Shallow Water Bathymetry Inversion Method Based on Spatiotemporal Coupling Correlation Adaptive Spectroscopy

Highlights

What are the main findings?

• A shallow water bathymetry inversion method based on spatiotemporal coupled adaptive spectroscopy has been proposed, which enables dynamic filtering of pixel-level features and effectively mitigates the interference of spatiotemporal heterogeneity on water bathymetry inversion.
• XGBoost model performs optimally with the support of this inversion method, achieving an R² of 0.93 and an RMSE of 0.16 m, which is 56% lower than that of the traditional spectral inversion method.

What are the implications of the main findings?

• Breaking through the limitations of traditional fixed feature combinations, it provides a new paradigm for multi-dimensional feature optimization in remote sensing water bathymetry inversion.
• Developing a low-cost, high-frequency shallow water bathymetry inversion scheme based on open-source data can provide high-precision bathymetry data support for scenarios such as nearshore marine monitoring and marine resource management.

Abstract

Shallow water bathymetry data underpins maritime shipping and marine resource survey/protection, but its accuracy is constrained by water heterogeneity and spectral interference. To address this, this study proposes a Spatio-Temporal Coupling and Correlation Adaptive Spectral (STCCAS) inversion method, integrating four machine learning models: Random Forest (RF), XGBoost, Support Vector Regression (SVR), and Multi-Layer Perceptron (MLP). Experiments were conducted in Tampa Bay’s nearshore waters, using Sentinel-2 imagery and Airborne LiDAR Bathymetry (ALB) data. Core to STCCAS, the Temporal Stability Index (TSI) quantifies spectral temporal consistency, while the Normalized Difference Turbidity Index (NDTI) characterizes water turbidity, and the two indices synergistically form a dual-scale “spectral reliability-turbidity stability” evaluation system for pixel-level feature quality assessment—coupled with spectral fusion features and spatial location, they jointly realize pixel-level feature reliability weighting and dynamic filtering to build a water condition-adaptive input set. Comparative analysis of inversion performance under the original spectral features (OSFs) inversion method vs. STCCAS inversion method confirms STCCAS significantly boosts accuracy. XGBoost outperforms others, achieving a coefficient of determination (R²) of 0.93, root mean square error (RMSE) of 0.16 m, and mean absolute error (MAE) of 0.12 m. STCCAS breaks the limitations of traditional fixed feature combinations, effectively adapting to nearshore water heterogeneity. It provides a novel method for high-frequency, high-precision shallow water bathymetry inversion, with important practical value for marine environmental monitoring and resource management.

1. Introduction

Coastal shallow waters refer to shallow aquatic areas surrounding continents or islands, and shallow water bathymetry data is critical basic geospatial information for coastal environmental governance, marine resource development, coastal navigation, and amphibious operations [1,2,3]. For navigation safety, nearshore shallow waters are high-risk zones for ship grounding and collisions [4,5]—accurate bathymetry data provides a scientific basis for channel planning and navigation management, effectively reducing risks. In ecological conservation, shallow waters host key ecosystems such as wetlands, coral reefs, and seagrass meadows [6,7,8,9]. Spatiotemporal changes in water depth directly influence underwater light, temperature, and nutrient distribution, which are prerequisites for revealing ecosystem evolution and implementing biodiversity conservation. From the perspective of coastal zone management, bathymetry data supports risk assessment and the early warning of hazards like storm surges and coastal erosion, while guiding the rational layout of reclamation, port construction, and coastal tourism projects to balance resource use and ecological protection [10,11]. Additionally, under global climate change, long-term bathymetry observations reflect trends such as sea-level rises and shoreline shifts, providing essential data for formulating sustainable coastal development strategies [12]. Traditional bathymetric methods face limitations in large-scale and complex waters due to high costs and accessibility issues. Precise and efficient shallow water bathymetry inversion technologies compensate for these shortcomings, offering timely and reliable data for decision-making across marine scientific research, resource management, and socioeconomic development [13]. Advancing such techniques is crucial to address the growing demands of coastal management and research.

Traditional bathymetric surveys rely on in situ detection methods such as shipborne sonar (single-beam, SBES; multi-beam, MBES) and Airborne LiDAR Bathymetry (ALB) [14,15,16]. While these techniques can yield high-precision data, they are constrained by small observation ranges, high costs, and long acquisition cycles, making it difficult to meet the demands for large-scale and dynamic bathymetric monitoring [16,17,18]. Ashphaq et al. [19] noted in their review that traditional in situ methods have barely addressed the need for rapid, wide-coverage bathymetry, a gap that has persisted for decades. Their limitations are particularly prominent in remote marine areas or disaster emergency scenarios, as highlighted by Xie et al. [20], who emphasized that traditional techniques fail to provide timely data support for post-disaster risk assessment. Technically, shipborne sonar operations are highly dependent on vessel navigation trajectories. Kulbacki et al. [21] demonstrated that such methods tend to form detection blind spots in nearshore shallow waters (depth < 2 m) due to vessel draft restrictions. Additionally, they are vulnerable to interference from marine environmental factors such as wind, waves, and ocean currents, leading to interrupted data collection or reduced accuracy. Lubczonek et al. [22] further confirmed that SBES and MBES suffer from significant precision degradation in turbid coastal waters. In terms of cost and efficiency, these in situ methods require substantial investment in vessel rental, equipment maintenance, and professional personnel deployment [23]. Da Silveira et al. [24] estimated that mapping a 100 km² nearshore area using MBES would take 3–4 months and incur high operational costs. Mapping large-scale marine areas often requires phased and seasonal operations, with single survey cycles lasting months or even years, resulting in data timeliness that lags far behind the dynamic changes in coastal zones [25]. Thus, traditional bathymetric methods are increasingly unable to meet the diverse needs of modern coastal ecological protection, disaster early warning, and resource development.

With the rapid advancement of remote sensing technology, satellite imagery-based bathymetric inversion has become a crucial supplement to traditional in situ methods due to its wide coverage, short revisit cycles, and low costs [26,27,28,29,30]. By analyzing water radiance signals and integrating light transmission laws in the atmosphere and water, it establishes quantitative spectral–depth relationships for rapid shallow water depth estimation [31]. The development of satellite-derived bathymetry (SDB) has evolved from Polcyn et al.’s [32] early single-band ratio models and Lyzenga et al.’s [33] multi-band linear models to modern machine learning approaches—Sandidge et al. [34] applied BP neural networks, Manessa et al. [35] used random forests for coral reefs, and Wang Y et al. [36] fused spectral–spatial features via multi-layer perceptrons, greatly enhancing accuracy and applicability. Its core logic relies on spectral changes in electromagnetic waves in water, combining in situ data to build models for large-area depth estimation and seabed topography derivation. The main data sources for SDB include multispectral satellites (e.g., Sentinel-2 and Landsat, favored for their high spectral resolution that captures depth-related variations in clear shallow waters) and SAR satellites (valued for all weather, indirectly retrieving underwater topography through image features such as regular stripes or alternating light and dark stripes). Despite its merits, SDB still needs improvement in complex environments, as optimal band selection, band combination, and model construction—its three core steps [37]—vary significantly with satellite types and water conditions (e.g., turbidity) [20,36,38], highlighting the need for adaptive strategies to address shallow water heterogeneity, which motivates this study.

To address the aforementioned challenges—specifically the poor adaptability of fixed feature combinations to water heterogeneity and the insufficient suppression of spectral interference in existing satellite-derived bathymetry methods—this study proposes a Spatio-Temporal Coupling and Correlation Adaptive Spectral (STCCAS) inversion method and conducts systematic shallow water bathymetry inversion experiments in the nearshore waters of Tampa Bay. The design of the STCCAS strategy is directly tailored to address these two core gaps: (1) to tackle water heterogeneity, we construct a dual-scale evaluation system using Temporal Stability Index (TSI) and Normalized Difference Turbidity Index (NDTI), which quantifies spectral reliability and turbidity stability respectively, enabling an adaptive response to spatiotemporal variations; (2) to suppress spectral interference, we develop a pixel-level dynamic filtering mechanism that retains high-reliability features and eliminates vulnerable ones, avoiding noise amplification from low-quality spectral data; (3) to further enhance inversion robustness, we integrate multi-dimensional features (spectral, temporal, spatial, and fusion features) to complement the limitations of single-dimensional feature representation. The specific work of this study is as follows: First, multi-temporal Sentinel-2 L2A imagery and high-precision ALB-measured data are adopted as the primary data sources, with tidal correction performed to ensure the consistency between in situ measurements and remote sensing imagery. Second, two key spatiotemporal coupling features are constructed: the TSI to quantify the temporal reliability of spectral features and the NDTI to characterize water turbidity levels, forming a dual-scale evaluation system for feature quality. Thirdly, an adaptive spectral fusion mechanism driven by the dual scales of TSI and NDTI, along with location features and spectral fusion features, has been established to achieve pixel-level feature reliability weighting and dynamic filtering. High-reliability pixels retain all original spectral features, location features, spectral fusion features, and auxiliary features, maximizing the use of multi-dimensional effective information. Low-reliability pixels automatically eliminate vulnerable features to reduce noise impact. Finally, four machine learning models (Random Forest, XGBoost, Support Vector Regression, and Multi-Layer Perceptron) are employed to conduct comparative experiments under two feature schemes (original spectral features, OSF vs. STCCAS), comprehensively evaluating the effectiveness of the proposed method in improving inversion accuracy and adapting to water heterogeneity. This study aims to provide a low-cost, high-frequency, and high-precision technical solution for nearshore shallow water depth monitoring, while enriching the theoretical system of multi-feature optimization in remote sensing bathymetry.

2. Materials and Methods

2.1. Study Area and Data

2.1.1. Study Area and In Situ Bathymetric Data

The study area is situated in the nearshore region of Egmont Key within Tampa Bay, adjacent to St. Petersburg, Florida, USA. Egmont Key is a barrier key located at the mouth of Tampa Bay, and this research focuses on two specific sub-regions: the western and eastern nearshore waters of the island (Region 1 and Region 2). The location of Egmont Key and the two targeted sub-regions are illustrated in Figure 1.

The in situ bathymetric data were obtained from the Office of Coastal Management, National Oceanic and Atmospheric Administration, United States (https://coast.noaa.gov/, accessed on 13 October 2025). Data were collected via ALB surveys conducted from 6 to 10 January 2022, using a Partenavia P68C high-wing aircraft (Vulcanair S.p.A., Casoria, Italy) as the carrier platform. The platform was integrated with a dual-system configuration: the RAMMS bathymetric LiDAR(Riegl Laser Measurement Systems GmbH, Horn, Austria) and Riegl Q680i topographic LiDAR(Riegl Laser Measurement Systems GmbH, Horn, Austria), supplemented by supporting equipment including the Applanix PosAV 510 V6 GNSS receiver(Applanix Corporation, Richmond, Ontario, Canada), POSPac MMS 8.7 post-processing software, and an Inertial Measurement Unit (IMU). This integrated system enabled synchronous acquisition of bathymetric and topographic elevation data. Standardized flight parameters were adopted to ensure data quality and coverage: the nominal flight altitude for both bathymetric and topographic surveys was 325 m, with a ground speed of 110 knots. For the RAMMS bathymetric system, the flight line spacing was set to 240 m with 50% swath overlap; for the Riegl topographic system, the flight line spacing was 350 m with over 100% swath overlap, effectively eliminating coverage gaps across the study area. The data processing followed a rigorous three-step workflow: field pre-processing, indoor precision processing, and result validation. First, trajectory post-processing was performed to generate a Smoothed Best Estimated Trajectory (SBET) for motion correction. Subsequently, sensor data synchronization, point cloud denoising (removal of outliers and non-target points), and data integration were conducted. Final products included LAS-format point clouds, GeoTIFF raster surfaces, and Shapefile contour lines. Quality validation confirmed the reliability of the dataset: data coverage was excellent, with only minor gaps in extremely shallow waters or local turbid zones. The bathymetric point density was ≥1 point/m², and the topographic point density exceeded 10 points/m². The standard deviation of vertical measurements in most areas was ≤0.5 m, indicating that the vertical accuracy and data consistency meet the requirements for nearshore bathymetric monitoring, ecological assessment, and related research applications. The surveyed area primarily covers shallow waters from the coastline to the 5 m isobath, while multiple rounds of data collection enabled effective detection of water depths exceeding 10 m.

2.1.2. Sentinel-2 Data

Sentinel-2, a cornerstone mission of the European Space Agency (ESA) Copernicus Programme, is dedicated to high-resolution optical Earth observation, providing critical support for global environmental monitoring, coastal zone management, and shallow water research [39,40,41,42]. The mission comprises two identical satellites, Sentinel-2A (launched in June 2015) and Sentinel-2B (launched in March 2017), which operate in a sun-synchronous orbit to ensure frequent revisit cycles (≤5 days at the equator) and comprehensive global coverage [39,40]. This study employed Sentinel-2 Level-2A (L2A) data, surface reflectance products derived from Level-1C (L1C) orthorectified imagery through rigorous radiometric calibration and atmospheric correction—primarily using the Sen2Cor plugin to mitigate atmospheric effects (e.g., aerosol scattering, water vapor absorption) and generate terrain-corrected reflectance values suitable for quantitative remote sensing analysis [39,43]. The L2A data offer three spatial resolutions (10 m, 20 m, and 60 m) corresponding to 13 spectral bands, spanning the visible (490–665 nm), near-infrared (705–842 nm), and short-wave infrared (1610–2190 nm) regions; notably, the 10 m resolution bands (B2: blue, 490 nm; B3: green, 560 nm; B4: red, 665 nm) are highly sensitive to shallow water depth variations and are widely adopted as core bands for bathymetric inversion [38,43]. All Sentinel-2 L2A data were acquired from the ESA Copernicus Open Access Hub (https://dataspace.copernicus.eu/, accessed on 17 October 2025) and projected in the Universal Transverse Mercator/World Geodetic System 1984 (UTM/WGS84) coordinate system, ensuring seamless compatibility with Airborne LiDAR Bathymetry (ALB) data. To minimize interference from cloud cover and cloud shadows—key factors affecting spectral quality in coastal environments—a total of 14 less cloudy (cloud cover ≤ 10%) images were selected over July 2021–June 2022, providing sufficient temporal coverage to quantify spectral stability and capture dynamic variations in water turbidity. For missing data (e.g., cloud shadows, data gaps) in individual images, a pixel-wise temporal interpolation method was adopted for processing: (1) for a target pixel with missing data in a single image, valid reflectance values from adjacent 3–5 clear images (before and after the target image acquisition time) were used for linear interpolation to fill the gap; (2) if a pixel had missing data in ≥2 images, it was marked as an invalid pixel and excluded from subsequent TSI/NDTI calculation and model training; (3) prior to interpolation, NDWI masking (NDWI > 0) was applied to ensure only water pixels were retained, avoiding land or cloud pixels affecting interpolation accuracy. This processing method ensures the completeness of the multi-temporal reflectance time series for each valid water pixel, laying a reliable foundation for calculating temporal stability indices (TSI/NDTI). Detailed information on the selected images is provided in

Table 1. Sentinel-2 imagery obtained in the study.

Index	Sentinel-2 Image File	Time	Cloud Cover (%)
1	S2B_MSIL2A_20211109T160459	09-11-2021 16:04	0.34
2	S2A_MSIL2A_20211124T160611	24-11-2021 16:06	0.03
3	S2B_MSIL2A_20211129T160619	29-11-2021 16:06	0.38
4	S2A_MSIL2A_20211224T160701	24-12-2021 16:07	0.04
5	S2B_MSIL2A_20211229T160649	29-12-2021 16:06	0.03
6	S2B_MSIL2A_20220108T160639	08-01-2022 16:06	9.76
7	S2A_MSIL2A_20220113T160631	13-01-2022 16:06	7.96
8	S2B_MSIL2A_20220118T160559	18-01-2022 16:05	0.45
9	S2A_MSIL2A_20220202T160501	02-02-2022 16:05	9.55
10	S2A_MSIL2A_20220212T160401	12-02-2022 16:04	5.73
11	S2A_MSIL2A_20220304T160151	04-03-2022 16:01	2.37
12	S2B_MSIL2A_20220329T155819	29-03-2022 15:58	0.03
13	S2B_MSIL2A_20220408T155819	08-04-2022 15:58	6.92
14	S2B_MSIL2A_20220508T155819	08-05-2022 15:58	2.36

.

2.2. Methodology

The main work of this study comprises the following components: First, Sentinel-2 images and ALB data were acquired for the study areas on the eastern and western sides of Egmont Key. Second, tidal correction was performed on the ALB bathymetric data and Sentinel-2 images to achieve temporal matching between the two datasets. Subsequently, the TSI and NDTI were calculated pixel-by-pixel based on 14 Sentinel-2 images. Additionally, the feature set was further expanded by incorporating the Normalized Difference Water Index (NDWI), band combination features (B3/B2, B4/B3), and pixel location information. Using this comprehensive feature set as input and ALB data as the validation reference, four machine learning models—Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Regression (SVR), and Multi-Layer Perceptron (MLP)—were trained to perform shallow water bathymetric inversion for Egmont Key. Finally, the inversion accuracy and applicable scenarios of each model were comparatively evaluated. The technical workflow of this study is illustrated in Figure 2.

2.2.1. In Situ Data Pre-Processing

Nearshore water depth is significantly influenced by tidal fluctuations, leading to temporal discrepancies between LiDAR in situ measurements and Sentinel-2 satellite imagery (acquired at different times). To ensure consistency between the two datasets and eliminate systematic errors caused by tidal variations, tidal correction was performed.

$$H_S=H_{Lidar}-T_{Lidar}+T_S$$

(1)

Tidal height data were retrieved from the National Oceanic and Atmospheric Administration (NOAA) Tides & Currents website (https://tidesandcurrents.noaa.gov/, accessed on 27 October 2025), which provides authoritative, long-term tidal observations for coastal stations across the United States. The nearest operational tidal station to the study area—St. Petersburg Pier, FL (Station ID: 8726520)—was selected due to its proximity and high data reliability. Based on the acquisition timestamps of LiDAR measurements and each Sentinel-2 image, the corresponding tidal heights were extracted: $T_{Lidar}$ = 74.5 cm (average tidal height during LiDAR surveys) and $T_S$ = 51.8 cm (tidal height at satellite overpass time). These values were substituted into the formula to adjust the LiDAR-measured depth to the actual water depth at the time of satellite imaging.

2.2.2. Sentinel-2 Image Pre-Processing

To prepare high-quality spectral data for shallow water bathymetric inversion, Sentinel-2 L2A images underwent a standardized processing workflow tailored to the study requirements. First, the images were clipped to the precise geographic boundary of the study area (eastern and western nearshore waters of Egmont Key) using vector data of the research extent, eliminating redundant off-area pixels to improve computational efficiency and focus on target regions. Second, sun glint correction was performed to mitigate the interference of solar specular reflection on water surface spectral signals—this was achieved by applying a threshold-based masking method combined with spectral angle matching, identifying and suppressing glint-affected pixels to ensure the authenticity of underwater spectral information. Third, the Normalized Difference Water Index (NDWI) was calculated using Equation (2), and pixels with NDWI > 0 were retained to accurately extract water bodies while excluding land, clouds, and cloud shadows. Finally, based on the spatial coordinates of Airborne LiDAR Bathymetry (ALB) in situ sampling points, the spectral attributes of corresponding pixels in the processed images were extracted, including the reflectance values of core sensitive bands (B2, B3, B4, B8) and derived band combination features (B3/B2, B4/B3), forming a foundational spectral dataset for subsequent model training and bathymetric inversion.

$$NDWI={\displaystyle \frac{{\rho }_{B3}-{\rho }_{B8}}{{\rho }_{B3}+{\rho }_{B8}}}$$

(2)

2.2.3. Feature Engineering

Feature engineering is the core component in achieving high-precision shallow water bathymetric inversion. Its objective is to construct an input feature set that adapts to the heterogeneity of nearshore water bodies by integrating multi-dimensional effective information and selecting high-reliability features. This study designs a feature system from three dimensions—spectral, temporal, and spatial—as follows:

Spectral characteristics and band combination features: Spectral characteristics serve as the foundation for retrieving water depth. Reflectance values from the core bands in Sentinel-2 L2A data that are sensitive to shallow water depth variations, namely the blue band (B2, 490 nm), green band (B3, 560 nm), red band (B4, 665 nm), and near-infrared band (B8, 842 nm), are selected as the original spectral features. Simultaneously, by incorporating the optical transmission laws of shallow water—where shorter-wavelength light (blue, green) has stronger penetration in shallow water and longer-wavelength light (red) is more rapidly attenuated with increasing depth—two key band combination features are constructed: the green–blue band ratio (B3/B2) and the red–green band ratio (B4/B3), aiming to enhance the discernibility of depth-related signals.

The Normalized Difference Water Body Index (NDWI) is introduced, which achieves effective separation of water body and non-water body information through the calculation of reflectance in the green band and near-infrared band (Equation (2)), thus limiting the effective range for subsequent feature extraction.

To quantify the temporal stability of spectral features and the dynamic changes in water turbidity, two types of temporal coupling features are constructed: TSI, based on 14 scenes of multi-temporal Sentinel-2 imagery, is used to conduct a temporal analysis on the reflectance of the core spectral bands (B2, B3, B4, B8) for each pixel. The spectral temporal consistency is quantified by calculating the ratio of standard deviation to mean (Equation (3)). Specifically, the standard deviation of reflectance over time is computed using Equation (4) to characterize temporal variability, while the mean reflectance is obtained via Equation (5) to represent the baseline spectral intensity, where $B_{\lambda ,t}$ represents the reflectance of the band $\lambda$ at time t. A larger TSI indicates that the spectral characteristics of the pixel are less affected by temporal fluctuations, indicating higher reliability—this is because TSI is defined as 1 minus the ratio of standard deviation (reflecting temporal variability) to mean reflectance (reflecting baseline spectral intensity); a smaller ratio of STD to mean implies more stable spectral signals over time, thus resulting in a larger TSI value.

$$TSI(B_{\lambda })=1-{\displaystyle \frac{STD(B_{\lambda ,t})}{Mean(B_{\lambda ,t})}}$$

(3)

$$STD(B_{\lambda ,t})=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^t{(B_{(\lambda ,i)}-{\overline{B}}_{\lambda })}^2}{t-1}}}$$

(4)

$$Mean(B_{\lambda ,t})={\displaystyle \frac{{\sum }_{i=1}^t{B}_{(\lambda ,i)}}{t}}$$

(5)

NDTI, by combining and calculating sensitive bands from multi-temporal images, characterizes the spatiotemporal variation in water turbidity levels. The core function is to identify reliable spectral data that are less affected by disturbances such as cloud shadows, waves, and instantaneous suspended matter by quantifying the temporal stability of water turbidity. The value range of NDTI is [0, 1]. The closer the value is to 1, the less the spectral characteristics of the pixel are affected by instantaneous interference, and the more reliable the reflectance data is. The calculation method of NDTI is as shown in Equation (6), where the Difference Turbidity Index (DTI) for each time step is first computed using Equation (7), and the average DTI of the time series is obtained via Equation (8). $B_{\lambda ,t}$ represents the reflectance of the band $\lambda$ at time t; and ${DTI}_{Max}$ and ${DTI}_{Min}$ refer to the pixel-wise temporal extreme values, i.e., the maximum and minimum values of the DTI time series calculated from 14 multi-temporal Sentinel-2 images for a single pixel, respectively.

$$NDTI={\displaystyle \frac{{DTI}_{Max}-DTI}{{DTI}_{Max}-{DTI}_{Min}}}$$

(6)

$${DTI}_t={\displaystyle \frac{B_{4,t}-B_{2,t}}{B_{4,t}+B_{2,t}}}$$

(7)

$$DTI={\displaystyle \frac{{\sum }_{i=1}^t{DTI}_t}{t}}$$

(8)

Two types of temporal features form a dual-scale evaluation system of “spectral reliability–water turbidity”, providing a basis for dynamic feature selection. The specific fusion logic is as follows: TSI quantifies the intrinsic temporal stability of spectral features (i.e., how consistently the pixel’s reflectance signals perform over time), while NDTI characterizes the external environmental stability (i.e., the fluctuation degree of water turbidity that affects spectral quality). The two indices are synergistically used to determine the reliability weight of each pixel: pixels with both high TSI (≥0.7) and high NDTI (≥0.7) are identified as high-reliability, retaining all multi-dimensional features; pixels with either TSI < 0.5 or NDTI < 0.5 are classified as low-reliability, automatically excluding easily disturbed spectral features (e.g., near-infrared band reflectance); for medium-reliability pixels (other combinations), feature retention is determined by the weighted sum of TSI and NDTI (weight coefficients: TSI = 0.6, NDTI = 0.4), ensuring an adaptive response to both spectral stability and turbidity changes.

Spatial location features: There is a potential correlation between the depth distribution of nearshore water bodies and their geographical spatial locations (such as indirect influences like offshore distance and topographic slope). Therefore, the planar coordinates (X, Y) of pixels are incorporated into the input set as positional features to capture the depth distribution patterns in the spatial dimension and supplement the deficiencies of spectral features.

Through the construction of the aforementioned multi-dimensional features, a comprehensive feature set encompassing spectral, temporal, and spatial dimensions is formed. The detailed composition of the feature set is summarized in

Table 2. Feature set constructed in the study.

Feature Type		Feature	Feature Description
Original Spectral Feature		B2 Reflectance	Blue Band (490 nm)
		B3 Reflectance	Green Band (560 nm)
		B4 Reflectance	Red Band (665 nm)
		B8 Reflectance	Near-infrared Band (833 nm)
Spectral Fusion Feature	Band Combination	B3/B2	Ratio of Green and Blue Bands
		B4/B3	Ratio of Red and Green Bands
	Water Body Index	NDWI	Normalized Difference Water Index
Temporal Feature		TSI	Temporal Stability of Spectral Features (B2, B3, B4, B8)
		NDTI	Temporal Stability of Water Turbidity
Location Feature		X	X Coordinate of Pixel (WGS 1984 UTM Zone 17N)
		Y	Y Coordinate of Pixel (WGS 1984 UTM Zone 17N)

. This lays the foundation for subsequent pixel-level feature reliability weighting and dynamic filtering based on the STCCAS inversion method, ultimately achieving the construction of high-precision inversion input data that adapts to water body heterogeneity.

2.2.4. Bathymetric Inversion Model

To comprehensively explore the adaptability of different machine learning paradigms in nearshore shallow water bathymetry inversion, this study selects four models— Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Regression (SVR), and Multi-Layer Perceptron (MLP)—for comparative experiments. Prior to model training, the dataset was partitioned into a training set and a test set following a spatially constrained strategy to avoid data leakage caused by spatial autocorrelation in remote sensing bathymetry data. (1) Partition ratio: 70% of the samples were used for model training, and 30% for performance validation. (2) Partitioning method: A spatially stratified random sampling approach was adopted. The study area was divided into non-overlapping 1 m × 1 m grid cells, and samples were randomly extracted from each grid according to the 7:3 ratio. This method ensures that both the training and test sets cover the full range of water depths and spatial distribution characteristics of the study area, effectively eliminating the overfitting risk associated with random partitioning and improving the generalization ability of the models. The core rationale lies in the fact that these four models cover typical architectures of ensemble learning, statistical learning, and deep learning, and each possesses unique advantages in handling high-dimensional features, nonlinear relationships, and noise interference, enabling targeted adaptation to the core challenges of nearshore water bathymetry inversion. Specifically, RF and XGBoost are representatives of ensemble learning [44,45]. The former utilizes multiple decision tree ensembles and random feature selection, exhibiting strong resistance to overfitting and efficient handling of multi-source features, effectively avoiding interference from single features [46]; the latter, through gradient boosting strategies and regularization mechanisms, can accurately capture nonlinear interactions between features, adapting to spectral water depth mapping fluctuations caused by turbidity heterogeneity in nearshore waters [47,48]. SVR, based on statistical learning theory, maps low-dimensional features to high-dimensional space through a kernel function, enabling the construction of complex nonlinear models without relying on a large number of samples, and is suitable for fine inversion in scenarios where spectral signals are disturbed [49,50,51]. MLP, as a shallow deep learning model, utilizes a multi-layer, fully connected structure and nonlinear activation functions to automatically learn high-order coupling patterns of features, adapting to the synergistic mechanism of multi-dimensional features [52,53,54]. By comparing these four different types of models, not only can the performance differences in each model in nearshore water bathymetry inversion be verified, but also the optimal model that is most suitable for the “multi-feature constrained adaptive spectral fusion strategy” can be selected, ensuring the reliability and generalization ability of the inversion results, while providing a reference for model selection in similar research.

Random Forest is a robust ensemble learning algorithm proposed by Breiman [55], which integrates multiple independent decision trees to achieve regression or classification tasks by leveraging the “bagging” strategy and randomized feature selection. During the training phase, the algorithm first generates multiple bootstrap samples with replacement from the original dataset to train individual decision trees, ensuring diversity among base learners. At each node split of a decision tree, only a random subset of features is considered to determine the optimal split threshold, which effectively reduces the correlation between trees and mitigates overfitting—a common limitation of single decision trees. For regression tasks, the final prediction result is derived from the average of outputs from all decision trees in the forest, balancing prediction accuracy and generalization ability. Owing to its strong capability in handling nonlinear relationships between features and targets, resistance to noise interference, and adaptability to high-dimensional data, the RF model has been widely applied in remote sensing bathymetric inversion and achieved excellent performance [23,29,35]. In this study, the RF model was configured with 200 decision trees, a maximum tree depth of 15, and a minimum of 5 samples required for node splitting (optimized via 5-fold cross-validation).

eXtreme Gradient Boosting, proposed by Chen and Guestrin [56], is an optimized implementation of the gradient boosting decision tree (GBDT) algorithm, renowned for its high efficiency, scalability, and robustness in handling complex regression tasks. Unlike the traditional GBDT, XGBoost integrates both L1 (Lasso) and L2 (Ridge) regularization terms into the objective function to penalize overly complex decision trees, effectively mitigating overfitting and improving the generalization ability of the model. The algorithm adopts a greedy strategy to iteratively construct additive decision trees: each new tree is trained to fit the residual errors of the combined predictions from all previous trees, and gradient descent is used to minimize the loss function. Additionally, XGBoost incorporates practical optimizations including column subsampling (random selection of feature subsets for tree splitting), built-in handling of missing values, and parallel computing for tree construction, which significantly accelerates training speed while maintaining prediction accuracy. XGBoost is particularly well-suited to modeling the nonlinear and non-stationary relationships between multi-dimensional features and water depth. Its strong capability to capture feature interactions and resistance to noise from turbid nearshore waters make it a competitive candidate for this study. In this study, the XGBoost model was optimized with a learning rate of 0.01, 300 base decision trees, L1 regularization coefficient of 0.1, L2 regularization coefficient of 1.0, and a maximum tree depth of 10.

Support Vector Regression is a regression variant of the Support Vector Machine (SVM) algorithm, rooted in statistical learning theory and kernel methods [57]. Unlike traditional regression models that minimize the sum of squared errors, SVR introduces an ε-insensitive loss function, which allows prediction deviations within a small threshold (ε) without penalization, enhancing the model’s robustness to noise [58]. A key advantage of SVR is its ability to map low-dimensional input features to a high-dimensional feature space via kernel functions, enabling the construction of an optimal hyperplane to model complex nonlinear relationships between features and water depth—this avoids the “curse of dimensionality” common in high-dimensional data processing. For shallow water bathymetric inversion, the radial basis function (RBF) was selected as the kernel function due to its flexibility in capturing non-stationary feature interactions in nearshore waters. Critical hyperparameters optimized for this study include the regularization parameter (C = 10) to balance model complexity and generalization, the ε-insensitive loss parameter (ε = 0.1) to control the width of the insensitive zone, and the RBF kernel bandwidth (γ = 0.1) to adjust the influence range of individual support vectors [6]. SVR’s strong performance in small-sample, high-dimensional scenarios makes it well-suited for this research, where it effectively models the nonlinear mapping between multi-source features and shallow water depth.

Multi-Layer Perceptron is a feedforward artificial neural network composed of an input layer, one or more hidden layers, and an output layer, capable of automatically learning complex nonlinear feature interactions through hierarchical computation [59]. Unlike shallow neural networks, MLP introduces nonlinear activation functions (e.g., ReLU) in hidden layers, enabling the model to capture nonlinear relationships between multi-dimensional features and shallow water depth. The training process relies on backpropagation algorithms to minimize the loss function (mean squared error, MSE) by iteratively adjusting weights and biases across layers, while regularization techniques (e.g., Dropout) are employed to mitigate overfitting. In this study, the MLP architecture was tailored to bathymetric inversion requirements: the input layer consists of multi-dimensional features, followed by two hidden layers with 64 and 32 neurons, respectively, and a linear output layer for water depth prediction. The ReLU activation function was selected for hidden layers to address the vanishing gradient problem, and a Dropout rate of 0.2 was applied to prevent overfitting to noisy spectral data in turbid waters. MLP’s ability to adapt to complex feature couplings makes it suitable for nearshore bathymetric inversion, where it integrates multi-source information to improve prediction accuracy. Key hyperparameters include a learning rate of 0.001, 100 training epochs, and a batch size of 32, balancing training efficiency and convergence performance.

3. Results

3.1. Temporal Features

Temporal features (TSI and NDTI) constructed in this study effectively quantify the temporal stability of spectral characteristics and the dynamic variation in water turbidity, laying a foundation for adaptive feature filtering in subsequent bathymetric inversion. The spatial distribution patterns of TSI across different Sentinel-2 core bands (B2, B3, B4, B8) and NDTI in the study area are shown in Figure 3.

For the TSI, which reflects the reliability of spectral features over time (lower TSI indicates stronger temporal fluctuation and lower spectral reliability), significant spatial heterogeneity is observed across all four core bands (Figure 3a–d). Generally, TSI values in offshore areas (far from the coastline) are closer to 1 (ranging from 0.8 to 1.0), indicating that spectral reflectance in these regions is less affected by temporal disturbances (e.g., nearshore runoff, suspended sediment resuspension, and short-term weather changes) and maintains high temporal consistency. In contrast, nearshore areas (within 1 km of the coastline) exhibit lower TSI values (0.4–0.6), especially in the western nearshore of Egmont Key (Region 2). This is attributed to the influence of coastal hydrodynamic processes (e.g., tidal currents, wave action) and terrigenous input (e.g., sediment and nutrient discharge), which cause frequent changes in water composition and thus lead to unstable spectral signals.

Among different bands, the visible bands (B2: blue, B3: green, B4: red) show higher overall TSI values compared to the near-infrared band (B8). This is because near-infrared radiation is strongly absorbed by water, and its reflectance is more sensitive to subtle changes in water turbidity and suspended matter concentration—even small temporal fluctuations in these factors can lead to significant variations in B8 reflectance. In contrast, visible bands have moderate penetration in shallow water and are less sensitive to minor turbidity changes, resulting in higher temporal stability.

The Normalized Difference Turbidity Index (NDTI) characterizes the temporal stability of water turbidity (higher NDTI indicates more stable turbidity and less interference from dynamic factors). As shown in Figure 3e, the spatial distribution of NDTI is highly consistent with that of TSI: offshore areas have NDTI values close to 1 (0.8–1.0), indicating stable turbidity conditions, while nearshore areas have lower NDTI values (0.1–0.5), reflecting frequent turbidity fluctuations. Notably, the lowest NDTI values (0.1–0.3) are concentrated in the eastern nearshore of Egmont Key (Region 1) and the estuarine-adjacent areas of Region 2, which are influenced by local runoff and shallow-water wave resuspension, leading to significant temporal changes in suspended sediment concentration.

3.2. Bathymetric Inversion

The bathymetric inversion results of four machine learning models (RF, XGBoost, SVR, MLP) under two feature strategies (OSF and STCCAS) in Region 1 (eastern nearshore) and Region 2 (western nearshore) are presented in Figure 4 and

Table 3. Performance of four models based on different strategies in Region 1 and Region 2.

Model	R2		RMSE(m)		MAE(m)
	Region 1	Region 2	Region 1	Region 2	Region 1	Region 2
RF-OSF	0.73	0.41	0.33	0.61	0.23	0.47
RF-STCCAS (variation)	0.92 (+0.19)	0.89 (+0.48)	0.18 (−0.15)	0.27 (−0.34)	0.13 (−0.10)	0.20 (−0.27)
XGBoost-OSF	0.68	0.32	0.36	0.67	0.25	0.50
XGBoost-STCCAS (variation)	0.93 (+0.25)	0.92 (+0.60)	0.16 (−0.20)	0.22 (−0.45)	0.12 (−0.13)	0.17 (−0.33)
SVR-OSF	0.71	0.37	0.33	0.63	0.25	0.49
SVR-STCCAS (variation)	0.92 (+0.21)	0.87 (+0.60)	0.18 (−0.15)	0.29 (−0.34)	0.13 (−0.12)	0.22 (−0.27)
MLP-OSF	0.71	0.39	0.33	0.61	0.24	0.47
MLP-STCCAS (variation)	0.91 (+0.20)	0.86 (+0.47)	0.19 (−0.14)	0.30 (−0.31)	0.14 (−0.10)	0.23 (−0.24)

. The results clearly demonstrate that the STCCAS inversion method significantly improves the inversion accuracy compared to the traditional OSF inversion method, and the performance of different models varies notably under the two strategies.

3.3. Evaluation of Model Accuracy

Based on the three key metrics (R², RMSE, MAE), a comprehensive evaluation of the inversion accuracy of each model under different strategies and regions is conducted, focusing on the magnitude of accuracy improvement and model adaptability.

Under the OSF inversion method, all four models exhibit limited inversion accuracy in both regions. In Region 1, the R² values of the models range from 0.68 (XGBoost) to 0.73 (RF), with RMSE between 0.33 m (RF, SVR, MLP) and 0.36 m (XGBoost), and MAE between 0.23 m (RF) and 0.25 m (XGBoost, SVR). In Region 2 (higher turbidity and stronger spatial heterogeneity), the OSF inversion method performs even worse: R² values drop to 0.32 (XGBoost) to 0.41 (RF), RMSE increases to 0.61 m (RF, MLP) to 0.67 m (XGBoost), and MAE reaches 0.47 m (RF, MLP) to 0.50 m (XGBoost). This indicates that traditional fixed spectral features are unable to adapt to the heterogeneity of nearshore waters, especially in turbid areas, where spectral interference leads to the severe degradation of inversion performance. In contrast, the STCCAS inversion method significantly enhances the inversion accuracy of all models. For Region 1, the R² of all models exceeds 0.91, with XGBoost-STCCAS achieving the highest R² (0.93), and the lowest RMSE (0.16 m), and MAE (0.12 m). Compared to XGBoost-OSF, the R² increases by 0.25, and the RMSE decreases by 0.20 m (a 56% reduction), which is consistent with the key findings highlighted in the study. RF-STCCAS, SVR-STCCAS, and MLP-STCCAS also show substantial improvements: R² increases by 0.19, 0.21, and 0.20 respectively, and RMSE decreases by 0.15 m, 0.15 m, and 0.14 m. In Region 2, the STCCAS inversion method achieves even more remarkable improvements. The R² of XGBoost-STCCAS surges from 0.32 (OSF) to 0.92, an increase of 0.60; RMSE decreases from 0.67 m to 0.22 m, and MAE drops from 0.50 m to 0.17 m. Similarly, RF-STCCAS, SVR-STCCAS, and MLP-STCCAS see their R² values increase by 0.48, 0.60, and 0.47 respectively, with RMSE reductions of 0.34 m, 0.34 m, and 0.31 m. This confirms that the STCCAS inversion method, through pixel-level feature reliability weighting and dynamic filtering, effectively mitigates the interference of spatiotemporal heterogeneity (e.g., turbidity fluctuations, nearshore runoff) on inversion results, and its adaptability to complex water environments is particularly prominent.

Among the four models, XGBoost exhibits the optimal overall performance under the STCCAS inversion method. In both regions, XGBoost-STCCAS achieves the highest R² and the lowest RMSE/MAE, which is attributed to its strong ability to capture nonlinear relationships between multi-dimensional features (spectral, temporal, spatial) and water depth, as well as the regularization mechanism that suppresses overfitting caused by noise features.

The accuracy evaluation results show clear differences in model adaptability to the STCCAS feature set. XGBoost has the strongest adaptability, with R² > 0.92 and RMSE < 0.22 m in both regions. Its ability to capture feature interactions and resist noise makes it the optimal model for shallow water bathymetry inversion under the STCCAS inversion method. RF exhibits good stability, with R² differences between the two regions of only 0.03 (STCCAS) and 0.32 (OSF), indicating that RF is less sensitive to regional environmental differences and is suitable for large-scale shallow water bathymetry monitoring. SVR performs well in clear water (Region 1, R² = 0.92) but has limited adaptability in turbid water (Region 2, R² = 0.87), which is attributed to the reduced effectiveness of kernel function mapping in high-noise feature environments. MLP has the weakest adaptability among the four models, with the lowest R² and highest RMSE in both regions under the STCCAS inversion method. This is due to the insufficient depth of the network structure, which cannot fully extract the high-order correlation information of multi-dimensional features.

For the OSF strategy (Figure 5a,e,i,m for Region 1; Figure 5c,g,k,o for Region 2), the residuals of all models exhibit significant dispersion and obvious systematic bias. In Region 1, the residuals of RF-OSF (Figure 5a) and MLP-OSF (Figure 5m) range from −1.5 m to 1.0 m, with a tendency of overestimation for shallow waters (<2 m) and underestimation for deeper waters (>3 m). XGBoost-OSF (Figure 5e) and SVR-OSF (Figure 5i) show similar bias patterns, with residual fluctuations exceeding ±1.0 m in partial depth intervals. In the more complex Region 2, the residual distribution of OSF-based models is more chaotic: RF-OSF (Figure 5c) and MLP-OSF (Figure 5o) have residuals spanning −3.0 m to 2.5 m, and XGBoost-OSF (Figure 5g) even exhibits extreme overestimation (residual > 2.0 m) for depths of 6–10 m. This indicates that traditional fixed spectral features fail to adapt to the spatiotemporal heterogeneity of nearshore waters, leading to unconstrained random errors and significant systematic deviations in inversion results.

In sharp contrast, the STCCAS strategy (Figure 5b,f,j,n for Region 1; Figure 5d,h,l,p for Region 2) significantly reduces residual dispersion and eliminates systematic bias. In Region 1, XGBoost-STCCAS (Figure 5f) achieves the most concentrated residual distribution, with over 95% of residuals falling within the range of −0.3 m to 0.3 m, and no obvious overestimation or underestimation tendency across the entire depth range (0–5 m). RF-STCCAS (Figure 5b), SVR-STCCAS (Figure 5j), and MLP-STCCAS (Figure 5n) also show similar optimization effects, with residual fluctuations reduced by more than 60% compared to the OSF strategy. Even in the turbid and heterogeneous Region 2, the STCCAS-based models maintain excellent residual stability: XGBoost-STCCAS (Figure 5h) limits residuals to −0.5 m to 0.5 m, and the residual distribution is uniformly scattered around the zero line without clustering or extreme values. RF-STCCAS (Figure 5d) and SVR-STCCAS (Figure 5l) exhibit slightly larger residual fluctuations but still avoid systematic bias, while MLP-STCCAS (Figure 5p) shows a slight underestimation for depths > 8 m but with residual amplitudes reduced by 58% compared to MLP-OSF.

The residual analysis further verifies the effectiveness of the STCCAS inversion method: the dual-scale “spectral reliability–turbidity stability” evaluation system and pixel-level dynamic filtering mechanism not only reduce random errors (reflected by reduced RMSE) but also eliminate systematic deviations caused by spectral interference and water heterogeneity. Among the four models, XGBoost-STCCAS demonstrates the most balanced residual distribution, which is attributed to its strong ability to capture nonlinear feature interactions and suppress noise, making it the optimal combination for shallow water bathymetry inversion in complex nearshore environments.

3.4. Mapping

Based on the optimal combination scheme (XGBoost STCCAS), shallow seawater bathymetry inversion mapping was completed in the study area, visually presenting the spatial distribution characteristics of nearshore water depth. By comparing pixel by pixel with ALB-measured data, the spatial reliability of the inversion results was quantified. The inversion result map (Figure 6a) and the measured difference map (Figure 6b) together constitute a complete characterization system of water depth distribution, providing visual data support for subsequent marine environmental monitoring and resource management.

4. Discussion

The core objective of this study is to address the limitations of traditional SDB methods in adapting to nearshore water heterogeneity and suppressing spectral interference. By proposing the STCCAS inversion method and comparing four machine learning models, this research achieves significant improvements in inversion accuracy. The following discussion focuses on the mechanisms underlying the key findings, comparisons with existing studies, model performance differences, and research limitations.

4.1. Advantages of STCCAS Inversion Method

This study constructs a multi-dimensional feature system integrating spectral, temporal, and spatial dimensions, laying a solid foundation for adaptive bathymetry inversion. In terms of inversion accuracy, the proposed STCCAS inversion method combined with the XGBoost model achieves exceptional performance—with R² of 0.93 and an RMSE of 0.16 m—outperforming most existing similar studies. Notably, the RMSE is reduced by 56% compared to traditional spectral inversion schemes, which fully confirms the STCCAS inversion method’s effectiveness in enhancing inversion precision. Additionally, this study adopts open-source Sentinel-2 data, developing a low-cost, high-frequency bathymetry inversion scheme. This not only tackles the high costs and long acquisition cycles associated with traditional in situ methods but also exhibits stronger practical applicability than studies relying on high-resolution commercial satellite data, as it eliminates the barriers of expensive data access.

The feature importance analysis of the STCCAS inversion method (Figure 7) further reveals the core driving factors of the high inversion accuracy, and quantifies the contribution of different features and feature types to the shallow water bathymetry inversion model, providing a clear theoretical basis for the rationality of the multi-dimensional feature construction in this study. Figure 7a presents the feature importance ranking of the STCCAS inversion method at the single-feature level, and the results show that the temporal features constructed in this study occupy the top positions of the importance ranking: NDTI has the highest importance score, followed by TSI of the green band (B3), red band (B4) and blue band (B2). This indicates that the turbidity stability and spectral temporal consistency of nearshore water bodies are the most critical factors affecting the accuracy of bathymetry inversion, which also verifies the scientificity of constructing the dual-scale “spectral reliability–turbidity stability” evaluation system in the STCCAS method—these two temporal features effectively capture the spatiotemporal heterogeneity of nearshore waters, and the dynamic filtering based on them can significantly reduce the interference of unstable spectral signals on the model. In addition, spatial location feature Y and TSI of the near-infrared band (B8) also show relatively high importance, reflecting that the spatial distribution pattern of water depth and the temporal stability of short-wave spectral signals also play an important role in the inversion process; the spectral fusion features (NDWI, B4/B3, B3/B2) and TSI of the green band (B3) have moderate importance, acting as effective supplements to the core temporal and spatial features and enriching the spectral information related to water depth.

We further quantify the importance proportion of different feature types in the XGBoost-STCCAS inversion method (Figure 7b), and the results show a clear hierarchical contribution of the four feature types (temporal features, spatial features, spectral fusion features, original spectral features) to the model. Temporal features (TSI + NDTI) account for the largest proportion of total importance, exceeding half of the total contribution, which is the absolute core of the STCCAS feature set; spatial features (X, Y coordinates) rank second in the importance proportion, which effectively make up for the deficiency of single spectral feature representation by capturing the spatial correlation of nearshore water depth distribution, and further improve the generalization ability of the model in heterogeneous water areas; spectral fusion features (band ratio, NDWI) account for a moderate proportion, optimizing and transforming the original spectral reflectance based on the optical transmission law of shallow water, enhancing the discernibility of depth-related spectral signals; the original spectral features have the lowest importance proportion in the STCCAS method, which is quite different from the traditional OSF inversion method that only relies on original spectral reflectance. This phenomenon fully demonstrates that the STCCAS method has broken through the limitations of relying on fixed original spectral features, and the introduction of temporal and spatial features has fundamentally improved the feature-driving mechanism of the bathymetry inversion model, making the model no longer limited by the interference of spectral heterogeneity, and thus achieving a substantial improvement in inversion accuracy.

The above feature importance analysis results are consistent with the core design logic of the STCCAS inversion method: the multi-dimensional feature set with temporal features as the core, spatial features as the supplement, and spectral fusion features as the auxiliary can effectively adapt to the spatiotemporal heterogeneity of nearshore waters. The high importance of temporal features also confirms that the suppression of spectral interference and the adaptation to water body heterogeneity are the key to improving the accuracy of satellite-derived bathymetry, which provides an important reference for the feature selection and optimization of subsequent shallow water bathymetry inversion research.

4.2. Mechanisms of Effectiveness

The remarkable accuracy improvement brought by the STCCAS inversion method stems from its innovative dual-scale feature evaluation and pixel-level dynamic filtering mechanism. First, the TSI and NDTI construct a “spectral reliability–turbidity stability” evaluation system that quantifies the quality of pixel features from temporal and environmental dimensions. As shown in the results, offshore areas with high TSI (0.8–1.0) and NDTI (0.8–1.0) have stable spectral signals and turbidity conditions, while nearshore areas with low TSI (0.4–0.6) and NDTI (0.1–0.5) are affected by terrigenous input and hydrodynamic disturbances, leading to unstable features. This quantitative evaluation enables the strategy to distinguish reliable and noisy features, avoiding the “one-size-fits-all” limitation of traditional fixed feature combinations.

Second, the dynamic filtering mechanism optimizes the input feature set according to pixel quality: high-reliability pixels retain all spectral, temporal, spatial, and fusion features to maximize information utilization, while low-reliability pixels eliminate vulnerable features to reduce noise interference. This adaptive adjustment effectively mitigates the negative impact of spatiotemporal heterogeneity—especially in turbid nearshore waters (Region 2), where the STCCAS inversion method increases the R² of XGBoost by 0.60 and reduces RMSE by 0.45 m. This mechanism aligns with the core demand of SDB for adaptive feature optimization in complex environments, breaking through the bottleneck of traditional methods that rely on fixed band combinations.

4.3. Limitations and Future Directions

Despite the significant achievements, this study has several limitations. First, the study area is limited to the nearshore waters of Egmont Key in Tampa Bay, with a water depth range of 0–10 m. The adaptability of the STCCAS inversion method to deeper environments or other types of nearshore environments (e.g., estuaries, coral reefs) needs further verification. Second, the feature set only includes TSI and NDTI as temporal features; future research can integrate more environmental variables (e.g., sea surface temperature, chlorophyll concentration) to enhance the comprehensiveness of feature evaluation. Third, the MLP model uses a shallow structure—deep learning models with more complex architectures (e.g., CNN, Transformer) may better capture high-dimensional feature couplings, further improving inversion accuracy.

Future research can focus on three directions: (1) expand the study area to different coastal types (estuaries, bays, open coasts) and water depth ranges (0–20 m) to verify the generalization ability of the STCCAS inversion method; (2) integrate multi-source remote sensing data (e.g., Sentinel-3 OLCI, ICESat-2) to enrich feature types and improve inversion stability; (3) optimize the dynamic filtering mechanism by introducing machine learning-based feature selection algorithms (e.g., recursive feature elimination) to adapt to more complex water environments.

5. Conclusions

To address the challenges of water heterogeneity and spectral interference in shallow water bathymetry inversion, this study proposes a Spatio-Temporal Coupling and Correlation Adaptive Spectral (STCCAS) inversion method and conducts comparative experiments with four machine learning models in the nearshore waters of Tampa Bay. The main conclusions are as follows:

The STCCAS inversion method constructs a multi-dimensional feature system integrating spectral, temporal, spatial, and fusion features. The TSI (quantifying spectral temporal consistency) and NDTI (characterizing turbidity stability) form a dual-scale evaluation system, and the pixel-level dynamic filtering mechanism effectively mitigates the interference of spatiotemporal heterogeneity.

Under the STCCAS inversion method, all four models achieve significant accuracy improvements. XGBoost performs optimally, with an R² of 0.93, RMSE of 0.16 m, and MAE of 0.12 m in Region 1—RMSE is 56% lower than the traditional original spectral feature (OSF) inversion method. In the more complex Region 2, XGBoost-STCCAS increases R² by 0.60 and reduces RMSE by 0.45 m, demonstrating strong adaptability to turbid waters.

Ensemble learning models (XGBoost, RF) are more suitable for the STCCAS feature set than statistical learning (SVR) and shallow deep learning (MLP) models. XGBoost’s ability to capture nonlinear feature interactions and resist noise makes it the optimal model for adaptive bathymetry inversion.

The STCCAS inversion method based on open-source Sentinel-2 data provides a low-cost, high-frequency, high-precision technical solution for shallow water bathymetry. It breaks through the limitations of traditional fixed feature combinations, establishes a new paradigm for multi-dimensional feature optimization in remote sensing bathymetry, and provides reliable data support for nearshore marine monitoring, resource management, and ecological protection.

The research enriches the theoretical system of adaptive spectral inversion and has important practical value for promoting the application of satellite-derived bathymetry in complex nearshore environments. Future research on expanding the application scope and optimizing the feature system will further enhance the generalization ability and accuracy of the method.