## 1. Introduction

In numerical weather prediction (NWP), the model initial conditions, also known as the analysis state, are produced as a combination of observations and a background state, usually provided by a short-term forecast from a previous model run. These two sources of information are appropriately weighted during the assimilation process, according to their respective error covariances represented in the so-called **R** and **B** matrices respectively.

Background errors are the result of two different errors: a *predictability error*, which corresponds to the growth of analysis error during the model integration, and a *model error* (Daley, 1992). The model error term is due to imperfections in the numerical model, arising, for instance, from approximations in the dynamics and in the physical parametrizations.

Monte Carlo methods, based either on the Kalman filter algorithm (the ensemble Kalman filter; Evensen, 2003) or on variational data assimilation (Belo Pereira and Berre, 2006; Berre *et al.*, 2007), are ongoing alternative or complementary approaches to deterministic assimilation systems, and they can provide estimates of flow-dependent background error covariances.

However, ensemble data assimilation systems are sometimes implemented in a perfect model framework. Consequently, they provide an estimation of the predictability error term while the model error component is omitted. As neglecting model error usually results in underestimated background error variances, the representation of model error has become an important aspect in the development of ensemble methods.

First investigations to account for model errors in ensemble systems lead to various strategies. Possible options include in particular multi-model/multi-physics approaches (Houtekamer *et al.*, 1996), stochastic physics (Buizza *et al.*, 1999), additive and multiplicative inflations (Constantinescu *et al.*, 2007) or the stochastic kinetic energy backscatter scheme (Shutts, 2005). These different model error representations have recently been evaluated and compared by Houtekamer *et**al.* (2009), which indicate that the inflation approach has the largest contribution in their model error simulation.

At Météo-France, an ensemble variational assimilation has been developed for the global operational model Arpège (Berre *et al.*, 2007) and has been successfully used in real time since July 2008 to provide flow-dependent background error variances to the operational 4D-Var assimilation (Raynaud *et al.*, 2011). The ensemble is run in a perfect model framework and estimated variances are inflated ‘offline’ (i.e. after the ensemble has been completed), on the basis of a posteriori diagnostics (Desroziers and Ivanov, 2001), to represent model error contributions. Multiplicative inflation is a simple and widely used technique to deal with all error sources of unknown origins.

The current ensemble system is, however, not entirely consistent since the offline multiplicative inflation applied to the variances is not accounted for in the background perturbation update. An improved configuration of the ensemble has therefore been developed, in which the multiplicative inflation is now performed within the ensemble by enlarging the amplitude of forecast perturbations. The aim of this paper is to describe the inflation procedure and to examine the effect of simulating model error in the ensemble system, in terms of both description of background errors and their impact on forecast scores.

The paper is organized as follows. Section 2 presents the variational ensemble data assimilation system developed at our centre. The adaptive tuning procedure of the multiplicative inflation factor and the updated ensemble configuration are detailed in section 3. Section 4 provides diagnostic results from a first experimentation of the perturbation inflation. Forecast scores of analysis–forecast experiments over a 3-week period, using background error variances from the inflated perturbations, are examined in section 5. Finally, conclusions and perspectives are given in section 6.