A state space model-based multivariate weather field unsupervised super-resolution reconstruction method, system, terminal device and storage medium

Abstract

The application discloses a kind of multivariate weather field unsupervised super-resolution reconstruction method, system, terminal equipment and storage medium based on state space model, it is related to meteorological data processing technical field.The method comprises the following steps: obtaining low-resolution multivariate weather field data and carrying out classification normalization processing and up-sampling, then input state space model in sequence form, obtain high-resolution reconstruction result;Reconstruction consistency loss function, spectral constraint loss function and adversarial training loss function are constructed, and based on the loss function constructed and high-resolution reconstruction result, the state space model is iteratively optimized and trained to obtain the super-resolution reconstruction model of training completion.The application can realize the high-resolution reconstruction of multivariate weather field under the condition of no matching high and low resolution data, while maintaining the physical consistency between different meteorological variables, and effectively restoring high-frequency detail information.

Description

Technical Field

[0001] This invention relates to the field of meteorological data processing technology, and in particular to an unsupervised super-resolution reconstruction method, system, terminal equipment, and storage medium for multivariable meteorological fields based on a state-space model. Background Technology

[0002] As intelligent systems increasingly demand higher precision in environmental perception, high-resolution meteorological data plays a crucial role in scenarios such as path planning, environmental modeling, and dynamic decision-making. However, existing meteorological data typically originates from numerical weather prediction models, which have low spatial resolution and cannot meet the needs for detailed local meteorological information. Therefore, reconstructing low-resolution meteorological fields into high-resolution meteorological fields has become an important research direction.

[0003] Existing meteorological super-resolution methods mainly fall into three categories: traditional numerical methods, supervised learning methods, and generative model methods. Traditional numerical methods, such as interpolation and dynamic downscaling, are computationally complex and time-consuming, making them difficult to meet the needs of real-time applications. Supervised learning methods rely on a large amount of paired high- and low-resolution sample data, but such paired data is difficult to obtain in real-world scenarios, severely limiting the model's generalization ability. In recent years, generative methods such as diffusion models have improved detail performance, but they generally suffer from high computational complexity, high training costs, and insufficient multivariate collaborative modeling capabilities. To address these issues, unsupervised methods attempt to achieve super-resolution reconstruction in the absence of paired data, but they still have significant shortcomings in multivariate meteorological scenarios: on the one hand, it is difficult to maintain the physical correlation and dimensional consistency between different meteorological variables; on the other hand, it lacks the ability to effectively model global long-distance dependencies and struggles to capture teleconnection structures in the meteorological field; furthermore, the ability to recover high-frequency details is insufficient, and the generated results are prone to over-smoothing, affecting physical consistency.

[0004] Therefore, there is an urgent need for a super-resolution reconstruction method for meteorological fields that can simultaneously achieve multivariate physical consistency, long-distance spatial dependency modeling, and high-frequency detail recovery without the need for paired data, in order to fill the gaps in existing technologies. Summary of the Invention

[0005] The technical problem this invention aims to solve is that, in the field of multivariate meteorological field super-resolution reconstruction, existing methods heavily rely on paired high- and low-resolution data, making it difficult to achieve high-precision reconstruction under unsupervised conditions. Furthermore, existing methods struggle to maintain physical consistency and dimensional relationships between different meteorological variables, and their ability to recover high-frequency details is insufficient, leading to over-smoothing in the reconstruction results. Therefore, an effective solution is urgently needed to address these technical problems.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides an unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model, the method comprising: Low-resolution multivariate meteorological field data is acquired, and the low-resolution multivariate meteorological field data is classified and normalized to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization process is used to perform different normalization processes according to the symmetry of the physical properties of the meteorological variables. After upsampling the normalized meteorological field data, it is input into the state space model in sequence form. The input sequence is modeled position by position through hidden state recursion to obtain high-resolution reconstruction results. A reconstruction consistency loss function, a spectrum constraint loss function, and an adversarial training loss function are constructed. The reconstruction consistency loss function is used to constrain the consistency between the high-resolution reconstruction result after downscaling and the low-resolution multivariate meteorological field data. The spectrum constraint loss function is used to constrain the consistency of the energy distribution between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain. The adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network. Based on the constructed loss function and the high-resolution reconstruction results, the state-space model is iteratively optimized and trained to obtain a trained super-resolution reconstruction model, wherein the trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

[0007] In one implementation, the step of acquiring low-resolution multivariate meteorological field data and performing classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data includes: Obtain raw multivariate meteorological field data that includes surface variables and multi-level atmospheric variables; The original multivariate meteorological field data is resampled to a unified low-resolution two-dimensional spatial grid and spliced ​​along the channel dimension to form the meteorological field input tensor. The variable channels in the meteorological field input tensor are divided into symmetric variables and asymmetric variables according to the symmetry of their physical properties. The symmetric variables include wind field components and precipitation variables, and the asymmetric variables include temperature variables, humidity variables, and geopotential height variables. For each symmetric variable in the meteorological field input tensor, symmetric variable normalization is performed, wherein the symmetric variable normalization includes dividing the symmetric variable by the standard deviation of the corresponding variable channel; For each asymmetric variable in the meteorological field input tensor, asymmetric variable normalization is performed, wherein the asymmetric variable normalization includes subtracting the mean of the corresponding variable channel from the asymmetric variable and then dividing by the standard deviation of the corresponding variable channel. The normalized meteorological field input tensor is used as the normalized meteorological field data.

[0008] In one implementation, the step of upsampling the normalized meteorological field data and inputting it as a sequence into a state-space model, and then performing position-by-position modeling on the input sequence through hidden state recursion to obtain a high-resolution reconstruction result includes: The normalized meteorological field data is upsampled to make its spatial size consistent with the target high resolution, thus obtaining upsampled meteorological field data. The two-dimensional spatial grid of the upsampled meteorological field data is flattened into a one-dimensional sequence according to a preset scanning path; The one-dimensional sequence is input into a state-space model, which encodes the meteorological field data at each position in the one-dimensional sequence through hidden state recursion to obtain an encoded feature sequence. After restoring the encoded feature sequence to a two-dimensional spatial layout, the features of each meteorological variable are fused to obtain a high-frequency residual signal; The upsampled meteorological field data is superimposed with the high-frequency residual signal through a residual connection structure to obtain the high-resolution reconstruction result.

[0009] In one implementation, the spectral constraint loss function is constructed, including: A two-dimensional Fourier transform is performed on the high-resolution reconstruction results output by the state-space model to obtain the spectral representation of each variable channel; The spectral representation is radially averaged to calculate the energy distribution within different frequency ranges, thus obtaining the radially averaged power spectrum. Based on the radial average power spectrum, the power spectrum difference between the high-resolution reconstruction result and the real high-resolution meteorological field data is calculated on a logarithmic scale in the frequency domain, and used as the spectral constraint loss function.

[0010] In one implementation, the adversarial training loss function is constructed, including: A discriminant network is constructed, which is used to compare the high-resolution reconstruction results generated by the state space model with the real high-resolution meteorological field data in local areas, and output the authenticity score of each local area. Using the state-space model as a generator, the discriminator loss is calculated based on the deviation between the score output by the discriminator network from the real high-resolution meteorological field data and the true label, and the deviation between the score output by the discriminator network from the high-resolution reconstruction results generated by the state-space model and the false label. The discriminator loss is used to optimize the discriminator network. The generator adversarial loss is calculated based on the deviation between the score output by the discriminant network and the true label of the high-resolution reconstruction result generated by the state-space model; The generator adversarial loss is used as the adversarial training loss function.

[0011] In one implementation, the iterative optimization training of the state-space model based on the constructed loss function and the high-resolution reconstruction result to obtain the trained super-resolution reconstruction model includes: The state-space model is pre-trained using the reconstruction consistency loss function and the spectral constraint loss function to obtain a pre-trained super-resolution reconstruction model. The pre-trained super-resolution reconstruction model is jointly optimized and trained using the adversarial training loss function, the reconstruction consistency loss function, and the spectral constraint loss function to obtain the trained super-resolution reconstruction model.

[0012] In one implementation, the method further includes: Acquire low-resolution multivariate meteorological field data to be reconstructed; The classification and normalization process is performed on the low-resolution multivariate meteorological field data to be reconstructed to obtain normalized data to be reconstructed. After upsampling the normalized data to be reconstructed, it is input into the trained super-resolution reconstruction model in sequence to obtain high-resolution reconstruction results. Based on the symmetry of the physical properties of meteorological variables, the high-resolution reconstruction results are classified and inversely normalized to obtain a high-resolution reconstructed meteorological field.

[0013] Secondly, embodiments of the present invention also provide an unsupervised super-resolution reconstruction system for multivariable meteorological fields based on a state-space model, the system comprising: The preprocessing module is used to acquire low-resolution multivariate meteorological field data and perform classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization processing is used to perform different normalization processing according to the symmetry of the physical properties of the meteorological variables. The preliminary reconstruction module is used to upsample the normalized meteorological field data and input it into the state space model in the form of a sequence. The input sequence is modeled position by position through hidden state recursion to obtain high-resolution reconstruction results. The loss function construction module is used to construct a reconstruction consistency loss function, a spectrum constraint loss function, and an adversarial training loss function. The reconstruction consistency loss function is used to constrain the consistency between the high-resolution reconstruction result after downscaling and the low-resolution multivariate meteorological field data. The spectrum constraint loss function is used to constrain the consistency of the energy distribution between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain. The adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network. The training module is used to iteratively optimize and train the state-space model based on the constructed loss function and the high-resolution reconstruction results to obtain a trained super-resolution reconstruction model, wherein the trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

[0014] Thirdly, embodiments of the present invention also provide a terminal device, the terminal device including a memory, a processor, and a multivariate meteorological field unsupervised super-resolution reconstruction program based on a state-space model stored in the memory and executable on the processor. When the processor executes the multivariate meteorological field unsupervised super-resolution reconstruction program based on a state-space model, it implements the steps of the multivariate meteorological field unsupervised super-resolution reconstruction method based on a state-space model as described in any of the above schemes.

[0015] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing a multivariable meteorological field unsupervised super-resolution reconstruction program based on a state-space model. When the multivariable meteorological field unsupervised super-resolution reconstruction program based on a state-space model is executed by a processor, it implements the steps of the multivariable meteorological field unsupervised super-resolution reconstruction method based on a state-space model as described in any of the above schemes.

[0016] Beneficial Effects: This invention discloses an unsupervised super-resolution reconstruction method, system, terminal device, and storage medium for multivariate meteorological fields based on a state-space model, relating to the field of meteorological data processing technology. The method first acquires low-resolution multivariate meteorological field data and performs classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data. Then, the normalized meteorological field data is upsampled and input into a state-space model in sequence form. The input sequence is modeled position-by-position through hidden state recursion to obtain a high-resolution reconstruction result. Next, a reconstruction consistency loss function, a spectral constraint loss function, and an adversarial training loss function are constructed. Finally, based on the constructed loss functions and the high-resolution reconstruction result, the state-space model is iteratively optimized and trained to obtain a trained super-resolution reconstruction model.

[0017] This invention enables accurate reconstruction of multivariate meteorological fields from low to high resolution without the need for pairing high and low resolution data. While maintaining the physical consistency and dimensional relationships between different meteorological variables, it effectively recovers high-frequency detail information, overcomes the problem of overly smooth reconstruction results, balances long-distance spatial dependency modeling capability and computational efficiency, reduces data acquisition costs, and improves the applicability and scalability of the method under different regions and climatic conditions. Attached Figure Description

[0018] Figure 1 The flowchart illustrates a specific implementation of the unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model, as provided in this invention.

[0019] Figure 2 This is a flowchart illustrating the unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model, as provided in an embodiment of the present invention.

[0020] Figure 3 A schematic diagram illustrating the impact of classification and normalization on spatial structure.

[0021] Figure 4 A schematic diagram illustrating the impact of classification and normalization on the distribution of variable values.

[0022] Figure 5 This is a schematic diagram comparing the spatial and spectral data of different reconstruction methods.

[0023] Figure 6 This is a schematic diagram of the principle of the unsupervised super-resolution reconstruction device for multivariable meteorological fields based on a state-space model provided in this embodiment of the invention.

[0024] Figure 7 This is a block diagram illustrating the internal structure of the terminal device provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0026] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content, operations, or steps, nor does it require execution in the described order. For example, some operations or steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0027] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0028] It should be understood that, in order to clearly describe the technical solutions of the embodiments of the present invention, the terms "first" and "second" are used in the embodiments of the present invention to distinguish identical or similar items with essentially the same function and effect. For example, the first control information and the second control information are only used to distinguish different control information and do not limit their order.

[0029] Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or the order of execution, and that the words "first" and "second" do not necessarily imply that they are different.

[0030] It should also be understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0031] As intelligent systems increasingly demand higher precision in environmental perception, high-resolution meteorological data plays a crucial role in scenarios such as path planning, environmental modeling, and dynamic decision-making. However, existing meteorological data typically originates from numerical weather prediction models, which have low spatial resolution, often at a grid scale of 1° to 2°, making it difficult to meet the needs for detailed local meteorological information. Therefore, reconstructing low-resolution meteorological fields into high-resolution meteorological fields has become an important research direction in this field.

[0032] Currently, existing meteorological super-resolution methods mainly fall into three categories: traditional numerical methods, supervised learning methods, and generative model methods.

[0033] Traditional numerical methods mainly include interpolation methods and dynamic downscaling methods. Interpolation methods fill high-resolution grids by mathematically interpolating low-resolution grid data. Although computationally fast, they struggle to recover high-frequency details in meteorological fields. Dynamic downscaling methods obtain high-resolution results by running regional numerical weather prediction models over high-resolution regions and using boundary conditions. They can maintain physical consistency better, but the computational process is complex and time-consuming, making it difficult to meet the needs of real-time applications.

[0034] Supervised learning methods construct deep neural networks and train models using a large amount of paired high- and low-resolution meteorological field sample data to learn the mapping relationship from low resolution to high resolution. These methods can achieve good reconstruction results when sufficient paired training data is available. However, in real-world scenarios, paired high- and low-resolution meteorological sample data are difficult to obtain: high-resolution meteorological data usually comes from costly reanalysis or assimilation systems, with limited coverage and time span; while low-resolution data is easy to obtain, paired samples that precisely correspond to high-resolution data in space and time are extremely scarce. This high dependence on paired data severely limits the generalization ability of supervised learning methods across different regions and climatic conditions.

[0035] In recent years, generative methods, represented by diffusion models, have been introduced into the field of meteorological super-resolution. Diffusion models generate high-resolution data from random noise through progressive denoising, which can improve the ability to represent details to a certain extent. However, these methods generally suffer from high computational complexity and slow inference speed, requiring multiple iterative denoising steps, making them difficult to apply to large-scale real-time meteorological data processing scenarios. In addition, existing generative methods are insufficient in multivariate collaborative modeling. When it comes to the joint super-resolution reconstruction of multiple meteorological variables such as wind field, temperature, humidity, and air pressure, it is difficult to maintain the physical correlation and consistency between different variables.

[0036] To address the aforementioned issue of strong dependence on paired data, unsupervised methods attempt to achieve super-resolution reconstruction in the absence of paired high- and low-resolution data. However, existing unsupervised methods still have the following significant shortcomings in multivariate meteorological field scenarios: First, it is difficult to maintain the physical correlation and dimensional consistency among different meteorological variables. Meteorological fields contain various variables with different physical properties. For example, wind components exhibit positive and negative symmetry, temperature and specific humidity are both positive, and precipitation is non-negative and its distribution is highly skewed. Existing unsupervised methods typically apply a uniform normalization method to all variables, disrupting the inherent physical symmetry and dimensional relationships between different variables. This leads to physical inconsistencies in the reconstruction results, such as a mismatch between wind direction and pressure gradient direction, and the disruption of the thermodynamic relationship between temperature and humidity.

[0037] Second, there is a lack of effective modeling capabilities for long-range global dependencies. Significant teleconnection structures exist in meteorological fields, with long-range spatial correlations between meteorological elements in multiple regions. Most existing methods are based on convolutional neural networks, whose receptive fields are limited by the local size of the convolutional kernel, making it difficult to effectively capture and model such cross-regional, large-scale spatial dependencies. This results in insufficient overall structural consistency in the reconstruction results.

[0038] Third, the high-frequency detail recovery capability is insufficient, and the generated results are prone to over-smoothing. High-frequency information in the meteorological field corresponds to fine-grained structures such as the spatial texture of precipitation, temperature gradient changes, and wind convergence and divergence. These details are crucial for local meteorological analysis and downstream applications. Existing unsupervised methods, lacking pixel-by-pixel supervision signals, often generate images that tend to be smoothed mean estimates, losing a large amount of high-frequency details. This results in a significant deviation between the power spectral density in the high-frequency region and the true high-resolution data.

[0039] Therefore, there is an urgent need for a meteorological field super-resolution method that can simultaneously achieve multivariate consistency, long-distance dependency modeling, and high-frequency detail recovery without requiring paired data.

[0040] This embodiment provides an unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model, such as... Figure 1 As shown, the specific steps include the following: Step S100: Obtain low-resolution multivariate meteorological field data, and perform classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization processing is used to perform different normalization processing according to the symmetry of the physical properties of the meteorological variables.

[0041] In this embodiment, low-resolution multivariate meteorological field data refers to a three-dimensional data set containing multiple meteorological elements with a relatively coarse spatial grid resolution. A multivariate meteorological field refers to a numerical field that simultaneously records multiple meteorological elements within the same geographic space, such as temperature, wind, humidity, and pressure fields. Multiple meteorological variable channels refer to treating each meteorological variable as an independent data channel, with multiple channels superimposed along the channel dimension to form a unified multi-channel tensor structure.

[0042] In this embodiment, there are a total of 71 variable channels, covering surface variables and atmospheric variables on multiple pressure layers.

[0043] Categorical normalization refers to the process of normalizing meteorological variables by not applying a uniform normalization formula to all variables, but rather classifying them into different categories based on the symmetry of their physical properties, and then performing different normalization operations on each category. The symmetry of the physical properties of meteorological variables refers to the distribution characteristics of variable values ​​in the positive and negative directions. Specifically, some meteorological variables, such as the horizontal and vertical components of wind fields, have clearly defined positive and negative directional meanings; positive values ​​represent one direction, negative values ​​represent the opposite direction, and zero values ​​have a clear physical zero-point meaning. Other meteorological variables, such as temperature and humidity, although all have positive values, do not have a physical positive-negative symmetry relationship. Therefore, variables with physical symmetry are normalized using a method that preserves the sign and zero-point meaning, while variables without physical symmetry are normalized using conventional mean and variance normalization methods. The classification normalization strategy ensures that the normalized data maintains numerical stability while preserving the physical relationships and dimensional proportions between different variables. This avoids the problem of physical information being destroyed in traditional unified normalization methods and provides a physical consistency basis for feature reconstruction of state-space models.

[0044] The computing platform and software environment used in this embodiment specifically employ a computing server equipped with an NVIDIA RTX 3090 GPU, an Intel Xeon processor, 64GB or more of memory, a Linux operating system (Ubuntu 20.04), Python 3.9 as the programming language, PyTorch 1.12 as the deep learning framework, and scientific computing libraries such as NumPy, SciPy, and xarray for data processing. This computing platform and software environment provide the necessary computational power and software support for the training and inference of the model in this embodiment, ensuring the reproducibility of the implementation process.

[0045] In one implementation, the step of acquiring low-resolution multivariate meteorological field data and classifying and normalizing the low-resolution multivariate meteorological field data to obtain normalized meteorological field data specifically includes the following steps: Step S110: Obtain raw multivariate meteorological field data containing surface variables and multi-level atmospheric variables; Step S120: Resample the original multivariate meteorological field data to a unified low-resolution two-dimensional spatial grid, and stitch them together according to the channel dimension to form a meteorological field input tensor; Step S130: Divide the variable channels in the meteorological field input tensor into symmetric variables and asymmetric variables according to the symmetry of physical properties. The symmetric variables include wind field components and precipitation variables, and the asymmetric variables include temperature variables, humidity variables and geopotential height variables. Step S140: For each symmetric variable in the meteorological field input tensor, perform symmetric variable normalization, wherein the symmetric variable normalization includes dividing the symmetric variable by the standard deviation of the corresponding variable channel; Step S150: For each asymmetric variable in the meteorological field input tensor, perform asymmetric variable normalization, wherein the asymmetric variable normalization includes subtracting the mean of the corresponding variable channel from the asymmetric variable and then dividing by the standard deviation of the corresponding variable channel. Step S160: Input the normalized meteorological field tensor of each variable as normalized meteorological field data.

[0046] In this embodiment, raw multivariate meteorological field data containing surface variables and multi-layered atmospheric variables are acquired. Specifically, the data source can be a reanalysis dataset released by a weather forecasting center. This dataset provides multivariate meteorological field data with temporal continuity and spatial consistency globally. The acquired multivariate meteorological field data is divided along the temporal dimension. Data from 2008 to 2018 is used as the training set for parameter training of the state-space model, and data from 2019 to 2022 is used as the test set to evaluate the generalization performance of the trained super-resolution reconstruction model. The training and test sets do not overlap temporally, effectively verifying the model's reconstruction capability under unseen meteorological conditions.

[0047] The main surface variables include 2-meter temperature (t2m), sea level pressure (msl), the horizontal component (u10) and vertical component (v10) of the 10-meter wind field, and precipitation (tp).

[0048] Multi-layered atmospheric variables include horizontal components u and v of the wind field, temperature t, specific humidity q, and geopotential height z, covering multiple pressure layers ranging from 50 hPa to 1000 hPa. All variables are organized according to channel dimension, with a total of 71 channels.

[0049] The original multivariate meteorological field data is resampled to a uniform low-resolution two-dimensional spatial grid. The original high-resolution data (HR) has a spatial resolution of 0.25°×0.25°, and low-resolution data (LR) is generated through average pooling or downsampling. The low-resolution grid is, for example, 1.5°×1.5°.

[0050] Figure 2 The S1 section on multivariate meteorological field data acquisition and preprocessing demonstrates the specific implementation process of input tensor construction. After resampling, all variable channels are concatenated along the channel dimension to form the meteorological field input tensor. The dimension of the input tensor is... ,in, This indicates that the number of variable channels is 71. and These correspond to a spatial grid with a height of 121 and a width of 240, respectively. This input tensor, i.e., the low-resolution data, can be represented as:

[0051] The input tensor is obtained by downsampling high-resolution data and is represented as:

[0052] in, Represents the set of real numbers. This indicates high-resolution data, and the downsampling process preserves large-scale spatial structure information.

[0053] Optionally, when constructing the low-resolution input tensor, auxiliary information can be injected into the input tensor to enhance the model's perception of spatial location, temporal context, and hierarchical structure. This auxiliary information specifically includes geographic coordinates (longitude and latitude coordinates of each grid point), grid index (row and column position of each grid point in two-dimensional space), barosphere number (identifier of the barosphere containing multiple atmospheric variables), and meteorological condition auxiliary information such as timestamps and seasonal markers. This auxiliary information helps the state-space model capture spatial and vertical hierarchical dependencies during the modeling process, while also providing temporal context for spectral reference sampling. This allows for the integration of low-resolution multivariate meteorological field data... The auxiliary information is concatenated along the channel dimension to form a multidimensional input tensor that can be directly input into the model, represented as:

[0054] In the classification and normalization process, the input tensor performs a normalization operation on the meteorological variable channel portion, while the auxiliary information channel retains its original values.

[0055] Figure 2 Section S2, Separate Explicit Preprocessing (SEP), demonstrates the specific implementation process of classification and normalization. The variable channels in the meteorological field input tensor are divided into symmetric and asymmetric variables based on the symmetry of their physical properties. Symmetric variables are those whose values ​​have positive and negative directional meanings, and whose zero values ​​have a clear physical meaning. In this embodiment, symmetric variables specifically include the u-component and v-component of the wind field, and precipitation tp. Asymmetric variables are those whose values ​​do not have a positive and negative symmetry relationship. In this embodiment, asymmetric variables specifically include temperature t, humidity q, and geopotential height z. Let the set of symmetric variable channels be denoted as […]. The set of asymmetric variable channels is denoted as .

[0056] For each symmetric variable in the meteorological field input tensor Then, perform symmetric variable normalization. Symmetric variable normalization uses proportional normalization, and its normalization formula is:

[0057] in, For variables The original value at a certain spatial location, For variables The normalized value at a certain spatial location, For variables The standard deviation over the entire training dataset. This normalization method only scales the variance of the variables without shifting the mean, thus preserving the sign symmetry of the variables and the physical meaning of the zeros. For example, positive values ​​of the u-component of a wind field represent westerly winds, and negative values ​​represent easterly winds. After dividing by the standard deviation, positive values ​​remain positive, negative values ​​remain negative, and zero values ​​remain zero, thus fully preserving the wind direction information.

[0058] For each asymmetric variable in the meteorological field input tensor Asymmetric variable normalization is performed. Asymmetric variable normalization uses the standard mean-variance normalization method, and its normalization formula is:

[0059] in, For variables The mean over the entire training dataset, For variables The standard deviation is calculated by subtracting the mean and then dividing by the standard deviation. This normalization method ensures that the normalized data has zero mean and unit variance, guaranteeing numerical stability and making it suitable for training subsequent deep learning models. For example, after this processing, temperature values ​​from different regions and different pressure levels are mapped to a comparable numerical range.

[0060] Finally, the normalized data of each variable are reassembled in the original channel order to obtain the normalized meteorological field data, i.e., the normalized input tensor. , is represented as:

[0061] This normalized meteorological field data maintains physical consistency and dimensional relationships among different variables while exhibiting stable numerical distribution characteristics, providing a standardized input basis for feature extraction and high-resolution reconstruction of state-space models.

[0062] Building upon this, further options include checking data integrity and handling outliers. Missing or outlier values ​​are imputed to ensure the integrity of the input tensor values.

[0063] The classification normalization strategy effectively avoids the loss of physical semantics caused by uniformly normalizing all variables, enabling the model to perceive the differences in physical attributes of different variables during training, thereby better maintaining the physical correlation between multiple variables in the reconstruction results.

[0064] Step S200: After upsampling the normalized meteorological field data, input it into the state space model in sequence form, and perform position-by-position modeling on the input sequence through hidden state recursion to obtain high-resolution reconstruction results.

[0065] In this embodiment, upsampling refers to the process of increasing the spatial size of low-resolution data to a target high resolution through interpolation or other methods. In this embodiment, bilinear interpolation can be used to implement the upsampling operation. Sequence format refers to flattening meteorological field data, which originally has a two-dimensional spatial layout, into a one-dimensional sequence structure arranged along one direction, row by row or column by column, according to a preset scanning order. State Space Model (SSM) is a type of neural network architecture that models sequence data by recursively updating state equations with hidden states as the core. Unlike traditional convolutional neural networks that aggregate information in a spatial neighborhood through local convolutional kernels, the state space model propagates information gradually along the sequence direction through a hidden state vector. The hidden state at each position integrates information from all previous positions. Hidden state recursion means that when the state space model traverses each position of the input sequence, it weights and combines the hidden state of the previous position with the current input according to a set of learnable parameters to generate the current hidden state. This hidden state is then mapped to obtain the current output, and so on, advancing position by position until the entire sequence is processed. Position-by-position modeling refers to the model encoding each spatial position in the sequence one by one. The encoding result of each step depends on the context information of all positions before that position, thereby capturing the global spatial dependencies.

[0066] In this embodiment, the normalized meteorological field data is first upsampled to ensure its spatial dimensions match the target high resolution. It is then flattened into a one-dimensional sequence and input into a state-space model. The model uses the aforementioned hidden-state recursive mechanism to perform position-by-position feature encoding, outputting a high-resolution reconstruction result. This transforms the global spatial dependencies of the two-dimensional meteorological field into long-range dependencies of the one-dimensional sequence. Leveraging the linear complexity advantage of the state-space model in modeling long sequences, it efficiently captures large-scale teleconnection structures within the meteorological field.

[0067] In one implementation, the step of upsampling the normalized meteorological field data and inputting it into the state-space model in sequence form, and then modeling the input sequence position by position through hidden state recursion to obtain a high-resolution reconstruction result, specifically includes the following steps: Step S210: Upsample the normalized meteorological field data to make its spatial size consistent with the target high resolution, and obtain upsampled meteorological field data; Step S220: Flatten the two-dimensional spatial grid of the upsampled meteorological field data into a one-dimensional sequence according to a preset scanning path; Step S230: Input the one-dimensional sequence into the state space model. The state space model encodes the meteorological field data at each position in the one-dimensional sequence through hidden state recursion to obtain the encoded feature sequence. Step S240: After restoring the encoded feature sequence to a two-dimensional spatial layout, the features of each meteorological variable are fused to obtain a high-frequency residual signal; Step S250: The upsampled meteorological field data and the high-frequency residual signal are superimposed through the residual connection structure to obtain the high-resolution reconstruction result.

[0068] In this embodiment, Figure 2 The S3 section, which focuses on global dependency modeling and feature reconstruction based on a state-space model, demonstrates the implementation process of the core modeling and reconstruction.

[0069] Specifically, the normalized meteorological field data is upsampled to make its spatial dimensions consistent with the target high resolution, resulting in upsampled meteorological field data. , is represented as:

[0070] The upsampling method is bilinear interpolation, which is simple and computationally inexpensive, and maintains the continuity of the large-scale structure of the meteorological field while expanding the spatial size. Although the spatial resolution of the upsampled data is improved, it lacks high-frequency detail information and presents a relatively smooth visual effect.

[0071] The two-dimensional spatial grid of the upsampled meteorological field data is flattened into a one-dimensional sequence according to a preset scanning path. The preset scanning path refers to the rule for mapping two-dimensional spatial locations to a one-dimensional sequence order. Specifically, it can use a row-first order, i.e., scanning row by row from left to right and top to bottom, or other custom scanning paths. This process can be represented as:

[0072] in, For the flattened one-dimensional sequence, This represents the sequence location index. The flattening operation arranges the meteorological variable values ​​for each spatial location in the scan order while preserving variable channel information, enabling the state-space model to capture the dependencies between different spatial locations at the sequence level.

[0073] A one-dimensional sequence is input into a state-space model. In this embodiment, the model is implemented using the Mamba architecture. The state-space model encodes the meteorological field data at each location in the one-dimensional sequence through hidden state recursion. The specific state recursion formula is as follows:

[0074]

[0075] in, For the first The hidden state at time step n, i.e., the hidden state at time step n in the sequence. The hidden state of each position, the hidden state vector of which encodes the global context information of the current position and all positions before it; For the first The input at each location is the meteorological field data corresponding to that location in the sequence; For the first Output features at each position; , and As input-dependent parameters, the values ​​of these three parameter matrices depend on the current input. The content is dynamically generated through linear projection.

[0076] The input-dependent parameterization mechanism enables the model to adaptively choose to retain or forget historical information, capturing the correlation strength between different spatial locations in the meteorological field. Control the way information decays and is transmitted between adjacent positions in the hidden state. Determine how the current input affects the update of the hidden state. The hidden state is then mapped back to the output space. Through the synergy of these three parameters, the state-space model effectively propagates long-distance spatially relevant information in the sequence, encoding potential large-scale structural features in the low-resolution meteorological field into the hidden state, thereby achieving efficient modeling of teleconnection structures.

[0077] In this embodiment, the state-space model consists of multiple stacked Mamba blocks. Each Mamba block includes a normalization layer for serialized features, a selective state propagation layer, and a residual backflow connection. In this embodiment, the parameters of the Mamba module include a hidden state dimension (state_dim=16), a local convolutional kernel size (local_conv=4), an expansion coefficient (expansion=2), and a hidden layer dimension (hidden_dim=96). By stacking multiple Mamba blocks, the global dependency modeling capability is gradually enhanced. After the state-space model processes all positions in the sequence, it yields the encoded feature sequence.

[0078] The encoded feature sequence is restored to a two-dimensional spatial layout, which involves rearranging the one-dimensional sequence into a two-dimensional spatial grid, following the inverse of the flattening operation. After restoring the two-dimensional layout, the features of surface variables and multi-layer atmospheric variables are fused, specifically through a fusion layer. The role of the fusion layer is to aggregate meteorological variable feature information from different pressure layers and the surface, ensuring cross-layer physical consistency while enhancing the expression of spatial and vertical dependencies.

[0079] By using a residual connection structure, the upsampled meteorological field data High-frequency residual signal from model output The results are then overlaid to obtain a high-resolution reconstruction. This process is represented as follows:

[0080] in, For the final high-resolution reconstruction result, This is the rough meteorological field after upsampling. This refers to the high-frequency residual signal predicted by the state-space model. It preserves the large-scale low-frequency structural information of the low-resolution input after upsampling. The state-space model learns and supplements high-frequency detail information from the global context, and the superposition of these two elements preserves both low-frequency structural information and high-frequency detail information. This residual learning approach reduces the difficulty for the model to directly predict the complete high-resolution meteorological field, allowing the model to focus on learning the differences between the input and the target, thereby improving training stability and reconstruction accuracy.

[0081] Step S300: Construct a reconstruction consistency loss function, a spectrum constraint loss function, and an adversarial training loss function, wherein the reconstruction consistency loss function is used to constrain the consistency between the high-resolution reconstruction result after downscaling and the low-resolution multivariate meteorological field data, the spectrum constraint loss function is used to constrain the consistency of energy distribution between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain, and the adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network.

[0082] In this embodiment, the reconstruction consistency loss function is a mathematical function used to measure the degree of difference between the high-resolution reconstruction result output by the model and the original low-resolution meteorological field data after downsampling back to low resolution. Downscaling refers to applying a spatial downsampling operation, such as average pooling, to the high-resolution data, reducing its spatial resolution back to the original low-resolution level. The reconstruction consistency loss function is a self-supervised constraint; it does not have paired high- and low-resolution labels during training, but it requires that the high-resolution result generated by the model, after degradation back to low resolution, can be restored to the original low-resolution input data, thereby ensuring the correctness of the macroscopic structure of the reconstruction result.

[0083] The spectral constraint loss function refers to a loss function that compares the energy distribution of the high-resolution reconstruction result output by the model from the spatial domain to the frequency domain using a Fourier transform, and then compares it with the energy distribution of the actual high-resolution meteorological field data in the frequency domain. The frequency domain is a representation space that uses frequency as the independent variable to describe the characteristics of a signal. Low-frequency components in the frequency domain correspond to the gradual changes and large-scale structure of the meteorological field, while high-frequency components correspond to the rapid changes and fine-grained texture of the meteorological field. Energy distribution consistency refers to the degree of matching between the power spectral density of the reconstructed result at different frequencies and the actual high-resolution data. Power spectral density reflects the energy concentration of the signal at different frequencies.

[0084] Adversarial training loss function refers to a loss function that uses a discriminative network to distinguish between generated and real data, driving the state-space model to generate more realistic high-resolution reconstruction results through adversarial game-like competition. The discriminative network determines whether the input is real high-resolution data or model-generated data by outputting a realism score for each local region of the input image. The state-space model acts as a generator, causing the discriminative network to misclassify the generated high-resolution reconstruction as real data. This adversarial training mechanism allows the generated weather field to gradually approximate the real high-resolution weather field in statistical distribution, thus achieving high-quality distribution alignment even without paired labels.

[0085] In one implementation, the spectral constraint loss function is constructed, specifically including the following steps: Step S310: Perform a two-dimensional Fourier transform on the high-resolution reconstruction result output by the state-space model to obtain the spectral representation of each variable channel; Step S320: Perform radial averaging on the spectrum representation, calculate the energy distribution in different frequency ranges, and obtain the radial average power spectrum; Step S330: Based on the radial average power spectrum, calculate the power spectrum difference between the high-resolution reconstruction result and the real high-resolution meteorological field data on a logarithmic scale in the frequency domain, and use it as the spectral constraint loss function.

[0086] In this embodiment, Figure 2 S4 in the paper, based on the spectral constraints and high-frequency detail enhancement, demonstrates the specific implementation process of constructing the spectral constraint loss function.

[0087] A two-dimensional Fourier transform is performed on the high-resolution reconstruction results output by the state-space model. Let... For the first The high-resolution reconstruction results of each variable channel are subjected to a two-dimensional fast Fourier transform to obtain the spectrum of that variable channel, denoted as: .

[0088] The Fourier transform converts meteorological field data from the spatial domain to the frequency domain, where each frequency component corresponds to a variation pattern at a certain spatial scale in the original space. For meteorological fields with rich texture and gradient changes, the high-frequency components have stronger energy, while for smooth and uniform meteorological fields, the energy is mainly concentrated in the low-frequency region.

[0089] Radial averaging is applied to the spectral representation to calculate the energy distribution across different frequency ranges. Radial averaging refers to averaging points with the center point (zero frequency) in the frequency domain as the center, averaging points with the same radial frequency across the frequency domain. All frequency components are grouped together, and the power spectral density of each frequency component within this group is calculated and averaged. Let... Indicates the first The set of frequency components within a radial frequency range Let be the number of elements in the set, then the th The variable channel in the first... Radial average power spectrum of each radial frequency range Defined as:

[0090] in, For high-resolution reconstruction results at frequency Fourier transform value at point, This represents the power spectral density corresponding to this frequency component. Radial averaging compresses the two-dimensional power spectral density into a one-dimensional radial frequency distribution curve, with the horizontal axis representing the radial frequency. , representing the reciprocal of the spatial scale, with the vertical axis representing the average energy at that frequency. In the radial average power spectrum curve, Low-frequency regions with smaller values ​​correspond to large-scale, gently sloping structures in the meteorological field. High-frequency regions with larger values ​​correspond to fine-grained texture and gradient information.

[0091] Based on the radial average power spectrum, the power spectrum difference between the high-resolution reconstruction result and the true high-resolution meteorological field data is calculated on a logarithmic scale in the frequency domain, and used as the spectral constraint loss function. , is represented as:

[0092] in, The total number of variable channels, For the first Real high-resolution meteorological field data for each variable channel This is the radial average power spectrum of real high-resolution data. This represents the smoothing L1 loss function, which exhibits the smoothing properties of L2 loss (squared loss) when the differences are small, and the robustness of L1 loss (absolute value loss) to outliers when the differences are large. This is the frequency weighting function.

[0093] In practice, higher weights are assigned to high-frequency regions, i.e., regions with larger k-values. This guides the model to focus more on its ability to recover high-frequency details. (Take the logarithm) The operation transforms the power spectrum from a linear scale to a logarithmic scale because power spectral density typically spans multiple orders of magnitude. The logarithmic transformation compresses the energy differences between different frequency ranges into a more compact numerical range, which facilitates model learning.

[0094] The spectral constraint loss function directly constrains the consistency of the power spectrum distribution between the generated results and the real data in the frequency domain. This allows the model to focus not only on pixel-level similarity in the spatial domain but also on structural differences in the frequency domain, especially information in high-frequency regions, during training. Frequency domain constraints effectively compensate for the problems of overly smoothed reconstruction results and loss of high-frequency details in existing methods. This makes the generated high-resolution meteorological field closer to the real high-resolution data in terms of fine-grained structures such as precipitation texture, temperature gradient, and wind convergence and divergence, and significantly reduces the power spectrum bias (PSD-Bias) index.

[0095] In one implementation, constructing the adversarial training loss function includes the following steps: Step S340: Construct a discriminant network, which is used to compare the high-resolution reconstruction results generated by the state space model with the real high-resolution meteorological field data in local areas, and output the authenticity score of each local area. Step S350: Using the state space model as a generator, calculate the discriminator loss based on the deviation between the score output by the discriminator network from the real high-resolution meteorological field data and the true label, and the deviation between the score output by the discriminator network from the high-resolution reconstruction result generated by the state space model and the false label. The discriminator loss is used to optimize the discriminator network. Step S360: Calculate the generator adversarial loss based on the deviation between the score output by the discriminant network and the true label of the high-resolution reconstruction result generated by the state space model; Step S370: Use the generator adversarial loss as the adversarial training loss function.

[0096] In this embodiment, Figure 2 The S5 section, based on distribution alignment and unsupervised reconstruction optimization, demonstrates the specific implementation process of constructing the adversarial training loss function.

[0097] In this embodiment, the discriminative network employs the PatchGAN architecture. Specifically, the PatchGAN discriminative network divides the input high-resolution image into several local regions (patch), outputs a realism score for each local region, and finally combines the scores of all regions to determine the authenticity of the entire image. Compared to a full-image discriminator that outputs a single score for the entire image, the PatchGAN discriminative network finely evaluates the spatial texture and local statistical characteristics of the image, thereby providing richer, finer-grained optimization signals. In this embodiment, the discriminative network is represented as follows: ,in The parameters of the discriminant network are used to determine its parameters. The high-resolution reconstruction results generated by the discriminant network from the state-space model are shown. and real high-resolution meteorological field data Local regions are compared separately, and the authenticity score of each local region is output. The closer the score is to the true label value, the more the discrimination network believes that the input comes from real data.

[0098] Using a state-space model as the generator, in an adversarial training framework, the generator aims to produce the most realistic high-resolution weather fields possible, causing the discriminator network to misclassify them as real data. The discriminator's goal is to accurately distinguish between real high-resolution weather fields and generated high-resolution weather fields. The two form an adversarial game, each optimizing its own network parameters.

[0099] Calculate the discriminator loss based on the authenticity score output by the discriminator network. The formula for calculating the discriminator loss is:

[0100] in, Represents true high-resolution meteorological field data After identifying the network The expected value of the deviation between the output rating and the true label value of 1. This represents the high-resolution reconstruction result generated by the state-space model. After identifying the network The expected value of the deviation between the output score and the all-false label value of 0. The discriminator loss function is used to optimize the parameters of the discriminator network. This enables the discriminator network to accurately distinguish between real and generated data. The discriminator loss function uses the least squares form. Compared with the adversarial loss of the traditional binary classification cross-entropy form, the least squares loss provides a smoother gradient signal, alleviates the gradient vanishing problem during training, and makes training more stable.

[0101] Based on the high-resolution reconstruction results generated by the state-space model, the deviation between the score output by the discrimination network and the true label is calculated, and the generator adversarial loss is then determined. :

[0102] in, This represents the high-resolution reconstruction result generated by the state-space model. After identifying the network The expected value of the deviation between the output score and the true label value of 1. In generator adversarial loss, the generator, i.e., the state-space model, hopes to produce high-resolution reconstructions. When the discriminant network makes its judgment, the score output by the discriminant network is as close as possible to the true label value of 1, meaning that the data is judged as real data by the discriminant network. By minimizing the generator adversarial loss, the parameters of the state-space model are gradually updated, making the generated high-resolution meteorological field increasingly closer to the statistical distribution of the real high-resolution meteorological field.

[0103] The adversarial training mechanism enables the model to gradually approximate the characteristics of real high-resolution data in terms of spatial texture, local statistical properties, and overall distribution, even in the absence of paired high- and low-resolution data. This achieves high-quality distribution alignment without relying on pixel-by-pixel labels.

[0104] Step S400: Based on the constructed loss function and the high-resolution reconstruction results, the state space model is iteratively optimized and trained to obtain a trained super-resolution reconstruction model, wherein the trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

[0105] In this embodiment, the state-space model is iteratively optimized and trained based on the constructed loss function and the high-resolution reconstruction results. Iterative optimization training refers to the process of calculating the value of each loss function through multiple epochs of forward propagation, calculating the gradient of the loss function with respect to the model parameters through the backpropagation algorithm, and updating the model parameters according to the gradient using the optimizer. This process is repeated until the model converges.

[0106] In this embodiment, the optimizer used for training is AdamW, and the learning rate is set to... The batch size is 1, and the total number of training rounds is set to 30.

[0107] A successfully trained super-resolution reconstruction model refers to a state-space model whose parameters have converged to an optimal state after the complete training process described above. This model can directly map input low-resolution multivariate meteorological field data into high-resolution multivariate meteorological field data with rich high-frequency details in an end-to-end manner. During the inference phase, the model performs one forward propagation to obtain the high-resolution reconstruction result.

[0108] In one implementation, the state-space model is iteratively optimized and trained based on the constructed loss function and the high-resolution reconstruction result to obtain a trained super-resolution reconstruction model, specifically including the following steps: Step S410: The state space model is pre-trained using the reconstruction consistency loss function and the spectral constraint loss function to obtain a pre-trained super-resolution reconstruction model; Step S420: The pre-trained super-resolution reconstruction model is jointly optimized and trained using the adversarial training loss function, the reconstruction consistency loss function, and the spectral constraint loss function to obtain the trained super-resolution reconstruction model.

[0109] In this embodiment, the state-space model is iteratively optimized and trained based on the constructed loss function and the high-resolution reconstruction results, using a two-stage training strategy.

[0110] The first stage is the pre-training stage. This involves reconstructing the consistency loss function. and spectrum-constrained loss function The state-space model is pre-trained to obtain a pre-trained super-resolution reconstruction model. In this pre-training phase, the overall training objective includes only two types of losses:

[0111] in, and These are preset weight coefficients for the reconstruction consistency loss and the spectral constraint loss, used to adjust the relative importance of the two losses in the overall training objective. The pre-training phase enables the state-space model to first learn basic reconstruction capabilities, meaning that the generated image, after downsampling, can maintain consistency with the original low-resolution input, while gradually approaching the energy distribution of the real high-resolution data in the frequency domain. The number of training epochs in the pre-training phase is determined based on the model's convergence; pre-training is completed when the model initially converges.

[0112] The second stage is the joint optimization training stage. After the pre-trained model has initially converged, an adversarial training loss function is introduced. The joint optimization training is performed together with the reconstruction consistency loss function and the spectral constraint loss function. The overall training objective of the joint optimization training phase is:

[0113] in, Preset weighting coefficients to counteract training loss. To ensure macroscopic consistency between low-resolution input and generated results, i.e., to provide self-supervised constraints. To ensure that the energy distribution of the generated results in the frequency domain is consistent with that of the real high-resolution data, frequency domain constraints are provided. By employing adversarial game theory, the generated results are statistically approximated to real high-resolution data, providing distribution alignment constraints. These three elements work together to constrain the training direction of the state-space model from different dimensions, enabling the final super-resolution reconstruction model to generate high-resolution multivariate meteorological fields with high physical consistency and rich high-frequency details even without paired data.

[0114] During the pre-training phase, the state-space model first establishes basic reconstruction capabilities under the guidance of a relatively simple loss function, avoiding problems such as training instability and pattern collapse that might occur if adversarial training is introduced in the early stages of training. Once the model has a certain basic reconstruction capability, adversarial training loss is introduced for fine-tuning, allowing the model to further optimize the statistical distribution characteristics of the generated results while maintaining the correct basic structure. This strategy effectively balances the relationship between training stability and result quality.

[0115] In one implementation, the method further includes the following steps: Step S510: Obtain the low-resolution multivariate meteorological field data to be reconstructed; Step S520: Perform the classification and normalization processing on the low-resolution multivariate meteorological field data to be reconstructed to obtain the normalized data to be reconstructed; Step S530: Upsample the normalized data to be reconstructed and input it into the trained super-resolution reconstruction model in sequence to obtain high-resolution reconstruction results; Step S540: Based on the symmetry of the physical properties of meteorological variables, the high-resolution reconstruction results are classified and inversely normalized to obtain a high-resolution reconstructed meteorological field.

[0116] In this embodiment, Figure 2The S6 high-resolution multivariate meteorological field output section demonstrates the specific implementation process of the model entering the inference application stage after training. First, the low-resolution multivariate meteorological field data to be reconstructed is acquired; the source and format of this data are consistent with the low-resolution data used in the training stage. Then, classification and normalization processing is performed on the low-resolution multivariate meteorological field data to be reconstructed, resulting in normalized data to be reconstructed. This classification and normalization processing is performed in exactly the same way as in the training stage.

[0117] After upsampling the normalized data to be reconstructed, it is input into the trained super-resolution reconstruction model in sequence to obtain high-resolution reconstruction results. During the inference phase, the model only performs forward propagation, does not calculate the loss function, and does not involve a discriminant network.

[0118] Based on the symmetry of the physical properties of meteorological variables, the high-resolution reconstruction results are subjected to classification and inverse normalization. Classification and inverse normalization is the inverse operation of classification and normalization.

[0119] Specifically, for symmetric variables, the normalized value is multiplied by the standard deviation of the corresponding variable channel. To restore the original physical dimensions, it is expressed as:

[0120] For asymmetric variables, the normalized value is multiplied by the standard deviation of the corresponding variable channel. Then add the mean of that channel. To restore the original physical dimensions, it is expressed as:

[0121] In the output stage, the high-resolution reconstructed meteorological field after classification and denormalization is channel-integrated and sorted according to the original meteorological variable order. This ensures that the channel arrangement of surface variables and multi-level atmospheric variables is consistent with the original data, guaranteeing the correct mapping of physical variables corresponding to different channels. The output high-resolution reconstructed meteorological field has the following dimensions: ,in The number of channels is a variable. and The height and width dimensions of a high-resolution spatial grid.

[0122] Spatial smoothing and outlier correction are performed on the output results after channel integration and sorting. Spatial smoothing can be achieved using local mean filtering or median filtering to slightly smooth the output results, eliminating local noise and artifacts that may be introduced during model generation while preserving high-frequency details. Outlier correction addresses anomalous values ​​that exceed the reasonable physical range of meteorological variables, such as negative absolute humidity values ​​or temperature values ​​outside the reasonable range. Threshold truncation or nearest-neighbor interpolation is used to correct these outliers, ensuring the output data is physically reasonable.

[0123] The output data is stored in a standardized data format, such as NetCDF or Zarr, which are widely used in meteorology as multidimensional array storage formats. In addition to meteorological variable values, the output data also includes spatial coordinate information, timestamps, and variable labels, so that subsequent meteorological analysis and environmental modeling systems can directly read and call them.

[0124] To verify the physical consistency and spatial structure of the reconstruction results, this embodiment also provides a visualization verification function, which displays the high-resolution meteorological field in the form of a two-dimensional planar map or a three-dimensional stereoscopic map, intuitively presenting the spatial distribution, gradient changes and high-frequency texture details of each meteorological variable, for qualitative evaluation of the reconstruction effect.

[0125] The output data can be directly used by downstream applications, including meteorological analysis, environmental modeling, path planning, and embodied agent environmental perception modules. To ensure the traceability and reproducibility of the results, the output data generation time, model version number, input data batch information, and processing parameter configuration are recorded each time an output is generated, ensuring complete traceability of any inference result.

[0126] Based on this, the advantages of this embodiment are demonstrated by setting up specific comparative tests.

[0127] Figure 3 A comparative image shows the spatial reconstruction effects of different normalization methods on multivariate meteorological fields. Specifically, Figure 3 Four processing methods—input image, standard normalization, cross-projection normalization, and the classification normalization (SEP) of this invention—were used to visually compare the reconstruction effects on three representative meteorological variables: total precipitation (tp), 10-meter meridional wind component (v10m, i.e., the wind speed component in the north-south direction), and 10-meter zonal wind component (u10m, i.e., the wind speed component in the east-west direction). The comparison results show that, compared to the standard method, classification normalization can effectively restore variable variability and improve the quality of spatial reconstruction.

[0128] Figure 4 A comparative chart showing the impact of Classification Normalization (SEP) on the numerical distribution of meteorological variables is presented. Figure 4The distributions of the 10-meter zonal wind component (u10m), 10-meter meridional wind component (v10m), and total precipitation (tp) after standard normalization and classification normalization (SEP) are presented in the form of kernel density estimation (KDE) curves, comparing them with the actual high-resolution data distributions. The figures show that, compared to standard normalization, classification normalization restores the dispersion of the distribution and alleviates the shrinkage phenomenon.

[0129] Figure 5 The diagram shows a comparison of the reconstruction effects of different super-resolution reconstruction methods in the spatial and frequency domains. Figure 5 Six methods or reference benchmarks were selected for comparison, including real high-resolution data, quantile delta mapping (QDM), bicubic interpolation, Clima climate downscaling, Corrdiff correlation diffusion downscaling, and the method proposed in this embodiment. In the spatial domain comparison, using sea level pressure (msl) and 2-meter temperature (t2m) as examples, the spatial texture differences between the high-resolution reconstruction results generated by different methods and the real high-resolution data were demonstrated. In the frequency domain comparison, the consistency of energy distribution between the reconstruction results of each method and the real data in the range from low to high frequencies was shown in the form of power spectral density (PSD) curves. The comparison results show that the method in this embodiment effectively improves the high-frequency reconstruction effect and is closer to the real spectrum.

[0130] Furthermore, in a typhoon case study, the actual typhoon path reconstructed based on the sea level pressure field was compared with the super-resolution prediction results. Taking a specific typhoon event as an example, the typhoon path extracted from real high-resolution sea level pressure data and the typhoon path extracted from the high-resolution sea level pressure field reconstructed by the method in this embodiment were simultaneously plotted on a spatial map. The comparison results showed that the reconstructed pressure field could produce a coherent path estimate, which was relatively close to the actual path.

[0131] This method achieves reconstruction accuracy close to that of supervised learning methods without requiring paired high- and low-resolution data. For typical meteorological variables (such as precipitation, temperature, and geopotential height), this method outperforms existing unsupervised methods in terms of root mean square error (RMSE), mean absolute error (MAE), and structural similarity index (SSIM). Taking precipitation as an example, the RMSE of this method reaches approximately 0.0012, a significant reduction compared to traditional unsupervised methods. Simultaneously, it also shows significant improvements in correlation index (ACC) and structural consistency. Compared to supervised methods that rely on paired data, the gap in key evaluation indicators is controlled within approximately 10%, indicating that high reconstruction accuracy can be maintained even with significantly reduced data dependence. Furthermore, by introducing a normalization strategy based on variable classification and a spectral constraint mechanism, this invention effectively maintains the physical correlation and dimensional consistency among multiple variables, while also improving the oversmoothing problem present in traditional methods. This method maintains a comparable level to existing methods in terms of power spectral density correlation (PSD-Corr) while significantly reducing power spectral bias (PSD-Bias). In particular, it can more accurately recover fine-grained structural information in the high-frequency region, thereby improving the spatial detail representation of meteorological fields.

[0132] In summary, this embodiment captures long-distance climate teleconnection features using the Mamba state-space model, and combines a physical consistency classification normalization strategy with high-frequency weighted radial power spectrum constraint loss to achieve accurate reconstruction of meteorological fields from a coarse resolution of 1.5° to a high resolution of 0.25°. This method can generate multivariate meteorological data with high physical consistency and high detail fidelity, providing reliable and rich high-resolution environmental information input for embodied agents and world models in real-time perception, intent understanding, and autonomous decision-making in complex dynamic environments.

[0133] like Figure 6 As shown in the figure, this embodiment of the invention provides an unsupervised super-resolution reconstruction system for multivariable meteorological fields based on a state-space model. The system includes: a preprocessing module 10, a preliminary reconstruction module 20, a loss function construction module 30, and a training module 40.

[0134] Specifically, the preprocessing module 10 is used to acquire low-resolution multivariate meteorological field data and perform classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization processing is used to perform different normalization processes based on the symmetry of the physical properties of the meteorological variables. The preliminary reconstruction module 20 is used to upsample the normalized meteorological field data and input it into a state-space model in sequence form. It then performs position-by-position modeling of the input sequence through hidden state recursion to obtain a high-resolution reconstruction result. The loss function construction module 30 is used to construct a reconstruction consistency loss function, a spectral constraint loss function, and an adversarial training loss function. The reconstruction consistency loss function is used to constrain the consistency between the downscaled high-resolution reconstruction result and the low-resolution multivariate meteorological field data. The spectral constraint loss function is used to constrain the energy distribution consistency between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain. The adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network. The training module 40 is used to iteratively optimize and train the state space model based on the constructed loss function and the high-resolution reconstruction result to obtain a trained super-resolution reconstruction model. The trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

[0135] Based on the above embodiments, the present invention also provides a terminal device, the principle block diagram of which can be as follows: Figure 7 As shown, the terminal device includes a processor, memory, network interface, display screen, and temperature sensor connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements an unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model. The display screen can be an LCD screen or an e-ink screen. The temperature sensor is pre-installed inside the terminal device to detect the operating temperature of the internal components.

[0136] Those skilled in the art will understand that Figure 7The block diagram shown is merely a partial structural diagram related to the present invention and does not constitute a limitation on the terminal device to which the present invention is applied. A specific terminal device may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0137] In one embodiment, a terminal device is provided, including a memory and one or more programs, wherein one or more programs are stored in the memory and configured to be executed by one or more processors, the one or more programs including instructions for performing operations as described in the embodiments of the methods above.

[0138] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0139] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0140] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for unsupervised super-resolution reconstruction of multivariable meteorological fields based on a state-space model, characterized in that, The method includes: Low-resolution multivariate meteorological field data is acquired, and the low-resolution multivariate meteorological field data is classified and normalized to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization process is used to perform different normalization processes according to the symmetry of the physical properties of the meteorological variables. After upsampling the normalized meteorological field data, it is input into the state space model in sequence form. The input sequence is modeled position by position through hidden state recursion to obtain high-resolution reconstruction results. A reconstruction consistency loss function, a spectrum constraint loss function, and an adversarial training loss function are constructed. The reconstruction consistency loss function is used to constrain the consistency between the high-resolution reconstruction result after downscaling and the low-resolution multivariate meteorological field data. The spectrum constraint loss function is used to constrain the consistency of the energy distribution between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain. The adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network. Based on the constructed loss function and the high-resolution reconstruction results, the state-space model is iteratively optimized and trained to obtain a trained super-resolution reconstruction model, wherein the trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

2. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, The process of acquiring low-resolution multivariate meteorological field data and classifying and normalizing the low-resolution multivariate meteorological field data to obtain normalized meteorological field data includes: Obtain raw multivariate meteorological field data that includes surface variables and multi-level atmospheric variables; The original multivariate meteorological field data is resampled to a unified low-resolution two-dimensional spatial grid and spliced ​​along the channel dimension to form the meteorological field input tensor. The variable channels in the meteorological field input tensor are divided into symmetric variables and asymmetric variables according to the symmetry of their physical properties. The symmetric variables include wind field components and precipitation variables, and the asymmetric variables include temperature variables, humidity variables, and geopotential height variables. For each symmetric variable in the meteorological field input tensor, symmetric variable normalization is performed, wherein the symmetric variable normalization includes dividing the symmetric variable by the standard deviation of the corresponding variable channel; For each asymmetric variable in the meteorological field input tensor, asymmetric variable normalization is performed, wherein the asymmetric variable normalization includes subtracting the mean of the corresponding variable channel from the asymmetric variable and then dividing by the standard deviation of the corresponding variable channel. The normalized meteorological field input tensor is used as the normalized meteorological field data.

3. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, The process of upsampling the normalized meteorological field data and inputting it into the state-space model in sequence form, then performing position-by-position modeling on the input sequence through hidden state recursion to obtain high-resolution reconstruction results includes: The normalized meteorological field data is upsampled to make its spatial size consistent with the target high resolution, thus obtaining upsampled meteorological field data. The two-dimensional spatial grid of the upsampled meteorological field data is flattened into a one-dimensional sequence according to a preset scanning path; The one-dimensional sequence is input into a state-space model, which encodes the meteorological field data at each position in the one-dimensional sequence through hidden state recursion to obtain an encoded feature sequence. After restoring the encoded feature sequence to a two-dimensional spatial layout, the features of each meteorological variable are fused to obtain a high-frequency residual signal; The upsampled meteorological field data is superimposed with the high-frequency residual signal through a residual connection structure to obtain the high-resolution reconstruction result.

4. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, Constructing the spectral constraint loss function includes: A two-dimensional Fourier transform is performed on the high-resolution reconstruction results output by the state-space model to obtain the spectral representation of each variable channel; The spectral representation is radially averaged to calculate the energy distribution within different frequency ranges, thus obtaining the radially averaged power spectrum. Based on the radial average power spectrum, the power spectrum difference between the high-resolution reconstruction result and the real high-resolution meteorological field data is calculated on a logarithmic scale in the frequency domain, and used as the spectral constraint loss function.

5. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, Construct the adversarial training loss function, including: A discriminant network is constructed, which is used to compare the high-resolution reconstruction results generated by the state space model with the real high-resolution meteorological field data in local areas, and output the authenticity score of each local area. Using the state-space model as a generator, the discriminator loss is calculated based on the deviation between the score output by the discriminator network from the real high-resolution meteorological field data and the true label, and the deviation between the score output by the discriminator network from the high-resolution reconstruction results generated by the state-space model and the false label. The discriminator loss is used to optimize the discriminator network. The generator adversarial loss is calculated based on the deviation between the score output by the discriminant network and the true label of the high-resolution reconstruction result generated by the state-space model; The generator adversarial loss is used as the adversarial training loss function.

6. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, Based on the constructed loss function and the high-resolution reconstruction results, the state-space model is iteratively optimized and trained to obtain a trained super-resolution reconstruction model, including: The state-space model is pre-trained using the reconstruction consistency loss function and the spectral constraint loss function to obtain a pre-trained super-resolution reconstruction model. The pre-trained super-resolution reconstruction model is jointly optimized and trained using the adversarial training loss function, the reconstruction consistency loss function, and the spectral constraint loss function to obtain the trained super-resolution reconstruction model.

7. The unsupervised super-resolution reconstruction method for multivariable meteorological fields based on a state-space model according to claim 1, characterized in that, The method further includes: Acquire low-resolution multivariate meteorological field data to be reconstructed; The classification and normalization process is performed on the low-resolution multivariate meteorological field data to be reconstructed to obtain normalized data to be reconstructed. After upsampling the normalized data to be reconstructed, it is input into the trained super-resolution reconstruction model in sequence to obtain high-resolution reconstruction results. Based on the symmetry of the physical properties of meteorological variables, the high-resolution reconstruction results are classified and inversely normalized to obtain a high-resolution reconstructed meteorological field.

8. An unsupervised super-resolution reconstruction system for multivariable meteorological fields based on a state-space model, characterized in that, The system includes: The preprocessing module is used to acquire low-resolution multivariate meteorological field data and perform classification and normalization processing on the low-resolution multivariate meteorological field data to obtain normalized meteorological field data. The multivariate meteorological field includes multiple meteorological variable channels, and the classification and normalization processing is used to perform different normalization processing according to the symmetry of the physical properties of the meteorological variables. The preliminary reconstruction module is used to upsample the normalized meteorological field data and input it into the state space model in the form of a sequence. The input sequence is modeled position by position through hidden state recursion to obtain high-resolution reconstruction results. The loss function construction module is used to construct a reconstruction consistency loss function, a spectrum constraint loss function, and an adversarial training loss function. The reconstruction consistency loss function is used to constrain the consistency between the high-resolution reconstruction result after downscaling and the low-resolution multivariate meteorological field data. The spectrum constraint loss function is used to constrain the consistency of the energy distribution between the high-resolution reconstruction result and the real high-resolution meteorological field data in the frequency domain. The adversarial training loss function is used to distinguish the authenticity of the high-resolution reconstruction result through a discriminant network. The training module is used to iteratively optimize and train the state-space model based on the constructed loss function and the high-resolution reconstruction results to obtain a trained super-resolution reconstruction model, wherein the trained super-resolution reconstruction model is used to perform super-resolution reconstruction of low-resolution multivariate meteorological field data.

9. A terminal device, characterized in that, The terminal device includes a memory, a processor, and a state-space model-based unsupervised super-resolution reconstruction program for multivariable meteorological fields, which is stored in the memory and can run on the processor. When the processor executes the state-space model-based unsupervised super-resolution reconstruction program for multivariable meteorological fields, it implements the steps of the state-space model-based unsupervised super-resolution reconstruction method for multivariable meteorological fields as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a multivariable meteorological field unsupervised super-resolution reconstruction program based on a state-space model. When the multivariable meteorological field unsupervised super-resolution reconstruction program based on a state-space model is executed by a processor, it implements the steps of the multivariable meteorological field unsupervised super-resolution reconstruction method based on a state-space model as described in any one of claims 1-7.

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