Four-dimensional variational data assimilation with a diabatic version of the NCEP global spectral model: System development and preliminary results

The formulation of the National Centers for Environmental Prediction four-dimensional variational dataassimilation (4D-Var) system is described. Results of applying 4D-Var over a one-week assimilation period, with a full set of physical parametrizations, are presented and compared with those of 3D-Var. The linearization has been performed without simplifications and, therefore, the tangent-linear and adjoint codes are consistent with the nonlinear physical parametrizations. The 4D-Var assimilation is similar in formulation to the 3D-Var analysis, except that observations are used at the appropriate time in 4D-Var. Compared with the 3D-Var runs, the 4D-Var results showed good convergences, smaller analysis increments, and a comparable fit of analyses and short-range forecasts to observations. A consistent improvement with the 4D-Var system is observed in short-range (six-hour) forecasts of all model variables except the specific humidity. The temperature analyses from 4D-Var were found to be better in most of the areas where the analysis errors from 3D-Var were largest, although the globally averaged root-mean-square difference in the 4D-Var temperature analysis was larger due to a very small degradation in some parts of the globe that include data-rich areas. The globally averaged root-mean-square difference in the 4D-Var specific-humidity analysis, compared with that of 3D-Var, was larger and was found to result from slightly increased analysis-error maxima in the 4D-Var results over data-sparse tropical regions. The 3 4 day forecasts from 4D-Var analyses compared more favourably than forecasts from the 3D-Var analyses with the targeted mid-Pacific dropwindsonde observations available from the 1998 North Pacific Experiment. Compared with conventional observations, a consistent improvement in the 1-5 day forecasts of wind and temperature was shown in the tropics and the southern hemisphere.