Block Krylov methods for accelerating ensembles of variational data assimilations

Mercier, François ; Gürol, Selime ; Jolivet, Pierre ; Michel, Yann ; Montmerle, Thibaut

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We consider the problem of efficiently solving ensembles of variational data assimilations in the context of numerical weather prediction. Running several assimilations notably allows to initialize ensemble prediction systems and to more accurately represent background error statistics, but is computationally expensive, limiting ensemble size. We propose a new class of algorithms for speeding up the minimization of the ensemble of data assimilations. It consists in using block Krylov methods to simultaneously perform the minimization for all members of the ensemble, instead of performing each minimization separately. We develop preconditioned block Krylov versions of the Full Orthogonal Method and of the Lanczos algorithm in both primal and dual space. The latter works in observation space that is usually of smaller dimension than the state space, giving thus an advantage in terms of memory requirements and computational cost. We describe and compare several parallelization strategies for speeding up the minimization and limiting the communications. These methods have been tested on a Quasi-Geostrophic system, consisting of a simplified atmospheric circulation model equipped with an ensemble of 3DVar schemes tuned to mimic some features of a limited area numerical weather prediction system. Experimentation shows that the number of iterations needed to converge is drastically reduced by the block Krylov approaches. We indicate that, while working in primal space does not allow to save significant computational time, working in the dual space may reduce the computational time by a factor 2-5 depending on ensemble size compared to standard Krylov methods, making our approach attractive for operational use.
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