The ECMWF initial ensemble perturbation strategy

Roberto Buizza

Scuola Universitaria Superiore Sant’Anna, Pisa, Italy

The European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble started operational forecast production on the 23rd of November 1992. In its first version, it simulated initial perturbations using a linear combination of singular vectors. Then, between 1998 and 2008, perturbations designed to take more into account observation, and model uncertainties were introduced to improve its reliability and accuracy (sharpness). In this contribution, the major changes introduced in the ensemble configuration between 1992 and 2008 are briefly reviewed.

1. Selective sampling using singular vectors

The initial design was based on two assumptions: (a) to focus on the simulation of initial uncertainties, and (b) to simulate them with singular vectors (SVs; Buizza et al 1993; Buizza & Palmer 1995; Molteni et al 1996). SVs, the perturbations with the fastest growth over a finite optimisation time interval, with growth measured with a dry total energy norm, were for the first time generated with a primitive equation model in 1991. They were computed with a simplified version of the ECMWF Integrated Forecast System that had a T21L19 (spectral triangular truncation with total wave number 21, and 19 vertical levels) resolution (Buizza et al 1993). Initial perturbations defined by a linear combination of orthonormal SVs, scaled to have local amplitudes comparable to analysis error estimates, guaranteed that the 33-member ensemble of T63L19 integrations had a reasonable spread (Molteni et al., 1996).

2. Simplified linear and adjoin physics, and the local projection operator

In the first operational ensemble, the SVs were computed without any adiabatic process apart for horizontal diffusion, and with a dry total energy norm. Operational diagnostics suggested that this first version of the operational ensemble had some weaknesses that needed to be addressed. Firstly, some SVs would show low-level, ‘non-meteorological’ structures, that when integrated non-linearly were dumped. The problem was addressed with the implementation of a linear and adjoint vertical diffusion and surface drag scheme (Buizza 1994a), which was then used for many years in variational data assimilation both at ECMWF and by the HIRLAM group. Secondly, during the boreal summer the global SVs would concentrate in the southern hemisphere, thus leading to too-low, unreliable spread in the northern hemisphere. This second weakness was addressed with a local projection operator (LPO), that allowed to localize the SVs (Buizza 1994b). These changes made it feasible to investigate the role that moist processes in perturbations’ growth (Coutinho et al., 2004), and to compute realistic SVs in the tropics (Barkmejier et al., 2001). The LPO also allowed us to contribute to targeted observation campaigns (Palmer et al., 1998; Buizza & Montani 1999).

3. Metrics, observations, and SVs

A further area that we thought required an in-depth investigation was the SVs sensitivity to the choice of the initial and final time metrics applied to measure the perturbation growth. Palmer et al. (1998) studied the sensitivity of the SV structures to metrics and concluded that the dry total energy norm used in operations was the most appropriate metric for ensemble prediction. Barkmeijer et al. (1999) explored the possibility of using the Hessian of the 3-dimensional variational assimilation system as the initial-time cost function, since this metric is sensitive to observations, its use would have made the initial perturbations sensitive to the observing system. Experiments indicated that the Hessian-SVs were too costly to compute and less effective than the total energy SVs, and thus these latter remained in operations.

4. Stochastic simulation of model uncertainties

At the end of 1998, the operational ensemble still only simulated initial uncertainties using SVs, computed now at higher resolution (T42L31) over different regions of the world using the LPO. The ensemble membership was now at 51, and the non-linear model resolution was T159L31. Following a comparison with the other two operational global ensembles (the American and the Canadian ones), we decided to investigate how we could simulate model uncertainties. Following the Canadian example, in 1998 we developed and implemented a stochastic scheme designed to simulate model uncertainties linked to the parameterized processes (Buizza et al., 1999). This improved substantially the ensemble reliability in the medium-range, especially in the tropical area where the dry-total-energy SVs were unable to induce enough spread in the ensemble. Thanks to the improved reliability, in 2006 the ensemble forecast length was extended to 15 days, and then in 2008 was joined in a seamless way with the operational monthly ensemble.

5. The Ensemble of Data Assimilations

In 1999, the ensemble initial perturbations were still not sensitive to observation uncertainties. We started exploring the possibility to use an ensemble of data assimilations (EDA), together with the SVs, to define the initial perturbations. Each EDA member was generated using stochastically perturbated observations and a stochastically perturbed model. EDA-based perturbations, defined initially by differences between EDA members, had substantially different characteristics than the SVs, and complemented them. When combined with SVs to define the initial conditions of the ensemble forecasts, they led to increased reliability, especially in the short forecast range, and they were thus included in operations (Buizza et al., 2008).

6. In summary

Today (November 2022), in the operational ECMWF ensemble, synoptic-scale (T42) targeted SVs are still used, combined with EDA-based perturbations to simulate the initial uncertainties, and an upgraded version of the stochastic scheme SPPT is active in all the ECMWF ensembles to simulate model uncertainties. During the 30 years of operations, the ensemble benefitted greatly from upgrades in data assimilation, the availability and use of better and more observations, and model improvements. Verification statistics indicate that thanks to all these changes, predictability in the medium range has been extended by about 1.5 days per decade (Buizza 2018).