Water depth estimation from Sentinel-2 imagery using advanced machine learning methods and explainable artificial intelligence

Abstract

The estimation of water depth in coastal areas and shallow waters is crucial for marine management and monitoring. However, direct measurements using fieldwork methods can be costly and time-consuming. Therefore, remote sensing imagery is a promising source of geospatial information for coastal planning and development. To this end, this study investigates advanced machine learning (ML) methods and redesigned morphological profiles for water depth estimation using high-resolution Sentinel-2 satellite imagery. The proposed framework involves three main steps: (1) morphological feature generation, (2) model training using several ML methods (Decision Tree, Random Forest, eXtreme Gradient BOOSTing, Light Gradient Boosting Machine, Deep Neural Network, and CatBoost), and (3) model interpretation using eXplainable Artificial Intelligence (XAI). The performance of the proposed method was evaluated in two different coastal areas (port and jetty) with reference data from accurate hydrographic data (Echo-sounder and differential global positioning systems). The statistical analysis revealed that the proposed method had high efficiency for depth estimation of the coastal area, achieving a best R² value of 0.96 and Root Mean Square Error (RMSE) of 0.27 m in water depth estimation in the shallow water of Chabahar Bay in the Oman Sea. Additionally, the higher impact and interaction of the morphological features were verified using XAI for water depth mapping.

Keywords:

• Explainable artificial intelligence
• coastal management
• depth estimation
• satellite derived bathymetry
• hydrography
• machine learning

1. Introduction

Water covers over 70 percent of the Earth’s surface, and accurately measuring water depth is essential for creating bathymetric maps. While conventional hydrographic surveying using Echo-sounder is the most accurate method for mapping the seabed and measuring water depth, it is expensive and time-consuming (Tajfirouz et al. 2022). Accurate seabed mapping is crucial for various purposes such as infrastructure development, subsea power cable monitoring, and geo-environmental applications (Evagorou et al. 2022). In particular, safe maritime transportation and navigation rely heavily on precise and current geospatial data, especially in coastal areas and shallow water. Marine infrastructure and transportation facilities, such as ports, channels, and jetties, require accurate seabed information to operate safely. However, the seabed is a dynamic surface that changes over time, and sedimentation can pose a threat to safe navigation, leading to significant socio-economic losses (Cesbron et al. 2021). Consequently, it is crucial to perform regular monitoring of shallow waters and coastal zones using bathymetric techniques (Salameh et al. 2019; Tajfirouz et al. 2022). Nonetheless, performing regular hydrographic surveying using conventional methods can be a daunting task, particularly in coastal areas and large regions. The process often involves extensive fieldwork, making it both time-consuming and expensive (Jagalingam et al. 2015; Ashphaq et al. 2021; Evagorou et al. 2022). Furthermore, the seasonal monsoon system in certain regions of the world can interrupt the continuous hydrography of the coastal zones. Additionally, conducting shorelines habitat and environment studies in rocky-cliff zones might be difficult and dangerous using sounding boats.

Alternatively, multispectral remote sensors mounted on satellites with revisiting time ranging from a few days to weeks have provided a cost-effective means for continuous earth observation (Seydi et al. 2022) and shallow water bathymetry (Lyzenga 1978; Stumpf et al. 2003; Mavraeidopoulos et al. 2019). The Sentinel-2 satellite has been providing freely available data since 2014 with a spatial resolution of 10–60 meters and a revisit time of 10 days. The satellite captures images in 13 different electromagnetic spectrums (bands), providing valuable information for various applications. Similarly, the Landsat-8 Operational Land Imager (OLI) has been delivering a nine-band dataset with a spatial resolution of 15–30 meters and a temporal resolution of 16 days since 2013. Therefore, satellite data presents a great potential for satellite-derived bathymetry, as it provides a resourceful platform for depth estimation. The depth estimation is based on the correlation between the light penetration through the water column in visible (RGB) and infrared bands, their electromagnetic wave absorption, and scattering (reflectance) (Mohamed et al. 2015; Mavraeidopoulos et al. 2019; LEDER 2020). The reflectance is recorded by the satellite-based sensors in Digital Numbers (DN) format. The intensity of electromagnetic waves then decreases with the increase in depth (Evagorou et al. 2022). Several satellite sensors, including Sentinel-2, Landsat-8, IKONOS, and SPOT6, have been evaluated for their effectiveness in bathymetry estimation, and some factors were identified as important factors influencing the final accuracy of the remote sensing technique (Stumpf et al. 2003; Jagalingam et al. 2015; Mohamed and Nadaoka 2017; Captain Najhan Md Said et al. 2018; Mavraeidopoulos et al. 2019; Evagorou et al. 2022). Accordingly, water surface reflection (low albedo), atmospheric effects, sun reflection, image pixel size, depth range, water quality (clear and shallow water up to 30 m), seabed characteristics, and adequate sample points were among the most significant factors. To overcome the aforementioned challenges in satellite-derived bathymetry, researchers have developed various radiometric correction techniques, water reflectance ratio models, and advanced algorithms (Lyzenga 1978). As a result, satellite-derived bathymetry has gained significant attention in research communities, with a focus on developing new methods and utilizing available data.

In order to effectively analyze multi-dimensional satellite datasets, statistical approaches and particularly machine learning (ML) methods have shown their ability and ease of applicability for tasks such as image classification (Seydi et al. 2022) and satellite-derived bathymetry (Ashphaq et al. 2021; Najar et al. 2022). For instance, support vector machine (SVM), random forest (RF), and artificial neural network (ANN) have been successfully used for depth extraction in clear and shallow water (Misra et al. 2018; Mohamed and Nadaoka 2017; Mohamed et al. 2015). A study by Mohamed and Nodaoka (2017) showed that using the red and green bands of Landsat-8 and SPOT6, the best Root Mean Square Errors (RMSEs) for depth extraction were 0.64 m, 0.84 m, 0.92 m, and 0.96 m for the RF, Multivariate Adaptive Regression Splines (MARS), Neural Network, and Generalized Linear Model (GLM) methods, respectively, in Alexandria port, Egypt, where the maximum depth was 10.5 m. Another study compared an ensemble learning-fitting algorithm of Least Squares Boosting (LSB) with the Principal Component Analysis (PCA) and GLM using SPOT4 bands in water depth less than 2 m, and obtained an RMSE of 0.15 m (Mohamed et al. 2016). In a study (Sagawa et al. 2019), the RF method was exploited to multi-temporal Landsat-8 images, resulting in an RMSE of 1.41 m for depths up to 20 m. Using WorldView-2/3 satellite data and ensemble ML methods such as SVM, Gaussian kernel, decision tree (DT), K-Nearest Neighbors (KNN), bagging tree, and subspace KNN, the mean RMSE of 2 m was achieved for depths up to 35 m, demonstrating excellent performance (Eugenio et al. 2022). Deep learning methods were also used with QuickBird imagery acquired in 2014, resulting in RMSEs ranging from 1.53 to 2.68 m when compared with a 1:125,000-scale nautical chart dating back to 2001 (Wan and Ma 2021). However, the lower spatial and temporal resolution of the sounding chart (as a ground truth depth) compared to the hydrographic map may have impacted the accuracy assessment of this experiment (Loomis 2009).

The existing research on satellite-derived bathymetry has primarily focussed on using simple ML and regression methods. However, more research is needed to investigate the use of advanced algorithms (e.g. GXboost, LightGBM, Catboost models) that can effectively model the complex relationships between dynamic factors in the water column and water depth estimation using satellite imagery (Ashphaq et al. 2021). By utilizing advanced and robust ML algorithms, the accuracy and reliability of water depth extraction can be improved. Therefore, further exploration and experimentation are necessary to identify the most effective and suitable algorithms for this task.

The use of ML algorithms in data modelling and information extraction can lead to a "black box" nature, where the underlying reasons for final decisions and operations by the ML operators are unclear, potentially leading to unjustified certainty (Roscher et al. 2020; Al-Najjar et al. 2022; Hasanpour Zaryabi et al. 2022). More specifically, it is important to have interpretability and explainability in ML models, as they can provide insights into the underlying reasons for the final decisions and operations made by these models (Roscher et al. 2020). The lack of transparency and interpretability in ML models’ interaction with datasets and contributors has led to the demand for explainable artificial intelligence (XAI). XAI has been the focus of significant research in many fields, including the medical industry (Tjoa and Guan 2021), flood prediction (Kadiyala and Woo 2022), landslide prediction (Al-Najjar et al. 2022), slope failure prediction (Maxwell et al. 2021), and heat-related mortality mapping (Kim and Kim 2022). The SHapley Additive Explanations (SHAP) is a widely used method for adding transparency to the function of ML models (Al-Najjar et al. 2022). Therefore, the aim of this research is to deploy the SHAP method to interpret the internal function of ML algorithms and explain the factors’ contribution through feature importance plots in the context of satellite-derived bathymetry.

For this study, high-resolution Sentinel-2 satellite imagery was acquired to estimate water depth using advanced ML methods (i.e. RF, eXtreme Gradient BOOSTing (XGBOOST), Light Gradient Boosting Machine (LightGBM), Deep Neural Network (DNN), and CatBoost). The proposed framework utilizes these advanced and ensemble MLs and compares their performance with other popular ML method (Decision Tree (DT)). Additionally, in response to the lack of transparency in ML-based methods used in previous studies on satellite-derived water depth estimation, we exploited SHAP to better understand the contribution of individual spectral bands and features. The key objectives of this research are:

1. Redesigning and evaluating a feature extraction approach that combines spatial and spectral features using morphological profiles

2. Comparing the performance of advanced and ensemble ML methods with commonly used ML method for water depth mapping

3. Deploying XAI through the SHAP method to better interpret the function of ML methods in water depth mapping

2. Materials and methods

2.1. Study areas and datasets

The study areas are located in Chabahar Bay, in the south of Iran, close to the northern boundary of the Oman Sea. For this study, two different coastal areas were selected (port and jetty with nearshore region). The site selection was based on: (1) the accessibility to highly accurate ground truth data (the hydrographic survey data) and (2) the availability of a cloud-free Sentinel image of the coastal region.

2.1.1. Case study 1

Beheshti port is a significant port located in Chabahar Bay, characterized by a hot desert climate with an average maximum temperature of 34 °C. This port is of strategic importance due to its access to international open waters, making it a crucial infrastructure for Iran’s international trade. Figure 1 depicts the study area’s geographical location and in-situ hydrographic data. For this study, a dataset of Sentinel-2 satellite imagery captured in January 2020 was used. The first study area covered 342 × 439 pixels, with each pixel grid being 10 × 10 m². A total of 7708 samples were extracted from the available hydrographic data in Chabahar port for training and testing purposes. The hydrography data was acquired by a single beam hydrographic survey Echo-sounder in January 2020, along pre-designed hydrographic lines (survey track) of 10 meters. The depth values varied from 0 to 17.8 m in Beheshti port. The depth accuracy was 0.05 m for depths lower than 5 m and 0.1 m for depths between 5 and 10 m, with a positioning accuracy of 0.5 m. Although the satellite imagery and the hydrographic survey were not acquired on the exact same date, the time difference between them is considered acceptable for this research, as the best available satellite image with less cloud coverage was used (Casal et al. 2020).

Figure 1. Geographical location and hydrographic data of the study areas; (a) Geographical location of the study areas in Iran, (b) Location of first and second study areas in Chabahar Bay, (c) RGB image of the first study area (Beheshti port) captured by Sentinel-2, (d) Beheshti port, hydrographic data.

2.1.2. Case study 2

Tis is a fishery jetty located in Chabahar Bay, north of Beheshti port. Figure 2(a) shows the Setinel-2 image captured in January 2020 from Tis port, and Figure 2(b) represents the in situ hydrographic dataset ranging from 0 to 6.2 m. The sampling dataset consisted of 1263 pixels from a total area of 208 × 109 pixels, which were extracted from the available hydrographic map on a scale of 1:2000. The hydrographic data were collected by a single beam Echo-sounder similar to the case study 1.

Figure 2. Second study area, Tis port: (a) Sentinel-2 image captured on January 2020; (b) in-situ hydrographic dataset.

2.2. Methodology

The water depth mapping flowchart in Figure 3 outlines the three main steps involved in estimating water depth: (1) data preparation (pre-processing) and feature extraction using morphological operators such as erosion and dilation, (2) training and tuning the parameters of the ML model for depth mapping, and (3) using XAI for model interpretation and assessing accuracy.

Figure 3. The flowchart of the proposed framework for depth estimation.

2.2.1. Feature extraction

Sentinel-2 Level-1C product with pre-applied radiometric and geometric corrections was used. After converting image pixel values to radiances and reflectance, atmospheric correction and sun-glint removal were applied using ENVI 5.2 software (FLAASH module) as a pre-processing step (Mohamed et al. 2015). Next, feature extraction is a conventional process in many applications of remote sensing, such as classification, damage assessment, and change detection. Due to the limitation of the multispectral imagery (i.e. the lower spectral resolution of Sentinel-2), it has been proven that the feature extraction can improve the final classification and mapping (El-Kenawy et al. 2021). To enhance the depth estimation process, a total of eleven spectral bands were employed for extracting morphological profile-based features, resulting in the generation of 72 spectral features. Consequently, a comprehensive set of 83 features, encompassing the 11 bands along with the 72 morphological features, was utilized as input for the machine learning (ML) models employed in the depth estimation.

There are two main groups of feature extraction techniques, namely (1) spectral features extraction (e.g. normalized vegetation index), which extracts information from the spectral characteristics of the images, and (2) spatial features extraction such as texture Gray-Level Co-occurrence Matrix (GLCM) features, which extract information based on the spatial relationships between pixels in the image.

Mathematical morphology is an unsupervised method that involves the use of extended morphological profiles for feature extraction. This framework was introduced by Plaza et al. (2003) for image classification. They developed the Morphological Profile (MP) approach to analyze both spatial and spectral features, which has been shown to be a robust and effective tool in many applications such as hyperspectral image classification and change detection (Licciardi et al. 2012; El-Kenawy et al. 2021). The MP utilizes the geodesic closing/opening transformations with an increasing structural element size to generate a set of opening and closing profiles (Garea et al. 2016). Additionally, an extended morphological profile can be constructed by stacking the MPs built using different features.

The two fundamental mathematical morphology operations are dilation and erosion (Licciardi et al. 2012). Erosion and dilation are the basic elements in the MP that are applied to a grayscale image with a specific structure element. This study involves a redesigning of Extended Morphological Profiles (EMP) based on a hierarchical morphological operator. In grayscale image analysis, each pixel’s intensity value is considered as the third dimension, corresponding to various features (Quackenbush 2004). Our proposed framework employs the output of a morphological layer in the individual stages as input for the next subsequent stages. Furthermore, the structure element size increases in each subsequent stage, using a 3 × 3, 5 × 5, and 7 × 7 kernel size filter. Figure 4 shows the general framework of the proposed feature extraction, consisting of three morphological erosion and dilation layers. The output of each layer is incorporated in the final output of the model, and the final output is constructed using the output of each layer in each stage

Figure 4. General structure of the proposed hierarchical morphological operator-based feature extraction framework.

The flat erosion operator can be defined for a grayscale input image data ($\mathcal{F}$) (are defined on the 2-D discrete space $Z^2$) with a structure element ($\mathcal{H}\subset Z^2$) as following (Frigato & Silva 2008): (1) $$(\mathcal{F}⨂\mathcal{ }\mathcal{H})(x,y){=}_{(\omega ,\phi )\in Z^2\left(\mathcal{H}\right)}^{\wedge }\mathcal{F}\left(x+\omega ,y+\phi \right),\mathrm{ }(x,y)\in Z^2\mathrm{ }$$(1) where $Z^2(\mathcal{H})$ represents the set of discrete spatial coordinates associated with pixels located in the neighbourhood defined by $\mathcal{H}$ and ∧ is the minimum operator. Similarly, the flat dilation can be defined as following: (2) $$(\mathcal{F}⨂\mathrm{ }\mathcal{H})(x,y){=}_{(\omega ,\phi )\in Z^2\left(\mathcal{H}\right)}^{\vee }\mathcal{F}\left(x-\omega ,y-\phi \right),\mathrm{ }(x,y)\in Z^2\mathrm{ }$$(2) where $\vee$ is the maximum operator.

2.2.2. Machine learning models

In this study, six supervised learning algorithms were used for depth mapping. Advanced ML methods, including XGBOOST, LightGBM, RF, CatBoost, and DNN, were compared with a regular ML algorithm, namely DT for satellite-derived bathymetry. The XGBOOST, LightGBM, RF, and CatBoost are ensemble-based models, while DNN is a deep learning-based model capable of extracting deep features from the input dataset. Further details on these algorithms are presented in the subsections below.

2.2.2.1. Random Forest (RF)

The RF algorithm is a supervised learning method that uses an ensemble of decision tree for regression and classification tasks (Sagawa et al. 2019). It generates multiple decision trees and aggregates their results to produce a final output. The RF model has two main user-defined parameters, the number of trees and the number of randomly selected predictor variables, which need to be set (Table 1).

Table 1. User-defined parameters of different ML models used in the study.

MODEL	Parameters
RF	Number of Trees = 155, Number of Randomly Selected Predictor Variables = 5
DNN	Number of Layers = 5, Activation Function = Rectified Linear Unit (Relu), Number of Hidden Layers = [150,150,150], Weight-Initializer = He-Normal, Optimizer = ADAM, Dropout Rate = 0.18
LightGBM	Number of Estimators = 150, Learning Rate = 0.1, Regularization Parameter = 0.9, Number of Leaves = 150, Maximum Depth = 9
CatBoost	Number of Estimators = 105, Learning Rate = 0.1, Subsample Ratio = 0.9
XGBOOST	Number of Estimators = 105, Learning Rate = 0.1, Maximum Depth = 20, Subsample Ratio = 0.7

2.2.2.2. eXtreme Gradient BOOSTing (XGBOOST)

One of the most popular and dominating methods applied over the past few years is XGBOOST, which is an ML system to scale up tree boosting algorithms (Wang et al. 2021). An XGBOOST prediction model is constructed by using a gradient descent approach to optimize a loss function of weak regression trees. The XGBOOST has several parameters to be set (i.e. the number of estimators, learning rate, regularization parameter, and optimal tree specific parameters determined in Table 1).

2.2.2.3. Light Gradient Boosting Machine (LightGBM)

To extract the information gained from every possible splitting point, conventional gradient-boosting decision tree scans all the instances of the data for each feature (Wang et al. 2021). The LightGBM takes the advantage of exclusive feature bundling and gradient-based one-side sampling procedures to enhance efficiency by reducing the number of features and samples, respectively. The training speed of LightGBM is faster, and the memory usage is lower than that of XGBOOST. Some tuning parameters of LightGBM are the number of estimators, learning rate, regularization parameter, and optimal tree specific parameters (Table 1).

2.2.2.4. Decision Tree (DT)

DT is one of the effective nonparametric techniques employed in numerous applications (Kalantar et al. 2021). DT is a sequential model that unites several basic tests by comparing a numeric feature to a threshold value (Al-Najjar and Pradhan 2021). Each tree’s nodes and branches make up the structure. Nodes represent features in the values to be predicted, and subsets define the values that nodes can take.

2.2.2.5. Deep Neural Network (DNN)

DNNs are artificial neural networks with more than one hidden layer between their inputs and outputs and feed-forward network (Najar et al. 2022). The benefit of deploying artificial models with deep architectures is their powerful tools for analyzing high-dimensional data at a high level or representing abstract features (Kalantar et al. 2021). These layers are trained to represent more and more abstract features of the input feature data. Figure 5 shows the DNN architecture for depth mapping. This framework has nine hidden layers with Rectified linear unit (Relu) activation function and an output layer with a linear activation function.

Figure 5. General structure of the DNN for water depth mapping.

2.2.2.6. CatBoost

The CatBoost is an ensemble supervised learning that employs binary decision trees as predictors, which is an implementation of gradient-boosting (Wang et al. 2021). This technique proposes an ordering principle to solve a very general gradient-boosting implementation problem. Gradient-boosting is completely dependent on the objectives of all training samples after several steps. Furthermore, the CatBoost combines symmetric decision trees into a single model, resulting in fewer parameters, faster training and testing, and a higher level of accuracy.

2.2.3 eXplainable Artificial Intelligence (XAI)

As one of the emerging strategies for improving trust in Artificial Intelligence (AI) systems, XAI encourages users to comprehend, trust, and manage a growing generation of artificially intelligent partners by deploying techniques such as XAI (Tjoa and Guan 2021). The interpretability level of ML models describes the extent to which humans can comprehend the reasoning behind a decision or replicate the results of the model (Miller 2019). SHAP is a representative method for model explanations. The SHAP algorithm explains the prediction operators of a black box regression. Using SHapley values, which were introduced in cooperative game theory for calculating the contributions of players to the payout (Kim and Kim 2022; Singh et al. 2022), is a post-hoc and local model-independent explanation method. A predictive model can be constructed by averaging over all possible orderings of features using SHAP, allowing one to analyze the importance of each input feature for a given instance, and providing local and global interpretability of input features (Al-Najjar et al. 2022). Accordingly, the SHAP method computes each feature contribution by comparing the expected model prediction to the actual one when adjusting for the particular feature. Using SHAP Equation (3)(3) $${\mathrm{\varnothing }}_{\mathrm{i}}=\mathrm{ }\sum _{\mathrm{S}\subseteq \mathrm{N}\backslash \left\{\mathrm{i}\right\}}\frac{\left|\mathrm{S}\right|!\left(\mathrm{n}\mathrm{ }\text{-}\mathrm{ }\left|\mathrm{S}\right|\text{-}\mathrm{ }1\right)!}{\mathrm{n}!}\left[\mathrm{v}\left(\mathrm{S}\mathrm{ }\cup \mathrm{ }\left\{\mathrm{i}\right\}\right)\text{-}\mathrm{ }\mathrm{v}\left(\mathrm{S}\right)\right] \mathrm{ }$$(3) , the contribution (${\mathrm{\varnothing }}_{\mathrm{i}}$) of $\mathrm{i}$ th feature is defined. Then, the sum of the SHAP value for each observation is calculated by Equation (4)(4) $$g\left(z^{\prime }\right)={\varnothing }_0+\sum _{\mathrm{i}=1}^{\mathrm{M}}{\varnothing }_{\mathrm{i}}{\mathrm{z}}^{\prime }{}_{\text{i }}$$(4) : (3) $${\mathrm{\varnothing }}_{\mathrm{i}}=\mathrm{ }\sum _{\mathrm{S}\subseteq \mathrm{N}\backslash \left\{\mathrm{i}\right\}}\frac{\left|\mathrm{S}\right|!\left(\mathrm{n}\mathrm{ }\text{-}\mathrm{ }\left|\mathrm{S}\right|\text{-}\mathrm{ }1\right)!}{\mathrm{n}!}\left[\mathrm{v}\left(\mathrm{S}\mathrm{ }\cup \mathrm{ }\left\{\mathrm{i}\right\}\right)\text{-}\mathrm{ }\mathrm{v}\left(\mathrm{S}\right)\right] \mathrm{ }$$(3) (4) $$g\left(z^{\prime }\right)={\varnothing }_0+\sum _{\mathrm{i}=1}^{\mathrm{M}}{\varnothing }_{\mathrm{i}}{\mathrm{z}}^{\prime }{}_{\text{i }}$$(4) where N defines the total number of features (i.e. 11 bands), $\mathrm{n}$ is the number of features in $\mathrm{N},$ $\mathrm{N}\backslash \left\{\mathrm{i}\right\}$ defines the set of the total number of features except $\mathrm{i}.\mathrm{ }\mathrm{S}$ denotes number of subset of N without feature $\mathrm{i},$ and $\mathrm{v}(\mathrm{N})$ defines the baseline value meaning the predicted output for each feature in N without knowing the feature values. M is the number of input features, $z^{\prime }ϵ$ {0, 1}^M and ${\varnothing }_0$ is a constant value (Al-Najjar et al. 2022; Kim and Kim 2022).

2.2.4. Model evaluation

The model evaluation is a vital process in depth water mapping. The sample dataset was divided into two main groups; training data (70%) and test dataset (30%). The model was trained based on the training dataset, and the result of the model was evaluated against the test dataset with corresponding pixels from reference hydrographic datasets. In this regard, we employed both quality measurement indices and visual interpretation. The most important accuracy assessment indices for regression methods are Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Explained Variance Score (EVS), Median Absolute Error (MeAE), and R². The RMSE calculates the error between the real value and the predicted value. The MAE, as the mean, evaluates the algorithm performance by comparing the prediction and actual values. The bigger value of EVS indicates better prediction. The R² is defined between −1 and 1, highlighting uncorrelated estimation to perfect positive correlation, respectively, to compare with observation and reference data (Ahmadi et al. 2020). Moreover, the scatter plot of predicted depth and actual depth was obtained.

3. Results

The current study utilized six ML methods and a redesigned morphological profile generation approach for water depth estimation using high-resolution Sentinel-2 satellite imagery. The findings of the ML methods, namely RF, XGBOOST, LightGBM, DT, DNN, and CatBoost, are reported below.

3.1. Feature extraction

Eleven spectral bands were fed into morphological profile-based feature extraction. Figure 6(a) shows the input original band 4 (as an example) undergoes the erosion. In the erosion process of feature extraction, shrinkage of the foreground structures occurred (Said and Jambek 2021) in band 4 (Figure 6b–d) leading to an increased background area (compared to the original input), while the dilation process broadened the foreground of the band (Figure 6e–g). Then, noise elimination and removing irrelevant detail within the image were obtained.

Figure 6. Feature extraction by MAPs for Band 4 Sentinel-2 dataset: (a) Original image, (b) Erosion, stage1, (c) Erosion, stage2, (d) Erosion, stage3, (e) Dilation, stage1, (f) Dilation, stage2, and (g) Dilation, stage3.

3.2. Depth estimation for case study 1, Beheshti port

The results of depth mapping are shown in Figure 7. In general, most models provided similar results, and smoothly depicted the depth differences between 18 m and zero. Besides, by visual inspection, the DT and RF models (Figure 7a,b) showed more rough and discrete classification to compare with the DNN, XGBOOST, LightGBM, and CatBoost, which provided smooth and soft results among different depth categories.

Figure 7. The results water depth mapping for Beheshti port, (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

The scatter plots of six ML algorithms for Beheshti port are presented in Figure 8. This plot compares the reference data (reality) with the results of the models (prediction) on the test samples. In an ideal condition, the red and blue dots are fitted in a line for a simple regression model, indicating a correlation between the two variables. Due to the models’ error, the scatter plots did not completely fit, and various intensities and correlations of red dots were seen among different models. Furthermore, the relationship between reference and estimated datasets in the result of the DT algorithm (Figure 8a) showed more fluctuation, depicting outliers in the modelling process. Other models provided quite a well-fit scatterplot, and among them, and the Catboost model showed the best performance (Figure 8f).

Figure 8. The scatter plot plots from different models in Beheshti port; (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

Statistical analyses of six ML models’ performance for depth estimation (in Beheshti port) are shown in Table 2. Among the applied ML models, the DT mainly showed the highest errors and uncertainty, with the RMSE value of 1.65 m and R² of 0.79. In contrast, the RF, XGBOOST, LightGBM, and CatBoost models achieved acceptable results by all the statistical indices and lower differences between the estimated and the actual values (the RMSEs better than 1 m). Among the six ML models, the XGBOOST algorithm provided the best performance for the depth estimation, with the RMSE of 0.88 m and R² of 0.94.

Table 2. The numerical performance analysis of different models in Beheshti port.

Method	MAE	EVS	MeAE	R2	RMSE
DT	0.82	0.79	0.34	0.79	1.65
RF	0.54	0.92	0.24	0.92	0.99
DNN	0.59	0.89	0.28	0.89	1.17
XGBOOST	0.50	0.94	0.26	0.94	0.88
LightGBM	0.52	0.94	0.27	0.94	0.90
CatBoost	0.53	0.94	0.30	0.94	0.91

3.3. Depth estimation for case study 2, Tis port

Figure 9 shows the result of depth mapping in Tis port. Predominantly, all the models provided similar smooth classes for depth estimation and classified the depth up to around 6 m except the DT model (Figure 9a), which classified the different depths as more distinct and rough in the whole region.

Figure 9. The results of depth mapping for Tis port using seven ML models; (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

In Figure 10, the scatter plots for Tis port are shown. Generally, the plots represented a good fit between the reference data (reality) and the prediction, highlighting a correlation between those variables. In details, the LightGBM, CatBoost, and XGBOOST (Figure 10d–f) were superior to the DT (Figure 10a) with more clustered dots.

Figure 10. The scatter plots for Tis port, (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

In Tis port, Models’ performances for depth estimation were evaluated against several statistical indices (Table 3). The DT algorithm showed maximum errors and minimum certainties amongst the ML models with an RMSE of 0.39 m and R² of 0.91. The best performance belonged to the LightGBM with an RMSE of 0.27 m and R² of 0.96, followed by the XGBOOST and CatBoost.

Table 3. The numerical performance analysis of different models in Tis port.

Method	MAE	EVS	MeAE	R2	RMSE
DT	0.26	0.91	0.16	0.91	0.39
RF	0.21	0.95	0.14	0.95	0.30
DNN	0.26	0.93	0.19	0.93	0.36
XGBOOST	0.19	0.95	0.14	0.95	0.28
LightGBM	0.19	0.96	0.13	0.96	0.27
CatBoost	0.20	0.95	0.13	0.95	0.28

3.4. Feature importance

The feature importance of ML models delivers significant information regarding the relation of spectral bands and features and their effects during modelling. The plot determines features’ global impact by ranking them. The result of XAI plot (Figure 11) showed that the dilation and erosion band-2 were predominantly the most effective feature for depth estimation by the models in Beheshti port. The dilation and erosion band-3 scored as the next significant feature. While the individual bands showed less impact among the features, and the significance of morphological features was higher than the original bands. For the DT (Figure 11a) model, the pattern of feature importance was quite different from other ML models. The XAI plot in Tis port (Figure 12) remarked the dilation and erosion band-3 as the most significant features, as well.

Figure 11. The feature importance results by XAI for Beheshti port, (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

Figure 12. The feature importance results by XAI for Tis port, (a) DT, (b) RF, (c) DNN, (d) XGBOOST, (e) LightGBM, and (f) CatBoost.

For more investigation regarding morphological profile-based feature extraction and its effect on the final results, we omitted the feature extraction phase and performed the satellite depth estimation, again in Beheshti port. The results of the evaluation of estimated depths are shown below (Table 4).

Table 4. The numerical performance analysis of different models without feature extraction phase in Beheshti port.

Method	MAE	EVS	MeAE	R2	RMSE
DT	1.21	0.66	0.54	0.66	2.12
RF	1.04	0.79	0.54	0.79	1.67
DNN	1.12	0.72	0.52	0.72	1.92
XGBOOST	1.02	0.80	0.54	0.80	1.60
LightGBM	1.08	0.79	0.62	0.79	1.64
CatBoost	1.01	0.81	0.55	0.81	1.59

By comparing Tables 2 and 4, it is clear that all evaluation indices were affected by the feature extraction phase. The RMSEs increased remarkably (from 22% up to 82%) by omitting the feature extraction step and the uncertainty (R²) propagated through the classification, and reliance on the estimations decreased.

4. Discussion

Geospatial data acquisition is a crucial step for depth mapping, but traditional field surveying workflows can be costly and time-consuming. To address the increasing demand for up-to-date information on coastal zones, satellite-derived bathymetry has emerged as a promising alternative, thanks to the availability of freely available satellite data and the ability to monitor large areas automatically. Implementing fully automated satellite-derived bathymetry in shallow waters and large regions using historical imagery is a key advantage that significantly reduces costs (Loomis 2009; Mohamed et al. 2016). In this study, morphological operations such as dilation and erosion have been employed to enhance the value of satellite image processing and feature extraction by preserving the data structure in both spectral and spatial feature space (Imani and Ghassemian 2019). Most single-band based algorithms assume homogeneity and constant water quality within a region, whereas multiple-band based algorithms are better suited to define heterogeneity and variation that are present in the real world (Su et al. 2008). Comparing the evaluation indices before and after the morphological operations confirmed the positive effect of deploying such feature extraction methods to achieve more accurate classification and water depth estimation. The contribution of features and their internal interactions with the ML models, also, emphasized on the impact of the morphological features. The SHAP method revealed that the morphological features such as erosion and dilation from band-3 (green) and band-2 (blue) ranked the utmost features for depth mapping. It was in agreement with a review paper (Ashphaq et al. 2021) that found the best spectral bandwidths for shallow water depth mapping are within the blue and green regions. The restricted number of training samples to compare with the huge size of the satellite image necessitates dimensionality reduction by exploiting feature extraction methods. Using dilation, pixels are added to the boundaries of objects within an image. Erosion, on the other hand, removes pixels from the boundaries of objects. The shrinking and enlarging image foreground led to enhance the image quality (Said and Jambek 2021), and deploying the morphological operations for feature extraction and depth mapping was successful. Mainly, the dilation and erosion result in smoother borders and de-noising by removing small objects (Said and Jambek 2021) that might better resemble seabed topography in coastal zones.

To further evaluate the reliability of the ML methods, several indices were used. The results of our experiment in Tis port were within the acceptable range (the RMSEs better than 0.39 m) by deploying all ML methods. However, in Beheshti port, the estimation accuracy dropped, especially when we used the DT method. The weak performance of the DT model is due to its simple structure without bagging and boosting, which suffers from a higher bias with simple trees and a higher variance with complex trees. In contrast, other models (i.e. XGBOOST, LightGBM) consider the complexity of depth estimation in their structure and perform better (Owen et al. 2020). The obtained accuracies by our methodology in both study areas were compatible with those of Mohamed and Nadaoka (2017), Sagawa et al. (2019), Eugenio et al. (2022), Wan and Ma (2021), and Caballero and Stumpf (2019). The depths estimated in the first and second study areas showed relative errors of less than 4.9% and 4.4% of the maximum depth, respectively, when employing the XGBOOST and LightGBM methods. Considering the maximum depth of the two regions, the depths were more accurately calculated in Tis port, as it represents more shallow water (depth up to 6 m) to compare with Beheshti port with deeper areas (depth up to 18 m). Also, it is found that satellite derived bathymetry can more efficiently retrieve the depth in water depths lower than 6 m (Stumpf et al. 2003; Caballero and Stumpf 2019). Additionally, the advanced methods such as RF, XGBOOST, LightGBM, and CatBoost outperformed other ML methods in the two study areas, and the use of advanced and ensemble ML models is more recommended than the DT. Our finding was confirmed by Mudiyanselage et al. (2022), as well. They combined individual bands from the Sentinel-2 and reported higher performance of the RF model for satellite derived bathymetry (up to 13.5 m). Moreover, in comparison to the 10 m spatial resolution of the Sentinel-2 data utilized in our experiment, Tonion et al. (2020) conducted a separate study where they employed a fusion process for multispectral datasets from three different satellites, achieving a higher spatial resolution of 3 m. They examined the RF model for satellite-derived bathymetry and obtained depths of up to 5 m. They reported an RMSE value of 0.228 m. It is worth noting that as the water depth increases, the accuracy of satellite-derived bathymetry tends to decrease. Therefore, our results align with the findings of Tonion et al. (2020) in terms of accuracy and certainty. Although the DNN methods did not perform as well as other advanced methods, their limitations were brought to the forefront, particularly the issue of limited training data samples. According to Najar et al. (2022), deep learning methods have been recognized for their ability to estimate water depth based on spectral information. However, their accuracy may not meet the requirements of specific applications. The main challenge in deriving water depth from satellite imagery lies in the availability of accurate hydrographic data to fine-tune the parameters, particularly the training samples.

However, in scenarios where rapid monitoring and coverage of larger areas are crucial, such as promptly reopening a port after a tsunami, the multispectral imagery itself may offer reasonably accurate water depth estimation (Ashphaq et al. 2021). The anthropogenic environment, including ports and jetties, is more susceptible to hazards and socioeconomic losses, necessitating regular and precise seabed monitoring. The first study area primarily consisted of man-made structures, such as harbours and docks, while the second study area encompassed a mixed environment of man-made structures (i.e. jetties) and a sandy near-shore region. The results of our experiment conducted in two ports in Iran demonstrated the effectiveness of the current method in a similar environment. Hydrographic survey data is typically accessible in limited sections of ports, jetties, and canals, where dynamic seabed conditions and sedimentation pose risks to navigation and vessels.

5. Conclusion

Traditionally, capturing water depth data relies on expensive technology with intensive fieldwork taking days to months. The satellite derived bathymetry, as a whole, delivers a suitable platform to carry out timely and costly surveying projects and aquatic habitats research. Data collection and sharing through the Sentinel Hub and its integration with the Landsat program is rapidly promoting the availability and seamless data over the globe. When large coastal environments need to be mapped, satellite bathymetry is an economical and practical solution. The variations of electromagnetic responses (i.e. absorption, emission, transmission, and reflection) in the satellite-based sensors and water depth measurement reinforce comprehensive data pre-processing and modelling. Then, the morphological operators can be satisfactorily deployed to eliminate surrounding noise in the jetties’ track and within the seabed in shallow water where boats and ships board and dock. The results from satellite bathymetry are affected by many factors, leading to uncertainties and higher value of RMSE and errors. Specifically, the accuracy of water depth estimation using passive (optical) sensors is highly influenced by the weather condition, water quality (turbidity), cloud cover, and seabed characteristics. Thus, using feature extraction methods and advanced models might improve data modelling and depth mapping accuracy. Here, we demonstrated that the advanced ML methods, specifically ensemble-based models (XGBOOST, LightGBM, RF, and CatBoost) outperformed the common ML algorithms. The present research provided more explainability and transparency within MLs’ complex modelling in satellite-derived bathymetry. It could promote trust among the decision-makers when using optical satellite-derived depths. The significant advantage of satellite derived bathymetry is the ability to derive water depth at high speed in a fully automated way. Soon, with the great potential and accuracy of remote sensing satellite data in water depth estimation and the availability of very high-resolution satellite data, conventional hydrographic surveying systems (e.g. Echo-sounder) will not be the best option. Therefore, satellites’ time series images (with regular revisiting times) will offer continuous records for coastal zone change detection, sedimentation, and monitoring. In shallow water and hard-to-access areas (e.g. ultra-shallow water, highly cliff zone with submerged debris, poor GNSS positioning in deep valleys and around bridges) this method might go far beyond time efficiency alone but safety. In addition to tackling the challenges in satellite depth estimation, future work will focus on exploring advanced ML techniques for different water turbidity conditions. This research will examine their applicability in various regions, including coastal wetlands, sandy areas, and lake environments, by considering the optimal spectral bands and potentially incorporating hyperspectral datasets. Once ground truth data becomes available, the transferability of the trained models will also be tested. Furthermore, by leveraging historical satellite images, the effectiveness of the current study will be extended to develop an operational system for real-time coastal zone monitoring, specifically focussing on sediment estimation rates.

Author contributions

Conceptualization, V.S., S.T.S. and B.K.; methodology, V.S., S.T.S. and B.K.; software, B.K.; validation, V.S., S.T.S., and B.K.; formal analysis, S.T.S., and B.K.; investigation, V.S., B.T. and B.K.; resources, V.S. and B.T.; data curation, V.S., and B.T.; writing original draft preparation, V.S. and B.K.; writing, review and editing, B.K., N.U and F.S.; visualization, B.K., N.U. and F.S.; supervision, B.K.; project administration, B.T.; funding acquisition, B.K. All authors have read and agreed to the published version of the manuscript

Acknowledgments

The authors would like to thank the Iran Ports & Maritime Organization (PMO) for providing the hydrographic data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Additional information

Funding

This research received no external funding.