Sub-grid parameterization of snow distribution for an energy and mass balance snow cover model

Abstract

Representation of sub-element scale variability in snow accumulation and ablation is increasingly recognized as important in distributed hydrologic modelling. Representing sub-grid scale variability may be accomplished through numerical integration of a nested grid or through a lumped modelling approach. We present a physically based model of the lumped snowpack mass and energy balance applied to a 26-ha rangeland catchment with high spatial variability in snow accumulation and melt. Model state variables are snow-covered area average snow energy content (U), the basin-average snow water equivalence (W a), and snow-covered area fraction (A f). The energy state variable is evolved through an energy balance. The snow water equivalence state variable is evolved through a mass balance, and the area state variable is updated according to an empirically derived relationship, A f W a †, that is similar in nature to depletion curves used in existing empirical basin snowmelt models. As snow accumulates, the snow covered area increases rapidly. As the snowpack ablates, A f decreases as W a decreases. This paper shows how the relationship A f W a † for the melt season can be estimated from the distribution of snow water equivalence at peak accumulation in the area being modelled. We show that the depletion curve estimated from the snow distribution of peak accumulation at the Upper Sheep Creek sub-basin of Reynolds Creek Experimental Watershed compares well against the observed depletion data as well as modelled depletion data from an explicit spatially distributed energy balance model. Comparisons of basin average snow water equivalence between the lumped model and spatially distributed model show good agreement. Comparisons to observed snow water equivalence show poorer but still reasonable agreement. The sub-grid parameterization is easily portable to other physically based point snowmelt models. It has potential application for use in hydrologic and climate models covering large areas with large model elements, where a computationally inexpensive parameterization of sub-grid snow processes may be important.

Introducing Hysteresis in Snow Depletion Curves to Improve the Water Budget of a Land Surface Model in an Alpine Catchment

“…Indeed, we demonstrated that the SCF increases faster than it decreases. The use of snow-depth measurements allowed us to confirm that the difference between SCF accumulation and ablation rates is due to the existence of a hysteresis in the SCD at the catchment scale, as Swenson and Lawrence (2012) and Luce et al (1999) highlighted in other environments. We then applied the CLSM in the upper Durance watershed.…”

“…The mean accumulation rate is 1.7 higher than the mean ablation rate, which means that the SCF increases faster than it decreases. This difference of variation rate strongly suggests the existence of a hysteresis in the SCD, as described by Luce et al (1999). Figure 3 shows, using snow-depth measurements, a hysteresis in the SCD of catchment 3.…”

“…At a small scale (26 ha), Luce and Tarboton (2004) highlighted the existence of a hysteresis in the SCD with different dynamics between accumulation and ablation periods. During accumulation, the snow-cover extent quickly reaches full coverage, after which the snowpack increases homogeneously in depth.…”

Independent evaluation of the SNODAS snow depth product using regional-scale lidar-derived measurements

“…Nevertheless, sub-grid spatial properties have been shown to have a significant effect on the accuracy of spatially distributed snow models (Luce et al, 1999;Liston, 2004;Skaugen and Randen, 2013), but the data sets required for parameter estimation and optimization are small and spatially sparse in high-elevation, tundra and shrubland environments (Elder et al, 1991;Sturm et al, 2001a, b;Hiemstra et al, 2002;Liston and Sturm, 2002;. Considerable variability in the spatial snow distribution can be introduced through the interaction between wind and snow with terrain and vegetation (Elder et al, 1991;Blöschl, 1999;Liston et al, 2007).…”

Advances in the use of observed spatial patterns of catchment hydrological response

“…Also, the general interest in spatial patterns, and availability of rapid position fixing via GPS, has made it more common to collect patterns of even ''traditional'' data such as snow depth or snow density. For example, the 26 ha upper sheep creek in the Reynolds creek watershed has snow depth patterns measured over several seasons [71,72] and Yang and Woo [122] and Young et al [123] collected patterns of snow-related variables in the Canadian Arctic. Along similar lines, McDonnell et al [73] measured a detailed pattern of soil depth to bedrock in the 41 ha Panola catchment for use as input data to a terrain-based model of water movement.…”