CN103698750A - HY-2 satellite scatterometer sea surface wind field retrieval method and device - Google Patents

Abstract

The invention provides an HY-2 satellite scatterometer sea surface wind field retrieval method and device. The method comprises the steps of building a physical geography module function; setting a target function based on the physical geography module function; searching for the local maximal wind speed and wind direction of the target function for each wind vector unit, and taking the obtained wind speed and wind direction as ambiguity solutions of the current wind vector unit; selecting ambiguity solutions corresponding to two maximal target values from the ambiguity solutions of the current wind vector unit, respectively comparing the two ambiguity solutions with an NCEP (National Centers for Environmental Prediction) forecast wind direction, and taking the ambiguity solution which is closest to the NCEP forecast wind direction as the initial field of the current wind vector unit in the comparative results; taking initial fields of all wind vector units as an ambiguity solution initial field of circle median filter, and performing ambiguity solution removal operation to obtain real data of a sea surface wind field. The HY-2 satellite scatterometer sea surface wind field retrieval method and device are adaptive to the requirements of ambiguity solution removal needed by the scatterometer wind field inversion under various complex environmental conditions, and the forecast accuracy is improved.

Description

Sea surface wind field inversion method and device for ocean second-number satellite scatterometer

Technical Field

The invention relates to the technical field of ocean microwave remote sensing, in particular to a sea surface wind field inversion method and device of an ocean second satellite scatterometer.

Background

The ocean surface wind field is a basic parameter which influences active factors of sea waves, ocean currents and water masses and ocean dynamics, and has important significance in monitoring the global ocean wind field, preventing and reducing disasters in coastal areas, guaranteeing the ocean environment and promoting ocean related scientific research. The satellite scatterometer has become the most important observation means of the global sea surface wind field due to the characteristics of all-time, all-weather, high space-time resolution, large coverage range and the like.

A satellite scatterometer is a calibrated radar that actively transmits electromagnetic waves to the sea surface and receives echo signals modulated by the sea surface. The radar echo signal will be determined by the transmitted signal together with the sea surface characteristics.When the wave length of the sea wave and the wave length of the electromagnetic wave transmitted by the radar meet the Bragg scattering condition, the phase of the backward scattering electromagnetic wave generated by each wave surface is the same, so that resonance is generated, and the echo energy is mainly determined by the electromagnetic wave generating the resonance. At the operating frequency of the microwave scatterometer, the sea surface wave satisfying the bragg resonance condition is a sea surface capillary wave, and the spectral density of the sea surface capillary wave is directly related to the wind speed on the sea surface. Therefore, the echo signal measured by the radar can acquire the information of the sea surface wind field. By processing the radar echo signals, a normalized backscattering coefficient (NRCS, or σ) can be derived that is only related to sea-surface conditions⁰) σ measured from a scatterometer⁰And (4) a sea surface wind field can be further extracted, and the information extraction process of the sea surface wind field is called wind vector inversion.

The ocean second satellite microwave scatterometer (HY 2-SCAT) is a microwave scatterometer capable of operating in a business mode, HY2-SCAT is mainly used for global sea surface wind field observation, the wind speed measuring range is 4-24 m/s, and the wind speed precision is 2 m/s or 10%; the wind direction measuring range is 0 ~ 360, and the wind direction precision is 20. The HY2-SCAT has working frequency of 13.256GHz, and is rotated around the sky bottom direction at a fixed elevation angle by pencil beams in a pencil beam conical scanning mode to form a certain ground coverage swath in the orbit-direction movement of the satellite platform; the scatterometer system comprises two polarization modes of VV and HH, which are observed respectively at different incidence angles, and multiple backscattering coefficients (sigma) of different polarization modes and different incidence angles can be obtained for the same resolution unit in the motion process of the platform⁰) And measuring results to overcome the multivalue fuzzy problem of sea surface wind field direction inversion. The internal wave beam adopts an HH polarization mode, the incident angle is 41 degrees, and the corresponding ground swath width is about 1350 km. The external wave beam adopts a VV polarization mode, the incident angle is 48 degrees, and the corresponding ground swath width is about 1700 km.

Currently available data products for marine satellite scatterometers are classified as L1B grade products, L2A grade products, L2B grade products, and L3 grade products. Products at all levels are simply introduced as follows:

the data for the L1B class product is scatterometer observations stored in time order of telemetry frames. Each telemetry frame includes 96 scatterometer measurement pulses, each measurement pulse including a backscatter coefficient, a geographic location of each pulse footprint, and parameters that describe information such as quality and uncertainty of the measurement data.

The L2A-level product file includes each radar backscatter sigma0 measurement taken by the satellite platform in one spatial orbit. In addition, the L2A product also contains some auxiliary data elements corresponding to each sigma0 measurement. These ancillary data elements list relevant information such as the position, quality, and uncertainty of each sigma0 measurement. Sigma0 in L2A products is grouped in units of wind vectors. Each wind vector unit row corresponds to an intersection cutting of the ground measurement swath. Each L2A wind vector cell is a 25km square. Therefore, 1624 rows of wind vector units are required to complete one complete coverage of the earth, where each orbit data is divided into 1624 × 76 wind vector units, 1624 for the down-orbit direction and 76 for the cross-orbit direction.

The data files of the L2B-grade product are organized in track units, i.e., the wind vector measurement data of each track constitutes one L2B file. Each data element in the L2B class product may be indexed by the row, column number of the wind vector unit. The extending direction of the wind vector unit rows in the L2B-level product is vertical to the lower starline, and the extending direction of the columns is consistent with the lower starline direction. The L2B grade product gives 4 wind speed and wind direction fuzzy solutions at most, and is arranged according to the likelihood value from high to low.

Data for the HY-2A scatterometer grade L3 product provides daily global sea surface wind field data in a grid of 0.25 ° x 0.25 ° size and separates the ascending and descending rails. When multiple wind vector cells fall within the same grid cell, then the data value is overwritten, rather than averaged. Therefore, only the most recent measurement per day is included in the scatterometer Level3 document.

Inverting the sea surface wind vector from the sea surface backscattering coefficients measured by the scatterometer requires solving three problems: and establishing a geophysical model, a wind vector solving algorithm and a fuzzy solving and removing algorithm. In the related art, a fuzzy solution removing algorithm usually adopts a round median filtering algorithm, and in essence, the round median filtering algorithm is a noise filtering algorithm, and when the algorithm is used for wind field fuzzy solution removing, the quality of a fuzzy solution initial field directly determines the effect of fuzzy solution removing. If the round median filtering fuzzy solution removing algorithm achieves a good effect, the conditions that at least more than 50% of solutions in an initial field are correct solutions and flaky fuzzy can not occur need to be met. In general, the above conditions are satisfied, but when the scatterometer is influenced by rainfall and the like, the initial field of the ambiguity solution of the scatterometer usually appears a flaky 180 ° ambiguity, and in this case, the round number filtering algorithm cannot achieve the effect of ambiguity solution removal well.

Disclosure of Invention

The invention aims to provide a sea surface wind field inversion method and a sea surface wind field inversion device for a marine second-number satellite scatterometer, so as to solve the problems.

The embodiment of the invention provides a sea surface wind field inversion method for a marine second satellite scatterometer, which comprises the following steps: establishing a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna; setting an objective function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein sigma_oiIs the actual measured backscattering coefficient, σ, of the scatterometer_mPredicting a backscattering coefficient when the corresponding wind speed is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion; for each wind vector unit, searching the wind speed and the wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit; respectively sorting the fuzzy solutions of each wind vector unit according to the corresponding objective function values from large to small; selecting two maximum fuzzy solutions corresponding to target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in a comparison result as an initial field of the current wind vector unit; and taking the initial fields of all the wind vector units as the fuzzy solution initial fields of the circular median filtering, and performing fuzzy solution removing operation to obtain real data of the sea surface wind field.

The embodiment of the invention also provides a sea surface wind field of the marine second satellite scatterometerAn inversion apparatus comprising: a geophysical model establishing module for establishing a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna; the fuzzy solution acquisition module is used for setting a target function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein sigma_oiIs the actual measured backscattering coefficient, σ, of the scatterometer_mFor the rear of the predicted corresponding wind speed V and the relative wind direction xThe backscattering coefficient N is the total number of backscattering coefficient measurement results for wind vector inversion; for each wind vector unit, searching the wind speed and the wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit; the initial field optimization module is used for respectively sequencing the fuzzy solutions of each wind vector unit from large to small according to the corresponding objective function values; selecting two maximum fuzzy solutions corresponding to target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in a comparison result as an initial field of the current wind vector unit; and the fuzzy solution removing module is used for taking the initial fields of all the wind vector units as fuzzy solution initial fields of the circle median filtering, and performing fuzzy solution removing operation to obtain real data of the sea surface wind field.

According to the method and the device provided by the embodiment of the invention, the fuzzy solution initial field of the wind direction optimization circular median filtering predicted by the NCEP (national centers for Environmental Prediction center) is introduced, so that the fuzzy solution can be more accurately removed, the inversion result of the sea surface wind field is more in line with the actual wind field, the requirement of fuzzy joint removal required by the scatterometer wind field inversion under various complex Environmental conditions is further met, and the Prediction accuracy is improved.

Drawings

FIG. 1 is a flow chart of a sea surface wind field inversion method for a marine second satellite scatterometer provided by an embodiment of the invention;

FIG. 2 is a schematic diagram illustrating a wind direction multi-solution generated by mirror symmetry and reflection symmetry of an antenna according to an embodiment of the present invention;

FIG. 3 is a flow chart of a method for full round number filtering provided by an embodiment of the present invention;

fig. 4 shows a structural block diagram of an offshore wind field inversion apparatus for a marine two-satellite scatterometer according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail below with reference to specific embodiments and with reference to the attached drawings.

Aiming at the defects that the traditional round-median filtering fuzzy solution removing algorithm has higher requirement on the accuracy of an initial field and can not remove sheet fuzziness and the like, the embodiment of the invention designs a more accurate fuzzy solution removing algorithm which is applied to the sea surface wind field inversion process of the satellite scatterometer so as to adapt to the requirement of fuzzy joint removal required by the scatterometer wind field inversion under various complex conditions. Based on the above, the embodiment of the invention provides a sea surface wind field inversion method and device for a marine second satellite scatterometer, and the following description is provided through the embodiment.

Referring to a flow chart of a sea surface wind field inversion method of a marine second satellite scatterometer shown in fig. 1, the method comprises the following steps:

step S102, establishing a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna;

step S104, setting a target function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> σ_oiIs the backscattering coefficient, sigma, actually measured by a scatterometer_mPredicting a backscattering coefficient when the corresponding wind speed is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion;

step S106, for each wind vector unit, searching the wind speed and the wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit;

in this embodiment, for each wind vector unit, the wind speed and wind direction of the local maximum of the objective function are found, and the wind speed and wind direction are taken as a potential solution of the wind vector unit (these solutions are called fuzzy solutions, and in general, there are 2-4 fuzzy solutions for each wind vector unit).

Step S108, sorting the fuzzy solutions of each wind vector unit from big to small according to the corresponding objective function values; selecting two maximum fuzzy solutions corresponding to the target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in the comparison result as an initial field of the current wind vector unit;

and step S110, taking the initial fields of all the wind vector units as fuzzy solution initial fields of the circular median filtering, and performing fuzzy solution removing operation to obtain real data of the sea surface wind field.

According to the method, the fuzzy solution can be removed more accurately by introducing the NCEP forecast fuzzy solution initial field of wind direction optimization circular number filtering, so that the inversion result of the sea surface wind field is more consistent with the actual wind field, the requirements of fuzzy joint removal required by the scatterometer wind field inversion under various complex environmental conditions are met, and the forecast accuracy is improved.

Before the step of comparing the two fuzzy solutions with the wind direction of the NCEP forecast, the following method may be adopted in the embodiment to obtain the wind direction of the NCEP forecast:

1) extracting observation longitude and latitude and observation time of the current wind vector unit, and recording the observation longitude and latitude and the observation time as MES _ Lat, MES _ Lon and PRD _ time respectively;

2) determining forecast data of two times of the NCEP forecast according to the observation time of the current wind vector unit, wherein the two times are recorded as time1 and time2 respectively;

3) extracting wind vectors of four angular points with the current wind vector unit as the center from the forecast data, wherein the wind vectors of the four angular points comprise: the longitude and latitude information and the warp and weft wind speed components of the four angular points are respectively recorded as Mer _ Lat_i、Mer_Lon_i、ZON_Met_i(time2)、ZON_Met_i(time1)、MER_Met_i(time2)、MER_Met_i(time 1); the variation range of the subscript i is 1-4, and the subscript i corresponds to 4 angular points respectively;

4) calculating a distance weight coefficient d_i(ii) a Wherein,

$d_i=\mathrm{ar}\cos \left(\begin{array}{c}\cos {(90-\mathrm{Mer}\_{\mathrm{Lat}}_i)}^{*}\cos (90-\mathrm{MES}\_\mathrm{Lat})\\ +\sin {(90-\mathrm{Met}\_{\mathrm{Lat}}_i)}^{*}\sin {(90-\mathrm{MES}\_{\mathrm{Lat}}_i)}^{*}\cos (\mathrm{Met}\_{\mathrm{Lon}}_i-\mathrm{MES}\_\mathrm{Lon})\end{array}\right);$

5) a temporal weight coefficient alpha is calculated, wherein, $a=\frac{\mathrm{time}2-\mathrm{PRD}\_\mathrm{time}}{\mathrm{time}2-\mathrm{timel}};$

6) interpolating the extracted wind vectors to a current wind vector unit, and obtaining the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction predicted by the NCEP through interpolation, wherein the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction are respectively marked as ZON _ Mean, MER _ Mean, SPD _ Met and DIR _ Met; in this embodiment, the wind vector data predicted by the NCEP is stored in the form of an equal longitude and latitude grid, and the marine second satellite scatterometer wind vector unit is a grid unit in a coordinate system with the wind direction and the along-orbit direction as coordinate axes, and the two data are not matched in a spatial relationship, so that the predicted data needs to be interpolated on the wind vector unit grid in an interpolation manner.

<math> <mrow> <mi>ZON</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>MER</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>MET</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>SPD</mi> <mo>_</mo> <mi>Met</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msqrt> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> </msqrt> </mrow> </math>

$+a^{*}\sqrt{\mathrm{ZON}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2+\mathrm{MER}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2}];$

DIR_Met=90-atan2(ZON_Mean,MER_Mean)/pi×180。

The method can be applied to wind field inversion of the HY-2A satellite scatterometer, and certainly, the method has universality for removing fuzzy solutions of sea wind fields of other satellite scatterometers. The fuzzy solution removal in the HY-2A satellite scatterometer wind field inversion process is taken as an example for explanation.

The HY-2A satellite scatterometer wind field inversion process comprises the following steps: and establishing a geophysical model, a wind vector solving algorithm and a fuzzy solving and removing algorithm. Wherein the geophysical model function describes a relationship between a sea surface wind vector and a radar backscattering coefficient. The general form of the geophysical model function is:

σ₀=F(V,χ,...,f,p,θ)（1）

wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; θ is the angle of incidence of the antenna.

The wind vector solving algorithm is mainly used for obtaining a wind vector solution of the sea surface through a geophysical model function and NRCS observation values of different azimuth angles of a sea surface wind vector bin. Since the biccosine distribution of the geophysical model is a nonlinear feature, the solution to the wind vector cannot be directly solved by directly substituting the backscattering coefficient into the geophysical model. The general solving algorithm adopts a maximum likelihood solving algorithm, a wind vector which enables the objective function shown in the formula (2) to obtain a local maximum value is searched to be used as a solution, and the solutions are sequenced according to the corresponding maximum likelihood values.

<math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein σ_oiFor actual measured backscattering of scatterometerCoefficient, σ_mAnd predicting a backscattering coefficient when the corresponding wind speed for the model is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion.

Due to the biccosine distribution characteristics of the geophysical model function itself and the effects of various measurement noises of the scatterometer, the solution algorithm will generally obtain multiple wind vector solutions (i.e., fuzzy solutions). Wind direction multi-solution elimination is to select the wind vector solution closest to the real wind vector from a series of multi-solution wind vectors.

In the process of wind vector inversion, a plurality of wind vector solutions can enable the target function formula (2) to take a maximum value, wherein only one solution is a real solution, and the rest solutions are called fuzzy solutions. Therefore, after the maximum likelihood solving method is used for obtaining the wind vector which enables the objective function to obtain the local maximum, the multi-solution removal of the wind direction, namely the fuzzy solution removal, is carried out, and the real solution can be obtained. The reason for the generation of the fuzzy solution is that the model function has a double harmonic property of cos (2 x), so that σ measured for each group⁰It is possible that 4 wind vector solutions satisfy the model function. Suppose sigma of downwind and upwind⁰For a certain wind speed, σ, with negligible asymmetry⁰The weathervaning relationship may be expressed as a cosine function. In the case of wind speed determination, for each σ⁰The value, w for a maximum of 4 wind directions satisfying the model function₁、w₂、w₃、w₄And the relationship is satisfied between them:

w₂=180°-w₁,w₃=180°+w₁,w₄=360°-w₁（3）

for convenience of explanation, W is assumed herein₁The wind direction is the true wind direction, and the schematic diagram of the wind direction multiple solution generated by the antenna mirror symmetry and the reflection symmetry is shown in fig. 2. For the antenna 1 in fig. 2, the ambiguity W2, W3 are caused by the reflection symmetry of the backscatter coefficients and the "upwind-upwind symmetry", respectively, whereas the ambiguity W4 is the result of the joint action of the two symmetries, in the case of only one antennaThe fuzzy wind direction W corresponding to FIG. 2 cannot be distinguished₂、W₃、W₄. In practice, two antennas with 90 ° angular difference are used in the actual design of SASS, in order to reduce the ambiguity. But the design has not proven to be as effective as desired. Since the two antenna angles differ by 90 °, for antenna 2 the ambiguity solution caused by reflection symmetry is exactly the same as the ambiguity solution W for antenna 1₄The ambiguity solution generated by the combined action of reflection symmetry and "downwind upwind symmetry" coincides with the ambiguity solution W2 of the antenna 1. In fact, as long as the angle difference between the two antennas is not an integer multiple of 90 °, theoretically, only two antennas can be eliminated, and the ambiguity generated by the reflection symmetry sum and the combined action of the reflection symmetry and the downwind upwind symmetry can be resolved. While the ambiguity due to "downwind upwind symmetry" with a 180 ° difference cannot be eliminated by increasing the number of antennas.

The model function is not completely symmetrical in practice, e.g. σ⁰The measurements in the downwind and upwind directions are not exactly the same. The true solution will always be the "maximum likelihood solution" after the wind field inversion if the errors introduced by the instrument and model functions are not accounted for. Even after errors caused by instrument and model functions are considered, the accuracy of the maximum likelihood solution obtained by wind field inversion to be a true solution can generally exceed 50%, so that the fuzzy solution can be eliminated by adopting a median filtering method. The circle-median filtering ambiguity resolution algorithm is briefly introduced as follows:

the scatterometer radar is used for accurately measuring sea surface backscattering, and a wind direction inversion error caused by near symmetry of downwind measurement and upwind measurement in the measurement process is similar to the problem of noise elimination in image processing. In a uniform and smooth image, a randomly-appearing bright spot or dark spot is easy to automatically distinguish, for the noise of the pulse type, a median filtering method is one of effective methods for eliminating, and similarly, in a uniform wind field, if a certain wind vector is opposite to or has a larger difference with the surrounding wind vectors, the median filtering method is also an effective method. At present, the wind direction multi-solution removal of the business operation scatterometer adopts a circle number filtering algorithm.

For rational number sequence x₀,x₁,…,x_n-1]When n is an odd number, the number x is the number^*The definition is as follows:

x^*

[x₀,x₁,...,x_n-1](formula 4)

And is greater than or equal to x in the sequence^*The sum of the number of (A) and (B) is less than or equal to x^*The number of (2) is equal. That is, if the sequence is monotonic, the median is exactly the middle of the sequence.

When n is an even number, there are two consecutive numbers x^* ₁，x^* ₂Satisfies the following numerical condition that x is less than or equal to x in the sequence^* ₁The sum of the number of (2) and x or more^* ₂Are equal, in which case a unique median number x is defined^*=（x^* ₁+x^* ₂）/2。

The median assumption data defined above is rational numbers between (— infinity, + ∞), but for circumferentially distributed data such as wind direction, the modulo of the data is 2 pi, i.e. the number with 2 pi as the period, and the median cannot be solved directly by the above method, early on, the wind vector is decomposed into two components in the cartesian coordinate system and filtered independently, but this causes incompatibility of wind speed and wind direction. Applying the median filtering technique to the filtering of directional data requires modifying the above definition. Distributing f (x) for any circle by using the definition given by Mardia when x belongs to [0,2 pi ]]Number of circles x^* ₁,x^* ₁+π,x^* ₂,x^* ₂+ π, … satisfies the medium condition:

the above formula is described in [ x ]^* _j,x^* _j+π]The total of (f), (x) is f (x) is in [0,2 π]Half of the whole interval. Unlike a conventional rational number sequence with only one number, a circular distribution may have multiple numbers, but by choosing the x closest to the average number x' of the circles^*As the only number of circles, namely:

wherein:

in fact, for n discrete datasets [ x ]₁,x₂,…,x_n]And the corresponding weight [ w₁,w₂,…,wn]Can approximate a circle histogram H_k(k =0,1, … L-1), where L is the number of strips into which the domain interval is divided. The value of f (x) on the kth strip is equal to the value of [ δ k, δ (k +1) ]]Where δ =2 pi/L, is the sum of the weights of all data in between. The point in the kth band is δ (k + 1/2). The circular average of the discrete data is calculated by:

then, the median band K can be obtained from the following equation^* ₁,K^* ₁+L/2,K^* ₂，K^* ₂+L/2,…

The midpoint angle value of each median strip is taken as the median angle, i.e.:

finally, the unique circle number is determined by selecting the nearest number angle to the circle mean.

The medium filtering is to open a window with a certain size in the sequence, and for the situation that a large error value exists on one point, because the number of the pollution points in the window taking the point as the center does not exceed half of the number, the medium filtering replaces the number of the window center with the medium number in the window coverage area, so as to achieve the purpose of eliminating the influence of the pollution points.

The method is particularly suitable for the problem of 180-degree fuzzy when a wind vector point is opposite to the surrounding adjacent points in direction by replacing error point data with noiseless adjacent point data in the median filtering, and particularly when the method is used in an atmospheric wind field, the median filtering cannot filter out low-frequency characteristics which are larger than a windowed window, such as a convergence line, a cyclone and the like and have severe changes in the wind direction. By phi_ij1，φ_ij2And … denotes a fuzzy wind direction (given in order by likelihood values), the wind direction inversion error is similar to impulse noise. True wind direction

j can be estimated as a signal value using maximum likelihood(first windfarm solution) as an observed value,

j + pi as an error value, the pulse model can be expressed as follows:

wherein delta_ij=[-1，0，1]Is an error model of wind direction inversion, ε_ij<<And pi represents other random errors in the inversion process. When delta_ijPhi at =0_ijRepresents the true wind direction when_ij=±1，

Corresponding to a pseudo solution at 180 deg. to the true wind direction.

The goal of wind direction ambiguity elimination is to eliminate from

(k =1,2,3, …) selecting a wind direction such that it is in the true direction of the windMost closely, in other words, the method renders non-volatile by selecting the subscript kAnd | is minimal. The true wind direction is unknown in the operation process, but the true wind direction can be estimated on each wind vector surface element by using a circle median filtering method. Firstly, selecting the number of circles with true wind direction equal to the wind vector in the window around the surface element, and then selecting a solution close to the true wind direction estimation from the fuzzy solutions. Finally, the true wind direction values are re-estimated based on these newly selected solutions. The above process of estimating true wind direction is iterated continuously until the selected wind vector is unchanged or the number of iterations exceeds a given maximum number. Note the book

An estimated value (also called reference wind direction) of the true wind direction, and the wind vector S obtained in the mth iteration^m _ijCan be expressed as:

wherein CMF represents the circle median filter operator over an NxN window, W_ijW is the weight of the surface element when the wind vector surface element does not contain any wind vector or the surface element is not on the swath_ij=0。

The physical basis of the vector median filtering technology is that the wind directions of wind vector surface elements are not independent, but have certain correlation with the wind directions of surrounding wind vector surface elements, a median is calculated through the wind directions of the surrounding wind vector surface elements, then the solution that the wind direction in the wind vector surface elements is closest to the median is assigned as a true value, the same operation is carried out on each wind vector surface element, and one iteration is completed. After a plurality of iterations and stable results, the multi-solution ambiguity elimination wind vector is obtained.

A method flow diagram for total circular number filtering as shown in fig. 3, the method comprising the steps of:

step S302, initializing, specifically including: setting window size N, setting bin weighting factor W_ij(ii) a Setting and selecting a first wind field solution as a wind vector S⁰ _ij= 1; setting the iteration number m = 0;

step S304, m = m + 1;

step S306, directly selecting a wind vector by using a circle median filtering method;

step S308, updating the selected wind vector;

step S310, judging whether the updated wind vector is converged, if so, ending the current process; if not, return to step S304.

The generation of the marine satellite scatterometer data product is completed by a marine satellite scatterometer data processing subsystem. After receiving a product manufacturing command sent by the operation control subsystem, starting a manufacturing process of products of corresponding grades, and reporting a product completion condition and a product file list to the operation control subsystem after the product is manufactured. And taking the 0-level product as input, and matching with other input auxiliary data to obtain the secondary and tertiary data products of the HY-2 satellite through processing such as internal calibration, external calibration, bin matching, landmark type identification, wind vector inversion, fuzzy solution removal, gridding and the like.

In this embodiment, the NCEP data naming rule: yhyymmdddh0 _ h1.nc, where fh is the NCEP forecast data identifier, yyymmdd is the year, month and day of the initial forecast, h0 is the time of the start of the forecast, and h1 is the time of the forecast. For example, fh.2013051000 — 18.nc represents a forecast product with a forecast time of 18 when the time of the forecast is 5 months, 10 days and 0 in 2013.

In this embodiment, the HY-2A satellite scatterometry data product naming rule takes an L2B-level marine wind field data product as an example, and the file naming rule is as follows: H2A _ SM 2 byyymdd _ nnn. H5. Wherein: H2A represents an HY-2 satellite; SM stands for load as scatterometer; 2B represents a data processing level of L2B; yyyy represents the year of the observation start time; mm represents the observation start time month; dd represents the day of the start of observation; YYYYMMDD represents the year, month and day covered by the product; NNNNN represents the number of tracks starting from the south-most end; h5 represents a file storage type in hdf5 format.

The round median filtering algorithm is basically a noise filtering algorithm, the fuzzy solutions of the first two objective function values are compared with the wind direction (NCEP forecast) of a third party, the fuzzy solution closest to the NCEP wind direction is selected as an initial field, and the initial field is optimized, so that the improvement of the round median filtering fuzzy solution removing algorithm is realized. The NCEP forecast initial field optimization technique is based on the fact that: in more than 85% of cases, the solution closest to the real wind field is the first or second fuzzy solution. Furthermore, the wind field streamlines can be roughly determined by these two solutions (but there is a directional ambiguity).

The fuzzy solution removal of the single-track data in the real-time data processing flow of the HY-2 scatterometer is taken as an example for explanation.

1. NCEP forecast data preparation

According to the current year, month and day, inquiring the NCEP data reported at 0 hour on the day by the NCEP file name at 8 nights every day in Beijing, extracting the NCEP forecast data of six times of 18 hours, 24 hours, 30 hours, 36 hours, 42 hours and 48 hours, and removing the preparation forecast wind field data for the fuzzy solution of the next day. The 24-48 hour forecast data is selected to ensure timeliness requirements for real-time processing. The forecast data at 18 is added to accommodate the orbit data for a single track across the sky. Because the marine second satellite scatterometer divides data products according to tracks, the data are processed track by track during data processing, and the starting time and the ending time of single track data are crossed over the day, which needs special processing.

2. And after the wind vector inversion process is finished, sequentially circulating according to wind vector units in the L2B-level product, and optimizing the fuzzy solution initial field. The method comprises the following specific steps:

1) and setting the row and column numbers of the wind vector units which need to be processed currently.

2) And extracting the observation longitude and latitude and the observation time of the current wind vector unit, and recording the observation longitude and latitude, the observation time and the observation time as MES _ Lat, MES _ Lon and PRD _ time respectively.

3) Forecast data for two epochs for subsequent interpolation processing is determined from the observed time. The two epochs are recorded as time1 and time2, respectively.

4) Longitude and latitude information of four corner point forecast data with the wind vector unit as the center and warp and weft wind speed components (the components are also called wind vectors) are extracted and recorded as Mer _ Lat_i、Mer_Lon_i、ZON_Met_i(time2)、ZON_Met_i(time1)、MER_Met_i(time2)、MER_Met_i(time 1). Wherein, the variation range of the subscript i is 1-4, which respectively corresponds to 4 angular points.

5) Calculating the distance weight coefficient di

$d_i=\mathrm{ar}\cos \left(\begin{array}{c}\cos {(90-\mathrm{Mer}\_{\mathrm{Lat}}_i)}^{*}\cos (90-\mathrm{MES}\_\mathrm{Lat})\\ +\sin {(90-\mathrm{Met}\_{\mathrm{Lat}}_i)}^{*}\sin {(90-\mathrm{MES}\_{\mathrm{Lat}}_i)}^{*}\cos (\mathrm{Met}\_{\mathrm{Lon}}_i-\mathrm{MES}\_\mathrm{Lon})\end{array}\right);$

(formula 15)

6) A time weight coefficient alpha is calculated, $a=\frac{\mathrm{time}2-\mathrm{PRD}\_\mathrm{time}}{\mathrm{time}2-\mathrm{timel}};$

7) and interpolating the extracted wind vector to a current wind vector unit, and marking the meridional wind speed, the latitudinal wind speed, the total wind speed and the wind direction obtained by interpolation as ZON _ Mean, MER _ Mean, SPD _ Met and DIR _ Met respectively.

$+a^{*}\sqrt{\mathrm{ZON}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2+\mathrm{MER}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2}];$

DIR _ Met =90-atan2(ZON _ Mean, MER _ Mean)/pi × 180 (formula 19)

8) Fuzzy solution removes initial field optimization

And selecting a solution with the wind direction closest to the NCEP forecast wind direction DIR _ Met from 2 fuzzy solutions of the current wind vector as an initial solution, and optimizing the fuzzy solution initial field. Where DIR _ diff (1), DIR _ diff (2) store the difference between the first and second ambiguity wind direction and the NCEP forecast wind direction DIR _ Met, respectively. The wind _ speed _ cmf and the wind _ dir _ cmf store initial field-optimized blur solutions, respectively. The program code for the optimization process is as follows:

dir_diff(1)=abs(model_dir(i,j)-wind_dir_cmf(i,j,1))

dir_diff(2)=abs(model_dir(i,j)-wind_dir_cmf(i,j,2))

if(dir_diff(1).gt.180)then

dir_diff(1)=360-dir_diff(1)

endif

if(dir_diff(2).gt.180)then

dir_diff(2)=360-dir_diff(2)

endif

if(dir_diff(2).lt.dir_diff(1))then

speed_temp=wind_speed_cmf(i,j,1)

dir_temp=wind_dir_cmf(i,j,1)

wind_speed_cmf(i,j,1)=wind_speed_cmf(i,j,2)

wind_dir_cmf(i,j,1)=wind_dir_cmf(i,j,2)

wind_speed_cmf(i,j,1)=speed_temp

wind_dir_cmf(i,j,1)=dir_temp

endif

9) repeating the steps 1) to 8) for the next wind vector unit until the fuzzy solutions of all the wind vector units of the track data are initialized.

3. Round-median fuzzy solution removal

And (5) adopting the optimized fuzzy solution initial field, starting circular number filtering and outputting a result.

Corresponding to the above method, the present embodiment further provides a sea surface wind field inversion apparatus of a satellite scatterometer, referring to fig. 4, the apparatus including:

a geophysical model building module 42 for building a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna;

a fuzzy solution obtaining module 44, configured to set an objective function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein sigma_oiIs the backscattering coefficient, sigma, actually measured by a scatterometer_mPredicting a backscattering coefficient when the corresponding wind speed is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion; for each wind vector unit, searching the wind speed and wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit;

the initial field optimization module 46 is configured to sort the fuzzy solutions of each wind vector unit according to their corresponding objective function values from large to small; selecting the largest fuzzy solutions corresponding to the two target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in the comparison result as the initial field of the current wind vector unit;

and the ambiguity resolution removing module 48 is configured to use the initial fields of all the wind vector units as ambiguity resolution initial fields of the circle median filtering, and perform ambiguity resolution removing operation to obtain real data of the sea surface wind field.

The device of the embodiment can remove the fuzzy solution more accurately by introducing the fuzzy solution initial field of the wind direction optimization circular number filtering of the NCEP forecast, so that the inversion result of the sea surface wind field more conforms to the actual wind field, the requirements of fuzzy joint removal required by the scatterometer wind field inversion under various complex environmental conditions are met, and the forecast accuracy is improved.

In a specific implementation, the apparatus may further include the following modules:

the first parameter extraction module is used for extracting the observation longitude and latitude and the observation time of the current wind vector unit in the fuzzy solution acquisition module, and the observation longitude and latitude and the observation time are respectively recorded as MES _ Lat, MES _ Lon and PRD _ time;

the forecast data determining module is used for determining forecast data of two times of the NCEP forecast according to the observation time of the current wind vector unit extracted by the first parameter extracting module, wherein the two times are respectively recorded as time1 and time 2;

a second parameter extraction module, configured to extract, from the forecast data, wind vectors of four corner points with a current wind vector unit as a center, where the wind vectors of the four corner points include: the longitude and latitude information and the warp and weft wind speed components of the four angular points are respectively recorded as Mer _ Lat_i、Mer_Lon_i、ZON_Met_i(time2)、ZON_Met_i(time1)、MER_Met_i(time2)、MER_Met_i(time 1); the variation range of the subscript i is 1-4, and the subscript i corresponds to 4 angular points respectively;

a distance weight coefficient calculation module for calculating a distance weight coefficient d_i(ii) a Wherein,

$d_i=\mathrm{ar}\cos \left(\begin{array}{c}\cos {(90-\mathrm{Mer}\_{\mathrm{Lat}}_i)}^{*}\cos (90-\mathrm{MES}\_\mathrm{Lat})\\ +\sin {(90-\mathrm{Met}\_{\mathrm{Lat}}_i)}^{*}\sin {(90-\mathrm{MES}\_{\mathrm{Lat}}_i)}^{*}\cos (\mathrm{Met}\_{\mathrm{Lon}}_i-\mathrm{MES}\_\mathrm{Lon})\end{array}\right);$

a time weight coefficient calculation module for calculating a time weight coefficient alpha, wherein,

$a=\frac{\mathrm{time}2-\mathrm{PRD}\_\mathrm{time}}{\mathrm{time}2-\mathrm{timel}};$

the NCEP forecast wind direction calculation module is used for interpolating the extracted wind vectors to the current wind vector unit, and interpolating to obtain the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction forecasted by the NCEP, and respectively marking the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction as ZON _ Mean, MER _ Mean, SPD _ Met and DIR _ Met;

<math> <mrow> <mi>ZON</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>MER</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>MET</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>SPD</mi> <mo>_</mo> <mi>Met</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msqrt> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> </msqrt> </mrow> </math>

$+a^{*}\sqrt{\mathrm{ZON}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2+\mathrm{MER}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2}];$

DIR_Met=90-atan2(ZON_Mean,MER_Mean)/pi×180。

the wind field of 16-48 hours, which is reported when the NCEP forecasts that the wind direction is 0, adopted by the embodiment can ensure the requirement on the timeliness in the operation of the data processing service of the ocean No. two scatterometer.

The above embodiment has a great improvement in the blur solution removing ability, and particularly, the blur solution removing ability under the conditions of rainfall and the like is greatly improved. Since the capability of the fuzzy solution elimination depends on instrument noise rather than weather physical conditions to a great extent, the elimination performance of the fuzzy solution can be greatly improved by adding physical factors to the selection of the fuzzy solution and the generation of the initial field. And comparing the fuzzy solutions of the first two objective function values with the third wind direction (such as a model wind vector or other wind fields), the performance of the initial field can be effectively improved. Applying median filtering on this basis, almost 100% filtering performance can be obtained.

It will be apparent to those skilled in the art that the modules or steps of the present invention described above may be implemented by a general purpose computing device, they may be centralized on a single computing device or distributed across a network of multiple computing devices, and they may alternatively be implemented by program code executable by a computing device, such that they may be stored in a storage device and executed by a computing device, or fabricated separately as individual integrated circuit modules, or fabricated as a single integrated circuit module from multiple modules or steps. Thus, the present invention is not limited to any specific combination of hardware and software.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. A sea surface wind field inversion method of a marine second satellite scatterometer is characterized by comprising the following steps:

establishing a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna;

setting an objective function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein sigma_oiIs the actual measured backscattering coefficient, σ, of the scatterometer_mPredicting a backscattering coefficient when the corresponding wind speed is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion;

for each wind vector unit, searching the wind speed and the wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit; respectively sorting the fuzzy solutions of each wind vector unit according to the corresponding objective function values from large to small; selecting two maximum fuzzy solutions corresponding to target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in a comparison result as an initial field of the current wind vector unit;

and taking the initial fields of all the wind vector units as the fuzzy solution initial fields of the circular median filtering, and performing fuzzy solution removing operation to obtain real data of the sea surface wind field.

2. The method according to claim 1, wherein said step of comparing said two fuzzy solutions with the wind direction predicted by the NCEP, respectively, is preceded by the step of:

extracting observation longitude and latitude and observation time of the current wind vector unit, and recording the observation longitude and latitude and the observation time as MES _ Lat, MES _ Lon and PRD _ time respectively;

determining forecast data of two times of the NCEP forecast according to the observation time of the current wind vector unit, wherein the two times are recorded as time1 and time2 respectively;

extracting wind vectors of four angular points with the current wind vector unit as the center from the forecast data, wherein the wind vectors of the four angular points comprise: the longitude and latitude information of the four angular points and the warp and weft wind speed components are respectively recorded as Mer _ Lat_i、Mer_Lon_i、ZON_Met_i(time2)、ZON_Met_i(time1)、MER_Met_i(time2)、MER_Met_i(time 1); the variation range of the subscript i is 1-4, and the subscript i corresponds to 4 angular points respectively;

calculating a distance weight coefficient d_i(ii) a Wherein,

$d_i=\mathrm{ar}\cos \left(\begin{array}{c}\cos {(90-\mathrm{Mer}\_{\mathrm{Lat}}_i)}^{*}\cos (90-\mathrm{MES}\_\mathrm{Lat})\\ +\sin {(90-\mathrm{Met}\_{\mathrm{Lat}}_i)}^{*}\sin {(90-\mathrm{MES}\_{\mathrm{Lat}}_i)}^{*}\cos (\mathrm{Met}\_{\mathrm{Lon}}_i-\mathrm{MES}\_\mathrm{Lon})\end{array}\right);$

a temporal weight coefficient alpha is calculated, wherein, $a=\frac{\mathrm{time}2-\mathrm{PRD}\_\mathrm{time}}{\mathrm{time}2-\mathrm{timel}};$

interpolating the extracted wind vectors to the current wind vector unit, and obtaining the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction predicted by the NCEP through interpolation, wherein the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction are respectively marked as ZON _ Mean, MER _ Mean, SPD _ Met and DIR _ Met;

<math> <mrow> <mi>ZON</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>MER</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>MET</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>SPD</mi> <mo>_</mo> <mi>Met</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msqrt> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> </msqrt> </mrow> </math>

$+a^{*}\sqrt{\mathrm{ZON}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2+\mathrm{MER}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2}];$

DIR_Met=90-atan2(ZON_Mean,MER_Mean)/pi×180。

3. the utility model provides a sea wind field inversion device of No. two satellite scatterometers in ocean which characterized in that includes:

a geophysical model establishing module for establishing a geophysical model function sigma₀= F (V, χ,.. F, p, θ); wherein σ₀Representing the backscattering coefficient corresponding to the sea surface; v is wind speed; χ is the relative azimuth of the wind direction; f is the working frequency of the scatterometer; p is a polarization mode; theta is the angle of incidence of the scatterometer antenna;

the fuzzy solution acquisition module is used for setting a target function based on the geophysical model function; wherein the objective function <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>-</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>oi</mi> </msub> <mo>-</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>ln</mi> <mrow> <mo>(</mo> <mi>Var</mi> <msub> <mrow> <mo>(</mo> <msub> <mi>&sigma;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Wherein sigma_oiFor actual measured back direction of the scatterometerScattering coefficient, σ_mPredicting a backscattering coefficient when the corresponding wind speed is V and the relative wind direction is chi, wherein N is the total number of backscattering coefficient measurement results for wind vector inversion; for each wind vector unit, searching the wind speed and the wind direction of the local maximum value of the objective function, and taking the searched wind speed and wind direction as the fuzzy solution of the current wind vector unit;

the initial field optimization module is used for respectively sequencing the fuzzy solutions of each wind vector unit from large to small according to the corresponding objective function values; selecting two maximum fuzzy solutions corresponding to target values from the fuzzy solutions of the current wind vector unit, comparing the two fuzzy solutions with the wind direction forecasted by the NCEP respectively, and taking the fuzzy solution which is closest to the wind direction forecasted by the NCEP in a comparison result as an initial field of the current wind vector unit;

and the fuzzy solution removing module is used for taking the initial fields of all the wind vector units as fuzzy solution initial fields of the circle median filtering, and performing fuzzy solution removing operation to obtain real data of the sea surface wind field.

4. The apparatus of claim 3, further comprising:

the first parameter extraction module is used for extracting the observation longitude and latitude and the observation time of the current wind vector unit in the fuzzy solution acquisition module, and the observation longitude and latitude and the observation time are respectively recorded as MES _ Lat, MES _ Lon and PRD _ time;

a forecast data determining module, configured to determine forecast data of two times of the NCEP forecast according to the observation time of the current wind vector unit extracted by the first parameter extracting module, where the two times are recorded as time1 and time2, respectively;

a second parameter extraction module, configured to extract, from the forecast data, a wind vector centered on the current wind vector unit, where the wind vectors at the four corners include: the longitude and latitude information of the four angular points and the warp and weft wind speed components are respectively recorded as Mer _ Lati and Mer _ Lon_i、ZON_Met_i(time2)、ZON_Met_i(time1)、MER_Met_i(time2), MER _ Meti (time 1); wherein the subscriptThe variation range of i is 1-4, and the i corresponds to 4 angular points respectively;

the distance weight coefficient calculation module is used for calculating a distance weight coefficient di; wherein,

$d_i=\mathrm{ar}\cos \left(\begin{array}{c}\cos {(90-\mathrm{Mer}\_{\mathrm{Lat}}_i)}^{*}\cos (90-\mathrm{MES}\_\mathrm{Lat})\\ +\sin {(90-\mathrm{Met}\_{\mathrm{Lat}}_i)}^{*}\sin {(90-\mathrm{MES}\_{\mathrm{Lat}}_i)}^{*}\cos (\mathrm{Met}\_{\mathrm{Lon}}_i-\mathrm{MES}\_\mathrm{Lon})\end{array}\right);$

a time weight coefficient calculation module for calculating a time weight coefficient alpha, wherein,

$a=\frac{\mathrm{time}2-\mathrm{PRD}\_\mathrm{time}}{\mathrm{time}2-\mathrm{timel}};$

the NCEP forecast wind direction calculation module is used for interpolating the extracted wind vectors to the current wind vector unit, and interpolating to obtain the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction forecasted by the NCEP, and respectively marking the warp-wise wind speed, the weft-wise wind speed, the total wind speed and the wind direction as ZON _ Mean, MER _ Mean, SPD _ Met and DIR _ Met;

<math> <mrow> <mi>ZON</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>MER</mi> <mo>_</mo> <mi>Mean</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> </mfrac> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>a</mi> <mo>*</mo> </msup> <mi>MER</mi> <mo>_</mo> <msub> <mi>MET</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>timel</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>;</mo> </mrow> </math>

<math> <mrow> <mi>SPD</mi> <mo>_</mo> <mi>Met</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mfrac> <mn>1</mn> <msub> <mi>d</mi> <mi>j</mi> </msub> </mfrac> </mrow> </mfrac> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <mo>*</mo> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msqrt> <mi>ZON</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>MER</mi> <mo>_</mo> <msub> <mi>Met</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>time</mi> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> </msqrt> </mrow> </math>

$+a^{*}\sqrt{\mathrm{ZON}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2+\mathrm{MER}\_{\mathrm{Met}}_i{\left(\mathrm{timel}\right)}^2}];$

DIR_Met=90-atan2(ZON_Mean,MER_Mean)/pi×180。

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