A variational data assimilation scheme for parameter estimation is developed and tested with a long-term tidal transport model. Long-term advective transport in a tidal environment is represented by the Lagrangian mean transport velocity that can be decomposed into two parts: the Eulerian transport velocity and the curl of a three-dimensional vector potential A. In the present study, the vector potential A is treated as a poorly known parameter field, and the optimal long-term advection transport field is obtained through adjusting the vector potential using a variational inverse data assimilation method to obtain the best fit between the model output and the data. Experiments were performed in an idealized estuary. Results showed that variational inverse data assimilation could successfully retrieve poorly known parameters in a long-term tidal transport model. The results also showed that the smooth best fit model state could be retrieved using a penalty method even when observed data are too sparse or contain noisy signals.