Varying-parameter modeling within ensemble architecture: Application to extended streamflow forecasting

Abstract Extended streamflow forecasting is nowadays important for early flood warning and risk mitigation under a changing climate. However, the absence of reliable estimates of the usual streamflow descriptors, at the considered time horizons, renders common input–output modeling approaches inapt for extended forecasting. For such a problem, system recurrence information is vital to produce relatively improved forecasts. Like any time series generated by complex systems, river flow can be represented by a time-varying parameter (TVP) model. TVP modeling frameworks often assume that the system evolution exhibits superstatistical random walks, and a number of statistical assumptions is followed upon, to infer better forecasts from the system. Also, the TVPs should hone a model's ability to capture system recurrence, which in this case translates to a number of state-based model structures. In this work, we develop an ensemble-based computationally efficient method that extracts useful cyclic-type TVPs which are strongly coupled over extended, but more continuous and less aggregated, time horizons. A multi-level modeling framework is proposed to facilitate the creation and direct use of updated parameter states to produce more reliable forecasts on the considered temporal resolutions. A dummy-variable optimization technique is also proposed within the state-updating procedure to allow smooth state transition. We show that the modeling framework produces stable results of parameter variations at different time horizons when applied to estimate the streamflow of Clearwater River. The proposed framework can incorporate exogenous descriptors at different levels without loss of generality and can be used for various forecasting applications.