When runoff no longer follows rainfall: a new index for diagnosing hydrological decoupling in semi-arid catchments

Hydrological systems in semi-arid regions are becoming non-stationary, with runoff increasingly decoupled from precipitation. This reflects both climate forcing and internal processes (e.g. storage and hydrological memory) not captured by conventional methods. We introduce the hydrological regime decoupling index (HRDI), a process-based metric combining runoff relative change, potential evapotranspiration relative change, residual water availability, and hydrological memory, with a moving window to track temporal change. Applied to three Algerian catchments, HRDI indicates strong decoupling in a karst basin (≈0.45), moderate in an arid basin (≈0.18), and weak in a Mediterranean basin (≈0.08). A clear regime shift appears only in the karst system. HRDI offers a simple, interpretable tool for detecting hydrological change in data-scarce semi-arid regions.