Using Phase Annealing to generate surrogate discharge time series

Phase randomization and its variants such as the Amplitude-adjusted (AAFT) and the Iterative amplitude adjusted (IAAFT) Fourier transform are used to check statistical significance of a given hypothesis and/or to generate time series that are similar to a reference in some statistical sense. These methods have the drawback of producing incorrect dependence structures e.g. empirical copula density, asymmetries and entropies. Recently, another form of such methods, “Phase Annealing”, was introduced, giving a possibility to generate n-dimensional realizations of a process under given constraint(s). The main concern using this method is the selection of correct objective function(s).

Here we show discharge time series generation using Phase Annealing with new objective functions. This allowed us to generate time series that are much longer than the reference, which in turn was helpful in establishing better distributions of floods.

We also show the generation of discharge time series at multiple locations that have the correct spatio-temporal dependences among all the series. Using the results, we generated full distributions of simultaneous extremes at observation locations.

Further uses may include clustering catchments that are likely to bring floods together and reliability analysis i.e. simulating distributions of failures for a system with many dependent/independent components. Drawbacks using this method are also shown.