Time-parallel incremental 4D-Var for two-dimensional rotating shallow water system

Bhatt, R. ORCID: https://orcid.org/0000-0001-7061-1817, Debreu, L. and Vidard, A. (2026) Time-parallel incremental 4D-Var for two-dimensional rotating shallow water system. Journal of Computational Physics, 564. 115164. ISSN 1090-2716 doi: 10.1016/j.jcp.2026.115164

Abstract/Summary

Incremental four-dimensional variational data assimilation (4D-Var) relies on repeated serial integrations of tangent-linear and adjoint models within its inner loop to minimize a cost function. While classical domain decomposition offers some spatial parallelism, it faces scalability issues as model resolution and complexity increase, motivating the need for effective time-parallel strategies. This study presents a practical approach for implementing a time-parallel incremental 4D-Var based on the Parareal algorithm applied to a two-dimensional rotating shallow water system. A Krylov-enhanced Parareal variant is introduced to improve convergence for relatively more hyperbolic problems and is coupled with an inexact conjugate gradient (CG) method that adaptively adjusts Parareal precision during minimization. Numerical experiments show that the proposed implementation attains the same minimization accuracy as standard CG while achieving a theoretical time-parallel speedup of about 6.8 when communication and implementation-specific overheads are neglected. In addition, the adaptive Parareal tolerance reduces the total Parareal iterations by roughly half relative to when standard CG is used with a fixed Parareal tolerance. Further inexact CG experiments under realistic observational settings demonstrate measurable wall-clock speedups and indicate that communication overhead and sequential adjoint integrations remain important limitations on achievable parallel efficiency. Diagnostics based on geostrophic balance confirm the dynamical consistency of the retrieved initial state, demonstrating the approach’s feasibility for moderately sized PDE-constrained optimization problems.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/130875
Identification Number/DOI	10.1016/j.jcp.2026.115164
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Elsevier
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