A practical approximation to optimal four-dimensional objective analysis

An iterative four-dimensional objective analysis scheme is described. The method is derived by approximating a variational algorithm, which should give an optimal four-dimensional analysis. The complete set of operationally available observations, the operational analysis, and forecast codes are used. The scheme differs from most other studies of optimal four-dimensional analysis, which make fewer approximations in the algorithm, but use simplified models and data. The scheme was developed by using the optimal interpolation analysis, nonlinear normal-mode initialization, and nested-grid forecast model from the Regional Analysis and Forecast System of NMC. To these were added an approximate adjoint model of the forecast and a code to implement a simple descent algorithm. Tests used the operational observation data base. The scheme was successful in producing a dynamically consistent four-dimensional analysis that fit the observations without totally impractical computer costs. However, for the one test case studied, the forecast from the scheme's analysis was slightly worse than that from the operational analysis. The tests highlighted some deficiencies of the current operational analysis, initialization, and forecast codes. They also indicated areas in which further development of the scheme is desirable, i.e., in the adjoint forecast model and analysis error estimation.