Steady state river quality modeling by sequential extended Kalman filters

Abstract

Sequential extended Kalman filters (EKF) are applied as a technique for steady state river water quality modeling. The approach was demonstrated by using water quality data collected over a 36.4‐mi (58.6 km) stretch of the Jordan River, Utah. Each EKF was used to represent a river reach in which hydraulic and quality characteristics were judged fairly uniform. Mean and variance boundary conditions between successive filters were adjusted to represent the effects of point loads and tributaries discharging into the main river. Approximate minimum variance estimates of the system state (water quality parameters) and confidence intervals on these estimates were provided by combining two independent estimates of the system)state. The independent estimates were based on (1) predictions from an ‘internally meaningful’ model of the stream transport processes and biochemical transformations and (2) measurements of the water quality parameters. The estimates were combined by a weighting procedure based on uncertainties associated with each estimate. A smoothing algorithm was also applied in order that estimates from passes of the filter procedure in both the downstream and upstream directions could be combined. In this way, information contained in the measurements was used both upstream and downstream of the location of the measurement. The calibration capability of the filter procedure was demonstrated by simultaneous estimation of the state vector and one of the model coefficients. This capability was also used to estimate simultaneously the rate of lateral loading for one of the water quality parameters. Simultaneous estimation of coefficients of lateral loading was shown to increase the uncertainty associated with filter estimates because of the inclusion of uncertainty associated with these coefficients and lateral loading rates.