The sensitivity of a model's stratospheric tape recorder to the choice of advection scheme

The sensitivity of a climate model's transport to the choice of numerical advection scheme is investigated using simulations of the stratospheric tape recorder. Significant differences are found between tracers advected with the Heun scheme (with centred spatial differencing) and tracers advected with a flux-limited total variation diminishing (TVD) scheme. The tape recorder simulated by the TVD scheme propagates upwards unrealistically fast: about three times faster than the tape recorder of the Heun scheme, even though the winds are identical. In contrast, the amplitude of the TVD scheme's tape recorder is more realistic than that of the Heun scheme, which is too strong in the middle stratosphere. Further off-line tracer experiments, using a family of conservative, upwind advection schemes, demonstrate how the tape: recorder's phase speed decreases as the order of the polynomial representing the tracer's subgrid variation is increased. It is found that schemes with more implicit vertical diffusion than a quasi third-order scheme produce a tape recorder with unacceptably fast upwards propagation. The sensitivity can only be reproduced in a one-dimensional model when winds with strong variability are used, highlighting a limitation of the traditional advection tests that use constant winds. The experiments also show that the numerical oscillations produced by non-monotonic methods, including the Heun scheme, can artificially strengthen the tape-recorder signal resulting in a unrealistic lack of attenuation with height. Finally, a full climate simulation using a higher-order, monotonic advection scheme is found to produce a tape recorder that is reasonably realistic, both in speed and amplitude.