Adaptive Parameter Estimation for Multisite Hydrologic Forecasting

Abstract

TWO stochastic modeling approaches for multisite hydrologic forecasting are presented in this work. The models are of ARMAX class expressed in state‐space formulations. The first approach, the adaptive partitioning, models a large catchment by shifting the locations in their time‐lags and modeling the flows of the different subsystems one at a time. The adaptive partitioning approach reintroduces the partitioning proposed by Wood in 1981 in an adaptive and more flexible form. The second approach, the cascading, divides the large catchment into groups of locations and models the groups as subsystems. In both approaches, the models' parameters and noise statistics are updated on‐line in an adaptive manner along with the states. For this purpose, the work proposes an evaluation/ forecasting algorithm based on the three parallel filter theory‐, a state‐space, parameter‐space, and a noise‐space filter. The algorithm is a synthesis and development of two preceding studies by Hebson and Wood, in 1985, and Bergman and Delleur, in 1985. The proposed evaluation/forecasting algorithm introduces a more flexible and comprehensive algorithm for the adaptive parameter‐noise statistics estimation of stochastic models. The two multisite hydrologic forecasting approaches use this tool in modeling large‐scale systems. In this work, the proposed algorithm and the two modeling approaches have been applied to daily stream‐flow forecasting of the Fraser River, Canada.