Total variation diminishing and mass conservative implementation of hydrological flow routing

- Unified computational framework for several flow routing schemes.
- Mass conservation by design regardless of the routing approach.
- High numerical robustness by the introduction of a total variation diminishing limiter.

SummaryHydrological flow routing methods are widely used as components of distributed hydrological models and in operational flow forecasting systems. The paper presents a novel approach to reformulate several of these routing schemes as a cascade of implicit pool routing models. Its numerical implementation is mass conservative and total variation diminishing, i.e. the solution does not oscillate or overshoot, for arbitrary time steps. It is shown that these numerical properties are achieved regardless of the accuracy of the scheme and its physical routing characteristics.Numerical experiments compare the computational performance and accuracy of the novel, reformulated approach with existing schemes including linear reservoir routing, nonlinear reservoir routing, and the Muskingum-Cunge method. We show that the approach can reproduce the original schemes, if these are already mass conservative, otherwise fixes the mass conservation in the reformulated version and improves the solution at sharp gradients by suppressing numerical oscillations, overshooting or negative flows.