An Improved Approach for Soil Moisture Estimation in Gully Fields of the Loess Plateau Using Sentinel-1A Radar Images

Abstract

As an essential ecological parameter, soil moisture is important for understanding the water exchange between the land surface and the atmosphere, especially in the Loess Plateau (China). Although Synthetic Aperture Radar (SAR) images can be used for soil moisture retrieval, it is still a challenge to mitigate the impacts of complex terrain over hilly areas. Therefore, the objective of this paper is to propose an improved approach for soil moisture estimation in gully fields based on the joint use of the Advanced Integral Equation Model (AIEM) and the Incidence Angle Correction Model (IACM) from Sentinel-1A observations. AIEM is utilized to build a simulation database of microwave backscattering coefficients from various radar parameters and surface parameters, which is the data basis for the retrieval modeling. IACM is proposed to correct the deviation between the local incidence angle at the scatterer and the radar viewing angle. The study area is located in the Loess Plateau of China, where the main land cover is mostly bare land and the terrain is complex. The Sentinel-1A SAR data in C-band with dual polarization acquired on October 19th, 2017 was adopted to extract the VV&VH polarimetric backscattering coefficients. The in situ measurements of soil moisture were collected on the same day of the SAR acquisition, for evaluating the accuracy of the SAR-derived soil moisture. The results showed that, firstly, the estimated soil moisture with volumetric content between 0% and 20% was in the majority. Subsequently, both the RMSE of estimation values (0.963%) and the standard deviation of absolute errors (0.957%) demonstrated a good accuracy of the improved approach. Moreover, the evaluation of IACM confirmed that the improved approach coupling IACM and AIEM was more efficient than employing AIEM solely. In conclusion, the proposed approach has a strong ability to estimate the soil moisture in the gully fields of the Loess Plateau from Sentinel-1A data.

1. Introduction

Soil moisture, a basic parameter of water cycle process in the ecosystem, plays a crucial role in multifarious applications such as ecological monitoring, hydrological cycle simulation, and climate change analysis [1,2,3,4]. Particularly in the Loess Plateau area (China), with the semi-arid environment and the fragile ecosystem, a comprehensive knowledge of the status of soil moisture helps to enhance the effectiveness of the ecological protection or restoration engineering, such as soil-water conservation, land reclamation, and vegetation restoration, thus making the soil moisture measurement more necessary [5,6,7,8,9]. However, in situ measurements of soil moisture are often difficult (or impossible) to access in the Loess Plateau gully fields because of the complex terrain and unstable slope. Also, the traditional field investigation methods can only provide local discrete information on the soil moisture. Estimation of the soil moisture at the regional scale would be better accomplished using remote sensing technology. Both optical and microwave remote sensing have been evidenced to be able to retrieve soil moisture, but optical images are strongly limited by the clouds and solar radiation conditions [10,11,12,13,14,15]. With more and more spaceborne SAR missions implementing and operating successfully, the active microwave remote sensing generally referring to SAR, has demonstrated its excellent potential to estimate the soil moisture due to the high sensitivity of backscattered radar signal to surface characteristics, together with the capacity for all-weather and all-time sensing [16,17,18,19,20,21].

Three basic types of microwave modeling methods for soil moisture retrieval from SAR radar images have been previously proposed: the empirical models [22,23,24,25], the semi-empirical models [26,27,28], and the theoretical models [29,30,31,32,33,34,35]. The empirical and semi-empirical models investigate the mathematical relations between radar backscattering coefficients and surface parameters based on a large number of in situ measurements, which usually provides a few fitted parameters that derived from the particular fields [36]. In other words, these models only perform well on similar surface profiles from the same SAR sensors, but have limitations when the parameters are unsuited to the particular conditions. As one of the basic theoretical models, the Integral Equation Model (IEM) has promoted the model parameters of surface profiles into a wider domain, successfully bridging the gap between the Small Perturbation Model (SPM) and the classical Kirchhoff [29,30], but it still has several flaws resulting from its assumptions. To optimize it, the Advanced IEM (AIEM) operates on the multiple scattering terms expression and the Fresnel reflection coefficients improvement, resulting in better microwave emissivity simulation for a wide range of roughness scales [30,31,32,33]. Considering that topographic parameters such as slope and aspect influence the return backscattered signal of SAR [37], soil moisture retrieval based on AIEM simulation in gully fields can be less reliable than that in the plains. Therefore, understanding and adequately incorporating the impacts of complex terrain are essential issues of soil moisture retrieval in gully fields of the Loess Plateau.

Although many studies on soil moisture estimation over bare soil, vegetation land, grassland, and agricultural soil have been reported [38,39,40,41,42], there is a dearth of research in gully fields. To explore the potentiality of soil moisture retrieval in gully fields from SAR data, this paper proposed an improved approach which utilizes the Incidence Angle Correction Model (IACM) to mitigate the impacts of topography on soil moisture modeling using remote sensing. The local incidence angle, rather than the radar viewing angle, is the exact parameter that can represent the reality in the gully fields. Therefore, IACM is used to compute the local incidence angle, which plays an important role in the basic retrieval model established by AIEM simulation database. Previous studies on soil moisture retrieval often adopt SAR data in C-band due to its high accessibility from several spaceborne SAR sensors (ERS-1/2, ENVISAT ASAR, and RADARSAT-1/2) [21,43,44,45,46,47,48]. Particularly in recent years, Sentinel-1A, launched by the European Space Agency (ESA), offers a finer spatiotemporal resolution data with totally open-access, greatly promoting the research and application of C-band SAR data for soil moisture estimation [49,50,51]. In conclusion, the main contribution of this paper is to broaden the application of soil moisture estimation from Sentinel-1A data to the Loess Plateau, and furthermore provide references for soil moisture estimation in other mountainous areas.

The organization of this paper is as follows: After a brief introduction in this section, Section 2 introduce the data set and study area in the Loess Plateau. Section 3 describes the methods for simulation process, the numerical analysis for retrieval modeling, and the local incidence correction. The results and discussion of the soil moisture estimation are presented in Section 4 and Section 5, respectively. Concluding remarks are provided in Section 6.

2. Study Area and Datasets

2.1. Study Area and In Situ Measurements

The study area, which belongs to the middle part of the Loess Plateau shown in Figure 1a, is located in Jingbian County, Shaanxi Province, China, with a central latitude of 37°22′N and a central longitude of 108°58′E. The region has a surface of about 110 km² and is characterized by rugged terrain and complicated gullies with elevation varying from 1200 m and 1700 m. In addition, the region provides a representative of the typical semi-arid circumstance with 455.76 mm/a precipitation and 1510.14 mm/a potential evapotranspiration, as shown in

Table 1. Seasonal values of precipitation and potential evapotranspiration in the study area.

Meteorological Data	Spring	Summer	Autumn	Winter	Annual
Precipitation (mm)	73.38	235.66	131.74	14.98	455.76
Potential evapotranspiration (mm)	527.54	533.58	285.34	163.68	1510.14

¹ Precipitation and potential evapotranspiration data were sourced from Jingbian meteorological station (No. 53735, China) from 2013 to 2017.

. The above-mentioned situations result in the land type mostly manifesting as sparse meadows and bare land, as shown in Figure 1b. Figure 1c shows the scenery of the region where bare land becomes the leading land type during the dry season from October to May (the following year), largely because of the continental monsoon climate.

To evaluate the accuracy of the soil moisture estimation, a network with sampling spacing larger than the pixel spacing of SAR images was constructed as 43 in situ measurements placed within the area shown in Figure 2a, whose border is marked in blue in Figure 1b. Within 2 hours before the acquisition time of Sentinel-1A (10:45 a.m. on October 19th, 2017, GMT), the volumetric soil moisture of the sampling sites was measured by the soil moisture sensing probe at a depth of approximately 5 cm, which is most closely related to the sensing ability of the C-band SAR data [43,52,53]. At each sampling site, soil moisture measurement below the surface 0 to 5 cm was derived from the average of 9 points formed as the double cross pattern (the shape of the British “Union Jack”) with 1 m spacing. The soil moisture results of 43 in situ measurements with approximately ±1% volumetric precision are presented in Figure 2b.

2.2. Remote Sensing Datasets

The SAR data were acquired by Sentinel-1A (5.405GHz) in interferometric wide swath (IW) mode with dual polarization (VV-VH) on October 19th, 2017 (https://scihub.copernicus.eu/). The level-1 Ground Range Detected (GRD) products, which had been projected to ground range using the Earth ellipsoid model WGS84 with approximately square pixel spacing of 10 m, were used to extract radar backscattering coefficients. The pixel value of the GRD products represents only the detected amplitude since the phase information has been discarded. Moreover, all bursts in all sub-swaths of the products had been seamlessly merged to form a single and contiguous ground range image per polarization.

Before further information extraction and image analysis, the GRD Sentinel-1A images were preprocessed. The preprocessing involved radiometric operation with respect to calibration and terrain flattening [54], thermal noise removal, speckle filter (refined Lee filter), SAR mosaic, and radiometric normalization, was implemented using the Sentinel Application Platform (SNAP, http://step.esa.int/main/download/). The preprocessed results were mapped as Figure 3 shown.

The Digital Surface Model (DSM) data collected for the topographic parameters inversion were AW3D30 products (http://www.eorc.jaxa.jp/ALOS/en/aw3d30/) with a horizontal resolution of 30 m mesh and a height accuracy of 5 m, released by Japan Aerospace Exploration Agency (JAXA). The products had mapped the land terrains through the utilization of 3 million scene archives acquired by the PRISM sensor on the Advanced Land Observing Satellite (ALOS) from 2006 to 2011. Figure 3c provided the topographic map in the study area generated from AW3D 30 products.

3. Methodology

As one of the analytical physical models that are most widely used, AIEM is employed for simulating the radar backscattering coefficients at various surface parameters over the study area. Considering that the AIEM had limited capability for dealing with the effect of complex topography, we proposed an improved retrieval approach to estimate soil moisture using Sentinel-1A radar data. The primary innovation of this approach is to append IACM into the preliminary retrieval model established by the simulation database, which efficiently mitigates the impacts from topographic factors. The process flow of soil moisture estimation is presented in Figure 4, and the detailed descriptions are introduced in the following sections.

3.1. Surface Roughness Parameters Combination Based on AIEM Simulation

Based on the IEM proposed by Fung et al. [29], Chen and Wu proposed an improved model, referred to as AIEM, by replacing the Fresnel reflection coefficients with a transition function for solving the discontinuities in surface roughness and permittivity. The good performance of AIEM in simulating the backscattering coefficients has been previously addressed [31,32,33]. Therefore, the AIEM was adopted in this study to simulate the radar backscattering coefficients from the configuration parameters of Sentinel-1A SAR sensor. For establishing a simulated database, the input parameters of AIEM is set as shown in

Table 2. Parameter setting of AIEM.

Parameters	Minimum	Maximum	Interval
Incidence angle $\theta$ (°)	10	70	1
Soil moisture $M_v$ (%)	5	35	1
Root mean square height $s$ (cm)	0.2	4	0.2
Correlation length $l$ (cm)	2	40	2
Frequency $fre$ (GHz)	5.405 (Sentinel-1A sensor parameter)
Auto-correlation function (ACF)	Generalized power-law spectral density function

.

The root mean square (RMS) height $s$ and the correlation length $l$ are the most used and basic parameters to describe surface roughness, which is essential for a fine simulation of the microwave scattering. According to in situ measurements, a data set of various surface roughness conditions was derived from the AIEM simulation database that satisfied the following settings: incidence angle $\theta$ is 35°; soil moisture $M_v$ is 20%. In a multivariate regression analysis from the data set, the numerical relation between the backscattering coefficients and the RMS height $s$ and the correlation length $l$ was developed as:

$${\sigma }_{vv}^0=9.204\ln \left(s\right)-5.314\ln \left(l\right)+2.913,$$

(1)

It is worth noting that an increase in the number of surface roughness parameters in a model will also increase the uncertainty of soil moisture retrieval, emphasizing the ill-posed problems in retrieval [55]. Therefore, we proposed a new description of surface roughness to unite the $s$ and the $l$ into only one comprehensive parameter, written as $R_s=\frac{s^{\sqrt{3}}}{l}$. In addition, then, Equation (1) was inverted to Equation (2).

$${\sigma }_{vv}^0=5.314\ln R_s+2.913,$$

(2)

Figure 5 plots the simulated backscattered radar signal for the VV polarization in C-band (5.405 GHz) at a 35° incidence angle. A strong correlation between the backscattering coefficients and the surface roughness can be clearly observed, which indicates that it is an effective approach to taking into account $R_s$ as one of the model parameters for addressing the ill-posed problems in the retrieval.

3.2. Implementation of the Retrieval Model

Over bare soil, the backscattering coefficient of the surface contribution ${\sigma }_{pp}^0$ (at the VV polarization, $pp=vv$) for the co-polarization is expressed as [43,56]:

$${\sigma }_{pp}^0=\frac{k^2}{2}{\left|f_{pp}\right|}^2{e}^{-4k^{2}rm{s}^2{\cos }^2\theta }\times {\displaystyle \sum }_{n=1}^{+\infty }\frac{{\left(4k^{2}rm{s}^2{\cos }^2\theta \right)}^n}{n!}{W}^{\left(n\right)}\left(2k\sin \theta ,0\right)$$

$$+\frac{k^2}{2}\mathrm{Re}\left(f_{pp}^{*}{F}_{pp}\right)e^{-3k^{2}rm{s}^2{\cos }^2\theta }\times {\displaystyle \sum }_{n=1}^{+\infty }\frac{{\left(4k^{2}rm{s}^2{\cos }^2\theta \right)}^n}{n!}{W}^{\left(n\right)}\left(2k\sin \theta ,0\right)$$

$$+\frac{k^2}{8}{\left|F_{pp}\right|}^2{e}^{-2k^{2}rm{s}^2{\cos }^2\theta }\times {\displaystyle \sum }_{n=1}^{+\infty }\frac{{\left(k^{2}rm{s}^2{\cos }^2\theta \right)}^n}{n!}{W}^{\left(n\right)}\left(2k\sin \theta ,0\right),$$

(3)

where:

$$f_{vv}=\frac{2R_v}{\cos \theta },$$

(4)

$$F_{vv}=2\frac{{\sin }^2\theta }{\cos \theta }\left[\left(1-\frac{{\epsilon }_r{\cos }^2\theta }{u_r{\epsilon }_r-{\sin }^2\theta }\right)\left(1-R_v\right)+\left(1-\frac{1}{{\epsilon }_r}\right){\left(1+R_v\right)}^2\right],$$

(5)

$$R_v=\frac{{\epsilon }_r\cos \theta -\sqrt{u_r{\epsilon }_r-{\sin }^2\theta }}{{\epsilon }_r\cos \theta +\sqrt{u_r{\epsilon }_r-{\sin }^2\theta }},$$

(6)

$R_v$ is the Fresnel coefficient; $u_r$ is the relative permittivity; Re is the real part of the complex number; $f_{pp}^{*}$ is the conjugate of the complex number $f_{pp}$; $W^{\left(n\right)}$ is the Fourier transform of the nth power of the surface correlation function [20]. Volumetric soil moisture $M_v$ can be inverted from dielectric constant ${\epsilon }_r$ by Dobson dielectric mixing model [57].

A statistical analysis of the AIEM simulation database indicated a strong logarithmic correlation between the backscattering coefficients and the soil moisture. As shown in Figure 6, the simulated backscattering coefficients are ideally correlated with the soil moisture at 30° incidence angle with 0.25 $R_s$. This reveals that a numerical expression for ${\sigma }_{\mathrm{vv}}^0$ as a function of $M_v$ can be written as Equation (7) provided that the roughness parameter and the incidence angle are certain.

$${\sigma }_{vv}^0=A\left(R_s,\theta \right)\ln \left(M_v\right)+f\left(R_s,\theta \right),$$

(7)

Analogously, the expression for ${\sigma }_{vv}^0$ as a function of $R_s$ can be given as Equation (8).

$${\sigma }_{vv}^0=B\left(M_v, \theta \right)\ln R_s+f\left(M_v, \theta \right),$$

(8)

Therefore, while considering both the soil moisture and surface roughness with only incidence angle given, the numerical form for ${\sigma }_{vv}^0$ is expressed as:

$${\sigma }_{vv}^0=A\left(\theta \right)\ln \left(M_v\right)+B\left(\theta \right)\ln R_s+C\left(\theta \right),$$

(9)

The backscattering coefficients for the VH polarization was simulated by adopting the cross-polarized ratio function that was previously proposed and reported by Oh et al [58,59,60]. After the VH-polarimetric backscattering coefficients ${\sigma }_{vh}^0$ had been computed, the numerical relation between cross-polarimetric backscattering coefficients and $R_s$ were computed as:

$$\Delta {\sigma }_{vv}^0=D\left(\theta \right)\ln R_s+E\left(\theta \right),$$

(10)

where $\Delta {\sigma }_{vv}^0$ is the differential backscattering coefficients of cross-polarization, which can be calculated as:

$$\Delta {\sigma }_{vv}^0={\sigma }_{vv}^0-{\sigma }_{vh}^0,$$

(11)

By combining Equation (10) and Equation (11), we eliminated the surface roughness parameter $R_s$. This process produces an obvious benefit that the retrieval model of soil moisture can be proposed as follows:

$${\sigma }_{vv}^0=A\left(\theta \right)\ln \left(M_v\right)+B\left(\theta \right)·\frac{{\sigma }_{vv}^0-{\sigma }_{vh}^0-E\left(\theta \right)}{D\left(\theta \right)}+C\left(\theta \right),$$

(12)

3.3. The Local Incidence Angle Inversion by the IACM

By understanding of the retrieval model of soil moisture, it is clear that the incidence angle $\theta$ at the ground scatterer is an essential parameter for the soil moisture estimation. The value of $\theta$ can refer directly to the radar viewing angle in the flat areas. However, as Figure 7 shows, in mountainous areas with rugged terrain, the local incidence angle at the scatterer is no longer adequately approximated by the value of radar viewing angle.

Aiming for incidence angle correction, the IACM was calculated based on the spatial relationship between the spaceborne SAR and the surface scatterer:

$$\theta ={\theta }_c+slope·\cos \delta ,$$

(13)

where ${\theta }_c$ is the radar viewing angle; slope represents the slope angle at the scatterer location, extracted from the AW3D DSM product; $\delta$ is the angle between the ground scatterer and the line of sight (LOS) as shown in Figure 8a, calculated as [61]:

$$\delta =aspect\pm \left(\beta -90°\right),$$

(14)

where the ascending mode corresponds to positive value, and the descending mode corresponds to negative value; aspect signifies the downslope direction, which is measured clockwise from 0° (due north) to 360° (again due north) [61]; $\beta$, the satellite heading angle, is equal to the deflection angle $\mathsf{\gamma }$ as Figure 8c shown, calculated as [62]:

$$\beta =arcsin\frac{\pm cos\alpha }{cos\xi },$$

(15)

where $\alpha$ is the orbital inclination, obtained from spaceborne SAR configuration; $\xi$ is the latitude of the center of the SAR image; the positive value is employed for the ascending mode, and the negative for the descending.

4. Results

4.1. Solution for Coefficients in the Retrieval Model

In the soil moisture retrieval model, expressed in Equation (12), there are still several coefficients of variables that need a definite numerical model for quantitative calculation, rather than only the notional expressions. Therefore, to observe the numerical relations between coefficients, i.e., $A\left(\theta \right)$, $B\left(\theta \right)$ and the incidence angle $\theta$, a large number of simulated backscattering coefficients based on AIEM were involved in the regression analysis and numerical modeling. The resultant numerical relations are presented in Figure 9, showing the response of the incidence angle $\theta$ to the function coefficients: $A\left(\theta \right)$, $B\left(\theta \right)$, $C\left(\theta \right)$, $D\left(\theta \right)$, $E\left(\theta \right)$, and the fitted curve.

4.2. The Local Incidence in the Study Area

Derived from the data description, the radar viewing angle at the central target of the Sentinel-1A radar images acquired on October 19th, 2017 is 39.24°. Figure 10 shows the inversion result in study area, with strongly differentiated topographic conditions based on the IACM. The spatial distribution of the local incidence angles present heterogeneity caused by the variation of slope and aspect. Specifically, in the Loess tableland, with a relatively flat terrain, the local incidence angles are mostly close to 39.24° (green color in Figure 10). On the other hand, in the Loess valley, with a large topographic relief, the local incidence angles differ significantly from the radar viewing angle, as shown in orange or blue color in Figure 10.

4.3. Soil Moisture Estimation

After the backscattering coefficients were extracted from SAR images and the local incidence angles were inverted, the estimation of soil moisture status over complex terrain land was computed based on the retrieval model given in Section 3.2. The map of volumetric soil moisture overlaying hillshade graph derived from AW3D30 product is shown in Figure 11, which reveals that land with volumetric soil moisture between 0% and 20% is predominant, mostly distributed in the Loess tableland, ridge and hills. Due to the regional dry climate and the strong differentia between evaporation and precipitation, soil moisture in such areas is low. Particularly in the Loess tableland with high topography and few vegetation, the soil moisture is between 0% and 10%. In the Loess gully areas formed by the Loess erosion, soil moisture is higher with volumetric content between 20% and 40%, largely because of surface water migration via seepage.

5. Discussion

5.1. Reliability Evaluation of Soil Moisture Estimation

As mentioned in Section 2.1, 43 in situ measurements over the verification area obtained within two hours before the acquisition time of Sentinel-1A data were used as validation data to evaluate the accuracy of the soil moisture estimation in terms of root mean square error (RMSE) and standard deviation of absolute error (SDAE). As a result of validating with in situ measurements, it is worth mentioning that the RMSE of estimation values is 0.963%, indicating a reliable performance of the retrieval methods. Moreover, the SDAE is 0.957%, indicating a small dispersion of the difference between the estimation value and in situ measurements (Figure 12b and

Table 3. The absolute errors statistic of soil moisture estimations on different topographical conditions.

Land Type	Mean (%)	SDAE (%)	RMSE (%)
Arable Land	0.162	0.875	0.890
Hill	0.173	0.347	0.388
Tableland	−0.02	1.386	1.386
Total	0.114	0.957	0.963

). The number of verification sites with absolute errors (AE) between −0.5% and 0.5% is 24, accounting for 56%, indicating stability of the estimation (Figure 12b).

The in situ measurements were divided into 3 types, including arable land, hill and tableland, according to the topographical condition. Figure 12 suggests that the different topographical conditions have different performances on soil moisture estimation. Firstly, the range of soil moisture observed is adequately representative because the estimated mean of soil moisture over arable land is the highest due to agricultural activities, reached 19.29%, while the estimated means over hill and tableland are 14.14%, 13.35%, respectively (Figure 12a). Furthermore, in terms of error evaluation, the finest retrieval takes place in the hill areas, where the SDAE and RMSE are smallest, with values equal to 0.347% and 0.388%, respectively. In the arable land areas, the SDAE and RMSE are 0.875% and 0.89%, respectively. The situation in tableland areas seems complex, with 1.386% SDAE and 1.386% RMSE (Table 3), due to the sparse distribution of a few low shrubs.

With respect to the roughness parameters, Zribi and Dechambre previously introduced the original roughness parameter $Z_s=s^2/l$ as a roughness parameter combination [22]. Since the numerical relations are based on sensor parameters and soil conditions in the AIEM, different forms of combined roughness parameter were developed by Yang et al. [63] and Kong et al. [64] over respective soil conditions. Therefore, the comprehensive roughness proposed in this paper is novel but appropriate for reducing the unknowns in the AIEM in the Loess Plateau region from Sentinel-1A.

Several studies on the soil moisture estimation over the Loess Plateau from SAR have been also reported [64,65,66]. Specifically, Zhang et al. estimated soil moisture over the western Loess Plateau area with a complicated landscape using ENVISAT ASAR data with VV polarization, and the result was strongly influenced by the terrain variation leading to the invalid estimations in the steep inhomogeneous slope of hill region [66]. Kong et al. retrieved soil moisture over the blown-sand area, namely Mu Us Desert located in the northern Loess Plateau, and the low soil moisture with major volumetric content between 0 and 15% corroborates our results well [64]. In summary, all the estimated results previously addressed indicated that soil moisture in the Loess Plateau is low.

5.2. Performance Evaluation of IACM

The gully fields of the Loess Plateau have several prominent characteristics that are important for soil moisture estimation, such as the semi-arid climate environment and the complex terrain condition. As mentioned in Section 2.1, bare land becomes the major constituent land type, which is attributed to the semi-arid environment, benefiting the retrieval stability on the basis of AIEM simulation. However, the regional terrain is certainly a factor that makes the soil moisture estimation harder, due to the dependence of the retrieval model on the local incidence angle.

To address this problem, this paper proposed a model, called IACM, for calculating the local incidence angle, thereby enhancing the estimation accuracy. To evaluate the performance of IACM, the volumetric soil moisture was repeatedly estimated under the same conditions except using IACM for the local incidence angle retrieval. The results evidence that coupling IACM and AIEM for soil moisture estimation in gully fields is much more efficient than only AIEM employed (Figure 13). The SDAE of estimation without IACM is 4.82%, which is 500% larger than that with IACM corrected (0.957%). Correspondingly, the RMSE of estimation without IACM is 4.83%, compared to 0.963% with IACM. As shown in Figure 13, soil moisture estimation over hill areas, which have the most complex terrain of the three topographical conditions, receives the most significant improvements with IACM. Therefore, taking advantage of IACM to retrieve local incidence angle can expand application of quantitative estimation based on microwave backscattering model to the fields with complex terrain.

6. Conclusions

In this study, we proposed an improved approach to estimate the bare land soil moisture in gully fields of the Loess Plateau from Sentinel-1A dual polarization data, based on the joint use of AIEM and IACM. To address the difficulty in acquiring surface roughness parameters in complicated gullies fields and the ill-posed problems in the retrieval, we adopted SAR images with dual polarization to establish two simulated numerical relations, and united both of them for eliminating the surface roughness parameters of the retrieval model. Additionally, we proposed to use IACM to calculate the local incidence angle and then appended it into the retrieval model to mitigate the influences of uneven terrain.

The results indicated that the overall status of soil moisture in the study area was generally dry, but differed by landform. The estimation accuracy of the improved approach was evaluated using the in situ measurements around the SAR observation time, with total SDAE 0.957% and RMSE 0.963%, indicating a good agreement between estimations and in situ measurements. Moreover, the improvements of soil moisture estimation promoted by introducing the IACM was evidenced when we compared it to the soil moisture with SDAE 4.82% and RMSE 4.83% using AIEM solely. The improved approach developed in this paper demonstrated its utility for the soil moisture estimation, particularly in the fields with complex terrain.

On the basis of this study, our further work will mainly focus on two aspects. One is to extend the soil moisture estimation fields to areas with diversified land cover, instead of just the bare land. The other is to explore the estimated time-series monitoring approaches for multi-temporal SAR images, that is more meaningful to dynamic monitoring and evolution prediction of ecosystem.