D. M. Gray

An evaluation of snow accumulation and ablation processes for land surface modelling

This paper discusses the development and testing of snow algorithms with specific reference to their use and application in land surface models. New algorithms, developed by the authors, for estimating snow interception in forest canopies, blowing snow transport and sublimation, snow cover depletion and open environment snowmelt are compared with field measurements. Existing algorithms are discussed and compared with field observations. Recommendations are made with respect to: (a) density of new and aged snow in open and forest environments; (b) interception of snow by evergreen canopies; (c) redistribution and sublimation of snow water equivalent by blowing snow; (d) depletion in snow-covered area during snowmelt; (e) albedo decay during snowmelt; (f) turbulent transfer during snowmelt; and (g) soil heat flux during meltwater infiltration into frozen soils. Preliminary evidence is presented, suggesting that one relatively advanced land surface model, CLASS, significantly underestimates the timing of snowmelt and snowmelt rates in open environments despite overestimating radiation and turbulent contributions to melt. The cause(s) may be due to overestimation of ground heat loss and other factors. It is recommended that further studies of snow energetics and soil heat transfer in frozen soils be undertaken to provide improvements for land surface models such as CLASS, with particular attention paid to establishing the reliability of the models in invoking closure of the energy equation. #1998 John Wiley & Sons, Ltd.

The Prairie Blowing Snow Model: characteristics, validation, operation

Abstract Physically based algorithms that estimate saltation, suspension and sublimation rates of blowing snow using readily available meteorological and land use data are presented. These algorithms are assembled into a model, the Prairie Blowing Snow Model (PBSM), and used to describe snow transport on fields in a Canadian Prairie environment. Validation tests of PBSM using hourly meteorological data indicate differences between modelled and measured seasonal snow accumulations between 4 and 13%. Application of the blowing snow model using meteorological records from the Canadian prairies shows that the annual proportion of snow transported above any specific height increases notably with mean seasonal wind speed. An observed decrease in annual blowing snow transport and sublimation quantities with increasing surface roughness height becomes more apparent with higher seasonal wind speeds and temperatures. The annual quantity of snow transported off a fetch increases with fetch length up to lengths of between 300 and 1000 m, then remains relatively constant or slowly declines. Within the first 300 m of fetch 38–85% of annual snowfall is removed by snow transport, the amount increasing with wind speed. Beyond 1000 m of fetch, blowing snow sublimation losses dominate over transport losses. In Saskatchewan, sublimation losses range from 44 to 74% of annual snowfall over a 4000 m fetch, depending on winter climate. Notably, as a result of steady-state transport, the sum of snowcover loss due to blowing snow transport and sublimation does not change appreciably from its 1000 m fetch value for fetches 500 to 4000 m. The transition from primarily transport to primarily sublimation losses at the 1000 m fetch distance may be useful in assessing the effect of scale in snow hydrology.

Evaporation from natural nonsaturated surfaces

Abstract Following a development similar to that used by Penman (1948) a general combination equation is derived to describe evaporation from nonsaturated surfaces. To account for departure from saturated conditions, the equation makes use of the concept of relative evaporation, the ratio of the actual to the potential evaporation, defined here as the evaporation rate which would occur under the existing atmospheric conditions if the surface were saturated at the actual surface temperature. A relationship is established between the relative evaporation and a dimensionless parameter called the relative drying power, the ratio of the drying power to the sum of the drying power and the net available energy (net radiation plus soil heat flux). The relationship is nondimensional and appears to be single-valued. The combination of this relationship with the general evaporation equation derived constitutes a simple model for obtaining estimates of evaporation from nonsaturated surfaces; no prior estimate of the potential evaporation is required, and the surface conditions of temperature and humidity need not be known.

APPLICATION OF A DISTRIBUTED BLOWING SNOW MODEL TO THE ARCTIC

Transportation, sublimation and accumulation of snow dominate snow cover development in the Arctic and produce episodic high evaporative fluxes. Unfortunately, blowing snow processes are not presently incorporated in any hydrological or meteorological models. To demonstrate the application of simple algorithms that represent blowing snow processes, monthly snow accumulation, relocation and sublimation fluxes were calculated and applied in a spatially distributed manner to a 68-km 2 catchment in the low Arctic of north-western Canada. The model uses a Landsat-derived vegetation classification and a digital elevation model to segregate the basin into snow ‘sources’ and ‘sinks’. The model then relocates snow from sources to sinks and calculates in-transit sublimation loss. The resulting annual snow accumulation in specific landscape types was compared with the result of intensive surveys of snow depth and density. On an annual basis, 28% of annual snowfall sublimated from tundra surfaces whilst 18% was transported to sink areas. Annual blowing snow transport to sink areas amounted to an additional 16% of annual snowfall to shrub‐tundra and an additional 182% to drifts. For the catchment, 19.5% of annual snowfall sublimated from blowing snow, 5.8% was transported into the catchment and 86.5% accumulated on the ground. The model overestimated snow accumulation in the catchment by 6%. The application demonstrates that winter precipitation alone is insuAcient to calculate snow accumulation and that blowing snow processes and landscape patterns govern the spatial distribution and total accumulation of snow water equivalent over the winter. These processes can be modelled by relatively simple algorithms, and, when distributed by landscape type over the catchment, produce reasonable estimates of snow accumulation and loss in wind-swept regions. #1997 John Wiley & Sons, Ltd.

Subsurface drainage from hummock-covered hillslopes in the Arctic tundra.

In the Arctic tundra, subsurface drainage occurs predominantly through the saturated zone within the layer of peat that mantles the hillslopes. In plan view, the peat cover is fragmented into a network of channels due to the presence of mineral earth hummocks. In cross section, the physical and hydraulic properties of the peat vary with depth and the water transmission characteristics (e.g. hydraulic conductivity) of the upper profile differ distinctly from those of the lower. Water flow through the peat is laminar, therefore the friction factor ( f ) and the Reynolds number (NR) are inversely related. Average values for the coefficientC of the relation f a C=NR; vary from ,300 near the surface to ,14,500 at depth. This large difference in C confirms that the larger-diameter soil pores of the living vegetation and lightly decomposed peat near the surface offer much less resistance to water motion than the finer-grained peat deeper in the profile. Also, the variability suggests that subsurface drainage is strongly affected by the position and thickness of the saturated zone within the peat matrix. A first approximation for a model or simulation of the flow regime may consider a peat profile with depth-varying, resistance properties in respect to subsurface flow. q 2000 Elsevier Science B.V. All rights reserved.

Estimating snowmelt infiltration into frozen soils

A general parametric correlation for estimating snowmelt infiltration into frozen soils is developed using the results from a numerical model, HAWTS. This model includes a set of partial differential equations that describe water and heat transport with phase changes in frozen soils. The model was run for soils with average textures ranging from sandy loam to clay. The relationship proposed relates infiltration to the total soil moisture saturation (water+ice) and temperature at the start of snow ablation, the soil surface saturation during melting, and the infiltration opportunity time—the time that meltwater is available at the soil surface for infiltration. The expression is calibrated to predict snowmelt infiltration in boreal forest and prairie environments. Comparisons of estimates of infiltration by the empirical relationship with those determined by field measurement suggest that the correlation will provide acceptable estimates of snowmelt infiltration into frozen mineral soils for use in operational hydrology schemes. Copyright

Synthesizing shallow seasonal snow covers

A method of synthesizing a snowfield from point field measurements, which is based on the fractal structure of the water equivalent, is presented. Two steps are involved in the synthesis. First, the method of fractal sum of pulses is used to generate the spatial distribution of the snow water equivalent in an array. Second, the synthetic snowfield is adjusted to take on the statistical properties of the natural snow cover. The two-parameter lognormal probability density function fitted to field data is used for this purpose. Examples of the application of the lognormal distribution for describing the water equivalent of snow covers on various landscapes encountered in a prairie environment are presented. The geometrical properties (fractal dimension(s)) of snow patches that result from melting a synthetic snow cover agree closely with those of patches of an ablated natural snow cover.

A parametric expression for estimating infiltration into frozen soils

This paper uses a numerical simulation to develop an expression for predicting infiltration of water into a frozen soil. The simulation is based on the continuity, energy and momentum equations, and uses well-known and accepted procedures to define the transport phenomena and the thermophysical properties of frozen soil. A parametric equation describing the variation in cumulative infiltration with time during quasi-steady-state flow in medium- and fine-textured soils is presented. The expression relates infiltration to initial soil saturation, soil surface saturation, soil hydraulic conductivity, initial soil temperature and infiltration opportunity time. Infiltration estimates by the expression demonstrate reasonable agreement with those determined by field measurement.

Snowmelt resulting from advection

Snowmelt can be estimated by applying an energy balance to a control volume of snow. A major problem with this method is the difficulty of obtaining accurate estimates of the turbulent transfers of sensible and latent heat. This paper uses a modified form of the Penman-Monteith equation, a combined aerodynamic-energy balance approach for calculating evaporation from vegetative surfaces, to estimate the energy available for snowmelt during large-scale advection. The modification requires knowledge of k, the ratio of the energy used for melting to the net energy available for phase changes (vaporization and melting). Comparisons between the melt flux determined by the Penman-Monteith equation and estimates derived from field measurements suggest a value of k in the range of 0.90-0.99. The modified Penman-Monteith equation is used in a detailed simulation of melting of a shallow prairie snow cover. This simulation incorporates the effects of a small-scale advection of energy from bare ground to adjacent patches. It is demonstrated that the contributions by large- and small-scale advective energy transfers to melt depend on the interactions between snow-covered area and meteorological variables.

Examination of Morton's CRAE model for estimating daily evaporation from field-sized areas.

Abstract Mortons complementary relationship areal evapotranspiration (CRAE) model was originally designed to provide regional estimates of monthly evapotranspiration. Often, however, hydrologists and others require estimates of evapotranspiration for field-sized land units under a specific land use, for shorter intervals of time. This paper examines CRAE with respect to the algorithms used to describe different terms and its applicability to reduced spatial and temporal scales. Daily estimates by CRAE of atmospheric radiation fluxes during the summer months are compared with monitored values. It is shown that errors in estimation of the extra-terrestrial flux, the transmittancy of clouds to short-wave radiation, the surface albedo and the net long-wave flux result in standard deviations of the difference between ‘modelled’ and ‘measured’ net all-wave radiation for 1-, 5- and 10-day periods of 2.58, 1.8 and 1.50 MJm −2 day −1 respectively. The assumption in CRAE that the vapour transfer coefficient is independent of wind speed may lead to appreciable error in computing evapotranspiration. A procedure for incorporating a wind correction factor is described and the improvement in estimating regional evaporation is illustrated. Comparisons of evapotranspiration estimates by CRAE and measurements obtained from soil moisture and precipitation observations in the semi-arid, cold-climate Prairie region of western Canada demonstrate that the assumptions that the soil heat flux and storage terms are negligible, lead to large overestimation by the model during periods of soil thaw.