Mixed‐Precision for Linear Solvers in Global Geophysical Flows.

Semi‐implicit (SI) time‐stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision arithmetic in the elliptic solvers. Precision levels as low as half (16 bits) are used and a detailed evaluation of the impact of reduced precision on the solver convergence and the solution quality is performed. This study is conducted in the context of a novel SI shallow‐water model on the sphere, purposely designed to mimic numerical intricacies of modern all‐scale weather and climate (W&C) models. The governing algorithm of the shallow‐water model is based on the non‐oscillatory MPDATA methods for geophysical flows, whereas the resulting elliptic problem employs a strongly preconditioned non‐symmetric Krylov‐subspace Generalized Conjugated‐Residual (GCR) solver, proven in advanced atmospheric applications. The classical longitude/latitude grid is deliberately chosen to retain the stiffness of global W&C models. The analysis of the precision reduction is done on a software level, using an emulator, whereas the performance is measured on actual reduced precision hardware. The reduced‐precision experiments are conducted for established dynamical‐core test‐cases, like the Rossby‐Haurwitz wavenumber 4 and a zonal orographic flow. The study shows that selected key components of the elliptic solver, most prominently the preconditioning and the application of the linear operator, can be performed at the level of half precision. For these components, the use of half precision is found to yield a speed‐up of a factor 4 compared to double precision for a wide range of problem sizes. Plain Language Summary: Numerical models of the Earth system are very important to predict weather and climate (W&C). The models are computationally expensive and run on supercomputers. If the models are enabled to run faster, model simulations can be enhanced—for example, via a higher resolution—and the accuracy of predictions can be improved. One way to enable the models to run faster is via the use of very low numerical precision. For example, via the use of so‐called half precision which is representing all variables of the simulation with only 16 bits, instead of the default value of 64 bits, reducing computational time by up to a factor of four. In this paper, we investigate whether numerical precision can be reduced down to half precision for parts of the linear solvers which are used in some W&C models. Linear solvers help to progress the model state in time and are responsible for a large fraction of the overall computational cost of model simulations. Key Points: A detailed study of mixed‐precision for linear solvers for weather and climate models is performed, including half precision with 16 bitsPrecision can be reduced in important parts of the solver but a naive approach to reduce precision everywhere does not workCompute time can be reduced by a factor four compared to double precision for parts that work in half precision [ABSTRACT FROM AUTHOR]