Spatiotemporal characterization of Ensemble Prediction Systems – the Mean-Variance of Logarithms (MVL) diagram

Abstract. We present a novel approach to characterize and graphically represent the spatiotemporal evolution of ensembles using a simple diagram. To this aim we analyze the fluctuations obtained as differences between each member of the ensemble and the control. The lognormal character of these fluctuations suggests a characterization in terms of the first two moments of the logarithmic transformed values. On one hand, the mean is associated with the exponential growth in time. On the other hand, the variance accounts for the spatial correlation and localization of fluctuations. In this paper we introduce the MVL (Mean-Variance of Logarithms) diagram to intuitively represent the interplay and evolution of these two quantities. We show that this diagram uncovers useful information about the spatiotemporal dynamics of the ensemble. Some universal features of the diagram are also described, associated either with the nonlinear system or with the ensemble method and illustrated using both toy models and numerical weather prediction systems.