A method for improving applicability of a high sea state and high frequency band model based on a SSA model

Abstract

The application provides a method for improving applicability of a medium-high sea state and high-frequency band model based on an SSA model, and belongs to the technical field of sea surface electromagnetic scattering simulation. Sea surface backscattering data and corresponding radar parameters are obtained, and synchronous sea surface environment information is obtained; the sea surface backscattering data, the radar parameters and the synchronous sea surface environment information are subjected to space-time matching to obtain a matching data set; the influence of sea foam on the relative dielectric constant of the sea surface and main scattering mechanisms is introduced into the SSA model, and on the basis of simplifying integral calculation of the SSA model, an expression of the approximate SSA is simplified according to main influence factors affecting integral precision of the SSA model, integral limits of the SSA model are analyzed and determined, and finally, a simulation result of sea surface electromagnetic scattering of a mixed sea surface is obtained.

Description

Technical Field

[0001] This invention belongs to the field of sea surface electromagnetic scattering simulation technology, and relates to an improved method for the applicability of SSA-based models in medium and high sea states and high frequency bands. Background Technology

[0002] Sea surface electromagnetic scattering simulation primarily uses computer modeling and numerical calculation methods to simulate the interaction process between electromagnetic waves and the sea surface and obtain corresponding scattering data. Benefiting from its advantages of being economical, efficient, and easy to implement, sea surface electromagnetic scattering simulation has been widely used in the study of the mechanism of microwave scattering at sea surface.

[0003] Currently, sea surface electromagnetic scattering simulation methods can be mainly divided into two categories: numerical methods and analytical approximation models. Numerical methods offer the advantage of high simulation accuracy, but require an extremely large amount of computation, especially when calculating electromagnetic scattering from electrically large sea surfaces, which consumes significant computational time and resources. Therefore, in practical applications, numerical methods are typically used only for one-dimensional sea surface electromagnetic scattering calculations or for verifying analytical approximation models. Compared to numerical models, analytical approximation models achieve a balance between accuracy and computational efficiency by setting assumptions and approximation conditions, thus performing sea surface electromagnetic scattering calculations with higher computational efficiency and gaining wider application. Commonly used analytical approximation models include the Geometric Optics (GO) method, the Small Perturbation Model (SPM), the Composite Surface Bragg Scattering Model (CB), the Two-Scale Model (TSM), and the Small Slope Approximation Model (SSA), among others.

[0004] The GO model is suitable for quasi-specular scattering simulations of the sea surface, and is commonly used in the small incident angle range close to 0°. The SPM model is suitable for Bragg scattering simulations of the sea surface, and is commonly used in the medium incident angle range. Compared to the GO and SPM models, the CB and TSM models have a wider range of applicable incident angles. The CB and TSM models assume that the sea surface is a superposition of large-scale and small-scale rough surfaces, and use local incident angle thresholds and cutoff wavenumbers to delineate the large-scale and small-scale rough surfaces of the sea surface, respectively. However, the selection of the delineation conditions lacks sufficient physical basis, which leads to uncertainties in the model. The SSA model uses the full spectrum to calculate electromagnetic scattering of the sea surface, and avoids the problem of selecting delineation conditions in the CB and TSM models, showing strong superiority in electromagnetic scattering simulations of the sea surface. However, the SSA model suffers from lower simulation accuracy in medium and high sea states and lower computational efficiency in the high-frequency band, which limits the applicability of the model in medium and high sea states and high-frequency band conditions. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes an improved method for the applicability of SSA-based models in medium-to-high sea states and high-frequency bands, comprising the following steps:

[0006] S1. Acquire sea surface backscatter data and corresponding radar parameters, and acquire synchronized sea surface environmental information;

[0007] S2. Perform spatiotemporal matching of sea surface backscattering data, radar parameters, and synchronized sea surface environmental information to obtain a matching dataset;

[0008] S3. The influence of marine foam on the relative permittivity and main scattering mechanism of the sea surface is introduced into the SSA model, and the integral calculation of the SSA model is simplified. Through the analysis of the SSA model expression, the integration limit of the SSA model is determined, and finally high-precision simulation results of sea surface electromagnetic scattering under high frequency band and medium-high sea state conditions are obtained.

[0009] Furthermore, the influence of marine foam on the relative permittivity of the sea surface and the main scattering mechanisms is introduced into the SSA model, including:

[0010] (1) Determine the proportion of regular sea surface and marine foam in mixed sea surface by using empirical relationships of white crown coverage;

[0011] The empirical relationship for white crown coverage is shown below:

[0012] ;

[0013] In the formula, Indicates the coverage rate of white crowns. Indicates the wind speed due to friction with the sea surface;

[0014] (2) Calculate the relative permittivity of conventional sea surface and marine foam using the Debye equation and the equivalent permittivity mixed formula, respectively;

[0015] The equivalent dielectric constant of the foam is calculated using the Refractive formula, as shown below:

[0016] ;

[0017] in, Foam porosity is defined as the proportion of air in a unit volume of seawater. This represents the relative permittivity of the foam. This represents the relative permittivity of seawater. The dielectric constant of air;

[0018] (3) Introduce Fresnel's reflection theorem to calculate the polarization correlation coefficient of marine foam;

[0019] (4) Based on the sea surface division results and the relative permittivity of seawater and marine foam, calculate the electromagnetic scattering of the sea surface of conventional sea surface and marine foam respectively, and obtain the electromagnetic scattering of the sea surface of mixed sea surface accordingly.

[0020] The normalized radar cross section (NRCS) of a mixed sea surface is represented as follows:

[0021] ;

[0022] In the formula, Indicates the NRCS of mixed sea surface. NRCS refers to marine foam. This refers to the NRCS of the normal sea surface.

[0023] Furthermore, based on the simplified integral calculation of the SSA model, the integration limits of the SSA model are determined through analysis of the SSA model expression, specifically including:

[0024] (1) Simplify the integral calculation of the SSA model;

[0025] (2) Determine the main factors affecting the accuracy of the integral results of the SSA model;

[0026] (3) Make reasonable approximations and simplifications to the expression of the SSA model, and on this basis, analyze and determine the integration limit of the SSA model and the number of nodes required for the unit interval.

[0027] Furthermore, the double integral involved in the SSA model is simplified into multiple single integrals through equivalent simplification, and the simplified autocorrelation function... Angle function integrals in the SSA model Represented as:

[0028] ;

[0029] ;

[0030] In the formula, Indicates radial distance. Indicates the incident azimuth angle. Denotes wave number, k B For Bragg wavenumber, , Represents the perpendicular projection components of the incident and scattered waves. Denotes the zeroth-order Bessel function of the first kind. Denotes the second-order Bessel function of the first kind. Denotes the Bessel function of the first kind of order 2n. Denotes the first-order modified Bessel function of order n. This represents a one-dimensional wave spectrum containing correction terms. This is the ratio term in the wave spectrum directional expansion function. It is the isotropic part of the autocorrelation function. It is the anisotropic part of the autocorrelation function.

[0031] Furthermore, the simplified expression for the SSA model is as follows:

[0032] ;

[0033] In the formula, For the expression of the SSA model, , Let represent the wavenumber vectors of the incident and scattered waves on the horizontal plane, respectively. This represents the first-order polarization correlation coefficient matrix. This represents a first-order modified Bessel function of the first kind.

[0034] Furthermore, the sensitivity of each term in the SSA model to the number of nodes required for the integration interval and the unit interval is analyzed. The SSA model expression is then approximated and simplified. The kernel functions used to analyze the number of nodes required for the integration interval and the unit interval after the approximation and simplification are expressed as follows:

[0035] ;

[0036] .

[0037] Furthermore, the simulation accuracy and computational efficiency of the evaluation model are validated using a matching dataset.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] First, the dimensionality of the SSA model's integral operation was reduced using Bessel functions, thus lowering the model's computational complexity. Based on this, the main contribution intervals of the integral part were analyzed through approximate simplification of the SSA model. The selection of integration limits and the number of nodes per unit interval was determined. By reducing redundant calculations, the computational efficiency of the model was improved, enhancing the computational efficiency of the SSA model for sea surface electromagnetic scattering simulation. This improvement was particularly pronounced at high frequencies. Furthermore, by introducing the influence of sea foam on the relative permittivity of the sea surface and the main scattering mechanisms, the accuracy of the SSA model's sea surface electromagnetic scattering simulation under medium to high sea states was improved. Attached Figure Description

[0040] Figure 1 A flowchart of the method for improving the applicability of SSA-based models in medium-to-high sea states and high-frequency bands;

[0041] Figure 2 A comparison chart of model simulation results and measured data for Ku-band HH polarization;

[0042] Figure 3 This is a comparison of model simulation results and measured data under Ka-band HH polarization high sea state conditions.

[0043] Figure 4 The graph shows the changing trend of the number of nodes required for computation of the improved SSA model under different incident angles in the Ka band when the wind speed in the upwind direction is 5 m / s and 15 m / s.

[0044] Figure 5 The graph shows the reduction in computational load of the improved model when the incident angle is 30°. Detailed Implementation

[0045] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0046] Example 1

[0047] 1. Construct the experimental dataset.

[0048] The experimental data used in this invention includes satellite data and buoy data, and an experimental dataset is constructed through data preprocessing. This dataset will be used to evaluate the performance of the improved applicability method for medium-to-high sea state and high-frequency band models based on the SSA model. Data preprocessing includes four parts: invalid data removal, wind speed data transformation, spatiotemporal data matching, and optimization of the quality of the matched data.

[0049] (1) Invalid data removal. Invalid data in satellite and buoy data are identified and removed by quality identification and data filling identification to ensure the validity of the data.

[0050] (2) Wind speed data conversion. Currently, the commonly used data standard for sea surface wind speed inversion results, wave spectrum input, and geophysical model function input is the wind speed at 10 m above the sea surface. However, the distance of the anemometers installed on the buoys from the sea surface is not uniform. Therefore, it is necessary to convert the wind speed data measured by the buoys into the equivalent wind speed U at 10 m above the sea surface. 10 .

[0051] ;

[0052] In the formula, Indicates the height above the sea surface Wind speed at that location.

[0053] (3) Spatiotemporal matching of data. To form a usable matching dataset, spatiotemporal matching of the collected satellite data and auxiliary data is required. The time window for spatiotemporal matching is set to 30 minutes, and the spatial window is set to 15 km. In spatiotemporal matching, satellite data within the time and spatial windows are filtered based on buoy data.

[0054] (4) Matching Data Quality Optimization. To improve the quality of the matching dataset, it is necessary to filter out matching data pairs affected by measurement errors. First, low-quality data is filtered out using satellite data quality indicators. Then, the standard deviation of all sea surface backscatter data within the same buoy data spatiotemporal window is calculated, and the portion of the matching data with a standard deviation exceeding 3dB is filtered out to reduce the impact of random errors. Finally, multiple quality-controlled matching data pairs within the same buoy data spatiotemporal window are averaged to generate the matching dataset.

[0055] 2. Improvement methods for the applicability of SSA model for sea surface electromagnetic scattering simulation in medium and high sea states and high frequency bands.

[0056] The expression for the SSA model is shown below:

[0057] ;

[0058] In the formula, Represents the normalized radar cross section. and These represent horizontal or vertical polarization, respectively. , Let represent the wavenumber vectors of the incident and scattered waves on the horizontal plane, respectively. It is a two-dimensional spatial vector. This represents the first-order polarization correlation coefficient matrix, and the perpendicular projection components of the incident and scattered waves. , and autocorrelation function It can be represented as follows:

[0059] ;

[0060] ;

[0061] In the formula, the correction term It can be represented as follows:

[0062] ;

[0063] In the formula, and These represent the incident and scattered angles, respectively. Example of radial direction. Represents the sea surface wave number vector. Represents a two-dimensional wave spectrum. Indicates wave number, Indicates wind direction. This represents the second-order polarization correlation coefficient matrix.

[0064] When using the SSA model to perform electromagnetic scattering calculations on the sea surface, the parts related to the sea surface mainly include: and .in It is mainly related to the selection of the wave spectrum. It is mainly related to the relative permittivity of the sea surface. First-order and second-order... Each item can be represented as follows:

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] In the formula, , , , , , , , and The subscripts VV, VH, HV, and HH represent the corresponding polarization modes, and subscripts (1) and (2) indicate that they are elements of the first-order or second-order polarization correlation coefficient matrix, respectively. and These represent the incident and scattered wave vectors, respectively. Represents the sea surface wave number vector. Represents the scalar and vector quantities of sea surface wave number. Let be the unit normal vector of the horizontal plane. This represents the relative permittivity of the rough surface. The angular frequency of the electromagnetic wave. For the speed of light, parameters , , , , and It can be calculated using the following formula:

[0074] ;

[0075] ;

[0076] When using the SSA model for sea surface electromagnetic scattering calculations, the relative permittivity of seawater is typically used as the relative permittivity of the rough surface. However, under high sea states, due to wave breaking, the sea surface is composed of both normal sea surface and sea foam. The dielectric properties of sea foam differ significantly from those of normal sea surface. Using the relative permittivity of seawater as the relative permittivity of the rough surface would lead to a significant reduction in computational accuracy. Furthermore, sea foam alters the primary scattering mechanism of the rough surface, resulting in differences from the polarization correlation coefficient matrix in the SSA model. Using the polarization correlation coefficient matrix from the SSA model to calculate the polarization correlation coefficient of the high sea state sea surface would affect the ability to characterize the polarization properties of sea surface scattering. In addition, the computational burden of calculating sea surface electromagnetic scattering using the SSA model largely depends on its complex integral operations.

[0077] In summary, to improve the applicability of the SSA model under medium-to-high sea states and high-frequency conditions, the proposed improvement method for the applicability of the SSA model under medium-to-high sea states and high-frequency conditions in this invention improves the simulation accuracy of the model under medium-to-high sea states by introducing the influence of sea foam on the relative permittivity of the sea surface and the main scattering mechanisms. It also improves the computational efficiency of the model by simplifying the integral calculation of the SSA model, determining the integration limits of the SSA model, and the number of nodes per unit interval. Specific steps are as follows: Figure 1 As shown.

[0078] like Figure 1 As shown, this invention corrects the influence of marine foam on the relative permittivity and main scattering mechanisms of the sea surface through three steps: sea surface composition classification, relative permittivity correction, and polarization correlation coefficient correction.

[0079] (1) Classification of sea surface composition.

[0080] To incorporate the impact of marine foam, this invention first uses an empirical relationship for canopy cover to quantify the proportion of marine foam on the sea surface. The empirical relationship for canopy cover used is as follows:

[0081] ;

[0082] In the formula, Indicates the coverage rate of white crowns. This indicates the wind speed caused by friction on the sea surface. When the speed is less than or equal to 0.11 m / s, the white crown coverage is 0, and the sea surface is entirely composed of the normal sea surface. When the speed is greater than 0.11 m / s, the sea surface consists of marine foam and the normal sea surface.

[0083] (2) Correction of relative permittivity.

[0084] Under low sea state conditions, when the sea surface is entirely composed of conventional sea surface, the relative permittivity of the sea surface can be calculated using the Debye equation.

[0085] Under medium to high sea states, the sea surface can be considered as a mixture of marine foam and normal sea surface, where the relative permittivity of the marine foam can be obtained using the equivalent permittivity mixing formula. This invention uses the Refractive formula to calculate the equivalent permittivity of the foam, which can be expressed as follows:

[0086] ;

[0087] in, Foam porosity is defined as the proportion of air in a unit volume of seawater. This represents the relative permittivity of the foam. This represents the relative permittivity of seawater. This represents the dielectric constant of air. In this invention, it will... It was set to 0.95, the same as the LOCEAN foam surface emissivity model.

[0088] (3) Polarization correlation coefficient correction.

[0089] Considering that marine foam produces quasi-mirror scattering, and its correlation matrix with the polarization in the SSA model... There are some differences. This invention introduces Fresnel's reflection theorem to calculate the polarization correlation coefficient of foamy sea surfaces, thereby correcting the polarization correlation coefficient term in the SSA model and improving the ability to characterize the scattering polarization characteristics of high sea state sea surfaces.

[0090] For convenience, in the following invention, the applicability-improved SSA model will be referred to as the modified SSA model, and the original, unmodified SSA model will be referred to as the original SSA model. Under medium-to-high sea state conditions, the electromagnetic scattering of the sea surface for normal sea surface and sea foam is calculated using both the original SSA model and the modified SSA model. The normalized radar cross section (NRCS) of the mixed sea surface can be expressed as follows:

[0091] ;

[0092] In the formula, Indicates the NRCS of mixed sea surface. NRCS refers to marine foam. This refers to the NRCS of the normal sea surface.

[0093] like Figure 1 As shown, this invention first utilizes Bessel functions to reduce the dimensionality of the SSA model's integral operation, thereby lowering the computational complexity of the SSA model. Based on this, through approximate simplification of the SSA model, the main contribution intervals of its integral part are analyzed, and the selection of integration limits and the number of nodes per unit interval is determined. By reducing redundant calculations, the computational efficiency of the model is improved.

[0094] (1) Simplification of integral operations in the SSA model.

[0095] Such as the SSA model and autocorrelation function As shown in the expression, to calculate the integral part of the SSA model, we first need to calculate... The present invention is achieved through, as follows: Figure 1 The process shown is as follows: It can be transformed into the following form using Euler's formula:

[0096] ;

[0097] For ease of representation, Represented in the following form

[0098] ;

[0099] In the formula, This represents a two-dimensional wave spectrum containing correction terms. This represents a one-dimensional wave spectrum containing correction terms. This is the ratio term in the wave spectrum directional expansion function. The above equation can be further expanded using Bessel functions into the following form:

[0100] ;

[0101] In the formula, Indicates the incident azimuth angle. Indicates 2 m The first-order Bessel function of the first kind, m It is a positive integer. For ease of calculation, the above formula includes... and The integrals of the terms are denoted as follows: and :

[0102] ;

[0103] ;

[0104] Calculating the integral of the above equation yields:

[0105] ;

[0106] akin, The integral can be transformed into the following form:

[0107] ;

[0108] because m For positive integers, using the integral property of the cosine function, the above equation can be simplified to:

[0109] Using the product-to-sum formula, the inner integral of the above equation can be expressed in the following form:

[0110] ;

[0111] The first term in the above formula is always 0, and the second term is 0 if and only if (1- m When (1-) is 0, the integral value is non-zero. m When ) is 0, It can be represented as follows:

[0112] ;

[0113] The autocorrelation function, simplified using the Bessel function, is expressed as:

[0114] ;

[0115] The simplified autocorrelation function no longer requires the calculation of a double integral; the reduction in the integration dimension significantly lowers the computational complexity of the autocorrelation function. The Bessel function plays a crucial role in this simplification.

[0116] After simplifying the autocorrelation function, a similar simplification is needed for the SSA model expression. Euler's formula can be used to integrate the angular functions in the SSA model expression. Transform into the following form

[0117] ;

[0118] In the formula, in the formula, Indicates the Bragg wavenumber. express The integral part, and Representing azimuth and wind direction respectively, the complex exponential function can be expressed in the following form.

[0119] ;

[0120] In the formula, m and n are both integers. Substituting the complex exponential function into... achievable

[0121] ;

[0122] In the formula, For the Dirac function, j Represents the imaginary unit. and Let m and n represent the first-order Bessel functions of the order m and n, respectively. First-order Bessel functions containing the imaginary unit can be transformed into first-order modified Bessel functions using mathematical relationships between Bessel functions, as shown below.

[0123] ;

[0124] In the formula, express n The first-order modified Bessel function of the order of 1. The transformed... It can be represented as

[0125] ;

[0126] In the formula, Let represent the 2n-th order Bessel function of the first kind. Using the above equation, the expression for the SSA model can be transformed into the following form.

[0127] ;

[0128] The transformed SSA model eliminates the need to calculate autocorrelation functions under multiple relative wind directions, and the integration calculation is simplified from two-dimensional to one-dimensional. If we assume that the number of nodes required for a single one-dimensional integration is... The computational cost required for two-dimensional integration is approximately One-dimensional integrals only require In practical applications of the SSA model, The value of is usually large, which indicates that the computational cost required for the simplified SSA model will be significantly reduced.

[0129] (2) Selection of integration limits for the SSA model.

[0130] Because the kernel function of the SSA model is quite complex, it is difficult to directly obtain the main contribution range of the kernel function. Therefore, this invention first approximates and simplifies the kernel function of the SSA model. Considering... With The sine or cosine functions of rate decay are similar, and In the positive real number field, greater than In the kernel function of the SSA model, the isotropic term contributes more to the integral result than the anisotropic term.

[0131] If the anisotropic part is discarded, the kernel function of the SSA model can be rearranged into the following form.

[0132] ;

[0133] Based on the above equation, approximating the kernel function can further simplify the structure. Firstly, utilizing the property that the first type of Bessel function is no greater than 1, we can approximate the kernel function in the above equation... It is approximately 1. Furthermore, the zeroth-order modified Bessel function of the first kind... Satisfy the following relationship

[0134] ;

[0135] In the formula, It refers to any variable.

[0136] Considering that the modified Bessel function of the first kind only monotonically affects the magnitude of the kernel function throughout the integration process, amplifying the modified Bessel function of the first kind will not reduce the main contribution interval of the kernel function and can reduce its impact on the integration result. Therefore, the modified Bessel function of the first kind is approximated as an exponential function to further simplify the kernel function. The kernel function after approximation and simplification can be expressed as follows:

[0137] ;

[0138] in, and When calculating backscattering, they are equal and both are affected by the incident wave frequency and incident angle (for ease of representation, hereinafter referred to as...). Represented as ). and It is mainly affected by the wave spectrum and wind speed.

[0139] Because the autocorrelation functions in the first-order and second-order SSA models differ little under the same environmental factors and radar parameters, their impact on the main contribution interval can be ignored. Therefore, taking the first-order SSA model and H-spectrum as an example, the corresponding... , and The autocorrelation function is fitted to the wind speed, thus obtaining the fitting results for different wind speeds:

[0140] ;

[0141] ;

[0142] In the formula, , and All of these are fitting parameters related to wind speed.

[0143] Based on a defined upper limit for integral truncation, this study investigates the required number of nodes for the integral part of the SSA model to ensure the accuracy of numerical integration. In the integral part of the SSA model, the oscillation frequency of the kernel function plays a dominant role in the number of nodes. The oscillations in the integral part of the SSA model are mainly contributed by the first-type Bessel function and the autocorrelation function during integration. When the autocorrelation function is close to 0, the oscillation frequency of the integral is dominated by the autocorrelation function, and the oscillation frequency is mainly related to the wind speed; conversely, when the autocorrelation function is close to 0, the oscillation frequency is mainly related to the wind speed. When the value is much greater than 0, the oscillation frequency of the integral is dominated by the Bessel function of the first kind, and the oscillation frequency is mainly related to the incident wave frequency.

[0144] Similar to the discussion of the main contribution interval, a discussion of the oscillation frequency also requires initial approximations and simplifications. First, let's consider... The effect on the oscillation frequency is approximated by a cosine function. Considering that the modified Bessel function of the first kind is monotonically increasing on the non-negative real number interval, and that the oscillation frequency is mainly affected by the rate of change of the function, i.e., the first derivative of the function, a simplified approximate expression is adopted. Furthermore, since the isotropic and anisotropic components of the SSA model integral have similar periodic variations and contribute similarly to the oscillation frequency, only the isotropic component is retained. In summary, the oscillation frequency of the integral can be approximated by the following equation:

[0145] .

[0146] In the formula, .

[0147] Example 2

[0148] Performance evaluation of the improved applicability method of the SSA model for medium and high sea states and high frequency bands.

[0149] To evaluate the performance of the improved model's applicability improvement method based on the SSA model for medium-high sea states and high frequency bands, this invention uses a constructed experimental dataset as input, taking radar parameters and environmental factors from the dataset to obtain simulated sea surface electromagnetic scattering data under different radar parameters and environmental factors. The RMSE between the model simulation results and measured data is used as the evaluation index to verify and evaluate the simulation accuracy of the improved model. A comparison between the model simulation results and measured data for Ku-band HH polarization under high sea states (wind speed greater than 15 m / s) is shown below. Figure 2 As shown. Figure 2 As shown, before the applicability improvement, the RMSE between the SSA model simulation results and the measured data was 1.35 dB, with the model simulation results slightly lower than the measured data. Compared with the applicability improvement, after the applicability improvement, the SSA model simulation results are closer to the measured data, and the RMSE between them has decreased to 0.80 dB, indicating a significant improvement in the accuracy of the model's electromagnetic scattering simulation.

[0150] Comparison of model simulation results and measured data for Ka-band HH polarization: Figure 3 As shown. Figure 3 As shown, the validation results under Ka-band conditions are similar to those under Ku-band conditions. Before the applicability improvement, the simulation results of the SSA model generally underestimated electromagnetic scattering from the sea surface. After the applicability improvement, the underestimation phenomenon of the simulation results was improved, and the RMSE compared with the measured data decreased from 1.43 dB to 1.21 dB.

[0151] When the Ka-band headwind speed is 5 m / s and 15 m / s, the number of nodes required for computation of the improved SSA model under different incident angles is as follows: Figure 4 As shown, after the applicability improvement, the number of nodes required for SSA model computation is positively correlated with the incident angle, and under the same waveband, the number of nodes is approximately linearly correlated with the incident angle. Unlike traditional methods, where the number of nodes required for SSA model computation is negatively correlated with the incident wave frequency under the same incident angle, this indicates that the applicability improvement method for SSA model in medium-high sea states and high-frequency bands effectively suppresses the problem of excessive computational complexity of SSA model in high-frequency bands. (Comparison) Figure 4 As shown in (a) and (b), under the same incident angle and waveband, increased sea state conditions reduce the number of nodes required for model computation. Furthermore, increased sea state conditions also reduce the difference in the number of nodes required for computation under different waveband conditions.

[0152] To more clearly reflect the computational efficiency improvement effect of the improved applicability method for SSA-based models in medium-high sea states and high-frequency bands, this invention quantifies the reduction in computational load of the improved model in C, X, Ku, and Ka bands, using an incident angle of 30° as an example. Figure 5 As shown, compared with traditional methods, the total number of computational nodes required for the improved SSA model is significantly reduced. This indicates that the improved applicability method for SSA models in medium-high sea states and high-frequency bands can effectively reduce the computational complexity of SSA models and significantly improve their computational efficiency. Comparing the quantization results in C, X, Ku, and Ka bands reveals that the proposed improvement method performs the worst in the C band, with a reduction in the number of computational nodes of approximately 75%-88%. The proposed improvement method performs the best in the Ka band, with a reduction in the number of computational nodes of more than 97%. In summary, the reduction in the number of nodes required in the C, X, Ku, and Ka bands is very significant, and the improved applicability method for SSA models in medium-high sea states and high-frequency bands proposed in this invention can significantly improve the computational efficiency of SSA models.

[0153] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for improving the applicability of SSA-based models in medium-to-high sea states and high-frequency bands, characterized in that, Includes the following steps: S1. Acquire sea surface backscatter data and corresponding radar parameters, and acquire synchronized sea surface environmental information; S2. Perform spatiotemporal matching of sea surface backscattering data, radar parameters, and synchronized sea surface environmental information to obtain a matching dataset; S3. The influence of marine foam on the relative permittivity of the sea surface and the main scattering mechanisms is introduced into the SSA model, and the integral calculation of the SSA model is simplified. Through analysis of the SSA model expression, the integration limit of the SSA model is determined, and finally, high-precision simulation results of sea surface electromagnetic scattering under high-frequency and medium-to-high sea state conditions are obtained, including: (1) Simplify the integral calculation of the SSA model; (2) Determine the main factors affecting the accuracy of the integral results of the SSA model; (3) Make reasonable approximations and simplifications to the expression of the SSA model, and on this basis, analyze and determine the integration limit of the SSA model and the number of nodes required for the unit interval; The double integrals involved in the SSA model are equivalently simplified into multiple single integrals, and the simplified autocorrelation function is obtained. Angle function integrals in the SSA model Represented as: ； ； In the formula, Indicates radial distance. Indicates the incident azimuth angle. Denotes wave number, k B For Bragg wavenumber, , Represents the perpendicular projection components of the incident and scattered waves. Denotes the zeroth-order Bessel function of the first kind. Denotes the second-order Bessel function of the first kind. Denotes the Bessel function of the first kind of order 2n. Denotes the first-order modified Bessel function of order n. This represents a one-dimensional wave spectrum containing correction terms. This is the ratio term in the wave spectrum directional expansion function. It is the isotropic part of the autocorrelation function. It is the anisotropic part of the autocorrelation function.

2. The method for improving the applicability of SSA-based models in medium-high sea states and high-frequency bands as described in claim 1, characterized in that, The influence of marine foam on the relative permittivity of the sea surface and the main scattering mechanisms is introduced into the SSA model, including: (1) Determine the proportion of regular sea surface and marine foam in mixed sea surface by using empirical relationships of white crown coverage; The empirical relationship for white crown coverage is shown below: ； In the formula, Indicates the coverage rate of white crowns. Indicates the wind speed due to friction with the sea surface; (2) Calculate the relative permittivity of conventional sea surface and marine foam using the Debye equation and the equivalent permittivity mixed formula, respectively; The equivalent dielectric constant of the foam is calculated using the Refractive formula, as shown below: ； in, Foam porosity is defined as the proportion of air in a unit volume of seawater. This represents the relative permittivity of the foam. This represents the relative permittivity of seawater. The dielectric constant of air; (3) Introduce Fresnel's reflection theorem to calculate the polarization correlation coefficient of marine foam; (4) Based on the sea surface division results and the relative permittivity of seawater and marine foam, calculate the electromagnetic scattering of the sea surface of conventional sea surface and marine foam respectively, and obtain the electromagnetic scattering of the sea surface of mixed sea surface accordingly. The normalized radar cross section (NRCS) of a mixed sea surface is represented as follows: ； In the formula, Indicates the NRCS of mixed sea surface. NRCS refers to marine foam. This refers to the NRCS of the normal sea surface.

3. The method for improving the applicability of SSA-based models in medium-high sea states and high-frequency bands as described in claim 1, characterized in that, The simplified expression for the SSA model is as follows: ； In the formula, For the expression of the SSA model, , Let represent the wavenumber vectors of the incident and scattered waves on the horizontal plane, respectively. This represents the first-order polarization correlation coefficient matrix. This represents a first-order modified Bessel function of the first kind.

4. The method for improving the applicability of SSA-based models in medium-high sea states and high-frequency bands as described in claim 3, characterized in that, The sensitivity of each term in the SSA model to the number of nodes required for the integration interval and the unit interval is analyzed. The SSA model expression is then approximated and simplified. The kernel functions used to analyze the number of nodes required for the integration interval and the unit interval after the approximation and simplification are expressed as follows: ； 。 5. The method for improving the applicability of SSA-based models in medium-high sea states and high-frequency bands as described in claim 1, characterized in that, The simulation accuracy and computational efficiency of the evaluation model were verified using a matching dataset.

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