The Relationship between Numerical Precision and Forecast Lead Time in the Lorenz’95 System

Abstract

Abstract We test the impact of changing numerical precision upon forecasts using the chaotic Lorenz’95 system. We find that in comparison with discretization and numerical rounding errors, the dominant source of errors are the initial condition errors. These initial condition errors introduced into the Lorenz’95 system grow exponentially at a rate according to the leading Lyapunov exponent. Given this information we show that the number of bits necessary to represent the system state can be reduced linearly in time without significantly affecting forecast skill. This is in addition to any initial reduction in precision to that of the initial conditions and also implies the potential to reduce some storage costs. An approach to vary precision locally within simulations, guided by the direction of eigenvectors of the growth and decay of forecast error (the “singular vectors”), did not show a satisfying impact upon forecast skill in relation to cost savings that could be achieved with a uniform reduction of precision. The error in a selection of ECMWF forecasts as a function of the number of bits used to store them indicates that precision might also be reduced in operational systems.