Boundary level hierarchical grid physical constraint variational assimilation method embedded in deep neural networks

Abstract

The application discloses a boundary level grid physical constraint variational assimilation method embedded in a deep neural network, comprising: establishing a momentum equation containing a boundary level grid turbulent friction term, wherein the boundary layer turbulent friction term is simulated through a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function with the momentum equation; training the deep neural network with a dataset constructed from historical numerical weather prediction model simulation results; linearizing the trained deep neural network to obtain a corresponding tangent linear operator and an adjoint operator, and embedding the tangent linear operator and the adjoint operator into the variational assimilation framework cost function; obtaining multi-source remote sensing observation data and a numerical weather prediction model background field, and solving an analysis field by taking minimization of the cost function as an objective, to complete data assimilation. The application can improve the data assimilation and numerical prediction level of disastrous weather such as typhoon, especially the observation assimilation level related to the boundary layer.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric science research and relates to variational assimilation methods under constraints, especially a boundary-level grid physical constraint variational assimilation method embedded with a deep neural network. Background Technology

[0002] High-resolution numerical weather prediction is an important way to improve the early warning capability of severe weather, and its forecasting effect largely depends on the assimilation of observational data to improve the initial field of the model. How to effectively assimilate multi-source remote sensing data (radar, satellite, etc.) has become a current research hotspot, as these data can make up for the shortcomings of conventional observations in terms of spatiotemporal resolution and physical variable detection capabilities.

[0003] Advanced data assimilation methods, through the consistency constraints of physical laws, aim to generate analytical fields that accurately describe the true state of the atmosphere, providing support for numerical weather prediction. Variational methods, or ensemble-variational hybrid assimilation methods based on variational frameworks, often employ weak constraints to introduce dynamic or physical constraints. Some studies have introduced model tendency constraints, diagnostic pressure equation constraints, steady momentum equation constraints, and large-scale analysis constraints into variational methods. While these constraints describe atmospheric dynamic processes, they often neglect the importance of subgrid physical processes that are not resolved.

[0004] For severe weather systems such as typhoons, boundary layer friction is crucial to boundary layer dynamics, determining the vertical structure of the boundary layer wind field and influencing convergence, divergence, and convection triggering. These factors are also very important for the evolution of typhoon structure and intensity. However, current assimilation schemes lack consideration for boundary layer friction effects, leading to incompatibility between assimilation analysis within the boundary layer and model nonlinear dynamics.

[0005] The current WRF (Weather Research and Forecasting) model's WRFDA (WRF data assimilation) assimilation system uses a frictionless assumption in the horizontal momentum equation constraint, which means it does not consider the frictional effects caused by the boundary layer. When applied to severe weather such as typhoons and strong convection, this can lead to deviations in the dynamic balance of the mid-to-low-level pressure field and wind field, resulting in unsatisfactory assimilation of observational data.

[0006] On the other hand, the development of artificial intelligence technology in recent years has brought new opportunities for improving data assimilation. The integration of machine learning and data assimilation is mainly reflected in two aspects: firstly, attempts are being made to construct a fusion framework, based on the unified theoretical foundation of Bayes' theorem, to develop data-driven alternative models based on recurrent neural networks, and to use deep learning to estimate the mode bias of the assimilation system; secondly, machine learning is being applied to improve key components of the assimilation system, such as alternative modeling of assimilation solvers, observation operators, background error covariance, and physical parameterization schemes. These advances are considered a deep integration of machine learning and data assimilation, especially providing new avenues for developing physical constraints. Machine learning simulators can not only accelerate the computation of physical processes, but also more easily develop tangent linear and adjoint models when simulating strongly nonlinear and discontinuous physical processes, thereby meeting assimilation requirements.

[0007] To address the problem that the WRFDA assimilation system cannot characterize the boundary layer turbulent friction effect, it is necessary to explore alternative methods based on machine learning to realize variational weak constraints. A new approach is proposed to establish the boundary layer friction effect in variational constraints using deep neural networks (DNNs). Summary of the Invention

[0008] The present invention aims to at least partially solve one of the technical problems existing in the related art.

[0009] The purpose of this invention is to integrate a deep neural network (DNN) into a variational framework, learn the horizontal wind field tendency contributed by the subgrid turbulent process in the parameterization of boundary layer physical processes through the DNN, and integrate the DNN simulator and its tangent linear and adjoint models into the weakly constrained momentum equation and the corresponding tangent linear and adjoint equations, thereby forming a boundary-level grid physical constraint variational assimilation method embedded with a deep neural network, improving the physical balance of assimilation of severe weather data such as typhoons, and enhancing numerical forecasting capabilities.

[0010] To achieve the above objectives, the present invention provides a boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network, comprising the following steps:

[0011] S1. Establish a momentum equation that includes boundary layer grid turbulent friction terms, wherein the boundary layer turbulent friction terms are simulated by a deep neural network; and construct a weak constraint term for the variational assimilation framework cost function using this momentum equation.

[0012] S2. The deep neural network is trained using a dataset constructed from historical numerical weather prediction model simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables.

[0013] S3. Linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the variational assimilation framework cost function;

[0014] S4. Obtain multi-source remote sensing observation data and the background field of numerical weather prediction model, and solve the analysis field with the goal of minimizing the cost function to complete the data assimilation.

[0015] A further preferred embodiment of the present invention is that the variational assimilation framework cost function in step S1 is expressed as:

[0016] ;

[0017] in, Represents the cost function, To observe the penalty items, This is the background penalty term corresponding to the static background error covariance. The background penalty term is the set of background error covariance. These are the weighting coefficients. It is a weak constraint term, defined as:

[0018] ;

[0019] in, The dynamic weights are a diagonal matrix with all diagonal elements having the same value. The momentum equation, which includes the boundary-level grid turbulent friction term, is expressed as:

[0020] ;

[0021] in, It is a horizontal wind field vector, containing wind field components. and ; It's air pressure. It is the height of position. It is atmospheric density. These are Coriolis parameters; This represents the boundary layer turbulent friction terms in two horizontal directions.

[0022] Preferably, for the boundary layer turbulent friction terms in both horizontal directions... Machine learning operators are used to simulate the horizontal wind field tendency generated by boundary layer parameterization in numerical models. and The boundary layer turbulent friction term in the horizontal momentum equation constraint is characterized by the tendency of the horizontal wind field, and is expressed as:

[0023] ;

[0024] ;

[0025] in, and These are the boundary layer wind tendencies in two horizontal directions obtained through machine learning simulation; the input features of the machine learning model include the horizontal wind components within the boundary layer. and ,temperature Water vapor mixing ratio and surface air pressure ;

[0026] Therefore, the momentum equation can be expressed as:

[0027] ;

[0028] in, Represents machine learning operators.

[0029] As a preferred approach, deep neural networks are used to construct machine learning operators. The deep neural network adopts a fully connected multi-layer neural network architecture, containing N-1 nonlinear layers with activation functions and 1 linear output layer. The output layer outputs the horizontal wind field tendency of the boundary layer. Both the input layer and the hidden layer maintain a fixed network width. The layer neural network operator is represented as:

[0030] ;

[0031] in, For the input vector, For the first The intermediate output of the layer, and They are the first The weight matrix and bias vector of the layer, This is the activation function.

[0032] Preferably, in step S2, the deep neural network is trained using a dataset constructed from historical WRF simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables; specifically:

[0033] Based on historical WRF simulation results, the horizontal wind components of each horizontal grid point within the boundary layer at each time step are extracted. and ,temperature Water vapor mixing ratio and surface air pressure As input to a deep neural network, the next time step and the current time step... , The vertical average difference is used as a label to construct a dataset for training the deep neural network;

[0034] In deep neural network training, mean squared error is used as the loss function, and a learning rate of 10 is used. -3 The Adam optimizer has a batch size of 1024 and a training cycle count of 100.

[0035] Preferably, in step S3, the trained deep neural network is linearized to obtain the corresponding tangent linear operator and adjoint operator; specifically:

[0036] For neural network operators By taking the derivative and applying the chain rule, the tangent linear operator of a deep neural network can be expressed as:

[0037] ;

[0038] in, and They represent and The disturbance It is a diagonal matrix whose diagonal elements are the derivatives of the activation function;

[0039] The adjoint operator of a deep neural network is obtained by transposing the tangent linear operator, and is expressed as:

[0040] ;

[0041] in, and Represent the outputs of any neural network right and The partial derivatives;

[0042] The tangent linear operator and adjoint operator of the deep neural network are respectively added to the tangent linear operator and adjoint operator constrained by the momentum equation. The tangent linear operator constrained by the momentum equation is expressed as:

[0043] ;

[0044] In this context, the overline symbol represents the background field state, and the apostrophe symbol represents the increment.

[0045] Preferably, in step S4, minimizing the cost function is the objective. Solving the analysis field depends on calculating the gradient of the cost function, and the cost function contains weak constraint terms. Item relative to increment The gradient is:

[0046] ;

[0047] in, Represents increment, It is the background field state. The momentum equation The adjoint operator, representing The matrix transpose.

[0048] In another aspect, the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, the computer instructions causing a computer to execute the above-described variational assimilation method of boundary-level grid physical constraints embedded in a deep neural network.

[0049] In another aspect, the present invention provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the above-mentioned boundary-level grid physical constraint variational assimilation method embedded in a deep neural network.

[0050] In another aspect, the present invention provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer performs the aforementioned variational assimilation method for boundary-level grid physical constraints embedded with a deep neural network.

[0051] Beneficial Effects: This invention's boundary-layer grid physical constraint variational assimilation method, embedded with a deep neural network, establishes an assimilation scheme considering boundary-layer grid physical constraints for severe weather numerical forecasting. Since general boundary layer physical parameterization schemes exhibit strong nonlinearity and discontinuity, incorporating them as constraints into variational assimilation algorithms using traditional methods for tangential and adjoint modeling is very difficult. Typically, simplified linearization schemes need to be developed first, and regularization constraints applied to the linearization physical process are used to suppress the abnormal growth of tangential perturbations, thus making it difficult to guarantee accuracy. This invention utilizes a deep neural network for machine learning training and simulation of the boundary layer parameterization scheme, establishing an alternative calculation of the boundary layer horizontal wind field tendency to characterize the boundary layer turbulent friction term within the horizontal momentum equation constraint. Furthermore, it constructs tangential and adjoint models of the deep neural network, correspondingly introducing them into the tangent and adjoint equations of the horizontal momentum equation to achieve gradient solving for the boundary layer turbulent friction term. Using WRF numerical model data as the background field, a variational assimilation scheme considering boundary layer physical constraints is established, improving the rationality and accuracy of the simulation. Attached Figure Description

[0052] Figure 1 This invention relates to a boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network;

[0053] Figure 2 The image shows the effect of the machine learning model in Example 1 predicting the boundary layer wind field trend.

[0054] Figure 3 This is a diagram showing the effect of the assimilation scheme in Example 1 on the sea level pressure field analysis of a typhoon;

[0055] Figure 4 This is a diagram showing the effect of the assimilation scheme in Example 1 on the intensity forecast of Typhoon Doksuri. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0057] The following is combined with Figures 1-4 This invention describes the boundary-level mesh physical constraint variational assimilation method for embedding deep neural networks.

[0058] Example 1: The existing WRF variational assimilation system adopts the frictionless assumption in the horizontal momentum equation constraint, that is, it does not consider the frictional effect caused by the boundary layer. When applied to severe weather such as typhoons and severe convection, if the scheme is not improved and it is applied directly, it will cause the dynamic balance of the middle and lower pressure field and wind field to deviate, resulting in unsatisfactory assimilation effect of observation data.

[0059] Therefore, this embodiment provides a boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network, such as... Figure 1 As shown, it includes the following steps:

[0060] The first step is to establish an improved variational weak constraint framework for the momentum equation.

[0061] In the current WRFDA assimilation system, the momentum equation constraint scheme does not consider the boundary layer friction effect, and the cost function is expressed as:

[0062] ;

[0063] in, Represents the cost function, To observe the penalty items, This is the background penalty term corresponding to the static background error covariance. The background penalty term is the set of background error covariance. These are the weighting coefficients. It is a weak constraint term, defined as:

[0064] ;

[0065] in, The dynamic weights are a diagonal matrix with all diagonal elements having the same value.

[0066] This is a momentum equation that includes boundary layer turbulent friction terms. Before introducing the boundary layer turbulent friction terms, this nonlinear momentum equation... The vector form is:

[0067] ;

[0068] In this embodiment, a subgrid boundary layer turbulent friction term is introduced, and the updated nonlinear momentum equation is expressed as follows:

[0069] ;

[0070] in, It is a horizontal wind field vector, containing wind field components. and ; It's air pressure. It is the height of position. It is atmospheric density. These are Coriolis parameters; This represents the boundary layer turbulent friction terms in two horizontal directions.

[0071] In order to incorporate the boundary level mesh friction term By explicitly incorporating momentum equation constraints, machine learning operators are employed to simulate the horizontal wind field tendency generated by boundary layer parameterization in numerical models. and The boundary layer turbulent friction term in the horizontal momentum equation constraint is characterized by the tendency of the horizontal wind field, and is expressed as:

[0072] ;

[0073] ;

[0074] in, and These are the boundary layer wind tendencies in two horizontal directions obtained through machine learning simulation; the input features of the machine learning model include the horizontal wind components within the boundary layer. and ,temperature Water vapor mixing ratio and surface air pressure ;

[0075] Therefore, the momentum equation can be expressed as:

[0076] ;

[0077] in, Represents machine learning operators.

[0078] The second step involves constructing machine learning simulation operators using deep neural networks. .

[0079] The deep neural network in this embodiment adopts a fully connected multi-layer neural network architecture. This multi-layer network contains N-1 non-linear layers with activation functions and 1 linear output layer. The output layer outputs the horizontal wind field tendency of the boundary layer. Both the input layer and the hidden layer maintain a fixed network width. The layer neural network operator is represented as:

[0080] ;

[0081] in, For the input vector, For the first The intermediate output of the layer, and They are the first The weight matrix and bias vector of the layer, The hyperbolic tangent function is chosen as the activation function because its derivative facilitates the calculation of the linear model. To simplify the formula, the distinction between the Nth layer and layers 1 to N-1 is not made here. It should be noted that in the Nth linear output layer, the activation function is always equal to 1.

[0082] Then, a deep neural network was used to establish a training model for the horizontal wind tendency of the boundary layer. For typhoon forecasting modeling, this embodiment selected WRF simulation results of individual typhoons from 2017-2021 as the training set, and individual typhoons from 2022-2023 as the validation and test sets. The training set contained typhoon data for 904 forecast times, totaling 24,910,624 samples; the validation set contained 3,747,616 samples; and the test set contained 3,306,720 samples.

[0083] Finally, the parameters of the neural network were adjusted, and the final configuration scheme was determined as follows: the input features include three-dimensional variables U, V, T, and Q, and P. s Two-dimensional variables are used, selecting only atmospheric variables below the 20th vertical layer of the model (below 1500 meters within the boundary layer) as features and labels. Each input sample is a column vector formed by the sequential arrangement of elements on a single column of the model grid, and each output sample is the horizontal wind field trend in the boundary layer on a single column of the model grid. and The column vectors are arranged in sequence. Mean squared error is used as the loss function. The model's input and output data are standardized by mean and standard deviation to ensure that the mean of the features and labels is zero and the standard deviation is one. After parameter tuning, the final hyperparameter configuration is: learning rate 10... -3 The Adam optimizer, with a batch size of 1024 and 100 training epochs. Features include... Each input dimension contains labels. One output dimension. Testing determined that the deep neural network simulator uses an architecture configuration with a network width of 87 nodes and a network depth of N=9 layers.

[0084] The third step is to linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the cost function of the variational assimilation framework.

[0085] Integrating deep neural networks into the variational assimilation framework also requires the development of their tangent linear model and adjoint model. This involves neural network operators. By taking the derivative and applying the chain rule, the tangent linear operator of a deep neural network can be expressed as:

[0086] ;

[0087] in, and They represent and The disturbance It is a diagonal matrix whose diagonal elements are the derivatives of the activation function;

[0088] The adjoint operator of a deep neural network is obtained by transposing the tangent linear operator, and is expressed as:

[0089] ;

[0090] in, and Represent the outputs of any neural network right and The partial derivatives;

[0091] The tangent linear operator and adjoint operator of the deep neural network are respectively added to the tangent linear operator and adjoint operator constrained by the momentum equation. The tangent linear operator constrained by the momentum equation is expressed as:

[0092] ;

[0093] In this context, the overline symbol represents the background field state, and the apostrophe symbol represents the increment.

[0094] The neural network model established in the second step is added as a machine learning operator L to the momentum equation constraint term. The tangent linear and adjoint models of the neural network established in the third step are added to the tangent linear model and adjoint model constrained by the momentum equation, respectively.

[0095] The fourth step is to acquire multi-source remote sensing observation data and the background field of numerical weather prediction models, and solve the analysis field with the goal of minimizing the cost function to complete the data assimilation.

[0096] Calculate constraint penalties The gradient of the cost function is calculated to achieve the improved variational assimilation system. Since the minimization process of variational assimilation depends on calculating the gradient of the cost function, the cost function... Item relative to increment The gradient is:

[0097] ;

[0098] in, Represents increment, It is the background field state. The momentum equation The adjoint operator, representing The matrix transpose.

[0099] Figure 1 A flowchart of the boundary-level mesh physical constraint variational assimilation method embedded with a deep neural network in this embodiment is given. The deep neural network boundary layer constraint module added to the new assimilation scheme is shown in the thick solid box. The improvements compared with the traditional scheme are: (1) Before online operation, the simulated values ​​of the boundary layer parameterization are used as labels, and the boundary layer wind field tendency is trained by the deep neural network to establish a simulation operator that represents the boundary layer turbulence friction term through machine learning. (2) The trained deep neural network is used to represent the boundary layer turbulence friction term L and it is introduced into the momentum equation constraint. (3) A tangent linear model of the deep neural network is developed. and adjoint model They are then introduced into the tangent linear model constrained by the momentum equation. and adjoint model In this process, a new gradient of the cost function is formed. The variational minimization of the new scheme is achieved through the conjugate gradient method.

[0100] To verify the consistency between the machine learning simulation and the labeled data. Figure 2 The prediction performance of deep neural networks on boundary layer wind field trends in the test dataset is presented. Figure 2 This indicates that the target value and the predicted value have extremely similar vertical distributions, with their mean differences approaching zero. The magnitude of their differences is approximately 10. -5The value is one to two orders of magnitude smaller than the target data value, indicating that the machine learning simulation has high accuracy.

[0101] Assimilation experiments were conducted on Typhoon Doksuri in 2023 using both the original assimilation scheme and the improved assimilation scheme of this embodiment. Figure 3 The typhoon pressure field structure after assimilating radar wind field data is presented. The original assimilation scheme yielded a minimum sea-level pressure of approximately 968 hPa, which does not match the weakening typhoon vortex wind field intensity after landfall. The improved assimilation scheme raises the minimum sea-level pressure to 978 hPa, close to the CMA optimal path observation value of 980 hPa. This indicates that incorporating a boundary layer turbulence friction term into the original assimilation scheme helps improve the wind-pressure balance within the boundary layer, resulting in a more accurate analysis field.

[0102] Using the analysis fields of the original assimilation scheme and the improved assimilation scheme as the initial forecast fields, an 18-hour forecast for Typhoon Doksuri was conducted. Figure 4 The results show that the improved assimilation scheme, based on the original scheme, further improved the typhoon intensity forecast. The original assimilation scheme had average forecast errors of 5.3 hPa and 3.1 ms for minimum sea level pressure and maximum near-surface wind speed, respectively. -1 The prediction errors corresponding to the improved assimilation scheme decreased to 3.9 hPa and 2.7 ms, respectively. 1 This indicates that assimilation schemes that consider boundary layer physical constraints contribute to improving typhoon intensity forecasting accuracy.

[0103] Example 2: This example provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network. The method includes the following steps:

[0104] S1. Establish a momentum equation that includes boundary layer grid turbulent friction terms, wherein the boundary layer turbulent friction terms are simulated by a deep neural network; and construct a weak constraint term for the variational assimilation framework cost function using this momentum equation.

[0105] S2. The deep neural network is trained using a dataset constructed from historical numerical weather prediction model simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables.

[0106] S3. Linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the variational assimilation framework cost function;

[0107] S4. Obtain multi-source remote sensing observation data and the background field of numerical weather prediction model, and solve the analysis field with the goal of minimizing the cost function to complete the data assimilation.

[0108] Example 3: This example provides an electronic device that may include a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions from the memory to execute a boundary-level mesh physical constraint variational assimilation method embedded with a deep neural network. This method includes the following steps:

[0109] S1. Establish a momentum equation that includes boundary layer grid turbulent friction terms, wherein the boundary layer turbulent friction terms are simulated by a deep neural network; and construct a weak constraint term for the variational assimilation framework cost function using this momentum equation.

[0110] S2. The deep neural network is trained using a dataset constructed from historical numerical weather prediction model simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables.

[0111] S3. Linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the variational assimilation framework cost function;

[0112] S4. Obtain multi-source remote sensing observation data and the background field of numerical weather prediction model, and solve the analysis field with the goal of minimizing the cost function to complete the data assimilation.

[0113] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0114] Example 4: This example provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a boundary-level mesh physical constraint variational assimilation method embedded with a deep neural network. The method includes the following steps:

[0115] S1. Establish a momentum equation that includes boundary layer grid turbulent friction terms, wherein the boundary layer turbulent friction terms are simulated by a deep neural network; and construct a weak constraint term for the variational assimilation framework cost function using this momentum equation.

[0116] S2. The deep neural network is trained using a dataset constructed from historical numerical weather prediction model simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables.

[0117] S3. Linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the variational assimilation framework cost function;

[0118] S4. Obtain multi-source remote sensing observation data and the background field of numerical weather prediction model, and solve the analysis field with the goal of minimizing the cost function to complete data assimilation.

[0119] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0120] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network, characterized in that, Includes the following steps: S1. Establish a momentum equation that includes boundary layer turbulent friction terms, wherein the boundary layer turbulent friction terms are simulated using a deep neural network; and construct a weak constraint term for the variational assimilation framework cost function based on this momentum equation; the variational assimilation framework cost function is expressed as: ； in, Represents the cost function, To observe the penalty, This is the background penalty term corresponding to the static background error covariance. This represents the background penalty term corresponding to the set background error covariance. These are the weighting coefficients. It is a weak constraint term, defined as: ； in, The dynamic weights are a diagonal matrix with all diagonal elements having the same value. The momentum equation, which includes the boundary-level grid turbulent friction term, is expressed as: ； in, It is a horizontal wind field vector, containing wind field components. and ; It's air pressure. It is the height of position. It is atmospheric density. These are Coriolis parameters; Let represent the boundary layer turbulent friction terms in two horizontal directions. Machine learning operators are used to simulate the horizontal wind field tendency generated by boundary layer parameterization in numerical models. and The boundary layer turbulent friction term in the horizontal momentum equation constraint is characterized by the tendency of the horizontal wind field, and is expressed as: ； ； in, and These are the boundary layer wind tendencies in two horizontal directions obtained through machine learning simulation; the input features of the machine learning model include the horizontal wind components within the boundary layer. and ,temperature Water vapor mixing ratio and surface air pressure ; Therefore, the momentum equation can be expressed as: ； in, Representing machine learning operators, these operators are constructed using deep neural networks. The deep neural network adopts a fully connected multi-layer neural network architecture, containing N-1 nonlinear layers with activation functions and 1 linear output layer. The output layer outputs the horizontal wind field tendency of the boundary layer. Both the input layer and the hidden layer maintain a fixed network width. The layer neural network operator is represented as: ； in, For the input vector, For the first The intermediate output of the layer, and They are the first Layer weight matrix and bias vector, For activation functions; S2. The deep neural network is trained using a dataset constructed from historical numerical weather prediction model simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and atmospheric state variables. S3. Linearize the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embed them into the cost function of the variational assimilation framework; specifically: For neural network operators By taking the derivative and applying the chain rule, the tangent linear operator of a deep neural network can be expressed as: ； in, and They represent and The disturbance It is a diagonal matrix whose diagonal elements are the derivatives of the activation function; The adjoint operator of a deep neural network is obtained by transposing the tangent linear operator, and is expressed as: ； in, and Represent the outputs of any neural network right and The partial derivatives; The tangent linear operator and adjoint operator of the deep neural network are respectively added to the tangent linear operator and adjoint operator constrained by the momentum equation. The tangent linear operator constrained by the momentum equation is expressed as: ； Among them, the overline symbol represents the background field state, and the apostrophe symbol represents the increment; S4. Obtain multi-source remote sensing observation data and the background field of numerical weather prediction model, and solve the analysis field with the goal of minimizing the cost function to complete the data assimilation.

2. The boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network according to claim 1, characterized in that, In step S2, the deep neural network is trained using a dataset constructed from historical WRF simulation results to learn the nonlinear mapping relationship between the horizontal wind field tendency in the boundary layer and atmospheric state variables; specifically: Based on historical WRF simulation results, the horizontal wind components of each horizontal grid point within the boundary layer at each time step are extracted. and ,temperature Water vapor mixing ratio and surface air pressure As input to a deep neural network, the next time step and the current time step... , The vertical average difference is used as a label to construct a dataset for training the deep neural network; In deep neural network training, mean squared error is used as the loss function, and a learning rate of 10 is used. -3 The Adam optimizer has a batch size of 1024 and a training cycle count of 100.

3. The boundary-level mesh physical constraint variational assimilation method embedded in a deep neural network according to claim 1, characterized in that, In step S4, minimizing the cost function is the objective. Solving the analysis field depends on calculating the gradient of the cost function, including the weak constraint terms in the cost function. Item relative to increment The gradient is: ； in, Represents increment, It is the background field state. The momentum equation The adjoint operator, representing The matrix transpose.

4. A non-transitory computer-readable storage medium, characterized in that, It stores computer instructions that cause the computer to execute the boundary-level grid physical constraint variational assimilation method for embedding deep neural networks as described in any one of claims 1-3.

5. An electronic device, characterized in that, include: The system includes a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor calls logical instructions from the memory to execute the boundary-level grid physical constraint variational assimilation method for embedding deep neural networks as described in any one of claims 1-3.

6. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer performs the boundary-level grid physical constraint variational assimilation method for embedding deep neural networks as described in any one of claims 1-3.

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