Tempered Stable Ornstein–Uhlenbeck Model for River Discharge Time Series with Its Application to Dissolved Silicon Load Analysis

Abstract

We identify stochastic process models describing the time series of inflow and outflow discharges of Obara Dam in Hii River, Japan. These models are based on tempered stable Ornstein–Uhlenbeck (TSOU) processes that have not been utilized in hydrological analysis but can capture both large and small fluctuation of the time series data. In addition, the models can be exactly simulated in a statistical sense by utilizing a recent tailored discretization algorithm, serving as efficient stochastic tools. We show that the identified models accurately reproduce statistical moments of the time series data and probability density functions. Based on the mathematical framework of backward stochastic differential equation (BSDE), the identified model is applied to a unique dynamic stochastic analysis of dissolved silicon (DSi) load flowing into the reservoir associated with Obara Dam. We thus contribute to the first application of TSOU processes and a BSDE to hydrological analysis.