Power-Law versus Michaelis-Menten Storage-Discharge Models: Evidence of Seasonal Divergence in the Ala River Basin, Nigeria

Storage-discharge diagnostics built from recession-limb analysis underpin much of the low-flow forecasting available to practitioners in data-scarce basins, yet the functional form linking discharge to catchment storage is rarely tested against genuine alternatives. This study evaluates whether Michaelis-Menten saturation kinetics, an equation transplanted from enzymology, can outperform the conventional power-law storage-discharge relationship in the Ala River Basin, Akure, Nigeria, using 46 years (1980 to 2025) of available GEOGLOWS retrospective discharge at a single reach. Storage was estimated for 373 qualifying recession events (4,230 daily pairs) by integrating future discharge across each recession limb. Three functional forms, linear, power-law, and Michaelis-Menten, were fitted and compared using R² and AIC, then stratified by season and event magnitude, and tested for temporal stability using bootstrap resampling, leave-one-event-out validation, and Mann-Kendall trend tests across nine 5-year blocks. The power law outperformed Michaelis-Menten overall and during the dry season, but Michaelis-Menten was consistently superior during the wet season across every independent 5-year window tested, with no significant trend detected in its saturation parameters. The assumption of a single master storage-discharge curve failed when stratified by event magnitude.