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

TL;DR

This paper introduces a parallelizable preconditioning strategy using randomized SVD for the incremental weak constraint 4D-Var data assimilation, improving convergence speed in the Lorenz 96 model.

Contribution

It proposes a novel time-parallel preconditioning method employing randomized SVD to enhance the efficiency of incremental weak constraint 4D-Var.

Findings

Accelerates minimization in initial iterations

Retains parallelism in the time domain

Improves results when CVT is effective

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.