Soil Moisture Retrieval by Integrating SAR and Optical Data over Winter Wheat Fields

Abstract

Soil moisture (SM) retrieval over agricultural fields using synthetic aperture radar (SAR) data is often hindered by the vegetation layer and soil roughness. Most SM inversion algorithms require in situ SM data for a calibration to eliminate these two disturbing factors, while collecting in situ data is a project that consumes a lot of manpower and resources. This paper aims to tentatively develop an inversion algorithm for retrieving SM in the absence of in situ SM in areas covered by winter wheat vegetation. Based on the analysis of the data set simulated by the Michigan Microwave Canopy Scattering (MIMICS) model, an improved ratio model is proposed to remove the effect of the vegetation layer. Through the parameterization of the advanced integral equation model (AIEM), the effect of the soil roughness on the inversion of soil moisture is eliminated. The spatial distribution of SM in winter wheat fields is obtained using the Sentinel-1 SAR and Sentinel-2 images. The comparison results between the inverted SM and the in situ measured data reveal a good correlation (R = 0.85, RMSE = 0.032 cm³·cm⁻³), and the result confirms that the algorithm developed only based on theoretical models can also effectively monitor the spatial changes of SM over winter wheat fields.

1. Introduction

Soil moisture (SM) is a key parameter that has an impact on the hydrological cycle and energy exchanges between the land and the atmosphere [1,2]. The accurate acquisition of SM with high temporal and spatial resolution is particularly important for precision irrigation, crop growth monitoring, and production estimation [3,4]. The synthetic aperture radar (SAR) has specific properties such as both a day/night data acquisition capability and high sensitivity to soil moisture, and it is widely used to estimate the surface SM in agricultural areas [5,6,7]. The soil roughness and the scattering of vegetation are two main disruptive factors in the research of soil moisture extraction using SAR data [8,9,10].

The Water Cloud Model (WCM) is usually used in most studies to invert the soil moisture information over areas covered with vegetation by combining SAR and optical remote sensing data [11,12,13]. The Normalized Difference Vegetation Index (NDVI) derived from optical remote sensing is often applied to estimate the Vegetation Water Content (VWC) which is the parameter required by the WCM to eliminate the vegetation impact [14,15,16]. Eliminating the effect of soil roughness is another thorny problem in the process of SM inversion. Some surface scattering models have been proposed to parameterize the surface roughness parameters and simulate the backscattering coefficient of the soil surface, such as the Oh model [17] and the Dubois model [18,19]. The problem with the methods mentioned above is the need for the in situ SM data to calibrate the parametrized model. Therefore, these algorithms have significant limitations in practical applications, especially in areas where the in situ SM data are difficult to obtain or cannot be measured in time. Fortunately, some theoretical models have been developed with higher simulation accuracy and flexibility, such as the PROSAIL model, the Advanced Integral Equation Model (AIEM) [20] and the Michigan Microwave Canopy Scattering (MIMICS) model [21]. However, the research on SM inversion based entirely on theoretical models is not very common in relevant previous studies.

In this study, an improved ratio model is proposed based on the simulation data set of the MIMICS to remove the vegetation layer effect. Based on the parameterization of the AIEM, the effect of the soil roughness on the inversion of soil moisture is eliminated. The Sentinel-1 SAR and Sentinel-2 optical data are collected to retrieve SM in winter wheat fields.

2. Study Area and Data

2.1. Study Area and Study Sites

An agricultural region in Hebei province of China is selected as the study area (37.70°–37.90° N, 116.29°–116.54° E, Figure 1). This area is located at the junction of Hengshui and Cangzhou, where it consists mainly of winter wheat agricultural fields on a flat landscape. The winter wheat crop is usually sown in October of the previous year, and it is harvested in June of the following year. The predominant soil texture of agricultural fields is loam with a clay percentage of about 16% and sand percentage of about 44 %.

2.2. Satellite Data and In Situ SM Data

The Sentinel-1 ascending SAR images were acquired on 16 April 2019, 28 April 2019, and 10 May 2019. The sentinel-1 SAR images are in VV and VH polarizations at an incidence angle that is close to 40°, with the spatial resolution of 10 m. All of the cloud-free Sentinel-2 satellite optical images during 1 April 2019 to 31 May 2019 were collected, and the specific acquisition dates of the images are listed in

Table 1. Some specific information on the Sentinel-2 optical data.

Date	Satellite Platform	Product Type	Relative Oribit Number
3 April 2019	S2B	MSIL2A	R075
5 April 2019	S2A	MSIL2A	R032
10 April 2019	S2B	MSIL2A	R032
15 April 2019	S2A	MSIL2A	R032
28 April 2019	S2A	MSIL2A	R075
30 April 2019	S2B	MSIL2A	R032
3 May 2019	S2B	MSIL2A	R075
10 May 2019	S2B	MSIL2A	R032
13 May 2019	S2B	MSIL2A	R075
15 May 2019	S2A	MSIL2A	R032
20 May 2019	S2B	MSIL2A	R032
23 May 2019	S2B	MSIL2A	R075
25 May 2019	S2A	MSIL2A	R032
28 May 2019	S2A	MSIL2A	R075

. The data preprocessing of SAR images, such as the orbit correction, noise filtering, radiometric calibration, and geocoding, was carried out using the SNAP tool (http://step.esa.int/main/toolboxes/snap, accessed on 1 January 2019). The Sentinel-2 images that were corrected for atmospheric effects were utilized to calculate the NDVI. Based on the method of time spline interpolation, the NDVI, on the same acquisition date as the SAR images, was obtained from the NDVI time-series data. Throughout the normal growth period of the plant, NDVI undergoes a smooth change. In addition, the temporal interpolation method used to obtain NDVI on the target date can partially reduce the uncertainty in the NDVI data itself which is caused by differences in atmospheric conditions at various dates. Therefore, the error introduced by the time interpolation method is ignored in this paper. The roads, water bodies, and buildings in the study area were masked. Finally, the Sentinel-1 and Sentinel-2 images were sampled to the resolution of 30 m for reducing the SAR speckle noise.

The in situ SM measurements were carried out on 28 April 2019. The soil moisture of 68 total fields was measured using calibrated Time Domain Reflectometry probes (TDR) with 5 cm length probes which could easily measure the average value of SM from the depth of 0 cm to 5 cm. The size of each field is in the range of more than 50 m with uniform winter wheat growth. In each field, the SM was measured at 9 different positions with intervals of more than 15 m between two adjacent points, and the SM of one field is the average of the SM values measured at 9 points. To calibrate the measured value of TDR, a defined volume of soil was sampled and weighed at certain points, then, the soil sample was dried using an oven, and the weight was measured to obtain the volumetric moisture content of the sampled fields in cm³·cm⁻³. The maximum value of measured SM is 0.34 cm³·cm⁻³, the minimum is 0.07 cm³·cm⁻³ and the mean is about 0.18 cm³·cm⁻³.

3. Methods

In this study, a set of combined semi-empirical approaches was constructed based entirely on three theoretical models (i.e., the PROSAIL model, the AIEM model, and the MIMICS model) for the retrieval of SM in winter wheat fields. The illustration is shown in Figure 2. In the first step, the LAI was estimated using the Sentinel-2-derived NDVI. Then, the LAI was transformed into the input parameters of the MIMICS model, and an improved ratio model for calculating the soil backscattering coefficient was developed based on a regression analysis of the simulation data set of the MIMICS model, while the soil backscattering coefficient was parameterized as a nonlinear function of SM and soil surface roughness through a statistical analysis of the data set simulated by the AIEM model. In the last step, the SM was calculated by using the Newton iteration method.

3.1. Estimation of LAI

In this study, NDVI was selected as a parameter for calculating the LAI due to its universality for most of the multispectral remote sensing data. The red band reflectance at 665 nm and the near-infrared band reflectance at 842 nm were used to calculate the NDVI according to Equation (1).

$$\mathrm{NDVI}=\frac{r_{842}-r_{665}}{r_{842}+r_{665}}$$

(1)

The PROSAIL model was used to simulate surface reflectance data with different LAI values. Based on the regression analysis of the simulated dataset, the e-index equation of NDVI was found to be a powerful expression for calculating the LAI using Formula (2), with the Pearson determination coefficient (R) of 0.998, as shown in Figure 3.

$$\mathrm{LAI}=0.11\times e^{3.83\times \mathrm{NDVI}}$$

(2)

3.2. The Improved Ratio Model

The ratio model was proposed by Joseph to eliminate the influence of the vegetation canopy on the radar backscattering coefficient. The model assumes that the ratio of the soil backscatter to the total backscatter is only related to the vegetation indices [22]. Based on the fact that the soil backscatter and the total surface backscatter are affected by both vegetation and soil moisture, the ratio model was modified as a nonlinear function of SM and LAI in this study.

$$\frac{{\sigma }_{pq}^{\mathrm{S}}}{{\sigma }_{pq}^{\mathrm{T}}}=f(\mathrm{SM},\mathrm{LAI})$$

(3)

where ${\sigma }_{pq}^{\mathrm{S}}$ represents the backscattering coefficient of the bare soil, ${\sigma }_{pq}^{\mathrm{T}}$ is the total backscattering coefficient of the radar, and the subscripts p and q denote the transmitting and receiving polarizations, respectively.

The MIMICS model can simulate the total surface backscattering coefficient and the backscattering coefficient of different components such as the vegetation, the soil and the interactive term between the two. Based on the simulation data set of the MIMICS model, the correct mathematical expression of the improved ratio model described by Equation (3) needed to be determined. The main input parameters of the MIMICS model listed in

Table 2. The main input parameters of MIMICS model.

Parameters	Value Range	Interval	Units
LAI	0.5~5.0	0.1	—
Leaf radius	1.0	—	cm
leaf thickness	0.2	—	mm
Leaf water content	75~85	5	%
Stem length	30~40	2	cm
Stem radius	0.1~0.2	0.05	cm
SM content	0.05~0.45	0.025	cm3·cm−3

under the configuration of the Sentinel-1 image were used to produce the simulation data set.

Based on the regression analysis on the simulated data set, the Formula (3) can be well expressed as a nonlinear function of SM and LAI as shown in Equations (4)–(6).

$$\frac{{\gamma }_{pq}^2\cdot {\sigma }_{pq}^{\mathrm{S}}}{{\sigma }_{pq}^{\mathrm{T}}}=\frac{f_{1pq}\left(\mathrm{SM}\right)\cdot \mathrm{LAI}+f_{2pq}\left(\mathrm{SM}\right)}{\mathrm{LAI}+f_{3pq}\left(\mathrm{SM}\right)}$$

(4)

with

$${\gamma }_{pq}=e^{-k_{pq}\cdot \mathrm{LAI}}$$

(5)

and

$$\begin{array}{l}{f}_{1pq}=a_{1pq}\cdot SM+b_{1pq}\\ f_{2pq}=a_{2pq}\cdot SM+b_{2pq}\\ f_{3pq}=a_{3pq}\cdot SM+b_{3pq}\end{array}$$

(6)

The empirical coefficients of a₁, b₁, a₂, b₂, a₃, b₃ and k obtained by fitting the MIMICS simulation data are listed in

Table 3. The empirical coefficients for Equation (4).

Polarization	a1	b1	a2	b2	a3	b3	k
VV	−1.73	−0.0530	12.3	0.214	11.3	0.157	0.292
VH	−0.807	−0.129	6.29	−0.0533	5.51	0.0216	0.225

with the Pearson determination coefficient (R) of 0.99 for both the VV and VH polarizations.

3.3. Parameterization of Soil Backscattering Model

The AIEM model can accurately simulate the backscattering coefficient of the soil surface under a wide range of conditions. The root mean square height (S) and the correlation length (L) were used to represent soil surface roughness in the AIEM model. For the case of agricultural soil, an exponential correlation function will generally give a good fit to the majority of experimental surfaces [23]. The parameters listed in

Table 4. The main input parameters of AIEM model.

Parameters	Value Range	Interval	Units
S	0. 25~2.5	0.05	cm
L	8~15	0.5	cm
SM	0.05~0.45	0.01	cm3·cm−3

were the inputs of the AIEM model to simulate the soil backscattering coefficients.

In this study, we use an effective roughness parameter Z with $Z=\raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$\sqrt{L}$}\right.$ to mix the effects of roughness on the soil backscattering coefficients. Based on the statistical analysis of the simulated data set, the soil backscatter was parameterized in Formula (7).

$${\sigma }_{pq}^{\mathrm{S}}=(a_{spq}\cdot Z^2+b_{spq}\cdot Z-c_{spq})\cdot {\mathrm{SM}}^{d_{spq}}$$

(7)

The empirical coefficients of a_s, b_s, c_s and d_s are obtained in

Table 5. The empirical coefficients for Equation (7).

Polarization	as	bs	cs	ds
VV	−1.51	2.01	−0.17	0.740
VH	−0.116	0.155	−0.0142	0.573

with R of 0.98 for both VV and VH polarization.

4. Results and Discussion

4.1. SM Inversion

The soil roughness was assumed to be a constant value from 16 April to 10 May. The multi-temporal Sentinel data on 16 April, 28 April, and 10 May were utilized to retrieve the SM and roughness Z, simultaneously, so the four unknowns were solved from six equations based on the Newton iteration method. In the process of solving the equation, the SM was limited to a range from 0.05 to 0.45, and the roughness of Z was limited to a range from 0.05 to 0.9. The spatial distribution of SM is shown in Figure 4.

The spatial distribution of SM on 16 April was very similar to that on 28 April with a slightly lower SM in the northern part of the study area. The spatial distribution of SM on 28 April was drier than the one on 16 April, while the SM distribution in the entire area on 10 May was generally higher. According to the local meteorological data, there was basically no rainfall from 16 April to 28 April, while a widespread rainfall in the study area occurred on 9 May, with rainfall exceeding 22 mm, so the soil moisture in the total study area remained high on 10 May.

The results showed that the SM value in the surrounding areas of the town was significantly higher than the value of the winter wheat areas. The field investigation revealed that there were a large number of scattered poplar and fruit trees in the surrounding area of the town. For the woodland areas, tree trunks and branches have a strong microwave scattering ability, and this is not involved in the algorithm. The algorithm attributes the strong scattering of branches to a high soil moisture content, so the soil moisture in the forested areas will be overestimated.

4.2. Validation

The comparison result shows a high correlation between the inverted SM and the in situ values, as shown in Figure 5, with an R of 0.85 and an RMSE of 0.032 cm³·cm⁻³. Figure 5 reveals that the inversion value is generally lower than the measured one, especially when the soil is relatively humid. The slight underestimation can be explained from the following: In the MIMICS model, the vegetation canopy is considered to be uniform, but the actual situation is that winter wheat has a typical ridge-row planting structure with large gaps in the canopy. Therefore, the MIMICS model will underestimate the contribution of the soil backscatter. Based on Equation (7), an underestimation of the soil backscattering coefficient will lead to an underestimation of the SM.

Different combinations of single-temporal, dual-temporal, and three-temporal data were used as data sources for retrieving the soil moisture, and the inversion accuracy of the soil moisture is listed in

Table 6. Inverted SM accuracy comparison under the data combination on different dates.

Data	28 April	16 April and 28 April	28 April and 10 May	16 April and 28 April and 10 May
R	0.56	0.79	0.77	0.85
RMSE/cm3·cm−3	0.061	0.041	0.044	0.032

.

When the single-temporal remote sensing data of 28 April were used as the data source, the soil moisture and soil roughness were solved simultaneously from the only two equations, and the inversion accuracy of soil moisture was the lowest one. When the dual-temporal data act as the data source, we obtained four equations for solving three unknowns, and the inversion accuracy of soil moisture was significantly improved. In the case of the three-temporal data, the inversion accuracy of soil moisture was further improved. The reason is that the dual-polarization SAR data are not completely independent, which causes a certain uncertainty in solving the SM and Z parameters simultaneously based on the single-temporal SAR data.

5. Conclusions

An algorithm for retrieving the SM is proposed in this paper based on the parameterization of some theoretical models. The spatial distribution of SM is estimated over an agricultural area in Hebei Province of China using both the Sentinel-1 and Sentinel-2 data. The encouraging comparison results (R = 0.85, RMSE = 0.032 cm³·cm⁻³) between the SM inversion results and the measured values confirm that it is feasible to develop the SM inversion algorithm based entirely on theoretical model simulations instead of the essential support of the in situ measured data.

Since the performance of the modified ratio model developed in this paper depends entirely on whether the input parameter configuration of the MIMICS model is consistent with the actual situation, it is not suitable for areas with a variety of unknown vegetation types. The differences between the vegetation types are significant, and the model-based simulations are only valid when the model input parameters match the actual vegetation type. Therefore, the empirical coefficients listed in Table 3 in this paper is only applicable to winter wheat and not to other vegetation types. However, the method proposed in this paper is completely independent of the in situ measured data, and it can well predict the changing trend of SM in the areas where the prior knowledge of the vegetation types has been known. Under the premise of correctly setting the input parameters of the scattering model, the method proposed in this paper can be effectively implemented to retrieve the soil moisture information especially in areas where in situ SM measurements are not easy to carry out.