Ensemble Riemannian data assimilation: towards large-scale dynamical systems

Abstract. This paper presents the results of ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) atmospheric circulation. The analysis state in this approach is inferred from joint distribution that optimally couples background probability likelihood function, enabling formal treatment systematic biases without any Gaussian assumptions. Despite risk curse dimensionality computation coupling distribution, comparisons with classic implementation particle filter stochastic Kalman demonstrate that, same size, presented methodology could improve predictability systems. In particular, under errors, root mean squared error can be reduced by 20 % (30 %) model.