Modeling the Snow Depth Variability With a High‐Resolution Lidar Data Set and Nonlinear Terrain Dependency

Abstract

In the mountains of Norway, snow depth (SD) is highly variable due to strong winds and open terrain. To investigate snow conditions on one of Europe's largest mountain plateaus, Hardangervidda, we conducted snow measurement campaigns in spring 2008 and 2009 using airborne lidar scanning at the approximate time of annual snow maximum (mid‐April). From 658 empirical distributions of SD at Hardangervidda, each comprised about 4,000 SD values sampled from a grid cell of 0.5 km2, quantitative tests have shown that the gamma distribution is a better fit for SD than the normal and log‐normal distributions. When aggregating snow and terrain data from 10 × 10 m to 0.5 km2, we find that the standard deviation of the terrain parameter squared slope, land cover, and the mean SD are highly correlated (0.7, 0.52, and 0.89) to the standard deviation of SD. A model for SD variance is proposed that, in addition to addressing the dependencies between the variability of SD and the terrain characteristics, also takes into account the observed nonlinear relationship between the mean and the standard deviation of SD. When validated against observed SD variance retrieved from the same area, the model explains 81–83% of the observed variance for spatial scales of 0.5 and 5.1 km2, which compares favorably to previous models. The model parameters can be determined from a GIS analysis of a detailed digital terrain and land cover model and will hence not increase the number of calibration parameters when implemented in environmental models.

Spatial Distribution and Scaling Properties of Lidar‐Derived Snow Depth in the Extratropical Andes

“… Finally, we compare the goodness of fit of three commonly used PDFs following Helbig et al (2015) and Skaugen and Melvold (2019): normal, lognormal, and the two‐parameter gamma functions (Equation ). In this way, we assess the entire domain and each elevation band using the Anderson‐Darling test (Delignette‐Muller & Dutang, 2015), which equally assesses the main body of the distribution and the tails.…”

“…Finally, we compare the goodness of fit of three commonly used PDFs following Helbig et al (2015) and Skaugen and Melvold (2019): normal, lognormal, and the two-parameter gamma functions (Equation 1).…”

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

“…Parametric SCD curves have disadvantages for practical applications such as numerical stability, computational efficiency and assuming an unimodal distribution which might be less appropriate for large grid cells covering heterogeneous surface such as mountainous terrain (e.g., Essery and Pomeroy, 2004;Swenson and Lawrence, 2012). Various closed functional forms for fSCAs are therefore applied in land surface and climate models (e.g., Douville et al, 1995;Roesch et al, 2001;Yang et al, 1997;Niu and Yang, 2007;Su et al, 2008;Swenson and Lawrence, 2012). Most of these parameterizations use simple relationships between fSCA and spatial mean HS or SWE.…”

“…Since recently, digital photogrammetry can also be applied to high-resolution optical satellite imagery (Marti et al, 2016;Deschamps-Berger et al, 2020;Eberhard et al, 2021;Shaw et al, 2020). Snow depth data at these high resolutions now enable statistical analyses of spatial snow depth patterns for various purposes (e.g., Melvold and Skaugen, 2013;Grünewald et al, 2013;Kirchner et al, 2014;Grünewald et al, 2014;Revuelto et al, 2014;Helbig et al, 2015;Voegeli et al, 2016;López-Moreno et al, 2017;Helbig and van Herwijnen, 2017;Skaugen and Melvold, 2019). Based on spatial snow depth data sets, σ HS could be related to terrain parameters.…”

“…Based on spatial snow depth data sets, σ HS could be related to terrain parameters. For instance, Helbig et al (2015) parameterized σ HS at the peak of winter using spatial mean HS and subgrid terrain parameters, namely a squared-slope-related parameter and terrain correlation length, and Skaugen and Melvold (2019) parameterized σ HS for the accumulation season using current spatial mean HS and stratifications according to landscape classes and standard deviations in squared slope. Though both approaches are promising and also somehow similar, e.g., both use the squared slope as a significant scale variable, they also differ, e.g., in the considered horizontal scale lengths at the development of the parameterization.…”