Efficient parameter estimation for a highly chaotic system

Abstract

We present a practical, efficient and powerful solution to the problem of parameter estimation in highly non-linear models. The method is based on the ensemble Kalman filter, and has previously been successfully applied to a simple climate model with steady-state dynamics. We demonstrate, via application to the well-known Lorenz model, that the method can successfully perform multivariate parameter estimation even in the presence of chaotic dynamics. Traditional variational methods using an adjoint model have limited applicability to problems of this nature, and the alternative of a brute force (or randomized) search in parameter space is prohibitively expensive for high-dimensional applications. The cost of our method is comparable to that of integrating an ensemble to statistical convergence, and therefore this technique appears to be ideally suited for probabilistic climate prediction.