A method is developed for the optimal estimation of the parameters in
a fully nonlinear model of flow in a channel. The data assimilated con
sist of values of the water surface elevation during a given interval.
The method is based on the adjoint method of optimal control. It is s
hown that accurate values of the parameters can be estimated, and the
estimates are stable with respect to random perturbations of the data
provided that data from a sufficient number of locations are available
for assimilation.