Derivation and analysis of spatial variability in master recession curves with mixed effects model

Abstract

Master recession curves, often modeled by the equation dQ/dt = -AQ^B, are widely used to analyze hydrological responses, develop hydrological models, and assess basin storage. However, traditional methods for deriving these curves often overlook the correlation between recession data of individual events. In this study, we applied three conventional methods and the mixed effects model that accounts for data correlation to derive master recession curves across 425 U.S. basins. The conventional methods include the lower envelope, point cloud regression, and two stage approaches. We evaluated the effectiveness of each method by comparing characteristic recession timescales and conducted stepwise regressions to investigate sources of cross-basin variability in the master recession curves. Key findings include: (1) master recession curve estimation is significantly sensitive to the fitting method (p < 0.05), with the sensitivity largely stemming from the high responsiveness of parameter A to the fitting approach; (2) the mixed effects model proves a valuable complement to traditional methods, with errors in recession timescale estimates from traditional methods being 1.78 to 30 times larger than those from the mixed effects model; (3) parameters A and B both vary considerably across basins even when derived with the same method, with parameter A showing more pronounced variability; and (4) parameter A’s spatial variability closely associates with vegetation cover, while parameter B’s variability shows a weaker and less consistent connection to geographic characteristics. The mixed effects model introduced here offers an alternative for deriving master recession curves, enhancing understanding of their spatial variability and providing insights for modeling master recession curves in data-scarce regions.