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On 15 March 2005, the Meteorological Service of Canada (MSC) proceeded to the implementation of a four-dimensional variational data assimilation (4DVAR) system, which led to significant improvements in the quality of global forecasts. This paper describes the different elements of MSC's 4DVAR assimilation system, discusses some issues encountered during the development, and reports on the overall results from the 4DVAR implementation tests. The 4DVAR system adopted an incremental approach with two outer iterations. The simplified model used in the minimization has a horizontal resolution of 170 km and its simplified physics includes vertical diffusion, surface drag, orographic blocking, stratiform condensation, and convection. One important element of the design is its modularity, which has permitted continued progress on the three-dimensional variational data assimilation (3DVAR) component (e.g., addition of new observation types) and the model (e.g., computational and numerical changes). This paper discusses some numerical problems that occur in the vicinity of the Poles where the semi-Lagrangian scheme becomes unstable when there is a simultaneous occurrence of converging meridians and strong wind gradients. These could be removed by filtering the winds in the zonal direction before they are used to estimate the upstream position in the semi-Lagrangian scheme. The results show improvements in all aspects of the forecasts over all regions. The impact is particularly significant in the Southern Hemisphere where 4DVAR is able to extract more information from satellite data. In the Northern Hemisphere, 4DVAR accepts more asynoptic data, in particular coming from profilers and aircrafts. The impact noted is also positive and the short-term forecasts are particularly improved over the west coast of North America. Finally, the dynamical consistency of the 4DVAR global analyses leads to a significant impact on regional forecasts. Experimentation has shown that regional forecasts initiated directly from a 4DVAR global analysis are improved with respect to the regional forecasts resulting from the regional 3DVAR analysis.

An experiment is being conducted to directly compare the impact of all assimilated observations on shortrange forecast errors in different forecast systems using an adjoint-based technique. The technique allows detailed comparison of observation impacts in terms of data type, location, satellite sounding channel, or other relevant attributes. This paper describes results for a ''baseline'' set of observations assimilated by three forecast systems for the month of January 2007. Despite differences in the assimilation algorithms and forecast models, the impacts of the major observation types are similar in each forecast system in a global sense. However, regional details and other aspects of the results can differ substantially. Large forecast error reductions are provided by satellite radiances, geostationary satellite winds, radiosondes, and commercial aircraft. Other observation types provide smaller impacts individually, but their combined impact is significant. Only a small majority of the total number of observations assimilated actually improves the forecast, and most of the improvement comes from a large number of observations that have relatively small individual impacts. Accounting for this behavior may be especially important when considering strategies for deploying adaptive (or ''targeted'') components of the observing system.

A new system that resolves the stratosphere was implemented for operational medium-range weather forecasts at the Canadian Meteorological Centre. The model lid was raised from 10 to 0.1 hPa, parameterization schemes for nonorographic gravity wave tendencies and methane oxidation were introduced, and a new radiation scheme was implemented. Because of the higher lid height of 0.1 hPa, new measurements between 10 and 0.1 hPa were also added. This new high-top system resulted not only in dramatically improved forecasts of the stratosphere, but also in large improvements in medium-range tropospheric forecast skill. Pairs of assimilation experiments reveal that most of the stratospheric and tropospheric forecast improvement is obtained without the extra observations in the upper stratosphere. However, these observations further improve forecasts in the winter hemisphere but not in the summer hemisphere. Pairs of forecast experiments were run in which initial conditions were the same for each experiment but the forecast model differed. The large improvements in stratospheric forecast skill are found to be due to the higher lid height of the new model. The new radiation scheme helps to improve tropospheric forecasts. However, the degree of improvement seen in tropospheric forecast skill could not be entirely explained with these purely forecast experiments. It is hypothesized that the cycling of a better model and assimilation provide improved initial conditions, which result in improved forecasts.

Two approaches can be used to solve the variational data assimilation problem. The primal form corresponds to the 3D/4D-Var used now in many operational NWP centres. An alternative approach, called dual or 3D/4D-PSAS, consists in solving the problem in the dual of observation space. Both forms use the same basic operators so that once one method is developed, it should be possible to obtain the other easily provided these operators have a modular form. It has been shown that, with proper conditioning of the minimization problem, the two algorithms should have similar convergence rates and computational performances. In the presence of nonlinearities, the incremental form of 3D/4D-Var extends the equivalence to the so-called 3D/4D-PSAS. The first objective of this paper is to present results obtained with the variational data assimilation of the Meteorological Service of Canada to show the equivalence between the 3D-Var and the PSAS systems. This exercise has forced us to have a close look at the modularity of the operational 3D/4D-Var which then makes it possible to obtain the 3D-PSAS scheme. This paper then focuses on these two quadratic problems that show similar convergence rates. However, the minimization of 3D-PSAS is examined more thoroughly as some parameters are shown to be determining elements in the minimization process. Lastly, preconditioning properties are studied and the Hessians of the two problems are shown to be directly related to one another through their singular vectors, which makes it possible to cycle the Hessian of the PSAS form.