Using local dynamics to explain analog forecasting of chaotic systems

Abstract

Analogs are nearest neighbors of the state of a system. By using analogs and their successors in time, one is able to produce empirical forecasts. Several analog forecasting methods have been used in atmospheric applications and tested on well-known dynamical systems. Although efficient in practice, theoretical connections between analog methods and dynamical systems have been overlooked. Analog forecasting can be related to the real dynamical equations of the system of interest. This study investigates the properties of different analog forecasting strategies by taking local approximations of the system's dynamics. We find that analog forecasting performances are highly linked to the local Jacobian matrix of the flow map, and that analog forecasting combined with linear regression allows to capture projections of this Jacobian matrix. The proposed methodology allows to estimate analog forecasting errors, and to compare different analog methods. These results are derived analytically and tested numerically on two simple chaotic dynamical systems.

arXiv commentArticle submitted to the Journal of Atmospheric Sciences

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Cited by in corpus (4)

• Probability distributions for analog-to-target distances
• Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification
• Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain
• Data-driven methods to estimate the committor function in conceptual ocean models