In this section, we consider nudging as a particular type of observers, e.g. Luenberger observer, or Kalman filters [81,73]. In most Kalman-type filters and observers, the gain matrices do not take into account the symmetries of the model. They are mainly designed to provide for each time step the optimal estimate of the system state. However, it seems interesting to preserve the model symmetries while adding a nudging term in the equations. Inspired by the recent works in observer design, we define symmetry-preserving nudging (or feedback) terms for a shallow-water model. This section summarizes the work presented in [22].