Distribution of snow depth variability

doi:10.1007/s11707-018-0714-z

Front. Earth Sci.

2018, Vol. 12

Issue (4) : 683-692 https://doi.org/10.1007/s11707-018-0714-z

RESEARCH ARTICLE

Distribution of snow depth variability

S.R. FASSNACHT^1,^2,^3,⁴(

), K.S.J. BROWN¹, E.J. BLUMBERG⁵, J.I. LÓPEZ MORENO⁶, T.P. COVINO^1,³, M. KAPPAS⁴, Y. HUANG⁷, V. LEONE⁸, A.H. KASHIPAZHA¹

¹. ESS-Watershed Science, Colorado State University, Fort Collins, CO 80523-1476, USA
². Cooperative Institute for Research in the Atmosphere, Fort Collins, CO 80523-1375, USA
³. Natural Resources Ecology Laboratory, Fort Collins, CO 80523-1499, USA
⁴. Geographisches Institut, Georg-August-Universität Göttingen, 37077 Göttingen, Deutschland
⁵. Geosciences, Colorado State University, Fort Collins, CO 80523-1482, USA
⁶. Instituto Pirenaico de Ecología, CSIC, Campus de Aula Dei, 50080 Zaragoza, España
⁷. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
⁸. Seconda Università degli Studi di Napoli, Viale Abramo Lincoln, 5, 81100 Caserta CE, Italia

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Abstract

Snow depth is the easiest snowpack property to measure in the field and is used to estimate the distribution of snow for quantifying snow storage. Often the mean of three snow depth measurements is used to represent snow depth at a location. This location is used as a proxy for an area, typically a digital elevation model (DEM) or remotely sensed pixel. Here, 11, 17, or 21 snow depth measurements were used to represent the mean snow depth of a 30-m DEM pixel. Using the center snow depth measurement for each sampling set was not adequate to represent the pixel mean, and while the use of three snow depth measurements improved the estimate of mean, there is still large error for some pixels. These measurements were then used to determine the variability of snow depth across a pixel. Estimating variability from few points rather than all in a measurement was not sufficient. The sampling size was increased from one to the total per pixel (11, 17, or 21) to determine how many point samples were necessary to approximate the mean snow depth per pixel within five percent. Binary regression trees were constructed to determine which terrain and canopy variables dictated the spatial distribution of the snow depth, the standard deviation of snow depth, and the sample size to within 5% of the mean per pixel. One location was measured in two years just prior to peak accumulation, and it is shown that there was little to no inter-annual consistency in the mean or standard deviation.

Keywords uncertainty sampling binary regression trees snow telemetry

Corresponding Author(s): S.R. FASSNACHT

Just Accepted Date: 14 May 2018 Online First Date: 21 June 2018 Issue Date: 20 November 2018

Cite this article:

S.R. FASSNACHT,K.S.J. BROWN,E.J. BLUMBERG, et al. Distribution of snow depth variability[J]. Front. Earth Sci., 2018, 12(4): 683-692.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-018-0714-z
https://academic.hep.com.cn/fesci/EN/Y2018/V12/I4/683

Fig.1 (a) Location map for the i. Togwotee Pass and ii. Joe Wright SNOTEL stations in Wyoming and Colorado, respectively. (b) Canopy density in percent for the area surveyed: i. Togwotee Pass was surveyed in 2009, and ii. Joe Wright was surveyed in 2009 (red symbols) and iii. 2010 (black symbols). (c) The snow depth sampling design at each sampling plot is i) 21 points for Togwotee Pass (2009), ii. 11 points for Joe Wright 2009, and iii. 17 points for Joe Wright 2010.

Fig.2 Comparison of (a) mean and (b) standard deviation comparison between 3 point statistics (grey diamonds) and plot statistics for three snow depth surveys about SNOTEL stations: i. Togwotee Pass in March 2009, ii. Joe Wright in May 2009, and iii. Joe Wright in May 2010. The center or 1 point snow depth is also compared to the pixel mean (open box). The maximum number of points per station-date are in parentheses.

Fig.3 Mean absolute difference from the pixel mean snow depth for all samples per pixel as a function of the number of points per pixel for the three sampling dates. The number in the (a) parentheses is the number of samples per pixel, while (b) is for only the 11 points in a row (as per Figure 1cii). The 5% difference threshold is shown as the dotted line.

Tab.1 Statistics mean summarizing the comparison of fewer sampling points (1, 3, or 5) to all sampling points (11, 17, or 21)

Tab.2 Statistics standard deviation summarizing the comparison of fewer sampling points (1, 3, or 5) to all sampling points (11, 17, or 21)

Fig.4 Joe Wright SNOTEL inter-annual (May 2009 and 2010) comparison of (a) mean snow depth, and (b) standard deviation for data at the 99 pixels within the same pixel (grey diamonds) and 70 sets of pixels that were within one pixel. A pixel is derived from the 30-meter U.S. Geological Survey (2018) digital elevation model<nationalmap.usgs.gov>. The Nash-Sutcliffe coefficient of efficiency statistic is not included as it is less than zero in all cases.

Fig.5 Togwotee Pass 2009 binary regression trees for depth to 5% of the mean per pixel. Boxes represent decision nodes with the true being the node to the left below. The value below the variable represents the mean value of all pixels remaining. Circles represent terminal nodes with the mean of the number of points to within 5% of snow depth, for the number of points (n) in that category.

Tab.3 Summary of the order of appearance in the binary regression tree for the (a) points to within 5% of the pixel mean from top (1) to last node (e.g., Fig. 2), (b) mean, and (c) standard deviation, and. The same number in the order list identifies that variable occurring more than once in the particular level. The fit statistic is the relative?standard errors using a minimum leaf size of 5% of total number of samples

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