A seawater depth inversion method integrating wave evolution numerical model

Abstract

The present invention provides a method for inverting seawater depth that integrates a numerical wave evolution model, comprising the following steps: Step 1: Obtaining the wave number of any sea area using remote sensing imagery; Step 2: Obtaining the characteristic wave period of offshore waves in a specific sea area; Step 3: Calculating the water depth based on the wave number and characteristic wave period using the dispersion relationship corresponding to linear wave theory; Step 4: Calculating the wave height and wave number using a numerical wave model; Step 5: Inverting the wave height and wave number using the nonlinear dispersion relationship to obtain the corrected water depth within the area of ​​interest; Step 6: Calculating the final water depth within the area of ​​interest using the numerical wave model based on the corrected water depth. The bathymetric model developed by the present invention is suitable for sea areas with relatively deeper water depths. In particular, the use of wave number information to obtain water depth significantly improves accuracy compared to methods using remote sensing wave height inversion. Furthermore, this method is fast and applicable to large-scale water depth calculations, making it suitable for rapid surveys of coastal resources.

Description

Technical Field

[0001] The invention relates to a seawater depth inversion method integrating a wave evolution numerical model. Background Art

[0002] The seabed topography reflects the changes in the seabed and is the most basic data for marine activities such as sediment migration and change research, underwater safe navigation, oil and gas exploration, and environmental monitoring (References: Jianhu Zhao. Modern ocean mapping [M]. Wuhan: Wuhan University Press, 2008; Sheng Xu. To become a maritime power with Chinese characteristics [J]. Qiushi, 2013(21): 41-42). The traditional method of water depth measurement uses shipborne sonar measurement (reference: Birkemeier WA, Mason C. The CRAB: Aunique nearshore surveying vehicle [J]. Journal of Surveying Engineering, 1984, 110 (1): 1-7). Although the measurement accuracy is high, its measurement cost is high in terms of economy and time, and it is not possible to carry out large-scale rapid measurement (reference: [4] Wang Jikun, Chen Zhenghua, Yu Kefu, et al. Study on multi-spectral remote sensing water depth inversion in coral reefs region [J]. Remote Sensing Technology and Application, 2018, 33 (1): 61-67; Jikun Wang, Zhenghua Chen, Kefu Yu, et al. Water depth information extraction with Multi-spectral remote sensing in coralreefs region [J]. Remote Sensing Technology and Application, 2018, 33 (1): 61-67).The development of remote sensing technology has provided a new means for water depth measurement (References: Li Xiurui. Application of WorldView-2 multi-spectral image in inversion of shallow water bathymetry in South China sea reefs [J]. Remote Sensing Information, 2016, 31(5): 114-121; Xiurui Li. Application of WorldView-2 multi-spectral image in inversion of shallow water bathymetry in South China sea reefs [J]. Remote Sensing Information, 2016, 31(5): 114-121; Tian Zhen. Study on bathymetry inversion models using multi-spectral or hyper-spectral data and bathyorographical mapping [D]. Shandong: Shandong University of Science and Technology, 2015; Zhen Tian. Study on bathymetry inversion models using multi-spectral or hyper-spectral data and bathyorographical mapping [D]. Shandong: Shandong University of Science and Technology, 2015).The water depth measurement technology based on remote sensing images has significant advantages such as large coverage, easy acquisition and low cost (References: Zhaokun Zhai, Shanlong Lu, Bao Zhu, et al. Research on remote sensing estimation model of water quality parameters of Panjiakou reservoir based on GF-1 satellite WFV data [J]. Journal of China Institute of Water Resources and Hydropower Research, 2018, 16(4): 297-306. Zhaokun Zhai, Shanlong Lu, Zhu Bao, et al. Water quality monitoring with GF1-WFV imagery in Panjiakou reservoir, Hebei province of China [J]. Journal of China Institute of Water Resources and Hydropower Research, 2018, 16(4): 297-306; Chu S, Cheng L, Ruan X, et al. Technical framework for shallow-water bathymetry with high reliability and no missing data based on time-series sentinel-2 images [J]. IEEE Transactions on Geoscience and Hydropower Research, 2018, 16(4): 297-306; Chu S, Cheng L, Ruan X, et al. Technical framework for shallow-water bathymetry with high reliability and no missing data based on time-series sentinel-2 images [J]. IEEE Transactions on Geoscience and Hydropower Research, 2018, 16(4): 297-306). RemoteSensing, 2019, 57(11): 8745-87863). Currently, there are two main types of bathymetry: bathymetry based on seabed reflected light intensity and bathymetry based on wave kinematics.

[0003] The measurement of visible light reflected from the seabed mainly includes photobathymetry, airborne laser bathymetry, optical remote sensing bathymetry and microwave radar bathymetry. References: Jiashuang Shen, Jingsheng Zhai, Guojun Zhai, et al. The research on the coastal topographic map and its surveying method [J]. Bulletin of Surveying and Mapping, 2007 (8): 29-32.

[0004] Ma Yi, Zhang Jie, Zhang Jingyu, et al. Research progress in shallow water depth optical remote sensing[J]. Advances in Marine Science, 2018, 36(3): 331-351.

[0005] Yi Ma,Jie Zhang,Jingyu Zhang,et al.Progress in shallow water depthmapping from optical Remote Sensing[J].Advances in Marine Science,2018,36(3):331--351.

[0006] Lyzenga D R.Passive remote sensing techniques for mapping water depth and bottom features[J].Applied Optics,1978,17(3):379-383.

[0007] Lyzenga D R.Shallow-water bathymetry using combined lidar and passivemultispectral scanner data[J].International Journal of Remote Sensing,1985,6(1):115-125.

[0008] Polcyn FC,Sattinger I J.Water Depth Determinations Using RemoteSensing Techniques[J].Remote Sensing of Environment,VI,1969,2:1017-1028.

[0009] Polcyn FC,Lyzenga D R.Calculations of water depth from ERTS-MSS data[C] / / Proceedings Symposium on Significant Results obtained from ERTS-1,1973:1433-1436.

[0010] Zhang Dong, Zhang Ying, Wang Wen, et al. Establishment of statistical correlation water depth remote sensing model[J]. Journal of Hohai University (Natural Science Edition), 1998(6):98-102.

[0011] Dong Zhang,Ying Zhang,Wen Wang,et al.Establishment of RS-Fathomingcorrelation model[J].Journal of Hohai University(Natural Sciences),1998(6):98-102。

[0012] Due to the absorption and scattering of seawater, electromagnetic waves are severely attenuated in seawater, so this type of method is only applicable to shallow water depths. In addition, the influence of seawater turbidity and background stray light such as the sun makes it unusable in turbid waters. In recent years, the method of directly or indirectly extracting wave information from remote sensing images and then using wave kinematics to invert water depth has gradually gained attention. As early as during World War II, people used aerial photos of beaches to determine wavelength and period, and used dispersion relations to infer water depth (Reference:

[16] Steers JA, Deacon GER, Wyatt AGN, et al. The Determination of Gradients on Enemy-Held Beaches: Discussion [J]. The Geographical Journal, 1947, 109 (1 / 3): 91-93). Bell et al. (reference: Bell P S. Shallowwater bathymetry derived from an analysis of X-band marine radar images of waves [J]. Coastal Engineering, 1999, 37(37): 513-527) used image analysis techniques to obtain wave velocity and direction from X-band radar images and inverted water depth based on linear wave theory. Leu et al. (reference: Leu LG, Kuo YY, Liu CT. Coastal bathymetry from the wave spectrum of SPOT images [J]. Coastal Engineering, 1999, 41(1): 21-41) used the wave spectrum bathymetry (WSB) method to extract wavelength and wave direction from SPOT satellite images and then infer water depth. The results showed that it had a high accuracy within 15 m. Abileah et al. (Reference: Abileah R. Mapping shallow water depth from satellite [C] / / Proceedings of the ASPRS annual conference, Reno, Nevada. 2006: 1-7) obtained wavenumbers from panchromatic multispectral images using a two-dimensional Fourier transform and then calculated the water depth near San Diego Bay based on the dispersion relationship.Leu et al. (Reference: Leu LG, Chang H W. Remote sensing in detecting the water depths and bed load of shallowwaters and their changes [J]. Ocean Engineering, 2005, 32(10): 1174-1198) used fast Fourier transform (FFT) to extract the wavelength of waves from SPOT-3 images and inverted the water depth based on the dispersion relationship. Error analysis showed that the inversion effect was good within 12 m. Holman et al. (Reference: Holman R, Plant N, Holland T. cBathy: A robust algorithm for estimating nearshore bathymetry [J]. Journal of Geophysical Research: Oceans, 2013, 118(5): 2595-2609) proposed a cbathy algorithm that uses Fourier transform and Kalman filtering to estimate nearshore water depth from wave velocity observations and applied it to the inversion of water depth at Mana Beach. Danilo et al. (Reference: Danilo C, Melgani F. Wave Period and Coastal Bathymetry Using Wave Propagation on Optical Images [J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(11): 6307-6319) used the wave tracking method to determine the wavelength and wave direction, and then estimated the water depth based on the dispersion relationship. Error analysis showed that the error was less than 15% within a water depth of 20 m outside the breaking zone. Shen Simin et al. (Reference: Shen Simin, Zhu Shouxian, Kang Yanyan, et al. Simulation analysis of remote sensing inversion of ocean wave wavelength and water depth based on fast Fourier transform method [J]. Journal of East China Normal University (Natural Science Edition), 2019(2): 184-194+208.

[0013] Simin Shen, Shouxian Zhu, Yanyan Kang, et al. Simulation analysis for Remote Sensing inversion of wavelength and water depth by the Fast FourierTransform method[J]. Journal of East China Normal University(Natural Science), 2019(2): 184-192) used ideal wavefront and numerical simulation results instead of remote sensing data to carry out simulation research, and discussed the influence of data resolution and sub-image length on the inversion of wave wavelength and water depth by the FFT method.

[0014] The aforementioned bathymetric methods based on remote sensing imagery primarily invert water depth by capturing spatial variations in wavelength using dispersion relationships. This method primarily accounts for the refraction of waves due to topographic variations. However, as waves propagate from offshore to nearshore, they are affected by islands and structures, resulting in shallow diffraction, reflection, and nonlinear variations. Summary of the Invention

[0015] Purpose of the invention: The technical problem to be solved by the present invention is to address the deficiencies of the existing technology and provide a seawater depth inversion method integrating a wave evolution numerical model, comprising:

[0016] Step 1: Use remote sensing images to obtain the wave number of any sea area;

[0017] Step 2, obtaining the characteristic wave period of offshore waves in a specific sea area;

[0018] Step 3: Calculate the water depth based on the wave number and characteristic wave period using the dispersion relationship corresponding to the linear wave theory;

[0019] Step 4: Based on the water depth obtained in step 3 and the characteristic wave period and characteristic wave height obtained in step 2, the wave height and wave number are calculated using a wave numerical model;

[0020] Step 5: Using wave height and wave number, the corrected water depth in the area of ​​interest is inverted according to the nonlinear dispersion relationship;

[0021] Step 6: Based on the corrected water depth, the final water depth of the area of ​​interest is calculated using the wave numerical model.

[0022] In step 1, the MATLAB FFT toolkit is used to process the WorldView-2 satellite remote sensing image to extract the wave number information; the resolution of the image panchromatic band is 0.5m, and the resolution of the multispectral band (including red, green, blue, and near-infrared bands) is 2m. Since the panchromatic data has strong noise, only the multispectral data is used, and the multispectral image is subjected to wavelet noise filtering.

[0023] In step 1, discrete Fourier transform (DFT) is a commonly used wavelength extraction method. The remote sensing image is divided into two or more N×N pixel sub-images using the discrete Fourier transform method. The image pixel resolution is recorded as ΔX, and the pixel value at the position (m1, m2) on the image is X(m1, m2). The Fourier coefficient F(k x ,k y ) and two-dimensional wave number energy spectrum Ψ(k x ,k y )(Reference: Leu LG, Chang H W.Remotely sensing in detecting the water depths and bed load of shallow waters and their changes[J].Ocean Engineering, 2005, 32(10):1174-1198.):

[0024]

[0025] Ψ(k x ,k y )=|F(k x ,k y )| 2

[0026] Where D = N * ΔX is the length of the subgraph, n x , n y The value is 1, 2, 3, ..., N; k x =n x k0, k y =n y k0 is the wave number in the x direction and the wave number in the y direction, k0 = 2π / D is the wave number resolution; e is a natural constant, and i is an imaginary number;

[0027] When N is a power of 2, the fast Fourier transform (FFT) is used instead of the discrete Fourier transform to calculate; the wave number k in the x direction corresponding to the highest value of the spectrum peak is extracted from the wave number energy spectrum px and the wave number k in the y direction py , and then calculate the wave number k.

[0028] In step 1, the wave number k is calculated using the following formula:

[0029]

[0030] Step 2 includes: Generally speaking, when waves move from deep water to shallow water, the wave period remains unchanged, and the wave period in shallow water (T S ) is approximately equal to the wave period in the adjacent deep water (T d Since the Worldview image does not cover the deep water area, the present invention uses the reanalysis wave product of the European Centre for Medium-Range Weather Forecasts (ECMWF) to obtain the period T d The significant wave height and average wave period of the South China Sea region corresponding to the Worldview image were obtained from the ECMWF. The significant wave height in the South China Sea region is 0.5 to 3 meters, and the significant wave height near Sanya Bay is 1 meter. The average wave period in the South China Sea is 2 to 8 seconds, and the average wave period near Sanya Bay is 6 seconds. In addition, according to the China Coastal Wave Database (CWAVE 1.0) (http: / / www.coast-hhu.com / ?page_id=323), the spectral peak period is 1.45 times the average wave period. Therefore, the spectral peak period corresponding to the Worldview image is 8.71 seconds, which means that the wave period is determined to be 8.71 seconds.

[0031] In step 3, the water depth h is calculated using the following formula:

[0032]

[0033] Wherein, σ = 2π / T is the circular frequency, T is the period, and g is the acceleration due to gravity.

[0034] In step 4, the governing equation of the wave numerical model is:

[0035]

[0036] in,

[0037]

[0038]

[0039]

[0040] f1 and f2 are the coefficients of the curvature term and the water depth slope term, respectively, which can improve the applicability of the equation to steep terrain changes. λ is the energy loss coefficient, α0 is the incident amplitude, β and γ are empirical parameters; φ is the velocity potential function, H0 is the incident wave height, and θ0 is the incident wave direction angle. are plane differential operators, C and C g are the wave phase velocity and group velocity, respectively.

[0041] Step 5 includes:

[0042] Step 5-1, establish the following nonlinear dispersion relationship:

[0043]

[0044] Where A represents the amplitude and σ is the circular frequency;

[0045] Step 5-2, rewrite formula (3) to obtain iterative relationship (4):

[0046]

[0047] Step 5-3, substitute the water depth h calculated in step 3 into the h on the right side of formula (4) to obtain a new h, recorded as h1, then substitute h1 into the h on the right side of formula (4) to obtain a new h, recorded as h2, and iterate until |h n -h n-1 |<ε, where ε is the set allowable error, h n is the final calculated water depth.

[0048] Step 6 includes the following steps:

[0049] Step 6-1: Substitute the water depth h calculated in step 5 n Denoted as h (1) Substitute into formula (2) to recalculate the wave height;

[0050] Step 6-2: Substitute the wave height and wave number into equation (4) to calculate the new water depth h (2) ;

[0051] Step 6-3, repeat steps 6-1 and 6-2 to calculate the new water depth h (2) Then, the water depth h is obtained through equations (2) and (3): (3) ; Repeat steps 6-3 until h (n) -h (n-1) <ε, select the tolerance ε=10 -8 ; At this time h (n) is the final water depth of the area of ​​interest.

[0052] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is executed, the seawater depth inversion method integrating the wave evolution numerical model is implemented.

[0053] Beneficial Effects: Compared to traditional methods that directly determine topography using visible light satellite remote sensing, the bathymetric model developed in this invention is applicable to relatively deeper waters. In particular, by utilizing wavenumber information to determine water depth, the accuracy is significantly improved compared to methods that rely on remote sensing wave height inversion. Furthermore, this method is fast and applicable to large-scale water depth calculations, making it suitable for rapid surveys of coastal resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0055] Figure 1 This is a schematic diagram of the remote sensing wave bathymetry model based on the gentle slope equation.

[0056] Figure 2 This is a map of the Berkhoff oval shoal topography and cross-section location.

[0057] Figure 3 It is the actual water depth and water depth inversion map.

[0058] Figure 4a 、 Figure 4b 、 Figure 4c 、 Figure 4d 、 Figure 4e 、 Figure 4f 、 Figure 4g 、 Figure 4h It is a comparison diagram of 8 sections between the water depth calculated by the remote sensing wave bathymetry model and the actual value.

[0059] Figure 5a This is a water depth error map calculated based on the remote sensing wave bathymetry model developed by the present invention.

[0060] Figure 5b This is a water depth error map calculated based on the linear dispersion relationship.

[0061] Figure 6 This is a schematic diagram of the water depth distribution of Sanya Bay (tidal correction value 1.22m).

[0062] Figure 7 It is the distribution map of remote sensing wavenumber data.

[0063] Figure 8 is the spatial distribution of wavenumbers.

[0064] Figure 9 It is the water depth map of Sanya Bay calculated by remote sensing wave bathymetry model.

[0065] Figure 10a 、 Figure 10b 、 Figure 10c 、 Figure 10d 、 Figure 10e 、 Figure 10f It is a comparison chart of the water depth calculated by the remote sensing wave bathymetry model and the six sections of the nautical chart.

[0066] Figure 11 It is a distribution map of relative errors between the water depth calculated based on the remote sensing wave bathymetry model and the nautical chart. DETAILED DESCRIPTION

[0067] This invention provides a method for inverting seawater depth by integrating a numerical model of wave evolution. The basic principle of the computational model is to invert water depth using wave number and wave height information while accounting for the effects of refraction and diffraction. Given the large errors in wave height information obtained by remote sensing, the results of wave numerical simulations are used as the final input data. Because the model needs to account for the influence of wave height, the wave numerical model employed should incorporate the nonlinear effects of waves. At present, the commonly used time-domain wave models include the Boussinesq equation model, the gentle slope equation model and the non-hydrostatic wave numerical model (reference: Jian Shi, Jinhai Zheng, Yixin Yan, et al. Review of non-hydrostatic numerical model for estuarial and coastal hydrodynamics [J]. Journal of Hohai University (Natural Sciences), 2017, 45(02): 167-174. Jian Shi, Jinhai Zheng, Yixin Yan, et al. Review of non-hydrostatic numerical model for estuarial and coastal hydrodynamics [J]. Journal of Hohai University (Natural Sciences), 2017, 45(02): 167-174). Since the control equations and boundary conditions of the Boussinesq equation model and the non-hydrostatic wave numerical model are relatively complex and the calculation efficiency is low, the results obtained need to further calculate the corresponding wave height and wave number information. Based on a comprehensive analysis of the advantages and disadvantages of various models, the present invention selects the gentle slope equation model.

[0068] Model development ideas can be found in Figure 1 Specifically, a set of water depths is preliminarily estimated based on the dispersion relationship based on the spatial variation of wavelength, and then the corresponding wave height spatial distribution is calculated based on the numerical model of the gentle slope equation. Then, the corrected water depth is calculated based on the obtained wave number and wave height using the nonlinear dispersion relationship. This correction is repeated multiple times. When the error between the current corrected water depth and the current calculated water depth is less than a certain value, the obtained water depth is considered to be the final result.

[0069] The spatial distribution of wavelength L (or wave number k) is obtained by remote sensing images and other methods. The dispersion relationship corresponding to the linear wave theory is:

[0070] σ 2 =gk tan h kh (1)

[0071] Where σ = 2π / T is the circular frequency (T is the period), g is the acceleration of gravity, k is the wave number, and h is the water depth. Equation (1) can be rewritten as:

[0072]

[0073] The above formula shows that within the range of real numbers, when the water depth is constant, the period and wavelength are in a one-to-one correspondence.

[0074] Remote sensing information can be used to determine the spatial distribution of wave elements at different times in a specific sea area. The most direct information is wavelength L and wave height H. Since actual ocean waves have wavelengths ranging from tens to hundreds of meters, and wave heights around one meter, remote sensing provides higher relative accuracy for wavelength, provided the horizontal and vertical accuracy are the same. The dispersion relationship reflects how wavelength changes with water depth, reflecting the influence of wave refraction. Therefore, given the known circular frequency σ and wave number k, the water depth h0 can be initially estimated using Equation (2).

[0075] For determining a specific season in a sea area, the characteristic period of offshore waves and the significant wave height are usually fixed, and the values ​​can be obtained by referring to existing research results (reference: Shi J, Zheng J, Zhang C, et al. A 39-year high-resolution wave hindcast for the Chinese coast: Model validation and waveclimate analysis [J]. Ocean Engineering, 2019, 183: 224-235). In addition, when actually calculating the water depth of a certain spatial range, it is necessary to divide the area of ​​interest into regular or irregular grids, and obtain the grid node information to obtain the water depth information of the entire sea area. The present invention uses a triangular grid to calculate the water depth of the area of ​​interest. The reason is that the gentle slope equation model used in the next section to calculate the wave evolution process uses this unstructured grid.

[0076] The estimated water depth data is combined with the wave period and characteristic wave height as input to calculate the wave height distribution of the area of ​​interest. The present invention adopts the extended gentle slope equation derived by Chandrasekera and Cheung (reference: Chandrasekera CN, Cheung KF. Extended linear refraction-diffraction model [J]. Journal of waterway, port, coastal, and ocean engineering, 1997, 123 (5): 280-286), adding the curvature term and the squared slope term of the terrain to improve the applicability of the equation to steep changes in water depth. Its control equation is

[0077]

[0078] Among them: f1 and f2 are functions of, φ is the velocity potential function, are plane differential operators, C and C g are the wave phase velocity and group velocity. The equations are based on a triangular mesh, and a hybrid finite element method with different types of interpolation functions in different regions is used to establish a numerical model (References: Zhenjun Zheng, Xiaozhou Ma, Yujin Dong, et al. Research on coupled oscillation between bat and slender harbor with variable water depth [J]. Engineering Mechanics, 2019, 36(09): 221-229; Zhenjun Zheng, Xiaozhou Ma, Yujin Dong, et al. Research on coupled oscillation between bat and slender harbor with variable water depth [J]. Engineering Mechanics, 2019, 36(09): 221-229).

[0079] The wave height and wave number are obtained by using the wave numerical model, and the water depth is further inverted based on the nonlinear dispersion relationship. The nonlinear dispersion relationship used in this invention is

[0080]

[0081] The above equation takes into account the influence of amplitude A (A = H / 2) on the dispersion relation. When A = 0, it degenerates into the linear dispersion relation (1). Since the water depth cannot be explicitly expressed as a function in equation (4), an iterative method is used to approximate the solution.

[0082]

[0083] Substitute the calculated water depth h0 into the right side of formula (5) to obtain h1, then substitute the calculated h1 into the right side of formula (5) to obtain h2, and so on, iterating until |h n -h n-1 |<ε(ε is the set allowable error, which is selected as 10 -8 . Where h n This is the final step to calculate the water depth. In this way, the water depth in the area of ​​interest can be obtained.

[0084] The calculated water depth h (1) Substitute into formula (2) to recalculate the wave height, and then substitute the obtained wave height and wave number into formula (4) to calculate the new water depth h (2) , ..., repeat the above steps until h (n) -h (n-1) <ε, select the tolerance ε=10 -8 ; At this time h (n) is the final water depth of the area of ​​interest.

[0085] Example

[0086] The present invention uses the elliptical shoal experiment conducted by Berkhoff et al. (reference: Berkhoff JCW, Booy N, Radder AC. Verification of numerical wave propagation models for simple harmonic linear water waves [J]. Coastal Engineering, 1982, 6 (3): 255-279) to verify the developed bathymetric model. Figure 2 As shown in the figure, an elliptical shoal is arranged on a uniform slope with a slope gradient of 1:50 and a water depth of 0.45 m in front of the slope. The incident regular wave has an amplitude of 0.0232 m and a period of 1.0 s. The angle between the incident wave direction and the slope gradient is 20°, and the computational domain is 21.5 m × 20.0 m.

[0087] Figure 4a 、 Figure 4b 、 Figure 4c 、 Figure 4d 、 Figure 4e 、 Figure 4f 、 Figure 4g 、 Figure 4h The comparison between the water depths of eight sections based on the water depth inversion model in this paper and the actual water depths is given, where the abscissa is the x or y coordinate of the experimental terrain, and the ordinate is the actual water depth corresponding to a certain x or y section and the water depth calculated by the bathymetric model; Figure 5a 、 Figure 5bThe error distributions between the water depths inverted using the two methods and the actual experimental terrain depths are presented, where the horizontal and vertical coordinates are the x and y coordinates of the experimental terrain, respectively, and Δh is the error between the water depths calculated using the two methods and the experimental terrain depths. The maximum error of the water depth inversion directly based on the dispersion relationship exceeds 20 mm, while the maximum error of the new water depth inversion model developed based on this invention is less than 3 mm, with an average error of only 0.13%.

[0088] Sanya Bay on Hainan Island was selected to further test the model's practical applicability. Located southwest of Sanya City, Sanya Bay is 14.6 km long from east to west and 11.5 km wide from north to south, with its mouth facing southwest. In recent years, with the rapid development of Sanya's tourism industry, numerous hotels and resorts have been built along the shores of Sanya Bay. Frequent and rapid bathymetry of the bay is essential for safe swimming and reliable predictions of the marine environment. Figure 6 The water depth distribution map of Sanya Bay is given, where the horizontal and vertical coordinates are the x and y coordinates of the study area, respectively, and depth is the water depth value on the chart.

[0089] Generally speaking, when waves move from deep water to shallow water, the wave period remains unchanged. The wave period in shallow water (T S ) is approximately equal to the wave period in the adjacent deep water (T d Since the Worldview image does not cover the deep water area, this study uses the reanalysis wave product of the European Centre for Medium-Range Weather Forecasts (ECMWF) to obtain the period T d The significant wave height and average wave period of the South China Sea region corresponding to the Worldview image were obtained from the ECMWF. The significant wave height in the South China Sea region is 0.5 to 3 meters, and the significant wave height near Sanya Bay is 1 meter. The average wave period in the South China Sea is 2 to 8 seconds, and the average wave period near Sanya Bay is 6 seconds. In addition, according to the China Coastal Wave Database (CWAVE 1.0) (http: / / www.coast-hhu.com / ?page_id=323), the spectral peak period is 1.45 times the average wave period. Therefore, the spectral peak period corresponding to the Worldview image is 8.71 seconds, which means that the wave period is determined to be 8.71 seconds.

[0090] The MATLAB FFT analysis toolkit is used to extract the wave number of Sanya Worldview remote sensing wave images. Figure 7 The wavenumber data obtained from remote sensing are presented, where the horizontal and vertical coordinates are the x and y coordinates of the study area, respectively, and k is the wavenumber value obtained by remote sensing. It can be seen that wavenumber k is concentrated in the x [649,800 m - 654,650 m] and y [2018,335 m - 2021,880 m] regions. Therefore, wavenumber k was screened within this range, resulting in 132 valid data points.

[0091] Draw a grid based on the above x, y range, interpolate the wave number k obtained by screening on the grid, and obtain the wave number spatial distribution diagram (see Figure 8 , where the horizontal and vertical coordinates are the x and y coordinates of the study area, respectively, and k is the interpolated wave value).

[0092] Based on remote sensing information, the wave number of the study area is obtained, and the dispersion relationship is used to calculate the initial water depth h1. The amplitude A of the corresponding area is calculated by substituting it into the gentle slope equation module. The new water depth is calculated based on the nonlinear dispersion relationship based on the wave number information, and so on. Finally, the water depth calculation result is obtained. The water depth map of Sanya Bay calculated by the remote sensing wave bathymetry model is shown below. Figure 9 As shown in the figure, the horizontal and vertical coordinates are the x and y coordinates of the study area, and depth is the water depth value corresponding to each point. The comparison diagram of the six calculated sections and the nautical chart is shown in the figure Figure 10a 、 Figure 10b 、 Figure 10c 、 Figure 10d 、 Figure 10e 、 Figure 10f As shown in the figure, the horizontal axis is the x or y coordinate of the study area, and the vertical axis is the actual water depth corresponding to a certain x or y section and the water depth calculated by the bathymetric model. The water depth calculated based on the water depth inversion model developed by the present invention is similar to the actual sea chart, showing a trend of gradually decreasing water depth from southwest to northeast, but in some local areas such as Figure 9 The main reason why the water depth in some areas such as the southwest end is inconsistent with the nautical chart is that the remote sensing wave number used in this invention has a large error compared with the actual value in this area (see Figure 7 and Figure 8 ). The figure shows the cross section Figure 10a 、 Figure 10b 、 Figure 10f Closest, cross section Figure 10d The difference between the two is the largest in deep water, with an overall average error of 11.58% in the prediction area (see Figure 11 , where the horizontal and vertical coordinates are the x and y coordinates of the study area, respectively, and the relative error is the relative error between the water depth calculated by the bathymetric model and the water depth on the nautical chart).

[0093] Water depth is essential data for studying nearshore hydrodynamics such as waves and tidal currents. However, measuring water depth is not only expensive but also impractical in some areas. Therefore, this paper has developed a bathymetric model based on satellite remote sensing data. Compared to traditional methods that directly determine topography using visible light satellite remote sensing, this bathymetric model is applicable to relatively deeper waters. Because this method utilizes both wave number and wave height information, it achieves higher inversion accuracy than methods that directly infer water depth from wave number dispersion. Figure 3Figure 1 shows the actual water depth map (left), the water depth inversion map based on the linear dispersion relationship (center), and the water depth inversion map based on the remote sensing wave bathymetry model developed by this invention (right). The horizontal and vertical coordinates are the x and y coordinates of the experimental terrain, respectively, and depth is the water depth value corresponding to each point. The water depth inversion example based on Sanya Bay shows that the accuracy of remote sensing wavenumber information directly affects the accuracy of the final model-derived water depth. Therefore, it is recommended to collect as much remote sensing image data as possible during application to obtain high-resolution and high-precision wavenumber data, which can greatly improve the prediction accuracy of the bathymetry model.

[0094] Comparisons with Berkhoff ellipse shoal experiments show that the model developed in this paper has an average error of 0.13%, a seven-fold improvement over previous methods for inverting water depth based on dispersion relationships. Further application of the new model to invert the nearshore topography of Sanya Bay, and comparisons with nautical charts, demonstrate that the proposed model can effectively infer the nearshore topography of Sanya Bay, with an average error of 11.58%. Areas with large local errors are primarily due to the low spatial resolution and accuracy of wavenumbers obtained from remote sensing imagery.

[0095] In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit, wherein the computer storage medium is capable of storing a computer program that, when executed by the data processing unit, executes the invention of a method for inverting seawater depth by integrating a wave evolution numerical model provided by the present invention, as well as some or all of the steps in each embodiment. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0096] Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of computer programs and their corresponding general hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, in essence or in other words, the part that contributes to the prior art, can be embodied in the form of a computer program, i.e., a software product. The computer program software product can be stored in a storage medium and includes several instructions for enabling a device including a data processing unit (which can be a personal computer, a server, a single-chip microcomputer, a MUU, or a network device, etc.) to execute the methods described in various embodiments of the present invention or certain parts of the embodiments.

[0097] The present invention provides a method for inverting seawater depth by integrating a numerical model of wave evolution. There are numerous methods and approaches for implementing this technical solution. The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A seawater depth inversion method integrating a wave evolution numerical model, characterized in that: The following steps are involved: Step 1: Use remote sensing images to obtain the wave number of any sea area; Step 2, obtaining the characteristic wave period of offshore waves in a specific sea area; Step 3: Calculate the water depth h based on the wave number and characteristic wave period using the dispersion relationship corresponding to the linear wave theory; Step 4: Based on the water depth obtained in step 3 and the characteristic wave period and characteristic wave height obtained in step 2, the wave height and wave number k are calculated using a wave numerical model; Step 5: Using wave height and wave number, the corrected water depth in the area of ​​interest is inverted according to the nonlinear dispersion relationship; Step 6: Based on the corrected water depth, the final water depth of the area of ​​interest is calculated using a wave numerical model; In step 4, the governing equation of the wave numerical model is: in, f1 and f2 are the coefficients of the curvature term and the water depth slope term, respectively; λ is the energy loss coefficient; α0 is the incident amplitude; β and γ are empirical parameters; φ is the velocity potential function; H0 is the incident wave height; θ0 is the incident wave direction angle; are plane differential operators, C and C g are the wave phase velocity and group velocity, respectively; Step 5 includes: Step 5-1, establish the following nonlinear dispersion relationship: Where A represents the amplitude and σ is the circular frequency; Step 5-2, rewrite formula (3) to obtain iterative relationship (4): Step 5-3, substitute the water depth h calculated in step 3 into the h on the right side of formula (4) to obtain a new h, recorded as h1, then substitute h1 into the h on the right side of formula (4) to obtain a new h, recorded as h2, and iterate until |h n -h n-1 |<ε, where ε is the set allowable error, h n is the final calculated water depth.

2. The method according to claim 1, characterized in that In step 1, the MATLAB FFT toolkit is used to process the WorldView-2 satellite remote sensing image to extract the wave number information; only multispectral data is used, and the multispectral image is subjected to wavelet denoising.

3. The method according to claim 2, characterized in that In step 1, the remote sensing image is divided into two or more N×N pixel sub-images using the discrete Fourier transform method. The image pixel resolution is denoted as ΔX, and the pixel value at position (m1, m2) on the image is X(m1, m2).

4. The method according to claim 3, characterized in that Step 1 also includes: calculating the Fourier coefficient F(k x ,k y ) and two-dimensional wave number energy spectrum Ψ(k x ,k y ): Ψ(k x ,k y )=|F(k x ,k y )| 2 Where D = N * ΔX is the length of the subgraph, n x , n y The value is 1, 2, 3, ..., N; k x =n x k0, k y =n y k0 is the wave number in the x direction and the wave number in the y direction, k0 = 2π / D is the wave number resolution; e is a natural constant, and i is an imaginary number; When N is a power of 2, fast Fourier transform is used instead of discrete Fourier transform; the wave number k in the x direction corresponding to the highest value of the spectrum peak is extracted from the wave number energy spectrum. px and the wave number k in the y direction py , and then calculate the wave number k.

5. The method according to claim 4, characterized in that In step 1, the wave number k is calculated using the following formula:

6. The method according to claim 5, characterized in that In step 3, the water depth h is calculated using the following formula: Wherein, σ = 2π / T is the circular frequency, T is the period, and g is the acceleration due to gravity.

7. The method according to claim 6, characterized in that Step 6 includes the following steps: Step 6-1: Substitute the water depth h calculated in step 5 n Denoted as h (1) Substitute into formula (2) to recalculate the wave height; Step 6-2: Substitute the wave height and wave number into equation (4) to calculate the new water depth h (2) ; Step 6-3, repeat steps 6-1 and 6-2 to calculate the new water depth h (2) Then, the water depth h is obtained through equations (2) and (3): (3) ; Repeat steps 6-3 until h (n) -h (n-1) <ε, select the tolerance ε=10 -8 ; At this time h (n) is the final water depth of the area of ​​interest.

8. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is executed, the method according to any one of claims 1 to 7 is implemented.

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