Near-inertia internal wave modeling method based on reverse echo observation array

Abstract

The invention belongs to the field of near-inertia internal wave modeling, and particularly relates to a near-inertia internal wave modeling method based on a reverse echo observation array, which comprises the following steps: arranging a reverse echo measurement device array in an observation area, and acquiring echo signals from the seabed to the sea surface; performing data cleaning and band-pass filtering on the signals, and extracting near-inertia internal wave signals; calculating the depth and the relative vorticity of a mixed layer by combining historical temperature-salinity data; calculating a wind input energy flux by using the wind stress data; calculating a net level energy flux by adopting a boundary integration method; judging whether the boundary energy flux influence is smaller than a threshold value or not, and if not, adjusting array layout; and finally establishing a multivariable linear model containing wind energy input, mixed layer depth, relative vorticity and energy flux. According to the method, the temporal-spatial resolution and prediction precision of near-inertia internal wave modeling are effectively improved, the problems that in a traditional method, the boundary effect is remarkable, and multi-factor comprehensive modeling is insufficient are solved, and the method is suitable for long-term efficient monitoring of a large-range marine environment.

Description

Technical Field

[0001] This invention belongs to the field of near-inertial internal wave modeling, specifically a near-inertial internal wave modeling method based on a reverse echo observation array. Background Technology

[0002] Near-inertial internal waves (NIWs) are an important physical phenomenon in the ocean, excited by wind stress, and are widely present in the upper waters of the global ocean. These waves play a crucial role in ocean energy transfer, water mass mixing, and biogeochemical cycles, profoundly impacting the global climate system and marine ecosystem. NIWs typically exhibit oscillations with periods close to their inertial period, and their energy can propagate from the sea surface down to depths of hundreds of meters, promoting vertical mixing in the ocean and thus influencing nutrient transport, carbon cycling, and the distribution of ocean heat. Therefore, accurately understanding and modeling NIWs is essential for oceanographic research, climate change prediction, maritime safety, and marine resource development. Scientists have long been dedicated to developing effective observation and modeling methods to capture the spatiotemporal characteristics and energy fluxes of NIWs.

[0003] Traditional near-inertial internal wave (NIW) research relies primarily on a range of ocean observation techniques, including buoy systems, acoustic Doppler current profilers, pressure sensors, and moored arrays. These devices are typically deployed at fixed locations, continuously monitoring parameters such as seawater velocity, temperature, salinity, and pressure to infer the generation, propagation, and attenuation processes of NIW. For example, buoys can provide long-term, single-point time-series data, while current meters can measure flow characteristics at different depths. These methods have accumulated valuable data over the past few decades, helping us to gain a preliminary understanding of the fundamental laws governing NIW. However, with the increasing demand for ocean observation, especially the need for high-precision ocean models in the context of global change, these traditional techniques have gradually revealed numerous limitations, making it difficult to meet the requirements of modern oceanographic research.

[0004] First, insufficient spatiotemporal resolution is a significant drawback of traditional methods. Near-inertial internal waves (NIWs) exhibit multi-scale and nonlinear characteristics, and their spatial distribution is often complexly influenced by factors such as seafloor topography, water mass structure, and atmospheric forcing. Traditional observation techniques, such as buoys or single-point current meters, typically provide only sparse point data due to high deployment costs and maintenance difficulties. This single-point or limited-point observation mode cannot comprehensively capture the spatiotemporal variability of NIWs over large areas. For example, in open seas or complex topographic regions, the wavefront of NIWs may exhibit strong spatial gradients, with significant changes in energy flux over short distances. Single-point observations can only reflect local information, easily missing key dynamic processes and leading to biases in regional energy budget estimations. Furthermore, temporal resolution is also limited; many traditional instruments have low sampling frequencies, making it difficult to distinguish high-frequency variations in NIWs, such as the rapid response of internal waves during storm events. This insufficient resolution not only affects the accuracy of short-term ocean forecasts but also restricts the improvement of long-term climate models, as NIWs are a crucial input for ocean mixing parameterization.

[0005] Secondly, existing research often focuses on the analysis of single factors, neglecting the combined effects of multiple environmental variables. The generation and evolution of near-inertial internal waves are the result of the interaction of multiple factors, including wind stress, mixing layer depth, relative vorticity, and background flow field. For example, wind stress is the main energy source of near-inertial internal waves, but its input efficiency is modulated by the mixing layer depth; when the mixing layer is shallow, wind energy more easily excites internal waves, while a deeper mixing layer may inhibit the generation of internal waves. Meanwhile, relative vorticity can change the frequency and propagation direction of internal waves by influencing the Coriolis parameter. However, traditional methods are limited by observational means and can usually only examine a single factor in isolation, such as analyzing wind stress data alone or calculating the mixing layer depth using temperature-salinity profiles. While this simplified analysis facilitates modeling, it cannot truly reflect the complexity of the ocean system, leading to systematic errors in model predictions. In practical applications, such as typhoon passage or seasonal changes, the coupling effect of multiple factors is particularly prominent. If the model fails to integrate these variables, it may underestimate the intensity of internal waves or misjudge their propagation paths, thus affecting marine disaster early warning and resource management.

[0006] Furthermore, boundary effects are becoming increasingly prominent in large-scale observations. When using array-based observation equipment, such as deploying multiple sensors or buoys, the calculation of energy flux at the array edges is easily affected by boundary conditions. Near-inertial internal waves may be reflected, refracted, or scattered when propagating to the array boundaries, generating spurious signals or amplifying errors. Traditional techniques for handling boundary effects are relatively crude, often relying on simple assumptions or empirical corrections, lacking universality. For example, in regional energy balance analysis, if boundary fluxes are not accurately quantified, it may lead to overestimation or underestimation of net energy flux, affecting the understanding of the energy cycle of the entire system. This problem is particularly severe in large-scale observation projects, such as global ocean observation systems, where boundary effects can introduce uncertainties, reducing the comparability and reliability of data.

[0007] In general, the limitations of traditional near-inertial internal wave modeling methods in terms of spatiotemporal resolution, multi-factor integration, and boundary control restrict their effectiveness in practical applications. With the development of marine observation technology and the deepening of interdisciplinary research, there is an urgent need for a new method that can balance high resolution, multivariate integration, and boundary optimization. This invention is proposed against this backdrop, aiming to overcome these bottlenecks through innovative technology and provide more reliable support for marine science and engineering applications. Summary of the Invention

[0008] The purpose of this invention is to provide a near-inertial internal wave modeling method based on a reverse echo observation array. By comprehensively considering multiple factors such as wind stress, mixing layer depth, and relative vorticity, and combining reverse echo measurement data, this method can efficiently extract near-inertial internal wave signals at a regional scale and accurately quantify their energy flux. This method offers advantages in terms of wider coverage, scientific rigor, stability, and economic efficiency in complex marine environments, and overcomes the shortcomings of existing near-inertial internal wave modeling methods mentioned in the background section.

[0009] The technical solution adopted by this invention to achieve the above objectives is: a near-inertial internal wave modeling method based on a reverse echo observation array, comprising the following steps:

[0010] Step S1: Deploy an array of reverse echo measurement devices in the near-inertial internal wave observation area and acquire echo signals from the seabed to the ocean surface;

[0011] Step S2: Perform data cleaning and bandpass filtering on the echo signal to extract the near-inertial internal wave signal;

[0012] Step S3: Based on the processed echo signal and historical temperature and salinity data within the observation area, the time series data of the mixing layer depth and relative vorticity in the observation area are calculated using the GEM method;

[0013] Step S4: Calculate the time series data of the mixed layer depth and relative vorticity of the observation area based on the lookup table, and calculate the time series data of the energy flux of wind input to the ocean using the wind stress dataset;

[0014] Step S5: Using the boundary integral method, calculate the net horizontal energy flux of near-inertial internal waves within the observation array, as well as the energy flux of wind input into the ocean in this region;

[0015] Step S6: Determine whether the influence of the boundary energy flux is less than the preset threshold. If yes, proceed to step S7; otherwise, return to step S1 and adjust the number and coverage of the reverse echo measurement array.

[0016] Step S7: Based on the energy flux of wind input to the ocean, the depth of the mixing layer, the relative vorticity, and the lateral energy flux of near-inertial internal waves, establish a multivariable linear model.

[0017] The coverage range of the reverse echo measurement device array is 200 km × 200 km to 600 km × 600 km; and adjacent reverse echo measurement devices are arranged in a square array on the ocean surface at intervals of 30 km to 60 km.

[0018] Step S2 includes the following steps:

[0019] Step S21: Data cleaning process, which includes the following steps:

[0020] Step S211: Outlier removal: Outliers in the echo signal are removed using the standard deviation method. Specifically, this includes calculating the mean and standard deviation of the echo signal data segment, setting a threshold of mean ± 3 standard deviations, and identifying data points that exceed this threshold range as outliers and removing them.

[0021] Step S212: Long-term drift correction: Using the pre-calibrated instrument drift rate and initial deviation parameters, long-term drift correction is performed on the echo signal after removing outliers to eliminate baseline drift caused by changes in instrument performance.

[0022] Step S213: High-frequency noise filtering: Apply a third-order Butterworth low-pass filter to filter the drift-corrected echo signal for 72 hours to remove high-frequency noise components and retain the effective low-frequency signal, including near-inertial internal waves.

[0023] Step S22: Near-inertial internal wave signal extraction and processing:

[0024] A third-order Butterworth phase-preserving bandpass filter is applied to filter the data-cleaned echo signal, wherein:

[0025] The passband frequency range of the bandpass filter is set to 0.95f to 1.05f; where f is the Coriolis frequency of the latitude of the observation area, to ensure coverage of the main energy distribution frequency band of near-inertial internal waves;

[0026] The cutoff frequency of the bandpass filter is set to ±2.5 hours to effectively separate near-inertial internal wave signals from interference signals in adjacent frequency bands.

[0027] The phase-preserving characteristic ensures that the phase relationship between the frequency components of the signal is not changed during the filtering process, thus maintaining the timing accuracy of the waveform.

[0028] Step S3 specifically includes:

[0029] Step S31: The historical profile data is interpolated onto a uniform pressure grid, with a pressure range from 0 to 1400 dbar at 2 dbar intervals, and the data is then calculated based on the corresponding τ. index Sort in ascending order;

[0030] Step S32: In each pressure layer p i Above, empirical functions of temperature and salinity versus propagation time were constructed using cubic spline interpolation:

[0031] T(p i ,τ)=f T (p i ,τ),S(p i ,τ)=f S (p i ,τ)

[0032] Wherein, T(p) i ,τ) and S(p i ,τ) represent the pressure layer p, respectively. i Temperature and salinity at propagation time τ. T (p i ,τ) and f S (p i ,τ) is an empirical function established based on CTD data;

[0033] The relationship between propagation time and temperature and salinity was constructed using cubic spline interpolation.

[0034] Step S33: Given the acoustic propagation time of any observed echo signal, reconstruct the temperature and salinity profile T from the lookup table after the same seasonal adjustment procedure. CPIES ,S CPIES ;

[0035] Step S34: Utilize the reconstructed temperature and salinity profile T CPIES ,S CPIES Calculate the mixing layer and relative vorticity.

[0036] Step S5 specifically includes:

[0037] Step S51: Calculate the disturbed physical quantity field:

[0038] Based on the reconstructed temperature and salinity profiles from the echo signals, the water density anomaly ρ′ is calculated.

[0039] Based on the static water relationship, the disturbance pressure p′ is derived by vertically integrating the water density anomaly ρ′.

[0040] The vertical mean of the disturbance pressure p′ is set to zero to remove the spurious baroclinic effect caused by stripe flow;

[0041] The perturbation velocity u′ is obtained by removing the time mean and depth mean from the observed instantaneous velocity.

[0042] Step S52: At each calculation point within the observation area, calculate the covariance between the disturbance velocity u′ and the disturbance pressure p′ to obtain the energy flux density vector F:

[0043] F =<u′p′> ;

[0044] Step S53: Calculate the net horizontal energy flux:

[0045] By integrating along the closed boundary of the array, the net horizontal energy flux F of the low-mode near-inertial internal wave in the observation region is obtained. NIIWs ;

[0046] Step S54: Simultaneously, in order to assess the contribution of wind stress to the local near-inertial energy budget, the wind-induced near-inertial energy flux WNEF is estimated as follows:

[0047] WNEF=<τ·u i >;

[0048] Where τ is wind stress, u i It is near-inertial velocity.

[0049] Step S53 specifically includes:

[0050] Step S531: Discretize the closed boundary of the array into multiple continuous boundary segments, each segment connecting two adjacent measuring devices;

[0051] Step S532: For each boundary line segment, calculate its normal vector. Calculate the component of the energy flux density vector F on the line segment in the normal direction.

[0052] Step S533: For each boundary segment, calculate the normal energy flux component F.⊥ Multiply by the length ΔL of the line segment to obtain the energy flux through the line segment;

[0053] Step S534: Summate the energy flux of all boundary segments on the closed boundary to obtain the total net horizontal energy flux F passing through the entire closed boundary. NIIWs =∑(F ⊥ ×ΔL).

[0054] In step S6, the influence of the boundary energy flux is determined, specifically as follows:

[0055] This is achieved by comparing the ratio of net horizontal energy flux to wind-induced near-inertial energy flux. The impact is considered to be less than a preset threshold when the following condition is met:

[0056]

[0057] Among them, F NIIWs WNEF is the net horizontal energy flux, and WNEF is the near-inertial energy flux caused by wind.

[0058] In step S6, if the influence of the boundary energy flux is greater than or equal to a preset threshold, the number and coverage of the reverse echo measurement array are adjusted, specifically as follows:

[0059] Step S61: Set the percentage threshold for energy flux

[0060] Step S611: Sort energy flux: sort the energy flux F for all boundary segments ⊥ Sort the data from largest to smallest and find the flux contribution of each boundary segment.

[0061] Step S612: Calculate the proportion: Calculate the proportion of the energy flux of each boundary segment to the net horizontal energy flux F. NIIWs The proportion H;

[0062] Step S613: Set a threshold: Set a percentage threshold M; for areas where the energy flux percentage H is less than the percentage threshold M, it is considered that the contribution is small, and the number of measurement stations in these areas is reduced; for areas where the energy flux percentage H is greater than or equal to the percentage threshold M, it is considered that the contribution is large.

[0063] Step S62: Adjust the number of array sites according to the net horizontal energy flux distribution:

[0064] Step S621: For areas with a small contribution to energy flux, i.e., areas M where the proportion of total energy flux H is lower than a set threshold, reduce the number of measurement stations in the area.

[0065] Step S622: Retain measurement stations in areas that contribute significantly to the total net energy flux, while removing areas that contribute less to reduce redundant data.

[0066] Step S63: Adjust the shape and coverage of the array:

[0067] Step S631: Adjust the shape of the array according to the spatial distribution of energy flux to conform to the regional ocean dynamics characteristics and reduce the influence of the array's boundary effects;

[0068] Step S632: For areas with small energy flux contribution, shrink the array coverage area, remove areas with small contribution, and retain measurement points in the core area to reduce redundant data acquisition and improve measurement accuracy and data quality.

[0069] Step S63: Optimize the layout of the remaining measurement stations:

[0070] The remaining measurement stations should be able to cover key ocean dynamic changes within the region; and the remaining stations should focus on areas that contribute significantly to the total net horizontal energy flux, enabling the capture of key dynamic processes such as near-inertial internal waves and backflow eddies.

[0071] In step S7, the multivariate linear model takes the following form:

[0072] F(NIIWs)=b1×WNEF+b2×MLD+b3×ζ+b4;

[0073] Where F(NIIWs) is the near-inertial internal wave energy, WNEF is the wind-induced near-inertial energy flux, MLD is the mixing layer depth, ζ is the relative vorticity, and b1, b2, b3, and b4 are the model coefficients.

[0074] Using goodness-of-fit R 2 F-test and error variance estimation S 2 Evaluate model performance.

[0075] The use of goodness of fit R 2 F-test and error variance estimation S 2 The model performance is evaluated as follows:

[0076] Step S71: Goodness of fit R 2 The assessment is expressed as:

[0077]

[0078] Among them, y i These are actual observed values. These are model predictions. It is the average of the actual observed values;

[0079] When R 2A value close to 1 indicates that the model fits the data very well and can effectively explain most of the variations in the data.

[0080] When R 2 A value greater than 0.8 indicates that the model explains a large proportion of the variation, and is generally considered to have good predictive ability.

[0081] When R 2 Between 0.5 and 0.8: The model may have some prediction errors, but it can still effectively capture the main features of the data and is suitable for engineering and research applications;

[0082] When R 2 Less than 0.5: The model's predictive ability is weak and needs to be improved or other independent variables need to be added;

[0083] Step S72: The evaluation of the F-test is expressed as:

[0084]

[0085] Where k is the number of independent variables and n is the sample size;

[0086] When the F-value is greater than 1, the result of the F-test is a significance level p-value; if the p-value is less than 0.05, it indicates that the independent variable in the model has a significant effect on the dependent variable.

[0087] A high F-value, such as F > 5, indicates that the regression model has significant predictive power.

[0088] An F-value close to 1 or low indicates that the model has a weak explanatory power for the dependent variable; more independent variables should be added or the model should be optimized.

[0089] The evaluation criteria are:

[0090] p < 0.05 indicates that the model is significant; p < 0.01 indicates that the model is significant at a higher confidence level.

[0091] Step S73: The error variance estimation S 2 The assessment is expressed as:

[0092]

[0093] Among them, y i These are actual observed values. Here, n represents the model's predicted value, n is the sample size, and k is the number of independent variables.

[0094] When S 2 The smaller the value, the better the model fits and the smaller the prediction error.

[0095] The present invention has the following beneficial effects and advantages:

[0096] This invention presents a near-inertial internal wave modeling method based on a reverse echo observation array. By integrating multi-source data and optimizing the observation layout, it significantly improves the accuracy and efficiency of near-inertial internal wave research. This method not only overcomes the limitations of traditional techniques but also introduces several innovative aspects, demonstrating broad advantages in marine environmental monitoring, climate research, and engineering applications.

[0097] First, this invention effectively solves the long-standing problem of insufficient spatiotemporal resolution. Traditional observation methods, such as buoys or single-point sensors, struggle to capture the dynamic changes of near-inertial internal waves at regional scales due to low deployment density and limited coverage. Near-inertial internal waves often exhibit strong spatial heterogeneity, with their beam structures potentially evolving rapidly with topography and current fields, characteristics that single-point data cannot reflect in two-dimensional or three-dimensional data. This invention achieves high-density synchronous observation from the seabed to the sea surface by deploying a large-scale array of reverse echo measurement devices. The array covers hundreds of kilometers, with station spacing optimized to 30 to 60 kilometers, forming a gridded layout that enables continuous monitoring of the generation, propagation, and dissipation of internal waves. This design significantly improves the spatial resolution and temporal continuity of the data; for example, hourly echo signal acquisition ensures the capture of high-frequency changes. Compared to traditional methods, this invention can more accurately quantify the spatial distribution of energy flux, especially in complex marine environments such as current confluence zones or submarine canyons, where its advantages are even more pronounced. High-resolution data also provides a more reliable validation benchmark for numerical models, contributing to improvements in climate prediction and ocean hybrid parameterization schemes.

[0098] Secondly, this invention achieves comprehensive analysis of multiple environmental factors, overcoming the limitations of single-variable modeling. The dynamics of near-inertial internal waves involve the coupling of multiple processes, including wind stress input, mixing layer modulation, and vorticity effects. Traditional studies often rely on scattered datasets, such as wind stress data from satellite remote sensing and temperature and salinity data from historical databases. These data may be mismatched in time and space, introducing additional errors. This invention utilizes inverse echo measurement technology to synchronously acquire echo signals, temperature and salinity profiles, and wind stress information from a unified platform. Key parameters such as mixing layer depth and relative vorticity are reconstructed using GEM methods and lookup tables. This integrated processing ensures data consistency and reduces system uncertainty. For example, in modeling, this invention integrates wind input energy, mixing layer depth, relative vorticity, and energy flux into a multivariate linear model, enabling the quantification of the contribution and interaction of each factor. This comprehensive approach not only improves prediction accuracy but also enhances the physical interpretability of the model, providing a new perspective for studying the response of internal waves to extreme events (such as storms or El Niño).

[0099] Third, this invention effectively controls the impact of boundary effects through advanced boundary integration methods and dynamic array adjustment. In large-scale observations, boundary flux is often the main source of error, and traditional techniques lack effective correction methods. This invention introduces the boundary integration method to calculate net horizontal energy flux and quantifies the boundary effect as a ratio to wind input energy, setting a threshold for real-time evaluation. If the boundary effect exceeds the limit, the system automatically optimizes the array deployment, such as shrinking low-contribution areas or strengthening high-energy sites. This adaptive mechanism ensures that the observation network always focuses on key dynamic processes and minimizes boundary interference. In contrast, traditional static arrays cannot dynamically respond to environmental changes, which may lead to data redundancy or omissions. The boundary handling of this method not only improves the reliability of energy flux calculation but also reduces operating costs because intelligent optimization reduces unnecessary equipment deployment.

[0100] Finally, this invention possesses efficient and economical long-term monitoring capabilities, making it suitable for large-scale marine environments. Compared to buoy or satellite remote sensing, inverse echo measurement technology offers advantages such as flexible deployment, ease of maintenance, and strong anti-interference capabilities. Array deployment can be adjusted based on actual sea conditions, avoiding the impact of harsh environments, and data acquisition is highly automated, making it suitable for long-term continuous observation. In terms of economy, this invention reduces redundant data acquisition and lowers the investment of manpower and resources by optimizing site layout. Simultaneously, high-precision modeling provides practical tools for marine disaster prevention, resource exploration, and climate change research; for example, it can be used for assessing the impact of internal waves on offshore platforms or monitoring marine carbon sinks. This high efficiency and economy make this invention widely applicable in global marine observation networks, especially in developing countries or remote sea areas, enabling low-cost and high-efficiency monitoring.

[0101] In summary, this invention achieves a technological leap in near-inertial internal wave research by integrating high-resolution observation, multi-factor modeling, and intelligent boundary control. Its advantages are not only reflected in scientific accuracy but also in expanding the boundaries of engineering applications, laying a solid foundation for sustainable ocean management. Attached Figure Description

[0102] Figure 1 This is a flowchart illustrating the near-inertial internal wave modeling of the present invention.

[0103] Figure 2 This is a schematic diagram showing the comparison between the modeling results of this invention and historical data. Detailed Implementation

[0104] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0105] How to use

[0106] 1. Method Overview

[0107] This method is specifically designed for near-inertial internal wave modeling. It acquires ocean echo signals by deploying an array of inverse echo measurement devices and combines this with multivariate data analysis to establish a linear predictive model. Its core advantages lie in improving spatiotemporal resolution and controlling boundary effects, making it suitable for long-term monitoring of large ocean areas. Users must ensure that the equipment meets marine environmental requirements and follow the steps outlined below to guarantee the accuracy of the results. The overall process revolves around data acquisition, signal processing, physical quantity calculation, and model optimization, emphasizing adaptive adjustments to cope with dynamic ocean changes.

[0108] 2. Detailed usage instructions

[0109] This section explains the implementation process of the method step by step, with each step corresponding to S1 to S7 in the claims, ensuring consistency with the patent data. The operation requires the use of a reverse echo measurement device, wind stress dataset, and calculation software tools. Equipment calibration and environmental assessment are recommended before implementation.

[0110] 2.1. Step 1: Deploy the reverse echo measurement device array

[0111] This step involves deploying a measurement array in the observation area to acquire echo signals from the seabed to the sea surface. Array deployment is fundamental to the method and directly affects data quality; users must select the optimal parameters based on ocean conditions.

[0112] (1) Determine the observation area: Select an active near-inertial internal wave area, and the array coverage should be controlled between 200 km × 200 km and 600 km × 600 km to ensure spatial representativeness. The area selection should avoid areas with strong currents or complex topography to reduce interference.

[0113] (2) Device deployment: The reverse echo measurement devices are arranged in a square array on the ocean surface, with adjacent devices spaced 30 to 60 kilometers apart. During deployment, a mooring system is required to secure the equipment, prevent drift, and ensure that the devices cover the entire water column vertically to capture complete echo signals.

[0114] (3) Signal acquisition: After starting the device, acquire echo signals at a frequency of no less than once per hour. During the acquisition process, the signal strength and quality need to be monitored in real time. If any abnormality is found, the device position or sampling rate should be adjusted in time.

[0115] The key to this step lies in the uniformity and stability of the array; users can optimize the deployment scheme through pre-experimentation. After completion, the data preprocessing stage begins.

[0116] 2.2. Step Two: Data Cleaning and Bandpass Filtering of Echo Signals

[0117] This step aims to extract the near-inertial internal wave component from the raw echo signal, removing noise and errors through data cleaning and filtering. The operation requires the use of the standard deviation method and a Butterworth filter to ensure signal purity.

[0118] (1) Data cleaning process: Perform the following sub-steps in sequence to eliminate instrument errors and environmental interference.

[0119] (a) Outlier removal: The signal is processed using the standard deviation method. The mean and standard deviation of the data segments are calculated, and a threshold is set at mean ± 3 standard deviations. Data points exceeding the threshold are automatically identified and deleted to avoid the influence of outliers.

[0120] (b) Long-term drift correction: Baseline correction is performed on the cleaned signal using pre-calibrated instrument parameters (such as drift rate and initial deviation). This operation eliminates drift caused by equipment aging and improves data consistency.

[0121] (c) High-frequency noise removal: A third-order Butterworth low-pass filter was used to filter the signal for 72 hours to remove high-frequency noise components. The filtered signal retained the effective low-frequency signal, laying the foundation for subsequent analysis.

[0122] (2) Near-inertial internal wave signal extraction: A third-order Butterworth phase-preserving bandpass filter was applied to filter the cleaned signal. The filter passband frequency was set to 0.95f to 1.05f (f is the Coriolis frequency, calculated based on the observation latitude), and the cutoff frequency was set to ±2.5 hours. The phase-preserving characteristic ensured the signal timing accuracy and effectively separated near-inertial internal waves from interference signals.

[0123] This step emphasizes automated processing; users can use software tools for batch operations, but the filtering effect needs to be verified periodically. The processed signal will be used for physical quantity calculations.

[0124] 2.3. Step 3: Calculate the mixing layer depth and relative vorticity based on echo signals and historical data.

[0125] This step utilizes the processed echo signal and historical temperature and salinity data to calculate the time series of the mixing layer depth and relative vorticity using the GEM method. The operation relies on lookup table construction and interpolation techniques to ensure parameter accuracy.

[0126] (1) Data preparation: Historical temperature and salinity profile data were interpolated onto a uniform pressure grid, with pressure ranging from 0 to 1400 dbar at 2 dbar intervals. The data were sorted by propagation time index for easy subsequent analysis.

[0127] (2) Construction of empirical functions: For each pressure layer, an empirical function of temperature and salinity is established using cubic spline interpolation, in the form T(p i ,τ)=f T (p i ,τ),S(p i ,τ)=f S (p i , τ), where τ is the propagation time. The function is derived based on CTD data and describes the relationship between variables.

[0128] (3) Profile Reconstruction: Given the propagation time of the observed echo signals, after applying a seasonal adjustment procedure, reconstruct the temperature profile T_CPIES and salinity profile S_CPIES from the lookup table. The reconstruction process must ensure data smoothness and physical plausibility.

[0129] (4) Calculation of physical quantities: The mixing layer depth and relative vorticity are calculated using the reconstructed profile. The mixing layer depth is determined based on the density threshold method, and the relative vorticity is derived from the geostrophic velocity gradient. The results are output as time series data.

[0130] This step requires integrating a historical database; users should ensure the timeliness and regional compatibility of the data. After calculation, the wind energy analysis phase begins.

[0131] 2.4. Step Four: Calculate the time series of wind input energy flux

[0132] This step uses a wind stress dataset to calculate the energy flux input from wind to the ocean. The process is simple and efficient, focusing on data integration and flux estimation.

[0133] (1) Data input: Obtain the wind stress dataset for the observation area. The data must be synchronized with the echo signal time. It is recommended to use satellite or buoy data sources to ensure reliability.

[0134] (2) Energy flux calculation: Directly apply the formula WNEF = <τ·u i >, where τ is wind stress, u i The velocity is near inertial. The calculated energy flux time series is used as the model input variable.

[0135] This step requires no complex processing, but it is necessary to verify the spatial representativeness of the wind stress data. Once completed, it is used together with the aforementioned physical quantities for energy flux analysis.

[0136] 2.5. Step Five: Calculate the net horizontal energy flux using the boundary integral method.

[0137] This step quantifies the net horizontal energy flux and wind input contribution within the observation array using the boundary integral method. The operation involves perturbation field calculations and vector integration, requiring assurance of numerical stability.

[0138] (1) Calculation of disturbed physical mass field: Based on the reconstructed temperature-salinity profile, the water density anomaly ρ′ is derived, and the disturbed pressure p′ is obtained by vertical integration. The vertical mean of p′ is set to zero to remove the interference of baroclinic effect; at the same time, the time mean is removed from the observed velocity to obtain the disturbed velocity u.

[0139] (2) Calculation of energy flux density vector: At each point in the array, calculate the covariance between the disturbance velocity u and the disturbance pressure p′ to obtain the energy flux density vector F =<u′p′> This step emphasizes spatial averaging to reduce random error.

[0140] (3) Net horizontal energy flux calculation: Discretize the array boundary into line segments, calculate the normal vector for each segment, and obtain the component F of the energy flux in the normal vector. ⊥ The total net horizontal energy flux F is obtained by weighted summation of line segment lengths. NIIWs =∑(F ⊥ ×ΔL).

[0141] (4) Wind input energy assessment: Simultaneously calculate the near-inertial energy flux WNEF caused by wind for subsequent boundary influence analysis.

[0142] This step is the core of the method; users need to use numerical integration tools to verify boundary closure. The result will be directly used for threshold determination.

[0143] 2.6. Step Six: Determine the impact of boundary energy flux and adjust the array.

[0144] This step assesses boundary effects and optimizes the observation network by dynamically adjusting the array. Operation is based on a ratio threshold to achieve adaptive control.

[0145] (1) Impact assessment: Calculate the net horizontal energy flux F NIIWs The ratio of the wind input energy flux (WNEF) to the wind energy flux. If the ratio is less than 0.1, it is considered a negligible boundary effect, and modeling can proceed directly; otherwise, array adjustment is performed.

[0146] (2) Array adjustment sub-step: When the ratio is ≥0.1, optimize the layout according to the following process.

[0147] (a) Set the percentage threshold: Sort the energy fluxes of all boundary segments, calculate the proportion H of each segment. Set the threshold M (based on actual requirements), and reduce the measurement sites in the area where H < M.

[0148] (b) Adjust the number of sites: Delete the sites in the low-proportion area (H < M), and retain the sites in the high-proportion area to reduce redundant data.

[0149] (c) Optimize the shape and range: According to the energy flux distribution, adjust the array shape to fit the ocean dynamics characteristics, and shrink the coverage range of the low-contribution area.

[0150] (d) Optimize the site layout: Ensure that the remaining sites cover key dynamic processes, such as near-inertial internal waves and vortex activities, to improve the monitoring efficiency.

[0151] (3) Iterative verification: After adjustment, repeat steps one to five, recalculate the ratio until the threshold condition is met.

[0152] This step emphasizes real-time feedback. Users can implement an automated loop through software, but attention should be paid to adjusting the frequency to avoid over-optimization.

[0153] 2.7. Step Seven: Establish a multivariable linear model and evaluate the performance

[0154] This step establishes a linear model based on the aforementioned variables to predict the energy of near-inertial internal waves. The operations include coefficient fitting and statistical verification to ensure the practicality of the model.

[0155] (1) Model establishment: Use the formula

[0156] F(NIIWs) = b1×WNEF + b2×MLD + b3×ζ + b4, where F(NIIWs) is the energy of near-inertial internal waves, MLD is the mixed layer depth, ζ is the relative vorticity, and b1 - b4 are the model coefficients. The coefficients are determined by least squares fitting.

[0157] (2) Performance evaluation: Apply three indicators to verify the model.

[0158] (a) Goodness of fit R 2 Evaluation: Calculate where yi is the observed value, is the predicted value. R 2 > 0.8 indicates strong model prediction ability, between 0.5 - 0.8 can be used for engineering applications, and if < 0.5, it needs to be optimized.

[0159] (b) F-test evaluation: Calculate the F value, and the formula is where k is the number of independent variables and n is the sample size. The p-value < 0.05 indicates that the model is significant, and F > 5 indicates high prediction ability.

[0160] (c) Error variance estimation S 2 Assessment: Calculation S 2 The smaller the value, the better the model fit.

[0161] Upon completion of this step, users will have access to reliable forecasting tools suitable for marine forecasting or research analysis. The model requires regular data updates to maintain accuracy.

[0162] 3. Usage Precautions and Summary

[0163] The following points should be noted when using this method: First, equipment deployment should avoid extreme weather to ensure data continuity; second, filter parameters need to be calibrated regularly during data processing to adapt to different sea areas; finally, it is recommended to combine the model with field verification to improve reliability. Overall, this method achieves efficient modeling of near-inertial internal waves through a systematic process. Users can flexibly adjust parameters based on this guide, but must strictly adhere to the numerical ranges specified in the claims, such as array coverage of 200-600 km, spacing of 30-60 km, and a threshold of 0.1, to avoid bias. This method is applicable to marine monitoring networks, climate change research, or marine engineering, and has high practical value and promising prospects for wider application.

[0164] Example 1: Deployment and Signal Acquisition of Reverse Echo Measurement Array

[0165] This embodiment involves deploying an array and acquiring echo signals within a near-inertial internal wave observation area. In the original embodiment, the array coverage area was set to 200 km × 200 km to 600 km × 600 km, with station intervals of 30 km to 60 km, arranged in a square pattern, and the signal acquisition frequency was no less than once per hour.

[0166] Operational Details: In actual deployment, users should choose sea areas with relatively stable sea conditions to avoid interference from strong currents or storms. The device should be secured using an anchoring system to ensure vertical coverage of the entire water column from the seabed to the surface. Before deployment, it is recommended to conduct a seabed topographic scan to optimize the array shape and reduce topographic shadowing effects. During signal acquisition, an automated system should be used to monitor signal strength in real time. If any anomalies are detected (such as device drift), the position or sampling rate should be adjusted promptly.

[0167] Environmental Adaptation: The array coverage area can be adjusted according to the size of the specific sea area, but it must be strictly controlled within 200-600 kilometers to balance spatial resolution and cost. For example, in open sea areas, a larger coverage area (such as 400 km × 400 km) can be selected, while in complex terrain areas, it can be appropriately reduced to the minimum to ensure data representativeness.

[0168] Data Foundation: This embodiment forms the basis of the method, emphasizing equipment stability and data continuity. Users need to periodically check the mooring status to prevent equipment displacement due to ocean dynamics (such as internal waves or tidal currents). Upon completion, the raw echo signal will be used for subsequent processing, providing input for the entire modeling process.

[0169] Example 2: Data Cleaning and Bandpass Filtering of Echo Signals

[0170] This embodiment preprocesses the acquired echo signal to extract near-inertial internal wave components. The original embodiment included data cleaning (outlier removal, long-term drift correction, and high-frequency noise filtering) and bandpass filtering sub-steps.

[0171] Enhanced cleaning: Outlier removal employs the standard deviation method, with a threshold set at mean ± 3 standard deviations. Outliers are identified and removed via automated scripts, improving efficiency. Long-term drift correction uses pre-calibrated instrument parameters (such as drift rate and initial deviation), which users must periodically update to adapt to changes in the marine environment. High-frequency noise filtering utilizes a third-order Butterworth low-pass filter for 72 hours to retain effective low-frequency signals. During operation, it is recommended to use visualization tools to monitor the filtering effect in real time to ensure that near-inertial internal wave components are not overly smoothed.

[0172] Filtering optimization: A third-order Butterworth phase-preserving filter is used for bandpass filtering, with the passband frequency set to 0.95f to 1.05f (f being the Coriolis frequency, dynamically calculated based on the observation latitude), and the cutoff frequency set to ±2.5 hours. The phase-preserving characteristic ensures signal timing accuracy and avoids waveform distortion. During implementation, users need to verify whether the passband range covers the main energy distribution of local near-inertial internal waves, and make fine adjustments if necessary.

[0173] Quality control: This step is crucial for data reliability. It is recommended to add batch processing capabilities to handle large-scale data. Additionally, intermediate results should be saved after cleaning for easy backtesting and verification. Once completed, the cleaned signal will be used for physical quantity calculations.

[0174] Example 3: Calculating the depth and relative vorticity of the mixing layer based on echo signals and historical data

[0175] This embodiment utilizes processed echo signals and historical temperature and salinity data to calculate the time series of mixing layer depth and relative vorticity using the GEM method. The original embodiment involved data interpolation, empirical function construction, and profile reconstruction.

[0176] Data processing extension: When interpolating historical profile data to a uniform pressure grid (pressure range 0-1400 dbar, interval 2 dbar), users should ensure data source consistency (e.g., using a public oceanographic database) and sort by propagation time index. Empirical functions are constructed using cubic spline interpolation to form the temperature T(p)... i,τ)=f T (p i ,τ) and salinity S(p i ,τ)=f S (p i The relationship between ,τ) enhances smoothness and physical plausibility.

[0177] Reconstruction Details: Profile reconstruction (T_CPIES, S_CPIES) includes seasonal adjustments to avoid interference from climate fluctuations. Further Emphasis: When calculating the mixing layer depth, cross-validation using a density threshold method can be performed; relative vorticity calculations must be based on the reconstructed profile and derived through the geostrophic relationship to ensure accurate results.

[0178] Integrated Application: The output of this embodiment serves as the model input, and users need to periodically update historical data to reflect environmental changes. In implementation, it is recommended to use standardized software (such as MATLAB or Python libraries) for automated calculations to reduce human error and improve efficiency.

[0179] Example 4: Calculation of wind input energy flux

[0180] This step uses a wind stress dataset to calculate the time series of energy flux input from wind to the ocean. The original embodiment directly applied the formula WNEF=<τ·u i >, where τ is wind stress, u i It is near-inertial velocity.

[0181] Data integration: Wind stress data can be sourced from satellite remote sensing or reanalysis datasets (such as ERA5), and must be time-synchronized with echo signals. During implementation, users should verify the spatial representativeness of the data, for example, by interpolating to fill in missing values ​​and avoid local biases.

[0182] Computational Simplification: This step is relatively straightforward, but emphasizes the importance of flux estimation for the model. Further Explanation: Wind input energy is the primary driving force of near-inertial internal waves; the calculation must ensure spatiotemporal matching between ui and τ, for example, by reducing noise through time averaging.

[0183] Efficiency Improvement: Calculations are automated through batch scripts, making it suitable for long-term monitoring projects. Once completed, the energy flux time series data will be integrated with other variables for model building.

[0184] Example 5: Calculation of Net Horizontal Energy Flux using Boundary Integral Method

[0185] This embodiment calculates the net horizontal energy flux and wind input contribution within the observation array using the boundary integral method. The original embodiment included calculation of the disturbed physical field, derivation of the energy flux density vector, and boundary integral.

[0186] Detailed Explanation of Perturbation Field: Based on the reconstructed temperature-salinity profile, calculate the water density anomaly p′, and obtain the perturbation pressure p′ through vertical integration. During the operation, set the vertical mean value of p′ to zero to remove the spurious baroclinic effect caused by the barotropic tide. The perturbation velocity u′ is obtained by removing the time mean and depth mean of the observed instantaneous velocity to ensure the purity of physical quantities.

[0187] Integration Optimization: The energy flux density vector F is calculated as the covariance of <u′p′>. When performing boundary integration, discretize the closed boundary of the array into line segments, and calculate the normal component F for each segment ⊥ and obtain the net horizontal energy flux F by weighted summation with the line segment lengths NIIWs . Users can use numerical integration tools to automate this process and improve accuracy.

[0188] Key Points for Verification: After calculating the wind input energy flux WNEF, a sensitivity analysis should be conducted to evaluate the boundary closure error. This embodiment is the core of the energy balance. It is recommended to add a real-time monitoring function to prevent calculation overflow.

[0189] Example 6: Judging the Influence of Boundary Energy Flux and Adjusting the Array

[0190] This embodiment evaluates the boundary effect and optimizes the observation network by dynamically adjusting the array. The original embodiment makes judgments and adjustments based on the ratio threshold (F NIIWs / WNEF < 0.1).

[0191] Expansion of Judgment: The ratio calculation emphasizes real-time performance, and users can set an automated alarm mechanism to trigger the adjustment process when the ratio ≥ 0.1. Expansion Explanation: The choice of the threshold 0.1 is based on the experience of ocean energy balance to ensure that the boundary influence is negligible; if the condition is not met, iterative adjustments are required until compliance.

[0192] Refinement of Adjustment: The array adjustment includes sorting the energy fluxes of the boundary line segments, calculating the proportion H, and setting the percentage threshold M. For regions where H < M, reduce the measurement sites; for regions where H ≥ M, retain the sites and optimize the layout. During the operation, users can define M according to actual needs (such as 5%), and pre-evaluate the adjustment strategy through simulation tests to reduce on-site risks.

[0193] Practical Suggestions: This step reflects the adaptability of the method. The expansion emphasizes that the shape of the array should conform to the characteristics of ocean dynamics, for example, reducing the coverage area in strong current regions. After adjustment, the previous steps need to be re-executed to ensure data consistency.

[0194] Example 7: Establishment and Performance Evaluation of Multivariable Linear Model

[0195] This embodiment establishes a multivariate linear model based on wind input energy flux, mixing layer depth, relative vorticity, and energy flux, and evaluates its performance. The original embodiment used the formula F(NIIWs)=b1×WHEF+b2×MLD+b3×ζ+b4, and used R… 2 F-test and S 2 Evaluate.

[0196] Modeling refinement: Coefficients b1-b4 are fitted using the least squares method. Users need to standardize the data during implementation to avoid the influence of units. The model can be designed for rolling updates to adapt to changes in time series, such as updating coefficients monthly or quarterly.

[0197] Evaluation enhancement: Goodness-of-fit R 2 In the evaluation, a value close to 1 indicates a high fit; further analysis is recommended to identify outliers. A p-value <0.05 in the F-test indicates a significant influence of the independent variable; users can interpret the results in conjunction with confidence intervals. Error variance estimation S 2 It emphasizes error control and is suitable for model optimization iteration.

[0198] Application scenarios: such as Figure 2 As shown, the modeling results can be used for ocean forecasting or climate research. The extension prompts users to periodically backtest the model, for example, by testing its generalization ability through cross-validation, to ensure long-term reliability.

[0199] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0200] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for near-inertial internal wave modeling based on inverse echo sounding array, characterized in that, The method comprises the following steps: Step S1: arranging an array of inverse echo measuring devices in a near-inertial internal wave observation area, and obtaining echo signals from the sea bottom to the sea surface; Step S2: performing data cleaning and band-pass filtering on the echo signals to extract near-inertial internal wave signals; Step S3: based on the processed echo signals and historical temperature and salinity data in the observation area, calculating time series data of the mixed layer depth and relative vorticity of the observation area using the GEM method; Step S4: calculating time series data of the mixed layer depth and relative vorticity of the observation area according to a lookup table, and calculating time series data of the energy flux input by the wind into the sea using a wind stress data set; Step S5: using a boundary integral method, calculating the net horizontal energy flux of the near-inertial internal wave in the observation array and the energy flux input by the wind into the sea in the region; Step S6: determining whether the influence of the boundary energy flux is less than a preset threshold, and if so, performing step S7; Otherwise, returning to step S1 and adjusting the number and coverage of the array of inverse echo measuring devices; Step S7: based on the energy flux input by the wind into the sea, the mixed layer depth, the relative vorticity and the horizontal energy flux of the near-inertial internal wave, establishing a multivariate linear model.

2. The method of claim 1, wherein, The coverage of the array of inverse echo measuring devices is 200 km x 200 km to 600 km x 600 km; and adjacent inverse echo measuring devices are arranged in a square array on the sea surface with an interval of 30 km to 60 km.

3. The method of claim 1, wherein, The step S2 comprises the following steps: Step S21: data cleaning processing, comprising the following steps in sequence: Step S211: outlier removal: using the standard deviation method to remove outliers in the echo signal, specifically including calculating the mean and standard deviation of the echo signal data segment, setting the threshold to the mean ± 3 standard deviations, identifying and removing data points outside the threshold range as outliers; Step S212: long-term drift correction: using the pre-calibrated instrument drift rate and initial bias parameters to correct the long-term drift of the echo signal after removing outliers, eliminating the baseline drift caused by changes in instrument performance; Step S213: high-frequency noise filtering: applying a 3rd order Butterworth low-pass filter to the drift-corrected echo signal for 72 hours of filtering, removing high-frequency noise components and retaining low-frequency effective signals including near-inertial internal waves; Step S22: near-inertial internal wave signal extraction processing: A 3rd order Butterworth phase-preserving band-pass filter is applied to filter the data-cleaning echo signal, wherein: The passband frequency range of the band-pass filter is set to 0.95f to 1.05f; wherein f is the Coriolis frequency at the latitude of the observation area, to ensure that the main energy distribution frequency band of the near-inertial internal wave is covered; The cutoff frequency of the band-pass filter is set to ± 2.5 hours to effectively separate the near-inertial internal wave signal from the interference signal in the adjacent frequency band; The phase-preserving characteristic ensures that the phase relationship between the frequency components of the signal is not changed during the filtering process, maintaining the time accuracy of the waveform.

4. The method of claim 1, wherein, The step S3 is specifically: Step S31: The historical profile data is interpolated onto a uniform pressure grid, with pressure ranging from 0 to 1400 dbar, with an interval of 2 dbar, and τ index ascending order; Step S32: At each pressure level p i Above, the empirical function of temperature and salinity versus travel time was constructed by cubic spline interpolation: T(p i ,τ)=f T (p i ,τ),S(p i ,τ)=f S (p i ,τ) where T(p i , t) and S(p i , t) represent temperature and salinity at pressure level p i and propagation time t, respectively. f T (p i , t) and f S (p i , t) are empirical functions established based on CTD data; A three-order spline interpolation method is used to construct and describe the relationship between the propagation time and the temperature and salinity; Step S33: Given any observed echo signal sound travel time, after the same seasonal adjustment procedure, reconstruct the temperature and salinity profiles T from the look-up table CPIES , S CPIES ; Step S34: Calculate the mixed layer depth and the relative vorticity using the reconstructed temperature and salinity profiles T CPIES , S CPIES , and the relative vorticity.

5. The method of claim 1, wherein, The step S5 is specifically: Step S51: Calculate the perturbation physical quantity field: Based on the temperature and salinity profiles reconstructed from the echo signals, calculate the water density anomaly p'; According to the hydrostatic relation, derive the perturbation pressure p' by vertically integrating the water density anomaly p'; Set the vertical mean value of the perturbation pressure p' to zero to remove the false baroclinic effect caused by the tidal current; Remove the time mean and depth mean of the observed instantaneous velocity to obtain the perturbation velocity u'; Step S52: At each calculation point in the observation area, calculate the covariance of the perturbation velocity u' and the perturbation pressure p' to obtain the energy flux density vector F: F = <u'p'> Step S53: Calculate the net horizontal energy flux: By integrating along the closed boundary of the array, the net horizontal energy flux F of the low-mode near-inertial internal waves in the observation region is obtained NIIWs ; Step S54: At the same time, in order to evaluate the contribution of wind stress to the local near-inertial energy budget, estimate the wind-induced near-inertial energy flux WNEF as: WNEF = <τ · u i >; where τ is the wind stress, u i is the near-inertial velocity.

6. The method of claim 5, wherein, The step S53, specifically: Step S531: Discretize the closed boundary of the array into multiple continuous boundary line segments, each connecting two adjacent measuring devices; Step S532: For each boundary line segment, calculate its normal vector and calculate the component of the energy flux density vector F on the normal direction of the line segment Step S533: For each boundary line segment, multiply the normal energy flux component F by the length ΔL of the line segment to obtain the energy flow flux through the line segment; Step S534: Summing the energy fluxes across all the boundary line segments on the closed boundary to obtain the total net horizontal energy flux F across the entire closed boundary NIIWs =∑(F ⊥ ×ΔL).

7. The method of claim 1, wherein, In step S6, the influence of the boundary energy flux is judged, specifically: By comparing the ratio of the net horizontal energy flux to the wind-induced near-inertial energy flux, it is considered that the influence is less than the preset threshold when the following conditions are met: where F NIIWs is the net horizontal energy flux, WNEFis the wind-induced near-kinetic energy flux.

8. The method of claim 1 or 7, wherein, In step S6, the influence of the boundary energy flux is greater than or equal to the preset threshold, and the number and coverage of the inverse echo sounding array are adjusted, specifically: Step S61: Set a percentage threshold for energy flux Step S611: Sort the energy flux: Sort the energy flux F of all the boundary segments in descending order ⊥ Sort the flux contribution of each boundary segment in descending order. Step S612: Calculate the proportion: calculate the proportion of the energy flux of each boundary line segment to the net level energy flux F NIIWs H; Step S613: Set a threshold: set a percentage threshold M; for regions with an energy flux proportion H less than the percentage threshold M, consider them to have less contribution and reduce the number of measuring stations in these regions; for regions with an energy flux proportion H greater than or equal to the percentage threshold M, consider them to have greater contribution; Step S62: Adjust the number of array stations according to the distribution of net horizontal energy flux: Step S621: For regions with less energy flux contribution, i.e., regions with a total energy flux proportion H lower than the set threshold M, reduce the number of measuring stations in the region; Step S622: Keep the measuring stations in regions with greater contribution to the total net horizontal energy flux, while delete regions with less contribution to reduce redundant data. Step S63: Adjust the shape and coverage of the array: Step S631: According to the spatial distribution of energy flux, adjust the shape of the array to conform to the shape of the regional ocean dynamics characteristics, and reduce the influence of the array boundary effect; Step S632: For regions with less energy flux contribution, shrink the coverage of the array to remove regions with less influence and keep the measuring points in the core region to reduce redundant data acquisition and improve measurement accuracy and data quality; Step S63: Optimize the layout of the remaining measuring stations: Make the remaining measuring stations cover the key ocean dynamics changes in the region; and the remaining stations should focus on regions with greater contribution to the total net horizontal energy flux to capture key dynamic processes of near-inertial internal waves and backflow eddies.

9. The method of claim 1, wherein, In step S7, the form of the multivariate linear model is: F(NIIWs) = b1 x WNEF + b2 x MLD + b3 x zeta + b4; where F(NIIWs) is the near-inertial internal wave energy, WNEF is the wind-induced near-inertial energy flux, MLD is the mixed layer depth, zeta is the relative vorticity, and b1, b2, b3, and b4 are model coefficients, respectively; Using the goodness of fit R 2 , the F-test and the error variance estimate S 2 Evaluate the model performance.

10. The method of claim 9, wherein, The use of goodness of fit R 2 , F-test and error variance estimate S 2 Evaluate model performance, specifically: Step S71: goodness of fit R 2 The evaluation of the goodness of fit R is expressed as: where y i is the actual observation, is the model prediction, is the mean of the actual observations; When R 2 Close to 1: indicates that the model fits well and can effectively explain most of the variation in the data; When R 2 Greater than 0.8: indicates that the model explains a large proportion of the variation and is generally considered to have good predictive power; When R 2 Between 0.5 and 0.8: The model can have some prediction errors, but it still captures the main characteristics of the data well enough for engineering and research applications; When R 2 Less than 0.5: The predictive power of the model is weak, and needs to be improved or other independent variables are needed. Step S72: evaluation of the F test, expressed as: where k is the number of independent variables, and n is the sample size; When the F value is greater than 1, the result of the F test is a significance level p value; if the p value is less than 0.05, it indicates that the independent variables in the model have a significant effect on the dependent variable; A higher F value, i.e., F > 5, indicates that the regression model has significant predictive power. F value close to 1 or lower: indicates that the model has weak explanatory power for the dependent variable, and more independent variables or optimization of the model should be added; The evaluation criteria are: p < 0.05, indicating that the model is significant; p < 0.01: indicates that the model is significant at a higher confidence level; Step S73: The error variance estimate S 2 is evaluated, and is expressed as: where y i is the actual observation, is the model prediction, n is the sample size, and k is the number of independent variables. When S 2 The smaller the value, the better the fitting effect of the model, and the smaller the prediction error.

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