Forecasting river temperatures in real time using a stochastic dynamics approach.

We address the growing need for accurate water temperature predictions in regulated rivers to inform decision support systems and protect aquatic habitats. Although many suitable river temperature models exist, few simultaneously model water temperature dynamics while considering uncertainty of predictions and assimilating observations. Here, we employ a stochastic dynamics approach to water temperature modeling that estimates both the water temperature state and its uncertainty by propagating error through a physically based dynamical system. This method involves converting the governing hydrodynamic and heat transport equations into a state space form and assimilating observations via the Kalman Filter. This model, called the River Assessment for Forecasting Temperature (RAFT), closes the heat budget by tracking heat movement using a robust semi-Lagrangian numerical scheme. RAFT considers key thermodynamic processes, including advection, longitudinal dispersion, atmospheric heat fluxes, lateral inflows, streambed heat exchange, and unsteady nonuniform flow. Inputs include gridded meteorological forecasts from a numerical weather prediction model, bathymetric cross-sectional geometry, and temperature and flow measurements at the upstream boundary and tributaries. We applied RAFT to an ∼100 km portion of the Sacramento River in California, downstream of Keswick Dam (a regulatory dam below Shasta Dam), at a spatial resolution of 2 km and a temporal resolution of 15 min. Model prediction error over a 6 month calibration period was on the order of 0.5°C. When temperature and flow gage data were assimilated, the mean prediction error was significantly less (0.25°C). The model accurately predicts the magnitude and timing of diel temperature fluctuations and can provide 72 h water temperature forecasts when linked with meteorological forecasts and real-time flow/temperature monitoring networks. RAFT is potentially scalable to model and forecast fine-grained one-dimensional temperature dynamics covering a broad extent in a variety of regulated rivers provided that adequate input data are available.