Adaptive ensemble reduction and inflation

In this paper we address the question of whether it is possible consistently to reduce the number of ensemble members at a late stage in the assimilation cycle. As an extension, we consider the question: given this reduction, is it possible to reintroduce ensemble members at a later time, if the accuracy is decreasing significantly? To address these questions, we present an adaptive methodology for reducing and inflating an ensemble by projecting the ensemble onto a limited number of its leading empirical orthogonal functions, through a proper orthogonal decomposition. We then apply this methodology with a global shallow-water-equations model on the sphere in conjunction with an ensemble filter developed at Florida State University and the Cooperative Institute for Research in the Atmosphere at Colorado State University. An adaptive methodology for reducing and inflating ensembles is successfully applied in two contrasting test cases with the shallow-water-equations model. It typically results in a reduction in the number of ensemble members required for successful implementation, by a factor of up to two. Copyright (C) 2007 Royal Meteorological Society.