A Multi-Temporal Satellite-Derived Bathymetry Fusion Method Based on Adaptive Segmented Rank-Statistic Fusion

Abstract

Satellite-derived bathymetry (SDB) provides an efficient approach for shallow-water mapping because of its wide spatial coverage and repeated observation capability. However, multi-temporal bathymetric results derived from optical imagery often exhibit substantial inconsistencies due to variations in atmospheric conditions, water optical properties, bottom reflectance, and imaging geometry. Moreover, different bathymetric intervals usually exhibit distinct uncertainty characteristics, while conventional global fusion methods generally apply a single statistical strategy to the entire depth range. To address this limitation, this study proposes an ICESat-2-constrained adaptive segment-wise rank-statistic fusion framework for multi-temporal SDB. The bathymetric range is adaptively divided into multiple depth intervals using ICESat-2 bathymetric control points, and the optimal rank-statistic fusion strategy is independently selected for each interval according to local RMSE evaluation. In this way, shallow-water outliers can be effectively suppressed, while deep-water systematic underestimation can be alleviated simultaneously. Experiments conducted in Ganquan Island, Dong Island, and Key Biscayne demonstrate that the proposed framework consistently outperforms individual single-scene results as well as conventional mean and median fusion methods. Compared with conventional mean and median fusion methods, the RMSE was reduced by up to 27.5%, while the coefficient of determination (R²) reached 0.95. Significant improvements were particularly observed in deeper bathymetric intervals and complex benthic environments. The results indicate that adaptive segmented rank-statistic fusion can effectively characterize bathymetric-dependent error variations and achieve unified optimization for shallow-water outlier suppression and deep-water bias correction.

1. Introduction

Bathymetric information in shallow coastal waters plays an important role in marine geomorphology analysis, navigation safety, coastal management, coral reef monitoring, and marine ecological studies [1,2,3]. Traditional bathymetric surveys mainly rely on shipborne single-beam or multibeam echo sounding systems and airborne LiDAR measurements. Although these methods can provide highly accurate depth measurements, they are usually expensive, time-consuming, and spatially constrained, making them unsuitable for large-scale and long-term shallow-water monitoring applications [4,5,6].

With the rapid development of optical remote sensing technology, Satellite-Derived Bathymetry (SDB) has become an effective approach for shallow-water mapping because of its wide spatial coverage, low operational cost, and repeated observation capability [7,8,9,10]. Optical bathymetric inversion mainly utilizes the attenuation characteristics of visible light in water bodies to establish relationships between spectral reflectance and water depth [1,11,12]. In recent years, multispectral satellite imagery acquired from Sentinel-2, Landsat-8, and WorldView platforms has been widely applied in shallow-water bathymetric studies, substantially improving bathymetric mapping efficiency and spatial coverage [13,14,15,16].

However, optical bathymetric inversion remains highly sensitive to atmospheric conditions, water optical properties, bottom substrate variability, wave disturbance, sun glint, and solar illumination geometry [8,17,18]. Significant differences often exist among bathymetric results derived from different acquisition times. In shallow-water regions, strong bottom reflectance and environmental disturbances can easily introduce unstable local fluctuations and abnormal bathymetric estimates. In deeper waters, optical signals are strongly attenuated by water absorption and scattering effects, resulting in decreasing spectral sensitivity and systematic bathymetric underestimation [11,12]. Consequently, single-scene bathymetric inversion results often exhibit limited robustness and significant temporal instability.

Previous studies mainly focused on multi-temporal compositing, temporal averaging, and statistical fusion strategies for improving SDB consistency and reducing environmental noise. Traganos et al. [9] demonstrated the potential of Google Earth Engine and Sentinel-2 for coastal bathymetric mapping. Poursanidis et al. [10] further showed that multi-source and multi-temporal observations could improve bathymetric stability under varying environmental conditions. Recent studies have also explored multi-image compositing and temporal optimization approaches to reduce uncertainty in satellite-derived bathymetry and improve mapping robustness. In addition, recent geospatial studies have highlighted the value of integrating remote sensing observations with GIS-based spatial analysis for improving the characterization of complex environmental processes [19]. These studies provide methodological support for developing robust geospatial analysis frameworks in coastal and marine environments.

Although these studies demonstrated that multi-temporal observations can effectively improve bathymetric stability, how to adaptively integrate bathymetric information from different depth intervals remains an important challenge.

The launch of the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) by NASA has provided an important opportunity for improving satellite-derived bathymetry [20,21]. Equipped with the Advanced Topographic Laser Altimeter System (ATLAS), ICESat-2 can provide high-precision photon-counting bathymetric observations in shallow coastal waters. Compared with conventional field surveys, ICESat-2 offers broader spatial coverage and higher data accessibility and has been increasingly applied in coastal bathymetric inversion and shallow-water topographic studies [22,23,24,25]. More importantly, ICESat-2 bathymetric photons provide reliable bathymetric control information for evaluating and optimizing multi-temporal bathymetric fusion strategies.

Although ICESat-2 bathymetric observations provide reliable bathymetric constraints, most existing fusion frameworks still rely on global statistical assumptions and rarely consider the substantial uncertainty differences among different bathymetric intervals. Consequently, local shallow-water instability and deep-water systematic underestimation are difficult to optimize simultaneously within a unified fusion framework. Therefore, developing a depth-dependent adaptive fusion strategy constrained by ICESat-2 bathymetric observations remains an important challenge for multi-temporal satellite-derived bathymetry.

To address these limitations, this study proposes an ICESat-2-constrained adaptive segment-wise rank-statistic fusion framework for multi-temporal satellite-derived bathymetry. The bathymetric range is adaptively divided into multiple depth intervals according to ICESat-2 bathymetric control points, and the optimal rank-statistic fusion strategy is independently selected for each interval based on local RMSE evaluation. In this way, different bathymetric intervals can automatically adopt different locally optimal statistical fusion strategies, thereby simultaneously suppressing shallow-water outliers and alleviating deep-water systematic underestimation. The proposed framework was evaluated in three representative shallow-water environments with different reef geomorphologies, benthic conditions, and bathymetric ranges, including Ganquan Island, Dong Island, and Key Biscayne.

The remainder of this paper is organized as follows. Section 2 introduces the study areas and datasets. Section 3 describes the proposed adaptive segment-wise rank-statistic fusion framework. Section 4 presents the experimental results and discussion. Finally, conclusions are summarized in Section 5.

2. Study Areas and Data

2.1. Study Areas

To evaluate the applicability and robustness of the proposed framework under different shallow-water environments, three representative coastal regions, namely Ganquan Island, Dong Island, and Key Biscayne, were selected as study areas, as shown in Figure 1. These regions exhibit substantial differences in bathymetric range, reef geomorphology, benthic composition, and water optical conditions, thereby providing comprehensive scenarios for validating the proposed method.

Ganquan Island and Dong Island are located in the Xisha Islands of the South China Sea, where coral reef geomorphology dominates the shallow-water environment. The water bodies in these regions generally exhibit high transparency and relatively stable optical conditions, making them suitable for satellite-derived bathymetric studies [26,27,28]. The relatively clear water conditions facilitate light penetration and provide favorable conditions for optical satellite-derived bathymetry.

Key Biscayne is characterized by extensive seagrass coverage, spatially variable bottom reflectance, and relatively complex water optical conditions. Compared with the coral reef environments of the South China Sea, stronger environmental heterogeneity is observed in this region, providing a representative scenario for evaluating the robustness of multi-temporal bathymetric fusion methods under complex shallow-water conditions [29].

Figure 1. Geographical locations of the three study areas.

Figure 1. Geographical locations of the three study areas.

2.2. Datasets

The datasets used in this study mainly include multi-temporal Sentinel-2 multispectral imagery, ICESat-2 ATL03 photon-counting bathymetric data, and reference bathymetric datasets. Sentinel-2 imagery was used to generate single-scene bathymetric inversion results, while ICESat-2 bathymetric photons were employed for adaptive segmentation and fusion strategy optimization. Reference bathymetric datasets were used for quantitative accuracy assessment.

2.2.1. Sentinel-2 Multi-Temporal Imagery

Sentinel-2 multispectral imagery was employed as the primary optical data source for bathymetric inversion in this study. Sentinel-2 was selected because it provides high spatial resolution, frequent revisit capability, free data access, and suitable visible spectral bands for shallow-water bathymetric inversion. These advantages have made Sentinel-2 one of the most widely used satellite datasets in SDB studies.

Sentinel-2 provides high spatial resolution, repeated observation capability, and multiple visible bands suitable for shallow-water bathymetric retrieval [30,31]. The blue band (B2), green band (B3), red band (B4), and near-infrared band (B8) were selected for bathymetric inversion because these bands contain important spectral information associated with water-column attenuation and benthic reflectance characteristics.

In this study, Sentinel-2 Level-2A surface reflectance products were acquired through the Google Earth Engine (GEE) platform. Atmospheric correction, cloud masking, image clipping, and spectral band extraction were performed before bathymetric inversion. Considering the strong penetration capability of visible bands in shallow waters, the blue, green, red, and near-infrared bands were selected as input features for bathymetric inversion [11,13].

To reduce the influence of environmental variability and cloud contamination, five cloud-free or low-cloud Sentinel-2 images were selected for each study area. All images were resampled to a unified spatial resolution of 10 m and projected into the same coordinate reference system to ensure spatial consistency among multi-temporal observations.

For Ganquan Island, the selected image dates were 24 February 2019, 1 March 2019, 26 March 2019, 4 July 2019, and 22 September 2019. For Dong Island, the selected dates were 6 March 2019, 14 July 2019, 19 July 2019, 22 September 2019, and 21 December 2019. For Key Biscayne, the selected dates were 6 January 2019, 5 February 2019, 9 August 2019, 28 October 2019, and 7 December 2019. The experimental datasets are presented in Table 1.

Table 1. Summary of experimental datasets.

Study Area	Location	Image Acquisition Dates	ICESat-2 ATL03 Data ID	Number of Valid Photons
Ganquan Island	111°35′24″ E, 16°30′36″ N	20190224, 20190301, 20190326, 20190704, 20190922	ATL03_20201119073024_08570907_006_01	10,899
			ATL03_20210717075633_03621201_006_01
			ATL03_20220114231625_03621401_006_01
			ATL03_20230815074804_08572007_006_01
Dong Island	112°43′48″ E, 16°39′36″ N	20190306, 20190714, 20190719, 20190922, 20191221	ATL03_20190319123621_12380207_006_02	4810
			ATL03_20201214061449_12380907_006_01
			ATL03_20210613213431_12381107_006_01
Key Biscayne	80°09′00″ W, 25°29′24″ N	20190106, 20190205, 20190809, 20191028, 20191207	ATL03_20220326083753_00501501_006_01	52,265
			ATL03_20230307042154_11701807_006_02
			ATL03_20230606000119_11701907_006_03
			ATL03_20240321215455_00502301_006_01

ICESat-2 ATL03 photon-counting data were obtained from the NASA Earthdata platform (https://search.earthdata.nasa.gov/).

Table 1. Summary of experimental datasets.

Study Area	Location	Image Acquisition Dates	ICESat-2 ATL03 Data ID	Number of Valid Photons
Ganquan Island	111°35′24″ E, 16°30′36″ N	20190224, 20190301, 20190326, 20190704, 20190922	ATL03_20201119073024_08570907_006_01	10,899
			ATL03_20210717075633_03621201_006_01
			ATL03_20220114231625_03621401_006_01
			ATL03_20230815074804_08572007_006_01
Dong Island	112°43′48″ E, 16°39′36″ N	20190306, 20190714, 20190719, 20190922, 20191221	ATL03_20190319123621_12380207_006_02	4810
			ATL03_20201214061449_12380907_006_01
			ATL03_20210613213431_12381107_006_01
Key Biscayne	80°09′00″ W, 25°29′24″ N	20190106, 20190205, 20190809, 20191028, 20191207	ATL03_20220326083753_00501501_006_01	52,265
			ATL03_20230307042154_11701807_006_02
			ATL03_20230606000119_11701907_006_03
			ATL03_20240321215455_00502301_006_01

ICESat-2 ATL03 photon-counting data were obtained from the NASA Earthdata platform (https://search.earthdata.nasa.gov/).

2.2.2. ICESat-2 ATL03 Bathymetric Data

ICESat-2 ATL03 photon-counting data were employed to generate bathymetric control points for adaptive fusion optimization and accuracy evaluation. Equipped with the Advanced Topographic Laser Altimeter System (ATLAS), ICESat-2 can provide high-precision bathymetric photon observations in shallow coastal waters. Previous studies demonstrated that ATL03 bathymetric photons can effectively support shallow-water bathymetric inversion and coastal topographic reconstruction [22,23,24,25].

This study utilized ATL03 Level-2 photon-counting data products as bathymetric control data. ATL03 datasets provide photon-level elevation, temporal, and geolocation information and have been increasingly applied in coastal bathymetric mapping studies [22,23,24,25]. The photon distributions of ATL03 in the three regions are shown in Figure 2.

Several preprocessing procedures were applied to the ATL03 datasets, including sea surface photon detection, seafloor photon extraction, and refraction correction [22]. After preprocessing, high-quality bathymetric control points were obtained for adaptive segmentation construction and fusion-strategy optimization.

A total of 10,899, 4810, and 52,265 valid bathymetric photons were extracted for Ganquan Island, Dong Island, and Key Biscayne, respectively. The higher photon density in Key Biscayne was mainly attributed to the larger number of available ICESat-2 tracks covering the study region.

Figure 2. Spatial distribution of the extracted ICESat-2 bathymetric photons.

Figure 2. Spatial distribution of the extracted ICESat-2 bathymetric photons.

2.2.3. Reference Bathymetric Data

Reference bathymetric datasets were used to quantitatively evaluate the performance of different bathymetric inversion methods.

For Ganquan Island and Dong Island, in situ bathymetric measurements were obtained from field surveys conducted by the First Institute of Oceanography, Ministry of Natural Resources of China. Bathymetric measurements were acquired using shipborne single-beam echo sounding systems combined with manual corrections, providing centimeter-level measurement accuracy. The field survey points covered different bathymetric intervals and effectively represented the actual seabed topography of the study regions.

For Key Biscayne, a high-resolution coastal DEM released by the National Oceanic and Atmospheric Administration (NOAA) was used as the reference dataset. The DEM was generated using the Riegl VQ-880-G airborne LiDAR system with a spatial resolution of 1 m and high vertical accuracy.

All reference datasets were transformed into the same coordinate reference system as the Sentinel-2 imagery and resampled to 10 m spatial resolution to ensure spatial consistency among different datasets. The distribution of in situ data across the three study areas is shown in Figure 3.

The reference bathymetric datasets were used for quantitative accuracy assessment of different bathymetric inversion results and for evaluating the performance of the proposed fusion framework in the three study areas.

Figure 3. Distribution of reference bathymetric datasets in the study areas.

Figure 3. Distribution of reference bathymetric datasets in the study areas.

3. Methodology

3.1. Framework Overview

Multi-temporal satellite-derived bathymetry is significantly affected by temporal variations in atmospheric conditions, water optical properties, solar illumination geometry, wave disturbance, and bottom substrate characteristics. Consequently, bathymetric inversion results derived from different acquisition times often exhibit substantial inconsistencies. In shallow-water regions, strong bottom reflectance and local environmental disturbances can easily introduce abnormal local fluctuations and extreme bathymetric estimates. In deeper waters, optical signals are strongly attenuated by water absorption and scattering effects, resulting in decreasing spectral sensitivity and systematic bathymetric underestimation. Therefore, different bathymetric intervals usually exhibit fundamentally different uncertainty characteristics.

Traditional global fusion methods generally apply a single statistical strategy to the entire bathymetric range and therefore cannot effectively accommodate the substantial error differences between shallow-water and deep-water regions. Mean fusion is often sensitive to local outliers in shallow waters, whereas median fusion may fail to compensate for systematic underestimation in deeper regions. As a result, conventional global fusion strategies are often insufficient for achieving optimal bathymetric performance across the full depth range.

To address these limitations, this study proposes an ICESat-2-constrained adaptive segment-wise rank-statistic fusion framework for multi-temporal satellite-derived bathymetry. The proposed framework consists of five major stages: (1) Sentinel-2 image preprocessing and water-region extraction; (2) ICESat-2 bathymetric photon preprocessing and bathymetric control-point generation; (3) multi-temporal single-scene bathymetric inversion using a BP neural network; (4) adaptive bathymetric segmentation constrained by ICESat-2 control points; and (5) segment-wise rank-statistic fusion and final bathymetric DEM reconstruction.

The core idea of the proposed framework is that different bathymetric intervals exhibit different uncertainty distributions and therefore may favor different statistical fusion strategies. Instead of applying a single global fusion rule, the proposed framework independently determines the optimal rank-statistic fusion strategy for each bathymetric interval according to ICESat-2-based accuracy evaluation. Consequently, shallow-water outliers can be effectively suppressed while deep-water systematic underestimation can be simultaneously alleviated.

The overall workflow of the proposed method is illustrated in Figure 4.

3.2. Data Preprocessing

3.2.1. Sentinel-2 Image Preprocessing and Water Extraction

Sentinel-2 Level-1C imagery was acquired and preprocessed on the Google Earth Engine (GEE) platform. Images with cloud coverage lower than 5% were selected to reduce atmospheric contamination and cloud interference. Atmospheric correction, cloud masking, image mosaicking, and study-area cropping were subsequently conducted to generate analysis-ready Sentinel-2 datasets.

Four Sentinel-2 bands, including the blue band (B2), green band (B3), red band (B4), and near-infrared band (B8), were employed for bathymetric inversion. These bands provide important spectral information associated with water-column attenuation and benthic reflectance characteristics.

To reduce the influence of land pixels and coastal interference on bathymetric inversion, water regions were extracted using the Normalized Difference Water Index (NDWI) proposed by McFeeters [32]. The NDWI is calculated as:

$$NDWI={\displaystyle \frac{Green-NIR}{Green+NIR}},$$

(1)

where Green and NIR represent the reflectance values of the green and near-infrared bands, respectively.

Pixels with NDWI values greater than 0.01 were classified as water regions. The extracted water mask was subsequently applied to all Sentinel-2 bathymetric inversion procedures.

3.2.2. ICESat-2 ATL03 Bathymetric Photon Preprocessing

ICESat-2 ATL03 photon-counting data were employed to generate bathymetric control points for subsequent fusion optimization and accuracy evaluation. ATL03 provides geolocated photon observations acquired by the Advanced Topographic Laser Altimeter System (ATLAS), which can penetrate shallow coastal waters and provide high-precision bathymetric information.

Because ATL03 photon data contain substantial noise photons originating from atmospheric scattering, solar background radiation, and water-column interference, bathymetric photon preprocessing was conducted prior to bathymetric control-point generation.

First, sea-surface photons were identified according to photon elevation distributions. Subsequently, underwater bathymetric photons were extracted from the water-column photon signals.

To suppress noise interference, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm proposed by Ester et al. [33] was employed for photon denoising. DBSCAN can effectively distinguish dense bathymetric photon clusters from sparse noise photons without requiring prior assumptions regarding data distribution. Neighboring photons satisfying the density threshold conditions were grouped into valid bathymetric clusters, whereas isolated photons were treated as noise and removed.

Because laser photons undergo refraction when passing through the air–water interface, underwater photon elevations are affected by geometric displacement. Therefore, a refraction correction model based on Snell’s law was applied to correct underwater photon positions and improve bathymetric accuracy. Following the refraction-correction strategy proposed by Parrish et al. [21], the corrected bathymetric photons were transformed into mean sea level elevations and subsequently used as bathymetric control points for adaptive segmentation and fusion evaluation.

The ATL03 photon processing workflow is shown in Figure 5. After preprocessing, high-quality bathymetric photons were finally obtained for subsequent bathymetric inversion and fusion optimization.

Figure 5. Preprocessing of ICESat-2 ATL03 bathymetric data.

Figure 5. Preprocessing of ICESat-2 ATL03 bathymetric data.

3.3. Multi-Temporal Single-Scene Bathymetric Inversion

To generate multi-temporal bathymetric candidates, single-scene bathymetric inversion was independently conducted for each Sentinel-2 image using a backpropagation (BP) neural network.

The BP neural network was employed as a stable baseline model for generating single-scene bathymetric estimates rather than as the primary methodological innovation of this study [34,35]. Compared with empirical linear or band-ratio models, BP neural networks can better characterize nonlinear relationships between multispectral reflectance and bathymetric variations under complex shallow-water conditions. The BP neural network architecture is shown in Figure 6.

The BP neural network consisted of an input layer, a hidden layer, and an output layer. Sentinel-2 spectral reflectance values from bands B2, B3, B4, and B8 were used as input variables, while ICESat-2 bathymetric elevations were employed as reference bathymetric targets.

The network structure included four input neurons, fifty hidden neurons, and one output neuron. The ReLU activation function was adopted during model training. The learning rate was set to 0.005, and the network was trained for 1000 epochs. All bathymetric samples were randomly divided into training and validation subsets using a 7:3 ratio. The network architecture and parameter settings were determined empirically according to repeated preliminary experiments and previous bathymetric inversion studies, aiming to achieve a balance between inversion accuracy and computational efficiency.

Because optical attenuation effects become increasingly significant in deeper waters, single-scene bathymetric inversion results commonly exhibit systematic underestimation in deep-water regions. To alleviate this issue, a quadratic residual-compensation model was subsequently established between ICESat-2 bathymetric control points and the initial bathymetric inversion results. The residual-compensation model was then applied to correct systematic depth-dependent inversion bias and improve the consistency of multi-temporal bathymetric estimates.

After residual correction, five corrected single-scene bathymetric DEMs were generated for subsequent adaptive segmentation and fusion analysis.

Figure 6. Architecture of the BP neural network used for bathymetric inversion.

Figure 6. Architecture of the BP neural network used for bathymetric inversion.

3.4. ICESat-2-Constrained Adaptive Bathymetric Segmentation

Different bathymetric intervals usually exhibit substantially different inversion-error characteristics in satellite-derived bathymetry because of variations in optical attenuation, bottom reflectance, and environmental conditions. In shallow-water regions, strong bottom reflectance and wave-induced disturbances can easily introduce abnormal local fluctuations and extreme bathymetric estimates. In contrast, deeper waters are more strongly affected by optical attenuation, resulting in decreasing spectral sensitivity and systematic bathymetric underestimation. Consequently, the uncertainty distributions of bathymetric estimates are highly depth-dependent.

Traditional global fusion methods generally assume that all bathymetric intervals follow similar uncertainty characteristics and therefore apply a single statistical strategy to the entire bathymetric range. However, such assumptions are often invalid in complex shallow-water environments where different depth intervals exhibit substantially different error mechanisms. To address this limitation, an ICESat-2-constrained adaptive bathymetric segmentation strategy was introduced prior to multi-temporal fusion, as shown in Figure 7.

Assuming that the valid bathymetric range covered by ICESat-2 bathymetric control points is:

$$D\in [Dmin,Dmax],$$

(2)

for a given segmentation number m, the bathymetric range was equally divided into multiple depth intervals. The interval width can be expressed as:

$$\Delta D={\displaystyle \frac{D_{max}-D_{min}}{m}}.$$

(3)

Accordingly, the s-th bathymetric interval can be represented as:

$$S_s=[D_{min}+(s-1)\Delta D, D_{min}+s\Delta D].$$

(4)

Unlike conventional global fusion strategies, the proposed segmentation framework independently evaluates local fusion performance within each bathymetric interval. In this way, different bathymetric intervals can adopt different optimal statistical fusion strategies according to their local uncertainty characteristics.

In this study, multiple candidate segmentation numbers were tested:

$$m\in \{6,8,10,12,14\}.$$

(5)

For each segmentation scheme, subsequent rank-statistic fusion and accuracy evaluation were independently conducted using ICESat-2 bathymetric control points. The candidate segmentation numbers were selected according to the bathymetric range and the distribution characteristics of ICESat-2 bathymetric control points. When the segmentation number is too small, depth-dependent uncertainty characteristics cannot be adequately represented. Conversely, excessively large segmentation numbers may result in insufficient samples within individual bathymetric intervals and reduce statistical reliability. The optimal segmentation number was finally determined according to the minimum overall RMSE of the fused bathymetric results.

The proposed adaptive segmentation framework establishes a depth-dependent local optimization mechanism for multi-temporal bathymetric fusion. Instead of relying on a single global statistical assumption, the framework allows different bathymetric intervals to independently select their locally optimal fusion strategies according to ICESat-2-constrained error distributions. Consequently, local instability in shallow waters and systematic underestimation in deeper regions can be simultaneously mitigated.

Figure 7. Adaptive bathymetric segmentation strategy proposed in this study.

Figure 7. Adaptive bathymetric segmentation strategy proposed in this study.

3.5. Segment-Wise Rank-Statistic Fusion Strategy

After adaptive bathymetric segmentation, rank-statistic fusion was independently conducted within each bathymetric interval. The fusion process is shown in Figure 8.

Because different temporal bathymetric observations are affected by varying atmospheric conditions, water optical properties, wave disturbance, bottom reflectance characteristics, and imaging geometries, substantial inconsistencies commonly exist among multi-temporal inversion results. Moreover, the uncertainty distributions of bathymetric estimates usually vary significantly with water depth.

In shallow-water regions, strong bottom reflectance and wave-induced disturbances may introduce temporally unstable extreme bathymetric estimates. Under such conditions, lower-order rank statistics generally exhibit stronger robustness against local outliers. In deeper waters, however, optical attenuation often leads to systematic bathymetric underestimation. Consequently, higher-order rank statistics may partially compensate for depth-dependent negative bias. These characteristics indicate that different bathymetric intervals may favor different statistical fusion strategies.

Rank statistics have been widely used in robust statistical analysis because of their resistance to abnormal values and noise interference [36,37]. Compared with conventional global mean fusion, rank-statistic fusion can effectively suppress unstable extreme estimates while preserving important bathymetric structures and spatial continuity.

For a given pixel, the multi-temporal single-scene bathymetric estimates can be expressed as:

$$\{d_1,d_2,\cdots ,d_n\},$$

(6)

where n denotes the number of temporal observations.

After sorting all bathymetric estimates in ascending order, the ordered sequence can be expressed as:

$$d_{(1)}\le d_{(2)}\le \cdots \le d_{(n)}.$$

(7)

Based on the ordered bathymetric sequence, five candidate rank-statistic fusion strategies were constructed, including minimum, second minimum, median, second maximum, and maximum values.

For each bathymetric interval, the RMSE values of all candidate rank-statistic strategies were calculated using ICESat-2 bathymetric control points. The optimal fusion strategy for each bathymetric interval was determined according to the minimum RMSE criterion.

Unlike traditional global mean or median fusion methods, the proposed framework allows different bathymetric intervals to independently adopt different optimal statistical strategies according to their local uncertainty distributions. Consequently, shallow-water outliers can be effectively suppressed, while deep-water systematic underestimation can be simultaneously alleviated.

Figure 8. Segment-wise adaptive rank-statistic fusion strategy proposed in this study.

Figure 8. Segment-wise adaptive rank-statistic fusion strategy proposed in this study.

3.6. Final Bathymetric DEM Reconstruction

After determining the optimal rank-statistic fusion strategy for each bathymetric interval, the final bathymetric DEM was reconstructed for the entire study area.

For each pixel, the median value of the multi-temporal bathymetric estimates was first used to determine its corresponding bathymetric interval. Subsequently, the optimal rank-statistic fusion strategy associated with that interval was applied to generate the final fused bathymetric value.

Through this procedure, different regions of the bathymetric DEM could automatically adopt different locally optimal statistical fusion strategies according to their depth-dependent uncertainty characteristics. Compared with conventional global fusion approaches, the proposed framework provides stronger adaptability to spatially heterogeneous bathymetric error distributions.

The final fused bathymetric DEM was subsequently used for quantitative accuracy evaluation and comparative analysis against conventional fusion strategies, including mean fusion and median fusion.

3.7. Accuracy Assessment

To quantitatively evaluate bathymetric inversion performance, the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE) were employed as evaluation metrics. These statistical metrics are commonly used in remote sensing accuracy assessment and bathymetric validation studies [38,39].

The RMSE is calculated as:

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N{(Z_i-{\widehat{Z}}_i)}^2}.$$

(8)

The MAE is calculated as:

$$MAE={\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N\mid Z_i-{\widehat{Z}}_i\mid .$$

(9)

The coefficient of determination is calculated as:

$$R^2=1-{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^N{(Z_i-{\widehat{Z}}_i)}^2}{{{\displaystyle \sum }}_{i=1}^N{(Z_i-\bar{Z})}^2}}.$$

(10)

where $Z_i$ represents the reference bathymetric value, ${\widehat{Z}}_i$ denotes the estimated bathymetric value, $\overline{Z}$ is the mean reference bathymetric value, and N represents the total number of validation samples.

To further evaluate the depth-dependent performance of different fusion strategies, the bathymetric range was additionally divided into multiple depth intervals, and segment-wise RMSE values were calculated for each interval. Through this procedure, the local performance characteristics of different fusion methods under varying bathymetric conditions could be systematically analyzed.

4. Results and Discussion

4.1. Bathymetry Results for Ganquan Island

4.1.1. Qualitative Evaluation

Figure 9 presents the bathymetric inversion results for Ganquan Island, including the worst single-scene result, the best single-scene result, the final fusion result, and the reference DEM.

Ganquan Island exhibits relatively smoother bathymetric variation and clearer water conditions. Nevertheless, considerable differences still exist among different single-scene inversion results. The worst single-scene result contains obvious local abnormal noise and exhibits significant underestimation in deeper reef-slope regions.

The best single-scene inversion result preserves the general coral reef morphology more effectively and reduces part of the random noise. However, local discontinuities and fragmented bathymetric patterns remain visible in several areas.

The fusion result generated by the proposed framework demonstrates significantly improved spatial continuity and bathymetric smoothness. Coral reef edges and transition structures are clearly represented, while local abnormal noise is effectively suppressed. Compared with single-scene results, the fusion DEM exhibits stronger consistency with the reference bathymetry, particularly in deeper reef-slope regions.

Overall, the proposed fusion framework effectively improves bathymetric reliability and spatial stability in clear-water coral reef environments.

4.1.2. Quantitative Evaluation

Table 2. Quantitative evaluation results for Ganquan Island.

Method	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed-Method
R2	0.92	0.84	0.88	0.85	0.89	0.95
RMSE	1.32	1.92	2.01	2.10	1.66	1.12
MAE	0.95	1.02	1.43	1.55	1.23	0.81

summarizes the quantitative evaluation results for Ganquan Island.

The worst single-scene result achieved an RMSE of 1.92 m and an R² value of 0.84. The best single-scene result achieved an RMSE of 1.32 m and an R² value of 0.92.

After applying the proposed adaptive segmented rank-statistic fusion framework, the RMSE was further reduced to 1.12 m, while the R² value increased to 0.95. Compared with the best single-scene result, the proposed method reduced the RMSE by approximately 15.2%. Compared with the worst single-scene result, the RMSE reduction reached approximately 46.7%.

The quantitative results indicate that multi-temporal fusion effectively improves bathymetric accuracy and reduces the instability caused by environmental variability among individual temporal observations.

4.1.3. Accuracy Analysis in Different Bathymetric Intervals

Table 3. RMSE comparison under different bathymetric intervals for Ganquan Island.

Depth Segmentation (m)	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed Method
(15, 20]	3.06	2.63	3.68	4.61	2.61	2.44
(10, 15]	1.73	1.81	2.74	2.88	1.95	1.50
(5, 10]	1.11	1.12	1.60	1.97	1.9	0.94
[0, 5]	0.90	2.54	1.42	0.90	0.85	0.59

presents the RMSE variations under different bathymetric intervals for Ganquan Island.

The worst single-scene result exhibits substantial error growth with increasing bathymetric depth. Although the best single-scene result demonstrates relatively improved stability, noticeable underestimation still exists in deep-water regions.

Compared with single-scene inversion results, the fusion framework maintains significantly lower RMSE values across all bathymetric intervals. The improvements are particularly evident in deep-water reef-slope regions, where spectral sensitivity decreases substantially.

These findings further demonstrate the effectiveness of the proposed fusion framework in improving bathymetric robustness and reducing depth-dependent systematic errors.

4.2. Bathymetric Results for Dong Island

4.2.1. Qualitative Analysis

Figure 10 presents the bathymetric inversion results for Dong Island, including the worst single-scene result, the best single-scene result, the final fusion result, and the reference DEM. Significant differences can be observed among different single-scene inversion results, particularly in deep-water regions and steep reef-slope areas.

The worst single-scene result exhibits substantial noise and obvious bathymetric discontinuities. In deep-water regions, severe underestimation occurs, accompanied by fragmented abnormal patches distributed along reef slopes. Moreover, local bathymetric structures become blurred, making it difficult to accurately characterize seabed topography.

Compared with the worst result, the best single-scene inversion preserves the overall geomorphological structure more effectively and reduces part of the local noise. However, spatial inconsistencies and local abnormal fluctuations remain noticeable in several regions, especially near steep bathymetric gradients.

The fusion result generated by the proposed framework demonstrates significantly improved spatial continuity and bathymetric stability. Coral reef boundaries and slope-transition structures are more clearly preserved, while deep-water underestimation is substantially alleviated. In addition, abnormal patches observed in single-scene inversion results are effectively suppressed, resulting in a bathymetric distribution that is more consistent with the reference DEM.

Overall, the multi-temporal fusion framework effectively integrates complementary information from different temporal observations and substantially improves the robustness of bathymetric inversion results in complex coral reef environments.

4.2.2. Quantitative Evaluation

Table 4. Quantitative evaluation results for Dong Island.

Method	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed Method
R2	0.80	0.81	0.75	0.62	0.78	0.88
RMSE	1.55	1.62	1.82	2.19	1.71	1.28
MAE	1.18	1.26	1.40	1.71	1.28	1.00

summarizes the quantitative evaluation results for Dong Island.

The worst single-scene inversion result produced an RMSE of 2.19 m and an R² value of 0.62. The best single-scene result achieved an RMSE of 1.55 m and an R² value of 0.80.

After applying the proposed fusion framework, the RMSE was reduced to 1.28 m, while the R² value increased to 0.88. Compared with the best single-scene result, the RMSE decreased by approximately 17.4%.

Compared with the worst single-scene result, the RMSE reduction reached approximately 41.6%. Even when compared with the best single-scene result, the fusion result still achieved a notable accuracy improvement. These findings indicate that multi-temporal fusion can effectively reduce the instability caused by environmental variability and imaging-condition differences among individual satellite observations.

4.2.3. Accuracy Analysis in Different Bathymetric Intervals

To further investigate bathymetric performance under different depth conditions, RMSE variations across different bathymetric intervals were analyzed, as shown in

Table 5. RMSE comparison under different bathymetric intervals for Dong Island.

Depth Segmentation (m)	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed Method
(15, 20]	4.11	4.11	4.67	5.86	4.19	3.23
(10, 15]	1.81	2.12	2.43	2.79	1.97	1.40
(5, 10]	1.27	1.32	1.53	1.64	1.39	1.05
[0, 5]	1.50	1.35	1.32	2.11	1.75	1.09

.

The worst single-scene result exhibits rapid RMSE growth with increasing bathymetric depth, particularly beyond 10 m depth, where systematic underestimation becomes increasingly severe. Although the best single-scene result demonstrates improved stability, its error still increases substantially in deeper waters.

By contrast, the fusion result maintains relatively stable RMSE values across all bathymetric intervals. The improvement is particularly significant in deep-water regions, indicating that multi-temporal fusion can effectively compensate for bathymetric underestimation caused by weak spectral sensitivity in deeper waters.

These results demonstrate that the proposed fusion framework substantially improves bathymetric consistency and depth adaptability under complex reef environments.

4.3. Bathymetry Results for Key Biscayne

4.3.1. Qualitative Evaluation

Figure 11 presents the bathymetric inversion results for Key Biscayne.

Compared with the coral reef environments of the South China Sea, Key Biscayne is characterized by relatively shallow bathymetry and more complex benthic conditions. Consequently, single-scene inversion results are more susceptible to benthic heterogeneity and water optical variability.

The worst single-scene result exhibits obvious abnormal patches and local bathymetric noise, particularly in seagrass-covered regions and benthic transition zones. The best single-scene result improves bathymetric continuity to some extent but still contains local inconsistencies and fragmented structures.

The fusion result generated by the proposed framework demonstrates substantially improved spatial smoothness and local-detail preservation. Abnormal noise observed in single-scene inversion results is effectively suppressed, while shallow-water bathymetric structures remain clearly identifiable.

Compared with the reference DEM, the fusion result exhibits stronger spatial consistency and better representation of benthic transition regions, demonstrating the robustness of the proposed framework under complex shallow-water environments.

4.3.2. Quantitative Evaluation

Table 6. Quantitative evaluation results for Key Biscayne.

Method	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed Method
R2	0.79	0.69	0.89	0.52	0.93	0.94
RMSE	0.72	0.69	0.40	1.16	0.32	0.29
MAE	0.47	0.35	0.29	0.67	0.22	0.21

summarizes the quantitative evaluation results for Key Biscayne.

The worst single-scene result achieved an RMSE of 1.16 m and an R² value of 0.52. The best single-scene result achieved an RMSE of 0.32 m and an R² value of 0.93.

The proposed fusion framework further reduced the RMSE to 0.29 m and increased the R² value to 0.94.

Compared with the best single-scene result, the RMSE decreased by approximately 9.4%. Compared with the worst single-scene result, the RMSE reduction reached approximately 75.0%, indicating substantial improvements in bathymetric stability and inversion consistency.

4.3.3. Accuracy Analysis in Different Bathymetric Intervals

Table 7. RMSE comparison under different bathymetric intervals for Key Biscayne.

Depth Segmentation (m)	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5	Proposed Method
(4, 6]	0.51	0.45	0.49	0.77	0.40	0.37
(2, 4]	0.44	0.3	0.31	0.6	0.26	0.23
[0, 2]	1.15	1.18	0.47	1.93	0.35	0.30

presents the RMSE variations across different bathymetric intervals for Key Biscayne.

Although the overall bathymetric range in Key Biscayne is relatively shallow, the worst single-scene result still exhibits noticeable error increases in benthically complex regions. The best single-scene result demonstrates improved stability but remains sensitive to local environmental variability.

The fusion result consistently maintains the lowest RMSE values across all bathymetric intervals, indicating that multi-temporal fusion can effectively suppress local abnormal noise and improve bathymetric consistency under complex shallow-water conditions.

4.4. Comparative Analysis of Different Fusion Methods

4.4.1. Qualitative Evaluation of Bathymetric Inversion Results

To further evaluate the effectiveness of different fusion strategies, qualitative comparisons among mean fusion, median fusion, and the proposed adaptive segmented rank-statistic fusion method were conducted for the three study areas. Figure 12 presents representative comparison results, including mean fusion, median fusion, the proposed method, and the reference DEM.

Overall, both mean fusion and median fusion can effectively reduce part of the random noise observed in single-scene bathymetric inversion results. However, substantial differences remain among the three fusion strategies in terms of spatial continuity, detail preservation, and deep-water representation capability.

Mean fusion produces relatively smooth bathymetric distributions and suppresses local fluctuations to some extent. Nevertheless, excessive smoothing effects are evident, particularly near coral reef boundaries and steep bathymetric gradients. Local geomorphological structures become blurred, and fine-scale bathymetric details are partially lost. In addition, deep-water regions still exhibit noticeable systematic underestimation.

Median fusion demonstrates stronger robustness against local outliers compared with mean fusion. Several abnormal high-value patches are effectively suppressed, resulting in improved local stability. However, median fusion still tends to underestimate deeper bathymetric regions because median statistics cannot effectively compensate for systematic low-bias errors commonly observed in deep-water inversion.

In contrast, the proposed adaptive segmented rank-statistic fusion method achieves substantially improved spatial continuity and bathymetric consistency. Coral reef boundaries, slope-transition structures, and benthic transition zones are more clearly preserved, while local abnormal noise and fragmented structures are effectively suppressed. Moreover, deep-water underestimation is significantly alleviated, resulting in bathymetric distributions that are considerably more consistent with the reference DEM.

These qualitative results indicate that the proposed framework can adaptively optimize fusion strategies according to local bathymetric error characteristics and achieve better balance between noise suppression and detail preservation.

4.4.2. Quantitative Evaluation of Bathymetric Inversion Results

To quantitatively compare the performance of different fusion strategies, statistical evaluation metrics including RMSE, MAE, and R² were calculated for all study areas.

Table 8. Quantitative comparison results of different fusion methods.

Study Area	Method	RMSE (m)	MAE (m)	R2
Ganquan Island	Mean Fusion	1.26	0.89	0.94
	Median Fusion	1.25	0.90	0.94
	Proposed Method	1.12	0.81	0.95
Dong Island	Mean Fusion	1.40	1.07	0.87
	Median Fusion	1.42	1.09	0.86
	Proposed Method	1.28	1.00	0.88
Key Biscayne	Mean Fusion	0.40	0.26	0.90
	Median Fusion	0.31	0.22	0.93
	Proposed Method	0.29	0.21	0.94

summarizes the quantitative evaluation results of mean fusion, median fusion, and the proposed adaptive segmented rank-statistic fusion method.

For Ganquan Island, mean fusion produced an RMSE of 1.26 m and an R² value of 0.94, whereas median fusion achieved an RMSE of 1.25 m and an R² value of 0.94. The proposed method achieved the best performance, with an RMSE of 1.12 m and an R² value of 0.95.

For Dong Island, mean fusion achieved an RMSE of 1.40 m and an R² value of 0.87, whereas median fusion produced an RMSE of 1.42 m and an R² value of 0.86. The proposed method further improved the bathymetric accuracy, achieving an RMSE of 1.28 m and an R² value of 0.88.

For Key Biscayne, mean fusion and median fusion achieved RMSE values of 0.40 m and 0.31 m, respectively. The proposed method further reduced the RMSE to 0.29 m and improved the R² value to 0.94.

Overall, the proposed adaptive segmented rank-statistic fusion framework consistently achieved the highest bathymetric accuracy across all study areas. Compared with conventional mean fusion and median fusion methods, the proposed framework substantially reduced bathymetric errors while improving correlation with reference bathymetric datasets.

To further evaluate the consistency between estimated and reference bathymetry, scatter plots between inversion results and reference bathymetric values were generated for the three study areas, as shown in Figure 13.

The scatter plots indicate that mean fusion and median fusion still exhibit noticeable deviations from the ideal 1:1 line, particularly in deeper bathymetric regions where systematic underestimation becomes increasingly evident. In contrast, the proposed adaptive segmented rank-statistic fusion framework produces scatter distributions that are considerably closer to the ideal fitting relationship, indicating improved bathymetric consistency and reduced depth-dependent systematic bias.

Compared with conventional global fusion strategies, the proposed method can adaptively optimize different bathymetric intervals according to their local error characteristics. As a result, shallow-water outliers are effectively suppressed, while deep-water underestimation is simultaneously alleviated, leading to improved spatial stability and overall bathymetric robustness across different shallow-water environments.

4.4.3. Residual Evaluation Based on Reference Bathymetric Data

To further investigate the spatial error characteristics of different fusion methods, residual spatial distributions based on in situ bathymetric data were analyzed. Residuals were calculated as the difference between reference bathymetric values and estimated bathymetric values. Figure 14 presents the residual spatial distributions of mean fusion, median fusion, and the proposed adaptive segmented rank-statistic fusion method for the three study areas.

For Ganquan Island, mean fusion demonstrates noticeable spatial smoothing effects and local abnormal residual clusters near coral reef boundaries. Median fusion improves local stability to some extent but still exhibits deep-water residual accumulation. The proposed method significantly suppresses these residual clusters and maintains stronger spatial consistency with the reference bathymetric dataset.

For Dong Island, mean fusion exhibits extensive negative residual distributions in deep-water regions, indicating significant systematic underestimation. Median fusion suppresses some local abnormal residuals but still contains striping residual patterns in steep reef-slope areas. In contrast, the proposed method produces substantially more uniform residual distributions and effectively reduces deep-water systematic errors.

For Key Biscayne, complex benthic conditions introduce considerable local residual noise into conventional fusion results. Mean fusion and median fusion both exhibit residual aggregation in benthic transition zones and seagrass-covered regions. By comparison, the proposed adaptive segmented rank-statistic fusion framework effectively suppresses abnormal residual distributions and generates considerably smoother residual patterns.

Overall, the residual analyses further demonstrate that conventional global fusion strategies cannot simultaneously achieve shallow-water outlier suppression and deep-water bias compensation. The proposed adaptive segmented rank-statistic fusion framework effectively improves bathymetric stability and spatial consistency by adaptively selecting optimal rank-statistic strategies for different bathymetric intervals.

4.5. Discussion

4.5.1. Advantages of the Proposed Method

Compared with conventional mean fusion and median fusion methods, the proposed adaptive segmented rank-statistic fusion framework exhibits several important advantages.

First, the proposed method can effectively adapt to different error characteristics across various bathymetric intervals. Traditional global fusion methods generally assume consistent error distributions throughout the entire bathymetric range, whereas shallow-water and deep-water regions often exhibit substantially different error mechanisms. By introducing adaptive bathymetric segmentation, the proposed framework enables segment-wise optimization according to local bathymetric characteristics, thereby substantially improving overall stability and accuracy.

Second, rank-statistic fusion demonstrates stronger robustness against local abnormal values compared with conventional mean fusion. Since satellite-derived bathymetry is highly sensitive to clouds, water turbidity, wave disturbances, and benthic heterogeneity, local abnormal bathymetric estimates frequently occur in single-scene inversion results. Rank-statistic fusion can effectively suppress the influence of such abnormal observations.

In addition, the proposed method does not require empirically determined weighting parameters or complicated optimization procedures. Therefore, it possesses good physical interpretability and engineering applicability. Experimental results from the three study areas consistently demonstrate stable performance, indicating strong cross-regional adaptability of the proposed framework.

4.5.2. Limitations and Future Work

Although the proposed method achieved promising results in all study areas, several limitations still exist.

First, equal-interval bathymetric segmentation was adopted in this study due to its simplicity and physical interpretability. However, in regions with highly complex bathymetric variations, equal-interval segmentation may not fully represent local error distributions. Future studies may further investigate more flexible adaptive segmentation strategies based on clustering methods or local error distributions.

Second, only Sentinel-2 multispectral imagery was used in this study. Different satellite sensors exhibit substantial differences in spatial resolution and spectral characteristics. Future work could integrate high-resolution satellite datasets such as WorldView, PlanetScope, and Chinese Gaofen imagery to further improve bathymetric inversion performance.

Third, ICESat-2 bathymetric photons may still be affected by wave disturbances and water turbidity in certain coastal regions, potentially introducing uncertainties into bathymetric control points. Future studies may combine airborne LiDAR measurements and additional field observations to further improve bathymetric control-point accuracy and spatial coverage.

Finally, this study mainly focused on static multi-temporal bathymetric fusion and did not explicitly consider tidal variations or seasonal environmental changes. Future work could integrate tidal correction and time-series analysis methods to achieve more stable long-term coastal bathymetric monitoring.

5. Conclusions

This study proposed an adaptive segmented rank-statistic fusion framework for multi-temporal satellite-derived bathymetry constrained by ICESat-2 bathymetric control points. The proposed method adaptively segments the bathymetric range according to ICESat-2 observations and automatically selects the optimal rank-statistic strategy within each bathymetric interval, thereby enabling segment-wise adaptive bathymetric optimization.

Experiments were conducted in Ganquan Island, Dong Island, and Key Biscayne, and the proposed framework was comprehensively compared with single-scene inversion results, conventional mean fusion, and median fusion methods. The main conclusions are summarized as follows.

(1)

Multi-temporal fusion can effectively improve the stability of satellite-derived bathymetry and reduce random inversion noise compared with single-scene bathymetric inversion.

(2)

Conventional mean fusion and median fusion methods can suppress part of the random noise; however, because they adopt global statistical strategies, systematic underestimation remains significant in deep-water regions.

(3)

The proposed adaptive segmented rank-statistic fusion method can automatically identify optimal fusion strategies according to local bathymetric error characteristics and consistently achieved the highest accuracy in all three study areas. The overall RMSE was reduced by up to 27.5%, while the R² value reached 0.95.

(4)

In shallow-water regions, median and lower-order rank statistics were more frequently selected, whereas deeper bathymetric intervals generally favored higher-order rank statistics. These findings indicate that different bathymetric intervals exhibit distinct uncertainty characteristics and therefore require different fusion strategies for optimal bathymetric reconstruction.

Overall, the proposed framework does not require empirical weighting parameters and exhibits strong robustness, physical interpretability, and cross-regional applicability. Therefore, it provides an effective and practical solution for large-scale high-accuracy shallow-water bathymetric mapping using multi-temporal satellite imagery.

Although the proposed framework achieved consistent improvements in all study areas, its performance still depends on the availability of ICESat-2 bathymetric control points and the quality of optical imagery. Future studies will further investigate the applicability of the proposed framework in additional coastal environments and explore more efficient optimization strategies to improve computational performance.