The established method for determining dike heights and dimensioning river training structures is to assess the resulting backwater by numerical modelling. The common consensus is that bottom friction determines the backwater and that momentum advection only has a local effect. We demonstrate that the numerical/artificial backwater contribution from the momentum advection approximation can be of the same order of magnitude as the bottom friction contribution, depending on the advection scheme. This is realized using a one-dimensional analysis and verified using a set of one- and two-dimensional test problems including a wavy bed case, flow over emerged and submerged groynes and finally an actual river. We compare first- and second-order accurate advection schemes and compute their artificial contribution to the backwater, for a range of practically-feasible grid resolutions. The tests demonstrate that the conservation/constancy properties of the scheme determine the size of this contribution, rather than the order of the scheme.