Age-Ranked Storage-Discharge Relations: A Unified Description of Spatially Lumped Flow and Water Age in Hydrologic Systems

Abstract

A storage-discharge relation tells us how discharge will change when new water enters a hydrologic system but not which water is released. Does an incremental increase in discharge come from faster turnover of older water already in storage? Or are the recent inputs rapidly delivered to the outlet, “short-circuiting” the bulk of the system? Here I demonstrate that the concepts of storage-discharge relationships and transit time distributions can be unified into a single relationship that can usefully address these questions: the age-ranked storage-discharge relation. This relationship captures how changes in total discharge arise from changes in the turnover rate of younger and older water in storage and provides a window into both the celerity and velocity of water in a catchment. This leads naturally to a distinction between cases where an increase in total discharge is accompanied by an increase (old water acceleration), no change (old water steadiness), or a decrease in the rate of discharge of older water in storage (old water suppression). The simple theoretical case of a power law age-ranked storage-discharge relations is explored to illustrate these cases. Example applications to data suggest that the apparent presence of old water acceleration or suppression is sensitive to the functional form chosen to fit to the data, making it difficult to draw decisive conclusions. This suggests new methods are needed that do not require a functional form to be chosen and provide age-dependent uncertainty bounds.