KR101731077B1 - Spherical high order filter for applications to global meteorological data and Method for controlling the same - Google Patents

Abstract

The present invention relates to a spherical coordinate system higher order FFDM filtering system for precursor meteorological data and to a control method thereof for enhancing computation efficiency and accuracy of calculation for spherical coordinate system weather data, A boundary condition setting module for setting a boundary condition, a hardness direction discretization module for discretizing grid data corresponding to an area by boundary condition setting using the spectral method with respect to the hardness direction, A directional FDM discretization module for discretizing a first order and a second derivative with respect to a direction, and a higher order filter equation discretization module for performing discretization of a higher order filter equation.

Description

Technical Field [0001] The present invention relates to a spherical coordinate system high-order FFDM filtering system and a control method thereof for global weather data,

More particularly, the present invention relates to a spherical coordinate system higher order FFDM filtering system for precursor meteorological data, which can increase the efficiency of calculation for spherical coordinate system weather data and increase the accuracy of calculation, and a control method thereof.

Recently, the image data to be processed in the fields such as weather and climate are becoming widespread, and it is becoming increasingly necessary to process such data at a high speed.

Accordingly, the digital filtering method for three-dimensional spatial data processing is required to have a high processing speed while maintaining accuracy.

The digital filtering method for three-dimensional spatial data processing generally uses the Legendre spectral method which uses the Legendre function as a basis function in the spherical surface.

However, as the resolution of the data increases, the processing speed (computation efficiency) deteriorates. In order to overcome these disadvantages, a double Fourier series (DFS) spectral method has been developed and is being used in the field of weather, climate and earth science.

In spectral method, which is one of the methods of solving differential equations, an arbitrary function is expanded into a series of basis functions satisfying the boundary condition, and the spatial derivative is represented by the derivative of the basis function.

The spectral method has high accuracy compared with other methods, for example, Finite Difference Mehod and the like, and maintains high efficiency almost in the calculation of nonlinear terms.

Because of these advantages, spectral methods are being used in most weather forecast models and climate models in each country at present.

However, the digital filter for the sector region on the spherical coordinate system using the double-Fourier series spectral method of the prior art has a high accuracy of calculation, but it has a drawback in that it takes a long calculation time as the number of gratings or degrees of freedom increases .

In addition, the digital filter using finite difference method and finite element method has a short computation time but low computational accuracy.

Therefore, it is required to develop a new filtering system that can improve the efficiency of calculation for the spherical coordinate system weather data and improve the accuracy of calculation.

Korean Patent No. 10-1491022 Korea Patent No. 10-0981983

In order to solve the problem of the digital filtering method for three-dimensional spatial data processing of the related art, the present invention provides a spherical coordinate system A coordinate system higher order FFDM filtering system and a control method thereof.

The present invention relates to a method for maximizing the accuracy of computation by applying a spherical higher order filter in a radar-finite difference method (FFDM) in a radial lattice system and for precise meteorological data for application to Ross Beau- A spherical coordinate system higher order FFDM filtering system and a control method thereof.

It is an object of the present invention to provide a spherical coordinate system higher order FFDM filtering system and a control method thereof for a precursor meteorological data which can improve the accuracy of calculation by processing a pentagonal diagonal matrix by applying a filter to the spherical coordinate system global meteorological data .

The present invention relates to a spherical coordinate system high-order FFDM (Fourier Transform Element) for precursor meteorological data in which an RMSE (Root Mean Square Error) characteristic varies according to resolution (the number of grid elements in the east-west direction) (Fourier Finite Difference Method) filtering system and a control method thereof.

The present invention relates to a sophisticated computation-efficient FFDM filtering system for spherical coordinate system weather data and a filtering method using the same, and a spherical coordinate system high-order FFDM filtering system and its control for precise meteorological data applicable to various fields as well as environmental meteorological fields The purpose of the method is to provide.

The objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

In order to accomplish the above object, a spherical coordinate system high-order FFDM filtering system for a precursor vapor phase data according to the present invention includes a boundary condition setting module for setting a size of a global area or a sector area of a spherical coordinate system, A longitudinal direction discretization module that discretizes lattice data by the spectral method with respect to the direction of hardness, and a latitudinal direction FDM which discretes the lattice data corresponding to the region by the boundary condition setting by the finite difference method with the first and second differentiation to the latitude direction A discretization module, and a higher order filter equation discretization module that performs discretization of higher order filter equations.

According to another aspect of the present invention, there is provided a method of controlling a spherical coordinate system high-order FFDM filtering system for a global warming data according to the present invention, the method comprising the steps of: setting a size of a global area or a sector area of a spherical coordinate system; A longitude discretization step of discretizing the corresponding lattice data by the spectral method with respect to the longitudinal direction; a latitude and longitude direction which discretizes the lattice data corresponding to the region by the boundary condition setting by the finite difference method A directional FDM discretization step, and a higher order filter equation discretization step, which performs discretization of the higher order filter equation by performing Helmholtz equation discretization and higher order Helmholtz equation discretization.

The spherical coordinate system higher order FFDM filtering system and the control method thereof for the precursor vapor phase data according to the present invention have the following effects.

First, for high - order FFDM filtering of Spherical Coordinate System for global meteorological data, it is possible to increase the efficiency of calculation for Spherical Coordinate System and to improve the accuracy of calculation.

Second, the accuracy of the calculation can be maximized by applying the sophisticated difference filter (FFDM) in the radar grid system, and it can be applied to the Ross-Beauwitz wave and weather data.

Third, the accuracy of the calculation can be improved by processing the pentagonal diagonal matrix by applying a filter to the spherical coordinate system global meteorological data.

Fourth, the Root Mean Square Error (RMSE) characteristics vary depending on the resolution (the number of lattice elements in the east-west direction), and errors can be reduced compared to the FFEM (Fourier Finite Element Method).

Fifth, the FFDM filtering system with high performance computing efficiency for the spherical coordinate system weather data and the filtering method using it can be applied to various fields as well as the environmental weather field.

1 is a schematic diagram of a spherical coordinate system high-order FFDM filtering system for the meteorological data according to the present invention
FIG. 2 is a flow chart illustrating a control process of a spherical coordinate system high-order FFDM filtering system for precursor meteorological data according to the present invention, in accordance with the present invention.
Fig. 3 is a graph showing the pole conditions of the coefficient of freedom
Fig. 4 shows the result of the FFDM digital filter, (d) the result of the FFEM digital filter, (b) the result of calculation from the analysis of the higher order filter, (c) Diagram
5 is a diagram showing a 500 hPa geopotential altitude according to the filtering scale
Fig. 6 shows a schematic diagram showing a 500 hPa geopotential high-speed coating and a velocity field during development of a tropical cyclone HALONG

Hereinafter, a preferred embodiment of a spherical coordinate system higher order FFDM filtering system and a control method thereof for the precursor vapor phase data according to the present invention will be described in detail.

The features and advantages of the spherical coordinate system higher order FFDM filtering system and the control method thereof for the precursor vapor data according to the present invention will be apparent from the following detailed description of each embodiment.

FIG. 1 is a block diagram of a spherical coordinate system high-order FFDM filtering system for precursor vapor phase data according to the present invention.

And FIG. 2 is a flowchart illustrating a control process of a spherical coordinate system high-order FFDM filtering system for precursor meteorological data according to the present invention.

The present invention maximizes the accuracy of computation by applying a sophisticated difference filter (FFDM) in a radial lattice system and increases the accuracy of computation by processing a pentagonal diagonal matrix.

Higher order Laplacian-type filters capable of isotropically sharp cut-off filtering on the spherical surface are essential for processing weather data.

The Galerkin method and the finite difference method are widely used among the methods of discretizing the Laplacian operator by the spherical coordinate system and processing the lattice data.

The higher order filter according to the present invention is performed by the inverse of the Helmholtz equation, and the spectral method and the finite difference method can be mixed to perform the discretization and inversion, so that a higher order filter can be constructed.

1, the boundary coordinate setting module 100, the longitudinal direction discretization module 200, the latitudinal direction FDM discretization module 300, and the latitudinal direction FDM disassembly module 300, And a higher order filter equation discretization module 400.

Here, the boundary condition setting module 100 is for setting the size of the global area or the sector area of the spherical coordinate system.

The size of the sector area set by the boundary condition setting module 100 may be a part of 0 to 360 degrees east to west, or a part or whole of -90 to 90 degrees north and south.

The hardness direction discretization module 200 includes a Laplacian operator module 21 for performing a spherical coordinate system Laplacian operation and a Helmholtz equation constituting a higher order filter of a spherical coordinate system for the hard direction discretization using the spectral method. A filter equation substitution module 24 for calculating and discretizing Helmholtz equation for the Fourier coefficient by substituting the filter equation, and a filter equation substitution module 24 for calculating the Helmholtz equation for the Fourier coefficient by substituting the filter equation, .

The latitudinal direction FDM discretization module 300 includes a first differential module 31 and a second differential module 32. The latitude direction FDM discretization module 300 divides the north and south regions into N lattice sections for the purpose of discretization in the latitudinal direction using a finite difference method, The first and second derivatives are discretized by the fourth order finite difference method.

The higher order filter equation discretization module 400 includes a Helmholtz equation discretization module 41 and a higher order Helmholtz discretization module 42 and performs the Helmholtz equation discretization and higher order Helmholtz equation discretization for the discretization of higher order filter equations.

The control process of the spherical coordinate system high-order FFDM filtering system for the precursor meteorological data according to the present invention is as follows.

A boundary condition setting step (S201) of setting a size of a global area or a sector area of the spherical coordinate system, as shown in FIG. 2, and a Laplacian computing step S202 for performing a spherical coordinate system Laplacian calculation for longitudinal direction discretization using the spectral method A variable transformation step of introducing a variable transformation using a Helmholtz equation constituting a high-order filter of a spherical coordinate system, a freezing element expansion step (S203) of expanding a hardness function to a freezing function, and a freezing coefficient (S204), and divides the north-south region into N grid regions (S205) for the purpose of discretization in the latitudinal direction using the finite difference method For the discretization of the higher order filter equations and the latitudinal direction FDM discretization step (S206), which is discretized by the difference finite difference method, And a high order filter equation dioxide step (S207) of performing a high-order equation and the Helmholtz equation dioxide dioxide.

Specifically, the description of the longitudinal direction discretization process using the spectral method is as follows.

The Sphere Coordinate System Laplacian operator is as shown in Equation (1).

Here,? And? Represent the longitude and latitude, respectively, and the Helmholtz equation constituting the high-order filter of the spherical coordinate system can be summarized as in Equation (2).

Here, ψ and F are integrable functions defined in spherical surfaces, respectively.

Since equation (1) is composed of a second order differential operator that is separated according to latitude and longitude, calculation using variable separation is possible.

And when we have a periodicity in the direction of hardness, we can develop a function of hardness as a series of degrees as follows.

은 복소수형태의 후리에계수를 나타낸다.Where m is the western and wavenumber. Re [*] is the real part of *, and

Represents the Fourier coefficient in complex form.

Substituting this into equation (2), a Helmholtz equation for the Fourier coefficients can be calculated.

에 따라 결정된다.Since cos θ = 0 at θ = ± π / 2, the term divided by cos θ in Equation (4) causes a singularity at the pole,

.

Equation 4 is a function of latitude only if m = 0 and singularity can be avoided in the pole according to the following properties.

으로 적용되며 수학식 6에서와 같은 관계를 나타낸다.Given the equidistant grid data,

And the relationship as shown in Equation (6) is shown.

Thus, the pole singularity disappears at m ≥ 2, and when m = 1, the pole singularity does not appear because the equation (6) is not satisfied.

The discretization of the latitude direction using the finite difference method is described as follows.

The transformed Laplacian operator is as follows.

Here, x = sin &thetas;

Here, k = 0, 1, 2 for m = 0, odd, even (m >

The term divided by cos? In Equation (7) is rearranged as Equation (6) as follows.

In the pole, equation (9) can be summarized as follows.

In order to realize discretization by applying the finite difference method, the region of north and south is divided into N lattice sections, and the light bulb including the poles consists of 2N * (N + 1) lattice points.

Equation (9) is discretized by a quadratic finite difference method in which the first and second derivatives are given as follows.

과 같이 격자 인덱스(index)를 의미한다.Where d (= π / N) represents the lattice spacing in radians and j (= 0, 1, 2, 3, ..., N)

And a grid index (index).

)To perform a derivative successfully, you need two shadow points at the pole. (

)

Fig. 3 is a graph showing the pole condition of the coefficient of freedom.

This condition can be expressed by the following equation.

The derivatives of Equation (10) can be applied to Equation (4) and Equation (8) to express a linear algebraic equation as a matrix equation.

The matrix related to the discrete Laplacian operator is a pentagonal diagonal matrix, and the Helmholtz equation of Equation (4) can be expressed by a matrix equation as shown in Equation (13).

Here, I, D and F are column vectors related to a unit matrix having a column and column size N + 1, a discrete Laplacian operator matrix [size of (N + 1) * (N + 1)], and a forcing function.

For a given function ψ, the spheric higher order filter of degree q is:

Here, * denotes a constant to which the filter is applied.

Equation (13) is divided into multiple Helmholtz equations composed of complex coefficients, and the filter is performed with successive inversion of the Helmholtz equation.

In the spherical coordinate system high-order FFDM filtering system and the control method thereof, the filter is applied to the spherical coordinate system global meteorological data, and the accuracy of the calculation can be improved by processing the pentagonal diagonal matrix.

The Root Mean Square Error (RMSE), which is the difference from the theoretical value, is shown by applying the filter according to the present invention to the Ross-Beauwitz wave, and is shown in Table 1 in comparison with the results of the FFEM digital filter.

Table 1 shows the error of the Ross-Beauwitz waves at the east-west wavenumber 4, where M is the number of grids in the east-west direction. And RMSE of each of FFDM and FFEM.

까지 다양하게 나타나고, FFDM의 오차는 해상도에 따라 FFEM의 오차보다 더 작게 나타나는 것을 알 수 있다.Depending on the resolution (east-west direction grid number M), RMSE is

And the error of the FFDM is smaller than the error of the FFEM according to the resolution.

The filtering of the Ross-Beauwitz wave using the spherical coordinate system high-order FFDM filtering system and the control method thereof for the meteorological data according to the present invention will be described as follows.

Fig. 4 shows the results of the FFDM digital filter, (d) the results of the FFEM digital filter, (b) the result of calculation from the analysis of the higher order filter, Fig.

으로 표현되는 동서파수 4의 로스비-하우어비츠 파동을 필터에 적용하였다.

And the Ross-Beauwitz waves of east-west wave number 4 are applied to the filter.

The Rossby-Hauer-Witz wave is one of the unique solutions of the Laplacian operator, so the interpretation solution of the higher-order filter is as follows.

The filtering was performed with N = 180 and γ = 1 / (20 × 21) ⁴ , and the results are compared with the results of the FFEM digital filter and shown in FIG. The results show that there is almost no visual difference.

The smoothing of the meteorological data is as follows.

The coefficient γ of the filter is a criterion for dividing the given data into smaller scale and larger scale.

으로 계수를 설정한다.The predetermined scale, N _f ,

.

FIG. 5 is a diagram showing a 500-hPa geopotential altitude according to the filtering scale.

Figure 5 compares the results for the three cases of N _{f 10} , 20, and 30 as a result of applying the observed geopotential altitude on January 1, 2015 to the filter.

The amplitude of the environmental field and the turbulence field varies with the value of N _f .

An example of applying the spherical coordinate system higher order FFDM filtering system and the control method thereof to the initialization of the hurricane prediction model will be described as follows.

FIG. 6 is a view showing a 500 hPa geopotential high-speed coating and a velocity field during development of a tropical cyclone HALONG.

In the initialization process of the prediction model of the typhoon, the environmental field is separated from the global observation field and the calculation is performed. In this process, a higher order filter is applied.

Fig. 6 shows the result of applying the observation data of August 11, 2014, when the tropical cyclone Halong (HALONG) developed in the Pacific Northwest, to the filter.

The turbulence fields including the environmental field and the tropical cyclone scale are accurately separated and compared with the results of the FFDM digital filter.

Fig. 6 (a) is the environmental field at the geopotential altitude, (b) is the turbulence of the tropical cyclone scale, and (c) and (d) are the same as (a) and (b) except the velocity field.

(e) is the difference between the synoptic geopotential altitudes calculated by the FFEM digital filter and the FFDM filter, and (f) is the same as (e) except that it is the velocity field.

In the spherical coordinate system high-order FFDM filtering system and control method for the precursor meteorological data according to the present invention, the accuracy of the calculation is maximized by applying the spherical higher order filter to the gridded-degree grating system in the gridded-degree grating system (FFDM) (RMSE) characteristics vary according to the resolution (the number of lattice elements in the east-west direction) and the errors are compared with the FFEM (Fourier Finite Element Method). .

As described above, it will be understood that the present invention is implemented in a modified form without departing from the essential characteristics of the present invention.

It is therefore to be understood that the specified embodiments are to be considered in an illustrative rather than a restrictive sense and that the scope of the invention is indicated by the appended claims rather than by the foregoing description and that all such differences falling within the scope of equivalents thereof are intended to be embraced therein It should be interpreted.

100. Boundary condition setting module 200. Hardness direction discretization module
300. Latitude direction FDM discretization module 400. Higher order filter equation discretization module

Claims (18)

A boundary condition setting module for setting a size of a global area or a sector area of the spherical coordinate system;
A hardness direction discretization module for discretizing lattice data corresponding to a region by boundary condition setting using a spectral method with respect to the hardness direction;
A latitudinal direction FDM discretization module which discretizes lattice data corresponding to a region by boundary condition setting by a finite difference method with a first order and a second differentiation with respect to a latitude direction;
And a higher order filter equation discretization module for performing discretization of the higher order filter equations. ≪ RTI ID = 0.0 > A < / RTI > 2. The method of claim 1, wherein the hardness direction discretization module is configured for longitudinal direction discretization using a spectral method,
A Laplacian operator module for performing a spherical coordinate system Laplacian operation,
A variable transformation module for introducing a variable transformation using a Helmholtz equation constituting a higher order filter of a spherical coordinate system;
A freeze water development module for performing a hard water function expansion in the freezing water series,
And a filter equation substitution module for calculating and discretizing the Helmholtz equation for the Fourier coefficient by substituting the filter equation into a spherical coordinate system higher order FFDM filtering system for the global warming data. 3. The apparatus of claim 2, wherein the Laplacian operator comprises:

ego,
Here,? And? Are longitude and latitude, respectively,
The Helmholtz equation, which constitutes a higher order filter of the spherical coordinate system,

ego,
Wherein the ψ and F are integrable functions defined in the spherical surface, respectively, for spherical coordinate system higher order FFDM filtering systems for precursor meteorological data. 3. The method according to claim 2, wherein, when having a periodicity in a hardness direction,

And developed with a freezing water,
Where m is the western and wavenumber. Re [*] is the real part of *, and

Characterized in that the Fourier coefficients of the complex form are represented by the Fourier coefficients of the spherical coordinate system. 3. The method of claim 2, wherein the Helmholtz equation for the Fourier coefficients is:

Lt; / RTI >
Since cos θ = 0 at θ = ± π / 2, the term dividing by cos θ causes singularity at the pole,

Dimensional FFDM filtering system for spherical coordinate system for the precursor vapor phase data. The method of claim 1, wherein the latitudinal direction FDM discretization module comprises:
It consists of a first differential module and a second differential module. It divides the region of north and north into N lattice sections for finite discretization using finite difference method, and discretizes the first and second derivatives by quaternary finite difference method Spherical Coordinate System Higher Order FFDM Filtering System for Bulb Meteorological Data. 7. The method according to claim 6,

Which is discretized by quaternary finite difference method,
Where d (= π / N) represents the lattice spacing in radians and j (= 0, 1, 2, 3, ..., N)

And a grid index (index) as shown in Equation (1). The spherical coordinate system higher order FFDM filtering system for the precursor meteorological data. The method of claim 1, wherein the higher order filter equation discretization module comprises:
A spherical coordinate system higher order FFDM filtering system for precursor meteorological data characterized by a Helmholtz equation discretization module and a higher order Helmholtz discretization module and performing the discretization of the Helmholtz equation discretization and the higher order Helmholtz equation for the discretization of higher order filter equations. 9. The method of claim 8, wherein the matrix associated with the discrete Laplacian operator is a pentagonal diagonal matrix,

Lt; / RTI >
Here, I, D and F are column vectors related to a unit matrix having a column and column size N + 1, a discrete Laplacian operator matrix [size of (N + 1) * (N + 1)], Spherical Coordinate System Higher Order FFDM Filtering System for Bulb Meteorological Data. 10. The method of claim 9, wherein the spherical higher order filter of degree q for a given function < RTI ID = 0.0 >

ego,
Here, * denotes a constant to which the filter is applied,
Wherein the matrix equation is divided into multiple Helmholtz equations with complex coefficients, and the filter is performed with successive inversion of the Helmholtz equation. A boundary condition setting step of setting a size of a global area or a sector area of the spherical coordinate system;
A hardness direction discretization step of discretizing the lattice data corresponding to the area by the boundary condition setting using the spectral method with respect to the hardness direction;
A latitudinal direction FDM discretization step of discretizing the lattice data corresponding to the area by the boundary condition setting by the finite difference method with the first and second differentiation for the latitude direction;
And a higher order filter equation discretization step in which the Helmholtz equation discretization and the higher order Helmholtz equation are discretized to perform discretization of the higher order filter equations. The method for controlling the spherical coordinate system higher order FFDM filtering system for precursor weather data. 12. The method of claim 11,
Performing a spherical coordinate system Laplacian operation,
Introducing a variable transformation using a Helmholtz equation constituting a higher order filter of the spherical coordinate system;
Performing a hard water function expansion on the hardness function;
And calculating a Helmholtz equation for the Fourier coefficient by discretizing the filter equation and discretizing the filtered Helmholtz equation. 13. The method of claim 12, wherein the Laplacian operator comprises:

ego,
Here,? And? Are longitude and latitude, respectively,
The Helmholtz equation, which constitutes a higher order filter of the spherical coordinate system,

ego,
Wherein the ψ and F are integrable functions defined in the spherical surface, respectively, for controlling the spherical coordinate system higher order FFDM filtering system for the global meteorological data. 13. The method according to claim 12, wherein, when having a periodicity in a hardness direction,

And developed with a freezing water,
Where m is the western and wavenumber. Re [*] is the real part of *, and

Characterized in that the Fourier coefficients of the complex form are represented by the Fourier coefficients. 13. The method of claim 12, wherein the Helmholtz equation for the Fourier coefficients is:

Lt; / RTI >
Since cos θ = 0 at θ = ± π / 2, the term dividing by cos θ causes singularity at the pole,

Wherein the step of determining the phase difference is performed according to the control method of the spherical coordinate system higher order FFDM filtering system for the precursor vapor phase data. 12. The method of claim 11, wherein in the latitudinal direction FDM discretization step,
Primary and secondary differentials,

Which is discretized by quaternary finite difference method,
Where d (= π / N) represents the lattice spacing in radians and j (= 0, 1, 2, 3, ..., N)

And a grid index (index) as shown in Equation (1). The control method of the spherical coordinate system higher order FFDM filtering system for the global meteorological data. 12. The method of claim 11, wherein in the higher order filter equation discretization step,
The matrix associated with the discrete Laplacian operator is a pentagonal diagonal matrix, and the Helmholtz equation,

Lt; / RTI >
Here, I, D and F are column vectors related to a unit matrix having a column and column size N + 1, a discrete Laplacian operator matrix [size of (N + 1) * (N + 1)], Control Method of Spherical Coordinate System Higher Order FFDM Filtering System for Bulb Weather Data. 18. The method of claim 17, wherein the spherical higher order filter of degree q for a given function < RTI ID = 0.0 >

ego,
Here, * denotes a constant to which the filter is applied,
Wherein the matrix equation is divided into multiple Helmholtz equations consisting of complex coefficients and the filter is performed with successive inversion of the Helmholtz equation.

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