Multi-ring layer strongly coupled data assimilation method based on cross-media localization correlation function

Abstract

The application provides a multi-sphere strong coupling data assimilation method based on a cross-medium localization correlation function, comprising the following steps: constructing a cross-medium localization correlation function, which is used for uniformly describing data assimilation scenes from weak coupling to strong coupling and from single medium to multi-medium cross; based on the cross-medium localization correlation function, performing localization processing on a background error covariance matrix generated by a coupling mode set to obtain a localized covariance matrix; embedding the localized covariance matrix into a pre-constructed four-dimensional ensemble variational assimilation (4DEnVar) framework to construct a strong coupling assimilation cost function; solving the cost function to obtain an optimal analysis increment, and updating a multi-sphere state according to the optimal analysis increment and a sea-land-air coupling mode. A complete strong coupling data assimilation system is constructed, which can accurately depict the correlation between cross-medium variables and realize efficient and robust assimilation performance.

Description

Technical Field

[0001] This invention relates to the field of multi-sphere data assimilation technology, and in particular to a multi-sphere strongly coupled data assimilation method based on cross-medium localization correlation functions. Background Technology

[0002] In Earth system prediction, data assimilation is a crucial step in fusing observations and models to construct a high-quality initial field. Its core challenge lies in accurately characterizing the complex interactions between multiple spheres, including the atmosphere, ocean, and land surface, thereby constructing an initial field with both high accuracy and consistency within a framework of dynamic coordination and physical conservation. Currently, the main drawback of weakly coupled data assimilation is that its sequential assimilation disrupts real-time feedback between spheres, easily leading to physical inconsistencies at interfaces. This "coupling bias" continuously increases during integration, impairing the reliability of medium- and long-term forecasts. Furthermore, it cannot directly utilize observations to correct states across spheres, limiting information utilization efficiency, and its solution is only globally suboptimal. Strongly coupled assimilation introduces cross-sphere background error covariance (BEC) during the assimilation process, updating the coupled system synchronously as a whole. This allows observational information from one sphere to directly and physically influence the analytical variables of other spheres through cross-sphere background error covariance. Strongly coupled assimilation maintains sphere coupling not only in the model forecasting step but also in the assimilation analysis step. Through the construction of cross-sphere background error covariance (BEC), it promotes the efficient transfer and collaborative utilization of observational information between spheres, simultaneously optimizing the states of multiple spheres, thereby effectively alleviating physical imbalances in key regions such as the land-atmosphere interface. The core bottleneck in the transition of strongly coupled assimilation from theory to operational application lies in how to accurately estimate and effectively utilize the cross-sphere background error covariance (BEC). Estimating BEC based on ensembles has inherent limitations; when the number of ensemble members is much smaller than the dimension of the model state variables, the estimated BEC matrix inevitably contains a large number of spurious long-range correlations. This problem is particularly prominent in coupled models with more variables and higher dimensions. Therefore, localization must be introduced in practical assimilation, i.e., for... Matrices impose constraints on spaces or variables to suppress spurious correlations, thereby ensuring the numerical stability of the assimilation process and the reliability of the analysis results.

[0003] Regarding the construction of localization correlation functions across different spheres, existing techniques have extended the single-sphere Gaspari-Cohn (GC) localization correlation function, developing a multivariate Gaspari-Cohn function. This function is constructed using convolution methods, maintaining the standard GC function within a single sphere. The cross-sphere function is newly constructed, capable of handling background error covariance between different spheres while preserving the positive semidefiniteness of the localization matrix. However, this method defines the localization correlation function formulas for different spheres and localization radii using piecewise functions, resulting in cumbersome formulas and complex implementation. Furthermore, it has only been tested in ideal scenarios and has not been applied to real numerical models. Summary of the Invention

[0004] This invention relates to a multi-sphere strongly coupled data assimilation method based on cross-medium localized correlation functions, in order to solve at least one of the above-mentioned technical problems.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical means: A multi-sphere strongly coupled data assimilation method based on cross-medium localized correlation functions includes the following steps: Construct cross-media localized correlation functions, which are used to uniformly describe data assimilation scenarios from weak coupling to strong coupling and from single medium to multi-media intersection; Based on the cross-medium localized correlation function, the background error covariance matrix of the sample estimate generated by the coupled mode set simulation is localized to obtain the localized covariance matrix. The localized covariance matrix is ​​embedded into a pre-constructed four-dimensional ensemble variational (4DEnVar) framework to construct a cost function for strongly coupled assimilation. The cost function is solved to obtain the optimal analysis increment, and the multi-sphere state is updated synchronously based on the optimal analysis increment and the sea-land-atmosphere coupling model.

[0006] In some embodiments, constructing cross-media localized correlation functions specifically includes: Define the dielectric coupling coefficient , where 0≤ ≤1; When spatial location in coupling mode and When located within the same medium domain, the localized correlation function of that medium itself is used as the cross-medium localized correlation function; Spatial location in coupling mode and When they belong to different media domains, the coupling coefficient of the media is used to determine their relationship. The relevant function values ​​of different media at the interface are combined and calculated.

[0007] In some embodiments, the cross-medium localization correlation function The mathematical expression is: ; in, and Indicates different spatial locations within the coupling mode. This represents the localized correlation function of the atmospheric domain. This indicates the atmospheric domain. express The localized correlation function, express .

[0008] In some embodiments, the cross-medium localization correlation function has backward compatibility, specifically including: When the dielectric coupling coefficient When = 0, the cross-medium localization correlation function degenerates into a classical uncoupled form; When the dielectric coupling coefficient When =1, the cross-medium localization correlation function completely ignores the physical differences between media, which is equivalent to treating heterogeneous media as the same medium.

[0009] In some embodiments, the background error covariance matrix generated by simulation from the set of coupled modes is localized, specifically including: For the cross-medium localized correlation function Matrix decomposition is performed to obtain a localized decomposition matrix, which is applicable to the localized correlation matrix in the case of multiple concentric layers across media. The expression is: ; in, For Kronecker product, Represents the localized correlation matrix of the atmospheric domain. express The localized correlation matrix.

[0010] In some embodiments, after obtaining the decomposition matrix of the localized correlation matrix, the method further includes: Suppose a set of state variable perturbations generated based on the perturbation of the coupled mode set. The corresponding background error covariance matrix is ; After localization, the matrix is ​​transformed into: ; in, The definition of .

[0011] In some embodiments, a scaling factor is introduced during the process of embedding the localized covariance matrix into a pre-constructed four-dimensional ensemble variational (4DEnVar) framework. ω The original set is perturbed and scaled to construct a scaled set. And characterize the analytical increment as This leads to the construction of a strongly coupled assimilation cost function.

[0012] In some embodiments, the method further includes a system integration step, which includes co-integrating the 4DEnVar method with a novel cross-medium efficient localization decomposition scheme and a general observation operator module into a sea-land-atmosphere coupled model platform to construct a complete strongly coupled data assimilation system, and obtaining the analysis field by iteratively calling the coupled model.

[0013] In some embodiments, the system integration step specifically includes: Initial samples are constructed based on sample generation technology; The ocean-land-atmosphere coupled model is driven to carry out ensemble simulation and background simulation. The output results are sent to the observation operator module and, together with the quality-controlled observation data, are input into the 4DEnVar solver equipped with a new cross-medium efficient localization decomposition scheme. The solver iteratively calls the sea-land-atmosphere coupled model to perform the calculation and finally obtains the analysis field; The forecast is driven by the analytical field, and cyclic assimilation is achieved based on the discreteness-preserving sample update strategy.

[0014] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0015] In one or more of the above specific embodiments, the multi-sphere strongly coupled data assimilation method based on cross-medium localization correlation function provided by the present invention has at least the following technical effects: Based on the physical fact that correlations significantly decay in observations of ocean-atmosphere and land-atmosphere interfaces, this method proposes a novel cross-medium correlation function. This function mathematically uniformly describes various cases from weak to strong coupling, and from single-medium to multi-medium intersections, possessing both formal simplicity and physical clarity. It provides a theoretically consistent and potentially applicable solution for localizing the background error covariance in strong coupling assimilation. Within the same medium, it retains the original function form; at different medium interfaces, the correlation decay is characterized by the medium coupling coefficient γ (0 ≤ γ ≤ 1). When γ = 0, the correlation function degenerates into a weakly coupled form; when γ = 1, the physical differences between media are completely ignored, treating heterogeneous media as a single medium.

[0016] A novel cross-medium localized correlation matrix is ​​efficiently decomposed, and based on this, the background error covariance matrix B in multi-sphere strong coupling assimilation is localized, thereby effectively solving the problem of localizing the cross-sphere background error covariance matrix in strong coupling data assimilation.

[0017] By integrating a novel cross-medium localization scheme with an advanced ensemble four-dimensional variational assimilation method and its supporting technologies, and combining it with an ocean-land-air coupling model, a complete strongly coupled data assimilation system is constructed. This system can accurately characterize the correlation between variables in a multi-sphere strongly coupled data assimilation method based on cross-medium localization correlation functions, achieving efficient and robust assimilation performance. Attached Figure Description

[0018] Embodiments of the invention will now be described by way of example only, with reference to the accompanying schematic diagrams, wherein: Figure 1 This is one of the flowcharts for the multi-concentric strongly coupled data assimilation method based on cross-medium localization correlation function provided by the present invention; Figure 2 The second flowchart is for the multi-concentric strongly coupled data assimilation method based on cross-medium localization correlation function provided by the present invention. Figure 3 For different A schematic diagram of the cross-sphere localization correlation function theory in the case of [missing information]; where, Figure 3 (a) is in the atmosphere Points and from the atmosphere to the ocean Point correlation; Figure 3 (b) is in the ocean Points and from the atmosphere to the ocean Point correlation; Figure 4 This is a schematic diagram of the electronic device of the present invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0020] Currently, two main technical paradigms exist internationally: weak coupling and strong coupling assimilation. Weak coupling assimilation, which assimilates each sphere sequentially or independently, is easy to implement and widely operational, but it also severs the inherent real-time physical connections and feedback mechanisms between spheres, easily introducing systemic "coupling bias." This bias accumulates during forecast integration, affecting the physical consistency of medium- and long-term forecasts; essentially, it is a suboptimal, path-dependent approximation. Strong coupling assimilation, on the other hand, synchronously fuses multi-sphere observations within the same assimilation window based on a unified Earth system state vector, and applies physical constraints using a background error covariance matrix that explicitly includes cross-medium covariance. Theoretically, this can yield a globally coordinated, physically balanced optimal analysis field, representing the development direction of next-generation Earth system numerical forecasting. From a scientific evolution perspective, promoting the paradigm shift from weak coupling to strong coupling is not only a necessary requirement for improving cross-scale and cross-sphere forecast consistency, but also a crucial scientific path to deepening the understanding of the Earth system's multi-sphere feedback mechanisms and achieving seamless forecasting and refined process management.

[0021] However, the operational deployment of strongly coupled assimilation faces several fundamental bottlenecks. First, the computational cost is exponential; constructing a high-dimensional background error covariance matrix B across all spheres demands computational resources at an exponential rate. Second, the theory of cross-medium error estimation is still incomplete; the error characteristics and observation frequencies of different spheres (such as the rapidly changing atmosphere and the slowly changing ocean) differ greatly, making it difficult to accurately characterize their cross-covariance. Furthermore, the scarcity of direct observations of key fluxes at the coupling interface further exacerbates the uncertainty in B matrix estimation. Traditional methods relying on finite set simulations are susceptible to sampling noise, easily leading to B matrix distortion and directly affecting the quality of assimilation analysis.

[0022] To address the challenges of modeling high-dimensional, nonlinear Earth systems, the introduction of artificial intelligence (AI) technology has become a noteworthy emerging research direction. For example, some scholars have proposed deep neural networks-ensemble-adjusted Kalman filters, attempting to capture complex nonlinear dependencies between variables using neural networks to improve cross-component error estimation in strongly coupled assimilation. Ideal experiments show that this method can improve analytical accuracy when the ensemble size is limited, especially for ocean variables. However, this type of research is currently in the preliminary theoretical verification stage, with a heavy computational burden. Its generalization ability and robustness under real complex models and multi-source observation conditions still need systematic testing. Overall, it remains a relatively preliminary attempt in cutting-edge exploration.

[0023] In summary, weakly coupled assimilation, with its mature technology and robust operation, supports the current mainstream operational forecasting system; while strongly coupled assimilation represents the future direction of pursuing higher accuracy in physical consistency. However, its development still faces multiple constraints, including high computational costs, an imperfect cross-sphere error estimation theory, and a scarcity of direct observations of interface fluxes. In recent years, data-driven methods, represented by artificial intelligence, have provided new ideas for fundamental problems such as error modeling and complex relationship representation, but most related research is still in the proof-of-concept or ideal experiment stage, and its transferability and reliability to real complex systems still need to be further tested.

[0024] However, if we re-examine the problem of strongly coupled data assimilation based on the widely used four-dimensional variational assimilation framework, its core can be expressed as the minimization of the following cost function: (1) (2) (3) (4) in, As background scene, Background error covariance matrix (abbreviated as) -matrix), for The observation vector at time t, The observation error covariance matrix, For the observation operator, S+1 is the assimilation window. Observation frequency within the forecast model. Initial state Integrate forward to the observation time: It is important to clarify that, based on the theoretical framework of the aforementioned optimal estimation, four-dimensional variational assimilation (4DVar) itself does not affect the forecast model. Whether it's a single component or a coupled form, no prior restrictions are imposed. In other words, a coupled model encompassing multiple spheres such as the atmosphere, ocean, and land surface can naturally be substituted into the framework as a holistic dynamic constraint. Simultaneously, the observation operator... Theoretically, it also has the ability to simultaneously fuse multi-source observation data from different spheres, provided that their errors are mutually independent or have a known covariance structure (this is often assumed in practice). (This is a diagonal matrix). Mathematically, strong coupling assimilation is theoretically feasible: its essence is to treat the coupled modes as a unified dynamical system and jointly assimilate observations from all relevant spheres within the same variational framework to seek a globally optimal solution. The universality of this framework lays a solid mathematical foundation for extending 4DVar to strongly coupled systems. At the same time, the above analysis clearly reveals the core challenge in implementing this framework: for coupled systems containing multiple spheres, a cross-sphere background error covariance matrix must be constructed that accurately characterizes the complex error correlation structure within and between each component. This is not only a key scientific challenge that must be overcome to move strong coupling assimilation from theory to practice, but also a major bottleneck currently facing the development of this field.

[0025] However, existing research on cross-sphere background error covariance still has significant limitations. For example, analysis of the cross-sphere covariance between air temperature, snow temperature, and land surface temperature based on single-point observation experiments reveals significant flow-dependent characteristics and influence from weather processes and land surface scenarios. Some scholars have used the WRF-Noah coupled model and NMC method to study the spatiotemporal variations of the covariance between soil moisture and atmospheric state variables, aiming to assess the potential impact of satellite soil moisture assimilation on atmospheric analysis. Other scholars have explored the covariance characteristics of land surface temperature and atmospheric variables during the rainy season. Most of these studies are limited to specific variables, specific regions, or idealized cases. While they reveal the complexity and flow-dependent nature of covariance, they fail to establish universally applicable and operationally feasible cross-sphere error models. Furthermore, studies using simplified conceptual models in some existing technologies have shown that the effectiveness of cross-sphere covariance is highly dependent on large sample sets and exhibits significant asymmetry—that is, observations of rapidly changing spheres can significantly improve the state of slowly changing spheres, while the improvement is limited. This further highlights the difficulty of accurately estimating and utilizing cross-sphere covariance in real-world coupled systems. Overall, while existing technologies have touched upon some characteristics of cross-sphere error covariance, most remain at the stage of case studies, ideal experiments, or simplified models, lacking a generalized modeling scheme that is applicable to real-world complex coupled systems and can be commercially deployed. How to break through the current localized and case-based research paradigm and develop a cross-sphere background error covariance model that balances physical constraints and computational feasibility remains a profound scientific problem that must be solved for strong coupling assimilation to move towards practical applications.

[0026] In fact, the current understanding of the background error covariance matrix The estimation mainly relies on two types of statistical methods: the classical NMC method and error statistics techniques based on ensemble forecasts. Among them, the ensemble forecast method can effectively capture the flow-dependent error characteristics, which helps to construct a more physically consistent and evolutionarily coordinated background error covariance. For coupled models, this method is particularly useful for characterizing the complex error cross-correlation relationships within and between different spheres.

[0027] However, ensemble estimation of cross-sphere background error covariance has inherent limitations; when the number of ensemble members is much smaller than the dimension of the model state variables, the estimated... The matrix inevitably contains a large number of spurious long-range correlations. This problem is particularly prominent in coupling modes with more variables and higher dimensions. Therefore, localization must be introduced in practical assimilation, i.e., for... - Matrices impose constraints on spaces or variables to suppress spurious correlations, thereby ensuring the numerical stability of the assimilation process and the reliability of the analysis results: (5) In the formula, the symbol " "" represents the Schür product (also known as element-wise product) between matrices of the same dimension, i.e., if A = B Let C be ai,j = bi,j × ci,j, where A, B, and C are matrices of the same dimension, and ai,j, bi,j, and ci,j are the (i,j)th elements of the corresponding matrices. For a single medium (such as the interior of the atmosphere), C is constructed as a fifth-order piecewise function (GC function, or other forms of distance revision functions can also be used), and its correlation decreases smoothly with the ratio of spatial distance di,j to localized radius d0, s = di,j / d0. (6) However, in multi-sphere strongly coupled assimilation, existing mature localization functions are only applicable to the internal workings of a single physical medium. For ensemble error covariance matrices spanning multiple spheres such as the atmosphere, ocean, and land surface, there is currently a lack of universally accepted and physically reasonable localization schemes. This deficiency makes it difficult to reliably constrain the cross-sphere background error covariance in coupled systems, becoming a key algorithmic bottleneck in the transition of strongly coupled assimilation from methodological research to practical applications. This highlights a core issue: although ensemble simulation can provide the background error covariance matrix... While providing reasonable estimates, their effective application in practical assimilation fundamentally depends on the reliable implementation of localization. Inaccurate or low-quality cross-sphere error covariance will directly lead to a decline in assimilation performance or even system failure. This explains why traditional assimilation often decouples different spheres, and has become a major constraint on the slow development of strongly coupled assimilation. Therefore, developing a localized correlation matrix and its supporting schemes that can simultaneously characterize the error correlation structure of multiple spheres and across media has become a key issue that urgently needs to be addressed.

[0028] Based on the mature experience of applying ensemble localization techniques in single-medium systems, this invention returns to this path and extends it to multi-medium coupled systems. Although the background error covariance matrix can be estimated through coupled mode ensemble simulation. The core bottleneck remains the efficient localization of the cross-medium error covariance. An ideal cross-medium localization framework should be backward compatible, naturally encompassing the single-medium case within a unified mathematical formulation, thus maintaining consistency and continuity with classical theory. Based on the physical fact that correlations significantly decay in ocean-atmosphere and land-atmosphere interface observations, this invention proposes a novel cross-medium correlation function. This function mathematically describes various cases from weak to strong coupling, and from single-medium to multi-medium intersections, possessing both formal simplicity and physical clarity. It provides a theoretically consistent and potentially applicable solution for the localization of background error covariance in strong coupling assimilation.

[0029] In summary, in strongly coupled data assimilation, although ensemble methods can effectively construct the background error covariance that varies with manifold patterns, However, traditional localization schemes are only applicable to single-sphere systems and are difficult to directly extend to multi-sphere systems. Existing cross-sphere localization research is mostly based on idealized models or case studies, and has not yet formed a unified, concise, and operationally applicable framework. Therefore, developing a universal localization scheme that combines physical rationality and computational feasibility remains a core challenge in this field.

[0030] Based on the above principles, in one specific implementation, such as Figure 1 As shown, the multi-sphere strongly coupled data assimilation method based on cross-medium localization correlation function provided by this invention includes the following steps: S110: Construct cross-media localized correlation functions, which are used to uniformly describe data assimilation scenarios from weak coupling to strong coupling and from single medium to multi-media intersection; S120: Based on the cross-medium localized correlation function, the background error covariance matrix of the sample estimate generated by the coupled mode set simulation is localized to obtain the localized covariance matrix. S130: Embed the localized covariance matrix into a pre-constructed four-dimensional ensemble variational (4DEnVar) framework to construct a cost function for strongly coupled assimilation; S140: Solve the cost function to obtain the optimal analysis increment, and update the multi-sphere state synchronously based on the optimal analysis increment and the sea-land-air coupling model.

[0031] Thus, the method provided by this invention achieves strong coupling data assimilation between multiple spheres (atmosphere, ocean, and land surface). By using a unified cross-medium localization correlation function, it overcomes the problem that traditional single-medium assimilation cannot effectively transmit interface information and cross-medium constraints. Combined with the 4DEnVar framework, it can significantly improve the analysis accuracy and physical consistency of the state variables of each medium in the coupled system while maintaining spatiotemporal consistency.

[0032] The construction of cross-media localized correlation functions specifically includes: Define the dielectric coupling coefficient , where 0≤ ≤1; Spatial location in coupling mode and When located within the same medium domain, the localized correlation function of that medium itself is used as the cross-medium localized correlation function; Spatial location in coupling mode and When they belong to different media domains, the coupling coefficient of the media is used to determine their relationship. The relevant function values ​​of different media at the interface are combined and calculated.

[0033] Thus, by introducing an adjustable dielectric coupling coefficient It enables continuous description of scenarios with different coupling strengths, which is compatible with traditional single-medium assimilation and supports strong coupling assimilation. It maintains the original physical and statistical properties in the same medium region and achieves smooth transition and energy transfer through interface correlation functions in the cross-medium region, avoiding abrupt changes or discontinuities at the interface.

[0034] The above cross-media localization correlation function The mathematical expression is: ; in, and Indicates different spatial locations within the coupling mode. This represents the localized correlation function of the atmospheric domain. This indicates the atmospheric domain. express The localized correlation function, express .

[0035] A cross-medium localized correlation function is defined in explicit mathematical form, making it computable and verifiable. The segmented definition ensures automatic switching of the corresponding correlation model in different media regions. In the interface region, controllable coupling is achieved through the medium coupling coefficient and the interface correlation value, providing a clear basis for subsequent matrix operations and numerical implementation.

[0036] Furthermore, the cross-medium localization correlation function has backward compatibility, specifically including: When the dielectric coupling coefficient When = 0, the cross-medium localization correlation function degenerates into a classical uncoupled form; When the dielectric coupling coefficient When =1, the cross-medium localization correlation function completely ignores the physical differences between media, which is equivalent to treating heterogeneous media as the same medium.

[0037] It is understandable that backward compatibility is achieved through parametric design, that is... When the value is 0, it reverts to traditional single-media assimilation, which facilitates comparison and verification with existing systems. When the value is 1, it achieves the maximum cross-media information fusion; intermediate values ​​support the adjustment of coupling strength as needed, improving the universality and engineering configurability of the method.

[0038] The background error covariance matrix generated by simulation from the coupled mode set is localized, specifically including: For the cross-medium localized correlation function Matrix decomposition is performed to obtain a localized decomposition matrix, which is applicable to the localized correlation matrix in the case of multiple concentric layers across media. The expression is: ; in, For Kronecker product, Represents the localized correlation matrix of the atmospheric domain. express The localized correlation matrix.

[0039] By transforming high-dimensional and complex cross-media correlation functions into locally localized correlation matrices through matrix decomposition, and by using Kronecker product to handle cross-media combinatorial relationships, storage and computational complexity are significantly reduced, making strong coupling assimilation under large-scale coupling modes engineering feasible.

[0040] Furthermore, after obtaining the decomposition matrix of the localized correlation matrix, the method further includes: Suppose a set of state variable perturbations generated based on the perturbation of the coupled mode set. The corresponding background error covariance matrix is ; After localization, the matrix is ​​transformed into: ; in, The definition of .

[0041] In this way, by providing a specific calculation form for the localized covariance, the matrix Hadamard product (element-wise multiplication) is transformed into an equivalent decomposable form, which facilitates efficient implementation in numerical models through matrix operations, while maintaining the positive definiteness, symmetry, and physical rationality of the background error covariance.

[0042] In the process of embedding the localized covariance matrix into the pre-constructed four-dimensional ensemble variational (4DEnVar) framework, a scaling factor is introduced. ω The original set is perturbed and scaled to construct a scaled set. And characterize the analytical increment as Furthermore, a strongly coupled assimilation cost function is constructed. By introducing a scaling factor ω, adaptive adjustment of the set perturbation amplitude is achieved, alleviating the sampling error and covariance underestimation problems caused by insufficient set members. The analysis increment is expressed as the product of the set and the localization factor, making the cost function structure clear and the gradient easy to calculate, which is conducive to efficient optimization solutions.

[0043] The method also includes a system integration step, which involves co-integrating the 4DEnVar method with a novel cross-medium efficient localization decomposition scheme and a general observation operator module into a sea-land-atmosphere coupled model platform to construct a complete strongly coupled data assimilation system. The system then iteratively calls the coupled model to perform calculations and obtain the analysis field. This elevates algorithmic innovation to a system-level solution, forming an end-to-end strongly coupled data assimilation system through deep integration with the general observation operator and coupled model platform. It supports multi-source observation data input and synchronous updates of multi-sphere models, exhibiting good modularity, portability, and scalability.

[0044] Specifically, the system integration steps include: Initial samples are constructed based on sample generation technology; The ocean-land-atmosphere coupled model is driven to carry out ensemble simulation and background simulation. The output results are sent to the observation operator module and, together with the quality-controlled observation data, are input into the 4DEnVar solver equipped with a new cross-medium efficient localization decomposition scheme. The solver iteratively calls the sea-land-atmosphere coupled model to perform the calculation and finally obtains the analysis field; The forecast is driven by the analytical field, and cyclic assimilation is achieved based on the discreteness-preserving sample update strategy.

[0045] The key processes and module interactions in system integration are designed through a closed loop of ensemble simulation-observation operator-solver-analysis field-forecasting-sample update, which ensures the dynamic consistency and long-term cyclic stability of the assimilation analysis and forecasting stages, and is conducive to operational use.

[0046] In one or more of the above specific embodiments, the multi-sphere strongly coupled data assimilation method based on cross-medium localization correlation function provided by the present invention has at least the following technical effects: Based on the physical fact that correlations significantly decay in observations of ocean-atmosphere and land-atmosphere interfaces, this method proposes a novel cross-medium correlation function. This function mathematically describes all cases from weak to strong coupling, and from single-medium to multi-medium intersections, combining formal simplicity with physical clarity. It provides a theoretically consistent and potentially applicable solution for localizing the background error covariance in strong coupling assimilation: within the same medium, it retains the original function form; at different medium interfaces, it characterizes the decay of correlation through the medium coupling coefficient γ (0≤γ≤1). When γ=0, the correlation function degenerates into a weakly coupled form; when γ=1, it completely ignores the physical differences between media, treating heterogeneous media as the same medium.

[0047] A novel cross-medium localized correlation matrix is ​​efficiently decomposed, and based on this, the background error covariance matrix B in multi-sphere strong coupling assimilation is localized, thereby effectively solving the problem of localizing the cross-sphere background error covariance matrix in strong coupling data assimilation.

[0048] By integrating a novel cross-medium localization scheme with an advanced ensemble four-dimensional variational assimilation method and its supporting technologies, and combining it with a sea-land-air coupling model, a complete strongly coupled data assimilation system is constructed. This system can accurately characterize the correlation between cross-medium variables and achieve efficient and robust assimilation performance.

[0049] To facilitate understanding, the following will be combined with... Figure 2 The technical solution provided by this invention will be described in general.

[0050] like Figure 2 As shown, it is divided into the following four steps: S1: Development of novel cross-medium correlation functions and their coupling with fast localization schemes.

[0051] This invention first extends mature single-medium localization methods to multi-medium coupled systems. The key lies in constructing a correlation function suitable for cross-medium scenarios to achieve efficient localization of error covariance. An ideal framework should be backward compatible, naturally encompassing the single-medium case within a unified mathematical formulation. Based on the physical understanding that "correlation at multi-concentric interfaces significantly decreases," this invention proposes the following novel cross-medium correlation function to support the assimilation of strongly coupled data (this embodiment focuses on the land...). )-gas( ) and the sea )-gas( The localized relationships in coupled systems are similar in the ocean-land system and will not be elaborated further. It should also be noted that the cross-medium interactions in land-atmosphere and ocean-atmosphere coupled systems are mainly vertical, while those in the ocean-land system are primarily horizontal. (7) in Indicates different spatial locations in the coupling mode. Its correlation coefficient. If the two points are located in the same medium (such as belonging to the atmospheric domain), then... The correlation coefficient of the medium itself is used directly. or Calculation; if two points belong to different media, then a media coupling coefficient is introduced. This coefficient is used to characterize the attenuation of correlation at the interface. It is typically much smaller than 1 to reflect the weak coupling characteristics of cross-medium interactions. Specifically, if we take... =0 means there is no instantaneous correlation between variables in different media; in this case, the coupled correlation degenerates into the classic uncoupled form. If we take =1, which completely ignores the physical differences between media, equivalent to treating heterogeneous media as the same medium. Thus, it can be seen that the constructed cross-media correlation function mathematically uniformly describes various cases from weak coupling to strong coupling, and from single medium to multi-media intersection, possessing both concise mathematical expression and clear physical connotation.

[0052] Figure 3 For different A schematic diagram of the cross-sphere localization correlation function theory in the case of [missing information]; where, Figure 3 (a) is in the atmosphere Points and from the atmosphere to the ocean Point correlation; Figure 3 (b) is in the ocean Points and from the atmosphere to the ocean Point correlation, the horizontal axis is the correlation coefficient, and the vertical axis is the vertical position; the number of atmospheric and ocean layers are set to 38 and 16 respectively, the interface position is 0, the height of the top of the atmosphere is 100 meters, and the depth of the bottom of the ocean is 80 meters.

[0053] This function uses the medium coupling coefficient The regulatory effect achieves a smooth transition of related features under different coupling states, and its variation law and physical meaning are as follows: Figure 2 As shown, when two points are located in the same medium, their correlation coefficient is consistent with the traditional single-medium case; however, if the two points belong to different media, the correlation coefficient changes due to the medium coupling coefficient. The correlation coefficient exhibits a significant decay at the interface.

[0054] Furthermore, based on the reconstruction decomposition approach for single-medium correlation matrices, this invention proposes a decomposition scheme for the localized correlation matrix (7) applicable to multi-layer cross-medium scenarios: (8) in, For Kronecker product.

[0055] Localized decomposition matrix of a single medium (such as atmosphere or ocean / land surface) By analyzing the correlation matrix of a single medium The decomposition yields: (9) This led to the development of a novel cross-medium correlation function and its coupling with a fast localization scheme.

[0056] After obtaining the decomposition matrix of the localized correlation matrix, subsequent calculations can be performed based on the 4DVar extended localization framework: Let the set of state variable perturbations be generated based on the perturbation of the coupled mode set. The corresponding background error covariance matrix can be estimated as follows: This requires the perturbation set to maintain a sufficient variance magnitude to ensure that... An accurate estimate. After localization, the matrix is ​​transformed into: ; in, The definition of .

[0057] S2: Coupling of a novel cross-medium correlation function-based fast localization decomposition with a four-dimensional set variational assimilation method (4DEnVar).

[0058] To simultaneously satisfy the high-precision approximation of the joint tangent linear operator, a sufficiently large constant scaling factor is introduced. ω (In reality, the vast majority of 4DEnVar takes...) ω =1), scaling the original perturbation set yields a new set. This compresses the sample variance to a sufficiently small order of magnitude to satisfy the infinitesimal perturbation assumption required for the tangent linear approximation. The linear representation of the analysis increment is then used. The expression for the localized background error covariance Substituting the cost functions of 4DVar and i4DVar, we get:

[0059] (10) The 4DEnVar problem can thus be solved within a unified localization framework. This method introduces a scaling factor. ωThis effectively distinguishes the different roles of the perturbation set in estimating the background error covariance and the approximate tangent linear operator, thereby alleviating the theoretical contradiction caused by the inconsistent perturbation amplitude requirements in the traditional ensemble variational method. Based on different solution schemes of formula (10), various 4DEnVar implementation paths can be further derived, which will not be discussed in detail here.

[0060] S3: The four-dimensional ensemble variational assimilation method (4DEnVar) with a novel cross-media efficient localization decomposition scheme is integrated with the general observation operator module into the coupled mode platform to build a strongly coupled data assimilation system.

[0061] The four-dimensional ensemble variational assimilation method (4DEnVar), equipped with a novel cross-media efficient localization decomposition scheme, and its supporting technologies (including sample generation and update techniques), will be integrated with a general observation operator module into the ocean-land-atmosphere coupled model platform to construct a complete strongly coupled data assimilation system. The specific process is as follows: First, initial samples are constructed based on sample generation technology; then, the ocean-land-atmosphere coupled model is driven to perform ensemble and background simulations, and the output results are sent to the observation operator module, along with quality-controlled observation data, and input into the 4DEnVar solver equipped with the novel cross-media efficient localization decomposition scheme; this solver iteratively calls the ocean-land-atmosphere coupled model to perform calculations, ultimately obtaining the analysis field; then, the analysis field drives the forecast, and cyclic assimilation is achieved based on a discreteness-preserving sample update strategy.

[0062] S4: Evaluation, verification and application of strongly coupled data assimilation systems.

[0063] Based on the above, a well-constructed, strongly coupled data assimilation system was built. Actual data assimilation experiments were conducted in key regions and on typical weather cases to evaluate, validate, and further verify the system.

[0064] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 4 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and model predictions. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The model predictions of the computer device store static and dynamic information data. The network interface of the computer device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the steps in the above method embodiments.

[0065] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. A specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0066] Corresponding to the above embodiments, this invention also provides a computer storage medium containing one or more program instructions. These one or more program instructions are used to execute the method described above.

[0067] The present invention also provides a computer program product, the computer program product including a computer program, the computer program being stored on a non-transitory computer-readable storage medium, and the computer being able to perform the above-described method when the computer program is executed by a processor.

[0068] In this embodiment of the invention, the processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, 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, or discrete hardware components.

[0069] The various methods, steps, and logic diagrams disclosed in the embodiments of this invention can be implemented or executed. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The processor reads information from the storage medium and, in conjunction with its hardware, completes the steps of the above methods.

[0070] The storage medium can be memory, such as volatile memory or non-volatile memory, or may include both volatile and non-volatile memory.

[0071] Among them, non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory.

[0072] Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (Synchlink DRAM, SLDRAM), and direct memory bus RAM (DRRAM).

[0073] The storage media described in the embodiments of the present invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0074] Those skilled in the art will recognize that, in one or more of the examples above, the functions described in this invention can be implemented using a combination of hardware and software. When applied as software, the corresponding functions can be stored in a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium. Computer-readable media include computer storage media and communication media, wherein communication media include any medium that facilitates the transmission of computer programs from one place to another. Storage media can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0075] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-sphere strongly coupled data assimilation method based on cross-medium localized correlation functions, characterized in that, Includes the following steps: Construct cross-media localized correlation functions, which are used to uniformly describe data assimilation scenarios from weak coupling to strong coupling and from single medium to multi-media intersection; Based on the cross-medium localized correlation function, the background error covariance matrix of the sample estimate generated by the coupled mode set simulation is localized to obtain the localized covariance matrix. The localized covariance matrix is ​​embedded into a pre-constructed four-dimensional set variational assimilation framework to construct a cost function for strongly coupled assimilation. The cost function is solved to obtain the optimal analysis increment, and the multi-sphere state is updated synchronously based on the optimal analysis increment and the sea-land-atmosphere coupling model.

2. The method according to claim 1, characterized in that, Constructing cross-media localized correlation functions, specifically including: Define the dielectric coupling coefficient , where 0≤ ≤1; When spatial location in coupling mode and When located within the same medium domain, the localized correlation function of that medium itself is used as the cross-medium localized correlation function; When spatial location in coupling mode and When they belong to different media domains, the coupling coefficient of the media is used to determine their relationship. The relevant function values ​​of different media at the interface are combined and calculated.

3. The method according to claim 2, characterized in that, The cross-medium localization correlation function The mathematical expression is: ； in, and Indicates different spatial locations within the coupling mode. This represents the localized correlation function of the atmospheric domain. This indicates the atmospheric domain. express The localized correlation function, express .

4. The method according to claim 3, characterized in that, The cross-media localization correlation function has backward compatibility, specifically including: When the dielectric coupling coefficient When = 0, the cross-medium localization correlation function degenerates into a classical uncoupled form; When the dielectric coupling coefficient When =1, the cross-medium localization correlation function completely ignores the physical differences between media, which is equivalent to treating heterogeneous media as the same media.

5. The method according to claim 1, characterized in that, The background error covariance matrix generated by simulation from the coupled mode set is localized, specifically including: For the cross-medium localized correlation function Matrix decomposition is performed to obtain a localized decomposition matrix, which is applicable to the localized correlation matrix in the case of multiple concentric layers across media. The expression is: ； in, For Kronecker product, Represents the localized correlation matrix of the atmospheric domain. express The localized correlation matrix.

6. The method according to claim 5, characterized in that, After obtaining the decomposition matrix of the localized correlation matrix, the method further includes: Suppose a set of state variable perturbations generated based on the perturbation of the coupled mode set. The corresponding background error covariance matrix is ; After localization, the matrix is ​​transformed into: ; in, The definition of .

7. The method according to claim 1, characterized in that, In the process of embedding the localized covariance matrix into a pre-constructed four-dimensional ensemble variational assimilation framework, a scaling factor is introduced. ω The original set is perturbed and scaled to construct a scaled set. And characterize the analytical increment as This leads to the construction of a strongly coupled assimilation cost function.

8. The method according to any one of claims 1-7, characterized in that, The method also includes a system integration step, which involves co-integrating the 4DEnVar method with a novel cross-medium efficient localization decomposition scheme and a general observation operator module into the ocean-land-atmosphere coupled model platform to construct a complete strongly coupled data assimilation system, and obtaining the analysis field by iteratively calling the coupled model.

9. The method according to claim 8, characterized in that, The system integration steps specifically include: Initial samples are constructed based on sample generation technology; The ocean-land-atmosphere coupled model is driven to carry out ensemble simulation and background simulation. The output results are sent to the observation operator module and, together with the quality-controlled observation data, are input into the 4DEnVar solver equipped with a new cross-medium efficient localization decomposition scheme. The solver iteratively calls the sea-land-atmosphere coupled model to perform the calculation and finally obtains the analysis field; The forecast is driven by the analytical field, and cyclic assimilation is achieved based on the discreteness-preserving sample update strategy.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-9.

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