Single-precision in the tangent-linear and adjoint models of incremental 4D-VAr

Journal article

The use of single-precision arithmetic in ECMWF’s forecasting model gave a 40% reduction in wall-clock time over double-precision, with no decrease in forecast quality. However, using reduced-precision in 4D-Var data assimilation is relatively unexplored and there are potential issues with using single-precision in the tangent-linear and adjoint models. Here, we present the results of reducing numerical precision in an incremental 4D-Var data assimilation scheme, with an underlying two-layer quasigeostrophic model. The minimizer used is the conjugate gradient method. We show how reducing precision increases the asymmetry between the tangent-linear and adjoint models. For ill-conditioned problems, this leads to a loss of orthogonality among the residuals of the conjugate gradient algorithm, which slows the convergence of the minimization procedure. However, we also show that a standard technique, reorthogonalization, eliminates these issues and therefore could allow the use of single-precision arithmetic. This work is carried out within ECMWF’s data assimilation framework, the Object Oriented Prediction System.

Authors: Hatfield, S; McRae, A; Palmer, T; Düben, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Meteorological Society
• Journal: Monthly Weather Review
• Volume: 148
• Issue: 4
• Pages: 1541-1552
• Publication date: 2020-03-26
• Acceptance date: 2019-12-17
• DOI: 10.1175/MWR-D-19-0291.1
• EISSN: 1520-0493
• ISSN: 0027-0644
• Language: English
• Keywords: optimization; algorithms; data assimilation; FFR; variational analysis