Temporal and spectral governing dynamics of Australian hydrological streamflow time series

Abstract

We use new and established methodologies in multivariate time series analysis to study the dynamics of 414 Australian hydrological stations' streamflow. First, we analyze our collection of time series in the temporal domain, and compare the similarity in hydrological stations' candidate trajectories. Then, we introduce a Whittle Likelihood-based optimization framework to study the collective similarity in periodic phenomena among our collection of stations. Having identified noteworthy similarity in the temporal and spectral domains, we introduce an algorithmic procedure to estimate a governing hydrological streamflow process across Australia. To determine the stability of such behaviours over time, we then study the evolution of the governing dynamics and underlying time series with time-varying applications of principal components analysis (PCA) and spectral analysis.