# Inferring Water Table Depth Dynamics from ENVISAT-ASAR C-Band Backscatter over a Range of Peatlands from Deeply-Drained to Natural Conditions

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## Abstract

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## 1. Introduction

_{d}and θ

_{w}, with θ

_{d}< θ

_{w}due to decreasing sensitivity with increasing aboveground biomass) in a normalization approach (with the equations given in Section 3.1.3) that is based on the assumptions that (i) for a certain vegetation state, σ° linearly depends on soil moisture; and that (ii) the incidence angle dependency changes over the year only due to changes of aboveground biomass and not due to soil moisture. Incidence angle dependency is parameterized directly from backscatter observations at multiple incidence angles (e.g., ERS scatterometers or Advanced Scatterometer (ASCAT)) typically by a second order Taylor series. The slope and curvature parameterize the vegetation dynamics for every day of the year and for every grid point.

_{d}= 25° and θ

_{w}= 40°, which have not been modified in subsequent applications since then. Since its introduction, the concept is routinely applied to generate soil moisture estimates from radar data [19]. Since soil moisture products have only been validated for mineral soils [20] due to the lack of easily accessible and good quality data from peat soils, it is unclear whether the concept can also improve the correlation between backscatter and soil moisture and/or water level over peatlands.

## 2. Data

#### 2.1. ENVISAT-ASAR Backscatter Intensity

#### 2.1.1. Environmental Scene Filter

#### 2.2. Ground-Based WTD Data in Peatlands

## 3. Methodology

#### 3.1. Incidence Angle Normalization and Cross-Over Angle Concept

#### 3.1.1. Linear Normalization with Constant Site-Specific Slope Parameter (β_{const})

_{r}= 40°:

_{const}(dB/degree) is the site-specific constant slope parameter of the linear regression between ASAR σ° (dB) and θ (degree) across all times, i.e., independent of water table, soil moisture, or vegetation conditions.

#### 3.1.2. Dynamical Site-Specific Slope (β_{doy})

_{doy}). At the coarse scale (ASCAT: 12.5 km), incidence angle dependency typically shows a clear seasonal pattern with shallow slopes (small negative β) in summer with denser vegetation and steep slopes (larger negative β) in winter with less biomass [34]. At the fine scale, which is, in our case, dominated by a mixture of grasslands and natural peatland vegetation, this might be often less systematic. Grasslands are typically cut once or several times per year leading to temporally low vegetation biomass in summer periods. As cut dates may vary considerably from year to year, it was not our goal to capture cut dynamics with our climatology time series.

#### Weighing

#### Ascending/Descending Incidence Angle Dependency

#### 3.1.3. Cross-Over Angle Concept

_{doy}, is used to normalize all ${\sigma}_{{\theta}_{\mathrm{i}}}^{\circ}(i)$ observed at time step i and arbitrary θ

_{i}to the cross-over angles θ

_{d}and θ

_{w}:

_{r}= 40°) at which all backscatter data will be compared:

_{r}-normalized backscatter values ${\sigma}_{{\theta}_{r}}^{\circ}\left(i\right)$ using:

_{r}and corrected for vegetation dynamics, and $\overline{{\sigma}_{{\theta}_{r}}^{d}}$ and $\overline{{\sigma}_{{\theta}_{r}}^{w}}$ are the temporally-averaged dry and wet reference backscatter coefficients at θ

_{r}. The quotient in Equation (6) corresponds to the scaling between 0 and 1 of Wagner et al. [18]. The second part of Equation (6) scales values to the average σ° range at θ

_{r}= 40° to make the magnitude of ${\sigma}_{{\theta}_{r},c}^{\circ}$ comparable across sites. Note that the effect of vegetation on the absolute level of ${\sigma}_{{\theta}_{r},c}^{\circ}$ is not corrected by the cross-over angle concept.

#### 3.2. Comparison of Backscatter with WTD Observations

#### 3.2.1. Application of Different Processing Configurations

- UNCOR: Uncorrected backscatter time series neglecting the incidence angle dependency
- CONST: Constant slope normalization (Section 3.1.1) [32]
- COASCAT: Application of the cross-over concept using site-specific β
_{doy}and curvature climatology from the corresponding ASCAT pixels at 12.5 km grid spacing (provided by TU Vienna). Approach as presented in Section 3.1.3, but additionally including curvature values for normalization (see Wagner et al. [18]). - COASAR: Application of the cross-over concept using site-specific slope climatology β
_{doy}derived from ASAR data (Section 3.1.2).

#### 3.2.2. Skill Metrics

## 4. Results

#### 4.1. Climatology of Site-Specific Slope Parameter Based on ASAR Data

_{doy}was similar for ASCAT and ASAR, with an offset towards lower (steeper) slope values for ASAR and a temporal shift of the peak value (here towards later times of the year for ASAR). On the other hand, there were also sites where the β

_{doy}for ASCAT and ASAR showed very different dynamics. For our peatland sites, the ASCAT slopes always showed a typical seasonal vegetation climatology, whereas for the ASAR data we also derived nearly constant incidence angle dependency over the year (Figure 4c).

#### 4.2. Comparison of Backscatter and Water Table Depth Time Series

_{r}= 40° using site-specific constant slope correction (CONST) and cross-over angle concept normalization based on slope climatologies derived from ASAR data (COASAR). Time series of descending and ascending data are shown separately in Figure 5a,b, respectively, and the corresponding scatterplot for both nodes is given in Figure 6 for the CONST method. The two figures show a number of typical features that we observed for many sites:

- There is a nearly linear increase of σ° with shallower water tables over most of the observed range of WTD, irrespective of the processing configuration (CONST, COASAR).
- The link between σ° and WTD becomes weaker towards the dry end of WTD. In Figure 6, the dependency seems to vanish at a WTD of approximately −1 m. We could not identify a systematic threshold WTD for all of our sites and, where present, it varied from about −0.5 to 1.5 m.
- The σ° time series enabled to monitor to some degree the interannual variability of WTD dynamics, i.e., anomalous dry or wet periods.
- The differences between descending and ascending σ° time series are remarkable during parts of the year, although not systematic over different sites.

#### 4.3. Skill Metrics for Different Backscatter Time Series

- The temporal correlation coefficient between σ° and WTD is rather independent of the mean WTD of a site. High R values of up to 0.8 can be observed for deeply-drained sites as well as for sites with shallow WTD (which comprise shallowly-drained, as well as natural sites).
- While at all sites a positive correlation can be observed, there is a strong variability of the absolute level of σ° across sites.

## 5. Discussion

#### 5.1. Differences between Descending and Ascending Data

#### 5.2. Impact of Different Processing Configurations

#### 5.2.1. Possible Optimization of Cross-Over Angles over Peatlands

_{d}and θ

_{w}directly from data analysis.

_{doy}together with a range of cross-angle combinations. For each pair of cross-angles, we evaluated the temporal skill metrics averaged across all drained and natural sites, and across both ascending and descending node. The pairs of cross-angles compose a grid of dry and wet cross-over angles from 15° to 45°, covering the range for which we determined the slope and assumed linearity. Under the assumption that the total backscatter amplitude due to changing moisture is smaller for states with high aboveground biomass than for states with low aboveground biomass [18], θ

_{d}must be smaller than θ

_{w}and the grid of cross-angle pairs is limited accordingly.

_{d}and θ

_{w}. Whereas R improves with decreasing θ

_{d}and θ

_{w}, anomR shows higher values with increasing θ

_{w}, but the anomR values are far less dependent on the cross-over angles than R. It is not possible to find a well-defined optimum for both metrics. A trade-off between optima of both metrics indicates optimal cross-over angles somewhere at θ

_{d}= 15° and θ

_{w}= 30°. It is however very questionable to suggest these angles as being more appropriate than the default angles. The fact that optimal angles for R would be in the range of negative angles (tested, not shown) indicates a general difficulty of the optimization of cross-over angles based on skill metrics. 66% of our slope climatologies showed a seasonal pattern that is negatively correlated with the seasonal pattern of the water table depth dynamics. We noticed, especially for sites with low R values, that R can be considerably improved by very low cross-over angles when the slope climatology showed this seasonal pattern. Low cross-over angles increase the influence of the vegetation dynamics on backscatter (see Figure 2). When the backscatter values themselves showed little correlation with WTD, the seasonal pattern of the slope climatology itself becomes a major predictor for WTD for low cross-over angles, which obviously results in spurious correlation. Backscatter time series from cross-over angles that were much smaller than 15° (not shown) were strongly smoothed with little remaining interannual variability due to the high impact of the invariant slope climatology. As a consequence, anomaly information gets lost which is, by its trend and averaged over all sites, seen in the pattern of anomR (Figure 10b).

#### 5.3. Potential and Limitations of C-Band Backscatter for Water Table Depth Monitoring

## 6. Conclusions

- backscatter is a good indicator for water table depth dynamics, but the interpretation seems to be more difficult for natural than for drained peatlands;
- the use of ENVISAT-ASAR (fine resolution) as opposed to ASCAT (coarse) has a high potential for future analysis over peatlands; and
- the use of various incidence angle correction techniques improved the correlation between backscatter and water table depth but differences between the various methods were small.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Illustration of the potential link between the remote sensing signal, here backscatter coefficient (σ°), and below-ground water table depth (WTD) via a ‘capillary bridge’, i.e., the capillary-connected top soil and vegetation moisture in shallow water table depth environments.

**Figure 2.**Illustration of the dependency of backscatter coefficients (σ°) to incidence angles (θ) with changing aboveground biomass. The slope and curvature are insensitive to soil moisture changes. At the cross-over angles (here indicated for a dry and a wet reference state, θ

_{d}and θ

_{w}, respectively), σ° is proposed to be rather independent of vegetation changes [18].

**Figure 3.**Locations of 179 peatland WTD reference sites across Germany, representing a subset of Bechtold et al. [21]. The base map (geological map 1:200,000, BGR) shows the distribution of peatlands.

**Figure 4.**Climatology time series examples of (

**a**,

**c**) slope and (

**b**,

**d**) curvature for two locations (

**a**,

**b**, lat: 53.995°N, lon: 12.233°E; c and d, lat: 53.694°N, lon: 8.822°E). Both footprints were dominated by grassland, but also included contributions from various other land covers. Curvature was not estimated for ASAR and set to 0.

**Figure 5.**Example time series (lat: 53.995°N, lon: 12.233°E) of a drained peatland location with intermediate temporal correlation statistics showing monitored water table depth (WTD) and backscatter ${\sigma}_{{\theta}_{r}}^{\circ}$ dynamics for (

**a**) descending, and (

**b**) ascending, pass after constant slope incidence angle normalization (CONST) and cross-over angle concept normalization based on slope climatologies derived from ASAR data (COASAR).

**Figure 6.**Corresponding scatterplot of data shown in Figure 5, indicating the observed correlation between water table depth (WTD) and backscatter ${\sigma}_{{\theta}_{r}}^{\circ}$ after constant slope incidence angle normalization (CONST) for descending and ascending nodes.

**Figure 7.**Temporal Pearson correlation coefficient and 95% confidence intervals for original (R) and anomaly time series (anomR) for the differently processed backscatter time series (NOCOR: no incidence angle correction, CONST: constant slope normalization, COASCAT: cross-over angle concept using ASCAT slope and curvature climatology, COASAR: cross-over angle concept using slope climatology derived from ASAR data). Skills are shown for (

**a**,

**b**) natural, and (

**c**,

**d**) drained sites, both for descending and ascending nodes.

**Figure 8.**Lines show the site-specific linear fits to backscatter (ascending data corrected using CONST method) and water table depth data for all peatland sites. Lines are colored by the temporal correlation coefficient (R) and drawn only for the inner 50% of the site-specific observed water table range for better readability.

**Figure 9.**Backscatter σ° from two 90-day windows covering the low and high slope periods of the example site and slope climatology from Figure 4a. Black solid line: wet reference; red solid line: dry reference; black dashed line: hypothetical (not-observed) dry reference in winter; red dashed line: hypothetical (not-observed) wet reference in summer.

**Figure 10.**Average time series (

**a**) R and (

**b**) anomR between observed WTD and backscatter estimates using various combinations of dry and wet cross-over angles. The metrics are averaged across all sites, ascending and descending node. The cross symbol indicates the commonly applied cross-over angles θ

_{d}= 25° and θ

_{w}= 40° at which R = 0.47 and anomR = 0.39 (see Table 1).

Method | R ± ½ CI ^{1} | anomR ± ½ CI |
---|---|---|

NOCOR | 0.37 ± 0.04 | 0.27 ± 0.05 |

CONST | 0.46 ± 0.04 | 0.38 ± 0.04 |

COASCAT | 0.42 ± 0.04 | 0.34 ± 0.04 |

COASAR | 0.47 ± 0.04 | 0.39 ± 0.04 |

^{1}The 95% confidence interval (CI) is narrower than shown in Figure 7 due to further aggregation over natural and drained sites, and descending and ascending nodes.

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**MDPI and ACS Style**

Bechtold, M.; Schlaffer, S.; Tiemeyer, B.; De Lannoy, G. Inferring Water Table Depth Dynamics from ENVISAT-ASAR C-Band Backscatter over a Range of Peatlands from Deeply-Drained to Natural Conditions. *Remote Sens.* **2018**, *10*, 536.
https://doi.org/10.3390/rs10040536

**AMA Style**

Bechtold M, Schlaffer S, Tiemeyer B, De Lannoy G. Inferring Water Table Depth Dynamics from ENVISAT-ASAR C-Band Backscatter over a Range of Peatlands from Deeply-Drained to Natural Conditions. *Remote Sensing*. 2018; 10(4):536.
https://doi.org/10.3390/rs10040536

**Chicago/Turabian Style**

Bechtold, Michel, Stefan Schlaffer, Bärbel Tiemeyer, and Gabrielle De Lannoy. 2018. "Inferring Water Table Depth Dynamics from ENVISAT-ASAR C-Band Backscatter over a Range of Peatlands from Deeply-Drained to Natural Conditions" *Remote Sensing* 10, no. 4: 536.
https://doi.org/10.3390/rs10040536