Physics-Informed Diffusion Model for HAB Forecasting in Hong Kong Coastal Waters

Harmful algal blooms (HABs) pose a persistent challenge to coastal ecosystems, fisheries, and public health, particularly in urbanized coastal regions subject to strong hydrodynamic forcing and meteorological variability. HAB dynamics emerge from the interaction of biologically driven growth processes and physically governed transport and dispersion, operating across disparate spatial and temporal scales. However, most existing data-driven forecasting approaches treat these processes implicitly and holistically, limiting physical interpretability, robustness under nonstationary forcing, and the ability to represent forecast uncertainty.

This study proposes a physics-informed diffusion-based framework for HAB forecasting in coastal environments, with the objective of explicitly separating biological and physical drivers within a generative probabilistic model. The central hypothesis is that decoupling meteorological and hydrodynamic forces can improve the physical consistency and generalizability of HAB forecasts while enabling uncertainty-aware prediction. To this end, future HAB states are formulated as conditional samples generated through a reverse diffusion process guided by physically meaningful environmental inputs.

The proposed framework adopts a dual-forcing architecture. A meteorological branch encodes atmospheric variables—including air temperature, precipitation, wind speed, and radiative forcing—that primarily regulate phytoplankton growth potential and bloom initiation. In parallel, a hydrodynamic branch incorporates tidal dynamics and wave-related information to represent advection, mixing, and dispersion processes governing the spatial evolution of algal biomass in coastal waters. Physical consistency is promoted by embedding the advection–diffusion equation as a soft constraint within the hydrodynamic latent space, encouraging mass-conserving and physically plausible transport behavior without imposing a fully deterministic dynamical model.

By leveraging diffusion probabilistic modeling, the framework generates ensemble-based forecasts that characterize the conditional probability distribution of future HAB states rather than single deterministic trajectories. Forecast outputs are formulated in terms of a probabilistic HAB severity index, facilitating interpretable, risk-informed early warning analogous to probabilistic weather forecasting systems. Model development is designed to integrate multi-source environmental datasets, including high-frequency meteorological observations, wave and tidal records, and routine coastal water-quality monitoring.

The framework is developed with a focus on tidally energetic coastal systems, with the Hong Kong coastal region serving as a representative application domain. Overall, this study outlines a physically interpretable and uncertainty-aware modeling paradigm for HAB forecasting and provides a conceptual foundation for next-generation early-warning systems in coastal environments.