Atmosphere data assimilation method, device and equipment and storage medium

Abstract

The invention provides an atmosphere data assimilation method and device, equipment and a storage medium. Relates to the technical field of computer science and atmospheric science fusion. The method comprises the following steps: adding a cost function, priori estimation and the gradient of the cost function into a gradient-based descent algorithm, adding posteriori estimation, and constructing a four-dimensional variation and ensemble Kalman filtering combined model based on Bayesian priori information; and carrying out data assimilation on atmosphere data based on the four-dimensional variation and ensemble Kalman filtering combined model. According to the method, an artificial intelligence technology is combined, especially deep learning and a Bayesian optimization adaptive algorithm are adopted, a traditional data assimilation algorithm is enhanced and optimized, and the method can be widely applied to prediction of extreme weather events such as high temperature and heat waves. Through assimilation of historical data and real-time observation data, the prediction precision of the future climate change trend is significantly improved, and more powerful support is provided for extreme weather early warning and decision making.

Description

Technical Field

[0001] This application relates to the field of the integration of computer science and atmospheric science, especially in the cross-field of data assimilation, deep learning, numerical analysis, and extreme climate analysis and prediction. In particular, it relates to an atmospheric data assimilation method, device, equipment, and storage medium. Background Art

[0002] Data assimilation technology has been widely used in the field of atmospheric science, especially in meteorological forecasting, climate modeling, environmental monitoring, etc. By combining observational data with numerical models, data assimilation can effectively improve prediction accuracy. Currently, in the field of atmospheric data assimilation, the following several common technologies mainly exist:

[0003] Kalman filtering is one of the earliest and most basic data assimilation methods, especially suitable for linear systems. Its basic idea is to estimate the mean and variance of the system state and adjust the predicted value by combining the current observational data. This method has a long application history in numerical weather forecasting and is usually used for real-time monitoring and short-term forecasting. However, its application is usually limited to low-dimensional systems or approximately linear systems. For high-dimensional, large-scale problems, especially atmospheric models, its efficiency is low, and it may face numerical instability.

[0004] EnKF is a Kalman filtering method based on the ensemble idea. By using multiple "samples" or "ensembles" to estimate the statistical characteristics of the system state, it avoids the difficulties encountered by the Kalman filtering method in high-dimensional problems. EnKF generates multiple state samples (ensembles) from a set of initial states and uses these samples to calculate the covariance matrix and optimize the data results. The EnKF method can effectively handle high-dimensional nonlinear systems and is more computationally efficient, especially suitable for real-time data assimilation processes. It is widely used in the fields of meteorology, oceanography, environmental monitoring, etc., especially playing an important role in numerical weather forecasting. However, at the same time, EnKF depends on a large number of ensemble members, and the computational resource requirements are high. In some extreme weather situations, such as when modeling complex weather systems, EnKF may face convergence problems.

[0005] Variational assimilation is an assimilation method based on the optimization idea. Its goal is to minimize the error between the model prediction and the observational data, usually by minimizing an objective function (such as a cost loss function). In atmospheric data assimilation, the variational assimilation method is usually applied to numerical weather forecasting models and can handle more complex nonlinear and high-dimensional systems. Currently, the widely used ones are still three-dimensional variational assimilation (3D-Var) and four-dimensional variational assimilation (4D-Var). However, both of the above two methods have high requirements for computational resources. For this reason, some related variant methods have been proposed to improve efficiency.

[0006] The method of combining four-dimensional variational and ensemble Kalman filtering (4DEnVar) is an improved method that combines variational assimilation and ensemble Kalman filtering (EnKF). It estimates the statistical properties of the system by introducing the ensemble method of EnKF and combines the variational method to optimize the initial conditions, thus improving the computational efficiency while ensuring high accuracy. Currently, 4DEnVar is also considered an excellent method that combines the accuracy of 4D-Var and the efficiency of EnKF, and it can achieve efficient data assimilation in complex systems such as weather forecasting. By using the ensemble idea in the variational framework, 4DEnVar can effectively reduce the computational cost while providing high accuracy, so this method is also the most widely used method in the field of data assimilation currently.

[0007] The main technologies in the current field of atmospheric data assimilation include classical Kalman filtering, variational assimilation methods, ensemble Kalman filtering (EnKF), and its derivative 4DEnVar method. These technologies have their own advantages and disadvantages and are suitable for different application scenarios and computational resources. In recent years, with the improvement of computing power and the development of artificial intelligence technology, deep learning and machine learning methods have begun to be introduced into the field of data assimilation, greatly expanding the application scope and effect of assimilation technologies. Therefore, the artificial intelligence-enhanced data assimilation technology proposed in this application will pay more attention to improving computational efficiency, accuracy, and the ability to handle nonlinear and high-dimensional systems, especially in the fields of high-temperature heatwave prediction and extreme climate change prediction, etc., which have important application potential. Summary of the Invention

[0008] This application provides an atmospheric data assimilation method, device, equipment, and storage medium, aiming to combine artificial intelligence technologies, especially deep learning and Bayesian optimization adaptive algorithms, to enhance and optimize traditional data assimilation algorithms, and can be widely applied to the prediction of extreme weather events such as high-temperature heatwaves. By assimilating historical data and real-time observation data, the prediction accuracy of future climate change trends is significantly improved, providing more powerful support for extreme weather warnings and decision-making.

[0009] In a first aspect, this application provides an atmospheric data assimilation method, including:

[0010] Adding a cost function, a prior estimate, and the gradient of the cost function to a gradient-based descent algorithm, and adding a posterior estimate to construct a combined model of four-dimensional variational and ensemble Kalman filtering based on Bayesian prior information;

[0011] Based on the combined model of four-dimensional variational and ensemble Kalman filtering, perform data assimilation on atmospheric data.

[0012] In a possible design, adding a cost function, a prior estimate, and the gradient of the cost function to a gradient-based descent algorithm includes:

[0013] The gradient of the cost function is given by:

[0014]

[0015] where ▽J(x0) represents the gradient of the cost function, x0 represents an optimized initial state vector expected to be found, B represents the background error covariance matrix, and x b represents the prior distribution of the state vector at time 0 of the state, represents a diagonal matrix composed of the observation error covariance matrix R of the overall time states from 0 to N represents the observed data, represents the observed data;

[0016] Using the following formula

[0017] ▽(x T Ax) = 2Ax; ▽(f(x) T Af(x)) = 2J(f) T Af(x) (2)

[0018] where, ▽(x T Ax) is the background field adjustment amount in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. ▽(f(x) T Af(x)) represents the joint action term of the background error covariance and the observation deviation in the gradient of the objective function. x represents a general parameter, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function between the background state, the observed data, and the state error, and J(f) represents the minimization function required in the optimization process;

[0019] Express J as the Jacobian determinant:

[0020]

[0021] where, represents the cost function of the observation deviation at the initial time. h0 represents h0(x0), which is the projection of the observation space at the initial time; m0 represents m0(x0), which is the time evolution of the model state; J(h i ) = h i , represents the linearized observed data, J(m i ) = m i , represents the tangent linear model data, that is, J(h i ) and J(m i ) are evaluated at x i ; J(h N (m 0→N(x0))) represents the observed deviation cost function after pattern integration; J(h N )J(m N-1 )…J(m0) represents the chain product of Jacobian matrices in gradient calculation, used to adjust the initial field to minimize the overall error; N represents the final moment to end the assimilation;

[0022] It can be obtained according to Equation (3):

[0023]

[0024] Among them, M t,0 = M t-1 M t-2 …M0

[0025] In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and its 0 to N respectively represent the model error covariance matrices under different time states; H0 represents the observation space projection at the initial moment, H1 represents the observation operator at time t = 1, H N represents the observation constraint at the end of the time window, M0 represents the single-time-step pattern integration operator, which describes the dynamic propagation of the initial error; M N,0 represents the integration chain within the time window, supporting multi-time-step observation constraints and flow-dependent difference modeling;

[0026] Define the preprocessing matrix U to satisfy B = UU T , after the Taylor expansion of h(X b + U w ) in the cost function, the cost function is expressed as:

[0027]

[0028] In the formula, J(w) represents the optimization objective function, w represents the optimization variable, representing the state increment or perturbation;

[0029] The gradient function of the cost function is expressed as:

[0030]

[0031] In the formula, ▽J(w) represents the gradient operator for the objective function;

[0032] Given a set of m joint state parameter vectors, the expression of the perturbation matrix is defined as:

[0033]

[0034] In the formula, X' b is defined as the perturbation matrix, Denotes the mean of the model output data in multiple time states, X b,i represents the model output data in the i-th time state;

[0035] The m set members X in Equation (8) b come from previous predictions or a known distribution N(X b , B), and using X b , approximate the background or prior error covariance matrix, expressed as:

[0036] B ≈ X b ′(X b ′) T (9)

[0037] By defining the use of the matrix X b , as a preprocessing matrix and transforming it into the ensemble space; then where w is a vector of length m;

[0038] In the case where the loss function and its gradient are as shown in the following formulas (10) and (11):

[0039]

[0040] The covariance matrix of the background state X b is approximated as: Approximated as:

[0041]

[0042] Derive the modified loss function ▽J(w):

[0043]

[0044] In the formula, Y' b represents the first derivative of the background state increment.

[0045] In a possible design, the posterior estimate is added in the following way:

[0046] By analyzing the error covariance matrix P a we get:

[0047]

[0048] In the formula, K represents the Kalman gain matrix, I represents the identity matrix, X' a represents the first derivative of the analyzed state data, and P b represents the background error covariance matrix, which describes the error and uncertainty of the background state estimate;

[0049] The Kalman gain matrix is expressed as:

[0050]

[0051] According to Equation (16), in all the following content, use Y b to approximate, so as to avoid calculating the tangent linear model and the linearized observation operator, where the analysis error covariance matrix becomes:

[0052]

[0053] Use Equation (18):

[0054]

[0055] Use to rewrite the original matrix, and obtain:

[0056]

[0057] In the formula, X' a satisfies

[0058] Define the expression of the posterior perturbation matrix as:

[0059]

[0060] In the formula, X a,i represents the numerical value of the analysis state X a at the i-th time state;

[0061] By substituting the posterior ensemble, we have:

[0062]

[0063] In the formula, X' a,i represents the first derivative of X a,i .

[0064] In a second aspect, the present application provides an atmospheric data assimilation device, and the device includes:

[0065] A model construction module, configured to add a cost function, a prior estimate, and a gradient of the cost function to a gradient-based descent algorithm, and add a posterior estimate to construct a combined model of four-dimensional variational and ensemble Kalman filtering based on Bayesian prior information;

[0066] A data assimilation module, configured to perform data assimilation on atmospheric data based on the combined model of four-dimensional variational and ensemble Kalman filtering.

[0067] Further, the model construction module is further configured to:

[0068] The gradient of the cost function is given by:

[0069]

[0070] where ▽J(x0) represents the gradient of the cost function, x0 represents an optimized initial state vector to be found, B represents the background error covariance matrix, and x b represents the prior distribution of the state vector at time 0 of the state, represents a diagonal matrix composed of the observation error covariance matrix R of the overall time states 0 to N, represents the observed data, represents the observed data;

[0071] Using the following formula:

[0072] ▽(x T Ax) = 2Ax; ▽(f(x) T Af(x)) = 2J(f) T Af(x) (2)

[0073] where ▽(x T Ax) is the background field adjustment in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. ▽(f(x) T Af(x)) represents the joint action term of the background error covariance and the observation deviation in the gradient of the objective function. x represents ordinary parameters, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function between the background state, the observed data, and the state error, and J(f) represents the minimization function required in the optimization process;

[0074] Express J as the Jacobian determinant:

[0075]

[0076] where represents the cost function of the observation deviation at the initial time. h0 represents h0(x0), which is the projection of the observation space at the initial time; m0 represents m0(x0), which is the time evolution of the model state; J(h i ) = h i , represents the linearized observed data, J(m i ) = m i , represents the tangent linear model data, that is, J(h i ) and J(m i ) are evaluated at x i ; J(h N (m 0→N (x0))) represents the cost function of the observation deviation after model integration; J(h N )J(mN-1 )…J(m0) represents the Jacobian matrix chain product in gradient calculation, which is used to adjust the initial field to minimize the overall error; N represents the final moment to end the assimilation;

[0077] It can be obtained from Equation (3):

[0078]

[0079] In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and its 0 to N respectively represent the model error covariance matrices under different time states; H0 represents the observation space projection at the initial moment, H1 represents the observation operator at time t = 1, and H N represents the observation constraint at the end of the time window, and M0 represents the single time step model integration operator, which describes the dynamic propagation of the initial error; M N,0 represents the integration chain within the time window, which supports multi-moment observation constraints and flow-dependent difference modeling;

[0080] Define the preprocessing matrix U to satisfy B = UU T , after the Taylor expansion of h(X b +U w ) in the cost function, the cost function is expressed as:

[0081]

[0082] In the formula, J(w) represents the optimization objective function, w represents the optimization variable, which represents the state increment or perturbation;

[0083] The gradient function of the cost function is expressed as:

[0084]

[0085] In the formula, ▽J(w) represents the gradient operator for the objective function;

[0086] Given a set of m joint state parameter vectors, the expression of the perturbation matrix is defined as:

[0087]

[0088] In the formula, X' b is defined as the perturbation matrix, represents the mean of the model output data under multiple time states, and X b,i represents the model output data of the i-th time state;

[0089] The m set members X in Equation (8) b come from previous predictions or known distributions N(Xb , B), using X b , approximate the background or prior error covariance matrix, expressed as:

[0090] B ≈ X b ′(X b ′) T (9)

[0091] By defining the use of matrix X b , as a preprocessing matrix and transform it into the ensemble space; then where w is a vector of length m;

[0092] In the case where the loss function and its gradient are as shown in the following formulas (10) and (11):

[0093]

[0094] For the covariance matrix of the background state X b approximate it as:

[0095]

[0096] Obtain the modified loss function ▽J(w):

[0097]

[0098] In the formula, Y' b represents the first derivative of the background state increment.

[0099] Furthermore, the model building module is further configured to:

[0100] By analyzing the error covariance matrix P a obtain:

[0101]

[0102] In the formula, K represents the Kalman gain matrix, I represents the identity matrix, X' a represents the first derivative of the analysis state data, and P b represents the background error covariance matrix, which describes the error and uncertainty of the background state estimate;

[0103] The Kalman gain matrix is expressed as:

[0104]

[0105] According to equation (16), in all subsequent content, use Y b ​approximate to avoid calculating the tangent linear model and the linearized observation operator, where the analysis error covariance matrix becomes:

[0106]

[0107] Using formula (18):

[0108]

[0109] Use to rewrite the original matrix, obtaining:

[0110]

[0111] where X' a satisfies

[0112] Define the expression of the posterior perturbation matrix as:

[0113]

[0114] where X a,i represents the numerical value of the analysis state X a at the i-th time state;

[0115] By substituting the posterior ensemble, we have:

[0116]

[0117] where X' a,i represents the first derivative of X a,i with respect to.

[0118] In a third aspect, an embodiment of the present application provides an electronic device, including: at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, so that the at least one processor executes the atmospheric data assimilation method described in the first aspect above and various possible designs of the first aspect.

[0119] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, in which computer-executable instructions are stored, and when a processor executes the computer-executable instructions, the atmospheric data assimilation method described in the first aspect above and various possible designs of the first aspect is implemented.

[0120] In a fifth aspect, an embodiment of the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, the atmospheric data assimilation method described in the first aspect above and various possible designs of the first aspect is implemented.

[0121] The atmospheric data assimilation method, device, equipment and storage medium provided by this application have at least the following beneficial effects:

[0122] This application solves the problems of high general computing resource requirements and unsatisfactory final effects in current data assimilation. By introducing the information of the Bayesian posterior perturbation matrix, it is possible to better compare and select the assimilated data, thereby significantly improving the accuracy of the data set in subsequent models and enhancing the training effect of the model.

[0123] Specifically, 4DEnVar makes the background error and the observation error reach an independent state by introducing the Bayesian optimization process, so as to avoid ignoring extreme meteorological data due to the model blindly pursuing the minimization of the loss function during the operation process; at the same time, in the deep learning part enhanced by AI, the perturbed observation method is adopted, so that each member of DA uses different observation errors to achieve and comply with the statistics of the observation errors. Compared with the high demand for high-level computing power in WRF-DA in traditional methods, this application adds AI deep learning to the operation process of the loss function, and through the Bayesian optimization process and enhanced error statistical modeling, avoids the missing of extreme data and the gradual accumulation of errors during the operation process of the loss function, ensuring the stability and accuracy of the final result. While improving the data assimilation accuracy, this application also greatly reduces the problem of excessive time and material consumption in the operation process of the assimilation model. Description of the Drawings

[0124] The drawings here are incorporated into the specification and constitute a part of this specification, showing the embodiments in line with this application, and are used together with the specification to explain the principles of this application.

[0125] Figure 1 It is a flowchart of an atmospheric data assimilation method provided by an embodiment of this application;

[0126] Figure 2 It is an image of the probability density distribution of the prior, posterior, and true values of four parameters during the data assimilation process provided by an embodiment of this application;

[0127] Figure 3 It is a comparison chart of the root mean square error between the assimilated data and the reference data provided by an embodiment of this application; among them, (a), the initial reference data (smoother); (b), the reference data set contains extreme meteorological elements;

[0128] Figure 4 It is a comparison of RMSE and its probability density distribution image during the assimilation process of the extreme meteorological data set provided by an embodiment of this application;

[0129] Figure 5 It is a schematic structural diagram of an atmospheric data assimilation device provided by an embodiment of this application.

[0130] Through the above-mentioned drawings, specific embodiments of the present application have been shown, and will be described in more detail hereinafter. These drawings and written descriptions are not intended to limit the scope of the concept of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by reference to specific embodiments. Detailed Embodiments

[0131] Exemplary embodiments will be described in detail herein, and examples thereof are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0132] In the technical solution of the present application, the processing of information such as financial data or user data, including collection, storage, use, processing, transmission, provision, and disclosure, complies with the provisions of relevant laws and regulations and does not violate public order and good customs.

[0133] It should be noted that in the embodiments of the present application, some industry-existing solutions such as certain software, components, models, etc. may be mentioned. They should be considered exemplary, and their purpose is only to illustrate the feasibility in the implementation of the technical solution of the present application, but it does not mean that the applicant has already or necessarily used this solution.

[0134] The technical solution of the present application and how the technical solution of the present application solves the above technical problems will be described in detail below with specific embodiments. These several specific embodiments below can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below with reference to the drawings.

[0135] Based on artificial intelligence enhancement, deep learning is combined with data assimilation to overcome the problem that the current data assimilation process consumes too much computing power and to improve the convergence of the assimilation problem to achieve the regional minimum loss function. For example, the high computing power and long running time required for running under the WRF-DA model; for Pytorch-based data assimilation tools such as OpenDA, DAPPER, PDAF, and TorchDA, there are large biases in extreme data assimilation processing, ignoring the requirements for the accuracy of extreme meteorological elements. At the same time, it is crucial that these data assimilation tools are mainly applicable to the explicit prediction and observation functions of the background state in the assimilation context. Existing data assimilation tools are still largely unable to fully handle the prediction and observation models represented by deep neural networks. Based on this, the embodiment of the present application provides an atmospheric data assimilation method, which is a new method that combines the 4DEnVar data assimilation algorithm with deep learning, which will help to provide a more advanced, comprehensive, accurate and simple solution for data assimilation.

[0136] Specifically, Figure 1 is a flowchart of an atmospheric data assimilation method provided by an embodiment of the present application. As Figure 1 shown, the atmospheric data assimilation method includes steps S10 to S20.

[0137] S10. Add the cost function, prior estimate, and gradient of the cost function to the gradient-based descent algorithm, and add the posterior estimate to construct a combined model of four-dimensional variational and ensemble Kalman filter based on Bayesian prior information.

[0138] S20. Based on the combined model of four-dimensional variational and ensemble Kalman filter, perform data assimilation on atmospheric data.

[0139] The atmospheric data assimilation method provided in this embodiment uses the combined method of four-dimensional variational and ensemble Kalman filter (4DEnVar) as the main data assimilation method. By combining Bayesian test information and the atmospheric physical state, background field data with smaller deviations is generated, improving the prediction ability of the subsequent AI model for extreme weather (such as extreme high temperature heatwaves). This embodiment also conducts research using meteorological data provided by ERA5, providing a large amount of research data for the verification of the data assimilation model.

[0140] The core of this method lies in constructing a combined 4D-Var and Ensemble Kalman Filter (4DEnVar) model based on Bayesian prior information. Initially, the original minimum loss matrix in the 4D-Var algorithm is optimized. Subsequently, by adding prior estimation, cost function, and the gradient of the cost function to the gradient-based descent algorithm, posterior estimation can be added on the basis of the 4DEnVar algorithm. Compared with the conventional 4DEnVar algorithm, the 4DEnVar algorithm enhanced by artificial intelligence in this embodiment considers more differences between extreme data and relatively stable data during the data assimilation process. Through the iteration of deep learning, the assimilated data obtained through training is used to learn and predict error statistics. Especially in high-dimensional problems, it reduces the demand for computing resources, and at the same time can effectively avoid the defect that the existing data assimilation methods blindly pursue the minimum loss function during the assimilation process, resulting in the inability to obtain extreme weather data ultimately, so as to improve the prediction fidelity and promote the dynamic update of the model state.

[0141] First, by adding the cost function, prior estimation, and the gradient of the cost function to the gradient-based descent algorithm, the diagonal matrix R in the loss function can be found in this part, and at this time the gradient of the cost function is given by the following formula:

[0142]

[0143] In the formula, ▽J(x0) represents the gradient of the cost function, x0 represents an optimized initial state vector expected to be found by this algorithm, B represents the background error covariance matrix, x b represents the prior distribution of the state vector at time 0, represents a diagonal matrix composed of R (observation error covariance matrix) for the overall time states from 0 to N, represents the observation data (the transformation from the state variable to the observation space), represents the observation data.

[0144] Among them, this embodiment uses the following formula:

[0145] ▽(x T Ax) = 2Ax; ▽(f(x) T Af(x)) = 2J(f) T Af(x) (2)

[0146] In the formula, ▽(x T Ax) can be understood as the background field adjustment amount in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. ▽(f(x) TAf(x) represents the joint action term of the background error covariance and the observation deviation in the gradient of the objective function, x represents the ordinary parameter, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function among the background state, the observation data, and the state error, and J(f) represents the minimization function required in the optimization process.

[0147] Here, J is the Jacobian determinant.

[0148]

[0149] In the formula, represents the cost function of the observation deviation at the initial time. h0 represents h0(x0), which is the observation space projection at the initial time; m0 represents m0(x0), which is the time evolution of the model state; J(h i ) = h i , represents the linearized observation data, J(m i ) = m i , represents the tangent linear model data, that is, J(h i ) and J(m i ) take values at x i ; J(h N (m 0→N (x0))) represents the cost function of the observation deviation after model integration; J(h N )J(m N-1 )…J(m0) represents the chain product of the Jacobian matrices in the gradient calculation, used to adjust the initial field to minimize the overall error; N represents the final assimilation end time.

[0150] And according to the above formula, it can be obtained that:

[0151]

[0152] Among them, M t,0 = M t-1 M t-2 …M0

[0153] In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and its 0 to N respectively represent the model error covariance matrices under different time states; H0 represents the observation space projection at the initial time, H1 represents the observation operator at time t = 1, H N represents the observation constraint at the end of the time window, M0 represents the single-time-step model integration operator, which describes the dynamic propagation of the initial error; M N,0 represents the integration chain within the time window, supporting multi-time observation constraints and flow-dependent difference modeling.

[0154] Here, in this embodiment, it is defined that the preprocessing matrix U satisfies B = UU T , and through the Taylor expansion of h(X b + U w ) in the cost function, the cost function can be further approximated as:

[0155]

[0156] In the formula, J(w) represents the optimization objective function, w represents the optimization variable, representing the state increment or perturbation.

[0157] And the gradient function of the cost function is given as:

[0158]

[0159] In the formula, ▽J(w) represents the gradient operator for the objective function.

[0160] Then, since the square root of a matrix is not uniquely existent, there will be multiple choices for the preprocessing partial matrix U in this embodiment. This embodiment selects to use deep learning based on AI reinforcement, and selects the most suitable preprocessing matrix through multiple iterations to ensure the accuracy of the Bayesian posterior information in the subsequent part.

[0161] Furthermore, in this embodiment, given a set of m joint state parameter vectors, the expression of the perturbation matrix can be defined as:

[0162]

[0163] b In the formula, X' is defined as the perturbation matrix, b,i represents the mean of the model output data under multiple time states, and X

[0164] represents the model output data at the i-th time state. b The m set members X b in the above formula can come from previous predictions (in this case, X b is the average of the m set members) or from a known distribution N(X b , B), such that X b = X b . Using X

[0165] B≈X b ′(X b ′) T (9)

[0166] Subsequently, by defining and using the matrix X b , as the preprocessing matrix of this embodiment and transforming it into the ensemble space, where w is a vector of length m.

[0167] X0 defined in the above way can effectively reduce problems in cases where the state or parameter vector is much larger than the ensemble size, and can also regularize problems in cases where the state or parameter vector contains elements of a contrasting order of magnitude. Even if the loss function becomes in the following form:

[0168]

[0169] and the gradient is:

[0170]

[0171] Here, in this embodiment, for the background state X b the covariance matrix of is approximated as

[0172]

[0173] Furthermore, the modified loss function ▽J(w) is obtained

[0174]

[0175] where Y' b represents the first derivative of the background state increment.

[0176] In the following part, this embodiment calculates the posterior information through a Bayesian optimization process to generate a reference posterior perturbation matrix. Among them, through the analysis of the error covariance matrix P a there is

[0177]

[0178] where K represents the Kalman gain matrix, I represents the identity matrix, X' a represents the first derivative of the analyzed state data, and P b represents the background error covariance matrix, which describes the error and uncertainty of the background state estimate.

[0179] The matrix K is the Kalman gain matrix, which is expressed as:

[0180]

[0181] According to the above formula, in all the following content, Y b can be used for approximation to avoid calculating the tangent linear model and the linearized observation operator, where the analysis error covariance matrix becomes:

[0182]

[0183] Use Equation (18):

[0184]

[0185] Use to rewrite the original matrix

[0186]

[0187] and satisfy

[0188] Finally, the expression of the posterior perturbation matrix is defined in this embodiment as

[0189]

[0190] In the formula, X a,i represents the analysis state X at the i-th time state a value of.

[0191] Therefore, here, in this embodiment, by substituting the posterior ensemble, we have:

[0192]

[0193] In the formula, X' a,i represents the first derivative of X a,i of.

[0194] Therefore, in addition to avoiding the calculation of the linearized observation operator and the tangent linear model, the 4DEnVar algorithm of the present invention also provides more comparison methods for the operator of data assimilation for the quality of the model results under the reference conditions of providing posterior uncertainty information.

[0195] The traditional 4DEnVar algorithm assumes that the errors of state variables are Gaussian distributed and uses a linear model to describe the errors and observation errors. However, in actual situations, the errors may have a complex non-linear structure. Therefore, in this embodiment, a deep neural network is used to learn the non-linear distribution characteristics of the state variable errors. These networks can automatically capture the complex patterns of errors through training samples (the differences between the assimilation model simulation data and the original reference data); at the same time, a generative adversarial network is used to generate an error field that conforms to the observed data to provide a more accurate error estimate, and the trained deep learning model is embedded in the 4DEnVar data assimilation process to replace the traditional error modeling and optimization steps. During the backpropagation process, the neural network can accelerate the optimization of the objective loss function of the 4DEnVar algorithm by adaptively adjusting the learning rate and weights, and thus optimize the entire assimilation process.

[0196] Based on the 4DEnVar model that combines four-dimensional variational and ensemble Kalman filtering based on Bayesian prior information constructed in the above manner, data assimilation is performed on the meteorological data provided by ERA5, and the results are as follows Figures 2 to 4 shown, where Figure 2 are the probability density distribution images of the prior, posterior, and true values of four parameters during the data assimilation process. The four parameters are p1, p2, k1, and k2 respectively. Figure 3 is a comparison chart of the root mean square error between the data after assimilation iteration and the reference data. Figure 4 is a comparison of RMSE and its probability density distribution image during the assimilation process of the extreme meteorological data set.

[0197] According to the above example, it can be obtained that the method provided in this embodiment can efficiently assimilate extreme climate phenomena (such as heatwaves) and other related meteorological data. This model effectively combines the Bayesian optimization process, the 4DEnVar data assimilation model, and deep learning in AI to generate better-quality post-assimilation stage data, thus making up for the problems of inaccurate post-assimilation data of current extreme meteorological elements and excessive computing power requirements during the assimilation process. This innovation ensures the accuracy and availability of data through multiple iterations of AI deep learning, playing a good role in the prediction process of various types of meteorological elements in subsequent large AI models.

[0198] In addition, this application also allows the operator to train a neural network for the state transformation function and the observation operator model to replace the traditional numerical model. This novel data assimilation method provides the ability to perform four-dimensional variational and ensemble Kalman filtering (4DEnVar) data assimilation using a non-explicit transformation function (represented by a neural network). This tool solves an important limitation faced by current data assimilation tools, that is, current tools are difficult to handle such non-explicit functions. By changing parameters such as the number of observations, the observation network, the ensemble size, the observation error, the numerical model, the reference trajectory, the inflation factor, and the localization length, the operator can create the data assimilation scenario they need as required.

[0199] In summary, the key to this method lies in its specific structure and implementation manner in aspects such as combining deep learning models and the 4DEnVar data assimilation method that includes Bayesian optimization process analysis. The detailed description and explanation of these key elements will help ensure the full protection of this technology.

[0200] The embodiment of this application also provides an atmospheric data assimilation device, as shown in Figure 5 shown, the atmospheric data assimilation device includes:

[0201] The model construction module 501 is configured to add a cost function, a prior estimate, and the gradient of the cost function to a gradient-based descent algorithm, and add a posterior estimate to construct a combined model of four-dimensional variational and ensemble Kalman filtering based on Bayesian prior information;

[0202] The data assimilation module 502 is configured to perform data assimilation on atmospheric data based on the combined model of four-dimensional variational and ensemble Kalman filtering.

[0203] In some embodiments, the model construction module is further configured to:

[0204] The gradient of the cost function is given by the following formula:

[0205]

[0206] In the formula, ▽J(x0) represents the gradient of the cost function, x0 represents an optimized initial state vector to be found, B represents the background error covariance matrix, and x b represents the prior distribution of the state vector at time 0 of the state, represents a diagonal matrix composed of the observation error covariance matrix R of the overall time states 0 to N, represents the observation data, represents the observation data;

[0207] Using the following formula:

[0208] ▽(x T Ax) = 2Ax; ▽(f(x) T Af(x)) = 2J(f) T Af(x) (2)

[0209] In the formula, ▽(x T Ax) is the background field adjustment amount in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. ▽(f(x) T Af(x)) represents the joint action term of the background error covariance and the observation deviation in the objective function gradient. x represents a general parameter, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function between the background state, the observation data, and the state error, and J(f) represents the minimization function required in the optimization process;

[0210] Express J as the Jacobian determinant:

[0211]

[0212] In the formula, The cost function representing the observation deviation at the initial time, where h0 denotes h0(x0), which is the projection of the observation space at the initial time; m0 denotes m0(x0), which is the time evolution of the model state; J(h i ) = h i , representing the linearized observation data, and J(m i ) = m i , representing the tangent linear model data, that is, J(h i ) and J(m i ) are evaluated at x i ; J(h N (m 0→N (x0))) represents the cost function of the observation deviation after model integration; J(h N )J(m N-1 )…J(m0) represents the chain product of the Jacobian matrices in the gradient calculation, used to adjust the initial field to minimize the overall error; N represents the final time when assimilation ends;

[0213] It can be obtained from Equation (3):

[0214]

[0215]

[0216] In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and its values from 0 to N respectively represent the model error covariance matrices under different time states; H0 represents the projection of the observation space at the initial time, H1 represents the observation operator at time t = 1, and H N represents the observation constraint at the end of the time window, M0 represents the single-time-step model integration operator, which describes the dynamic propagation of the initial error; M N,0 represents the integration chain within the time window, supporting multi-time-step observation constraints and flow-dependent difference modeling;

[0217] Define the preprocessing matrix U to satisfy B = UU T . After the Taylor expansion of h(X b + U w ) in the cost function, the cost function is expressed as:

[0218]

[0219] In the formula, J(w) represents the optimization objective function, w represents the optimization variable, representing the state increment or perturbation;

[0220] The gradient function of the cost function is expressed as:

[0221]

[0222] In the formula, ▽J(w) represents the gradient operator for the objective function;

[0223] Given a set of m joint state parameter vectors, the expression of the perturbation matrix is defined as:

[0224]

[0225] In the formula, X' b is defined as the perturbation matrix, represents the mean of the model output data at multiple time states, and X b,i represents the model output data at the i-th time state;

[0226] The m set members X in formula (8) b come from previous predictions or a known distribution N(X b , B), and using X b , approximate the background or prior error covariance matrix, expressed as:

[0227] B≈X b ′(X b ′) T (9)

[0228] By defining the use of the matrix X b , as a preprocessing matrix and transforming it into the ensemble space; then where w is a vector of length m;

[0229] In the case where the loss function and its gradient are as shown in formulas (10) and (11) below:

[0230]

[0231] The covariance matrix of the background state X b is approximated as:

[0232]

[0233] The modified loss function ▽J(w) is obtained:

[0234]

[0235] In the formula, Y' b represents the first-order derivative of the background state increment.

[0236] In some embodiments, the model construction module is further configured to:

[0237] Obtained by analyzing the error covariance matrix P a :

[0238]

[0239] In the formula, K represents the Kalman gain matrix, I represents the identity matrix, and X' a represents the first derivative of the analyzed state data, and P b represents the background error covariance matrix, which describes the error and uncertainty of the background state estimate;

[0240] The Kalman gain matrix is expressed as:

[0241]

[0242] According to Equation (16), in all the following content, use Y b to approximate it in order to avoid calculating the tangent linear model and the linearized observation operator, where the analysis error covariance matrix becomes:

[0243]

[0244] Use Equation (18):

[0245]

[0246] Use to rewrite the original matrix, and obtain:

[0247]

[0248] In the formula, X' a satisfies

[0249] Define the expression of the posterior perturbation matrix as:

[0250]

[0251] In the formula, X a,i represents the value of the analyzed state X at the i-th time state X a ;

[0252] By substituting the posterior ensemble, we have:

[0253]

[0254] In the formula, X' a,i represents the first derivative of X a,i .

[0255] An embodiment of the present application provides an electronic device. The electronic device may include: a processor and a memory. Among them, the processor and the memory can communicate; Exemplarily, the processor and the memory communicate through a communication bus.

[0256] The processor executes the computer-executable instructions stored in the memory, enabling the processor to execute the solutions in the above embodiments. The processor may be a general-purpose processor, including a Central Processing Unit (CPU), a network processor (NP), etc.; it may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0257] The communication bus may be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into an address bus, a data bus, a control bus, etc. The transceiver is used to implement communication between the database access device and other computers (such as clients, read-write libraries, and read-only libraries). The memory may include Random Access Memory (RAM), and may also include non-volatile memory.

[0258] The electronic device provided by the embodiments of this application may be the terminal device in the above embodiments.

[0259] The embodiments of this application also provide a computer-readable storage medium, in which computer instructions are stored. When the computer instructions run on a computer, the computer is enabled to execute the technical solutions of the atmospheric data assimilation method in the above embodiments.

[0260] The embodiments of this application also provide a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium, and when at least one processor executes the computer program, the technical solutions of the atmospheric data assimilation method in the above embodiments can be implemented.

[0261] In several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces, and the indirect coupling or communication connection of devices or modules can be in electrical, mechanical or other forms.

[0262] The modules described as separate components may or may not be physically separated. The components shown as modules may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to implement the solution of this embodiment.

[0263] In addition, in each embodiment of the present application, the functional modules can be integrated in a processing unit, or each module can exist physically alone, or two or more modules can be integrated in a unit. The unit formed by the above modules can be implemented in the form of hardware or in the form of a hardware plus software functional unit.

[0264] The integrated modules implemented in the form of software functional modules can be stored in a computer-readable storage medium. The above software functional modules are stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods in each embodiment of the present application.

[0265] It should be understood that the above processor can be a central processing unit (Central Processing Unit, abbreviated as CPU), and can also be other general-purpose processors, digital signal processors (Digital Signal Processor, abbreviated as DSP), application specific integrated circuits (Application Specific Integrated Circuit, abbreviated as ASIC), etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in combination with the invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

[0266] The memory may include high-speed RAM memory and may also include non-volatile storage NVM, such as at least one disk memory, and can also be a USB flash drive, a mobile hard disk, a read-only memory, a disk or an optical disc, etc.

[0267] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0268] The above storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disc. The storage medium can be any available medium accessible by a general-purpose or special-purpose computer.

[0269] An exemplary storage medium is coupled to the processor, enabling the processor to read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an Application Specific Integrated Circuits (ASIC). Of course, the processor and the storage medium can also exist as discrete components in an electronic control unit or a master control device.

[0270] Those of ordinary skill in the art can understand that all or part of the steps for implementing the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments; and the foregoing storage medium includes: various media such as ROM, RAM, magnetic disks, or optical discs that can store program codes.

[0271] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not intended to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. An atmospheric data assimilation method, characterized in that: The method comprises: The cost function, prior estimate and the gradient of the cost function are added to the gradient-based descent algorithm, and the posterior estimate is added to construct a four-dimensional variational and ensemble Kalman filter combined model based on Bayesian prior information; Based on the four-dimensional variational and ensemble Kalman filter combined model, data assimilation is performed on the atmospheric data.

2. The atmospheric data assimilation method according to claim 1, characterized in that: The cost function, the prior estimate, and the gradient of the cost function are added to the gradient-based descent algorithm, including: The gradient of the cost function is given by: In the formula, represents the gradient of the cost function, x0 represents an optimized initial state vector that is expected to be found, B represents the background error covariance matrix, x b represents the prior distribution of the state vector at state 0, represents a diagonal matrix composed of the observation error covariance matrix R of the overall time state 0~N, represents the simulated observation value after the observation operator maps the initial state vector x0 of the mode to the observation space, Represents a collection of actual observation data; Using the following formula In the formula, is the background field adjustment in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. represents the joint effect of the background error covariance and the observation bias in the objective function gradient, x represents the common parameter, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function between the background state, the observation data and the state error, and J(f) represents the minimization function required in the optimization process; Express J as the Jacobian: In the formula, represents the cost function of the observation deviation at the initial moment, h0 represents h0(x0), which is the observation space projection at the initial moment; m0 represents m0(x0), which is the time evolution of the mode state; J(h i )=h i , represents the linearized observation data, J(m i )=m i , represents the tangent linear model data, that is, J(h i ) and J(m i ) in x i The value at which J(h N (m 0→N (x0))) represents the observation bias cost function after model integration; J(h N )J(m N-1 )...J(m0) represents the Jacobian matrix chain product in the gradient calculation, which is used to adjust the initial field to minimize the overall error; N represents the final end of the assimilation moment; According to formula (3), we can get: Among them, M t,0 =M t-1 M t-2 ...M0 In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and 0 to N represent the error covariance matrix of the model under different time states; H0 represents the observation space projection at the initial moment, H1 represents the observation operator at time t = 1, and H N represents the observation constraint at the end of the time window; M0 represents the single time step mode integration operator, describing the dynamic propagation of the initial error, M N,0 Represents the integral chain within the time window, supporting multi-time observation constraints and flow dependency difference modeling; Define the preprocessing matrix U to satisfy B = UU T , after h(X b +U w ), the cost function is expressed as: In the formula, J(w) represents the optimization objective function, w represents the optimization variable, which represents the state increment or disturbance; The gradient function of the cost function is expressed as: In the formula, represents the gradient operator for the objective function; Given a set of m joint state parameter vectors, the expression defining the perturbation matrix is: Where X' b Defined as the perturbation matrix, represents the mean of the model output data at multiple time states, X b,i It represents the model output data of the i-th time state; The m set members X in formula (8) b From previous predictions or known distributions N(X b ,B), using X b , the approximate background or prior error covariance matrix, expressed as: B≈X′ b (X′ b ) T (9) Using the matrix X by definition b , as the preprocessing matrix and transformed into the integrated space; then Where w is a vector of length m; When the loss function and its gradient are as follows: Background state X b The covariance matrix of Approximately: The modified loss function is obtained In the formula, Y' b Represents the first derivative of the background state increment.

3. The atmospheric data assimilation method according to claim 2, characterized in that: The posterior estimate is added as follows: By the error covariance matrix P a The analysis yields: Where K represents the Kalman gain matrix, I represents the identity matrix, and X' a Represents the first-order derivative of the analyzed state data, P b represents the background error covariance matrix, describing the error and uncertainty of the background state estimation; The Kalman gain matrix is ​​expressed as: According to formula (16), in all the following contents, Use Y b To approximate, in order to avoid calculating the tangent linear model and linearizing the observation operator, the analytical error covariance matrix becomes: Using formula (18): use To rewrite the original matrix, we get: Where X' a satisfy The expression for defining the posterior perturbation matrix is: Where, X a,i Indicates the analysis state X at the i-th time state a The value of By substituting the posterior set into: Where X' a,i Represents X a,i The first derivative of .

4. An atmospheric data assimilation device, characterized in that: The device comprises: A model building module is configured to add the cost function, the prior estimate and the gradient of the cost function into a gradient-based descent algorithm, and add the posterior estimate to build a four-dimensional variational and ensemble Kalman filter combined model based on Bayesian prior information; The data assimilation module is configured to perform data assimilation on the atmospheric data based on the four-dimensional variational and ensemble Kalman filter combined model.

5. The atmospheric data assimilation method according to claim 4, characterized in that: The model building module is further configured to: The gradient of the cost function is given by: In the formula, represents the gradient of the cost function, x0 represents an optimized initial state vector that is expected to be found, B represents the background error covariance matrix, x b represents the prior distribution of the state vector at time 0, represents a diagonal matrix composed of the observation error covariance matrix R of the overall time state 0~N, represents the observed data, represents observation data; Use the following formula: In the formula, is the background field adjustment in the observation space, which drives the analysis field to converge to the optimal solution in the subsequent data assimilation process. represents the joint effect of the background error covariance and the observation bias in the objective function gradient, x represents the common parameter, A represents the background observation value after the background field is transformed by the observation operator, f(x) represents the matching function between the background state, the observation data and the state error, and J(f) represents the minimization function required in the optimization process; Express J as the Jacobian: In the formula, represents the cost function of the observation deviation at the initial moment, h0 represents h0(x0), which is the observation space projection at the initial moment; m0 represents m0(x0), which is the time evolution of the mode state; J(h i )=h i , represents the linearized observation data, J(m i )=m i , represents the tangent linear model data, that is, J(h i ) and J(m i ) in x i The value at which J(h N (m 0→N (x0))) represents the observation bias cost function after model integration; J(h N )J(m N-1 )…J(m0) represents the Jacobian matrix chain product in the gradient calculation, which is used to adjust the initial field to minimize the overall error; N represents the final end of assimilation; According to formula (3), we can get: In the formula, represents a mathematical mapping that maps the state of the model from the state space to the observation space; M represents the model error covariance matrix, which describes the error structure of the model itself, and its 0~N represent the error covariance matrix of the model under different time states; H0 represents the observation space projection at the initial moment, H1 represents the observation operator at time t=1, and H N represents the observation constraint at the end of the time window, M0 represents the single time step mode integration operator, describing the dynamic propagation of the initial error; M N,0 Represents the integral chain within the time window, supporting multi-time observation constraints and flow dependency difference modeling; Define the preprocessing matrix U to satisfy B = UU T , after h(X b +U w ), the cost function is expressed as: In the formula, J(w) represents the optimization objective function, w represents the optimization variable, which represents the state increment or disturbance; The gradient function of the cost function is expressed as: In the formula, represents the gradient operator for the objective function; Given a set of m joint state parameter vectors, the expression defining the perturbation matrix is: Where X' b Defined as the perturbation matrix, represents the mean of the model output data at multiple time states, X b,i It represents the model output data of the i-th time state; The m set members X in formula (8) b From previous predictions or known distributions N(X b ,B), using X b , the approximate background or prior error covariance matrix, expressed as: B≈X′ b (X′ b ) T (9) Using the matrix X by definition b , as the preprocessing matrix and transformed into the integrated space; then Where w is a vector of length m; When the loss function and its gradient are as follows: Background state X b The covariance matrix of Approximately: The modified loss function is obtained In the formula, Y' b Represents the first derivative of the background state increment.

6. The atmospheric data assimilation method according to claim 5, characterized in that: The model building module is further configured to: By the error covariance matrix P a The analysis yields: Where K represents the Kalman gain matrix, I represents the identity matrix, and X' a Represents the first-order derivative of the analyzed state data, P b represents the background error covariance matrix, describing the error and uncertainty of the background state estimation; The Kalman gain matrix is ​​expressed as: According to formula (16), in all the following contents, Use Y b To approximate, in order to avoid calculating the tangent linear model and linearizing the observation operator, the analytical error covariance matrix becomes: Using formula (18): use To rewrite the original matrix, we get: Where X' a satisfy The expression for defining the posterior perturbation matrix is: Where, X a,i Indicates the analysis state X at the i-th time state a The value of By substituting the posterior set into: Where X' a,i Represents X a,i The first derivative of .

7. An electronic device, characterized in that: include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the atmospheric data assimilation method according to any one of claims 1 to 3.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the atmospheric data assimilation method according to any one of claims 1 to 3.

9. A computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the atmospheric data assimilation method according to any one of claims 1 to 3 is implemented.

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