaturated flow in layered soils, Adv. Water Resour., 34, 1012–1025, <a href="http://dx.doi.org/10.1016/j.advwatres.2011.05.011">https://doi.org/10.1016/j.advwatres.2011.05.011</a>, 2011.

van Genuchten, M. T.: A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils, Soil Sci. Soc. Am. J., 44, 892–898, <a href="http://dx.doi.org/10.2136/sssaj1980.03615995004400050002x">https://doi.org/10.2136/sssaj1980.03615995004400050002x</a>, 1980.

Vionnet, V., Brun, E., Morin, S., Boone, A., Faroux, S., Le Moigne, P., Martin, E., and Willemet, J.-M.: The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2, Geosci. Model Dev., 5, 773–791, <a href="http://dx.doi.org/10.5194/gmd-5-773-2012">https://doi.org/10.5194/gmd-5-773-2012</a>, 2012.

Waldner, P. A., Schneebeli, M., Schultze-Zimmermann, U., and Flühler, H.: Effect of snow structure on water flow and solute transport, Hydrol. Process., 18, 1271–1290, <a href="http://dx.doi.org/10.1002/hyp.1401">https://doi.org/10.1002/hyp.1401</a>, 2004.

Walter, B., Horender, S., Gromke, C., and Lehning, M.: Measurements of the pore-scale water flow through snow using Fluorescent Particle Tracking Velocimetry, Water Resour. Res., 49, 7448–7456, <a href="http://dx.doi.org/10.1002/2013WR013960">https://doi.org/10.1002/2013WR013960</a>, 2013.

Winstral, A., Elder, K., and Davis, R. E.: Spatial Snow Modeling of Wind-Redistributed Snow Using Terrain-Based Parameters, J. Hydrometeorol., 3, 524–538, <a href="http://dx.doi.org/10.1175/1525-7541(2002)003<0524:SSMOWR>2.0.CO;2">https://doi.org/10.1175/1525-7541(2002)003<0524:SSMOWR>2.0.CO;2</a>, 2002.

Yamaguchi, S., Katsushima, T., Sato, A., and Kumakura, T.: Water retention curve of snow with different grain sizes, Cold Reg. Sci. Technol., 64, 87–93, <a href="http://dx.doi.org/10.1016/j.coldregions.2010.05.008">https://doi.org/10.1016/j.coldregions.2010.05.008</a>, 2010.

Zanotti, F., Endrizzi, S., Bertoldi, G., and Rigon, R.: The GEOTOP snow module, Hydrol. Process., 18, 3667–3679, <a href="http://dx.doi.org/10.1002/hyp.5794">https://doi.org/10.1002/hyp.5794</a>, 2004.