  Semi-implicit 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. The essential components of a
representative elliptic solver are run at precision levels as low as half (16
bits), and accompanied with a detailed evaluation of the impact of reduced
precision on the solver convergence and the solution quality.
  A detailed inquiry into reduced precision requires a model configuration that
is meaningful but cheaper to run and easier to evaluate than full
atmosphere/ocean models. This study is therefore conducted in the context of a
novel semi-implicit shallow-water model on the sphere, purposely designed to
mimic numerical intricacies of modern all-scale weather and climate (W&C)
models with the numerical stability independent on celerity of all wave
motions. 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 solver GCR, proven in advanced atmospheric applications. The
classical longitude/latitude grid is deliberately chosen to retain the
stiffness of global W&C models posed in thin spherical shells as well as to
better understand the performance of reduced-precision arithmetic in the
vicinity of grid singularities. Precision reduction is done on a software
level, using an emulator. The reduced-precision experiments are conducted for
established dynamical-core test-cases, like the Rossby-Haurwitz wave number 4
and a zonal orographic flow.
  The study shows that selected key components of the elliptic solver, most
prominently the preconditioning, can be performed at the level of half
precision.
