Improving model fidelity and sensitivity for complex systems through empirical information theory
Author Affiliations
Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
Contributed by Andrew J. Majda, April 12, 2011 (sent for review March 3, 2011)
Abstract
In many situations in contemporary science and engineering, the analysis and prediction of crucial phenomena occur often through complex dynamical equations that have significant model errors compared with the true signal in nature. Here, a systematic information theoretic framework is developed to improve model fidelity and sensitivity for complex systems including perturbation formulas and multimodel ensembles that can be utilized to improve both aspects of model error simultaneously. A suite of unambiguous test models is utilized to demonstrate facets of the proposed framework. These results include simple examples of imperfect models with perfect equilibrium statistical fidelity where there are intrinsic natural barriers to improving imperfect model sensitivity. Linear stochastic models with multiple spatiotemporal scales are utilized to demonstrate this information theoretic approach to equilibrium sensitivity, the role of increasing spatial resolution in the information metric for model error, and the ability of imperfect models to capture the true sensitivity. Finally, an instructive statistically nonlinear model with many degrees of freedom, mimicking the observed non-Gaussian statistical behavior of tracers in the atmosphere, with corresponding imperfect eddy-diffusivity parameterization models are utilized here. They demonstrate the important role of additional stochastic forcing of imperfect models in order to systematically improve the information theoretic measures of fidelity and sensitivity developed here.
coarse graining, inadequate resolution
Footnotes
1To whom correspondence should be addressed. E-mail:jonjon@cims.nyu.edu.
Author contributions: A.J.M. designed research; A.J.M. and B.G. performed research; and A.J.M. wrote the paper.
The authors declare no conflict of interest.
Freely available online through the PNAS open access option.
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