Jérôme Vialard, Javier Zavala-Garay, Andrew M. Moore, Youmin Tang, Kamran Sahami, Richard Kleeman, David L. T. Anderson, Michael Fisher, Anthony T. Weaver, Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado [Boulder]-National Oceanic and Atmospheric Administration (NOAA), Rosenstiel School of Marine and Atmospheric Science (RSMAS), University of Miami [Coral Gables], University of Northern British Columbia [Prince George] (UNBC), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), Laboratoire d'Océanographie et du Climat : Expérimentations et Approches Numériques (LOCEAN), Muséum national d'Histoire naturelle (MNHN)-Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Institut Pierre-Simon-Laplace (IPSL (FR_636)), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-École polytechnique (X)-Centre National d'Études Spatiales [Toulouse] (CNES)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-École polytechnique (X)-Centre National d'Études Spatiales [Toulouse] (CNES)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Department of Physics [Denver], University of Colorado [Denver], European Centre for Medium-Range Weather Forecasts (ECMWF), CERFACS, Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Muséum national d'Histoire naturelle (MNHN)-Institut Pierre-Simon-Laplace (IPSL (FR_636)), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-École polytechnique (X)-Centre National d'Études Spatiales [Toulouse] (CNES)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)
The optimal forcing patterns for El Niño–Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air–sea interaction processes. Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.