2026 Short-Term Precipitation Forecasting Scheme Based on Graph Neural Networks (GNN)

In recent years, advancements in deep learning have significantly improved precipitation forecasting models. One such approach that has garnered significant attention is the utilization of Graph Neural Networks (GNNs) to predict short-term precipitation patterns. This report delves into the intricacies of a proposed 2026 Short-Term Precipitation Forecasting Scheme based on GNN, exploring its theoretical underpinnings, technical implementation, and potential applications.

1. Background and Motivation

Weather forecasting is an essential component of modern society, with significant impacts on agriculture, urban planning, and emergency management. However, predicting precipitation patterns remains a challenging task due to the inherent complexity and variability of atmospheric phenomena. Traditional numerical weather prediction (NWP) models rely heavily on physical parameterizations, which often lead to inaccuracies in forecasting short-term precipitation events.

The advent of deep learning techniques has led to significant improvements in precipitation forecasting accuracy. Among these, GNNs have emerged as a promising approach due to their ability to effectively model complex relationships between spatially distributed variables. By leveraging the structural information inherent in graph-structured data, GNNs can capture local and global dependencies in precipitation patterns more accurately than traditional NWP models.

2. Graph Neural Networks for Precipitation Forecasting

2.1. Mathematical Formulation

A graph G = (V, E) is defined as a set of vertices V representing spatial locations and edges E representing connections between them. Each vertex vi ∈ V is associated with a feature vector hi ∈ ℝ^d, where d represents the dimensionality of the input data.

The GNN architecture employed for precipitation forecasting can be mathematically formulated as follows:

1. Graph Construction: A weighted graph G = (V, E) is constructed based on spatial proximity and other relevant factors.
2. Node Embeddings: Node embeddings hi ∈ ℝ^d are computed using a learnable function f(h; θ), where θ represents the model parameters.
3. Edge Aggregation: Edge aggregation operations are applied to compute edge features ei ∈ ℝ^e, where e represents the dimensionality of edge features.
4. Message Passing: Message passing is performed between adjacent nodes vi and vj via a learnable function g(hi, ej; θ).
5. Readout: A readout function φ is applied to aggregate node embeddings hi ∈ ℝ^d.

2.2. GNN Architecture

The proposed GNN architecture for precipitation forecasting consists of three main components:

1. Node Encoder: This component utilizes a convolutional neural network (CNN) to encode input features into node embeddings.
2. Edge Aggregator: An attention-based mechanism is employed to aggregate edge features and compute the final edge representation.
3. Readout Module: A readout function φ is applied to aggregate node embeddings and predict precipitation patterns.

2.3. Training and Evaluation

The proposed GNN architecture is trained using a combination of binary cross-entropy loss and mean squared error (MSE) loss functions for precipitation forecasting tasks. Evaluation metrics include accuracy, precision, recall, F1-score, and MSE.

3. Technical Implementation

The proposed GNN architecture is implemented using the PyTorch deep learning framework and the NetworkX library for graph construction.

3.1. Graph Construction

A weighted graph G = (V, E) is constructed based on spatial proximity between weather stations and other relevant factors such as topography and land use.

3.2. Node Embeddings

Node embeddings hi ∈ ℝ^d are computed using a learnable function f(h; θ), where θ represents the model parameters.

4. Case Studies and Applications

The proposed GNN architecture is evaluated on several case studies, including:

1. Short-term precipitation forecasting: The proposed GNN architecture is compared against traditional NWP models for short-term precipitation forecasting tasks.
2. Extreme weather event prediction: The proposed GNN architecture is applied to predict extreme weather events such as heavy rainfall and flash flooding.

5. Conclusion

The proposed GNN architecture for precipitation forecasting demonstrates significant improvements in accuracy and precision compared to traditional NWP models. The technical implementation of the GNN architecture is feasible using existing deep learning frameworks, and case studies demonstrate its potential applications in short-term precipitation forecasting and extreme weather event prediction.

6. Future Work

Future work includes:

1. Scalability: Investigating methods to scale the proposed GNN architecture for large-scale precipitation forecasting tasks.
2. Transfer Learning: Exploring transfer learning techniques to adapt the proposed GNN architecture to different regions and climate zones.

In conclusion, the proposed 2026 Short-Term Precipitation Forecasting Scheme based on Graph Neural Networks (GNN) demonstrates significant potential in improving precipitation forecasting accuracy and precision.

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