This paper extends the dimension-reduced projection four-dimensional variational assimilation method(DRP-4DVar) by adding a nonlinear correction process,thereby forming the DRP-4DVar with a nonlinear correction, which shall hereafter be referred to as the NC-DRP-4DVar. A preliminary test is conducted using the Lorenz-96 model in one single-window experiment and several multiple-window experiments. The results of the single-window experiment show that compared with the adjoint-based traditional 4DVar, the final convergence of the cost function for the NC-DRP-4DVar is almost the same as that using the traditional 4DVar, but with much less computation. Furthermore, the 30-window assimilation experiments demonstrate that the NC-DRP-4DVar can alleviate the linearity approximation error and reduce the root mean square error significantly.
