A method for inverting internal solitary wave amplitude based on SWOT observation data

Abstract

The present invention relates to the technical field of marine remote sensing image processing, and discloses a method for inverting internal solitary wave amplitudes based on SWOT observation data. The method comprises the following steps: obtaining L3 sea surface height anomaly data from the SWOT satellite Ka-band radar interferometer, performing preprocessing, respectively, performing adaptive noise filtering, maximum inter-class variance method enhancement, and morphological edge detection, performing overlap analysis, retaining pixels determined to be valid as sea surface height anomaly data of internal solitary wave disturbances; inverting the first-order amplitude of the internal solitary wave; introducing a nonlinear term in the extended KdV equation to perform nonlinear correction on the vertical mode function; and inverting to obtain the higher-order amplitudes of the internal solitary wave. The method disclosed in the present invention can extract real and effective internal solitary wave disturbance information as the input source for amplitude inversion, thereby achieving accurate inversion of large-amplitude internal solitary waves, thereby expanding the technical potential of the SWOT satellite in quantitative research and practical applications of internal solitary waves.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean remote sensing image processing, and in particular to an internal solitary wave amplitude inversion method based on SWOT observation data. Background Art

[0002] Internal solitary waves, a nonlinear wave phenomenon prevalent in the inner ocean, play a crucial role in influencing ocean mixing, material transport, nutrient distribution, and marine engineering safety. In recent years, the precise observation and inversion of internal solitary waves' physical parameters, particularly amplitude inversion, have become key technical challenges in marine science research and practical applications. While existing optical remote sensing and synthetic aperture radar technologies have been widely used to identify the spatial distribution of internal solitary waves, they still have significant limitations in quantitatively observing sea surface height anomalies and detecting three-dimensional structures, making it difficult to accurately invert large-scale internal solitary wave amplitudes.

[0003] The rapid development of three-dimensional imaging radar altimeter technology has provided a new means to address these issues. In particular, the Ka-band Radar Interferometer (KaRIn) aboard the Surface Water and Ocean Topography (SWOT) satellite, launched on December 16, 2022, offers high spatial resolution (250 m) and wide swath (100 km left and right) sea surface height observation capabilities. This provides centimeter-level accuracy for sea surface height variation, laying a crucial foundation for internal solitary wave disturbance feature extraction and amplitude inversion.

[0004] However, the SWOT satellite still faces the following key technical challenges in the application of internal solitary wave amplitude inversion: on the one hand, the ocean background environment is complex, and the internal solitary wave disturbance signal in the SWOT sea surface height data is easily masked by background noise. It is urgent to develop an extraction method that can effectively highlight the characteristics of the internal solitary wave disturbance and provide high-quality input data for subsequent amplitude inversion; on the other hand, there is currently a lack of inversion methods based on SWOT sea surface height observation data and adapted to the amplitude of large-amplitude internal solitary waves. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides an internal solitary wave amplitude inversion method based on SWOT observation data, so as to extract real and effective internal solitary wave disturbance information as the input source for amplitude inversion, thereby realizing the accurate inversion of large-amplitude internal solitary waves, thereby expanding the technical potential of SWOT satellites in the quantitative research and practical application of internal solitary wave dynamic processes.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A method for inverting internal solitary wave amplitude based on SWOT observation data includes the following steps:

[0008] Step 1: Obtain L3 sea surface height anomaly data from the SWOT satellite Ka-band radar interferometer, and use quality identification and threshold screening methods to remove abnormal pixels and large-scale background fields;

[0009] Step 2: Adaptively filter the data obtained in step 1 to remove the small-scale noise areas caused by non-inner solitary wave disturbances. Then, the maximum inter-class variance method is used to enhance the stripe features in the sea surface height anomaly data. The enhanced data is then subjected to connectivity analysis.

[0010] Step 3, using the Sobel operator to perform morphological edge detection on the data obtained in step 1;

[0011] Step 4: Perform overlapping analysis on the pixels retained after processing in steps 2 and 3, and retain the pixels that are determined to be valid in both steps as the sea surface height anomaly data of internal solitary wave disturbance; use this data as the height change caused by the internal solitary wave on the sea surface to invert the first-order amplitude of the internal solitary wave;

[0012] Step 5: Based on the first-order amplitude of the internal solitary wave obtained by inversion, the nonlinear term in the extended KdV equation is introduced to perform nonlinear correction on the vertical modal function to obtain the corrected nonlinear vertical modal function; the corrected nonlinear vertical modal function is used to invert the high-order amplitude of the internal solitary wave.

[0013] In the above scheme, in step 1, the unedited sea surface height anomaly data contained in the unsmoothed variant of the SWOT satellite Ka-band radar interferometer L3 sea surface height anomaly data is selected as the basic data source for extracting internal solitary wave disturbance information.

[0014] In the above solution, step 1 specifically includes the following processing steps:

[0015] Step 1.1: Based on the quality identifiers provided in the L3 unsmoothed variant of the SWOT satellite Ka-band radar interferometer, the unedited sea surface height anomaly data are quality-labeled. The labeling rules used include: selecting Flag 102 to remove pixels with default value errors; selecting Flag 101 to remove pixels in land areas; selecting Flag 100 to remove pixels with swath edge artifacts; selecting Flag 70 to remove pixels affected by spacecraft events; selecting Flag 50 to remove pixels with errors in coastal and polar regions; and selecting Flag 20 to remove pixels affected by sea ice. Through the above labeling process, potentially low-quality or anomalous data are removed.

[0016] Step 1.2: After the quality marking process in step 1.1, the abnormal sea surface height data is subjected to a threshold screening method to remove abnormal pixels. The specific method is as follows: the average value of the global abnormal sea surface height data is calculated, and the reasonable data value range is set to ±50 cm. Pixels outside this range are judged as abnormal pixels and are removed.

[0017] In step 1.3, download the global gridded sea surface height anomaly data with a spatial resolution of 1 / 8° and a temporal resolution of 1 day provided by the Copernicus Marine Service as background field data; perform pixel-by-pixel subtraction between the observation data after removing abnormal pixels obtained in step 1.2 and the background field data to obtain sea surface height anomaly data with large-scale background changes removed.

[0018] In the above scheme, the specific method of step 2 is as follows:

[0019] Step 2.1, adaptive noise filtering: Calculate the global histogram of the sea surface height anomaly data and remove the anomaly data below the 20th percentile and above the 99.9th percentile. Based on this, perform mean filtering on the global data using a 3×3 window to further smooth the local noise.

[0020] Step 2.2: The maximum inter-class variance method is used to enhance the internal solitary wave fringe features of the noise-filtered data: First, a 50×50 pixel sliding window is used to perform local adaptive Otsu segmentation; second, an overall Otsu segmentation is performed on the global data to improve the recognition of the internal solitary wave fringe features;

[0021] In step 2.3, connectivity analysis is performed on the data after feature enhancement in step 2.2. The number of pixels in the connected area is calculated, and the area with less than 500 connected pixels is eliminated to remove the small-scale noise area not disturbed by the internal solitary wave and highlight the internal solitary wave stripe characteristics.

[0022] In the above scheme, the specific method of step 3 is as follows:

[0023] Step 3.1: Use a 3×3 window to calculate the Sobel operator in the x-direction and y-direction respectively;

[0024] Step 3.2, modulo the calculation results of the Sobel operator in the x-direction and y-direction;

[0025] Step 3.3: Calculate the global histogram of the Sobel operator modulus and remove data points below the 60% quantile as non-edge pixels.

[0026] In step 3.4, a 3×3 window mean filter is applied to the remaining data to further smooth the edge features.

[0027] In the above scheme, the first-order amplitude of the internal solitary wave in step 4 is The calculation formula is as follows:

[0028] ;

[0029] Where, represents the first-order amplitude of the internal solitary wave; SSHA is the sea surface height anomaly data obtained due to internal solitary wave disturbance; g is the gravitational acceleration; z is the depth integration variable; H is the water depth, which is provided by the gridded water depth dataset of the global ocean bathymetry dataset; is the floating frequency at depth z, calculated from the water density profile provided by the WOA2023 monthly average grid layered data; is the vertical mode function at depth z, which is solved according to the homogeneous eigenvalue problem and needs to be standardized to maximize =1; the following formula is the solution formula:

[0030] ;

[0031] ;

[0032] Where, is the linear phase velocity, Indicates that the vertical mode function at the sea surface and seabed is 0.

[0033] In the above scheme, in step 5, the nonlinear term is calculated as follows:

[0034] ;

[0035] ;

[0036] Where, is the nonlinear coefficient in the continuous hierarchical model, and its calculation formula is as follows:

[0037] ;

[0038] Where, Indicates that the nonlinear value at the sea surface and seabed is 0;

[0039] For nonlinear terms To perform standardization:

[0040] ;

[0041] in, is a nonlinear term; represents the nonlinear term after normalization;

[0042] C is an undetermined constant and needs to be used This condition determines To make The corresponding depth;

[0043] Corrected nonlinear vertical mode function for:

[0044] .

[0045] In the above scheme, in step 5, the high-order amplitude of the internal solitary wave The inversion formula is as follows:

[0046] ;

[0047] Where, SSHA is the sea surface height anomaly data obtained due to internal solitary wave disturbance; g is the gravitational acceleration; z is the depth integration variable; H is the water depth, which is provided by the gridded water depth dataset of the global ocean bathymetry dataset; Indicates depth The floating frequency at represents the modified nonlinear vertical mode function at depth z.

[0048] Through the above technical solution, the internal solitary wave amplitude inversion method based on SWOT observation data provided by the present invention has the following beneficial effects:

[0049] 1. Optimization preprocessing method based on SWOT observation data

[0050] The present invention uses unedited sea surface height anomaly data of the unsmoothed variant of SWOT KaRIn L3 and filters the raw observation data according to specific Flag tags (Flag 20, 50, 70, 100, 101, and 102) to remove abnormal pixels including those caused by land areas, sea ice effects, swath edge artifacts, spacecraft event interference, and polar errors. At the same time, a global threshold is introduced to remove abnormal extreme values, thereby improving the quality of the raw data for internal solitary wave information extraction.

[0051] 2. Efficient extraction algorithm for internal solitary wave disturbance information

[0052] The proposed internal solitary wave information extraction algorithm utilizes the global sea surface height anomaly reanalysis product provided by the Copernicus Ocean Service to eliminate large-scale background variations and effectively isolate internal solitary wave signals. Furthermore, adaptive noise filtering (including global histogram-based upper and lower truncation and 3×3 window mean filtering) and a maximum inter-class variance dual-scale segmentation method are used to enhance the internal solitary wave streak characteristics. Combined with Sobel morphological edge detection and connected domain analysis, small pixels with non-volatility are removed, significantly improving the integrity and accuracy of internal solitary wave disturbance extraction.

[0053] 3. High-precision nonlinear inversion model for large-amplitude internal solitary waves

[0054] This paper constructs a nonlinear amplitude inversion method suitable for large-amplitude internal solitary waves. The first-order amplitude of the internal solitary wave is calculated based on sea surface height anomaly data extracted using SWOT. The nonlinear term T(z) in the extended KdV equation is further introduced to obtain a vertical modal function that accounts for nonlinear effects. This results in a strongly nonlinear internal solitary wave amplitude inversion model, enabling high-precision inversion of the internal solitary wave amplitude. The inversion process combines the WOA2023 ocean stratification data with the depth data of the Global Ocean Bathymetry Dataset, demonstrating excellent environmental adaptability and parameter versatility, enabling high-precision inversion of large-amplitude internal solitary waves in different regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments or the prior art.

[0056] Figure 1 This is a flow chart of a method for inverting internal solitary wave amplitude based on SWOT observation data disclosed in the present invention;

[0057] Figure 2 It is the unsmoothed and unedited raw sea surface height anomaly data of SWOT KaRIn L3 level;

[0058] Figure 3 is the pre-processed sea surface height anomaly data;

[0059] Figure 4 The internal solitary wave fringe feature map is obtained based on enhancement processing and edge detection;

[0060] Figure 5 Detailed illustration of the SWOT internal solitary wave feature extraction results in the western Indian Ocean region according to an embodiment of the present invention, wherein (a) is a sea surface backscatter coefficient (NRCS) image of the western Indian Ocean region acquired by the SWOT satellite; (b) is the sea surface height anomaly of the solitary wave disturbance in the western Indian Ocean extracted from the SWOT sea surface height anomaly data after processing by the method of the present invention;

[0061] Figure 6 Detailed illustration of the SWOT internal solitary wave feature extraction results in the Andaman Sea region according to an embodiment of the present invention. In the figure, (a) is the surface backscatter coefficient (NRCS) image of the Andaman Sea region acquired by the SWOT satellite; (b) is the sea surface height anomaly of the Andaman Sea internal solitary wave disturbance extracted from the SWOT sea surface height anomaly data after being processed by the method of the present invention. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0063] The present invention provides an internal solitary wave amplitude inversion method based on SWOT observation data, such as Figure 1 As shown, the following steps are included:

[0064] Step 1: Obtain the L3 sea surface height anomaly data from the SWOT satellite Ka-band radar interferometer, and use the quality identification and threshold screening method to remove abnormal pixels and large-scale background fields.

[0065] The unedited sea surface height anomaly data contained in the unsmoothed variant of the SWOT satellite Ka-band radar interferometer (KaRIn) L3 (Level-3) sea surface height anomaly data is selected as the basic data source for extracting internal solitary wave disturbance information, such as Figure 2 shown.

[0066] The acquired data is processed as follows:

[0067] Step 1.1: Based on the quality identifiers (Flags) provided in the L3 unsmoothed variant of the SWOT satellite Ka-band radar interferometer, the unedited sea surface height anomaly data are quality-labeled. The labeling rules used include: selecting Flag 102 to remove pixels with default value errors; selecting Flag 101 to remove pixels in land areas; selecting Flag 100 to remove pixels at the edge of the swath; selecting Flag 70 to remove pixels affected by spacecraft events; selecting Flag 50 to remove pixels with errors in coastal and polar regions; and selecting Flag 20 to remove pixels affected by sea ice. Through the above labeling process, potentially low-quality or anomalous data are removed.

[0068] Step 1.2: After the quality marking process in step 1.1, the abnormal sea surface height data is subjected to a threshold screening method to remove abnormal pixels. The specific method is as follows: the average value of the global abnormal sea surface height data is calculated, and the reasonable data value range is set to ±50 cm. Pixels outside this range are judged as abnormal pixels and are removed.

[0069] Step 1.3, remove large-scale background fields: Download the global gridded sea surface height anomaly data with a spatial resolution of 1 / 8° and a temporal resolution of 1 day provided by the Copernicus Marine Service (CMS) as background field data; perform pixel-by-pixel subtraction between the observation data after removing abnormal pixels obtained in step 1.2 and the background field data to obtain the sea surface height anomaly data with large-scale background changes removed, as shown in the figure. Figure 3 As shown, the background noise is effectively suppressed.

[0070] In step 2, the data obtained in step 1 are subjected to adaptive noise filtering. The maximum inter-class variance method (Otsu method) is then used to enhance the stripe features in the sea surface height anomaly data. The enhanced data are then subjected to connectivity analysis to remove small-scale noise areas not caused by internal solitary wave disturbances.

[0071] The specific method is as follows:

[0072] Step 2.1, adaptive noise filtering: Calculate the global histogram of the sea surface height anomaly data and remove the anomaly data below the 20th percentile and above the 99.9th percentile. Based on this, perform mean filtering on the global data using a 3×3 window to further smooth the local noise.

[0073] Step 2.2: The maximum inter-class variance method is used to enhance the internal solitary wave fringe features of the noise-filtered data: First, a 50×50 pixel sliding window is used to perform local adaptive Otsu segmentation; second, an overall Otsu segmentation is performed on the global data to improve the recognition of the internal solitary wave fringe features;

[0074] Step 2.3: Perform connectivity analysis on the data after feature enhancement in step 2.2, calculate the number of pixels in the connected area, and remove areas with less than 500 connected pixels to remove small-scale noise areas not disturbed by internal solitary waves and highlight the internal solitary wave stripe features, such as Figure 4 As shown, the abnormal changes in sea surface height caused by internal solitary wave disturbances are clearly demonstrated.

[0075] Step 3: Perform morphological edge detection on the data obtained in step 1 using the Sobel operator.

[0076] The specific method is as follows:

[0077] Step 3.1: Use a 3×3 window to calculate the Sobel operator in the x-direction and y-direction respectively;

[0078] Step 3.2, modulo the calculation results of the Sobel operator in the x-direction and y-direction;

[0079] Step 3.3: Calculate the global histogram of the Sobel operator modulus and remove data points below the 60% quantile as non-edge pixels.

[0080] In step 3.4, a 3×3 window mean filter is applied to the remaining data to further smooth the edge features.

[0081] In step 4, the pixels retained after processing in steps 2 and 3 are overlapped and analyzed, and the pixels judged as valid in both steps are retained as the sea surface height anomaly data of internal solitary wave disturbance. This data is used as the height change caused by the internal solitary wave on the sea surface to invert the first-order amplitude of the internal solitary wave.

[0082] First-order amplitude of internal solitary wave The calculation formula is as follows:

[0083] ;

[0084] Where, represents the first-order amplitude of the internal solitary wave; SSHA is the extracted sea surface height anomaly data of internal solitary wave disturbance; g is the gravitational acceleration; z is the depth-integrated variable; H is the water depth, provided by the gridded bathymetric data set of the General Bathymetric Chart of the Oceans (GEBCO); is the floating frequency at depth z, calculated from the water density profile provided by the WOA2023 monthly average grid layered data; is the vertical mode function at depth z, which is solved according to the homogeneous eigenvalue problem (Taylor-Goldstein equation) and needs to be normalized to maximize =1; the following formula is the solution formula:

[0085] ;

[0086] ;

[0087] Where, is the linear phase velocity, Indicates that the vertical mode function at the sea surface and seabed is 0.

[0088] Step 5: Based on the first-order amplitude of the internal solitary wave obtained by inversion, the nonlinear term in the extended KdV (Korteweg-deVries) equation is introduced to perform nonlinear correction on the vertical modal function to obtain the corrected nonlinear vertical modal function. The corrected nonlinear vertical modal function is used to invert the high-order amplitude of the internal solitary wave.

[0089] Nonlinear terms is calculated as follows:

[0090] ;

[0091] ;

[0092] Where, is the nonlinear coefficient in the continuous hierarchical model, and its calculation formula is as follows:

[0093] ;

[0094] Where, Indicates that the nonlinear value at the sea surface and seabed is 0;

[0095] For nonlinear terms To perform standardization:

[0096] ;

[0097] in, is a nonlinear term; represents the nonlinear term after normalization;

[0098] C is an undetermined constant and needs to be used This condition determines To make The corresponding depth;

[0099] Corrected nonlinear vertical mode function for:

[0100] .

[0101] Internal solitary wave high-order amplitude The inversion formula is as follows:

[0102] ;

[0103] Where, SSHA is the extracted sea surface height anomaly data of internal solitary wave disturbance; g is the gravitational acceleration; z is the depth integration variable; H is the water depth, which is provided by the gridded water depth dataset of the global ocean bathymetry dataset; Indicates depth The floating frequency at represents the modified nonlinear vertical mode function at depth z.

[0104] Figure 5 (a) is the NRCS image of the western Indian Ocean region acquired by the SWOT satellite; Figure 5 Middle (b) is the sea surface height anomaly caused by solitary wave disturbance in the western Indian Ocean extracted from the SWOT sea surface height anomaly data after being processed by the method of the present invention. Figure 6 (a) is the surface backscatter coefficient (NRCS) image of the Andaman Sea region acquired by the SWOT satellite; Figure 6 Figure (b) shows the Andaman Sea internal solitary wave disturbance sea surface height anomaly extracted from the SWOT sea surface height anomaly data after processing using the method of the present invention. It can be seen that the method of the present invention can accurately extract the sea surface height anomaly of internal solitary wave disturbances.

[0105] The method for extracting and inverting internal solitary wave information based on SWOT satellite observation data proposed in the present invention fully utilizes the high spatial resolution and wide-swath sea surface height anomaly data provided by the SWOT satellite, and combines it with the reanalysis of ocean gridded data to effectively suppress the interference of ocean background noise on the extraction of internal solitary wave disturbance characteristics, and significantly improves the extraction accuracy and integrity of internal solitary wave disturbance characteristics. At the same time, the large-amplitude internal solitary wave amplitude inversion model established can fully consider nonlinear characteristics and achieve high-precision inversion of internal solitary wave amplitudes. This method provides a reliable technical means for dynamic monitoring of the marine environment, early warning of internal solitary wave disasters, and assessment of marine engineering safety risks, and has good application prospects and promotion value.

[0106] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for inverting internal solitary wave amplitude based on SWOT observation data, characterized in that: The steps include: Step 1: Obtain L3 sea surface height anomaly data from the SWOT satellite Ka-band radar interferometer, and use quality identification and threshold screening methods to remove abnormal pixels and large-scale background fields; Step 2: Adaptively filter the data obtained in step 1 to remove the small-scale noise areas caused by non-inner solitary wave disturbances. Then, the maximum inter-class variance method is used to enhance the stripe features in the sea surface height anomaly data. The enhanced data is then subjected to connectivity analysis. Step 3, using the Sobel operator to perform morphological edge detection on the data obtained in step 1; Step 4: Perform overlapping analysis on the pixels retained after processing in steps 2 and 3, and retain the pixels that are determined to be valid in both steps as the sea surface height anomaly data of internal solitary wave disturbance; use this data as the height change caused by the internal solitary wave on the sea surface to invert the first-order amplitude of the internal solitary wave; Step 5: Based on the first-order amplitude of the internal solitary wave obtained by inversion, the nonlinear term in the extended KdV equation is introduced to perform nonlinear correction on the vertical modal function to obtain the corrected nonlinear vertical modal function; the corrected nonlinear vertical modal function is used to invert the high-order amplitude of the internal solitary wave.

2. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 1 is characterized in that: In step 1, the unedited sea surface height anomaly data contained in the unsmoothed variant of the SWOT satellite Ka-band radar interferometer L3 sea surface height anomaly data is selected as the basic data source for extracting internal solitary wave disturbance information.

3. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 2 is characterized in that: Step 1 specifically includes the following processing steps: Step 1.1, based on the quality identifier provided in the L3 unsmoothed variant of the SWOT satellite Ka-band radar interferometer, the obtained unedited sea surface height anomaly data is quality-marked; The identification rules used include: selecting Flag102 to remove default value error pixels; selecting Flag101 to remove land area pixels; selecting Flag100 to remove swath edge artifact pixels; selecting Flag70 to remove spacecraft event-affected pixels; selecting Flag50 to remove coastal and polar error pixels; selecting Flag20 to remove sea ice-affected pixels. Through the above identification processing, potential low-quality or abnormal data are removed. Step 1.2: After the quality marking process in step 1.1, the abnormal sea surface height data is subjected to a threshold screening method to remove abnormal pixels. The specific method is as follows: the average value of the global abnormal sea surface height data is calculated, and the reasonable data value range is set to ±50 cm. Pixels outside this range are judged as abnormal pixels and are removed. In step 1.3, download the global gridded sea surface height anomaly data with a spatial resolution of 1 / 8° and a temporal resolution of 1 day provided by the Copernicus Marine Service as background field data; perform pixel-by-pixel subtraction between the observation data after removing abnormal pixels obtained in step 1.2 and the background field data to obtain sea surface height anomaly data with large-scale background changes removed.

4. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 1 is characterized in that: The specific method of step 2 is as follows: Step 2.1, adaptive noise filtering: Calculate the global histogram of the sea surface height anomaly data and remove the anomaly data below the 20th percentile and above the 99.9th percentile. Based on this, perform mean filtering on the global data using a 3×3 window to further smooth the local noise. Step 2.2: The maximum inter-class variance method is used to enhance the internal solitary wave fringe features of the noise-filtered data: First, a 50×50 pixel sliding window is used to perform local adaptive Otsu segmentation; second, an overall Otsu segmentation is performed on the global data to improve the recognition of the internal solitary wave fringe features; In step 2.3, connectivity analysis is performed on the data after feature enhancement in step 2.

2. The number of pixels in the connected area is calculated, and the area with less than 500 connected pixels is eliminated to remove the small-scale noise area not disturbed by the internal solitary wave and highlight the internal solitary wave stripe characteristics.

5. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 1 is characterized in that: The specific method of step 3 is as follows: Step 3.1: Use a 3×3 window to calculate the Sobel operator in the x-direction and y-direction respectively; Step 3.2, modulo the calculation results of the Sobel operator in the x-direction and y-direction; Step 3.3: Calculate the global histogram of the Sobel operator modulus and remove data points below the 60% quantile as non-edge pixels. In step 3.4, a 3×3 window mean filter is applied to the remaining data to further smooth the edge features.

6. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 1, characterized in that: The first-order amplitude of the internal solitary wave in step 4 The calculation formula is as follows: ； Where, represents the first-order amplitude of the internal solitary wave; SSHA is the sea surface height anomaly data obtained due to internal solitary wave disturbance; g is the gravitational acceleration; z is the depth integration variable; H is the water depth, which is provided by the gridded water depth dataset of the global ocean bathymetry dataset; is the floating frequency at depth z, calculated from the water density profile provided by the WOA2023 monthly average grid layered data; is the vertical mode function at depth z, which is solved according to the homogeneous eigenvalue problem and needs to be standardized to maximize =1; the following formula is the solution formula: ； ； Where, is the linear phase velocity, Indicates that the vertical mode function at the sea surface and seabed is 0.

7. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 6, characterized in that: In step 5, the nonlinear term is calculated as follows: ； ； Where, is the nonlinear coefficient in the continuous hierarchical model, and its calculation formula is as follows: ； Where, Indicates that the nonlinear value at the sea surface and seabed is 0; For nonlinear terms To perform standardization: ； in, is a nonlinear term; represents the nonlinear term after normalization; C is an undetermined constant and needs to be used This condition determines To make The corresponding depth; Corrected nonlinear vertical mode function for: 。 8. The internal solitary wave amplitude inversion method based on SWOT observation data according to claim 1, characterized in that: In step 5, the high-order amplitude of the internal solitary wave The inversion formula is as follows: ； Where, SSHA is the sea surface height anomaly data obtained due to internal solitary wave disturbance; g is the gravitational acceleration; z is the depth integration variable; H is the water depth, which is provided by the gridded water depth dataset of the global ocean bathymetry dataset; Indicates depth The floating frequency at represents the modified nonlinear vertical mode function at depth z.

Images