The Canadian Meteorological Centre (CMC) started running an Ensemble Prediction System in January 1996 with an ensemble of eight members (Houtekamer et al. 1996; Lefaivre et al. 1997). This set using eight different versions of the spectral model (SEF) was extended to sixteen members in September 1999 by adding eight different versions of the Global Environmental Multi-scale model (GEM). The models differ in their physical parameterizations and their dynamical cores. The horizontal resolution was increased in June 2001: the SEF models went from TL95 to TL149 with an equivalent increase from 1.5 degrees to 1.2 degrees for the grid point GEM model (Pellerin et al. 2003).

An ensemble Kalman filter (EnKF) has been implemented for atmospheric data assimilation. It assimilates observations from a fairly complete observational network with a forecast model that includes a standard operational set of physical parameterizations. To obtain reasonable results with a limited number of ensemble members, severe horizontal and vertical covariance localizations have been used.It is observed that the error growth in the data assimilation cycle is mainly due to model error. An isotropic parameterization, similar to the forecast-error parameterization in variational algorithms, is used to represent model error. After some adjustment. it is possible to obtain innovation statistics that agree with the ensemble-based estimate of the innovation amplitudes for winds and temperature. Currently, no model error is added for the humidity variable, and, consequently, the ensemble spread for humidity is too small. After about 5 days of cycling. fairly stable global filter statistics are obtained with no sign of filter divergence.The quality of the ensemble mean background field, as verified using radiosonde observations. is similar to that obtained using a 3D variational procedure. In part, this is likely due to the form chosen for the parameterized model error. Nevertheless, the degree of similarity is surprising given that the background-error statistics used by the two procedures are rather different, with generally larger background errors being used by the variational scheme.A set of 5-day integrations has been started from the ensemble of initial conditions provided by the EnKF. For the middle and lower troposphere. the growth rates of the perturbations are somewhat smaller than the growth rate of the actual ensemble mean error. For the upper levels, the perturbation patterns decay for about 3 days as a consequence of diffusive model dynamics. These decaying perturbations lend to severely underestimate the actual error that grows rapidly near the model top.

The ensemble Kalman filter (EnKF) has been proposed for operational atmospheric data assimilation. Some outstanding issues relate to the required ensemble size, the impact of localization methods on balance, and the representation of model error.To investigate these issues, a sequential EnKF has been used to assimilate simulated radiosonde, satellite thickness, and aircraft reports into a dry, global, primitive-equation model. The model uses the simple forcing and dissipation proposed by Held and Suarez. It has 21 levels in the vertical, includes topography, and uses a 144 x 72 horizontal grid. In total, about 80 000 observations are assimilated per day.It is found that the use of severe localization in the EnKF causes substantial imbalance in the analyses. As the distance of imposed zero correlation increases to about 3000 km, the amount of imbalance becomes acceptably small.A series of 14-day data assimilation cycles are performed with different configurations of the EnKF. Included is an experiment in which the model is assumed to be perfect and experiments in which model error is simulated by the addition of an ensemble of approximately balanced model perturbations with a specified statistical structure. The results indicate that the EnKF, with 64 ensemble members, performs well in the present context.The growth rate of small perturbations in the model is examined and found to be slow compared with the corresponding growth rate in an operational forecast model. This is partly due to a lack of horizontal resolution and partly due to a lack of realistic parameterizations. The growth rates in both models are found to be smaller than the growth rate of differences between forecasts with the operational model and verifying analyses. It is concluded that model-error simulation would be important, if either of these models were to be used with the EnKF for the assimilation of real observations.

An ensemble Kalman filter may be considered for the 4D assimilation of atmospheric data. In this paper, an efficient implementation of the analysis step of the filter is proposed. It employs a Schur (elementwise) product of the covariances of the background error calculated from the ensemble and a correlation function having local support to filter the small (and noisy) background-error covariances associated with remote observations. To solve the Kalman filter equations, the observations are organized into batches that are assimilated sequentially. For each batch, a Cholesky decomposition method is used to solve the system of linear equations. The ensemble of background fields is updated at each step of the sequential algorithm and, as more and more batches of observations are assimilated, evolves to eventually become the ensemble of analysis fields. A prototype sequential filter has been developed. Experiments are performed with a simulated observational network consisting of 542 radiosonde and 615 satellite-thickness profiles. Experimental results indicate that the quality of the analysis is almost independent of the number of batches (except when the ensemble is very small). This supports the use of a sequential algorithm. A parallel version of the algorithm is described and used to assimilate over 100 000 observations into a pair of 50-member ensembles. Its operation count is proportional to the number of observations, the number of analysis grid points, and the number of ensemble members. In view of the flexibility of the sequential filter and its encouraging performance on a NEC SX-4 computer, an application with a primitive equations model can now be envisioned.

No abstract available. Corresponding author address: Peter Jan van Leeuwen, IMAU, Utrecht University, P.O. Box 80005, 3508 TA Utrecht, the Netherlands. Email: leeuwen@fys.ruu.nl

The possibility of performing data assimilation using the flow-dependent statistics calculated from an ensemble of short-range forecasts (a technique referred to as ensemble Kalman filtering) is examined in an idealized environment. Using a three-level, quasigeostrophic, T21 model and simulated observations, experiments are performed in a perfect-model context. By using forward interpolation operators from the model state to the observations, the ensemble Kalman filter is able to utilize nonconventional observations. In order to maintain a representative spread between the ensemble members and avoid a problem of inbreeding, a pair of ensemble Kalman filters is configured so that the assimilation of data using one ensemble of short-range forecasts as background fields employs the weights calculated from the other ensemble of short-range forecasts. This configuration is found to work well: the spread between the ensemble members resembles the difference between the ensemble mean and the true state, except in the case of the smallest ensembles. A series of 30-day data assimilation cycles is performed using ensembles of different sizes. The results indicate that (i) as the size of the ensembles increases, correlations are estimated more accurately and the root-mean-square analysis error decreases, as expected, and (ii) ensembles having on the order of 100 members are sufficient to accurately describe local anisotropic, baroclinic correlation structures. Due to the difficulty of accurately estimating the small correlations associated with remote observations, a cutoff radius beyond which observations are not used, is implemented. It is found that (a) for a given ensemble size there is an optimal value of this cutoff radius, and (b) the optimal cutoff radius increases as the ensemble size increases.

An evaluation of the analyses of the large-scale global circulation produced by the Canadian Meteorological Centre (CMC) is undertaken by intercomparing them to the corresponding analyses of two independent analysis centres: the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP; formerly the National Meteorological Center).The evaluation is done by constructing the mean of the analyses from the three centres and then computing the deviations of the analyses from each of the three centres from the mean. Results are presented for January and July over a sc-year period for the moisture field, the mass field and the wind field.The results suggest that the CMC analyses, like those from the other two centres, have strengths and weaknesses and do not stand out as being consistently better or worse than the other two. In general, the analyses agree well in mid-latitudes and northern polar regions and exhibit poor agreement in the tropics and southern polar regions. The results also indicate that data assimilation systems continue to have great difficulty in analysing the moisture field.

Both the numerical models used in atmospheric data assimilation and the forward interpolation from the analysis mesh to the observations are subject to discretization errors. To examine the effect of these errors, a generalized Kalman filter, in which both model and observation errors are functions of the signal, is formulated. Far from the red model error spectrum assumed in many studies, the formulation yields a model error spectrum which increases with wavenumber to reach a maximum at the truncation limit. The resulting second-moment equations are studied in the context of the one-dimensional linear advection equation and, even for this simple equation, found to be quite complex. For example, it is found that signal/error correlations, not normally considered in standard Kalman filter theory, can play an important role. Two types of (semi-Lagrangian) model discretization and two types of forward interpolation are examined in this paper. The first type uses Fourier interpolation (and has no error), while the second type uses cubic spline interpolation (and has amplitude and phase errors). To facilitate understanding of the general case, various simpler cases are considered first, e.g., the case of a uniform observation network with the same number of observations as analysis meshpoints reveals important analogies between the forward interpolation error and the model discretization error. It is found that the perfect-model assumption can result in degeneracy for any observation network when the signal/error correlation is properly accounted for. The case of a single observation (coinciding with an analysis gridpoint) strikingly illustrates the importance of the signal/error correlations and suggests that simple model error parametrization based purely on the model discretization error, and neglecting these correlations, would seriously underestimate the forecast and analysis errors. In this paper, it is assumed that the analysis mesh can resolve all scales in the signal. The effect of unresolved scales is considered in a companion paper.

The improvement of analysis and data assimilation techniques can have a large impact, as shown here in the context of the Canadian global and regional data assimilation systems. Both of these systems utilize the same analysis component that was recently changed as follows: (a) a completely 3D algorithm replaced the previous split 3D scheme, which involved separate vertical and horizontal steps; (b) the assimilation of SATEM data was revised and is now done in terms of thicknesses over relatively thick layers; (c) an additional analysis level (at 925 hPa) was added and a derived temperature analysis replaced the former temperature analysis; (d) observation and forecast error statistics were revised; and (e) a correction procedure was introduced for certain types of radiosondes to offset the negative impact of solar and longwave radiation.While many of these changes are interrelated, preventing a systematic evaluation of each in isolation, it is shown that the revised 3D algorithm eliminates a problem that sometimes occurred in areas of dense surface data, SATEM data have a large positive impact in the Southern Hemisphere, and the radiosonde bias-correction scheme very significantly reduces the geopotential height bias observed previously in the upper atmosphere over certain regions, such as western North America.The overall evaluation of the analysis changes shows that in general the new analysis results in more accurate 6-h forecasts, with the largest improvements in the Tropics and especially in the Southern Hemisphere. In conjunction with these forecast gains, the evaluation of the general circulation statistics for August also show significant changes: the new analyses are more energetic, exhibiting a substantially stronger Hadley circulation and stronger zonal winds about Antarctica. The global forecasts from the revised analysis system consistently exhibit a significantly more rapid spinup of global precipitation as compared to the previous system.

For many aspects of numerical weather prediction it is important to have good error statistics. Here one can think of applications as diverse as data assimilation, model improvement, and medium-range forecasting. In this paper, a method for producing these statistics from a representative ensemble of forecast states at the appropriate forecast time is proposed and examined. To generate the ensemble, an attempt is made to simulate the process of error growth in a forecast model. For different ensemble members the uncertain elements of the forecasts are perturbed in different ways.First the authors attempt to obtain representative initial perturbations. For each perturbation, an independent 6-h assimilation cycle is performed. For this the available observations are randomly perturbed. The perturbed observations are input to the statistical interpolation assimilation scheme, giving a perturbed analysis. This analysis is integrated for 6 h with a perturbed version of the T63 forecast;model, using perturbed surface fields, to obtain a perturbed first guess for the next assimilation. After cycling for 4 days it was found that the ensemble statistics have become stable.To obtain perturbations to the model, different model options for the parameterization of horizontal diffusion, deep convection, radiation, gravity wave drag, and orography were selected. As part of the forecast error is due to model deficiencies, perturbing the model will lead to an improved ensemble forecast. This also creates the opportunity to use the ensemble forecast. for model sensitivity experiments.It is observed that the response, after several assimilation cycles, to the applied perturbations is strongly nonlinear. This fact makes it difficult to motivate the use of opposite initial perturbations. The spread in the ensemble of first-guess fields is validated against statistics available from the operational data assimilation scheme. It is seen that the spread in the ensemble is too small. Apparently, the simulation of the error sources is incomplete. In particular, we might have to generate less conventional perturbations to the model.

The ability of a digital filter technique to control high-frequency gravity wave noise in numerical weather forecasts based on the primitive equations is examined in the context of a global data assimilation system. The method uses a 12-h forward integration of the complete model to generate a time series that is filtered to give a balanced model state valid 6 h into the integration. This state is free of high-frequency noise and serves as a background held for the next analysis. The technique is referred to as digital filter finalization. The technique is first applied to a long model run in order to identify the impact of the chosen cutoff period in the design of the filter on a properly balanced model state. The robustness of the technique to typical imbalances between the mass and wind fields produced by an operational statistical interpolation procedure is also examined. Results of data assimilation experiments performed with the digital filter finalization and with the currently-operational adiabatic nonlinear normal mode initialization scheme are compared. The digital filter finalization technique examined here is shown to be an accurate, consistent and very simple way to remove the undesirable high-frequency noise from a global model forecast.

The first part of this paper presents the results of a study of the structure of the observed residuals, or differences, between radiosonde data and the short-range forecasts that are used as trial fields in an operational hemispheric data assimilation scheme. The study is based on fitting appropriate functional representations to horizontal correlations of observed height and wind residuals. Rather than represent the height residuals by the sum of a degenerate second-order autoregressive function and an additive constant to account for long-wave error, as in a previous study, we use a representation consisting of a sum of two degenerate third-order autoregressive functions of the form (1 + cr + c2r2/3) exp(−cr), where r represents radial distance. For the wind residuals, we use the functional form that follows by geostrophy. In addition to examining the structure of the horizontal and vertical correlations, we also present other statistics relating to the performance of the data assimilation procedure, such as vertical profiles of the magnitude of the observed wind and height residuals for various regions. In the second part of the paper, the results of the study are used as a basis for specifying interpolation statistics for the objective analysis. To evaluate the impact of the new interpolation statistics, various objective measures of analysis performance are examined and parallel 48-h forecasts are performed. It is found that significant improvements result when the new interpolation statistics are used in the data assimilation procedure.