The Kalman Filter with Colored Noise and Its Application to the Flood Forecasting of a River Basin

To control the divergence of the filter efficaciously, the Kalman filter algorithm with colored noise is applied in this study for predicting the rainfall and the flow of rivers during flooding. To facilitate rainfall forecasting, an autoregressive moving average (ARMA) model is fitted to hourly rainfall. The adopted runoff model is the V-shaped kinematic-wave conceptual model. Hydrodynamic models of overland flow and channel flow are derived from the kinematic-wave approximation. These two systems are connected in a series to form a state-space system. By using the algorithm which the Kalman filter provides, state variables can be predicted and the measured rainfall or streamflow can be used to correct and update the estimated state variables. These updated state variables then provide the basis for the computation of N-step ahead forecasts, so as to forecast rainfall during the next few hours and be applied in real-time flood forecasting.