Criteria for resolution-scales and parameterisation of compartmental models of hydrological and ecological mass flows

SummaryThe effect of compartment resolution-scale, i.e. number of compartments and compartment size, on prediction of transport of water and solute mass in watersheds is analysed by using numerical discretisation and temporal moments methods. The one-dimensional advection–diffusion model is used as a theoretical frame of reference for representing transport along a single series of compartments along a pathway in the surface water or ecosystem. Criteria for parameterisation of compartment models and error estimates are derived for two cases: (1) requiring an exact match with the advection–diffusion model; and (2) requiring as good match as possible with a simplified compartment model using a small number of compartments. The matching criteria are based on a comparison of numerical discretisation and temporal moments of the compartmental backflow model with those of the one-dimensional advection–diffusion equation. We derived solutions in terms of temporal moments of both the advection–diffusion equation and compartmental backflow model with arbitrary input concentration vs. time boundary condition. This approach can be used to translate parameters between the models and analyse the error caused by any arbitrary structure of the compartmental model as a function of boundary conditions and the physical parameters of the advective–diffusive equation. Data from tracer experiments were compared with model predictions to provide a practical frame of reference.