Boundary hierarchical grid physical constraint variation assimilation method of embedded deep neural network

Abstract

The invention discloses a boundary hierarchical grid physical constraint variation assimilation method embedded with a deep neural network, which comprises the following steps: establishing a momentum equation containing a boundary hierarchical grid turbulence friction item which is simulated through the deep neural network; constructing a weak constraint term of a variational assimilation framework cost function by using the momentum equation; training the deep neural network by using a data set constructed by a historical numerical weather forecast mode simulation result; 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; and acquiring multi-source remote sensing observation data and a numerical weather forecast mode background field, and solving an analysis field by taking the cost function minimization as a target to complete data assimilation. According to the method, the data assimilation and numerical forecasting level of disastrous weather such as typhoon can be improved, and particularly the observation assimilation level related to a boundary layer can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of atmospheric science, and relates to a variational assimilation method under constraints, in particular to a boundary level grid physical constraint variational assimilation method embedded with a deep neural network. BACKGROUND

[0002] High-resolution numerical weather prediction is an important way to improve the warning ability of disastrous weather, and its prediction effect depends largely on the improvement of the initial field of the observation data assimilation model. How to effectively assimilate multi-source remote sensing data (radar, satellite, etc.) has become a current research hotspot, which can make up for the lack of conventional observation in the spatial and temporal resolution and the detection ability of physical variables.

[0003] Advanced data assimilation methods strive to generate an analysis field that accurately describes the real state of the atmosphere through the consistency constraint of physical laws, providing support for numerical prediction. The variational method or ensemble-variational hybrid assimilation method based on the variational framework often uses weak constraint to introduce dynamic constraints or physical constraints. Some studies introduce model tendency constraints, diagnostic pressure equation constraints, steady momentum equation constraints and large-scale analysis constraints in the variational method. Although these constraints describe the atmospheric dynamic process, they often ignore the importance of the unresolved sub-grid physical process.

[0004] For strong weather systems such as typhoons, boundary layer friction is very important to the dynamics of the boundary layer, determines the vertical structure of the boundary layer wind field, and will affect the convergence and divergence and the triggering of convection, which are also very important for the evolution of typhoon structure and intensity. However, the current assimilation scheme lacks consideration of the effect of boundary layer friction, resulting in incompatibility between the assimilation analysis and the nonlinear dynamics of the model in the boundary layer.

[0005] The current WRF (Weather Research and Forecasting) model WRFDA (WRF data assimilation) assimilation system uses the no-friction assumption in the horizontal momentum equation constraint, i.e. it does not consider the effect of friction caused by the boundary layer. When applied to typhoons and strong convection, it will cause deviations in the dynamic balance of the pressure field and wind field in the middle and low layers, resulting in unsatisfactory observation data assimilation effect.

[0006] On the other hand, in recent years, the development of artificial intelligence technology brings new opportunities for data assimilation improvement. The combination of machine learning and data assimilation mainly reflects two aspects: on the one hand, it tries to build a fusion framework, based on the unified theoretical basis of Bayes theorem, develops a data-driven substitute model based on recurrent neural network, and estimates the assimilation system's model bias using deep learning; on the other hand, machine learning is applied to improve key components of the assimilation system, such as the assimilation solver, the observation operator, the background error covariance and the alternative modeling of the physical parameterization scheme. These developments are regarded as the deep integration of machine learning and data assimilation, especially providing a new way for the development of physical constraints. Machine learning simulators can not only accelerate the calculation of physical processes, but also make it easier to develop tangent linear and adjoint models in the case of simulating strong nonlinear and discontinuous physical processes, thus meeting the assimilation needs.

[0007] In view of the problem that the WRFDA assimilation system cannot represent the boundary layer turbulent friction effect, it is necessary to explore an alternative method based on machine learning to realize variational weak constraint, and a new idea of establishing the boundary layer friction effect in the variational constraint through a deep neural network (DNN) is proposed. SUMMARY

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

[0009] The present application aims to at least solve one of the technical problems existing in the related art to some extent.

[0010] In order to achieve the above-mentioned purpose, the present application provides a boundary layer grid physical constraint variational assimilation method embedded with a deep neural network, comprising the following steps:

[0011] S1, establishing a momentum equation containing a boundary layer grid turbulent friction term, wherein the boundary layer turbulent friction term is simulated by a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function with the momentum equation;

[0012] S2, training the deep neural network with a data set constructed from historical numerical weather prediction model simulation results, learning the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the atmospheric state variables;

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

[0014] S4, obtaining multi-source remote sensing observation data and numerical weather prediction model background field, solving an analysis field to minimize the cost function, and completing data assimilation.

[0015] The further preferred technical solution of the present application is that the variational assimilation framework cost function in step S1 is represented as:

[0016] Among them, the cost function is represented as, the observation penalty term is represented as, the background penalty term corresponding to the static background error covariance is represented as, the background penalty term corresponding to the ensemble background error covariance is represented as, the weight coefficient is represented as, the weak constraint term is defined as:

[0017] Among them, the dynamic weight is a diagonal matrix, and the diagonal elements have the same value; the momentum equation containing the boundary layer grid turbulence friction term is represented as:

[0018] Among them, the horizontal wind field vector contains wind field components and ; the air pressure is represented as, the geopotential height is represented as, the atmospheric density is represented as, the Coriolis parameter is represented as; the two horizontal direction boundary layer turbulence friction terms are represented as.

[0019] As preferred, for the two horizontal direction boundary layer turbulence friction terms , a machine learning operator is used to simulate the horizontal wind field tendency generated by the numerical model boundary layer parameterization and , and the horizontal wind field tendency is used to represent the boundary layer turbulence friction term in the horizontal momentum equation constraint, which is represented as:

[0020] Among them, and are the boundary layer wind tendencies in the two horizontal directions obtained by machine learning simulation; the input features of the machine learning model include the horizontal wind components in the boundary layer​​​​​ and temperature , water vapor mixing ratio and surface pressure ;

[0021] Accordingly, the momentum equation is expressed as: ;

[0022] wherein, represents a machine learning operator.

[0023] As a preference, the machine learning operator is constructed by a deep neural network , which adopts a fully connected multi-layer neural network architecture, contains N-1 nonlinear layers with activation functions and 1 linear output layer, the output layer outputs the boundary layer horizontal wind field tendency, the input layer and the hidden layer both maintain a fixed network width, the first layer neural network operator is expressed as: ;

[0024] wherein, is an input vector, is an intermediate output of the first layer, and are a weight matrix and a bias vector of the first layer, respectively, is an activation function.

[0025] As a preference, the deep neural network is trained by the dataset constructed by the historical WRF simulation results in step S2, to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the atmospheric state variables; specifically:

[0026] According to the historical WRF simulation results, the horizontal wind components and , temperature , water vapor mixing ratio and surface pressure of each horizontal grid point in the boundary layer at each time step are extracted as the deep neural network input, the , vertical average difference of the next time step and the current time step are taken as labels, and the deep neural network is trained by the dataset.

[0027] In the deep neural network training, the mean square error is taken as the loss function, the Adam optimizer with a learning rate of 10 -3 is adopted, the batch size is 1024, and the training period is 100.

[0028] As preferred, the trained deep neural network in step S3 is linearized to obtain the corresponding tangent-linear operator and adjoint operator; specifically:

[0029] The neural network operator is differentiated and the chain rule is applied to express the tangent-linear operator of the deep neural network as: ;

[0030] where and denote the perturbations of and respectively, is a diagonal matrix whose diagonal elements are composed of the derivatives of the activation function;

[0031] The adjoint operator of the deep neural network is obtained by transposing the tangent-linear operator, and is expressed as: ;

[0032] where and denote the partial derivatives of the arbitrary neural network output with respect to and respectively;

[0033] The tangent-linear operator and adjoint operator of the deep neural network are added to the tangent-linear operator and adjoint operator of the momentum equation constraint, respectively, and the tangent-linear operator of the momentum equation constraint is expressed as: ;

[0034] where the overline symbol denotes the background field state, and the prime symbol denotes the increment.

[0035] As preferred, in step S4, the gradient of the cost function with respect to the increment is solved to minimize the cost function, where the weak constraint term in the cost function is: ;

[0036] where represents the increment, is the background field state, is the adjoint operator of the momentum equation , and denotes the matrix transpose of .

[0037] In another aspect of the present application, a non-transitory computer readable storage medium is provided, which stores computer instructions, and the computer instructions cause a computer to perform the boundary-level grid physical constraint variational assimilation method embedded with a deep neural network.

[0038] In yet another aspect of the present application, an electronic device is provided, which comprises 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 invokes logical instructions in the memory to perform the boundary-level grid physical constraint variational assimilation method embedded with a deep neural network.

[0039] In still another aspect of the present application, a computer program product is provided, which comprises a computer program stored on a non-transitory computer readable storage medium, and the computer program is executed by a processor to cause a computer to perform the boundary-level grid physical constraint variational assimilation method embedded with a deep neural network.

[0040] Beneficial effects: The boundary-level grid physical constraint variational assimilation method embedded with a deep neural network of the present application establishes an assimilation scheme considering boundary-level grid physical constraints for strong weather numerical prediction. Since a general boundary layer physical parameterization scheme has strong nonlinearity and discontinuity, it is very difficult to use a traditional method to perform tangent linearization and adjoint modeling if it is to be added as a constraint to a variational assimilation algorithm. Generally, a simplified linearization scheme needs to be developed first, and the linearized physical process needs to be regularized to suppress the abnormal growth of tangent linear perturbations, so it is difficult to ensure accuracy. The present application uses a deep neural network to perform machine learning training and simulation on the boundary layer parameterization scheme, establishes a substitute calculation of the boundary layer horizontal wind field tendency, and uses it to represent the boundary layer turbulent friction term in the horizontal momentum equation constraint; further, tangent linear and adjoint models of the deep neural network are constructed, which are correspondingly introduced into the tangent and adjoint equations of the horizontal momentum equation to realize gradient solution of the boundary layer turbulent friction term. Taking WRF numerical model data as a background field, a variational assimilation scheme considering boundary layer physical constraints is established to improve the rationality and accuracy of simulation. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The boundary-level grid physical constraint variational assimilation method embedded with a deep neural network of the present application;

[0042] Figure 2 The effect diagram of the machine learning model of embodiment 1 for predicting the boundary layer wind field tendency;

[0043] Figure 3 The effect diagram of the assimilation scheme of embodiment 1 for analyzing the sea level pressure field of a typhoon;

[0044] Figure 4 Figure of the effect of assimilation scheme of Example 1 on the intensity prediction of Typhoon "Doksu". DETAILED DESCRIPTION

[0045] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below with reference to the drawings in the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application, and they should not be understood as limiting the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work should fall within the protection scope of the present application. In the description of the present application, it should be understood that the terms used are only for the purpose of description and should not be understood as indicating or implying the relative importance.

[0046] The technical solutions in the present application will be described below with reference to the drawings in the present application. Figures 1-4 The boundary level grid physical constraint variational assimilation method embedded with a deep neural network is described.

[0047] Example 1: The existing WRF variational assimilation system adopts a no-friction assumption in the horizontal momentum equation constraint, that is, the friction effect caused by the boundary layer is not considered. When applied to typhoons and severe convective weather, if the scheme is not improved and directly applied, it will cause deviation in the dynamic balance of the middle and low layer pressure field and wind field, resulting in unsatisfactory observation data assimilation effect.

[0048] Therefore, the present embodiment provides a boundary level grid physical constraint variational assimilation method embedded with a deep neural network, as shown in Figure 1 The method comprises the following steps:

[0049] Firstly, an improved momentum equation variational weak constraint framework is established.

[0050] In the current WRFDA assimilation system, the momentum equation constraint scheme does not consider the boundary layer friction effect, and the cost function is represented as: ;

[0051] wherein, represents the cost function, is an observation penalty term, is a background penalty term corresponding to the static background error covariance, is a background penalty term corresponding to the ensemble background error covariance, is a weight coefficient, is a weak constraint term, which is defined as: ;

[0052] wherein, is the power weighting, which is a diagonal matrix with the same value on the diagonal;

[0053] is the momentum equation with the boundary layer turbulence friction term, where the nonlinear momentum equation is expressed in vector form as ;

[0054] The updated nonlinear momentum equation with the subgrid boundary layer turbulence friction term is expressed as ;

[0055] where is the horizontal wind field vector, which includes the wind field components and ; is the air pressure, is the geopotential height, is the atmospheric density, is the Coriolis parameter; denotes the two horizontal boundary layer turbulence friction terms.

[0056] To explicitly add the boundary layer grid friction term into the momentum equation constraint, a machine learning operator is used to simulate the horizontal wind field tendency and generated by the numerical model boundary layer parameterization, which is expressed as ; ;

[0057] where and are the two horizontal boundary layer wind tendencies simulated by the machine learning model; the input features of the machine learning model include the horizontal wind components and , temperature , water vapor mixing ratio , and surface air pressure ;

[0058] Accordingly, the momentum equation is expressed as ;

[0059] where represents the machine learning operator.

[0060] In the second step, a deep neural network is used to construct the machine learning simulation operator .

[0061] The deep neural network of the embodiment adopts a fully connected multi-layer neural network architecture, which contains N-1 nonlinear layers with activation functions and 1 linear output layer, the output layer outputs the boundary layer horizontal wind field tendency, the input layer and the hidden layer maintain a fixed network width, the first The layer neural network operator is expressed as: ;

[0062] wherein, is an input vector, is the intermediate output of the first layer, and are the weight matrix and the bias vector of the first layer, is an activation function, and the hyperbolic tangent function is selected as the activation function because the derivative is convenient for calculating the tangent linear model. In order to simplify the formula expression, the first N layer and the first 1~N-1 layer are not distinguished here, and it needs to be specially pointed out that the activation function is always equal to 1 in the Nth linear output layer.

[0063] Then, a training model of the boundary layer horizontal wind tendency is established by using the deep neural network. For typhoon forecasting modeling, the WRF simulation results of typhoon cases from 2017 to 2021 are selected as the training set, and the typhoon cases from 2022 to 2023 are selected as the verification set and the test set. The training set contains 904 forecast times of typhoon data, a total of 24,910,624 sample data; the verification set contains 3,747,616 sample data; and the test set contains 3,306,720 sample data.

[0064] Finally, the neural network is parameter adjusted, and the final configuration scheme is determined as follows: the input features include U, V, T, Q three-dimensional variables and P s two-dimensional variables, only the atmospheric variables of the model vertical 20 layers below (1500 meters below the boundary layer) are selected as the features and the labels. Each input sample is a column vector formed by sequentially arranging each element on the model grid single column, and each output sample is a column vector formed by sequentially arranging the boundary layer horizontal wind field tendency and on the model grid single column. The mean square error is used as the loss function, and the input and output data of the model are standardized by mean and standard deviation, so that the feature quantity and the label quantity have a mean of zero and a standard deviation of one. After parameter optimization, the final hyperparameter configuration is: the learning rate is 10 -3 , the Adam optimizer is used, the batch size is 1024, and the training period is 100. The features include input dimensions, and the labels include an output dimension. The architecture configuration of the deep neural network emulator was determined by testing to have a network width of 87 nodes and a network depth of N = 9 layers.

[0065] Third, the trained deep neural network is linearized to obtain the corresponding tangent-linear operator and adjoint operator, and the tangent-linear operator and adjoint operator are embedded into the cost function of the variational assimilation framework.

[0066] It is also necessary to develop the tangent-linear model and adjoint model of the deep neural network integrated into the variational assimilation framework. The derivative of the neural network operator is derived and the chain rule is applied to express the tangent-linear operator of the deep neural network as ;

[0067] where and denote the perturbations of and respectively, is a diagonal matrix whose diagonal elements are composed of the derivative of the activation function;

[0068] The adjoint operator of the deep neural network is obtained by transposing the tangent-linear operator and is expressed as ;

[0069] where and denote the partial derivatives of the arbitrary neural network output with respect to and respectively;

[0070] The tangent-linear operator and adjoint operator of the deep neural network are added into the tangent-linear operator and adjoint operator of the momentum equation constraint, respectively, and the tangent-linear operator of the momentum equation constraint is expressed as ;

[0071] where the overline symbol denotes the background field state and the prime symbol denotes the increment.

[0072] The neural network model established in the second step is added as the machine learning operator L into the momentum equation constraint term, and the tangent-linear and adjoint models of the neural network established in the third step are added into the tangent-linear model and adjoint model of the momentum equation constraint, respectively.

[0073] Fourth, the multi-source remote sensing observation data and the numerical weather prediction model background field are obtained, and the analysis field is solved to complete the data assimilation by minimizing the cost function.

[0074] The constraint penalty term of the cost function, an improved variational assimilation system is implemented. Since the minimization process of variational assimilation relies on the calculation of the gradient of the cost function, the gradient of the cost function with respect to the increment

[0075] wherein, represents the increment, is the background field state, is the adjoint operator of the momentum equation , and denotes the matrix transpose.

[0076] Figure 1 The flowchart of the boundary layer grid physical constraint variational assimilation method embedded with the deep neural network of the present embodiment is given, and the deep neural network boundary layer constraint module added by the new assimilation scheme is given in the thick solid line box. Compared with the traditional scheme, the improvements are as follows: (1) Before online operation, the simulation value parameterized by the boundary layer is taken as the label, the deep neural network is trained to obtain the boundary layer wind tendency, and the machine learning simulation operator representing the boundary layer turbulent friction term is established. (2) The trained deep neural network is used to represent the boundary layer turbulent friction term L, which is introduced into the momentum equation constraint. (3) The tangential linear model and the adjoint model of the deep neural network are developed and introduced into the tangential linear model and the adjoint model of the momentum equation constraint, respectively, to form the new cost function gradient , and the variational minimization calculation of the new scheme is realized by the conjugate gradient method.

[0077] In order to verify the consistency between the machine learning simulation and the label data, Figure 2 the prediction effect of the deep neural network on the boundary layer wind tendency in the test data set is given. Figure 2 It is shown that the average vertical distribution of the target value and the predicted value is very similar, and the difference between their average values is close to zero. The difference in the order of magnitude is about 10 -5 , which is one to two orders of magnitude smaller than the target data value, indicating that the machine learning simulation accuracy is high.

[0078] The original assimilation scheme and the improved assimilation scheme of the present embodiment are applied to assimilate Typhoon “Doksuri” in 2023. Figure 3 ​​​​The typhoon pressure field structure after assimilating the radar wind field data is given. The sea level minimum pressure of the original assimilation scheme is about 968 hPa, which does not match the weakened typhoon vortex wind field intensity after landing. The sea level minimum pressure of the improved assimilation scheme rises to 978 hPa, which is close to the 980 hPa of the CMA best path observation. This shows that adding the boundary layer turbulent friction term in the original assimilation scheme helps to improve the wind-pressure balance relationship in the boundary layer, making the analysis field more accurate.

[0079] The 18-hour forecast of typhoon "Dusuo" is carried out with the analysis field of the original assimilation scheme and the improved assimilation scheme as the initial field of prediction, respectively. Figure 4 It is shown that the prediction test corresponding to the improved assimilation scheme further improves the typhoon intensity prediction level on the basis of the original assimilation scheme. The average prediction error of the sea level minimum pressure and the near-surface maximum wind speed of the original assimilation scheme is 5.3 hPa and 3.1 m / s -1 , respectively, and the prediction error of the improved assimilation scheme decreases to 3.9 hPa and 2.7 m / s 1 , respectively. It is shown that the assimilation scheme considering the boundary layer physical constraint helps to improve the typhoon intensity prediction level.

[0080] Embodiment 2: The embodiment provides a non-transitory computer readable storage medium, which stores computer instructions, the computer instructions causing a computer to execute a boundary layer hierarchical grid physical constraint variational assimilation method embedded in a deep neural network, the method comprising the following steps:

[0081] S1, establishing a momentum equation containing a boundary layer hierarchical grid turbulent friction term, wherein the boundary layer turbulent friction term is simulated by a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function with the momentum equation;

[0082] S2, training the deep neural network with a dataset constructed from historical numerical weather prediction model simulation results, learning the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the atmospheric state variables;

[0083] S3, linearizing the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embedding the variational assimilation framework cost function;

[0084] S4, obtaining multi-source remote sensing observation data and numerical weather prediction model background field, minimizing the cost function to solve the analysis field, and completing data assimilation.

[0085] Embodiment 3: The electronic device can include a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other through the communications bus. The processor can invoke a logical instruction in the memory to execute a boundary level grid physical constraint variational assimilation method embedded with a deep neural network, which includes the following steps:

[0086] S1, establishing a momentum equation containing a boundary level grid turbulent friction term, wherein the boundary layer turbulent friction term is simulated by a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function with the momentum equation;

[0087] S2, training the deep neural network with a dataset constructed from historical numerical weather prediction model simulation results, learning the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the atmospheric state variables;

[0088] S3, linearizing the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embedding the variational assimilation framework cost function;

[0089] S4, obtaining multi-source remote sensing observation data and numerical weather prediction model background field, and solving the analysis field to complete data assimilation by minimizing the cost function.

[0090] In addition, the logical instructions in the memory described above can be implemented in the form of a software functional unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product, which is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various program code storage media.

[0091] Embodiment 4: provided is a computer program product, the computer program product comprising a computer program, the computer program being stored on a non-transitory computer-readable storage medium, and the computer program being executable by a processor to enable a computer to execute a boundary-layer hierarchical grid physical constraint variational assimilation method embedded in a deep neural network, the method comprising the following steps:

[0092] S1, establishing a momentum equation containing a boundary-layer hierarchical grid turbulent friction term, wherein the boundary-layer turbulent friction term is simulated by a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function based on the momentum equation;

[0093] S2, training the deep neural network with a dataset constructed based on historical numerical weather prediction model simulation results, and learning a nonlinear mapping relationship between a boundary layer horizontal wind field tendency and atmospheric state variables;

[0094] S3, linearizing the trained deep neural network to obtain a corresponding tangent linear operator and adjoint operator, and embedding the tangent linear operator and the adjoint operator in the variational assimilation framework cost function;

[0095] S4, obtaining multi-source remote sensing observation data and a numerical weather prediction model background field, and solving an analysis field to complete data assimilation by minimizing the cost function.

[0096] The apparatus embodiments described above are merely illustrative, wherein the units shown as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment according to actual needs. Those skilled in the art can understand and implement it without creative labor.

[0097] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software plus a necessary general hardware platform, and of course can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0098] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A boundary level grid physics constrained variational assimilation method embedded in a deep neural network, characterized in that, Comprising the following steps: S1, establishing a momentum equation containing a boundary layer grid turbulence friction term, wherein the boundary layer turbulence friction term is simulated by a deep neural network; and constructing a weak constraint term of a variational assimilation framework cost function with the momentum equation; S2, training the deep neural network with a dataset constructed from historical numerical weather prediction model simulation results, learning the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the atmospheric state variables; S3, linearizing the trained deep neural network to obtain the corresponding tangent linear operator and adjoint operator, and embedding them in the variational assimilation framework cost function; S4, obtaining multi-source remote sensing observation data and numerical weather prediction model background field, minimizing the cost function to solve the analysis field and complete data assimilation.

2. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network according to claim 1, wherein, The variational assimilation framework cost function in step S1 is represented as: ； wherein, represents a cost function, is an observation penalty, is a background penalty corresponding to a static background error covariance, is a background penalty corresponding to an ensemble background error covariance, is a weighting coefficient, is a weak constraint term, which is defined as: ； wherein, is a power weight, which is a diagonal matrix with the same value on the diagonal elements; is the momentum equation with the boundary layer hierarchy grid turbulent friction term, expressed as: ； where is the horizontal wind field vector, containing the wind field components and ; is the air pressure, is the geopotential height, is the atmospheric density, is the Coriolis parameter; denotes two horizontal directional boundary layer turbulence friction terms.

3. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network according to claim 2, wherein, For the two horizontal-direction boundary layer turbulent friction terms A machine learning operator is employed to simulate the horizontal wind field tendency resulting from the numerical model boundary layer parameterization and The boundary layer turbulent friction terms are represented in the horizontal momentum equation constraint as a function of the horizontal wind field tendency, denoted as: ； ； wherein, and are two horizontal wind tendency of the boundary layer simulated by machine learning; the input features of the machine learning model include the horizontal wind components and , temperature , water vapor mixing ratio , and surface pressure ; Accordingly, the momentum equation is represented as: ； wherein, represents a machine learning operator.

4. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network according to claim 3, wherein, Building machine learning operators with deep neural networks , the deep neural network employs a fully connected multi-layer neural network architecture comprising N-1 non-linear layers with activation functions and 1 linear output layer, the output layer outputs the boundary layer horizontal wind field tendencies, the input layer and the hidden layers all maintain a fixed network width, the first layer neural network operator is represented as: ； where, is an input vector, is the intermediate output of the layer, and are the weight matrix and bias vector of the layer, respectively, is an activation function.

5. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network of claim 1, wherein, In step S2, the deep neural network is trained with a dataset constructed from historical WRF simulation results to learn the nonlinear mapping relationship between the boundary layer horizontal wind field tendency and the 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 the training of deep neural networks, the mean square error is used as the loss function, the learning rate is 10 -3 , the Adam optimizer is used, the batch size is 1024, and the number of training cycles is 100.

6. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network according to claim 4, wherein, In step S3, the trained deep neural network is linearized to obtain the corresponding tangent linear operator and adjoint operator; specifically: Neural network operators Taking the derivative and applying the chain rule, the tangential linear operator of a deep neural network is expressed as: ； where and denote and perturbations of is a diagonal matrix whose diagonal elements consist of the derivative of the activation function; The adjoint operator of the deep neural network is obtained by transposing the tangent linear operator, represented as: ； wherein, and denote the partial derivatives of the arbitrary neural network outputs with respect to and respectively. The tangent linear operator and adjoint operator of the deep neural network are added to the tangent linear operator and adjoint operator of the momentum equation constraint, respectively, wherein the tangent linear operator of the momentum equation constraint is represented as: ； Wherein, the overline symbol represents the background field state, and the prime symbol represents the increment.

7. The boundary-level hierarchical mesh physical constraint variational assimilation method embedded deep neural network according to claim 6, wherein, In step S4, the minimization of the cost function is targeted, the gradient of the cost function is relied on for solving the analysis field, the weak constraint term in the cost function is the gradient of the increment ； wherein represents an increment, is a background field state, is a momentum equation is an adjoint operator, and denotes a matrix transpose.

8. A non-transitory computer-readable storage medium, comprising: A computer program product comprising computer instructions stored on a non-transitory computer readable storage medium, the computer program being executed by a processor, the computer executing the method of embedding a deep neural network in a boundary layer grid physical constraint variational assimilation method according to any one of claims 1-7.

9. An electronic device, comprising: 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 the logical instructions in the memory to execute the method of embedding a deep neural network in a boundary layer grid physical constraint variational assimilation method according to any one of claims 1-7.

10. A computer program product, characterised in that, The computer program product comprises a computer program, the computer program is stored on a non-transitory computer readable storage medium, the computer program is executed by a processor, the computer executes the method of embedding a deep neural network in a boundary layer grid physical constraint variational assimilation method according to any one of claims 1-7.

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