Revision Method for the Fog Boundary Layer Parameterization Scheme Based on a Multi-Scale Physical Coupling Network

Abstract

The present invention discloses a correction method for fog boundary layer parameterization scheme based on a multi-scale physical coupling network, which relates to the cross field of numerical weather prediction and artificial intelligence. The aim is to improve the performance of different boundary layer parameterization schemes in the WRF model, construct a fusion framework of physical model and deep learning, adopt a dual-branch heterogeneous network structure, combine spatio-temporal attention mechanism, and establish a non-linear mapping relationship between the deviations of different parameterization schemes and the large-eddy simulation turbulence characteristics; by correcting the systematic deviations existing in the parameterization scheme, improve the analytical ability of the turbulence structure and optimize the physical description of the boundary layer process; compared with the traditional boundary layer scheme, it significantly improves the accuracy of fog area simulation, and the root mean square errors of fog area visibility, liquid water content and liquid water path are reduced by 66.7%, 50% and 58.3% respectively, effectively solving the problem of insufficient representation of turbulence intermittency in the stable boundary layer by traditional methods, and providing a new paradigm for the refined prediction of fog generation and dissipation processes.

Description

Technical Field

[0001] The present invention relates to the intersection of numerical weather forecasting and artificial intelligence, and in particular to a method for correcting a fog boundary layer parameterization scheme based on a multi-scale physical coupling network. Background Art

[0002] Boundary layer parameterization schemes are a core component of numerical weather forecast models, directly affecting the simulation accuracy of turbulent mixing, cloud microphysical processes, and radiation effects. In fog simulations, especially under stable boundary layer conditions, existing classical boundary layer schemes (such as YSU, ACM2, and QNSE) mostly rely on local K theory or the first-order closed turbulence assumption, assuming that turbulence statistics are linearly related to the mean gradient. However, atmospheric turbulence exhibits significant intermittent, nonlocal transport, and anisotropic characteristics. These traditional turbulence parameterization assumptions make it difficult to accurately characterize actual processes, resulting in weak simulations of the inversion layer top structure, low cooling rates, loss of intermittent turbulent bursts, underestimated nighttime turbulent kinetic energy, delayed simulations of liquid water condensation and evaporation processes, increased fog top height prediction errors, and dramatic visibility changes, but also sluggish or distorted model responses.

[0003] Taking radiation fog as an example, its formation relies on the coordinated evolution of surface radiation cooling and turbulence weakening. However, traditional approaches inadequately characterize the radiation-turbulence coupling process. They only use simple stability functions to modify the turbulent exchange coefficient, which is unable to dynamically respond to changes in local cooling rates, making it difficult to reproduce the true timing of fog formation and dissipation. Furthermore, in complex terrain conditions (such as basins, canyons, and mountains), the topographically driven thermal circulation (such as valley winds and slope winds) and the local turbulence enhancement effects further exacerbate the heterogeneity and non-stationarity of the boundary layer structure. Traditional parameterization schemes can maintain a certain degree of accuracy under simple terrain conditions, but the prediction error is significantly amplified under complex terrain, manifesting as small fog area coverage, underestimated fog top height, early or delayed life cycle prediction, and other problems. In response to the limitations of the above physical schemes, researchers have proposed introducing high-order turbulence closure, local / non-local mixed correction terms, turbulent energy spectrum parameterization and other methods to improve model accuracy. However, there are still strong parameter dependence, sensitivity to initial fields and parameter selection, difficulty in ensuring physical consistency, increased computing costs, and reduced real-time business application capabilities of NWP systems. Limited by prior physical assumptions, performance degrades significantly under extremely stable or local strong radiation cooling conditions.

[0004] In recent years, data assimilation techniques have been introduced to improve the output of initial fields and parameterization schemes. However, they rely on high-quality observational data and have limited effectiveness in data-sparse regions. With the rise of deep learning in the meteorological field, parameterization correction methods based on neural networks have gradually received attention. However, existing deep learning models still have deficiencies in multi-scale feature extraction, spatio-temporal dependence modeling, and physical constraint integration. Especially in the simulation of fog in complex terrain areas, the generalization ability and accuracy of the models are limited. Therefore, there is an urgent need for a deep learning method that can effectively extract multi-scale spatio-temporal features, integrate physical constraints, and improve the accuracy of fog simulation. Summary of the Invention

[0005] To overcome the deficiencies of traditional boundary layer parameterization schemes in fog simulation, the present invention proposes a method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network to solve the problem of insufficient accuracy in fog simulation by existing boundary layer parameterization schemes under stable conditions.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network, comprising the following steps:

[0008] S1. Use the numerical weather prediction model WRF to generate multi-parameterized boundary layer simulation data, and the input data includes thermodynamic variables, water substance variables, and dynamic field variables;

[0009] S2. Generate an initial feature tensor by processing the input data through feature encoding, and use the multi-head attention mechanism to screen out key variables with relatively large weights affecting the evolution of the fog area;

[0010] S3. Construct a multi-scale physical coupling network SMAP-Net, and extract the temperature-humidity phase state features and cloud-water phase state features at different scales through a double-branch heterogeneous network structure;

[0011] S4. Fuse the features of the double branches through the spatio-temporal coupling attention module ST-CAM, and use three-dimensional convolutional spatio-temporal encoding, bidirectional GRU time series modeling, and dynamic attention weighting to jointly model the non-linear relationships of turbulence, radiation, and phase change;

[0012] S5. Embed a physical constraint loss function in the decoding stage, including the mass-momentum conservation equation and the visibility gradient matching term, and perform collaborative optimization of data-driven features and physical laws through adaptive weight allocation to correct the boundary layer variables;

[0013] S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content, and visibility, and improve the simulation accuracy of the liquid water path LWP and liquid water content LWC in the fog area.

[0014] As a further preferred solution of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S2, the specific implementation of the encoding stage includes:

[0015] S2.1. The input variables include temperature T, relative humidity RH, water vapor mixing ratio Qv, cloud water content Qc, rain water content Qr, ice crystal content Qi, snow content Qs, air pressure P, and vertical velocity W. The input data is organized into a three-dimensional spatio-temporal tensor with dimensions H×W×T×C, where H×W represents the spatial resolution, T represents the time step, and C represents the number of variable channels;

[0016] S2.2. Extract spatio-temporal local features through a parallel three-dimensional convolutional layer. The convolutional kernel size of the three-dimensional convolutional layer is 3×3×3, the stride is 1, and the padding is 1; generate an initial feature tensor , where represents the number of output channels, and use the ReLU activation function for non-linear transformation;

[0017] S2.3. Use the multi-head attention mechanism to screen the initial feature tensor , and the calculation formula is as follows:

[0018] Among them, , , are the query, key, and value vectors respectively, is a learnable linear transformation matrix. Each matrix is responsible for linearly transforming the channel dimension of the input feature tensor , keeping the dimension unchanged and continuously updated during training to optimize the attention calculation, realize the re-weighting of information between channels and the feature subspace mapping, so that different variable combinations can adapt to the subsequent correlation modeling, is the dimension of the key vector, and the attention mechanism is configured as heads, where is an adjustable hyperparameter, and the filtered feature tensor is output to highlight the key variables that have a greater impact on the evolution of the fog area.

[0019] As a further preferred solution of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S3, the specific implementation of the temperature and humidity phase branch includes:

[0020] S3.1. The input variables are temperature T, relative humidity RH, water vapor mixing ratio Qv, and air pressure P. Extract spatio-temporal local features through three-dimensional convolution. The convolutional kernel size of the three-dimensional convolution is 3×3×3, the stride is 1, and the padding is 1, and generate an initial feature tensor , where the number of output channels is 64;

[0021] S3.2. Adopt a 4-level Dense Block stacking structure. Each level contains a bottleneck structure, which successively includes: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, and 1×1×1 convolution for dimensionality increase. The features of the previous layer and the current layer are concatenated in channels through skip connections, and a feature tensor is output. , where the number of output channels is 4×64 = 256 to enhance the feature reuse ability;

[0022] S3.3. Enhance the feature response of the inversion layer top and the humidity jump region through the channel-spatiotemporal hybrid attention CSTA mechanism. The calculation formula is as follows: Where, represents the global average pooling result along the spatial-temporal dimension, is a learnable weight matrix used to model the dependencies between channels, is the Sigmoid activation function to generate the channel attention weights, represents element-wise multiplication, is the output feature tensor of the Dense Block. The addition operation retains the original feature information, and an enhanced feature tensor is output. .

[0023] As a further preferred solution of the fog boundary layer parameterization scheme correction method based on the multi-scale physical coupling network of the present invention, in step S3, the U-Transformer module of the cloud water phase branch includes:

[0024] S3.4. The input variables are cloud water content Qc, rain water content Qr, ice crystal content Qi, and snow content Qs. Multi-scale features are extracted through a U-shaped encoding-decoding structure. The input data dimension is H×W×T×4, where the number of channels is 4;

[0025] S3.5. The encoder adopts 2-level downsampling and combines a multi-scale adaptive position encoding MSPE block layer. Let the original three-dimensional coordinates of each position point be , where , are spatial coordinates, is the time index. For each dimension , different scale sets are selected, where is a positive integer used to control the number of frequency resolution levels of the encoding, and the absolute position encoding is calculated: Where, is the coordinate on the dimension , is the single-dimensional encoding vector, and the encoding vectors of each dimension are concatenated: Among them, is the complete absolute position encoding, and for each scale introduce learnable weights , which are used to adjust the importance of features at different scales; for any two positions and in the attention calculation, calculate the coordinate difference: Map the coordinate difference to the relative position encoding through a lightweight MLP:

[0026] This relative position encoding has the same dimension as the hidden dimension of the MSPE block. In each MSPE block layer, add the absolute position encoding of each position to the input features after linear mapping, and use the relative position encoding as the bias term for attention weight calculation to adjust the attention intensity between different positions, thereby enhancing the modeling ability of multi-scale spatio-temporal relationships;

[0027] S3.6. The decoder uses a 3×3×3 convolutional kernel with a stride of 2 and skip connections through 2-level upsampling to fuse low-level local features and high-level semantic information, and outputs a multi-scale cloud water phase state feature tensor .

[0028] As a further preferred solution of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S4, the implementation of the spatio-temporal coupling attention module ST-CAM includes:

[0029] S4.1. The input feature tensor is the output of the temperature-humidity phase state branch and the cloud water phase state branch, with a dimension of H×W×T×C. Build a multi-resolution feature pyramid using 3D convolutional kernels with dilation rates of 1, 2, and 4 respectively. The size of the 3D convolutional kernel is 3×3×3, the stride is 1, and the padding is same. The output feature channel numbers are set to , , , where < < , to achieve dimensionality increase operation. Fuse the features of the three scales into a unified feature tensor through a 1×1×1 convolutional layer, whose number of channels is

[0030] S4.2. Model the lag effect of the development of the inversion layer along the time axis through a bidirectional GRU, and the input feature tensor Unfolding along the time axis into a sequence , the bidirectional GRU contains 2 layers, the hidden state dimension of each layer is 128, the activation function is tanh, and the hidden state update formula is:

[0031] , wherein, is the update gate, is the reset gate, , , , , , are learnable weight matrices, , , are bias terms, is the Sigmoid activation function, is the element-wise multiplication, is the unidirectional hidden state, and the bidirectional GRU generates the final hidden state through forward and backward calculations , enhancing the ability of temporal dynamic modeling;

[0032] S4.3. Calculate the correlation weights between grid points using the spatial self-attention mechanism to generate a dynamic attention map, and the calculation formula is as follows: where SA represents the spatial attention mechanism, which is used to calculate the attention weights based on the feature similarity between grid points, , , are the query, key, and value vectors respectively, , , are linear transformation matrices, and each matrix linearly transforms the number of channels of the input , keeping the number of channels unchanged, and re-encoding the semantic representation of each grid point in different feature subspaces to provide an adapted feature subspace mapping for subsequent attention score calculation, is the key vector dimension, outputting the attention-weighted feature tensor, and then multiplying it element-wise with to generate the final fused feature tensor .

[0033] As a further preferred solution of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S5, the physical constraint loss function includes:

[0034] S5.1. The pixel-level reconstruction loss uses the weighted mean square error (WMSE) to constrain the consistency between the correction field and the large eddy simulation (LES) data, and is defined as: wherein, represents the value obtained by the correction model SMAP-Net at the position ( )'s predicted correction field, is the true value of the LES simulation, is the dynamic weight, and the calculation formula is: where, is the position 's terrain height, is the fog top height, is the standard deviation. The weight design weights the deviation between the terrain height and the fog top height in the form of a Gaussian function, thereby enhancing the error constraint of the key layer near the fog top in the loss function and improving the simulation accuracy of the key area;

[0035] S5.2. The mass-momentum conservation term strengthens the physical self-consistency by minimizing the residual of the Navier-Stokes equation and is defined as: where, is the air density, is the three-dimensional wind speed vector, is the air pressure, is the gravitational acceleration, represents the divergence of the mass flux and is used to constrain the continuity equation, represents the material derivative of the wind speed, represents the balance relationship between the inertial force, pressure gradient force, and gravity in momentum conservation, , are hyperparameters for adjusting the weights of the two terms and are obtained through grid search and cross-validation;

[0036] S5.3. The visibility gradient matching term uses a contrastive loss function to maximize the similarity between the visibility feature and the surface temperature feature, so as to strengthen the sensitivity of the model to radiative cooling and fog layer changes. This loss function is defined as: where, is the feature vector of the visibility field, is the feature vector of the surface temperature field, is the negative sample feature vector, is the cosine similarity function, is the temperature parameter. The feature vectors are extracted by a three-layer convolutional neural network CNN. Each layer uses a fixed-size 3×3 convolutional kernel, and the number of output channels increases layer by layer to capture different levels of spatial patterns and semantic information;

[0037] S5.4. The total loss function is the weighted sum of each part: where, and are adaptive weight parameters and are dynamically optimized through a small multi-layer perceptron MLP; MLP contains two fully connected layers, and the input is the of the current training epoch, , , the output is and , and the optimization objective is to minimize the prediction error on the validation set.

[0038] As a further preferred solution of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, it includes the SMAP-Net model, and the SMAP-Net model includes a double-branch feature extraction module, a spatio-temporal coupling attention module, and a physical constraint loss function module;

[0039] The double-branch feature extraction module extracts the temperature-humidity phase state features and cloud-water phase state features respectively through a double-branch heterogeneous network structure. Among them, the temperature-humidity phase state branch uses the Dense Block and CSTA mechanisms to capture the multi-scale features of temperature and humidity, and the cloud-water phase state branch uses the U-Transformer module to extract the spatial distribution features of cloud-water content;

[0040] The spatio-temporal coupling attention module fuses the double-branch features output by the multi-scale physical coupling network module, performs spatio-temporal encoding using 3D convolution, models the temporal dependence relationship through bidirectional GRU, and combines the dynamic attention weighting mechanism to jointly model the non-linear relationship between turbulence, radiation, and phase change, and outputs an optimized fog area feature representation;

[0041] The physical constraint loss function module embeds physical constraints during the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, and optimizes the consistency between the data-driven features and physical laws through adaptive weight allocation, improving the generalization ability of the model under complex terrain conditions.

[0042] Compared with the prior art by adopting the above technical solutions, the present invention has the following technical effects:

[0043] 1. By designing a double-branch heterogeneous network structure, the present invention respectively uses the Dense Block and U-Transformer modules to extract local details and large-scale evolution features for the different physical properties of the temperature-humidity phase state and the cloud-water phase state. The temperature-humidity phase state sub-module strengthens the fine extraction of local structures such as the top of the inversion layer and humidity gradient, and the cloud-water phase state sub-module captures the multi-scale dynamic evolution during the processes of cloud-water condensation, sedimentation, and freezing. Overall, it makes up for the problem of insufficient fine-grained process characterization of traditional parameterization schemes under low turbulence intensity conditions.

[0044] 2. The present invention embeds multiple physical constraints such as mass conservation, momentum conservation, and visibility gradient matching during the training process. Through the joint optimization strategy, while improving the prediction accuracy, it ensures the consistency of the internal physical relationship between output variables, effectively enhancing the stability and reliability of the model under complex weather scenarios such as the development of the inversion layer and the intermittent outbreak of turbulence, and having strong business application value.

[0045] 3. Under complex terrain conditions, the present invention can accurately capture the multi-scale modulation effects of terrain on local radiative cooling, turbulence weakening, and fog generation and evolution. At the same time, by introducing a deep learning framework, it effectively reduces the dependence on large-scale and high-density observational data, reduces the sensitivity of numerical models to the quality of external input data, and improves the applicability of the model in data-sparse regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention;

[0047] Figure 2 It is a structural diagram of the overall SMAP-Net network model of the present invention;

[0048] Figure 3 It is a structural diagram of the U-Transformer feature extraction network of the present invention;

[0049] Figure 4 It is a structural diagram of the ST-CAM feature fusion network of the present invention;

[0050] Figure 5 It is a comparison diagram of the correlation coefficient matrices of the SMAP-Net of the present invention and each model on multi-physical quantity pairs;

[0051] Figure 6 It is a spatial distribution diagram of the liquid water content of the SMAP-Net of the present invention and each model;

[0052] Figure 7 It is a scatter diagram of the correction accuracy of the liquid water path of the SMAP-Net of the present invention and each model;

[0053] Figure 8 It is a spatio-temporal comparison diagram of the visibility of the SMAP-Net of the present invention and different parameterization schemes. DETAILED DESCRIPTION OF THE INVENTION

[0054] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the application will be further elaborated in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments made by other researchers in the field based on this embodiment belong to the protection scope of the present invention. At the same time, for the step numbers in the embodiments of the present invention, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0055] In one embodiment of the present invention, the flow chart of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network is as Figure 1As shown in the figure, it includes the following steps:

[0056] S1. Generate multi-parameterized boundary layer simulation data using the Weather Research and Forecasting (WRF) model. The specific process is as follows:

[0057] Input the ERA5 reanalysis data (horizontal resolution 0.25°×0.25°, time resolution 6 hours) as the initial field and boundary conditions into the WRF model, and configure the WRF model parameters, including physical parameterization schemes (boundary layer schemes ACM2, YSU, QNSE) and grid settings (horizontal resolution 3 km, vertical resolution 50 layers, top pressure 50 hPa), to generate simulation results with a horizontal resolution of 3 km. The simulation data includes thermodynamic variables such as temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), air pressure (P), water substance variables such as cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), snow content (Qs), and dynamic field variables such as vertical velocity (W).

[0058] S2. Generate an initial feature tensor by processing the input data through feature encoding, and use the multi-head attention mechanism to screen key variables. The specific implementation includes the following steps:

[0059] S2.1. The input variables include temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), snow content (Qs), air pressure (P), and vertical velocity (W). Organize these variables into a three-dimensional spatio-temporal tensor with dimensions H×W×T×C, where H×W represents the spatial resolution, T represents the time step, and C = 9 represents the number of variable channels;

[0060] S2.2. Extract spatio-temporal local features through a parallel three-dimensional convolutional layer. The convolutional kernel size is 3×3×3, the stride is 1, and the padding is 1 to retain the spatial and time dimensions of the input tensor and generate an initial feature tensor , with the number of output channels being 64. Use the ReLU activation function to perform a non-linear transformation on the features to enhance the expression ability of the model;

[0061] S2.3. Use the multi-head attention mechanism to screen the initial feature tensor to highlight the variables that have a greater impact on the evolution of the fog area (such as temperature gradient, humidity distribution). The calculation formula is as follows: where , , are the query, key, and value vectors respectively, is a learnable linear transformation matrix, and each matrix is responsible for transforming the input feature tensor Perform a linear transformation on the channel dimension, keeping the dimension unchanged and continuously updating it during the training process to optimize the attention calculation, achieve re-weighting of information between channels and feature subspace mapping, so that different variable combinations can adapt to subsequent correlation modeling. is the dimension of the key vector, and the attention mechanism is configured with 8 heads to output the filtered feature tensor. to highlight the key variables that have a greater impact on the evolution of the fog area.

[0062] S3. Construct a multi-scale physical coupling network (SMAP-Net), extract temperature-humidity phase state features and cloud-water phase state features through a double-branch heterogeneous network structure. The overall structure of SMAP-Net is as Figure 2 shown, and specifically includes the following processes:

[0063] S3.1. The input variables of the temperature-humidity phase state branch are temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), and air pressure (P). Spatiotemporal local features are extracted through 3D convolution (convolution kernel size is 3×3×3, stride is 1, padding is 1) to generate the initial feature tensor. where the number of output channels is 64;

[0064] S3.2. Adopt a 4-level Dense Block stacking structure, each level contains a bottleneck structure, and the bottleneck structure successively includes: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, and 1×1×1 convolution for dimensionality increase. The features of the previous layer and the current layer are concatenated in channels through skip connections to output the feature tensor. where the number of output channels is 4×64 = 256 to enhance the feature reuse ability;

[0065] S3.3. Enhance the feature response of the inversion layer top and the humidity jump area through the channel-spatiotemporal hybrid attention (CSTA) mechanism. The calculation formula is as follows: where, represents the global average pooling result along the space-time dimension, is a learnable weight matrix used to model the dependencies between channels, is the Sigmoid activation function to generate the channel attention weights, represents element-wise multiplication, is the output feature tensor of the Dense Block, and the addition operation retains the original feature information to output the enhanced feature tensor. .

[0066] S3.4. The input variables of the cloud-water phase state branch are cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), and snow content (Qs). Multi-scale features are extracted through a U-shaped encoding-decoding structure. The structure is as Figure 3As shown, the input data dimension is H×W×T×4, where the number of channels is 4;

[0067] S3.5. The encoder adopts 2-level downsampling and combines with the multi-scale self-adaptive position encoding MSPE block layer. Let the original three-dimensional coordinates of each position point be , where , are spatial coordinates, is the time index. For each dimension , select different scale sets , where , and calculate the absolute position encoding: where, is the component of the coordinate on the dimension , is the single-dimension encoding vector. Concatenate the encoding vectors of each dimension:

[0068] where, is the complete absolute position encoding. Introduce a learnable weight for each scale to adjust the importance of features at different scales; for any two positions and in the attention calculation, calculate the coordinate difference: Map the coordinate difference to the relative position encoding through a lightweight MLP: where, matches the hidden dimension of the MSPE block. In each MSPE block layer, add the result after linearly mapping to the input feature, and use as the attention score bias term to enhance the multi-scale spatio-temporal modeling ability;

[0069] S3.6. The decoder fuses the low-level local features and high-level semantic information through 2-level upsampling (using a 3×3×3 convolution kernel with a stride of 2) and skip connections, and outputs the multi-scale cloud water phase state feature tensor .

[0070] S4. Fuse the features of the two branches through the spatio-temporal coupled attention module (ST-CAM) to model the non-linear relationship between turbulence, radiation and phase change. The structure of ST-CAM is as Figure 4 shown, and the specific steps are as follows:

[0071] S4.1. The input feature tensor is the output of the temperature-humidity phase branch and the cloud water phase branch, with a dimension of H×W×T×128. A multi-resolution feature pyramid is constructed using 3D convolutional kernels with dilation rates of 1, 2, and 4 respectively (size 3×3×3, stride 1, padding same), and the number of output channels is 64, 128, and 256 respectively. They are fused into a unified feature tensor through 1×1×1 convolution to expand the receptive field and capture multi-scale spatio-temporal patterns;

[0072] S4.2. The lag effect of the development of the temperature inversion layer is modeled along the time axis through a bidirectional GRU. The input feature tensor is unfolded into a sequence along the time axis . The bidirectional GRU contains 2 layers, with the hidden state dimension of each layer being 128, the activation function being tanh, and the hidden state update formula being: , where, is the update gate, is the reset gate, , , , , , are learnable weight matrices, , , are bias terms, is the Sigmoid activation function, is the element-wise multiplication, is the unidirectional hidden state, and the bidirectional GRU generates the final hidden state through forward and backward calculations to enhance the ability of temporal dynamic modeling.

[0073] S4.3. The spatial self-attention mechanism is used to calculate the correlation weights between grid points to generate a dynamic attention map. The calculation formula is as follows: where , , are the query, key, and value vectors respectively, , , are linear transformation matrices. Each matrix linearly transforms the number of channels of the input while keeping the number of channels unchanged, and re-encodes the semantic representation of each grid point in different feature subspaces to provide an adapted feature subspace mapping for subsequent attention score calculation. is the key vector dimension. The output attention-weighted feature tensor is multiplied element-wise with to generate the final fused feature tensor .

[0074] S5. Embed a physical constraint loss function during the decoding stage to optimize the correction results of the boundary layer variables, specifically including the following steps:

[0075] S5.1. The pixel-level reconstruction loss uses weighted mean square error (WMSE) to constrain the consistency between the correction field and large eddy simulation (LES) data, defined as: where, represents the predicted correction field of the model at position ( ), is the true value of the LES simulation, is the dynamic weight, and the calculation formula is: where, is the terrain height at position , is the fog top height, is the standard deviation, and the weight design highlights the prediction accuracy in the area near the fog top;

[0076] S5.2. The mass-momentum conservation term strengthens physical self-consistency by minimizing the residual of the Navier-Stokes equation, defined as: where, is the air density, is the three-dimensional wind speed vector, is the air pressure, is the acceleration due to gravity, represents the divergence of the mass flux, constraining the continuity equation, is the material derivative of the wind speed, and combines the pressure gradient and gravity terms to reflect momentum conservation , are hyperparameters, determined by grid search and cross-validation;

[0077] S5.3. The visibility gradient matching term maximizes the similarity between visibility and surface temperature features through contrastive loss, defined as: where, is the feature vector of the visibility field, is the feature vector of the surface temperature field, is the negative sample feature vector, is the cosine similarity function, is the temperature parameter, and the feature vectors are extracted through a three-layer convolutional neural network (CNN), with a 3×3 convolutional kernel used in each layer, and the number of channels being 64, 128, and 256 respectively;

[0078] S5.4. The total loss function is the weighted sum of each part: where, and are adaptive weight parameters, dynamically optimized through a small multi-layer perceptron (MLP). The MLP contains two fully connected layers, and the input is the current training epoch , , , the output is and , and the optimization goal is to minimize the prediction error on the validation set.

[0079] S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content, and visibility, and improve the simulation accuracy of the liquid water path (LWP) and liquid water content (LWC) in the fog area.

[0080] The present invention also includes a multi-scale physical coupling network (SMAP-Net) model, and the multi-scale physical coupling network (SMAP-Net) model includes a dual-branch feature extraction module, a spatio-temporal coupling attention module, and a physical constraint loss function module;

[0081] The dual-branch feature extraction module extracts the temperature-humidity phase state features and cloud water phase state features through a dual-branch heterogeneous network structure. Among them, the temperature-humidity phase state branch uses the Dense Block and CSTA mechanisms to capture the multi-scale features of temperature and humidity, and the cloud water phase state branch uses the U-Transformer module to extract the spatial distribution features of cloud water content;

[0082] The spatio-temporal coupling attention module fuses the dual-branch features output by the multi-scale physical coupling network module, performs spatio-temporal encoding using 3D convolution, models the temporal dependence relationship through bidirectional GRU, and combines the dynamic attention weighting mechanism to jointly model the non-linear relationship between turbulence, radiation, and phase change, and outputs an optimized fog area feature representation;

[0083] The physical constraint loss function module embeds physical constraints during the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, and optimizes the consistency between the data-driven features and physical laws through adaptive weight allocation, and improves the generalization ability of the model under complex terrain conditions.

[0084] In addition, to systematically evaluate the performance advantages of the multi-scale physical coupling network (SMAP-Net) proposed by the present invention in the multi-physical quantity collaborative correction in the radiation fog boundary layer parameterization, the present invention comprehensively compares the performance of SMAP-Net with traditional boundary layer parameterization schemes and existing deep learning models in a complex fog area environment. Figure 5 This is a comparison chart of the correlation coefficient matrices of SMAP-Net and each model for multi-physical quantity pairs of the present invention. The results show that SMAP-Net has the highest consistency with the LES benchmark value, and the average deviation of all variable pairs is only 0.03, highlighting its superior ability to capture the collaborative interaction between thermodynamic and microphysical variables. To further evaluate the physical consistency of each model in fog area simulation. Figure 6Shows the spatial distribution map of the liquid water content of the SMAP-Net of the present invention and each model. The results show that SMAP-Net can relatively accurately reproduce the distribution characteristics of the LWC in the fog area. Especially in complex terrain areas, its simulation results are highly consistent with the LES true value.

[0085] Finally, the present invention selects a typical strong dense fog event for case analysis. Figure 7 Is the scatter plot of the liquid water path correction accuracy of the SMAP-Net of the present invention and each model, which is used to evaluate the deviation of each model compared with the LES true value. From the results, SMAP-Net highly coincides with the reference line at most points, and its root mean square error of the liquid water path is significantly better than the traditional boundary layer parameterization scheme. Figure 8 Is the spatio-temporal comparison map of visibility between the SMAP-Net of the present invention and different parameterization schemes. The results show that the SMAP-Net model can accurately reproduce the fog outbreak process, with a low error from the observation time. Thanks to its dynamic learning ability for the non-equilibrium state of radiative cooling, the fog area boundary is highly coupled with the terrain undulation, especially showing a fog patch distribution at the sub-kilometer scale in karst basins and narrow valleys, which is significantly improved compared with the traditional scheme.

[0086] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network, characterized in that, It includes the following steps: S1. Use the numerical weather prediction model WRF to generate multi-parameterized boundary layer simulation data. The input data includes thermodynamic variables, water substance variables, and dynamic field variables. S2. Generate an initial feature tensor by processing the input data through feature encoding, and use the multi-head attention mechanism to screen out the key variables with greater influence weights on the evolution of the fog area. S3. Construct a multi-scale physical coupling network SMAP-Net, and extract the temperature-humidity phase state features and cloud-water phase state features at different scales through a dual-branch heterogeneous network structure. S4. Fusion the dual-branch features through the spatio-temporal coupling attention module ST-CAM, and adopt three-dimensional convolutional spatio-temporal encoding, bidirectional GRU time series modeling, and dynamic attention weighting to jointly model the non-linear relationship between turbulence, radiation, and phase change. In step S4, the implementation of the spatio-temporal coupling attention module ST-CAM includes: S4.

1. The input feature tensor is the output of the temperature-humidity phase branch and the cloud water phase branch, with dimensions of H×W×T×C. A multi-resolution feature pyramid is constructed using 3D convolutional kernels with dilation rates of 1, 2, and 4 respectively. The size of the 3D convolutional kernel is 3×3×33, the stride is 1, and the padding is same. The output feature channel numbers are set to C1, C2, and C3 respectively, where C1 < C2 < C3, to achieve the dimension increase operation. The features of the three scales are fused into a unified feature tensor F through a 1×1×1 convolutional layer fused , whose number of channels is C f , to expand the model's receptive field and capture the multi-scale spatio-temporal evolution pattern, and enhance the modeling ability of the fog area boundary layer variables; S4.

2. Model the lag effect of the development of the temperature inversion layer along the time axis through bidirectional GRU, and input the feature tensor F fused Unfold it into a sequence along the time axis The bidirectional GRU contains 2 layers, the hidden state dimension of each layer is 128, the activation function is tanh, and the hidden state update formula is: z t = σ(W z F t + U z h t-1 + b z ), r t = σ(W r F t + U r h t-1 + b r )C1C2C3C f Among them, z t is the update gate, r t is the reset gate, W z , W r , W h , U z , U r , U h are learnable weight matrices, b z , b r , b h are bias terms, σ is the Sigmoid activation function, ⊙ is the element-wise multiplication, h t is the unidirectional hidden state, and the bidirectional GRU generates the final hidden state through forward and backward calculations Enhance the ability of temporal dynamic modeling; S4.

3. Use the spatial self-attention mechanism to calculate the correlation weights between grid points and generate a dynamic attention map. The calculation formula is as follows: Among them, SA represents the spatial attention mechanism, which is used to calculate the attention weights based on the feature similarity between grid points. They are the query, key, and value vectors respectively. is the linear transformation matrix, and each matrix linearly transforms the number of channels of the input h t while keeping the number of channels unchanged, re-encodes the semantic representation of each grid point in different feature subspaces, and provides an adapted feature subspace mapping for subsequent attention score calculation. d s is the key vector dimension, outputs the attention-weighted feature tensor, and then multiplies it element-wise with F fused to generate the final fused feature tensor F stcam ; S5. In the training optimization process, introduce a physical constraint loss function, including the mass-momentum conservation equation and the visibility gradient matching term, and perform collaborative optimization of data-driven features and physical laws through adaptive weight allocation to correct the boundary layer variables. S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content, and visibility, to improve the simulation accuracy of the liquid water path LWP and liquid water content LWC in the fog area.

2. The correction method for the fog boundary layer parameterization scheme based on the multi-scale physical coupling network according to claim 1, wherein In step S2, the specific implementation of the encoding stage includes: S2.

1. The input variables include temperature T, relative humidity RH, water vapor mixing ratio Qv, cloud water content Qc, rain water content Qr, ice crystal content Qi, snow content Qs, air pressure P, and vertical velocity W. Organize the input data into a three-dimensional spatio-temporal tensor with dimensions of H×W×T×C, where H×W represents the spatial resolution, T represents the time step, and C represents the variable channel number. S2.

2. Extract spatio-temporal local features through a parallel three-dimensional convolutional layer. The size of the convolutional kernel of the three-dimensional convolutional layer is 3×3×3, the stride is 1, and the padding is 1; generate an initial feature tensor where C out represents the number of output channels, and a ReLU activation function is used for non-linear transformation; S2.

3. Use the multi-head attention mechanism to screen the initial feature tensor F init The calculation formula is as follows: Among them, W Q F init , W K F init , W V F init are the query, key, and value vectors respectively, and W Q , W K , W V ∈R 64×64 is a learnable linear transformation matrix. Each matrix is responsible for linearly transforming the channel dimension of the input feature tensor F init , keeping the dimension unchanged and continuously updated during training to optimize the attention calculation, realize the re-weighting of information between channels and the feature subspace mapping, so that different variable combinations can adapt to the subsequent correlation modeling, and d k is the dimension of the key vector. The attention mechanism is configured with N head heads, where N head is an adjustable hyperparameter, and the output is the filtered feature tensor F select ∈R H×W×T×64 to highlight the key variables that have a greater impact on the evolution of the fog area.

3. The correction method for the fog boundary layer parameterization scheme based on the multi-scale physical coupling network according to claim 1, characterized in that, In step S3, the specific implementation of the temperature-humidity phase state branch includes: S3.

1. The input variables are temperature T, relative humidity RH, water vapor mixing ratio Qv, and air pressure P. Spatiotemporal local features are extracted through three-dimensional convolution. The size of the convolution kernel of the three-dimensional convolution is 3×3×3, the stride is 1, and the padding is 1, generating an initial feature tensor F thermo ∈R H×W×T×64 , where the number of output channels is 64; S3.

2. Adopt a 4-level stacked Dense Block structure, each level contains a bottleneck structure, and the bottleneck structure sequentially includes: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, and 1×1×1 convolution for dimensionality increase. The features of the previous layer and the current layer are concatenated in channels through skip connections, and the output feature tensor F dense ∈R H×W×T×256 is obtained, where the number of output channels is 4×64 = 256 to enhance the feature reuse ability; S3.

3. Enhance the feature response of the inversion layer top and the humidity jump region through the channel-spatio-temporal hybrid attention CSTA mechanism. The calculation formula is as follows: Among them, GAP(F dense ) represents the global average pooling result along the spatio-temporal dimension, W c is a learnable weight matrix for modeling the dependencies between channels, σ is the Sigmoid activation function that generates the channel attention weights, represents element-wise multiplication, F dense is the output feature tensor of the Dense Block, and the addition operation preserves the original feature information, outputting the enhanced feature tensor 4. The correction method for the fog boundary layer parameterization scheme based on the multi-scale physical coupling network according to claim 1, wherein In step S3, the U-Transformer module of the cloud-water phase state branch includes: S3.

4. The input variables are cloud water content Qc, rain water content Qr, ice crystal content Qi, and snow content Qs. Extract multi-scale features through a U-shaped encoding-decoding structure. The input data dimension is H×W×T×4, where the number of channels is 4. S3.

5. The encoder adopts 2-level downsampling and combines with the multi-scale self-adaptive position encoding MSPE block layer. Let the original three-dimensional coordinates of each position point be p = (p x , p y , p t ), where p x , p y are spatial coordinates, and p t is the time index. For each dimension d ∈ {x, y, t}, different scale sets {2 k π∣k = 0,..., K - 1} are selected, where K is a positive integer used to control the number of frequency resolution levels of the encoding, and the absolute position encoding is calculated: E d (p d ) = [sin(2 0 πp d ), cos(2 0 πp d ),..., sin(2 K-1 πp d ), cos(2 K-1 πp d )] where p d is the component of coordinate p in dimension d, and E d (p d ) is the single-dimension encoding vector. Concatenate the encoding vectors of each dimension: E abs (p) = Concat(E x (p x ), E y (p y ), E t (p t )) Among them, E abs (p) is the complete absolute position encoding, and a learnable weight w k is introduced for each scale k to adjust the importance of features at different scales; for any two positions p i and p j in the attention calculation, calculate the coordinate difference: Δp ij = p i - p j Map the coordinate difference Δp ij to relative position encoding through a lightweight MLP: E rel (p i ,p j ) = MLP(Δp ij ) The relative position encoding E rel (p i , p j ) has the same dimension as the hidden dimension of the MSPE block. In each MSPE block layer, the absolute position encoding E abs (p) is added to the input features after being linearly mapped, and the relative position encoding E rel (p i , p j ) is used as a bias term for calculating the attention weights to adjust the attention intensity between different positions, thereby enhancing the modeling ability of multi-scale spatio-temporal relationships; S3.

6. The decoder uses a 3×3×3 convolutional kernel with 2-level upsampling, a stride of 2, and skip connections to fuse low-level local features and high-level semantic information, and outputs a multi-scale cloud water phase state feature tensor F cloud .

5. The correction method for the fog boundary layer parameterization scheme based on the multi-scale physical coupling network according to claim 1, wherein In step S5, the physical constraint loss function includes: S5.

1. The pixel-level reconstruction loss uses the weighted mean square error WMSE to constrain the consistency between the correction field and the large eddy simulation LES data, which is defined as: Among them, represents the predicted correction field of the correction model SMAP-Net at position (i, j), is the true value of the LES simulation, w i,j is the dynamic weight, and the calculation formula is: where h i,j is the terrain height at position (i, j), and h fog is the fog top height, σ is the standard deviation, and the weight design weights the deviation between the terrain height and the fog top height in the form of a Gaussian function, thereby enhancing the error constraint of the key layer near the fog top in the loss function and improving the simulation accuracy of the key area; S5.

2. The mass-momentum conservation term strengthens the physical self-consistency by minimizing the residual of the Navier-Stokes equation, which is defined as: where ρ is the air density, u is the three-dimensional wind speed vector, p is the air pressure, and g is the acceleration due to gravity. represents the divergence of the mass flux and is used to constrain the continuity equation. represents the material derivative of the wind speed. represents the balance relationship among the inertial force, pressure gradient force, and gravity in the momentum conservation. λ1 and λ2 are hyperparameters for adjusting the weights of the two terms, which are obtained through grid search and cross-validation. S5.

3. The visibility gradient matching term uses a contrast loss function to maximize the similarity between the visibility feature and the surface temperature feature to enhance the sensitivity of the model to radiative cooling and fog layer changes. This loss function is defined as: Among them, f VIS is the eigenvector of the visibility field, and f T is the eigenvector of the surface temperature field. f k is the negative sample eigenvector, sin(.,.) is the cosine similarity function, τ is the temperature parameter, and the eigenvector is extracted by a three-layer convolutional neural network CNN. Each layer uses a 3×3 convolutional kernel with a fixed size, and the number of output channels increases layer by layer to capture spatial patterns and semantic information at different levels; S5.

4. The total loss function is the weighted sum of each part: L total = L WMSE + αL phys + βL cont Among them, α and β are adaptive weight parameters, dynamically optimized by a small multi-layer perceptron (MLP); the MLP contains two fully connected layers, and the input is L of the current training epoch WMSE , L phys , L cont , and the output is α and β. The optimization objective is to minimize the prediction error on the validation set.

6. A system for correcting a fog boundary layer parameterization scheme based on the multi-scale physical coupling network according to any one of claims 1 to 5, characterized in that, It includes a multi-scale physical coupling network model, and the multi-scale physical coupling network model includes a dual-branch feature extraction module, a spatio-temporal coupling attention module, and a physical constraint loss function module; The dual-branch feature extraction module extracts the temperature-humidity phase state features and the cloud-water phase state features respectively through a dual-branch heterogeneous network structure. Among them, the temperature-humidity phase state branch uses the Dense Block and CSTA mechanisms to capture the multi-scale features of temperature and humidity, and the cloud-water phase state branch uses the U-Transformer module to extract the spatial distribution features of cloud-water content; The spatio-temporal coupling attention module fuses the dual-branch features output by the multi-scale physical coupling network module, performs spatio-temporal encoding using 3D convolution, models the temporal dependence relationship through a bidirectional GRU, and combines a dynamic attention weighting mechanism to jointly model the non-linear relationship between turbulence, radiation, and phase change, and outputs an optimized fog area feature representation; The physical constraint loss function module embeds physical constraints during the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, and optimizes the consistency between the data-driven features and physical laws through adaptive weight allocation, improving the generalization ability of the model under complex terrain conditions.

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