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Exploring Overall and Component Complexities via Relative Complexity Change and Interacting Complexity Amplitudes in
Dragutin T Mihailović1, Slavica Malinović-Milićević2,3
1Faculty of Natural Sciences, Department of Physics, University of Novi Sad, 21000 Novi Sad, Serbia.
Entropy (Basel, Switzerland)
|October 28, 2025
Summary
Researchers quantified river system complexity using Kolmogorov complexity (KC) metrics. This analysis revealed patterns in U.S. river streamflow, temperature, precipitation, and dynamics, offering new insights into hydrological complexity.
Area of Science:
- Hydrology and Environmental Science
- Complex Systems Theory
- Time Series Analysis
Background:
- Quantifying streamflow complexity is challenging due to environmental and dynamic influences.
- Understanding system complexity is crucial for effective water resource management.
- Existing methods may not fully capture the intricate interactions within river systems.
Purpose of the Study:
- To apply Kolmogorov complexity (KC) metrics to analyze U.S. river streamflow complexity.
- To investigate the contributions of temperature, precipitation, and river dynamics (Lyapunov exponent) to overall system complexity.
- To visualize and quantify the relative changes in complexity across different river systems and time scales.
Main Methods:
- Utilized Kolmogorov complexity spectrum (KC spectrum) and Kolmogorov complexity plane (KC plane) metrics.
- Analyzed monthly streamflow time series from 1879 U.S. river gauge stations (1950-2015).
- Calculated normalized KC spectra, master/individual amplitudes, and relative change in complexities (RCC).
Main Results:
- Visualized interactive master and individual amplitudes on overlapping two-dimensional KC planes.
- Quantified the relative change in complexities (RCC) for streamflow and its components.
- Identified distinct complexity patterns across U.S. rivers based on normalized amplitude intervals.
Conclusions:
- Kolmogorov complexity metrics provide a robust framework for assessing hydrological system complexity.
- The study reveals how environmental factors and river dynamics interact to shape streamflow complexity.
- Findings contribute to a deeper understanding of U.S. river system behavior and variability.
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