Echo attenuation compensation and KAN network-based ground wave radar significant wave height inversion method

Abstract

The application provides a ground wave radar significant wave height inversion method based on echo attenuation compensation and KAN network, and belongs to the field of ocean remote sensing and ground wave radar signal processing. The method constructs a global sample set composed of observation time, distance unit and azimuth sector, extracts first-order and second-order spectral integrals, peak value, azimuth correlation statistics, effectiveness mask, relative wind direction and water depth and other features; the training set is used to statistically average the energy class spectral feature attenuation coefficients of adjacent distance units according to distance, sea state and azimuth conditions, and an echo attenuation coefficient lookup table is established; a KAN-HFR wave height inversion model is trained, the reference wave height is obtained at the reference distance unit in the near shore, the energy feature of the next distance unit is compensated by table lookup, and the inversion is recursively performed unit by unit; and a two-dimensional significant wave height field is output after quality control and space-time smoothing. The application can reduce the wave height underestimation caused by echo attenuation at middle and long distances, and improve the global inversion stability and spatial continuity.

Description

Technical Field

[0001] This invention relates to the fields of marine remote sensing observation, ground wave radar signal processing, and wave parameter inversion technology, specifically to a ground wave radar effective wave height inversion method based on echo attenuation compensation and KAN network. Background Technology

[0002] High-frequency ground wave radar mainly utilizes high-frequency electromagnetic waves that diffract along the sea surface to conduct large-scale continuous observations of the sea surface. It has been widely used in monitoring ocean currents, sea surface wind fields, and ocean wave parameters, and is an important means of monitoring marine dynamic environmental parameters.

[0003] Compact ground-wave radars with a monopole cross-ring system offer advantages such as flexible deployment and lower cost. They primarily retrieve the significant wave height of the sea surface through the first and second-order spectral features of the echo Doppler spectrum. Existing ground-wave radar significant wave height retrieval methods mostly focus on single-point modeling approaches such as fixed buoy points or fixed detection units. This typically involves establishing empirical relationships or deep learning models based on the radar echo spectral characteristics of a specific spatial location and the corresponding wave height label.

[0004] However, the energy of the ground wave radar echo spectrum gradually decreases as the detection distance increases, causing the wave height-related features such as the first-order spectrum and second-order spectrum to decrease significantly at medium and long distances. This makes the effective wave height inversion model prone to underestimation, affecting the accuracy of effective wave height detection.

[0005] Therefore, there is an urgent need for an effective wave height inversion method that can be applied to the entire detection grid of ground wave radar and comprehensively consider distance propagation attenuation and sea state modulation, so as to improve the inversion accuracy of ground wave radar in the medium and long range and form reliable two-dimensional effective wave height distribution results. Summary of the Invention

[0006] (a) Technical problems to be solved

[0007] The purpose of this invention is to propose a compact ground wave radar global effective wave height measurement method based on echo attenuation compensation and the Kolmogorov-Arnold-Network (KAN) neural network model, so as to reduce the wave height underestimation caused by mid-to-long-range spectral energy attenuation and improve the inversion accuracy and spatial continuity of the two-dimensional wave height field.

[0008] (II) Technical Solution

[0009] This invention includes the following steps:

[0010] Step 1: Construction of ground wave radar feature sample set.

[0011] To unify the spatial reference of ground wave radar echo spectrum with ERA5 sea state, wind field and water depth data, and to construct the input features and label data required for effective wave height inversion, feature extraction and spatial registration of radar echo spectrum are performed.

[0012] First, the first and second order echo spectra are extracted from the ground wave radar echo spectrum to obtain the energy integrals and peak values ​​of the first and second order spectra. Specifically, the integrals of the positive and negative first and second order spectra are... Perform averaging:

[0013]

[0014] Simultaneously, MUSIC direction finding was performed on the first-order echo spectrum to obtain the first-order spectral amplitude and its effectiveness mask in different orientations.

[0015] For the range-azimuth detection grid of ground wave radar, the latitude and longitude positions of each observation unit are calculated based on the latitude and longitude of the radar station, the range unit interval, and the center angle of the azimuth sector, thus forming a latitude and longitude grid of ground wave radar global detection units.

[0016] Based on this grid, bilinear interpolation is performed on the significant wave height of ECMWF ERA5. For any ground wave radar observation unit, its latitude and longitude position is denoted as (…). Assume this location is at grid point ERA5 ( ), ( ), ( )and( Within the rectangular area enclosed by the observation cell, the ERA5 significant wave height is obtained using the following bilinear interpolation method:

[0017]

[0018] Among them are:

[0019]

[0020] and These represent the normalized relative positions of the observation units in the longitude and latitude directions, respectively, and are used to determine the weighting coefficients in the bilinear interpolation process.

[0021] Obtain spatially registered ERA5 effective wave height data for network training labels and testing to verify ground truth.

[0022] In addition, water depth data is interpolated to the latitude and longitude grid of the ground wave radar to distinguish between land and sea areas and characterize local water depth environmental conditions.

[0023] After the above processing, a unified matching of radar echo spectral characteristics, sea state, wind field, and water depth information is achieved. The spatially registered features include: first-order spectral energy integral. First-order spectral peak Second-order spectral energy integral Second-order spectral peak The first-order spectral amplitude A in different directions ( Effectiveness mask M, ERA5 effective wave height Water depth D, wind field components and the latitude and longitude location of the radar observation unit ( ).

[0024] Step 2: Construct a lookup table for ground wave radar echo attenuation coefficients based on sea state information.

[0025] Because the echo energy of ground wave radar attenuates at medium to long distances, the accuracy of effective wave height inversion is affected when establishing an inversion model using radar echo spectrum characteristics and their corresponding wave height labels. To address this, this invention statistically analyzes the differences in echo spectrum energy of ground wave radar at different distance cells and sea states, obtaining a lookup table of ground wave radar echo attenuation coefficients based on sea state information.

[0026] First, based on the ERA5 effective wave height H(r) corresponding to the ground wave radar detection range unit r, the sea state is divided into boxes h for wave heights of 0-5m with a step size of 0.5m.

[0027] Within each distance cell and sea state sub-cell (r, h), for energy-related spectral characteristics such as first-order spectral integrals, the ratio of echo energy between adjacent distance cells is calculated to obtain the energy attenuation coefficient.

[0028]

[0029] in, Represents the energy class spectral characteristics of the j-th type. Represents the first-order spectral integral. Represents the second-order spectral integral. Indicates the peak value of the first-order spectrum. Indicates the peak value of the second-order spectrum; r is the current distance cell, and H is the sea state sub-cell to which the significant wave height belongs. This refers to the directional sector.

[0030] Then, the energy attenuation coefficients of ground wave radar echoes at different distances and sea conditions at multiple times are statistically analyzed, and the average values ​​of the attenuation coefficients under various conditions are taken to form a lookup table of ground wave radar echo energy attenuation coefficients.

[0031] Step 3: Construction of an effective wave height inversion model based on the KAN-HFR network.

[0032] After completing the spatial registration and sample matching of ground wave radar echo spectral characteristics, ERA5 significant wave height, wind field information and water depth data, a KAN-HFR significant wave height inversion network was constructed based on the sample data of the nearshore effective observation unit. This network was used to establish the nonlinear mapping relationship between radar spectral characteristics and significant wave height, and to provide an initial inversion model for subsequent two-dimensional detection domain global recursive inversion.

[0033] First, to eliminate the differences in units and numerical ranges among different input features, avoid large-value features from dominating the model training process, and improve the stability and convergence efficiency of the KAN-HFR model training, the i-th input feature is normalized using the minimum and range of the training set:

[0034]

[0035] in, This represents the original value of the i-th input feature. and Let represent the minimum and maximum values ​​of the i-th input feature in the training set, respectively; the normalization result is limited to the range [0, 1], and the validation and testing phases only call the normalization parameters saved during the training phase.

[0036] For an m-dimensional normalized input vector The output of the KAN model is represented as:

[0037]

[0038] in, Let be the unary internal function acting on the j-th input feature in the q-th branch. Let be the unary external function of the q-th branch, and 2m+1 be the number of hidden summation branches. The internal and external functions are expanded using B-spline basis functions.

[0039]

[0040]

[0041] For B-spline basis functions of a preset order and node range, and These are the parameters to be trained.

[0042] During training, the KAN-HFR network uses mean squared error as the loss function:

[0043]

[0044] Where N is the number of training samples, Let i be the effective ERA5 wave height of the i-th training sample. Output for the KAN model.

[0045] The spline coefficients of the internal and external functions are updated according to the preset number of iterations. Training stops when the validation set error no longer decreases or reaches the maximum number of iterations. The model with the smallest validation error, spline parameters, and normalization parameters are saved to obtain the target KAN model.

[0046] Using the dataset of radar observation samples, spectral features, sea state, wind field and water depth information obtained in step one, a KAN effective wave height inversion network is constructed and trained as a single-range unit KAN-HFR network.

[0047] In each effective azimuth sector Within, select the nearest effective reference unit. As an anchor point, the original input feature X(t, , Input the KAN-HFR model to obtain the reference significant wave height. :

[0048]

[0049] Step 4: Ground wave radar echo compensation and global wave height recursive inversion.

[0050] First, based on the reference wave height obtained in step three... Based on the current distance unit r and wave height For the sea state sub-cell, the attenuation coefficient of the adjacent range cell is looked up in the ground wave radar echo attenuation coefficient lookup table obtained in step two, and the weighted compensation factor of the echo spectrum characteristics of the next range cell is applied for compensation.

[0051]

[0052] in, , () represents the energy spectrum characteristics after compensation.

[0053] Then, the compensated features of the next range cell are input into the KAN-HFR inversion model to obtain the effective wave height estimate of that range cell:

[0054]

[0055] Based on this result, the estimated wave height is used as a new sea state reference to determine its sea state sub-cell and find the attenuation coefficient corresponding to the next distance cell.

[0056] Following the above method, the effective detection range is progressively increased from near-shore to far-distance units until the maximum effective detection range is reached, thus forming a full-domain effective wave height covering the two-dimensional detection domain of the ground wave radar:

[0057]

[0058] in, This represents the global effective wave height field within the two-dimensional detection domain of the ground wave radar at time t. Represents distance unit r and azimuth sector The effective wave height inversion value at that location, This represents the unit with the furthest effective detection range. This represents the set of effective azimuth sectors.

[0059] (III) Beneficial Effects

[0060] The advantages of this invention are as follows:

[0061] First, this invention addresses the problem of echo spectrum energy attenuation with increasing detection distance by establishing a lookup table for ground wave radar echo attenuation coefficients and compensating for the attenuation of the aforementioned energy spectrum characteristics, thereby mitigating the underestimation of effective wave height at medium and long distances.

[0062] Secondly, this invention employs a recursive approach from near to far anchor points. In each azimuth radial direction, the sea state binning and compensation ratio are updated using the inverted wave height of the previous distance cell, and then echo spectrum compensation and wave height inversion are performed on the next distance cell. This method transforms one-time long-distance energy compensation into a distance-cell-by-distance update, reducing the accumulation of errors caused by inconsistencies between the fixed compensation factor and the actual sea state. Attached Figure Description

[0063] Figure 1 The flowchart of the ground wave radar effective wave height full-domain inversion method based on distance-sea state joint attenuation compensation provided by the present invention is shown.

[0064] Figure 2 This is a schematic diagram of the ground wave radar echo attenuation curve provided by the present invention.

[0065] Figure 3 This is a schematic diagram illustrating the construction of the ground wave radar echo attenuation coefficient lookup table provided by the present invention.

[0066] Figure 4 This is a schematic diagram of the KAN-HFR effective wave height inversion network structure provided by the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be understood that the described embodiments are for explaining the invention and are not intended to limit the scope of protection of the invention.

[0068] Unless otherwise defined, the technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art. The term "ocean cell" as used herein refers to a radar detection grid defined by a range cell and an azimuth sector. The term "target KAN-HFR model" as used herein refers to an effective wave height inversion model that has been trained and whose normalized parameters and spline function parameters have been saved.

[0069] This invention provides a compact ground wave radar full-domain significant wave height measurement method based on echo attenuation compensation and the Kolmogorov-Arnold-Network (KAN) neural network model. The overall process is as follows: Figure 1 As shown, it mainly includes four parts: ground wave radar feature extraction and spatial registration, construction of ground wave radar echo attenuation coefficient lookup table based on sea state information, construction of effective wave height inversion network based on KAN-HFR model, echo compensation and global wave height recursive inversion.

[0070] Step 1: Construction of ground wave radar feature sample set.

[0071] To unify the spatial reference of ground wave radar echo spectrum with ERA5 sea state, wind field and water depth data, and to construct the input features and label data required for effective wave height inversion, feature extraction and spatial registration of radar echo spectrum are performed.

[0072] First, wave height-related features are extracted from the ground wave radar echo spectrum, including first-order spectral integrals, second-order spectral integrals, first-order peak values, and second-order peak values. Simultaneously, MUSIC direction finding is performed on the first-order echo spectrum to obtain the first-order spectral amplitude and its mask at different azimuths. Furthermore, the energy integrals of the first-order and second-order spectra on both the positive and negative frequencies are obtained. Perform averaging:

[0073]

[0074] For the range-azimuth detection grid of ground wave radar, the latitude and longitude positions of each observation unit are calculated based on the latitude and longitude of the radar station, the range unit interval, and the center angle of the azimuth sector, thus forming a latitude and longitude grid of ground wave radar global detection units.

[0075] Based on this detection unit, the significant wave height of ECMWF ERA5 is interpolated. For any ground wave radar detection unit, its latitude and longitude position is denoted as (…). Assume this location is at grid point ERA5 (). ), ( ), ( )and( Within the rectangular area enclosed by the given information, the significant wave height of ECMWF ERA5 corresponding to this detection unit is obtained using bilinear interpolation.

[0076]

[0077] Among them are:

[0078]

[0079] and These represent the normalized relative positions of the observation units in the longitude and latitude directions, respectively, and are used to determine the weighting coefficients in the bilinear interpolation process.

[0080] Obtain spatially registered ERA5 effective wave height data for network training labels and testing to verify ground truth.

[0081] Water depth is provided by the ETOPO global topography and water depth dataset and spatially interpolated based on the above-mentioned ground wave radar latitude and longitude grid to distinguish between land and sea areas and characterize local water depth environmental conditions.

[0082] After the above processing, unified matching of radar echo spectral characteristics, sea state, wind field, and water depth information is achieved. The spatially registered features include: first-order spectral energy integral. First-order spectral peak Second-order spectral energy integral Second-order spectral peak The first-order spectral amplitude A in different directions ( Effectiveness mask M, ERA5 effective wave height Water depth D, wind field components and the latitude and longitude location of the radar observation unit ( ).

[0083] Step 2: Construct a lookup table for ground wave radar echo attenuation coefficients based on sea state information.

[0084] First, the ERA5 significant wave height is divided into multiple equally spaced sea state bins (h) within the 0-5m range with a step size of 0.5m: 0-0.5m, 0.5-1m, and 1-1.5m. Within each range cell and sea state bin (r, h), the ratio of echo energy between adjacent range cells is calculated based on energy spectral characteristics such as the first-order spectral integral, to obtain the energy attenuation coefficient.

[0085]

[0086] in, Represents the energy class spectral characteristics of the j-th type. Represents the first-order spectral integral. Represents the second-order spectral integral. Indicates the peak value of the first-order spectrum. Indicates the second-order spectral peak value; r is the current distance cell, and H is the sea state sub-cell to which the significant wave height belongs. This refers to the directional sector.

[0087] The adjacent attenuation ratio describes the proportion of spectral energy retention between two consecutive range cells, while the cumulative attenuation ratio describes the overall attenuation of the target range cell relative to the near-shore reference range cell.

[0088] Then, the ground wave radar echo energy attenuation coefficients at different distances and sea states at multiple times were statistically analyzed, and their averages were taken to obtain the final result as shown below. Figure 2 and Figure 3 The ground wave radar echo energy attenuation curve and coefficient lookup table are shown.

[0089] In some implementations, the maintenance coefficient is limited to the range of [kmin, 1], and the compensation ratio of adjacent distance cells is expressed as:

[0090]

[0091] Step 3: Construction of an effective wave height inversion model based on the KAN-HFR network.

[0092] KAN is an interpretable neural network model based on the Kolmogorov-Arnold representation theorem. Its core idea is to transform the fixed activation functions located at nodes in traditional neural networks into learnable univariate functions located on the edges, and then use spline functions to parameterize these edge functions. Compared to traditional multilayer perceptrons, KAN can adaptively learn the nonlinear transformation of input variables during feature propagation and achieve nonlinear combinations of multidimensional features through an additive structure. Therefore, it has good applicability in characterizing the complex mapping relationship between ground wave radar echo spectrum characteristics, sea state environmental factors, and significant wave height.

[0093] First, to eliminate the differences in units and numerical ranges among different input features, avoid large-value features from dominating the model training process, and improve the stability and convergence efficiency of the KAN-HFR model training, the i-th input feature is normalized using the minimum and range of the training set:

[0094]

[0095] in, This represents the original value of the i-th input feature. and represents the minimum and maximum values ​​of the i-th input feature in the training set, respectively; the normalization result is limited to the range [0, 1]. During the testing phase, only the minimum, range, and output scale parameters saved during the training phase are called, and the normalization parameters are not recalculated using the test data.

[0096] Based on the spatial registration results obtained in step one, each ground wave radar observation unit is constructed as an input sample for the KAN-HFR network. This sample consists of ground wave radar echo spectral features and their matched wind field and water depth data, denoted as the normalized input feature vector. For an m-dimensional normalized input vector... The KAN output is represented as:

[0097]

[0098] in, Let be the unary internal function acting on the j-th input feature in the q-th branch. Let be the unary external function of the q-th branch, and 2m+1 be the number of hidden summation branches. KAN learns unary functions on the edges instead of the combination of fixed activation functions and linear weights in traditional multilayer perceptrons to express the nonlinear mapping between radar spectral features and effective wave height.

[0099] The inner and outer functions are expanded using B-spline basis functions:

[0100]

[0101]

[0102] in, For B-spline basis functions of a preset order and node range, and These are the parameters to be trained. By updating the spline coefficients, the error between the effective wave height of the model output and the ERA5 label is reduced.

[0103] For example, the KAN-HFR network has an input dimension m of 6 and a hidden summation branch number of 2m+1, or 13; the internal and external functions each use 7 spline control coefficients. The internal spline parameter matrix has a size of 7×78, and the external spline parameter matrix has a size of 7×13. These dimensions are used to illustrate an implementable structure and do not constitute a limitation on the input dimension, number of branches, or number of spline nodes.

[0104] KAN-HFR network training uses mean squared error as the objective function:

[0105]

[0106] Where N is the number of training samples, Let i be the effective ERA5 wave height of the i-th training sample. This represents the output of the trained inversion model. The spline coefficients of the internal and external functions are updated according to a preset number of iterations. Training stops when the validation set error no longer decreases or reaches the set number of iterations, and the model with the smallest validation error is saved as the target KAN-HFR model.

[0107] Based on the unified matching sample set obtained in step one, the KAN-HFR effective wave height inversion network is constructed and trained to obtain the following results: Figure 4 The single-range cell KAN-HFR inversion model is shown. This sample set has been uniformly registered with ground wave radar echo spectral characteristics, sea state, wind field, water depth, and spatial location information, and therefore can be directly used for model training and validation.

[0108] In each effective azimuth sector Within, select the nearest effective reference unit. As the anchor point for inversion, the original input features at the anchor point are used. , Input the target KAN-HFR model to obtain the reference significant wave height. :

[0109]

[0110] Step 4: Ground wave radar echo compensation and global wave height recursive inversion.

[0111] Based on the reference wave height obtained in step three Based on the current distance unit r and wave height The sea state sub-cell is assigned to, and the attenuation coefficient of the adjacent range cell is found in the ground wave radar echo attenuation coefficient table obtained in step two. The echo spectrum characteristics of the next range cell are then analyzed based on the attenuation coefficient c. Compensation will be provided.

[0112]

[0113] in, , () represents the energy spectrum characteristics after compensation.

[0114] Then, the compensated echo spectral characteristics, effectiveness mask, relative wind direction, and water depth are input into the KAN-HFR inversion model to obtain the effective wave height estimate for this distance cell:

[0115]

[0116] Based on this result, As a new sea state reference, the sea state bin is redefined, the attenuation coefficient is found for compensation, and the significant wave height is retrieved by inputting the KAN-HFR network. Following this method, the effective detection range is recursively calculated from nearshore to far-distance cells until the maximum effective detection range is reached, thus forming the full-domain significant wave height covering the two-dimensional detection domain of the ground wave radar.

[0117]

[0118] in, This represents the global effective wave height field within the two-dimensional detection domain of the ground wave radar at time t. Represents distance unit r and azimuth sector The effective wave height inversion value at that location, This represents the unit with the farthest effective detection range. This represents the set of effective azimuth sectors.

[0119] In some specific cases, step four performs a reasonable range check and compensation limiting on the KAN output. Let the allowable effective wave height range be [...]. , The effective wave height after amplitude limiting is expressed as follows:

[0120]

[0121] Range smoothing is applied to significant wave heights in the same azimuth, and time smoothing is applied to continuous time results within 2 hours for the same ground wave radar detection cell. The smoothing window and weights can be adaptively adjusted based on range, sea state, and local gradients to suppress isolated anomalies while minimizing the attenuation of true wave height variations.

[0122] The target KAN model is evaluated using root mean square error, mean absolute error, bias, and correlation coefficient. Root mean square error, mean absolute error, and bias are expressed as follows:

[0123]

[0124] Where N represents the total number of samples. This represents the effective wave height inversion value corresponding to the i-th sample. This represents the true effective wave height corresponding to the i-th sample. In addition to the overall indicators, evaluation indicators are statistically analyzed according to distance range and sea state bins to determine the stability of the model under near, medium, and long distances and different sea state conditions.

[0125] In this experimental case study, measured data from a SeaSonde compact ground wave radar at a near-shore observation station were used for verification, with a range cell spacing of approximately 5.82 km. Continuous time independent partitioning was employed. During the training phase, ground wave radar echo attenuation coefficients and KAN-HFR models were established, while all parameters were fixed during the testing phase.

[0126] Based on 119,064 independent test samples, the wave height inversion scheme without compensation for echo spectrum characteristics had an RMSE of 0.619 m, a MAE of 0.473 m, a Bias of -0.382 m, and a correlation coefficient R of 0.670. After recursive compensation, the RMSE was 0.539 m, the MAE was 0.403 m, the Bias was -0.145 m, and the R was 0.681. After further applying window smoothing filtering to the inverted global effective wave height, the RMSE was 0.493 m, the MAE was 0.368 m, the Bias was -0.166 m, and the R was 0.722.

[0127] According to the distance cell, the wave height inversion scheme without compensation for echo spectrum characteristics has a wave height inversion RMSE of approximately 0.380 m in the 8th distance cell, and the RMSE increases to approximately 0.785 m in the 20th distance cell; after recursive compensation, the RMSE in the 20th distance cell is approximately 0.638 m, an improvement of approximately 0.147 m.

[0128] The results show that the present invention can reduce the systematic underestimation at medium and long distances and improve the continuity of the global wave height field.

[0129] This invention is not limited to the above-described embodiments. Those skilled in the art can adjust the distance range, sea state binning, input feature combination, number of KAN branches, number of spline nodes, number of iterations, amplitude limit range, and smoothing method without departing from the spirit of this invention; such equivalent substitutions or modifications should all fall within the protection scope of the claims of this invention.

Claims

1. A method for inverting the effective wave height of ground wave radar based on echo attenuation compensation and KAN network, characterized in that, Includes the following steps: (1) Extract the echo spectrum features of compact ground wave radar and the first-order spectrum frequency features in different directions, construct an ocean unit determined by the range unit and the azimuth sector, match the external effective wave height label, wind field and water depth data according to the time and latitude of the ocean unit to obtain the global sample set, and divide the global sample set into training set, validation set and independent test set according to the continuous time period. (2) Using only the training set, according to the range cell and the sea state of the significant wave height, the energy spectrum characteristic ratio between adjacent range cells at the same observation time is statistically analyzed and the average is obtained to obtain the ground wave radar echo attenuation coefficient lookup table, and the compensation ratio of adjacent range cells is determined according to the echo attenuation coefficient in the echo attenuation coefficient lookup table. (3) Select nearshore effective distance unit samples from the training set, the validation set and the independent test set respectively, normalize the input features in the selected samples, and use the nearshore effective distance unit samples selected from the training set to construct and train the nearshore single distance unit KAN-HFR effective wave height inversion network to obtain the target KAN-HFR model. (4) For each effective azimuth sector, select the near-shore effective range cell as the anchor point, input the echo spectrum characteristics at the anchor point into the target KAN-HFR model to obtain the reference effective wave height; find the compensation ratio according to the current range cell and the sea state bin to which the reference effective wave height belongs, compensate the energy spectrum characteristics of the next range cell and input them into the same target KAN-HFR model; use the obtained effective wave height as the new sea state reference, and iterate from the near shore to the far distance cell by cell, and perform quality control and smoothing on the inversion results to obtain the global effective wave height field of the two-dimensional detection domain of the ground wave radar.

2. The method for inverting the effective wave height of ground wave radar based on echo attenuation compensation and KAN network according to claim 1, characterized in that, The formation of the global sample set in step (1) includes: (1) Based on the ground wave radar station, the range unit and azimuth sector are divided according to the radar range resolution and preset azimuth interval. Each ocean unit is represented as a combination of range unit and azimuth sector. The longitude and latitude of the ocean unit are calculated according to the radar station latitude and longitude, the distance between the center of the range unit and the center angle of the azimuth sector. (2) Extract the first-order spectral integral, second-order spectral integral, first-order spectral peak and second-order spectral peak from the ground wave radar echo spectrum, and average the corresponding features of the energy integral on both sides of the positive and negative frequencies; extract the first-order spectral frequency points and their effectiveness masks in different directions from the autocorrelation spectrum of the monopole antenna. (3) Match the external significant wave height label, wind field data and water depth data according to the observation time and latitude and longitude of the ocean unit. The water depth data is spatially matched once, and the wind field data is converted into the form of the angle relative to the direction of incoming waves of the ocean unit.

3. The method for inverting the effective wave height of ground wave radar based on echo attenuation compensation and KAN network according to claim 1, characterized in that, The construction of the return attenuation coefficient lookup table in step (2) includes: (1) Within each range cell and sea state sub-bin (r, h), for the energy spectrum characteristic of the first-order spectral integral, the ratio of the echo energy of adjacent range cells is calculated to obtain the energy attenuation coefficient: ； In the formula, Represents the energy class spectral characteristics of the j-th type. Represents the first-order spectral integral. Represents the second-order spectral integral. Indicates the peak value of the first-order spectrum. Indicates the peak value of the second-order spectrum; r is the current distance cell, and H is the sea state sub-cell to which the significant wave height belongs. For directional sectors; (2) When the number of effective samples of the combination of distance unit and sea state sub-box is lower than the preset threshold, the echo attenuation coefficient of the previous adjacent sea state sub-box is used as the selection value, and the compensation ratio is determined according to the energy attenuation coefficient. (3) Limit the echo attenuation coefficient of each sub-box to a preset range. Within [1], its reciprocal, after being clipped, is used as the compensation ratio c(r,H) for adjacent distance cells: 。 4. The method for inverting the effective wave height of ground wave radar based on echo attenuation compensation and KAN network according to claim 1, characterized in that, The nearshore single-distance cell KAN-HFR significant wave height inversion network construction described in step (3) includes: (1) Select near-shore effective distance unit samples from the global sample set as network training samples, divide the training set, validation set and independent test set according to continuous time periods, and normalize the input features using training set statistics; (2) Using echo spectrum energy characteristics, first-order spectral frequency points and their effectiveness masks, relative wind direction and water depth as inputs, and effective wave height as output, a KAN-HFR model is constructed; the KAN-HFR model is based on Kolmogorov-Arnold representation, and its univariate internal function and univariate external function are expanded using B spline basis functions, and the spline coefficients are updated through training; (3) The mean squared error is used as the training target. The parameters of the KAN-HFR model are updated using the training set. The target KAN-HFR model with the minimum network structure, number of iterations and validation error is determined using the validation set. The independent test set does not participate in model training and parameter selection.

5. The method for inverting the effective wave height of ground wave radar based on echo attenuation compensation and KAN network according to claim 1, characterized in that, The specific process of recursively extrapolating from nearshore to distant distance units as described in step (4) includes: (1) Establish a sequence of range cells arranged from near to far within each effective azimuth sector, select the near effective cells as anchor points, and input the anchor point features without range attenuation compensation into the target KAN-HFR model to obtain the reference effective wave height H0: ； (2) Based on the current distance cell and the sea state bin to which the current inverted significant wave height belongs, obtain the compensation ratio from the echo attenuation coefficient lookup table, and compensate for the energy spectrum characteristics of the next distance cell: ； (3) Re-input the compensated energy class spectrum features into the same target KAN-HFR model to obtain the effective wave height of the next distance cell: ； (4) Using the effective wave height of the next range cell as the new sea state reference, the compensation ratio of the sea state sub-cell and the next adjacent range cell is re-determined, and the compensation and inversion are repeated along the same azimuth radial direction until the farthest effective range cell of the corresponding azimuth sector is reached, thereby forming the full-domain effective wave height covering the two-dimensional detection domain of the ground wave radar: ； in, This represents the global effective wave height field within the two-dimensional detection domain of the ground wave radar at time t. Represents distance unit r and azimuth sector The effective wave height inversion value at that location, This represents the unit with the farthest effective detection range. This represents the set of effective azimuth sectors.

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