Active Layer Thickness Estimation from X-Band SAR Backscatter Intensity

The active layer above the permafrost, which seasonally thaws during summer is an important parameter for monitoring the state of permafrost. Its thickness is typically measured locally, but a range of methods, which utilize information from satellite data, exist. Mostly, the Normalized Difference Vegetation Index (NDVI) obtained from optical satellite data is used as proxy. The applicability has been demonstrated mostly for shallow depths of Active Layer Thickness (ALT) below approximately 70 cm. Some permafrost areas including central Yamal are, however, characterized by larger ALT. Surface properties 5 including vegetation structure are also represented by microwave backscatter intensity. So far, the potential of such data for estimating ALT has not been explored. We therefore investigated the relationship between ALT and X-Band SAR backscatter of TerraSAR-X (averages for 10 x 10 m window) in order to examine the possibility of delineating ALT on a continuous and larger spatial coverage in this area and compare it to the already established method of using NDVI from Landsat (30 m). Our results show that the mutual dependency of ALT and TerraSAR-X backscatter on land cover types induces :::::: suggests : a connec10 tion of both parameters. A range of 5 dB can be observed for an ALT range of 100 cm (40 140 cm) and an R2 of 0.66 has been determined over the calibration sites. An increase of ALT with increasing backscatter can be determined. The RMSE over a comparably heterogeneous validation site with maximum ALT of > 150 cm is 20 cm. Deviations are larger for measurement locations with mixed vegetation types (especially partial coverage by cryptogam crust) with respect to the spatial resolution of the satellite data. 15


Introduction
Permafrost is defined as soil or rock that remains at or below 0 • C for two or more consecutive years (Harris et al., 1988) and currently underlies some 25 % of the Earth's land surface (Huggett, 2007).Due to global warming extensive areas where permafrost is presently within a degree or two below the melting point could be destabilized (Smith, 1990).At the global scale, increased ground temperatures could facilitate further climatic changes by releasing greenhouse gases that are currently sequestered in the upper layer of permafrost by increasing the annual thaw depth (Kane et al., 1991;Gomersall and Hinkel, 2001;Shiklomanov and Nelson, 1999;Schaefer et al., 2011;Schuur et al., 2015).The top layer of ground subject to annual thawing and freezing in areas underlain by permafrost is defined as the active layer (Permafrost Subcommittee, 1988).In this layer most ecological, hydrological and biochemical activities take place (Kane et al., 1991;Brown et al., 2000).Furthermore it is an essential climate variable for monitoring permafrost regions (Schaefer et al., 2015), making it an important factor not only at the regional but also at the the global scale.The activelayer thickness (ALT) is predominately controlled by ambient temperature but is also influenced by insulation layers such as snow cover and vegetation, slope, drainage, soil type, organic layer thickness and water content (Leibman, 1998;Shiklomanov and Nelson, 1999;Hinkel and Nelson, 2003;Kelley et al., 2004;Melnikov et al., 2004;Vasiliev et al., 2008).Due to the interaction between these surface and subsurface factors that can be spatially highly variable, ALT may vary substantially over short lateral distances (Shiklomanov and Nelson, 1999;Leibman et al., 2012).
Near-surface permafrost area is projected to decrease within the next century (IPCC, 2013).Changes in activelayer thickness have been already observed for Yamal (Leibman et al., 2015), where ATL spatial patterns are unknown outside of the sites with in situ measurements.
Analytical procedures exist to estimate ALT, such as the Stefan solution (Harlan and Nixon, 1978) or the Kudryavtsev equation.While the Stefan solution links the seasonal thaw depth to the accumulated surface thawing-degree days, the Kudryavtsev equation accounts for the effects of snow cover, vegetation, soil moisture, thermal properties and regional climate (Kudryavtsev et al., 1974;Yershov, 1998;Shiklomanov and Nelson, 1999).These methods, although accurate, are labor-intensive and limited in spatial coverage (Gangodagamage et al., 2014).
While traditional in situ measuring methods like probing with metal rods are very inefficient at the regional scale, remote sensing holds great potential to delineate ALT with continuous and larger spatial coverage.ALT can be derived by empirical relationships between probe measurements and a physical attribute measurable by remote sensing (Schaefer et al., 2015).Investigations have been made using the normalized difference vegetation index (NDVI) (McMichael et al., 1997;Kelley et al., 2004), digital elevation data and land cover classes (Nelson et al., 1997;Peddle and Franklin, 1993).Especially optical data have been used to retrieve vegetation characteristics (see Table 1).A combination with derivatives of digital elevation models (DEMs) has been shown to be of added value (Peddle and Franklin, 1993;Leverington and Duguay, 1996;Gangodagamage et al., 2014).Application of high-resolution optical satellite data in combination with high-resolution digital elevation data from airborne measurements have been shown to be useful for mapping ALT but are very limited in spatial extent.Subsurface thermal properties are also derived from land cover classes, but applicability has been demonstrated only for the permafrost transition zones so far (Bartsch et al., 2016).
Recently, subsidence rates have been used as input for modeling ALT (Schaefer et al., 2015).Synthetic aperture radar has been exploited using interferometric analyses (In-SAR, which provides seasonal ground subsidence) in combination with soil properties to estimate ALT without using empirical relationships with probing data (Schaefer et al., 2015).
Most previous remote-sensing approaches (Leverington and Duguay, 1996;McMichael et al., 1997;Sazonova and Romanovsky, 2003;Schaefer et al., 2015) have utilized data with spatial resolutions of 30 m and coarser and been conducted in areas with shallow ALT (less than approximately 70 cm; see Table 1).Many regions such as the Yamal Penin-sula are, however, characterized by a larger ALT range.Deeper active layers have been modeled by analytical approaches (e.g., Sazonova and Romanovsky, 2003) or by incorporating only a few ALT classes (e.g., Leverington and Duguay, 1996).For Yamal, previous tests indicate that ALT below 70, within the range of 70-100 and above 100 cm can be distinguished using NDVI (Leibman et al., 2015).
SAR backscatter intensity has so far not been investigated for ALT estimation.Radar backscatter at X-band is also related to vegetation coverage, especially shrubs (Duguay et al., 2015), due to volume scattering, similarly to the NDVI.The microwave signal interacts with leaves in the shrub canopy due to the comparably short wavelength (∼ 3 cm).Leaf size of willows often exceeds this wavelength, and stems can have significantly larger diameters (Widhalm et al., 2016).Also vegetation water content may influence the return signal, but no dedicated investigations for tundra species exist.The overall backscatter intensity of a certain surface area is also influenced by surface roughness with respect to the wavelength, as well as by soil moisture.A higher moisture content leads to a higher dielectric constant and therefore higher backscatter values and additionally a reduction in penetration depth.X-band investigations in tundra (Lena Delta) suggest that such variations can occur (Zwieback et al., 2016), but results from Antonova et al. (2016) showed no sensitivity to precipitation over the same area.
In this study we hypothesize that there is a relationship between local ALT and X-band measurements, based on the influence of ALT affecting features on backscatter strength.Like ALT, backscatter is dependent on vegetation cover.Furthermore shrubs, which can be monitored with X-band data, can be related to snow cover due to their characteristic of retaining snow (Domine et al., 2016).Moreover the terrain in this region is closely linked to drainage and water content, which influence ALT.These characteristics in turn influence the predominant vegetation, which, including soil moisture, can be captured with microwave backscatter.We use in situ records from several sites in the proximity of a long-termmonitoring site on the Yamal Peninsula and discuss the results with respect to previous approaches which use remotely sensed information as a proxy for ALT.
2 Study area and datasets

The Vaskiny Dachi monitoring site
The Vaskiny Dachi research station (70 • 20 N, 68 • 51 E) was established in 1988 and is situated on the central Yamal Peninsula in a system of highly dissected alluviallacustrine-marine plains and terraces.It is located within a region of continuous permafrost where tundra lakes and river flood plains are the most prominent landscape features (Leibman et al., 2015).Dense dwarf shrubs (Betula nana) are widespread in the watersheds.Well-drained hill-  Leibman, 2014).
The study area is characterized by continuous permafrost.ALT ranges between 40 cm in peat and up to 120 cm on sandy, poorly vegetated surfaces (Melnikov et al., 2004;Vasiliev et al., 2008;Leibman et al., 2011Leibman et al., , 2012)).There are extremes observed on high-centered sandy polygons, which can be 1-1.5 m high and up to 10 m in diameter, with an active layer exceeding 2 m.Spatial changes in ground temperature are controlled by the redistribution of snow which results from strong winds characteristic for tundra environments and the highly dissected relief of central Yamal (Dvornikov et al., 2015).The lowest ground temperature is characteristic for hilltops with sparse vegetation where snow is blown away.The warmest are areas with high willow shrubs, due to the retention of snow, found on slopes, in valleys and lake depressions.While the spatial distribution of ALT depends on lithology and surface covers, temporal fluctuations are controlled by ground temperature, summer air temperature and summer precipitation (Leibman et al., 2015).

In situ measurements
In 1993 a Circumpolar Active Layer Monitoring (CALM) site was established at Vaskiny Dachy, placed on the top and slope of a highly dissected plain affected by landslides, with sandy to clayey soils.The CALM program, designed to observe the response of the active layer and near-surface permafrost to climate change, currently incorporates more than 100 sites.The International Permafrost Association serves as the international facilitator for the CALM network, which is now part of the WMO Global Terrestrial Network for Permafrost (GTN-P) (Brown et al., 2000).
Within the Greening of the Arctic (GOA) project of the International Polar Year (IPY), which was funded by NASA's Land-Cover and Land-Use Change (LCLUC) Program, three additional monitoring sites were established in the Vaskiny Dachi area (Walker et al., 2009).Study sites were established within areas with more or less homogeneous vegetation.The site Vaskiny Dachi-1 (VD-1) has clay soils, and the vegetation is heavily grazed sedge and dwarf-shrub-moss tundra.Soils at Vaskiny Dachi-2 (VD-2) are a mix of sand and clay; its vegetation is heterogeneous but dominated by dwarf birch, small reed grass and sedge, cowberries and mosses.At Vaskiny Dachi-3 (VD-3) the soils are sandy and the vegetation is a dry dwarf-shrub-lichen tundra (Walker et al., 2009).
The ALT is measured by a metal probe according to CALM protocol.This involves a late-season mechanical probing, in this case late August, when ALT is near its endof-season maximum.A 1 cm diameter graduated steel rod is inserted into the soil to the depth of resistance to determine the depth of thaw (Brown et al., 2000).
ALT is measured at a spacing of 10 m within the 100 × 100 m grid at the CALM site, resulting in 121 measuring points.The VD sites each feature five transects.At VD-1 and VD-2 these transects form grids of 50 × 50 m.Transects are 12.5 m apart, and ALT is measured every 5 m, resulting in 55 measurement points per site.The transects at VD-3 are arranged in areas of homogeneous vegetation (Walker et al., 2009).The site of VD-3 features higher ALT values, most likely because of the present sandy soils, which yield a greater conductivity and water permeability (higher convective heat exchange).The CALM grid site is far more heterogeneous than the other VD sites and holds patches of dry cryptogam crust, grasses and mosses; low and high shrubs; and some wet sedge spots.Cryptogam crust is encountered at the concave hilltop, while high shrubs were mostly located at the landslides (Fig. 8).Here, ALT is locally higher due to the high salinity of clayey deposits which contain no ice under negative temperature and do not resist to probing.
In August 2015, we carried out a dedicated vegetation survey of each CALM grid point, where we determined the dominant vegetation cover within a 3 × 3 m area (Fig. 1).The following classes are distinguished: cryptogam crust, low shrubs (< 15 cm), medium shrubs (15-30 cm), high shrubs (> 30 cm), grass and moss, a class where sedges dominate and classes of mixed vegetation.Further information on vegetation has been collected outside of the ALT measurement sites in August 2014.Over 60 points were registered, but only 36 of these points could be further used because of low homogeneity with respect to the spatial resolution of the satellite data.This survey included the most dominant classes of the region and therefore covered more types than can be found at the VD sites or the CALM grid: low shrubs (< 20 cm), medium shrubs (20-60 cm), high shrubs (> 60 cm), cryptogam crust, and a mixture of grasses and sedges.
Furthermore we conducted moisture measurements at the CALM grid.We used the Delta-T WET Sensor with a handheld HH2 Moisture Meter to measure the moisture content of the top 5 cm at each grid point on three dates in August 2015.

X-band data
X-band data have so far been used to investigate surface deformations like thaw subsidence and frost heave (Beck et al., 2015;Zhang et al., 2016;Wang et al., 2016), to monitor tundra shrub growth (Duguay et al., 2015) or to date drained thermokarst lake basins (Regmi et al., 2012) related to permafrost research.Backscatter information from data of the TerraSAR-X mission have been used for this study.The digital elevation model available from the TanDEM-X mission has been used as an auxiliary dataset for TerraSAR-X data preprocessing.
The German national SAR satellite system TerraSAR-X is based on a public-private partnership agreement between the German Aerospace Center (DLR) and EADS Astrium GmbH.It was launched in June 2007 and started its operational service at the beginning of 2008 (DLR, 2009).The satellite flies in a sun-synchronous, dawn-dusk orbit with an 11-day repeat period.TerraSAR-X features an advanced high-resolution X-band synthetic aperture radar with a center frequency of 9.65 GHz, corresponding to a wavelength of about 3.1 cm.TerraSAR-X operates in SpotLight, StripMap and ScanSAR mode with various polarizations.In this study HH (horizontally sent and horizontally received) polarized images of StripMap mode were used, which image strips of 30 km width at 3 m resolution (Werninghaus et al., 2004).
Six images from August 2014 and 2015 (three images per year) were obtained as SSC (single-look slant range complex) and have been acquired in the same ascending orbit and beam (incidence angle range 27.3-30.3• ).
The TanDEM-X mission is an extension of the TerraSAR-X mission, co-flying a second satellite of nearly identical capability in a close formation.This enables the acquisition of highly accurate cross-and along-track interferograms without the inherent accuracy limitations imposed by repeatpass interferometry due to temporal decorrelation and atmospheric disturbances (Krieger et al., 2007).In this study the TanDEM-X Intermediate DEM (IDEM, ∼ 12 m pixel spacing, < 10 m absolute horizontal and vertical accuracy) was used for terrain correction, which, compared to the final TanDEM-X DEM product, might have limitations with respect to product quality and completeness (Wessel, 2013 ) and compare the already-established approach of using NDVI for ALT delineation to the approach introduced in this study of utilizing TerraSAR-X backscatter.

Methodology
In microwave remote sensing the radar backscatter is dependent on sensor parameters like incidence angle, polarization and wavelength and also on geometric parameters such as surface roughness and vegetation structure, as well as soil properties.Shorter wavelengths do not penetrate as much as longer wavelengths into vegetation and soil; therefore short wavelengths like X-band rather yield information about the upper layers of vegetation (Ulaby et al., 1982).The assumption for this study is that surface roughness variations play a minor role regarding spatial backscatter differences across the study site.Backscatter increases with increasing vegetation height for X-band in tundra, which originates from volume scattering and double bounce (leading to higher backscatter) rather than surface roughness (Ullmann et al., 2014).It can be also expected that soil moisture variations are not reflected in X-band measurements when vegetation cover is present.The assumption is that volume scattering and double bounce in vegetation are the main contributors to spatial differences in backscatter.Several studies have exemplified the separability of tundra shrubs from their surroundings (Ullmann et al., 2014;Duguay et al., 2015).In Antonova et al. (2016) it is shown that X-band time series analysis allows for a clear discrimination of major landscape elements in tundra regions.
The local vegetation patterns are influenced by terrain and soil moisture and also correlate with snow cover thickness, which are all ALT-influencing factors (Shiklomanov and Nelson, 1999;Gomersall and Hinkel, 2001;Kelley et al., 2004).Areas with shrubs have higher snow cover, which prevents the ground from cooling in the winter.The ALT might therefore also be higher than in the surrounding area.Based on results of previous studies which utilized the vegetation in-dex NDVI (Table 1) and the mutual dependency of NDVI and radar backscatter on vegetation coverage, it is expected that a relationship between X-band backscatter measurements and ALT is given.We compiled a dataset based on TerraSAR-X which allows the investigation of this relationship.This included for SAR common preprocessing steps to account for variations due to viewing geometry.
Six TerraSAR-X images from August 2014 and 2015 were processed (three images per year).It is assumed that within this time stable phenological conditions can be expected.Utilizing the software NEST (Next ESA SAR Toolbox), range-Doppler terrain correction was performed with a TanDEM-X Intermediate DEM (∼ 12 m resolution) in order to orthorectify the images and to compensate for distortions due to topographical variations and the tilt of the sensor.Images were processed to a pixel spacing of 2 m, and a radiometric normalization was applied to account for incidence-angledependent sensitivity.The so-called resulting σ 0 values were then converted into decibels.The term backscatter refers in the following to these values, which represent the normalized measure of the radar return.SAR data are affected by so called speckle, which is a noise-like effect.It can be understood as an interference phenomenon due to a number of scatterers within each resolution cell.The images were therefore further averaged over time, and a spatial filter (average value of the cells in the neighborhood was calculated: 5 × 5 cells -10 m) was applied to subdue this noise.
Backscatter and NDVI values for the sites VD-1, VD-2 and VD-3 were extracted and compared to the mean ALT values of 2014 and 2015 of each measuring point.The relationship of backscatter values and ALT was examined by varying representations.Box plots for ALT classes and for backscatter classes are shown in Fig. 4. ALT values were separated into 10 cm classes, and the backscatter classes ranged 1 dB, allowing a representative number of sampling points per class (7 and 13 points minimum per class, respectively).σ 0 values as well as NDVI values were additionally compared directly to ALT by scatterplots (Fig. 5).Fitted linear functions were applied to characterize the relationship between TerraSAR-X backscatter and NDVI as well as ALT values of the sites VD-1, VD-2 and VD-3.The coefficient of determination (R 2 = 1 − (y i −y) 2 , the proportion of the variance in the dependent variable that is predictable from the independent variable) was calculated for the regression lines which involved all VD sites, as well as for regression lines for each VD site separately (Table 2).Validation has been undertaken using ALT measurements at the CALM grid.Root mean square error (RMSE) was calculated, representing the modeled ALT (linear regression of all VD sites) versus the measured ALT at the CALM site.Moreover χ 2 was determined, which also accounts for observational uncertainties.An observational uncertainty of 4 cm was assumed for the probe measurements, which has been investigated by Leibman (1998) for sandy soils (2-4 cm) in this region.The mod-Table 2. R 2 between X-band backscatter and NDVI (22 July 2014 and 10 August 2015) and ALT.R 2 has been calculated for all calibration sites combined (VD-1,2 and 3) and separately (ALT range for VD-1: 56-108 cm; VD-2: 45-102 cm; VD-3: 90-140 cm).RMSE values represent the modeled ALT (linear regression of sites VD-1, VD-2 and VD-3) versus the measured ALT at the CALM site.χ 2 statistics compare the modeled and measured ALT at the CALM site under consideration of observational uncertainties.

Dataset
R 2 (VD-1, RMSE (cm)  eled and measured ALT values at the CALM grid were further compared by scatterplots depicting the different vegetation types (Fig. 7) in order to investigate their impact.Backscatter statistics have also been derived for different vegetation classes from locations of the 2014 survey outside of the ALT measurement sites (Fig. 2).These locations represent relatively homogeneous sites (with respect to TerraSAR-X spatial resolution).The ALT sites, especially the CALM grid, are comparably heterogeneous and therefore of limited applicability for determination of backscatter dependence on vegetation type.The relation of vegetation type and soil moisture was examined for the CALM grid using moisture measurements of August 2015 (Fig. 3).

Results
The assumption that backscatter increases with increasing amount of vegetation could be confirmed for the Vaskiny Dachi area (Fig. 2).There is a difference of about 2 dB between the median for shrubs less than 20 cm and those larger than 60 cm.σ 0 values for the grass-sedge class do, however, exceed these values.Cryptogam crust backscatter is on the same order of magnitude as shrubs between 20 and 60 cm height.Although the sparse vegetation in these areas consists mostly of lichen and volume scattering within is negligible, these spots often show higher surface roughness or even hummocks, which may lead to a rise in backscatter amount.The box plot of Fig. 3, which shows the relationship between soil moisture and vegetation types at the CALM grid, reveals that the lowest soil moisture is encountered for areas with www.the-cryosphere.net/11/483/2017/The Cryosphere, 11, 483-496, 2017  cryptogam crust, while higher shrubs and especially sedges dominate in areas of high soil moisture.Class statistics (Fig. 4) indicate a relationship between σ 0 and larger thaw depths.Low backscatter values dominate in areas with low ALT, and high backscatter values coincide with high ALT.However, the median σ 0 for shallow ALT does not decrease with decreasing ALT at the same rate as for deeper ALT.The scatterplots of the filtered σ 0 and ALT values of the sites VD-1 to VD-3 also indicate this correlation (see Fig. 5).It also becomes apparent that the change in slope that is visible in the box plot of Fig. 4 is caused by different backscatter values of the sites VD-1 and VD-2 (Fig. 5).Nevertheless σ 0 increases generally with increasing ALT.The overall higher ALT values of VD-3 are reflected by their higher backscatter values.A range of 5 dB can be observed for an ALT range of 100 cm (40-140 cm).
A coefficient of determination of 0.66 was obtained for the linear regression of backscatter and ALT values (see Table 2).The mathematical form of the regression line is given in Fig. 5.The standard error of the intercept is 14.00 and  0.96 for the slope, respectively.R 2 for the individual VD sites showed higher values for VD-3 than for VD-1 and VD-2, which both feature lower ALT values.The linear regression which incorporated all calibration sites (VD-1, VD-2 and VD-3) yielded an RMSE of 20 cm at the CALM grid site and 25 cm for χ 2 .Some VD points showed a backscatter variability of more than 1 dB between the acquisitions of 2014 and 2015.An exclusion of these points would slightly increase the coefficients of determination, but no positive effect could be found with RMSE values at the CALM grid.
The relationship found between TerraSAR-X backscatter and ALT is not as pronounced at the CALM validation site as at the other plots.In particular, a patch at the highest elevation of the CALM grid was expected to show higher ALT values according to the calculations from the satellite data (Figs.7 and 6).There are also some spots with slightly higher ALT than predicted.This applies to ALT larger than 125 cm.With the exception of the area around the hilltop, the pat-terns derived with TerraSAR-X resemble those of the in situ measurements.
A deeper active layer can be found in areas with high shrubs as well as cryptogam crust at the CALM site (see Fig. 6).Extremes of ALT can further be encountered at the clay-rich landslides with relatively sparse vegetation, classified as "other" in Fig. 6.Thinner active layers were encountered at zones with grass and moss or low shrubs (see Fig. 6).Residuals increase for depths larger than 125 cm, especially in case of dominance of cryptogam crusts.
In Fig. 7 a map of the calculated ALT is given for the entire TerraSAR-X scene (open water bodies are masked out).Linear features are expected to be false values as they can be attributed to artificial objects.They show low as well as high ALT values depending on surface roughness and material (air strip and rail track, respectively).Values across the scene range between 60 and 180 cm.ALT is higher in drained or partially drained lake basins.
www.the-cryosphere.net/11/483/2017/The Cryosphere, 11, 483-496, 2017 Derived scatterplots of NDVI and ALT values also reveal a relationship within the observed NDVI range of 0.46-0.65 (Fig. 5).The standard error of the intercept is 9.21 for 22 July 2014 and 11.60 for 10 August 2015, and 15.80 and 20.21 for the slope, respectively.Both NDVI images showed even larger coefficients of determination (about 0.73-0.75)than the TerraSAR-X approach (Table 2).The achieved RMSE at the validation site is, however, about 7 cm larger than when using the TerraSAR-X backscatter values.Furthermore, when using only site VD-3, which has the highest range and total thickness of the active layer, comparable to the values at the CALM grid, the linear regression for the backscatter values has a coefficient of determination of 0.622, while for NDVI values it is only 0.017 and 0.002, respectively (Fig. 5).The NDVI-derived ALT values for the CALM site range at most between 70 and 100 cm for 22 July 2014 and between 60 and 110 cm for 10 August 2015, while measured values have a range of 60-150 cm.

Discussion
The assumption that X-band backscatter variations result mostly from differences in volume scattering in vegetation over tundra does not seem to be valid for the selected sites.Radar backscatter is dependent on volume scattering, surface roughness and soil moisture.The influence of all these effects can be perceived in Fig. 2. For shrubs a major contributor to backscatter is the volume scattering that takes place within the vegetation.A rise in volume indicated by shrub height clearly gives rise to backscatter amount.This effect is also described in Duguay et al. (2015), where areas with high shrubs show higher backscatter values.A pronounced relationship was, however, not found for X-band in HH by Ullmann et al. (2014) over the MacKenzie Delta.They applied a smaller spatial filter of 3 × 3 and used data from the end of the growing season (mostly September) when plant decay is already expected to take place.A season-related reduction of leaves on shrubs could lead to a decrease in volume scattering and therefore lower backscatter values.The magnitude of backscatter for cryptogam crust, which predominantly occurs on sandy soils, can be attributed neither to volume scattering in vegetation nor to soil moisture (Figs. 2  and 3).Surface roughness or partial interaction within the upper soil may lead to higher backscatter than for grass and low shrubs < 20 cm.
High soil moisture is typical for the class sedges (Fig. 3), giving rise to the backscatter amount.Additionally the so called double bounce effect, which may occur for sedges and grass in standing water, can lead to an increase of received backscatter (Fig. 2).
Using backscatter intensity at only one polarization (as available for this study) does not allow distinguishing between surface and volume scattering.Polarimetric analyses (using other combinations of H and V polarizations) may help to distinguish the scattering mechanism contributions (see e.g.Ullmann et al., 2014).Data acquired at different polarizations are, however, not available for the study site.
The above described influences on radar backscatter can be linked to ALT-controlling factors.The effect of shrubs on ALT has been described contradictorily by different authors.On the one hand shrubs have been said to have a cooling effect due to shading in the summer (Blok et al., 2010;Lawrence and Swenson, 2011;Pearson et al., 2013), leading to shallower ALT.In other publications (Domine et al., 2016;Myers-Smith and Hik, 2013) shrubs have been linked with ground warming due to the isolating effect of snow cover.Shrubs trap wind-blown snow and limit snow erosion by wind.It seems that the prevailing effect of cooling or warming may be caused by the length of the winter or summer season.For the CALM site it can be shown that shrubs coincide with deeper ALT (Fig. 6).However it needs to be noted that shrubs are found here on saline clay, which, as stated before, can lead to higher ALT values measured by probing.In clayey saline soils (with ALT values > 130 cm at the CALM site) the freezing point is different from zero and probes can be inserted to greater depths (Leibman, 1998).
Soil moisture is another factor that influences microwave backscatter and ALT.It increases the backscatter amount due to the rise of the dielectric constant.It may also lead to higher ALT, caused by an increased heat flux and an enhanced conductive transfer of heat into subsurface layers (Gross et al., 1990;Shiklomanov et al., 2010).For the Yamal region the measured moisture content is influenced strongly by lithology.While sandy soils are found to be dry, clayey saline soils often hamper infiltration and show higher soil moisture or even standing water.Although barren sandy areas are dryer, they have been shown to have maximal ALT (Leibman et al., 2015) due to higher heat flux, increased by infiltration of rain water.Cryptogam crust is typically found on high-centered sandy polygons in the study area.For these points the following restrictions of the used approach become apparent.Most points for which the modeled ALT shows high deviations from the in situ data have or lie close to spots of cryptogam crust.The volume scattering for areas with cryptogam crusts is expected to be very low (as described in the Sect.4), but the recorded σ 0 is comparable to medium shrub heights which have a lower thaw depth.The higher σ 0 values could be due to higher surface roughness.The moisture content itself may also contribute to σ 0 ; however soil moisture values for areas with cryptogam crust have been shown to be very low (see Fig. 3).Heterogeneity regarding vegetation coverage may also contribute.Especially sites with mixed types show high deviations (see Fig. 6).
The redistribution of water and consequently also the occurring vegetation is controlled not only by lithology but also by topography (see Fig. 8), which has been shown to be useful in delineating ALT (Peddle and Franklin, 1993;Leverington and Duguay, 1996;Gangodagamage et al., 2014).Although we did not use topographic information in our study in order to derive ALT, it is indirectly introduced into our measurements through its effects on vegetation and moisture.For future studies the potential of refining the backscatter approach by incorporating topographic information could be explored.
The comparison of the produced ALT map to the ALT measurements at the CALM grid showed that some points within the validation dataset from the CALM grid are not well represented by the map (Fig. 7).These sites also deviate in the probe data.For instance for one of these points an ALT of > 170 cm was measured in 2014, which is about almost double the values of the surrounding points, and in 2015 only 116 cm was registered.Such an extreme variability of ALT could be explained by an interface between a sandy active layer and a clayey permafrost at this location.
Regarding the delineated ALT map for the entire TerraSAR-X scene (Fig. 7), it needs to be considered that neither the calibration data (VD sites) nor the validation site (CALM grid) included lowlands with extensive wetlands, as can be found in this region.Because of the lack of ALT measurements for these areas, the shown map is only representative for parts of the region, while lowlands would need further verification and could be masked out using a DEM.The higher ALT in drained lake basins does agree with findings of Schaefer et al. (2015) around Barrow.They, however, argue that their algorithm actually overestimates ALT at these locations.
The comparison of Landsat-8-derived NDVI values and ALT revealed a negative correlation (see Fig. 5), which is contrary to most studies of other regions (Gangodagamage et al., 2014;McMichael et al., 1997).However Leibman et al. (2015) previously obtained similar results for the Yamal region at the CALM grid.Results suggest that NDVI is higher for sites with grasses, mosses and sedges than for medium to high shrubs (Salix), although the near infrared used is influenced by plant cell structure and vegetation biomass.These shrubs do, however, coincide with very wet soils (Fig. 3) and are growing within partially waterlogged depressions.The sensitivity of NDVI to water (Raynolds and Walker, 2016) might have an impact over these sites.Furthermore a differ-ence between the training datasets becomes apparent.Both VD-1 and VD-2 lie within a similarly lower ALT range, but especially the acquisition of 22 July 2014 shows clearly higher NDVI values for VD-1 than for VD-2.This points to different vegetation types.A difference is also observed for the X-band backscatter, where VD-1 shows slightly lower backscatter values than VD-2.The backscatter differences could be explained by a slightly higher surface roughness, which is, however, not pronounced enough to have a sufficient influence on the site's snow cover or even ALT.Moreover vegetation at VD-2 is rather heterogeneous and also includes patches of sedges or reeds, which could increase the amount of backscatter.While VD-1 and to a small amount even VD-3 also shows sedge vegetation, these sandier sites show a different kind of grass (Carex bigelowii instead of Calamagrostis holmii).Moreover a clear difference between Landsat acquisitions of 22 July 2014 and 10 August 2015 exists due to differences in vegetation and their respective phenological cycles (Bratsch et al., 2016), which are in turn influenced by terrain features and consequent draining conditions.
The advantages and disadvantages of the new approach with respect to previous studies could be demonstrated by application of the NDVI approach over the same site and using the same training dataset.Investigations presented in this paper showed that the introduced approach of using TerraSAR-X backscatter values to delineate ALT values is suitable to provide estimates higher than 30 m resolution over unsaturated soils with ALT ranging from 40 to 140 cm in areas outside of high-centered sandy polygons.One previous study that was conducted within comparable ALT ranges used NDVI and land cover information derived from Landsat data in combination with DEM data to derive three classes of ALT (Leverington and Duguay, 1996).A 93 % agreement rate for three different ALT classes was obtained.In contrast to our study, Leverington and Duguay (1996) used "bestestimate" ALT values from either a pit value or the average of pit and probe measurements, and fixed ALT classes.In our study we used measurements for single points from grid points within a 100 × 100 m raster of high heterogeneity.All but one measured ALT value fall into only one ALT class (70-150 cm) used by Leverington and Duguay (1996).The given accuracy can therefore not be compared.
The used TerraSAR-X data have been acquired in StripMap mode, which has a swath width of 30 km.This sensor can, however, also acquire data over 270 km when using the Wide ScanSAR mode (40 m resolution).This would allow the transfer of the approach to larger regions.The incidence angle range investigated thus far is, however, very limited.Differences in the described backscatter-ALT relationship due to incidence angle effects would need to be considered.

Conclusions
The common dependency of ALT and X-band backscatter values (HH, approximately 30 • incidence angle) on land cover types as well as the interrelation of terrain, vegetation, soil moisture and snow cover yields a correlation which can be used to derive ALT with an RMSE of 20 cm over a longterm-monitoring site in central Yamal.It can be shown that in general higher ALT values correspond with higher backscatter values for the tested ALT range of 40-140 cm.The accuracy is lower over sites with mixed vegetation types within the pixels.Especially contributions from areas with little vegetation (cryptogam crusts) alter the relationship between backscatter and ALT.Soil moisture and/or surface roughness influence the signal over these sites.Polarimetric SAR analyses which allows distinguishing different scattering mechanisms might be suitable to tackle these issues.This could, however, not be tested due to unavailability of such satellite data.Results indicate a better performance than NDVI for higher ALT, but investigations with higher-spatial-resolution optical data would be required for confirmation.

Data availability
ALT information of the CALM site is available via GTNP or via the following link: https://www2.gwu.edu/~calm/data/webforms/r5_f.html(Leibmann, 2016).Soil moisture and temperature measurements as well as mean backscatter values for the CALM points will be provided via https://www.pangaea.de/.
Author contributions.Barbara Widhalm performed all data analyses, collected moisture and vegetation information at the CALM site, and compiled the manuscript.Annett Bartsch contributed to the development of the concept of the approach as well as to the manuscript.Marina Leibmann and Artem Khomutov collected the active-layer measurements at the long-term-monitoring sites as well as the vegetation information at sites outside of the ALT monitoring sites and contributed to the interpretation and discussion of the results.
Competing interests.The authors declare that they have no conflict of interest.

Figure 2 .
Figure 2. Box plot for backscatter values of various vegetation types.The points used were recorded within a field campaign in 2014.Backscatter values were extracted from the temporally averaged and spatially filtered image of August 2014 and 2015 acquisitions.

Figure 3 .
Figure 3. Box plot for mean soil moisture values of three acquisition dates in late August 2015 for vegetation types at the CALM grid.

Figure 4 .
Figure 4. Box plots showing median, minimum and maximum values; first and third quartile and outliers of the ALT; and backscatter values of the sites VD-1, VD-2 and VD-3.Left: σ 0 statistics for ALT classes (10 cm).Right: ALT statistics for backscatter classes (1 dB).

Figure 5 .
Figure 5. Upper left: comparison between σ 0 and ALT values at the sites VD-1 to VD-3.Points with differences of more than 1 dB between 2014 and 2015 are marked by circles.Linear regression for σ 0 and ALT values of all sites in black and for site VD-3 in red.Bottom: comparison between NDVI (22 July 2014 and 10 August 2015) and ALT values at the sites VD-1 to VD-3.Linear regression for NDVI and ALT values of all sites in black and for site VD-3 in red.

Figure 6 .
Figure 6.Comparison between predicted and measured ALT values at the CALM grid with differentiation between vegetation types for TerraSAR-X and NDVI approaches.

Figure 7 .
Figure 7. Left: calculated ALT map for all TerraSAR-X scenes, based on TerraSAR-X backscatter values.Right: calculated ALT map (background raster, based on X-band backscatter) for the CALM grid compared to in situ measurements (circles).

Figure 8 .
Figure 8.Comparison of topographic units (source CALM metadata, Earth Cryosphere Institute, Siberian Branch of the Academy of Sciences (SB RAS)) and vegetation type (survey of August 2015) at the CALM grid, illustrating the interrelation of certain topographic features and specific vegetation covers.

Table 1 .
Studies which used satellite data for determination of active-layer thickness (ALT): type of satellite data, accuracy and active-layer ranges.