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The MVL diagram: A diagnostic tool to characterize ensemble simulations

This work illustrates the usefulness of some recent spatiotemporal analysis tools in the field of weather and climate simulation. To this aim we present a recent characterization of spatiotemporal error growth (the so called mean-variance logarithmic (MVL) diagram, Primo et al. 2005, Gutiérrez et al. 2008). Behind a simple calculation procedure, the MVL diagram comes from a sound theoretical basis borrowed from the growth of rough interfaces (López et al. 2004), and has several applications as a diagnostic tool in the characterization of ensemble prediction systems. Namely, it is useful in characterizing (1) the initial perturbations applied in a simulation, (2) the model dynamics, acting as a fingerprint for different models and (3) the climatological fluctuations of the perturbations specific of each model. As opposite to the standard temporal analysis (spatially-averaged or single-point), the MVL spatiotemporal analysis accounts for the nontrivial localization of fluctuations, thus allowing disentangling the effects of the different initialization procedures (random, lagged, singular vectors) and the different model formulations.
We show an application of this diagram using a coupled ocean-atmosphere Ensemble Prediction System (Fernández et al. 2009); in particular we consider the DEMETER multimodel seasonal hindcast and focus on both initial conditions (three different perturbation procedures) and model errors (seven coupled GCMs). We show that the shared building blocks of the GCMs (atmospheric and ocean components) impose similar dynamics among different models and, thus, contribute to poorly sampling the model formulation uncertainty. We also illustrate how multiple scales in dynamical systems impose non-trivial effects on the growth of perturbations.