Fractional snow-covered area: scale-independent peak of winter parameterization

Nora Helbig,Marie Dumont,César Deschamps-Berger,Simon Gascoin,Yves Bühler,Jeff S Deems,Lucie Eberhard,Tobias Jonas,Jesus Revuelto

doi:10.5194/tc-15-615-2021

Abstract

Abstract. The spatial distribution of snow in the mountains is significantly influenced through interactions of topography with wind, precipitation, shortwave and longwave radiation, and avalanches that may relocate the accumulated snow. One of the most crucial model parameters for various applications such as weather forecasts, climate predictions and hydrological modeling is the fraction of the ground surface that is covered by snow, also called fractional snow-covered area (fSCA). While previous subgrid parameterizations for the spatial snow depth distribution and fSCA work well, performances were scale-dependent. Here, we were able to confirm a previously established empirical relationship of peak of winter parameterization for the standard deviation of snow depth σHS by evaluating it with 11 spatial snow depth data sets from 7 different geographic regions and snow climates with resolutions ranging from 0.1 to 3 m. An enhanced performance (mean percentage errors, MPE, decreased by 25 %) across all spatial scales ≥ 200 m was achieved by recalibrating and introducing a scale-dependency in the dominant scaling variables. Scale-dependent MPEs vary between −7 % and 3 % for σHS and between 0 % and 1 % for fSCA. We performed a scale- and region-dependent evaluation of the parameterizations to assess the potential performances with independent data sets. This evaluation revealed that for the majority of the regions, the MPEs mostly lie between ±10 % for σHS and between −1 % and 1.5 % for fSCA. This suggests that the new parameterizations perform similarly well in most geographical regions.

Highlights

Whenever there is snow on the ground, there will be large spatial variability in snow depth
(2) Based on a spatial scale analysis, we introduced scale-dependent parameters in peak of winter parameterization of Helbig et al (2015) for σHS such that the new fractional snow-covered area (fSCA) parameterization can be reliably applied for grid cell sizes starting at 200 m and increasing to 5 km
We evaluate the performances by deriving the twosample Kolmogorov–Smirnov test (K-S test) statistic values D (Yakir, 2013) for the pdfs and by computing the normalized root mean square error (NRMSE) for quantile–quantile plots (NRMSEquant; normalized by the range of measured quantiles, max-min) for probabilities with values in the range of [0.1, 0.9]

Summary

Introduction

Whenever there is snow on the ground, there will be large spatial variability in snow depth. In mountainous terrain, this spatial distribution of snow is significantly influenced by topography due to corresponding spatial variations in wind, precipitation, and shortwave and longwave radiation and in steep terrain due to avalanches that may relocate the accumulated snow. A parameter which describes how much of the ground is covered by snow is the fractional snow-covered area (fSCA). FSCA is tightly linked to snow depth (HS) and in particular to its spatial distribution. A fSCA is able to bridge the spatial mean HS and the actual observed snow coverage. Sound fSCA models are crucial since for the same spatial mean HS in early winter and in late spring, the associated fSCA can be completely different (e.g., Luce et al, 1999; Niu and Yang, 2007; Magand et al, 2014)

Methods

Results

Discussion

Conclusion