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

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 yet unobserved low and high flows. The simulation approach consists of seven steps: 1) fitting the theoretical Kappa distribution, 2) normalization and deseasonalization, 3) Fourier transformation, 4) random phase generation, 5) inverse Fourier transformation, 6) back transformation, and 7) simulation. The simulation approach is applicable both to 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.

How Probable Is Widespread Flooding in the United States?

“…In order to increase the number of available (potentially regional) flood events for the regional frequency analysis, we use the stochastic streamflow generation model PRSim.wave (Phase Randomization Simulation), a direct continuous approach. PRSim.wave was proposed by Brunner and Gilleland (2020) to generate streamflow time series at multiple sites and is based on an earlier version of the model ( PRSim ), which was originally proposed to simulate streamflow at individual sites (Brunner, Bárdossy, et al, 2019). Both versions of the model are implemented in the R‐package PRSim (Brunner & Furrer, 2019).…”

“…PRSim.wave was proposed by Brunner and Gilleland (2020) to generate streamflow time series at multiple sites and is based on an earlier version of the model ( PRSim ), which was originally proposed to simulate streamflow at individual sites (Brunner, Bárdossy, et al, 2019). Both versions of the model are implemented in the R‐package PRSim (Brunner & Furrer, 2019). In contrast to other stochastic models used for flood hazard analyses, which usually simulate individual flood events, PRSim simulates continuous streamflow time series.…”

Future shifts in extreme flow regimes in Alpine regions

“…In a third step, the inverse Fourier transform is applied to transform the data from the spectral domain back to the temporal domain. A step by step description of the stochastic simulation procedure and more background information on the Fourier transform are provided in Brunner et al (2019a) and references therein.…”

“…An application of the simulation procedure to four example catchments in Switzerland has shown that both seasonal statistics and temporal correlation structures of discharge can be well reproduced (Brunner et al, 2019a). We therefore used this method to stochastically simulate 1500 years of discharge for each of the 19 regions in our data set.…”

“…Despite their favorable characteristics, such methods based on the Fourier transform have been rarely applied in hydrology (Fleming et al, 2002). We apply the approach of phase randomization in combination with the flexible Kappa distribution (Hosking, 1994) to simulate stochastic discharge time series as proposed by Brunner et al (2019a). Among these simulated series, extreme regimes can be identified.…”