Data assimilation

Hannart A, Carrassi A, Bocquet M, Ghil M, Naveau P, Pulido M, Ruiz J, Tandeo P. DADA: data assimilation for the detection and attribution of weather and climate-related events. Climatic Change [Internet]. 2016;136 (2) :155–174. Publisher's VersionAbstract

We describe a new approach that allows for systematic causal attribution of weather and climate-related events, in near-real time. The method is designed so as to facilitate its implementation at meteorological centers by relying on data and methods that are routinely available when numerically forecasting the weather. We thus show that causal attribution can be obtained as a by-product of data assimilation procedures run on a daily basis to update numerical weather prediction (NWP) models with new atmospheric observations; hence, the proposed methodology can take advantage of the powerful computational and observational capacity of weather forecasting centers. We explain the theoretical rationale of this approach and sketch the most prominent features of a ``data assimilation–based detection and attribution'' (DADA) procedure. The proposal is illustrated in the context of the classical three-variable Lorenz model with additional forcing. The paper concludes by raising several theoretical and practical questions that need to be addressed to make the proposal operational within NWP centers.

Carrassi A, Ghil M, Trevisan A, Uboldi F. Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system. Chaos. 2008;18 (2) :023112.Abstract

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.

Ghil M, S. Coho JT, Bube K, Isaacson E. Dynamic Meteorology: Data Assimilation Methods. In: Bengtsson L, Ghil M, Källén E Applied Mathematical Sciences. Vol. 36. Dynamic Meteorology - Data Assimilation Methods. Springer-Verlag ; 1981. pp. 139–224.