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.

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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.

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We examine the large‐scale effects of organized convective systems in the tropical western Pacific observed during the Tropical‐Ocean Global‐Atmosphere Coupled Ocean‐Atmosphere Response Experiment (TOGA COARE). In a case‐study approach, we examine realizations of a supercluster, associated with the onset of the December 1992 westerly wind burst, in the T213 operational medium‐range weather forecasting model of the European Centre for Medium‐Range Weather Forecasts (ECMWF). We idealize a supercluster as a hierarchy of three interacting scales, namely organized cumulonimbu 𝒞1 mesoscale convective systems 𝒞2, and the supercluster component 𝒞3. It is shown that the ECMWF model represents this hierarchy as a 𝒞3‐like surrogate whose influence dominates the effect of parametrized convection. This causes over‐prediction of the model tendencies which, in the case of zonal momentum, is explained in elementary terms. The structure of the resolved‐scale momentum flux is explained by Moncrieff's (1992) archetypal theory of organized convection which has been verified against observations and cloud‐resolving model data‐sets. the parametrization of subgrid‐scale convective momentum‐flux in the ECMWF model, based on a momentum mixing concept, produces subgrid‐scale tendencies that are physically different from transports associated with cumulonimbus convection in a shear flow. We outline a strategy for parametrizing the momentum flux by the 𝒞1 component based on the archetypal model. the 𝒞2 component, which is part‐resolved and part‐parametrized, is at odds with the assumptions of scale separation underpinning parametrization. It is argued that this component should be represented as part of the prognostic treatment of convectively generated cirrus. Finally, we suggest cloud‐resolving modelling studies to further quantify the structure and large‐scale impact of superclusters in a westerly‐wind‐burst environment, ranging from idealized models to models having data assimilation capability.

The first two papers of this series describe the development of the operational four-dimensional variational assimilation (4D-Var) configuration implemented at the European Centre for Medium-Range Weather Forecasts (ECMWF). The basic features are a &hour incremental 4D-Var set-up with two minimization steps, using very simplified physics in the first minimization and a more complete set of linear physics in the second. This paper describes the validation of this configuration. Prior to implementation, 12 weeks of experimentation showed a consistent improvement relative to 3D-Var. After an additional 6 weeks of encouraging parallel operation with the then current operational suite, 4D-Var with physics was introduced in operations at ECMWF in November 1997. The difference in scores is statistically significant, and the fast-growing components of the 4D-Var analysis errors are shown to be smaller than their 3D-Var counterparts. The performance of this new operational assimilation system is studied for the month of January 1998, for which the 4D-Var analyses exhibit more realistic baroclinic waves than the 3D-Var, especially in the Pacific area. A case-study illustrates the improvement one can expect in forecast terms in the mid latitudes. The 4D-Var system improved the forecast skill in the Tropics in general.Observing-system experiments show that the current 4D-Var operational system benefits from the assimilation both of satellite data and conventional observations.