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4. Concluding remarks

The TTD method as used in the paper seems to have some advantages over other techniques. For example, the TTD can identify the regions of barriers and mixing regions. The TTD can give air parcel exchange rate across given surfaces in quantitative manner. The times and locations of the passages judged as effective can be traced. The results depend little on the initial conditions: For example, the results at a time after integration from a start 10 days before are similar to those from a start 20 days before.

On the other hand, the TTD method seems to have some disadvantages. The determination of the time threshold is not rigorously objective but empirical. The physical meaning of the values of the time threshold, for example, 7 days in this case, should be pursued. The given surface for the TTD should be selected depending on purposes. We selected potential vorticity equivalent latitude in this case. The selection might not be appropriate for quasi-isentropic transport problem in some cases.

Future works along the line of this research may include the followings. The analysis for the 1997 Arctic winter will be continued to have comprehensive results. The extended results from TTD will be combined with the extension of estimate of descent rate in the polar vortex by Kanzawa et al. (2000) on the basis of long-lived tracer data of satellite sensor ILAS (Sasano et al., 1999): It will give an integrated view of the Arctic polar vortex of 1997. The TTD method will also be applied to the Antarctic vortices to identify the differences of the Antarctic vortex and the 1997 Arctic vortex which is considered to be similar to the Antarctic one, and other Arctic vortices to investigate their interannual variability. The TTD method might be applicable also to other important issues such as the "sub-tropical barriers" and tropopause exchanges.

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