Holger Lange
Seniorforsker
Sammendrag
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.
Sammendrag
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhibit a bewildering diversity of spatiotemporal patterns, indicating the intricate nature of processes acting on a large range of time scales. Nonlinear dynamics is an obvious framework to investigate catchment time series. We analyzed selected long-term data from three headwater catchments in the Bramke valley, Harz mountains, Lower Saxony in Germany at common biweekly resolution for the period 1991 to 2023. For every time series, we performed gap filling, detrending, and removal of the annual cycle using singular system analysis (SSA), and then calculated metrics based on ordinal pattern statistics: the permutation entropy, permutation complexity, and Fisher information, as well as their generalized versions (q-entropy and α-entropy). Further, the position of each variable in Tarnopolski diagrams is displayed and compared to reference stochastic processes, like fractional Brownian motion, fractional Gaussian noise, and β noise. Still another way of distinguishing deterministic chaos and structured noise, and quantifying the latter, is provided by the complexity from ordinal pattern positioned slopes (COPPS). We also constructed horizontal visibility graphs and estimated the exponent of the decay of the degree distribution. Taken together, the analyses create a characterization of the dynamics of these systems which can be scrutinized for universality, either across variables or between the three geographically very close catchments.
Sammendrag
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