State space model for river temperature prediction

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Abstract
A stochastic state space model for the estimation of river temperature is presented, setting the stage for its implementation in optimal control algorithms. Physical processes modeled include advection, diffusion, and environmental heat exchange; the mathematical formulation is one dimensional. The deterministic formulation uses a hybrid characteristics‐finite differences numerical scheme for the solution of the governing equations. The stochastic formulation accounts for uncertainty due to model assumptions, errors in the model inputs and parameters, and river temperature measurements. Model use is demonstrated by the estimation of temperatures in a 5‐mile (8 km) reach of the Des Plaines River, Illinois, below the Joliet power station. River temperature measurements and hydrological and meteorological data are used to estimate the model parameters; model formulation and limitations are assessed based on the model application results. The stochastic formulation improves river temperature estimation, as measured by the mean, variance‐covariance, correlation, and range of the residuals.

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