Estimating salt content of vegetated soil at different depths with Sentinel-2 data

Measurement of SSC

The soil samples were first dried, ground, and then screened with a 2.0-mm sieve to remove the small stones and wood pieces. The processed samples were mixed with water to make soil solution (the ratio of soil to water is 1:5). Eight hours after the solution was prepared, its electrical conductivity (EC_1:5, ds/cm) was measured by conductivity meter (DDS-307A; Shanghai Youke Instrument Branch, Shanghai, China), and then the SSC (%) was calculated by the empirical formula (1) , which was developed by Huang et al. (2018) in their research in HID. (1)${\displaystyle SSC=\left(0.2882\times {\text{EC}}_{1:5}\right)+0.0183.}$

Statistical characteristics of SSC

We selected five depths (0∼20 cm, 20∼40 cm, 40∼60 cm, 0∼40 cm and 0∼60 cm) in this study, and the SSC of 0∼40 cm was the mean value of 0∼20 cm and 20∼40 cm and that of 0∼60 cm was the mean value of 0∼20 cm, 20∼40 cm and 40∼60 cm. The sample points were sequenced according to the SSC, and then one of every three samples were selected as the validation dataset so that the ranges of calibration and validation datasets were consistent and evenly distributed. The statistical characteristics of SSC are shown in Table 1.

Selection of spectral index

In this study, we selected 32 widely used spectral indices, including salinity index, vegetation index and drought index. The indices and the relevant formulae are shown in Table 3.

Soil line fitting

As has been shown in the Nir-Red scatterplot of several studies, when the horizontal and vertical coordinates are the red and Nir bands, respectively, a series of corresponding points of the digital number values of the red and Nir infrared wavelengths of the bare soil approximate to fit into a straight line, which is called soil line (Wu et al., 2014a). Three spectral indices (PVI, PDI and VAPDI) used in this study were based on the concept of soil line. Eight hundred pure bare pixels (NDVI <0.1) were identified by visual interpretation using conventional soil line extraction for soil line fitting. R ², M, and I were 0.9694, 1.0984, and 0.0152, respectively (Fig. 2).

Full subset selection

According to the least squares method, the full subset selection is a method to select the optimal combinations by traversing all possible combinations of the full IV set (the IV set includes 12 bands and 32 indices). The calculation of the full subset selection takes the following steps: When the number of IVs is P, P models can be built according to K, the number of IVs input into the model (1 ≤ K ≤ P, K is integer), and there are $C_P^K$ combinations of IVs for each model (Zhang et al., 2019b). Therefore, based on the calibration dataset, the optimal combination of the IVs for each model was selected according to the maximum of the adjusted coefficient of determination (R²_adj). Afterwards, based on the R²_adj, root mean square error (RMSE), mean absolute error (MAE), Akaike information criterion (AIC) and Bayesian information criterion (BIC), the optimal model from P models at each depth was selected on the ground of the validation dataset. Considering the computational magnitude problem of full subset selection, the value of K was taken from 2 to 6.

Among the five criteria, R²_adj can improve the accuracy of the comparison between the models with different numbers of IVs and samples. As the number of IVs in the model increases, R²_adj will not necessarily increase (Srivastava, Srivastava & Ullah, 1995), which mitigates the difference among the coefficient of determination caused by the number of IVs. RMSE and MAE are indicators to evaluate the model inversion error; AIC and BIC measure the goodness of model fit. Smaller values of AIC and BIC mean the model can explain the dependent variable (DV) with fewer IVs (Atkinson et al., 2012). The equations are shown in Eqs. (2)–(6) (2)${\displaystyle R_{\mathrm{a}dj}^2=1-\left(1-\frac{\sum _{i=1}^n{\left({\hat{y}}_i-\overline{y}\right)}^2}{\sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}\right)\frac{\left(n-1\right)}{\left(n-k\right)}}$ (3)${\displaystyle RMSE=\sqrt{\frac{\sum _{i=1}^n{\left({\hat{y}}_i-y_i\right)}^2}{n}}}$ (4)${\displaystyle MAE=\frac{1}{n}\sum _{i=1}^n\left|{\hat{y}}_i-y_i\right|}$ (5)${\displaystyle AIC=2k+n\left[ln\left(RSS\right)\right]}$ (6)${\displaystyle BIC=n\left[ln\left({\hat{\sigma }}^2\right)\right]+k\times ln\left(n\right)}$

where ${\hat{y}}_i$, y_i and $\overline{y}$ are the predicted, measured, and the average of measured values of the model, respectively; n is the number of samples; k is the number of free parameters in the model; RSS is the squared sum of the residuals between the measured and predicted data; ${\hat{\sigma }}^2$ is the error variance.

BPNN Model

BPNN algorithm, proposed by Rumelhart, Hinton & Williams (1986), has a strong nonlinear mapping capability and can adjust the internal parameters of the system according to the error between the output and actual value via the error back propagation algorithm. Topologically, the BPNN model consists of three layers: the input, hidden, and output layers (Fig. 4) (Wang et al., 2018). After extensive pre-testing, the BPNN model in this study used the optimal combination of IVs as the input layer, SSC as the output layer, and the number of hidden layers was set as 2. The transfer functions of the input and output layers were linear, and the hidden layers were tangent-S. The target error and network learning rate were 0. 65 ×10⁻³ and 0.05, respectively. In order to eliminate the effect of different dimensions on data analysis, the input layer and output layer data were normalized (so were the other three models). MATLAB was used to build the BPNN model (so were the other three models). Details of BPNN can be found in Xiao et al. (2020) and Chen et al. (2015).

SVM Model

SVM is a machine learning algorithm based on the principle of structural risk minimization. It focuses on transforming the input data into a high-dimensional feature space using nonlinear transformations for classification and regression (Chen et al., 2015). This algorithm enjoys such advantages as avoiding discrete values, mitigating overlearning and reducing computation. This study adopted the widely used radial basis kernel (RBF) (Zhang et al., 2019b) as the kernel function of SVM. The penalty parameter (C) and the nuclear parameter (g) of the RBF have a great effect on the model stability, so a grid-searching technique was used to find the best parameters of C and g (at 0∼20 cm 20∼40 cm 40∼60 cm ∼40 cm and 0∼60 cm, the C was 724, 1024, 1024, 1024 and 1024, respectively, the g was 0.0313, 0.0028, 0.0039, 0.0156 and 0.01, respectively).

ELM Model

ELM is a machine learning algorithm proposed by Huang, Zhu & Siew (2006). It is the same as BPNN in structure, a traditional three-layer neural network (Fig. 4). Its main difference is that the execution does not require adjustments to the input weights of the network or the biases of the hidden elements. Therefore, ELM can reduce the influence of such subjective factors as choice of parameters, and speed up computation while ensure accuracy (Ahila, Sadasivam & Manimala, 2015; Prasad et al., 2019). After extensive pre-testing, this study adopted sigmoid as the activation function, and the number of hidden nodes was set as 6. Detailed principles of ELM can be found in Zhu et al. (2020).

RF Model

RF is a machine learning algorithm proposed by Breiman (2001). Based on multiple decision tree theory, this algorithm can be used for classification and regression. RF uses the bootstrap method to extract training sets from the input data, and randomly generates variables to build decision tree models. Thus, the decision made by a random forest model is based on the ensemble of decisions made by numerous decision trees (Fig. 5) (Zhou et al., 2020; Du et al., 2015). After extensive pre-testing, the minimum number of observations per tree leaf (minleaf) and the number of decision trees (ntree) were set as 5 and 10, respectively (the two parameters were determined by the out-of-bag errors and training set cross-validation) (Zhang et al., 2019a).

Model accuracy evaluation

R²_adj, RMSE, and MAE were used to evaluate the inversion of calibration and validation model. Among the three criteria, R²_adj can avoid the errors caused by the different number of IVs in each model. The closer its value is to 1, the better fit the model has. The smaller the RMSE and MAE are, the smaller the deviation between the predicted and measured values are. The equations are shown in Eqs. (2)–(4).

Analysis of BPNN model

The optimal combination (after the full subset selection) of IVs at each depth was input into the BPNN model for training to obtain the SSC inversion model. The accuracy of calibration and validation models are shown in Table 5.

The model performance was optimal at 20∼40 cm, with the R²_adj of around 0.6 for both calibration and validation models, indicating a good fitting and generalization performance. Its RMSE (0.15%) and MAE (0.11%) were relatively low, indicating their good control of inversion errors. The model had the worst performance at 0∼20 cm, with the lowest R²_adj (below 0.48) of the calibration and verification model, and the RMSE (both above 0.17%) and MAE (0.13%) were the highest at the five depths. At 40∼60 cm, the model performance was second only to 20∼40 cm, with a relatively good fitting and low inversion error. The performance of the model at 0∼40 cm and 0∼60 cm was similar. The R²_adj and MAE were around 0.51 and 0.12%, respectively, but the RMSE at 0∼40 cm was greater than that at 0∼60 cm, suggesting that some samples had some relatively big errors.

Overall, the BPNN model worked best at 20∼40 cm, followed by 40∼60 cm, and worked worst at 0∼20 cm. The other two depths had better similar results.

Analysis of SVM model

The optimal combination (after the full subset selection) of IVs at each depth was input into the SVM model for training to obtain the SSC inversion model. The accuracy of calibration and validation models are shown in Table 6.

The model performance was optimal at 40∼60 cm, with R²_adj of 0.58 and 0.55 for the calibration and validation models, respectively, and its RMSE and MAE were the lowest. The performance of the model at 20∼40 cm and 0∼40 cm was similar, second only to 40∼60 cm. Comparatively, 20∼40 cm was slightly better in fitting of validation model. At 0–20 cm, the model performance was still the worst. Its RMSE (above 0.16%) and MAE (above 0.12%) indicated a bad control of inversion error. But its R²_adj was around 0.5, the model at this depth still had a good fitting. At 0∼60 cm, the R²_adj of the calibration and verification models were 0.59 and 0.52, respectively, showing a slight overfitting.

Overall, the SVM model worked best at 40∼60 cm, followed by 20∼40 cm and 0∼40 cm. The worst performance of the model was found at 0∼20 cm.

Analysis of ELM model

The optimal combination (after the full subset selection) of IVs at each depth was input into the ELM model for training to obtain the SSC inversion model. The accuracy of calibration and validation models are shown in Table 7.

The model performance was optimal at 20∼40 cm, with the highest R²_adj (above 0.6) and lowest inversion error. The model was still the worst at 0∼20 cm, mainly because the inversion error was the largest. But it still had a good fitting (R²_adj ≈ 0.5). The performance of the model at 0∼60 cm was slightly better than that at 0∼20 cm. The model performance was satisfactory and similar at 40∼60 cm and 0∼40 cm.

In general, the ELM model worked best at 20∼40 cm, but worst at 0∼20 cm and 0∼60 cm (0∼60 cm was slightly better). This model had relatively good performance at the other two depths.

Analysis of RF model

The optimal combination (after the full subset selection) of IVs at each depth was input into the RF model for training to obtain the SSC inversion model. The accuracy of calibration and validation models are shown in Table 8.

The RF model performed well at all five depths, with R²_adj all above 0.5. The model performance was still optimal at 20∼40 cm. The R²_adj of the calibration and validation models were 0.68 and 0.63, respectively, which were significantly better than at the other depths. Its RMSE (below 0.14%) and MAE (below 0.11%) indicated that the inversion error was well controlled. At 0∼40 cm, the model performance was second only to that at 20∼40 cm. The result was worst at 0∼60 cm. Its RMSE and MAE were around 0.15% and 0.12%, respectively, indicating a relatively high inversion error. However, its R²_adj also reached 0.53. The model performance at 0∼20 cm was slightly better than that at 0∼60 cm because the former’s R²_adj of the calibration and validation models were higher (0.03 and 0.01 higher, respectively) than that of the latter. There was some overfitting at 40∼60 cm.

In general, the RF model had a good performance at all depths, working best at 20∼40 cm. The performance was relatively poor at 0∼20 cm and 0∼60 cm (0∼20 cm was slightly better). The scatterplot of measured and predicted SSC of the four models at the best depth are shown in Fig. 7.

Evaluation of inversion depths

The inversion performance of each model at different depths has been discussed in detail (the Section of Model calibrations and validations). In this section, the sensitivity of Sentinel-2 to SSC at different depths was evaluated by analyzing the combined performance of all models at each depth (Fig. 8). At 20∼40 cm, the R²_adj was significantly higher than that of other depths (Figs. 8A–8E), and each model was able to achieve a good fitting and generalization performance. At this depth, the RMSE and MAE of the calibration models were the lowest, and those of the validation models were also relatively low (Figs. 8F–8O). It indicated that all models were able to control the inversion errors at 20∼40 cm. Therefore, 20∼40 cm was the optimal depth for the Sentinel-2 data for SSC inversion. The R²_adj at 0∼20 cm and 0∼60 cm was relatively low overall, and the inversion error at 0∼20 cm was the highest among all depths (Fig. 8). The overall fitting at 40∼60 cm and 0∼40 cm was satisfactory, and the inversion error at 40∼60 cm was better controlled (Fig. 8). Therefore, Sentinel-2 had the lowest sensitivity at 0∼20 cm. At 0∼60 cm, it was slightly better than 0∼20 cm. The inversion performance was good at 40∼60 cm and 0∼40 cm, and that at 40∼60 cm was relatively better.

As is analyzed above, the sensitivity of Sentinel-2 to SSC at different depths in the vegetated area was as follows: 20∼40 cm > 40∼60 cm > 0∼40 cm >0∼60 cm >0∼20 cm.

Evaluation of inversion models

In this section, the SSC inversion ability of each model was evaluated by analyzing the combined performance at all depths of each model (Fig. 9). The overall R²_adj of the RF model was higher than that of the other models (Figs. 9A–9D). Although some overfitting occurred at 40∼60 cm, the model still had a good fitting and generalization performance. The RF model had the lowest RMSE and MAE at all depths (Figs. 9E–9L), and the inversion error was especially well controlled at 0∼20 cm where the inversion errors of other models were all high. Therefore, the RF model was the optimal model for SSC inversion. The BPNN model fitted relatively poorly at most depths (Figs. 9A–9D), and the MAE of BPNN model was high at all depths (Figs. 9I–9L). Therefore, the BPNN model had a relatively slightly poor SSC inversion ability. The SVM and ELM models had better fitting and generalization performance, and their inversion errors were relatively low (Fig. 9). The ELM model was obviously better for the inversion at 20∼40 cm than that of SVM model. Therefore, both of them have satisfactory SSC inversion performance though ELM model was slightly better.

When R²_adj, RMSE and MAE were all taken into consideration, the SSC inversion capability of all models was as follows: RF model > ELM model > SVM model > BPNN model.