Adaptive ensemble member size reduction and inflation

In this paper we address the question of given a set of ensemble members of a certain size is there a way to consistently reduce the number of ensemble members at a later stage in the assimilation cycles. An extension to this is given this reduction is it possible to reintroduce the ensemble members at a later time if the order of accuracy is decreasing, is also considered. To address this problem we present an adaptive methodology for reducing and inflating ensemble size by projecting the ensemble on to a limited number of its leading Empirical Orthogonal Functions (EOFs) through a Proper Orthogonal Decomposition (POD). We then apply this methodology with a global shallow water equations model on the sphere in conjunction with a ensemble filter under development at Florida State University and the Cooperative Institute for Research in the Atmosphere at Colorado State University. An adaptive methodology for reducing and inflating ensemble size was successfully applied for the chosen test cases resulting typically in a reduction of up to a factor of half in the number of members of ensemble required for successful implementation.