Utah Water Research Laboratory An Energy Balance Snowmelt Model for use in Spatially Distributed Hydrologic Models David G. Tarboton Tanveer G. Chowdhury Thomas H. Jackson Charlie Luce Utah Water Research Laboratory Utah State University email: dtarb@cc.usu.edu www: http://www.engineering.usu.edu/dtarb/snow/snow.html

Objectives (Snowmelt model design considerations) Physically based calculation of snow energy balance. Simplicity. Small number of state variables and adjustable parameters. Transportable. Applicable without calibration at different locations. Match diurnal cycle of melt outflow rates for erosion prediction. Match overall accumulation and ablation for water balance. • Distributed by application over a spatial grid.

Papers: Luce, C. H., D. G. Tarboton and K. R. Cooley, (1999), "Subgrid Parameterization Of Snow Distribution For An Energy And Mass Balance Snow Cover Model," Hydrological Processes, 13: 1921-1933, special issue from International Conference on Snow Hydrology, Brownsville, Vermont, 6-9 October, 1998. Luce, C. H., D. G. Tarboton and K. R. Cooley, (1998), "The Influence of the Spatial Distribution of Snow on Basin-Averaged Snowmelt," Hydrological Processes, 12(10-11): 1671-1683. Luce, C. H., D. G. Tarboton and K. R. Cooley, (1997),"Spatially Distributed Snowmelt Inputs to a Semi-Arid Mountain Watershed," in Proceedings of the Western Snow Conference, Banff, Canada, May 5-8, 1997. Tarboton, D. G. and C. H. Luce, (1996), "Utah Energy Balance Snow Accumulation and Melt Model (UEB)," Computer model technical description and users guide, Utah Water Research Laboratory and USDA Forest Service Intermountain Research Station. Tarboton, D. G., T. G. Chowdhury and T. H. Jackson, (1995),"A Spatially Distributed Energy Balance Snowmelt Model," in Biogeochemistry of Seasonally Snow-Covered Catchments, ed. K. A. Tonnessen et al., Proceedings of a Boulder Symposium, July 3-14, IAHS Publ. no. 228, p.141-155. (These are available on the internet: http://www.engineering.usu.edu/dtarb/)

(Qsi-Qr) + (Lin - Lout) + Qh + Qe + Qg + Qp - dU/dt = Qm Snow Energy Exchanges Qsn Qle (Qsi-Qr) + (Lin - Lout) + Qh + Qe + Qg + Qp - dU/dt = Qm Qsi Lin Lout Qr Modified from D. Cline

Snow Model Physics and Parameterizations Inputs Wind Fluxes dependent on surface temperature Q (T ,T ) Q (e ,T ) Q (T ) h a s e a s le s Thermally active layer State variables Snow Energy Content U Q Water Equivalence W D Soil e Q Q g m Snow Model Physics and Parameterizations

{ { Model Structure Predictor + Corrector Numerical Integration

Surface Energy Balance External Forcing Surface temperature dependent fluxes Depth sensitivity to diurnal temperature fluctuation Energy Balance /Equilibrium at surface If Ts > 0 oC  Conduction cannot accommodate surface energy inputs  Surface melt is generated. Set Ts = 0 oC  Additional energy is advected downwards by surface melt inflow

Surface Energy Balance – With Forest Canopy External Forcing Surface temperature dependent fluxes Depth sensitivity to diurnal temperature fluctuation Energy Balance /Equilibrium at surface If Ts > 0 oC  Conduction cannot accommodate surface energy inputs  Surface melt is generated. Set Ts = 0 oC  Additional energy is advected downwards by surface melt inflow

Melt Outflow Calculation

Shortwave Radiation

Atmospheric Transmissivity Bristow, K. L. and G. S. Campbell, (1984), "On the Relationship Between Incoming Solar Radiation and the Daily Maximum and Minimum Temperature," Agricultural and Forest Meteorology, 31: 159-166.

Reflective Properties of Snow Modified from D. Cline

Albedo Dickinson, R. E., A. Henderson-Sellers and P. J. Kennedy, (1993), "Biosphere-Atmosphere Transfer Scheme (BATS) Version 1e as Coupled to the NCAR Community Climate Model," NCAR/TN-387+STR, National Center for Atmospheric Research.

Shortwave Radiation & Snow Why does snow albedo decrease over time? Modified from D. Cline, Handbook of Snow

Effect of Illumination angle Dickinson, R. E., A. Henderson-Sellers and P. J. Kennedy, (1993), "Biosphere-Atmosphere Transfer Scheme (BATS) Version 1e as Coupled to the NCAR Community Climate Model," NCAR/TN-387+STR, National Center for Atmospheric Research.

Calibration Data: Central Sierra Snow laboratory winter of 85/86. 1. Drive model with net radiation input. • Match overall accumulation and ablation of W • Match surface temperatures 2. Drive model with observed incident radiation. • Adjust albedo parameters so that observed and net radiation matches. 3. Compare Melt Outflow

Calibration of zo and Ks to match observations with Net Radiation Input

Surface conductance Ks adjusted to match diurnal surface temperature fluctuations

Surface conductance Ks adjusted to match diurnal surface temperature fluctuations

Drive with incident solar radiation, adjust albedo.

Confirm agreement between modeled and observed Net Radiation

Calibrate Ksat to match Melt Outflow

Upper Sheep Creek

Snow drifts at Reynolds Creek Experimental Watershed

Snow drift at Upper sheep Creek

Snow drift at Upper sheep Creek

Drift adjustment factor Contours at 0.5, 0.9, 1.5, 2.5, 4 and 6.

Day 407 2/11/93 Observed Basin Averages Snow Water Equivalent Observed: 209 mm Modeled: 301 mm Cumulative Precipitation from 10/29/92: 369 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 428 3/4/93 Observed Basin Averages Snow Water Equivalent Observed: 269 mm Modeled: 339 mm Cumulative Precipitation from 10/29/92: 418 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 448 3/24/93 Observed Basin Averages Snow Water Equivalent Observed: 220 mm Modeled: 233 mm Cumulative Precipitation from 10/29/92: 471 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 464 4/9/93 Observed Basin Averages Snow Water Equivalent Observed: 166 mm Modeled: 191 mm Cumulative Precipitation from 10/29/92: 487 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 471 4/16/93 Observed Basin Averages Snow Water Equivalent Observed: 145 mm Modeled: 181 mm Cumulative Precipitation from 10/29/92: 489 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 485 4/30/93 Observed Basin Averages Snow Water Equivalent Observed: 133 mm Modeled: 152 mm Cumulative Precipitation from 10/29/92: 499 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 498 5/13/93 Observed Basin Averages Snow Water Equivalent Observed: 75 mm Modeled: 96 mm Cumulative Precipitation from 10/29/92: 518 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 505 5/20/93 Observed Basin Averages Snow Water Equivalent Observed: 37 mm Modeled: 42 mm Cumulative Precipitation from 10/29/92: 525 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Day 511 5/26/93 Observed Basin Averages Snow Water Equivalent Observed: 19 mm Modeled: 21 mm Cumulative Precipitation from 10/29/92: 525 mm Simulated Snow water equivalent in m Contour interval 0.5 m

Location

USU lysimeter drainage farm Cache Valley

Sawing weighing lysimters

Weighing lysimeter to measure sublimation

USU lysimeter drainage farm Cache Valley

Observed and Modeled snow water equivalent, USU drainage farm

Vertical temperature profiles

Temperature time series at different depths

Comparison of measured and modeled energy content

Theory Semi infinite domain heat conduction For diurnal fluctuation at surface Amplitude

Model Options

Model options contd.

Modified Model – SWE comparison Uncertainty due to extremely strong wind Discrepancy in snowfall and extreme strong wind λ=0.33 kJ/m/K/hr r=1 Lc=0.02 De =0.1 m z0=0.010 m

Comparisons of snow water equivalent in 1986 at CSSL

Comparisons of accumulative melt in 1986 at CSSL.

Comparisons of meltwater outflow rate in 1986 at CSSL

Comparisons of surface temperature of snow in 1986 at CSSL

Using the UEB Model Input files Weather file Model Parameter File Site Variable File Diurnal temperature range parameter file (Bristow – Campbell)

Weather File 5 16 86 0. 6. 21852.20 1.240756 0.56845 6.506857 0.000000 1.828394 0.500000 9.600000 0.000000 475.250000 11.290192 0.000000 2.304491 0.435833 9.600000 1585.991455 475.500000 15.373524 0.000000 2.724709 0.353000 9.600000 1489.272705 475.750000 12.223524 0.000000 1.113130 0.321000 9.600000 0.000000 476.000000 12.023525 0.000000 2.205397 0.405500 7.700000 0.000000 476.250000 16.306858 0.000000 1.765063 0.275167 7.700000 1582.527466 476.500000 18.256859 0.000000 2.963130 0.265500 7.700000 1323.753052 476.750000 … Month day year hour time_step U W age Time steps to skip Columns of Air temp (C) Precip rate (m/hr) Wind Speed (m/s) Relative Humidity as a fraction Daily Air temperature range Incoming Shortwave Net Radiation (kJ/m2/hr) …

Parameter File (param.dat) Free format file containing model parameters

Parameter File (param.dat) contd. Free format file containing model parameters

Site Variables (sitev.dat) 0.0 1.0 88500 0 0.1 0 125.0 39.32

Diurnal temperature range file (bcparam.dat)