Classification of environmental time series using ordinal pattern dynamics and complexity metrics

Long-term monitoring of ecosystems is the only direct method to provide insights into the system dynamics on a range of timescales from the temporal resolution to the duration of the record. Time series of typical environmental variables reveal a striking diversity of trends, periodicities, and long-range correlations. Using several decades of observations of water chemistry in first-order streams of three adjacent catchments in the Harz mountains in Germany as example, we calculate metrics for these time series based on ordinal pattern statistics, e.g. permutation entropy and complexity, Fisher information, or q-complexity, and other indicators like Tarnopolski diagrams. The results are compared to those obtained for reference statistical processes, like fractional Brownian motion or ß noise. After detrending and removing significant periodicities from the time series, the distances of the residuals to the reference processes in this space of metrics serves as a classification of nonlinear dynamical behavior, and to judge whether inter-variable or rather inter-site differences are dominant. The classification can be combined with knowledge about the processes driving hydrochemistry, elucidating the connections between the variables. This can be the starting point for the next step, constructing causal networks from the multivariate dataset.