A method for predicting internal waves in the ocean based on satellite remote sensing data

Abstract

The application discloses a kind of ocean internal wave prediction methods based on satellite remote sensing data, it is first obtained the multi-source satellite remote sensing image of target sea area, establishes multi-source satellite remote sensing internal wave peak line data set;Then construct internal wave numerical model, in the calculation domain range of each two-dimensional section, internal wave numerical model is used to carry out internal wave numerical simulation calculation, and then internal wave generation statistical data set is obtained, finally construct internal wave generation statistical model, and obtain initial internal wave peak line.On this basis, the internal wave peak line in remote sensing image is matched with initial internal wave peak line, and then the corresponding initial peak line information and initial arrival time field and at N two-dimensional section generation time of generation source in Luzon Strait are obtained, finally construct internal wave initial arrival time error statistical model, correct initial arrival time field, to obtain the corrected arrival time field, to construct internal wave propagation model, realize the prediction of internal wave peak line.

Description

Technical Field

[0001] This invention belongs to the field of internal wave prediction technology, specifically relating to a method for predicting ocean internal waves based on satellite remote sensing data. Background Technology

[0002] Internal ocean waves are small- to medium-scale wave phenomena occurring in stable density-stratified seawater, widely distributed across global oceans. Their generation mechanism primarily stems from the interaction between barotropic currents and seabed topography, which excites the stable stratified seawater to generate internal waves. The maximum amplitude of internal ocean waves occurs within the ocean interior, and their wave frequencies lie between buoyancy and inertial frequencies, with their restoring force mainly being reduced gravity. However, since the reduced gravity generated by the density difference in stratified seawater is only on the order of one-thousandth of gravity, the amplitude of internal ocean waves is much larger than that of ocean waves, but their impact on sea surface undulation is negligible. Furthermore, internal ocean waves have significant impacts on vertical mixing in the upper ocean, nutrient transport, marine engineering, and underwater navigation; therefore, research on prediction techniques for internal ocean waves has significant scientific value and practical implications.

[0003] The development of internal wave prediction technology has always been an important topic in the field of marine science. Among the existing marine internal wave prediction technologies, Jackson (2009) established an internal wave propagation model based on empirical formulas. This model obtains the internal wave arrival time field by establishing a functional relationship between internal wave propagation velocity and seawater depth, thereby realizing internal wave propagation prediction. However, in the process of internal wave propagation, since only the single influencing factor of water depth is considered, while other factors such as seawater stratification, internal wave amplitude, and background current field are ignored, the arrival time error predicted by the model gradually accumulates with the increase of propagation time. Zhang and Li (2022) proposed an internal wave prediction method based on machine learning. This method can effectively obtain the internal wave propagation velocity field and realize internal wave prediction by training a large number of remote sensing data pairs. However, there is a significant technical drawback: this method must rely on remote sensing data to provide the initial crest line information of the internal wave, which may bring many limitations in practical applications. Gong et al. (2023) proposed a marine internal wave prediction method based on the three-dimensional MITgcm numerical model. However, due to the high computational complexity and large computational resource consumption of this method, it suffers from low computational efficiency in long-term internal wave prediction applications, making it difficult to achieve operational use. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting ocean internal waves based on satellite remote sensing data.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] A method for predicting ocean internal waves based on satellite remote sensing data, specifically including steps (1) to (6).

[0007] (1) Input the internal wave generation date into the A-wave generation statistical model, and output the A-wave on the first to N two-dimensional cross sections, respectively, from the source, the eastern ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. and the corresponding maximum eastward tidal current. The maximum eastward tidal current corresponds to the tidal range. And solve them separately. and The average value is obtained. and .

[0008] Input the internal wave generation date into the B-wave generation statistical model, and output the B-wave on the first to N two-dimensional cross sections, respectively, from the source, the western ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. And the corresponding maximum eastward tidal current value was obtained. The maximum eastward tidal current corresponds to the tidal range. The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak And the tidal range corresponding to the weak wave peak And solve them separately. , , and The average value is obtained. , , and .

[0009] (2) Based on the time difference of A wave arriving at the western boundary of the generation area of ​​the first to N two-dimensional cross sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the region where the A-wave is generated, and use this average internal wave propagation velocity to determine the time difference in which the A-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the A-wave, and the formation time of the initial crest line of the A-wave is determined. .

[0010] Based on the time difference of B-wave arrival at the western boundary of the region generating the first to N two-dimensional cross-sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the B-wave generation region, and use this average internal wave propagation velocity to determine the time difference in which the B-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the B-wave, and the formation time of the initial crest line of the B-wave is determined. .

[0011] (3) Using the internal wave propagation velocity-water depth function relationship, calculate the latitude and longitude coordinates of the i-th row and j-th column of the target sea area. speed of propagation The propagation speed corresponding to all latitude and longitude coordinates in the target sea area The set of values ​​represents the velocity field within the internal wave propagation region. The internal wave propagation velocity-water depth function relationship is: .

[0012] in, Indicates the internal wave at latitude and longitude coordinates. The speed of propagation at that location; Represents latitude and longitude coordinates Water depth at the location; parameters =2.971 m / s; B1=0.003; B2=1390.758 m.

[0013] (4) For the initial wave crest line of wave A determined in step (2), propagate within the target sea area using the velocity field calculated in step (3), and use the fast travel algorithm to solve the equation to obtain the coordinate point of the i-th row and j-th column of the initial wave crest line of wave A within the target sea area. earliest time .

[0014] For the initial crest line of the B wave determined in step (2), it propagates within the target sea area using the velocity field calculated in step (3). The fast travel algorithm is used to solve the equation of the equation to obtain the coordinate point of the i-th row and j-th column of the initial crest line of the B wave within the target sea area. earliest time .

[0015] Simultaneously obtain the coordinates of the i-th row and j-th column point within the target sea area. The corresponding maximum buoyancy frequency , depth of the mezzanine Seabed topography height .

[0016] (5) Input the statistical model of A-wave arrival time error, output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the A wave.

[0017] Will Input the B-wave arrival time error statistical model, output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the B wave.

[0018] (6) Based on the corrected arrival time field of the initial peak line of wave A and the corrected arrival time field of the initial peak line of wave B, calculate the arrival position of the initial peak line of wave A and the initial peak line of wave B in step (2) under a given propagation time, or the arrival time of a given position, so as to realize the prediction of the internal wave peak line.

[0019] The internal waves are A-waves and B-waves, and the target sea area has a latitude and longitude range of 114°E to 123°E and 19°N to 23°N.

[0020] Specifically, the methods for constructing the statistical models for A-wave generation and B-wave generation include S1 to S4.

[0021] S1. Acquire multi-source satellite remote sensing images of the target sea area and establish a multi-source satellite remote sensing internal wave peak line dataset.

[0022] S2. In the target sea area, based on the spatial distribution characteristics of the internal wave crest line in the remote sensing image and the location of the underwater mooring observation point in the target sea area, select N two-dimensional cross sections, N≥3. Each two-dimensional cross section represents a two-dimensional numerical simulation calculation domain. On each two-dimensional cross section, the two-dimensional MITgcm numerical model is used to construct the internal wave numerical model for internal wave numerical simulation calculation.

[0023] S3. Based on the numerical simulation results of the internal waves, determine the generation location, generation time, and generation range of the internal waves, using the time of the maximum eastward tidal current in the barotropic tidal current time series diagram at the generation source. This indicates the generation time of the internal wave at the source.

[0024] S4. Construct a statistical model for internal wave generation, specifically including steps S401 to S403.

[0025] S401. Within the computational domain of each two-dimensional section, the internal wave numerical model constructed in step S2 shall be subjected to internal wave numerical simulation calculations for no less than two years.

[0026] S402. Based on the numerical simulation results, for wave A, in the first two-dimensional cross section, based on the Hovmöller diagram of this two-dimensional cross section within a certain time period, and using the Hovmöller diagram, extract the maximum value of the eastward tidal current on the eastern ridge. , Corresponding tidal range And A wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seabed topography in the source region Similarly, extract the corresponding second two-dimensional cross-section within this time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. .

[0027]

[0028] For wave B, the Hovmöller plot for a certain time period is obtained in the first two-dimensional section, and the maximum eastward tidal current value of the western ridge is extracted using the Hovmöller plot. , Corresponding tidal range B wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. East Mountain Ridge Positive Pressure Tidal Wave Weak Peak , Corresponding tidal range Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seabed topography in the source region Similarly, extract the corresponding second two-dimensional cross-section within this time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. .

[0029] .

[0030] S403, Multiple matrices for different time periods A statistical data set on A-wave generation is constructed, and then input into an MLP feedforward artificial neural network to build a statistical model for A-wave generation. The input to the statistical model for A-wave generation is... The output is .

[0031] Multiple matrices for different time periods A statistical data set of B-wave generation is constructed. This statistical data set of B-wave generation is then input into an MLP feedforward artificial neural network to construct a statistical model of B-wave generation. The input to the statistical model of B-wave generation is... The output is .

[0032] Specifically, the method for constructing the statistical model of the arrival time error of wave A or wave B includes steps S6-S7.

[0033] S6. First, based on the generation date of a certain internal wave crest line in the remote sensing image, the A-wave generation statistical model, and the B-wave generation statistical model, determine k initial A-wave crest lines and k initial B-wave crest lines. Then, based on the internal wave propagation model of the initial arrival time field, determine k initial predicted internal wave crest lines for A-wave and k initial predicted internal wave crest lines for B-wave corresponding to the k initial A-wave crest lines and k initial predicted internal wave crest lines for A-wave. Finally, calculate the values ​​of the internal wave crest line and the k initial predicted internal wave crest lines for A-wave in the remote sensing image, respectively. The average distance between the line and k initial predicted internal wave crest lines of B-wave is used to determine the initial crest line corresponding to the initial predicted internal wave crest line with the smallest average distance. This initial crest line is the initial crest line corresponding to that internal wave crest line in the remote sensing image. The initial crest line information, the initial arrival time field, and the generation time of N two-dimensional sections at the generation source in the Luzon Strait are retained. The initial crest line information includes the initial crest line position, formation time, and internal wave type (A-wave or B-wave). The internal wave type is also the type of internal wave crest line in the remote sensing image. S6 includes steps S601 to S605.

[0034] S601. Based on the acquisition time of the remote sensing image, determine k possible generation dates for a certain internal wave crest line in the remote sensing image. For each generation date, apply the A-wave generation statistical model and the B-wave generation statistical model to obtain the time difference between the arrival of the internal wave at the western boundary of the generation area of ​​the first to N two-dimensional cross sections. Then, determine the average propagation velocity of the internal wave at the first to N two-dimensional cross sections within the generation area. Using the corresponding average propagation velocity of the internal wave, under a given time difference, determine the position of the internal wave after propagating through the corresponding given time difference to reach the first to N two-dimensional cross sections. Connect the positions reaching the first to N two-dimensional cross sections in sequence to obtain the initial crest line. Finally, obtain k initial A-wave crest lines and k initial B-wave crest lines corresponding to the k generation dates.

[0035] S602. Using the internal wave propagation velocity-water depth function relationship, calculate the latitude and longitude coordinates of the i-th row and j-th column point within the target sea area. speed of propagation The propagation speed corresponding to all latitude and longitude coordinates in the target sea area The set of is the velocity field within the region of internal wave propagation.

[0036] S603. For the k initial crest lines of A-waves and k initial crest lines of B-waves determined in step S601, propagate them within the target sea area using the velocity field calculated in step S602. Use the fast travel algorithm to solve the equation to obtain the coordinate point of the i-th row and j-th column of each initial crest line within the target sea area. earliest time And the initial wave crest line of wave B reaches the coordinate point in the i-th row and j-th column within the target sea area. earliest time The set of earliest arrival times for all coordinate points within the target sea area constitutes the initial arrival time field of the initial wave crest line. Based on the initial arrival time field, A-wave propagation models and B-wave propagation models are established, and the arrival positions of the corresponding initial wave crest lines at the remote sensing observation time are calculated, resulting in k initial predicted internal wave crest lines for A-waves and k initial predicted internal wave crest lines for B-waves.

[0037] S604. Calculate the distance between any initial predicted internal wave crest line and the same internal wave crest line in the remote sensing image. Select and retain only the initial predicted internal wave crest line with the smallest average distance. The initial crest line corresponding to the initial predicted internal wave crest line with the smallest average distance is the initial crest line corresponding to the same internal wave crest line in the remote sensing image.

[0038] S605. Repeat steps S601 to S604 until the initial crest lines corresponding to the internal wave crest lines in all acquired remote sensing images are obtained. After completion, the initial crest line information corresponding to the internal wave crest lines in the remote sensing images, the initial arrival time field, and the average values ​​of the eastward tidal current maximum value, the corresponding tidal range, the barotropic weak wave peak value, and the corresponding tidal range of the barotropic weak wave peak value at the N two-dimensional cross-sections at the source of the Luzon Strait are retained and recorded. The initial crest line information includes the initial crest line position, formation time, and internal wave type. The internal wave type is also the type of internal wave crest line in the remote sensing image.

[0039] If the internal wave crest line in the remote sensing image determined in step S604 is an A wave, then extract the generation times of the first to N two-dimensional sections of the internal wave crest line at the source location in the Luzon Strait. The corresponding maximum value of the eastward tidal current Tidal range and solve and The average value is obtained. and .

[0040] If the internal wave crest line in the remote sensing image determined in step S604 is a B wave, then extract the generation time of the internal wave crest line in the remote sensing image at the first to N two-dimensional sections at the generation source. The corresponding maximum value of the eastward tidal current Tidal range The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak extreme value and corresponding and solve , , and The average value is obtained. , , and .

[0041] S7. Construct a statistical model for the initial arrival time error of internal waves.

[0042] S7 specifically includes steps S701 to S703.

[0043] S701. From step S1, it can be seen that the internal wave crest line in the remote sensing image is composed of several spatial points. Assume the latitude and longitude coordinates of a certain spatial point on the internal wave crest line in the remote sensing image are... Determine latitude and longitude coordinates of the points in the initial arrival time field corresponding to the remote sensing image. Corresponding initial arrival time value )or Then calculate the latitude and longitude coordinates of that point. Initial arrival time error )or ). , .

[0044] In the formula, The acquisition time of the internal wave crest line in the remote sensing image. This refers to the initial peak formation time corresponding to the internal wave crest line in the remote sensing image. Simultaneously, the latitude and longitude coordinates are determined. The corresponding stratification parameter, buoyancy frequency maximum value , mezzanine depth and topographic parameters water depth .

[0045] S702. If step S6 determines that the internal wave crest line in the remote sensing image is an A wave, then each spatial point in the corresponding internal wave crest line of the remote sensing image will be... Corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along an A-wave crest line form a multidimensional array. Multiple A-wave crest lines result in multiple multidimensional arrays, which constitute the statistical data set of the A-wave initial arrival time error.

[0046] If step S6 determines that the internal wave crest line in the remote sensing image is a B wave, then each spatial point of the internal wave crest line in the remote sensing image is... The corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image , , and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along a B-wave crest line form a multidimensional array. Multiple B-wave crest lines result in multiple multidimensional arrays, which constitute the statistical data set of the initial arrival time error of the B-wave.

[0047] S703. Input the initial arrival time error statistics set of wave A into the MLP feedforward artificial neural network, using the initial arrival time error... Using the distribution pattern as the learning objective, a statistical model of A-wave arrival time error is constructed. When applied, for a given latitude and longitude coordinate point, the statistical model outputs the corresponding predicted initial arrival time error. .

[0048] The initial arrival time error statistics set of B-wave is input into the MLP feedforward artificial neural network to obtain the initial arrival time error. Using the distribution pattern as the learning objective, a statistical model of B-wave arrival time error is constructed. When applied, for a given latitude and longitude coordinate point, the statistical model outputs the corresponding predicted initial arrival time error. .

[0049] This invention first acquires multi-source satellite remote sensing images of the target sea area and establishes a multi-source satellite remote sensing internal wave crest line dataset. Then, it constructs an internal wave numerical model to determine the generation location, generation time, and generation range of internal waves. Within the computational domain of each two-dimensional cross-section, the internal wave numerical model is used to perform internal wave numerical simulation calculations for no less than two years, obtaining potential temperature data sets (referred to as potential temperature field data) and horizontal and vertical flow field data for N two-dimensional cross-sections over two years. This yields an internal wave generation statistical data set, and finally, an internal wave generation statistical model is constructed to obtain the initial internal wave crest line. Based on this, the internal wave crest line in the remote sensing image is matched with the initial internal wave crest line to obtain the corresponding initial crest line information, the initial arrival time field, and the generation time of N two-dimensional cross-sections at the generation source in the Luzon Strait. Finally, an internal wave initial arrival time error statistical model is constructed. This model is used to correct the initial arrival time field, obtaining the corrected arrival time field, thereby constructing an internal wave propagation model to predict the internal wave crest line.

[0050] Compared with the prior art, the present invention has the following advantages: (1) The statistical data set of internal wave generation covers the key parameters affecting internal wave generation, including barotropic tidal current parameters ( ), layering parameters ( , (1) The statistical model of internal wave generation ensures the accuracy of the output results of the established generation statistical model; (2) The generation statistical model uses the maximum time of the eastward current in the barotropic tidal time series diagram to represent the generation time of the internal wave, which simplifies the determination of the generation time in the prediction process of ocean internal waves; (3) The establishment of the internal wave generation statistical model can replace the calculation of complex numerical models. Under the condition that the generation date of the internal wave is known, the position of the initial wave crest line and the formation time of the internal wave can be obtained quickly and accurately, thereby solving the problem that the input of the initial wave crest line of the propagation model depends on remote sensing data; (4) In the existing propagation model, only the influence of seawater depth on the propagation speed of internal waves is considered, while the influence of other factors is ignored, which leads to the accumulation of the initial arrival time error as the propagation distance and propagation time increase. The establishment of the initial arrival time error statistical model aims to learn the distribution law of the initial arrival time error. It incorporates the factors affecting the propagation speed of internal waves into the input feature space of the model, including topographic parameters (H), stratification parameters (H), and topographic parameters (H). , Barotropic tidal parameters characterizing the influence of internal wave amplitude magnitude Geographical location parameters characterizing background flow field and mesoscale eddy influence. The initial arrival time parameter characterizing the propagation time effect. This allows the propagation model to follow the physical laws of wavefront propagation while significantly improving the accuracy of prediction through data-driven methods; (5) The internal wave prediction method described in this invention can automatically call the generation statistical model to form the initial wave crest line of the internal wave when the internal wave generation date is given at the generation source, and input the initial wave crest line into the propagation model to realize the prediction of the arrival time or arrival location of the internal wave crest line. This method has high computational efficiency and is convenient for business operation. Attached Figure Description

[0051] Figure 1 This diagram illustrates the internal wave generation time, the initial wave crest line predicted by the statistical model, the internal wave crest line predicted by the A-wave propagation model in the initial arrival time field (red curve), the internal wave crest line predicted by the A-wave propagation model in the corrected arrival time field (green curve), and the internal wave crest line observed by remote sensing (blue curve) involved in the ocean internal wave prediction process of this invention.

[0052] Figure 2 This is a comparison and verification diagram of the internal wave crest lines between the numerical model and the remote sensing image. Among them, (a) is the Envisat / ASAR remote sensing image imaged at 14:10:22 (UTC) on August 4, 2009; (b) is the time series diagram of the isotherm distribution at the intersection of the second two-dimensional section and the internal wave crest line A1 in the remote sensing image; (c) is the time series diagram of the isotherm distribution at the intersection of the second two-dimensional section and the internal wave crest line B1 in the remote sensing image; and (d) is the time series diagram of the isotherm distribution at the intersection of the second two-dimensional section and the internal wave crest line A2 in the remote sensing image. The white triangles point to the location of the internal wave in the numerical simulation results, and the white dashed lines represent the imaging time of the remote sensing image.

[0053] Figure 3 Hovmöller plot (a) plotted for potential temperature data of the second two-dimensional cross section depth, time series plot of east-west barotropic tidal current on the east ridge (b) and corresponding topographic profile of the second two-dimensional cross section (c).

[0054] Figure 4 Hovmöller plot (a) of potential temperature data for the second two-dimensional cross section depth, time series plot of east-west barotropic tidal current on the western ridge (b) and corresponding topographic profile of the second two-dimensional cross section (c).

[0055] Figure 5 This is a horizontal-vertical flow field distribution diagram, where u represents the horizontal velocity and w represents the vertical velocity.

[0056] Figure 6 This is a scatter plot of the test set results for the statistical model of the initial arrival time error of wave A.

[0057] Figure 7 This is a scatter plot of the test set results for the statistical model of the initial arrival time error of wave B.

[0058] Figure 8 This is a comparison diagram of the prediction results of the model described in this invention and remote sensing images.

[0059] Figure 9 This is a flowchart illustrating the prediction of an inner wave for a given generation date based on the A-wave generation statistical model and the A-wave arrival time error statistical model of this invention.

[0060] Figure 10 This is a flowchart illustrating the prediction of an inner wave for a given generation date based on the B-wave generation statistical model and the B-wave arrival time error statistical model of this invention. Detailed Implementation

[0061] The present invention will be further described below through specific embodiments.

[0062] Example 1

[0063] The ocean internal wave prediction method based on satellite remote sensing data involved in this embodiment specifically includes steps S1 to S8.

[0064] S1. Acquire multi-source satellite remote sensing images of the target sea area and establish a multi-source satellite remote sensing internal wave crest line dataset. The satellite remote sensing internal wave crest line dataset includes the latitude and longitude coordinates of the spatial points constituting each internal wave crest line and the acquisition time of each internal wave crest line. S1 specifically includes steps S101 to S102.

[0065] S101. The target sea area in this embodiment has a latitude and longitude range of 114°E to 123°E and 19°N to 23°N. In the target sea area, the interaction between the barotropic current and the submarine ridge (east and west ridges of the Luzon Strait) will generate disturbances, forming two different types of internal waves (baroclinic motion), A waves and B waves. The internal waves described in this invention are A waves and B waves. According to the observation data of the mooring, A waves have relatively large amplitudes and narrow waveforms, usually appearing as a significant leading wave followed by several solitons; B waves have relatively small amplitudes and wide waveforms, usually appearing as a single waveform. Ocean internal waves are a small-to-medium scale wave phenomenon occurring in stable density-stratified seawater. During their movement and propagation, they induce convergence / divergence effects in the sea surface current field, thereby modulating the sea surface roughness. This modulation effect causes ocean internal waves to appear as alternating bright and dark stripes in remote sensing images. This embodiment collects 200 multi-source satellite remote sensing images of the target sea area containing internal wave characteristic stripes. The multi-source refers to the data coming from multiple different independent or complementary satellite platforms, sensors or observation systems, such as at least two of ERS-1 / 2SAR, Envisat / ASAR, Radarsat-2 / SAR and GF-3 / SAR.

[0066] S102. The multi-source satellite remote sensing images are input into the remote sensing image processing platform (Envi). After geo-correction and radiometric correction, the crest lines of the internal wave characteristic fringes are extracted through the image enhancement and edge detection function modules. Simultaneously, the latitude and longitude coordinates of the spatial points of the internal wave crest lines and the acquisition time information are recorded to form a satellite remote sensing internal wave crest line dataset for the target sea area. This dataset includes the latitude and longitude coordinates of the spatial points constituting each internal wave crest line and the acquisition time of the internal wave crest line. The geo-correction process maps each pixel in the remote sensing image to its corresponding latitude and longitude coordinates.

[0067] S2. Construct the internal wave numerical model. S2 specifically includes steps S201 to S202.

[0068] S201. Constructing an internal wave numerical model: In the target sea area, based on the spatial distribution characteristics of the internal wave crest line in the remote sensing image and the location of the underwater mooring observation point in the target sea area, select N two-dimensional cross sections, N≥3. Each two-dimensional cross section represents a two-dimensional numerical simulation calculation domain. On each two-dimensional cross section, use the two-dimensional MITgcm numerical model to construct an internal wave numerical model for internal wave numerical simulation calculation, and output the potential temperature field data and horizontal and vertical flow field data for a certain period of time within the calculation domain.

[0069] This embodiment specifically selects three two-dimensional cross-sections, referred to as the first, second, and third two-dimensional cross-sections for ease of explanation. Each two-dimensional cross-section represents a two-dimensional numerical simulation computational domain, with the computational domains for all three cross-sections ranging from 116°E to 122.3°E. On each two-dimensional cross-section, a two-dimensional MITgcm numerical model is used to construct a numerical model for internal wave numerical simulation calculations. Specifically, the eastern boundary of the numerical model employs fixed boundary conditions, through which barotropic currents are introduced into the two-dimensional numerical simulation computational domain, outputting potential temperature field data as well as horizontal and vertical flow field data. The western boundary of the numerical model employs free boundary conditions. The numerical model adopts a homogeneous ocean stratification condition. Furthermore, to prevent internal wave reflection, a 50-kilometer-wide sponge layer is set at each of the eastern and western boundaries of the numerical model to absorb baroclinic energy.

[0070] S202. Verify the internal wave numerical model: Select some spatiotemporally representative satellite remote sensing internal wave data to verify the internal wave numerical model. Specifically, on each two-dimensional cross-section, use the potential temperature field data obtained in step S201 to draw isotherm distribution maps (e.g., ...). Figure 2 As shown in the figure, the numerical model constructed in step S201 was compared and verified with the internal wave crest line observed by remote sensing, confirming that the numerical model has high simulation accuracy.

[0071] Taking the second two-dimensional cross-section as an example, in this embodiment, the numerical models for A-waves and B-waves are validated. Statistical results show that in the deep-water area east of 118°E, the root mean square error of the arrival time of A-waves and B-waves is relatively small, at 0.77 h; while in the continental slope area west of 118°E, this error increases to 1.18 h due to factors such as topography. The results indicate that the numerical model maintains good consistency with remote sensing observation data, especially exhibiting high simulation accuracy in the deep-water area east of 118°E.

[0072] S3. Determine the generation location, generation time, and generation range of the internal wave. S3 specifically includes steps S301 to S302.

[0073] S301. Using the potential temperature data of each two-dimensional cross section at the corresponding depth of the mezzanine (the depth of the mezzanine refers to the depth at which the vertical temperature gradient of the ocean is greatest), draw a Hovmöller diagram, track the generation and propagation process of internal waves, and accurately identify their generation location and generation time at the generation source. Simultaneously, the time series diagram of the barotropic tidal flow at the source was obtained, and through comparative analysis, the moment of the maximum eastward tidal flow value in the time series diagram of the barotropic tidal flow at the source was determined. It can be used to represent the generation time of an internal wave at the source. .

[0074] For example, Figure 3 (a) in the figure is a Hovmöller plot plotted from the potential temperature data of the second two-dimensional cross-section at the depth of the stratum. Figure 3 (b) in the diagram is the time series diagram of the east-west barotropic tidal current on the East Ridge. Figure 3 (c) in the figure is the topographic profile of the second two-dimensional section. Figure 4 (a) in the figure is a Hovmöller plot plotted from the potential temperature data of the second two-dimensional cross-section at the depth of the stratum. Figure 4 (b) in the figure is the time series diagram of the east-west barotropic tidal current on the western ridge. Figure 4 (c) in the diagram represents the topographic profile of the second two-dimensional section. The barotropic tidal current time series diagram reveals a clear mixture of semi-diurnal and diurnal tidal components at the source. Two adjacent peaks of the semi-diurnal component overlap with the peaks and troughs of the diurnal component, respectively, resulting in a barotropic tidal current pattern based on the semi-diurnal cycle, alternating between strong and weak double peaks. Specifically, the peaks of the semi-diurnal and diurnal components superimpose to form a strong peak (corresponding to the maximum eastward tidal current value), while the peaks of the semi-diurnal and diurnal components superimpose to form a weak peak. The maximum eastward tidal current value is determined based on the barotropic tidal current time series diagram. The moment when the eastward tidal current reaches its maximum value. , Corresponding tidal range ( for (The difference between it and the previous barotropic trough), the moment of the maximum eastward tidal current. Previous barotropic tidal wave weak peak , Corresponding tidal range ( for (The difference between it and the previous barotropic trough).

[0075] Specifically, from Figure 3 (a) indicates that the A-wave was generated in the second two-dimensional section on August 4, 2009. Located on the eastern ridge, the time of its formation was ,from Figure 3 (b) in the equation determines that the maximum eastward tidal current along the eastern ridge of the Luzon Strait is... , correspond The corresponding time of the maximum eastward tidal current is .

[0076] from Figure 4 (a) indicates that the location of wave B generation in the second two-dimensional section on August 4, 2009 was [location missing]. Located on the western ridge, it was formed at the time of [date missing]. ,from Figure 4 (b) in the equation can determine the maximum value of the eastward tidal current along the western ridge. , correspond The corresponding time of the maximum eastward tidal current is .at the same time, The previous peak value of the weak wave of the positive pressure tidal current on the eastern ridge ,as well as Corresponding tidal range It can be determined that, such as Figure 3 As shown in (b) of the diagram.

[0077] Statistical results show that: and The average time deviation was 5.8 ± 9 minutes. and The average time deviation is 7.2 ± 8 minutes. The tidal cycle at the source is predominantly a semi-diurnal tide of 12.48 hours. Therefore, for both waves A and B, the time difference between their generation time and the moment when the eastward tidal current reaches its maximum value does not exceed 2% of the tidal cycle. Thus, the generation time of wave A is considered to be the moment when the eastward tidal current reaches its maximum value on the eastern ridge. The generation time of wave B coincides with the maximum value of the eastward tidal current along the western ridge. This allows for a more accurate and rapid determination of the internal wave generation time.

[0078] S302. Based on the generation location determined in step S301 and the fact that in the area east of 120.5°E, remote sensing images are difficult to capture obvious internal wave crest lines, thus the generation area range of internal waves can be determined.

[0079] In this embodiment, the A-wave generation regions in the three two-dimensional cross-sections are (120.5°E, 121.9°E), (120.5°E, 121.8°E), and (120.5°E, 121.8°E), respectively. The B-wave generation regions are (120°E, 120.85°E), (120°E, 120.8°E), and (120°E, 120.8°E), respectively.

[0080] S4. Construct a statistical model for internal wave generation. S4 specifically includes steps S401 to S403.

[0081] S401. Within the computational domain of each two-dimensional section, the internal wave numerical model constructed in step S201 is subjected to internal wave numerical simulation calculations for no less than two years to obtain a set of potential temperature data (referred to as potential temperature field data) and horizontal and vertical flow field data for N two-dimensional sections within two years.

[0082] S402. In order to ensure the accuracy of the output results of the established statistical model, key parameters affecting the generation of internal waves are used in the establishment process, including barotropic tidal current parameters, stratification parameters and topographic parameters.

[0083] Using the horizontal and vertical flow field data obtained in step S201, a horizontal-vertical flow field distribution map is plotted. Figure 5 Analysis revealed that the formation of wave B was related not only to the maximum eastward tidal current value on the western ridge but also to the strengthening effect of the weak wave peak in the first half of the diurnal tidal cycle on the eastern ridge. Specifically, from... Figure 5 The horizontal-vertical flow field distribution diagrams reveal that both the west and east ridges contribute to the generation of wave B. At t=14h, when the barotropic tidal current is at its weak peak, a significant downflow occurs on the east side of the east ridge. This wave gradually propagates to the east side of the west ridge at t=24h, reinforcing the downflow generated on the east side of the west ridge at the peak of the eastward tidal current, thus forming a distinct internal wave characteristic structure at t=31h. In other words, the horizontal flow field exhibits opposite directions between upper and lower layers, while the vertical flow field displays a strong alternation of downflow and upflow. Wave A, however, is only related to the peak of the eastward tidal current on the east ridge. Therefore, the statistical model for wave A generation uses the peak of the eastward tidal current on the east ridge and its corresponding tidal range as the barotropic tidal current parameters, while the statistical model for wave B generation uses the peak of the eastward tidal current on the west ridge and its corresponding tidal range, and the weak peak of the barotropic tidal current on the east ridge and its corresponding tidal range.

[0084] Specifically, for wave A, in the first two-dimensional cross section, the Hovmöller diagram for a certain time period of the two-dimensional cross section is obtained based on the numerical simulation results in step S401, and the maximum value of the eastward tidal current on the eastern ridge is extracted using the Hovmöller diagram. , Corresponding tidal range And A wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seafloor topography in the source region Similarly, the topographic parameters included in the data are extracted to obtain the corresponding data for the second two-dimensional cross-section within the same time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. .

[0085] .

[0086] Specifically, for wave B, in the first two-dimensional cross section, the Hovmöller diagram for a certain time period of the two-dimensional cross section is obtained based on the numerical simulation results in step S401, and the maximum value of the eastward tidal current on the western ridge is extracted using the Hovmöller diagram. , Corresponding tidal range B wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. East Mountain Ridge Positive Pressure Tidal Wave Weak Peak , Corresponding tidal range Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seafloor topography in the source region The terrain parameters, including those for the second two-dimensional section, are extracted similarly within this time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. .

[0087] .

[0088] S403, the multiple sets of matrices for different time periods A statistical data set on A-wave generation is constructed, and then input into an MLP feedforward artificial neural network to build a statistical model for A-wave generation. The input to the statistical model for A-wave generation is... The output is .

[0089] The matrices of multiple different time periods A statistical data set of B-wave generation is constructed. This statistical data set of B-wave generation is then input into an MLP feedforward artificial neural network to construct a statistical model of B-wave generation. The input to the statistical model of B-wave generation is... The output is .

[0090] Specifically, the statistical data sets generated by wave A and wave B are divided into training, validation, and test sets at a ratio of 60%, 20%, and 20%, respectively. The training set is used for adjusting model weights, the validation set is used for monitoring model overfitting and selecting the optimal network structure, and the test set is used to finally evaluate the model's generalization ability, with the root mean square error of the test set serving as an objective measure of the performance of the generative statistical model.

[0091] In this embodiment, statistical models for A-wave and B-wave generation are established using the method described above combined with a feedforward artificial neural network (MLP). The results show that the root mean square error (RMSE) of the A-wave generation statistical model test set is 0.23 hours, and the RMSE of the B-wave generation statistical model test set is 0.24 hours. Furthermore, the time difference between the A-wave generation source and the western boundary of the generation region at different two-dimensional cross-sections ranges from 12 hours to 16.8 hours, while the time difference between the B-wave generation source and the western boundary of the generation region at different two-dimensional cross-sections ranges from 7.2 hours to 12 hours.

[0092] Based on the root mean square error results of the test set, it is demonstrated that the generative statistical model can replace the MITgcm numerical model, and quickly and relatively accurately calculate the A wave at the first to Nth two-dimensional sections of the eastern ridge. After the time is generated, the time difference to the western boundary of the corresponding generation region is as follows: And B waves at the first to Nth two-dimensional sections of the western ridge respectively After the time is generated, the time difference to the western boundary of the corresponding generation region is as follows: .

[0093] S5. Determine the initial crest line position and formation time of the internal wave: Based on the time difference between the arrival of the internal wave at the western boundary of the generation area of ​​the first to N two-dimensional cross-sections, the average propagation velocity of the internal wave at the first to N two-dimensional cross-sections within the generation area can be accurately calculated. Using the corresponding average propagation velocity of the internal wave, given a time difference, the position of the internal wave reaching the first to N two-dimensional cross-sections after propagating through the corresponding given time difference can be determined. Connecting the positions reaching the first to N two-dimensional cross-sections sequentially yields the initial crest line, and the formation time of the initial crest line is determined.

[0094] like Figure 1 For wave A, based on the time difference of arrival at the western boundary of the region generated by the first to N two-dimensional cross-sections. The average propagation velocity of the virus in the first to N two-dimensional cross-sections within the generated region was calculated. . use At a given time difference At that time, calculations were performed separately. The position of reaching the first to N two-dimensional cross-sections (X) 1A Y 1A ), (X) 2A Y 2A ), (X) 3A Y 3A )……(X) NA Y NA ), These represent the time differences between the generation times of wave A in the first two-dimensional section and the generation times of the second to Nth two-dimensional sections, respectively. Let X be the time difference between the generation times of the A-wave in the first two-dimensional section and the second two-dimensional section, where '-' indicates phase lag and '+' indicates phase advance. 1A Y 1A ), (X) 2A Y 2A ), (X) 3A Y 3A )……(X) NA Y NA Connecting these points sequentially as the initial crest lines of the internal wave propagation model, the formation time of the initial crest lines is... Theoretically, wave A reaches (X) at the same time. 1A Y 1A ), (X) 2A Y 2A ), (X) 3A Y 3A )……(X) NA Y NA ), given (X) 1A Y 1A ), (X) 2A Y 2A), (X) 3A Y 3A )……(X) NA Y NA It needs to be within the region where the A wave is generated, therefore The minimum value within its range (12 hours to 16.8 hours) should be taken.

[0095] For B-waves, the time difference between the arrival of B-waves at the western boundary of the generation region of the first to N two-dimensional cross-sections is used. The average propagation velocity of the virus in the first to N two-dimensional cross-sections within the generated region was calculated. . use At a given time difference At that time, it can be calculated The position of reaching the first to N two-dimensional cross-sections (X) 1B Y 1B ), (X) 2B Y 2A ), (X) 3B Y 3B )……(X) NB Y NB ), These represent the time differences between the generation times of the B wave at the first two-dimensional section and the generation times at the second to Nth two-dimensional sections, respectively. Let X be the time difference between the generation times of the A-wave in the first two-dimensional section and the second two-dimensional section, where '-' indicates phase lag and '+' indicates phase advance. 1B Y 1B ), (X) 2B Y 2A ), (X) 3B Y 3B )……(X) NB Y NB ) Connect the positions of the initial wave crests, which serve as the initial wave propagation model, in sequence. The formation time of the initial wave crests is . Theoretically, wave B reaches (X) at the same time. 1B Y 1B ), (X) 2B Y 2A ), (X) 3B Y 3B )……(X) NB Y NB ), given (X) 1B Y 1B ), (X) 2B Y 2A ), (X) 3B Y 3B )……(X) NB Y NB It needs to be within the region where B-waves are generated, therefore The minimum value within its range (7.2 hours to 12 hours) should be taken.

[0096] Specifically, the A wave in the first two-dimensional section... Generate at the source at all times, and then use V 1A The average velocity propagates along the first two-dimensional cross-section to the western boundary of the generation region, over time... Later spread to (X) 1A Y 1A Similarly, the internal wave in the second two-dimensional section is at... Generate at the source at all times, and then use V 2A The average velocity propagates along the second two-dimensional cross-section to the western boundary of the generation region, over time... Later spread to (X) 2A Y 2A The internal wave at the third two-dimensional section is Generate at the source at all times, and then use V 3A The average velocity propagates along the third two-dimensional cross-section to the western boundary of the generation region, over time... Later spread to (X) 3A Y 3A And according to the result of step S4, The minimum value within its range should be taken, which is 12 hours. Similarly, The minimum value within its range should also be taken, which is 7.2 hours.

[0097] Based on the statistical model of internal wave generation, given the known generation date of the internal wave, the initial crest position and formation time of the internal wave can be determined. Specifically, taking the statistical model of A-wave generation as an example, by inputting the generation date (year, month, day) of the internal wave at the source, the A-wave generation statistical model automatically retrieves N two-dimensional cross-sections (taking three two-dimensional cross-sections as an example) from that generation date to generate barotropic tidal current time-series data at the eastern ridge of the source, as well as seawater stratification parameter data. Topographic parameters of the average height of the eastern ridge Based on the barotropic tidal current time series data at the East Ridge, the system automatically calculates and generates the maximum eastward tidal current time at each two-dimensional section of the East Ridge on the specified date. As the generation time of A wave within the generation date, the corresponding eastward tidal current maximum value of each two-dimensional section is extracted. and tidal range A matrix is ​​formed. This matrix is ​​then input into the A-wave generation statistical model to obtain the time difference between the A-wave's self-generation and the western boundary of the generation region at different two-dimensional cross-sections. Then, in step S5, based on the given time difference... The initial peak position and the initial peak formation time are obtained.

[0098] S6. First, based on the k possible generation dates of a certain internal wave crest line in the remote sensing image, the A-wave generation statistical model, and the B-wave generation statistical model, determine k initial A-wave crest lines and k initial B-wave crest lines; then, based on the internal wave propagation model of the initial arrival time field, determine the k initial predicted internal wave crest lines of A-wave and k initial predicted internal wave crest lines of B-wave corresponding to the k initial A-wave crest lines and k initial predicted internal wave crest lines of B-wave; finally, calculate the relationship between the internal wave crest line in the remote sensing image and the k initial predicted internal wave crest lines of A-wave. The average distance between the wave crest line and k initially predicted internal wave crest lines of B-wave is used to determine the initial wave crest line corresponding to the initial predicted internal wave crest line with the smallest average distance. This initial wave crest line is the initial wave crest line corresponding to that internal wave crest line in the remote sensing image. The initial wave crest line information, the initial arrival time field, and the generation time of N two-dimensional sections at the generation source in the Luzon Strait are retained. The initial wave crest line information includes the initial wave crest line position, formation time, and internal wave type (A-wave or B-wave). The internal wave type is also the type of internal wave crest line in the remote sensing image. S6 specifically includes steps S601 to S605.

[0099] S601. Based on the acquisition time of the remote sensing image, determine k possible generation dates of a certain internal wave crest line in the remote sensing image. For each generation date, apply the A-wave generation statistical model and the B-wave generation statistical model, as well as step S5, to obtain k initial A-wave crest lines and k initial B-wave crest lines corresponding to the k generation dates. Retain the initial crest line information and the corresponding generation date. The initial crest line information includes the initial crest line position, formation time, and internal wave type (A-wave or B-wave).

[0100] After forming in the generation region, the internal wave continues to propagate forward within the propagation region and is captured by the remote sensing image, thus becoming the internal wave crest line. Since the generation time of this internal wave crest line in the remote sensing image is unknown, it is assumed that it may have generated within 1 to k days before the remote sensing observation time. Therefore, k possible generation dates of the internal wave at the generation source can be determined, denoted as year, month, and day X. Using the statistical models for A-wave generation and B-wave generation respectively, and combining them with step S5, k possible initial crest lines of A-wave and k possible initial crest lines of B-wave are obtained. For example, after an internal wave is generated in the Luzon Strait region, it will gradually propagate westward until it dissipates. The entire evolution process takes about 4 days. Assuming that the satellite remote sensing image was acquired on July 6, 2024, and k is 4, then the possible generation dates of the internal wave are July 2, 2024, July 3, 2024, July 4, 2024, and July 5, 2024. Each possible generation date corresponds to two initial crest lines, namely an A-wave initial crest line and a B-wave initial crest line.

[0101] S602. Using the internal wave propagation velocity-depth function relationship proposed by Jackson (2009), calculate the latitude and longitude coordinates of the i-th row and j-th column point within the target sea area. speed of propagation , The value is the latitude range of the target sea area. The value is the longitude range of the target sea area. and as well as and The intervals between them can be determined as needed, such as 1° or (1 / 60)°. The propagation speeds corresponding to all latitude and longitude coordinates in the target sea area. The set of is the velocity field within the region of internal wave propagation.

[0102] The relationship between internal wave propagation velocity and water depth is: .

[0103] in, Indicates the internal wave at latitude and longitude coordinates. The speed of propagation at that location; Represents latitude and longitude coordinates Water depth at the location; parameters =2.971 m / s; B1=0.003; B2=1390.758 m.

[0104] S603. For the k initial crest lines of A-waves determined in step S601, propagate them within the target sea area using the velocity field calculated in step S602. Use the fast travel algorithm to solve the equation of the equation to obtain the coordinate point of the i-th row and j-th column of each initial crest line within the target sea area. earliest time The set of earliest arrival times for all coordinate points within the target sea area constitutes the initial arrival time field of the initial crest line of the A-wave. Based on the initial arrival time field of the initial crest line of the A-wave, the arrival position of the corresponding initial crest line at the remote sensing observation time is calculated, i.e., the initial predicted inner wave crest line of the A-wave. The initial predicted inner wave crest line of the A-wave is represented by contour lines of the time difference between the remote sensing observation time and the formation time of the initial crest line determined in step S601. This step yields k initial predicted inner wave crest lines of the A-wave.

[0105] For the k initial crest lines of B-waves determined in step S601, they are propagated within the target sea area using the velocity field calculated in step S602. The fast travel algorithm is used to solve the equation of the equation to obtain the coordinate point of the i-th row and j-th column of each initial crest line within the target sea area. earliest time The set of earliest arrival times for all coordinate points within the target sea area constitutes the initial arrival time field of the initial crest line of the B-wave. Based on the initial arrival time field of the initial crest line of the B-wave, the arrival position of the corresponding initial crest line at the remote sensing observation time is calculated, i.e., the initial predicted inner wave crest line of the B-wave. The initial predicted inner wave crest line of the B-wave is represented by contour lines of the time difference between the remote sensing observation time and the formation time of the initial crest line determined in step S601. This step yields k initial predicted inner wave crest lines of the B-wave.

[0106] The fast-moving algorithm solves the equation as follows: .

[0107] S604. Calculate the distance between any initial predicted internal wave crest line of A wave and initial predicted internal wave crest line of B wave and the corresponding internal wave crest line (actual internal wave crest line) in the remote sensing image. Select and retain only the initial predicted internal wave crest line with the smallest average distance. The initial crest line corresponding to the initial predicted internal wave crest line with the smallest average distance is the initial crest line corresponding to the corresponding internal wave crest line in the remote sensing image. Retain the initial crest line information, the initial arrival time field, and the generation time of N two-dimensional sections at the generation source in the Luzon Strait. The initial crest line information includes the initial crest line position, formation time, and internal wave type (A wave or B wave). The internal wave type is also the type of the internal wave crest line in the remote sensing image.

[0108] For example, if a satellite remote sensing image was acquired at 12:00:00 on July 6, 2024, and k is 4, then the possible generation dates of the internal wave are July 2, 2024, July 3, 2024, July 4, 2024, and July 5, 2024. Taking July 5, 2024 as an example, assuming that the initial peak line of the A wave corresponding to July 5, 2024 forms at 13:00:00 on July 5, 2024, the time difference between the generation at 12:00:00 on July 6, 2024 and 13:00:00 on July 5, 2024 is 25 hours. Connecting the latitude and longitude coordinates with an arrival time of 25 hours in the corresponding time field yields a contour line with a time difference of 25 hours, which is the initial predicted internal wave peak line. Calculate the distance between the initial predicted internal wave peak line and the internal wave peak line in the satellite remote sensing image (the actual internal wave peak line). Calculate the distance between the initial predicted internal wave crest line corresponding to the prediction generation dates of July 2, 2024, July 3, 2024, and July 4, 2024, and the distance between the initial predicted internal wave crest line and the corresponding internal wave crest line in the satellite remote sensing image, and select and retain only the initial predicted internal wave crest line with the smallest average distance.

[0109] S605. Repeat steps S601 to S604 until the initial crest lines corresponding to the internal wave crest lines in all acquired remote sensing images are obtained. After completion, the initial crest line information corresponding to the internal wave crest lines in the remote sensing images, the initial arrival time field, and the generation times of N two-dimensional sections at the source in the Luzon Strait must be retained and recorded. The average value of the eastward tidal current maximum, the tidal range corresponding to the eastward tidal current maximum, the peak value of the barotropic weak wave preceding the peak value of the eastward tidal current, and the average value of the tidal range corresponding to the peak value of the barotropic weak wave are determined from the generation times of each two-dimensional section.

[0110] If the internal wave crest line in the remote sensing image determined in step S604 is an A wave, then extract the generation time of the internal wave crest line in the remote sensing image obtained in step S605 at the first to N two-dimensional sections of the source in the Luzon Strait. The corresponding maximum value of the eastward tidal current Tidal range And solve them separately. and The average value is obtained. and .

[0111] If the internal wave crest line in the remote sensing image determined in step S604 is a B wave, then extract the generation time of the internal wave crest line in the remote sensing image at the first to N two-dimensional sections at the generation source. The corresponding maximum value of the eastward tidal current Tidal range The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak and corresponding And solve them separately. , , and The average value is obtained. , , and .

[0112] As explained above, the velocity field and initial arrival time field can be used to predict the internal wave crest line formed during remote sensing observation. However, due to the large error in the initial arrival time field, the prediction accuracy is low. Therefore, this application introduces an initial arrival time error statistical model to correct the initial arrival time field, thereby improving the prediction accuracy.

[0113] S7. Construct a statistical model for the initial arrival time error of the internal wave, specifically including steps S701 to S703.

[0114] S701. From step S1, it can be seen that the internal wave crest line in the remote sensing image is composed of several spatial points. Assume the latitude and longitude coordinates of a certain spatial point on the internal wave crest line in the remote sensing image are... Based on the initial arrival time field corresponding to the internal wave crest line in the remote sensing image, the latitude and longitude coordinates are determined. Corresponding initial arrival time value )or Then calculate the latitude and longitude coordinates of the point according to the following formula. Initial arrival time error )or ). , .

[0115] In the formula, The acquisition time of the internal wave crest line in the remote sensing image. This refers to the initial peak formation time corresponding to the internal wave crest line in the remote sensing image. Simultaneously, the latitude and longitude coordinates are determined. The corresponding stratification parameter, buoyancy frequency maximum value , mezzanine depth and topographic parameters water depth .

[0116] S702. If step S6 determines that the internal wave crest line in the remote sensing image is an A wave, then each spatial point in the corresponding internal wave crest line in the remote sensing image will be... Corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along an A-wave crest line form a multidimensional array. Multiple A-wave crest lines result in multiple multidimensional arrays, which constitute the statistical data set of the A-wave initial arrival time error.

[0117] If step S6 determines that the internal wave crest line in the remote sensing image is a B wave, then each spatial point of the internal wave crest line in the remote sensing image is... The corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image , , and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along a B-wave crest line form a multidimensional array. Multiple B-wave crest lines result in multiple multidimensional arrays, which constitute the statistical data set of the initial arrival time error of the B-wave.

[0118] S703. Input the initial arrival time error statistics set of wave A into the MLP feedforward artificial neural network, using the initial arrival time error... Using the distribution pattern of A-waves as the learning objective, a statistical model of A-wave arrival time error is constructed. During the construction process, the input to the statistical model of A-wave initial arrival error consists of multiple sets of data. The output is the corresponding In application, for a given latitude and longitude coordinate point, the statistical model for A-wave arrival time error outputs the corresponding predicted initial arrival time error. .

[0119] The initial arrival time error statistics set of B-wave is input into the MLP feedforward artificial neural network to obtain the initial arrival time error. Using the distribution pattern of the wave as the learning objective, a statistical model of the arrival time error of wave B is constructed. During the construction process, the initial arrival error statistical model of wave B is input with multiple sets of data. The output is the corresponding In application, for a given latitude and longitude coordinate point, the B-wave arrival time error statistical model outputs the corresponding predicted initial arrival time error. .

[0120] Specifically, the statistical data sets of the initial arrival time error of wave A and wave B are divided into training set, validation set, and test set according to the proportions of 60%, 20%, and 20%, respectively. The training set is used for model weight adjustment, the validation set is used for monitoring model overfitting and selecting the optimal network structure, and the test set is used to finally evaluate the generalization ability of the model. The root mean square error of the test set is used as an objective measure of the performance of the initial arrival time error model.

[0121] In this embodiment, the initial arrival time error statistical models for waves A and B are established by combining the above method with the MLP feedforward artificial neural network. Figure 6 and Figure 7 These are scatter plots drawn from the test set results of the statistical model for the initial arrival time error of A-waves and B-waves, respectively. The horizontal axis represents the latitude coordinates. True initial arrival time error or The vertical axis represents latitude and longitude coordinates. Predicted initial arrival time error or According to statistics, the root mean square error of the statistical model test set for the initial arrival time error of wave A is 1.80 hours, and the root mean square error of the statistical model test set for the initial arrival time error of wave B is 1.96 hours.

[0122] S8. Construct an internal wave propagation model based on the modified arrival time field. The internal wave propagation model specifically includes: for the latitude and longitude coordinates of the i-th row and j-th column within the target sea area... The initial arrival time value corresponding to a certain initial wave crest line is calculated based on steps S602 and S603. and The statistical model of the initial arrival time error of wave A and wave B, constructed based on step S7, can output coordinate points. Predicted initial arrival time error and Thus, the corrected arrival time is obtained. and , The set of corrected arrival times for all coordinate points within the target sea area constitutes the corrected arrival time field of the initial crest line of the internal wave. Based on this, A-wave propagation models and B-wave propagation models based on the corrected arrival time field can be constructed respectively. The corrected arrival time field of the internal wave propagation model allows for the prediction of the internal wave crest line. That is, given a propagation time, the arrival position of the internal wave crest line can be predicted by drawing propagation time contour lines; or, given the arrival position of the internal wave crest line, the arrival time of the internal wave crest line can be predicted by accessing the corrected arrival time value corresponding to that position.

[0123] For the test set partitioned in step S703, the distribution of the initial arrival time error and its statistical model predicted output value is as follows: Figure 6 As shown in the figure. For the test set data, statistical analysis shows that in the initial prediction, the root mean square error (RMSE) of the A-wave propagation model based on the initial arrival time field was 2.31 hours, and the RMSE of the B-wave propagation model based on the initial arrival time field was 2.81 hours. After the statistical model of initial arrival error learned the distribution pattern of the initial arrival error, the RMSE of the A-wave propagation model based on the modified arrival time field decreased to 1.80 hours, and the RMSE of the B-wave propagation model based on the modified arrival time field decreased to 1.96 hours. The former improved by 22%, and the latter by 30%. Considering both internal wave types, in the initial prediction, the RMSE of the internal wave propagation model based on the initial arrival time field was 2.48 hours. After the statistical model of initial arrival error learned the distribution pattern of the initial arrival error, the RMSE of the internal wave propagation model based on the modified arrival time field decreased to 1.85 hours, an overall improvement of 25%.

[0124] Figure 8 This is a remote sensing image acquired by the Envisat / ASAR satellite at 02:05:04 (UTC) on March 9, 2004. The black curve represents the prediction result of the model described in this invention at the time of the remote sensing observation. Figure 8As shown, the root mean square errors between the spatial locations and predicted locations on the A3, A4, and B2 wave crest lines are 3.40 km, 5.75 km, and 4.12 km, respectively. Comparative analysis of the predicted results and the inner wave crest lines in the remote sensing images indicates that the invention described in this application can accurately predict the arrival location of the inner wave crest lines, and exhibits good consistency with the remote sensing images in terms of the geometric morphology and distribution interval characteristics of the inner wave crest lines.

[0125] In summary, the statistical models for A-wave generation, B-wave generation, A-wave arrival time error, and B-wave arrival time error were constructed to predict the inner wave on a given generation date. The specific process is steps (1) to (6).

[0126] like Figure 9 and 10 As shown, (1) the internal wave generation date is input into the A-wave generation statistical model, and the A-wave is output on the first to N two-dimensional cross sections, respectively, from the source, the eastern ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. and the corresponding maximum eastward tidal current. The maximum eastward tidal current corresponds to the tidal range. And solve them separately. and The average value is obtained. and .

[0127] Input the internal wave generation date into the B-wave generation statistical model, and output the B-wave on the first to N two-dimensional cross sections, respectively, from the source, the western ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. And the corresponding maximum eastward tidal current value was obtained. The maximum eastward tidal current corresponds to the tidal range. The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak And the tidal range corresponding to the weak wave peak And solve them separately. , , and The average value is obtained. , , and .

[0128] (2) Based on the time difference of A wave arriving at the western boundary of the generation area of ​​the first to N two-dimensional cross sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the region where the A-wave is generated, and use this average internal wave propagation velocity to determine the time difference in which the A-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the A-wave, and the formation time of the initial crest line of the A-wave is determined. .

[0129] Based on the time difference of B-wave arrival at the western boundary of the region generating the first to N two-dimensional cross-sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the B-wave generation region, and use this average internal wave propagation velocity to determine the time difference in which the B-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the B-wave, and the formation time of the initial crest line of the B-wave is determined. .

[0130] (3) Using the internal wave propagation velocity-water depth function relationship, calculate the latitude and longitude coordinates of the i-th row and j-th column of the target sea area. speed of propagation The propagation speed corresponding to all latitude and longitude coordinates in the target sea area The set of values ​​represents the velocity field within the internal wave propagation region. The internal wave propagation velocity-water depth function relationship is: .

[0131] in, Indicates the internal wave at latitude and longitude coordinates. The speed of propagation at that location; Represents latitude and longitude coordinates Water depth at the location; parameters =2.971 m / s; B1=0.003; B2=1390.758 m.

[0132] (4) For the initial wave crest line of wave A determined in step (2), propagate within the target sea area using the velocity field calculated in step (3), and use the fast travel algorithm to solve the equation to obtain the coordinate point of the i-th row and j-th column of the initial wave crest line of wave A within the target sea area. earliest time .

[0133] For the initial crest line of the B wave determined in step (2), it propagates within the target sea area using the velocity field calculated in step (3). The fast travel algorithm is used to solve the equation of the equation to obtain the coordinate point of the i-th row and j-th column of the initial crest line of the B wave within the target sea area. earliest time .

[0134] Simultaneously obtain the coordinates of the i-th row and j-th column point within the target domain. The corresponding maximum buoyancy frequency , depth of the mezzanine Seabed topography height .

[0135] (5) Input A-wave arrival time error statistical model output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the A wave.

[0136] Will Input B-wave arrival time error statistical model output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the B wave.

[0137] (6) Based on the corrected arrival time field of the initial peak line of wave A and the corrected arrival time field of the initial peak line of wave B, calculate the arrival position of the initial peak line of wave A and the initial peak line of wave B in step (2) under a given propagation time, or the arrival time of a given position, so as to realize the prediction of the internal wave peak line.

Claims

1. A method for predicting ocean internal waves based on satellite remote sensing data, characterized in that, Specifically, the following steps are included: (1) Input the internal wave generation date into the A-wave generation statistical model, and output the A-wave on the first to N two-dimensional cross sections, respectively, from the source, the eastern ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. and the corresponding maximum eastward tidal current. The maximum eastward tidal current corresponds to the tidal range. And solve them separately. and The average value is obtained. and ; Input the internal wave generation date into the B-wave generation statistical model, and output the B-wave on the first to N two-dimensional cross sections, respectively, from the source, the western ridge of the Luzon Strait. The time difference between the arrival time at the western boundary of the corresponding generation region after the time is generated. And obtain the corresponding maximum value of the eastward tidal current. The maximum eastward tidal current corresponds to the tidal range. The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak And the tidal range corresponding to the weak wave peak And solve them separately. , , and The average value is obtained. , , and ; (2) Based on the time difference of A wave arriving at the western boundary of the generation area of ​​the first to N two-dimensional cross sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the region where the A-wave is generated, and use this average internal wave propagation velocity to determine the time difference in which the A-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the A-wave, and the formation time of the initial crest line of the A-wave is determined. ; Based on the time difference of B-wave arrival at the western boundary of the region generating the first to N two-dimensional cross-sections It can accurately calculate the average internal wave propagation velocity of the first to N two-dimensional sections within the B-wave generation region, and use this average internal wave propagation velocity to determine the time difference in which the B-wave passes. After propagation, the positions reaching the first to Nth two-dimensional cross-sections are sequentially connected to obtain the initial crest line of the B-wave, and the formation time of the initial crest line of the B-wave is determined. ; (3) Using the internal wave propagation velocity-water depth function relationship, calculate the latitude and longitude coordinates of the i-th row and j-th column of the target sea area. speed of propagation The propagation speed corresponding to all latitude and longitude coordinates in the target sea area The set of values ​​represents the velocity field within the internal wave propagation region. The relationship between the internal wave propagation velocity and water depth is: ; in, Indicates the internal wave at latitude and longitude coordinates. The speed of propagation at that location; Represents latitude and longitude coordinates Water depth at the location; parameters =2.971 m / s; B1=0.003; B2=1390.758 m; (4) For the initial wave crest line of wave A determined in step (2), propagate within the target sea area using the velocity field calculated in step (3), and use the fast travel algorithm to solve the equation to obtain the coordinate point of the i-th row and j-th column of the initial wave crest line of wave A within the target sea area. earliest time ; For the initial crest line of the B wave determined in step (2), it propagates within the target sea area using the velocity field calculated in step (3). The fast travel algorithm is used to solve the equation of the equation to obtain the coordinate point of the i-th row and j-th column of the initial crest line of the B wave within the target sea area. earliest time ; Simultaneously obtain the coordinates of the i-th row and j-th column point within the target sea area. The corresponding maximum buoyancy frequency , depth of the mezzanine Seabed topography height ; (5) Input the statistical model of A-wave arrival time error, output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the A wave. Will Input the B-wave arrival time error statistical model, output coordinates Corrected arrival time The corrected arrival time set of all coordinate points in the target sea area obtained through this step is the corrected arrival time field of the initial crest line of the B wave. (6) Based on the corrected arrival time field of the initial peak line of wave A and the corrected arrival time field of the initial peak line of wave B, calculate the arrival position of the initial peak line of wave A and the initial peak line of wave B in step (2) under a given propagation time, or the arrival time of a given position, so as to realize the prediction of the inner wave peak line. The internal waves are A waves and / or B waves, and the target sea area is in the latitude and longitude range of 114°E to 123°E and 19°N to 23°N.

2. The ocean internal wave prediction method based on satellite remote sensing data according to claim 1, characterized in that, The methods for constructing the statistical models for A-wave generation and B-wave generation include S1 to S4; S1. Acquire multi-source satellite remote sensing images of the target sea area and establish a multi-source satellite remote sensing internal wave peak line dataset; S2. In the target sea area, based on the spatial distribution characteristics of the internal wave crest line in the remote sensing image and the location of the underwater mooring observation point in the target sea area, select N two-dimensional cross sections, N≥3. Each two-dimensional cross section represents a two-dimensional numerical simulation calculation domain. On each two-dimensional cross section, the two-dimensional MITgcm numerical model is used to construct the internal wave numerical model for internal wave numerical simulation calculation. S3. Based on the numerical simulation results of the internal waves, determine the generation location, generation time, and generation range of the internal waves, using the time of the maximum eastward tidal current in the barotropic tidal current time series diagram at the generation source. This indicates the generation time of the internal wave at the source. S4. Construct a statistical model for internal wave generation, specifically including steps S401 to S403; S401. Within the computational domain of each two-dimensional section, the internal wave numerical model constructed in step S2 shall be subjected to internal wave numerical simulation calculations for no less than two years. S402. Based on the numerical simulation results, for wave A, in the first two-dimensional cross section, based on the Hovmöller diagram of this two-dimensional cross section within a certain time period, and using the Hovmöller diagram, extract the maximum value of the eastward tidal current on the eastern ridge. , Corresponding tidal range And A wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seabed topography in the source region Similarly, extract the corresponding second two-dimensional cross-section within this time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. ; ； For wave B, the Hovmöller plot for a certain time period is obtained in the first two-dimensional section, and the maximum eastward tidal current value of the western ridge is extracted using the Hovmöller plot. , Corresponding tidal range B wave The time difference between the arrival time at the western boundary of the generation region is generated at each moment. East Mountain Ridge Positive Pressure Tidal Wave Weak Peak , Corresponding tidal range Simultaneously, based on the configuration of the first two-dimensional cross-sectional numerical model, stratification parameters within the same time period are extracted, including the maximum buoyancy frequency. , depth of the mezzanine and the average height of the seabed topography in the source region Similarly, extract the corresponding second two-dimensional cross-section within this time period. The third two-dimensional section corresponds to ...and the Nth two-dimensional section corresponding to The data within the same time period are arranged into the following matrix. Through this step, multiple sets of matrices for different time periods can be obtained within the simulation time range of step S401. ; ； S403, Multiple matrices for different time periods A statistical data set on A-wave generation is constructed, and then input into an MLP feedforward artificial neural network to build a statistical model for A-wave generation. The input to the statistical model for A-wave generation is... The output is ; Multiple matrices for different time periods A statistical data set of B-wave generation is constructed. This statistical data set of B-wave generation is then input into an MLP feedforward artificial neural network to construct a statistical model of B-wave generation. The input to the statistical model of B-wave generation is... The output is .

3. The ocean internal wave prediction method based on satellite remote sensing data according to claim 1, characterized in that, The method for constructing the statistical model of A-wave arrival time error or the statistical model of B-wave arrival time error includes steps S6-S7. S6. First, based on the generation date of a certain internal wave crest line in the remote sensing image, the A-wave generation statistical model, and the B-wave generation statistical model, determine k initial A-wave crest lines and k initial B-wave crest lines. Then, based on the internal wave propagation model of the initial arrival time field, k initial A-wave crest lines and k initial B-wave crest lines are determined, along with k initial predicted internal wave crest lines of A-wave and k initial predicted internal wave crest lines of B-wave. Finally, the average distance between the internal wave crest line in the remote sensing image and the k initial predicted internal wave crest lines of A-wave and k initial predicted internal wave crest lines of B-wave are calculated respectively. The initial crest line corresponding to the initial predicted internal wave crest line with the smallest average distance is determined to be the initial crest line corresponding to the internal wave crest line in the remote sensing image. The initial crest line information, the initial arrival time field, and the generation time of N two-dimensional sections at the generation source in the Luzon Strait are retained. The initial crest line information includes the initial crest line position, formation time, and internal wave type. The internal wave type is also the type of internal wave crest line in the remote sensing image. S6 includes steps S601 to S605. S601. Based on the acquisition time of the remote sensing image, determine k possible generation dates for a certain internal wave crest line in the remote sensing image. For each generation date, apply the A-wave generation statistical model and the B-wave generation statistical model to obtain the time difference between the arrival of the internal wave at the western boundary of the generation area of ​​the first to N two-dimensional cross sections. Then, determine the average propagation velocity of the internal wave at the first to N two-dimensional cross sections within the generation area. Using the corresponding average propagation velocity of the internal wave, under a given time difference, determine the position of the internal wave after propagating through the corresponding given time difference to reach the first to N two-dimensional cross sections. Connect the positions of the first to N two-dimensional cross sections in sequence to obtain the initial crest line. Finally, obtain k initial A-wave crest lines and k initial B-wave crest lines corresponding to the k generation dates. S602. Using the internal wave propagation velocity-water depth function relationship, calculate the latitude and longitude coordinates of the i-th row and j-th column point within the target sea area. speed of propagation The propagation speed corresponding to all latitude and longitude coordinates in the target sea area The set of these is the velocity field within the region of internal wave propagation; S603. For the k initial crest lines of A-waves and k initial crest lines of B-waves determined in step S601, propagate them within the target sea area using the velocity field calculated in step S602. Use the fast travel algorithm to solve the equation to obtain the coordinate point of the i-th row and j-th column of each initial crest line within the target sea area. earliest time And the initial wave crest line of wave B reaches the coordinate point in the i-th row and j-th column within the target sea area. earliest time The earliest arrival time set of all coordinate points within the target sea area is the initial arrival time field of the initial wave crest line. Based on the initial arrival time field, the A-wave propagation model and B-wave propagation model are established, and the arrival position of the corresponding initial wave crest line at the remote sensing observation time is calculated, resulting in k initial predicted inner wave crest lines of A-wave and k initial predicted inner wave crest lines of B-wave. S604. Calculate the distance between any initial predicted internal wave crest line and the same internal wave crest line in the remote sensing image. Select and retain only the initial predicted internal wave crest line with the smallest average distance. The initial crest line corresponding to the initial predicted internal wave crest line with the smallest average distance is the initial crest line corresponding to the same internal wave crest line in the remote sensing image. S605. Repeat steps S601 to S604 until the initial wave crest line corresponding to the internal wave crest line in all the acquired remote sensing images is obtained. After completion, the initial wave crest line information corresponding to the internal wave crest line in the remote sensing images, the initial arrival time field, and the average values ​​of the eastward tidal current maximum value, the tidal range corresponding to the eastward tidal current maximum value, the barotropic weak wave peak value before the eastward tidal current maximum value time, and the tidal range corresponding to the barotropic weak wave peak value are retained and recorded. The initial wave crest line information includes the initial wave crest line position, formation time, and internal wave type. The internal wave type is also the type of internal wave crest line in the remote sensing image. If the internal wave crest line in the remote sensing image determined in step S604 is an A wave, then extract the generation times of the first to N two-dimensional sections of the internal wave crest line at the source location in the Luzon Strait. The corresponding maximum value of the eastward tidal current Tidal range And solve and The average value is obtained. and ; If the internal wave crest line in the remote sensing image determined in step S604 is a B wave, then extract the generation time of the internal wave crest line in the remote sensing image at the first to N two-dimensional sections at the generation source. The corresponding maximum value of the eastward tidal current Tidal range The moment when the eastward tidal current reaches its maximum value. Previous barotropic tidal wave weak peak extreme value and corresponding And solve , , and The average value is obtained. , , and ; S7. Construct a statistical model for the initial arrival time error of internal waves. S7 specifically includes steps S701 to S703. S701. From step S1, it can be seen that the internal wave crest line in the remote sensing image is composed of several spatial points. Assume the latitude and longitude coordinates of a certain spatial point on the internal wave crest line in the remote sensing image are... Determine latitude and longitude coordinates of the points in the initial arrival time field corresponding to the remote sensing image. Corresponding initial arrival time value )or Then calculate the latitude and longitude coordinates of that point. Initial arrival time error )or ), , ; In the formula, The acquisition time of the internal wave crest line in the remote sensing image. Determine the initial peak formation time corresponding to the internal wave peak in the remote sensing image, and simultaneously determine the latitude and longitude coordinates. The corresponding stratification parameter, buoyancy frequency maximum value , mezzanine depth and topographic parameters water depth ; S702. If step S6 determines that the internal wave crest line in the remote sensing image is an A wave, then each spatial point in the corresponding internal wave crest line of the remote sensing image will be... Corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along an A-wave peak line form a multidimensional array. Multiple A-wave peak lines result in multiple multidimensional arrays, which are the statistical data set of the initial arrival time error of A-wave. If step S6 determines that the internal wave crest line in the remote sensing image is a B wave, then each spatial point of the internal wave crest line in the remote sensing image is... The corresponding one-dimensional array Corresponding to the internal wave crest line in the remote sensing image , , and Combine to obtain a one-dimensional array In a remote sensing image, multiple spatial points along a B-wave peak line form a multidimensional array. Multiple B-wave peak lines result in multiple multidimensional arrays, which are the statistical data set of the initial arrival time error of the B-wave. S703. Input the initial arrival time error statistics set of wave A into the MLP feedforward artificial neural network, using the initial arrival time error... Using the distribution pattern as the learning objective, a statistical model of A-wave arrival time error is constructed. When applied, for a given latitude and longitude coordinate point, the statistical model outputs the corresponding predicted initial arrival time error. ; The initial arrival time error statistics set of B-wave is input into the MLP feedforward artificial neural network to obtain the initial arrival time error. Using the distribution pattern as the learning objective, a statistical model of B-wave arrival time error is constructed. When applied, for a given latitude and longitude coordinate point, the statistical model outputs the corresponding predicted initial arrival time error. .

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