KR101758234B1 - Apparatus for data assimilation and method for data assimilation - Google Patents

Abstract

The present invention relates to a data assimilation method and apparatus.
To this end, according to the present invention, there is provided a data moving method of a gaseous numerical model including at least one grid-shaped cell, characterized in that a first variable at a cell point which is a center of gravity of the at least one grid- Calculating a first ensemble analysis mean vector value and a first ensemble analysis perturbation matrix value using a prediction field; Calculating a first weight at an edge point of the first cell using the ensemble analysis mean vector values of neighboring cells of a first one of the cells and calculating a first weight at an edge point of the first cell, Calculating a second weight at the first cell edge point using the ensemble analysis perturbation matrix values of the cells; And calculating a second ensemble analysis mean vector value using the first weight and calculating a second ensemble analysis perturbation matrix value using the second weight.

Description

 [0001] APPARATUS FOR DATA ASSIMILATION AND METHOD FOR DATA ASSIMILATION [0002]

 The present invention relates to a data assimilation method and apparatus.

 Many of the recent weather forecasting models are no longer in a rectangular grid. The MPAS model under development by the US National Weather Research Center (NCAR) is also using Arakawa C grid staggering in a unique grid structure called Centroidal Voronoi tessellation. The wind defined in the edge point of the MPAS's unique grid structure is calculated not only by the east-west winds and the north-south winds but also by the direction perpendicular to the hexagonal sides. The total number of edge points is about three times more. Therefore, it is not easy to apply K to the wind field specific to the MPAS defined at the edge point, even if K is simply calculated assuming all variables at the cell point. In fact, there is a precedent in NCAR where the ensemble data assimilation technique is applied to the MPAS model. It is assumed that the wind point of the MPAS is converted into the east-west wind / north-south wind component by the cell point, After calculating K, we calculate the increment of the wind parameter at the cell point and then convert it to the incremental value of the edge specific MPAS wind. In other words, model data converted to wind variables at the cell point are used for data assimilation, and after the data assimilation is performed, the wind point of the cell point is converted to the MPAS wind point of the edge point. In this method, which is called "incremental interpolation of analysis", a wind variable defined at the edge point is converted into a cell point, and in the process of converting the wind variable updated by the data acquisition at the cell point back to the edge point, In particular, in the case of lower winds of complex terrain, the error that occurs in the conversion process can be large enough to be ignored.

 SUMMARY OF THE INVENTION The present invention is directed to a method and apparatus for data assimilation to solve the above problems.

 According to an embodiment of the present invention, there is provided a data moving method of a gaseous numerical model including at least one grid-shaped cell, Calculating a first ensemble analysis mean vector value and a first ensemble analysis perturbation matrix value using a predicted field of a first variable at cell points; Calculating a first weight at an edge point of the first cell using the ensemble analysis mean vector values of neighboring cells of a first one of the cells and calculating a first weight at an edge point of the first cell, Calculating a second weight at the first cell edge point using the ensemble analysis perturbation matrix values of the cells; And calculating a second ensemble analysis mean vector value using the first weight and calculating a second ensemble analysis perturbation matrix value using the second weight.

According to another aspect of the present invention, there is provided a data moving device for a vapor-phase numerical model including at least one grid-shaped cell, the cell moving device comprising: a cell point which is a center of gravity of the at least one grid- A calculation module for calculating a first ensemble analysis mean vector value and a first ensemble analysis perturbation matrix value using a predicted field of a first variable in the first ensemble analysis mean vector value; Calculating a first weight at an edge point of the first cell using the ensemble analysis mean vector values of neighboring cells of a first one of the cells and calculating a first weight at an edge point of the first cell, A weighting module for calculating a second weight at the first cell edge point using the ensemble analysis perturbation matrix values of the cells; And an extraction module for calculating a second ensemble analysis mean vector value using the first weight and calculating a second ensemble analysis perturbation matrix value using the second weight.

 As described above, according to the present invention, by providing the data assimilation method and apparatus, the Kalman gain matrix K calculation can be avoided without requiring a lattice transformation.

Further, according to the present invention, spatial interpolation between cell point-edge points of an existing technique caused by a model lattice point becomes unnecessary.

According to the present invention, the Kalman gain matrix corresponding to the edge point need not be calculated separately, and all the desired information can be calculated only by light calculation of the simple arithmetic mean.

Further, according to the present invention, the weather prediction can be implemented very efficiently in terms of accuracy and calculation cost.

BRIEF DESCRIPTION OF DRAWINGS FIG. 1 is a block diagram illustrating a data moving apparatus. FIG.
Fig. 2 is a diagram for explaining a data assimilation process.
Fig. 3 is a view for explaining only the observation information around the lattice points to obtain the data assimilation result value.
FIG. 4 is a view for explaining the setting of the data moving radius in consideration of the triangular lattice structure.
5 is a diagram for explaining a unique lattice structure of the NCAR MPAS model.
6 is a diagram for explaining a calculation process of a vector value and a matrix value corresponding to a wind parameter at an edge point of the present invention.
7 is a flowchart for explaining a data assimilation method.

 One embodiment of the present invention will be described in detail with reference to the accompanying drawings. In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear.

BRIEF DESCRIPTION OF DRAWINGS FIG. 1 is a block diagram illustrating a data moving apparatus. FIG.

,

,

및

이며 이에 대한 구체적인 내용은 도 2 내지 도 7에서 후술한다. 또한 전술한 제 1 셀 및 제 2 셀은 적어도 하나 이상의 변을 공유하여 인접할 수 있다. Referring to FIG. 1, the data moving apparatus may include a calculation module 100, a weight module 110, and an extraction module 120. The calculation module 100 calculates information about an ensemble analysis average vector value for a first variable (temperature information, humidity information, or atmospheric pressure information) at a cell point, which is the center of gravity of the first cell among a plurality of grid- And the first information and the second information on the basis of information on the ensemble analysis perturbation matrix value.
In addition, the calculation module 100 calculates information on the ensemble analysis average vector value for the second variable (temperature information, humidity information, or atmospheric pressure information) at the center of gravity of the second cell among the plurality of grid-shaped cells, The third information and the fourth information can be calculated based on the information on the perturbation matrix value. The above first information, second information, third information and fourth information are

,

,

And

And details thereof will be described later with reference to FIG. 2 to FIG. Also, the first cell and the second cell may be adjacent to each other by sharing at least one side.

및

이며 이에 대한 구체적인 내용은 도 2 내지 도 7에서 후술한다. The weighting module 110 may calculate the first weight using the first information and the third information, and may calculate the second weight using the second information and the fourth information. The first weight and the second weight are

And

And details thereof will be described later with reference to FIG. 2 to FIG.

The extraction module 120 calculates the information on the ensemble analysis mean vector value for the wind information at the edge point using the first weight and calculates the wind information at the edge point using the second weight The information on the ensemble analysis perturbation matrix value for < RTI ID = 0.0 > In addition, the above-mentioned edge points may be located on at least one side shared by the first cell and the second cell described above.

Fig. 2 is a diagram for explaining a data assimilation process.

는 예측모델의 예단 변수를 포함하는 벡터로서 대개 바람, 온도, 습도, 압력 등의 기상요소에 대한 평균값이다. 참고로 위 첨자 a는 결과에 대한 값을 의미하며 위 첨자 b는 예측에 대한 값을 의미한다. Referring to FIG. 2, FIG. 2 illustrates a MPAS ensemble prediction process in which the observation data and the observation operator are used to integrate the LETKF data at every 6 hours using the LETKF data assimilation method. When integrating only the predictive model with time without data assimilation, the prediction error increases continuously with time, so that the accuracy of the phenomenon to be predicted may decrease sharply. Therefore, in order to improve the accuracy of the prediction, the above-described data assimilation can estimate the error of the prediction model in real time by integrating the prediction model having different initial conditions. If the initial conditions are slightly different, the prediction uncertainty of the predicted model can be judged to be large if the results of the predictive model described above largely differ. However, even if the initial conditions are different, the prediction uncertainty of the prediction model may be considered to be low if the results of the prediction model are fairly similar. The prediction uncertainty can be estimated through the standard deviations of the results of the prediction models described above, and the prediction model values can be updated while comparing the observation data and the observation data errors. Therefore, it can be used to improve initial condition of prediction model by using observational data (assimilation), and integrating prediction model periodically can increase accuracy of prediction model. The LETKF data assimilation method updates the initial values for all parameters of the ensemble prediction, ie, weather information such as air pressure, wind, temperature, and humidity. Equation (1) below means how the mean value of the ensemble prediction parameters is updated. Equation (2) indicates how much the value of the perturbation of each ensemble prediction parameter is. In Equation (1)

Is a vector containing the predictor variables of the predictive model and is usually an average value for weather elements such as wind, temperature, humidity, and pressure. For reference, superscript a means the value for the result and superscript b means the value for the prediction.

는 앙상블 예측의 평균 벡터값,

는 앙상블 예측의 섭동에 대한 값 즉, 각각의 앙상블 예측에서

를 뺀 값을 열로 하는 행렬이다.

는 각각의 모델 격자점 주변에 분포한 관측 자료 정보를 포함하는 벡터값이며,

는 관측 공간으로 변환된 앙상블 예측 정보를 평균한 벡터값이고, K는 앙상블 개수이다.

는 분석장 오차 공분산 행렬로서 앙상블 공간에서 정의되며,

에 상당하는 값이나 관측 공간으로 변환된 값이다. 이때 예측 모델 값은 관측 연산자 H에 의해 관측 공간으로 변환된다. R은 관측 오차 공분산 행렬 값이며,

는 표본 오차를 줄이기 위한 팽창계수로서 시공간적으로 계산된다. 마지막으로

으로 앙상블 공간에서 계산되는 Kalman gain matrix로서, 모델오차가 클 경우 관측을 더 많이 반영하고 모델 오차가 관측 오차보다 적다고 판단될 때는 관측 자료를 거의 반영하지 않는 방식으로 결정된다. 또한 본원발명의 경우, 도 1에서 전술한 추출모듈은 제 1 변수가 온도, 습도 및 기압에 대한 정보일 경우, 제 1 가중치 및 제 2 가중치를 적용하지 않고 전술한 수학식 1 및 수학식 2에 의해 제 2 의 앙상블 예측의 평균 벡터값과 앙상블 예측 섭동 행렬 값을 산출할 수 있다. Described above

Is an average vector value of the ensemble prediction,

The value for the perturbation of the ensemble prediction, that is, for each ensemble prediction

Is a matrix obtained by subtracting a value obtained by subtracting the number

Is a vector value including observation data information distributed around each model lattice point,

Is a vector value obtained by averaging the ensemble prediction information converted into the observation space, and K is the number of ensembles.

Is an analytical field error covariance matrix defined in an ensemble space,

Or a value converted to the observation space. At this time, the prediction model value is converted into the observation space by the observation operator H. R is the observed error covariance matrix value,

Is the expansion coefficient to reduce the sampling error. Finally

Is a Kalman gain matrix calculated in an ensemble space that reflects more observations when the model error is large and does not reflect the observed data when the model error is less than the observation error. In the case of the present invention, the extraction module described above with reference to FIG. 1 may be configured such that, when the first parameter is information on temperature, humidity, and atmospheric pressure, the first and second weights are not applied, The average vector value of the second ensemble prediction and the ensemble predictive perturbation matrix value can be calculated.

The process of sequential LETKF data assimilation is described in detail as follows.

를 계산하는 단계, (5) 각각의 모델 격자점에 대한 분석장을 계산하기 위해 국지화 영역 내의

을 이용하여 전술한 수학식 1과 수학식 2를 계산하여 분석장을 계산하는 단계. 전술한 국지화 영역은 보통 수백 km 영역으로 정하며, 국지화 영역 내에서 격자점에 더 가까운 정보일수록 더 크게 반영하는 국지화 가중치 함수를 사용할 수 있다.(1) Integrating the model predictions started at the initial condition of t-6, which is 6 hours before, for the time t, for 9 hours until -3 or +3, (2) (3) a step of preparing the background data of the 9-hour prediction starting from the condition (the ensemble analysis field at t-6), (3) the material assimilation among the observation data collected within -3 hours or +3 hours from the time t , And (4) transforming the background field into the same space as the observation data

(5) calculating the analytical field for each model grid point in the localized region

And calculating the analytical field by calculating Equations (1) and (2). The above-described localized region is usually defined as a region of several hundred km, and a localized weight function can be used that reflects more the information closer to the lattice point in the localized region.

 Fig. 3 is a view for explaining only the observation information around the lattice points to obtain the data assimilation result value.

 Referring to FIG. 3, in the case of the first diagram of FIG. 3, the above-described LETKF data assimilation in FIG. 2 is performed in the vicinity of a lattice point to obtain an analytical field (i.e., a result of data assimilation) The use of only the observation information of Fig. In the case of the first diagram of FIG. 3, a description will be given of a method of calculating using only the model prediction result converted from the surrounding observation information and the observation information when updating the prediction model. For example, in order to calculate the analytical field of a grid point indicated by a circle in FIG. 1, the calculation module or the extraction module sets an appropriate radius, that is, a localization region (circle shape) (Black diamond) and the model predicted value interpolated to the observation point.

 In the case of the second drawing in Fig. 3, a grid called Arakawa C grid staggering is described. Scalar variables such as temperature, humidity, and pressure can be defined in the center of the grid point. Also, the vector variables, east - west wind field, can be defined at the center of the left and right sides of the grid, and the north and south wind fields can be defined at the center of the grid north - south direction. Therefore, in the case of the regional model, the north and south wind fields have one grid point in the north-south direction and the east-west wind field may have one grid in the east-west direction.

 FIG. 4 is a view for explaining the setting of the data moving radius in consideration of the triangular lattice structure.

를 가지고 Kalman gain matrix를 3번 각각 계산하게 되면 계산 비용이 3배로 늘어날 수 있다. MPAS 모델의 경우 독특한 격자 구조에 Arakawa C grid staggering이 적용될 수 있다. 이에 대한 구체적인 설명은 도 5에서 언급한다.Referring to FIG. 4, a diamond mark in FIG. 4 indicates observation data. The circles (50, 51, 52) indicated by dotted or solid lines mean the radius of the data assimilation. Also, the diamond (53), which is filled with black, is included in all the circles indicated by dotted lines or solid lines. Conversely, a diamond 54 filled with dots may or may not be included in a dotted line or a solid line circle, so that the observation data of the diamond display point filled with dots may not be used if not included. If grid staggering exists as shown in FIG. 4, the setting of the data moving radius set in the first drawing of FIG. 3 becomes complicated. In the data assimilation, the model error can be analyzed by multivariate analysis, including not only the spatio - temporal correlation but also the correlation between the variables. Therefore, in principle, different data assimilation radii can be used as shown in FIG. 4 in order to calculate the analytical fields of the variables defined at positions slightly offset from each other. As shown in FIG. 4, since different data assimilation radii are three,

To calculate the Kalman gain matrix three times, the calculation cost can be tripled. For the MPAS model, Arakawa C grid staggering can be applied to a unique grid structure. A detailed description thereof will be given in Fig.

5 is a diagram for explaining a unique lattice structure of the NCAR MPAS model.

Referring to FIG. 5, FIG. 5 illustrates the use of Arakawa C grid staggering in a unique lattice structure called the MPAS model Centroidal Voronoi tessellation. The wind defined by the edge point of the MPAS 'unique grid structure computes the wind in the direction orthogonal to the hexagonal sides, not the existing east-west winds and north-south winds. In the MPAS model shown in FIG. 5, the total number of edge points is about three times greater than the total number of cell points. Therefore, it is highly likely that the range of error will increase if K is calculated assuming that all variables are simply at the cell point. In addition, an error may occur in converting the wind variables defined at the edge point to the cell points and converting the wind variables updated by the data acquisition at the cell points back to the edge points.

FIG. 6 is a diagram for explaining a calculation process of a vector value and a matrix value corresponding to a wind parameter at an edge point of the present invention.

과

를 얻은 다음, 바람 변수에 대해서만 분석 증분을 edge point의 MPAS의 바람장으로 내삽/변환한다면, 본 발명은 전술한 수학식 1에서

는

로, 전술한 수학식 2에서

는

로 내삽/변환(치환) 할 수 있다. 전술한

는 각각 K X 1 차원의 벡터, K X K 차원의 행렬로서 모델 공간에서 정의되는 값이 아니기 때문에 모델 격자점에 의해 야기되었던 기존 기법의 cell point-edge point간의 공간 내삽이 불필요하다. 전술한 수학식 1 및 수학식 2를 치환하면 아래와 같다.Referring to FIG. 6, the prior art describes an analytical incremental interpolation by calculating Equations 1 and 2 above, assuming that all variables are at cell points

and

And then interpolates / converts the analytical increment to the wind field of the MPAS of the edge point only for the wind variables,

The

In the above-mentioned equation (2)

The

(Substitution). Described above

Is a KX 1 -dimensional vector, which is not a value defined in the model space as a matrix of KXK dimensions. Therefore, spatial interpolation between the cell point-edge points of the existing technique caused by the model lattice point is unnecessary. The following equations (1) and (2) are substituted as follows.

를 계산하고, 수학식 3 및 수학식 4를 통해 바람 변수를 제외한 온도, 습도, 기압 변수에 대해

를 계산하고, edge point의 바람 변수의 경우는 도 6과 같이Specifically, during the process of LETKF data assimilation described in FIG. 2, in the process (2), the wind variable of the edge point is converted into the observation space directly from the edge point without being converted to the cell point

(3) and Equation (4) are used to calculate the temperature, humidity, and atmospheric pressure variables except wind parameters

And the wind variable of the edge point is calculated as shown in FIG. 6

를 이용하여 아래 제시된 분석장을 계산한다.Lt; / RTI > Equations 5 and 6

To calculate the analytical field given below.

This technique can be called weight interpolation, and since the edge point is the middle value of adjacent cell points, it can be obtained by simple arithmetic mean, and it is not necessary to calculate Kalman gain matrix corresponding to edge point separately. All the desired information can be calculated with only light calculation.

7 is a flowchart for explaining a data assimilation method.

Referring to FIG. 7, in a data visualization method of a vapor phase numerical model including a plurality of grid cells, a plurality of grid cells include a first cell and a second cell, May be adjacent to each other by sharing at least one side.
The data moving method is based on the information about the ensemble analysis average vector value for the first variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the first cell, 2 information based on the information on the ensemble analysis mean vector value for the second variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the second cell, Calculating a first weight using the first information and the third information, calculating a second weight using the second information and the fourth information, and calculating a second weight using the first weight, and the second weight is used to calculate information about the ensemble analysis perturbation matrix value for the wind information at the edge point, The information may comprise the step of calculating. Further, the above-mentioned edge points may be located on at least one side shared by the first cell and the second cell.
The calculation module calculates the first information and the second information based on the information about the ensemble analysis mean vector value for the first variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the first cell Computing the third information and the fourth information based on the information about the ensemble analysis average vector value for the second variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the second cell Can be performed. The description thereof has been given above with reference to Figs. 1 to 6.
The weighting module may calculate the first weight using the first information and the third information, and calculate the second weight using the second information and the fourth information. The description thereof has been given above with reference to Figs. 1 to 6.
The extraction module calculates information on an ensemble analysis mean vector value for wind information at an edge point using the first weight and calculates an ensemble analysis mean vector value for the wind information at the edge point using the second weight, And calculating information on the matrix value. The description thereof has been given above with reference to Figs. 1 to 6.

delete

100: Calculation module
110: Weight module
120: Extraction module

Claims (8)

A method of data animation of a meteorological model including a plurality of grid cells,
Wherein the plurality of lattice-like cells include a first cell and a second cell, the first cell and the second cell are adjacent by sharing at least one side,
Based on the information on the ensemble analysis mean vector value for the first variable and the information about the ensemble analysis perturbation matrix value at a cell point which is the center of gravity of the first cell,

And the second information

;
Based on the information on the ensemble analysis mean vector value for the second variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the second cell,

And the fourth information

;
By using the first information and the third information,

And using the second information and the fourth information to calculate a second weight

; And
Calculating information on an ensemble analysis mean vector value for wind information at an edge point using the first weight and performing an ensemble analysis for the wind information at the edge point using the second weight value; And calculating information on the perturbation matrix value,
Wherein the edge points are located on the at least one side shared by the first cell and the second cell.  The method of claim 1, wherein the first variable and the second variable are at least one of temperature information, humidity information, and atmospheric pressure information. A data moving apparatus for a vapor-phase numerical model including a plurality of grid-shaped cells,
Wherein the plurality of lattice-like cells include a first cell and a second cell, the first cell and the second cell are adjacent by sharing at least one side,
Based on the information on the ensemble analysis mean vector value for the first variable and the information about the ensemble analysis perturbation matrix value at a cell point which is the center of gravity of the first cell,

And the second information

Based on the information on the ensemble analysis mean vector value for the second variable and the information about the ensemble analysis perturbation matrix value at the cell point which is the center of gravity of the second cell,

And the fourth information

A calculation module for calculating a calculation result;
By using the first information and the third information,

And using the second information and the fourth information to calculate a second weight

A weight module for calculating a weight module; And
Calculating information on an ensemble analysis mean vector value for wind information at an edge point using the first weight and performing an ensemble analysis for the wind information at the edge point using the second weight value; And an extraction module for calculating information on the perturbation matrix value,
Wherein the edge point is located on the at least one side shared by the first cell and the second cell.        The apparatus of claim 3, wherein the first variable and the second variable are at least one of temperature information, humidity information, and atmospheric pressure information. delete delete delete delete

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