A study of ensemble size and shallow water dynamics with the Maximum Likelihood Ensemble Filter

In this paper we perform a study using the Maximum Likelihood Ensemble Filter, MLEF, developed at the Cooperative Institute for Research in the Atmosphere (CIRA), Colorado State University (CSU), and Florida State University (FSU), with CSU’s 2-dimensional shallow water equations model on the sphere. The aim of this study is to find the optimal number of ensemble members, with respect to the root mean square (rms) error of the three state variables in the shallow water equations model, such that the rms error is a minimum. After ascertaining this number, we vary the size of the observations sets for three different Rossby-Haurwitz waves in the shallow water equations model. These waves generate different types of dynamics from fast, shallow motions to fast, tall waves with vortices, to a flow similar to geostrophic balance. We show that, for faster flows, we require less ensemble members than for slow balanced flows. We also present an explanation for this behavior in the form of hybrid Lyapunov-bred vectors.