DA Theory and Mathematics

p1-14 January 21 15:10-16:10

Single-precision in 4D-Var: The impact of rounding errors on the tangent-linear and adjoint models

S. Hatfield (University of Oxford), P. Dueben (ECMWF), A. McRae (University of Oxford) and T. Palmer (University of Oxford)


The use of single-precision arithmetic has been found to deliver a 40% reduction of wall-clock time in the ECMWF model, compared with double-precision. Using single-precision would permit a larger ensemble size in the ensemble prediction system which may result in a higher forecast skill for no extra cost. However, single-precision in 4D-Var is as yet unexplored and there are potential issues with using single-precision in the tangent linear and adjoint models used for minimising the incremental 4D-Var cost function. Here we will present preliminary results of a precision reduction in an incremental 4D-Var data assimilation scheme applied to a two layer quasigeostrophic model with a conjugate gradient minimizer. We use the Object Oriented Prediction System (OOPS) of ECMWF. we will show how reducing precision increases the asymmetry between the tangent linear and adjoint models. We will discuss the loss of conjugacy of the search directions due to rounding errors, a standard problem that is exacerbated when using single-precision, and how to fix this. We will also discuss other relevant parameters such as the problem size and the condition number of the Hessian.

Contact information

Mr. Sam Hatfield University of Oxford