Complexity Analysis of Environmental Time Series.

Area of Science:

• Environmental Science
• Hydrology
• Ecology

Background:

• Forested catchments are key terrestrial ecosystems studied across environmental science disciplines.
• Time series data of water, matter fluxes, and nutrient concentrations reveal complex spatiotemporal patterns.
• Nonlinear dynamics offers a framework for investigating intricate catchment processes across various timescales.

Purpose of the Study:

• To analyze long-term hydrological and biogeochemical data from three headwater catchments in the Bramke valley, Germany (1991-2023).
• To characterize the dynamics of these catchment systems using nonlinear methods and ordinal pattern statistics.
• To investigate potential universality in system dynamics across different variables and between closely located catchments.

Main Methods:

• Data preprocessing including gap filling, detrending, and annual cycle removal using Singular System Analysis (SSA).
• Calculation of ordinal pattern statistics: permutation entropy, permutation complexity, Fisher information, q-entropy, and α-entropy.
• Analysis using Tarnopolski diagrams, comparison with stochastic processes (fractional Brownian motion, fractional Gaussian noise, β noise), Complexity from Ordinal Pattern Positioned Slopes (COPPS), and horizontal visibility graphs.

Main Results:

• Characterization of catchment system dynamics through a suite of nonlinear metrics.
• Comparison of observed dynamics with reference stochastic processes and deterministic chaos models.
• Assessment of potential universality in dynamics across variables and between the three studied catchments.

Conclusions:

• The study provides a comprehensive characterization of catchment system dynamics using advanced nonlinear analytical techniques.
• Findings contribute to understanding the complex interplay of processes governing water and nutrient fluxes in forested ecosystems.
• The approach allows for scrutiny of universality, offering insights into broader ecological and hydrological principles.