Koopman Fourier Diffusion for Storm River Forecasting During Extreme Storm Events

Abstract

Accurate prediction of river water levels over extended temporal horizons remains a formidable challenge in hydrological forecasting, particularly under the volatile conditions induced by severe storm events. Traditional physical models and conventional deep learning architectures often struggle to capture the complex, non-linear dynamics inherent in rapid hydrological fluctuations. This paper proposes a novel framework that integrates Koopman operator theory and Fourier analysis within a diffusion-based generative model to achieve robust, long-horizon river level forecasting. By utilizing the Koopman operator, the methodology maps the intricate, non-linear hydro-meteorological state space into an infinite-dimensional linear space, where the system dynamics become significantly more tractable. Simultaneously, the Fourier transform decomposes these dynamics in the frequency domain, enabling the model to capture multi-scale periodic patterns such as seasonal variations and flash storm impulses. The diffusion model acts as the core predictive engine, leveraging the linearly transformed frequency features to generate highly accurate future state trajectories through a learned denoising process. Comprehensive evaluations against established benchmarks demonstrate that the proposed architecture not only minimizes accumulation errors in long-term predictions but also exhibits superior stability and responsiveness during extreme weather anomalies. The approach establishes a new paradigm for resilient infrastructure planning and disaster mitigation.