Satellite-borne GNSS-R wave period estimation method based on incident angle lookup table and two-step empirical model formula

Abstract

The invention discloses a spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula, and belongs to the technical field of spaceborne GNSS-R wave period estimation, and the method comprises the following steps: S1, analyzing the correlation between two spaceborne GNSS-R observation values, i.e., a bistatic radar cross section and a leading edge slope, and effective wave height and wave period parameters; s2, constructing a wave period estimation empirical model; S3, optimizing the constructed wave period estimation empirical model; s4, estimating a satellite-borne GNSS-R wave period; according to the method, the wave periods of the low-wind-speed sea condition and the high-wind-speed sea condition are estimated through the two-step empirical model formula considering the incident angle dependency, the estimation result is accurate, meanwhile, the current situation that the current satellite-borne GNSS-R technology is not widely applied to the wave period estimation aspect, that is, no reliable estimation method exists is solved, and the method is suitable for large-scale popularization and application. And the complex relationship between the low-wind-speed and high-wind-speed sea condition wave parameters and the GNSS-R observation value and the influence of the incident angle dependency on the wave period estimation precision are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of on-board GNSS-R wave period estimation, and particularly relates to an on-board GNSS-R wave period estimation method based on an incident angle look-up table and a two-step empirical model formula. Background Art

[0002] Ocean waves are key factors in the ocean dynamic system, and their research is of great significance for multiple fields such as ocean engineering, shipping safety, climate change, environmental protection, and ocean resource development.

[0003] Currently, research methods for ocean waves include the on-board GNSS-R technology, which can accurately estimate parameters such as sea surface height, significant wave height, sea surface wind speed, sea surface salinity, wind direction, and sea ice thickness. However, there are still the following drawbacks:

[0004] 1. Under complex sea conditions, especially under high wind speed sea conditions, the relationship between GNSS-R signals, significant wave height, and wave period is more complex than that under low wind speed sea conditions, and is different from the relationship between GNSS-R observations and wave parameters under low wind speeds. Therefore, formulas cannot be shared for estimation, resulting in the fact that the current on-board GNSS-R technology has not been widely applied in wave period estimation, that is, there is no method for estimating wave period using on-board GNSS-R technology.

[0005] 2. The accuracy of estimating wave period using GNSS-R observations is affected by different incident angle conditions, resulting in the fact that the current on-board GNSS-R technology cannot accurately estimate wave periods under both low wind speed and high wind speed sea conditions simultaneously.

[0006] In view of this, an on-board GNSS-R wave period estimation method based on an incident angle look-up table and a two-step empirical model formula is designed to solve the above problems. Summary of the Invention

[0007] To solve the problems raised in the above background art, the present invention provides an on-board GNSS-R wave period estimation method based on an incident angle look-up table and a two-step empirical model formula, which has the characteristics of solving the above problems.

[0008] To achieve the above object, the present invention provides the following technical solution: An on-board GNSS-R wave period estimation method based on an incident angle look-up table and a two-step empirical model formula, comprising the following steps:

[0009] S1: Analyze the correlation between two on-board GNSS-R observations, namely the bistatic radar cross-section and the front slope, and the parameters of significant wave height and wave period.

[0010] S2: Based on the correlation between the two on-board GNSS-R observations and the parameters of significant wave height and wave period analyzed, construct an empirical model for wave period estimation:

[0011] The expression of the empirical model for wave period estimation under low wind speed sea conditions is as follows:

[0012]

[0013] Where: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope, and a(θ), b(θ), c(θ) and d(θ) respectively represent the model fitting parameters that vary with the incident angle θ;

[0014] The expression of the empirical model for wave period estimation under high wind speed sea conditions is as follows:

[0015] T NBRCS (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ)

[0016] T LES (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ)

[0017] Where: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope, and a1(θ), b1(θ), a1(θ), b2(θ) and c(θ) respectively represent the model fitting parameters that vary with the incident angle θ;

[0018] S3: Optimize the constructed empirical model for wave period estimation;

[0019] S4: Estimate the wave period of spaceborne GNSS-R based on the optimized empirical model for wave period estimation.

[0020] Furthermore, the specific steps of the step S1 include:

[0021] The period parameter T of the wave is obtained from the zero-order spectral moment m0 and the fourth-order spectral moment m4 measured by the sensor, and the expression is:

[0022]

[0023] Where: T represents the period parameter of the wave, m0 represents the zero - order spectral moment, and m4 represents the fourth - order spectral moment; among them, the expression of the zero - order spectral moment m0 is:

[0024]

[0025] Where: SWH represents the significant wave height of the sea surface;

[0026] The expression of the fourth - order spectral moment m4 is:

[0027]

[0028] Where: S 2 represents the variance of the sea - surface slope, g represents a certain constant related to some characteristics of the wave, and σ(θ) represents the observed value of the bistatic radar cross - section at the incident angle (θ);

[0029]

[0030] Where: R(θ) represents the Fresnel reflection coefficient at the incident angle (θ), and MSS represents the mean - square slope;

[0031] That is, the correlation expression between the observed value of the bistatic radar cross - section and the significant wave height and wave period parameter is:

[0032] T i ~(m0 / m4) 1 / 4 = f(σ(θ), SWH)

[0033] Where: σ(θ) represents the observed value of the bistatic radar cross - section at the incident angle (θ), and SWH represents the significant wave height of the sea surface;

[0034] The sea state is divided into low - wind - speed sea state and high - wind - speed sea state. Due to different wind speeds, the wave period parameter T is different;

[0035] Assume that the low - wind - speed sea - state condition is set as the wind speed less than 10 m / s and the NBRCS value ≥ 40, and the high - wind - speed sea - state condition is set as the wind speed ≥ 10 m / s and the NBRCS value < 40;

[0036] Taking the observed value of the bistatic radar cross - section and the significant wave height as input variables, the correlation expression between the observed value of the bistatic radar cross - section and the significant wave height and wave period parameter is:

[0037] T = f(NBRCS, SHW)

[0038] Where: NBRCS represents the observed value of the normalized bistatic radar cross - section, and SWH represents the significant wave height of the sea surface;

[0039] Similarly, the correlation expression between the observed value of the leading edge slope and the significant wave height and wave period parameters can be deduced as follows:

[0040] T = f(LES, SHW)

[0041] Where: LES represents the normalized leading edge slope, and SWH represents the significant wave height of the sea surface.

[0042] Furthermore, the specific steps of the said step S2 include:

[0043] Eliminate the incidence angle dependence in low wind speed and high wind speed sea conditions;

[0044] Based on the correlation expressions between the bistatic radar cross-section observation values and the leading edge slope observation values and the significant wave height and wave period parameters, construct an empirical model for wave period estimation in low wind speed and high wind speed sea conditions:

[0045] The expression of the empirical model for wave period estimation in low wind speed sea conditions is:

[0046]

[0047] Where: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of the bistatic radar cross-section observation value and the leading edge slope observation value at the incidence angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross-section and the leading edge slope, and a(θ), b(θ), c(θ) and d(θ) respectively represent the model fitting parameters that vary with the incidence angle θ;

[0048] The expression of the empirical model for wave period estimation in high wind speed sea conditions is:

[0049] T NBRCS (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ)

[0050] T LES (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ)

[0051] Where: T NBRCS (θ) and T LES(θ) represents the wave period values of the bistatic radar cross-section observation values and the front slope observation values at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a1(θ), b1(θ), a2(θ), b2(θ) and c(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0052] Further, in step S2, the specific steps for eliminating the incident angle dependence under low wind speed and high wind speed sea conditions include:

[0053] Divide the incident angles in the range of 0 - 70° into different subsets at 1° intervals;

[0054] Estimate the fitting parameters with the data within each subset and establish an independent fitting model for each subset;

[0055] Save the fitting coefficients of each subset and construct an incident angle look-up table;

[0056] Based on the incident angle look-up table, eliminate the dependent terms of the incident angle under low wind speed and high wind speed sea conditions.

[0057] Further, the specific steps of step S3 include:

[0058] Optimization of the wave period estimation empirical model under low wind speed sea conditions:

[0059] Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model, and the expression of the loss function is:

[0060]

[0061] In the formula: T NBRCS and T LES represent the wave period values of the bistatic radar cross-section observation values and the front slope observation values respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively;

[0062] Optimization of the wave period estimation empirical model under high wind speed sea conditions:

[0063] Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model, and the expression of the loss function is:

[0064] loss NBRCS =∑(T NBRCS-a1(θ)·exp(b1(θ)·SWH)+a2(θ)·exp(b2(θ)·NBRCS)+c(θ)) 2

[0065] loss LES =∑(T LES -a1(θ)·exp(b1(θ)·SWH)+a2(θ)·exp(b2(θ)·LES)+c(θ)) 2

[0066] where: T NBRCS and T LES represent the wave period values of the bistatic radar cross section observation value and the front slope observation value respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross section and the front slope respectively, and a1(θ), b1(θ), a2(θ), b2(θ) and c(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0067] Furthermore, step S2 further includes:

[0068] The expression of the empirical model for wave period estimation under high wind speed sea conditions is:

[0069]

[0070] where: T NBRCS (θ) and T LES (θ) represent the wave period values of NBRCS and LES observation values at the incident angle θ respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross section and the front slope respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0071] Furthermore, step S3 further includes:

[0072] Optimization of the empirical model for wave period estimation under high wind speed sea conditions:

[0073] Minimize the loss function of the empirical model for wave period estimation based on the fminsearch optimization algorithm. The expression of the loss function is:

[0074]

[0075] where: T NBRCS and T LESThe wave period values represented by the bistatic radar cross-section observation value and the front slope observation value respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0076] Further, the step S2 further includes:

[0077] The step S2 further includes:

[0078] The expression of the empirical model for wave period estimation under high wind speed sea conditions is:

[0079] T NBRCS (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·NBRCS) + e(θ))

[0080] T LES (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·LES) + e(θ))

[0081] In the formula: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of NBRCS and LES observations at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a(θ), b(θ), c(θ), d(θ) and e(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0082] Further, the step S3 further includes:

[0083] Optimization of the empirical model for wave period estimation under high wind speed sea conditions:

[0084] Based on the fminsearch optimization algorithm, minimize the loss function of the empirical model for wave period estimation. The expression of the loss function is:

[0085] loss NBRCS = ∑(T NBRCS - a(θ)·SWH b(θ) + c(θ)·log(d·NBRCS) + e(θ))) 2

[0086] loss LES = ∑(T LES - a(θ)·SWH b(θ) + c(θ)·log(d·LES) + e(θ))) 2

[0087] Where: T NBRCS and T LES respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value. SWH represents the significant wave height of the sea surface. NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope. a(θ), b(θ), c(θ), d(θ) and e(θ) respectively represent the model fitting parameters that vary with the incident angle θ.

[0088] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0089] The present invention estimates the wave period of low wind speed sea conditions and high wind speed sea conditions with a two-step empirical model formula considering the incident angle dependence term, and the estimation result is accurate. At the same time, it solves the current situation that spaceborne GNSS-R technology has not been widely applied in wave period estimation, that is, there is no reliable estimation method, as well as the complex relationship between wave parameters and GNSS-R observation values under low wind speed and high wind speed sea conditions and the problem of the influence of the incident angle dependence term on the accuracy of wave period estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is a flowchart of the method of the present invention;

[0091] Figure 2 is an inversion result diagram of the power fitting model based on NBRCS and LES observation values under low wind speed sea conditions of the present invention;

[0092] Figure 3 is an inversion result diagram of the exponential function relationship fitting model based on NBRCS and LES observation values under high wind speed sea conditions of the present invention;

[0093] Figure 4 is an inversion result diagram of the fractional relationship fitting model based on NBRCS and LES observation values under high wind speed sea conditions of the present invention;

[0094] Figure 5 is an inversion result diagram of the combined relationship fitting model with power term and logarithmic term based on NBRCS and LES observation values under high wind speed sea conditions of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0095] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0096] Embodiment 1

[0097] See the appendix Figure 1 , the present invention provides the following technical solutions: A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula, comprising the following steps:

[0098] S1: Analyze the correlation between two spaceborne GNSS-R observation values, namely the bistatic radar cross section and the front slope, and the significant wave height and wave period parameters;

[0099] S2: Based on the correlation between the two spaceborne GNSS-R observation values and the significant wave height and wave period parameters analyzed, construct an empirical model for wave period estimation:

[0100] The expression of the empirical model for wave period estimation under low wind speed sea conditions is:

[0101]

[0102] In the formula: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of the bistatic radar cross section observation value and the front slope observation value at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross section and the front slope, and a(θ), b(θ), c(θ) and d(θ) respectively represent the model fitting parameters that vary with the incident angle θ;

[0103] The expression of the empirical model for wave period estimation under high wind speed sea conditions is:

[0104] T NBRCS (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ)

[0105] T LES (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ)

[0106] In the formula: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of the bistatic radar cross section observation value and the front slope observation value at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross section and the front slope, and a1(θ), b1(θ), a1(θ), b2(θ) and c(θ) respectively represent the model fitting parameters that vary with the incident angle θ;

[0107] S3: Optimize the constructed empirical model for wave period estimation;

[0108] S4: Estimate the wave period of spaceborne GNSS-R based on the optimized empirical model for wave period estimation.

[0109] Specifically, the specific steps of step S1 include:

[0110] The period parameter T of the wave is obtained from the zero-order spectral moment m0 and the fourth-order spectral moment m4 measured by the sensor, and the expression is:

[0111]

[0112] In the formula: T represents the wave period parameter, m0 represents the zero-order spectral moment, and m4 represents the fourth-order spectral moment; among them, the expression of the zero-order spectral moment m0 is:

[0113]

[0114] In the formula: SWH represents the significant wave height of the sea surface;

[0115] The expression of the fourth-order spectral moment m4 is:

[0116]

[0117] In the formula: S 2 represents the variance of the sea surface slope, g represents a constant related to certain characteristics of the wave, and σ(θ) represents the observed value of the bistatic radar cross section at the incident angle (θ);

[0118]

[0119] In the formula: R(θ) represents the Fresnel reflection coefficient at the incident angle (θ), and MSS represents the mean square slope;

[0120] That is, the correlation expression between the observed value of the bistatic radar cross section and the significant wave height and the wave period parameter is:

[0121] T i ~(m0 / m4) 1 / 4 = f(σ(θ), SWH)

[0122] In the formula: σ(θ) represents the observed value of the bistatic radar cross section at the incident angle (θ), and SWH represents the significant wave height of the sea surface;

[0123] The sea state is divided into low wind speed sea state and high wind speed sea state. Due to different wind speeds, the wave period parameter T is different;

[0124] Assume that the condition of the low wind speed sea state is that the wind speed is less than 10 m / s and the NBRCS value ≥ 40, and the condition of the high wind speed sea state is that the wind speed ≥ 10 m / s and the NBRCS value < 40;

[0125] Taking the bistatic radar cross-section observation value and the significant wave height as input variables, the correlation expression between the bistatic radar cross-section observation value, the significant wave height, and the wave period parameter is:

[0126] T = f(NBRCS, SHW)

[0127] Where: NBRCS represents the normalized bistatic radar cross-section observation value, and SWH represents the significant wave height of the sea surface;

[0128] Similarly, the correlation expression between the leading edge slope observation value, the significant wave height, and the wave period parameter can be deduced as:

[0129] T = f(LES, SHW)

[0130] Where: LES represents the normalized leading edge slope, and SWH represents the significant wave height of the sea surface.

[0131] Specifically, the specific steps of step S2 include:

[0132] Eliminating the incidence angle dependence under low wind speed and high wind speed sea conditions;

[0133] Based on the correlation expressions between the bistatic radar cross-section observation value, the leading edge slope observation value, and the significant wave height and wave period parameters, an empirical model for wave period estimation under low wind speed and high wind speed sea conditions is constructed:

[0134] The expression of the empirical model for wave period estimation under low wind speed sea conditions is (power fitting model):

[0135]

[0136] Where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross-section observation value and the leading edge slope observation value at the incidence angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and leading edge slope respectively, and a(θ), b(θ), c(θ), and d(θ) represent the model fitting parameters that change with the incidence angle θ;

[0137] The expression of the empirical model for wave period estimation under high wind speed sea conditions is (fitting model with exponential function relationship):

[0138] T NBRCS (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ)

[0139] T LES(θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ)

[0140] Where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross - section observation value and the front - slope observation value at the incident angle θ respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross - section and the front - slope respectively. a1(θ), b1(θ), a2(θ), b2(θ) and c(θ) represent the model fitting parameters varying with the incident angle θ respectively.

[0141] Specifically, in step S2, the specific steps for eliminating the incident - angle dependence under low - wind - speed and high - wind - speed sea conditions include:

[0142] Divide the incident angles in the range of 0 - 70° into different subsets at intervals of 1°;

[0143] Estimate the fitting parameters with the data within each subset and establish an independent fitting model for each subset;

[0144] Save the fitting coefficients of each subset and construct an incident - angle look - up table;

[0145] Eliminate the incident - angle dependent terms under low - wind - speed and high - wind - speed sea conditions based on the incident - angle look - up table.

[0146] Specifically, the specific steps of step S3 include:

[0147] Optimization of the wave - period estimation empirical model under low - wind - speed sea conditions:

[0148] Minimize the loss function of the wave - period estimation empirical model based on the fminsearch optimization algorithm. The expression of the loss function is:

[0149]

[0150] Where: T NBRCS and T LES represent the wave - period values of the bistatic radar cross - section observation value and the front - slope observation value respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross - section and the front - slope respectively. a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively;

[0151] Optimization of the wave - period estimation empirical model under high - wind - speed sea conditions:

[0152] Minimize the loss function of the wave - period estimation empirical model based on the fminsearch optimization algorithm. The expression of the loss function is:

[0153] loss NBRCS =∑(T NBRCS -a1(θ)·exp(b1(θ)·SWH)+a2(θ)·exp(b2(θ)·NBRCS)+c(θ)) 2

[0154] loss LES =∑(T LES -a1(θ)·exp(b1(θ)·SWH)+a2(θ)·exp(b2(θ)·LES)+c(θ)) 2

[0155] Where: T NBRCS and T LES are the wave period values ​​of the bistatic radar cross section observation and the leading edge slope observation, SWH is the effective wave height on the sea surface, NBRCS and LES are the normalized bistatic radar cross section and leading edge slope, respectively. a1(θ), b1(θ), a2(θ), b2(θ) and c(θ) are the model fitting parameters that vary with the incident angle θ.

[0156] Embodiment 2

[0157] The difference between this embodiment and the first embodiment is that:

[0158] Specifically, step S2 also includes:

[0159] The expression of the constructed empirical model for wave period estimation under high wind speed sea conditions is (fitting model of fractional relationship):

[0160]

[0161] Where: T NBRCS (θ) and T LES (θ) represents the wave period value of NBRCS and LES observations at the incident angle θ, SWH represents the effective wave height on the sea surface, NBRCS and LES represent the normalized bistatic radar cross section and leading edge slope, respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters that vary with the incident angle θ.

[0162] Specifically, step S3 also includes:

[0163] Optimization of the empirical model for wave period estimation in high wind speed sea conditions:

[0164] Based on the fminsearch optimization algorithm, the loss function of the empirical model for wave period estimation is minimized. The expression of the loss function is:

[0165]

[0166] where: T NBRCS and T LES respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value. SWH represents the significant wave height of the sea surface. NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope. a(θ), b(θ), c(θ), and d(θ) respectively represent the model fitting parameters that vary with the incident angle θ.

[0167] Example 3

[0168] The difference between this example and Example 2 is that:

[0169] Specifically, step S2 further includes:

[0170] Step S2 further includes:

[0171] The expression of the empirical model for wave period estimation under high wind speed sea conditions constructed (a fitting model with a combined relationship of power terms and logarithmic terms) is:

[0172] T NBRCS (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·NBRCS) + e(θ))

[0173] T LES (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·LES) + e(θ))

[0174] where: T NBRCS (θ) and T LES (θ) respectively represent the wave period values of NBRCS and LES observation values at the incident angle θ. SWH represents the significant wave height of the sea surface. NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope. a(θ), b(θ), c(θ), d(θ), and e(θ) respectively represent the model fitting parameters that vary with the incident angle θ.

[0175] Specifically, step S3 further includes:

[0176] Optimization of the empirical model for wave period estimation under high wind speed sea conditions:

[0177] Based on the fminsearch optimization algorithm, minimize the loss function of the empirical model for wave period estimation. The expression of the loss function is:

[0178] loss NBRCS = Σ(T NBRCS - a(θ)·SWH b(θ)+c(θ)·log(d·NBRCS)+e(θ))) 2

[0179] loss LES =∑(T LES -a(θ)·SWH b(θ) +c(θ)·log(d·LES)+e(θ))) 2

[0180] In the formula: T NBRCS and T LES respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value, SWH represents the significant wave height of the sea surface, NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope, and a(θ), b(θ), c(θ), d(θ) and e(θ) respectively represent the model fitting parameters that vary with the incident angle θ.

[0181] Verification:

[0182] Download the CYGNSS GNSS-R L1 V3.2 version observation data, ERA5 wind speed data, ERA5 significant wave height data, ERA5 wave period data, and WW3 wave period data from January 2020 to December 2020 from relevant websites. Among them, the CYGNSS GNSS-R L1 V3.2 version observation data includes the normalized bistatic radar cross-section (NBRCS), the front slope (LES), and the incident angle (θ) at the specular reflection point. The ERA5 wind speed data includes the wind speed data at 10 m above the ERA5 sea surface. The ERA5 significant wave height data includes the combined wind wave and swell significant wave height data of ERA5. The ERA5 wave period data includes the ERA5 peak wave period data. The WW3 wave period data includes the peak wave period data of the third-generation wave model (WW3);

[0183] Process the downloaded data. The CYGNSS GNSS-R L1 V3.2 version observation data, ERA5 wind speed data, and WW3 wave period data are respectively matched and aligned using linear interpolation and bilinear interpolation algorithms in terms of time and space resolution. Use the wind speed data at 10 m above the ERA5 sea surface to determine whether the sea state is a low wind speed sea state or a high wind speed sea state. Based on the MATLAB 2019b software platform, use the CYGNSS GNSS-R NBRCS and LES observation values, ERA5 significant wave height and wave period data to construct and train a wave period estimation model, and use the WW3 wave period data as reference data to verify the solution accuracy of the wave period estimation model;

[0184] Refer to the appendix Figure 2 to show the inversion results of the power fitting model based on NBRCS and LES observation values under low wind speed sea conditions;

[0185] See the appendix Figure 3 , showing the inversion results of the exponential function relationship fitting model based on NBRCS and LES observations under high wind speed sea conditions;

[0186] See the appendix Figure 4 , showing the inversion results of the fractional relationship fitting model based on NBRCS and LES observations under high wind speed sea conditions;

[0187] See the appendix Figure 5 , showing the inversion results of the combined relationship fitting model with power terms and logarithmic terms based on NBRCS and LES observations under high wind speed sea conditions;

[0188] At the same time, under low wind speed sea conditions, the accuracy statistics of the comparison between the wave period estimated by the power fitting model based on NBRCS and LES observations and the WW3 wave period data are shown in Table 1:

[0189] Table 1: Accuracy statistics of the comparison between the wave period estimated by the power fitting model based on NBRCS and LES observations and the WW3 wave period data under low wind speed sea conditions

[0190] Accuracy index NBRCS observations LES observations RMSE(s) 2.19 2.26 Bias(s) 0.01 0.01 CC 0.61 0.64 MAPE 17.03％ 18.51％

[0191] Under high wind speed sea conditions, the accuracy statistics of the comparison between the wave period estimated by different fitting models based on NBRCS and LES observations and the WW3 wave period data are shown in Table 2:

[0192] Table 2: Accuracy statistics of the comparison between the wave period estimated by different fitting models based on NBRCS and LES observations and the WW3 wave period data under high wind speed sea conditions

[0193]

[0194] From appendix Figure 2 to appendix Figure 5 and Tables 1 to 2, it can be seen that:

[0195] This application can be used for ocean wave period estimation;

[0196] For low wind speed sea conditions, the power fitting model developed based on NBRCS and LES observations has good estimation performance. Among them, the NBRCS observations are slightly better than the LES observations, and the accuracies of RMSE, Bias, CC, and MAPE are better than 2.19 s, 0.01 s, 0.61, and 17.03% respectively;

[0197] For high wind speed sea conditions, when the three models are compared with the WW3 reference data, good estimation accuracy is achieved. For the NBRCS observed values, the fitting model with an exponential function relationship has the best performance, and the accuracies of RMSE, Bias, CC, and MAPE are better than 2.21 s, -0.35 s, 0.64, and 14.67% respectively; for the LES observed values, the fitting model with an exponential function relationship and the fitting model combining power terms and logarithmic terms have comparable performance; when comparing the estimation performances of the two observed values, the accuracies are basically the same, and the NBRCS observed values are slightly better than the LES observed values.

[0198] Based on the above analysis, the present application has good practicability and reliability, and can effectively solve the problems of the complex relationship between wave parameters and GNSS-R observed values under low wind speed and high wind speed sea conditions and the influence of the incident angle dependence term on the estimation accuracy of wave period.

[0199] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula, characterized in that It includes the following steps: S1: Analyze the correlation between the bistatic radar cross section and the front slope, two spaceborne GNSS-R observation values, and the significant wave height and wave period parameters; S2: Based on the correlation between the two spaceborne GNSS-R observation values and the significant wave height and wave period parameters analyzed, construct an empirical model for wave period estimation: The expression of the empirical model for wave period estimation under low wind speed sea conditions is: Where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross-section observation and the front slope observation at the incident angle θ, respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross-section and the front slope, respectively. a(θ), b(θ), c(θ), and d(θ) represent the model fitting parameters that vary with the incident angle θ; The expression of the empirical model for wave period estimation under high wind speed sea conditions is: T NBRCS T(θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ) T LES (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ) where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value at the incident angle θ, respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross-section and the front slope, respectively. a1(θ), b1(θ), a1(θ), b2(θ) and c(θ) represent the model fitting parameters varying with the incident angle θ; S3: Optimize the constructed empirical model for wave period estimation; S4: Estimate the wave period of spaceborne GNSS-R based on the optimized empirical model for wave period estimation.

2. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 1, characterized in that: The specific steps of step S1 include: The period parameter T of the wave is obtained from the zero-order spectral moment m0 and the fourth-order spectral moment m4 measured by the sensor, and the expression is: In the formula: T represents the wave period parameter, m0 represents the zero-order spectral moment, and m4 represents the fourth-order spectral moment; Among them, the expression of the zero-order spectral moment m0 is: In the formula: SWH represents the significant wave height of the sea surface; The expression of the fourth-order spectral moment m4 is: where: S 2 represents the variance of the sea surface slope, g represents a certain constant related to some characteristics of the wave, and σ(θ) represents the observed value of the bistatic radar cross section at the incident angle (θ); In the formula: R(θ) represents the Fresnel reflection coefficient at the incident angle (θ), and MSS represents the mean square slope; That is, the correlation expression between the bistatic radar cross section observation value and the significant wave height and wave period parameters is: T i ~(m0 / m4) 1 / 4 = f(σ(θ), SWH) In the formula: σ(θ) represents the bistatic radar cross section observation value at the incident angle (θ), and SWH represents the significant wave height of the sea surface; The sea conditions are divided into low wind speed sea conditions and high wind speed sea conditions. Due to different wind speeds, the wave period parameter T of the wave is different; It is assumed that the low wind speed sea condition is set as the wind speed less than 10 m / s and the NBRCS value ≥ 40, and the high wind speed sea condition is set as the wind speed ≥ 10 m / s and the NBRCS value < 40; Taking the bistatic radar cross section observation value and the significant wave height as input variables, the correlation expression between the bistatic radar cross section observation value and the significant wave height and wave period parameters is: T = f(NBRCS, SHW) In the formula: NBRCS represents the normalized bistatic radar cross section observation value, and SWH represents the significant wave height of the sea surface; Similarly, the correlation expression between the leading edge slope observation value and the significant wave height and wave period parameters can be deduced as: T = f(LES, SHW) In the formula: LES represents the normalized leading edge slope, and SWH represents the significant wave height of the sea surface.

3. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 2, characterized in that: The specific steps of step S2 include: Eliminate the incident angle dependence under low wind speed and high wind speed sea conditions; Based on the correlation expressions between the bistatic radar cross section observation value and the leading edge slope observation value and the significant wave height and wave period parameters, construct an empirical model for wave period estimation under low wind speed and high wind speed sea conditions: The expression of the empirical model for wave period estimation under low wind speed sea conditions is: Where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross - section observation value and the front slope observation value at the incident angle θ respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross - section and the front slope respectively. a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ; The expression of the empirical model for wave period estimation under high wind speed sea conditions is: T NBRCS (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ) T LES (θ) = a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·LES) + c(θ) where: T NBRCS (θ) and T LES (θ) represent the wave period values of the bistatic radar cross-section observation and the front slope observation at the incident angle θ, respectively. SWH represents the significant wave height of the sea surface. NBRCS and LES represent the normalized bistatic radar cross-section and the front slope, respectively. a1(θ), b1(θ), a2(θ), b2(θ), and c(θ) represent the model fitting parameters that vary with the incident angle θ.

4. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 3, characterized in that: In step S2, the specific steps for eliminating the incident angle dependence under low wind speed and high wind speed sea conditions include: Divide the incident angles in the range of 0 - 70° into different subsets at intervals of 1°; Estimate the fitting parameters with the data within each subset and establish an independent fitting model for each subset; Save the fitting coefficients of each subset and construct an incident angle look-up table. Eliminate the dependence on the incident angle under low wind speed and high wind speed sea conditions based on the incident angle lookup table.

5. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 4, characterized in that: The specific steps of step S3 include: Optimization of the wave period estimation empirical model under low wind speed sea conditions: Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model. The expression of the loss function is: Where: T NBRCS and T LES respectively represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value. SWH represents the significant wave height of the sea surface. NBRCS and LES respectively represent the normalized bistatic radar cross-section and the front slope. a(θ), b(θ), c(θ) and d(θ) respectively represent the model fitting parameters varying with the incident angle θ; Optimization of the wave period estimation empirical model under high wind speed sea conditions: Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model. The expression of the loss function is: loss NBRCS = ∑(T NBRCS - a1(θ)·exp(b1(θ)·SWH) + a2(θ)·exp(b2(θ)·NBRCS) + c(θ)) 2 loss LES = ∑(T LES - a1(θ)·exp(b1(θ)·SWH)+a2(θ)·exp(b2(θ)·LES)+c(θ)) 2 where: T NBRCS and T LES represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a1(θ), b1(θ), a2(θ), b2(θ) and c(θ) represent the model fitting parameters varying with the incident angle θ respectively.

6. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 5, characterized in that: Step S2 further includes: The expression of the constructed wave period estimation empirical model under high wind speed sea conditions is: where: T NBRCS (θ) and T LES (θ) represent the wave period values of NBRCS and LES observations at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross section and the leading edge slope respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively.

7. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 6, characterized in that: Step S3 further includes: Optimization of the wave period estimation empirical model under high wind speed sea conditions: Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model. The expression of the loss function is: where: T NBRCS and T LES represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a(θ), b(θ), c(θ) and d(θ) represent the model fitting parameters varying with the incident angle θ respectively.

8. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 7, characterized in that: Step S2 further includes: Step S2 further includes: The expression of the constructed wave period estimation empirical model under high wind speed sea conditions is: T NBRCS (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·NBRCS) + e(θ)) T LES (θ) = a(θ)·SWH b(θ) + c(θ)·log(d·LES) + e(θ)) Where: T NBRCS (θ) and T LES (θ) represent the wave period values of NBRCS and LES observations at the incident angle θ, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross section and the front slope respectively, and a(θ), b(θ), c(θ), d(θ) and e(θ) represent the model fitting parameters varying with the incident angle θ respectively.

9. A spaceborne GNSS-R wave period estimation method based on an incident angle lookup table and a two-step empirical model formula according to claim 8, characterized in that: Step S3 further includes: Optimization of the wave period estimation empirical model under high wind speed sea conditions: Based on the fminsearch optimization algorithm, minimize the loss function of the wave period estimation empirical model. The expression of the loss function is: loss NBRCS = Σ(T NBRCS - a(θ)·SWH b(θ) + c(θ)·log(d·NBRCS) + e(θ)) 2 loss LES = Σ(T LES - a(θ)·SWH b(θ) + c(θ)·log(d·LES) + e(θ)) 2 Where: T NBRCS and T LES represent the wave period values of the bistatic radar cross-section observation value and the front slope observation value respectively, SWH represents the significant wave height of the sea surface, NBRCS and LES represent the normalized bistatic radar cross-section and the front slope respectively, and a(θ), b(θ), c(θ), d(θ) and e(θ) represent the model fitting parameters varying with the incident angle θ respectively.

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