Hydrologic exchange fluxes (HEFs) vary significantly along river corridors due to spatiotemporal changes in discharge and geomorphology. This variability results in the emergence of biogeochemical hot-spots and hot-moments that ultimately control solute and energy transport and ecosystem services from the local to the watershed scales. In this work, we use a reduced-order model to gain mechanistic understanding of river bank storage and sinuosity-driven hyporheic exchange induced by transient river discharge. This is the first time that a systematic analysis of both processes is presented and serves as an initial step to propose parsimonious, physics-based models for better predictions of water quality at the large watershed scale. The effects of channel sinuosity, alluvial valley slope, hydraulic conductivity, and river stage forcing intensity and duration are encapsulated in dimensionless variables that can be easily estimated or constrained. We find that the importance of perturbations in the hyporheic zone's flux, residence times, and geometry is mainly explained by two-dimensionless variables representing the ratio of the hydraulic time constant of the aquifer and the duration of the event (Γ_d) and the importance of the ambient groundwater flow ( ). Our model additionally shows that even systems with small sensitivity, resulting in small changes in the hyporheic zone extent, are characterized by highly variable exchange fluxes and residence times. These findings highlight the importance of including dynamic changes in hyporheic zones for typical HEF models such as the transient storage model.