A multi-temporal satellite image shallow water depth inversion method and system based on laser depth measurement guidance

Abstract

This invention provides a method and system for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry. The method includes: extracting water body pixels from Sentinel-2 imagery; extracting water depth photons from satellite-borne laser bathymetry data and performing refraction correction to obtain water depth values ​​along the orbital direction; utilizing the strong correlation between the water depth values ​​along the orbital direction and the reflectivity of the blue and green bands of Sentinel-2 imagery to calculate multi-temporal image fusion weights and generate a weighted fused image; based on water column layer-by-layer inversion and / or seabed classification inversion strategies, dividing the weighted fused image into multiple homogeneous regions according to the water penetration capabilities of blue and green light; using LLM and / or LRM to invert water depth layer by layer in the multiple homogeneous regions; and fusing the results of different regions through a buffer zone to obtain the water depth inversion result for the entire shallow sea area. This invention can achieve high-precision and high-stability shallow water depth inversion.

Description

Technical Field

[0001] This invention relates to the field of remote sensing mapping and marine information acquisition technology, and in particular to a method and system for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry. Background Technology

[0002] Shallow water depth information is crucial foundational data for coastal topographic mapping, marine ecological environment monitoring, nautical chart updates, and marine resource development and management. Traditional shallow water depth sounding primarily relies on shipborne or airborne sonar and laser depth sounding methods. While these methods offer high accuracy, they suffer from high operating costs, limited coverage, and long implementation cycles. Furthermore, they are difficult to conduct large-scale, long-term continuous observations in remote islands, uninhabited waters, and areas with complex environmental conditions.

[0003] With the development of satellite remote sensing technology, shallow water depth inversion methods based on optical satellite imagery have gradually become an important technical means to obtain nearshore water depth information. These methods typically utilize the attenuation characteristics of different bands in multispectral imagery within the water body to establish a model relating water reflectance to water depth, thereby achieving the inversion of shallow water depth. However, existing water depth inversion methods based on single-temporal satellite imagery are easily affected by instantaneous environmental factors such as cloud cover, wave disturbance, ship wakes, and solar flares, leading to significant errors in the inversion results and even the loss of water depth information, thus limiting their reliability in practical applications.

[0004] To mitigate the impact of transient noise in single-temporal images on the accuracy of water depth inversion, existing research has proposed multi-temporal satellite image water depth inversion methods. These methods improve the stability and completeness of water depth inversion by fusing optical image data from different temporal phases. Current multi-temporal methods typically employ temporal median filtering, mean combination, outlier removal, or weighting based on image spectral features to fuse multi-temporal images before water depth inversion, or to invert each temporal image separately and then overlay the results. Furthermore, with the development of spaceborne laser altimetry, some studies have begun to explore combining spaceborne laser bathymetry data with optical satellite imagery to reduce reliance on in-situ measured water depth data and improve the accuracy of water depth inversion. Overall, existing multi-temporal satellite image water depth inversion methods still have the following shortcomings:

[0005] (i) Multi-temporal image fusion lacks physical constraints and is susceptible to interference from anomalous images.

[0006] Existing multi-temporal shallow water depth retrieval methods typically rely on median filtering, mean combination, outlier removal, or weighting strategies based on the spectral characteristics of the images themselves to fuse optical images from different temporal phases during the image fusion stage. These methods do not adequately incorporate physical measurement data that directly reflects true water depth information as constraints. When anomalies such as cloud cover, wave disturbances, or ship wakes exist in the images involved in the fusion, these anomalous images may still occupy a high weight during the fusion process.

[0007] The aforementioned drawbacks lead to distortion of spectral information in local areas of the fused image, which in turn affects the stability and accuracy of the subsequent water depth inversion model. In particular, in nearshore areas with complex environmental conditions or large differences in image quality, the inversion results are prone to systematic biases.

[0008] (ii) Ignoring the differences in optical penetration of water columns makes it difficult to ensure the accuracy of inversion in different water depth regions.

[0009] Existing technologies mostly employ a uniform water depth inversion model to invert the entire study area, typically assuming that the optical properties of water bodies remain consistent spatially, without distinguishing the differences in penetration ability between shallow and deep water areas at different spectral bands. Since shallow water areas are more sensitive to short-wavelength spectra such as the green band, while effective information in deep water areas mainly comes from the blue band with stronger penetration, the uniform model struggles to maintain high inversion accuracy simultaneously across different water depth ranges.

[0010] This drawback makes existing methods susceptible to surface noise interference in shallow water areas, and prone to accuracy degradation due to spectral signal attenuation in deep water areas, thus limiting the spatial consistency of shallow water depth inversion results.

[0011] (iii) The impact of seabed sediment differences on water depth inversion was not fully considered.

[0012] Existing shallow water depth inversion methods generally assume that seabed sediment types remain constant in time and space, or do not explicitly incorporate sediment classification information during the inversion process. Differences in the optical reflectivity of different sediment types can alter the attenuation behavior of water reflection signals. If these differences are not distinguished, sediment variations can easily be misinterpreted as changes in water depth, thus introducing additional errors.

[0013] This problem is particularly prominent in nearshore areas where coral reefs, sandy beaches, and rocky bottoms are interspersed, which can easily lead to discontinuities or inconsistencies in the accuracy of water depth inversion results between different bottom areas. Summary of the Invention

[0014] To address at least some of the problems of existing multi-temporal shallow water depth inversion methods, such as the inversion results being easily affected by abnormal images, difficulty in balancing the inversion accuracy of different water depth regions, and the tendency for inversion results to be discontinuous or inconsistent in accuracy between different seabed regions, this invention provides a shallow water depth inversion method and system based on laser bathymetry-guided multi-temporal satellite imagery, which can achieve high-precision and high-stability shallow water depth inversion.

[0015] In a first aspect, the present invention provides a method for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry, comprising:

[0016] Water pixels are extracted from Sentinel-2 images, water depth photons are extracted from spaceborne laser depth sounding data and refraction correction is performed to obtain water depth values ​​along the orbital direction.

[0017] By utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of blue and green bands in Sentinel-2 images, the fusion weights of multi-temporal images are calculated to generate weighted fused images.

[0018] Based on water column layer inversion and / or bottom sediment classification inversion strategies, the weighted fused image is divided into multiple homogeneous regions according to the water penetration ability of blue and green light, and the water depth of the multiple homogeneous regions is inverted layer by layer using LLM and / or LRM.

[0019] By fusing the results from different regions through a buffer zone, the water depth inversion results for the entire shallow sea area are obtained.

[0020] In this embodiment of the invention, spaceborne laser bathymetry data is introduced as a physical constraint for multi-temporal image fusion. Unlike existing techniques that rely solely on statistical or spectral features for multi-temporal image fusion, this invention, for the first time, introduces spaceborne laser bathymetry data into the multi-temporal image fusion process. It utilizes the physical correlation between laser bathymetry values ​​and the water penetration mechanism of optical images to perform guided weighting of images from different temporal phases. This improvement provides a clear physical constraint basis for the multi-temporal image fusion process, enabling effective identification and suppression of anomalous images severely affected by instantaneous interference from clouds, waves, and ship wakes during the fusion stage, significantly improving the quality of the fused images and the stability of water depth retrieval.

[0021] In this embodiment of the invention, water bodies are stratified and water depth is retrieved by region based on spectral penetration characteristics. Addressing the problem that existing technologies generally use a unified model to retrieve different water depth regions, making it difficult to balance accuracy in shallow and deep water areas, this invention performs water column stratification based on the differences in penetration ability of different spectral bands in the fused image within the water body. By establishing separate water depth retrieval models within different water column layers, this invention can adaptively model the optical characteristics of different water depth ranges, thereby avoiding the problem of the unified model failing simultaneously in shallow and deep water areas and improving the overall water depth retrieval accuracy.

[0022] In this embodiment of the invention, a depth-independent seabed classification is introduced to reduce interference from seabed differences. Existing technologies typically ignore differences in seabed types during depth inversion. This invention classifies seabed areas in fused images by constructing depth-independent spectral feature indices, and performs depth inversion separately within different seabed regions. This improvement effectively reduces systematic errors caused by differences in seabed reflectivity, ensuring high consistency and continuity of depth inversion results in nearshore areas with complex seabed variations.

[0023] This invention proposes a regional inversion framework that integrates water column stratification and sediment classification. Instead of simply improving water column stratification or sediment classification individually, this invention synergistically incorporates both into the water depth inversion process. Inversion models are constructed separately for different water column layers and different sediment regions, and the results are then fused. Through this water column-sediment synergistic regional inversion framework, this invention can simultaneously address the dual impacts of water depth and sediment changes in complex nearshore environments, further improving the accuracy and robustness of water depth inversion results.

[0024] In this embodiment of the invention, stable and high-precision inversion is achieved without the need for in-situ measured water depth data. This invention utilizes spaceborne laser bathymetry data to replace traditional in-situ measured water depth data as crucial constraint information for the inversion model, thus eliminating reliance on shipborne or airborne measured data for the water depth inversion process. This improvement significantly expands the applicability of shallow water depth inversion technology to remote islands and reefs, uninhabited waters, and areas where on-site measurements are difficult to conduct.

[0025] Furthermore, the extraction of water pixels from Sentinel-2 images includes:

[0026] The modified normalized difference water index (MNDWI) of Sentinel-2 imagery is calculated according to the following formula, and pixels with an MNDWI value greater than 0.2 are extracted as water pixels.

[0027]

[0028] in, and These represent the green band and mid-infrared band reflectance of the Sentinel-2 image, respectively. The value range is [-1, 1].

[0029] Furthermore, the extraction of water depth photons from spaceborne laser bathymetry data and the subsequent refraction correction to obtain the water depth value along the orbital direction includes:

[0030] Based on the spatial density of photons, photons are distributed to different levels of the quadtree;

[0031] Perform pre-pruning on the quadtree constructed in the previous step;

[0032] The frequency histogram of the quadtree depth of the remaining nodes after pre-pruning is analyzed. Based on the distribution characteristics of the frequency histogram, the isolation threshold in different depth ranges is automatically determined. Based on the isolation threshold, the water depth photons are extracted from the remaining photons.

[0033] By matching the ID of the deep-water photons and the distance along the photon propagation trajectory, surface photons and seabed photons belonging to the same laser emission pulse are matched to reconstruct the propagation path of the laser emission pulse in the water.

[0034] Based on the reconstructed propagation path of the laser emission pulse in the water, the elevation distribution of photons on the sea surface is fitted to calculate the refraction angle of the laser emission pulse on the sea surface. The water depth value of the seabed photons is corrected according to the refraction angle to obtain the water depth value along the orbital direction.

[0035] Furthermore, the method of utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of the blue and green bands of Sentinel-2 images to calculate multi-temporal image fusion weights and generate weighted fused images includes:

[0036] The Gaussian weights of the images at each time phase are calculated using the following formula:

[0037]

[0038] in, It is the first Index of landscape images Indicates the first Gaussian weights for scene images This refers to the water depth along the track direction. yes variance These are the blue and green band reflectances of the Sentinel-2 image, respectively. It is an exponential function with the natural constant e as its base. This indicates the preset scaling factor;

[0039] The Gaussian weights of all images are normalized according to the following formula:

[0040]

[0041] in, Indicates the number of images. Indicates the first Normalized weights of scene images;

[0042] The fused image is obtained according to the following formula:

[0043]

[0044] in, This represents the i-th fused image. Indicates for fusion The original first Scene images, express The weights;

[0045] Furthermore, the water column stratification inversion strategy includes:

[0046] For each time phase of the image, the green band reflectance was statistically analyzed. Each gray level Number of pixels And calculate the normalized probability distribution:

[0047]

[0048] in, The total number of pixels in the image;

[0049] Assuming a segmentation threshold It can effectively divide images into shallow water and deep water, traversing all possible thresholds. Choose the threshold that maximizes the inter-class variance. The image is divided into two parts: shallow water and deep water.

[0050]

[0051] The segmentation threshold is calculated according to the following formula. Inter-class variance :

[0052]

[0053] in, and The pixel probability and average grayscale of shallow water are calculated using the following formulas:

[0054]

[0055]

[0056] and The pixel probability and average grayscale of deep water are calculated using the following formulas:

[0057]

[0058]

[0059] in, This represents the maximum gray level of the green band.

[0060] Furthermore, the aforementioned substrate classification and inversion strategy includes:

[0061] For each time phase image, a number of pixels are extracted at equal intervals from the image to ensure that the extracted pixels cover sandy and coral-bearing beaches at different water depths; the ratio of slow attenuation coefficients in the blue, green, and red bands is calculated using the following formula:

[0062]

[0063]

[0064]

[0065] in, and For band and reflectivity, and For band and The variance, and For band and covariance; and Indicates the intermediate coefficients used for sediment classification;

[0066] Construct depth-invariant index (DII) models for the green and blue bands, the blue and red bands, and the green and red bands respectively, according to the following formulas:

[0067]

[0068] in, Indicates the intermediate coefficients used for sediment classification;

[0069] Using the DII model to convert images into... , and The three-band pseudo-color images were combined and clustered using the iterative self-organizing data analysis algorithm ISODATA to divide the seabed into two types of substrate regions: sandy and coral-based.

[0070] Furthermore, the method of using LLM and LRM to invert water depth layer by layer in the multiple homogeneous regions includes:

[0071] The LRM model is represented as:

[0072]

[0073] in, For the region The water depth, For the region The slope of the LRM, and area In the middle, the intercept of LRM when the water depth is 0, This indicates the preset scaling factor;

[0074] The LLM model is represented as:

[0075]

[0076] in, For the region The water depth, and For the region linear regression coefficients and This represents the reflectance of the fused image at band j, and the reflectance of the fused image in the deep water area at band j.

[0077] Secondly, the present invention provides a shallow water depth inversion system based on multi-temporal satellite imagery guided by laser bathymetry, comprising:

[0078] The data preprocessing module is used to extract water body pixels from Sentinel-2 images, extract water depth photons from spaceborne laser bathymetry data and perform refraction correction to obtain water depth values ​​along the orbital direction.

[0079] The multi-temporal image fusion module is used to calculate the multi-temporal image fusion weights by utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of the blue and green bands of Sentinel-2 images, and to generate a weighted fused image.

[0080] The partition inversion module is used to divide the weighted fused image into multiple homogeneous regions according to the water penetration ability of blue and green light based on water column layer inversion and / or bottom sediment classification inversion strategies, and use LLM and / or LRM to invert the water depth of the multiple homogeneous regions layer by layer.

[0081] The inversion fusion module is used to fuse results from different regions through a buffer to obtain the water depth inversion results for the entire shallow sea area.

[0082] Thirdly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method as described in the first aspect.

[0083] Fourthly, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method described in the first aspect.

[0084] The beneficial effects of this invention are as follows:

[0085] (1) Improve the reliability and physical interpretability of multi-temporal image fusion. This invention introduces spaceborne laser bathymetry data as a physical constraint in the multi-temporal image fusion process, so that image fusion no longer relies solely on statistical or empirical rules, thereby effectively reducing the impact of abnormal images on the fusion results. Compared with existing multi-temporal fusion methods, the fused images generated by this invention have a higher signal-to-noise ratio and better spatial continuity, providing a more reliable data foundation for subsequent water depth inversion.

[0086] (2) Enhancing the stability and anti-interference capability of water depth inversion in complex nearshore environments. To address common nearshore noise interference such as cloud cover, wave disturbance, and ship wakes, this invention effectively weakens the impact of transient interference in the fused image through a weighted fusion mechanism guided by laser bathymetry. Compared with existing technologies, this invention can maintain relatively stable water depth inversion results under complex environmental conditions, reducing local anomalies and missing results.

[0087] (3) Balancing inversion accuracy across different water depth ranges to improve overall water depth inversion consistency. This invention utilizes water column stratification based on spectral transmittance characteristics to establish separate water depth inversion models for different water depth ranges, avoiding the problem of inconsistent accuracy in shallow and deep water areas with a single model. Compared to existing methods using a single model, this invention achieves more balanced inversion accuracy in both shallow and relatively deep water areas, improving the spatial consistency of water depth inversion results.

[0088] (4) Reducing the impact of seabed sediment differences on water depth inversion results. This invention introduces a seabed sediment classification mechanism during the water depth inversion process, performing water depth inversion separately in different seabed sediment regions, effectively reducing systematic errors caused by differences in seabed sediment reflection characteristics. Compared with existing technologies that ignore the influence of seabed sediment, this invention can obtain more continuous and stable water depth inversion results in nearshore areas with complex seabed sediment variations.

[0089] (5) Reduce reliance on in-situ measured water depth data and expand application scenarios. This invention uses spaceborne laser bathymetry data to replace traditional in-situ measured water depth data as inversion constraints, so that the water depth inversion process no longer depends on shipborne or airborne measurements. Compared with existing technologies that require a large amount of in-situ data, this invention is more suitable for remote islands and reefs, uninhabited sea areas and areas where it is difficult to conduct on-site measurements, significantly expanding the applicable scope of shallow water depth inversion technology.

[0090] (6) Enhance the practical value and engineering application potential of shallow water depth inversion results. By introducing the synergistic effect of physical constraints, multi-temporal fusion, water column stratification and seabed classification, this invention can improve the accuracy of water depth inversion while ensuring the integrity of the results. It has strong engineering feasibility and promotion and application value, and is suitable for application in coastal zone mapping, marine ecological monitoring and related geographic information system updates. Attached Figure Description

[0091] Figure 1 A flowchart illustrating a method for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry, provided for an embodiment of the present invention;

[0092] Figure 2 A schematic diagram of the three research areas provided in an embodiment of the present invention;

[0093] Figure 3 The signal photon extraction and refraction correction results provided for embodiments of the present invention are: (a) Culebra, (b) Oahu, (c) Niihau; where gray dots represent noise photons, blue dots represent signal photons, and magenta dots represent seabed photons after refraction correction.

[0094] Figure 4 The fused images generated using the method of the present invention (also known as the MTSB method) provided for embodiments of the present invention are: (a) Culebra, (b) Oahu, and (c) Niihau.

[0095] Figure 5 The water column layering results of the fused images provided in this embodiment of the invention are: (a) Culebra, (b) Oahu, (c) Niihau; where red pixels represent land, green pixels represent shallow water, and blue pixels represent deep water.

[0096] Figure 6 Substrate classification results of fused images provided for embodiments of the present invention: (a) Culebra, (b) Oahu, (c) Niihau; wherein, dark blue pixels represent land, yellow pixels represent sandy substrate, and gray pixels represent rocky substrate;

[0097] Figure 7 Scatter plots and error distribution histograms of Culebra provided for embodiments of the present invention: (a) water column stratification and LRM model, (b) water column stratification and LLM model, (c) substrate classification and LRM model, (d) substrate classification and LLM model, (e) water column stratification, substrate classification and LRM model, and (f) water column stratification, substrate classification and LLM model;

[0098] Figure 8 Scatter plots and error distribution histograms of Oahu provided for embodiments of the present invention: (a) water column stratification and LRM model, (b) water column stratification and LLM model, (c) substrate classification and LRM model, (d) substrate classification and LLM model, (e) water column stratification, substrate classification and LRM model, and (f) water column stratification, substrate classification and LLM model;

[0099] Figure 9 Scatter plots and error distribution histograms of Niihau provided for embodiments of the present invention: (a) water column stratification and LRM model, (b) water column stratification and LLM model, (c) substrate classification and LRM model, (d) substrate classification and LLM model, (e) water column stratification, substrate classification and LRM model, and (f) water column stratification, substrate classification and LLM model.

[0100] Figure 10 The water depth inversion results obtained from the fused images generated by the MTSB method using water column stratification, substrate classification, and LLM model provided in this embodiment of the invention are: (a) Culebra, (b) Oahu, (c) Niihau. The depth range is from 0 to -30 m.

[0101] Figure 11 To compare the RMSE inversion of the FRTR, median filtering, TSBF, MIWC, and MTSB methods provided in this embodiment of the invention, (a) LRM model and (b) LLM model are used. In this model, the orange line represents the FRTR method, the green line represents the median filtering method, the blue line represents the TSBF method, the pink line represents the MIWC method, and the magenta line represents the MTSB method.

[0102] Figure 12 Comparison of Culebra images and their corresponding water depth inversion results provided in embodiments of the present invention. (a)-(c) Images generated by median filtering, TSBF, and MIWC methods; (d)-(g) Water depth results obtained by image inversion using the LLM model, generated by FRTF, median filtering, TSBF, and MIWC methods; (h)-(k) Images from (a), (b), and (c) and... Figure 4 (a) is a partial view of the area corresponding to the red box; (l)-(p) are (d), (e), (f), (g) and... Figure 10 (a) A partial view of the part corresponding to the red box in the middle;

[0103] Figure 13Comparison of Oahu images and their corresponding water depth inversion results provided in embodiments of the present invention. (a)-(c) Images generated by median filtering, TSBF, and MIWC methods; (d)-(g) Water depth results obtained by image inversion using the LLM model, generated by FRTF, median filtering, TSBF, and MIWC methods; (h)-(k) Images from (a), (b), and (c) and... Figure 4 (a) is a partial view of the area corresponding to the red box; (l)-(p) are (d), (e), (f), (g) and... Figure 10 (a) A partial view of the part corresponding to the red box in the middle;

[0104] Figure 14 Comparison of Niihau images and their corresponding water depth inversion results provided in embodiments of the present invention. (a)-(c) Images generated by median filtering, TSBF, and MIWC methods; (d)-(g) Water depth results obtained by image inversion using the LLM model, generated by FRTF, median filtering, TSBF, and MIWC methods; (h)-(k) Images from (a), (b), and (c) and... Figure 4 (a) is a partial view of the area corresponding to the red box; (l)-(p) are (d), (e), (f), (g) and... Figure 10 (a) A partial view of the part corresponding to the red box in the middle;

[0105] Figure 15 A schematic diagram of a shallow water depth inversion system based on laser bathymetry-guided multi-temporal satellite imagery provided in an embodiment of the present invention;

[0106] Figure 16 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0108] This invention can be applied to the acquisition of water depth information in nearshore shallow sea areas, and is suitable for applications such as coastal topographic mapping, marine ecological monitoring, nautical chart preparation, island and reef and uninhabited sea area survey, marine resource management, and data updating and analysis of related geographic information systems.

[0109] This invention provides a method for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry, such as... Figure 1The multi-temporal nearshore bathymetry framework shown takes multi-temporal Sentinel-2 L2A imagery and spaceborne laser bathymetry data (ICESat-2 ATL03 data in this embodiment) as input, and includes the following steps:

[0110] S101: Extract water pixels from Sentinel-2 images, extract water depth photons from spaceborne laser depth sounding data and perform refraction correction to obtain water depth values ​​along the orbital direction.

[0111] Specifically, the research area of ​​this invention includes three regions: Culebra Island in Puerto Rico, Oahu Island and Niihau Island in the Hawaiian Islands. For example... Figure 2 As shown in (a), Culebra Island is located on the southwestern edge of the Caribbean Sea (longitude: 18.25°–18.35°N, latitude: 65.15°–65.35°W), covering an area of ​​approximately 26 square kilometers and boasting a long coastline. Located about 32 km from the main island of Puerto Rico, Culebra Island has clear waters, making it an ideal location for depth inversion. In 2019, scientists from the National Oceanic and Atmospheric Administration (NOAA) used the Riegl VQ-880-G II lidar system to precisely measure the underwater topography of Culebra Island and generate a seabed topographic map in Geotiff format. The measured data has a spatial resolution of 1 m, a planar accuracy better than 0.35 m, and an elevation accuracy of 0.1 m, and is freely available from the NOAA website.

[0112] like Figure 2 As shown in (b), Oahu is the third largest island in the Hawaiian archipelago, and Waimanalo Beach is located in the southeast of Oahu (longitude: 21.33°–21.37°N, latitude: 157.65°–157.72°W), covering an area of ​​approximately 7.7 square kilometers. Waimanalo Beach also boasts a long coastline and clear waters, with a seabed composed of coral reefs and sand, making it suitable for depth inversion studies. The water depth of this beach was collected using a Scanning Hydrographic Operations Airborne LiDAR System (SHOALS), with point cloud spacing between 3 and 15 cm and elevation error less than 0.15 m. This set of measured data was resampled to a spatial resolution of 3 m and also incorporated into the study as measured data.

[0113] like Figure 2As shown in (c), Niihau Island is the westernmost main island of the Hawaiian Islands (longitude: 21.72°–22.06°N, latitude: 160.00°–160.28°W), covering an area of ​​approximately 180 square kilometers. The island has sparse human activity and possesses a large, undeveloped pristine coastline and coral reef ecosystem, requiring detailed water depth data to aid in the analysis of its coastal ecological environment. Reference data was acquired using a Leica Hawkeye 4X airborne lidar system. After point cloud filtering and interpolation optimization, the raw point cloud data was transformed into a high spatial resolution DEM product, with accuracy meeting the requirements of the NOAA data processing workflow.

[0114] The Sentinel-2 L2A imagery product encompasses 12 bands, ranging from near-ultraviolet to shortwave infrared. After atmospheric and orthorectification correction, the L2A imagery is suitable for depth inversion tasks. From January 2023 to April 2024, 20 L2A imagery scenes were selected for Culebra. Additionally, 20 imagery scenes were selected each between January 2023 and December 2024 for depth inversion in Oahu and Niihau.

[0115] In this embodiment, the spaceborne laser bathymetry data used is ICESat-2 ATL03 data. ICESat-2 ATL03 data meticulously records the latitude, longitude, time, and altitude of globally geolocated photons, and is recorded in HDF5 format according to laser stripes. These photons have undergone precise orientation and orbit determination, possessing extremely high accuracy, and can be downloaded free of charge from the National Snow and Ice Data Center (NSIDC). As shown in Table 1, eight data tracks from five ICESat-2 ATL03 datasets were used in the Culebra experiment, two data tracks from two datasets were used for the Oahu study, and four data tracks from another two datasets were used to invert the water depth of Niihau.

[0116] Table 1. Detailed information on the study area and corresponding data.

[0117]

[0118] This step is a data preprocessing step. In this embodiment, considering that water exhibits high reflectivity in the green band (corresponding to Sentinel-2 band 3: 560 nm) and extremely low reflectivity in the mid-infrared band (corresponding to Sentinel-2 band 11: 1610 nm) due to strong absorption by the water, this embodiment of the invention uses the Modified Normalized Difference Water Index (MNDWI) to extract accurate water areas from the image. Specifically, the image is calculated according to the following formula... ,extract Pixels with a value greater than 0.2 are designated as water pixels.

[0119]

[0120] in, and These represent the green band and mid-infrared band reflectance of the Sentinel-2 image, respectively. The value range is [-1, 1].

[0121] In this embodiment, a pre-pruned quadtree isolation method is used to extract water depth photons from raw spaceborne laser bathymetry data. The pre-pruned quadtree isolation method mainly includes three steps: First, the quadtree isolation step: based on the spatial density of photons, photons are distributed to different levels of the quadtree; second, the pre-pruning step: the isolation process is checked, and pre-pruning is performed on the quadtree constructed in the previous step to reduce underwater noise interference; finally, by analyzing the frequency histogram of the quadtree depth, isolation thresholds within different depth ranges are automatically determined, and water depth photons are extracted from the remaining photons based on these isolation thresholds, achieving accurate extraction of water depth photons.

[0122] However, the extracted water depth photons did not fully account for the refraction effects of laser propagation in the atmospheric-oceanic medium, resulting in deviations in photon elevation. To address this, this invention further introduces a refraction correction method based on photon parameters: First, by associating the ID of the water depth photon with the distance along its propagation trajectory to photons belonging to the same laser emission pulse from the sea surface and seabed, the propagation path of the laser emission pulse in the water is reconstructed. Next, sea surface fluctuations are fitted, the refraction angle of the laser emission pulse from air to the sea surface is calculated, and based on this refraction angle, the refraction error of the water depth value of the seabed photon is corrected according to Snell's law, accurately obtaining the water depth on the ICESat-2 data trajectory. The water depth results from different photon propagation trajectories are spatially superimposed to obtain the ICESat-2 water depth value.

[0123] Figure 3The results of photon extraction and refraction correction at deep water are: (a) Culebra, (b) Oahu, (c) Niihau; where gray dots represent noise photons, blue dots represent signal photons, and magenta dots represent seabed photons after refraction correction.

[0124] S102: Utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of the blue and green bands of Sentinel-2 images, calculate the fusion weights of multi-temporal images and generate a weighted fused image.

[0125] Specifically, current image fusion weight allocation in multi-temporal depth inversion largely relies on statistical methods such as temporal median filtering or standard deviation weighting, or spectral thresholds based on near-infrared reflectance. While these methods can partially suppress transient noise interference, their weight calculation mechanisms lack physical constraints and are prone to systematic biases in areas with changes in water column or seabed sediment.

[0126] Therefore, this embodiment considers incorporating ICESat-2 water depth values ​​as a physical constraint into the image fusion weight calculation to avoid wasting spectral-laser collaborative information. The water penetration mechanism of laser bathymetry and optical remote sensing are inherently physically related. The 532 nm blue-green laser of ICESat-2 and the blue and green bands of Sentinel-2 both belong to the water transmission window and are jointly affected by water absorption and scattering.

[0127] Based on this mechanism, this invention proposes an image weighting method guided by ICESat-2 depth. The Sentinel-2 image is interpolated using ICESat-2 depth photons to extract the blue and green band reflectance at the corresponding locations of these depth photons. and Construct a Gaussian weighting function for the images at each time phase:

[0128]

[0129] in, It is the first Index of landscape images This refers to the ICESat-2 depth sounding value, while That is its variance. This is the ratio of the reflectance of the green to blue bands of the image. The scaling factor is 0.1 in this embodiment. This weighting function uses a Gaussian kernel to convert the deviation between the laser depth measurement result and the optical reflectivity into probability weights. The greater the deviation, the lower the image fusion weight for the current time phase, thereby suppressing pixel contamination caused by environmental noise.

[0130] The fusion weights of all images are normalized:

[0131]

[0132] in, Indicates the number of images.

[0133] Output normalized weight matrix It was used for multi-temporal image fusion, thereby quantifying the synergistic law of water penetration between spaceborne lasers and multispectral images, and providing a physically interpretable basis for weight allocation for multi-temporal image fusion.

[0134] Therefore, a fused image can be obtained through weighted fusion. This provides a data foundation for subsequent steps:

[0135]

[0136] in, This represents the i-th fused image. Indicates for fusion The original first Scene images, express The weight.

[0137] S103: Based on the water column layer inversion and / or bottom sediment classification inversion strategy, the weighted fused image is divided into multiple homogeneous regions according to the water penetration ability of blue and green light, and the water depth of the multiple homogeneous regions is inverted layer by layer using LLM and / or LRM respectively.

[0138] Specifically, current multi-temporal studies all assume that water quality does not change over time, employing a globally uniform model that ignores the spatiotemporal heterogeneity of water body optical properties. They fail to model the spectral sensitivity at different depth intervals in a tiered manner, making them susceptible to the combined effects of shallow noise and deep signal attenuation, thus accumulating inversion errors. Furthermore, these studies do not consider the impact of water column on spectral penetration, equating the spectral characteristics of the fused image with those of any single temporal phase, which can easily lead to mismatches in spectral penetration capabilities. In fused images, blue light typically has stronger penetration than green light. This makes green light sensitive to shallow details, while blue light is more robust to weak signals at deeper depths.

[0139] To address this, this invention proposes a layered depth inversion method based on the spectral penetration capability of fused images, which uses the Otsu method to binarize the green band reflectance. This method achieves the stratification of shallow and deep water. The core idea of ​​the Otsu method is to determine the optimal segmentation threshold by maximizing the inter-class variance. In this embodiment, "∧" is used to distinguish the reflectance of the original image and the fused image; the image without this symbol represents the reflectance of the original image, and vice versa.

[0140] When using the Otsu method, it is necessary to calculate the green band reflectance in the fused image. Each gray level Number of pixels And calculate the normalized probability distribution:

[0141]

[0142] in, This represents the total number of pixels.

[0143] Assuming a segmentation threshold It can effectively divide images into shallow water and deep water. Specifically, the pixel probability of shallow water... and average gray level It can be represented as:

[0144]

[0145]

[0146] Similarly, the pixel probability of deep water and average gray level It can be represented as:

[0147]

[0148]

[0149] in, This represents the maximum gray level of the green band.

[0150] Therefore, the segmentation threshold can be obtained. The following are the inter-class variances:

[0151]

[0152] Therefore, iterate through all possible thresholds. Choose the threshold that maximizes the inter-class variance. The image is divided into two parts: shallow water and deep water.

[0153]

[0154] The accuracy of water depth inversion in shallow sea areas is significantly affected by the type of sandy and coral reef substrate. Differences in the reflectivity of different substrates alter the attenuation behavior of optical signals. Current multi-temporal bathymetry studies assume that the substrate does not change over time and do not consider the influence of substrate distribution before water depth inversion, which easily introduces errors. However, most islands and reefs lack substrate data for different temporal phases, and most supervised classification methods are affected by water depth, making them difficult to apply directly.

[0155] Existing research in optical shallow water theory has introduced water body characteristics that can be used for unsupervised classification of nearshore sediments. On the one hand, water exhibits attenuation. Different wavelengths of light have different attenuation coefficients in water, but the relationship between the reflectivity of the same sediment and water depth can be described by a radiative transfer model. On the other hand, sediment exhibits reflectivity invariance. For the same sediment, the ratio of reflectivity across different wavelengths is independent of water depth and depends only on the sediment type. Therefore, this invention proposes a sediment classification method based on the Depth Invariant Index (DII). By constructing a logarithmic transformation and band combination, the contribution of water depth to the reflected signal is eliminated, extracting an index that reflects only the differences in sediment. In practical applications, sediment classification includes the following two steps:

[0156] Step (1): Calculate and construct the DII model.

[0157] Specifically, 400 pixels are extracted at equal intervals from the image to ensure that these pixels cover sandy and coral-bearing beaches at different water depths. The diffuse attenuation ratios for the blue, green, and red bands are calculated using the following formula:

[0158]

[0159]

[0160]

[0161] in, and To fuse images in band and reflectivity, and For band and The variance, and For band and covariance, and This represents the intermediate coefficients used for sediment classification. Therefore, DII models can be constructed for the green and blue bands, the blue and red bands, and the green and red bands respectively, according to the following formulas:

[0162]

[0163] in, This represents the intermediate coefficient used for sediment classification.

[0164] Step (2): Use the DII model to convert the image into a digital representation of the image. , and Combined three-band pseudo-color images. The three-band pseudo-color images were clustered using the Iterative Self-Organizing Data Analysis Technique Algorithm (ISODATA) to achieve substrate classification.

[0165] Specifically, the ISODATA algorithm randomly selects several pixels as initial cluster centers and calculates the Euclidean distance from each pixel to each cluster center, assigning it to the nearest cluster. Subsequently, the mean of each cluster is recalculated as the new cluster center, and the number of clusters is dynamically adjusted during iterative calculations until the maximum number of iterations is reached. Ultimately, the seabed is divided into two types of substrate areas, with areas of higher reflectivity labeled as sandy areas and those of lower reflectivity labeled as coral substrate areas.

[0166] In this embodiment of the invention, a "homogeneous region" refers to a region with the same depth, or the same substrate, or a region with the same depth and the same substrate.

[0167] After water column stratification or substrate classification, the image is divided into different regions for water depth inversion. The LRM model is represented as follows:

[0168]

[0169] in, For the region The water depth, For the region The slope of the LRM, and area In the figure, the intercept of the LRM is when the water depth is 0. p represents the proportionality coefficient, which is fixed at 1000 in this embodiment.

[0170] The LLM model is represented as:

[0171]

[0172] in, For the region The water depth, and For the region The linear regression coefficients, and This represents the reflectance of the fused image at band j and the reflectance of the fused image in the deep water area at band j; the reflectance of the fused image in the deep water area is set to be the same.

[0173] S104: By fusing the results from different regions through a buffer zone, the water depth inversion results for the entire shallow sea area are obtained.

[0174] Specifically, to fuse water depth results from different regions, a buffer with a radius of 3 pixels is generated, centered on the region boundary. For pixels within the buffer, their neighborhood windows are extracted, and a Gaussian kernel function is applied for weighted averaging to achieve boundary smoothing and fusion of water depth results from different regions.

[0175] S105: Accuracy verification.

[0176] Specifically, measured data from each study area were used to verify the accuracy of the inversion results. Mean absolute error (MAE) ), root mean square error ( ) and correlation coefficient The formula is:

[0177]

[0178]

[0179]

[0180] in, Represents the number of samples. This represents the value of the measured data. Indicates the inversion result, This represents the average value of the measured data.

[0181] The verification results are as follows:

[0182] (a) ICESat-2 Deep Water Photon Assessment

[0183] Table 2. Accuracy Assessment of ICESat-2 Deep Water Photons

[0184]

[0185] Figure 3 This section presents examples of ICESat-2 data processing results across three study areas. Gray dots represent noisy photons, blue dots represent signal photons, and magenta dots represent seabed photons after refraction correction. It can be observed that noisy photons are effectively removed, and the density of seabed photons gradually decreases with increasing water depth. After the ICESat-2 laser pulses propagate through the atmosphere-ocean medium, refraction causes the actual water depth to be less than the depth recorded in the original data.

[0186] Table 2 shows that the accuracy verification of ICESat-2 data preprocessing can obtain high-precision depth measurement results. Specifically, the Culebra results have a MAE of 0.31 m and an RMSE of 0.50 m, indicating a slightly undulating seabed that accurately reflects underwater topography up to a depth of 34.40 m. The Oahu results have a MAE of 0.28 m and an RMSE of 0.46 m, with a maximum detected depth of 30.23 m, indicating a gentle seabed change. The Niihau results have a maximum detected depth of 36.27 m, a MAE of 0.24 m, and an RMSE of 0.51 m.

[0187] (ii) Integration of imagery, water column stratification, and substrate classification

[0188] Current research mostly sets the weights for fused images based on image pixel information, but it lacks the ability to pre-identify noise in the image, which will negatively impact the quality of the fused image. For example... Figure 4 As shown, we fused 20 Sentinel-2 images in each experimental area using the MTSB method. The results showed no significant noise distribution in the fused images, indicating that the image weighting was guided by laser bathymetry data, and the interference of transient noise such as clouds, waves, and ship wakes was suppressed.

[0189] Furthermore, the fused images obtained using the MTSB method clearly reveal the water depth transition and seabed distribution in the study area. The water depth changes in Culebra and Oahu are relatively gradual, with the fused images transitioning from brighter spectral features in shallower areas to deeper spectral features in deeper water. In the bay directly south of Culebra's main island, the spectral transition is particularly slow. The fused images of Oahu clearly show changes in the seabed sediment. Brighter spectral areas represent sandy seabeds, while darker areas correspond to coral reefs and rocky beaches. In contrast, the fused images of Niihau show more rapid spectral changes, indicating more pronounced underwater topographic variations in this area. Shallows are only distributed along the coastal zone, while the water depth in the Niihau area increases rapidly with increasing distance from the coastline.

[0190] Subsequently, high-quality fused imagery was used for water column stratification and sediment classification. The core idea of ​​water column stratification is to divide nearshore areas into shallow and deep water columns based on spectral characteristics. This allows the fused imagery to also consider the impact of water quality changes on depth inversion, constructing inversion models for different water depth ranges with varying optical characteristics. The Otsu algorithm was used to calculate the green band of the fused imagery, dividing the continuous water body region into... Figure 5 The results are shown below. Red pixels represent land areas, green pixels represent shallow water, and blue pixels represent deep water.

[0191] like Figure 5 As shown in (a), Culebra's shallow waters surround the landmass, with large areas of shallow water distributed around its main island and eastern islands. Although the distribution of these areas is irregular, it echoes the island's outline. Figure 5 As shown in (b) of the diagram, in Oahu, shallow water bodies are distributed along the coastal zone, occupying a large area of ​​the nearshore region and gradually extending into the sea. For example... Figure 5 As shown in (c), the shallow waters of Niihau are relatively concentrated and account for a low proportion, mainly distributed in the northwestern edge area of ​​the island.

[0192] Overall, shallow water bodies are generally distributed along the land, which is consistent with natural patterns. The boundaries between shallow and deep water bodies delineated using the MTSB method are clear and can well reflect the water column situation in the study area, providing a foundation for more accurate inversion of nearshore water depth.

[0193] Furthermore, the fused imagery was also used to delineate different substrate regions. The MTSB method calculates the DII based on pixel values, making substrate classification in the fused imagery unaffected by water depth. Subsequently, the fused imagery is transformed into... , and Combined three-band pseudo-color images, and the background was divided into sections using the ISODATA algorithm as follows: Figure 6 The results are shown below. Dark blue pixels represent land, yellow pixels represent sandy substrates, and gray pixels represent rocky substrates such as coral reefs or exposed rocks.

[0194] like Figure 6 As shown in (a), the sandy substrate of Culebra is mainly distributed in a ring around the island, while the rocky substrate is mainly distributed along the coastal area of ​​the bay in the south of the main island and other areas far from the coastline. Figure 6 As shown in (b), sandy and rocky beaches are interspersed in Oahu. Specifically, sandy beaches are found around the northern coastline of Oahu, while the southern coastline is predominantly rocky. In contrast, as... Figure 6 As shown in (c), a continuous and relatively uniformly wide yellow sandy beach is distributed along the northwestern land edge of Niihau, while the southeastern part of the island is mainly composed of rocky beaches.

[0195] Overall, DII-based seabed classification can accurately divide the fused images of the study area into regions with different seabed textures, allowing multi-temporal depth inversion to take into account the impact of seabed texture changes, thereby further improving the accuracy of depth inversion.

[0196] Therefore, the MTSB method proposed in this invention can achieve high-quality fusion of multi-temporal images through a laser-guided weighting strategy, while the synergistic analysis of spectral stratification and seabed classification further enriches the physical basis for multi-temporal water depth inversion. The stratification strategy and seabed classification reduce the uncertainty in water depth inversion, providing advantages for more accurate depth inversion in nearshore environments.

[0197] (III) Inversion results based on MTSB

[0198] The previous section qualitatively analyzed the results of image fusion, water column stratification, and sediment classification. This section compares the inversion results with measured data to quantitatively analyze the impact of different strategies and models on inversion accuracy. We designed six combinations of different inversion strategies and models for water depth inversion: (a) water column stratification and LRM model, (b) water column stratification and LLM model, (c) sediment classification and LRM model, (d) sediment classification and LLM model, (e) water column stratification, sediment classification, and LRM model, and (f) water column stratification, sediment classification, and LLM model.

[0199] Figure 7 , 8 Images 9 and 1 respectively show the scatter plots and histograms of errors obtained from different inversion combinations in Culebra, Oahu, and Niihau. The left side of each image shows the scatter distribution between the inversion results and the reference data. The black dashed line represents the 1:1 line, the magenta line represents the fitting result, and the accuracy indicators and the fitting model are marked on the image. The right side of each image shows the histogram distribution of the inversion error at the reference depth. These are divided into 10 m depth intervals, with the MAE and RMSE for different depth intervals marked within them.

[0200] Among the inversion results, Culebra achieved the highest inversion accuracy, with an average MAE of 1.27 m and an average RMSE of 1.49 m. Oahu followed closely with an average MAE of 1.33 m and an average RMSE of 1.54 m. Niihau had the lowest inversion accuracy, but still achieved an average MAE of 1.67 m and an RMSE of 1.90 m. Figure 7 , 8 The scatter plots for Figure 9 and 9 show that the inversion results obtained by the MTSB method are in high agreement with the reference data, and the consistency variation among different inversion results is small. For example... Figure 7 As shown in (a), the correlation is lowest (0.95) when using a combination of water column stratification and LRM model to invert Culebra water depth. Figure 8As shown in (e), the highest correlation (0.98) was observed when using a combination of water column stratification, sediment classification, and the LRM model to retrieve Oahu water depth. Furthermore, all combinations effectively retrieved nearshore water depth. Figure 9 As shown in (a), the error is greatest when using a combination of water column stratification and LRM model to invert the Niihau water depth, with a MAE of 1.91 m and an RMSE of 2.10 m. Figure 7 As shown in (f), the best results were achieved when using water column stratification, sediment classification, and the LLM model to invert the Culebra water depth, with a MAE of 1.12 m and an RMSE of 1.32 m. It can be concluded that the proposed MTSB method can effectively invert nearshore water depth and obtain high-precision inversion results.

[0201] Further analysis Figure 7 The error histograms for 9 and 1 show that water depth is the main factor affecting inversion accuracy. With increasing water depth, both MAE and RMSE of the inversion results gradually increase. For Culebra, the inversion results of water column stratification and LRM models are most affected by water depth (e.g., ...). Figure 7 (a)). When the water depth is in the range of -30 to -20 m, the MAE is 1.56 m and the RMSE is 1.80 m. When the water depth is in the range of -10 to 0 m, the MAE is 0.97 m and the RMSE is 1.12 m. Increasing the water depth increases the MAE by 31.25% and the RMSE by 37.78%. For Niihau, the inversion accuracy under the combination of water column stratification, sediment classification, and LRM model is most affected by depth (e.g., Figure 9 (e)). When the water depth increased from the -10 ~ 0 m range to the -30 ~ -20 m range, the MAE increased by 35.12%, while the RMSE increased by 30.80%.

[0202] In Fig. 8, Oahu's error distribution appears to provide a set of counterexamples. The inversion accuracy initially decreases as the water depth increases from -10 to 0 m to -20 to -10 m. However, the inversion error decreases further with increasing water depth. Combined with... Figure 8 Scatter plot analysis shows that there are fewer scatter points in the range of -30 to -20 m. The pixels corresponding to these scatter points may happen to correspond to high-quality inversion results, so that the deepest region is not necessarily the least accurate in the overall results.

[0203] Furthermore, when using the same inversion strategy, the LLM model consistently achieves slightly higher inversion accuracy than the LRM model. In the inversion results after water column stratification, the LRM model has an average MAE of 1.57 m and an average RMSE of 1.80 m. In contrast, the LLM model has an average MAE of 1.49 m and an average RMSE of 1.70 m. In the inversion results after sediment classification, the LRM model has an average MAE of 1.46 m and an average RMSE of 1.65 m. In contrast, the LLM model has an average MAE of 1.39 m and an average RMSE of 1.58 m. When both water column stratification and sediment classification are used simultaneously, the LRM model has an average MAE of 1.42 m and an average RMSE of 1.64 m. In comparison, the LLM model has an average MAE of 1.26 m and an average RMSE of 1.47 m. These results demonstrate that the LLM model can better capture the spectral characteristics of nearshore images and perform water depth inversion with higher accuracy.

[0204] The analysis above also reveals that water column stratification and sediment classification have different impacts on inversion accuracy. Specifically, the average MAE after water column stratification of the fused image and subsequent water depth inversion is 1.53 m, and the average RMSE is 1.75 m. Sediment classification divides the fused image into sandy and rocky regions and uses separate models to invert water depth. The average MAE after sediment classification is 1.46 m, and the average RMSE is 1.62 m. The sediment classification strategy has higher accuracy than the water column stratification strategy. When stratification and classification strategies are combined, the accuracy of water depth inversion is further improved. When water column stratification and sediment classification are performed simultaneously, the average MAE of the inversion results is 1.34 m, and the average RMSE is 1.56 m, which is higher than the accuracy when either strategy is used alone. This result indicates that the MTSB method, which considers both water column and sediment, has good water depth inversion capabilities.

[0205] In summary, it can be found that the accuracy is always best when using water column stratification and sediment classification strategies and inverting water depth through an LLM model. Figure 10 The results show the water depth obtained by the MTSB method through water column stratification, sediment classification, and LLM model inversion. Among them, the Culebra results show the best accuracy, with an MAE of 1.12 m and an RMSE of 1.32 m. The accuracy was 0.97. The water depth in Culebra gradually transitions from 0 m near the shore to >-30 m offshore. The water depth changes are relatively gentle and shallower in the southern bay of the main island and along the coast of the eastern islands. Oahu's results were the next most accurate, with an MAE of 1.25 m and an RMSE of 1.48 m. The accuracy is 0.97. The water depth variation at Oahu is relatively smooth, with large areas of flat seabed near the shore. As the water depth increases, the seabed topography of Oahu begins to show some undulation. The Niihau results have the lowest accuracy, with an MAE of 1.40 m and an RMSE of 1.61 m. In the Niihau water depth results, the water depth transition within the northwest shoal is gentle, while the water depth along the southeast coast increases rapidly from 0 m to >-30 m. Therefore, the proposed MTSB method not only generates high-quality fused images but also obtains satisfactory water depth inversion results, thus verifying the effectiveness of the method.

[0206] This section further compares the MTSB method with previously proposed methods, and clarifies the conclusions stated above. It quantitatively analyzes the inversion accuracy of different methods and demonstrates their performance; it also evaluates the impact of the number of multi-temporal images, the model, and the inversion strategy on accuracy. Furthermore, it presents and quantitatively analyzes the results of different combinations to understand the specific differences between different methods and models.

[0207] (iv) Quantitative comparison of MTSB with other methods

[0208] To comprehensively evaluate the inversion performance of the MTSB method, four existing inversion methods were selected for comparison. The FRTR method first inverts water depth using images from different time phases, then applies median filtering to the multi-temporal results to obtain the final result. The remaining comparison methods all employ the FFTR strategy. The Median method performs median filtering on multi-temporal images to obtain a fused image before performing water depth inversion. The TSBF method uses outlier removal techniques to construct the optimal fused image and uses it for water depth inversion. The MIWC method assigns weights to pixels based on near-infrared information from the images, thereby generating a fused image and completing the water depth inversion.

[0209] The average RMSE of these methods when retrieving water depth is shown as follows: Figure 11 As shown, as the number of images increases from 1 to 20, the RMSE of all methods under different models shows a gradual decreasing trend, indicating that increasing the number of images can effectively improve the inversion accuracy. For example, the initial inversion accuracy of the MTSB method using LRM and LLM models both exceeded 2 m, while when the number of images increased to 20, the RMSE dropped to below 2 m, demonstrating a significant advantage of multi-temporal observation.

[0210] like Figure 11As shown in (a), when using the LRM model, the RMSE of the FRTF method decreased from 2.71 m when the number of images was 1 to 2.29 m when the number of images was 20. The increase in the number of images reduced the error of the FRTF method by 0.42 m. This change was smaller than that of other methods, and its RMSE remained at a relatively high level among all methods. This indicates that the FRTF method is not very effective in utilizing multi-temporal images, especially when the number of images is large, and its improvement in inversion accuracy is limited.

[0211] In contrast, when using the LRM model, the MTSB method reduced the error from 2.33 m to 1.53 m. As the number of images increased, the error of the MTSB method decreased by 0.80 m, significantly outperforming the FRTF method. This indicates that under the LRM model, the MTSB method is more effective at fusing multi-temporal images and performing inversion, exhibiting better accuracy.

[0212] like Figure 11 As shown in (b), when using the LLM model, the RMSE of the FRTF method decreased from 2.71 m to 2.26 m. Although the error decreased slightly, the accuracy was still not as good as other methods. Similarly, under the LLM model, the RMSE of the MTSB method decreased from 2.24 m to 1.47 m, showing a more significant improvement in accuracy and ultimately the smallest RMSE. This indicates that when using the LLM model, MTSB also exhibits better accuracy.

[0213] Comparing the methods themselves, the FRTF method first inverts each image individually before fusing the results, while other methods first fuse multi-temporal images before performing a unified inversion. Figure 11 It can be seen that the FFTR method has a significantly better RMSE than the FRTF method under both LRM and LLM models, indicating that the FFTR method can more effectively avoid the interference of image noise and obtain more accurate results.

[0214] From a model perspective, under the same method, using the LLM model almost always yields better inversion accuracy. For example, the MIWC method achieves a final RMSE of 1.80 m using the LRM model, while this drops to 1.65 m using the LLM model. The Median method achieves a final RMSE of 2.00 m using the LRM model, while the LLM model achieves 1.74 m. This indicates that the LLM model outperforms the LRM model in inverting water depth.

[0215] Looking at the error trends of different methods, most methods show a rapid decrease in RMSE when the number of images increases from 1 to 10, indicating that the newly added images at this stage can supplement more information from different time phases. When the number of images exceeds 10, the rate of decrease tends to slow down. For methods such as TSBF and MIWC, the RMSE decrease is less than 0.1 m between 10 and 20 images, and the accuracy tends to stabilize.

[0216] Analysis of the combined strategies and models revealed that the optimal combination is the MTSB method paired with the LLM model. This combination achieved a final RMSE of 1.47 m, the lowest among all combinations, with minimal error fluctuation. This combination not only leverages the advantages of the MTSB method in fusing multi-temporal images but also utilizes the superior depth modeling capabilities of the LLM model, demonstrating the best multi-temporal image depth inversion performance.

[0217] (v) Qualitative analysis of MTSB and other methods

[0218] Although the preceding sections evaluated the error performance of various methods through quantitative experiments, this section employs qualitative analysis to visually compare the fused images and water depth inversion results obtained by different methods, thereby providing a more comprehensive evaluation of the methods' applicability, in order to further verify their practical effectiveness and reveal specific images of environmental disturbances. It is worth noting that, considering the previous sections have verified the superior water depth inversion capability of the LLM model, the water depth inversion results presented in this section are all obtained by combining different water depth inversion methods with the LLM model.

[0219] Figure 12 The image shows the fused and inverted Culebra images. For example... Figure 12 As shown in (i) and (n), the TSBF method exhibits a disadvantage when faced with large areas of cloud cover, resulting in significant deviations in the retrieved water depth, which differ considerably from the results of other methods. In contrast, the water depth results generated by the other methods more accurately reflect the continuous variation characteristics from shallow to deep water areas, demonstrating better stability and noise resistance.

[0220] Figure 13 The image fusion and inversion results for Oahu are presented. FRTF, Median, TSBF, and MIWC methods are used in… Figure 13 The areas circled in yellow are significantly affected by cloud noise. Furthermore, ocean waves also cause abnormal variations in image pixel values. The reflection noise caused by ocean waves... Figure 13 In (e), (f), and (g), obvious stripe interference is formed on the right side. In contrast, the fused image generated by the MTSB method suppresses this type of noise interference better, and the water depth inversion results are smoother and more consistent in spatial distribution, with clearer details.

[0221] Figure 14 This presents the fused imagery of Niihau and the corresponding inversion results. The region exhibits dramatic changes in water depth and complex topography, posing higher demands on image fusion methods. Nevertheless, various methods generally handle these complex variations well; multi-temporal fusion effectively suppresses spectral disturbances caused by clouds and waves, yielding a water depth distribution map with good continuity. However, the MTSB method performs better in reconstructing fine topographic structures and smoothing boundaries, demonstrating stronger adaptability.

[0222] Further analysis Figure 12 and Figure 13 The yellow circle in the image reveals that clouds are the most common interference factor. Clouds not only directly obscure water information, but their shadows also cause abnormal local reflectance, disrupting the normal spectral characteristics of the water body and making it difficult for the inversion model to accurately estimate water depth. Furthermore, waves and ship tracks can produce striped interference in some areas, which are easily misinterpreted as topographic changes by water depth inversion methods, thus reducing inversion accuracy.

[0223] The MTSB method introduces ICESat-2 laser photon depth as a guide, providing a physical basis for the image fusion process. The resulting fused image effectively suppresses noise interference. The multi-temporal fusion mechanism allows transient interference to be mitigated by the averaging effect of multi-temporal data; different multi-temporal fusion methods all achieve water depth results superior to those of single-temporal methods. Combined with the quantitative analysis above, increasing the number of images involved in the fusion further enhances noise resistance, and the MTSB method demonstrates significant advantages in this process.

[0224] In summary, the MTSB method performs exceptionally well in qualitative analysis, especially in complex environments such as shallow water transition zones and deep water edge areas, maintaining high accuracy and stability in water depth retrieval. Compared to methods like FRTF, Median, TSBF, and MIWC, MTSB effectively handles transient disturbances such as clouds, waves, and ship tracks, achieving a good balance between detail preservation and result consistency. Therefore, the MTSB method demonstrates greater adaptability in multi-temporal satellite image fusion and nearshore water depth retrieval, showing promising application prospects.

[0225] Based on the same inventive concept, such as Figure 15 As shown, this embodiment of the invention also provides a shallow water depth inversion system based on laser bathymetry-guided multi-temporal satellite imagery, including a data preprocessing module, a multi-temporal image fusion module, a zonal inversion module, and an inversion fusion module.

[0226] Specifically, the data preprocessing module extracts water body pixels from Sentinel-2 images, extracts water depth photons from spaceborne laser bathymetry data and performs refraction correction to obtain water depth values ​​along the orbital direction; the multi-temporal image fusion module utilizes the strong correlation between water depth values ​​along the orbital direction and the reflectivity of the blue and green bands of Sentinel-2 images to calculate the multi-temporal image fusion weights and generate a weighted fused image; the partition inversion module uses a water column layered inversion and / or bottom sediment classification inversion strategy to divide the weighted fused image into multiple homogeneous regions according to the water penetration ability of blue and green light, and uses LLM and / or LRM to invert the water depth of the multiple homogeneous regions layer by layer; the inversion fusion module uses a buffer to fuse the results of different regions to obtain the water depth inversion results for the entire shallow sea area.

[0227] It should be noted that the multi-temporal satellite imagery shallow water depth inversion system provided in this embodiment of the invention is for implementing the above method. Its specific functions can be referred to the above method embodiments, and will not be repeated here.

[0228] This invention proposes a multi-temporal satellite imagery method and system for shallow water depth inversion. It uses ICESat-2 laser bathymetry data to replace in-situ water depth measurements and fuses multi-temporal Sentinel-2 images. By constructing a laser-guided image weighting mechanism, high-quality fused images are generated. Simultaneously, it combines spectral stratification strategies and seabed classification methods to establish water depth inversion models for regions with different depths and seabed types, fusing them to obtain a complete water depth distribution map. This system effectively fills the gaps in existing research by lacking physical constraints and neglecting the time-varying nature of water and seabed, and exhibits stronger adaptability in various environments.

[0229] Experiments conducted in three representative nearshore areas—Culebra, Oahu, and Niihau—demonstrate that the method and system of this invention achieve higher inversion accuracy and correlation compared to previously proposed methods, and exhibit greater stability in areas affected by cloud cover, waves, and ship wake interference. Furthermore, this invention systematically analyzes the performance differences of various methods at different depths, under different water conditions and sediment environments from both quantitative and qualitative perspectives, further validating the comprehensive advantages of this invention.

[0230] In summary, the method and system of this invention provide an efficient and reliable solution for realizing long-term dynamic shallow water depth inversion on a global scale in uninhabited areas. It has broad application prospects in coastal zone ecological monitoring, marine resource management, and other fields.

[0231] Furthermore, it should be noted that this invention can be implemented based on existing spaceborne laser depth sounding data and multi-temporal optical satellite remote sensing images, without relying on dedicated or customized hardware equipment. It can be implemented in existing remote sensing data processing platforms and computing environments, and has good engineering feasibility and repeatability.

[0232] This invention is applicable to water depth inversion in nearshore shallow sea areas and can be applied to sea areas with different geographical locations, water conditions and seabed types. It has good adaptability to water transparency and seabed topography complexity and can meet the water depth information acquisition needs in various application scenarios.

[0233] This invention is not limited to specific spaceborne laser depth sounding data sources or optical satellite image types. Without departing from the technical concept of this invention, it can be adapted to spaceborne laser depth sounding data from different sources as well as optical remote sensing images with different resolutions and band configurations, and has good scalability and compatibility.

[0234] This invention can be implemented on a general-purpose computer or server platform through software programs, or it can be integrated into a remote sensing data processing system or geographic information system. Its specific implementation form does not constitute a limitation on the scope of protection of this invention.

[0235] Figure 16 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 16 As shown, the electronic device may include: a processor 1601, a communications interface 1602, a memory 1603, and a communication bus 1604, wherein the processor 1601, the communications interface 1602, and the memory 1603 communicate with each other through the communication bus 1604. Processor 1601 can call logic instructions in memory 1603 to execute a shallow water depth inversion method based on laser bathymetry-guided multi-temporal satellite imagery. This method includes: extracting water body pixels from Sentinel-2 images; extracting water depth photons from satellite-borne laser bathymetry data and performing refraction correction to obtain water depth values ​​along the orbital direction; calculating multi-temporal image fusion weights based on the strong correlation between the water depth values ​​along the orbital direction and the reflectivity of the blue and green bands of Sentinel-2 images, generating a weighted fused image; dividing the weighted fused image into multiple homogeneous regions according to the water penetration capabilities of blue and green light based on water column layering inversion and / or seabed classification inversion strategies; using LLM and / or LRM to invert water depth layer by layer in the multiple homogeneous regions; and fusing the results of different regions through a buffer to obtain the shallow sea depth inversion result for the entire shallow sea area.

[0236] Furthermore, when the logical instructions in the aforementioned memory 1603 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0237] This invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer can execute a method for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry, provided in the above-described method embodiments.

[0238] This invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the shallow water depth inversion method based on laser bathymetry-guided multi-temporal satellite imagery provided in the above-described method embodiments.

[0239] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0240] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for shallow water depth inversion based on multi-temporal satellite imagery guided by laser bathymetry, characterized in that, include: Water pixels are extracted from Sentinel-2 images, water depth photons are extracted from spaceborne laser depth sounding data and refraction correction is performed to obtain water depth values ​​along the orbital direction. By utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of blue and green bands in Sentinel-2 images, the fusion weights of multi-temporal images are calculated to generate weighted fused images. Based on water column layer inversion and / or bottom sediment classification inversion strategies, the weighted fused image is divided into multiple homogeneous regions according to the water penetration ability of blue and green light, and the water depth of the multiple homogeneous regions is inverted layer by layer using LLM and / or LRM. By fusing the results from different regions through a buffer zone, the water depth inversion results for the entire shallow sea area are obtained.

2. The shallow water depth inversion method based on multi-temporal satellite imagery guided by laser bathymetry according to claim 1, characterized in that, The extraction of water body pixels from Sentinel-2 images includes: The modified normalized difference water index (MNDWI) of Sentinel-2 imagery is calculated according to the following formula, and pixels with an MNDWI value greater than 0.2 are extracted as water pixels. in, and These represent the green band and mid-infrared band reflectance of the Sentinel-2 image, respectively. The value range is [-1, 1].

3. The shallow water depth inversion method based on multi-temporal satellite imagery guided by laser bathymetry according to claim 2, characterized in that, The process of extracting water depth photons from spaceborne laser depth sounding data and performing refraction correction to obtain water depth values ​​along the orbital direction includes: Based on the spatial density of photons, photons are distributed to different levels of the quadtree; Perform pre-pruning on the quadtree constructed in the previous step; The frequency histogram of the quadtree depth of the remaining nodes after pre-pruning is analyzed. Based on the distribution characteristics of the frequency histogram, the isolation threshold in different depth ranges is automatically determined. Based on the isolation threshold, the water depth photons are extracted from the remaining photons. By matching the ID of the deep-water photons and the distance along the photon propagation trajectory, surface photons and seabed photons belonging to the same laser emission pulse are matched to reconstruct the propagation path of the laser emission pulse in the water. Based on the reconstructed propagation path of the laser emission pulse in the water, the elevation distribution of photons on the sea surface is fitted to calculate the refraction angle of the laser emission pulse on the sea surface. The water depth value of the seabed photons is corrected according to the refraction angle to obtain the water depth value along the orbital direction.

4. The shallow water depth inversion method based on laser bathymetry-guided multi-temporal satellite imagery according to claim 1, characterized in that, The method of utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of the blue and green bands of Sentinel-2 images to calculate multi-temporal image fusion weights and generate weighted fused images includes: The Gaussian weights of the images at each time phase are calculated using the following formula: in, It is the first Index of landscape images Indicates the first Gaussian weights for scene images This refers to the water depth along the track direction. yes variance These are the blue and green band reflectances of the Sentinel-2 image, respectively. It is an exponential function with the natural constant e as its base. This indicates the preset scaling factor; The Gaussian weights of all images are normalized according to the following formula: in, Indicates the number of images. Indicates the first Normalized weights of scene images; The fused image is obtained according to the following formula: in, This represents the i-th fused image. Indicates for fusion The original first Scene images, express The weight.

5. The shallow water depth inversion method based on multi-temporal satellite imagery guided by laser bathymetry according to claim 1, characterized in that, The water column stratification inversion strategy includes: For each time phase of the image, the green band reflectance was statistically analyzed. Each gray level Number of pixels And calculate the normalized probability distribution: in, The total number of pixels in the image; Assuming a segmentation threshold It can effectively divide images into shallow water and deep water, traversing all possible thresholds. Choose the threshold that maximizes the inter-class variance. The image is divided into two parts: shallow water and deep water. The segmentation threshold is calculated according to the following formula. Inter-class variance : in, and The pixel probability and average grayscale of shallow water are calculated using the following formulas: and The pixel probability and average grayscale of deep water are calculated using the following formulas: in, This represents the maximum gray level of the green band.

6. The shallow water depth inversion method based on multi-temporal satellite imagery guided by laser bathymetry according to claim 1, characterized in that, The aforementioned substrate classification and inversion strategy includes: For each time phase image, a number of pixels are extracted at equal intervals from the image to ensure that the extracted pixels cover sandy and coral-bearing beaches at different water depths; the ratio of slow attenuation coefficients in the blue, green, and red bands is calculated using the following formula: in, and For band and reflectivity, and For band and The variance, and For band and covariance; and Indicates the intermediate coefficients used for sediment classification; Construct depth-invariant index (DII) models for the green and blue bands, the blue and red bands, and the green and red bands respectively, according to the following formulas: in, Indicates the intermediate coefficients used for sediment classification; Using the DII model to convert images into... , and The three-band pseudo-color images were combined and clustered using the iterative self-organizing data analysis algorithm ISODATA to divide the seabed into two types of substrate regions: sandy and coral-based.

7. The shallow water depth inversion method based on multi-temporal satellite imagery guided by laser bathymetry according to claim 1, characterized in that, The method of using LLM and LRM to invert water depth layer by layer in the multiple homogeneous regions includes: The LRM model is represented as: in, For the region The water depth, For the region The slope of the LRM, and area In the middle, the intercept of LRM when the water depth is 0, This indicates the preset scaling factor; The LLM model is represented as: in, For the region The water depth, and For the region The linear regression coefficients, and This represents the reflectance of the fused image at band j, and the reflectance of the fused image in the deep water area at band j.

8. A shallow water depth inversion system based on multi-temporal satellite imagery guided by laser bathymetry, characterized in that, include: The data preprocessing module is used to extract water body pixels from Sentinel-2 images, extract water depth photons from spaceborne laser bathymetry data and perform refraction correction to obtain water depth values ​​along the orbital direction. The multi-temporal image fusion module is used to calculate the multi-temporal image fusion weights by utilizing the strong correlation between water depth values ​​along the orbital direction and the reflectance of the blue and green bands of Sentinel-2 images, and to generate a weighted fused image. The partition inversion module is used to divide the weighted fused image into multiple homogeneous regions according to the water penetration ability of blue and green light based on water column layer inversion and / or bottom sediment classification inversion strategies, and use LLM and / or LRM to invert the water depth of the multiple homogeneous regions layer by layer. The inversion fusion module is used to fuse results from different regions through a buffer to obtain the water depth inversion results for the entire shallow sea area.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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