SUMMARYAn ensemble-based probabilistic precipitation forecasting scheme has been developed that blends an extrapolation nowcast with a downscaled NWP forecast, known as STEPS: Short-Term Ensemble Prediction System. The uncertainties in the motion and evolution of radar-inferred precipitation fields are quantified, and the uncertainty in the evolution of the precipitation pattern is shown to be the more important. The use of ensembles allows the scheme to be used for applications that require forecasts of the probability density function of areal and temporal averages of precipitation, such as fluvial flood forecasting-a capability that has not been provided by previous probabilistic precipitation nowcast schemes. The output from a NWP forecast model is downscaled so that the small scales not represented accurately by the model are injected into the forecast using stochastic noise. This allows the scheme to better represent the distribution of precipitation rate at spatial scales finer than those adequately resolved by operational NWP. The performance of the scheme has been assessed over the month of March 2003. Performance evaluation statistics show that the scheme possesses predictive skill at lead times in excess of six hours.

ABSTRACT: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

The Met Office has developed an ensemble-variational data assimilation method (hybrid-4DEnVar) as a potential replacement for the hybrid four-dimensional variational data assimilation (hybrid-4DVar), which is the current operational method for global NWP. Both are four-dimensional variational methods, using a hybrid combination of a fixed climatological model of background error covariances with localized covariances from an ensemble of current forecasts designed to describe the structure of ''errors of the day.'' The fundamental difference between the methods is their modeling of the time evolution of errors within each data assimilation window: 4DVar uses a linear model and its adjoint and 4DEnVar uses a localized linear combination of nonlinear forecasts. Both hybrid-4DVar and hybrid-4DEnVar beat their three-dimensional versions, which are equivalent, in NWP trials. With settings based on the current operational system, hybrid-4DVar performs better than hybrid-4DEnVar. Idealized experiments designed to compare the time evolution of covariances in the methods are described: the basic 4DEnVar represents the evolution of ensemble errors as well as 4DVar. However, 4DVar also represents the evolution of errors from the climatological covariances, whereas 4DEnVar does not. This difference is the main cause of the superiority of hybrid-4DVar. Another difference is that the authors' 4DVar explicitly penalizes rapid variations in the analysis increment trajectory, while the authors' 4DEnVar contains no dynamical constaints on imbalance. The authors describe a four-dimensional incremental analysis update (4DIAU) method that filters out the high-frequency oscillations introduced by the poorly balanced 4DEnVar increments. Possible methods for improving hybrid-4DEnVar are discussed.

ABSTRACT: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.

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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.

An important aspect of ensemble forecasting is that the resulting probabilities are reliable (i.e., the forecast probabilities match the observed frequencies). In the medium-range forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble spread should be representative of the uncertainty in the mean, whereas in the seasonal forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble forecasts should have the same climatological variance as the truth. In this note, the authors emphasize that both of these requirements are necessary for reliability and they clarify that a popular calibration method actually achieves both of these requirements.

ABSTRACT: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 BackgroundThe resolutions of modern numerical weather/ocean models and observation density have greatly increased in recent years in order to resolve the dynamic processes at smaller scales (such as convective scales in the atmosphere and eddies in the ocean). As a consequence, the computational cost required for data assimilation (DA) has also increased. To reduce the computational cost, methods like variational analysis (3D-Var and 4D-Var) focus on reducing the computation during the minimization process of the cost function. For example, 4D-Var is solved using the incremental form (Courtier et al., 1994) in which the so-called inner loop is carried out by running the adjoint model at a lower resolution with simplified physics.For the ensemble methods such as Ensemble Kalman Filter, the computational cost can be alleviated by allowing the analysis to be computed in parallel in local regions (Keppenne and Rienecker, 2002;Ott et al., 2004;Hunt et al., 2007). However, the computational burden for such local analyses is still constrained by the ensemble size * Correspondence to: Shu-Chih Yang, Department of Atmospheric Sciences, National Central University, Jhongli, Taiwan, 320. E-mail: shuchih.yang@atm.ncu.edu.tw † The contribution of N. E. Bowler was written in the course of his employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland. and the total number of local regions in a high-resolution model. It is possible to reduce the computation further by carrying out the ensemble analyses on a coarser resolution, as done with incremental variational analyses, and then interpolating to the finer resolution. We will show that such an interpolation step degrades the accuracy of the analysis, compared to a full-resolution analysis.In this study, we investigate the feasibility of a method to reduce the computational cost in the assimilation procedure. This method is developed following a suggestion of Bowler (2006, Section 6.4), who computed the transform matrix deriv...