Analogy-based Offline Ensemble Kalman Filter Paleoclimate Data Assimilation System, Method and Electronic Device

Abstract

The present invention discloses an offline ensemble Kalman filter paleoclimate data assimilation system, method and electronic device based on analogy. The data assimilation method is carried out under the assimilation framework of the ensemble Kalman filter. Before assimilation of observations, based on an analogy method, ensemble prior members are selected through certain criteria (root mean square error or correlation coefficient relative to the observations) to replace the traditional static ensemble prior members randomly selected, so as to update the ensemble mean and ensemble perturbation. Compared with the 'online' cyclic assimilation method, the huge computational amount of the forward integration of the ensemble model is reduced. Compared with the usual 'offline' assimilation method that repeatedly uses randomly selected prior ensembles, the present invention can construct a more accurate prior ensemble average, capture the 'flow-dependent' background field error covariance information at the same time, and can further reduce the error after assimilation.

Description

Technical Field

[0001] The present invention relates to a method for reconstructing paleoclimate fields, and is an assimilation system, method, and electronic device based on analogy and ensemble Kalman filtering. Background Art

[0002] Understanding paleoclimate phenomena can improve the prediction skills of future climate change. The reconstruction of paleoclimate fields uses paleoclimate proxy indicators to evaluate the climate state. Most paleoclimate field reconstruction methods use multiple linear regression to obtain climate field variables, but are limited by the non-linear relationship between proxy indicators and climate variables.

[0003] Correspondingly, paleoclimate data assimilation is a method of combining the dynamic system constraints of climate models and proxy observation information to find the optimal estimate of the climate system state. Among them, traditional ensemble-based data assimilation techniques use the ensemble of analysis fields updated by observations at the previous moment as the initial conditions of the ensemble model to integrate forward to obtain the prior ensemble for the next cycle of assimilation, which is called 'online' cyclic ensemble assimilation. However, due to the short predictability of the model compared to the time scale of observations, and the large computational cost required for ensemble model integration. An 'offline' ensemble data assimilation method has been proposed, which constructs a background field ensemble from existing climate simulations. 'Offline' and 'online' have been systematically compared, and no significant improvement has been found for the 'online' method compared to the 'offline' method.

[0004] Therefore, the offline ensemble-based paleoclimate data assimilation method is widely used in paleoclimate field reconstruction. The prior ensemble members are often randomly selected from existing long-term climate simulations. At the same time, to prevent the reconstructed climate field from being affected by the randomness of each selection, the same selected ensemble is reused in each assimilation. Another ensemble-based paleoclimate data assimilation method is to use a degenerated particle filter to select the optimal simulation from the simulations of the ensemble model. However, even with a large number of ensembles, the selected particles are still affected by the curse of dimensionality. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention provides an assimilation method using analogy and ensemble Kalman filtering (hereinafter simply referred to as AOEnKF). AOEnKF first selects prior ensemble members from a group of long-term climate simulations. The selection criterion is that the root mean square error (RMSE) between the ensemble field and the observations is the smallest or the correlation coefficient is the largest. The obtained prior ensemble members thus capture the 'flow-dependent' background field error covariance matrix. Then, by assimilating climate proxy data into the prior ensemble members, posterior ensemble members can be obtained. The prior ensemble members obtained by AOEnKF according to the present invention do not require ensemble model integration to obtain the 'flow-dependent' background field error covariance matrix compared with the 'online' cyclic assimilation, and the computational cost is smaller. Compared with the traditional 'offline' static prior ensemble members based on ensemble assimilation methods, it can better spread the proxy data information to the climate field. It can be seen that the assimilation method described in the present invention can combine the advantages of the analogy method and the ensemble Kalman filtering to better reconstruct the paleoclimate field.

[0006] To achieve the above technical objectives, the present invention will adopt the following technical solutions:

[0007] An offline ensemble Kalman filtering paleoclimate data assimilation method based on analogy first screens prior ensemble members from the state variable samples x simulated in a group of control experiments according to specific criteria using the observations y, and then updates the posterior ensemble mean of the obtained prior ensemble members through the Kalman gain matrix according to the update formula of the ensemble square root filter and the posterior ensemble perturbations Specifically, it includes the following steps:

[0008] Step 1: Given a group of state variable samples x simulated in control experiments and the observations y

[0009] Step 2: Select prior ensemble members according to different criteria before assimilating the observations

[0010] Before assimilating the observations, first interpolate the state variable samples x into the observations y, and then, based on each state variable sample x of the state variable samples x j The initial N samples arranged in order selected from the state variable samples x according to the principle that the root mean square error relative to the observations y is the smallest or the correlation coefficient is the largest constitute the prior ensemble members;

[0011] Step 3: Assimilate the observations using the obtained prior ensemble members

[0012] Use the square root filter to assimilate the observations y with the error covariance matrix R, first update the posterior ensemble mean and the i-th posterior ensemble perturbation i = 1,..., N; then the posterior ensemble mean and the posterior ensemble perturbations Adding them together gives N posterior ensemble members.

[0013] Preferably, when the criterion for selecting prior ensemble members from the state variable samples x is that each state variable sample x of the state variable samples x j has the minimum root mean square error with respect to the observation y, each state variable sample x j The root mean square error RMSE with respect to y is expressed as:

[0014]

[0015] where: the observation y represents a p×1 observation variable; y m represents the m-th observation variable in the observation y; H(x j,m ) represents transforming the state variable sample x j into the observation space y m , that is, the estimate of the observation y j obtained from the state variable sample x m .

[0016] Meanwhile, the samples of the N prior ensemble members are sorted in ascending order according to the corresponding root mean square error RMSE.

[0017] Preferably, when the criterion for selecting prior ensemble members from the state variable samples x is that each state variable sample x of the state variable samples x j has the maximum correlation coefficient with respect to the observation y, each state variable sample x j The correlation coefficient with respect to y is expressed as:

[0018]

[0019] where: the observation y represents a p×1 observation variable; y′ represents the observation space anomaly field obtained by subtracting the spatial average of the observation y from the observation y; y′ m represents the m-th variable in the observation space anomaly field y′; H(x j,m )′ represents the anomaly field of the estimate of the observation y j obtained from the state variable sample x m minus the spatial average of the obtained observation estimate.

[0020] Meanwhile, the samples of the N prior ensemble members are sorted in descending order according to the corresponding correlation coefficients.

[0021] Posterior ensemble mean The update formula is:

[0022]

[0023] Posterior ensemble perturbation The update formula is as follows:

[0024]

[0025] Where: represents the ensemble mean of the N prior members obtained in step two; ρ is the localization matrix, represents the Schur product;

[0026] X f is the background covariance P f = X f X fT the square root of, represents the ensemble perturbation of the i-th member of the N prior members obtained in step two, H2 is the observation operator that maps the model variables to the observed variables, and H1 is the Jacobian matrix of the partial derivative of the observation with respect to the model variables.

[0027] Another technical objective of the present invention is to provide an offline ensemble Kalman filter paleoclimate data assimilation system based on analogy, including:

[0028] An acquisition module for acquiring the observation y with the error covariance matrix R to be assimilated;

[0029] An assimilation module built based on the assimilation framework of the ensemble Kalman filter;

[0030] Before assimilating the observation, the assimilation module first interpolates the state variable samples x into the observation y, and then, according to the principle that the root mean square error of each state variable sample x j of the state variable samples x with respect to the observation y is the smallest or the correlation coefficient is the largest, the initial N sorted samples selected from the state variable samples x form the prior ensemble members;

[0031] At the assimilation time, the assimilation module uses square root filtering to assimilate the observation y with the error covariance matrix R, first updates the posterior ensemble mean and the i-th posterior ensemble perturbation i = 1,..., N; then adding the posterior ensemble mean and the posterior ensemble perturbation can obtain N posterior ensemble members.

[0032] Preferably, the criterion for the assimilation module to select the prior ensemble members from the state variable samples x is that each state variable sample x j of the state variable samples x is sorted in descending order of the correlation coefficient with respect to the observation y; the correlation coefficient of each state variable sample x j with respect to y is expressed as:

[0033]

[0034] Among them: the observation \(y\) represents a \(p\times1\) observation variable; \(y'\) represents the observation spatial anomaly field obtained by subtracting the spatial average from the observation \(y\); \(y'\) m represents the \(m\)th variable in the observation spatial anomaly field \(y'\); \(H(x\) j,m )' represents the anomaly field of the observation estimate obtained by subtracting its spatial average from the estimate of the observation \(y\) obtained from the state variable sample \(x\). j m

[0035] Preferably, for each sample of the \(N\) prior ensemble members selected from the state variable sample \(x\) by the assimilation module, they are sorted in ascending order of the root mean square error RMSE of each state variable sample \(x\) j relative to \(y\); where, the root mean square error RMSE of each state variable sample \(x\) j relative to \(y\) is:

[0036]

[0037] Among them: the observation \(y\) represents a \(p\times1\) observation variable; \(y\) m represents the \(m\)th observation variable in the observation \(y\); \(H(x\) j,m ) represents the conversion of the state variable sample \(x\) j to the observation space \(y\) m , that is, the estimate of the observation \(y\) j obtained from the state variable sample \(x\). m

[0038] Preferably, the update formulas for the posterior ensemble mean and the posterior ensemble perturbation at the assimilation time are respectively:

[0039]

[0040]

[0041] In the formula: represents the ensemble mean of the \(N\) ensemble prior members obtained in step two; \(\rho\) is the localization matrix, represents the Schur product;

[0042] X f is the square root of the background covariance \(P\) f =X f X fT ; ​​​Denote the ensemble perturbation of the \(i\)-th member among the \(N\) ensemble prior members obtained in Step 2. \(H_2\) is the observation operator that maps the model variables to the observed variables, and \(H_1\) is the Jacobian matrix of the partial derivative of the observations with respect to the model variables.

[0043] The third technical objective of the present invention is to provide an electronic device, including: at least one processor, at least one memory, a communication interface, and a bus; wherein, the processor, the memory, and the communication interface complete communication with each other through the bus; the communication interface is used for information transmission between the electronic device and the communication devices of other electronic devices; the memory stores program instructions executable by the processor, and the processor can execute the above-mentioned method by invoking the program instructions.

[0044] According to the above technical solution, compared with the prior art, the present invention has the following beneficial effects:

[0045] Based on the analogy method, the present invention selects ensemble prior members through certain criteria (RMSE or correlation coefficient relative to the observations), instead of the traditional static ensemble prior members randomly selected, to update the ensemble mean and ensemble perturbation. Compared with the 'online' cycling assimilation method, the huge computational amount of the ensemble model forward integration is reduced. Compared with the usual 'offline' assimilation method that repeatedly uses randomly selected prior ensembles, the present invention can construct a more accurate prior ensemble mean, and at the same time capture the 'flow-dependent' background field error covariance information, which can further reduce the error after assimilation. Description of the Drawings

[0046] Figure 1 It is a flowchart of the present invention.

[0047] Figure 2 It is a sequence of RMSE varying with different localization values for the 'online' cycling ensemble Kalman filter (CEnKF), 'offline' ensemble Kalman filter (OEnKF), offline ensemble Kalman filter based on the RMSE criterion analogy (AOEnKF_E), and offline ensemble Kalman filter based on the correlation coefficient criterion analogy (AOEnKF_C): circles indicate that the RMSE of OEnKF is significantly different from that of other experiments (passed the 99% confidence test), and crosses indicate that the RMSE of AOEnKF_E and AOEnKF_C is significantly different (passed the 99% confidence test).

[0048] Figure 3 It is a schematic structural diagram of the electronic device of the present invention. Detailed Embodiments

[0049] In order to better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the drawings.

[0050] It should be clear that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0051] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The singular forms "a", "said", and "the" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0052] It should be understood that the term "and / or" used herein is only a correlative relationship describing related objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the related objects before and after.

[0053] Embodiment 1

[0054] As Figure 1 shown, for the offline ensemble Kalman filter paleoclimate data assimilation method based on analogy of the present invention, first, prior ensemble members are selected from a set of state variable samples simulated by control experiments according to different criteria (the minimum RMSE between the model and the observations or the maximum correlation coefficient), and then the obtained prior ensemble members are used to update the ensemble mean and ensemble perturbation by applying the ensemble square root filter. Applying this assimilation method can further improve the analysis field. The specific steps are as follows:

[0055] Step 1. Given a set of state variables and observations simulated by control experiments

[0056] 1.1. Given a set of state variable samples simulated by control experiments

[0057] x f Samples X from a set of state variables simulated by a control experiment n×T ={x1,…,x T}, where T is the number of state variable samples; n is the dimension of the state variables. The control experiment is obtained by integrating a single model for a period of time.

[0058] 1.2. Given the observations to be assimilated

[0059] Given the observations y with the error covariance matrix R, it is generally assumed that the observation errors are uncorrelated, and R is a diagonal matrix, and the diagonal elements are the error variances of the observed variables.

[0060] Step 2. Select prior ensemble members according to different criteria before assimilating the observations

[0061] Before the assimilation observation, the state variables are first interpolated into the observation space, and then the prior ensemble members are constructed based on the criterion of the minimum root mean square error (RMSE) or the principle of the maximum correlation coefficient between the state variables and the observations. Specifically, they are elaborated as follows:

[0062] 2.1. Selecting prior ensemble members based on the minimum root mean square error criterion (abbreviated as AOEnKF_E)

[0063] AOEnKF_E is to select prior ensemble members Based on the criterion of the minimum root mean square error (RMSE) (first interpolating the state variables into the observation space). For each state variable sample x j (j = 1,…, T), x j The RMSE with respect to y can be expressed as

[0064]

[0065] By sorting the RMSE in ascending order, the first N samples are selected as the prior ensemble members for this assimilation time.

[0066] 2.2. Selecting prior ensemble members based on the maximum correlation coefficient criterion (abbreviated as AOEnKF_C)

[0067] AOEnKF_C selects the prior ensemble members Based on the correlation coefficient between the state variables and the observations (first interpolating the state variables into the observation space). For each state variable sample x j (j = 1,…, T), x j The correlation coefficient with y can be expressed as

[0068]

[0069] where the prime indicates the spatial anomaly field obtained by subtracting the spatial average. By sorting the correlation coefficients in descending order, the first N samples are selected as the prior ensemble members for this assimilation time.

[0070] 2.3. Selecting a suitable localization scheme

[0071] Select a suitable localization function to localize the influence of the observations and reduce the spurious correlation between the observations and the state variables. Commonly used localization functions such as the Gaspari and Cohn (GC; Gaspari and Cohn 1999) function are determined by a single characteristic scale parameter. The localization function is applied to the Kalman gain matrix as shown in step (3.1) during assimilation.

[0072] Step 3. Use the obtained prior set members to assimilate the observations

[0073] Use the square root filter to assimilate the observation y with the error covariance matrix R. First, update the ensemble mean of the posterior set members and the perturbation of the i-th (i = 1, …, N) posterior set member, and then add the posterior ensemble mean and the posterior ensemble perturbation to obtain N posterior set members. The specific calculation formula is as follows:

[0074] 3.1. Update the ensemble mean

[0075] The update formula for the ensemble mean of the posterior set members is:

[0076]

[0077] where: ρ is the localization matrix, denotes the Schur product; denotes the ensemble mean of the N ensemble prior members selected by AOEnKF_E or AOEnKF_C described in Step 2;

[0078] X f is the square root of the background covariance P f = X f X fT and denotes the ensemble perturbation of the i-th member of the N ensemble prior members selected by AOEnKF_E or AOEnKF_C described in Step 2. H2 is the observation operator that maps the model variables to the observation variables, and H1 is the Jacobian matrix of the partial derivative of the observation with respect to the model variables.

[0079] 3.2. Update the ensemble perturbation

[0080] The update formula for the perturbation of the i-th (i = 1, …, N) posterior set member is:

[0081]

[0082] where: denotes the ensemble perturbation of the i-th member of the N ensemble prior members selected by AOEnKF_E or AOEnKF_C described in Step 2; X f is the square root of the background covariance P f = X f X fT and H1 is the Jacobian matrix of the partial derivative of the observation with respect to the model variables; ρ is the localization matrix, denotes the Schur product.

[0083] 3.3. Obtain the posterior ensemble members

[0084] The posterior ensemble mean and the posterior ensemble perturbations are added together to obtain N posterior ensemble members.

[0085] 3.4. Evaluate the results of the assimilation experiment

[0086] When the assimilation experiment is over, the time series of the root mean square error is averaged as a standard to evaluate the results of the assimilation experiment.

[0087] Example 2

[0088] Based on the analogy-based offline ensemble Kalman filter paleoclimate data assimilation method of the present invention to assimilate observations, taking the Lorenz (2005) model as an example, the performance of the present invention is tested with the single-scale mode II without model error, and the error results are compared with those using the traditional static grab, 'offline' ensemble Kalman filter (OEnKF, Hakim 2016) method. The results of the sensitivity test show that the present invention is superior to the traditional assimilation method in different ensemble sizes, localization scales, observation errors, and observation densities.

[0089] Step 1: Given a set of state variables and observations simulated by a control experiment

[0090] The single-scale mode II of the L05 model only contains one large-scale slow process variable. Let X be the slow process variable, and the single-scale mode II can be written as:

[0091]

[0092] The subscript n represents the grid point number, K is a constant, and F is the forcing term. The advection term is written as:

[0093]

[0094] where ∑' is a special summation operator, which is the same as the general summation operator except that the first and last terms are divided by 2. When K is even, J = K / 2, when K is odd, J = (K - 1) / 2,

[0095] The total number of grid points N = 960, and the constant K is selected as 32. The forcing term F is 16. The true value is the same as the model parameters of the control experiment, indicating that there is no model error in the control experiment.

[0096] 1.1. Given a set of state variable samples simulated by a control experiment

[0097] x fSamples from the state variables from a control experiment simulation, where the control experiment is obtained by integrating the above L05 single-scale model II for a period of time. The control experiment is averaged every 6000 integration time steps (~120h) to obtain the independent prior ensemble member samples X n×T ={x1,...,x T}.

[0098] 1.2. Given the observations to be assimilated

[0099] Given the observations y with the error covariance matrix R, it is generally assumed that the observation errors are uncorrelated, and R is a diagonal matrix with the diagonal elements being the error variances of the observed variables. The observations are generated by adding random perturbations following the normal distribution N(0,R) to the average of the true values over a period of time (~120h). The default observation error variance size is 4.0. The default observation network is one observation per 8 grid points (a total of 120 observation grid points). One observation is generated for every 6000 integration time steps of averaging (~120h).

[0100] Step 2. Select prior ensemble members according to different criteria before assimilating the observations

[0101] 2.1. Select prior ensemble members based on the minimum root mean square error criterion

[0102] AOEnKF_E is to select prior ensemble members based on the criterion of minimum root mean square error (RMSE) (first interpolate the state variables into the observation space). For each state variable sample x j (j = 1,…,T), x j The RMSE relative to y can be expressed as

[0103]

[0104] By sorting the RMSE in ascending order, the first N samples are selected as the prior ensemble members for this assimilation time

[0105] 2.2. Select prior ensemble members based on the maximum correlation coefficient criterion

[0106] AOEnKF_C selects the ensemble prior members based on the correlation coefficient between the state variables and the observations (first interpolate the state variables into the observation space). For each state variable sample x j (j = 1,…,T), x j The correlation coefficient with y can be expressed as

[0107]

[0108] where the apostrophe represents the spatially anomalous field obtained by subtracting the spatial average. By sorting the correlation coefficients in descending order, the first N samples are selected as the prior ensemble members for this assimilation time.

[0109] 2.3. Select an appropriate localization scheme

[0110] The Gaspari and Cohn (GC; Gaspari and Cohn 1999) function is used as the localization function, which is determined by a single characteristic scale parameter. The localization function is applied to the Kalman gain matrix during assimilation as shown in step (3.1). An appropriate value for the characteristic scale of the GC function needs to be selected to obtain the best results.

[0111] Step 3. Assimilate the observations with the obtained prior ensemble members

[0112] N ensemble prior members have been selected through AOEnKF_E or AOEnKF_C and the observation y, is the ensemble mean, is the ensemble perturbation of the i-th member, is the background covariance P f = X f X fT is the square root of. The observation operator H maps the model variables to the observation variables. H is the Jacobian matrix of the partial derivative of the observation with respect to the model variables. The observation y with the assimilation error covariance matrix R is used with square root filtering.

[0113] 3.1. Update the ensemble mean

[0114] The posterior ensemble mean is updated by the formula

[0115]

[0116] where ρ is the localization matrix, denotes the Schur product

[0117] 3.2. Update the ensemble perturbations

[0118] The update formula for the perturbation of the i-th (i = 1,..., N) ensemble member is

[0119]

[0120] 3.3. Obtain the posterior ensemble members

[0121] The N posterior ensemble members are obtained by adding the posterior ensemble mean and the posterior ensemble perturbations.

[0122] 3.4. Evaluate the results of the assimilation experiment

[0123] After the assimilation experiment ends, the time series of the root mean square error is averaged as the standard to evaluate the results of the assimilation experiment. Each data assimilation method conducts an assimilation experiment for 1000 months. Figure 2 It shows the variation of the average of the 1000-month time series of RMSE of each assimilation method with different localization values. CEnKF and OEnKF have almost the same error, which proves that the single-scale L05 model has almost no memory of the initial conditions, and the predictability of the model is shorter than the time scale of the observations. For AOEnKFs, AOEnKF_E and AOEnKF_C have similar performances, and the RMSE is significantly reduced compared to OEnKF. This proves that the 'flow-dependent' background field error covariance information included in the prior ensemble members can improve the assimilation effect.

[0124] Example 3

[0125] Based on the above paleoclimate data assimilation method, the present invention provides an analog-based offline ensemble Kalman filter paleoclimate data assimilation system, including: an acquisition module for acquiring the observation y with an error covariance matrix R to be assimilated; an assimilation module built based on the assimilation framework of the ensemble Kalman filter; before assimilating the observation, the assimilation module first interpolates the state variable samples x into the observation y, and then, according to each state variable sample x of the state variable samples x j The initial N sorted samples selected from the state variable samples x according to the principle of the minimum root mean square error or the maximum correlation coefficient relative to the observation y form the prior ensemble members; at the assimilation moment, the assimilation module uses square root filtering to assimilate the observation y with an error covariance matrix R, first updates the posterior ensemble mean and the i-th posterior ensemble perturbation Then the posterior ensemble mean and the posterior ensemble perturbation are added to obtain N posterior ensemble members.

[0126] The assimilation module can implement each process that can be achieved in the embodiment of the paleoclimate data assimilation method of the present invention, and achieve the same beneficial effects. To avoid repetition, it will not be described in detail here.

[0127] Example Four

[0128] Based on the above paleoclimate data assimilation method, the present invention provides an electronic device, including: at least one processor, at least one memory, a communication interface, and a bus; wherein, the processor, the memory, and the communication interface complete communication with each other through the bus; the communication interface is used for information transmission between this electronic device and communication devices of other electronic devices; the memory stores program instructions executable by the processor, and the processor can execute the above paleoclimate data assimilation method by invoking the program instructions.

[0129] Specifically, the processor is used to obtain the observation y with the error covariance matrix R to be assimilated.

[0130] The processor has an assimilation module built based on the assimilation framework of the ensemble Kalman filter; the assimilation module, based on specific criteria, uses the obtained observation y to screen prior ensemble members from a set of state variable samples x simulated in a group of control experiments, and then, according to the update formula of the ensemble square root filter, updates the posterior ensemble mean of the obtained prior ensemble members through the Kalman gain matrix and the posterior ensemble perturbation The specific criteria are: based on each state variable sample x of the state variable samples x j The principle of the minimum root mean square error or the maximum correlation coefficient relative to the observation y.

[0131] In this embodiment, the assimilation module in the processor can also implement each process that can be implemented in the embodiment of the paleoclimate data assimilation method of the present invention, and achieve the same beneficial effects. To avoid repetition, it will not be elaborated here.

[0132] The embodiments of the present application have been described above with reference to the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present application, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the present invention and the claims, and all belong to the protection scope of the present invention.

Claims

1. An analog-based offline ensemble Kalman filter paleoclimate data assimilation method, characterized in that First, according to specific criteria, the prior ensemble members are screened from the state variable samples x simulated in a set of control experiments using the observation y. Then, according to the update formula of the ensemble square root filter, the obtained prior ensemble members are updated through the Kalman gain matrix to obtain the posterior ensemble mean and the posterior ensemble perturbation The specific criteria are as follows: based on each state variable sample x of the state variable samples x j the principle of the minimum root mean square error or the maximum correlation coefficient with respect to the observation y; The data assimilation method specifically includes the following steps: Step 1: Given a set of state variable samples x simulated by a control experiment and an observation y; Step 2: Select prior ensemble members according to different criteria before assimilating the observation; Before assimilation observations, the state variable sample x is first interpolated into the observation y, and then, based on each state variable sample x of the state variable sample x j According to the principle that the root mean square error relative to the observation y is the smallest or the correlation coefficient is the largest, the initial N ordered samples selected from the state variable sample x form the prior ensemble members; Step 3: Use the obtained prior ensemble members to assimilate the observation; Use the square root filter to assimilate the observation \(y\) with the error covariance matrix \(R\), and update the posterior ensemble mean first as well as the \(i\)-th posterior ensemble perturbation for \(i = 1,\ldots,N\); then add the posterior ensemble mean and the posterior ensemble perturbation to obtain \(N\) posterior ensemble members.

2. The analog-based offline ensemble Kalman filter paleoclimate data assimilation method according to claim 1, wherein When the criterion for selecting prior ensemble members from the state variable samples x is that each state variable sample x of the state variable samples x j has the smallest root mean square error relative to the observation y, each state variable sample x j The root mean square error RMSE relative to y is expressed as: where: the observation \(y\) represents a \(p\times1\) observation variable; \(y_m\) m m represents the \(m\)-th observation variable in the observation \(y\); \(H(x\) j,m j,m ) represents the conversion of the state variable sample \(x\) j j to the observation space \(y\) m m , that is, the estimate of the observation \(y\) j j obtained from the state variable sample \(x\) m m ; Meanwhile, each sample of the N prior ensemble members is sorted in ascending order according to the corresponding root mean square error RMSE.

3. The analog-based offline ensemble Kalman filter paleoclimate data assimilation method according to claim 1, characterized in that, When the criterion for selecting prior ensemble members from the state variable samples x is that each state variable sample x of the state variable samples x j has the largest correlation coefficient with respect to the observation y, each state variable sample x j The correlation coefficient with respect to y is expressed as: where: the observation \(y\) represents a \(p\times1\) observation variable; \(y'\) represents the observation spatial anomaly field obtained by subtracting the spatial mean from the observation \(y\); \(y'\) m represents the \(m\) -th variable in the observation spatial anomaly field \(y'\); \(H(x j,m )'\) represents the anomaly field of the observation estimate obtained by subtracting its spatial mean from the estimate of the observation \(y\) obtained from the state variable sample \(x j ; meanwhile, each sample of the \(N\) prior ensemble members is sorted in descending order according to the corresponding correlation coefficient. m ​ 4. The analog-based offline ensemble Kalman filter paleoclimate data assimilation method according to claim 2 or 3, characterized in that Posterior ensemble mean The update formula is as follows: Posterior ensemble perturbation The update formula is as follows: In the formula: represents the ensemble mean of the N prior members obtained in Step 2; ρ is the localization matrix, represents the Schur product; X f is the background covariance P f = X f X fT is the square root of denotes the ensemble perturbation of the i-th member of the N ensemble prior members obtained in step 2, H2 is the observation operator that maps the model variables to the observation variables, and H1 is the Jacobian matrix of the partial derivative of the observation with respect to the model variables.

5. An offline ensemble Kalman filter paleoclimate data assimilation system based on analogy, characterized in that, Including: An acquisition module for acquiring an observation y whose error covariance matrix to be assimilated is R; An assimilation module built based on the assimilation framework of the ensemble Kalman filter; Before assimilating the observations, the assimilation module first interpolates the state variable sample x into the observation y, and then, based on the principle that each state variable sample x of the state variable sample x has the smallest root mean square error or the largest correlation coefficient relative to the observation y, the first N ordered samples selected from the state variable sample x form the prior ensemble members; j The first N ordered samples selected from the state variable sample x according to the principle of the smallest root mean square error or the largest correlation coefficient relative to the observation y form the prior ensemble members; At the assimilation moment, the assimilation module uses the square root filter to assimilate the observation y with the error covariance matrix R, and first updates the posterior ensemble mean and the i-th posterior ensemble perturbation where i = 1, …, N; then the posterior ensemble mean and the posterior ensemble perturbation are added together to obtain N posterior ensemble members.

6. The analog offline ensemble Kalman filter paleoclimate data assimilation system according to claim 5, wherein The criterion for the assimilation module to select prior ensemble members from the state variable samples x is that each state variable sample x of the state variable samples x j is sorted in descending order of the correlation coefficient with respect to the observation y; Each state variable sample x j The correlation coefficient relative to y is expressed as: where: the observation \(y\) represents a \(p\times1\) observation variable; \(y'\) represents the observation spatial anomaly field obtained by subtracting the spatial average from the observation \(y\); \(y' m represents the \(m\)th variable in the observation spatial anomaly field \(y'\); \(H(x j,m )'\) represents the anomaly field of the observation estimate obtained by subtracting its spatial average from the estimate of the observation \(y\) obtained from the state variable sample \(x j . m ​ 7. The analog offline ensemble Kalman filter paleoclimate data assimilation system according to claim 5, characterized in that Each sample of the N prior ensemble members selected by the assimilation module from the state variable samples x is sorted in ascending order of the root mean square error RMSE of each state variable sample x j with respect to y; wherein, each state variable sample x j The root mean square error RMSE relative to y is as follows: where: the observation \(y\) represents a \(p\times1\) observation variable; \(y\) m represents the \(m\) -th observation variable in the observation \(y\); \(H(x\) j,m ) represents the conversion of the state - variable sample \(x\) j to the observation space \(y\) m , that is, the estimate of the observation \(y\) j obtained from the state - variable sample \(x\) m .

8. The analog offline ensemble Kalman filter paleoclimate data assimilation system according to claim 6 or 7, characterized in that The posterior ensemble mean at the assimilation time of the assimilation module and the posterior ensemble perturbation have the following update formulas respectively: In the formula: represents the ensemble mean of the N prior members obtained in Step 2; ρ is the localization matrix, represents the Schur product; X f is the background covariance P f = X f X fT is the square root of, denotes the ensemble perturbation of the i-th member of the N ensemble prior members obtained in step two, H2 is the observation operator that maps the model variables to the observation variables, and H1 is the Jacobian matrix of the partial derivative of the observation with respect to the model variables.

9. An electronic device, characterized in that, Including: At least one processor, at least one memory, a communication interface, and a bus; wherein, the processor, the memory, and the communication interface complete communication with each other through the bus; The communication interface is used for information transmission between this electronic device and communication devices of other electronic devices; the memory stores program instructions executable by the processor, and the processor can execute the method described in claim 1 by invoking the program instructions.

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