Abstract:

[Objective] Three-dimensional variational data assimilation is a core technique in numerical weather prediction. Traditional primal-form methods optimize in a high-dimensional control space and are therefore computationally expensive. Although the dual-form reduces the optimization dimension by solving in observation space, deploying it within the current GSI architecture still requires handling deep coupling in the legacy operator chain, numerical stability issues, and degraded discrete adjoint consistency. [Methods] This paper proposes a dual-form quasi-Newton framework based on the Unified Control Variable Transform, which reduces the optimization dimension by solving in observation space and achieves engineering deployment by reusing existing operator chains in a low-intrusive manner. [Results and Limitations] In a single regional 3D-Var configuration, the proposed dual-form solver achieves convergence behavior comparable to that of the primal-form quasi-Newton solver (lsqrt-qn) while delivering an overall 5.1× speedup; the L-BFGS curvature-history recursion is accelerated by 2600×. Relative to LS-PCG, the best-performing solver in the current operational configuration, the proposed solver is about 1.9× faster, with less than a 1% difference in cost-function reduction. However, its performance across a broader range of cases and different parameter settings still requires further evaluation. [Conclusions] These results show that the dual reduced-dimensional solver can be introduced into existing operational systems in a low-intrusive manner while preserving analysis quality and improving computational efficiency. This provides an engineering-feasible implementation for introducing dual reduced-dimensional solvers into existing operational systems.

Key words: 3D-Var, GSI, dual-form quasi-Newton method, unified control variable transform, low-intrusive integration