Quart. J. Roy. Met. Soc. (1999), 125, 635-655.
Five methods of diagnosing the synoptic-scale mass exchange across the tropopause are investigated and compared with each other. Three of them are derived from Wei's (1987) general formula using pressure, potential temperature, and potential vorticity as vertical coordinates. The fourth method involves the computation of a large number of trajectories. The fifth method evaluates the flux directly as the difference between the motion of the air and the motion of the tropopause. The methods are tested in the context of a case study. An episode with strong convective heating in a decaying cut-off cyclone was selected. A consistent data set was obtained through a special ECMWF-model run with enhanced output storage.
There was a large cross-tropopause mass exchange during the episode. It is found that the different diagnostic methods yield quite different results. Those versions of Wei's formula which predominantly draw on standard information like wind, temperature and pressure turn out to be unreliable, as they suffer from strong cancellation of large terms. Tests with the direct technique reveal that the problem lies in the lack of consistency between the model data and the diagnosed location of the tropopause. The amount of cancellation is substantially reduced when full use is made of model information about the non-conservative fields in Wei's general formula with potential vorticity as vertical coordinate. This formulation also allows a straightforward interpretation of the net flux in terms of individual physical processes. The trajectory method, which does not require information about the nonconservative fields, also yields reasonable estimates for the cross-tropopause mass flux. The problems with the different methods and their differences show up especially clearly in a second model run in which all non-conservative processes are switched off.