Accelerating Flood Warnings by 10 Hours: The Power of River Network Topology in AI-enhanced Flood Forecasting

TL;DR

The study addresses the underutilization of river network topology in GNN-based flood forecasting, which stems from over-squashing in tree-like river networks and high resistance distances $R_{u,v}$. It introduces a dense graph transformation using a Gaussian kernel on inter-node distances, with $\mathcal{D}_{i,j} = \exp(-||d_{i,j}||^2/(2\sigma^2))$, to densify connections and lower effective resistance, enabling GNNs to capture distal river interactions. Across six GNN architectures, the dense topology yields superior long-horizon predictive performance, achieving 24-hour forecasts whose accuracy rivals EA-LSTM's 14-hour forecasts (a 71% improvement in horizon) and providing an average lead-time advantage of about 10 hours over the baseline. The approach demonstrates that appropriately dense, topology-aware representations can significantly enhance early flood warning capabilities, especially for rare, large-spike events, and suggests hybrid modeling opportunities that balance topology with attention mechanisms for varying hydrological conditions.

Abstract

Climate change-driven floods demand advanced forecasting models, yet Graph Neural Networks (GNNs) underutilize river network topology due to tree-like structures causing over-squashing from high node resistance distances. This study identifies this limitation and introduces a reachability-based graph transformation to densify topological connections, reducing resistance distances. Empirical tests show transformed-GNNs outperform EA-LSTM in extreme flood prediction, achieving 24-h water level accuracy equivalent to EA-LSTM's 14-h forecasts - a 71% improvement in long-term predictive horizon. The dense graph retains flow dynamics across hierarchical river branches, enabling GNNs to capture distal node interactions critical for rare flood events. This topological innovation bridges the gap between river network structure and GNN modeling, offering a scalable framework for early warning systems.

Figures (4)

• Figure 1: Visual exploration and quantitative analysis of river network topology.a) Visualization of an actual river network topology, showing the natural tree-like structure with multiple tributaries converging into main streams. b) Comparison of resistance distance distributions between dense and topology graphs, where the dense graph (blue line) shows lower resistance distances overall compablack to the topology graph (green line), indicating better information flow. c) Conceptual illustration of the bottleneck problem in tree-like structures, where information must pass through critical nodes that can become congested. d,e) Quantifying resistance distance through electrical analogy: When injecting 1A current at node A and extracting it at node B, the measublack voltage difference $V(A)-V(B)$ represents the resistance distance. The dense graph structure (e) blackuces this voltage difference from 2V to 0.625V compablack to the topology graph (d), demonstrating improved connectivity.
• Figure 2: In this study, we evaluate the performance of mainstream GNNs by analyzing their Nash-Sutcliffe efficiency across different types of adjacency matrices (dense, topological, and isolated) over varying pblackiction horizons. Additionally, the EA-LSTM model is employed as a baseline for comparison, allowing us to emphasize the superior long-term forecasting capabilities of GNNs relative to EA-LSTM.
• Figure 3: Figure \ref{['fig:nse_dist_mlp']} and \ref{['fig:nse_dist_lstm']} illustrate the performance of six different GNNs on LamaH-CE. We compares the NSE trends of the models under three scenarios: dense adjacency, EA-LSTM, and isolated adjacency. Overall, the NSE across different discharge, dense adjacency significantly outperforming both isolated adjacency and EA-LSTM.
• Figure 4: We compablack the GCN pblackiction results using dense and isolated adjacency matrices for spiked large flood events, evaluating both short-term (3-hour) and long-term (12-hour) forecasts.