A resampling method for generating synthetic hydrological time series with preservation of cross‐correlative structure and higher‐order properties

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Abstract
Based on existing techniques in nonlinear physics that work in the Fourier domain, we develop a multivariate, wavelet‐based method for the generation of synthetic discharge time series. This approach not only retains the cross‐correlative structure of the original data (which makes it preferable to principal component methods that merely preserve the correlations) but also replicates the nonlinear properties of the original data. We argue that the temporal asymmetry of the typical hydrograph is the most important form of nonlinearity to preserve in the synthetic data. Using the derivative skewness as a measure of asymmetry and an example data set of 35 years of daily discharge data from 107 gauging stations in the United States, we compare two approaches that preserve the asymmetry of the original records. We generate synthetic data and then study the properties of fitting a generalized extreme value distribution to the annual maxima for a total flux time series. The synthetic series provides error bands for the fitted distribution that give a different way of assessing credible return periods. It is found that the best approach for studying extremes is to match the asymmetry of each series individually, rather than to formulate a global threshold criterion.

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