Accuracy Assessment of Numerical Morphological Models based on Reduced
Sustainable river management often requires long-term morphological
simulations. As the future is unknown, uncertainty needs to be accounted
for, which may require probabilistic simulations covering a large
parameter domain. Even for one-dimensional models, the simulation times
can be long. One of the strategies to speed up simulations is
simplification of models by neglecting terms in the governing
hydrodynamic equations. Examples are the quasi-steady model and the
diffusive wave model, both widely used by scientists and practitioners.
Here, we establish under which conditions these simplified models are
accurate. Based on the results of linear stability analyses of the St.
Venant-Exner equations, we assess migration celerities and damping of
infinitesimal, but long riverbed perturbations. We did this for the full
dynamic model, i.e. no terms neglected, as well as for the simplified
models. The accuracy of the simplified models was obtained from
comparison between the characteristics of the riverbed perturbations for
simplified models and the full dynamic model. We executed a spatial-mode
and a temporal-mode linear analysis and compared the results with
numerical modelling results for the full dynamic and simplified models.
The numerical results match best with the temporal-mode linear stability
analysis. The analysis shows that the quasi-steady model is highly
accurate for Froude numbers up to 0.7, probably even for long river
reaches with large flood wave damping. Although the diffusive wave model
accurately predicts flood wave migration and damping, key morphological
metrics deviate more than 5% (10%) from the full dynamic model when
Froude numbers exceed 0.2 (0.3).