CN114070262A - Additional disturbance integrated hybrid ensemble Kalman filtering weather forecast assimilation method and device thereof - Google Patents

Additional disturbance integrated hybrid ensemble Kalman filtering weather forecast assimilation method and device thereof Download PDF

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CN114070262A
CN114070262A CN202111250600.XA CN202111250600A CN114070262A CN 114070262 A CN114070262 A CN 114070262A CN 202111250600 A CN202111250600 A CN 202111250600A CN 114070262 A CN114070262 A CN 114070262A
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kalman gain
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CN114070262B (en
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雷荔傈
谈哲敏
王仲睿
张进
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Nanjing University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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Abstract

The invention discloses an additional disturbance integrated hybrid ensemble Kalman filtering weather forecast assimilation method and device. The weather forecast assimilation method estimates a static background error covariance matrix through a set of climate state set disturbances, and therefore a mixed Kalman gain matrix is obtained. Compared with the commonly used mixing method for averaging the Kalman gains obtained by the covariance of the static and flow related background errors, the method adopts the mixed Kalman gain to update the posterior set mean value
Figure DEST_PATH_IMAGE001
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 46780DEST_PATH_IMAGE002
. Mixture number with ensemble perturbation updated by ensemble Kalman filtering in generalCompared with the assimilation method, the method can update the set disturbance by using the hybrid Kalman gain, overcomes the problem of inconsistency of a separated hybrid assimilation system and an integrated Kalman filtering system, and can further reduce the error after assimilation under the condition that the mixing weight and other assimilation parameters are properly selected.

Description

Additional disturbance integrated hybrid ensemble Kalman filtering weather forecast assimilation method and device thereof
Technical Field
The invention relates to a numerical weather forecast assimilation method, belonging to a variation assimilation and collective assimilation-based mixed assimilation method and a device thereof.
Background
Data assimilation is a technology for finding the optimal estimation of the system state by combining the prior information and observation of the power system.
Common data assimilation methods are the variational and collective assimilation methods. In order to combine the advantages of collective and variational assimilation while minimizing the disadvantages of both methods, a hybrid collective-variational assimilation method is proposed. Previous studies have shown that the mixed ensemble-variational assimilation approach is superior to the variational or ensemble approach alone, and has been widely used for regional and global model numerical weather forecasting.
The hybrid ensemble-variational assimilation method typically uses a variational framework to solve for the hybrid analysis deltas, while the ensemble members are updated using ensemble kalman filtering, making the ensemble average equal to the analysis field solved by the hybrid method. The mixed mode uses a mixed method to update the ensemble average under the variation framework, but the posterior ensemble disturbance is updated by using a separate ensemble Kalman filtering system. The inconsistencies present in such separate hybrid assimilation systems and the ensemble kalman system may result in non-optimal results.
Therefore, chinese patent 202010646132.7 discloses a method for assimilating data in numerical weather forecast based on triple multi-layer perceptron, which is based on the traditional analysis period, obtains a training data set composed of a background field and an observation sequence, optimizes the results of two types of analysis fields by using a first perceptron model and a second perceptron model, and optimizes the outputs of the first perceptron and the second perceptron by using a third perceptron model, and couples the three-dimensional variation data assimilation method with the analysis field of the kalman filter data assimilation method, so that the data assimilation effect in numerical weather forecast is better, thereby ensuring that the assimilation performance of the method is effectively improved compared with the traditional method. The difficulty in introducing neural network learning algorithms during assimilation is how to guarantee the effectiveness of the training data set, which generally depends on the number of labeled samples and the training period.
Therefore, the dilemma faced by the developers is how to develop a hybrid assimilation method, which can realize hybrid assimilation under a single ensemble kalman filtering framework to solve the inconsistency problem caused by the separated assimilation systems.
Disclosure of Invention
The invention provides an integrated hybrid assimilation algorithm for calculating analysis increment by using an ensemble Kalman filtering framework instead of a variation framework aiming at the defects of the prior art. The newly proposed integrated mixed ensemble Kalman filtering assimilation method (IHGEnKF) with additional disturbance estimates a static background error covariance matrix through a set of climate state ensemble disturbance, and therefore a mixed Kalman gain matrix is obtained. In contrast to conventional hybrid methods that combine static and flow-dependent background error covariances to obtain a Kalman gain, the integrated hybrid assimilation method may utilize the information of the estimated static background error covariance plus the flow-dependent background error covariance to update both the ensemble mean and the ensemble perturbation (specifically, the hybrid Kalman gain is used to update the posterior ensemble mean)
Figure 361795DEST_PATH_IMAGE001
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 493699DEST_PATH_IMAGE002
). Compared with the EVIL which generates the posterior set from the minimization process, the integrated hybrid assimilation algorithm does not need a large number of iterations and is easily applied to the existing set Kalman filtering system. And the problem of inconsistency of a separated hybrid assimilation system and an integrated Kalman filtering system is solved, and the errors after assimilation can be further reduced under the condition that the hybrid weight and other assimilation parameters (such as a local parameter and an expansion parameter) are properly selected.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
an integrated mixed ensemble Kalman filtering weather forecast assimilation method with additional disturbance is carried out under the framework of ensemble Kalman filtering, and comprises the following steps:
step one, a set of forecast sets and observation data required to be assimilated are given
Acquiring the circulation set disturbance of a given prediction set, and calculating the corresponding background error covariance based on the acquired circulation set disturbance;
step two, extracting climate state set disturbance
2.1, integrating the forecast set at a given moment for a period of time before after assimilation observation based on the forecast set at the given moment, and obtaining a climate state time sequence after continuous cycle assimilation;
2.2, randomly extracting a group of data from the climate state time sequence acquired in the step 2.1 to form climate state set disturbance;
2.3, according to the climate state set disturbance obtained in the step 2.2, calculating the corresponding climate state background error covariance by referring to the calculation mode of the background error covariance in the step one;
step three, calculating the mixed Kalman gain and the mixed reduced Kalman gain
3.1, at the moment that the assimilation observation is needed, respectively calculating an estimated Kalman gain and an estimated Kalman reduction gain based on the background error covariance obtained in the first step, and respectively and correspondingly calculating the estimated climate state Kalman gain and the estimated climate state Kalman reduction gain based on the climate state background error covariance obtained in the second step by referring to the calculation modes of the estimated Kalman gain and the estimated Kalman reduction gain;
3.2, after the estimated Kalman gain and the estimated climate state Kalman gain obtained in the step 3.1 are weighted and averaged, the mixed Kalman gain can be calculated; after the estimated Kalman gain reduction and the estimated climate state Kalman gain reduction obtained in the step 3.1 are weighted and averaged, the mixed Kalman gain reduction can be calculated;
step four, using the mixed Kalman gain matrix and the mixed reduced Kalman gain assimilation observation data
For a given observation to be assimilated in step (3.2), the mean of the posterior set is updated during the assimilation process using the Kalman gain obtained in step
Figure 862101DEST_PATH_IMAGE003
Updating the posterior set disturbance by the mixed Kalman gain reduction obtained in step 3.2
Figure 3232DEST_PATH_IMAGE004
；
Step five, obtaining a posterior cycle set
Perturbing the updated posterior set
Figure 907734DEST_PATH_IMAGE004
And updated posterior aggregate mean
Figure 944960DEST_PATH_IMAGE003
Adding to obtain posterior cyclic set members corresponding to the prior cyclic set members one by one; the a posteriori loop set members are used to integrate into the next assimilation loop.
Preferably, in step one, the given set of predictions is a
Figure 895599DEST_PATH_IMAGE005
Of a set size ofN；
The ensemble average of the forecast ensemble is:
Figure 450208DEST_PATH_IMAGE006
；
first of forecast ensembleiA member of a set
Figure 333851DEST_PATH_IMAGE007
The aggregate perturbation of (c) is:
Figure 745240DEST_PATH_IMAGE008
；
cyclic ensemble perturbation of forecast ensembleXComprises the following steps:
Figure 589700DEST_PATH_IMAGE009
；
background error covariance
Figure 72634DEST_PATH_IMAGE010
。
Preferably, in step two, random extraction is carried out from the climate state time sequenceN c Data to form said disturbance set of climatic states
Figure 184684DEST_PATH_IMAGE011
：
Figure 32554DEST_PATH_IMAGE012
Covariance of climate state background error
Figure 488943DEST_PATH_IMAGE013
。
Preferably, in extracting from the time series of climatic statesN cBefore the disturbance of each climate state set, an expansion coefficient suitable for a given forecast set is selected to expand the dispersion of the given forecast set.
Preferably, in step 3.1, the estimated kalman gain is:
Figure 385355DEST_PATH_IMAGE014
the estimated reduced kalman gain is:
Figure 446852DEST_PATH_IMAGE015
estimated climate state kalman gain:
Figure 262361DEST_PATH_IMAGE016
estimated climate state reduction kalman gain:
Figure 81413DEST_PATH_IMAGE017
in the formula:Xa cyclic ensemble perturbation representing a forecast ensemble;
Figure 843832DEST_PATH_IMAGE018
representing a climate state set disturbance;
Figure 556573DEST_PATH_IMAGE019
representing the background error covariance;
Figure 683929DEST_PATH_IMAGE020
representing the covariance of the climate background error, H1Is a Jacobian matrix for observing the partial derivatives of the mode variables,
Figure 114911DEST_PATH_IMAGE021
represents the product of Shuer; y is a given observation to be assimilated and R is an error covariance matrix for the given observation to be assimilated.
Preferably, in step 3.2, the hybrid kalman gain is:
Figure 415442DEST_PATH_IMAGE022
the hybrid reduced kalman gain is:
Figure 356591DEST_PATH_IMAGE023
in the formula: k is the estimated kalman gain,
Figure 779482DEST_PATH_IMAGE024
(ii) is an estimated climate state kalman gain;
Figure 635443DEST_PATH_IMAGE025
reducing the kalman gain for the estimation;
Figure 411769DEST_PATH_IMAGE026
reducing a Kalman gain for the estimated climate state; 1-
Figure 364681DEST_PATH_IMAGE027
Weighting coefficients in the hybrid Kalman gain for the estimated Kalman gain or weighting coefficients in the hybrid reduced Kalman gain for the estimated reduced Kalman gain;
Figure 896157DEST_PATH_IMAGE027
for the weight coefficients of the estimated climate state Kalman gain in the hybrid Kalman gain or the weight coefficients of the estimated climate state reduced Kalman gain in the hybrid reduced Kalman gain,
Figure 911517DEST_PATH_IMAGE028
is a localized matrix of the image data that is,
Figure 616168DEST_PATH_IMAGE029
representing the schuler product.
Preferably, the posterior ensemble mean is updated with the hybrid Kalman gain
Figure 33374DEST_PATH_IMAGE030
：
Figure 735751DEST_PATH_IMAGE031
Mixed Kalman gain reduction to update posterior aggregate perturbations
Figure 628620DEST_PATH_IMAGE004
：
Figure 257003DEST_PATH_IMAGE032
In the formula: 1-
Figure 122191DEST_PATH_IMAGE027
Weighting coefficients in the hybrid Kalman gain for the estimated Kalman gain or weighting coefficients in the hybrid reduced Kalman gain for the estimated reduced Kalman gain;
Figure 792207DEST_PATH_IMAGE033
an ensemble average representing the ensemble of forecasts,
Figure 782159DEST_PATH_IMAGE034
representing aggregate perturbations;
Figure 828613DEST_PATH_IMAGE027
weighting coefficients of the estimated climate state Kalman gain in the hybrid Kalman gain or weighting coefficients of the estimated climate state reduced Kalman gain in the hybrid reduced Kalman gain; k is the estimated kalman gain,
Figure 548307DEST_PATH_IMAGE024
(ii) is an estimated climate state kalman gain;
Figure 530170DEST_PATH_IMAGE025
reducing the kalman gain for the estimation;
Figure 866473DEST_PATH_IMAGE026
reducing a Kalman gain for the estimated climate state;H 2 is an observation operator, H is a Jacobian matrix of observing the mode variables to make partial derivatives,
Figure 654300DEST_PATH_IMAGE028
is a localized matrix of the image data that is,
Figure 166184DEST_PATH_IMAGE035
represents the product of Shuer; y is a given observation to be assimilated and R is an error covariance matrix for the given observation to be assimilated.
Another technical object of the present invention is to provide an additional disturbance integrated hybrid ensemble kalman filter weather forecast assimilation device, including:
the acquisition module is used for acquiring observation data needing assimilation;
an assimilation module built based on an assimilation framework of ensemble Kalman filtering and updating the mean value of the posterior ensemble by adopting a mixed Kalman gain
Figure 178003DEST_PATH_IMAGE003
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 470444DEST_PATH_IMAGE004
To perform uniform mixing and assimilation processing on the observed data;
the hybrid Kalman gain is calculated after weighted averaging of the estimated Kalman gain and the estimated climate state Kalman gain, and the hybrid reduced Kalman gain is calculated after weighted averaging of the estimated reduced Kalman gain and the estimated climate state Kalman gain;
the estimated Kalman gain and the estimated reduced Kalman gain are respectively obtained by calculating the background error covariance at the moment of assimilation observation, and the estimated climate state Kalman gain and the estimated climate state reduced Kalman gain are respectively obtained by calculating the climate state background error covariance at the moment of assimilation observation;
the background error covariance is given by a set size ofNIs obtained by calculating the forecast set, the climate state background error covariance is obtained by the set sizeN c The climate state set disturbance is obtained by calculation, and the climate state set disturbance is obtained by random extraction from a period of climate state time sequence; the climatic time series is given by a set size ofNThe forecast set of (2) is integrated for a period of time before the time when the observation needs to be assimilated, and is obtained by continuous cyclic assimilation.
It is still another technical object of the present invention to provide an electronic apparatus, comprising: at least one processor, at least one memory, a communication interface, and a bus; the processor, the memory and the communication interface complete mutual communication through the bus; the communication interface is used for information transmission between the electronic equipment and communication equipment of other electronic equipment; the memory stores program instructions executable by the processor, which when called by the processor are capable of performing the methods described above.
A fourth technical object of the present invention is to provide an electronic device, a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method described above.
According to the technical scheme, compared with the prior art, the invention has the following beneficial effects:
the method approximates the static background error covariance by estimating the background error covariance through the climate state disturbance set, can realize a mixed assimilation method in the frame of the ensemble Kalman filtering, and adopts the mixed Kalman gain to update the posterior ensemble mean value
Figure 232601DEST_PATH_IMAGE030
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 723625DEST_PATH_IMAGE002
. Compared with the conventional mixed data assimilation method for updating the set disturbance by the ensemble Kalman filtering, the method can update the set disturbance by the mixed Kalman gain, overcome the problem of inconsistency of a separated mixed assimilation system and the ensemble Kalman filtering system, and further reduce the errors after assimilation under the condition that the mixed weight and other assimilation parameters (such as a localization parameter and an expansion parameter) are properly selected.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
In fig. 2: (a) shows that model II has a first mode error ofFIf =16, each assimilation method [ ensemble square root filter (EnSRF), mixed covariance assimilation: (HCDA), additional disturbance integrated mixed set Kalman filtering assimilation method (IHGEnKF)]RMSE time series of (a); (b) shows that model II has a second mode error ofF=18, methods for assimilation [ ensemble square root filter (EnSRF), mixed covariance assimilation (HCDA), disturbance-added Integrated Mixed ensemble Kalman Filter assimilation method (IHGEnKF)]RMSE time series of (a); (c) shows that model III has a first mode error ofF=16, methods of assimilation [ ensemble square root filter (EnSRF), mixed covariance assimilation (HCDA), Integrated Mixed ensemble Kalman Filter assimilation with additional perturbation (IHGEnKF)]RMSE time series of (a); (d) shows that model III has a second mode error ofF=18, methods for assimilation [ ensemble square root filter (EnSRF), mixed covariance assimilation (HCDA), disturbance-added Integrated Mixed ensemble Kalman Filter assimilation method (IHGEnKF)]RMSE time series of (1).
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
As shown in FIG. 1, the weather forecast assimilation method of the augmented disturbance integrated hybrid ensemble Kalman filter provided by the invention extracts the climate state ensemble disturbance in the frame of the ensemble Kalman filter, and updates the ensemble mean and the ensemble disturbance by using the mixed background error covariance obtained by calculation of the climate state ensemble disturbance and the cycle ensemble disturbance, thereby realizing hybrid assimilation. The mixed assimilation method can be used for further improving the forecast. The method comprises the following specific steps:
step one, a group of forecast sets and observations are given
1.1. Given a set of forecast sets
Given a set of collection sizesNForecast collection
Figure 109607DEST_PATH_IMAGE005
}, the ensemble average may be computed
Figure 295869DEST_PATH_IMAGE006
Of 1 atiA member of a set
Figure 487816DEST_PATH_IMAGE007
Set of disturbances of
Figure 708713DEST_PATH_IMAGE008
. To facilitate calculation of background error covariance for assimilation, aggregate perturbations can be written in the form of the square root of background error covariance
Figure 265596DEST_PATH_IMAGE009
Then background error covariance
Figure 329367DEST_PATH_IMAGE010
。
Given observations requiring assimilation
Given an observation y with an error covariance matrix R, it is generally assumed that the observation errors are uncorrelated, R is a diagonal matrix with diagonal elements being the error variances of the observation variables.
Step two, extracting climate state set disturbance before assimilation observation
And forward integration is carried out on the ensemble forecasting members, the prior ensemble is disturbed and expanded at the moment of needing assimilation observation to enlarge the dispersion, a proper localization scheme is selected in advance to be applied to assimilation, and the climate state ensemble disturbance is extracted to calculate the covariance of the mixed background error.
Covariance dilation spread
And selecting a proper expansion coefficient, and applying to prior set disturbance before assimilation to enlarge set dispersion and prevent filter divergence.
Selecting an appropriate localization scheme
The impact of observations is localized by selecting appropriate localization functions to reduce spurious correlations between observations and state variables, commonly used localization functions such as Gaspari and Cohn (GC; Gaspari and Cohn 1999) functions, determined by a single feature scale parameter. The localization function is applied to the kalman gain matrix as shown in step (4.1) at the time of assimilation.
Extracting climate state set disturbances
At the time of need of assimilation observation, extracting from a climate state time sequenceN c Disturbing chinese continental county state set
Figure 934792DEST_PATH_IMAGE036
Written as the square root of the background error covariance:
Figure 338092DEST_PATH_IMAGE012
then the covariance of the climate state background error
Figure 862614DEST_PATH_IMAGE013
。
Step three, calculating a hybrid Kalman gain matrix
Calculate byNKalman gain (in English: Kalman gain) estimated by members of ensemble prediction:
Figure 787582DEST_PATH_IMAGE014
estimated reduced Kalman gain (in English: reduced Kalman gain):
Figure 321332DEST_PATH_IMAGE015
calculating to obtain an estimated climate state Kalman gain according to the covariance of the climate state background error:
Figure 579138DEST_PATH_IMAGE016
similar climate state reduction kalman gains are:
Figure 415507DEST_PATH_IMAGE017
kalman gain of the hybrid of
Figure 188291DEST_PATH_IMAGE037
Hybrid Kalman gain reduction of
Figure 463414DEST_PATH_IMAGE023
Weight of
Figure 513410DEST_PATH_IMAGE038
The same as the expansion coefficient, localized parameters need to be adjusted to be optimal.
In the above formula, the first and second carbon atoms are,
Figure 645314DEST_PATH_IMAGE018
and
Figure 843077DEST_PATH_IMAGE039
as such, all represent a disturbance in the set of climate states.
Step four, using mixed Kalman gain assimilation observation
The hybrid assimilation is based on a collective square root filtering system. By observation operatorsH 2 Is that the observation operator maps the mode variables to the observation space, H1Is a Jacobian matrix for observing the partial derivatives of the mode variables,
Figure 593995DEST_PATH_IMAGE028
is a localized matrix of the image data that is,
Figure 623131DEST_PATH_IMAGE035
representing the schuler product.
Updating ensemble averages
Updating posterior ensemble averages with hybrid Kalman gain
Figure 129199DEST_PATH_IMAGE003
Equivalent to mixed analytical increments:
Figure 984897DEST_PATH_IMAGE031
4.2. update set perturbation
Updating the posterior set perturbation with the hybrid kalman gain:
Figure 664140DEST_PATH_IMAGE032
step five, obtaining a posterior cycle set
5.1. Obtaining a posterior cyclic set
The average of posterior set and the disturbance of posterior set are added to obtainNA posteriori cycle set membership. This is achieved byNThe members of the posterior cycle set are integrated to the next cycle of assimilation.
Evaluation of assimilation test results
The time series of root mean square errors were obtained after completion of the assimilation experiments and the results of the assimilation experiments were evaluated using the RMSE average over the selected analysis period as a standard.
Example 1
The performance of the method is tested by using a mixed Kalman gain assimilation observation under the framework of integrated square root filtering, taking a Lorenz (2005) model as an example, in single-scale and double-scale modes and mode errors with different degrees, and compared with error results of the integrated square root filtering and mixed Kalman gain assimilation (HGDA, Penny 2014) method. The sensitivity test result shows that the method is superior to the traditional mixed assimilation method in different set sizes, swelling degrees and localization scales.
Step one, a group of forecast sets and observations are given
The Lorenz (2005) model has two scales to choose from, single scale mode II only contains one large scale slow process variable, double scale mode III contains fast and slow process variables. Is provided with
Figure 751045DEST_PATH_IMAGE040
For slow process variables, the single-scale mode II can be written as:
Figure 100118DEST_PATH_IMAGE041
wherein the content of the first and second substances,
Figure 334790DEST_PATH_IMAGE042
denotes the time of day, subscriptnRepresents the number of the lattice point and the number of the lattice point,Kis a constant number of times, and is,F is a forcing term.
The advection entry is written as:
Figure 427511DEST_PATH_IMAGE043
,
wherein
Figure 368922DEST_PATH_IMAGE044
Is a special summation operator, which is the same as the general summation operator except that the first term and the last term are divided by 2.KWhen it is even numberJ=K/2，
Figure 279109DEST_PATH_IMAGE045
；KWhen it is oddJ=(K-1)/2，
Figure 610865DEST_PATH_IMAGE046
。
Introducing a fast process variable
Figure 569593DEST_PATH_IMAGE047
The double scale model III can be written as:
Figure 693407DEST_PATH_IMAGE048
wherein the content of the first and second substances,
Figure 617239DEST_PATH_IMAGE049
is a mode integral variable. Coefficient of performanceb=10 determines
Figure 764186DEST_PATH_IMAGE047
Relative to
Figure 323344DEST_PATH_IMAGE050
Frequency and amplitude of (d). Coefficient of couplingc=3 determine
Figure 177030DEST_PATH_IMAGE050
And
Figure 163441DEST_PATH_IMAGE047
the coupling strength of (2). By
Figure 673050DEST_PATH_IMAGE049
Deconstructed
Figure 144221DEST_PATH_IMAGE050
And
Figure 180310DEST_PATH_IMAGE047
comprises the following steps:
Figure 540884DEST_PATH_IMAGE051
Figure 396845DEST_PATH_IMAGE053
total number of lattice pointsN=960, smooth scaleISelection of 12, constantKAnd 32 is selected. Constant numberαAndβthe values of (a) need to satisfy: when in use
Figure 438750DEST_PATH_IMAGE049
In thatn-IAndn+Iwhen the angle changes quadratically between the two,
Figure 329346DEST_PATH_IMAGE040
is equal to
Figure 657559DEST_PATH_IMAGE049
Then, thenαTaken as the sum of the values of 0.1241,βthis was taken to be 0.0137. By forcing the termFDifferent values of (c) can introduce different degrees of mode errors, and the embodiment makes the forcing term F of the value be 15 and the forcing term F of the experiment be 16 and 18, wherein the assignment of the two forcing terms F during the experiment means that the forcing term F =16 corresponds to a smaller mode error (first mode error) experiment and the forcing term F =18 corresponds to a larger mode error (second mode error) experiment.
Given a set of forecast sets
The truth value and the initial condition of the set member are obtained by extracting from a set composed of a plurality of independent states. Setting a group of forecast collection
Figure 938499DEST_PATH_IMAGE005
Of a set size ofN. Ensemble averaging
Figure 377570DEST_PATH_IMAGE006
Of 1 atiA member of a set
Figure 122672DEST_PATH_IMAGE054
Set of disturbances of
Figure 995688DEST_PATH_IMAGE055
. For the convenient calculation of background error covariance during assimilation, the aggregate perturbation is written in the form of the square root of the background error covariance
Figure 888558DEST_PATH_IMAGE009
Then background error covariance
Figure 334583DEST_PATH_IMAGE010
。
Given observations requiring assimilation
Given an observation y with an error covariance matrix R, it is generally assumed that the observation errors are uncorrelated, R is a diagonal matrix with diagonal elements being the error variances of the observation variables. Obey normal distribution by adding to truthN(0,R) To make observations. The default observation error variance size is 1.0. The default observation network is one observation for every 4 grid points (240 observation grid points total). One observation is generated every 50 integration time steps (-6 h).
Step two, extracting climate state set disturbance before assimilation observation
And forward integration is carried out on the ensemble forecasting members, the prior ensemble is disturbed and expanded at the moment of needing assimilation observation to enlarge the dispersion, a proper localization scheme is selected in advance to be applied to assimilation, and the climate state ensemble disturbance is extracted to calculate the covariance of the mixed background error. Default number of sets of climate state disturbancesN c Is 800.
Covariance dilation spread
Constant expansion coefficients (Anderson and Anderson 1999) are used to expand the set dispersion to prevent filter divergence. And selecting a proper expansion coefficient, and applying to prior set disturbance before assimilation.
Selecting an appropriate localization scheme
Gaspari and Cohn (GC; Gaspari and Cohn 1999) functions are used as localization functions, determined by a single feature scale parameter. The localization function is applied to the kalman gain matrix as shown in step (4.1) at the time of assimilation. The characteristic scale of the GC function requires the selection of appropriate values to obtain the best results.
Extracting climate state set disturbances
The climate time series was obtained by 1 year integration at any initial condition. At the moment of need of assimilation observation, from climateDecimation in a time series of statesN c Disturbing chinese continental county state set
Figure 606295DEST_PATH_IMAGE036
Written as the square root of the background error covariance:
Figure 541890DEST_PATH_IMAGE012
then the covariance of the climate state background error
Figure 859739DEST_PATH_IMAGE013
。
Step three, calculating a hybrid Kalman gain matrix
Calculate byNKalman gain estimated by members of the ensemble prediction:
Figure 781559DEST_PATH_IMAGE014
estimated reduced kalman gain:
Figure 297991DEST_PATH_IMAGE015
calculating to obtain an estimated climate state Kalman gain according to the covariance of the climate state background error:
Figure 342170DEST_PATH_IMAGE016
the estimated climate state reduction kalman gain is:
Figure 819419DEST_PATH_IMAGE017
kalman gain of the hybrid of
Figure 669563DEST_PATH_IMAGE037
Hybrid Kalman gain reduction of
Figure 243764DEST_PATH_IMAGE023
Weight of
Figure 629484DEST_PATH_IMAGE038
The same as the expansion coefficient, localized parameters need to be adjusted to be optimal. The parameters used for the adjustment of this example are as follows:
Figure 984242DEST_PATH_IMAGE056
the upper row is model II, the lower row is model III, the left column is parameter F =16, and the right column is F = 18.
Step four, using mixed Kalman gain assimilation observation
The hybrid assimilation is based on a collective square root filtering system. By observation operatorsH 2 Mapping mode variables to observation space, H1Is a Jacobian matrix for observing the partial derivatives of the mode variables,
Figure 310181DEST_PATH_IMAGE057
is a localized matrix of the image data that is,
Figure 676571DEST_PATH_IMAGE035
representing the schuler product.
Updating ensemble averages
Updating posterior ensemble averages with hybrid Kalman gain
Figure 124870DEST_PATH_IMAGE003
Equivalent to mixed analytical increments:
Figure 639028DEST_PATH_IMAGE031
4.2. update set perturbation
Updating the posterior set perturbation with the hybrid kalman gain:
Figure 440762DEST_PATH_IMAGE032
step five, obtaining a posterior cycle set
5.1. Obtaining a posterior cyclic set
The average of posterior set and the disturbance of posterior set are added to obtainNA posteriori cycle set membership. This is achieved byNThe members of the posterior cycle set are integrated to the next cycle of assimilation.
Evaluation of assimilation test results
The time series of root mean square errors were obtained after completion of the assimilation experiments and the results of the assimilation experiments were evaluated using the RMSE average over the selected analysis period as a standard. Each data assimilation method was performed for 360 days, and some assimilation parameters (expansion coefficient, localization and mixing weight) were changed according to the experiment, except for some default parameters. The first 10 days were discarded to avoid the effect of error desaturation, and the last 350 days were used to obtain optimal assimilation parameters and to evaluate assimilation performance.
FIG. 2 shows the RMSE time series for each assimilation method for models II and III with different modal errors. When only slow process variables are present, the RMSE of the hybrid data assimilation method (HGDA) is smaller than the ensemble square root filter (EnSRF), as shown in both (a) and (b) of fig. 2. This demonstrates the advantage of updating the ensemble mean using mixed background error covariance compared to using pure sampled background error covariance. The integrated hybrid integrated Kalman filter with additional perturbation (IHGEnKF) yields a similar RMSE and is smaller than the HGDA. This demonstrates the advantage of updating the set disturbance with the hybrid kalman gain by additional climate disturbances. Similar results were obtained when fast process variables were included, as shown in fig. 2 (c), (d), indicating that there is still an advantage in updating the ensemble perturbation using the hybrid kalman gain in the presence of fast process variables.
Example 2
The embodiment discloses an integrated mixed ensemble Kalman filtering weather forecast assimilation device with additional disturbance, which comprises: the device comprises an acquisition module and an assimilation module which are mutually connected in a communication manner; wherein:
the acquisition module is used for acquiring observation data needing assimilation;
an assimilation module built based on an assimilation framework of ensemble Kalman filtering and updating the mean value of the posterior ensemble by adopting a mixed Kalman gain
Figure 51872DEST_PATH_IMAGE030
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 608755DEST_PATH_IMAGE002
To perform uniform mixing and assimilation processing on the observed data;
the hybrid Kalman gain is calculated after weighted averaging of the estimated Kalman gain and the estimated climate state Kalman gain, and the hybrid reduced Kalman gain is calculated after weighted averaging of the estimated reduced Kalman gain and the estimated climate state Kalman gain;
the estimated Kalman gain and the estimated reduced Kalman gain are respectively obtained by calculating the background error covariance at the moment of assimilation observation, and the estimated climate state Kalman gain and the estimated climate state reduced Kalman gain are respectively obtained by calculating the climate state background error covariance at the moment of assimilation observation;
the background error covariance is given by a set size ofNThe climate state background error covariance is obtained by calculating a climate state set disturbance, and the climate state set disturbance is obtained by randomly extracting from a period of climate state time sequence; the climatic time series is given by a set size ofNThe forecast set of (2) is integrated for a period of time before the time when the observation needs to be assimilated, and is obtained by continuous cyclic assimilation.
Example 3
The present embodiment provides an electronic device, including: at least one processor, at least one memory, a communication interface, and a bus; the processor, the memory and the communication interface complete mutual communication through the bus; the communication interface is used for the electronic equipment andinformation transmission between communication devices of other electronic devices; the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the method of the above embodiment. Examples include: under the framework of ensemble Kalman filtering, acquiring observation data to be assimilated, and acquiring a set of forecast ensembles. At the time needing assimilation observation, respectively calculating and obtaining a background error covariance and a climate state time sequence on the basis of a given forecast set, and randomly extracting a group of data from the climate state time sequence to form climate state set disturbance; and then calculating the climate state background error covariance by referring to a calculation mode of the background error covariance on the basis of the disturbance of the climate state set. In addition, the estimated Kalman gain and the estimated reduced Kalman gain can be respectively calculated according to the background error covariance, the estimated climate state Kalman gain and the estimated climate state reduced Kalman gain are respectively calculated according to the climate state background error covariance, the mixed Kalman gain is calculated according to the estimated Kalman gain and the estimated climate state Kalman gain, and the mixed reduced Kalman gain is calculated according to the estimated reduced Kalman gain and the estimated climate state reduced Kalman gain. Finally, updating the posterior set mean value according to the mixed Kalman gain
Figure 282313DEST_PATH_IMAGE003
Updating the posterior aggregate perturbation based on the blended reduced Kalman gain
Figure 277951DEST_PATH_IMAGE004
To finally obtain the posterior set members.
The above-described embodiments of the electronic device and the like are merely illustrative, where the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may also be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Example 4
The present embodiments disclose a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, the computer is capable of performing the methods provided by the above embodiments, for example, comprising: acquiring observation data to be assimilated, and acquiring a set of forecast sets. At the time needing assimilation observation, respectively calculating and obtaining a background error covariance and a climate state time sequence on the basis of a given forecast set, and randomly extracting a group of data from the climate state time sequence to form climate state set disturbance; and then calculating the climate state background error covariance by referring to a calculation mode of the background error covariance on the basis of the disturbance of the climate state set. In addition, the estimated Kalman gain and the estimated reduced Kalman gain can be respectively calculated according to the background error covariance, the estimated climate state Kalman gain and the estimated climate state reduced Kalman gain are respectively calculated according to the climate state background error covariance, the mixed Kalman gain is calculated according to the estimated Kalman gain and the estimated climate state Kalman gain, and the mixed reduced Kalman gain is calculated according to the estimated reduced Kalman gain and the estimated climate state reduced Kalman gain. Finally, updating the posterior set mean value according to the mixed Kalman gain
Figure 681250DEST_PATH_IMAGE030
Updating the posterior aggregate perturbation based on the blended reduced Kalman gain
Figure 591393DEST_PATH_IMAGE002
To finally obtain the posterior set members.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.

Claims (10)

1. An integrated hybrid ensemble Kalman filtering weather forecast assimilation method with additional disturbance is characterized by being carried out under the frame of ensemble Kalman filtering and comprising the following steps:
step one, a set of forecast sets and observation data required to be assimilated are given
Acquiring the circulation set disturbance of a given prediction set, and calculating the corresponding background error covariance based on the acquired circulation set disturbance;
step two, extracting climate state set disturbance
2.1, integrating a period of time in the forward direction at the moment needing assimilation observation based on a given forecast set, and continuously and circularly assimilating to obtain a climate state time sequence;
2.2, randomly extracting a group of data from the climate state time sequence acquired in the step 2.1 to form climate state set disturbance;
2.3, according to the climate state set disturbance obtained in the step 2.2, calculating the corresponding climate state background error covariance by referring to the calculation mode of the background error covariance in the step one;
step three, calculating the mixed Kalman gain and the mixed reduced Kalman gain
3.1, at the moment that the assimilation observation is needed, respectively calculating an estimated Kalman gain and an estimated Kalman reduction gain based on the background error covariance obtained in the first step, and respectively and correspondingly calculating the estimated climate state Kalman gain and the estimated climate state Kalman reduction gain based on the climate state background error covariance obtained in the second step by referring to the calculation modes of the estimated Kalman gain and the estimated Kalman reduction gain;
3.2, after the estimated Kalman gain and the estimated climate state Kalman gain obtained in the step 3.1 are weighted and averaged, the mixed Kalman gain can be calculated; after the estimated Kalman gain reduction and the estimated climate state Kalman gain reduction obtained in the step 3.1 are weighted and averaged, the mixed Kalman gain reduction can be calculated;
step four, using the mixed Kalman gain matrix and the mixed reduced Kalman gain assimilation observation data
For the observation data required to be assimilated given in the step, updating the mean value of the posterior set by using the hybrid Kalman gain obtained in the step 3.2, and updating the disturbance of the posterior set by using the hybrid reduced Kalman gain obtained in the step 3.2 in the assimilation process
Figure 103947DEST_PATH_IMAGE001
；
Step five, obtaining a posterior cycle set
Perturbing the updated posterior set
Figure 746018DEST_PATH_IMAGE001
And updated posterior aggregate mean
Figure 3824DEST_PATH_IMAGE002
Adding to obtain posterior cyclic set members corresponding to the prior cyclic set members one by one; the a posteriori loop set members are used to integrate into the next assimilation loop.
2. The method according to claim 1, wherein in step one, the given set of predictions is a
Figure 964827DEST_PATH_IMAGE003
Of a set size ofN；
The ensemble average of the forecast ensemble is:
Figure 612977DEST_PATH_IMAGE004
；
first of forecast ensemblei set members
Figure 684838DEST_PATH_IMAGE005
The aggregate perturbation of (c) is:
Figure 62730DEST_PATH_IMAGE006
；
cyclic ensemble perturbation of forecast ensembleXComprises the following steps:
Figure 804421DEST_PATH_IMAGE007
；
background error covariance
Figure 330080DEST_PATH_IMAGE008
。
3. The method for assimilating weather forecast with additional disturbance according to claim 2, characterized in that in step two, the weather state time series is randomly extractedN c Data to form said disturbance set of climatic states
Figure 815419DEST_PATH_IMAGE009
：
Figure 47818DEST_PATH_IMAGE010
Covariance of climate state background error
Figure 350623DEST_PATH_IMAGE011
。
4. The perturbed integrated hybrid ensemble Kalman filter weather forecast assimilation method of claim 3, characterized in that it is extracted from the time series of climatic statesN cBefore disturbance of each climate state set, the expansion coefficient suitable for the given forecast set is selected to expand the given forecast setThe dispersion of (2).
5. The additively perturbed integrated hybrid ensemble kalman filtering weather forecast assimilation method according to claim 1 or 3, characterized in that in step 3.1, the estimated kalman gain is:
Figure 471901DEST_PATH_IMAGE012
the estimated reduced kalman gain is:
Figure 885564DEST_PATH_IMAGE013
estimated climate state kalman gain:
Figure 972469DEST_PATH_IMAGE014
estimated climate state reduction kalman gain:
Figure 587121DEST_PATH_IMAGE015
in the formula:Xa cyclic ensemble perturbation representing a forecast ensemble;
Figure 556214DEST_PATH_IMAGE016
representing a climate state set disturbance;
Figure 711252DEST_PATH_IMAGE017
representing the background error covariance;
Figure 590346DEST_PATH_IMAGE018
representing the covariance of the climate background error, H1Is a Jacobian matrix for observing the partial derivatives of the mode variables,
Figure 500533DEST_PATH_IMAGE019
represents the product of Shuer; y is a given observation to be assimilated and R is an error covariance matrix for the given observation to be assimilated.
6. The method for integrating additive disturbance and Kalman filtering weather forecast assimilation according to claim 1 or 5, is characterized in that in step 3.2, the Kalman gain is as follows:
Figure 832289DEST_PATH_IMAGE020
the hybrid reduced kalman gain is:
Figure 791018DEST_PATH_IMAGE021
in the formula: k is the estimated kalman gain,
Figure 383673DEST_PATH_IMAGE022
(ii) is an estimated climate state kalman gain;
Figure 838663DEST_PATH_IMAGE023
reducing the kalman gain for the estimation;
Figure 985610DEST_PATH_IMAGE024
reducing a Kalman gain for the estimated climate state; 1-
Figure 544768DEST_PATH_IMAGE025
Weighting coefficients in the hybrid Kalman gain for the estimated Kalman gain or weighting coefficients in the hybrid reduced Kalman gain for the estimated reduced Kalman gain;
Figure 398454DEST_PATH_IMAGE025
kalman augmentation of estimated climate statesA weight coefficient in a hybrid Kalman gain or a weight coefficient of an estimated climate state reduced Kalman gain in a hybrid reduced Kalman gain;
Figure 119285DEST_PATH_IMAGE026
is a localized matrix of the image data that is,
Figure 753529DEST_PATH_IMAGE027
representing the schuler product.
7. The perturbed integrated HYBRID AGAINST WEA method according to claim 6, wherein the posterior ensemble mean is updated with the HYBRID Kalman gain
Figure 991744DEST_PATH_IMAGE002
：
Figure 824570DEST_PATH_IMAGE029
Mixed Kalman gain reduction to update posterior aggregate perturbations
Figure 919565DEST_PATH_IMAGE001
：
Figure 713209DEST_PATH_IMAGE031
In the formula: 1-
Figure 879748DEST_PATH_IMAGE025
Weighting coefficients in the hybrid Kalman gain for the estimated Kalman gain or weighting coefficients in the hybrid reduced Kalman gain for the estimated reduced Kalman gain;
Figure 675404DEST_PATH_IMAGE033
presentation forecastThe set average of the set is then determined,
Figure 206879DEST_PATH_IMAGE035
representing aggregate perturbations;
Figure 612453DEST_PATH_IMAGE025
weighting coefficients of the estimated climate state Kalman gain in the hybrid Kalman gain or weighting coefficients of the estimated climate state reduced Kalman gain in the hybrid reduced Kalman gain; k is the estimated kalman gain,
Figure 192470DEST_PATH_IMAGE022
(ii) is an estimated climate state kalman gain;
Figure 937572DEST_PATH_IMAGE023
reducing the kalman gain for the estimation;
Figure 436686DEST_PATH_IMAGE024
reducing a Kalman gain for the estimated climate state;H 2 is an observation operator, and the operator is,
Figure 204922DEST_PATH_IMAGE026
is a localized matrix of the image data that is,
Figure 447685DEST_PATH_IMAGE036
represents the product of Shuer; y is a given observation to be assimilated and R is an error covariance matrix for the given observation to be assimilated.
8. An integrated hybrid ensemble Kalman filter weather forecast assimilation device with additional disturbance, comprising:
the acquisition module is used for acquiring observation data needing assimilation;
an assimilation module built based on an assimilation framework of ensemble Kalman filtering and updating the mean value of the posterior ensemble by adopting a mixed Kalman gain
Figure 47293DEST_PATH_IMAGE002
Updating posterior ensemble perturbations with blended Kalman gain reductions
Figure 858254DEST_PATH_IMAGE001
To perform uniform mixing and assimilation processing on the observed data;
the hybrid Kalman gain is calculated after weighted averaging of the estimated Kalman gain and the estimated climate state Kalman gain, and the hybrid reduced Kalman gain is calculated after weighted averaging of the estimated reduced Kalman gain and the estimated climate state Kalman gain;
the estimated Kalman gain and the estimated reduced Kalman gain are respectively obtained by calculating the background error covariance at the moment of assimilation observation, and the estimated climate state Kalman gain and the estimated climate state reduced Kalman gain are respectively obtained by calculating the climate state background error covariance at the moment of assimilation observation;
the background error covariance is given by a set size ofNIs obtained by calculating the forecast set, the climate state background error covariance is obtained by the set sizeN c The climate state set disturbance is obtained by calculation, and the climate state set disturbance is obtained by random extraction from a period of climate state time sequence; the climatic time series is given by a set size ofNThe forecast set of (2) is integrated for a period of time before the time when the observation needs to be assimilated, and is obtained by continuous cyclic assimilation.
9. An electronic device, comprising: at least one processor, at least one memory, a communication interface, and a bus; the processor, the memory and the communication interface complete mutual communication through the bus; the communication interface is used for information transmission between the electronic equipment and communication equipment of other electronic equipment; the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of claim 1.
10. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of claim 1.
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