Four-dimensional variational assimilation

Summary

Four-dimensional variational assimilation, or 4D-Var, is a method of data assimilation that fits a model trajectory to all the observations made during a time window. It chooses the initial state of the window that minimises a cost function. The cost measures the misfit to a background estimate and to the observations along the trajectory. The gradient of the cost function is computed by a backward integration of the adjoint model, which makes the method an optimal control problem. It is used to produce the initial conditions of several major operational weather forecasting systems.