Radar remote sensing-based inversion model of soil salt content at different depths under vegetation

Overview of research site

The experiment was conducted in the Shahaoqu Irrigation Area (SIA) of the Hetao Irrigation District, Inner Mongolia, China (Fig. 1). SIA totals about 6,000 hectares (15 km from north to south and 4 km from west to east). The south is higher than the north, and the average altitude is 1,034–1,037 m. The soil samples were identified as silty clay loam and sandy loam according to the USDA system (Soil Texture Calculator NRCS, https://www.nrcs.usda.gov). The main vegetation includes corn, wheat and sunflower. Located in the mid-temperate zone, SIA is slightly influenced by the warm southeast monsoon and greatly affected by the dry and cold northwest monsoon. This area is cold and dry all the year round, with an average temperature of about 7 °C, an average annual precipitation and evaporation of 140 and 2,000 mm, respectively (Zhang et al., 2018). The irrigation method here is mainly flood irrigation from the Yellow River, supplemented by submersible irrigation. Long-term inappropriate irrigation has led to secondary salinization in this area.

Soil sample collection and chemical analysis

This research is supported by the program of Diagnosing and Estimating Techniques and Methods of Soil Moisture and Salt Content at Different Depths, a subitem of the State Key Development Program of Water Saving, Sewage Reduction and Salinity Control Technology and its Application in the Farmland, which was approved by Chinese Ministry of Science and Technology on March 29, 2020. HID administration approved the experiment in accordance with the program No. (2017YFC0403302) rather than issuing a field permit. The soil samples were collected from July 15 through 18, 2019 when SIA was covered with vegetation. In selecting the sampling points, such local conditions as salinity and vegetation coverage were taken into consideration. The five-point sampling method was adopted, and a hand-held ring knife was utilized to conduct stratified sampling at 0–10, 10–20, 20–40 and 40–60 cm. GPS was used to record the longitude and latitude information of the sampling points. In total, 114 sampling plots (each plot has five sampling points) were established, and the soil samples were collected into the prepared aluminum boxes, weighed and carried to the laboratory. The obtained soil samples were placed in the oven at 105 °C for 8 h. to be dried completely, and then the dried samples were weighed again and ground to remove the large particles. Next, the soil solution (the mass ratio of distilled water to the processed soil was 5:1) was prepared, and its conductivity was measured with a conductivity meter (Leici DDS-307A; Shanghai Yoke Instruments Co., Ltd., Shanghai, China). The empirical formula SSC = 0.2882 EC_1:5 + 0.0183 was used to calculate the SSC. According to the four grades of saline-alkali soil, the 114 treated soil samples were classified into four types: non-saline soil (0–0.2%), slightly salinized soil (0.2–0.5%), strongly salinized soil (0.5–1.0%), and salinized soil (>1.0%). The sample analysis is shown in Table 1. The SSC of 0–40 cm was the average value of the measured SSC at 0–20 and 20–40 cm, and the SSC of 0–60 cm was the average value of the measured SSC at 0–20, 20–40 and 40–60 cm.

Remote sensing data acquisition and pretreatment

Sentinel-1, with a short revisit period and a dual-polarization channel (Gao et al., 2020), can provide continuous images of HIA. The radar satellite image used in this experiment was obtained from Sentinel-1 transiting at 13:46 on July 17, 2019, and the imaging time was almost synchronous with the ground sampling time. The mode of Sentinel-1 image used in this experiment was terrain observation by progressive scans (TOPS), in which the corresponding coverage range was 25 km × 25 km, the ground resolution was 5 m × 20 m, the data was of grade one, and the product data was Ground Range Detected (GRD). The dual-polarization channels are Vertical-horizontal (VH) and Vertical-Vertical (VV). Radar satellite image data were downloaded from ESA data access center (https://scihub.copernicus.eu/userguide/).

Sentinel-1 radar remote sensing image was preprocessed in SNAP and ENVI. The image processing process was as follows: (1) precision orbit calibration, (2) thermal noise elimination, (3) radiometric terrain correction, (4) speckle noise removal, (5) geometric terrain correction, and (6) radar backscattering coefficient (VV and VH) extraction. The speckle noise was processed with a filter of Refined Lee and the terrain correction was based on the digital elevation model generated by the Shuttle Radar Topography Mission (SRTM).

Polarization combination index construction and best subset selection

Researches indicated that ground object features can be reflected by the magnitude of radar backscattering coefficient (Yu et al., 2020; Stamenkovic et al., 2017). Due to the limited ground object information in a single backscattering coefficient, in this study, twelve sets of polarization combination indices were generated from the two groups of backscattering coefficients through a series of mathematical operations so as to reflect more ground object information. For convenience, all the polarization combination indices were renamed and shown in Table 2.

Best subset selection (BSS) is used to select variable sets for multiple regression. Its principle is, according to all the different combinations of independent variables, to use partial least squares to perform fit analysis on each combination so as to select the only model whose combination has the best performance. Therefore, BSS is often used in variable selection. Its calculation is as follows: Let K be the number of independent variables (K = 1,2,…, P); 1~P models of predicative variables are fitted. Among the 1~P models, P optimal models were selected when the R² reached the maximum and R_MSE the minimum after adjustment by validation sets. According to the R² and R_MSE after adjustment, an optimal combination of independent variables was selected from P models. The BSS in this study was mainly conducted in LEAPS of R3.5.1.

Construction of salinity inversion models

To ensure the generalization ability and robustness of the model, the total soil samples (n = 114) were randomly divided as calibration set (76 samples) and validation set (38 samples) at the ratio of 2:1. The samples were cross validated using stratified 3-fold cross validation.

Previous studies have shown that the optimal machine learning methods for SSC inversion accuracy vary from research areas (Hoa et al., 2019). Therefore, this study adopted four commonly used machine learning methods: PLSR, QR, SVM and ELM. These methods have demonstrated good universality and stability in soil salinity study (Wang et al., 2020; Hu, Liu & Peng, 2019). Some main characteristics of these methods are outlined as follows.

PLSR models

PLSR is a statistical analysis based on multiple elements (Zhou et al., 2018). As an improved version of least square regression, PLSR enjoys more flexible problem-solving ability because it integrates principal component analysis, multiple linear regression and canonical correlation analysis. Its basic principle is as follows: components are interactively extracted from variables X and Y, and according to principal component analysis, the independent and dependent variable matrices can be decomposed into two matrices multiplied by each other:

(1) $$Y=U(n\times a)Q(a\times m)=F$$

(2) $$X(n\times p)=T(n\times a)P(a\times p)=E$$where n represents the sample size, p is the independent variable, m is the number of dependent variables, a is the number of principal components, E and F are the random error matrix. In model construction and sample prediction, the leave-one-out method was adopted. Cross-validation was used to determine the number of principal components. The establishment and prediction of PLSR model were completed in MatlabR2016b.

QR models

Quantile Regression (QR), proposed by Bassett and Koenker in 1978, is mainly used to study the relationship between conditional quantiles of two variables (Broniatowski et al., 2019). In this study, it handled the relationship between the independent and dependent variables. According to the conditional quantile of the dependent variables, the regression model is derived from fitting. The QR modeling in this study mainly has the following three advantages: (1) It needs no standard normal changes or random perturbations for all variables. It is known from experience that the model accuracy will increase when the variables are perturbed. (2) The abnormal points will not cause too much interference to the model accuracy, so the QR model has a good stability. (3) If the parameters of any quantile are given, the changes of dependent variables caused by the influence of parameters becomes interpretable when the parameters are different. The rationale of QR is as follows: a random sample of the dependent variable Y is $\left\{y_1,y_2,y_3,\cdot \cdot \cdot y_n\right\}$, the sample quantile linearity under the quantile condition $\tau$ should meet the following equation:

(3) $$\begin{array}{c}min\\ \beta \in R\end{array}(\sum _{i=1}^n{y}_i-x_i^{{}^{\prime }}\beta (\tau ))$$where $y_i$ represents the dependent variable and $\beta$ the unknown parameter. For any $0<\tau <1$, the formula for parameter estimate is:

(4) $${\beta }^{{}^{\prime }}=\arg min\sum _{i=1}^n{y}_i-x_i^{{}^{\prime }}\beta (\tau )$$when the test function is substituted into Eq. (5), which is rewritten as Eq. (6), the parameter $x^{{}^{\prime }}\beta (\tau )$ is obtained. Then, the obtained parameter is the unique regression quantile.

(5) $$\begin{array}{c}min\\ \beta R\end{array}\left[\sum _{i:y_{i\ge x_i^{{}^{\prime }}\beta (\tau )}}\tau \left|y_i-x_i^{{}^{\prime }}\beta (\tau )\right|+\sum _{i:y_{i\ge x_i^{{}^{\prime }}\beta (\tau )}}(1)-\tau \left|y_i-x_i^{{}^{\prime }}\beta (\tau )\right|\right]$$where $\beta (\tau )$ represents the solution of the minimization problem. The QR model establishment and prediction were completed in Eviews 9.

SVM models

SVM, based on statistical theory and structure minimization, employs nonlinear mapping to transform the data into higher-dimensional feature space, in which linear model fit of dependent variables is carried out (Nakagawa et al., 2007). SVM can avoid redundant discrete values of traditional regression models and “over-learning” in variable analysis (Kisi & Cimen, 2012). Recently, the application of SVM has gradually shifted from image recognition and classification to regression problems. The rationale of SVM model is as follows: with the constraint of the condition of

$$\{\begin{array}{c}{y}_i\left[(\omega \cdot x_i)+b\right]\ge 1-{\xi }_i\\ {\xi }_i\ge 0\end{array}$$

(6) $$(i=1,2,\cdot \cdot \cdot ,l)$$

find the minimum of function

(7) $$\mathrm{\Phi }(\omega ,\xi )={\displaystyle \frac{1}{2}(\omega \cdot \omega )+c(\sum _{i=1}^n{\xi }_i)}$$where $c$ represents the penalty coefficient used to control the equilibrium of the boundary of error $\xi$. ${\alpha }_i$ represents the Lagrange multiplier, and it is transformed into a quadratic function, thereby the extreme value is found. With the constraint of

$$\{\begin{array}{c}\sum _{i=1}^n{y}_i{\alpha }_i=0\\ 0\le {\alpha }_i\le c\end{array}$$

(8) $$(i=1,2,\cdot \cdot \cdot ,l)$$

find the maximum of

(9) $$W(\alpha )=\sum _{j=1}^l{\alpha }_i-{\displaystyle \frac{1}{2}\sum _{i,j-1}^l{\alpha }_i}{\alpha }_j{y}_i{y}_j(x_i\cdot x_j)$$

Then the optimal discriminant function is

(10) $$f(x)=\mathrm{sgn}\{\sum _{i=1}^l{\alpha }_i{\alpha }_{j}K(x_i\cdot x_j)+b$$where the kernel function $K(x_i\cdot x_j)$ is RBF (the Gaussian radial basis function)

(11) $$K(x_i\cdot x_j)=\exp \left(-\gamma {\Vert x_j-x_i\Vert }^2\right),\gamma >0$$

In this study, the SVR analysis of the SVM model was performed in E1071 of R3.5.1, where the kernel function was RBF, Gamma = 0.07, and Cost = 100.

ELM model

As a neural network ELM, proposed by Huang Guangbin (Bai, Huang & Wang, 2016), differs from other neural networks in its feedforward with a single hidden layer (Zhao et al., 2012). Its training process is simple, and the only operation is to set the number of nodes in the feedforward network. Compared with the traditional neural networks, ELM needs no adjustment of the connection weights of the input and hidden layers or the number of valves in the hidden layers. Moreover, this model has strong nonlinear fitting ability and high learning speed. The algorithm is as follows:

(12) $$\text{φ}(x)=h(x)H^T({\displaystyle \frac{I}{C}+H{H}^T{)}^{-1}}T={\left[\begin{array}{c}k(x,x_1)\\ \begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}\\ k(x,x_N)\end{array}\right]}^T({\displaystyle \frac{1}{C}+{\mathrm{\Omega }}_{EML}{)}^{-1}}T$$

(13) $$k(a,b)=\exp (-\Vert a-b\Vert {)}^2/\sigma$$

(14) $${\mathrm{\Omega }}_{ELM(i,j)}=k(x_i,x_j)$$where H represents the hidden layer matrix of the neural network, and k is the number of neurons in the hidden layer, which is usually set as RBF nucleus; I is the identity matrix. C is the kernel parameter that needs optimizing; and T is the vector of the predicted target value.

Four machine learning models were constructed with the SSC at different depths as the dependent variables and all the indexes before BSS and the optimal indexes after BSS as independent variables, respectively. The model construction was carried out in R3.5.1.

Evaluation index of model accuracy

The coefficient of determination (R²), root mean square error (R_MSE) and correlation coefficient (r) of the model were used for model accuracy evaluation. The formulae of the three evaluation indexes are as follows:

(15) $$r={\displaystyle \frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n{(x_i-\overline{x})}^2\sqrt{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}}}$$

(16) $$R^2={\displaystyle \frac{{\sum }_{i=1}^n{({\hat{y}}_i-\overline{y})}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(17) $$R_{MSE}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{({\hat{y}}_i-y_i)}^2}{n}}}$$where ${\mathrm{x}}_{\mathrm{i}}$ represents the value of backscattering coefficient, and $\overline{x}$ the average value of backscattering coefficient; ${\mathrm{y}}_{\mathrm{i}}$ the measured SSC value, and ${\hat{y}}_i$ the predicted SSC value; $\overline{y}$ the average SSC; and $\mathrm{n}$ the sample number.

In addition, Ratio of Performance to Deviation (RPD) was used to evaluate the model stability. The formula of RPD is as follows:

$$\mathrm{R}\mathrm{P}\mathrm{D}=\sqrt{\sum _{i=1}^n{\displaystyle \frac{{\left(y_i-\overline{y}\right)}^2}{n\cdot R_{MSE}}}}$$

Previous studies have divided the models into three categories (Chang et al., 2001): (1) when RPD ≥ 2.00, the model has the highest stability and reliable prediction ability; (2) When 1.40 ≤ RPD ≤ 2.00, the model has good stability and prediction ability; and (3) when RPD < 1.40, the model is unstable.

Division of modeling and validation sets

The collected ground data were divided into four grades in terms of salinity. According to laboratory physical and chemical analysis, all the soil samples were divided as modeling and validation sets. The salt content distribution of the total samples, modeling and validation samples at different depths is shown in Fig. 2.

As Fig. 2 shows, the distribution of these three types of samples at different depths is basically the same, indicating the partitioning of modeling and validation sets is reasonable.

Optimal variable combinations by the BSS

According to all the combinations of the given variables, the BSS was used to figure out all the random combinations at the seven depths. Based on these combinations and the R² of the validation sets, the combinations of the independent variables at the seven depths were identified. The optimal combinations of independent variables (OC_IV) at each depth determined by the R² and R_MSE are shown in Table 3.

As Table 3 shows, the two backscattering coefficients plus 12 polarization combination indices, after BSS, generated six optimal independent variables at 0–10, 10–20 and 0–40 cm, respectively. The OC_IV were $V_H$, $V_1$, $V_4$, $H_1$, $H_2$, and $H_5$ when the variable combination was at 0–10 cm; the OC_IV for 10–20 cm were $V_H$, $V_7$, $H_1$, $H_2$, $H_3$, and $H_4$; and the OC_IV for 0–40 cm was $V_V$, $V_3$, $V_4$, $H_2$, $H_4$, and $H_5$. It also shows that as the sampling depth increased the R² of each depth under the OC_IV presented an increase-and-decrease trend and then reached the maximum value of 0.846 at 0–40 cm. As the depth increased, the R_MSE first decreased and then increased.

Construction and validation of PLSR-based SCC models

Construction of PLSR-based SCC models

In this section, PLSR is used for model construction. The model accuracy comparison in Fig. 3 shows: (1) the PLSR model based on the OC_IV after BSS and the PLSR model before BSS had similar results: both models displayed the best performance when the soil depth was 10–20 cm although their model accuracy was somewhat different; the R_MSEc of the modelling set before BSS was 0.09% while the R_MSEp of validation set was 0.1%, showing only a slight difference between the R_MSEc and R_MSEp. (2) Except for 10–20 cm, the model accuracy after BSS was generally lower than that before BSS, which was preliminarily speculated to be related to the decrease of the number of independent variables after BSS.

Validation of PLSR-based SCC models

PLSR models of SSC at different depths were constructed on the basis of the OC_IV through BSS (Fig. 4). As Fig. 4 shows, the predicted values were mainly concentrated in zones I and II, and only one predicted value of 0–10 cm was distributed in zone IV. However, no predicted values of 0–10, 0–20 and 40–60 cm appeared in zone III. At 0–10 and 0–40 cm, the R² of the modeling and validation sets were 0.04 and 0.03, respectively, showing a relatively small difference. At these two depths, the R_MSE differences of the modeling and validation sets were 0.12 and 0.03, while the R_MSEp and R_MSEc were 0.20% and 0.14%, respectively. At 0–20 cm, the difference between R_c² and R_p² was the greatest (up to 0.15), and the R_MSE difference was also the largest (0.20).

In general, the PLSR model had a satisfying prediction at 0–60 cm. At this depth, the R_c² of the modeling and the validation sets were 0.47 and 0.35, respectively; the difference between R_c² and R_p ² was 0.12 while the difference between R_MSEc and R_MSEp was 0.02. When the sampling depth was 10–20 cm, the predicted values all appeared in zones I, II and III, and one predicted value was very close to zone IV, and the model fit curve was close to function y = x. At this depth, the corresponding R_c² and R_p² were 0.4 and 0.32, the R_MSEc and R_MSEp were 0.21% and 0.29%, respectively, so there was no overfitting and the model displayed satisfactory prediction. As Figs. 4C–7 shows, at 0–20 cm, the model had the worst prediction performance because the model fit function obviously deviated from function y = x, and the R_c² and R_p² were only 0.27 and 0.12, respectively.

The comparison of all the prediction figures of SSC at different depths showed that, after BSS of OC_IV, the fit curve of the measured and predicted SSC at 10–20 cm was closer to the function y = x. The fit accuracy of the PLSR model for 10–20 cm was higher than the predicted values for the other six depths.

Construction and validation of QR-based SSC models

Construction and verification of ELM-based SSC models

Verification of ELM-based SSC models

Figure 8 gives the results of ELM models of SSC at different depths constructed after BSS.

After BSS, the ELM models of SSC at the seven depths had no overfitting. The predicted values were concentrated in the vicinity of non-salinized soil and slightly salinized soil in zones I and II. At 20–40 and 40–60 cm, no predicted values appeared in zone IV, indicating the failure of OC_IV of the ELM model in predicting the values of salinity after BSS. At 0–10 cm, the model failed to predict the value of severely salinized soil in zone III. However, at other depths, the ELM model had predicted values in zones I, II, III and IV, which preliminarily indicated that the ELM model had better performance than PLSR model in salinity estimation at the seven depths.

Among the models for the seven depths, the model effect was relatively poor at 40–60 cm: the R_c² and R_p² were 0.26 and 0.16, respectively, and the R_MSEp and R_MSEc were both less than the model error of 0.4%. The differences of the R_c² and R_p² at 0–10, 0–20 and 40–60 cm reached 0.14, −0.18 and 0.1, respectively, and were relatively large. Meanwhile, the differences of R_MSEp and R_MSEc reached −0.13%, 0.31% and −0.22%, respectively, and were also relatively large, indicating a poor model stability at these three depths. At 10–20, 20–40 and 0–60 cm, the differences between the R_c² and R_p² were 0.09, −0.05 and 0.05, respectively, and were relatively small. The differences of the R_MSEp and R_MSEc were 0.19%, 0.07% and 0.12%, respectively, and were also small, indicating the stability of the ELM model at these three depths. At 0–40 cm, the difference between R_c² and R_p² was 0.04, and the difference between R_MSEp and R_MSEc is −0.03%, indicating that the ELM model was most stable at 0–40 cm.

In general, at 10–20, 0–20 and 0–60 cm, the fit curve for the ELM models was closer to the distribution trend of function y = x. At 10–20 cm, the R_c² and R_p² of ELM model had the best effect, reaching 0.53 and 0.44, respectively. Meanwhile, the R_MSEp and R_MSEc were 0.29% and 0.10%, respectively, indicating that 10–20 cm was the optimal inversion depth for ELM model.

Construction and validation of SVM-based SSC models

Construction of SVM-based SSC models

In this section, SVM is used to for the model construction. As the comparison of model accuracy in Fig. 9 shows, before BSS, the R_MSE of both the modeling and validation sets were relatively high at 0–60 cm while the R² was relatively low. The R² of the modeling and validation sets at 10–20 cm was the highest among all the seven depths. Compared with the SVM model before BSS, in the SVM model after BSS, the R² of the modeling and validation sets at other depths were increased except for the decrease of R_p² in the validation set at 40–60 cm, and the R_MSE of the model decreased and remained stable after BSS.

Validation of SVM models

After BSS, the prediction effect of the SVM model for seven different depths is shown in Fig. 10. As is shown, the SVM model based on the OC_IV at the seven depths after BSS displayed no overfitting. The predicted values were concentrated in zones I and II, and at each depth, the predicted values appeared in zones III and IV. This trend was also consistent with the distribution of ground measured data, indicating the suitability of the SVM model for SSC estimation at different depths.

After BSS, the R_MSEs of the SSC inversion models at the seven depths were all less than 0.4%. At 40–60 cm, the SVM model prediction was relatively poor: the R_c² and R_p² reached the minimum of 0.37 and 0.23, respectively, and the difference between the R_MSEp and R_MSEc was −0.19%, indicating the instability of the SVM model at this depth. At 20–40, 0–40 and 0–60 cm, the differences between the R_c² and R_p² (0.01, −0.04 and 0.06, respectively) as well as that between the R_MSEp and R_MSEc (−0.09%, −0.01% and 0.13%) were both relatively small, indicating the relative stability of the SVM model at these three depths. At 0~–10 cm, 10–20 cm, 0–20 cm, the absolute values of the difference of the R² reached 0.18, 0.11 and 0.13, respectively; and the difference of the R_MSE (−0.07%, 0.07% and 0.09%, respectively) were relatively small. At 10–20 cm, the R_c² and R_p² reached their maximum of 0.56 and 0.67, respectively; the R_MSEp and R_MSEc were 0.19% and 0.12%, respectively; and the model fit curve was close to the distribution of function y = x. It showed that the optimal depth for SVM was 10–20 cm.

Model comparison and analysis

With the OC_IV at different depths after BSS as independent variables, the inversion models of SSC at different depths were constructed. For the same soil depth, the fit of each model is shown in Fig. 11. Indices of R_c², R_MSEc, R_p², R_MSEp and RPD were used to evaluate the prediction ability of PLSR, ELM, SVM models for different depths so that the optimal inversion model was screened out (Table 4). As is shown, PLSR had the lowest stability (RPD = 1.42) while SVM had the highest stability (RPD = 1.85).

Table 4:

Comparison of soil salinity inversion models at different depths.

Model	Optimal depth (cm)	Rc2	RMSEc	Rp2	RMSEp	RPD
PLSR	10–20	0.4	0.21	0.22	0.29	1.46
QR	0–20	0.36	0.17	0.48	0.56	1.63
ELM	0–40	0.27	0.26	0.23	0.29	1.42
SVM	10–20	0.56	0.19	0.67	0.12	1.85

DOI: 10.7717/peerj.13306/table-4

As Fig. 11 shows, the fit curves of PLSR, ELM and SVM models for the depth of 0–10 cm were compact, indicating that the three models have the same estimation ability at this depth. Among the three models constructed for 0–20, 0–40 and 0–60 cm, PLSR had relatively poor fit. The fit curve of SVM was smoother than that of PLSR and ELM at these three depths; and the R² of SVM model reached 0.57 at 0–40 cm. At 20–40 cm, the fit accuracy of PLSR, ELM and SVM models (with R² of 0.32, 035 and 0.43 respectively) was relatively high, indicating the stability of the three models at this depth.

The comparison showed that at 10–20 cm the model fit accuracy of PLSR, ELM and SVM reached 0.40, 0.53, and 0.56, respectively, and the three models had the best model fit curve.

Estimation performance of the four models

It should be noted that there are few studies on radar remote sensing-based estimation of SSC especially under vegetation due to the lack of a simple and effective radar backscattering model for SSC inversion. Therefore, the use of radar images together with optimal machine learning methods is important for the inversion of SSC under vegetation. For this reason, four machine learning methods were used to model the relationship between Sentinel-1 radar images and the measured soil salinity.

Due to the non-negligible effects of environmental factors such as geographical patterns and agricultural activities on soil salinity, the general relationship between Sentinel-1 signals and soil salinity is highly nonlinear (Bai et al., 2020). This complicated relationship poses a challenge to SSC inversion models. As is known in the previous section, the performance of the four models in validation data set ranked as follows: SVM > QR > ELM > PLSR. The R² and R_MSE of the SVM model reached 0.67% and 0.12%, respectively. Xu et al. (2020) associated pixel brightness of digital images of surface soil with soil salinity, and evaluated the accuracy of PLSR and RF in terms of the R_MSE and R². The results showed that the R_MSE of RF was 3.31 g/kg smaller than that of PLSR, the R² of RF was 0.13 larger than that of PLSR. Chen et al. (2020b) used UAV remote sensing data together with four machine learning methods to build SSC models of sunflower in different growth stages and different soil depths. The comparison showed that SVM, BPNN and ELM outperformed PLSR, and BPNN had the best performance (R² = 0.718, R_MSE = 0.062%).

To sum up, our study showed that nonlinear models (SVM, QR and ELM) outperformed the linear model (PLSR) in prediction accuracy and stability, and this result agrees favorably with that of Taghadosi & Hasanlou (2021) and Wang et al. (2021a). In model construction, the nonlinear models adopted in this study enjoyed the following advantages. The SVM model has good robustness because it can grasp the key samples and eliminate redundant samples. More importantly, it can minimize the sample errors and reduce the upper bound of the model prediction errors using the limited sample information, thus improving its generalization and anti-noise disturbance abilities (Jing et al., 2012). The QR model can more comprehensively characterize the conditional distribution of the explained variables, and the estimation results are more robust to the outliers. The ELM uses the regularization method to calculate unknown variables in order to achieve infinite proximity to the target variables of any continuous system. In general, because of their stronger analytical ability, nonlinear models are more stable and accurate (Farahmand, Sadeghi & Farahmand, 2020). Therefore, they have become powerful tools for SSC monitoring.

Optimal inversion depth

The study showed that 0–20 cm was the best inversion depth of SSC under vegetation. In the study area, the period when the soil was under full vegetation was the middle and later stages of irrigation. In this period, the salt carried by the irrigation water would migrate upwards and aggregate at the shallow soil depths (<30 cm) due to the strong evaporation. The active root layer is in 10–30 cm, so the effect of soil salt on crop growth is closely related to the root zone (Kumar et al., 2021). Therefore, the depth of active root layer is a major reason for the difference of inversion accuracy at different depths. The optimal inversion depth of 0–20 cm is reasonable because this depth is within the active root layer. In the same study area, Tan et al. (2020) also found the optimal inversion depth was 0–20 cm (R² = 0.875, R_MSE = 0.7%) when they monitored soil moisture content in the root zone of mature corn using UAV multi-spectral remote sensing. Because 20–60 cm is beyond the active root layer, the prediction accuracy was unsatisfactory at this depth. Overall, the difference of inversion accuracy in soil depths is not only a statistical result of the inversion models but also the co-result of salt migration and vegetation physiological response.

In this study, the optimal SSC inversion depth of 0–20 cm stemmed from the full consideration of different depths under vegetation as well as the actual irrigation situation in the study area. This result was consistent with that of previous studies. Therefore, the result of this study has more practical value.

Influence of other factors

In this study, soil salinity under vegetation was monitored via Sentinel-1 images of vegetation growth indirectly. However, both soil moisture and salinity have been identified as important factors influencing vegetation growth, especially under water deficit conditions (Wang et al., 2019a; Hassani, Azapagic & Shokri, 2020; Zhang et al., 2021). Therefore, ignoring the effect of soil moisture on vegetation may introduce additional errors in SSC estimation (Liu et al., 2020). Meanwhile, vegetation coverage is also a non-negligible factor affecting the Sentinel-1 signal (Dinh et al., 2018). Existing researches indicate that Sentinel-1 signal is more affected by soil than vegetation in areas with low vegetation coverage (Li, Chen & Xu, 2019). Textural characteristics and roughness of the soil also have some impact on the SSC inversion (Ren et al., 2016; Karthikeyan et al., 2019). In this regard, categorizing the vegetation coverage may be an effective solution to this problem (Lykhovyd, 2021). Therefore, in the future, appropriate models should be selected according to the different categories of vegetation coverage. In addition, human activities can also cause uncertainty in the estimation results (Martínez-Sánchez et al., 2011). For example, the diffuse irrigation used in the study area can exacerbate the extreme distribution of soil salinity, causing great salt accumulation in the topsoil at low topography (Huang et al., 2018; Mao et al., 2020). However, vegetation cover can mask this information, leading to salinity underestimation by the model. In conclusion, future work should focus on coupling existing monitoring models with soil salinity formation mechanisms to achieve more accurate SSC estimation with remote sensing.