#### 3.1. Data Analysis of Beigong Reservoir Samples

According to the GPS locations of the 36 sample points, after the preprocessing of the UAV-borne HRS images, the spectral curves of the remote sensing reflectance obtained from the images are shown in

Figure 4. Distinct bimodal characteristics are apparent in the reflectance curves. The main reflection peak appears in the wavelength range of 560–590 nm, and the secondary reflection peak is located in the infrared band between 790 nm and 900 nm. Since the overall SSC in the reservoir is low, the first peak is formed above the second peak. A reflection peak appears at a wavelength of 700 nm. When the SSC increases, the reflection peak moves toward the long wave direction (“red shift”) [

35]. Therefore, the curves of the remote sensing reflectance have the obvious spectral characteristics of suspended solids and can be used for the study of SSC inversion.

The 36 water samples were tested in the laboratory, and a line chart of the SSC is shown in

Figure 5. The SSC values of samples 1–6 and 19 were high, generally exceeding 10 mg/L. Sample 2 had the highest concentration of 18 mg/L. Conversely, the test results of samples 22–36 were at a lower level. When combined with

Figure 1, it is further found that the turbid area is generally concentrated in the west bank of the reservoir, especially in the southwest direction near the shore, while the SSC at the north bank is at a medium level.

Table 2 lists the descriptive statistical information of the SSC, including the number of samples, the minimum (Min), the Maximum (Max), the mean, the standard deviation (SD) and the coefficient of variation (CV). The SSC is low overall (Min = 2 mg/L, Max = 18 mg/L, mean = 5.86 mg/L, SD = 4.61 mg/L, CV = 0.79), which is in line with the actual water quality conditions of a drinking water source. The standard deviation is 4.61 mg/L, which is slightly less than the mean value, and the degree of data variation is not large. Therefore, it can be preliminarily judged that there are no abnormal sample points, and that the test results of the 36 samples can be used for the SSC estimation.

After the spectral curves of the remote sensing reflectance extracted from the UAV-borne HRS images were preprocessed by maximum and minimum normalization, first-order differential pretreatment, continuum removal, and the band ratio model, Pearson’s correlation analysis was performed between the spectral curves and the WQPs (such as SSC). The results of the correlation coefficients in descending order are shown in

Figure 6. The maximum positive correlation coefficient between the original remote sensing reflectance and SSC is 0.65 (

Figure 6a). There are 58 spectral correlation coefficients higher than 0.6, which are mainly concentrated in the 700–900 nm band, indicating that the reflectivity of this band range is sensitive to changes in SSC. Gitelson [

12] stated that the 700–900 nm band is the best band for remote sensing inversion of SSC. Compared with the original spectra, the correlation coefficient of the max-min normalization (

Figure 6b) decreases in the maximum positive correlation, the largest negative correlation increases to −0.57, and the overall correlation increases insignificantly. The correlation coefficient of the first-order differential pretreatment (

Figure 6c) shows no significant change in the maximum positive correlation, but the largest negative correlation of −0.73 appears near the 660 nm band. The continuum removal (

Figure 6d) result shows high correlation in the 600–650 nm band, but the overall improvement is not obvious compared to the original remote sensing reflectance.

The band ratio model can eliminate the interference of water surface roughness and background noise, and is thus a commonly used contrast enhancement operation in remote sensing quantitative inversion. The exhaustive method was used to calculate the band ratio. By calculating the ratio of the 225 bands with each other, 50,400 characteristic variables were obtained. The Pearson’s correlation coefficients of each characteristic variable with SSC were then calculated, and are arranged in descending order in

Figure 6e. The results show that the maximum correlation coefficient is 0.73, the correlation coefficient of 135 characteristic variables is greater than 0.7, and the maximum negative correlation is −0.72. Compared with the other spectral pretreatments, the correlation of the band ratio model result is increased significantly. Therefore, the band ratio model is suitable for the study of SSC inversion modeling.

#### 3.2. Data Analysis of Shahu Port Samples

The spectral waveform (

Figure 7) collected in the study area is similar to that in the first study area, but the spectral reflectance (near 1%) of the polluted riverway is lower than East Lake and the Yangtze River. This is due to the comprehensive effect of various WQPs such as water-insoluble particulate matter, colored dissolved organic matter (CDOM), and chlorophyll-a (Chl-a) [

36,

37]. The absorption coefficient of CDOM in polluted water is high, while the backscattering of water is controlled by inorganic particulate matter. The common contribution of various factors results in “low scattering and high absorption” of the riverway. The quantitative inversion method based on statistical methods explores the relationship between a single water quality index and the spectra above the water surface without considering the complex underwater optical field. This is significant for the discussion of quantitative inversion technology based on UAV hyperspectral data.

A total of 29 bottles of water samples were collected from SP, East Lake, and the Yangtze River. The concentration curve of suspended solids in laboratory tests is shown in

Figure 8. Sample points 1–9 came from SP, and the SSC was above 200 mg/L, while SSC in East Lake and the Yangtze River was relatively low. According to the descriptive statistics (

Table 3), the overall SSC in the second study area (Min = 26.64 mg/L, Max = 578 mg/L, mean = 173.74 mg/L, SD = 154.64 mg/L, CV = 0.89) is higher than in BR, which involves different water quality conditions in different waters.

The Pearson correlation coefficients between the spectra of the second study area images after preprocessing and suspended matter concentration are shown in

Figure 9. There was no positive correlation between original remote sensing reflectance (

Figure 9a) and SSC, and the maximum negative correlation of −0.789 appears near the 557 nm band. After normalization (

Figure 9b), the correlation between spectra and SSC increased significantly. The correlation between 400–552 nm is greater than 0.6, and the maximum negative correlation of −0.85 appears near the 581 nm band. Compared with the correlation of the original spectra with the WQPs (such as SSC), the first order differential (

Figure 9c), the continuum removal (

Figure 9d) and the band ratio (

Figure 9e) have improved, but they have little change compared with the normalization. In addition, considering the influence of spectral normalization on eliminating the differences caused by different observation environments and the difficulty of UAV image processing, the normalized spectra were selected as the input variables of LSSVM.

#### 3.3. Particle Swarm Optimization-based Least Squares Support Vector Machine Modeling

The training samples were uniformly selected in the study area, and the PSO-LSSVM algorithm was used to model the SSC inversion, as shown in

Figure 10. For BR dataset, the ratio models whose correlation coefficient with SSC was greater than 0.7 were selected as the input variable of the PSO-LSSVM model, and the predicted SSC was used as the output variable.

Firstly, the initial state of the particle swarm needed to be set before undertaking the PSO optimization. The default values were used except for the particle size (5, 10, 15, 20…) and the maximum iteration (50, 100, 150, 200, …). We attempted different particle sizes and maximum iterations by enumeration to prevent the LSSVM model from over-fitting. Finally, for the BP dataset, we confirmed the particle size = 10, maximum iteration = 50, extreme value of inertia factor (${\omega}_{\mathrm{min}}$ = 0.1, ${\omega}_{\mathrm{max}}$ = 0.9), and acceleration constant (${c}_{1}$ = 2, ${c}_{2}$ = 2). The initial values of the particle velocity and position were calculated based on the initial state of the particle swarm. For the SP dataset, the maximum iteration = 100, and the other parameters were the same.

During the iteration, the RMSE of the predicted result was calculated each time, as well as the current local and global fitness of the particle, i.e., pbest and gbest. At the same time, the inertia factor $\omega $ was calculated according to the formula $\omega ={\omega}_{\mathrm{max}}-(ite{r}_{i}-1)\cdot ({\omega}_{\mathrm{max}}-{\omega}_{\mathrm{min}})/iter$, where iter represents the number of iterations.

When entering the next iteration, pbest and gbest were used to update the current particle velocity and position. This method was iterated sequentially until the maximum number of iterations was reached. If the stopping condition was not met, the speed and position of the particle were continued to be updated. After stopping the iteration, the LSSVM model was trained according to the currently obtained optimal parameters. Due to PSO, one of optimization methods, it is not necessary to directly tune LSSVM parameters. After iteration, PSO calculated a and b (Equation (13)) at the minimum fitness. Finally, the UAV-borne HRS image inversion was performed using this model.

Figure 11 shows the fitness curve of the PSO optimization process. For BR, it can be seen that the PSO quickly converges at the beginning of the optimization process, where the fitness value decreases significantly, and then remains at 0.85 mg/L. When iterating nearly 40 times, the fitness decreases slightly to 0.75 mg/L and then remains stable again. At this time,

${R}^{2}$ (0.98), RMSE (0.68 mg/L), and MAPE (12.66%) values remain at a good level. When the data of the second study area were used as input variables, the root mean square error decreased from 32.18 mg/L to 28.56 mg/L, and it did not change after 20 iterations.

To verify the validity of the model, the remaining samples were used as test samples to estimate the SSC. The inversion results of the training set and test dataset are shown in

Figure 12. The predicted values and the true values of all the samples are evenly distributed on the diagonal, indicating that the inversion results are good, and that the model can be used for the inversion of SSC.

#### 3.4. Accuracy Evaluation of the PSO-LSSVM and Other Models

The SSC inversion of inland waters is still a popular and difficult problem. Scholars have proposed a large number of classical algorithm models for the modeling and prediction of WQPs. Doxaran et al. [

38] proposed the use of the sensitivity of the near-infrared band to SSC for the Gironde estuary in France, and modeled the SSC using the band ratio model. Therefore, in this study, we attempted to use the band ratio model to predict the SSC in a variety of common remote sensing inversion models, including exponential function (EF), logarithmic function (LogF), quadratic polynomial (QP), linear function (LinF), and power function (PF) models, to explore whether the traditional empirical or semi-empirical methods were suitable for the inversion of the WQPs of inland waters. For BR, the correlation coefficient between the ratio of the remote sensing reflectance (

${R}_{595}/{R}_{499}$) and SSC reached a maximum of 0.733. The ratio (

${R}_{595}/{R}_{499}$) was used as the input variable of the above five empirical models, and SSC was used as the output variable. The inversion accuracy results are listed in

Table 4. For second study area SP, after normalization, the band (

${R}_{581}$) with the highest correlation with SSC was selected as the input variable of five semi-empirical models. The retrieval results are shown in

Table 5.

In addition, the competitive adaptive reweighted sampling (CARS) algorithm combined with partial least squares (PLS) and RF regression models was also in the comparison experiments (

Table 4 and

Table 5).

Information redundancy is sometimes caused by too many feature variables, and some useless information may be mixed, which, in turn, reduces the inversion accuracy. The CARS algorithm can solve such a problem. CARS selects the wavelengths with large absolute values of regression coefficients in the PLS model through adaptive reweighted sampling (ARS) technology, and removes the wavelengths with low weights, thus playing the role of characteristic band selection. PLS has the advantages of the three analytical methods of principal component analysis, canonical correlation analysis, and multiple linear regression analysis. PLS is, thus, widely used in water quality parameter inversion. The fitting process of PLS does not involve parameter adjustment. However, before fitting, the CARS algorithm should be applied to select effective characteristics. The number of Monte Carlo sampling runs selected was 50.

The RF algorithm is one of the most commonly used algorithms at present, and its training speed and precision are high, making it popular with many researchers. Even if the algorithm is based on no parameter adjustment, as long as enough trees are used, the predicted results of the model will not show too much offset. Therefore, the RF algorithm was also introduced as a comparison to verify its practicability in predicting SSC. For BR dataset, the maximum number of features used by a single decision tree (MNF = 3) and number of subtrees established (NS = 5) is simply adjusted. When MNF and NS continued to increase, over-fitting was unavoidable, and the accuracy of test data no longer increased. For SP dataset, we tried several different values of MNF (1, 2, 3, 4, 5, …, 10) and NS (5, 10, 20, 30, …, 100), and confirmed MNF = 2 and NS = 6. Other parameters are default values and not adjusted.

In

Table 4, comparing the inversion results of all the models, PSO-LSSVM shows the best effect in predicting SSC. Although the prediction accuracy of the test dataset (

${R}^{2}$ = 0.95, RMSE = 0.75 mg/L, MAPE = 13.38%) is lower than the prediction accuracy of the training set (

${R}^{2}$ = 0.98, RMSE = 0.68 mg/L, MAPE = 12.66%), based on the fact that the minimum value of the actual measured SSC is only 2 mg/L, the inversion result is very good. In addition, the RF regression model also shows good performance (

${R}^{2}$ = 0.888, RMSE = 1.13 mg/L, MAPE = 17.56%) in estimating the SSC of the training data, and the inversion accuracy is only slightly lower than that of PSO-LSSVM. Therefore, the RF algorithm could also be used as a research direction for water quality parameter inversion, providing more reference for water quality monitoring methods. However, compared with the RF and PSO-LSSVM models, the prediction effect of the other models is far from ideal. The

${R}^{2}$ values of the training data are always less than 0.6, and the RMSE is generally above 3 mg/L. The effectiveness of the prediction results cannot be guaranteed at this low concentration of suspended solids. One difference with PSO-LSSVM is that the test data of the other models predict better results than the training data. The prediction accuracy of the verification data of the quadratic polynomial is very good (

${R}^{2}$ = 0.804, RMSE = 1.5 mg/L, MAPE = 27.5%), and the prediction ability is second only to the RF algorithm.

In

Table 5, similarly, PSO-LSSVM is the best approach to retrieve SSC. The fitting accuracy of validated data (

${R}^{2}$ = 0.964, RMSE = 28.56 mg/L, MAPE = 13.12%) is slightly better than that of the training data (

${R}^{2}$ = 0.957, RMSE = 31.63 mg/L, MAPE = 17.96%). RF has good performance both in training data fitting (

${R}^{2}$ = 0.810, RMSE = 66.38 mg/L, MAPE = 41.87%) and test data retrieval (

${R}^{2}$ = 0.740, RMSE = 77.21 mg/L, MAPE = 47.30%). Compared with BR, the five semi-empirical models in SP all perform well, especially LogF, QP, and LinF, whose accuracy of training data are close to 0.75, which is much better than the semi-empirical model in BR. It is speculated that this may be related to the high correlation between the input variables of modeling and the retrieved WQPs.

In summary, regarding the SSC inversion based on UAV-borne HRS images, several inversion models were compared for two study areas. In the areas, the overall performance of multiple models is generally consistent. We found that PSO-LSSVM is better than other classical models. When the input variables are the same, RMSE shows the advantages and disadvantages of the inversion results of different models. The output of LSSVM model is closer to the fitting curve. Then, comparing the inversion results of different study areas by using the determinant coefficients and MAPE, PSO-LSSVM performed well in both areas, which proved that the model was suitable for the current datasets. In addition, we also found that Random forest had a good performance both in the simplicity of super-parameters adjustment and inversion accuracy, and this model can be studied in the future. The fitting results of semi-empirical model are stable. Comparing the two study areas, it is found that higher the correlation between water quality parameters and input variables is, higher the inversion accuracy of semi-empirical models. However, the PLS method with feature extraction is not suitable for the current datasets.

#### 3.5. UAV Image Inversion Based on PSO-LSSVM

Figure 13 shows the results of the inversion of SSC for the UAV-borne HRS images using the PSO-LSSVM algorithm. Due to some problems with the GPS information of the ground control points, some of the edge regions of the spliced image after the geometric correction still cannot be completely overlapped (the area of the red frame). However, the site radiation correction was based on the average position of the 5 × 5 window spectra extracted from the empirical position, so as to minimize the influence of positional deviation between the aerial double-high image pixels and the ground-measured points. In addition, there is a noticeable strip-like chromatic aberration on the image, which is due to the splicing of multiple UAV-borne strip images. Therefore, the inversion results shown only reflect the trend of the SSC distribution in the reservoir, and the prediction results at individual pixel points are not considered here.

According to the inversion results, the maximum SSC in the reservoir is 16.92 mg/L, and the lowest is 0.81 mg/L, which is consistent with the laboratory test results (

$SS{C}_{\mathrm{max}}$ = 18 mg/L,

$SS{C}_{\mathrm{min}}$ = 2 mg/L). The points marked on

Figure 13 are the actual values of SSC at the sampling points.

Further observations are shown in

Figure 13. The predicted SSC for the remote sensing imagery is consistent with the observed results in the field. The suspended solids in the southwest part of BR are regionally clustered, and the overall color is close to red. The predicted concentration of suspended solids is above 14 mg/L in this area, which is the highest in the whole reservoir. From

Figure 1 (sampling distribution map), the samples collected in the red area are samples 2–6, which are completely consistent with the results shown in

Figure 5 (actual measured SSC curve). The measured concentration in this area is 14–18 mg/L. During the field sampling, it was found that a large amount of white foam floated on the surface of the water where the water pollution was serious.

In addition, the inversion image shows that the SSC near the shore is generally high, at about 8 mg/L. In particular, many areas near the shore in the eastern part of the reservoir appear as small-scale red areas. The SSC toward the center of the lake decreases significantly, and is mostly around 2 mg/L. This is due to the human and animal activities along the shore, which result in increased turbidity near the shore. However, the area near the lake center is quiet, with few external disturbances, resulting in low SSC.

In the second experiment, we used the established model to retrieve the UAV-borne HRS images from a riverway in SP, as shown in

Figure 14. The points marked on the figure are the actual values of SSC at the sampling points. According to the legend, there is higher SSC in the first half of the riverway, i.e., sampling points 1–5. The average laboratory concentration reaches 411.4 mg/L. The SSC in the second half of the riverway is around 300 mg/L, which is consistent with the laboratory test results of the sample points. It is speculated that the difference of SSC distribution in the riverway may be caused by the different flow direction and width of the riverway. The water flowed from the southwest to the northeast. The initial point passed through a polluted area, which led to increased SSC. Later, due to the widening of the riverway and the precipitation of particulate matter insoluble in water, SSC in the later section decreases. In addition, a clear black area is visible on the edge of the channel on the image. Compared with the original image, it is found that the area is extracted by NDWI and is indeed the water. However, due to the sun’s oblique illumination, the edge of the water is covered by the shadow, and the remote sensing reflectance is low. Therefore, when the experimenter collects the ground-measured spectra, it should try to avoid the shadow area. The gray at the beginning of the river is due to the serious exposure caused by UAV photography, which results in the image masking effect.