  An adjoint based technique is applied to a shallow water model in order to
estimate the influence of the model's parameters on the solution. Among
parameters the bottom topography, initial conditions, boundary conditions on
rigid boundaries, viscosity coefficients Coriolis parameter and the amplitude
of the wind stress tension are considered. Their influence is analyzed from
three points of view: 1. flexibility of the model with respect to a parameter
that is related to the lowest value of the cost function that can be obtained
in the data assimilation experiment that controls this parameter; 2.
possibility to improve the model by the parameter's control, i.e. whether the
solution with the optimal parameter remains close to observations after the end
of control; 3. sensitivity of the model solution to the parameter in a
classical sense. That implies the analysis of the sensitivity estimates and
their comparison with each other and with the local Lyapunov exponents that
characterize the sensitivity of the model to initial conditions. Two
configurations have been analyzed: an academic case of the model in a square
box and a more realistic case simulating Black Sea currents. It is shown in
both experiments that the boundary conditions near a rigid boundary influence
the most the solution. This fact points out the necessity to identify optimal
boundary approximation during a model development.
