Sensitivity of global mixing and fluxes to isolated transport barriers

Effects of isolated transport barriers on the global mixing and fluxes of a tracer are investigated, where a barrier is defined as a local minimum in effective diffusivity. An idealized 1D model with a prescribed diffusivity profile, with or without forcing, is used to show that the structure, flux, and decay rates of the tracer are all very sensitive to the barrier geometry, particularly when it is deep and narrow. Although the tracer gradients and the variance dissipation are concentrated to the barrier region, the flux shows a more global response to the barrier, decreasing everywhere. The harmonic mean of effective diffusivity is proposed as a useful first-order predictor of the global transport. This 1D model is used to diagnose the isentropic transport in the upper troposphere and lower stratosphere with offline transport calculations driven by the Met Office winds. The global tracer variance in these calculations decays approximately exponentially, and the time-mean decay rate and tracer structure are well captured by the gravest 1D eigenmode with the time-averaged effective diffusivity. However, the decay rate and the flux of the full solution are 15%-20% smaller than those of the eigenmode because of a negative temporal correlation between the effective diffusivity and the gradient. The vertical and decadal variations of the decay rates are consistent with the corresponding variations in the harmonic mean effective diffusivity. To the extent that the global mixing is sensitive to the local barrier properties, and to the extent that the latter are sensitive to the errors in advecting winds and model numerics, modeling of global atmospheric transport remains a challenge. This may explain, at least partially, the disparate model estimates reported in the literature.