The problem of time-continuous meteorological data assimilation is addressed. An optimal control method is proposed and studied for a simple well-posed 2D atmospheric model and continuous in time and space observations. An existence result for the optimal control problem is given. Then the first-order necessary conditions of optimality are explicited using a forced version of the linearized adjoint model; allowing the use of a classical descent method to solve the problem. The reliability of the method is shown on some numerical tests. Finally, the existence and characterization results of an optimal control are extended to the case of observations distributed in time.