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A new method for generating ensemble predictions based on an ensemble of data assimilations has been developed. Using an ensemble of four-dimensional ensemble-variational minimizations provides an approach which is close to the Met Office's operational data assimilation system and less computationally expensive than other alternatives. In developing this system, several inflation schemes have been compared. One form of additive inflation, based on analysis increments, was developed and found to be very effective at increasing the overall ensemble spread and correcting systematic biases in the model. However, the analysis increments are not flow-dependent since they are randomly drawn from a long archive. It was decided to scale back their amplitude to avoid them dominating the overall performance. Of the other inflation schemes considered, it was found that relaxation-to-prior-perturbations was the most effective at maintaining the ensemble spread. However, this scheme also produced perturbations which are too large-scale and too balanced. The relaxation-to-prior-spread scheme performed well in many respects, but required a relaxation factor greater than one to produce an acceptable spread. Therefore these two schemes were combined in order to mitigate the drawbacks of each. This combination proved successful and was used in final testing of the ensemble against the currently operational ensemble transform Kalman filter (ETKF). The ETKF has its perturbations centred around a high-resolution ‘deterministic’ analysis. This was seen to be an important benefit, and the new ensemble system also benefited from being recentred around the high-resolution analysis. This recentred system has slightly lower forecast skill than the ETKF over a variety of variables, due to the fact that the spread of this ensemble is less than the spread of the ETKF ensemble. The deficiency of the spread of the new ensemble system will be addressed in ongoing work.

Hybrid four-dimensional ensemble-variational (4DEnVar) data assimilation is a method which avoids using a linear and adjoint model by relying on an input ensemble to propagate analysis increments in time. Previous studies have shown that hybrid 4DEnVar performs worse than hybrid four-dimensional variational (4D-Var) assimilation. Given hybrid 4DEnVar's heavy reliance on the ensemble, this comparison may be affected by the quality of the input ensemble. Here we investigate how improvements to the ensemble system affect hybrid 4D-Var and how they affect the comparison with hybrid 4DEnVar. Using the Met Office's operational ensemble generation scheme (the ensemble transform Kalman filter, ETKF) it is found that hybrid 4D-Var gains little benefit from using an enlarged ensemble as input (176 as opposed to 23 members). By contrast, hybrid 4DEnVar benefits more from the increased ensemble size, and it benefits further when the weighting given to the ensemble covariance is increased. Both data assimilation methods benefit when the input ensemble is changed from using the ETKF to using an ensemble of 4DEnVars. Both schemes also show further benefit when a large ensemble (200 members) of 4DEnVars is used, and when a large weight is given to the covariance information from this ensemble. Thus, improving the ensemble covariance used in assimilation (ensemble generation method and ensemble size) and increasing its weight can have substantial benefits. Given that both hybrid 4D-Var and hybrid 4DEnVar benefit from improvements to the input ensemble, the relative performance is largely unaffected by the ensemble changes and hybrid 4D-Var performs better than hybrid 4DEnVar for all input ensembles.

It has long been known that verification of a forecast against the sequence of analyses used to produce those forecasts can under-estimate the magnitude of forecast errors. Here we show that under certain conditions the verification of a short-range forecast against a perturbed analysis coming from an ensemble data assimilation scheme can give the same root-mean-square error as verification against the truth. This means that a perturbed analysis can be used as a reliable proxy for the truth. However, the conditions required for this result to hold are rather restrictive: the analysis must be optimal, the ensemble spread must be equal to the error in the mean, the ensemble size must be large and the forecast being verified must be the background forecast used in the data assimilation. Although these criteria are unlikely to be met exactly it becomes clear that for most cases verification against a perturbed analysis gives better results than verification against an unperturbed analysis. We demonstrate the application of these results in a idealised model framework and a numerical weather prediction context. In deriving this result we recall that an optimal (Kalman) analysis is one for which the analysis increments are uncorrelated with the analysis errors.

The Met Office Global and Regional Ensemble Prediction System (MOGREPS) uses an on-line inflation factor calculation to calibrate the spread of the ensemble in space and time and counteract the tendency of the Ensemble Transform Kalman Filter (ETKF) to underestimate analysis uncertainty. Sonde measurements are augmented with ATOVS brightness temperature observations to provide sufficient coverage across the globe. This paper describes how the scheme has been extended to improve the vertical distribution of spread. Separate inflation factors are derived for each of three ‘bands’ of model levels, loosely representing the boundary layer, troposphere and stratosphere. A continuous profile is ensured by linearly interpolating between the band centres. The error/spread relationship observed in each ATOVS channel is mapped onto the three bands using a set of weights obtained by integrating the appropriate Jacobians over the range of pressures covered by each band. These weights are found to be approximately constant, thanks to the small number of bands and the fact that near-surface channels are not used over land. The revised initial perturbations lead to increased near-surface spread which persists throughout the 72 h forecast and carries through to improved probabilistic scores. However, the near-surface spread remains too small due to insufficient growth of spread by the forecast model. This suggests perturbation of sea-surface temperatures, soil initial conditions, soil properties and boundary-layer physics as priorities for future work.

The Met Office is currently developing an ensemble-based data-assimilation system for use in numerical weather prediction (NWP). In an effort to inform those developments, a simple model has been used to compare a number of different flavours of ensemble Kalman filter (EnKF). As in many previous studies, deterministic (square-root) filters are seen to perform better than stochastic (perturbed-observations) filters. Two previously proposed methods for mitigating the effects of perturbing the observations were tested. These modified stochastic filters improved performance, but were still worse than the deterministic filters. Very little difference was seen between the performance of the various deterministic filters tested. The typical approach to localization in the Local Ensemble Transform Kalman Filter (LETKF) is based solely on the distance between each observation and the model point being updated. It takes no account of the inter-observation distance and we argue that this is incorrect. However, the difference between covariance localization and observation localization is only relevant when the assimilation is not weak and hence it did not affect performance in these tests. If a hybrid covariance matrix is used to update the ‘deterministic’ forecast around which the ensemble is centred, then using the same covariance matrix when updating the perturbations is seen to be beneficial in a stochastic filter. This is not the case in the square-root filter, due to restrictions imposed by its formulation. Tests with a nonlinear observation operator indicate better behaviour when observations are assimilated simultaneously rather than sequentially. An ensemble of variational minimizations has some advantages in this situation. These results, along with other considerations, have led the Met Office to develop a 4-dimensional ensemble-variational (4D-En-Var) system for data assimilation and ensemble generation.

The Met Office Global and Regional Ensemble Prediction System (MOGREPS) uses an online inflation factor calculation to calibrate the spread of the ensemble in space and time and counteract the tendency of the Ensemble Transform Kalman Filter (ETKF) to underestimate analysis uncertainty. Until 2008, this calibration mechanism relied entirely on sonde and wind profiler data, and was only applied locally in the Extratropics. By producing more appropriate estimates of the error variance of ATOVS brightness temperature observations, it has become possible to include these in the inflation factor calculation. This in turn provides sufficient data to apply localisation uniformly over the globe. The new scheme improves the latitudinal distribution of spread in comparison to forecast error, especially in the Tropics. Issues remain with the vertical distribution of spread, which are addressed by work to be reported in a future paper. © 2011 Crown Copyright, the Met Office. Published by John Wiley & Sons, Ltd.

The Met Office has been routinely running a short-range global and regional ensemble prediction system (EPS) since the summer of 2005. This article describes a major upgrade to the global ensemble, which affected both the initial condition and model uncertainty perturbations applied in that ensemble. The change to the initial condition perturbations is to allow localization within the ensemble transform Kalman filter (ETKF). This enables better specification of the ensemble spread as a function of location around the globe. The change to the model uncertainty perturbations is the addition of a stochastic kinetic energy backscatter scheme (SKEB). This adds vorticity perturbations to the forecast in order to counteract the damping of small-scale features introduced by the semi-Lagrangian advection scheme. Verification of ensemble forecasts is presented for the global ensemble system. It is shown that the localization of the ETKF gives a distribution of the spread as a function of latitude that better matches the forecast error of the ensemble mean. The SKEB scheme has a substantial effect on the power spectrum of the kinetic energy, and with the scheme a shallowing of the spectral slope is seen in the tail. A k−5/3 slope is seen at wavelengths shorter than 1000 km and this better agrees with the observed spectrum. The local ETKF significantly improves forecasts at all lead times over a number of variables. The SKEB scheme increases the rate of growth of ensemble spread in some variables, and improves forecast skill at short lead times. ©Crown Copyright 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.

The Met Office has been routinely running a short-range ensemble prediction system since the summer of 2005. This system consists of two component ensembles, a global ensemble that provides lateral boundary conditions to a regional ensemble. The global ensemble calculates the initial condition perturbations using a local version of the ensemble transform Kalman filter (ETKF). This article details tests of an ETKF run specifically for the regional ensemble. The perturbations using the ETKF for the regional ensemble contain more detail on small scales and less power on large scales. This extra small-scale detail persists for less than 18 h. These perturbations are overall smaller than the ones derived from the global ensemble, since they have been explicitly scaled to match the average error of the ensemble mean forecast at T + 6 h. Aside from the difference in the overall scaling of the perturbations, the skill of the two ensembles is very similar, with slightly higher skill being seen when the perturbations are derived from the global ensemble. The ETKF for the regional ensemble was implemented during May 2007. This change has recently been reversed, following these results. These comparisons may shed some light on whether the regional ensemble is providing a ‘dynamical downscaling’ of the global ensemble, or unique information of its own. In these tests the ensemble run with perturbations from the global ensemble was slightly more skilful than the regional perturbations ensemble, indicating that improving on dynamical downscaling is likely to be difficult. ©Crown Copyright 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.

We have investigated a method to substantially reduce the analysis computations within the Local Ensemble Transform Kalman Filter (LETKF) framework. Instead of computing the LETKF analysis at every model grid point, we compute the analysis on a coarser grid and interpolate onto a high-resolution grid by interpolating the analysis weights of the ensemble forecast members derived from the LETKF. Because the weights vary on larger scales than the analysis increments, there is little degradation in the quality of the weight-interpolated analyses compared to the analyses derived with the high-resolution grid. The weight-interpolated analyses are more accurate than the ones derived by interpolating the analysis increments. Additional benefit from the weight-interpolation method includes improving the analysis accuracy in the data-void regions, where the standard LEKTF with the high-resolution grid gives no analysis corrections due to a lack of available observations. Copyright © Royal Meteorological Society and Crown Copyright, 2008

The Met Office has recently introduced a short-range ensemble prediction system known as MOGREPS. This system consists of global and regional ensembles, with the global ensemble providing the boundary conditions and initial-condition perturbations for the regional ensemble. Perturbations to the initial conditions are calculated using the ensemble transform Kalman filter, which is a computationally-efficient version of the ensemble Kalman filter. Model uncertainties are represented in the system through a series of schemes designed to tackle the structural and subgrid-scale sources of model error. This paper describes the set-up of the system, and provides justification for the initial-condition and model perturbation schemes chosen. An outline of the structure of the perturbations generated by the system is presented, along with performance results, including verification from case studies and routine running. MOGREPS has been on trial within the operational suite at the Met Office since August 2005. On 20 October 2006 it was decided that this system should be made fully operational, with implementation expected in summer 2008. Results show a good performance. The regional ensemble is more skilful than the global ensemble, and compares favourably to the ECMWF ensemble for the forecast variables examined in this study. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland. Published by John Wiley & Sons,Ltd

An experiment has been performed, using a simple chaotic model, to compare different ensemble perturbation strategies. The model used is a 300 variable Lorenz 95 model which displays many of the characteristics of atmospheric numerical weather prediction models. Twenty member ensembles were generated using five perturbation strategies, error breeding, singular vectors, random perturbations (RPs), the Ensemble Kalman Filter (EnKF) and the Ensemble Transform Kalman Filter (ETKF). Based on normal verification methods, such as rank histograms and spread of the perturbations, the RPs method performs as well as any other method—this illustrates the limitations of using a simple model. Consideration of the quality of the background error information provided by the ensemble gives a better assessment of the ensemble skill. This measure indicates that the EnKF performs best, with the ETKF combined with RPs being the next most skillful. It was found that neither the ETKF, error breeding nor singular vectors provided useful background information on their own. Central to the success of the EnKF is the localization of the background error covariance which removes spurious long-range correlations within the ensemble. Computationally efficient versions of the EnKF (such as the ETKF) cannot accommodate covariance localization and their performance is seen to suffer. Applying the ETKF to a series of local domains has been tested, which allows covariance localization whilst remaining computational efficient, and this has been found to be nearly as effective as the EnKF with covariance localization.