1. 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
www:

2. 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.

3. 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: , 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):
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
(These are available on the internet:

6. (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

7. 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

8. { { Model Structure Predictor + Corrector Numerical Integration

9. 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

10. 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

11. Melt Outflow Calculation

12. Shortwave Radiation

13. 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:

14. Reflective Properties of Snow
Modified from D. Cline

15. 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.

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

17. 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.

18. 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

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

20. Surface conductance Ks adjusted to match diurnal surface temperature fluctuations

21. Surface conductance Ks adjusted to match diurnal surface temperature fluctuations

22. Drive with incident solar radiation, adjust albedo.

23. Confirm agreement between modeled and observed Net Radiation

24. Calibrate Ksat to match Melt Outflow

25. Upper Sheep Creek

26. Snow drifts at Reynolds Creek Experimental Watershed

27. Snow drift at Upper sheep Creek

28. Snow drift at Upper sheep Creek

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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. Location

40. USU lysimeter drainage farm Cache Valley

41. Sawing weighing lysimters

42. Weighing lysimeter to measure sublimation

44. USU lysimeter drainage farm Cache Valley

45. Observed and Modeled snow water equivalent, USU drainage farm

46. Vertical temperature profiles

47. Temperature time series at different depths

48. Comparison of measured and modeled energy content

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

50. Model Options

51. Model options contd.

52. 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= De =0.1 m
z0=0.010 m

54. Comparisons of snow water equivalent in 1986 at CSSL

55. Comparisons of accumulative melt in 1986 at CSSL.

56. Comparisons of meltwater outflow rate in 1986 at CSSL

57. Comparisons of surface temperature of snow in 1986 at CSSL

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

59. Weather File …
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) …

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

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

62. Site Variables (sitev.dat)

63. Diurnal temperature range file (bcparam.dat)