15 cruises in-situ data were collected in typical lakes in China in this study. The sampling locations are shown in Figure 1. The principle of selecting lakes in this study is the area, salinity, spatial distribution and temporal distribution of lakes. In terms of lake area, 7 lakes are larger than 1,000 k m 2 , 5 lakes between 100 k m 2 and 1,000 k m 2 , and 3 lakes smaller than 100 k m 2 . From the salinity of the lake, Qinghai Lake and Bosten Lake are salt water lakes, and the other lakes are freshwater lakes. In terms of spatial distribution, these lakes are distributed in five major regions of China, namely, Northeast, Northwest, Central, South and Southwest. And it covers the eastern China from high latitude to low latitude. From the time distribution of the data, the collection time of these sample points is from March to December. Water quality samples in different seasons are taken from some typical lakes, as shown in Table 1. In addition, limited by the number of sampling points, this paper adopts reasonable sampling principles in different lakes to improve the spatial representation.

The remote sensing images of broad bandwidth satellites are from the China Centre for Resources Satellite Data and Application (https://data.cresda.cn/). The remote sensing images come from 8 sensors of 7 satellites, including GF1-PMS, GF1-WFV, GF1B-PMS, GF1C-PMS, GF1D-PMS, GF6-PMS, HJ2A-CCD, and HJ2B-CCD. Their band setting is the same: blue/band 1, green/band 2, red/band 3, and near-infrared/band 4, four spectral bands. The spectral response functions of each sensor are highly similar (Figures 2, 3). The networked joint observation of multiple sensors can meet the requirements of daily full-coverage observation of the whole of China, which is suitable for the dynamic monitoring of lakes in China. Twenty-two broad bandwidth remote sensing images matching the field sampling data were downloaded. The time window is within 1 day of the on-site sampling time. The Second Simulation of a Satellite Signal in the Solar Spectrum vector code (6sV) was used to complete the atmospheric correction of each satellite data, which was used in producing remote sensing products for the TSM concentration in lakes.

The in-situ data include the water spectrum data and the TSM concentration data in lakes. The determination of the TSM concentration adopts the laboratory measurement method, and the process of drying, roasting, and weighing is carried out in the laboratory. The water spectral data are measured by the water spectrometer model RAMSES produced by the German TRIOS company, and the measurement method is the water surface measurement method.

The in-situ spectral data of the lakes is equivalent to the water remote sensing reflectance through the integral band operation (Martins et al., 2017). As shown in Formula 1: R r s γ i = ∑ j = 1 n F i γ j R r s γ j ∑ j = 1 n F i γ j (1) Where R r s γ i ( s r − 1 ) is water remote sensing reflectance; F i is the spectral response function of the i th band of the broadband satellite sensor synchronized with the in-situ data.

The water spectrum data were used to simulate the true values of remote sensing reflectance observed by satellite sensors. Three spectral data of three different TSM concentrations of 6 mg/L, 26 mg/L, and 48 mg/L were selected, and Formula 1 was used to simulate the remote sensing reflectance of eight sensors (Figure 2). Table 2 showed that the MAPE of broad bandwidth satellite remote sensing reflectance under different TSM concentrations was 2.11%, indicating that different broad bandwidth satellites transferred about 2% error in the retrieval model.

The FUI is one of the monitoring data of traditional water quality optical properties. The FUI is closely related to changes in water quality parameters and has strong potential and advantages in monitoring water quality on a regional and global long-term scale. Moreover, the FUI extracted from satellite images has higher accuracy and is closely related to the TSM concentration. The remote sensing extraction of the FUI has strong stability and can convert between different sensors (Wernand et al., 2013; Garaba et al., 2015; Li et al., 2016). Based on the Forel-Ule Scale, the color of natural water is divided into 21 color levels, from dark blue to reddish brown (Novoa et al., 2013; Wang et al., 2014). Therefore, The FUI are added to supplement the input feature dataset of the machine learning model. The calculation method of the FUI refers to the research paper of Li et al. (Wang et al., 2021).

Machine learning models can automatically identify and capture the characteristics of training data and develop predictive models with good performance (Reichstein et al., 2019). Several representative machine learning models are used in the TSM retrieve in water quality, including linear regression, support vector regression, random forest, and BP neural network. To ensure the accuracy and generalization of the retrieved model, The in-situ data and spectral data were divided into the training dataset (N = 230), validation dataset (N = 100), test dataset (Lake Chagan (2021-08-31), Lake Changdang). Water spectral characteristic variables are used to estimate the TSM concentration to check the performance of the machine learning models.

The mean absolute percentage error (MAPE), the mean absolute error (MAE), and the root mean square error (RMSE) are used to evaluate the performance of the TSM concentration retrieval model. Their formulas are as follows: M A P E = 100 % N ∑ i = 1 N E i − M i M i (5) M A E = 1 N ∑ i = 1 N E i − M i (6) R M S E = 1 N ∑ i = 1 N E i − M i 2 (7) where N is the total number of data, i represents a single data; M and E are measured values and estimated values, respectively.

Figure 4 showed the change differences in the TSM concentration in each lake. This difference reflected the impact of human life on the water environment of the lake. For example, Qinghai Lake and Lake Bosten were located in the central and western parts of China. Because the lakes are governed and protected by the local government, and the TSM concentration were lower. The highest values of TSM concentration in Lake Chagan and Lake Xingkai were more significant than 100 mg/L. They were located near towns in northern China, so they were highly vulnerable to human activities. The TSM concentration in all samples ranged from 1 to 126 mg/L, averaging 40 mg/L. It showed that our lake dataset contains the R r s γ i of the lake type of 0–130 mg/L, and did not contain the lakes with high TSM concentration higher than 130 mg/L.

Based on the four bands of blue (Band 1), green (Band 2), red (Band 3), and near-infrared (Band 4), band combinations (Band 3/Band 2, Band 3/Band 1, Band 3/Band 4, Band 2*Band 3/Band 1) and the FUI were used as the feature variables for the TSM concentration retrieve (Du et al., 2020; Liu et al., 2021). However, if there was a strong correlation between the feature variables, it may lead to multicollinearity of the dataset, affecting the solution’s spatial instability. The Mean Decrease Impurity (MDI) feature selection method in Scikit-learn were used to reduce the dimensionality of the feature dataset. The feature importance ranking was shown in Figure 5. Band 3/Band 2 features variables had the highest proportion of importance, which was 0.44. The importance of the top four feature variables accounted for more than 80%. Therefore, the final selected four feature variables, Band 3/Band 2, FUI, Band 4, and Band 3/Band 4, were used to retrieve the TSM concentration.

The following comparative analysis on the TSM retrieve model were conducted: evaluated the retrieved model of TSM concentration in the existing documented; compared and evaluated four machine learning methods; considered the influence of FUI on the accuracy of TSM retrieve model.

Six existing documented models were compared in this study (Table 3). Figure 6 showed the retrieval performance of the six models in existing datasets. All TSM concentration retrieve models were generally underestimated at high values. Overestimation occurred in the low-value area. The performance of Model 2 and Model 5 was the most prominent, and their predicted values was concentrated between 20 and −60 mg/L, and they were not sensitive to low and high TSM concentration. Although the fitting coefficients of Model 1, Model 3, and Model 6 were above 0.4, the MAPEs were all above 54%, indicating obvious faults in the shallow value area (<10 mg/L) and other value areas. Therefore, the existing documented models often exhibited high dispersion and error characteristics when targeting different types of lakes and were not suitable for joint retrieve research of TSM concentration in multiple lakes.

Machine learning algorithms had good performance for feature capture of training datasets. The retrieved results of the four machine-learning models were shown in Figure 7 (Table 2). The statistical indicators of the validation dataset showed that among the four machine learning models, the RF model ( R 2 = 0.83 , M A P E = 25.5 % ) and BP model ( R 2 = 0.80 , M A P E = 22.7 % ) show good performance (slope close to 1) and relatively low error. In contrast, the SVR model ( R 2 = 0.55 , M A P E = 114.4 % ) algorithm showed good learning performance in the low-value area, but underestimated the TSM concentration (>50 mg/L) in the high-value area, the results of LR model ( R 2 = 0.59 , M A P E = 94.3 % ) also showed that the high-value area was underestimated, and its dispersion was high. Therefore, we considered the RF and BP models as candidate models for the TSM retrieval model.

The FUI divided water bodies into different categories, covering an extensive range of natural water optical features. The FUI was added into the machine learning model. Figures 7E, F, G, H) showed the accuracy changes of the four machine learning models after adding the FUI. The MAE of the four machine learning models on the test dataset was reduced from 16.06 mg/L, 15.30 mg/L, 8.06 mg/L, and 7.52 mg/L to 15.14 mg/L, 15.21 mg/L, 6.69 mg/L, 6.92 mg/L (Table 4). At the same time, RMSE decreased by an average of 1.48 mg/L among the four models. By comparing the RF model (Figures 7D, H), it was found that in the TSM concentration of 30–50 mg/L, the FUI effectively captured the change characteristics, which significantly improved the performance of the model on the validation dataset. Figures 7G, H showed that the FUI can make the machine learning model converge better and improve the training accuracy of the BP model and RF model ( R F : R 2 = 0.97 , B P : R 2 = 0.91 ) and Validation accuracy ( R F : R 2 = 0.88 , B P : R 2 = 0.88 ). The resulted showed that the FUI could improve the accuracy of the TSM retrieval model in the machine-learning model.

The RF model and BP model were used to retrieve the TSM concentration in Lake Chagan (2021-8-31) and Lake Changdang (Figure 8). The Lake Chagan dataset was used to verify the generalization ability of the TSM model for the machine learning model in different phases of the same lake. The Lake Changdang dataset was used to demonstrate the generalization ability of machine learning in different lakes and time phases. The resulted showed that the prediction model of the RF model and BP model had the best performance in Lake Chagan ( R F : R 2 = 0.935 , B P : R 2 = 0.885 ) and Lake Changdang ( R F : R 2 = 0.898 , B P : R 2 = 0.752 ) showed good performance. But the RF model was superior to the BP model in the statistical indicators of MAPE and RMSE. And the MAE of the RF model was less than 2 mg/L, which showed that compared with the BP model, the RF model had a better generalization ability, and its prediction results of TSM concentration could be effectively guaranteed.

The RF model was used to retrieve the TSM concentration in Lake Bosten, Lake Chagan, and Lake Changdang in this study. Lake Bosten was used to verify the retrieval accuracy of the TSM concentration used for modeling. Lake Chagan and Lake Changdang were to prove the generalization performance of the RF model. The remote sensing images of the three lakes used were the HJ2A-CCD image on 31 August 2021, the GF1B-PMS image on 15 September 2021, and the GF1-PMS image on 2 November 2022. The imaging time of the remote sensing image and the on-site sampling time were both carried out on the same day, and the verification validity of the in-situ data could be guaranteed. Figures 9A–C showed the validation results of retrieving TSM concentrations in three lakes. The MAPEs of the three lakes were 5.3%, 8.1%, and 12.1%, respectively, and the results reached relatively high precision. Compared with the retrieved results of the water spectra data of Lake Chagan and Lake Changdang (Figures 8A, B), the retrieval accuracy of remote sensing images needed to be higher. The reason may be that the accuracy error images of radiometric and atmospheric correction models limited remote sensing images. There was a certain error between the remote-sensing spectrum data and the in-situ spectrum data. For example, the retrieve of TSM concentration in Lake Changdang had an overestimation (>10 mg/L) in the high-value area (60–75 mg/L). At the same time, the in-situ spectral data of (Figure 8B) could better invert the high-value area of TSM concentration. Lake Bosten was the largest freshwater lake in China. The water quality environment had always been good, and the TSM concentration was deficient (0–15 mg/L). The TSM concentration in Lake Chagan and Lake Changdang was relatively high (33–89 mg/L, 32–84 mg/L). The reason may be that the two lakes are located on the edge of the city and are greatly affected by human activities such as agriculture and industry.

The RF model proposed in this study preliminarily solves the applicability of broad bandwidth satellites to retrieve the TSM concentration in different types of water. But the RF model also has certain limitations. First, the machine learning model requires a large amount of in-situ data, enabling it to capture the water spectral features of various TSM concentrations. The ideal training data should collect long-term continuous water spectrum and TSM concentration data in various typical lakes in China so that the spectral characteristics of these types of lakes can fully characterize the changes in TSM concentration. However, the acquisition cost of these data is relatively high in actual work. Therefore, 22 water experiment data from 15 lakes were selected as the dataset in this sutdy. There is a certain need for more training data. The range of TSM concentration can only cover the range of 0–120 mg/L, and there is a lack of training data for highly turbid water (TSM>10 0 mg/L). This makes the RF model proposed has a better retrieve effect for water bodies with medium and low suspended solids concentrations. Still, the accuracy must be verified more in high turbid water bodies. Secondly, this study is the first attempt to use a combination of multiple broad bandwidth satellites to retrieve the TSM. The true value of remote sensing reflectance of each broad bandwidth satellite is calculated by Formula 5. However, although the bands of these broad bandwidth satellites are similar, there are certain differences in the sensitivity of their sensors to different bands. This results in a certain error ( M A P E ≈ 2 % ) when the true value of the reflectance formed corresponds to different satellites after spectral equivalence. Using the equivalent true data of these different satellites to carry out unified modeling research will increase the uncertainty of the TSM retrieved model to a certain extent. The evaluation of this uncertainty still needs to be verified through continuous experiments.

This study attempts to use various broad bandwidth satellites to carry out comprehensive TSM concentration retrieval. The purpose is to develop a TSM retrieve model compatible with various high-resolution broad bandwidth satellites to meet the requirements of water dynamic monitoring. RF and various neural network models have good model generalization ability, and the quality of the accuracy of the TSM retrieve model is primarily affected by the amount of data. The RF model proposed is to obtain the optimal model in the existing dataset. In the future research, on the one hand, the research team will continue to accumulate water quality data of typical lakes in China, the model will continue to iterate and update. We will continue to optimize the model to obtain a broad bandwidth satellite TSM retrieve model with better stability and accuracy. On the other hand, the bandwidth and spectrum of broad bandwidth satellite sensors are very similar. Therefore, we consider building these satellites into virtual constellations, carry out research on the normalization of remote sensing spectra of broadband satellites, and eliminate observation errors between different sensors. The coordinated operation among satellites can meet the demand of regional lakes dynamic observation.