Abstract: Dynamical equations,observations and their statistics are all important information for presenting the states of unsteady flows.Under the framework of inverse problems,a variational model is developed to fuse all available information for improving the computation of unsteady flows.In the paper,the appropriate optimal control problems are firstly defined for controlling possible numerical errors from inaccurate initial conditions,boundary conditions and unknown physical parameters.Then,the general variational method and its numerical algorithm are suggested to solve these optimal control problems of unsteady flows.Also,we derive the adjoint equations of one-and two-dimensional shallow equations with the forms for practical purpose.It directly serves for real engineering applications.With the proposed variational model,the tidal flows in one reach of the Pearl River are investigated.Results show that the model can well reconstruct tidal flow states when data are unavailable at some boundaries,unlike the direct model.