A prerequisite to studying phenomena in the winter stratospheric polar vortex is the separation of measurements inside and outside the dynamical barrier of the vortex edge. We describe a technique to accurately determine the inner edge of the vortex boundary region from measurements of potential temperature and a trace gas, such as N2O, and apply it to in situ aircraft and balloon measurements from the SOLVE/THESEO 2000 Arctic campaign. The method may be used to refine the Nash algorithm, which, due to the inherently coarser resolution of potential vorticity on which it is dependent, may misidentify the inner edge by more than 400 km and omit the identification of small, extravortex filaments within the vortex.
 In the stratosphere of each hemisphere during autumn, diminishing sunlight in the polar region induces a pressure gradient between the pole and midlatitudes, giving rise to increased circumpolar winds [Schoeberl and Hartmann, 1991]. The band of high winds, termed the polar night jet, forms a dynamical barrier to transport into the vortex [Hartmann et al., 1989; Schoeberl et al., 1992; Pierce et al., 1994]. The decreasing polar temperatures in autumn also create a downward motion of the polar air column, commonly called diabatic descent or subsidence [Schoeberl and Hartmann, 1991]. Both of these effects serve to produce a distinct contrast in air composition inside and outside the polar vortex. Under special circumstances, such as persistent tropospheric blocking [Plumb et al., 1994], material may occasionally cross into the vortex, and strong distortion of the vortex caused by planetary wave breaking can move material out of the vortex [e.g., Waugh et al., 1994; Konopka et al., 2002]. In general, however, a strong barrier exists between the vortex and the rest of the stratosphere.
 Determining the location of this transport barrier, or vortex edge, is important for many studies of polar ozone loss. The air inside the vortex contains levels of trace chemicals that are often substantially different from air outside the vortex in the midlatitude surf zone. This distinction is primarily caused by the physical isolation of the vortex, which may persist for many months. For example, chemical ozone loss occurring in the coldest regions of the stratosphere is often located within the polar vortex, so that high concentrations of ozone-destroying compounds, as well as low ozone levels, can be maintained because there is little opportunity for mixing with the rest of the atmosphere. Also, several km of subsidence over the winter produces a distribution of trace gases substantially different from air outside the vortex on the same potential temperature or theta (θ) surface [e.g., Loewenstein et al., 1989, 1990]. Without a reliable, accurate method of delineating the vortex edge, vortex studies may be compromised by extravortex data that have not been filtered out of a vortex data set.
 Ertel's potential vorticity (PV) is a quasi-conserved quantity [Holton, 1992] of great utility in analyzing the polar vortex. Basically a measure of the angular momentum of an air parcel, its magnitude is larger inside the vortex than outside, and it generally exhibits a strong gradient in the region of the polar night jet. Nash et al.  developed a method of defining the vortex edge using PV which has become widely accepted by the stratospheric research community. This method expresses PV as a function of equivalent latitude [Butchart and Remsberg, 1986], and then locates the vortex edge, referred to in our paper as the “middle” edge, by maximizing the product of the PV gradient and the average wind speed along PV isolines. Nash et al. also defined a vortex boundary region by the inflection points (second derivative extrema) in PV near the middle edge, which serve as “error bars” for the middle edge. In this paper, we refer to these points as the “inner” (poleward) and “outer” (equatorward) edges of the vortex boundary region.
 While the Nash method has proven to be fairly robust, it was intended primarily for determining the vortex edge in the context of a hemispheric picture. The resolutions of the analyzed PV and wind fields are limited, due to the sparse coverage of the observational radio sonde network; practical considerations lead to the choice of a fairly large grid size for reported PV data, typically 1 degree of latitude (110 km) or larger. Most other schemes for defining the vortex edge which have been employed [e.g., Loewenstein et al., 1990; Bauer et al., 1994; Gao et al., 2001] utilize PV in ways similar to Nash, and thus these approaches suffer from the same drawbacks. There are some ways to improve upon the resolution limitation by various trajectory methods [e.g., Plumb et al., 1994], but these still rely on wind fields which are assimilated from the same sparse network, and thus are susceptible to accumulated errors.
 Many atmospheric trace gases with large vertical gradients, such as N2O, CH4, CO2 and HF, exhibit significant changes in concentration across the vortex edge at altitudes typical of the NASA ER-2 research aircraft (∼20 km) [e.g., Loewenstein et al., 1989, 1990; Russell and Pierce, 2000]. As an example, Figure 1 shows the ER-2 flight of 11 March 2000, measured during the SOLVE/THESEO 2000 (Stratospheric Aerosol and Gas Experiment III (SAGE III) Ozone Loss and Validation Experiment/Third European Stratospheric Experiment on Ozone 2000) campaign. In black are 10-second average data points of N2O versus θ, taken from the unified N2O [Hurst et al., 2002] and the Meteorological Measurement System (MMS) [Scott et al, 1990; Gaines et al., 1992] data sets, respectively. In this flight, the ER-2 crossed from inside to outside the vortex relatively early in the flight, and spent most of the flight outside the vortex. Portrayed in N2O:θ coordinates, three phenomenologically distinct regions are apparent. On the left-hand side of Figure 1, a tight, essentially straight line correlation (above 370 K) is seen at the minimum N2O value for a given θ, typical of air within the polar vortex. Using the binning technique described below, we find that, for any given ER-2 flight from the winter of 1999/2000, the N2O on a constant θ surface inside the vortex has an average variability of ∼6 ppb. This compact relationship indicates that the air has been well mixed, the result of a long isolation time for this winter. On the right-hand side of Figure 1, a region of maximum N2O versus θ also forms a line, though it is much less compact. Air exhibiting this type of correlation originates from the midlatitude surf zone, where air is continually mixed over distances of thousands of kilometers, resulting in less homogeneity [Schoeberl and Hartmann, 1991]. The difference between the vortex and midlatitude correlations is understood to be the result of subsidence, whereby the vortex forms in the autumn from essentially midlatitude air, and undergoes substantial radiative cooling over the winter, causing the potential temperature of air parcels to drop [Schoeberl and Hartmann, 1991]. The third region comprises the space between these two limits, and its pattern is generally found in air near the vortex edge, illustrating the strongly inhomogeneous character of that region. This is the vortex boundary region referred to by Nash et al. .
 We see in the above example that air with even a small amount of midlatitude content will exhibit a detectable change from the vortex N2O:θ correlation. Thus it is possible to define a vortex edge based on deviations from a vortex tracer:θ correlation, which may be much more sensitive than the prediction of the Nash algorithm, because it is derived entirely from high-resolution measurements. In this paper, we choose N2O as our tracer, and examine the two vortex-crossing flights made by the NASA ER-2 aircraft during the SOLVE/THESEO 2000 campaign in the Arctic winter of 1999/2000. In addition, as an example, one intravortex flight is examined which exhibited significant filamentation; that is, small segments of the flight contained air whose N2O:θ correlations indicated significant midlatitude content.
 Our method consists of constructing a vortex “reference” N2O data set for each flight, called N2Ovor, which is based on the N2O:θ correlation from a profile measured on another flight which remained entirely inside the vortex, was free of filaments, and which occurred within a few days of the flight of interest. Such flights were readily available for the period we examined (January and March 2000). For flights which do not satisfy these criteria, there are several remedies which may be applied; these are discussed in the next section. For earlier periods of the winter, where recent vortex formation and possible differential diabatic descent [Pierce et al., 1994] may produce a less homogenous vortex, such a correlation may not be available, and in this case our technique may not be applicable.
 To distinguish between vortex and extravortex air in a given flight, the difference between the measured N2O and N2Ovor is examined. When the difference is smaller than a prescribed cutoff, the air is considered to be characteristic of vortex air. Once the vortex boundary region is entered, however, the difference rapidly increases, reflecting the mixing in of midlatitude air. The approach can be generalized to any trace gas measured with sufficient precision and time resolution, and whose correlation with θ is easily distinguishable between vortex and extravortex air, as illustrated in Figure 1.
 The edge defined by this N2O approach is sensitive to the inner edge of the vortex boundary region, where vortex air and midlatitude air begin to mix, rather than to the middle edge as defined by the Nash criterion. This is to be expected, as erosion by planetary wave breaking maintains a sharp distinction in tracer levels at the inner edge of the vortex boundary region [Schoeberl et al., 1992]. Thus, rather than comparing our N2O-derived edge directly with the Nash criterion's PV-derived middle edge, comparison is made with the Nash inner edge. It is expected that this inner edge may not be as robust as the middle edge, because it is calculated from the second derivative of PV, which is a less sharply peaked function, and more susceptible to noise, than the product of the PV gradient and the average wind speed [Nash et al., 1996]. However, the PV-derived inner edge is the quantity most directly comparable to the N2O-derived edge.
 The extension of this method to detect the outer edge of the vortex boundary region is difficult because of the considerable variation of N2O at a given θ in the midlatitudes. Hence the determination of a reference N2O:θ correlation is impracticable and was not attempted. The higher variation stems from transport of both tropical air, and occasionally polar air, into the midlatitude surf zone [Schoeberl and Hartmann, 1991].
 We will demonstrate that our method offers a considerable refinement of the Nash method for defining the vortex inner edge. It will also be shown that the method can be used to effectively detect filaments of midlatitude air within the vortex, as well as vortex filaments present outside the vortex; neither type of filament was distinguishable using the Nash method for the flights presented here. The main drawback of our technique is the limited spatial and temporal coverage of high-resolution tracer data in most winters, and in cases where tracer data are not available, the Nash criterion should still be used to specify the location of the vortex edge. However, for most ER-2 or balloon-based measurements, tracer data are almost always available in tandem with measurements of chemically active species. Thus, when separation of vortex and extravortex air parcels is required, we highly recommend using our tracer method as a refinement of, or in lieu of, the Nash criterion.
2. Data and Method
 For this study, we utilized unified N2O [Hurst et al., 2002], a derived SOLVE product based on data from the four N2O instruments on board the ER-2 (the Airborne Chromatograph for Atmospheric Trace Species IV (ACATS IV) [Elkins et al., 1996; Romashkin et al., 2001], the Aircraft Laser Infrared Absorption Spectrometer (ALIAS) [Webster et al., 1994], the Argus instrument [Jost et al., 1998], and the Whole Air Sampler (WAS) [Heidt et al., 1989; Schauffler et al., 1999]). Potential temperature (θ) was calculated from temperature and pressure measurements made by the onboard Meteorological Measurement System (MMS) instrument [Scott et al., 1990; Gaines et al., 1992]. Modified PV [Lait, 1994] maps and flight curtain data were supplied by the NASA Goddard Space Flight Center (GSFC) Atmospheric Chemistry and Dynamics Branch, using analyzed temperatures and winds from the NASA GSFC Data Assimilation Office (DAO) [Nash et al., 1996]. The hemispheric maps were represented on a 1° × 1° grid. The flight curtain data were created from aircraft flight tracks using bilinear interpolation in the two horizontal directions, and a log-pressure cubic spline fit in the vertical direction. All ER-2 flights originated from Kiruna, Sweden, located at 68°N, 20°E. The following ER-2 flights were employed for this study (date of flight given as yyyymmdd): 20000127 and 20000311, which crossed the vortex edge; 20000307, which did not cross outside the vortex but exhibited filamentation; and 20000312, which was used to generate N2Ovor for the 20000307 and 20000311 flights. In addition, N2O data were used from the University of Frankfurt, Germany cryosampler (BONBON) [Schmidt et al., 1987] on board a balloon payload launched from Esrange, Sweden (68°N, 21°E) on 20000127. Pressure and temperature associated with the BONBON flight were measured by onboard sensors operated by the Centre National d'Études Spatiales (CNES) and University of Frankfurt teams, respectively. BONBON data were used to create N2Ovor for the ER-2 flight of the same date.
 All ER-2 data were first binned into 10-s intervals so that N2O, θ and PV could be placed on the same time axis. The three quantities defined by the Nash method were expressed in terms of PV (the middle edge, hereafter PVmid, and the inner and outer edges of the vortex boundary region, hereafter PVin and PVout). These quantities were calculated for several θ surfaces, and then were linearly interpolated for every bin of the flight.
 Calculation of N2Ovor first required constructing an N2O:θ correlation curve from a “reference” flight, that is, a flight (1) whose correlation curve was approximately linear, indicating an absence of filaments; (2) which took place well within the vortex (PV > PVin according to the Nash criterion), so that the correlation would not be influenced by midlatitude air; and (3) which occurred within a few days of the flight of interest. For this last point, we have examined the 1999/2000 subsidence in detail in another paper [Greenblatt, et al., 2002]. The average change in θ between 23 January and 2 February 2000 was found to be 0.41 ± 0.34 K/day, or, using the mean slope of N2O:θ for January–March 2000 (2.0 ppb/K), 0.80 ± 0.68 ppb/day. Between 26 February and 12 March, the average rate was 0.10 ± 0.25 K/day, or 0.20 ± 0.50 ppb/day. Thus, compared with the average scatter within each N2O:θ correlation curve (∼6 ppb), differences of a few days between the reference flight and the flight of interest amounted to a negligible shift due to subsidence.
 All three criteria were satisfied for the flights described in this paper; however, if a flight does not satisfy the requirements, several remedies can be taken to utilize an imperfect flight. Segments of the flight which are deemed too close to the edge of the vortex can be removed, and if the remaining data span the range of θ values required, linear interpolation can be used to fill in the missing segments. This approach can also be used to remove filaments, though the binning technique described below generally removes the effects of small filaments by virtue of their relatively small contribution to the average. Another option is to combine data from several flights occurring close in time to construct a composite reference correlation. For the situation when there is no reference flight available close enough in time, it may be necessary to “evolve” a correlation curve using calculated heating rates, which can be obtained from a number of stratospheric chemical transport models [e.g., Rosenfield et al., 1994; Strahan et al., 1994; Chipperfield, 1999; Konopka et al., 2002].
 The reference correlation was constructed by one of two methods. For the ER-2 reference flight, N2O data (Figure 1, red symbols) were binned in 5 K θ intervals, and averaged using reported uncertainties as weights (Figure 1, blue symbols). In this way, minor filaments present in the data were excluded by virtue of their comparatively small contribution to the average. For the flight of 20000312, the maximum value of θ was 466 K, whereas the vortex-crossing flight of 20000311 reached 474 K. Thus, in order to extend the dynamic range of the reference correlation to represent these higher θ values, the section of the flight from 440 to 460 K was used to linearly extrapolate the correlation to 474 K (Figure 1, green line). For the reference flight using BONBON N2O (not shown), the reporting was sparse (up to 25 K separation between points) compared with the ER-2 data, so linear interpolation was used to generate an N2O value for each 5 K θ interval.
 To generate N2Ovor for the flight of interest, the measured θ for each bin of the flight was used to linearly interpolate an N2O value from the reference N2O:θ correlation curve. N2Ovor was physically interpreted to be the expected N2O level if that air mass were located deep inside the vortex.
 We chose the BONBON flight as the 20000127 reference because the data satisfied the requirements for a good reference better than all of the nearby ER-2 flights (five flights occurring within seven days of 20000127). However, we tried using four of these flights as references (20000123, which had several large filaments, was not used), with very similar results to BONBON: each predicted crossings of the inner edge which differed from the BONBON-based predictions by 60 s or less; at typical ER-2 cruise speeds (∼210 m s−1), this is about 13 km. We have examined the vortex portion of the 20000127 ER-2 flight against the BONBON flight, and found no substantial differences, indicating a well-mixed vortex in the regions sampled. We have also compared a BONBON flight on 20000301 with an ER-2 flight on 20000305, both of which took place within the vortex, and found excellent agreement between the two data sets, eliminating possible calibration offsets.
 To define the inner edge according to our method, a positive cutoff was established to apply to the difference ΔN2O = N2O − N2Ovor. We have chosen the 3-σ uncertainty in ΔN2O, which is the sum (in quadrature) of the uncertainties in N2O and N2Ovor, as our cutoff. This level, approximately 20 ppb for all flights, provides a conservative (>99% confidence limit), objective criterion for discrimination, and is successful in picking out the first major departure of ΔN2O from baseline noise very early in each transition (within a few tens of seconds in the flight track data) for the flights considered here.
3. Results and Discussion
 The flight of 20000127 is shown in Figure 2. In the top panel, N2Ovor appears in blue, and the measured N2O appears in black when ΔN2O = N2O − N2Ovor was below the cutoff value, and in red when it was above the cutoff. The bottom panel shows the two Nash quantities, PVin (blue) and PVmid (purple), and PV is shown in several colors, depending on its value relative to the Nash quantities. While we feel that the only relevant comparison to the N2O-derived edge is PVin, we have also included PVmid in all these plots for reference. Vertical dashed lines on both panels indicate where, according to our algorithm, a major crossing of the inner edge occurred.
 In this flight, the ER-2 took off from Kiruna, Sweden, and headed southeast into Russia. According to the PV profile, the ER-2 crossed PVin, the inner edge, at 36030 universal time (UT) s, and crossed PVmid, the middle edge, at ∼36200 UT s. Our method, however, indicates that N2O departed from N2Ovor briefly at 36600 UT s, followed by a more permanent departure at 36740 UT s. This second departure is indicated in Figure 2 by the vertical dashed line, and represents our best determination of the inner edge crossing. In the second half of the flight, the ER-2 turned around, performed a descent/ascent dip, and returned to Kiruna. The PV crossed PVmid several times from 47030 to 48450 UT s, before increasing above PVmid permanently at 48570 UT s; PV crossed PVin briefly at ∼48800 UT s and permanently increased above PVin at 49190 UT s. By contrast, ΔN2O dropped below the cutoff criterion at 46970 UT s, indicated by a second dashed line.
 There are additional departures of N2O above the cutoff level (indicated in red in Figure 2): one early in the flight, and several after the main return to the vortex. These features are correlated with anomalies in other tracer fields, such as CO2 (not shown). These departures could indicate air of mixed origin well within the vortex; a study by H.-J. Jost et al. (Mixing events revealed by anomalous tracer relationships in the Arctic vortex during winter 1999/2000, submitted to Journal of Geophysical Research, 2002) reported that midlatitude filaments are common in the vortex, appearing in ∼15% of the ER-2 flight data for SOLVE/THESEO 2000. However, the size of the deviations (∼15–25 ppb N2O) is much smaller than those encountered during the extravortex segments of the flights.
 This flight clearly shows the large time differences which can exist between the PVin-based and the N2O-based crossings: 710 s on the outbound leg of the flight, and 2220 s on the return leg, corresponding to ∼149 and ∼466 km, respectively, assuming that the ER-2 was traveling perpendicular to the vortex edge in this flight. These differences are significantly larger than the PV map grid size (∼110 km in latitude) from which PVin was calculated. In this flight, the use of PVin to determine the vortex region produces an overly conservative estimate of the vortex edge, resulting in the exclusion of about 500 km of vortex air. This is not necessarily an undesirable result, as it guarantees that only vortex air is included. However, the numerous segments tagged as midlatitude filaments by our method were not distinguishable using the Nash method, and therefore would still be included, contaminating the vortex data set.
 Differences between the PVmid-based and N2O-based crossing times are slightly smaller (540 and 1600 s, or about 113 and 336 km, respectively). Using PVmid as the vortex cutoff also results in a conservative estimate of the vortex edge for this flight, but with the same limitation of including midlatitude filaments as the PVin cutoff.
 We now discuss the second vortex-crossing flight of 20000311 (Figure 3). In this flight, the ER-2 ascended out of Kiruna and immediately headed southwest toward Scotland. The bottom panel shows that PV crossed PVin at 33240 UT s (with a small recrossing at 33410 UT s), and crossed PVmid at 33760 UT s, remaining at very low values until the latter half of the flight. The N2O method indicates that the ER-2 encountered a small, vortex edge filament at ∼32700 UT s, and crossed into the boundary region at 33060 UT s. After almost 30 min. of progress away from the inner edge, N2O rapidly rejoined N2Ovor for 430 s (∼90 km). This feature was not represented by the PV data, except perhaps as a small bump. However, the Lagrangian model CLaMS [Konopka et al., 2002] predicted a vortex filament at the location indicated by the N2O anomaly, attributed to shearing off of the outer layers of the polar vortex as a result of transport of air from low and midlatitudes into the polar region. Konopka et al. ultimately attributed this filament break-off to upper stratospheric warming events in February and March 2000, and, according to the CLaMS model, the lifetime of these filaments exceeded two weeks before they were mixed with the ambient air.
 After reaching the coast of Scotland, the ER-2 performed a profile dip, then turned back toward Scandinavia. N2O rejoined N2Ovor at 45710 UT s, where it remained for the duration of the flight. The Nash method showed PV crossing PVmid at 44800 UT s, and crossing PVin at 45130 UT s.
 The time differences between the N2O-based and PVin-based crossings are smaller than for 20000127: 180 and 580 s for the outbound and inbound legs, respectively, or ∼38 and ∼122 km. These distances are close to or below the intrinsic grid size of the PV maps, demonstrating that, for this flight, the sharp gradient in PV followed the gradient in N2O fairly well. The differences between the N2O-based and PVmid-based crossings are 700 and 910 s (∼147 km and ∼191 km), worse than for PVin, but not significantly different from those seen for PVmid in the 20000127 flight.
 Unlike the 20000127 flight, however, the use of PVin to determine the vortex region for the 20000311 flight would result in the inclusion of extravortex segments on both the inbound and outbound legs of the flight, and the use of PVmid would result in the inclusion of even more extravortex air parcels. Thus, in general, neither PVin nor PVmid can be used as a reliable PV cutoff level for the exclusion of midlatitude air parcels from a vortex data set. However, in the absence of adequate tracer data, PVin would still be a “safer” cutoff level to use than PVmid, resulting in less extravortex air parcels being included in a vortex data set.
Figure 4 shows the flight of 20000307, which, according to PV maps, remained within the vortex, inside the PVmid contour. In this flight, the ER-2 took off from Kiruna and flew east into Russia, then headed northwest, performed a descent/ascent dip, and finally returned south to Kiruna. On the top panel, showing N2O and N2Ovor, two large deviations are apparent on either side of the dip, from 43190 to 44020 UT s (a ∼174 km segment) and from 46170 to 46570 UT s (an ∼84 km segment). There are also two small regions in the same vicinity, as well as a region at the very beginning of the flight, which exceed the cutoff criterion. The PV, shown on the bottom panel, never crosses PVin, though it does approach the inner edge near 35500 UT s, and again near 45500 UT s. Thus, while the Nash method indicates that the ER-2 came close to the inner edge at a few points during the flight, it predicts a flight occurring entirely inside the vortex.
 The observed elevated levels of N2O (and other gases, such as O3, not shown) in the vortex for this flight are similar to those observed during the second Airborne Arctic Stratospheric Expedition (AASE 2). Model runs by Plumb et al.  using the contour advection with surgery (CAS) technique predicted intrusions of midlatitude air inside the vortex at locations where aircraft based instruments observed enhanced aerosol and N2O. Tracking these air masses back in the model showed that they were entrained into the vortex about six days earlier when the vortex was distorted by a strong ridge, and had formed two centers. A similar distortion of the vortex occurred at the end of February 2000, with, however, a much weaker second center, and was likely to be the source of the intrusions seen in the 20000307 flight. As shown by Plumb et al. , such features are generally too small to be revealed in PV maps. It appears that both phases of enhanced N2O observed in this flight belong to the same filament, sampled first on the ER-2 descent and again on ascent.
4. Summary and Conclusions
 We presented a tracer-based method of defining the inner edge of the vortex boundary region that offers a way of discriminating vortex from extravortex air based on high-resolution, in situ measurements. The high sensitivity of the technique is due to the large contrast of N2O across the vortex edge on a potential temperature surface. Agreement with the Nash inner edge defined by PV > PVin ranges from 180 to 2220 s or 38 to 466 km at ER-2 speeds, respectively. The sometimes large discrepancies between the two methods are most likely due to the limited resolution of the radio sonde network on which the PV calculations are based. The agreement between the Nash-derived middle edge (PVmid) commonly used in vortex studies and the inner edge as determined from our method is not much different in range (540–1600 s), though using PVmid as a vortex cutoff generally led to inclusion of more extravortex air parcels in a data set. This is expected, as the PVmid-based and N2O-based edges relate to different quantities, i.e., the middle of the vortex region and the innermost significant departure from a vortex N2O:θ correlation.
 Our method is also highly effective at detecting filaments of midlatitude origin, as shown for the flights of 20000127 and 20000307, as well as vortex filaments existing outside the main vortex, demonstrated on the vortex edge-crossing flight of 2000311. The Nash criterion is not sensitive to these cases.
 The Nash criterion as applied to analyzed PV is entirely adequate for identification of the vortex edge on a large scale, such as in hemispheric maps. However, it is not always reliable for delineating vortex from extravortex air parcels in high-resolution data sets: we have shown that even when the conservative inner edge of the Nash criterion (PV > PVin) is used, extravortex air parcels were still included in the resulting data set. Therefore, when high-resolution tracer data are available, and when a vortex reference tracer:θ correlation as described in this paper can be determined, we recommend the use of our technique to exclude extravortex segments from flight data. In the absence of such data, the Nash criterion might be used to remove extravortex segments, but this approach is not a guarantee that such segments will be excluded, and therefore extreme caution should be exercised.
 We are indebted to Michael Kurylo and Phil DeCola (NASA Headquarters) for providing funding for our participation in SOLVE/THESEO 2000. J. B. Greenblatt is grateful for funds provided by the National Research Council, which made his research at NASA Ames possible. Thanks go to Jeff Grose (NASA Ames) for his expertise in all aspects of the Argus instrument operations. We are grateful to Katja Drdla and Anthony Strawa (NASA Ames) for reading an early draft of this paper. We thank Paul Konopka (Forschungszentrum Jülich) for interpretation of the extravortex filament encounter of 20000311, and we appreciated the suggestions of Eric Nash (NASA Goddard), which helped to strengthen our explanation of the Nash method. Thanks also to Ross Salawitch (Caltech/JPL) for providing the initial motivation to pursue the technique described herein.