• Introduction
• Method and data
• Results
• Concluding remarks
• Acknowledgements
• References

1. Introduction

The degrees of isolation of the polar vortex of the stratosphere have been extensively discussed in relation to the ozone depletion problem by isentropic advection in which air parcels or material contours are advected by large-scale winds from objective analysis data sets (e.g., Haynes and Shuckburgh (2000) and references therein). Haynes and Shuckburgh (2000) has recently applied the effective diffusivity diagnostic introduced by Nakamura (1996) to an artificial "test tracer" field in order to identify barriers to transport and mixing regions not only for the "winter polar vortex-edge barrier" but also for the "sub-tropical barrier" in the stratosphere.

In this paper, we describe a method of objectively identifying barriers of the polar vortex edge to quasi-isentropic transport and of quantifying the permeability of the barriers on the basis of the time threshold diagnostics (TTD) developed by Sugata (2000) as a method of quasi-isentropic advection of air parcels. The method is applied to the polar vortex in the 1996/1997 Northern Hemisphere winter. The winter is well-known in that the polar vortex was maintained until the beginning of May, i.e., the Arctic polar vortex was stable and maintained abnormally long to bring about anomalously low ozone over the Arctic in March (e.g., Newman et al., 1997).

2. Method and data

The time threshold diagnostics (TTD) was developed for estimating effective flux of air parcels across given surfaces. The method considers the motion of an air parcel passing through a given surface and defines effective passages if the residence time of the parcel on one side of the surface before the passage and that of the other side after it are both larger than a specified time threshold. We use ECMWF meteorological analysis data of 2.5 * 2.5 degrees in geographic longitude and latitude, 15 levels between 1000-10 hPa, and 4 times per day.

Trajectory calculations using ECMWF horizontal and vertical (dp/dt) wind data are first done. Initially air parcels are set at 11 levels of 10 hPa-interval between 110 and 10 hPa with 10404 air parcels at each pressure level in the Northern Hemisphere (1-degree interval in latitude from 0 to 89 degrees North and 2-degree interval in longitude at the equator with weight of cosine of latitude in other latitudes). An air parcel thus represents the same weight of air mass. Positions (longitudes, latitudes, and pressures) of the air parcels, i.e., trajectories, are calculated by integration from the initial condition. We use a fourth-order Runge-Kutta-Gill scheme at a time step of 30 minutes by using wind data linearly interpolated in time from ECMWF wind data. The positions are archived at 6-hour interval as well as Ertel's potential vorticities and potential temperatures for every parcel. The trajectory calculations are carried out for one month such as December 1996, January, February, March, and April 1997. The time integration is started from 15 days before the beginning of each month and is extended to 15 days after the end of the month. The period of time integration should be less than a given period because density of air parcels may become too much inhomogeneous after the integration over the given period under some circumstances. We set one month as the given period empirically for this case. The addition of about 15 days before is necessary for the TTD method in this case because the critical value of TTD, i.e., the time threshold, is determined as a result after the trajectory calculation.

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

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.

Acknowledgements

This research is partially supported by the International Cooperative Study on Stratospheric Change and its Role in Climate of the Science and Technology Agency of Japan.

References

Haynes, P. and Shuckburgh, E. (2000): Effective diffusivity as a diagnostic of atmospheric transport. Part I: stratosphere. J. Geophys. Res, 105, D18, 22777-22794.

Kanzawa, H., Shiotani, M., Suzuki, M., Yokota T., and Sasano, Y. (2000): Structure of the polar vortex of the Arctic winter of 1996/1997 as analyzed from long-lived tracer data of ILAS and meteorological data. Quadrennial Ozone Symposium, Sapporo, Japan, 3-8 July 2000. (Proceedings: p.253-254)

Nakamura, N. (1996): Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate. J. Atmos. Sci., 53, 1524-1537.

Newman, P.A., Gleason, J.F., McPeters, R.D., and Stolarski, R.S. (1997): Anomalously low ozone over the Arctic. Geophys. Res. Lett, 2689-2692.

Sasano, Y., Suzuki, M., Yokota, T., and Kanzawa, H. (1999): Improved Limb Atmospheric Spectrometer (ILAS) for stratospheric ozone layer measurements by solar occultation technique. Geophys. Res. Lett., 26, No.2, 197-200.

Sugata, S. (2000): Time threshold diagnostics: A mixed Lagrangian-Eulerian method for describing global tracer transport. J. Meteorol. Soc. Japan, 78, No. 3, 258-277.