We designed our aerial surveys to achieve horizontal spatial resolutions of <0.05 m to observe centimeter-scale differences in snow depths throughout the entire study site (De Michele et al., 2016; Fierz et al., 2009). We used a commercially available DJI Phantom 4 UAS equipped with a 20-megapixel camera and a real-time kinematic (RTK) global navigation satellite system (GNSS) with the DJI DRTK2 GNSS mobile station. We conducted repeated autonomous pre-programmed UAS missions flying in a grid pattern at a constant 50 m above ground level based on a 1 m resolution DSM collected prior to winter flights. Our flight imagery was collected with 70 % front/side image overlap, resulting in <2 cm per pixel average ground sampling distance and approximately 550 overlapping images each field day, similar to Goetz and Brenning (2019). A data gap exists between 17 March 2020 and 14 May 2020, due to the onset of the COVID-19 pandemic.

To constrain topographic error in postprocessing, we collected 25 stationary and easily recognizable ground control points with high-resolution RTK GNSS survey equipment during the snow-free season to incorporate into the digital surface models. Due to variable snow cover, we used a partial selection of the 25 ground control points, typically 3–10 points, in each individual model by selecting points that were not covered by snow. To constrain snow depth observation error, each field day we deployed and surveyed at least four snow depth validation point targets prior to flights in safe, accessible locations within the study area and manually measured snow depths at each point immediately after the flights (described further in Sect. 3.3).

For each field date, we processed the overlapping imagery to derive snow depth maps using three steps: postprocessing kinematic (PPK) location corrections, SfM processing of imagery for DSM creation, and DSM differencing to derive snow depth.

We postprocessed the UAS location data to improve the quality of the RTK GNSS positions and ensure accurate coregistration of output models using RTKLIB (Takasu, 2009) and the R software environment (R Core Team, 2021) in the WGS84 geographic coordinate system (EPSG:4326). Using the National Geodetic Survey CORS MTSU reference station (∼21 km from the study site), the National Aeronautics and Space Administration's daily global positioning systems broadcast ephemeris data, and the UAS RINEX and timestamp files, our PPK processing resulted in horizontal positional accuracies of less than 0.1 m and vertical positional accuracies of less than 0.2 m for most UAS photo locations (Table A1). This additional step was necessary due to limited satellite connectivity of the RTK system from the poor sky view of high-relief topography at our study site.

We completed SfM photogrammetric processing using the software package Agisoft Metashape Pro Version 1.6.6 (Agisoft, 2020), which generates 3-D surface models from overlapping imagery and point matching (Alidoost and Arefi, 2017; Carbonneau and Dietrich, 2017; Gabrlik et al., 2018; Nolan et al., 2015). We filtered, aligned, and reduced the error of the geolocated imagery before the addition of ground control points for final batch processing. Finally, we ensured accurate coregistration by aligning the vertical and horizontal positions of the snow-covered models to available snow-free ground control points and the snow-free 8 July 2020 model (Adams et al., 2018). Utilizing fewer ground control points and UASs equipped with RTK provides similar accuracies as traditional ground-control point-driven SfM workflows (Eberhard et al., 2021; Revuelto et al., 2021). This processing workflow produced a DSM interpolated from a dense point cloud and an orthomosaic for further analysis. We used simple DSM-differencing techniques to calculate snow depths throughout our site by subtracting a snow-free DSM collected on 8 July 2020 from each snow-covered DSM, resulting in snow depth DSMs used for further spatial-variability analysis. We removed poor-quality DSMs if deemed unacceptable through comparison with probed snow depths, visual inspection, and expert judgment (Table A2). Examples of these thresholds include observed limited point matching while processing, inaccurate DSM reconstruction surfaces, unrealistic snow depths, and unrealistic snow depth distributions. Unrealistic snow depths are negative snow depth values and values filtered by expert judgment.

We collected traditional manual snow depth measurements through in situ probing primarily within the lower elevations of the research area. These geolocated validation point snow depths were used for error assessment of UAS-derived snow depths. We collected manual snow depth measurements at four or more random locations within avalanche-safe areas of the study site at deployed 1 m2 markers on each field day. To determine the 1 m2 average, variation, and range at validation points, we probed manual in situ snow depths at the center and four corners of each deployed marker (López-Moreno et al., 2011). We used the 1 m2 averages as our individual validation point measurements. We collected location information for each of these manual snow depth measurements with handheld GPS units (3–5 m accuracy). Additionally, we manually collected a single in situ avalanche crown profile in the upper elevations of the couloir on 28 February 2020, which included total snow depth, 25 individual snow layer thicknesses, grain type and size measurements, and an extended column test (ECT) as per Greene et al. (2016). We calculated summary statistics for manual snow depth measurements and their UAS-derived equivalent depths for each field day (Table A3).

We completed an assessment of error by calculating mean, standard deviation, root mean square error (RMSE) (Eq. 1), and normalized median absolute deviation (NMAD) (Eq. 2) values for the differences between UAS-derived and probed snow depths for both the complete set of snow depth DSMs and a subset with poor-quality models of the meadow removed. RMSE is defined as 1RMSE=1n∑i=1nPi-Oi2, where n is the number of observations, P is the predicted value, and O is the observed value. NMAD is represented by 2NMAD=1.4826×medianxi-xmedian, where 1.4826 is the scale factor for comparison with standard deviation, xi is the difference in measured snow depths for point i, and xmedian is the median of the dataset of differences.

Our error assessment followed a condensed version of the accuracy and precision measures presented in Adams et al. (2018) and Eberhard et al. (2021). The mean difference and RMSE are common measures of accuracy. Standard deviation and NMAD are common measures of precision, with NMAD being more resistant to outliers. We extracted the 1 m2 median and inner quartile range (IQR) values from the corresponding snow depth DSM for each manually collected snow depth measurement location and used the median value for error assessment.

In preparation for variability analysis, we detrended each snow depth DSM with regular grids to focus analysis on the resultant residual surfaces as per Lutz and Birkeland (2011). Detrending allowed us to calculate omnidirectional variograms. First, we masked individual vegetation features, such as trees, out of all DSMs while attempting to retain some snow surface between features. We used QGIS version 3.20.1 (QGIS.org, 2021) and the SAGA-GIS plugin's DTM filter tool (Vosselman, 2000) to filter out localized vertical spikes in elevation in the snow-free 8 July 2020 DSM and applied a 0.1 m buffer along the masked feature boundaries to account for minor vegetation shifts due to wind or snow creep (Table A3). We checked this mask against high-resolution orthoimagery produced in the SfM workflow to ensure accuracy and applied this mask to each DSM included in our analysis.

We created detrended surfaces for each DSM using elevation, aspect, and distance from ridge as independent variables potentially contributing to snow depth trends. We extracted elevation, aspect, and distance-from-ridge raw surfaces from the snow-free 8 July 2020 DSM. Then, we calculated trend surfaces by selecting the most significant (lowest p value) independent variable resulting from a least squares linear regression for snow depth and each independent variable for each individual DSM. We subtracted the resultant trend surface from the raw snow depth DSM to produce detrended residual DSMs for each field day. If no independent variables proved significant (p>0.05), we detrended the DSMs by subtracting the mean snow depth from the raw snow depth DSM instead. A final correction using a 3 standard deviation filter and expert judgment removed erroneous outlier data from the detrended residual snow depth DSMs (Höhle and Höhle, 2009).

To examine the spatial relationships of snow depth distributions in our two study sites, we used variogram analysis. Variograms are useful for determining spatial structure and correlation of variables whose scaling behavior is unknown. Variograms are a visual representation of semivariance values calculated between point pairs at a variety of lag distances. The experimental variogram can be calculated as 3γ^h=12Nh∑(i,j)N(h)zj-zi2, where N(h) is the number of point pairs at the given lag distance h, and zi and zj are detrended snow depth values from individual points separated by a lag distance h (Webster and Oliver, 2007). The resultant semivariance values γ^ can be plotted against their lag distances, and we can determine the separation distance h at which point-pair values are still correlated. This autocorrelation point is defined as the “sill” in terms of semivariance γ^ and the “range” in terms of lag distance h. The sill represents the overall variance of the input data. The range represents the maximum distance where point values are still correlated and is generally calculated as the lag distance at 95 % of the sill. Point pairs further apart than the range are considered not correlated and spatially independent. The nugget represents the potential measurement error and is the variance resulting from measurement error and natural variation found over distances shorter than the minimum sampling resolution. We calculated experimental omnidirectional variograms of the detrended residual snow depth DSMs at a variety of spatial resolutions and fit spherical models in the R software environment (R Core Team, 2021). Spherical models are well suited for 3-D spatial analysis, are commonly used in similar variogram analyses, and fit the majority of our 170 experimental variograms (Kronholm, 2004; Kronholm et al., 2004; Kronholm and Birkeland, 2007; Webster and Oliver, 2007). Additionally, alternative models, such as exponential, Gaussian, and log–log linear, were utilized to fit snow depth spatial-variability variograms in previous studies (Mendoza et al., 2020).

First, we resampled the detrended residual DSMs from their original 0.02 m spatial resolution to 0.05, 0.1, 0.25, 0.5, 1, 2.5, 5, 10, and 20 m horizontal spatial resolutions using four resampling methods: nearest neighbor (Schön et al., 2015), cubic convolution, mean aggregation, and median aggregation. We used paired-point correlations of the nearest-neighbor resampled results with aggregated mean, aggregated median, and cubic-convolution resampling techniques to compare the effects of each resampling method on variability calculations. We chose the nearest-neighbor resampling technique to avoid oversmoothing observed using an aggregation or a cubic-convolution resampling technique, and to avoid the uncertainty associated with the possibility of out-of-range values calculated through cubic-convolution techniques (Roy and Dikshit, 1994; Fassnacht and Deems, 2006). We then calculated experimental variograms of both sites for each resolution for each field day with both nearest-neighbor and cubic convolution resampled DSMs and fit spherical models to each of these independent experimental variograms using the R package “gstat” (Pebesma, 2004). To estimate the goodness of fit of the spherical models, we calculated RMSE and NMAD values for the fit of the spherical models to the experimental variograms. The maximum distance considered for our variogram calculations was set to one-third of the maximum distance between point pairs within the two scenes, and we used minimum lag distances equal to the minimum point pair distances. Previous work used one-half of the maximum distance between point pairs as the maximum distance considered for variogram calculations, which would result in the comparison of point pairs at greater lag distances (Schirmer and Lehning, 2011; Clemenzi et al., 2018; Mendoza et al., 2020). Our focus on complex terrain, our relatively small study site extent, and the large number of points to be compared with our high-resolution DSMs motivated our decision for a smaller maximum distance considered for variogram calculations (Blöschl, 1999). Due to the large number of points contained in the high-resolution DSMs (0.02, 0.05, and 0.1 m) and the computing power required for variogram analysis of such large datasets, we used a random sample of 3 million points to process the experimental variograms for these three resolutions. To ensure reproducibility, we used a pre-set seed when randomly sampling. We applied a local polynomial regression (LOESS) fit from the R package “stats” to the fit spherical models to produce the seasonally averaged resolution-specific variograms (R Core Team, 2021). We utilized the United States Geological Survey (USGS) Yeti supercomputer for all of our variogram calculations and model fitting (Falgout and Gordon, 2022).

We calculated the coefficient of variation (CV) (Eq. 3) of the vegetation-masked and outlier-removed snow depth DSMs in the R software environment (R Core Team, 2021) defined as 4CV=σμ, where σ is standard deviation and μ is mean snow depth. We calculated the CV values for a variety of nearest-neighbor resampled resolutions to ensure consistent results and to reduce the computational load of calculating 0.02 m resolution snow depth DSMs.

We compared manual in situ validation-point snow depth measurements (n=70) with our DSM-differenced snow depths to assess error in our UAS-derived snow depths (Fig. 2). The seasonal mean, standard deviation, RMSE, and NMAD of differences between probed and UAS-derived snow depths show the effect of poor model quality on snow depth measurements (Table 1). The daily mean, standard deviation, and RMSE of differences between UAS-derived and probed snow depths varied considerably throughout the season (Table A2) and showed an increase in accuracy and a slight decrease in precision throughout the season (Fig. A1).

We collected all validation snow depth measurements, except the crown profile of the 26 February 2020 avalanche, in the lower elevations of the Hourglass and throughout the meadow in order to avoid exposure to snow avalanches. We observed large ranges of measured snow depths within these vegetated areas. For example, the ranges of probed snow depths measured within the 1 m2 validation points (n=70) were as high as 0.49 m, with an average range of 0.13 m. This assessment is not a comprehensive assessment of error, because our validation snow depths were primarily collected at random locations in the safe lower slopes, and this assessment is therefore biased towards comparisons of measurements in the meadow. Although far from a complete accuracy assessment, our single manual snow depth measurement from upper elevations at the crown of the avalanche (top of the couloir) exhibited a snow depth difference of only 0.01 m (1.90 m measured vs. 1.89 m UAS-derived), which is well within the typical error of manual measurement.

The DSM detrending analysis identified elevation as the most significant independent variable for each day at our study site. Therefore, we detrended all snow depth DSMs using the elevation surface derived from the 8 July 2020 snow-free DSM (Fig. 3). Complete time series plots of vegetation-masked and detrended snow depth maps of the Hourglass and meadow are provided in the Appendix (Figs. A7 and A8).

We resampled and compared the vegetation-masked and detrended DSMs from their original 0.02 m spatial resolution to 0.05, 0.1, 0.25, 0.5, 1, 2.5, 5, 10, and 20 m horizontal spatial resolutions using nearest-neighbor, cubic convolution, aggregated mean, and aggregated median methods. We compared the resampled snow depth DSMs by calculating correlation coefficients for all cell values for each pairing of resampling techniques. All resampling techniques are highly correlated at DSM resolutions finer than 1 m, with average correlations of 0.99, 0.98, and 0.97 for 0.25, 0.5, and 1 m resolutions, respectively (Fig. A2). At each resolution step greater than 1 m, correlations between the nearest-neighbor, cubic convolution, aggregated mean, and aggregated median methods decrease differentially between the Hourglass and the meadow but remain consistent between resampling methods. In the Hourglass, average correlations decrease to 0.92, 0.87, 0.77, and 0.73 for 2.5, 5, 10, and 20 m resolutions, respectively. In the meadow, average correlations decrease to 0.94, 0.92, 0.91, and 0.87 for 2.5, 5, 10, and 20 m resolutions, respectively.

We calculated experimental variograms (Fig. A3) and compared the results of the spherical-fit variogram models from the two distinct topographies within our study site and each field day at a variety of spatial resolutions using two different resampling techniques, nearest neighbor and cubic convolution. The two resampling techniques produced similar experimental variograms with only a few instances of lower residual semivariance observed in the cubic convolution resampled data. Subtle differences in the experimental variograms between the two resampling techniques influenced the spherical-fit models (Fig. A4). The cubic-convolution approach fails to register the initial sill break point (around 15 m) of the experimental variogram and fits a larger range with an associated larger sill value in several spherical-fit variograms (Fig. A5). The RMSE and NMAD values for the spherical-fit models were consistently higher for the Hourglass than the meadow, with the highest values found at spatial resolutions finer than 0.5 m and at 20 m (Table A5). We found consistent differences in the range, nugget, and sill (semivariance) values of the Hourglass and the meadow sites. The Hourglass exhibits a smaller range of autocorrelation, greater sill values, and greater nugget values than the meadow, when including all dates and snow depth DSM resolutions (Table 2). Specifically, the Hourglass exhibited consistently more snow depth spatial variability on individual field days (Fig. 4) and more seasonal variability in its patterns of spatial variability than the meadow (Fig. 5). These results reflect the given substratum of the two sites. The meadow's more homogenous ground cover and topography are reflected in less variability overall and spatial autocorrelation over greater distances. In contrast, the steep, rocky terrain of the Hourglass is reflected in the more dynamic seasonal patterns of spatial variability and shorter distances of autocorrelation. The 20 m resolution variograms frequently misrepresent the spatial-variability patterns of finer resolutions, and this is perhaps due to the relatively small study sites creating far fewer point pairs of snow depths to calculate the variograms from, therefore being less resistant to outliers.

Temporally, the greatest semivariance values exist earlier in the winter at both the Hourglass and meadow at all resolutions. Variability then decreases throughout mid-winter and increases slightly after the first substantial spring melt event that occurred approximately 2 weeks prior to 14 May 2020. Autocorrelation range generally increased within both the Hourglass and the meadow throughout the winter (Fig. 6), followed by pronounced increases in the spring. Sill values were consistently greater at the Hourglass compared to the meadow throughout the season (Fig. 6) and were relatively similar across all resolutions except 20 m at the Hourglass couloir where greater variability exists throughout the season. Temporally, sill values generally decreased at the Hourglass couloir site and remained consistent at the meadow throughout the winter. Additionally, at the Hourglass, the sill increased at finer resolutions because of a large natural avalanche on 26 February 2020.

Snow depth DSM spatial resolution affected the calculated variograms, resulting in larger autocorrelation range, sill, and nugget values present in coarser-resolution variograms (Fig. 7). At the Hourglass, 0.5 m resolution models accurately represented the spherical-fit variograms of all finer resolutions (0.02, 0.05, 0.1, and 0.25 m) and consistently resulted in autocorrelation range values of ∼10 m. The 1 m resolution snow depth DSMs captured the pattern of the finer-resolution variograms on all but three of the observation dates (21 February, 14 May, and 25 May) but aligned more closely with coarser-resolution variograms (2.5, 5, 10, and 20 m) on those three observation dates and exhibited larger, more variable autocorrelation ranges consistently throughout the winter. At the meadow, 2.5 m resolution models accurately represented the spherical-fit variograms of all finer resolutions (0.02, 0.05, 0.1, 0.5, and 1 m) on all observation dates. The 5 m resolution differed from finer-resolution patterns when seasonally averaged, and the 10 m resolution differed from the patterns on a single date and more so when seasonally averaged (Fig. 5). Snow depth DSM resolutions of 20 m in both topographies and all observation dates failed to capture the patterns of spatial variability found in finer resolutions.

We compared the calculated coefficient of variation over time at the Hourglass and meadow. Resultant coefficients of variation were similar across a variety of snow depth DSM resolutions. As such we present the 0.5 m resolution results here. Coefficient of variation values were greater at the Hourglass when compared to the meadow on every observation day (Fig. 8). The seasonal pattern of variability in the Hourglass started higher in January, decreased, then remained consistent through March and peaked in May concurrently with the onset of ablation. At the meadow, the variability decreased throughout the season before peaking in May with the onset of ablation.

Comparisons between DSM-differenced and probed snow depths highlight the challenge of sampling spatially representative snow depth measurements with underlying vegetation. The 1 m2 validation point measurements had an average range of 0.13 m, while the mean difference between DSM-differenced snow depths and in situ probed snow depths was 0.27 m (Table 1). Both of these point and observational tool measurement differences, as well as our additional error estimates, could be attributed to the vegetation captured in the snow-free 8 July 2020 DSM. This vegetated surface had greater than 0.5 m of vertical variability across horizontal distances less than 1 m and compressed at an unquantified and spatially heterogenous rate under the gradually increasing snowpack. This vegetation effect is largely confined to the lower elevations of our study site, which is also primarily where we collected our validation point measurements. Vegetation effect is a recognized weakness of UAS-derived snow depth measurement and helps explain the differences we observed between the DSM-differenced snow depths and probed validation point measurements in this study (Bühler et al., 2016).

Previous research identified wind direction as a contributing variable to their spatial-variability findings (Clemenzi et al., 2018; Deems et al., 2006; Mendoza et al., 2020; Mott and Lehning, 2010; Mott et al., 2018). Our results suggest that elevation is the most significant predictor in directional snow distribution bias in our dataset, and we detrended the DSMs on this metric.

Our project analyzed the spatial variability of snow depth across spatial resolutions spanning 3 orders of magnitude (0.02 to 20 m). Given this large resampling need, we were interested in the effects of resampling techniques on the resultant spatial variability. Previous research identifies oversmoothing as a concern with resampling methods which rely on averaging because it results in decreasing the absolute magnitude of observed variance (Fassnacht and Deems, 2006; Melvod and Skaugen, 2013). We found very high correlation of residual snow depths (Sect. 4.2) between all resampling techniques at spatial resolutions finer than 1 m (Fig. A2). As resolution increased beyond 1 m, correlation begins to decrease, especially in the more heterogenous terrain of the Hourglass. Closer inspection of cell-by-cell differences reveals the cubic convolution and aggregated mean methods producing unrealistic snow depth residual artifacts near areas of greater snow depth variability, such as the avalanche crown, near cornices, and in the upper start zone. This is probably due to these resampling techniques' limited resistance to outliers. Additionally, we observed very similar patterns in the experimental variograms between nearest-neighbor and cubic-convolution methods (Fig. A3). Consistently slightly lower semivariance values in cubic-convolution resampled experimental variograms point towards potential oversmoothing of the natural variability seen in the nearest-neighbor resampled experimental variograms. On the other hand, subtle differences in the cubic convolution experimental variograms propagated larger differences in the spherically fit models (Fig. A4) and resulted in both greater ranges of autocorrelation and higher semivariance values (Figs. A5 and A6). The range and semivariance values observed at 0.25, 0.5, and 1 m resolutions resembled those found at 2.5 and 5 m resolutions in the nearest-neighbor spherically fit models. As spatial resolutions coarsen, averaging resampling methods produce longer ranges (Fassnacht and Deems, 2006) and, with that, higher sill values. We are confident that nearest-neighbor resampling methods depict the true patterns of spatial variability of snow depth at fine resolutions within our study area because of the preservation of real observed snow depth values and the high correlation to other resampling methods. Given the diverging results at resolutions greater than 1 m, we urge careful consideration of resampling techniques for coarser spatial resolutions in future work.

Many previous studies utilized 1 m resolution sampling grids (Clemenzi et al., 2018; De Michele et al., 2016; Deems et al., 2013; López-Moreno et al., 2015; Mendoza et al., 2020; Meyer and Skiles, 2019; Trujillo et al., 2009) but without detailed analysis to determine if this resolution is sufficient to capture the patterns of spatial variability. Our results indicate 1 m resolution is an insufficient resolution to capture the complete pattern of snow depth spatial variability in the steep, complex mountain terrain of the Hourglass. At our site, 0.5 m resolution results capture the spatial-variability patterns seen in all finer resolutions (0.02, 0.05, 0.1, and 0.25 m) in each observation day at the Hourglass (Fig. 5), while the 1 m resolution only captures these patterns on 7 of our 11 observation days. Maximum variation exists within a 15 m range for all sub-0.5 m resolution variograms with a decreasing variance as the range continues to grow beyond the sill. Coarser-resolution variograms exhibit increasing variance at greater ranges, with increasing variance beyond the sill. While 1 m, and even 2.5 m, resolutions have similar ranges as finer-resolution models on some observation days, the mean range values increase dramatically between 0.5 m (15 m), 1 m (29 m), and 2.5 m (48 m) resolutions and decrease minimally below 0.5 m resolutions (10 to 12 m for 0.02 and 0.25 m resolutions, respectively) (Table 2 and Fig. 7). Our results suggest that a 0.5 m sampling resolution is the coarsest sampling resolution necessary to capture all small-scale spatial variability of snow depth in the complex mountain terrain of our study site.

However, our results suggest 2.5 m resolution sampling grids are adequate to capture spatial variability in the protected terrain at the meadow. The finer-resolution patterns evident in the mean variograms of the meadow are similar to the 2.5 m resolution, while the 5, 10, and 20 m resolutions differ distinctly with generally larger range values (Fig. 5). The autocorrelation range values at the meadow scale directly with snow depth DSM resolution, while the sill values remain consistent across all snow depth DSM resolutions (Fig. 7). Given this relationship, the 2.5 m resolution captures both the fine- and coarse-resolution patterns in the meadow. This distinct difference in snow depth spatial variability between complex and simple terrain provides evidence of the contrasting snow distributions in the two mountain topographies.

Previous research reported autocorrelation range values for snow depths of 15–25 m in a variety of mountain terrain with an additional correlated scaling break above 50 m (Fassnacht and Deems, 2006; Clemenzi et al., 2018; López-Moreno et al., 2015; Mendoza et al., 2020; Trujillo et al., 2009). We found consistently less than 20 m range values in the steep, complex terrain in the Hourglass at finer spatial resolutions and greater than 50 m range values in the meadow at all resolutions (Table 2). Our results also suggest that the range of autocorrelation increased throughout the winter at both sites. We attribute this to increasingly homogenous snow depth distributions over larger distances due to wind redistribution near ridges (Mott and Lehning, 2010; Trujillo et al., 2007) and small-scale redistribution processes (Mott et al., 2011). Increasingly leptokurtic distributions evident in scene-wide violin plots, especially at the meadow, indicate that snow depth distributions were largely concentrated near the mean snow depth for each given observation day (Fig. A9) and became more uniform as snow depth increased.

Our results show that snow depth variability generally decreased throughout the season in the complex terrain of the Hourglass (Fig. 8). This suggests that a deeper snowpack tends to decrease the spatial variability of snow depth as terrain and vegetation features become less influential on snow depth distribution across space (Deems et al., 2006; Elder et al., 1991; Harder et al., 2016; Trujillo et al., 2009). There was a slight increase in snow depth variability at the Hourglass following two notable events: a natural avalanche on 26 February and the first major spring melt during the first half of May (Fig. 4). An increase in sill values and a clear distribution change of snow depth residuals provide evidence for these snow depth distribution shifts (Fig. A9). The spring-melt-aligned increase in spatial variability is similar to changes during ablation periods reported by López-Moreno et al. (2015) who used the coefficient of variation as the measure of variability over the course of 8 observation days spread over two winters.

Snow depth DSM creation through UAS and SfM photogrammetry workflows is distinctly challenged by snow surface conditions and their interaction with local lighting (Bühler et al., 2016, 2017; Goetz and Brenning, 2019). DSMs from certain observation days had to be removed from further analysis due to poor quality, which can be attributed to homogenous snow surfaces that occurred due to either recent snowfall with minimal wind, cloud cover producing low light, or a combination of both. The wind-sheltered and nearly flat terrain of the meadow limited the influence of surface-texture-creating processes, such as wind redistribution and natural snow sluffing, resulting in uniform minimally textured snow surfaces and more observed days removed from further analysis (Table A3). These poor-quality models affected errors in snow depth measurement (Tables 1, A4) and, once removed, the error in our remaining models was comparable to the reported error margins of other similar UAS-derived snow depth research (Adams et al., 2018; Eberhard et al., 2021; Revuelto et al., 2021). Therefore, we are confident that our retained UAS-derived snow depth observations in steep mountain terrain are accurate.

The analytical approach used in this study is limited by computational resource availability. The processing time for variogram analysis scaled directly with snow depth DSM resolutions (Fig. A10) and increased exponentially at finer resolutions while processing in parallel on the USGS Yeti supercomputer (specifications online). We utilized a simple random sample of 3 million points for all 0.02 and 0.05 m resolution DSMs to avoid memory overloading. Processing times for high-resolution DSM analysis at resolutions finer than 0.5 m offered little additional value (see Figs. 5, 6, and 7) given the computational requirements, thereby supporting a spatial sampling grid of 0.5 m for snow depth spatial-variability analysis.

Our results are from a thorough analysis of a single study site and under the influence of only the interactions of the local topography and meteorological events from one winter season. The spatially limited in situ snow depth validation measurements are not completely representative of our entire research site, particularly at upper elevations near the ridgeline. Additionally, our snow depth measurement errors from the UAS–SfM photogrammetry process may contribute to snow depth spatial-variability error, but these errors are challenging to accurately quantify (Redpath et al., 2018) and likely contribute a trivial amount (Adams et al., 2018; Eberhard et al., 2021; Revuelto et al., 2021). We also attempted to account for these small errors by conducting repeated UAV flights over the course of a season, using ground control points from the same locations on both snow-free and snow-covered sampling flights, and choosing a site with a relatively deep snowpack (Goetz and Brenning, 2019). Future snow depth spatial-variability research should consider observing a wider variety of complex mountain terrain features, different snow and avalanche climates, as well as using additional remote sensing tools for further validation or comparison.