Stochastic simulation of streamflow and spatial extremes: a continuous, wavelet-based approach

Manuela I Brunner,Eric Gilleland

doi:10.5194/hess-24-3967-2020

Abstract

Abstract. Stochastically generated streamflow time series are used for various water management and hazard estimation applications. They provide realizations of plausible but as yet unobserved streamflow time series with the same temporal and distributional characteristics as the observed data. However, the representation of non-stationarities and spatial dependence among sites remains a challenge in stochastic modeling. We investigate whether the use of frequency-domain instead of time-domain models allows for the joint simulation of realistic, continuous streamflow time series at daily resolution and spatial extremes at multiple sites. To do so, we propose the stochastic simulation approach called Phase Randomization Simulation using wavelets (PRSim.wave) which combines an empirical spatio-temporal model based on the wavelet transform and phase randomization with the flexible four-parameter kappa distribution. The approach consists of five steps: (1) derivation of random phases, (2) fitting of the kappa distribution, (3) wavelet transform, (4) inverse wavelet transform, and (5) transformation to kappa distribution. We apply and evaluate PRSim.wave on a large set of 671 catchments in the contiguous United States. We show that this approach allows for the generation of realistic time series at multiple sites exhibiting short- and long-range dependence, non-stationarities, and unobserved extreme events. Our evaluation results strongly suggest that the flexible, continuous simulation approach is potentially valuable for a diverse range of water management applications where the reproduction of spatial dependencies is of interest. Examples include the development of regional water management plans, the estimation of regional flood or drought risk, or the estimation of regional hydropower potential. Highlights. Stochastic simulation of continuous streamflow time series using an empirical, wavelet-based, spatio-temporal model in combination with the parametric kappa distribution. Generation of stochastic time series at multiple sites showing temporal short- and long-range dependence, non-stationarities, and spatial dependence in extreme events. Implementation of PRSim.wave in R package PRSim: Stochastic Simulation of Streamflow Time Series using Phase Randomization.

Highlights

Stochastic models are used to generate long time series or large event sets showcasing the full variability of a phenomenon
They randomized the phases resulting from the continuous wavelet transform instead of the real-valued amplitudes. This approach has the advantage of being non-parametric, avoids assumptions about the distribution and dependence structure of the data, allows for multiple realizations, and can be extended to multiple sites by randomizing the phases for multiple time series in the same way (Prichard and Theiler, 1994; Schreiber and Schmitz, 2000). We investigate whether such a wavelet-based phase randomization approach allows for a realistic representation of spatial dependence in both continuous streamflow time series and spatial extremes
While the median of the observed low- and high-flow distributions is well met by the simulated medians, again the simulations allow for the generation of extreme low and high flows going beyond the observed values because of the use of the theoretical kappa distribution

Summary

Introduction

Stochastic models are used to generate long time series or large event sets showcasing the full variability of a phenomenon. If the focus is on such extreme events, event-based instead of continuous simulation approaches are often employed (e.g., Bracken et al, 2016; Diederen et al, 2019; Quinn et al, 2019) This strategy requires an a priori definition of extreme events and leads to a loss of temporal information, e.g., on the season of occurrence. Continuous simulation approaches allow for the simulation of time series including, but not limited to, extreme events which are provided together with their time of occurrence.

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Discussion

Conclusion