Velocities, celerities and the basin of attraction in catchment response

Abstract

AbstractCatchment systems are interestingly nonlinear, but their dynamics are constrained from being unduly chaotic by mass and energy balance requirements. There have been no attempts in hydrology that we know of that have tried to map both the flow and transport dynamics of a catchment in any form of phase space. In part, this is because of the high dimensionality of the space–time patterns of response; in part because there is sufficient uncertainty about the input and output fluxes estimated by measurement that this might be expected to obscure any attractor‐like behaviour. In this study we explore the basin of the catchment attractor for the Multiple Interacting Pathway (MIPs) model that in previous papers has been shown to give good results for the small Gårdsjön catchment in Sweden. MIPs is based on particle tracking techniques and gives results for both the flow responses and for the travel and residence time responses of water in the catchment. Here it is used to provide consistent values of fluxes, total storage, travel time distributions and residence time distributions for a long simulation period. The nature of those responses in storage and input dimensions is then investigated. The results suggest that the range of behaviours is hysteretic in interesting ways and constrained by the forcing inputs, with space filling of trajectories in the basin of attraction as should be expected of a forced dissipative system. The range of behaviours exhibited defines a space that the responses of any simpler emulator model will need to span. © 2015 The Authors Hydrological Processes Published by John Wiley & Sons Ltd.