Simulating climate with a synchronization-based supermodel.

The SPEEDO global climate model (an atmosphere model coupled to a land and an ocean/sea-ice model with about 250.000 degrees of freedom) is used to investigate the merits of a new multi-model ensemble approach to the climate prediction problem in a perfect model setting. Two imperfect models are generated by perturbing parameters. Connection terms are introduced that synchronize the two models on a common solution, referred to as the supermodel solution. A synchronization-based learning algorithm is applied to the supermodel through the introduction of an update rule for the connection coefficients. Connection coefficients cease updating when synchronization errors between the supermodel and solutions of the "true" equations vanish. These final connection coefficients define the supermodel. Different supermodel solutions, but with equivalent performance, are found depending on the initial values of the connection coefficients during learning. The supermodels have a climatology and a climate response to a CO2 increase in the atmosphere that is closer to the truth as compared to the imperfect models and the standard multi-model ensemble average, showing the potential of the supermodel approach to improve climate predictions.

Introduction to focus issue: Synchronization in large networks and continuous media-data, models, and supermodels.

The synchronization of loosely coupled chaotic systems has increasingly found applications to large networks of differential equations and to models of continuous media. These applications are at the core of the present Focus Issue. Synchronization between a system and its model, based on limited observations, gives a new perspective on data assimilation. Synchronization among different models of the same system defines a supermodel that can achieve partial consensus among models that otherwise disagree in several respects. Finally, novel methods of time series analysis permit a better description of synchronization in a system that is only observed partially and for a relatively short time. This Focus Issue discusses synchronization in extended systems or in components thereof, with particular attention to data assimilation, supermodeling, and their applications to various areas, from climate modeling to macroeconomics.