Chaotic Analysis of Streamflow Dynamics through Dynamical Systems Theory: A Case Study of the Gilvan Sub-Watershed, Iran

Authors
Z. Abdollahi 1
H. Shadman 1
R. Kazemi 2
G. Rostamizad 1
1 Soil Conservation and Watershed Management Research Department, Zanjan Agricultural and Natural Resources Research and Education Center, AREEO, Zanjan, Iran
2 Soil Conservation and Watershed Management Research Institute, Agricultural Research, Education and Extension Organization (AREEO), Tehran, Iran
10.22034/ECOPERSIA.13.3.287
Abstract
Aims: Understanding the dynamic nature of river discharge is essential for effective water management, particularly in regions subject to climatic and hydrological variability. This study applies chaos theory to detect nonlinear patterns in the monthly discharge of the Gilvan Sub-Watershed, a tributary of the Qezel Ozan River in northwestern Iran, integrating spectral noise diagnostics with implications for adaptive management.

Materials & Methods: Monthly discharge data (1963–2017) from the Gilvan hydrometric station were analyzed using phase space reconstruction. Optimal parameters—time delay of 2 months (Average Mutual Information) and embedding dimension of 6 (False Nearest Neighbors)—were applied. The correlation dimension was estimated using the Grassberger–Procaccia algorithm, and the largest Lyapunov exponent was computed to assess system sensitivity.

Findings: A significant decreasing trend in streamflow (p < 0.001) was detected, averaging 0.16 m³.s-1month-1 over the study period. The correlation dimension (2.3) indicated a low-dimensional attractor, while the positive largest Lyapunov exponent (0.08) confirmed sensitivity to initial conditions, a hallmark of chaos. These results suggest that streamflow dynamics are shaped by variable precipitation, snowmelt, evaporation, and anthropogenic factors.

Conclusion: The presence of chaos implies fundamental limits to long-term predictability and supports the need for nonlinear modeling in water management. Recognizing such complexity is vital for sustainable resource planning under changing climatic conditions. However, this study did not explicitly assess the mechanical effects of dams or other hydraulic infrastructure, and its findings may be influenced by data quality and spatial coverage—issues that warrant further investigation.
Keywords
Chaos Theory
Lyapunov exponent
Nonlinear Hydrology
River Discharge

Subjects

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