Croatian Karst River Flows: Insights from Hurst Exponent Analysis

This study investigates long-term persistence in the daily water levels of the Čabranka and Kupa rivers in Croatia using Hurst exponent analysis. Daily water level data, spanning several decades for each river, were analyzed to determine the Hurst exponent (H) and assess the presence of long-range dependence. The analysis employed Hurst–Kolmogorov (HK) dynamics and climacogram analysis, established methods for identifying long-range dependence in time series data. Climacograms were constructed to visually assess the scaling behavior of the variance, and linear regression was applied to estimate the Hurst exponent (H) within a range of time scales (10–100 days) to ensure statistical robustness.

Results reveal significant long-term persistence in both river systems, with Hurst exponents (H) consistently exceeding 0.5, a threshold indicating the presence of long-range dependence. High coefficients of determination (R²) support the reliability of the linear fits. Potential contributing factors to this observed persistence, including climatic influences (e.g., rainfall patterns, snowmelt), geological characteristics of the river basins, and the impact of human activities (e.g., dam operations, water withdrawals), are discussed.

The implications of these findings are substantial for water resource management in the region. The presence of long-term persistence necessitates the incorporation of this characteristic into hydrological models to improve forecasting accuracy and inform sustainable water management strategies. Further research will focus on investigating the relative contributions of various factors to the observed persistence and developing improved hydrological models that explicitly account for long-range dependence. This enhanced understanding will allow for more robust and reliable water resource management strategies in the face of increasing climate variability and human pressures on these vital water resources.