This paper compares and integrates different strategies to characterize the
variability of end-of-winter snow depth and its relationship to topography in
ice-wedge polygon tundra of Arctic Alaska. Snow depth was measured using
in situ snow depth probes and estimated using ground-penetrating radar (GPR)
surveys and the photogrammetric detection and ranging
(phodar) technique with an unmanned aerial system (UAS). We found
that GPR data provided high-precision estimates of snow depth
(RMSE

Snow plays a critical role in ecosystem functioning of the
Arctic tundra environment through its impacts on soil hydrothermal processes
and energy exchange (e.g., Callaghan et al., 2011). Snow insulates the ground
from intense cold during the Arctic winter, limiting the heat transfer
between the air and the ground (Zhang, 2005). Snow depth affects active layer
and permafrost temperatures throughout the year (Gamon et al., 2012;
Stieglitz et al., 2003), and increased snow depth has resulted in permafrost
degradation (Osterkamp, 2007). Snow's insulating capacity enhances conditions
for active soil microbial processes and

In order to investigate controls of snow on ecosystem properties,
high-resolution estimates of snow are needed over large spatial regions. This
is especially true in ice-wedge polygon tundra, which dominates a large
portion of the high Arctic (Zona et al., 2011). The ice wedges develop when
frost cracks occur in the ground, and vertical ice wedges grow laterally over
years (Leffingwell, 1915; MacKay, 2000). Soil movement associated with
ice-wedge development creates small-scale topographic variations –

Snow depth characterization in Arctic tundra environments has traditionally been performed using snow depth probes (Benson and Sturm, 1993; Hirashima et al., 2004; Derksen et al., 2009; Rees et al., 2014; Dvornikov et al., 2015) or modeled using terrain and vegetation information (Sturm and Wagner, 2010; Liston and Sturm, 1998; Pomeroy et al., 1997). Recently, there have been several new techniques for estimating snow depth in high resolution and in a noninvasive and spatially extensive manner. Ground-penetrating radar (GPR) has been widely used to characterize snow cover in alpine, arctic and glacier environments (e.g., Harper and Bradford, 2003; Machguth et al., 2006; Gusmeroli and Grosse, 2012; Gusmeroli et al., 2014). GPR measures the radar reflection from the snow–ground interface, which can be used to estimate snow depth. GPR can be collected by foot, snowmobile or airborne methods. In addition, light detection and ranging (lidar) and photogrammetric detection and ranging (phodar) airborne methods have recently been used to estimate snow depth at local and regional scales (e.g., Deems et al., 2013; Harpold et al., 2014; Nolan et al., 2015). Both techniques measure the snow surface elevation, using laser in lidar or a camera with a structure-from-motion (SfM) algorithm in phodar. Both approaches allow us to estimate snow depth by subtracting the snow-free elevation from the snow surface elevation. While there is potential for providing detailed information about local-scale snow variability using lidar and phodar snow depth estimates, these techniques have not been extensively tested in ice-wedge polygonal tundra environments.

Such indirect geophysical methods are, however, known to have increased snow depth uncertainty relative to direct measurements (here ground-based snow depth probe measurements) (e.g., Hubbard and Rubin, 2005). The uncertainty of the snow depth probe measurements is sub-centimeter to several centimeters depending on the surface vegetation (Berezovskaya and Kane, 2007). In contrast, the snow depth estimates obtained using GPR can be affected by uncertainty associated with radar velocity, which depends on snow density (Harper and Bradford, 2003). In the environments with complex terrain such as ice-wedge polygonal tundra, GPR-based snow estimates could also be influenced by the errors stemming from radar positioning and ray path assumptions. The airborne lidar/phodar-based methods are subject to the errors associated with georeferencing, processing and calibration (e.g., Deems et al., 2013; Nolan et al., 2015). The accuracy of the airborne methods is usually several tens of centimeters, which is lower than the snow depth probe measurements.

Integrating different types of snow measurements can take advantage of the strengths of various techniques while minimizing the limitations stemming from using a single method. Bayesian approaches have proven to be useful for integrating multiscale, multi-type datasets to estimate spatially heterogeneous terrestrial system parameters in a manner that honors method-specific uncertainty (e.g., Wikle et al., 2001; Wainwright et al., 2014, 2016). Bayesian methods also permit systematic incorporation of expert knowledge or process-specific information, such as the relationships between datasets and parameters. In particular, snow depth is known to be affected by topography and wind direction (e.g., Benson and Sturm, 1993; Anderson et al., 2014; Dvornikov et al., 2015). To our knowledge, such Bayesian data integration methods have never been applied to estimate end-of-winter snow variability using multiple types of datasets.

The primary objectives of this study are to (1) compare point-scale snow depth probe, GPR and UAS-based phodar approaches for characterizing snow depth and the associated resolution and accuracy of the GPR and phodar methods; (2) quantify the spatial variability of end-of-winter snow depth in ice-wedge polygonal tundra landscape; (3) explore the relationship between snow depth and topography; and (4) develop a Bayesian method to integrate multiscale, multi-type data to estimate snow depth over a lidar digital elevation model (DEM) covering an ice-wedge polygonal tundra landscape. In Sect. 2, we describe our site and datasets, including snow depth probes, ground-based GPR and UAS-based phodar. In Sect. 3, we present the methodology to analyze the indirect snow depth measurements from GPR and phodar as well as to evaluate the heterogeneity of snow depth in relation to both microtopography (i.e., ice-wedge polygons) and macrotopography (i.e., large-scale gradient, drained thaw lake basins and interstitial upland tundra). We then develop a Bayesian geostatistical approach to integrate the multiscale datasets to estimate snow depth over the lidar domain. The snow measurement and estimation results are presented in Sect. 4 and discussed in Sect. 5.

Snow survey data were collected within a study site (approximately

Ice-wedge polygons are prevalent in the region, including low-centered
polygons in drained thaw lake basins and high-centered polygons with
well-developed troughs in the upland tundra (Hinkel et al., 2003; Wainwright
et al., 2015). The dominant plants are mosses (

Three long transects and four representative plots were chosen within the
study site to explore snow variability and its relationship to topography
(Fig. 1). Typical for low-gradient tundra terrain, ice-wedge
polygons and microtopographic variations
are superimposed on macrotopographic trends at the study site. The elevation
is higher in the center of the domain (interstitial upland tundra) and lower
near the drainage features in the south. The elevation is also relatively
lower in the drained thaw lake basins (DTLB) region, which is located in the
northeastern and northwestern edges of the study site. The four intensive
plots (A–D), each

Airborne lidar data were collected at the site on 4 October 2005 and used to
provide a high-resolution DEM of the snow-free ground
at

The majority of the snow depth data were collected on 6–12 May 2012, during
which no snowfall occurred and little change in snow depth was observed. Snow
depth was measured in the four intensive study plots and along three transect
lines (Fig. 1). Two sets of snow depth measurements using a snow depth probe
were collected. The “fine-grid” dataset was aimed to characterize the
fine-scale heterogeneity by

A second “coarse-grid” set of snow depth measurements covered the entire
area in plots A–D (

Ground-based GPR data were acquired over the four study plots and along the
three 500 m transects (Peterson et al., 2015b). The instrument (Mala ProEx
with 500 MHz antenna) was pulled on a sled. In each plot, we acquired the
GPR data at 0.1 m intervals (triggered by an odometer wheel) along 37 lines
of 4 m spacing. The start and end coordinates of each transect were surveyed
with a RTK DGPS and used to georeference the measurement locations. We
compared the distance from the wheel with the distance on tape and confirmed
that the difference is generally very small at this site. The error of
horizontal positioning is estimated to be about 0.1

The GPR reflection signal from the bottom of snowpack (i.e., the ground
surface) was clear, which allowed us to measure the travel time between the
top and bottom of snowpack. The GPR processing routine consisted of
(1) zero-time adjustment, (2) average tracer removal, (3) picking the travel
time (manually with automated snapping in the
ProMAX^{®} software) of the reflected GPR signal
that traveled from the snow surface to the snow-ground interface and back to
the snow surface and (4) dividing this travel time
by two to obtain a one-way travel time between the snow surface and ground
surface. We processed the GPR data including travel-time picking before
accounting for topography. More details on GPR processing and theory can be
found in Annan (2005) and Jol (2009), while more detailed explanation on the
use of GPR in the tundra can be found in Hubbard et al. (2013). Differing
from previous studies (e.g., Harper and Bradford, 2003), we did not observe
echoes from snow layering. This is possibly because of the low antenna
frequency (500

Additional campaigns were carried out in 2013–2015 along the 500 m
transects only. UAS-based phodar data were collected in July 2013 and 2014 to
estimate snow-free ground surface elevation and in May 2015 for estimating
snow depth along the transects (Dafflon et al., 2015). To make these
measurements, we lifted a consumer-grade digital camera (Sony Nex-5R) to
about 40

The snow-free ground surface elevation measurements were then subtracted from the snow surface data to estimate the snow depth over the area. The snow depth probe measurements were taken at 183 locations along one of the 500 m transects to validate the phodar-based snow depth estimates. The locations were marked on a measurement tape, the start and end coordinates of which were surveyed with a RTK DGPS and used to georeference the measurement locations.

Snow depth can be inferred by multiplying GPR one-way travel time by radar
velocity. The radar velocity is determined with the dielectric constant, which depends on snow density in dry
snow (Tiuri, et al., 1984; Harper and Bradford, 2003). Depending on site
conditions, the snow density can vary in both vertical and horizontal
directions (Proksch et al., 2015). In this study, we assume that the
depth-averaged radar velocity – which is a function of depth-averaged snow
density – is sufficient for estimating snow depth. Thus, we compute the
radar velocity based on the known snow depth from co-located snow depth probe
measurements as (radar velocity)

Identifying co-located points between the GPR and snow depth probe
measurements, however, is not a trivial task in polygonal ground, since the
topography and snow depth can vary significantly within a meter. To address
these issues, we investigate the correlations between the radar velocity and
the submeter-scale variability of topography. To link the DEM elevation data
to the snow depth probe and GPR data, we selected the DEM elevation
(

We first evaluate the accuracy of the phodar-derived digital surface model
(DSM) by comparing it to the RTK GPS elevation measurements along the 500 m
transects acquired in 2011. Since the phodar-derived DSM was obtained at very
high lateral resolution (

To quantify the topographic effects in a complex terrain of ice-wedge
polygons and to partition micro- and macrotopography, we apply the wavelet
transform method to the airborne lidar DEM, which is commonly used for 2-D
image processing. The wavelet approach has been applied to DEM
in geomorphic studies, including
terrain analysis and landslide analysis (Bjørke and Nilsen, 2003;
Kalbermatten, 2010; Kalbermatten et al., 2012). In this transform, a
high-pass filter (a mother wavelet) and a low-pass filter (a father wavelet)
are applied to decompose the DEM into four images at each scale: low-pass,
high-pass horizontal, high-pass vertical and high-pass diagonal images. The
scale is a parameter in the wavelet transform, representing the width of the
filter and the scale of topographic variability (Kalbermatten et al., 2012).
Depending on the scale of the wavelet transform, the method yields different
images, corresponding to different scales of topographic features. We define
this wavelet scale as a

Correlations between the topographic metrics and snow depth are identified
using the Pearson product-moment correlation coefficient (Anderson et
al., 2014). At each spatial scale, we can compute micro- and macrotopographic
metrics such as slope and curvature as well as their correlations with
corresponding probe-measured snow depth. The curvature is of particular
interest, since Dvornikov et al. (2015) reported strong correlations between
snow surface curvature and snow depth as well as a dependency of this
correlation on the DEM resolution (the lower resolution led to lower
correlation coefficients). Note that the DEM resolution (0.5

A geostatistical approach has been used to investigate the spatial variability of snow depth as well as the scales of variability (Anderson et al., 2014). The standard geostatistical analysis starts with creating an empirical variogram, followed by estimating the spatial correlation parameters (Diggle and Ribeiro Jr., 2007). The spatial correlation parameters include (1) magnitude of variability (or spatial heterogeneity) as variance, (2) fraction of correlated and uncorrelated variability (nugget ratio), (3) spatial correlation length (range) and (4) covariance model (i.e., the shape of decay in the spatial correlation as a function of distance), such as exponential and spherical models. The covariance models (equivalent to variogram models) can be selected to minimize the weighted sum of squares during variogram fitting.

Such spatial variability and correlation are particularly important for
interpolating the sparse in situ snow depth measurements. The interpolation
can be applied not only for snow depth itself but also for snow surface (snow
depth plus elevation) or residual snow depth after removing topographic
correlations in the regression analysis. The same geostatistical analysis
method is therefore performed for snow surface and residual snow depth. We
used the geoR package in statistical software R (Ribeiro Jr. and Diggle,
2001;

We first define that the snow depth at each pixel

We assume a linear model to describe the snow depth field,

Multivariate normal distribution defined for each variable.

The data model for the snow depth probe measurements defines the snow depth
probe data

Radar velocity as a function of

The data model for the GPR data describes the GPR data

The posterior distribution of the snow depth conditioned on the datasets

Elevation and snow depth in plots A, B, C and D. Panel

Our results (based on the GPR data and tile probe data collected in May 2012)
indicate that the estimated radar velocity itself does not have a systematic
dependency on (or trend with) the snow depth or submeter-scale variability of
topography in May 2012 (Fig. 2a and b). The correlation coefficient between
the radar velocity and snow depth is 0.11 and between the radar velocity and
submeter-scale variability is 0.15. The variability of the radar velocity,
however, depends on those two factors (i.e., the variability of snow depth
and topography). Hence, the variability is higher in areas with shallower
snow depths (Fig. 2a). The SD of the radar velocity is
0.039

Using the mean velocity value in May 2012, the calculated GPR-based snow
depth estimates were compared with the snow depth probe measurements
(Fig. 2c). The correlation between the measured and estimated snow depth is
high (the correlation coefficient is 0.88), with the RMSE being 5.4

Figure 3 shows the lidar DEM as well as snow depth probe measurements and GPR estimates in plots A–D (May 2012). The lidar DEM (Fig. 3a) illustrates the difference among four plots in terms of both macro- and microtopography. For example, plot A has better defined polygon rims and troughs than plot D, although plots A and D are both low-centered polygons. Plot B has round-shaped high-centered polygons, while plot C has flat-centered polygons with well-defined troughs. The average size of polygons is also different, with smaller polygons in plot B and larger polygons in plots A, C and D. In addition, these figures illustrate some macrotopographic trends. Plot C is gradually sloping down towards the east, and plot D has a depression (i.e., DTLB) in the northeastern half.

In Fig. 3b shows the snow depth probe data collected using the fine-grid and
coarse-grid scheme collected in May 2012. The fine-grid data reveal the
detailed heterogeneity of snow depth around a single polygon. For example,
the fine-grid data in plot A show the snow depth distribution in a
low-centered polygon, including thin snow along the polygon rim and thick
snow at the polygon center and trough. Comparison of the fine-grid snow data
with the DEM reveals the microtopographic effect such that the troughs and
center of the polygon have larger snow depth. The coarse-grid dataset covers
the entire plot, although it is much more difficult to ascertain the
relationship between the snow depth and microtopography. The snow depth probe
data show that the snow depth is highly variable, ranging from 0.2 to
0.8

In Fig. 3c, the May 2012 snow depth was estimated from GPR using a fixed
radar velocity 0.25

Box plots of

In the region of the 500 m transects, the phodar-derived snow-free DSMs
(Fig. 4a) collected in July 2013 and August 2014 were first compared with the
RTK DGPS data (acquired in 2011) in Table 2, using the different schemes to
identify co-location. We included the results of both years to confirm the
consistency between the two snow-free DSM products at the same terrain.
Although all the schemes yielded an excellent accuracy (the RMSE less than
7.0

The phodar-derived snow depth (Fig. 4b) around the 500 m transects in May 2015 reveals a similar pattern of snow distribution as the GPR data in Fig. 3, having deeper snow in the troughs and the centers of low-centered polygons. The high-resolution image of the phodar data reveals more detail of the microtopographic effect than the interpolated image of the GPR data, particularly in the narrow troughs. The large aerial coverage also shows the minimal effect of macrotopography: while the elevation decreases towards south, the snow depth does not have a large-scale trend.

Root mean square error (RMSE) between the phodar-derived DSM and RTK DGPS elevation measurements based on the three schemes: nearest neighbor, average, and minimum elevation within the 0.5 m radius.

Figure 5 shows the box plots of the snow depth, elevation and
microtopographic elevation (

The absolute elevation distribution varies among the four plots (Fig. 5b),
although the snow depth for each of the plots has similar median values and
distributions. Plot A (well-defined low-centered polygons), for example, is
at a higher elevation than plots C (flat-centered polygons) and D
(low-centered polygons in DTLB), but the difference in the average snow depth
is not statistically significant (Table 3). The microtopographic elevation is
computed based on the wavelet transform with the scale of 32

Among the topographic indices of macro- and microtopography, the snow depth
in May 2012 (measured by the snow depth probe) was significantly correlated
only to the microtopographic elevation for all plots (Fig. 6a). The
correlation coefficient changes with the scale of the wavelet transform that
separates micro- and macrotopography. The correlation coefficient is up to

Correlation coefficients between snow depth and topographic metrics
as a function of the wavelet scale:

A significant correlation between snow depth and wind factor of
macrotopography was identified only in plot D (low-centered polygons in DTLB;
Fig. 6b). The correlation coefficient is up to 0.41 at the scale of
38

Estimated geostatistical parameters and covariance models for snow depth, snow surface and residual snow depth.

The estimated mean snow depth across the site (in meters) based on

The estimated standard deviation of snow depth across the site (in
meters) based on

Spatial correlation exists for all three variables in May 2012: snow depth,
snow surface and residual snow depth after removing the correlation to the
microtopographic elevation (Table 4). The correlation range is less than
20

Based on the snow-topography analysis in Sect. 4.2, we included the linear
correlation between snow and microtopographic elevation in Eq. (1) to
describe the snow variability in May 2012. We used the Shapiro–Wilk
normality test to confirm that the residual of the linear correlation,
defined by

The Bayesian estimated mean snow depth field over the full study domain in May 2012 (Fig. 7a) captures the effects of microtopography, such as more snow accumulation in polygon troughs and centers of low-centered polygons. The snow depth does not have any large-scale trends over the full study domain, which is different from the lidar DEM in Fig. 1b, but consistent with the interpolated GPR snow depths depicted in Fig. 3c and the measured UAS snow depth measurements depicted in Fig. 4b. The variability is larger in the southern region where there are high-centered polygons with deep troughs.

Estimated mean and confidence intervals from the Bayesian method,
compared to the probe-measured snow depth by

In addition, we compared this result (Fig. 7a) with the mean field
from estimating the snow surface
elevation and subtracting the ground surface elevation (Fig. 7b). In this
estimation, we used the same Bayesian algorithm
described in Sect. 3.4, except that we removed the topographic
correlations and assumed a standard geostatistical model for snow surface
(Diggle and Ribeiro Jr., 2007). In other words, we had the same algorithm
except that we modified Eq. (1) to

The estimated SD of the Bayesian-derived snow depth over the study domain (Fig. 8a) also shows a significant difference from the one based on the snow surface interpolation (Fig. 8b). This SD represents the uncertainty in the estimation. In both cases, the SD is smaller near the measurement locations along the transects and within the four plots. However, when the topographic correlation is included (Fig. 8a), the SD increases more rapidly as the pixel is farther away from the data points. This is due to the fact that the spatial correlation range is small for the residual snow depth after removing the topographic correlation (Table 4).

Validation of the snow depth estimates over the study area (plots A–D and
the 500 m transects) was performed by comparing the estimates with the snow
depth probe data (May 2012) not used in the Bayesian snow depth estimation.
We selected 100 points randomly from the snow depth probe data (all the
locations in plots A–D and the 500 m transects), using a uniform
distribution. The validation results (Fig. 9) show that the estimated
confidence interval captures the probe-measured snow depth. The estimated
snow depth is distributed along with the one-to-one line without any
significant bias. The estimation, including the topographic correlation
(Fig. 9a), has a tighter confidence interval and better estimation results
than the one from interpolating the snow surface (Fig. 9b). The RMSE for the
Bayesian method of estimating snow depth including the topographic
correlation is 6.0

Our analysis showed that GPR data provided the end-of-winter snow depth
distribution with high accuracy (RMSE

UAS-based phodar provided an attractive alternative for estimating snow depth
at high resolution over a large area. With much less labor and time,
UAS-based phodar can provide many more sample points than GPR. The
phodar-based snow depth, however, was less accurate than ground-based GPR or
snow depth probe measurements (RMSE

The phodar-based approach is expected to continue its trajectory of continuous improvements in terms of technical aspects, ease of use and accuracy. At the time of our campaign, we were allowed to use only a kite due to regulations, which led to a limited number of pictures that could be used to reconstruct the DSM. The accuracy will significantly improve with the use of a light unmanned aerial vehicle (UAV). Although UAS-based lidar acquisition technology continues to improve (e.g., Anderson and Gaston, 2013), as is expected to be a powerful alternative to characterize snow, the lidar device is still significantly more expensive than a conventional camera (roughly by factor of 100). Given that the vegetation height is fairly small in the Arctic tundra, the phodar technique is an affordable alternative.

For all the types of measurements, accurate positioning was critical in the polygonal tundra due to microtopography. The GPS snow depth probe (Snow-Hydro), for example, had a positioning error larger than several meters and required extra post-processing to correct the locations. However, measuring the RTK DGPS at all the snow depth measurement locations would not be realistic since it would take time. We found that having a measurement tape and measuring the start and end points by the DGPS was a reasonable approach, when the snow surface is smooth and hard. In this study, we used the snow depth probe data as the true snow depth to compare with other measurements (i.e., GPR, phodar, and Bayesian estimation). To improve the accuracy further, it would be necessary to quantify the uncertainty in the snow depth probe associated with the vegetation and other issues (Berezovskaya and Kane, 2007).

The end-of-year snow depth distribution at the ice-wedge polygons was highly variable over a short distance in May 2012. The snow depth was, however, significantly correlated with the microtopographic elevation, suggesting that the snow depth could be described by microtopography. The wind-blown snow transport leads to significant snow redistribution and fills microtopographic lows (i.e., troughs and centers of low-centered polygons) with thicker snow pack (e.g., Pomeroy et al., 1993). The redistribution also results in the smooth snow surface, following the macrotopography. The exception was observed at the edge of the DTLB, where the abrupt change in macrotopography led to increased accumulation in the depression. This is a similar effect to that observed along the riverbanks by Benson and Sturm (1993). Although the tundra ecosystem studies have focused on the effect of microtopography (e.g., Zona et al., 2011), the macrotopography also may be important when we characterize snow distribution over a larger area.

The “average” (or median) snow depth over a hundred-meter scale (i.e., the size of plots A–D), however, was fairly uniform across the site despite the different polygon types in May 2012. Plots A (well-defined low-centered polygons) and C (flat-centered polygons), for example, have different polygon types, but they have a similar median snow depth. This is because microtopography and microtopographic features (i.e., polygon troughs, rims) mainly control the snow distribution. Plot B (small high-centered polygons) is an exception, having smaller median snow depth than the other plots. Plot B has the largest variability in microtopography, characterized by the small round high-centered polygons, like numerous small mounds (Fig. 3). Such mounds are prone to erosion by the wind, and hence lead to less snow trapping and accumulation.

Identifying such correlations between snow depth and topography requires an effective approach to separate micro- and macrotopography. Our wavelet analysis revealed that the separation scale depends on the polygon sizes; for example, the larger polygons in plots A (well-defined low-centered polygons) and C (flat-centered polygons) lead to a larger separation scale than the smaller polygons in plot B (small high-centered polygons). It is a challenge to map macrotopography accurately over a larger area, particularly at the present site, where different types and sizes of polygons mix together. Although we used the same scale for the estimation, an improved polygon delineation algorithm will possibly enable us to separate micro- and macrotopography in the future (e.g., Wainwright et al., 2015).

The developed Bayesian approach enabled us to estimate the snow depth
distribution over a large area based on the lidar DEM and the correlation
between the snow depth and topography. Although this paper only used the
ground-based GPR and snow depth probe measurements collected at the same
time, phodar could be easily included in the same framework. The Bayesian
method allowed us to integrate three types of datasets (lidar DEM, snow depth
probe and GPR) in a consistent manner and also provided the uncertainty
estimate for the estimated snow depth. Taking into account the topographic
correlation explicitly improved the accuracy of estimation significantly
(RMSE

Our approach can be extended to snow estimates over both time and space. The correlations between snow depth and topography may change over time. In early and later winter, for example, the snow depth would be more affected by curvature and slope of microtopography, since the microtopographic lows (troughs and centers of the low-centered polygons) are not filled by snow. It would be possible to quantify the seasonal changes in the topography–snow correlations by designing a full season ground-based measurement campaign and acquisition of remote sensing snow depth measurements (by phodar or lidar) that monitored the same site over several years to account for interannual variability. The Bayesian method presented here is flexible enough to account for changes in parameters over time for the spatiotemporal data integration (e.g., Wikle et al., 2001). Although physically based snow distribution models can be used for the same purposes (e.g., Pomeroy et al., 1993; Liston and Sturm, 1998, 2002), it is difficult to parameterize all the processes, such as sublimation and turbulent transport. Our data-driven approach provides a powerful alternative to distribute snow depth based on various datasets.

In this study, we explored various strategies to
estimate the end-of-year snow depth distribution over an Arctic ice-wedge
polygon tundra region. We first developed an effective methodology to
calibrate GPR and phodar in the presence of submeter-scale variability of
topography. We then investigated the characteristics and accuracy of three
observational platforms: snow depth probe, GPR and phodar. The phodar-derived
snow depth estimates have great potential for accurately characterizing snow
depth over larger regions (with an RMSE of 4.6

We investigated the spatial variability of the snow depth and its dependency
on the topographic metrics. At the peak snow depth during our data
acquisition, the snow depth was highly correlated with microtopographic
elevation (the correlation coefficient of up to

The Bayesian method was effective at integrating different measurements to estimate snow depth distribution over the site. Although our estimation is based on the data collected from a one-time campaign, and the correlations to topography may change over time, the approach developed here is expected to be applicable for estimating both spatial and temporal variability of snow depth at other sites and in other landscapes.

Datasets are available upon request by contacting the corresponding author (Haruko M. Wainwright, hmwainwright@lbl.gov). The datasets are also available through the data digital object identifiers (DOIs) on the NGEE Arctic data portal (

In MCMC, we sample each variable sequentially conditioned on all the other variables. In other words, when we update one variable (or one vector), we assume that the other variables are known and fixed. After sampling thousands of sets of the variables, the distribution of those samples converges to the posterior distribution. Each vector is sampled as follows.

The snow depth field is sampled from the distribution

Posterior distributions during the Gibbs sampling.

The workflow of the Bayesian geostatistical approach from the data is included in Fig. B1. The snow depth probe data and lidar DEM are used to (a) identify the correlations between topography and snow depth (Sect. 3.3) after identifying the representative scale of macro- and micro-topography in the wavelet analysis, (b) quantify the variogram parameters and (c) create a process model in Eq. (1). The GPR data are analyzed to estimate the radar velocity and to quantify the correlations to the snow depth probe (Sect. 3.1). At the end (the last column in Fig. B1), all the parameters are assembled for the estimation using MCMC (Appendix A).

Workflow of the Bayesian geostatistical estimation.

The authors declare that they have no conflict of interest.

The Next-Generation Ecosystem Experiments (NGEE) Arctic project is supported by the Office of Biological and Environmental Research in the DOE Office of Science. This NGEE Arctic research is supported through contract number DE-AC0205CH11231 to Lawrence Berkeley National Laboratory. We gratefully acknowledge Stan Wullschleger in Oak Ridge National Laboratory, project PI. We thank Craig Tweedie at University of Texas, El Paso, for providing the lidar dataset and Sergio Vargas from University of Texas, El Paso, for providing kite-based landscape imaging advice. We also thank G. Chambon, N. Eckert and one anonymous reviewer for the helpful comments. Edited by: G. Chambon Reviewed by: N. Eckert and one anonymous referee