This paper presents results of a comparison between four‐dimensional variational assimilation (4D‐Var). using a 6‐hour assimilation window and simplified physics during the minimization, and three‐dimensional variational assimilation (3D‐Var). Results have been obtained at ‘operational’ resolution T213L31/T63L31. (T defines the spectral triangular truncation and L the number of levels in the vertical, with the first parameters defining the resolution of the model trajectory, and the second the resolution of the inner‐loop.) The sensitivity of the 4D‐Var performance to different set‐ups is investigated. In particular, the performance of 4D‐Var in the Tropics revealed some sensitivity to the way the adiabatic nonlinear normal‐mode initialization of the increments was performed. Going from four outer‐loops to only one (as in 3D‐Var), together with a change to the 1997 formulation of the background constraint and an initialization of only the small scales, helped to improve the 4D‐Var performance. Tropical scores then became only marginally worse for 4D‐Var than for 3D‐Var. Twelve weeks of experimentation with the one outer‐loop 4D‐Var and the 1997 background formulation have been studied. The averaged scores show a small but consistent improvement in both hemispheres at all ranges. In the short range, each two‐ to three‐week period has been found to be slightly positive throughout the troposphere. The better short‐range performance of the 4D‐Var system is also shown by the fits of the background fields to the data. More results are presented for the Atlantic Ocean area during FASTEX (the Fronts and Atlantic Storm‐Track Experiment), during which 4D‐Var is found to perform better. In individual synoptic cases corresponding to interesting Intensive Observing Periods, 4D‐Var has a clear advantage over 3D‐Var during rapid cyclogeneses. The very short‐range forecasts used as backgrounds are much closer to the data over the Atlantic for 4D‐Var than for 3D‐Var. The 4D‐Var analyses also display more day‐to‐day variability. Some structure functions are illustrated in the 4D‐Var case for a height observation inserted at the beginning, in the middle or at the end of the assimilation window. The dynamical processes seem to be relevant, even with a short 6‐hour assimilation period, which explains the better overall performance of the 4D‐Var system.
The adjoint method has been used to calculate the sensitivity of short-range forecast errors to the initial conditions. The gradient of the energy of the day 2 forecast error with respect to the initial conditions can be interpreted as a sum of rapidly growing components of the analysis error. An analysis modified by subtracting an appropriately scaled vector, proportional to the gradient, provides initial conditions for a 'sensitivity integration' that can be used to diagnose the effect of initial-data errors on forecast errors.Statistics of sensitivity calculations for the month of April 1994 characterize the sensitivity patterns as smallscale, middle or lower tropospheric structures which are tilted in the vertical. The general pattern of these structures is known to be associated with the fastest possible growth of forecast error. When used as initial perturbations, they evolve rapidly into synoptic-scale structures, propagating both downstream and to higher atmospheric levels.On average, the sensitivity integration corrects for about a tenth of the day 2 forecast error, which indicates that indeed not all of the error is in the fastest-amplifying modes. But the fraction of the error corrected at day 2 is important for an improvement in the medium-range, as this fraction continues to grow substantially in the non-linear regime. These results have proved that there is still scope for great improvement in the medium-range forecast, particularly over Europe, by a better description of the initial conditions. The sensitivity experimentation suggests that many cases of major forecast-errors may be explained by defects in the analysis. A small but well-chosen change in the analysis can frequently improve the forecast quality.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.