Wavenumber spectrum slope calibration method and system for dual GNSS buoy wide-swath altimeter

Abstract

The present application belongs to the field of marine remote sensing measurement technology, and specifically relates to a dual GNSS buoy wide-swath altimeter wavenumber spectrum slope calibration method and system. The present application combines the wavenumber spectrum-frequency spectrum model, processes and numerically analyzes the frequency spectrum data obtained by the buoy, and thus quantitatively evaluates the wavenumber spectrum slope of the wide-swath satellite altimeter. This technical solution effectively compensates for the shortcomings of traditional single-point measurement, reduces the evaluation cost and implementation difficulty, and realizes reliable verification of the wavenumber spectrum characteristics of the two-dimensional sea surface height in the spatial domain of the wide-swath altimeter.

Description

Technical Field

[0001] The present application belongs to the field of marine remote sensing measurement technology, and specifically relates to a method and system for calibrating the slope of a wavenumber spectrum of a dual GNSS buoy wide-swath altimeter. Background Art

[0002] Wide-swath satellite altimeters (such as SWOT) are a new generation of ocean measurement altimeters with advantages such as wide-swath observation and high spatial resolution. This type of altimeter can provide more accurate sea surface height (SSH) measurement data and can capture the spatial and temporal characteristics of the ocean over a large range. However, the existing sea surface height assessment methods for traditional sub-satellite point altimeters are not applicable to wide-swath altimeters. This is because traditional technologies usually rely on a single GNSS buoy or tide gauge station for point-to-point comparison, focusing mainly on the sea surface height (SSH) comparison in the time domain, but the error of the wide-swath altimeter is mainly reflected in the wavenumber spectrum in the spatial domain. The existing assessment methods cannot directly perform spatial domain evaluation of the wavenumber spectrum of the two-dimensional sea surface height measured by the wide-swath altimeter, resulting in the inability to accurately calibrate.

[0003] In the prior art, common sea surface height measurement and evaluation methods, such as single GNSS buoy observations, can usually only provide SSH time series data in the time domain. This method can effectively calibrate the changes in sea surface height in the time dimension, but cannot reflect spatial fluctuations, that is, changes in the sea surface wavenumber spectrum. The measurement data of wide-swath altimeters, especially for changes in sea surface height over a large area of ​​sea, require an evaluation of the spatial wavenumber spectrum. The prior art lacks an efficient and economical method that can combine the wavenumber spectrum information in the spatial domain and frequency domain for calibration and verification.

[0004] In the process of accurate calibration of wide-swath altimeters, the traditional point-to-point comparison method cannot meet the evaluation requirements of its spatial domain two-dimensional sea surface height measurement data. In addition, although directly deploying a large number of GNSS buoys to obtain spatial wavenumber spectra is a feasible method, this not only requires high costs, but also has considerable technical difficulties in implementation, especially when deployed in a large area of ​​sea, it is difficult to achieve large-scale deployment. Therefore, the existing evaluation methods have great limitations in cost and implementation complexity, and a low-cost, efficient and convenient calibration solution is urgently needed. Summary of the invention

[0005] In view of the problems and defects in the above background, the present invention proposes an innovative wavenumber spectrum calibration method. This method uses only two sets of GNSS buoy data and combines the wavenumber spectrum-frequency spectrum model to derive and quantitatively evaluate the wavenumber spectrum slope of the wide-swath altimeter by analyzing the frequency spectrum information measured by the GNSS buoy. Its technical solution is:

[0006] A dual GNSS buoy wide-swath altimeter wavenumber spectrum slope calibration method comprises the following steps:

[0007] S1. GNSS buoy data preprocessing;

[0008] S2. GNSS buoy sea surface height frequency spectrum calculation;

[0009] S3. Calculation of frequency spectrum of GNSS buoy differences;

[0010] S4. Estimation of wavenumber spectrum slope by combining numerical model and GNSS buoy spatial difference frequency spectrum;

[0011] S5. Spatially differentiated SSH frequency spectrum of GNSS buoys;

[0012] S6. Calculate the GNSS buoy frequency spectrum ratio;

[0013] S7. Calibration of the slope of the wavenumber spectrum of a wide swath altimeter.

[0014] Preferably, the GNSS buoy data preprocessing in step S1 includes inverse pressure effect correction and true sea surface height calculation, and the method is as follows:

[0015] Correction for adverse pressure effects:

[0016] Calculated pressure anomaly , the correction amount of sea level is calculated according to the inverse pressure effect formula, and the change of sea level caused by the inverse pressure effect It is inversely proportional to the air pressure anomaly, and the calculation formula is:

[0017] ;

[0018] in: is the reference density of seawater; is the acceleration due to gravity;

[0019] The air pressure data collected by the GNSS buoy is compared with the reference air pressure to obtain air pressure anomalies and air pressure anomalies. The calculation is as follows:

[0020] ;

[0021] in: is the atmospheric pressure measured in real time at the buoy location, is the reference air pressure value;

[0022] True sea surface height calculation:

[0023] To obtain the corrected sea surface height, the calculated inverse pressure correction is Subtract it from the original sea surface height, that is:

[0024] ;

[0025] in: is the corrected true sea surface height; is the original uncorrected sea surface height.

[0026] Preferably, the GNSS buoy data preprocessing in step S1 includes the removal of tidal components, and nonlinear least squares fitting is performed on the main tidal components to separate significant tidal signals and deduct them from the buoy SSH time series. The specific implementation is as follows:

[0027] S1-01. Determine several main tidal components based on the tidal characteristics of the target sea area and the tidal observations or numerical simulation results over the years;

[0028] S1-02. Fitting the observed data:

[0029] ;

[0030] It represents the change of tidal height obtained by tidal fitting over time. is the number of main tidal components selected, For the The amplitude of the tidal component, For the The angular frequency corresponding to the tidal component is For the The initial phase of the tidal component, for time;

[0031] S1-03. During the fitting process, the amplitude of each component in the above tidal model is and the first phase Perform nonlinear least squares solving;

[0032] S1-04. Subtract the tidal signal from the original SSH time series to obtain the sea surface height after removing the main tidal component:

[0033] ;

[0034] in: is the residual sea surface height sequence after deducting the tidal component, is the tidal height sequence obtained by fitting, is the time series of sea surface height after inverse pressure correction ;

[0035] S1-05. Use low-pass filter to process SSH data;

[0036] S1-06. Use linear interpolation method to supplement missing data.

[0037] Preferably, step S2 uses a piecewise Fourier transform method to perform spectrum analysis on the time series:

[0038] First, the long SSH data sequence is divided into segments of a certain length, each containing sampling points and apply a window function to each segment to reduce spectrum leakage;

[0039] Then, a discrete Fourier transform is performed on the windowed data; the Fourier transform is as follows:

[0040] For each piece of data Perform Fourier transform to get the frequency domain expression :

[0041] ;

[0042] ;

[0043] in: For frequency The complex frequency domain result at is the sampling point in the time series;

[0044] Calculate the intensity of the frequency spectrum, that is, the frequency spectrum power density, frequency The frequency spectrum power density at It is expressed as:

[0045] ;

[0046] Average the frequency spectra of multiple segments of data:

[0047] ;

[0048] in It is The frequency spectrum of the segment data.

[0049] Preferably, the frequency spectrum of the GNSS buoy difference in step S3 is calculated as follows:

[0050] First, calculate the SSH difference between the two floats ;

[0051] Then, the frequency spectrum is calculated for the difference data:

[0052] For difference data Perform Fourier transform to obtain the frequency spectrum , which represents the frequency spectrum power density at each frequency point. The frequency spectra of multiple difference data are averaged to obtain the final difference frequency spectrum .

[0053] Preferably, in step S4, the frequency spectrum of the sea surface height time series collected by the GNSS buoy is analyzed by Fourier transform to obtain the frequency spectrum of the sea surface height , the specific method is as follows:

[0054] Wavenumber-spectrum model :

[0055] ;

[0056] is the overall amplitude of the spectrum, and are the transition points of wave number and frequency, respectively. and Control the shape of the spectrum;

[0057] Separation Frequency spectrum, Defined as the wave number Points:

[0058] ;

[0059] Considering the symmetry of the integral, the integral can be simplified to:

[0060] ;

[0061] make ,but , the integral becomes:

[0062] ;

[0063] Define the constant term , the integral is further simplified to:

[0064] ;

[0065] Using the integral formula:

[0066] ;

[0067] ;

[0068] is the gamma function, let , then the original integral becomes:

[0069] ;

[0070] Substitute the integral result into Frequency spectrum expression:

[0071] ;

[0072] Substituting Con into the equation, we get:

[0073] ;

[0074] ;

[0075] Similarly, we can get:

[0076] ;

[0077] ;

[0078] Can be ordered:

[0079] ;

[0080] ;

[0081] but:

[0082] ;

[0083] ;

[0084] in: is the spectrum slope obtained by power law fitting of the high frequency part of the frequency spectrum, is the slope of the wavenumber spectrum.

[0085] Preferably, the method for calculating the spatial difference SSH frequency spectrum of the GNSS buoy in step S5 is as follows:

[0086] Assume the sea surface height field is , and its wavenumber-frequency joint spectrum is ,satisfy:

[0087] ;

[0088] in yes The space-time Fourier transform of yes The complex conjugate of

[0089] Two distances The inter-buoy SSH differences are:

[0090] ;

[0091] The Fourier transform is:

[0092] ;

[0093] The power spectrum of the difference is:

[0094] ;

[0095] ,

[0096] We can get:

[0097] ;

[0098] If defined is the semivariogram, then:

[0099] ;

[0100] Therefore, the ratio formula is:

[0101] ;

[0102] In the formula Indicates wave number The spatial distance between the two buoys dependencies.

[0103] Preferably, step S6 calculates the GNSS buoy frequency spectrum ratio in the following manner:

[0104] The frequency spectrum is obtained by calculating the spectrum of the SSH time series collected by the GNSS buoy. , perform power law fitting on the high frequency part of the frequency spectrum to obtain the spectrum slope , the turning frequency It is estimated by identifying the turning point in the spectrum where the spectrum transitions from a flat region to a steep decay;

[0105] By setting different wavenumber spectrum slopes Ratio of values The model prediction is then compared with the actual results of GNSS buoy measurements to determine the optimal wavenumber spectrum slope. .

[0106] Preferably, step S7 is to calibrate the slope of the wide swath altimeter wavenumber spectrum, and the method is as follows:

[0107] The Welch method is used to calculate the wavenumber spectrum of each one-dimensional along-track subset in the data set. The wavenumber spectra of each sub-segment calculated are horizontally averaged to obtain a comprehensive wavenumber spectrum across directions. The power law of the obtained wavenumber spectrum is fitted by the least squares method to calculate the slope of the spatial wavenumber spectrum of SSH measured by the satellite. ;

[0108] Comparison of the slope of the wavenumber spectrum obtained from GNSS buoy measurements and the slope of the wavenumber spectrum measured by a wide-swath satellite altimeter , calculate the wavenumber spectrum slope error between the two:

[0109] ;

[0110] in: is the slope of the wavenumber spectrum measured by the GNSS buoy; is the slope of the wavenumber spectrum measured by the wide-swath satellite altimeter; is the wavenumber spectrum slope error between the two.

[0111] A dual GNSS buoy wide swath altimeter wavenumber spectrum slope calibration system is used to implement the dual GNSS buoy wide swath altimeter wavenumber spectrum slope calibration method.

[0112] Compared with the prior art, the present invention has the following beneficial effects:

[0113] 1. High-precision wavenumber spectrum slope estimation: The present invention can accurately estimate the spatial wavenumber spectrum slope of sea surface fluctuations through the joint numerical model of two GNSS buoys. This method does not need to rely on traditional high-cost satellite data, and can obtain results consistent with high-precision satellite data under low-cost conditions, greatly improving the estimation accuracy of the wavenumber spectrum slope.

[0114] 2. Simplified satellite calibration verification: The present invention estimates the wavenumber spectrum slope through GNSS buoy data, providing an effective tool for calibration verification of wide-swath altimeter satellites (such as SWOT). This method can reduce the reliance on expensive satellite data and significantly reduce the cost of satellite calibration.

[0115] 3. Wide applicability: The method of the present invention can adapt to different sea areas and climatic conditions, and is widely used in ocean wave analysis and satellite data calibration, which not only improves the flexibility of application, but also enhances the wide applicability of the technology.

[0116] 4. Cost reduction: Compared with traditional high-cost satellite observation data, the present invention achieves a significant reduction in the cost of sea surface fluctuation monitoring and satellite calibration through a low-cost GNSS buoy combined with a numerical model. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Figure 1 This is the flow chart of this application;

[0118] Figure 2 It is a schematic diagram of the ratio calculation process;

[0119] Figure 3 This is a comparison chart of the slopes of the wide-swath satellite altimeter wavenumber spectra. DETAILED DESCRIPTION

[0120] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0121] The present invention relates to a wavenumber spectrum slope calibration method for a dual GNSS buoy wide-swath altimeter. The method utilizes a limited number of GNSS buoys (two buoy systems in this solution) to measure the time series of sea surface height, and combines the wavenumber spectrum-frequency spectrum coupling model to derive the wavenumber spectrum characteristics of the sea surface height in the spatial domain, thereby providing quantitative calibration and verification for the wide-swath altimeter data. The technical solution of the present invention has the advantages of simple structure, low cost, convenient operation, and the ability to simultaneously obtain time and space information, and is suitable for field verification and subsequent data processing of marine remote sensing data.

[0122] 1. GNSS buoy data observation:

[0123] The method of the present invention first selects two observation positions in the target sea area and deploys two independent GNSS buoys, with a distance of about 10 kilometers between them. The design purpose of the above spacing is to conduct targeted observations of changes in ocean surface height at a scale less than 10 kilometers, so as to evaluate the wavenumber spectrum slope of sea surface height within the sub-mesoscale (i.e., less than 10 kilometers). The wavenumber spectrum slope is closely related to the energy cascade mechanism of ocean dynamic processes (such as near-geostrophic balance, sub-mesoscale eddy generation and frontal dynamics, etc.), and has a key reference value for wide-swath satellite radar altimeter data calibration and other aspects.

[0124] Each of the GNSS buoys includes a geodetic-grade GNSS receiver and a high-gain antenna to ensure the accuracy and stability of sea surface height measurements.

[0125] The present invention requires that the data observation duration of the above-mentioned GNSS buoys is not less than 2 months, and high-frequency (e.g., 1 Hz or higher) sea surface height records are maintained during this period. Through long-term continuous observation, the SSH changes under sub-mesoscale dynamic processes can be fully captured, ensuring complete coverage of sub-mesoscale ocean dynamic processes.

[0126] In the system described in the present invention, two GNSS buoys are provided with corresponding data acquisition and transmission modules to send sea surface height, air pressure, temperature and other relevant sensor information to the shore-based data center for aggregation and backup in real time or quasi-real time.

[0127] 2. GNSS buoy data preprocessing:

[0128] After completing the GNSS buoy data collection and preliminary solution, the method of the present invention obtains the original sea surface height time series, and the original time series data needs to be systematically preprocessed to ensure the accuracy and stability of the observation results. The present invention proposes the following specific implementation steps:

[0129] 2.1 Effectiveness screening:

[0130] To ensure data validity, the present invention performs a preliminary quality check on the observation records, removes observation segments with abnormal GNSS positioning solution status or signal loss, and removes outliers that are obviously inconsistent with the actual sea conditions (such as extreme value jumps that occur frequently). This step can be completed based on the observation residuals with set thresholds and epoch positioning solution quality indicators (such as GDOP, number of reference satellites, etc.).

[0131] 2.2 High sea state elimination:

[0132] When eliminating high sea conditions, the present invention uses sea surface height (SSH) data collected at a frequency of 1 Hz to separate high-frequency fluctuation signals caused by gravity waves through high-pass filtering, and then performs statistical analysis on the high-frequency fluctuation signals at hourly intervals to calculate significant wave heights in the form of the four-fold mean error method (i.e., SWH=4×standard deviation). If the SWH in a certain hour period exceeds 5 meters, it is determined that the buoy may have excessive measurement errors due to the large swing of waves during this period. Based on this, the present invention automatically shields or marks the data of this period as invalid values, thereby avoiding the pollution of the overall data quality by extreme sea conditions and ensuring the reliability and accuracy of the data used for subsequent wave number spectrum slope calibration. This method can flexibly adjust the threshold of significant wave height according to actual observation needs to adapt to the marine environmental conditions of different sea areas or time periods.

[0133] 2.3 Correction of adverse air pressure effect:

[0134] In ocean remote sensing measurements, sea surface height (SSH) is often significantly affected by changes in atmospheric pressure. The inverse pressure effect caused by changes in the pressure field will cause the sea surface height to rise and fall, thereby affecting the measurement accuracy. Therefore, in order to obtain true sea surface height data, the sea surface height changes caused by abnormal atmospheric pressure must be corrected. To this end, the present invention provides a method for correcting the inverse pressure effect based on GNSS buoy measurement data, and the specific steps are as follows:

[0135] (1) Calculation of air pressure anomaly:

[0136] In the present invention, the air pressure data collected by the GNSS buoy is compared with the reference air pressure to obtain the air pressure anomaly. Calculated by the following formula:

[0137] ;

[0138] in: is the atmospheric pressure measured in real time at the buoy position (unit: Pa), It is the reference air pressure value (unit: Pa), which is usually the standard air pressure or average air pressure provided by meteorological models or historical data.

[0139] (2) Correction for adverse pressure effect:

[0140] Calculated pressure anomaly , calculate the correction of sea level height according to the inverse pressure effect formula. Change of sea level height caused by inverse pressure effect It is inversely proportional to the air pressure anomaly, and the calculation formula is:

[0141] ;

[0142] in: The change in sea surface height after correction for the adverse pressure effect (in meters); is the abnormal air pressure (unit: Pa); is the reference density of seawater (unit: ),Pick ; is the acceleration due to gravity (unit: ), usually taken .

[0143] (3) Calculation of true sea surface height:

[0144] To obtain the corrected sea surface height, the calculated inverse pressure correction is Subtract it from the original sea surface height. That is:

[0145] ;

[0146] in: is the corrected true sea surface height (unit: meter); is the original uncorrected sea surface height (unit: meter).

[0147] 2.4 Removal of tidal components:

[0148] In order to accurately identify and deduct the influence of tide on sea surface height change, the present invention further performs nonlinear least square fitting on the main tidal components after effectively eliminating high-frequency sea surface fluctuations and high sea conditions, so as to separate the significant tidal signal and deduct it from the buoy SSH time series. The specific implementation is as follows:

[0149] (1) Selection of main tidal components:

[0150] The present invention first determines several main tidal components based on the tidal characteristics of the target sea area and the tidal observations or numerical simulation results over the years, including but not limited to M2, S2, K1, O1, etc. If necessary, it can be expanded to other common or known important components (such as N2, P1, etc.) to adapt to the actual tidal conditions in different sea areas.

[0151] (2) Establishment of tidal fitting model:

[0152] In order to separate these main tidal components in the SSH time series, the present invention adopts the following simplified tidal model to fit the observed data:

[0153] ;

[0154] in: It represents the change of tidal height obtained by tidal fitting over time. is the number of the selected main tidal components (e.g. M2, S2, K1, O1, etc.), For the The amplitude of each tidal component (in meters), For the The angular frequency corresponding to each tidal component (unit: radians per second), is the initial phase of the component (unit: radian), is the time (in seconds or hours, depending on the application).

[0155] (3) Nonlinear least squares fitting:

[0156] During the fitting process, the present invention aims at the amplitude of each component in the above tidal model. and the first phase Perform nonlinear least squares solution. In specific implementation, numerical optimization methods such as trust region method and Levenberg-Marquardt algorithm can be used to perform the following optimization objectives on the observed SSH data:

[0157] ;

[0158] in: The SSH sequence measured for the buoy at time The value of is the total number of buoy observation epochs.

[0159] (4) Tidal signal subtraction:

[0160] After completing the above nonlinear least squares fitting and obtaining the main tidal component parameters (i.e. and ), the present invention deducts the tidal signal from the original SSH time series to obtain the sea surface height after removing the main tidal component:

[0161] ;

[0162] in: is the residual sea surface height sequence after deducting the tidal component, is the tidal height sequence obtained by fitting, is the time series of sea surface height after inverse pressure correction .

[0163] (5) Data filtering:

[0164] In order to remove the influence of high-frequency waves on sea surface height (SSH) data, the present invention uses a low-pass filter to process the SSH data collected at 1 Hz. First, the filter window is set to 30 minutes to ensure that the high-frequency wave components with a period of less than 30 minutes are filtered out. A 4th-order Butterworth low-pass filter is used, and the cutoff frequency is set to 0.000555 Hz. The filtering process is carried out by Fourier transform and filter frequency response function For the original data Filter to obtain smoothed sea surface height data ,Right now:

[0165] ;

[0166] in: represents the Fourier transform of the original sea surface height data, is the frequency response function of the Butterworth filter, Represents the inverse Fourier transform.

[0167] This process effectively removes high-frequency wave signals and retains low-frequency ocean dynamic changes, providing accurate data support for subsequent wave number spectrum analysis. The response function of the Butterworth low-pass filter is:

[0168] ;

[0169] in: is the signal frequency; is the frequency response; is the cut-off frequency, which indicates the maximum frequency that the signal can pass (unit: Hz); is the order of the filter, which controls the steepness of the filter.

[0170] (6) Data interpolation and continuity:

[0171] In order to process missing data and ensure the temporal continuity of sea surface height (SSH) data, the present invention uses linear interpolation method to supplement the missing data. and There are missing data points between them, and the interpolation process can be performed using the following formula:

[0172] ;

[0173] in: is the interpolation point between and between; is the interpolated data point; and The time points and The known data at .

[0174] Through the above series of preprocessing steps, the present invention can obtain high-precision, spatiotemporally continuous and relatively low-noise GNSS buoy SSH data, providing reliable data support for the subsequent wide-swath satellite radar altimeter wavenumber spectrum slope calibration. Especially in sub-mesoscale dynamic research, the above method can effectively eliminate the interference caused by extreme sea conditions and meteorological factors, making the final wavenumber spectrum slope evaluation more consistent with the intrinsic characteristics of actual ocean physical processes.

[0175] 3. Calculation of sea surface height frequency spectrum of independent GNSS buoy:

[0176] In order to obtain the frequency distribution characteristics of the sea surface height (SSH) observed by the GNSS buoy, the present invention adopts the segmented Fourier transform method to perform spectrum analysis on the time series. First, the long-term SSH data sequence is divided into a certain length (e.g., each segment contains The data is divided into segments (sampling points) and a window function (such as Hann window) is applied to each segment to reduce spectrum leakage. Then, a discrete Fourier transform (DFT) is performed on the windowed data. The key steps of spectrum calculation are as follows:

[0177] (1) Fourier transform:

[0178] For each piece of data Perform Fourier transform to get the frequency domain expression .

[0179] ;

[0180] in: For frequency The complex frequency domain result at is the sampling point in the time series, is a discrete frequency.

[0181] (2) Frequency spectrum intensity:

[0182] Calculate the intensity of the frequency spectrum (i.e., frequency spectrum power density), frequency The frequency spectrum power density at It can be expressed as:

[0183] ;

[0184] (3) Spectrum averaging:

[0185] Average the frequency spectra of multiple segments of data to reduce the impact of random noise:

[0186] ;

[0187] in It is The frequency spectrum of the segment data.

[0188] 4. Calculation of frequency spectrum of GNSS buoy differences:

[0189] In order to analyze the frequency characteristics of the sea surface height difference between two GNSS buoys (GB1, GB2), the present invention first calculates the SSH difference between the two buoys The frequency spectrum of the difference data is then calculated. The difference data is calculated using the same method as for independent GNSS buoys. Perform Fourier transform to obtain the frequency spectrum , represents the frequency spectrum power density at each frequency point. The frequency spectrum of multiple difference data is averaged to obtain the final difference frequency spectrum , in order to reduce the impact of noise on the results.

[0190] 5. Estimation of wavenumber spectrum slope by combining numerical model and GNSS buoy spatial difference frequency spectrum:

[0191] The frequency spectrum of the sea surface height is obtained by Fourier transforming the time series of sea surface height collected by the GNSS buoy. To this end, the following wavenumber-spectrum model is used :

[0192] ;

[0193] in: is the overall amplitude of the spectrum, and are the transition points of wave number and frequency, respectively. and Controls the shape of the spectrum.

[0194] Separation Frequency spectrum, Defined as the wave number Points:

[0195] ;

[0196] Considering the symmetry of the integral, the integral can be simplified to:

[0197] ;

[0198] make ,but , the integral becomes:

[0199] ;

[0200] Define the constant term , the integral is further simplified to:

[0201] ;

[0202] Using the integral formula:

[0203] ;

[0204] in is the beta function, is the gamma function. Let , then the original integral becomes:

[0205] ;

[0206] Substitute the integral result into Frequency spectrum expression:

[0207] ;

[0208] After substituting Con, we get:

[0209] ;

[0210] in:

[0211] ;

[0212] Similarly, we can get:

[0213] ;

[0214] ;

[0215] Due to parameters It mainly controls the edge of the wavenumber spectrum, so it does not affect the slope of the middle spectrum. , ,but:

[0216] ;

[0217] in: is the spectrum slope obtained by power law fitting of the high frequency part of the frequency spectrum, is the slope of the wavenumber spectrum.

[0218] 6. Spatially differentiated SSH frequency spectrum of GNSS buoys:

[0219] Assume the sea surface height field is , and its wavenumber-frequency joint spectrum is ,satisfy:

[0220] ;

[0221] in yes The space-time Fourier transform of yes The complex conjugate of .

[0222] Two distances The inter-buoy SSH difference is , whose Fourier transform is:

[0223] ;

[0224] The power spectrum of the difference is:

[0225] ;

[0226] because , we can get:

[0227] ;

[0228] If defined is the semivariogram, then:

[0229] ;

[0230] Therefore, the ratio formula is:

[0231] ;

[0232] This formula provides a quantitative description of the spatial spectrum of the difference in sea surface height between two buoys. By comparing the frequency spectrum with the difference spectrum, we can deeply analyze the temporal frequency characteristics of ocean surface waves, as well as their spatial distribution and transmission characteristics. Indicates wave number The spatial distance between the two buoys This term describes the propagation and attenuation characteristics of sea surface waves in space at different wave numbers. This expression shows that longer wavelength waves (low wave numbers) are more strongly correlated between the two buoys, while shorter wavelength waves (high wave numbers) are weaker. The ratio calculation can assist the slope of the wave number spectrum This ratio can be used to verify the consistency between actual observation data and theoretical models, thus providing an important reference for the calibration of the wavenumber spectrum slope of high-resolution satellite observation data.

[0233] 7. Model parameter estimation:

[0234] In order to calculate the GNSS buoy frequency spectrum ratio, it is first necessary to determine the spectrum slope , Turn frequency And the turning wave number The frequency spectrum is obtained by calculating the spectrum of the SSH time series collected by the GNSS buoy. , perform power law fitting on the high frequency part of the frequency spectrum to obtain the spectrum slope . Transition frequency It is estimated by identifying the turning point in the spectrum where the spectrum transitions from a flat region to a steep decay. The empirical scale used is 250km.

[0235] According to the characteristics of ocean dynamics, the present invention sets different wave number spectrum slopes. Numeric value (range is , with an interval of 0.5) The model prediction is then compared with the actual results of GNSS buoy measurements to determine the optimal wavenumber spectrum slope. .

[0236] 8. Wide swath altimeter wavenumber spectrum slope calibration:

[0237] use It can be further used for calibration verification of the slope of the wavenumber spectrum of SSH measured by a wide-swath altimeter.

[0238] Before calculating the satellite wavenumber spectrum, the calibration satellite measurement coverage of 100 km before and after the test sea area is determined according to the GNSS buoy position. The linear trend of the wide-swath along-track SSH data is removed to eliminate the influence of large-scale changes and ensure that the data only reflects the mesoscale and sub-mesoscale fluctuation components. Then, interpolation processing is performed on the missing data to achieve the continuity of the data set and avoid spectrum estimation errors caused by missing data.

[0239] The Welch method is used to calculate the wavenumber spectrum of each one-dimensional along-track subset in the data set. Specifically, the data set is divided into multiple sub-segments along the satellite orbit direction, and the length of each sub-segment is 20km. The corresponding wavenumber spectrum information is obtained by performing spectrum analysis on each sub-segment.

[0240] The wave number spectra of each sub-segment calculated are horizontally averaged to obtain a comprehensive wave number spectrum across directions. This step can accurately reflect the spatial distribution characteristics of SSH fluctuations in the direction of the satellite ground track and in the vertical direction.

[0241] Finally, the power law fitting of the obtained wave number spectrum was performed by the least squares method, and the slope of the spatial wave number spectrum of SSH measured by the satellite was calculated. .

[0242] Comparison of the slope of the wavenumber spectrum obtained from GNSS buoy measurements and the slope of the wavenumber spectrum measured by a wide-swath satellite altimeter , the wave number spectrum slope error between the two can be calculated. The error calculation formula is as follows:

[0243] ;

[0244] in: is the slope of the wavenumber spectrum measured by the GNSS buoy; is the slope of the wavenumber spectrum measured by the wide-swath satellite altimeter; is the wavenumber spectrum slope error between the two, expressed as a percentage.

[0245] The error value reflects the consistency and deviation between the two measurement methods in estimating the wavenumber spectrum slope. Through this error calculation method, the present invention can compare the results of different measurement methods, verify the accuracy of wide-swath satellite altimeter measurement in practical applications, and provide a basis for satellite data calibration.

[0246] Attached Figure 2 To calculate the ratio Schematic diagram showing the slope of different wavenumber spectra ( ) under the frequency ratio The relationship with frequency is =4 is most consistent with the measured GNSS results.

[0247] Attached Figure 3 Shows the slope of the wavenumber spectrum of the Wide Swath Satellite Altimeter (SWOT satellite) SSH =3.84, so the relative error of the slope of the wide-swath satellite altimeter wavenumber spectrum can be estimated 4%.

[0248] The system is constructed to run the method of the present application. Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0249] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A dual GNSS buoy wide-swath altimeter wavenumber spectrum slope calibration method, characterized in that: The following steps are involved: S1. GNSS buoy data preprocessing; S2. GNSS buoy sea surface height frequency spectrum calculation; S3. Calculation of frequency spectrum of GNSS buoy differences; S4. Estimation of wavenumber spectrum slope by combining numerical model and GNSS buoy spatial difference frequency spectrum; S5. Spatially differentiated SSH frequency spectrum of GNSS buoys; S6. Calculate the GNSS buoy frequency spectrum ratio; S7. Calibration of the slope of the wavenumber spectrum of a wide swath altimeter.

2. The dual GNSS buoy wide swath altimeter wavenumber spectrum slope calibration method according to claim 1, characterized in that: The GNSS buoy data preprocessing in step S1 includes the correction of the adverse pressure effect and the calculation of the true sea surface height, and the method is as follows: Correction for adverse pressure effects: Calculated pressure anomaly , the correction amount of sea level is calculated according to the inverse pressure effect formula, and the change of sea level caused by the inverse pressure effect It is inversely proportional to the air pressure anomaly, and the calculation formula is: ； in: is the reference density of seawater; is the acceleration due to gravity; The air pressure data collected by the GNSS buoy is compared with the reference air pressure to obtain air pressure anomalies and air pressure anomalies. The calculation is as follows: ； in: is the atmospheric pressure measured in real time at the buoy position, is the reference air pressure value; True sea surface height calculation: To obtain the corrected sea surface height, the calculated inverse pressure correction is Subtract it from the original sea surface height, that is: ； in: is the corrected true sea surface height; is the original uncorrected sea surface height.

3. The dual GNSS buoy wide swath altimeter wavenumber spectrum slope calibration method according to claim 1, characterized in that: The GNSS buoy data preprocessing in step S1 includes the removal of tidal components, and the nonlinear least squares fitting of the main tidal components is performed to separate the significant tidal signals and deduct them from the buoy SSH time series. The specific implementation method is as follows: S1-01. Determine several main tidal components based on the tidal characteristics of the target sea area and the tidal observations or numerical simulation results over the years; S1-02. Fitting the observed data: ； in: It represents the change of tidal height obtained by tidal fitting over time. is the number of main tidal components selected, For the The amplitude of the tidal component, For the The angular frequency corresponding to the tidal component is For the The initial phase of the tidal component, for time; S1-03. During the fitting process, the amplitude of each component and the first phase Perform nonlinear least squares solution; S1-04. Subtract the tidal signal from the original SSH time series to obtain the sea surface height after removing the main tidal component: ； in: is the residual sea surface height sequence after deducting the tidal component, is the tidal height sequence obtained by fitting, is the time series of sea surface height after inverse pressure correction ; S1-05. Use low-pass filter to process SSH data; S1-06. Use linear interpolation method to supplement missing data.

4. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: Step S2 uses the segmented Fourier transform method to perform spectrum analysis on the time series: First, the long SSH data sequence is divided into segments of a certain length, each containing sampling points and apply a window function to each segment; Then, a discrete Fourier transform is performed on the windowed data; the Fourier transform is as follows: For each piece of data Perform Fourier transform to get the frequency domain expression : ； ； in: For frequency The complex frequency domain result at is the sampling point in the time series, is the wave number; Calculate the intensity of the frequency spectrum, that is, the frequency spectrum power density, frequency The frequency spectrum power density at It is expressed as: ； Average the frequency spectra of multiple segments of data: ； in It is The frequency spectrum of the segment data.

5. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: The frequency spectrum of the GNSS buoy difference in step S3 is calculated as follows: First, calculate the SSH difference between the two floats: ； Then, the frequency spectrum is calculated for the difference data: For difference data Perform Fourier transform to obtain the frequency spectrum , which represents the frequency spectrum power density at each frequency point. The frequency spectra of multiple difference data are averaged to obtain the final difference frequency spectrum .

6. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: In step S4, the frequency spectrum of the sea surface height time series collected by the GNSS buoy is analyzed by Fourier transform to obtain the frequency spectrum of the sea surface height , the specific method is as follows: Wavenumber-spectrum model : ； is the overall amplitude of the spectrum, and are the transition points of wave number and frequency, respectively. and Control the shape of the spectrum; Separation Frequency spectrum, Defined as the wave number Points: ； Considering the symmetry of the integral, the integral can be simplified to: ； make ,but , the integral becomes: ； Define the constant term , the integral simplifies to: ； Using the integral formula: ； ； is the gamma function, let , then the original integral becomes: ； Substitute the integral result into Frequency spectrum expression: ； Substituting Con into the equation, we get: ； ； Similarly, we can get: ； ； Can be ordered: ； ； but: ； ； in: is the spectrum slope obtained by power law fitting of the high frequency part of the frequency spectrum, is the slope of the wavenumber spectrum.

7. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: The calculation method of the spatial difference SSH frequency spectrum of the GNSS buoy in step S5 is as follows: Assume the sea surface height field is , and its wavenumber-frequency joint spectrum is ,satisfy: ； in yes The space-time Fourier transform of yes The complex conjugate of Two distances The inter-buoy SSH differences are: ； The Fourier transform is: ； The power spectrum of the difference is: ； ， We can get: ； If defined is the semivariogram, then: ； Therefore, the ratio formula is: ； In the formula Indicates wave number The spatial distance between the two buoys dependencies.

8. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: Step S6 calculates the GNSS buoy frequency spectrum ratio in the following way: The frequency spectrum is obtained by calculating the spectrum of the SSH time series collected by the GNSS buoy. , perform power law fitting on the high frequency part of the frequency spectrum to obtain the spectrum slope , the turning frequency It is estimated by identifying the turning point in the spectrum where the spectrum transitions from a flat region to a steep decay; By setting different wave number spectrum slopes Ratio of values The model prediction is then compared with the actual results of GNSS buoy measurements to determine the optimal wavenumber spectrum slope. .

9. The method for calibrating the wavenumber spectrum slope of a dual GNSS buoy wide-swath altimeter according to claim 1, characterized in that: Step S7: calibrate the slope of the wide swath altimeter wavenumber spectrum, the method is as follows: The Welch method is used to calculate the wavenumber spectrum of each one-dimensional along-track subset in the data set. The wavenumber spectra of each sub-segment calculated are horizontally averaged to obtain a comprehensive wavenumber spectrum across directions. The power law of the obtained wavenumber spectrum is fitted by the least squares method to calculate the slope of the spatial wavenumber spectrum of SSH measured by the satellite. ; Comparison of the slope of the wavenumber spectrum obtained from GNSS buoy measurements and the slope of the wavenumber spectrum measured by a wide-swath satellite altimeter , calculate the wavenumber spectrum slope error between the two: ； in: is the slope of the wavenumber spectrum measured by the GNSS buoy; is the slope of the wavenumber spectrum measured by the wide-swath satellite altimeter; is the wavenumber spectrum slope error between the two.

10. A dual GNSS buoy wide swath altimeter wavenumber spectrum slope calibration system, characterized in that: A method for calibrating the slope of a wavenumber spectrum of a dual GNSS buoy wide-swath altimeter as described in any one of claims 1 to 9.

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