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 data‐assimilation (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.