Estimating background-error variances with the ECMWF Ensemble of Data Assimilations system: some effects of ensemble size and day-to-day variability

Ensemble of data assimilations (EDA) methods have been shown to be able to provide flow-dependent estimates of analysis and background error statistics. For this reason, they potentially present a way to overcome one of the main limitations of current variational data assimilation systems. However, the limited number of ensemble members which can be realistically run in an operational context and the stochastic nature of the EDA approach lead to high levels of sampling noise in the relevant ensemble statistics. To answer this problem, an 'objective filtering' technique of the sample ensemble variances proposed by Raynaud et al. in 2009 has been implemented at ECMWF. In this article we present a comparison of the ability of ensemble data assimilation systems of different sizes (10 to 50 members) to represent flow-dependent background-error variances. In particular, the ensemble-based variances are examined in the cases of the severe storm Klaus (24 January 2009) over France and the Atlantic tropical hurricane Ike (1-14 September 2008). Our results show that, while a relatively small ensemble (10 members) can be sufficient to resolve the larger-scale error structures connected to an extratropical cyclogenesis, a larger ensemble is beneficial to resolve more localised anomalies like those connected with a hurricane. In this sense, the objective filtering technique provides a useful indication of the spatial scales the ensemble is able to resolve in a statistically robust way. The day-to-day variability of the ensemble statistics and how this affects the objective spatial filtering procedure are also examined. Our conclusion is that a time-independent implementation of the filter based on a climatology of truncation wave numbers results in more robust ensemble statistics estimates, and ultimately in improved forecast skill scores. Copyright (c) 2011 Royal Meteorological Society