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3. Results

3.1 Edge latitude and time threshold

The results are described in potential temperature than in pressure as a vertical coordinate. The lower boundary is set at 450 K and the upper boundary is at 650 K. The equivalent latitude on the basis of Ertel's potential vorticity is used as a latitude coordinate. An analysis of absolute sum of southward and northward effective fluxes at 1-degree interval equivalent latitude from 56 to 76 degrees North in number of air parcels per day and in per cent per day of the total number of air parcels northward of the latitude for the time threshold of 1 day, 2 days, 3 days, 5 days, 7 days, 11 days, and 15 days is made. Minimum fluxes of the absolute sum are seen around 66-degree equivalent latitude for the time threshold larger than 5 or 7 days. Minimum values of the northward flux are seen at latitude a few degrees lower than those of the southward flux. The TTD method thus identifies the barriers of quasi-isentropic transport as the region of the minimum effective flux.

The polar vortex edge is thus determined as the surface of in degrees of equivalent latitude, which is approximately 3.3*10^-5 K m²/kg/s of Ertel's potential vorticity at 450 K potential temperature, from the TTD result. An analysis of the sum of absolute values of southward and northward effective fluxes as a function of the time threshold values shows that the sum decreases as the time threshold becomes larger than around 5 or 7 days.

Hereafter we adopt the 66-degree equivalent latitude as the polar vortex edge and 7 days as the time threshold of TTD.

3.2 Temporal variation of effective fluxes

An analysis of temporal variation of southward and northward effective fluxes at the edge of 66-degree equivalent latitude in per cent of the total number of air parcels northward of the edge for 450-650 K layer shows low effective fluxes during the period from about day 40 through day 100. Table 1 shows a summary of the results. Northward flux is larger than southward flux in December 1996 and January 1997 when the vortex was developing while vice versa in April when the vortex is gradually becoming unstable: This is reasonable.

3.3 Quiet period in March 1997

As shown in Table 1, the effective flux toward the outside of the edge (southward flux) is 0.25 %/day and that toward the inside (northward flux) is 0.2 %/day in March 1997 where the percentage is defined against the total volume of the polar vortex air within the edge boundary. The characteristic vortex filling time is thus estimated to be over 1 year in March, which indicates strong isolation of the polar vortex.

3.4 Mixing period in April 1997

The positions of the air parcels identified as effective passages across the 66-degree equivalent latitude are plotted on Ertel's potential vorticity (PV) maps at 500 K potential temperature at 6-hour interval in normal geographic coordinate. The analysis shows that episodic events of southward fluxes occurred associated with protrusion of a tongue of PV contours outward from the polar vortex around 12-15 April over north of Japan and around 17-19 April over Eastern Europe. Northward flux events are not clearly associated with intrusion of a tongue into the polar vortex.

Table 1 Effective flux of northward (inward to the polar vortex) and southward (outward from the polar vortex) at the 66-degree equivalent latitude in per cent (%) of the total number of the parcels northward of 66-degree per day for the potential temperature layer of 450-650 K in the lower stratosphere as a function of periods of 5 months and each month with the beginning, middle, and end oh each month.



	Period				Effective Flux
			Northward	(%/day)		Southward	(%/day)
Dec 1996	Apr 1997	(5 months)	0.67			0.48
Dec 1996	1-31		1.60			0.76
		1-10		1.85			0.74
		11-20		1.29			11-20
		21-31		1.65			0.77
Jan 1997	1-31		0.84			0.53
		1-10		1.08			0.55
		11-20		0.31			0.25
		21-31		1.09			0.77
Feb	1-28		0.38			0.30
		1-10		0.53			0.44
		11-20		0.22			0.23
		21-28		0.40			0.21
Mar	1-31		0.20			0.25
		1-10		0.14			0.28
		11-20		0.20			0.30
		21-31		0.25			0.17
Apr	1-31		0.31			0.54
		1-10		0.10			0.21
		11-20		0.56			1.13
		21-30		0.27			0.28

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