A Multi-Scale Dynamical Model for Extreme Atmospheric Events: Coupling Navier–Stokes Transport with Multiplicative Chaos Cascades

We developed a multi-scale stochastic model for atmospheric events capable of generating extreme precipitation leading to flooding. The framework combines a deterministic continuum-mechanical backbone based on an augmented Navier–Stokes system with a probabilistic multiplicative cascade representing unresolved sub-grid intermittency. The cascade is conditioned dynamically through optimal transport constraints and shown to approximate a stochastic continuity equation in measure space. Extreme rainfall statistics were derived using Gaussian multiplicative chaos theory, yielding power-law tail behaviour governed by a physically parametrised intermittency coefficient. The model provides a principled bridge between fluid mechanics, stochastic geometry, and statistical risk estimation.