A supCBI process with application to streamflow discharge and a model reduction

TL;DR

This paper introduces a novel stochastic model called supCBI for streamflow discharge time series, capturing subexponential autocorrelation, and demonstrates its application and reduction to semi-Markov chains for hydrological data analysis.

Contribution

The paper presents the supCBI process as a new non-Markovian model for streamflow, with analytical formulas and a reduction method to semi-Markov chains for improved modeling.

Findings

supCBI accurately reproduces autocorrelation in hydrological data

Analytical formulas for moments and autocorrelation are derived

Semi-Markov chain reduction effectively models high- and low-flow regimes

Abstract

We propose a new stochastic model for streamflow discharge timeseries as a jump-driven process, called a superposition of continuous-state branching processes with immigration (a supCBI process). It is a non-Markovian model having the capability of reproducing the subexponential autocorrelation found in the hydrological data. The Markovian embedding as a version of matrix analytic methods is applied to the supCBI process, successfully yielding analytical formulae of statistical moments and autocorrelation. The supCBI process is identified at study sites, where hourly streamflow discharge data are available. We also consider another Markovian embedding as a model reduction of the supCBI process to a continuous-time binary semi-Markov chain of high- and low-flow regimes. We show that waiting times can be modeled using a mixture of exponential distributions, suggesting that semi-Markov chains serve as effectively reduced models of the supCBI process.