A multivariate cross-frequency interaction manba-based gnss rainfall prediction method

Abstract

This invention discloses a multivariate cross-frequency interactive Manba method for GNSS rainfall prediction. First, tropospheric water vapor content (PWV), temperature, humidity, air pressure, wind speed, and actual rainfall over the GNSS observation station are acquired to construct an observation vector. A dynamic maximum information coefficient criterion is used to screen key rainfall factors, reducing data redundancy and interference. Then, a cross-frequency interactive Manba model is designed, decomposing the key factors into low-frequency trend components and high-frequency abrupt change components through time-frequency transformation. The model first learns the low-frequency trend characteristics and then dynamically adjusts the scanning parameters of the high-frequency abrupt change components, coupling to obtain a cross-frequency feature tensor. This feature tensor is input into a PatchTST time-series model, and convolution operations are used to capture the physical critical points before rainfall, generating an evolution feature vector. Finally, based on this feature vector, the rainfall prediction result is output through a quantile loss function. This invention enhances the ability to capture long-term rainfall characteristics while maintaining the prediction sensitivity for sudden rainfall, achieving high-precision rainfall prediction.

Description

Technical Field

[0001] This invention relates to the field of meteorological and hydrological monitoring technology, and in particular to a multivariate cross-frequency interactive Manba GNSS precipitation prediction method. Background Technology

[0002] Rainfall forecasting has significant applications in urban flooding early warning, flash flood prevention, aviation meteorological support, and traffic safety. In particular, accurate short-term rainfall forecasting is a key technology for improving meteorological disaster prevention and control capabilities and emergency response efficiency.

[0003] Existing rainfall forecasting technologies mainly include extrapolation forecasting methods based on meteorological radar and satellite remote sensing, physical forecasting methods based on numerical weather prediction models, and statistical or data-driven forecasting methods based on historical observation data. Rainfall forecasting methods based on meteorological radar and satellite remote sensing typically rely on observed precipitation echoes or cloud system evolution characteristics to achieve short-term forecasts by extrapolating the movement, development, or attenuation trends of precipitation systems. These methods have a certain predictive capability when precipitation systems have already formed and have a clear structure; however, their predictive effectiveness for the initial stages of rainfall, weak rainfall processes, and localized heavy rainfall depends heavily on the quality of echo identification, and their forecast stability and lead time are limited.

[0004] Numerical weather prediction models simulate rainfall processes by solving atmospheric physical equations, which can characterize the evolution of large-scale weather systems. However, in short-term, fine-scale rainfall prediction, they are highly sensitive to initial field errors, have high computational complexity, are difficult to meet real-time requirements, and are insufficient in characterizing local and sudden rainfall events.

[0005] With the development of Global Navigation Satellite System (GNSS) technology, atmospheric precipitable water (PWV) retrieved from GNSS has been widely used in rainfall monitoring and short-term forecasting research because it can continuously and stably reflect changes in the total amount of atmospheric water vapor. Meanwhile, multi-source meteorological elements such as temperature, pressure, and humidity acquired by automatic weather stations provide richer observational information for characterizing rainfall formation mechanisms. Against this backdrop, areal rainfall prediction methods that integrate GNSS-PWV with multi-source surface meteorological observation data have gradually become a research hotspot.

[0006] In recent years, deep learning methods have been widely used in time series forecasting, with some studies attempting to model precipitation processes using recurrent neural networks (RNNs), convolutional neural networks (CNNs), or traditional attention mechanisms. However, existing techniques still have the following significant shortcomings when handling multivariate forecasts that couple GNSS water vapor data with surface meteorological elements: 1. Nonlinear Coupling and Redundancy Interference of Heterogeneous Variables: With the increase in observation methods (such as GNSS-PWV, air pressure, temperature and humidity, wind speed, etc.), the dimensionality of input variables increases dramatically, and extremely complex nonlinear relationships exist between variables. Existing models mostly use full input or simple correlation analysis, which is difficult to effectively remove redundant noise, leading to the model being prone to overfitting. There is an urgent need for a mechanism that can accurately quantify nonlinear relationships and automatically screen key rainfall factors based on the dynamic maximum information coefficient (MIC) criterion to reduce data redundancy and improve feature purity.

[0007] 2. Imbalance between Macro-Trends and Local Abrupt Changes, and Computational Bottlenecks: Rainfall is driven by both large-scale circulation (low-frequency trends) and local convection initiation (high-frequency abrupt changes). Traditional models struggle to balance these two vastly different temporal patterns within a single architecture. While the Transformer architecture possesses long-range modeling capabilities, its quadratic computational complexity limits its performance in processing long sequences. Furthermore, existing attention mechanisms are often based on static weight allocation, making it difficult to characterize the physical critical points before rainfall triggering (such as nonlinear disturbances leading to rapid water vapor saturation), resulting in significant smoothing or lag effects in the prediction of sudden, severe convective weather. Therefore, it is urgent to introduce Mamba (state-space model) with linear complexity for cross-frequency interactive modeling, and combine it with PatchTST's block semantic extraction and convolution operators to accurately pinpoint rainfall precursors.

[0008] 3. Lack of Physical Consistency Feature Extraction and Uncertainty Quantification: Rainfall processes exhibit strong randomness, non-stationarity, and physical evolution characteristics. Existing prediction models tend to output single "point prediction" values, ignoring the semantic coherence of physical variables in the spatiotemporal dimensions before rainfall occurs, and failing to reflect the fluctuation range of prediction results at different confidence levels. This output method, lacking risk assessment information, is insufficient to meet the needs of "worst-case" assessments in high-risk scenarios such as urban flooding warnings and flash flood disaster prevention. Therefore, there is an urgent need to construct an interval prediction model that can integrate convolutional enhancement evolution features and is based on a quantile loss function to provide probabilistic early warning information with both high accuracy and reliability. Summary of the Invention

[0009] A multivariate cross-frequency interactive Manba method for GNSS precipitation prediction includes the following steps: Step 1: Collect GNSS-inverted atmospheric precipitable water (PWV) data and synchronous observation data from multiple ground rain gauges and meteorological stations within the target area. After cleaning, normalization, and time alignment, construct a historical sliding window with a length of [missing information]. Multivariate original observation feature matrix ; Step 2: Construct a dynamic screening module for rainfall factors, which will filter the original observation feature matrix. Mapping to features The correlation weights of each variable were calculated, and the dynamic maximum information coefficient (MIC) criterion was used to iteratively select a subset of key rainfall factors from the original feature matrix. ; Step 3: Design a cross-frequency interactive Mamba (CFI-Mamba) model, and use the time-frequency transformation method to integrate key rainfall factors. The data is decomposed into low-frequency trend components and high-frequency detail components. The Mamba model first learns features from the low-frequency trend components and then dynamically adjusts the scanning parameters of the high-frequency detail components accordingly, deeply coupling the dual-frequency features to generate a fused feature tensor. ; Step 4: Construct a temporal prediction model based on PatchTST, using convolution operations on the feature tensor. Processing is performed to capture the physical critical point before rainfall occurs, generating an evolutionary feature vector reflecting the characteristics of sudden rainfall changes. ; Step 5: Construct an interval prediction output layer based on the quantile expected risk minimization criterion, and utilize feature vectors. Solve for the optimal model parameters and output the predicted interval and center value of the surface rainfall at future times.

[0010] The present invention is further configured such that, in step two, the dynamic screening module for rainfall factors is modeled as a dynamic optimization problem in the feature subspace, and the specific calculation is as follows: Define the original feature as For candidate variable vectors Construct a dynamic maximum information coefficient functional ; in the In each iteration, the variable that maximizes the functional is selected. Add to selected collection :

[0011] in, Represents the target rainfall vector; Indicates the first The subset of key rainfall factors selected before the next iteration; This represents the maximum information coefficient operator, used to measure the strength of nonlinear correlations between variables; In the selected set The expectation operator on the variable is used to measure and eliminate redundant projections between candidate variables and the selected variable set.

[0012] The present invention is further configured such that, in step three, a cross-frequency interactive Mamba (CFI-Mamba) learning model is designed, the feature extraction process of which includes: (1) Use the time-frequency transformation method to transform the variable subset output in step two. Mapped to the frequency domain, high-pass and low-pass filters are used to separate the high-frequency detail components that reflect instantaneous fluctuations. With low-frequency trend components that reflect long-term evolution patterns ; (2) Low-frequency guided cross-frequency selective scanning: Constructing a cross-frequency interactive state space architecture based on low-frequency feature modulation. First, the low-frequency component is extracted from the first Mamba block. The temporal dependency features are used to generate an environmental state memory vector. Innovatively establishes a mapping function between low-frequency memory and high-frequency parameters. ,use Dynamically generating the selectivity parameter matrix for processing high-frequency components (Step size coefficient) (Input projection matrix) and (Output projection matrix) enables the high-frequency branch to dynamically adjust its sensitivity to sudden signals based on the current atmospheric background environment; its controlled state equation is expressed as:

[0013] in, It is an adaptive parameter discretized by a hardware-aware parallel association operator through low-frequency features, which realizes cross-scale collaborative feature extraction of "trend perception of the whole and high frequency locking of the local". (3) Calculate the structural similarity (SSIM) between the output feature maps of each branch. If the similarity is higher than the preset threshold, redundant channels are removed. Finally, the dual-frequency features are deeply coupled to generate a cross-frequency feature tensor. .

[0014] The present invention is further configured such that, in step four, a feature enhancement module based on PatchTST and local convolution is constructed, which captures the physical critical features before rainfall through the following mathematical logic: (1) Multidimensional spatiotemporal block mapping: The cross-frequency feature tensor generated in step three is mapped to the multidimensional spatiotemporal block mapping. (in For the number of channels, Divide the sequence into several semantically overlapping subsequence blocks (within the sequence length). ,in The block length, The number of blocks. This is determined by a learnable projection matrix. Each patch is mapped to a high-dimensional latent space and positional encoding is superimposed. Its mathematical expression is:

[0015] (2) Dynamic convolution scanning guided by physical critical point: For nonlinear perturbations of meteorological parameters (such as PWV and humidity) before rainfall, a multi-scale one-dimensional dilated convolution operator is introduced. Using different expansion rates Capture the gradient jump characteristics of multiple frequency bands and define the critical change response function. :

[0016] in, For activation function, This represents a convolution operation. This operator is specifically used to quantify the change in the second derivative of the feature tensor within a local window, thereby pinpointing the physical critical point triggered by rainfall. (3) Channel-independent self-attention evolutionary encoding: The Transformer architecture is used to independently model the temporal correlations of each physical channel. A multi-head self-attention mechanism is employed to calculate the inter-dependency weights between patches, capturing the long-term meteorological evolution logic. Its attention score matrix... The calculation is as follows:

[0017] This represents time series blocks for a single physical channel; Let represent the learnable query, key, and value projection matrices, respectively. and The dot product operation is used to measure the strength of nonlinear correlation between different time blocks; This represents the normalized activation function; This represents the scaling factor.

[0018] (4) Global context evolution vector synthesis: The attention-encoded and convolution-enhanced features are then global pooled and aggregated using a multilayer perceptron to generate the final evolved feature vector. :

[0019] in Indicates global average pooling; Indicates the flattening operation; For feature splicing operators; This represents a multilayer perceptron.

[0020] The present invention is further configured such that, in step five, the quantile loss function is constructed as a functional for minimizing the expected risk, as follows: Define the model parameter set as The problem of predicting the conditional distribution of rainfall on the target surface is transformed into solving the following objective function. Minimum value: in, For the set of quantiles, It is an asymmetric quantile norm. This is the indicator function; the model outputs the corresponding quantile by minimizing this expected risk. The prediction boundary below Indicates the distribution of data The expectation operator on.

[0021] A multivariate cross-frequency interactive Manba GNSS rainfall prediction method is implemented through a monitoring system. The monitoring system includes a data sensing layer, comprising a GNSS receiver and a ground rain gauge network, used to collect and calculate PWV and rainfall data; a calculation and processing layer, which incorporates a dynamic rainfall factor screening module and a deep learning inference engine, used to perform variable screening and multi-scale feature fusion calculations; and an early warning release layer, which generates a areal rainfall change trend map and confidence interval based on quantile prediction results, and triggers an alarm when the lower limit of the prediction exceeds a threshold.

[0022] The beneficial effects of this invention are as follows: 1. Achieved accurate dimensionality reduction and noise reduction for complex nonlinear meteorological factors: This invention introduces a factor selection mechanism based on Dynamic Maximum Information Coefficient (MIC). Unlike traditional linear correlation analysis or static mutual information strategies, Dynamic MIC can accurately quantify the complex nonlinear and nonfunctional coupling relationships between GNSS-PWV, surface meteorological elements, and rainfall. By iteratively evaluating the effective information contribution and redundant overlap among variables, it adaptively eliminates interference noise, ensuring a high signal-to-noise ratio for the model input features, thereby significantly reducing computational overhead while improving prediction accuracy.

[0023] 2. Breakthrough in the collaborative modeling bottleneck of long-term trends and short-term mutations: The cross-frequency interactive Mamba (CFI-Mamba) architecture designed in this invention achieves deep decoupling of meteorological evolution logic through time-frequency transformation. Its core innovation lies in establishing a dynamic modulation mechanism of "low-frequency guiding high-frequency": utilizing low-frequency trend characteristics to adjust the selective scanning parameters in the high-frequency component processing in real time. This design perfectly aligns with the physical law of "large-scale circulation modulating local convection," enabling the model to stably capture the long-term evolution trend of rainfall while maintaining extremely high trigger sensitivity to sudden rainfall signals.

[0024] 3. Significantly enhanced ability to capture the physical critical point of rainfall: This invention addresses the lag or extreme value smoothing issues present in traditional models for heavy rainfall prediction by deeply integrating PatchTST block mapping with local convolution operations. Patch semantic extraction ensures the local coherence of meteorological evolution, while the multi-scale convolution operator acts like a "pattern scanner," accurately pinpointing changes in the second derivative (physical critical points) before rainfall triggers, such as drastic fluctuations in water vapor and sudden drops in air pressure. This combination of "global semantics + local abrupt change recognition" enables the model to identify precursor signals of severe convective weather earlier and more accurately.

[0025] 4. Provides quantitative information on uncertainty that has value for risk assessment: This invention abandons the traditional single-point prediction model and uses a quantile loss function to construct an interval prediction model. By outputting the rainfall range at different confidence levels (such as the risk of heavy rainfall corresponding to high quantiles), the model can quantify the randomness and uncertainty of the rainfall process. This provides a scientific "worst-case" assessment basis for high-risk decision-making scenarios such as urban flood control and early warning of flash floods and geological disasters, greatly improving the practicality and reliability of GNSS rainfall prediction technology. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the prediction process of a multivariate cross-frequency interactive Manba GNSS rainfall prediction method proposed in this invention. Figure 2 This is a network model architecture diagram of a multivariate cross-frequency interactive Manba GNSS rainfall prediction method proposed in this invention. Detailed Implementation The technical solution of this patent will be further described in detail below with reference to specific embodiments.

[0027] The embodiments of this patent are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this patent, and should not be construed as limiting this patent.

[0028] Reference Figure 1-2 A multivariate cross-frequency interactive Manba method for GNSS precipitation prediction includes the following steps: Step 1: Data Construction and Preprocessing 1. Multi-source heterogeneous data acquisition and inversion First, this invention establishes an integrated air-ground monitoring network. Multiple GNSS base stations deployed within the target watershed acquire dual-frequency GNSS observation files (standard RINEX format) and precise ephemeris data. Using differential precise point positioning (PPP) technology, the tropospheric delay term (ZTD) is calculated, and then atmospheric precipitable water (PWV) is retrieved. The physical inversion formula is as follows:

[0029] Where ZHD is the dry delay component. The conversion coefficient from wet delay to precipitation is given.

[0030]

[0031] This coefficient takes into account the thermodynamic properties of water vapor and the propagation characteristics of electromagnetic waves in the atmosphere, serving as a bridge between signal delay and actual water vapor content. The physical constants in the formula include: Water vapor gas constant. It reflects the thermodynamic properties of water vapor; atmospheric refractive index and This describes the degree to which water vapor affects the refraction of electromagnetic waves. The Bevis empirical formula is used to calculate the average atmospheric temperature T. m :T m =70.2+0.72T t , among which, T t These are surface air temperatures, sourced from weather stations. These constants are physical quantities precisely measured in laboratories, ensuring the accuracy of the conversion.

[0032] 2. Resampling of multi-rate data Because the processing frequency of GNSS data (usually 15 or 30 minutes) is inconsistent with the acquisition frequency of ground meteorological stations (usually 1 minute or 10 minutes), this invention uses a sliding window averaging method to resample all data to a uniform time step. (For example ).

[0033] For continuous variables (such as PWV and temperature), linear interpolation or mean calculation methods are used; for discrete cumulative variables (such as rainfall), interval accumulation methods are used.

[0034] Ensure that all features are strictly aligned in the time dimension.

[0035] 3. Original observation feature matrix Construction Aligned Integrating several meteorological variables, a historical sliding window length of [length missing] is constructed. The original observation feature matrix :

[0036] Each row represents a vector of all meteorological factors at a specific time step.

[0037] 4. Nonlinear normalization processing To eliminate the influence of different physical units (such as air pressure in hPa and rainfall in mm) on the model convergence speed and weight allocation, this invention modifies the matrix... Perform deviation standardization:

[0038] in, For the first The feature in the first The original value at each moment, These are the minimum and maximum values ​​of the feature in the historical sequence, respectively; the processed matrix. All elements are mapped to the [0,1] interval and used as input for the subsequent dynamic factor selection module.

[0039] Step 2: Dynamic screening of rainfall factors based on maximum joint mutual information In order to remove redundant noise and identify key inducing factors (such as sudden changes in air pressure and sudden increases in PWV) from multi-source meteorological data, this step models the screening process of precipitation factors as an iterative optimization problem of feature subspace: 1. Initialize the feature set Set the original feature set as The complete set consists of candidate variables such as GNSS-PWV obtained in step one and normalized, as well as air pressure, temperature, humidity, and wind speed at each station; a subset of key variables has been selected. Initialized as an empty set, the target rainfall vector is .

[0040] 2. Dynamic Maximum Information Coefficient Calculation Mechanism The dynamic maximum information coefficient (MIC) is used as a screening criterion to measure the nonlinear "net gain" of candidate variables on the prediction target. A functional of the dynamic maximum information coefficient is constructed. ; in the In each iteration, the variable that maximizes the functional is selected. Add to selected collection :

[0041] in, Represents the target rainfall vector; Indicates the first The subset of key rainfall factors selected before the next iteration; This represents the maximum information coefficient operator, used to measure the strength of nonlinear correlations between variables; In the selected set The expectation operator on the variable is used to measure and eliminate redundant projections between candidate variables and the selected variable set.

[0042] Step 3: Cross-frequency interactive Mamba feature deep coupling learning and redundancy pruning This step aims to refine the optimal subset of variables selected in step 2. Deep feature extraction is performed using a frequency-domain enhanced multi-scale selective state-space network to capture the evolution of rainfall dynamics across different time-frequency dimensions.

[0043] 3.1 Frequency Domain Decoupling and Multi-Scale Component Generation Define the sequence of variable subsets output in step two as follows: This invention first utilizes a time-frequency transformation method to map time-series signals to the frequency domain, thereby achieving multi-scale deconstruction of features.

[0044] Low-frequency trend components The long-term accumulation trend and seasonal background evolution of atmospheric water vapor were characterized by extraction using a low-pass filter.

[0045] High-frequency detail components The instantaneous meteorological fluctuation signals induced by strong convection, such as sudden drops in air pressure and sudden changes in wind speed, are extracted using a high-pass filter.

[0046] 3.2 Low-frequency environmental feature extraction and state memory construction Low frequency components The first Mamba block is input, and its selective scanning mechanism is used to model long-period temporal dependencies. The hidden states of low-frequency components are extracted to generate an environment state memory vector. This vector represents the strength of the current atmospheric environment's support for rainfall occurrence and the background evolution stage.

[0047] 3.3 Innovative cross-frequency interaction mechanism: low-frequency guided high-frequency adaptive scanning The core of this invention lies in constructing a cross-frequency interaction logic based on low-frequency feature modulation, enabling the model to dynamically adjust its sensitivity to local abrupt changes according to the atmospheric background.

[0048] Mapping function construction: Establishing nonlinear mapping functions , low-frequency memory vector Selective scan control matrix mapped to high-frequency branches:

[0049] Parameter dynamic modulation: Real-time intervention of high-frequency components using generated low-frequency control parameters. The scanning process. Its controlled discretized state-space equation is expressed as:

[0050] in, These are adaptive parameters discretized using a hardware-aware parallel associative operator based on low-frequency features. This mechanism achieves cross-scale collaboration by "globally sensing trends and locking in local high frequencies." When the low-frequency background indicates a critical rainfall state, the step size coefficient... The dynamic reduction improves the sampling sensitivity of the high-frequency branch to subtle signal changes.

[0051] 3.4 Feature Pruning Based on Structural Similarity To reduce the number of model parameters and improve inference efficiency, this invention introduces a feature map structure similarity (SSIM) pruning strategy. The system calculates the output feature map of each convolutional branch. Similarity between : (9)

[0052] in, The mean of the feature map, For variance, For covariance, To maintain computational stability, a constant is used. If the similarity exceeds a preset threshold... (e.g., 0.9) indicates that the two channels have extracted highly repetitive evolutionary features. The system will automatically remove one of the convolutional channels, thereby achieving model lightweighting and compressing model size.

[0053] 3.5 Residual Fusion and Tensor Generation After the above pruning process, the outputs of each branch are transformed through residual connection. Generate the final fused feature tensor :

[0054] in, This represents the cascading operation of feature channels. This step effectively enhances the model's ability to represent complex weather systems through the nonlinear fusion of multi-scale features.

[0055] Step 4: Extraction of rainfall evolution features based on PatchTST coupled with multi-scale convolution To address the challenges of modeling long-distance temporal dependencies and accurately capturing physical critical points in rainfall forecasting, this step utilizes the PatchTST architecture combined with local convolution operators to deeply mine cross-frequency feature tensors. The evolutionary logic in: 4.1 Multidimensional Spatiotemporal Block Mapping (Patching & Embedding) transforms the cross-frequency feature tensor generated in step three into a multidimensional spatiotemporal block mapping. (in For the number of channels, The sequence length is divided into several semantically overlapping subsequence blocks along the time dimension. ,in The block length, The number of blocks. Utilizing a learnable projection matrix. Each patch is mapped to a high-dimensional latent space and positional encoding is superimposed. To preserve the local semantic coherence of rainfall evolution, its mathematical expression is as follows:

[0056] 4.2 Dynamic Convolution Scan Guided by Physical Critical Points To capture the "physical critical point" of meteorological parameters (such as PWV and humidity) caused by nonlinear perturbations before rainfall, a multi-scale one-dimensional dilated convolution operator is introduced. By setting different expansion rates The operator can capture gradient jump characteristics under different receptive fields. Define the critical change response function. :

[0057] in, For activation function, This represents the convolution operation. By quantizing the change of the second derivative of the feature tensor within a local window, this operator can accurately pinpoint precursor signals such as sudden spikes in water vapor saturation before a heavy rainstorm.

[0058] 4.3 Channel-independent self-attention evolutionary encoding A channel-independent Transformer encoder is used to independently model the temporal correlation of each physical channel. A multi-head self-attention mechanism is employed to calculate the inter-dependency weights between patches, and its attention score matrix is ​​used. The calculation is as follows:

[0059] This represents time series blocks for a single physical channel; Let represent the learnable query, key, and value projection matrices, respectively. and The dot product operation is used to measure the strength of nonlinear correlation between different time blocks; This represents the normalized activation function; This represents the scaling factor.

[0060] 4.4 Global Context Evolution Vector Synthesis: Global trend features encoded through attention With convolution-enhanced local critical features The components are then fused. Core components are extracted using Global Average Pooling (GAP), and multilayer perceptron (MLP) is used for dimensionality transformation and nonlinear aggregation to generate the final evolutionary feature vector. :

[0061] in Indicates global average pooling; Indicates the flattening operation; For feature splicing operators; This represents a multilayer perceptron. This vector... It deeply integrates the macroscopic evolution trend of rainfall occurrence with microscopic precursors of sudden changes, providing highly discriminative feature inputs for subsequent interval prediction.

[0062] Step 5: Output of areal rainfall interval prediction based on quantile regression To quantify the uncertainty of rainfall forecasting, this invention abandons the traditional single-value forecasting and adopts an interval forecasting scheme.

[0063] 1. Multiquantile prediction layer Using the context evolution feature vector containing mutation information generated in step four This is mapped to multiple quantile output units through a fully connected layer. The quantile set is defined as follows: It typically includes low quantiles (e.g., 0.1, corresponding to the lower limit of prediction), middle quantiles (e.g., 0.5, corresponding to the center value of prediction), and high quantiles (e.g., 0.9, corresponding to the upper limit of prediction).

[0064] 2. Training with combined loss function Define the model parameter set as The problem of predicting the conditional distribution of rainfall on the target surface is transformed into solving the following objective function. Minimum value:

[0065] in, For the set of quantiles, It is an asymmetric quantile norm. This is the indicator function; the model outputs the corresponding quantile by minimizing this expected risk. The prediction boundary below Indicates the distribution of data The expectation operator on.

[0066] 3. Results Output and Application Based on the solved optimal parameters, the model outputs the predicted range and center value of future areal rainfall in real time: Numerical prediction: Output The predicted value corresponding to the time is used as the central reference value for areal rainfall.

[0067] Confidence interval assessment: based on the lower and upper quantile boundaries. This constitutes the prediction interval. Dynamic early warning logic: If the prediction interval... A narrow range indicates that atmospheric water vapor evolution conforms to historical patterns, and the prediction is highly reliable; if the range widens significantly, it indicates that there is a great risk of random mutations in the rainfall process, and the system should automatically raise the warning level based on the upper limit of the prediction.

[0068] Experimental Results and Validation 1. Experimental Setup and Data Sources: To comprehensively evaluate the effectiveness of the proposed method, we compared it with various baseline models, including traditional deep learning models (LSTM, Transformer, Informer, DeepAR) and traditional machine learning methods (LightGBM). The data for this study came from seven monitoring stations deployed in Hefei City, Anhui Province (2021-2024). We used data from January 2021 to December 2023 as the training set, and data from January 2024 to June 2024 as the validation set for hyperparameter tuning and early termination. Finally, we used data from June 2024 to October 2025 as an independent test set to evaluate the model's generalization performance. We referred to the "Classification of Short-Term Imminent Rainfall Intensity" standard (DB34 / T1592-2012) to classify rainfall intensity into multiple levels (e.g., light rain). Moderate rain ,heavy rain ,rainstorm The predicted value is the cumulative rainfall in the hour following the occurrence of rainfall.

[0069] 1. Evaluation Indicators Explanation: To fully verify the superiority of this invention in interval prediction, the following multidimensional indicators are adopted: Let... for The actual rainfall observation value at that moment, To predict the upper limit of the interval, This is the lower limit of the prediction interval. This is the predicted median value (or median) of the interval. This represents the total number of samples in the test set.

[0070] ①PICP (Predicted Interval Coverage): Reflects reliability. The calculation formula is:

[0071] in, This is a Boolean value indicating whether the observed value falls within the interval. .

[0072] ② MPIW (Mean Prediction Interval Width): Reflects the sharpness of the prediction. The narrower the interval, the higher the reference value of the warning. The calculation formula is:

[0073] ③CWC (Predicted Interval Coverage Score): A comprehensive metric. It penalizes models when the PICP (Predicted Interval Coverage Score) falls below a set confidence level, and measures the model's ability to compress the width while maintaining coverage.

[0074]

[0075] in: It is a preset confidence level (typically set to 0.9 in this patent). It is the penalty coefficient (usually a large value, such as 50); It is a step function: if ,but like ,but .

[0076] ④RMSE (Root Mean Square Error): A regression accuracy indicator for the central value of an interval. Calculation formula:

[0077] 2. Main Experiment Results: Table 1 shows the comparison of interval prediction performance at a 90% confidence level ( The present invention compares the method (Ours) with current mainstream probabilistic prediction and deep learning models.

[0078] Table 1: Comparison of areal rainfall prediction performance at 90% confidence level

[0079] This invention achieves a high reliability of 91.2% for PICP while significantly compressing the inter-frequency inter-inverter width (MPIW) to 2.18 mm, which is 28.5% narrower than the second-best performing Informer model (3.05 mm). This leap forward is directly attributed to the CFI-Mamba cross-frequency interaction mechanism in this invention: by dynamically guiding high-frequency parameters through low-frequency trends, the model can accurately eliminate non-physical "predictive bloat" caused by water vapor disturbances, providing highly precise early warning information while ensuring that predictions do not "miss" reports.

[0080] On the comprehensive performance index CWC, this invention achieved 0.82, a reduction of 33.8% compared to Informer (1.24) and 50.3% compared to the traditional deep learning model LSTM-QR (1.65). This performance leap demonstrates the superiority of the PatchTST and locally dilated convolutional collaborative architecture adopted in this invention—by capturing the "physical critical point," the model can quickly converge the prediction interval before heavy rainfall occurs, effectively solving the "response lag" phenomenon of traditional models when facing non-stationary rainfall sequences.

[0081] With an RMSE of only 1.98 mm, this method is the only one among all the comparative models to fall below the 2.0 mm mark. This demonstrates that the present invention is not only accurate in probability distribution estimation, but also most closely approximates actual observations in predicting the absolute value of rainfall. This high-precision "point-to-surface" performance is attributed to the dynamic MIC variable selection and similarity pruning strategy mentioned in this invention. This strategy filters out redundant noise that interferes with regression accuracy at the source, ensuring the purity of the model input.

[0082] Data results show that while maintaining a high coverage rate of 91.2%, MPIW remains at an extremely low level. This suggests that even during the test set period of drastic weather fluctuations (2024-2025), this invention can still provide highly deterministic warning intervals through the quantile loss function, rather than avoiding errors by blindly expanding the interval range, demonstrating strong engineering application value.

[0083] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A multivariate cross-frequency interactive Manba method for GNSS rainfall prediction, characterized in that, Includes the following steps: Step 1: Collect GNSS-inverted atmospheric precipitable water (PWV) data and synchronous observation data from multiple ground rain gauges and meteorological stations within the target area. After cleaning, normalization, and time alignment, construct a historical sliding window with a length of [missing information]. Multivariate original observation feature matrix ; Step 2: Construct a dynamic screening module for rainfall factors, which will filter the original observation feature matrix. Mapping to features The correlation weights of each variable are calculated, and the key rainfall factor subset is iteratively selected from the original feature matrix using the dynamic maximum information coefficient criterion. ; Step 3: Design a cross-frequency interactive Mamba model and use the time-frequency transformation method to integrate key rainfall factors. The data is decomposed into low-frequency trend components and high-frequency detail components. The Mamba model first learns features from the low-frequency trend components and then dynamically adjusts the scanning parameters of the high-frequency detail components accordingly, deeply coupling the dual-frequency features to generate a fused feature tensor. ; Step 4: Construct a temporal prediction model based on PatchTST, using convolution operations on the feature tensor. Processing is performed to capture the physical critical point before rainfall occurs, generating an evolutionary feature vector reflecting the characteristics of sudden rainfall changes. ; Step 5: Construct an interval prediction output layer based on the quantile expected risk minimization criterion, and utilize feature vectors. Solve for the optimal model parameters and output the predicted interval and center value of the surface rainfall at future times.

2. The GNSS rainfall prediction method using multivariate cross-frequency interactive Manba as described in claim 1, characterized in that, In step two, the dynamic screening module for rainfall factors is modeled as a dynamic optimization problem in the feature subspace, and the specific calculation is as follows: Define the original feature as For candidate variable vectors Construct a dynamic maximum information coefficient functional ; in the In each iteration, the variable that maximizes the functional is selected. Add to selected collection : in, Represents the target rainfall vector; Indicates the first The subset of key rainfall factors selected before the next iteration; This represents the maximum information coefficient operator, used to measure the strength of nonlinear correlations between variables; In the selected set The expectation operator on the variable is used to measure and eliminate redundant projections between candidate variables and the selected variable set.

3. The GNSS rainfall prediction method using multivariate cross-frequency interactive Manba as described in claim 1, characterized in that, Step three involves designing a cross-frequency interactive Mamba learning model, the feature extraction process of which includes: The time-frequency transformation method is used to transform the variable subset output in step two. Mapped to the frequency domain, high-pass and low-pass filters are used to separate the high-frequency detail components that reflect instantaneous fluctuations. Low-frequency trend components that reflect long-term evolution patterns ; Low-frequency guided cross-frequency selective scanning: Constructing a cross-frequency interactive state space architecture based on low-frequency feature modulation; First, low-frequency components are extracted from the first Mamba block. The temporal dependency features are used to generate an environmental state memory vector. Innovatively establishes a mapping function between low-frequency memory and high-frequency parameters. ,use Dynamically generating the selectivity parameter matrix for processing high-frequency components Step size factor, Input projection matrix and The output projection matrix enables the high-frequency branch to dynamically adjust its sensitivity to abrupt signals based on the current atmospheric background environment; its controlled state equation is expressed as: in, and It is an adaptive parameter discretized by a hardware-aware parallel association operator through low-frequency features, which realizes cross-scale collaborative feature extraction of "trend perception of the whole and high frequency locking of the local". Calculate the structural similarity (SSIM) between the output feature maps of each branch. If the similarity is higher than a preset threshold, redundant channels are removed. Finally, the dual-frequency features are deeply coupled to generate a cross-frequency feature tensor. .

4. The GNSS rainfall prediction method using multivariate cross-frequency interactive Manba as described in claim 1, characterized in that, In step four, a feature enhancement module based on PatchTST and local convolution is constructed, which captures the critical physical features before rainfall through the following mathematical logic: Multidimensional spatiotemporal block mapping: This involves mapping the cross-frequency feature tensor generated in step three. ,in For the number of channels, The sequence length is used to divide the sequence into several semantically overlapping subsequence blocks. ,in The block length, Number of blocks; through a learnable projection matrix Each patch is mapped to a high-dimensional latent space and positional encoding is superimposed. Its mathematical expression is: Physically critical point-guided dynamic convolutional scanning: This approach introduces a multi-scale one-dimensional dilated convolution operator to address nonlinear perturbations in pre-rainfall meteorological parameters, such as precipitation and humidity. ; Utilizing different expansion rates Capture the gradient jump characteristics of multiple frequency bands and define the critical change response function. : in, For activation function, This represents a convolution operation; this operator is specifically used to quantify the changes in the second derivative of the feature tensor within a local window, thereby locking the physical critical point triggered by rainfall. Channel-independent self-attention evolutionary encoding: The Transformer architecture is used to independently model the temporal correlation of each physical channel; a multi-head self-attention mechanism is used to calculate the interdependence weights between patches to capture the long-term meteorological evolution logic; its attention score matrix... The calculation is as follows: in, This represents time series blocks for a single physical channel; Let represent the learnable query, key, and value projection matrices, respectively. and The dot product operation is used to measure the strength of nonlinear correlation between different time blocks; This represents the normalized activation function; Represents scaling factor; Global context evolution vector composition: The attention-encoded and convolution-enhanced features are then global pooled and aggregated using a multilayer perceptron to generate the final evolved feature vector. : in, Indicates global average pooling; Indicates the flattening operation; For feature splicing operators; This represents a multilayer perceptron.

5. In step five of claim 1, the quantile loss function is constructed as a functional for minimizing expected risk, as follows: Define the model parameter set as The problem of predicting the conditional distribution of rainfall on the target surface is transformed into solving the following objective function. Minimum value: in, For the set of quantiles, It is an asymmetric quantile norm. This is the indicator function; the model outputs the corresponding quantile by minimizing this expected risk. The prediction boundary below Indicates the distribution of data The expectation operator on.

6. A GNSS rainfall prediction method based on multivariate cross-frequency interactive Manba as described in any one of claims 1-5, implemented through a monitoring system, characterized in that, The monitoring system includes a data sensing layer, which contains a GNSS receiver and a ground rain gauge network, used to collect and calculate PWV and rainfall data; and a calculation and processing layer, which has a built-in dynamic screening module for rainfall factors and a deep learning inference engine, used to perform variable screening and multi-scale feature fusion calculations. The early warning release layer generates a trend map of areal rainfall changes and confidence intervals based on quantile prediction results. An alarm is triggered when the lower limit of the prediction exceeds the threshold.

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