Adaptive prediction of hydrologic series by Walsh-Kalman model

Abstract

Abstract The orthogonal Walsh series are proposed as an effective model to account for periodicities in observed hydrologic series. Their combinations with the Kalman filter lead to a real-time prediction procedure of the state variables which are monthly hydrologic variables. General formulations of adaptive parameter and state estimates are presented and subsequently their application is performed for monthly flow and rainfall volume sequences. The Walsh series are attractive because of their piecewise linearity over controllable finite periods, their orthogonality and their symmetry, in addition to their simplicity in the basic calculations, which are additions and subtractions. The method has been applied to monthly stream flow data from Turkey and the U.S.A., and monthly rainfall data from Saudi Arabia as a representative of extremely arid zones. Comparison with the already available results indicates that the Walsh functions lead to better adaptive predictions than the Fourier series when combined with the Kalman procedure.