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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.

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