Mar 22, 2015

Energy Balance of Prairie Snowmelt

Snowmelt refers to the phase change of ice into water, which is involved with energy absorption. If net incoming radiation is negative then it refers as condensation and if net incoming radiation is positive it refers to melting. The net energy is the amount of energy used for phase change and transfer of radiation, convection, conduction, and advection flux into snowpack and the rate of change of internal energy. The amount of energy is estimated using simple empirical equation, which uses readily available measured meteorological variables.
Figure- Energy balance control volume (Pomeroy et al., 2007)
Snow is a highly porous and sintered material and it consists of ice granule and air. The temperature of snow is almost near to melting temperature. Snow on the ground is under continuous transformation or metamorphism. Near melting point temperature, snow becomes a mixture of ice, air and water. Snowpack consists of permeable heterogeneous layers and can be changed with wind redistribution and metamorphism. The relative density of snow normally varies from 0.004 to 0.34 and it depends on the metamorphism of snowflakes (Dingman, 2002; Fierz et al., 2009; Helgason & Pomeroy, 2012). Metamorphism of snow is done in four stages.
Figure- Snowpack metamorphism (Dingman, 2002)
Snow melting can be divided into three phases i.e. warming phase, ripening phase and output phase. In the warming phase, snowpack absorb ambient energy and raises the average snowpack temperature. At the end of this phase, snowpack becomes isothermal at 0oC. In the ripening phase, snowpack absorbed energy, which is used to melt snow. Meltwater is stored in the pore space of snowpack by using surface tension of water. At the end of this phase, snowmelt runoff initiates. In the output phase, further absorption of energy produces snowmelt runoff and participate on other hydrologic processes i.e. infiltration, overland runoff, evaporation etc. (Dingman, 2002).
Net radiation is the sum of net shortwave and longwave radiation. Net radiation flux is dominated by net shortwave radiation. (Gray et al., 1986b; Male & Granger, 1981). Granger (1977) neglected advective fluxes, as they are negligible comparing solar radiation and sensible heat transfer flux. The energy budget equation can be expressed as:

QM + QN +QH + QE + QG + QD = dU/dt

Here, QM is energy available for snowmelt, QN is net radiation (Kin: incoming shortwave, Kout: outgoing shortwave, Lin: incoming longwave and Lout: outgoing longwave), QH is turbulent flux of sensible heat, QE is turbulent flux of latent energy, QG is ground heat flux, Qd is energy due to advection from external sources, T is the incoming and outgoing advective energy, P is advective flux from precipitation and dU/dt is the rate of change of internal energy. The fluxes of energy directed towards the control volume are taken as positive; those directed away from the volume are negative. The net radiation, QN is composed of the sum of net longwave and net shortwave fluxes (Pomeroy et al., 2007).

The shortwave radiation is composed of direct beam and diffuse components of beam. Diffusion or reflection occurs due to clouds or other surfaces and atmospheric constituents. The amount of shortwave radiation depends on turbidity of atmosphere or albedo (Granger & Gray, 1990). Gray et al. (1986a) estimates net shortwave radiation with respect to surface albedo as: K* = Kin (1 - α); where, Kin is incoming shortwave radiation and α is albedo. Granger & Gray (1990) shows that net incoming shortwave radiation is the sum of direct beam and diffuse sky radiation. Shook & Pomeroy (2011) applied several sources (i.e. NARR, NCEP) and methods (i.e. semi empirical, Campbell-Bristow-Walter, regression) of shortwave radiation estimation.

Albedo or mean reflectance is the ratio of reflected shortwave flux. Snow grain size and density are the factors of albedo change. In prairies, the rate of change of albedo is not constant. Wind transported soil, fall of new snow changes albedo. The amount of albedo variation is very small under clear sky condition. Though albedo is not generally measured in climatologic stations, it can be estimated using the color, ripeness, wetness, age and other properties of snow. Albedo varies over different periods of snow melting. Net shortwave radiation estimation using albedo shows reasonable results (Gray & Landine, 1987; Gray et al., 1986b). Gray & Landine (1987) shows that the factors of albedo depletion rate is-
  • time of year
  • occurrence of melt
  • snow events
  • underlying ground
  • patchy snow cover
Underlying ground surface can transfer previously absorbed solar radiation into snowpack and expedite snowmelt. However, the attenuation of radiation is dependent on particle size, density, structure, wetness, and foreign matter content in snowpack.

Shortwave radiation is the dominant in the solar radiation flux, but longwave radiation can contribute similar or higher in some cases. During the stages of early melting, solar energy is low and albedo is high. In this time longwave dominates the solar radiation. The amount of longwave radiation is higher under cloudy sky and high albedo conditions. High albedo causes high emissivity of soil surface, which reduces the amount of shortwave radiation. The variation of longwave radiation depends of temperature, humidity and cloud cover of atmosphere. In uneven surface, ground longwave emission also contributes longwave irradiance and causes spatial variability of snowmelt (Granger & Gray, 1990; Sicart et al., 2006). Most of the longwave radiation is received at the surface, which comes from the near-surface layer of the atmosphere.

Convective energy is transferred in sensible heat and latent heat form. Heat transfer is carried to or from snow surface by turbulent eddies and it occurs in the 2-3 m layer of atmosphere just above the snow surface. Energy advected from adjacent patches of snow and bare ground also contribute energy for snowmelt (Gray & Landine, 1988; Morris, 1989). Sensible heat energy is function of physical temperature, wind speed and latent heat energy is function of vapour pressure, wind speed.

Snowmelt normally exhibits diurnal pattern as it receives radiation in the daytime and energy flow stops at night. Nighttime energy deficiency is compensated by change in the internal energy of snowpack. For shallow snowpack, this change of internal energy is higher comparing deep snowpack. Often the amount of change in internal energy is neglected, because the amount of energy is small comparing other major energy terms (Gray & Landine, 1988).

Net energy balance controls the snowmelt rate. Comparing mountainous or forest area, energy intake in the Prairie plain land is significantly high and it causes immediate steep peak flow just after the inception of snow melting process. Shortwave solar radiation is the dominant part of net solar radiation. However, at the beginning of snow meting season, snow surface albedo is high. High albedo leads to less net shortwave radiation and higher longwave radiation. Convective and advective heat transfer is occurs in a form of turbulent eddies. The amount of turbulent sensible heat and latent heat exchange is low comparing net solar radiation in the Prairies. The amount of change of internal heat flux is very insignificant comparing other major energy term. Change in internal energy is the result of diurnal energy reception pattern. Researchers faced difficulties to understand the effect of patchiness and bare ground on snowmelt as well as physical measurement of the turbulent heat flux. Recently these problems have been addressed in several publications and overall understanding improved.


References:
Dingman, S. L. (2002). Physical Hydrology (2nd ed.). Prentice Hall.

Essery, R., & Pomeroy, J. W. (2004). Implications of spatial distributions of snow mass and melt rate for snow-cover depletion: theoretical considerations. Annals of Glaciology, 38(1), 261–265. doi:10.3189/172756404781815275Granger, R. J. (1977). Energy exchange during melt of a prairie snowcover. University of Saskatchewan.

Granger, R. J., & Gray, D. M. (1990). A net radiation model for calculating daily snowmelt in open environment. In Paper presented in 8th Northern Res. Basins Symposium (Vol. 21, pp. 217–234). Abisko, Sweden: Nordic Hydrology.

Granger, R. J., Gray, D. M., & Dyck, G. E. (1984). Snowmelt infiltration to frozen Prairie soils. Canadian Journal of Earth Sciences, 21(6), 669–677. doi:10.1139/e84-073

Gray, D. M., & Landine, P. G. (1987). Albedo model for shallow prairie snow covers. Canadian Journal of Earth Sciences, 24(9), 1760–1768. doi:10.1139/e87-168

Gray, D. M., & Landine, P. G. (1988). An energy-budget snowmelt model for the Canadian Prairies. Canadian Journal of Earth Sciences, 25(8), 1292–1303. doi:10.1139/e88-124

Gray, D. M., Landine, P. G., & Granger, R. J. (1985). Simulating infiltration into frozen Prairie soils in streamflow models. Canadian Journal of Earth Sciences, 22 (3), 464–474.

Gray, D. M., Pomeroy, J. W., & Granger, R. J. (1986a). Prairie snowmelt runoff. In Conference Commemorating the Official Opening of the National Hydrology Research Centre (pp. 49–68). Saskatoon.

Gray, D. M., Pomeroy, J. W., & Landine, P. G. (1986b). Development and performance evaluation of energy balance snowmelt models. Edmonton, Alberta.

Male, D. H., & Granger, R. J. (1981). Snow surface energy exchange. Water Resources Research, 17(3), 609–627. doi:10.1029/WR017i003p00609

Male, D. H., & Gray, D. . (1981). Snowcover ablation and runoff. In D. M. Gray & D. H. Male (Eds.), Handbook of Snow: principles, processes, management & use (pp. 360–436). Ontario: Pergamon Press Canada Ltd.

McKay, G. A. (1970). Precipitation. In D. M. Gray (Ed.), Handbook on the principles of hydrology. Port Washington, NY: Water Information Center, INC.

Pomeroy, J. W., & Brun, E. (2001). Physical properties of snow. In H. G. Jones, J. W. Pomeroy, D. A. Walker, & R. W. Hoham (Eds.), Snow Ecology: an Interdisciplinary Examination of Snow-covered Ecosystems (pp. 45–118). Cambridge, UK: Cambridge University Press.

Pomeroy, J. W., Fang, X., & Ellis, C. (2012). Sensitivity of snowmelt hydrology in Marmot Creek, Alberta, to forest cover disturbance. Hydrological Processes, 26(12), 1891–1904. doi:10.1002/hyp.9248

Pomeroy, J. W., Gray, D. M., Brown, T., Hedstrom, N. R., Quinton, W. L., Granger, R. J., & Carey, S. K. (2007). The cold regions hydrological model: A platform for basing process representation and model structure on physical evidence. In Hydrological Processes (Vol. 21, pp. 2650–2667). doi:10.1002/hyp.6787

Pomeroy, J. W., Gray, D. M., Shook, K. R., Toth, B., Essery, R. L. H., Pietroniro, A., & Hedstrom, N. (1998). An evaluation of snow accumulation and ablation processes for land surface modelling. Hydrological Processes, 12(15), 2339–2367. doi:10.1002/(SICI)1099-1085(199812)12:15<2339::aid-hyp800>3.0.CO;2-L

Pomeroy, J. W., Shook, K., & Fang, X. (2014). Improving and Testing the Prairie Hydrological Model at Smith Creek Research Basin. Saskatoon, SK.

Pomeroy, J. W., Shook, K., Fang, X., & Brown, T. (2013). Predicting spatial patterns of inter-annual runoff variability in the Canadian Prairies. In G. Blöschl, M. Sivapalan, T. Wagener, A. Viglione, & H. Savenije (Eds.), Runoff Prediction in Ungauged Basins. Synthesis across Processes, Places and Scales (pp. 283–289). Cambridge, UK: Cambridge University Press.

Shaw, D. A., Vanderkamp, G., Conly, F. M., Pietroniro, A., & Martz, L. W. (2012). The Fill-Spill Hydrology of Prairie Wetland Complexes during Drought and Deluge. Hydrological Processes, 26(20), 3147–3156. doi:10.1002/hyp.8390

Shook, K., & Pomeroy, J. W. (2011). Synthesis of incoming shortwave radiation for hydrological simulation. Hydrology Research, 42(6), 433–446.

Shook, K., Pomeroy, J. W., Spence, C., & Boychuk, L. (2013). Storage dynamics simulations in prairie wetland hydrology models: Evaluation and parameterization. Hydrological Processes, 27, 1875–1889. doi:10.1002/hyp.9867

Sicart, J. E., Pomeroy, J. W., Essery, R. L. H., & Bewley, D. (2006). Incoming longwave radiation to melting snow: observations, sensitivity and estimation in Northern environments. Hydrological Processes, 20(17), 3697–3708. doi:10.1002/hyp.6383