Derber, J., 1989: A variational continuous assimilation technique. Monthly Weather Review, 117 (11), 2437-2446.

Abstract: A variational assimilation technique is presented which continuously adjusts a model solution by introducing a correction term to the model equations. The technique is essentially a modification of the adjoint technique. The Variational Continuous Assimilation (VCA) technique optimizes the correction to the model equations rather than the initial conditions as is done in the adjoint technique.
The VCA-technique characteristics were examined by inserting independent analyses into a simple quasi-geostrophic model using both the VCA technique and the adjoint technique. Because the model equations do not have to be satisfied exactly in the VCA technique, some of the effects of systematic model errors can be removed from the assimilation. Thus, the VCA technique was able to consistently fit the data better than the adjoint technique. Predictions from the results from the assimilation techniques showed that the forecast from the adjoint technique's solution was consistently inferior to those from the VCA technique and those from the Geophysical Fluid Dynamics Laboratory's (GFDL's) First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) IIIb analyses. As a by-product of the VCA technique, an empirical correction for the model's systematic error is produced. Application of this correction during a forecast produced substantially improved simulations.