A generalized Damköhler number for classifying material processing in hydrological systems

Abstract. Assessing the potential for transfer of pollutants and nutrients across catchments is of primary importance under changing land use and climate. Over the past decade the connectivity/disconnectivity dynamic of a catchment has been related to its potential to export material; however, we continue to use multiple definitions of connectivity, and most have focused strongly on physical (hydrological or hydraulic) connectivity. In contrast, this paper constantly focuses on the dynamic balance between transport and material transformation, and defines material connectivity as the effective transfer of material between elements of the hydrological cycle. The concept of exposure timescales is developed and used to define three distinct regimes: (i) which is hydrologically connected and transport is dominated by advection; (ii) which is hydrologically connected and transport is dominated by diffusion; and (iii) which is materially isolated. The ratio of exposure timescales to material processing timescales is presented as the non-dimensional number, N_E, where N_E is reaction-specific and allows estimation of relevant spatial scales over which the reactions of interest take place. Case studies within each regime provide examples of how N_E can be used to characterise systems according to their sensitivity to shifts in hydrology and gain insight into the biogeochemical processes that are signficant under the specified conditions. Finally, we explore the implications of the N_E framework for improved water management, and for our understanding of biodiversity, resilience and chemical competitiveness under specified conditions.