  In recent years, it has been convincingly shown that weather forecasting
models can be run in single-precision arithmetic. Several models or components
thereof have been tested with even lower precision than this. This previous
work has largely focused on the main nonlinear `forward' model. A nonlinear
model (in weather forecasting or otherwise) can have corresponding tangent
linear and adjoint models, which are used in 4D variational data assimilation.
The linearised models are plausibly far more sensitive to reductions in
numerical precision since unbounded error growth can occur with no possibility
of nonlinear saturation. In this paper, we present a geophysical experiment
that makes use of an adjoint model to calculate sensitivities and perform
optimisation. Using software emulation, we investigate the effect of degrading
the numerical precision of the adjoint model. We find that reasonable results
are obtained with as few as 10 significand bits, equal to the significand
precision in the IEEE half-precision standard.
