Sub-grid parameterization of snow distribution for an energy and mass balance snow cover model

Representation of sub-element scale variability in snow accumulation and ablation is increasingly recognized as important in distributed hydrologic modelling, Representing sub-grid scale variability may be accomplished through numerical integration of a nested grid or through a lumped modelling approach. We present a physically based model of the lumped snowpack mass and energy balance applied to a 26-ha rangeland catchment with high spatial variability in snow accumulation and melt. Model state variables are snow-covered area average snow energy content (U), the basin-average snow water equivalence (W a ), and snow-covered area fraction (A f ). The energy state variable is evolved through an energy balance. The snow water equivalence state variable is evolved through a mass balance, and the area state variable is updated according to an empirically derived relationship, A f (W a ), that is similar in nature to depletion curves used in existing empirical basin snowmelt models. As snow accumulates, the snow covered area increases rapidly. As the snowpack ablates, A f decreases as W a decreases. This paper shows how the relationship A f (W a ) for the melt season can be estimated from the distribution of snow water equivalence at peak accumulation in the area being modelled. We show that the depletion curve estimated from the snow distribution of peak accumulation at the Upper Sheep Creek sub-basin of Reynolds Creek Experimental Watershed compares well against the observed depletion data as well as modelled depletion data from an explicit spatially distributed energy balance model. Comparisons of basin average snow water equivalence between the lumped model and spatially distributed model show good agreement, Comparisons to observed snow water equivalence show poorer but still reasonable agreement. The sub-grid parameterization is easily portable to other physically based point snowmelt models. It has potential application for use in hydrologic and climate models covering large areas with large model elements, where a computationally inexpensive parameterization of sub-grid snow processes may be important.

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

[2]  Eric A. Anderson,et al.  National Weather Service river forecast system: snow accumulation and ablation model , 1973 .

[3]  Murugesu Sivapalan,et al.  Scale issues in hydrological modelling , 1995 .

[4]  J. Dozier,et al.  Rapid Calculation Of Terrain Parameters For Radiation Modeling From Digital Elevation Data , 1989, 12th Canadian Symposium on Remote Sensing Geoscience and Remote Sensing Symposium,.

[5]  J. Dozier,et al.  Rapid calculation of terrain parameters for radiation modeling from digital elevation data , 1990 .

[6]  Keith Beven,et al.  A Discussion of Distributed Hydrological Modelling , 1990 .

[7]  C. Duffy,et al.  SELF-AFFINE SCALING AND SUBSURFACE RESPONSE TO SNOWMELT IN STEEP TERRAIN , 1991 .

[8]  David G. Tarboton,et al.  The Influence of the Spatial Distribution of Snow on Basin-Averaged Snowmelt , 1998 .

[9]  W. Allard.  Snow Hydrology: Summary Report of the Snow Investigations. Published by the North Pacific Division, Corps of Engineers, U.S. Army, Portland, Oregon, 1956. 437 pages, 70 pages of plates, maps and figs., 27 cm.* , 1957 .

[10]  L. B. Leopold,et al.  Water In Environmental Planning , 1978 .

[11]  M. Wigmosta,et al.  A distributed hydrology-vegetation model for complex terrain , 1994 .

[12]  M. Levent Kavvas,et al.  Physics of the spatially averaged snowmelt process , 1997 .

[13]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[14]  R. Moore.  The probability-distributed principle and runoff production at point and basin scales , 1985 .

[15]  Albert Rango,et al.  Development and testing of a Snowmelt-Runoff forecasting technique , 1990 .

[16]  Eli Skop,et al.  Scale Issues in Hydrological Modeling , 1996 .

[17]  R. Allan Freeze,et al.  Mathematical simulation of subsurface flow contributions to snowmelt runoff, Reynolds Creek Watershed, Idaho , 1974 .

[18]  Günter Blöschl,et al.  Entering the Era of Distributed Snow Models , 1994 .

[19]  K. Tonnessen,et al.  Biogeochemistry of seasonally snow-covered catchments , 1995 .

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

[21]  David S. Bowles,et al.  Recent advances in the modeling of hydrologic systems , 1991 .

[22]  D. Lettenmaier,et al.  Effects of Subgrid Spatial Heterogeneity on GCM-Scale Land Surface Energy and Moisture Fluxes , 1996 .

[23]  E. Anderson,et al.  A point energy and mass balance model of a snow cover , 1975 .

[24]  Keith Beven,et al.  Linking parameters across scales: Subgrid parameterizations and scale dependent hydrological models. , 1995 .

[25]  D. Tarboton,et al.  Spatially Distributed Snowmelt Inputs to a Semi-Arid Mountain Watershed , 1997 .

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

[27]  G. Flerchinger,et al.  Groundwater response to snowmelt in a mountainous watershed , 1991 .

[28]  Jeff Dozier,et al.  Automated Mapping of Montane Snow Cover at Subpixel Resolution from the Landsat Thematic Mapper , 1996 .

[29]  G. Blöschl,et al.  Distributed Snowmelt Simulations in an Alpine Catchment: 2. Parameter Study and Model Predictions , 1991 .

[30]  R. Jordan.  A One-dimensional temperature model for a snow cover : technical documentation for SNTHERM.89 , 1991 .

[31]  E. Morris,et al.  Modelling Snowmelt-Induced Processes , 1988 .

[32]  David G. Tarboton,et al.  A Spatially Distributed Energy Balance Snowmelt Model , 1993 .

[33]  E. Morris.  Physics-Based Models of Snow , 1991 .