The results of many numerical simulations on both the linearized and nonlinear shallow water models are reported in [22]. The following feedback terms have been considered:
for the fluid height, and
for the velocity, where 
and 
are defined by equations (3.62) and (3.63). Several values of the parameters 
, 
, 
and 
are considered, as well as several levels of observation noise. A comparison between the standard nudging (or Luenberger observer) and this observer is also given in [22].
All these simulations show the interest of such a choice of invariant gains. They provide better results than the standard nudging, even on the nonlinear system, because the error converges faster, the residual error is smaller, and noise is better filtered. Indeed the observer is nearly insensible to gaussian white noise. The numerical experiments also confirm that, as predicted by the theory, it is possible to correct the non-observed variables with the observed ones, thanks to model coupling.
Note that the computational cost of such an observer is not much larger than for the standard nudging, as we have considered a truncated convolution integral instead of the complete convolution over the whole domain. The truncation radius can be set equal to at most 
pixels in similar experiments.
Several other gain functions should now be studied to see if it is possible to filter other types of observation noise. Some experiments will also be carried out in the case of sparse observations, both in time and space.