# Soil Moisture Retrieval Using Multistatic L-Band SAR and Effective Roughness Modeling

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## Abstract

**:**

^{3}/m

^{3}, with the best performance observed for the cross-polarized backscatter signal. In addition, different experimental SAR monostatic and bistatic configurations are evaluated in this study using the proposed retrieval technique. Results illustrate that the soil moisture retrieval performance increases by using backscatter data in multiple polarizations simultaneously, compared to the case where backscatter observations in only one polarization mode are used. Furthermore, the retrieval performance of a multistatic system has been evaluated and compared to that of a traditional monostatic system. The recent BELSAR campaign (in 2018) provides time-series of experimental airborne SAR measurements in two bistatic geometries, i.e., the across-track (XTI) and along-track (ATI) flight configuration. For both configurations, bistatic observations are available in the backward region. The results show that the simultaneous use of backscatter and bistatic scattering data does not result in a profound increase in retrieval performance for the bistatic configuration flown during BELSAR 2018. As theoretical studies demonstrate a strong improvement in retrieval performance when using backscatter and bistatic scattering coefficients in the forward region simultaneously, the introduction of additional bistatic airborne campaigns with more promising multistatic SAR configurations is highly recommended.

## 1. Introduction

_{v}) is an essential variable in the hydrological cycle both at the global and local scale, since it plays a critical role in the water and energy balance, affecting crop development, and controlling runoff processes. Acquiring ground measurements of soil moisture is labor intensive. Therefore, ground measurements are often limited in spatial coverage and to few snapshots in time. Remote sensing provides a means of monitoring soil moisture over a range of spatial and temporal scales [1]. It is well known that Synthetic Aperture Radar (SAR) systems are capable of observing soil moisture, with relatively high spatial resolution, typically about 5–20 m [2]. Studies by Schmugge [3] and Ulaby et al. [4,5] illustrated a relationship between the radar backscatter signal and the soil moisture content. Several models have been developed and evaluated over the last decades to retrieve soil moisture from the SAR backscattering coefficient (see [6,7] for an overview). The Integral Equation Model (IEM) is one of the most frequently used scattering models that performs well for bare or sparsely vegetated land surfaces [8].

## 2. Materials and Methods

#### 2.1. Study Site

#### 2.2. Airborne SAR Data

^{2}/m

^{2}) at the original incidence angle ${\theta}_{\mathrm{i}}$, and $\sigma {}_{\mathrm{SAR},\mathrm{ref}}^{0}$ is the backscattering coefficient (m

^{2}/m

^{2}) at the reference incidence angle ${\theta}_{\mathrm{ref}}$, in this case 40°.

^{2}/m

^{2}) at the ${\theta}_{\mathrm{s}}$ zenith scattering angle, and $\sigma {}_{\mathrm{BISAR},\mathrm{ref}}^{0}$ is the bistatic scattering coefficient (m

^{2}/m

^{2}) at the reference ${\theta}_{\mathrm{ref}}$ zenith scattering angle, in this case 40°.

#### 2.3. Ground Measurements

^{3}/m

^{3}, which corresponds to very dry conditions. The average soil moisture content for bare-wheat soils is 0.05, 0.134 and 0.127 m

^{3}/m

^{3}, with a standard deviation of 0.008, 0.033 and 0.029 m

^{3}/m

^{3}, respectively, on 30 July, 28 August and 10 September. Especially during the July flight campaign, soil moisture values were found to be low. Furthermore, it should be stressed that the dynamic range of soil moisture is limited, which is not ideal for developing and testing soil moisture retrieval techniques. Therefore, soil moisture observations over the bare Orgeval study site have been added in order to test the retrieval approach over a wider range of soil moisture conditions (0.030–0.22 m

^{3}/m

^{3}).

^{3}.

#### 2.4. Effective Roughness Modeling as a Tool for Soil Moisture Retrieval

_{v})-observations for agricultural fields with a smooth to medium smooth roughness state. In the study of Lievens et al. [28], the best soil moisture retrieval results were obtained when s was fixed at a predefined value of 2 cm, and l was estimated using regression model parameters a = −8.833 and b = −102.7 for L-band HH SAR backscatter observations. The modeled effective correlation lengths have then propagated through an iterative inversion scheme of the IEM [8] for the retrieval of the soil dielectric constant, which may then be converted to volumetric soil moisture using the four-component dielectric mixing model [37]. The performance of the linear model has been assessed through cross-validation. The observed and retrieved soil moisture showed good agreement with RMSE close to 4 vol% and R${}^{2}$ values of approximately 0.87. For a detailed description of the developed technique, we refer to [28].

^{3}/m

^{3}) are inserted in the dielectric mixing model to compute corresponding soil dielectric constants. Subsequently, these dielectric constants are used as input to the Oh model and AIEM, together with the modeled s- and l-values, and associated backscatter coefficients (HH, VV and HV) are simulated. The retrieved soil moisture value is then reported as the one for which the difference in simulated and observed backscatter is minimal. Once all linear regression models are propagated through the iterative inversion scheme, an optimal linear regression model can be determined. This best linear regression is defined, as the one resulting in the best soil moisture retrieval results, evaluated by the Kling–Gupta Efficiency [38]. The modeled surface roughness parameters corresponding with this best linear regression are defined as the effective roughness parameters ($R{}_{\mathrm{eff}}$). The Kling–Gupta Efficiency (KGE) is a goodness-of-fit measure between observed and simulated soil moisture and is defined as

#### 2.5. Experimental Set-Up

^{2}) and Root-Mean-Square Error (RMSE) are used to evaluate the retrieval performance of the different SAR configurations.

^{3}/m

^{3}) are inserted in the Oh model and AIEM together with the modeled s- and l-values, and associated backscatter coefficients (HH, VV and HV) are calculated. When single-polarized backscatter data are considered, the following cost function can then be evaluated

^{3}/m

^{3}) are inserted in the Oh model and AIEM, together with the modeled s- and l-values, and associated backscatter coefficients (HH, VV and HV) are calculated. For multi-polarized data, the following cost function has been introduced

^{3}/m

^{3}) are inserted in the AIEM, together with the modeled l-values, and associated backscatter and bistatic scattering coefficients are calculated. The following cost function is then evaluated to retrieve soil moisture from backscatter observations

## 3. Results and Discussion

#### 3.1. Backscatter Simulations and Soil Moisture Retrieval Using In Situ Measured Surface Roughness Parameters

_{v}). We found that the field average scattering signal of bare-maize soils is generally higher than that of bare-wheat soils, especially in cross-polarization mode (not shown here). Since soil moisture content and surface roughness are similar for bare-wheat and bare-maize soils, the strong scattering signal of bare-maize soils could result from large crop residues of maize that were still present on the soil surface after harvest. Due to the fact that no information is available regarding crop residue cover in the BELSAR dataset, the data of maize fields are not taken into account in this study.

^{3}/m

^{3}, the Oh model tends to underestimate the cross-polarized backscatter coefficient. The origin of this discrepancy might be in the calibration or normalization process of SAR data, in the parameterization of surface roughness or in the model itself, which does not simulate all physical interactions for the cross-polarization. This strong underestimation might also be due to the fact that the radar response is below the noise equivalent sigma zero (NESZ = −31 dB). Therefore, the results presented here related to cross-polarization should be interpreted with caution.

^{3}/m

^{3}. Instead, calibrated or effective roughness parameters can be used in the retrieval process.

#### 3.2. Modeling Effective Root-Mean-Square Height s from SAR Backscatter

#### 3.3. Modeling Effective Correlation Length l from SAR Backscatter and Bistatic Scattering

#### 3.4. Soil Moisture Retrieval Based on Effective Roughness Modeling

^{3}/m

^{3}. These retrieval results are much better compared to what we found when using in situ measured surface roughness parameters in the retrieval process (see Figure 5). Furthermore, in Figure 10, similar results are obtained for the two strategies, illustrating the robustness of the developed retrieval technique. The best results are obtained for the cross-polarization mode HV, with errors below 0.04 m

^{3}/m

^{3}and a maximum R${}^{2}$ value of 0.626. The co-polarization mode VV also yields accurate soil moisture retrieval results. For the co-polarization mode HH, the retrieval results are slightly worse with R${}^{2}$ values lower than 0.55 and errors equal to or slightly larger than 0.04 m

^{3}/m

^{3}.

#### 3.5. Evaluating Different Soil Moisture Retrieval Approaches

^{3}/m

^{3}and a correlation coefficient of 0.665. This is in line with what we expect and could be linked to the BELSAR sensitivity study of Bouchat et al. [44], whereby a higher sensitivity to soil moisture and a lower sensitivity to surface roughness was observed when the combination of dual-polarized backscatter was evaluated. For the AIEM, the retrieved versus observed soil moisture based on single-polarized data is represented in Figure 10 (bottom line) and the retrieved versus observed soil moisture based on multi-polarized data is represented in Figure 11 (right). For the AIEM, using multi-polarized data in the retrieval process does not result in a profound increase in retrieval performance, the retrieval performance is rather similar to the one obtained with single-polarized SAR data in VV and HV polarization.

^{3}/m

^{3}and $\Delta $R

^{2}= +0.028 for XTI flight configuration and $\Delta $RMSE = −0.002 m

^{3}/m

^{3}and $\Delta $R

^{2}= +0.066 for ATI flight configuration. This limited increase in retrieval performance was expected given the flight configuration of the BELSAR campaign with short along-track and especially short across-track baseline, and corresponding small bistatic angles. Because of this, the scattering mechanisms involved in the monostatic and bistatic geometry are similar, resulting in the fact that the bistatic scattering coefficients do not give substantial added value to the backscattering. The model-based theoretical study of Pierdicca et al. [15] highlights that the scattering mechanism of the monostatic and bistatic system should be sufficiently different in order to increase the retrieval performance if both scattering coefficients are used simultaneously in the retrieval process. Bistatic scattering in the forward region was therefore desired, with a special focus on the specular and orthogonal direction. These findings are in agreement with the BELSAR sensitivity study of Bouchat et al. [44] where no increase in sensitivity to soil moisture was observed when considering backscatter and bistatic scattering coefficients simultaneously. Given this, the introduction of additional bistatic airborne campaigns with more promising active-passive SAR configurations is highly recommended in order to further verify the improvement in soil moisture retrieval performance.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The BELAIR Hesbania test site, with the winter wheat and maize fields in green and red, respectively, and all the other agricultural fields inventoried on the anonymous cadastral map for agricultural land provided in Wallonia’s land-parcel identification system (Système Intégré de Gestion et Contôle (SIGeC)) in grey. The four parallel flight tracks are represented by colored arrows.

**Figure 4.**Simulated versus observed field average bare soil SAR backscatter for HH (

**left**), VV (

**middle**) and HV (

**right**) polarization. Backscatter simulations are performed with the semi-empirical Oh model and in situ measured root-mean-square heights.

**Figure 5.**Retrieved field-average soil moisture values using in situ measured root-mean-square heights in the retrieval process with the Oh model against observed field-average soil moisture values, using single-polarized backscatter data.

**Figure 6.**Kling–Gupta Efficiency (KGE) values for a range of linear regression models (slope a ranging from 0.001 to 0.20 and intercept b ranging from 0 to 8), obtained by inverting the Oh model for HH (

**left**) VV (

**middle**) and HV (

**right**) normalized bias-corrected backscatter coefficients.

**Figure 7.**Simulated versus observed field average bare soil SAR backscatter for HH (

**left**), VV (

**middle**) and HV (

**right**) polarization. Backscatter simulations are performed with the physically-based AIEM and in situ measured roughness parameters.

**Figure 8.**Simulated versus observed field average bare soil SAR bistatic scattering in XTI flight configuration for HH (

**left**) and VV (

**right**) polarization. Bistatic scattering simulations are performed with the physically-based AIEM and in situ measured roughness parameters.

**Figure 9.**Simulated versus observed field average bare soil SAR bistatic scattering in ATI flight configuration for HH (

**left**) and VV (

**right**) polarization. Bistatic scattering simulations are performed with the physically-based AIEM and in situ measured roughness parameters.

**Figure 10.**Simulated field-average soil moisture values based on effective roughness modeling for the Oh model and AIEM against observed field-average soil moisture values for HH (

**left**), VV (

**middle**) and HV (

**right**) polarization. The top line represents the first validation technique performed with the Oh model. The middle line represents the second validation technique, i.e., leave-one-out cross-validation, performed with the Oh model. The bottom line represents the first validation technique performed with the AIEM.

**Figure 11.**Simulated field-average soil moisture values based on effective roughness modeling for the Oh model (

**left**) and AIEM (

**right**) against observed field-average soil moisture values, using multi-polarized backscatter data.

**Figure 12.**Simulated field-average soil moisture values based on effective roughness modeling for the AIEM against observed field-average soil moisture values.

**Left**: using HH- and VV-polarized backscatter data of the BELSAR campaign.

**Middle**: using HH- and VV-polarized backscatter and XTI bistatic scattering data of the BELSAR campaign.

**Right**: using HH- and VV-polarized backscatter and ATI bistatic scattering data of the BELSAR campaign.

Active-Passive SAR System | |

Central Frequency | 1.375 GHz |

Polarization | HH, VV, HV and VH |

Signal Bandwidth | 50 MHz |

Along-track baseline | ∼400 m |

Across-track baseline | ∼25 m |

Zenith incidence angle range ${\theta}_{\mathrm{i}}$ | 20°–55° |

Zenith scattering angle range ${\theta}_{\mathrm{s}}$ | 20°–55° |

Average azimuth scattering angle ${\varphi}_{\mathrm{s}}$ ATI | −171.6° |

Average azimuth scattering angle ${\varphi}_{\mathrm{s}}$ XTI | −179.2° |

**Table 2.**Regression model parameters for estimating the effective s-values for the Oh model from normalized backscatter observations.

L-Band Backscatter | ${\mathit{a}}_{\mathbf{best}}$ | ${\mathit{b}}_{\mathbf{best}}$ | KGE_{max} |
---|---|---|---|

HH | 0.083 | 2.88 | 0.723 |

VV | 0.056 | 2.16 | 0.768 |

HV | 0.025 | 1.87 | 0.791 |

**Table 3.**Regression model parameters for estimating the effective l-values for the AIEM from normalized backscatter observations, whereby s is set at 1.75 cm.

L-Band | ${\mathit{a}}_{\mathbf{best}}$ | ${\mathit{b}}_{\mathbf{best}}$ | KGE_{max} |
---|---|---|---|

HH | −1.7 | −5.7 | 0.566 |

VV | −7 | −77.1 | 0.720 |

HV | −8.5 | −203.3 | 0.682 |

**Table 4.**Regression model parameters for estimating the effective l-values for the AIEM from normalized bistatic scattering observations, whereby s is set at 1.75 cm.

L-Band | ${\mathit{a}}_{\mathbf{best}}$ | ${\mathit{b}}_{\mathbf{best}}$ | KGE_{max} | |
---|---|---|---|---|

XTI | HH | −1.3 | 0.9 | 0.667 |

VV | −7.9 | −91 | 0.617 | |

ATI | HH | −1.2 | 2.4 | 0.664 |

VV | −8 | −90.9 | 0.575 |

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Tronquo, E.; Lievens, H.; Bouchat, J.; Defourny, P.; Baghdadi, N.; Verhoest, N.E.C.
Soil Moisture Retrieval Using Multistatic L-Band SAR and Effective Roughness Modeling. *Remote Sens.* **2022**, *14*, 1650.
https://doi.org/10.3390/rs14071650

**AMA Style**

Tronquo E, Lievens H, Bouchat J, Defourny P, Baghdadi N, Verhoest NEC.
Soil Moisture Retrieval Using Multistatic L-Band SAR and Effective Roughness Modeling. *Remote Sensing*. 2022; 14(7):1650.
https://doi.org/10.3390/rs14071650

**Chicago/Turabian Style**

Tronquo, Emma, Hans Lievens, Jean Bouchat, Pierre Defourny, Nicolas Baghdadi, and Niko E. C. Verhoest.
2022. "Soil Moisture Retrieval Using Multistatic L-Band SAR and Effective Roughness Modeling" *Remote Sensing* 14, no. 7: 1650.
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