Parsing Synthetic Aperture Radar Measurements of Snow in Complex Terrain: Scaling Behaviour and Sensitivity to Snow Wetness and Landcover

: This study investigates the spatial signatures of seasonal snow in Synthetic Aperture Radar (SAR) observations at different spatial scales and for different physiographic regions. Sentinel-1 C-band (SAR) backscattering coefficients (BSC) were analyzed in the Swiss Alps (SA), in high elevation forest and grasslands in Grand Mesa (GM), Colorado, and in North Dakota (ND) croplands. GM BSC exhibit 10dB sensitivity to wetness at small scales (~100 m) over homogeneous grassland. Sensitivity decreases to 5 dB in the presence of trees, and it is demonstrated that VH BSC sensitivity enables wet snow mapping below the tree-line. Area-variance scaling relationships show minima at ~100 m and 150-250 m respectively in barren and grasslands in SA and GM, increasing up to 1 km and longer in GM forests and ND agricultural fields. The spatial organization of BSC (as described by 1D-directional BSC wavelength spectra) exhibits multi-scaling behavior in the 100 -1,000 m range with a break at (180-360 m) that is also present in UAVSAR L-band measurements in GM. Spectral slopes in GM forested areas steepen during accumulation and flatten in the melting season with mirror behavior for grasslands reflecting changes in scattering mechanisms with snow depth and wetness, and vegetation mass and structure. Overall, this study reveals persistent patterns of SAR scattering variability spatially organized by land-cover, topography and regional winds with large inter-annual variability tied to precipitation. This dynamic scaling behavior emerges as an integral physical expression of snowpack variability that can be used to model sub-km scales and for downscaling applications.

interface. Volume scattering is practically undetectable at C-and L-bands for shallow snowpacks, in which case the backscatter at the snow-ground interface is dominant [34]. The sensitivity of backscattering coefficients to snow cover condition in the Alps was examined by many in the past including Matzler (1996) and Strozzi et al. (1997) [28,35]. In particular, Strozzi and Matzler (1998) [36] demonstrated that C-band radar measurements with an incidence angle of 30° could be used to distinguish wet from dry snow and snow-free areas. The capability to discriminate between dry-refrozen and wet snow at microwave frequencies is likewise well established [19,37]. Nagler and Rott (2000) [24] used ERS-2 (European Remote Sensing satellite 2) and RADARSAT-1 imagery to identify wet snow in the Austrian Alps. This work was followed by an improved approach using dual polarimetric bi-temporal Sentinel-1 SAR data to monitor snowmelt [25]. To integrate across scales from the SAR nominal measurement scale (10's m) to landscape scale, including the scales representative of unambiguous physical processes in state-of-the-science models (100 m -kms), remains however a critical challenge [38].
The goal of this study is to investigate the temporal evolution of the spatial signatures of seasonal snow in SAR observations at different spatial scales and for different physiographic regions using multi-temporal Sentinel-1 dual polarization C-band observations. L-band UAVSAR (Uninhabited Aerial Vehicle Synthetic Aperture Radar) observations are also available for one of the study regions.
The focus is on quantifying and interpreting the impact of spatial variability on SAR BSC imagery with an eye toward inferring constraints for physically-based snow models using spectral scaling analysis. In particular, the temporal evolution of the spectral slope (scaling factor) and local changes in spectral slope (scaling breaks) with scale are interpreted in the light of snowpack condition, landcover, and landform. This information can be used to capture (parameterize) scale-aware subgridscale variability in coupled snow hydrology-microwave models, and to downscale snow products (e.g. passive microwave) as illustrated by [68] for soil moisture. In addition, the scaling characteristics can be used to upscale or downscale the results of coupled-snow hydrology-microwave models observing system simulators (OSS) to the desired scale in forward mode and in data-assimilation experiments. The study regions and the data are described in Section 2. Section 3 describes the processing steps followed to derive the BSC from Sentinel-1 measurements, including the Cloud-Pottier (CP) decomposition the dual polarization SAR data to derive the Alpha and entropy parameters. Section 4 presents the results of the multi-temporal analysis of backscattering, Entropy and Alpha parameters for different regions, and the spatial scaling analysis toward elucidating how the SAR BSC intensity changes with topography and land cover, followed by conclusion and discussion concerning the suitability of SAR measurements in Section 5. Supplementary data presented in Tables and Figures are referred to using the notation S# throughout the manuscript.

Study Regions
Three different study sites characterized by deep seasonal snowpacks (depth > 1 m) were selected to investigate the snowpack properties from Sentinel-1 SAR imagery ( Figure 2). The first study region is Grand Mesa, Colorado (CO), USA (38°54' -39°06'N, 107°42' -108°20'W). This is one of NASA's Snow Experiment (SnowEx) primary field sites, where an intense field campaign was conducted in February 2017, hereafter referred to as SnowEx'17. SnowEx's primary goal is to enable development and, or systematic evaluation of alternative snow remote-sensing technologies, methods and retrieval algorithms using extensive in-situ measurements [38,39].
The Swiss Federal Office of Meteorology and Climatology (MeteoSwiss) maintains climatological stations to monitor weather and snowpack properties at different terrain elevations in this region, most located above the tree-line. The Swiss Alps site is characterized by steep complex topography in the 800-3000 m elevation range and heterogeneous land cover including barren land, grassland, deciduous forests, urban areas, and lakes. In contrast, Grand Mesa is characterized by elevated flat terrain with complex land cover ( Figure 3) including grassland, shrubs, and meadows of closed canopy evergreen forest with deciduous forest in adjacent slopes [39,40]. SNOTEL stations Snow cover is maximum over Grand Mesa from November through March and minimum from June to September for the 2016-2019 period ( Figure 4). June and July images serve as snow-free baseline. Snow cover over the Swiss Alps shows similar seasonality ( Figure 5), although snow accumulation begins in September and decreases in October due to the warmer temperatures and high precipitation in the form of rainfall rather than snow [41]. In North Dakota, considerable snow accumulation occurs during February and March when the entire study region is covered with snow until it melts in April ( Figure 6).    Land-cover Classification -The spectral variability vegetation index (SVVI) is used to classify vegetation due its refined sensitivity as compared to NDVI (Normalized Difference Vegetation Index) and application to both natural and agricultural land-uses [42]. SVVI is calculated as the difference between the standard deviation (SD) of all Landsat bands (excluding thermal) and the SD of all three infrared bands, as follows SVVI derived from Landsat-8 data over Grand Mesa was used here to distinguish grassland, forest and snow cover features as shown in Figure 7. Nevertheless, despite superior performance as

Backscattering Coefficient Estimation
The standard framework for processing the Sentinel-1 Single Look Complex (SLC) data is presented in Figure 8. Radiometric and geometric corrections are applied to the Sentinel-1 SAR data to derive the normalized backscattering coefficients. Thermal noise due to the background energy of the SAR receiver is removed from the VV and VH intensity images (this background energy is independent of the received signal of the SAR sensor). Next, radiometric calibration was performed which converts the digital number of the image pixel to the corresponding backscatter intensity for both polarization channels, and phase information is preserved to extract the coherency matrix (https://sentinel.esa.int/web/sentinel/technical-guides/sentinel-1-sar).
The Terrain Observation with Progressive Scans SAR (TOPSAR) technique is applied in the IW mode of Sentinel-1 acquisitions to achieve large swath widths with enhanced radiometric performance [43]. The IW mode acquisition consists of three swaths. Each swath has a single image for each polarization channel, thus a single SLC image consists of six images for dual polarization channels. Due to the coherent addition of scattered signals within a pixel, constructive and destructive interference occurs depending on the relative phase of each scattered signal. Speckle is an inherent problem of the SAR system, and the Lee speckle filter [44] with a width of five pixels (75m) was applied to remove the speckles of the backscattered elements. SAR data have different topographical distortions (i.e. layover, foreshortening, shadowing) that depend on acquisition geometry. A geometric terrain correction is necessary to convert the data from slant range geometry into a gridded map. Specifically, the Range-Doppler terrain correction is applied, which is a robust approach that takes into account topography, and orbit and velocity information from the satellite. While computing the Sentinel-1 backscattering coefficient (BSC), local terrain variation and their impact on the BSC is not considered. So the local incidence angle is used to represent the local terrain variation as proposed by Kellendorfer et. al (1998) [45]. This is called radiometric corrected backscattering coefficient. The BSC of an illuminated target area is highly dependent on the incident angle of the signal. At small incidence angles the backscattered intensity is high compared to that at higher incidence angles over the same illuminated area. Thus, the cosine correction [46] is applied to the georeferenced data to minimize the backscatter variation due to the incidence angle. Finally, radiometric and geometric corrected normalized BSC coefficients for VV and VH polarization channels are derived.

Coherency Metrics (Entropy -Alpha Estimation)
The CP (Cloude-Pottier) polarimetric decomposition [47,48] is an incoherent decomposition technique based on the eigenvalues and eigenvectors from the coherency matrix that was originally developed for fully polarimetric SAR data (intensity and phase at HH, VV, and HV polarizations).
The Entropy and Alpha parameters obtained from the CP decomposition reveal scattering characteristics of the SAR signal that can be tied to scattering mechanisms of the snowpack [49][50][51].
Here, a modified CP decomposition approach is applied to the Sentinel-1 data coherency matrix generated from the debursted SLC image (Section 3.1) which includes only VV and VH channels. The scattering matrix captures the complete scattering characteristics of each pixel in an image as follows, where SVV, SVH and SHV represent the co-and cross-pol BSC at VV, VH and HV polarization respectively. Due to the constraints of the reciprocity theorem, the cross polarization elements in the scattering matrix are similar in the monostatic backscattering case, i.e., SHV = SVH. These elements can be represented by the corresponding Pauli vector kp: where the operator T represents the conjugate transpose. The coherency matrix [T2] is obtained from the product of the Pauli vector and its conjugate: Using the eigenvalue and eigenvector based incoherent target decomposition technique, [T2] can be decomposed into its corresponding rank-1 coherency matrix T2 as follows: where λi are the eigenvalues of the rank-1 coherency matrix. The normalized eigenvalues (Pi) can be interpreted as pseudo probability measures derived from the eigenvalues: Shannon's Entropy (H) is subsequently estimated from the normalized eigenvalues (Pi): Following [44], the eigenvectors u of the averaged coherency matrix can be expressed as This could be further written as a revised eigenvector parameterization of a 2 x 2 unitary matrix as Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 January 2020 doi:10.20944/preprints202001.0300.v1 where 1 , 2 represent the target's scattering mechanisms, and β, δ and ϕ are used for the estimation of target orientation angles. The roll invariant mean dominant scattering parameter � is calculated in terms of the pseudo probabilities as follows: In the remainder of the manuscript, � is referred to as Alpha. Generally, it is expected that Entropy is low for fresh snow cover and increases with wetness. Conversely, Alpha is high for fresh snow and decreases with wetness. Entropy and Alpha respectively increase and decrease with surface roughness. Entropy is high (> 0.7) for vegetated areas whereas Alpha takes values in the intermediate

Scaling Analyses
The spatial characteristics of snowpack properties as captured by SAR measurements were examined by quantifying the changes in the variance as a function of area, and by tracking changes the spatial statistics between overpasses based on the slope of the power spectra of individual images as per Kim and Barros (2002) [52]. To isolate homogeneous areas for scaling analysis, backscattering images for Grand Mesa, Swiss Alps, and the North Dakota areas were subset into areas of homogeneous land cover with areas ~4-16 km 2 . The BSC intensity images were aggregated from 225 m 2 to ~16 km 2 using the aggregation scheme summarized in Table 5. Note that the speckle removal described in Section 3.1 to improve signal-to-noise ratio (SNR) is expected to introduce a scaling break above and below the LRS filter scale. in the zonal (x) and meridional (y) directions is calculated for scaling analysis as following [53,54]. If k x ( ) and k y � � are wavenumbers (wavelengths) corresponding to x and y directions, in the range of scales where the power spectrum |F′(k γ )| 2 exhibits power-law behaviour where γ can be x or y and C is a constant, the spectral slope β γ along direction γ is estimated by applying the log transform to Eq. (12a) as follows: The spectral slope is the metric (scaling factor) that explains the transfer of backscatter energy across scales. A change in slope between adjacent scales (scaling break) is indicative of a change in scaling behavior. Here, the underlying premise is that scaling breaks and changes in scaling factor can be attributed to physical changes in the snowpack that impact backscattering mechanisms.

Snow wetness mapping
The BSC difference between wet and dry snow or snow-free surfaces has long been explored to detect and map wet snow [22]. The threshold polarization ratio algorithm proposed by [25] to map wet snow was applied to the Sentinel-1 SAR data for the three study regions. Both VV and VH polarization BSC ratios with respect to a reference image (e.g. summer conditions) as a function of the local incidence angle were utilized to determine the appropriate threshold values to detect wet snow based on LandSat-8 visible imagery and SCA-NDSI maps. Different threshold values were estimated for each of the three study regions due to different topography and SAR viewing geometry.
Following [25], the reference image is the average of multiple SAR images from summer and early winter for snow free conditions to reduce noise. Results from the analysis of BSC variance with scale (see Section 4) suggest a minimum is reached at ~250 m, and therefore the wet snow detection algorithm is applied to the SAR data at 240 m resolution to strike a balance between spatial resolution and accuracy. BSC image pairs are co-registered based on the SRTM 30m DEM and a multichannel intensity filter was applied [55]. Finally, weighted averages of RVV=VVwinter/VVsummer and RVH=VHwinter/VHsummer at different times were determined based on the local incidence angle following Nagler et al. (2016) [25].
The most commonly used wet snow mapping algorithm [24] was successfully applied previously to map wet snow at high elevations above the treeline, and it worked well in this study for North Dakota and the Swiss Alps areas, but it failed in Grand Mesa due to the presence of evergreen forest. To address this limitation, the approach from [25] was modified to take advantage of VH BSC sensitivity (~ 5 dB for snow on-off in the forest). The backscattering coefficients (VV and VH) derived for summer (reference) and all winter Sentinel 1 overpasses with same acquisition geometry (descending mode in Grand Mesa) are used to calculate the ratios RVV = VVwinter/VVsummer and RVH = VHwinter/VHsummer. A weighted average polarization RAvg image is then estimated as follows: where k = 0.5, 1 = -0.5 and 2 = 2. To discriminate wet from dry snow and snow-free areas over forest and other land covers is done based on the threshold of -1.2 dB of the average polarization ratio image (RAvg). This value is selected based on the histogram of polarization ratio images over the different land cover classes based on the analyses of snow cover during the accumulation (October-March), melting (April-may) and snow-free (July-August) seasons.

Temporal Variability of SAR Measurements over Complex Terrain
The temporal variability of backscatter measurements over snow covered areas has been documented for many different geographic regions with a focus on sensitivity to snow condition and snow mass [26,28,[33][34][35][56][57][58]. Generally, BSC slightly increases over the course of the (dry) snow accumulation season [66]. The change of snow BSC from snow free BSC is strongly depend on (1) local weather including winds and precipitation regimes, (2) local soils and vegetation, and (3) the timing of the snow and snow-free observations.
Here, the temporal evolution of Sentinel-1 BSC sensitivity for Grand Mesa, Swiss Alps, and North Dakota is shown in Figure 9 taking advantage of multiple overpasses of Sentinel-1 C-Band dualpolarization (VV and VH). Seasonal BSC intensity is significantly different over grassland for both polarizations in Grand Mesa. VH BSC is 3 dB lower for dry snow vis-à-vis snow-free conditions, but VV BSC shows no difference, although VV BSC differs by 5 dB between fresh snow (Dec-Jan) and melting season conditions (Apr-May). This is in contrast with [28] reported that the backscattering coefficient for dry snow was 5 dB lower than snow-free conditions at C-band irrespective of the polarization in the Swiss Alps at mid-elevations (~ 2,500 m), which highlights the importance of regional controls in seasonal backscattering. Sentinel-1 data over the Grand Mesa were acquired in descending mode at 07:00 LT (Local Time), and thus the surface of the snowpack is always frozen in late winter at the time of overpass. Diurnal melt-refreeze processes (Figures S6(a-f)) result on increased snow surface roughness as well as rough ice-water and, or ice-soil snowpack interfaces due to the refreezing of the daytime meltwater that can percolate deep into the snowpack [62]. Meltrefreeze cycles along with increases in diffuse scattering caused by the larger snow grain sizes in old Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 January 2020 doi:10.20944/preprints202001.0300.v1 snow and due to wind sintering explain therefore the BSC increase from early spring (smooth wet snow) to late spring and early summer conditions (refrozen crusted wet snow) [63]. In early winter, from December to March, dielectric discontinuities in the snowpack tied to heterogeneous stratigraphy strongly impact the backscattering signal. In particular, if the event-scale snow accumulation is small, heterogeneous layering in the snowpack leads to strong backscattering [63].
In the Swiss Alps, the Sentinel-1 data were acquired in ascending pass at 19:15 LT. Both VV and VH BSC are ~5dB higher in the accumulation season than in Grand Mesa and in North Dakota due to strong scattering at the dry snowpack-ground interface because of the rock surfaces and steep terrain.
In April-May, VV and VH BSC decrease both relative to dry-snow and snow-free conditions due to surface melting. Indeed, the Sentinel-1 imagery shows strong spatial organization of BSC behavior with slope and aspect, and thus direct solar radiation, which is indicative of afternoon surficial Note that, in addition to surface radiative effects, wind driven coarsening and roughing of the snowpack surface should also be influenced by the diurnal cycle of ridge-valley wind patterns, thus introducing persistent spatial variability that varies locally with time-of-day and with landform.
Therefore, BSC sensitivity in complex terrain is necessarily regional and even local. The advantage of satellite revisits is that it is possible to learn a local climatology (time-varying patterns) of BSC sensitivity from tracking its variability in space and time, which can be interpreted subsequently in the light of snow physical condition using a snow physics model or ground-based observations. More extensive discussion follows in Section 4.2 in the context of scaling analysis.

Space-Time Scaling Behavior
Variance Scaling -To examine the evolution of spatial variability with time, we first focus on the relationship between variance (2 nd order moment of the spatial distribution of BSC) with area for three (4×4 km 2 ) areas of homogeneous land-cover identified in Figure 3 as land-cover within B, that is the variance is minimum at the spatial scales corresponding to uniform land-cover (e.g. grass meadows versus forest-patch length-scales). Finally, the variability observed at A, B and C was maximum in summer (snow-free) and decreases to a minimum in early winter (fresh snow cover). Warm weather episodes during the accumulation season result in surface melt followed by overnight refreeze (e.g. 20 April, 2018). Over forested areas (areas B and C), the minimum variance is reached at larger spatial scales in the range 1-2 km 2 , although it increases at larger scales due to changes in topography at the edges of area C (see Figures 2 and 3).  independence of frequency suggests that the physical basis of BSC scaling behavior is robust for dry snow conditions and there is therefore potential to explore multi-frequency SAR data for retrieving snow properties without extensive calibration using ground observations [65].
The intra-seasonal persistence of spectral slopes during the accumulation season is present in 2018 as well, but the spectral slopes change dramatically (see selected spectra in Figure 14d S2(a-b)).
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 January 2020 doi:10.20944/preprints202001.0300.v1 Figures 15a-b show there are significant differences in spectral slopes between grassland and mixed and forest areas with high (low) spectral slope ratios in the y-direction (x-direction) for snowfree conditions in late May (5/31) and before the full greening of the Mesa by end of June (6/24, see Figure S5 for NDVI maps). Note the increasingly steeper slopes for VV BSC in the x-direction in the forest as snow wetness increases and peaks by the end of April (4/25) for snow-on conditions in contrast with the behavior for grassland in the y-direction (Figure 15b). The decreases after the onset of the melting season show that attenuation due to snow wetness on the ground counterbalances volume scattering by the canopy above leading to a significant increase in spectral slope ratios. No synthesis of contrasting scaling between forest (orange, area C) and grassland (blue, are A) in part (a).
The Sentinel-1 BSC spectra over the Swiss Alps shows multi-scaling behavior with scaling breaks at ~ 180 m and ~ 360 m for snow-on conditions ( Figure 16, Table S3) with single-scaling for snow-free conditions. Note that the selected area ( Figure 2) for scaling analysis is above the tree-line, and thus vegetation should not be playing a role here. At pixels where meteorological stations exist in the Swiss Alps ( Figure S1(a)) the relationship between BSC and snow depth is ambiguous ( Figure S2 (ab)). This suggests that snow mass is wrapped on the terrain filling (accumulating) the terrain roughness (depressions) at scales below 360 m. The variation of VV and VH BSC with slope ( Figure   17a) is only apparent in the spring (Apr-May) during the melt season. There is however high all-year sensitivity to aspect (sun exposure, ascending and descending pass acquisitions and local incidence angle) with a difference of 7 dB between the North-East and North-West slopes for VV polarization in contrast with the North and South slopes that show the same BSC for all seasons ( Figure 17b). As in Grand Mesa, the sensitivity to aspect captures differences in insolation patterns that are indicative of spatial variability on daytime surface melt followed by nocturnal refreeze cycles that strongly impact the microphysics of the snow surface during the accumulation season. Wet snow attenuation effects consistent with the minimum BSC magnitude independent of slope and aspect (Figures 17a   and 17b) explain the distinct spectral slopes at small scales on May 18, 2018 in the y-direction ( Figure   16, bottom row). Nonlinear behavior of heterogeneous snowpacks in the melt season reflects the changing patterns of SCA for scales < 360 m (see also [8,72]).
The impact of wind-driven snow redistribution is out of the scope of this work. In particular, it is expected that "snowform" should reflect wind climatology in the planetary boundary layer that is closely modulated by regional  Whereas the minimum WSCA occurs by end of May, the time rate of WSCA change in the forested areas is slower compared to other land covers suggesting that light extinction through the canopy plays a significant role in reducing incoming shortwave radiation, and thus preserving the snowpack.

Wet Snow Mapping
As expected the algorithm detects well wet snow above the tree line in the Swiss Alps ( Figure 19b) capturing weather related variability such as new snowfall and melting events in April and May. Landsat imagery of the region that is mostly snow-free by the end of May. However, the BSC changes during the snow melt [63] can potentially lead to the temporary underestimation of wet snow areas.
Using the summer BSC image as a reference for wet snow mapping can lead to overestimation in areas of densely vegetated deciduous forest and underestimation for dry snow in barren areas with high BSC, both relatively small in Grand Mesa. Also, the selection of threshold for the wet snow mapping is highly dependent on local soil surface, vegetation covers and observation period, and thus it should be calibrated locally.

Conclusion
ESA's spaceborne Sentinel-1 dual-polarization SAR data offers high spatial and temporal polarimetric BSC imagery to monitor seasonal snowpacks globally. This study reports a comprehensive effort to examine the spatial information content of these data in the light of snow physics. First, the data show large ambiguity in the relationship between BSC magnitude and snow mass, with the underlying ground surface dominating the signal during snow accumulation and a difference in BSC magnitude greater than 5 dB attributed to rocky terrain. In GM, BSC exhibit 10 dB sensitivity to wetness at small scales (~100 m) over homogeneous grassland. Sensitivity decreases to 5 dB in the presence of trees, and it is demonstrated that VH BSC sensitivity enables wet snow mapping below the tree-line. VV and VH BSC trends (positive, negative) in the early snow melting season strongly depend on the time of data acquisition (morning, evening), which demonstrates the importance of melt-refreeze cycles on surface roughness and microphysics. Parameters Entropy and Alpha derived from the coherency matrix showed little sensitivity to snowpack changes during the accumulation season in all cases, which is attributed in part to the lack of full polarimetric information in Sentinel-1 data.
Previously, [25] demonstrated a wet snow mapping algorithm that was adopted here to map wet snow using Sentinel-1 data. The algorithm that worked well in the Swiss Alps failed in Grand Grand Mesa, increasing up to 1 km and longer for forested areas in Grand Mesa and agricultural fields in North Dakota. These scales can be viewed as measurement optima, that is the scales at which the average of the measured BSC Lm is representative of the local mean value of the field measured at scale l (Lm > l). Spectral analysis reveals two scaling regimes at sub-km scale with scaling breaks around ~180-360 m. These scaling regimes as measured by the spectral slopes are reliable within the same accumulation season and exhibit strong sensitivity to snow mass and snow wetness when trees are present. This is in keeping with work in the peer-reviewed literature highlighting the reliability of snowpack melting patterns at regional scale consistent with topography and landform as discussed in Section 4.2. Nevertheless, large inter-annual variability as illustrated for the case of Grand Mesa suggests that snowmelt patterns organized by topography and vegetation can explain the scaling breaks at small scales, the regional spatial variability of snowpack conditions (surface roughness, microphysics, LWC) varies strongly with local weather including snowfall that determines snow accumulation, and wind-driven snow redistribution. Indeed, variance-area and spectral scaling differences between regions of complex topography (Grand Mesa and the Swiss Alps) and smooth topography in North Dakota suggest the hypothesis that BSC multi-scaling behavior may be attributed to scattering mechanisms controlled by heterogeneous stratigraphy and surface roughness at small mesoscales (100's m) vis-à-vis snow mass modulated by regional winds (snow-form) at larger mesoscales (kms).
This work demonstrates time-varying spectral slopes are an emergent metric of the overall scattering behavior of heterogeneous snowpacks. More extensive multi-year multi-site analysis is required to investigate whether the scaling break positions identified here are fixed conditional on climate, topography and land-cover, that is cold region physiography, or they also exhibit interannual variability as the spectral slopes for example in response to changes in wind climatology.
Further research will focus on elucidating the scattering budget (volume scattering, surface and interface scattering) of heterogeneous snowpacks and developing model constraints and a data assimilation framework to capture snow physics heterogeneity at sub-km scale.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1. Figure S1(a). Spatial distribution of meteorological stations in the Swiss Alps region.          Table S1(a). Spectral slopes of Sentinel-1 BSC for the grassland region in Grand Mesa, CO in 2017.        Author Contributions: AB conceived the work; SM processed the Sentinel-1 data, conducted data analysis, and produced graphics and quantitative summaries with guidance from AB; SM and AB jointly wrote the manuscript.