Velocities and celerities without additional assumptions - a particle tracking approach.

Abstract:

The difference between velocities and celerities in catchment responses has often been neglected in hydrology but is critical to the consideration of both hydrograph and residence time distributions. The difference is important because it implies a scale dependence in the way in which flow and residence times are related. McDonnell and Beven (2014) recently reviewed the issues and made a plea for more data sets to be collected that cover both hydrograph and tracer characteristics. Models of catchment response generally require additional mixing or dispersion assumptions to reproduce both flow and tracer responses. If, however, a modelling strategy can follow the velocities of flow within the system, then the celerities should follow deductively. Hydrological modelling has classically done the inverse; fitting hydrographs before trying to reproduce tracer data and residence time distributions. One modelling method for starting with velocities is the particle tracking approach, for which one example is the Multiple Interacting Pathways (MIPs) model of Davies et al (2011, 2013). This has been used in the past to test hypotheses about local velocity distributions in reproducing both tracer and flow data and to demonstrate the scale dependence of catchment responses (Davies and Beven, 2014). This will be taken further in this paper to demonstrate the form of the attractors for both flow and residence times and how they might be used as a way of evaluating the consistency of observational data.