A method for calculating effective henry's reflectance coefficient based on sea wave spectrometer

Abstract

The application discloses a kind of effective Fennel reflection coefficient calculation method based on sea wave spectrometer, first by least square fitting anisotropic quasi-speculum scattering formula, the slope variance component of observation azimuth is obtained;The variation law of the slope variance component with azimuth is fitted with azimuth cosine function, to obtain the total slope variance of the detected sea surface, slope variance component fluctuation rate and sea surface wave propagation direction;Then by the slope variance component along the wave propagation direction and total slope variance, the distribution of the slope variance component perpendicular to the detection azimuth with observation azimuth is obtained;Finally, by calculating the non-standardized correlation coefficient between observation azimuth and the slope variance perpendicular to observation azimuth angle, the 0 degree effective Fennel reflection coefficient of different incident angle beams can be obtained according to quasi-speculum scattering formula, and the effective Fennel reflection coefficient of Ku band at 0 degree incident angle can be obtained by averaging the results of each beam with wind speed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ocean remote sensing, and particularly relates to an effective Fresnel reflection coefficient calculation method based on a wave spectrum instrument. BACKGROUND

[0002] Currently, the way to measure sea waves in a large area is to use a satellite-borne radar. Small incidence angle microwave backscattering can describe the roughness of the sea surface, and the sea surface backscattering mechanism and sea surface measurement can be used for remote sensing to obtain sea surface information based on various platforms such as satellite-borne or airborne radars. In order to describe the backscattering of the sea surface to the microwave at a small incidence angle, the two-scale model theory of sea surface scattering is introduced. According to the theory, the sea surface is represented as small-scale ripples covering large-scale waves (compared with the radar wavelength). Therefore, the concept of cutoff wavenumber is introduced, and the wave spectrum is divided into large-scale waves and small ripples. In the framework of Kirchhoff approximation, the mechanism of electromagnetic wave backscattering on the sea surface at a small incidence angle is quasi-specular scattering. The electromagnetic wave is incident on the sea surface vertically, and the backscattering radar cross section (RCS) generated by the sea surface depends on the mean square slope (mss) of the large-scale wave. However, the small ripples covering the large-scale wave will cause the appearance of diffuse (resonance) scattering, thereby reducing the strength of the backscattering signal. In order to consider this effect, the concept of effective reflection coefficient (ERC) is introduced to replace the Fresnel coefficient in the RCS formula.

[0003] The rain radar data of the TRMM satellite can be used to analyze the dependence of ERC on the wind speed. When moving, the radar scans through the incidence angle change in the direction perpendicular to the flight trajectory. The dependence of RCS on the incidence angle is measured, which can be used to invert the slope variance component along the scanning direction. However, since the slope variance component is only calculated along one azimuth angle, and the ERC is calculated based on the assumption of isotropy of the large-scale wave. Using this incorrect assumption is due to the lack of slope variance component measurement at different azimuth angles. Therefore, an error will be generated when calculating the ERC. The wave spectrum instrument SWIM carried on the CFOSAT satellite first measures at 24 azimuth angles, so the anisotropy of the sea wave can be considered when calculating the ERC. In this case, the slope variance component of the sea surface in different azimuth directions can be calculated, and the total slope variance and wave propagation direction of the sea surface are further calculated, and combined with the normalized backscattering cross section at different incidence angles, the ERC can be calculated according to the quasi-specular scattering formula. The accurate calculation of ERC has good practical value for Ku-band sea surface detection. SUMMARY

[0004] The application aims to solve the problem that the effective Fresnel reflection coefficient at 0 degree of incidence angle cannot be accurately calculated according to the normalized backscattering coefficient in the existing quasi-specular scattering theory of sea surface due to the small wave diffraction effect.

[0005] The technical scheme of the application is as follows: a method for calculating the effective Fresnel reflection coefficient based on a wave spectrum instrument, comprising the following steps:

[0006] Step 1: according to the quasi-specular scattering theory considering the anisotropy of sea surface, i.e. formula (1) below, the formula (2) obtained by transformation processing is as follows,

[0007]

[0008]

[0009] In the formula, ERC is the effective Fresnel reflection coefficient at 0 degree of incidence angle of sea surface, θ is the incidence angle, φ is the antenna observation azimuth angle, σ0(θ, φ) is the normalized backscattering coefficient at the observation incidence angle θ and the antenna observation azimuth angle φ; mss xx is the slope variance component in the observation azimuth angle direction, mss yy is the slope variance component in the direction perpendicular to the observation azimuth angle, mss xy is the non-normalized correlation coefficient between the slope variance in the observation azimuth angle and the slope variance in the direction perpendicular to the observation azimuth angle, and e is the natural constant.

[0010] Step 2: for a fixed antenna observation azimuth angle φ, the normalized backscattering coefficient at the observation incidence angle θ is denoted as σ0(θ), and formula (2) is least square fitted by using formula (3) as follows to obtain a first order polynomial;

[0011] y(θ)=a·tan 2 θ+b (3)

[0012] In the formula, a and b are the coefficients to be fitted, and y(θ) is a function of the incidence angle θ; a and b are obtained by the following two formulas:

[0013]

[0014]

[0015] Wherein, A and B represent two independent variables of the function F(A, B), min[F(A, B)] represents the minimum value of the function F(A, B), denotes the arguments that minimize the function F(A,B); the slope variance component of a certain antenna observation azimuth direction is calculated as follows:

[0016]

[0017] Step three, calculate the non-standardized correlation coefficient mss between the slope variance of the observation azimuth and the slope variance of the observation azimuth vertical direction xy ;

[0018]

[0019] where constA is a constant related to the slope variance of the sea surface only and does not change with the antenna observation azimuth angle;

[0020] Step four, calculate the effective Fienup reflection coefficient at different incident angles θbeam and different relative wind directions

[0021]

[0022] Step five, average to obtain the effective Fienup reflection coefficient at different relative wind directions at the sea surface 0-degree incident angle

[0023]

[0024] where θ(i) is the incident angle of the i-th beam, is the effective Fienup reflection coefficient at the incident angle θ(i) and the relative wind direction , and N is the number of used incident angles θ.

[0025] Further, in step three, the specific steps are as follows:

[0026] Each antenna observation azimuth direction obtains a mss xx For each 0-180 degree observation, the obtained mss xx is fitted according to formula (10) with the change of the antenna observation azimuth angle φ mss xx (φ) to obtain the three unknown parameters in formula (10), i.e., the total slope variance of the sea surface mss total , the slope variance component fluctuation rate Δmss, and the wave propagation direction

[0027]

[0028] Calculate the slope variance component mss yy ​The formula is as follows:

[0029] mss yy (φ)=mss total -mss xx (φ) (11)

[0030] Based on the azimuth angle φ of the spectrometer beam rotation and the obtained wave propagation direction When the two differ by 0 degrees, the constant value constA is calculated using the following formula;

[0031]

[0032] in, and These are the observation direction and the slope variance components perpendicular to the observation direction when the observation azimuth and wave propagation direction are consistent.

[0033] Furthermore, formula (10) is fitted using formula (13) to obtain the three unknown parameters in formula (10);

[0034]

[0035] In the formula, g, h and The coefficients to be fitted are z(φ), which is a function of the antenna observation azimuth angle φ; g, h, and It is obtained from the following two equations:

[0036]

[0037]

[0038] Where G, H, and Ψ represent the three independent variables of the function F'(G,H,Ψ), and min[F'(G,H,Ψ)] represents taking the minimum value of the function F'(G,H,Ψ). Let G be the independent variable that minimizes the function F'(G,H,Ψ) when different values ​​of G, H, and Ψ are taken.

[0039] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0040] 1. The unstandardized correlation coefficient mss between the variance of the slope in the observation azimuth direction and the variance of the slope in the direction perpendicular to the observation azimuth angle in the quasi-mirror scattering theory proposed in this invention is calculated. xy The method of squaring utilizes and the direction of wave propagation Based on these characteristics, the slope variance component (mss) in the direction of wave propagation can be obtained by rotating the spectrometer for detection. xx The slope variance component perpendicular to the wave propagation direction (mss)yy , so the effective Fresnel reflection coefficient of any observation azimuth can be calculated

[0041] 2. The method for calculating the ERC can utilize the radar backscatter coefficient (NRCS) on different beams of the SWIM, so that multiple measurements can be averaged to obtain more reliable ERC results.

[0042] 3. The method for calculating the ERC can calculate the ERC at different antenna observation azimuths, so as to obtain the variation of the ERC at different relative wind directions. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is the overall flowchart of the method for calculating the effective Fresnel reflection coefficient of the Ku band at 0° incidence angle;

[0044] Figure 2 is the flowchart of the non-standardized correlation coefficient mss xy of the square of the slope variance of the observation azimuth and the slope variance of the vertical direction of the observation azimuth;

[0045] Figure 3 is the graph of the effective Fresnel reflection coefficient calculated by the 6th beam of the wave spectrum instrument varying with the wind speed and the wind direction;

[0046] Figure 4 is the graph of the average value of the effective Fresnel reflection coefficient calculated by the 3456th beam of the wave spectrum instrument varying with the wind speed and the wind direction. DETAILED DESCRIPTION

[0047] The technical solutions of the present application will be further described below in combination with the drawings and examples.

[0048] The effective Fresnel reflection coefficient calculation method based on the wave spectrum instrument according to the present application has the overall flowchart as shown in Figure 1 , and the specific steps are as follows:

[0049] Step 1: According to the quasi-specular scattering theory considering the anisotropy of the sea surface, i.e., the following formula (1), the formula (2) obtained by transformation processing of the formula (1) is obtained,

[0050]

[0051]

[0052] In the formula, ERC is the effective Fresnel reflection coefficient of the sea surface at 0° incidence angle, θ is the incidence angle, φ is the antenna observation azimuth, σ0(θ, φ) is the normalized backscatter coefficient at the observation incidence angle θ and the antenna observation azimuth φ; mss xxis the slope variance component in the observation azimuth direction, mss yy is the slope variance component in the perpendicular direction of the observation azimuth, mss xy is the non-standardized correlation coefficient between the slope variance in the observation azimuth and the slope variance in the perpendicular direction of the observation azimuth, e is the natural constant.

[0053] Step two, for a fixed antenna observation azimuth φ, the normalized backscattering coefficient at the observation incidence angle θ is denoted as σ0(θ), formula (2) is least square fitted by using the following formula (3) to obtain a first order polynomial:

[0054] y(θ) = a tan 2 θ + b (3)

[0055] In the formula, a and b are the coefficients to be fitted, y(θ) is the function of the incidence angle θ; a and b are obtained by the following two formulas,

[0056]

[0057]

[0058] Wherein, A and B represent two independent variables of the function F(A, B), min[F(A, B)] represents taking the minimum value of the function F(A, B), represents taking the independent variable that minimizes the function F(A, B) when A and B are different; the slope variance component in the observation azimuth of a certain antenna is calculated by using the following formula:

[0059]

[0060] Step three, the non-standardized correlation coefficient mss xy between the slope variance in the observation azimuth and the slope variance in the perpendicular direction of the observation azimuth is calculated, and the flow is shown in Figure 2 ;

[0061]

[0062] In the formula, constA is a constant related to the slope variance of the sea surface and does not change with the antenna observation azimuth.

[0063] Step four, the effective Bragg reflection coefficient at different incidence angles θ and different relative wind directions

[0064]

[0065] Step five, the The average processing obtains the effective Finnell reflection coefficient of the sea surface at 0 degree incident angle at different relative wind directions

[0066]

[0067] Where θ(i) is the incident angle of the i-th beam, is the effective Finnell reflection coefficient at the incident angle θ(i) and the relative wind direction , and N is the number of the used incident angles θ.

[0068] In step three, an mss xx is obtained for each antenna observation azimuth direction. xx The mss xx (φ) obtained for each 0-180 degree observation range is actually related to three unknown parameters in formula (10), i.e. the total slope variance of the sea surface mss total , the slope variance component fluctuation rate Δmss and the wave propagation direction According to formula (10), fitting is performed to obtain the three unknown parameters in formula (10).

[0069]

[0070] The slope variance component mss yy in the vertical observation azimuth direction is calculated, and the formula is as follows:

[0071] mss yy (φ) = mss total -mss xx (φ) (11)

[0072] According to the azimuth angle φ of the wave spectrum instrument beam rotation and the obtained wave propagation direction When the difference between the two is 0 degree, the constant value constA is calculated using the following formula:

[0073]

[0074] Wherein, and are the observation direction and the slope variance component perpendicular to the observation direction when the observation azimuth direction and the wave propagation direction are consistent; by fitting formula (10) through formula (13), the three unknown parameters in formula (10) are obtained, and the cosine function fitting formula is obtained.

[0075]

[0076] In the formula, g, h and are coefficients to be fitted, z(φ) is a function of the antenna observation azimuth angle φ; g, h and are obtained from the following two equations:

[0077]

[0078]

[0079] where G, H and Ψ represent three independent variables of the function F'(G, H, Ψ), min[F'(G, H, Ψ)] represents taking the minimum value of the function F'(G, H, Ψ), representing the independent variables that minimize the function F'(G, H, Ψ) when taking different G, H, Ψ.

[0080] According to formula (7), the non-standardized correlation coefficient mss xy between the observation azimuth slope variance and the observation azimuth vertical slope variance is calculated.

[0081] Figure 3 is the effective Fresnel reflection coefficient variation graph with wind speed and wind direction calculated by the 6th beam of the spectrum instrument of the method of the present application; Figure 4 is the effective Fresnel reflection coefficient average variation graph with wind speed and wind direction calculated by the 3456th beam of the spectrum instrument of the method of the present application. Analysis shows that the method for calculating ERC proposed by the present application realizes multiple measurement and averaging, and obtains more reliable ERC results; ERC can be calculated at different antenna observation azimuths, thereby obtaining the variation of ERC at different relative wind directions.

[0082] The above is only the preferred embodiment of the present application and is not used to limit the present application. Those skilled in the art can make various modifications or equivalent replacements to the present application within the spirit and protection scope of the present application, and such modifications or equivalent replacements should also be considered to fall within the protection scope of the technical scheme of the present application.

Claims

1. A method for calculating an effective Fresnel reflection coefficient based on a wave spectrum meter, characterized by, The specific steps are as follows: Step one, according to the quasi-specular scattering theory considering the sea surface anisotropy, that is, formula (1) below, the formula (2) obtained by transformation processing is as follows, where ERC is the effective Fresnel reflectance at normal incidence, θ is the incidence angle, φ is the antenna look direction, and σ0(θ, φ) is the normalized backscatter coefficient at look incidence angle θ and antenna look direction φ; mss xx is the slope variance component in the look direction, mss yy is the slope variance component in the direction perpendicular to the look direction, mss xy is the non-normalized correlation coefficient between the slope variance in the look direction and the slope variance in the direction perpendicular to the look direction, and e is the natural constant. Step two, for a fixed antenna observation azimuth angle φ, the normalized backscattering coefficient when the observation incidence angle is θ is expressed as σ0(θ), formula (2) is least square fitted by using formula (3) as follows, to obtain a first order polynomial; y(θ) = a tan 2 θ + b (3) In the formula, a and b are the coefficients to be fitted, and y(θ) is a function of the incidence angle θ; a and b are obtained by the following two formulas: where A and B represent two arguments of the function F(A, B), min[F(A, B)] represents taking the minimum value of the function F(A, B), representing the argument that minimizes the function F(A, B) for different A, B; the slope variance component of a certain antenna observation azimuth direction is calculated as follows: Step three, calculate the non-normalized correlation coefficient mss between the variance of the slope of the observed azimuth and the variance of the slope of the observed perpendicular to the azimuth xy the square of the slope of the observed azimuth; In the formula, constA is a constant related only to the sea surface slope variance and does not change with the antenna observation azimuth angle; Step four, the effective Fresnel reflection coefficient at different incident angles θ and different relative wind directions φ are calculated respectively by using the following formula ​ Step five, the averaging to obtain the effective Fresnel reflection coefficient at sea level for 0 degree incidence angle for different relative wind directions where θ(i) is the incidence angle of the i-th beam, is the effective Fresnel reflection coefficient at the incidence angle θ(i) and the relative wind direction N is the number of incidence angles θ used.

2. The method according to claim 1, wherein, In step three, the specific steps are as follows: One mss is obtained for each antenna observation azimuth xx For each observation in the range 0-180 degrees, the obtained mss xx The mss as a function of the antenna observation azimuth angle φ xx (φ) is fitted according to equation (10) to obtain the three unknown parameters in equation (10), namely the total slope variance of the sea surface mss total , the slope variance component fluctuation rate Δmss and the wave propagation direction The slope variance component mss of the vertical observation azimuth direction is calculated yy The formula is as follows: mss yy (φ) = mss total - mss xx (φ) (11) According to the azimuth angle φ of the beam rotation of the spectrometer and the determined wave propagation direction When the difference is 0 degrees, the constant value constA is calculated using the following formula; wherein and are the observed direction and the slope variance component perpendicular to the observed direction, respectively, when the observed azimuth and the wave propagation direction are aligned.

3. The method according to claim 2, wherein the method is based on a wave spectrum meter. The three unknown parameters in formula (10) are obtained by fitting formula (10) through formula (13); where g, h and are coefficients to be fitted, z(φ) is a function of the antenna observation azimuth angle φ; g, h and are obtained from the following two equations: where G, H and Ψ represent three arguments of the function F'(G, H, Ψ), min[F'(G, H, Ψ)] represents the minimum value of the function F'(G, H, Ψ), represent the arguments that minimize the function F'(G, H, Ψ) for different G, H, Ψ.

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