Water quality forecasting with transient-aware modeling for non-stationary environmental time series

Water quality is jointly shaped by environmental and anthropogenic factors, and the resulting monitoring data often exhibit non-stationary characteristics with transient and abrupt signals. Conventional forecasting models have difficulty accommodating these distributional shifts: they often produce delayed predictions or lose accuracy near abrupt-change points. This study proposes a state-space forecasting framework for complex aquatic dynamics, in which parallel temporal and spectral branches learn complementary time-domain and frequency-domain representations. The spectral-attention Mamba architecture integrates long-range temporal dependencies with frequency- and phase-domain interactions in a joint latent space. To reduce the feature smoothing typical of conventional reconstructions, we further introduce a Laplace-domain transient decoder, which maps latent features to stable complex poles and constructs a damped-oscillation basis for transient forecasting. This formulation is motivated by the damped and oscillatory patterns observed in water-quality records. Experiments on three heterogeneous monitoring datasets demonstrate competitive forecasting performance, with the largest improvements observed for irregular multiscale dynamics and long-horizon forecasting, whereas the gains are more limited for strongly periodic sequences. The event-based analysis further indicates lower mean temporal-lag errors for selected variables under non-stationary conditions.