On time-parallel preconditioning for the state formulation of incremental weak constraint 4D-Var

Abstract

Using a high degree of parallelism is essential to perform data assimilation efficiently. The state formulation of the incremental weak constraint four-dimensional variational data assimilation method allows parallel calculations in the time dimension. In this approach, the solution is approximated by minimising a series of quadratic cost functions using the conjugate gradient method. To use this method in practice, effective preconditioning strategies that maintain the potential for parallel calculations are needed. We examine approximations to the control variable transform (CVT) technique when the latter is beneficial. The new strategy employs a randomised singular value decomposition and retains the potential for parallelism in the time domain. Numerical results for the Lorenz 96 model show that this approach accelerates the minimisation in the first few iterations, with better results when CVT performs well.

arXiv comment12 pages, 5 figures

References in corpus (4)

• On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
• Enhanced parallelization of the incremental 4D-Var data assimilation algorithm using the Randomized Incremental Optimal Technique (RIOT)
• A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
• Randomised preconditioning for the forcing formulation of weak constraint 4D-Var