Technical note: Stochastic simulation of streamflow time series using phase randomization

Manuela I Brunner,András Bárdossy,Reinhard Furrer

doi:10.5194/hess-23-3175-2019

Abstract

Abstract. Stochastically generated streamflow time series are widely used in water resource planning and management. Such series represent sets of plausible yet unobserved streamflow realizations which should reproduce the main characteristics of observed data. These characteristics include the distribution of daily streamflow values and their temporal correlation as expressed by short- and long-range dependence. Existing streamflow generation approaches have mainly focused on the time domain, even though simulation in the frequency domain provides good properties. These properties comprise the simulation of both short- and long-range dependence as well as extension to multiple sites. Simulation in the frequency domain is based on the randomization of the phases of the Fourier transformation. We here combine phase randomization simulation with a flexible, four-parameter kappa distribution, which allows for the extrapolation to as yet unobserved low and high flows. The simulation approach consists of seven steps: (1) fitting the theoretical kappa distribution, (2) normalization and deseasonalization of the marginal distribution, (3) Fourier transformation, (4) random phase generation, (5) inverse Fourier transformation, (6) back transformation, and (7) simulation. The simulation approach is applicable to both individual and multiple sites. It was applied to and validated on a set of four catchments in Switzerland. Our results show that the stochastic streamflow generator based on phase randomization produces realistic streamflow time series with respect to distributional properties and temporal correlation. However, cross-correlation among sites was in some cases found to be underestimated. The approach can be recommended as a flexible tool for various applications such as the dimensioning of reservoirs or the assessment of drought persistence. Highlights. Stochastic simulation of streamflow time series for individual and multiple sites by combining phase randomization and the kappa distribution. Simulated time series reproduce temporal correlation, seasonal distributions, and extremes of observed time series. Simulation procedure suitable for use in water resource planning and management.

Highlights

Generated streamflow time series are used in various applications of water resource planning and management
We use phase randomization to simulate stochastic streamflow time series to be used in various water resource management studies
The stochastic streamflow generator based on phase randomization has been shown to produce realistic streamflow time series with respect to both distributional properties and temporal correlation

Summary

Introduction

Generated streamflow time series are used in various applications of water resource planning and management. Generated time series mimic the characteristics of observed data and represent sets of plausible realizations of streamflow sequences (Ilich, 2014; Borgomeo et al, 2015; Tsoukalas et al, 2018b). They are essential for many uncertainty studies in hydrology because they can serve as input for deterministic. Brunner et al.: Stochastic simulation of streamflow time series water system models in which they allow for the propagation of natural variability and uncertainty (Tsoukalas et al, 2018b)

Methods

Results

Conclusion