Enhancing Turbidity Modeling in the Mississippi River Using Machine Learning and Sentinel‐2 Remote Sensing Data: A Generalizability Analysis

1. Introduction

Monitoring river water quality is paramount for developing effective, sustainable management strategies and preserving both freshwater water resources for agricultural irrigation and domestic/industrial use, as well as for safeguarding the health of these invaluable aquatic ecosystems. However, anthropogenic and natural processes can disrupt the physical-chemical balance in a river. This leads to the endangerment of water quality, negatively impacting human health and aquatic biodiversity and causing significant economic implications worldwide [1,2,3,4]. To cite a few, diverse parameters can be used to monitor water quality, such as dissolved oxygen, chlorophyll, and salt concentrations [4,5,6]. Among the set of possible water quality parameters, turbidity is often deemed the most relevant indicator for water quality. This optical property of water indicates how the light incident to the water body is scattered, absorbed, or directly transmitted. Its importance lies in its ability to indirectly provide information about other parameters, as it is vastly influenced by them [7,8].

Traditional ways of measuring turbidity in water, such as turbidimeters, nephelometry, and spectrometry, consist of gathering water samples and often providing reliable results. However, they have the downside of being expensive, prone to human error, and do not offer the capacity for real-time monitoring of turbidity [7,9,10]. A viable strategy to overcome this hindrance is the use of remote sensing. The ever-increasing geospatial data from satellite devices allowed the implementation of data-driven approaches, such as Machine Learning (ML) [11]. The combined usage of ML and satellite information covering a vast spatial area allows monitoring spatiotemporal variations of water quality parameters, including turbidity [12]. Furthermore, compared to other approaches, such as numerical methods, ML has a more straightforward implementation, has improved computational performance, and can generalize data remarkably well for time-series applications [13,14,15].

Using ML models with the sizeable spatiotemporal coverage of satellite images proved valuable for water monitoring, as corroborated in previous studies [11]. In the work of Silveira Kupssinskü et al. [16], the authors implemented several ML paradigms to estimate future levels of chlorophyll-a (Chla) and Total Suspended Solids (TSS) for two locations in Brazil. The models were trained with Sentinel-2 and unmanned aerial vehicle imagery. The authors achieved satisfactory results for the ML applications, which consistently outputted coefficient of determination (R²) values greater than 80%. In the work conducted by Zhang et al. [17], the authors estimated Chla on lakes located in China using a Support Vector Machine (SVM) and Landsat-8 images. The assessed model successfully predicted the concentration of Chla, reaching R² = 77% and Root Mean Squared Error (RMSE) of 22.64 μg/L. In their work, Ma et al. [18] investigated the use of Sentinel-2 imagery for turbidity prediction in lakes in China. Again, the ML paradigms, especially forest-based approaches, offered competitive results for water quality assessment, returning R² values greater than 80%. Another comprehensive study was conducted in [19], which investigated twelve different ML algorithms for phosphorous modeling in reservoirs in China using Landsat-8 satellite data. Again, the ML paradigms showed excellence in predicting time-series data from remotely sensed images, where a tree-based approach was the best-performing model with an R² of 85%. Another ML paradigm investigated in past studies was the Group Method of Data Handling (GMDH), which has been used for different hydrological applications, such as predicting water quality [20], Chla [21], and turbidity [22]. Nonetheless, there is still a gap in the knowledge regarding using GMDH with satellite data for turbidity modeling.

As discussed above, the ML models are paramount in hydrological applications, particularly concerning water quality management when combining ground-based monitoring with remotely sensed datasets. Thus, the present study seeks to advance our knowledge on the details of training and testing machine learning algorithms, namely eXtreme Gradient Boosting (XGBoost), Random Forests (RF), GMDH, Support Vector Regression (SVR), k-Nearest Neighbors (kNN) and Least Absolute Shrinkage and Selection Operator (LASSO) to model turbidity levels on the Mississippi River, USA. Every method was implemented individually at each monitoring station along the Mississippi River and collectively across all stations. This approach aimed to assess the methods’ generalization on specific locations and the broader river system. To this end, the models were trained and tested with Sentinel-2 remote sensed data. The specific objectives of this study are:

• A thorough investigation of the influence of the Sentinel-2 spectral bands and several indexes on ML applications for turbidity modeling in a large spatial area.
• Use of parameter selection strategy to determine the best inputs for the ML models.
• Evaluate the performance of the GMDH ML model for turbidity modeling using satellite imagery.
• Generalizability analysis of the modelling approaches considering specific stations and their collective datasets for turbidity modeling.

2. Materials and Methods

2.1. Study Site Location

The Mississippi River, a critical hydrological source in the USA, ranks as the second largest river in the country. It spans over 3.7 thousand kilometres from its source in Minnesota to its termination at the Gulf of Mexico. The Mississippi River provides resources for 15 million people at its upper basin alone and serves over 50 cities along its course. The Mississippi River has a discharge flow rate greater than 600 thousand cubic meters per second at its delta. Its watershed also upholds significant natural, hydrological, and economic resources, encompassing over 250 lakes, covering more than 3.2 million square kilometres, including 32 American states and 2 Canadian provinces, encompassing more than 40% of the total continental USA area [23,24]. Given its extension, the Mississippi River and its watershed house a vast biodiversity and cultural sites for its inhabitants [25,26].

Given its significance, the preservation of the Mississippi River has become paramount for river management agencies [27]. However, anthropogenic activities undermine the Mississippi River’s environmental stability, altering its hydrological dynamics and landscape [27,28]. Additionally, the Missouri River, the most important tributary of the Mississippi River, is a significant source of sediments, which can also negatively impact the Mississippi River equilibrium. Given the current global warming and climate change scenario, this is a vital concern, endangering the riverine population relying on its waters, mainly at its delta [29].

The data used in this study is made publicly available by the United States Geological Survey (USGS) (data available at https://help.waterdata.usgs.gov/, accessed on 22 February 2024). The USGS is the state agency responsible for compiling and collecting water-use data for the American Government since the 1950s, stratified into several categories [30]. A total of 12 monitoring stations were used in this study, encompassing locations for both the Mississippi and the Missouri rivers. Each station records daily turbidity data, comprising the years 2018 to 2023. The geographical location of the monitoring stations, the Mississippi River, its basin and principal tributaries are presented in Figure 1 [31,32]. The statistical information for the dataset is presented in Table 1. A complete statistical analysis of the data can be found in the supplementary material.

2.2. Sentinel-2 Imagery

2.2.1. Spectral Data

The Sentinel-2 constellation comprises two polar-orbiting satellites led by the European Space Agency (ESA). The first satellite, Sentinel-2A, was launched back in 2015. The second, Sentinel-2B, was launched two years later, in 2017. Both monitor the Earth in the same sun-synchronous orbit. The main goal of the Sentinel-2 constellation is to monitor Earth’s environment, providing remotely sensed data to track changes in its climate, with a revisiting time of 5 days after the launching of Sentinel-2B [33,34,35]. The Multispectral Instruments (MSI) present in the constellation are state-of-the-art equipment that can provide information within a wide range of spatial coverage, registering data in thirteen different spectral bands [34,36,37]. Table 2 compiles the configuration for the MSI equipment in the Sentinel-2 constellation.

This study collected remote sensed data using Level-1C processing. The collected data goes through rigorous monthly quality checks to maintain its integrity. [39]. The satellite imagery is sectioned into different parts for this processing level based on the UTM/WGS84 projection. For each tile, whose limits are separated by a distance of 100 km, the radiometric values are calculated using top-of-the-atmosphere reflectances, later converted to irradiance [40,41].

2.2.2. Spectral Indices

The spectral indices are mathematical formulations that combine different satellite bands to extract more information from the satellite data. The usage of spectral indices can be found in the literature with applications in various areas of knowledge, such as monitoring crops [42,43], vegetation [44,45], and also water quality [46,47], to cite a few.

In the present study, the influence of several indices for the modeling of turbidity levels in the Mississippi River was investigated. Table 3 compiles the 17 indices assessed and their intended original usage.

It is possible to notice that many of the mentioned indices in Table 3 are not directly related to water assessment. However, including indices not directly related to water quality may still provide insight for the predictive model, thus improving the turbidity modeling.

In the final stage of the process, the revisit time of Sentinel-2 was synchronized with the date of the turbidity sample acquisition. This synchronization ensured that the remote sensing data and the turbidity sample shared the same collection date, allowing their comparison. The entire dataset was randomly split into training and testing data with this information, following an 80/20 ratio.

2.3. Machine Learning Models

In this work, turbidity was modeled using several ML models. It is important to disclose that deep learning (DL) models were not implemented in this work. This is because DL paradigms require extensive datasets, as well as long computational times. Previous works show that DL performance can yield similar and even inferior outcomes compared to classical ML approaches, when the dataset size is not sufficiently broad [79,80,81]. Therefore, the implementation of DL models in this study was not considered, as the available data for each monitoring station amounts to 2453 for the period under investigation.

The implemented ML structures are briefly discussed as follows.

2.3.1. Tree-Based ML Models

Tree-based paradigms are popular approaches applied to time-series problems. They are versatile models that handle non-linear problems for either classification or regression. Fundamentally, it consists of splitting the multidimensional predictive space into smaller regions. This approach offers a good interpretation of its results and may offer competitive performance to more advanced ML models when combined with resampling approaches, such as bagging [82,83].

Two different tree-based models were implemented in the present study. The first is called Random Forest (RF). This approach consists of training many independent tree models using the bagging resample. Thus, each tree is trained using a subsample of the total predictors, i.e., the spectral bands and indexes [82,83]. Later, these trees are combined into a larger model, which is called an ensemble model. This approach reduces the model variance, improving its output [84].

The second tree-based model implemented was the eXtreme Gradient Boosting (XGBoost) [85]. This is also an ensemble model and an improved version of the RF paradigm. Its theory consists of combining weaker ML models to combine them sequentially, each one improving its predecessor’s residual errors. This creates small trees, which will slowly learn the underlying patterns in the dataset. The resulting model is more robust to overfitting, with less variance and more generalization capacity [82,83].

2.3.2. Self-Structured ML Model

Another methodology investigated in this study was the Group Method of Data Handling (GMDH). It was first proposed in the 1960s, as an approximation model using a reduced dataset with high non-linearity between the inputs and outputs [21,86,87]. This model does not require hyperparameter tuning, as it selects its best configuration automatically [88]. Despite being a relatively old ML model, its application to time-series problems, including hydrology-related applications, has been positively validated by previous research [89,90,91].

2.3.3. Support Vector Regression ML Model

The Support Vector Regression (SVR) model comes from the Support Vector Machine (SVM) paradigm, a versatile approach able to handle linear and non-linear problems [83]. To this end, the SVR uses a kernel trick, which consists of using a kernel trick and kernel functions that allow the model to handle the dataset in higher dimensions. This benefits the model twofold: by being computationally efficient and allowing it to retrieve non-linear relationships within the dataset that could not be detected in simpler dimensions [92]. However, a significant limitation of the SVR lies in its inability to handle extensive datasets efficiently, resulting in longer computational training times [93,94].

2.3.4. k-Nearest Neighbour ML Model

The k-Nearest Neighbour (kNN) model was another paradigm investigated in this study. This is another versatile model that performs both classification and regression strategies. When applied to regression cases, the kNN attributes the mean value to the unknown point based on its neighbors [82,92,95]. This approach is more straightforward than classification, where kNN classifies the new point based on a voting system by its neighbors, which may be scattered in a possibly high-dimensional space.

2.3.4. The Least Absolute Shrinkage and Selection Operator ML Model

The Least Absolute Shrinkage and Selection Operator (LASSO) is a linear approach that was investigated in this work. This methodology combines parameter selection with a regularization strategy to avoid overfitting [84,96]. Thus, the LASSO paradigm seeks to provide the best-fitting regression hyperplane describing the data.

2.4. Evaluation Metrics

To compare the performance of the proposed ML models, one of the most used metrics for ML applications in time-series problems is the coefficient of determination (R²) [97]. It is an indicator of the amount of variance in the output that the predictors explain. It offers more information about the regression model output while also providing good interpretability [98].

2.5. Data Preprocessing

Before using the dataset to train the ML models, we first cleaned the dataset, removing outliers and incorrect values. Afterwards, we investigated different normalization strategies. Normalization often improves ML models’ performance by setting the dataset values to the same order of magnitude [13]. The first preprocessing methodology was the standard normalization. It sets the dataset mean to zero and its standard deviation to one. The second normalization implemented was the Yeo-Johnson. This normalization strategy seeks to reduce the skewness in the data, approximating it to a normal distribution. To this end, the Yeo-Johnson transformation implements power transformations, ensuring that all data values are positive [99]. A combination between Yeo-Johnson and standard normalization was investigated as well. The case where no normalization was applied to the dataset was also evaluated as input for the models.

3. Results

3.1. Parameter Selection

The best parameters among bands and spectral indexes were selected before feeding the ML models with the data. To this end, the forward stepwise parameter selection was performed [82]. This approach consists of adding one predictor at a time and verifying if its inclusion improved the model’s performance in terms of reduced error. In this study, we first selected the best indices among the ones presented in Table 2. The benchmarking model to evaluate the parameters was the XGBoost, where the R² metric was assessed. The results for the best indices are depicted in Figure 2.

From Figure 2, the selected indices were the NDGI, GCI, AWEI, GNDVI, SWM, 3BSI, NDMI, EVI, BSI, SAVI, MSI, NDWI, and NDSI, achieving an R² equal to 74%. Analysing both Figure 2 and Table 2, we can conclude that the predictive model benefited from indices related to both water and vegetation. Indices related to glaciers and snow also promoted improvements in turbidity modeling, as demonstrated by the selection of NDGI and NDSI. Although it may seem counterintuitive, including such indices befits the ML model by conveying relevant spatiotemporal data. Additionally, the selection of the best set of spectral bands is presented in Figure 3.

Figure 3 shows that the best Sentinel-2 bands for turbidity modeling were B02 and B06, achieving an R² of 76%, promoting an improvement of 2% compared to the indices’ selection alone. Analyzing Table 1, B02 has a spectral range around the blue spectrum, with a high spatial resolution of 10 meters. Additionally, B06 conveys information ranging on the red edge of the vegetation of the light spectrum, with a high spatial resolution of 20 meters. It’s worth noting that we incorporated the cubic root of the predictors as a predictive parameter. This was done to mitigate data skewness and bring the distribution closer to normal [100]. Henceforth, the results presented for the turbidity modeling are based on the selected parameters presented in Figure 2 and Figure 3, and the cubic root of each predictor.

3.2. Turbidity Modeling Results

The ML models were built using Python and Scikit-Learn [101]. Besides the GMDH model, which is a self-organizing approach, the hyperparameters were determined using the GridSearch tool for Scikit-Learn with 5 cross-validations. Such methodology proved to yield good outputs for time-series applications [95]. The results achieved by the models for each monitoring station are presented in Table 4, for each monitored station, as presented in Figure 1.

Table 4 elucidates that the best results in terms of coefficient of determination are achieved at the Missouri River at St. Joseph station. At this location, the best-performing model was kNN, achieving an R² value of 86.7%, while the second-best model was RF, achieving an R² of 85.1%. At the Missouri River at Randolph and Mississippi River stations at Baton Rouge, the R² value was also superior to 80%. The GMDH approach yielded the best results for both of them, followed by XGBoost and SVR, respectively.

Contrarywise, the lowest R² was achieved at E. Fk. Black R. bl Lower Taum Sauk Reservoir station, where RF output a 25.7% for the coefficient of determination, while the second-best performing model at this location was XGBoost, with R² of 25.2%. Other locations where the coefficient of determination fell below 30% included the East Fork Black River near Lesterville and the Mississippi River at Clinton. In both cases, the XGBoost model was the best-performing approach, followed by SVR and kNN.

For the monitoring station Mississippi River at Dam 13 near Fulton, it was not possible to derive an optimal model using the available data. As can be observed from Table 1, reduced values for range and standard deviation of turbidity indicate a lack of variability in the data. At this station, the measured turbidity is practically constant, leading to a poor generalization by the ML model and a degenerated R² value.

As informed by Table 4, considering the best-performing models, not normalizing the dataset usually provided the best outcomes. For some cases, the normal standardization improved the modeled turbidity value a couple of times at stations Mississippi River at Keokuk and the Mississippi River at Baton Rouge. Combining Yeo-Johnson and normal standardization improved turbidity modeling only at station Missouri River at Hermann.

The rank of the best-performing and second best-performing models is presented in Table 5 as follows.

Table 5 elucidates that the most common best-performing model was GMDH, which bested the remaining paradigms four out of eleven times. It was closely followed by the XGBoost approach, the best-performing model three times. Considering both XGBoost and RF, the three-based methodology surpassed the GMDH. In this case, it is safe to say that these models offer a more general approach for modeling turbidity, posing as a more viable alternative.

To underscore the non-linear behaviour of the turbidity, we compared it with the coefficient of determination of each stations using different statistical metric. To this end, we removed the stations with fewer turbidity samples, according to Table 1, namely Missouri at Hermann, Mississippi at Clinton, and Mississippi at Dam 13. This relationship is depicted in the following Figure 4.

Figure 4 reveals a strong second-order relationship between mean turbidity values and the coefficient of determination for each monitoring station. Figure 4 illustrates that there exists a natural limitation for increments on turbidity values. Examining the plotted data, we observe that the R² value for the modeled turbidity shows an upward trend in the range of 4 FNU to 57 FNU. Interestingly, the R² shows stabilization at an r-squared value of 88.7%, with turbidity value of 44 FNU. Beyond this threshold, the regression line for the modeled turbidity starts to show a downwards behaviour, indicating that an increase in turbidity is likely to result in data dispersion without necessarily improving the models’ outcomes. This is seen by the right-most point in Figure 4, representing the station Missouri River at Randolph, MO, where the coefficient of determination is 87% for a mean turbidity value of 57 FNU.

The models’ performance were investigated to verify the their generalization capacity using information from all the monitoring stations to model turbidity values. The best-performing approaches are presented in Table 6.

Considering the whole monitoring station data, the best model was the XGBoost, reaching a coefficient of determination of 75.7% using no normalization. The RF model was the second-best performing methodology, achieving an R² of 70.7% also without normalization. Compared with the results from Table 4, which provide an average R² value of 59.5%, the models trained using all the samples showed a superior overall performance.

4. Discussion

4.1. Bands and Indices Selection

Earlier research has demonstrated the significance of individual and combined bands in assessing turbidity values. In a previous study [18], the authors confirmed a positive Pearson correlation for both these categories using remote sense data from Sentinel-2. Specifically, bands 1 through 5 exhibited a strong positive correlation with turbidity, achieving a Pearson correlation coefficient exceeding 70%. In the case of combined bands, bands 2, 3, 4, 5, and 8 they also displayed a superior positive correlation, reaching a correlation value of 70%. In the study conducted by Zhu et al. [102], the authors used the Shapley additive explanations (SHAP) analysis [103] to determine the importance of bands for water quality estimation, including turbidity, using machine learning models and Sentinel-2 images for Shenzen Bay, China. Their findings revealed that bands 2 through 8A (Table 2) contributed the most to determining turbidity.

In [104], the authors concluded that every band improved turbidity estimation in the North Tyrrhenian Sea, Italy . They found that bands 5, 6, 7, and 8A contributed the most to this end. In another study by Psychalas et al. [105], their results showed significant contributions from bands 4, 5, 8A, 11, and 12 for identifying highly turbid waters in reservoirs. Specifically, the contributions from bands 11 and 12 were attributed to the variety of land classes and cloud formations present in their remote sensing data.

In our study, a comprehensive analysis of Table 2 and Table 3 reveals that bands 8, 3, 11, 4, and 2 are the five most relevant attributes in terms of frequency, in that order. Our findings are following the results from the literature. This alignment allows us to affirm the significance of the red spectrum bands and the green and blue bands in modeling turbidity values. As discussed by Maimouni et al. [106], due to the high reflectance of turbid water, the Sentinel-2 bands related to the visible spectrum are particularly influential for monitoring water turbidity due to the high reflectance of this type of water. Additionally, SWIR and NIR bands can enhance turbidity modeling in highly murky waters. These wavelengths are more adept at gathering information about the turbidity in such waters, especially when the spectral reflectance is saturated.

Furthermore, our study underscores the critical role of high spatial resolution in turbidity modeling, as band 11 is the only one with a spatial resolution worse than 10 m. The spatial resolution is important for turbidity modeling as it can better identify and convey finer spatial information to the model, thus improving its performance [107]. The importance of spatial resolution was also attested and discussed in previous studies related to water quality monitoring [108,109,110].

4.2. Turbidity Modeled Using for Each Monitoring Station

Assessing the performance of the ML approaches for each monitoring station, we concluded that proper turbidity modeling depends on the availability of a dataset containing a wide range of turbidity values. The models perform better when applied to a specific location, i.e., when implemented to model turbidity at specific monitoring stations. This is due to the reduced variance in the data, which tends to improve the model’s performance. This can be seen in Table 4, where the individual models can achieve R² values over 88%. Interestingly, kNN outperformed more complex models for the Missouri River at St. Joseph station. This can be explained by the fact that kNN, being a non-parametric approach [82], maybe more resistant to noisy data. Furthermore, the architecture of kNN is specifically designed to identify similar data points. Given that the data from the station above exhibits this characteristic, kNN can accurately capture the turbidity levels surrounded by similar instances.

The LASSO model, which is a linear approach, also surpassed the non-linear models for the Missouri River near Council Bluffs station. This can be explained by the data available at the mentioned station. Being the LASSO a linear model, it is suited to perform linear regression on linear data, which may be the case at the station. Additionally, this approach applies parameter selection using L1 regularization, which can reduce the error related to the variance while focusing on more relevant features [96].

Interestingly, each assessed model achieved the best result at least once. The “no free lunch” theorem [111] can be used to explain this phenomenon. In the ML field, this theorem explains that no “one-fit-all” model exists. The best-suited ML approach depends on the designed task and data availability. Different models may excel due to their inherent strengths and weaknesses for particular tasks but perform similarly on average when provided with a sufficiently large amount of data.

4.3. Comparison with Results from the Literature

The performance of the proposed model was compared with results from the literature, compiled in Table 7. At this point, it is crucial to emphasize that direct comparison between different ML models is difficult. Each ML model possesses unique characteristics, with different methodologies and geographic contexts, leading to varying performances. Nevertheless, comparing the metrics from these models remains a valid benchmarking approach for evaluating ML performances across different applications [112,113].

In the work by [104], the authors implemented two different ML models to estimate turbidity in the North Tyrrhenian Sea, Italy, from April 2015 to December 2021. Their results showed a good performance for both proposed models, linear and a kernel-based approaches. Compared to our results in Table 4, we observe a very similar performance with the LASSO model and the stepwise linear regression proposed by those authors, both paradigms reached values around 73%. Regarding kernel-based models, again, we observe similarities between their results, where our SVR model was slightly outperformed by a marginal difference of 9%, and a marginal difference of 9% slightly outperformed our SVR model. Still, our work’s results for GMDH and kNN are significantly superior, showing that they can better identify non-linear relationships related to turbidity modeling. Considering all the monitoring stations, the XGboost approach performed better, achieving an R² value of almost 75.7%. It is essential to note that Magrì et al.‘s work focuses on modeling turbidity in an oceanic scenario, where turbidity concentrations remain relatively stable across seasons. Additionally, their spatial coverage is significantly narrower than ours. These characteristics may limit their model’s generalization due to the specific context and data availability.

Ma and colleagues [18] investigated several machine-learning models to assess turbidity in lakes in Northeastern China from June to September 2018. Their results showed that the XGBoost model was the top performer, achieving an R² value of 88%. Compared to the XGBoost model in our study, the models used by these authors demonstrated significant superiority. Their results are on par with the coefficient of determination achieved by kNN and GMDH. When evaluating the performance XGBoost model considering all the monitoring station data, we observe that our proposed approach falls short compared to the results presented by Ma et al. However, the significant discrepancy between the output of these models can be explained by the shorter time window investigated on their study and the fact that their research was conducted on lakes. As previously noted, the study spanned four months. This limited timeframe might not capture significant fluctuations in turbidity values, resulting in a dataset with lower variance. Additionally, lakes typically exhibit more stable turbidity values, which can enhance the predictive accuracy of machine-learning models.

In the study by Katlane et al. [108], the authors used a semi-empiric approach to evaluate turbidity values using remote sensing data for a lagoon in Tunisia. The authors harnessed Sentinel-2 and PRecursore IperSpettrale della Missione Applicativa (PRISMA) satellite imagery for the year 2021. Their proposed semi-empirical approach showed good performance in predicting turbidity at their location, with an R² of 88%. Compared to our models using individual station data, its performance is matched by kNN and GMDH. On the other hand, the XGBoost approach, which used all the sample data, performed inferiorly to the one reported by their study. Again, their reduced temporal coverage and more stable turbidity values for the given location can explain their superiority over our models, at the expense of a less general predictive approach.

Chen et al. [111] present a novel self-optimizing model for water quality determination on an urban river in China. Using remote sensing data from GF-1C satellite for the year 2021, the authors showed that the best result achieved for turbidity modeling was an R² of 67.9%, a value well below the range of the output found in our study. When compared to our study, specifically when all the monitoring stations are considered, it is possible to visualize a better performance of the latter, which improved turbidity modeling by around 8%.

In another work [115], the authors used multispectral images captured by an unmanned aerial vehicle to feed an ML model determining water quality in Changlin River, China, from February to June 2023. After appraising several predictive models, the authors found that the best results were provided by the CBR approach, which reached a coefficient of determination of 92% for turbidity. Such value surpasses the ones presented in Table 4, where the best model achieves a maximum R² of 88.7%. The models using all available data from the monitoring stations also fall short when compared to their results. Again, we state that this discrepancy may be due to the improved spatial resolution and reduced time window in their study, factors that are presumed to enhance the output of their model.

5. Conclusions

In this study, we implemented several ML paradigms to model turbidity for the Mississippi River, USA. We utilized remote sensing data from the Sentinel-2 mission and applied forward stepwise selection to identify the optimal input parameter set. To this end, we investigated several attributes containing the 13 bands of the Sentinel-2 satellite and spectral indices.

The selection of the best input parameters proved that it is beneficial for the model to combine both bands and indices, as they can convey spatiotemporal information for the predictive model. A comprehensive analysis of the selected inputs revealed that bands 8, 3, 11, 4, and 2 are the five most relevant attributes for turbidity modeling, which agrees with the literature.

Additionally, the individual results from the ML models exhibited considerable variation. Upon investigating this outcome, we found that the performance of the ML models was heavily dependent on the data availability for each site, particularly the amount of data in the third quantile. As shown in Table 4, the GMDH architecture generally produced superior performance among the individual models considered. Tree-based models like XGBoost and Random Forest (RF) achieved comparable results, demonstrating their potential for accurate turbidity modeling.

On average, the individual models reached an R² value of 59.5%. The methodology using XGBoost and all the monitoring station data was also investigated. Its result proved to be significantly superior to the mean performance of the models using data from individual stations, achieving a coefficient of determination of 75.7%.

A comparison with the literature values showed that the results found in this study are competitive, deeming the proposed methodology an important tool for turbidity characterization from remote sensing data.

The assessment of water quality, turbidity included, is paramount for informed decision-making related to new legislation and water management strategies. To enhance the effectiveness of this process, future research could consider incorporating additional spectral indices and employing advanced image processing techniques.

To achieve better results in this scenario, future works may include the addition of more indices, as well as the usage of higher-level image processing. by integrating information from other satellites, such as Landsat-8. The incorporation of these elements has the potential to reduce dataset variance, thereby enhancing the accuracy of turbidity modeling for the target location.