Extended assimilation and forecast experiments with a four-dimensional variational assimilation system

Results of four-dimensional variational assimilations, 4D-Var, in cycling mode, over a few two-week assimilation periods are presented. 4D-Var is implemented in its incremental formulation, with a high-resolution model with the full physical parametrization package to compare the atmospheric states with the observations, and a low-resolution model with simplified physics to minimize the cost-function. The comparison of 4D-Var using several assimilation windows (6, 12 and 24 hours) with 3D-Var (the equivalent of 4D-Var with no time-dimension) over a two-week period shows a clear benefit from using 4D-Var over a 6 or 12-hour window compared to the static 3D-Var scheme. It also exhibits some problems with the forecasts started using 4D-Var over a 24-hour window. The poorer performance of 4D-Var over a relatively long assimilation window can be partly explained by the fact that in these experiments, the tangent-linear and adjoint models used in the minimization are only approximations of the assimilating model (having lower resolution and crude physics). The error these approximations introduce in the time evolution of a perturbation affects the convergence of the incremental 4D-Var, with larger discontinuities in the values of the cost-function when going from low to high resolution for longer assimilation windows. Additional experiments are performed comparing 4D-Var using a 6-hour window with the SD-Var system. Two additional 2-week periods show a consistent improvement in extratropical forecast scores with the 4D-Var system. The main 4D-Var improvements occur in areas where the 3D-Var errors were the largest. Local improvement can be as large as 35% for the root-mean-square of the 5-day-forecast error, averaged over a two-week period. A comparison of key analysis errors shows that, indeed, 4D-Var using a 6-hour window is able to reduce substantially the amplitude of its fast-growing error components. The overall fit to observations of analyses and short-range forecasts from 3D-Var and 4D-Var is comparable. in active baroclinic areas, the fit of the background to the data is considerably better for the 4D-Var system, resulting in smaller increments. It appears that in these areas (and in particular over the west Atlantic), 4D-Var is able to better use the information contained in the observations. The ability of 4D-Var to extrapolate some aircraft data in the Vertical with a baroclinic tilt is illustrated. Problems exist in the tropics and mountainous areas due partly to a lack of physics in the tangent-linear model. Possible improvements to the system (the introduction of more physics; better behaviour of the incremental approach owing to a line search at high resolution) are also discussed.