A method for GNSS rainfall prediction and attribution of water vapor balance constrained PINN network
By combining the water vapor balance constrained PINN network with ConvLSTM and the atmospheric water vapor balance equation, the problem of existing models violating physical common sense in extreme weather was solved, achieving more accurate and interpretable rainfall prediction and improving the application effect of meteorological disaster prevention and mitigation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI XINGBEI INTELLIGENT TESTING TECHNOLOGY CO LTD
- Filing Date
- 2026-02-11
- Publication Date
- 2026-06-12
AI Technical Summary
Existing rainfall prediction models ignore the law of mass conservation in atmospheric physical processes, resulting in predictions that violate physical common sense during extreme weather or in areas with insufficient training data. Furthermore, they cannot explain the physical mechanisms of rainfall formation, thus limiting their application in practical meteorological disaster prevention and mitigation.
A water vapor balance constrained PINN network is adopted, data is acquired through GNSS ground observation stations, a four-dimensional input tensor is constructed, and a ConvLSTM network is combined to capture spatiotemporal features. The atmospheric water vapor balance equation is introduced as a physical constraint, and a hybrid loss function is designed for training to ensure that the model output conforms to atmospheric dynamics, while providing interpretable analysis of the causes of precipitation.
It significantly improves the accuracy and interpretability of rainfall forecasts, avoids non-physical prediction results, provides more refined and real-time water vapor evolution characteristics, and enhances the model's predictive ability in extreme events and the trust of weather forecasters.
Smart Images
Figure CN122196399A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of meteorological forecasting technology, and in particular to a GNSS precipitation prediction and attribution method using a water vapor balance constrained PINN network. Background Technology
[0002] In the past, rainfall prediction mainly relied on numerical weather prediction (NWP) models, which used complex dynamic equations for simulation. However, this method is computationally expensive, time-consuming, and suffers from a "start-up" effect, making it difficult to meet the timeliness requirements of short-term nowcasting. In recent years, with the development of deep learning technology, many existing methods have established rainfall prediction models based on pure data-driven approaches (such as CNN and LSTM), utilizing massive amounts of historical data to mine rainfall patterns, achieving significant breakthroughs in computational efficiency.
[0003] However, while the aforementioned data-driven methods offer advantages in prediction speed, they are essentially "black box" models, neglecting the laws of mass conservation (such as water vapor balance) that must be followed in atmospheric physics. This often leads to predictions that defy physical principles when facing extreme weather or areas with insufficient training data coverage (such as negative precipitation or false heavy precipitation under water vapor-free conditions). Furthermore, existing deep learning models cannot explain the physical mechanisms of precipitation formation (whether it is local water vapor accumulation or external transport), making it difficult for forecasters to judge the reliability of model predictions and limiting their application in practical meteorological disaster prevention and mitigation. Therefore, there is room for improvement. Summary of the Invention
[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a GNSS precipitation prediction and attribution method using a water vapor balance-constrained PINN network. Its advantages lie in significantly improving the accuracy of precipitation prediction and the interpretability of precipitation causes.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for GNSS precipitation prediction and attribution using a water vapor balance-constrained PINN network includes the following steps: Step 1: Acquire data from GNSS ground observation stations and ground meteorological sensors to obtain meteorological data at T time points. ; Then, the tropospheric atmospheric precipitation at T time points is obtained through inversion. This allows for the construction of the four-dimensional model input tensor at T time points. ;in, , , , , , , These are the wind field, temperature, surface air pressure, altitude, geographical latitude, surface evaporation, and actual rainfall of the target area at time point t. Step 2: Calculate the potential rainfall at time point t. Data and Provided , By introducing the atmospheric water vapor balance equation as a physical constraint, the model output is ensured to conform to atmospheric dynamics, thus obtaining the theoretical rainfall prediction value. Thus, the theoretical rainfall prediction values at T time points are obtained. ; Step 3: Construct the backbone network and process the input tensors Spatiotemporal feature extraction is performed to obtain the hidden layer state. Then, the original prediction output module is constructed and the hidden layer state is... The data is input into the system for rainfall prediction processing, and the system outputs preliminary rainfall prediction values. Finally, a hybrid loss function is constructed and the model is trained to update the preliminary rainfall forecast. ; Step 4: Calculate the preliminary rainfall forecast value at time t using the preliminary rainfall forecast formula. Fine-tune the parameters and ensure the output is non-negative to obtain the final rainfall prediction value at time t. This allows us to obtain the final rainfall forecast values at T time points. ; Step 5: Design an interpretable quantitative analysis method based on the deconstruction of precipitation physics terms; output the physical causes of precipitation based on the proportions of each term in the water vapor balance.
[0006] The present invention is further configured such that, in step one, water vapor inversion is performed using GNSS ground observation station data, and the total zenith delay is obtained by calculating the GNSS data at T time points using precise single-point positioning. Then, the zenith delay at T time points is obtained using the following formula. Then, the possible rainfall at T time points can be calculated using the following inversion formula. ; in, It is the water vapor conversion factor.
[0007] The present invention is further configured to include the rainfall at the t-th time point. Data and surface meteorological data Wind field provided Temperature air pressure Perform spatiotemporal alignment to construct the four-dimensional input tensor at time t. This allows us to obtain the model input tensors at T time points. .
[0008] The present invention is further configured such that the water vapor balance equation in step two is: in, This is the water vapor divergence operator.
[0009] The present invention is further configured such that, in step three, a ConvLSTM unit is used to capture the spatiotemporal characteristics of meteorological data; and the model input tensor at time point t is used. The input is fed into the backbone network, thereby capturing its spatiotemporal features using the following formula to obtain the hidden state at time point t. This allows us to obtain the hidden states at T time points. ; in, Input tensor to the model at time t , , , These are the input gate, forget gate, and output gate at time t, respectively. The cell state at time t, The cell state at time t-1 Let t be the hidden state. Let be the hidden state at time t-1; Use the Sigmoid activation function; , , , For the bias of each gate; , , , , , , , , , , The subscripts represent the model weights and indicate the connection relationships. This is the convolution operator; This represents element-wise multiplication of matrices; It is the hyperbolic tangent activation function.
[0010] The present invention is further configured to store the hidden state of the ConvLSTM layer at time t. After a The convolutional layer is mapped to the preliminary rainfall prediction value; thus, the preliminary rainfall prediction value at time t is obtained using the following formula. This allows us to obtain preliminary rainfall forecasts for T time points. ; .
[0011] The present invention is further configured to output the network at time t. Inputting this into the water vapor balance constraint equation yields the physical residual at time t. As shown in the following formula:
[0012] Based on this, design the total loss function at time t. Includes data loss at time t. and physical loss As shown in the following formula:
[0013] in, For the sample size, The weighting coefficient for the physical loss term; Then, during the training phase, minimize the total loss function at time t. To optimize network parameters and update preliminary rainfall forecasts This allows us to obtain the updated preliminary rainfall forecasts for the T time points. .
[0014] The present invention is further configured such that the preliminary rainfall prediction formula is: ;in, To correct the hyperparameters of the coefficients, This is the activation function used to ensure that the final rainfall forecast value is not negative.
[0015] The present invention is further configured such that, in step five, the four-dimensional model at time t is input as a tensor. Included rainfall Wind field The following formula can be used to convert the local water vapor conversion contribution at time t. Contribution to water vapor convergence transport ; .
[0016] The present invention is further configured to use the obtained local water vapor conversion contribution at time t. Contribution to water vapor convergence transport The dominant factor of the rainfall mechanism at time t is calculated using the following formula. This leads to the understanding of the causes of rainfall at T time points. ;
[0017] in, To ensure numerical stability and prevent the denominator from being zero; if Rainfall is dominated by water vapor transport. The dominant type of rainfall is local accumulation; This is then classified as mixed rainfall.
[0018] The beneficial effects of this invention are as follows:
[0019] 1. This invention innovatively introduces the atmospheric water vapor balance equation as a physical constraint (PhysicsLoss) for the neural network, forcing the model to obey the law of conservation of mass while learning data patterns. This not only avoids non-physical prediction results such as negative precipitation and significantly improves the model's prediction accuracy in extreme precipitation events, but also ensures that the prediction results conform to the principles of atmospheric dynamics.
[0020] 2. This invention utilizes all-weather, high temporal resolution atmospheric precipitable water (PWV) data retrieved from the Global Navigation Satellite System (GNSS) to effectively compensate for the shortcomings of traditional radar and rain gauges in terms of temporal continuity and spatial coverage, providing more refined and real-time water vapor evolution characteristics for short-term nowcasting.
[0021] 3. This invention addresses the four-dimensional spatiotemporal characteristics of meteorological data by employing a Convolutional Long Short-Term Memory (ConvLSTM) network as its backbone architecture. Compared to traditional neural networks, this architecture utilizes convolutional operations instead of fully connected layers, enabling it to simultaneously capture the spatial movement characteristics and temporal evolution trends of rain clouds, thereby achieving a higher-fit prediction model in a shorter training time.
[0022] 4. This invention can quantify the contribution ratio of "local water vapor conversion" and "external water vapor transport" to rainfall, automatically determine whether rainfall is dominated by local convection or external transport, and provide a physical confidence score. This provides meteorologists with intuitive physical attribution analysis, greatly enhancing the transparency and credibility of artificial intelligence models in practical disaster prevention and mitigation applications. Attached Figure Description Figure 1 This is a schematic diagram illustrating the workflow of a GNSS precipitation prediction and attribution method using a water vapor balance constrained PINN network proposed in this invention.
[0023] Figure 2 This is a schematic diagram of the PINN network model for a GNSS precipitation prediction and attribution method using a water vapor balance constrained PINN network proposed in this invention. Figure 3 This is a schematic diagram illustrating the prediction performance of the PINN network model under heavy rain conditions in a GNSS rainfall prediction and attribution method based on a water vapor balance constrained PINN network proposed in this invention. Figure 4This is a schematic diagram of the prediction of GNSS rainfall under light to moderate rain conditions using the PINN network model of the water vapor balance constrained PINN network proposed in this invention. Detailed Implementation
[0024] The technical solution of this patent will be further described in detail below with reference to specific embodiments.
[0025] 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.
[0026] In this embodiment, a GNSS precipitation prediction and attribution method using a water vapor balance-constrained PINN network includes: 1. Performing water vapor inversion through a GNSS ground observation station to obtain the precipitable water volume (PWV) in the troposphere above the station, and simultaneously acquiring various meteorological data (wind field, temperature, and air pressure) for the region to construct a four-dimensional input tensor; 2. Using a Physical Information Neural Network (PINN) based on ConvLSTM (CL-PINN) to extract the spatiotemporal features of the four-dimensional input tensor, while introducing the water vapor balance equation as a physical constraint into the loss function, thereby training the network to achieve a preliminary prediction of precipitation; 3. Designing a physical residual correction strategy to fine-tune the preliminary prediction value output by the network to obtain the final precipitation prediction value; 4. Designing an interpretable quantitative analysis method based on the deconstruction of precipitation physics terms to calculate the dominant precipitation factor and achieve physical attribution analysis of precipitation.
[0027] Reference Figure 1 A method for GNSS precipitation prediction and attribution using a water vapor balance-constrained PINN network includes the following steps: Step 1: The tropospheric precipitation potential (PWV) of the region is obtained through GNSS ground observation stations and multi-source data of temperature, air pressure and wind field of the region are obtained through meteorological sensors to construct a four-dimensional input tensor.
[0028] Data from GNSS ground observation stations and ground meteorological sensors were acquired. GNSS signals possess all-weather, high temporal resolution characteristics, enabling them to penetrate clouds and fog to detect atmospheric water vapor content, compensating for the limitations of optical remote sensing during rainfall. Multi-source data, including wind field and air pressure, were fused to construct a complete "atmospheric thermodynamic environment field," providing the neural network with the material basis (water vapor) and dynamic conditions (wind field) for rainfall occurrence. Meteorological data at T time points were obtained. , Then, the tropospheric atmospheric precipitation at T time points is obtained through inversion. This allows for the construction of model input tensors at T time points. .in, , , , , , , These are the wind field, temperature, surface air pressure, altitude, latitude, surface evaporation, and actual rainfall of the target area at time point t.
[0029] Step 1.1: GNSS data PWV inversion. Water vapor is inverted using GNSS ground observation data. Precise point positioning is used to calculate the total zenith delay (PWV) of GNSS data at T time points. Then, using equation (1), the zenith delay at T time points is obtained. Then, the possible rainfall at T time points is calculated by inversion using equation (2). GNSS signals experience a delay during atmospheric propagation, where ZTD comprises the dry delay (ZHD) caused by dry gases and the wet delay (ZWD) caused by water vapor. After accurately subtracting the ZHD using a model (such as the Saastamoinen model), the remaining ZWD is converted using a conversion factor. This can be mapped to the liquid water equivalent (PWV) within the atmospheric column. (1) (2) Among them It is the water vapor conversion factor.
[0030] Step 1.2: Model Input Construction. The potential rainfall at time point t... Data and surface meteorological data Wind field provided Temperature air pressure Perform spatiotemporal alignment to construct the four-dimensional input tensor at time t. This allows us to obtain the model input tensors at T time points. This data structure is specifically adapted to subsequent convolutional neural networks, enabling them to simultaneously extract the spatial distribution characteristics (such as the distribution of water vapor gradients) and temporal evolution characteristics (such as the transport trend of wind fields) of meteorological elements.
[0031] Step 2: Design the water vapor balance constraint equations. The possible rainfall at time point t... Data and Provided , Introducing the atmospheric water vapor balance equation (3) as a physical constraint ensures that the model output conforms to atmospheric dynamics, thus obtaining the theoretical rainfall prediction value. Thus, the theoretical rainfall prediction values at T time points are obtained. Introducing this equation as a "soft constraint" into a neural network can not only calculate a theoretical rainfall value based on physical derivation, but also prevent purely data-driven models from producing predictions that violate common sense physics (such as predicting heavy rain in the absence of water vapor transport and local accumulation). (3) Among them, This is the water vapor divergence operator.
[0032] Step 3: Construction and training of the PINN physical information neural network based on ConvLSTM. See details in the following section. Figure 2 As shown. This step is the core of the method, employing an "encoder-decoder" structure. The PINN (Physics-Informed Neural Network) architecture is characterized by the network learning not only from labeled data but also supervised by the residuals of physical equations, achieving a dual drive from data-driven and physical mechanisms. First, the backbone network is constructed and the input tensor... Spatiotemporal feature extraction is performed to obtain the hidden layer state. Then, a preliminary prediction output module is constructed and the hidden layer state is... The data is input into the system for rainfall prediction processing, and the system outputs preliminary rainfall prediction values. Finally, a hybrid loss function is constructed and the model is trained to update the preliminary rainfall forecast. .
[0033] Step 3.1: Construct the backbone network. Use ConvLSTM units to capture the spatiotemporal features of the meteorological data. Input the model tensor at time point t. The input is fed into the backbone network, thereby capturing its spatiotemporal features using equation (4) to obtain the hidden state at time point t. This allows us to obtain the hidden states at T time points. The reason for choosing ConvLSTM is that rainfall processes exhibit significant spatiotemporal nonstationarity. Traditional LSTM can only process one-dimensional time series, ignoring the spatial movement of clouds; while ordinary CNNs cannot remember historical states. ConvLSTM introduces convolution operations within LSTM units. It retains the long short-term memory capability of LSTM and has the spatial feature extraction capability of CNN, making it very suitable for simulating the formation and dissipation process of rain clouds. (4) Among them, Input tensor to the model at time t , , , These are the input gate, forget gate, and output gate at time t, respectively. The cell state at time t, The cell state at time t-1 Let t be the hidden state. Let be the hidden state at time t-1; Use the Sigmoid activation function; , , , For the bias of each gate; , , , , , , , , , , The subscripts represent the model weights and indicate the connection relationships. This is the convolution operator; This represents element-wise multiplication of matrices; It is the hyperbolic tangent activation function.
[0034] Step 3.2: Construct the initial prediction output module. This involves storing the hidden states of the ConvLSTM layer at time t. After a The convolutional layer is mapped to the preliminary rainfall prediction value. Therefore, the preliminary rainfall prediction value at time t is obtained using equation (5). This allows us to obtain preliminary rainfall forecasts for T time points. . (5)
[0035] Step 3.3: Construct a hybrid loss function for model training. The output of the network at time t... Inputting this into the water vapor balance constraint equation designed in step 2, we obtain the physical residual at time t. As shown in equation (6). (6) Based on this, design the total loss function at time t. Includes data loss at time t. and physical loss As shown in Equation (7): Through joint optimization, the network is forced to find the optimal solution in the solution space that conforms to both the data distribution and the physical constraints, thereby improving the generalization ability of the model. (7) Among them, For the sample size, This represents the weighting coefficient for the physical loss term.
[0036] Then, during the training phase, minimize the total loss function at time t. To optimize network parameters and update preliminary rainfall forecasts This allows us to obtain the updated preliminary rainfall forecasts for the T time points. .
[0037] Step 4: Design the physical residual correction for the final rainfall prediction output. Use equation (8) to calculate the initial rainfall prediction value at time t in the network. Fine-tune the parameters and ensure the output is non-negative to obtain the final rainfall prediction value at time t. This allows us to obtain the final rainfall forecast values at T time points. . (8) Among them, To correct the hyperparameters of the coefficients, This is the activation function used to ensure that the final rainfall forecast value is not negative. The specific effect is as follows: Figure 3 , Figure 4 As shown.
[0038] Step 5: Design an interpretable quantitative analysis method based on the deconstruction of precipitation physics. Based on the proportions of each term in the water vapor balance, output the physical causes of precipitation. This quantitative attribution analysis not only provides prediction results but also offers the physical basis for "why this rain is happening," greatly enhancing weather forecasters' trust in AI models and providing scientific support for disaster prevention and mitigation decisions (such as whether to focus on strong winds or severe convective weather defense).
[0039] Step 5.1 Physical Attribution Decomposition Vector. Input the four-dimensional model at time t into the tensor. Included rainfall Wind field Equation (9) is used to convert the local water vapor conversion contribution at time t. Contribution to water vapor convergence transport . (9)
[0040] Step 5.2: Quantify the dominant factors of precipitation mechanisms and analyze the causes of precipitation. The local water vapor transformation contribution at time t will be obtained. Contribution to water vapor convergence transport The dominant factor of the rainfall mechanism at time t is calculated using equation (10). This leads to the understanding of the causes of rainfall at T time points. . (10) Among them, This is a numerically stable term to prevent the denominator from being zero. If This rainfall event is dominated by moisture transport, indicating that it was primarily caused by a large influx (convergence) of external moisture, such as rainfall brought by typhoons, frontal rainfall, or warm, moist air transport belts. Close attention should be paid to changes in upstream wind fields and moisture flux. The rainfall was mainly caused by local accumulation, indicating that the rainfall was primarily due to drastic phase changes in water vapor within the local atmospheric column (such as strong surface evaporation and convective instability), similar to afternoon thunderstorms in summer or localized severe convective weather. Local thermal instability and vertical motion should be closely monitored. This is then classified as mixed rainfall, meaning it is caused by a combination of local factors and external transport.
[0041] Step 6: Select the benchmark models XGBoost, DeepAR, and LSTM, and compare the prediction results with the rainfall prediction performance of the proposed method (CL-PINN) under heavy rain conditions. The root mean square error (RMSE) and mean absolute error (MAE) are used as evaluation indicators of the model performance results. The experimental results in Table 1 show that the CL-PINN model has a good prediction effect in rainfall prediction.
[0042] Table 1
[0043] The goal of this invention is to predict, analyze, and evaluate rainfall causes in areas where GNSS ground observation stations are located, aiming to improve the accuracy of rainfall prediction and more effectively and rationally evaluate the evolution trend of natural disasters to meet the needs of practical engineering applications.
[0044] 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 method for GNSS precipitation prediction and attribution using a water vapor balance-constrained PINN network, characterized in that, Includes the following steps: Step 1: Acquire data from GNSS ground observation stations and ground meteorological sensors to obtain meteorological data at T time points. ; Then, the tropospheric atmospheric precipitation at T time points is obtained through inversion. This allows for the construction of the four-dimensional model input tensor at T time points. ;in, , , , , , , These are the wind field, temperature, surface air pressure, altitude, geographical latitude, surface evaporation, and actual rainfall of the target area at time point t. Step 2: Calculate the potential rainfall at time point t. Data and Provided , By introducing the atmospheric water vapor balance equation as a physical constraint, the model output is ensured to conform to atmospheric dynamics, thus obtaining the theoretical rainfall prediction value. Thus, the theoretical rainfall prediction values at T time points are obtained. ; Step 3: Construct the backbone network and process the input tensors Spatiotemporal feature extraction is performed to obtain the hidden layer state. Then, the original prediction output module is constructed and the hidden layer state is... The data is input into the system for rainfall prediction processing, and the system outputs preliminary rainfall prediction values. Finally, a hybrid loss function is constructed and the model is trained to update the preliminary rainfall forecast. ; Step 4: Calculate the preliminary rainfall forecast value at time t using the preliminary rainfall forecast formula. Fine-tune the parameters and ensure the output is non-negative to obtain the final rainfall prediction value at time t. This allows us to obtain the final rainfall forecast values at T time points. ; Step 5: Design an interpretable quantitative analysis method based on the deconstruction of precipitation physics terms; output the physical causes of precipitation based on the proportions of each term in the water vapor balance.
2. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 1, characterized in that, In step one, water vapor inversion is performed using GNSS ground observation station data, and the total zenith delay is obtained by solving the GNSS data at T time points using precise single-point positioning. Then, the zenith delay at T time points is obtained using the following formula. Then, the possible rainfall at T time points can be calculated using the following inversion formula. ; in, It is the water vapor conversion factor.
3. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 2, characterized in that, The rainfall at time point t Data and surface meteorological data Wind field provided Temperature air pressure Perform spatiotemporal alignment to construct the four-dimensional input tensor at time t. This allows us to obtain the model input tensors at T time points. .
4. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 1, characterized in that, The water vapor balance equation in step two is: in, This is the water vapor divergence operator.
5. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 1, characterized in that, In step three, a ConvLSTM unit is used to capture the spatiotemporal characteristics of meteorological data; the model input tensor at time point t is then used. The input is fed into the backbone network, thereby capturing its spatiotemporal features using the following formula: Get the hidden state at time point t. This allows us to obtain the hidden states at T time points. ; in, Input tensor to the model at time t , , , These are the input gate, forget gate, and output gate at time t, respectively. The cell state at time t, The cell state at time t-1 Let t be the hidden state. Let be the hidden state at time t-1; Use the Sigmoid activation function; , , , For the bias of each gate; , , , , , , , , , , The subscripts represent the model weights and indicate the connection relationships. This is the convolution operator; This indicates element-wise multiplication of matrices; It is the hyperbolic tangent activation function.
6. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 5, characterized in that, The hidden state of the ConvLSTM layer at time t. After a The convolutional layer is mapped to the preliminary rainfall prediction value; thus, the preliminary rainfall prediction value at time t is obtained using the following formula. This allows us to obtain preliminary rainfall forecasts for T time points. ; .
7. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 6, characterized in that, The output of the network at time t Inputting this into the water vapor balance constraint equation yields the physical residual at time t. As shown in the following formula: Based on this, design the total loss function at time t. Includes data loss at time t. and physical loss As shown in the following formula: in, For the sample size, The weighting coefficient for the physical loss term; Then, during the training phase, minimize the total loss function at time t. To optimize network parameters and update preliminary rainfall forecasts This allows us to obtain the updated preliminary rainfall forecasts for the T time points. .
8. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 1, characterized in that, The preliminary rainfall prediction formula is as follows: ;in, To correct the hyperparameters of the coefficients, This is the activation function used to ensure that the final rainfall forecast value is not negative.
9. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 1, characterized in that, In step five, the four-dimensional model at time t is input into the tensor. Included rainfall Wind field The following formula can be used to convert the local water vapor conversion contribution at time t. Contribution to water vapor convergence transport ; 。 10. The GNSS precipitation prediction and attribution method for a water vapor balance constrained PINN network according to claim 9, characterized in that, The local water vapor conversion contribution at time t will be obtained. Contribution to water vapor convergence transport The dominant factor of the rainfall mechanism at time t is calculated using the following formula. This leads to the understanding of the causes of rainfall at T time points. ; in, To ensure numerical stability and prevent the denominator from being zero; if Rainfall is dominated by water vapor transport. The dominant type of rainfall is local accumulation; This is then classified as mixed rainfall.