The Energy Budget Method is based on the Utah Energy Balance (UEB) model (Tarboton and Luce, 199619; Luce, 200020; Tarboton and Luce, 200121; You, 200422). The UEB snowmelt model is a physically-based energy and mass balance model. Energy is exchanged between the snowpack, the air above, and the soil below.
Tutorials describing example applications of this snowmelt method, including parameter estimation and calibration, can be found here: Calibrating Gridded Snowmelt: Upper Truckee River, California15 and Calibrating Point Snowmelt: Swamp Angel Study Plot, Colorado16. A tutorial illustrating how to use the Uncertainty Analysis to evaluate Hybrid Snow parameter sensitivity can be found here: Evaluating Gridded Hybrid/RTI Snowmelt Parameter Sensitivity17. Descriptions of the user interface features pertaining to this method can be found here: Hybrid Snow section of the User's Manual18.
where is net shortwave radiation, is incoming longwave radiation, is advected heat from precipitation, is ground heat flux, is outgoing longwave radiation, is sensible heat flux, is latent heat flux due to sublimation/condensation, and is advected heat removed by meltwater.
Depiction of Energy Budget Snow Method Iterative Solver
The surface energy balance is:
Surface heat conduction describe the exchange of heat from the snow surface into the snowpack. Snow surface heating varies dramatically over the course of a day and over longer time periods resulting in a nonlinear temperature profile. Nonlinearity in snowpack temperature profile is largely caused by daily temperature fluctuations at the surface, which have a sinusoidal pattern.
Surface Heat Conduction
HEC-HMS uses the modified force-restore with shallow snow correction method. The force-restore method estimates the driving flux at the surface as sinusoidal (since daily temperature fluctuations follow an
approximately sinusoidal pattern). However, the force-restore method may be a poor approximation because the temperature gradient does not cycle on a daily time scale. Temperature variation (and heat fluxes) with depth is caused by lower frequency fluctuations. Therefore, the heat fluxes caused by lower frequency variability are superimposed on the gradient in daily average temperature.
The low frequency effective depth is used to associate a frequency with a distance used in the daily average gradient estimate:
where is the soil thermal diffusivity, is the frequency of low-frequency temperature variation, and
The surface heat flux is computed as:
where is daily average surface temperature and is daily average depth average snowpack temperature.
•
•
•
•
•
•
•
•
•
•
•
The shallow snow correction involves computation of an effective thermal depth of combined snowpack and ground and a weighted thermal conductivity when the thermal damping depth extends into the ground. The shallow snowpack correction is applied when the snow depth is less than the effective depth.
Heat conduction scheme for combined snow/soil system (You, 2004)
Applicability and Limitations of Snow Accumulation and Melt Methods
The following table contains a list of various advantages and disadvantages regarding the aforementioned snowmelt methods available for use within HEC-HMS. However, these are only guidelines and should be supplemented by knowledge of, and experience with, the methods and the watershed in question.
Method Advantages Disadvantages
Temperature
Index "Mature" method that has been used successfully in thousands of studies throughout the U.S.
Easy to set up and use
Only requires precipitation and air temperature boundary conditions More parsimonious than other methods
May be too simple for some situations Limited snowpack outputs compared to other methods
Hybrid/
Radiation- derived Temperature Index
Incorporates factors such as short and longwave radiation into snowmelt equations
Can incorporate terrain slope, aspect, and shading
More snowpack outputs than Temperature Index method
Requires more meteorologic boundary conditions than Temperature Index Less mature than other methods
•
•
•
•
•
•
•
Method Advantages Disadvantages
Energy Budget Incorporates factors such as short and longwave radiation, sensible heat flux, sublimation, condensation, and wind into snowmelt equations
Can incorporate terrain slope, aspect, and shading
Lots of snowpack outputs available including SWE, snow density, snow depth, snowpack temperature, snowpack energy, albedo, etc.
Requires many meteorologic boundary conditions
Computationally intensive
Solution isn’t guaranteed to converge Much less parsimonious than other methods
Snowmelt References
Allen, R. G., Walter, I. A., Elliott, R., Howell, T., Itenfisu, D., and Jensen, M. (2005). "The ASCE Standardized Reference Evapotranspiration Equation." ASCE, Reston, VA.
Anderson, E. (2006). "Snow accumulation and ablation model - SNOW-17, NWSRFS User Documentation."
U.S. National Weather Service, Silver Springs, MD.
Follum, M. L., Downer, C. W., Niemann, J. D., Roylance, S. M., and Vuyovich, C. M. (2015). "A radiation-derived temperature-index snow routine for the GSSHA hydrologic model." Journal of Hydrology, 529, 723-736.
Follum, M. L., Niemann, J. D., and Fassnacht, S. R. (2019). "A comparison of snowmelt-derived streamflow from temperature-index and modified-temperature-index snow models." Hydrological Processes, 33, 3030-3045.
Luce, C. H. (2000). "Scale Influences on the Representation of Snowpack Processes." [Doctoral dissertation - Utah State University].
Luce, C. H. and Tarboton, D. G. (2001). "A modified force-restore approach to modeling snowsurface heat fluxes." Proceedings of The 69th Annual Meeting of the Western Snow Conference, Sun Valley, Idaho.
Oke, T. R. (1987). Boundary Layer Climates. Second Edition. Methuen: London and New York
Sturm, M., et al. (1995). A Seasonal Snow Cover Classification System for Local to Global Applications DOI:
http://dx.doi.org/10.1175/1520-0442(1995)008<1261:ASSCCS>2.0.CO;223
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 (http://www.engineering.usu.edu/dtarb/).
USACE. (1987). SSARR Model, Streamflow Synthesis and Reservoir Regulation. User Manual. (Reprinted 1991). U.S. Army Corps of Engineers, North Pacific Division, PO Box 2810, Portland, OR 97208-2870
USACE. (1956). Snow Hydrology. Summary Report Of The Snow Investigations. North Pacific Division, Corps of Engineers, U.S. Army, Portland, Oregon. 30 June 1956.
You, J. (2004). "Snow Hydrology: The Parameterization of Subgrid Processes within a Physically Based Snow Energy and Mass Balance Model." [Doctoral dissertation - Utah State University].