Consistent operational ensemble variational assimilation

a. Ensemble of perturbed assimilations versus deterministic square-root filters The principles of ensemble data assimilation (EnDA) are relatively simple and general. In this study, we will focus on the use of perturbed assimilations, based, on one hand, on explicit observation perturbations (representative of observation errors), and on the other hand, on background perturbations which are either fully implicit (from the perturbed previous data assimilation cycles) or partly explicit (to represent model error contributions). Applying this approach to a Kalman filter algorithm corresponds to an ensemble Kalman filter (EnKF). Similarly, its application to a variational algorithm leads to an ensemble vari-ational assimilation (EnVar), such as the one which is operational at Météo-France since 2008. Such an EnVar system is very easy to implement and run from an existing variational system, as each member is basically quite similar to a usual variational assimilation experi-ment (albeit less expensive, depending for instance on horizontal resolution and number of outer-loops). It may be mentioned also that there are other variants called deterministic square-root filters (e.g. Tippett et al 2003). They are based on a linear transformation of backgroun