A reappraisal of the Kalman filtering technique, as applied in river flow forecasting

Abstract

Some applications of the Kalman filtering technique in river flow forecasting are critically reviewed. It is argued that when the flow forecasting model is assumed to be an autoregressive moving average (ARMA) model and the corresponding flow data are considered to be free of measurement errors, the minimum mean-square error forecasts obtained by using the ‘conventional’ Box and Jenkins-type time series forecasting method are identical with those obtained by using the Kalman filtering technique. However, with the assumption of the presence of measurement errors in the river flow time series, the use of Kalman filtering technique assumes relevance, but this type of application results in reduced forecast efficiency as evaluated by the degree of matching attained, in the least-squares sense, of the forecasted flows with the measured flows. In the absence of measurement error, referred to as the pure prediction scenario, it is demonstrated that a simpler degenerate set of Kalman filter equations results, in which the Kalman gain plays no part in the prediction, i.e. the application of the general Kalman filter becomes redundant.