CN117216509A - Spatial wind field assimilation method - Google Patents
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Abstract
The application discloses a space wind field assimilation method, which is used for acquiring wind field observation data and wind field background field data; performing gridding processing according to the observation data and the background field data, and filtering abnormal values of the gridding processing data; assimilation error proportional coefficient determination is carried out on the data after the filtering treatment, and a background error covariance matrix B, an observation error covariance matrix R and an observation operator H in the assimilation process are determined through a covariance model according to the proportional coefficient; and obtaining an assimilation calculation weight matrix K according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, and carrying out iterative assimilation on the space wind field through a Kalman filtering algorithm according to the weight matrix K. The method combines a Kalman filtering algorithm, greatly reduces the data assimilation time, can improve the assimilation precision, and has important significance for wind field forecast.
Description
Technical Field
The application relates to the field of atmosphere data assimilation, in particular to a spatial wind field assimilation method.
Background
In a specific near space, detection tools such as a space/air/ground satellite and the like provide a large amount of observation data with wide space distribution and high resolution, and along with the increasing attention and importance of each country of the strategic value of the near space, how to fully utilize the available detection data to research the change characteristics of the wind field in the near space, improve the forecasting precision of the numerical mode of the atmospheric wind field in the near space, provide scientific basis and guarantee for the development and utilization of the near space, and become one of research hotspots.
For accurate prediction, the method is a key difficult problem to be solved urgently, but the existing wind field data assimilation method, such as a variation method, is perfect in theory, but has respective limitations in the actual operation process, cannot assimilate data in high frequency, real time and fast, and becomes a bottleneck of accurate wind field prediction.
Disclosure of Invention
The application aims to provide a space wind field assimilation method which can realize the high-frequency, real-time and rapid assimilation process of wind field data so as to overcome the defects of the prior art,
in order to achieve the above object, the present application provides the following solutions:
a method of spatial wind farm assimilation, the assimilation method comprising:
acquiring wind field observation data and wind field background field data;
performing gridding processing according to the observation data and the background field data, and filtering abnormal values of the gridding processing data;
assimilation error proportional coefficient determination is carried out on the data after the filtering treatment, and a background error covariance matrix B, an observation error covariance matrix R and an observation operator H in the assimilation process are determined through a covariance model according to the proportional coefficient;
and obtaining an assimilation calculation weight matrix K according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, and carrying out iterative assimilation on the space wind field through a Kalman filtering algorithm according to the weight matrix K.
Optionally, the method for determining the covariance matrix R of the observed error according to the covariance model comprises the following specific steps:
wherein i, j represents an observation point, R ij Error covariance value η between observation points o Is a scaling factor.
Optionally, the background error covariance matrix B is determined according to the covariance model, which specifically includes:
B ij ＝σ i σ j ρ ij
in B of ij As the error covariance value between observation points ρ ij Is the correlation coefficient, eta b Is a super parameter. Because the observed value is generally closer to the true value, the observed value should occupy a larger proportion and take eta b ＝20η o . L (r), L (H) represents the correlation length in the horizontal direction and the height direction, respectively, r ij ，H ij The distances between grid points in the horizontal direction and the height direction are indicated, respectively.
Optionally, the assimilation calculation weight matrix K is obtained according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, which comprises,
K＝BH T (HBH T +R) -1
wherein B is a background error covariance matrix, R is an observation error covariance matrix, H is an observation operator, and K is an assimilation calculation weight matrix.
Optionally, the kalman filtering algorithm performs iterative assimilation on the spatial wind field, and the specific process is as follows: and predicting the background field change in the near space through a background field model based on the background field at the current moment, and correcting a background field prediction structure based on the observed value to obtain a final assimilation result.
Optionally, predicting the near space background field through the background model comprises the following specific processes:
in the middle ofFor the background field at the next moment, +.>For the state analysis value after assimilation at the present moment, < >>For the background field at the current moment, < > and->Delta t in (a) is the assimilation time window, tau is the time-dependent scale,/->The background field for the next moment calculated for the model, < >>Covariance matrix for background field at next moment,/-, for background field at next moment>Is an assimilated covariance matrix, +.>Covariance matrix of background field for current time, < ->Covariance matrix of background field calculated for model of next moment.
Optionally, the background field prediction structure is modified based on the observed value to obtain a final assimilation result, which comprises the following specific processes:
X a ＝X b +K(Y-HX b )
B a ＝B-BH T (HBH T +R) -1 HB
wherein X is a Is an analysis value, X b Is the background field value predicted by the background field model, B is the background field error covariance matrix, Y represents the state value of the observed field, H represents the observation operator, R represents the observed field error covariance matrix, K is the gain matrix, B a Is an assimilated analytical field covariance matrix.
According to the specific embodiment provided by the application, the application discloses the following technical effects:
the application improves the existing wind field data assimilation method and improves the data assimilation precision, and simultaneously, the application can lead the prediction error to develop along with the development of model power, and the prediction error in the optimal interpolation is given, and the state and the change of the model are separated; in addition, compared with the traditional variation method, the application provides the mean value of the state quantity and the corresponding error covariance, so that the scheme is easier to realize.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a diagram illustrating a spatial wind farm assimilation method according to the present application;
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The application aims to provide a space wind field assimilation method, which comprises the steps of obtaining wind field observation data and wind field background field data; performing gridding processing according to the observation data and the background field data, and filtering abnormal values of the gridding processing data; assimilation error proportional coefficient determination is carried out on the data after the filtering treatment, and a background error covariance matrix B, an observation error covariance matrix R and an observation operator H in the assimilation process are determined through a covariance model according to the proportional coefficient; and obtaining an assimilation calculation weight matrix K according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, and carrying out iterative assimilation on the space wind field through a Kalman filtering algorithm according to the weight matrix K.
In order that the above-recited objects, features and advantages of the present application will become more readily apparent, a more particular description of the application will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the spatial wind field assimilation method of the present application comprises: acquiring wind field observation data and wind field background field data;
performing gridding processing according to the observation data and the background field data, and filtering abnormal values of the gridding processing data;
assimilation error proportional coefficient determination is carried out on the data after the filtering treatment, and a background error covariance matrix B, an observation error covariance matrix R and an observation operator H in the assimilation process are determined through a covariance model according to the proportional coefficient;
and obtaining an assimilation calculation weight matrix K according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, and carrying out iterative assimilation on the space wind field through a Kalman filtering algorithm according to the weight matrix K.
Specifically, the covariance matrix R of the observation error is determined according to the covariance model, and the specific process is as follows:
wherein i, j represents an observation point, R ij Error covariance value η between observation points o Is a scaling factor.
Specifically, a background error covariance matrix B is determined according to a covariance model, and the specific process is as follows:
B ij ＝σ i σ j ρ ij
in B of ij As the error covariance value between observation points ρ ij Is the correlation coefficient, eta b Is a super parameter. Because the observed value is generally closer to the true value, the observed value should occupy a larger proportion and take eta b ＝20η o . L (r), L (H) represents the correlation length in the horizontal direction and the height direction, respectively, r ij ，H ij The distances between grid points in the horizontal direction and the height direction are indicated, respectively.
Specifically, according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, an assimilation calculation weight matrix K is obtained, which comprises,
K＝BH T (HBH T +R) -1
wherein B is a background error covariance matrix, R is an observation error covariance matrix, H is an observation operator, and K is an assimilation calculation weight matrix.
Specifically, the Kalman filtering algorithm performs iterative assimilation on the spatial wind field, and the specific process is as follows: and predicting the background field change in the near space through a background field model based on the background field at the current moment, and correcting a background field prediction structure based on the observed value to obtain a final assimilation result.
Specifically, the background field in the near space is predicted by a background model, and the specific process is as follows:
in the middle ofFor the background field at the next moment, +.>For the state analysis value after assimilation at the present moment, < >>For the background field at the current moment, < > and->Delta t in (a) is the assimilation time window, tau is the time-dependent scale,/->The background field for the next moment calculated for the model, < >>Covariance matrix for background field at next moment,/-, for background field at next moment>Is an assimilated covariance matrix, +.>Covariance matrix of background field for current time, < ->For the next momentCovariance matrix of background field calculated by model.
Specifically, the background field prediction structure is corrected based on the observed value to obtain a final assimilation result, and the specific process is as follows:
X a ＝X b +K(Y-HX b )
B a ＝B-BH T (HBH T +R) -1 HB
wherein X is a Is an analysis value, X b Is the background field value predicted by the background field model, B is the background field error covariance matrix, Y represents the state value of the observed field, H represents the observation operator, R represents the observed field error covariance matrix, K is the gain matrix, B a Is an assimilated analytical field covariance matrix.
In this embodiment, the observation operator H represents a mapping from the observation wind field to the background wind field. Most of the time H is a matrix with different numbers of rows and columns. The number of rows is equal to the number of meshes occupied by observation, and the number of columns is equal to the number of background meshes. The element of H consists of 0 and 1, and when the observed value is absent, the corresponding column number element is set to 0, and the presence is set to 1. The concrete representation is as follows:
in this embodiment, the horizontal wind field of HWM14 is used as the background field to obtain the atmospheric horizontal wind field data of Yunnan region with the height range of 80-100km, 1000km×1000km (centered on curved line), and the meteor radar, intermediate frequency radar, FPI foundation wind field observation data and space foundation tid/tid and ICON/MIGHTI wind field observation data of Yunnan region.
The covariance model reflects the correlation between the data, and the error covariance includes both errors and correlations of errors. The assimilation process is a process in which data and a background model are fused with each other, and thus, the error covariance model thereof includes both the error covariance of the data and the error covariance of the background model.
The observation data are considered to be independent of each other, and thus, the observation error covariance matrix R can be represented by a diagonal matrix, that is:
wherein i, j represents an observation point, R ij Error covariance value η between observation points o Is a proportionality coefficient, the ratio determines the weight of the observed value in the assimilation system, if the ratio is increased, the corresponding error covariance is increased, and the weight of the observed value is naturally decreased, and vice versa. At the same time, considering that we believe more about the observation rather than the model state, this ratio is usually small, in this embodiment we set η o ＝0.01。
Because the errors between the observations are uncorrelated, the spatially correlated information can only be transferred to the assimilation analysis results via the background field error covariance matrix B.
Covariance models based on gaussian theory are a common modeling method in data assimilation. As with the observed field error modeling approach, the Gao Sixie variance model also assumes that the background error is proportional to the square of the background value. In addition, the gaussian model assumes gaussian correlation between background field data and is divided into horizontal correlation and vertical correlation. The calculation method is as follows:
B ij ＝σ i σ j ρ ij
in B of ij As the error covariance value between observation points ρ ij Is the correlation coefficient, eta b Is a super parameter. Because the observed value is generally closer to the true value, the observed value should occupy a larger proportion and take eta b ＝20η o . L (r), L (H) represents the horizontal direction and the height direction, respectivelyRelated length, r ij ，H ij The distances between grid points in the horizontal direction and the height direction are indicated, respectively.
Under the assumption that the wind field in the near space is horizontally and vertically separable, the wind field in the near space can be calculated by the horizontal correlation and the vertical correlation respectively, and the horizontal correlation can be divided into the warp correlation and the weft correlation.
(1) Horizontal correlation
In the embodiment, the wind field data of the HWM14 model is utilized to calculate the background field level correlation of the winding region, and the seasonal average value of the wind field in the vicinity space of the HWM14 model is used as a true value to carry out statistical analysis on the error of the HWM14 model. The model data is divided according to the world time, season and altitude, and detailed division conditions are shown in table 1.
Table 1 data set partitioning condition table
Based on the conditions, the adjacent space wind field correlation coefficients under different conditions are respectively counted, and can be used in assimilation according to the correlation conditions. In the case of sample covariance estimation, the usual method is empirical covariance estimation, which is the maximum likelihood estimate of covariance, unbiased, i.e. it converges to true (overall) covariance when given many observations. However, where the number of samples is less than the variable dimension, the empirical covariance estimate is not the optimal estimate of the covariance, which may cause the covariance matrix to be of a non-full rank, causing the matrix to be non-inverted, and regularizing it to reduce its variance is often beneficial.
The present embodiment uses a Ledoit-Wolf shrink covariance estimator to estimate HWM14 model error covariance. The Ledoit-Wolf shrink covariance estimation is a generalized linear combination based on a covariance matrix and an identity matrix, and generally performs better when the number of samples is smaller than the variable dimension, and can ensure that the covariance matrix is a positive definite matrix. After covariance estimation M is obtained, the following formula is utilized to obtain the horizontal correlation coefficient of the wind field in the near space.
Where trace is the trace of the matrix. And defining a region with a correlation coefficient larger than 0.75 as a correlation region, wherein the correlation length is the distance from the reference point to the boundary of the correlation region, and assuming that the wind field horizontal correlation in the region of the labyrinth has no change in the height direction.
(2) Vertical correlation
In the embodiment, the wind field error of the model background of the region of the trefoil is statistically analyzed by utilizing the wind field observation data of the trefoil radar in 2022 year, so that the vertical correlation of the wind field in the near space is further obtained, and the condition that the vertical correlation of the wind field in the region of the trefoil has no change in the horizontal direction is assumed. The vertical correlation area was set to 80-100km with a height resolution of 2km, again estimated using a ledit-Wolf shrink covariance estimator. The region with the correlation coefficient larger than 0.75 is defined as a correlation region, and the correlation length is the distance from the reference point to the boundary of the correlation region.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present application have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present application and the core ideas thereof; also, it is within the scope of the present application to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the application.
Claims (7)
1. A method of spatial wind farm assimilation, comprising:
acquiring wind field observation data and wind field background field data;
performing gridding treatment according to wind field observation data and wind field background field data, and filtering abnormal values of the gridding treatment data;
assimilation error proportional coefficient determination is carried out on the data after the filtering treatment, and a background error covariance matrix B, an observation error covariance matrix R and an observation operator H in the assimilation process are determined through a covariance model according to the proportional coefficient;
and obtaining an assimilation calculation weight matrix K according to the background error covariance matrix B, the observation error covariance matrix R and the observation operator H, and carrying out iterative assimilation on the space wind field through a Kalman filtering algorithm according to the weight matrix K.
2. The spatial wind farm assimilation method according to claim 1, wherein the determining the observed error covariance matrix R according to the covariance model comprises the following steps:
wherein i, j represents an observation point, R ij Error covariance value η between observation points o Is a scaling factor.
3. The spatial wind farm assimilation method according to claim 1, wherein the background error covariance matrix B is determined according to a covariance model, and the specific process is as follows:
B ij ＝σ i σ j ρ ij
in B of ij As the error covariance value between observation points ρ ij Is the correlation coefficient, eta b Is a super parameter. Because the observed value is generally closer to the true value, the observed value should occupy a larger proportion and take eta b ＝20η o . L (r), L (H) represents the correlation length in the horizontal direction and the height direction, respectively, r ij ，H ij The distances between grid points in the horizontal direction and the height direction are indicated, respectively.
4. The spatial wind field assimilation method according to claim 1, wherein the assimilation calculation weight matrix K is obtained according to a background error covariance matrix B, an observation error covariance matrix R and an observation operator H, comprising,
K＝BH T (HBH T +R) -1
wherein B is a background error covariance matrix, R is an observation error covariance matrix, H is an observation operator, and K is an assimilation calculation weight matrix.
5. The spatial wind farm assimilation method according to claim 1, wherein the kalman filter algorithm iterates assimilation of the spatial wind farm, comprising,
and predicting the background field change in the near space through a background field model based on the background field at the current moment, and correcting a background field prediction structure based on the observed value to obtain a final assimilation result.
6. The method of spatial wind farm assimilation according to claim 5, wherein predicting the near-spatial background field by the background model comprises,
in the middle ofFor the background field at the next moment, +.>For the state analysis value after assimilation at the present moment, < >>For the background field at the current moment, < > and->Delta t in (a) is the assimilation time window, tau is the time-dependent scale,/->The background field for the next moment calculated for the model, < >>Covariance matrix for background field at next moment,/-, for background field at next moment>Is an assimilated covariance matrix, +.>Covariance matrix of background field for current time, < ->Covariance matrix of background field calculated for model of next moment.
7. The method of spatial wind farm assimilation according to claim 5, wherein the background field prediction structure is modified based on the observed value to obtain a final assimilation result, comprising,
X a ＝X b +K(Y-HX b )
B a ＝B-BH T (HBH T +R) -1 HB
wherein X is a Is an analysis value, X b Is the background field value predicted by the background field model, B is the background field error covariance matrix, Y represents the state value of the observed field, H represents the observation operator, R represents the observed field error covariance matrix, K is the gain matrix, B a Is an assimilated analytical field covariance matrix.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117874982A (en) * | 2024-01-30 | 2024-04-12 | 中国气象局地球系统数值预报中心 | Multivariable-fusion Beidou navigation and exploration station network layout method, system and equipment |
| CN118409325A (en) * | 2024-07-02 | 2024-07-30 | 中国人民解放军国防科技大学 | Scatterometer wind field super-resolution method based on self-adaptive two-dimensional variation assimilation |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117874982A (en) * | 2024-01-30 | 2024-04-12 | 中国气象局地球系统数值预报中心 | Multivariable-fusion Beidou navigation and exploration station network layout method, system and equipment |
| CN117874982B (en) * | 2024-01-30 | 2024-09-20 | 中国气象局地球系统数值预报中心 | Multivariable-fusion Beidou navigation and exploration station network layout method, system and equipment |
| CN118409325A (en) * | 2024-07-02 | 2024-07-30 | 中国人民解放军国防科技大学 | Scatterometer wind field super-resolution method based on self-adaptive two-dimensional variation assimilation |
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