Combining Analog Method and Ensemble Data Assimilation: Application to the Lorenz-63 Chaotic System

Nowadays, ocean and atmosphere sciences face a deluge of data from space, in situ monitoring as well as numerical simulations. The availability of these different data sources offers new opportunities, still largely underexploited, to improve the understanding, modeling, and reconstruction of geophysical dynamics. The classical way to reconstruct the space-time variations of a geophysical system from observations relies on data assimilation methods using multiple runs of the known dynamical model. This classical framework may have severe limitations including its computational cost, the lack of adequacy of the model with observed data, and modeling uncertainties. In this paper, we explore an alternative approach and develop a fully data-driven framework, which combines machine learning and statistical sampling to simulate the dynamics of complex system. As a proof concept, we address the assimilation of the chaotic Lorenz-63 model. We demonstrate that a nonparametric sampler from a catalog of historical datasets, namely, a nearest neighbor or analog sampler, combined with a classical stochastic data assimilation scheme, the ensemble Kalman filter and smoother, reaches state-of-the-art performances, without online evaluations of the physical model.