Ozone observations made by the Airborne Raman Ozone, Temperature, and Aerosol Lidar (AROTEL) and Differential Absorption Lidar (DIAL) on board the NASA DC-8 aircraft, the NOAA in situ instrument on board the NASA ER-2 aircraft, and Third European Stratospheric Experiment on Ozone 2000 (THESEO 2000) ozonesondes are analyzed by applying a quasi-conservative coordinate mapping technique. Measurements from the late winter/early spring SAGE III Ozone Loss and Validation Experiment (SOLVE) period (January through March 2000) are incorporated into a time-varying composite field in a potential vorticity-potential temperature coordinate space; ozone loss rates are calculated both with and without diabatic effects. The average loss rate from mid-January to mid-March near the 450 K isentropic surface in the polar vortex is found to be approximately 0.03 ppmv/d.
 Since the discovery of the Antarctic ozone hole by Farman et al. , stratospheric researchers have monitored the ozone layer, watching for signs of similar chemical processes over the Arctic regions. To detect ozone loss, researchers have collected and analyzed measurements from satellite instruments such as the Total Ozone Mapping Spectrometer (TOMS) [e.g., Newman et al., 1997] and Microwave Limb Sounder (MLS) [e.g., Manney et al., 1997]. Just as important, however, have been data from American and European field experiments such as the Airborne Arctic Stratospheric Expeditions (AASE I and II) and the European Arctic Stratospheric Ozone Experiment (EASOE), as outlined by Turco et al. , Rodriguez , and Pyle et al. , respectively. Measurements from such experiments typically involve a large number of species from relevant families of atmospheric constituents, and these data—frequently of high spatial and temporal resolution—enable a fairly detailed understanding of the chemical processes associated with stratospheric ozone loss [see, for example, Salawitch et al., 1993].
 During the winter of 1999–2000, the SAGE III Ozone Loss and Validation Experiment (SOLVE) was carried out simultaneously with the Third European Stratospheric Experiment on Ozone 2000 (THESEO 2000) campaign. Meteorological and trace gas constituent data were collected by many different in situ and remote sensing instruments. These included measurements of stratospheric ozone by airborne lidars, an airborne UV-absorption photometer, and ozonesondes.
 Given the variety of ozone measurements taken by different instruments at different times and scattered locations, it is desirable to put these data into a consistent wide-scale meteorological framework. As outlined by Schoeberl and Lait , constituent mapping using quasi-conserved coordinates can be a useful technique for this purpose. A composite field of trace gas constituent measurements is constructed in a vortex-relative coordinate system using potential vorticity (PV) and potential temperature (θ) as abscissa and ordinate, respectively. Then, given gridded meteorological fields of PV and θ, one can map the composite into real space, creating a three-dimensional field of the reconstructed constituent. Schoeberl et al.  and Lait et al.  demonstrated examples of this “PV-θ” technique. Related techniques have been employed by Manney et al. , Lary et al. , and Kyrö et al. .
 In this paper, we refine the PV-θ technique and use it to investigate ozone depletion observed during the late winter/early spring of 2000. Section 2 describes the data used in this analysis, and section 3 describes the enhanced technique. Results are presented in section 4, and the conclusions follow.
2.1. Meteorological Data
 PV-θ analysis requires that each measurement be associated with a value of PV and θ, and PV at least must be obtained from gridded meteorological analyses. Three sources of such analyses were used for this work. The NASA Goddard Space Flight Center's Data Assimilation Office (DAO) product for the SOLVE period is obtained from their GEOS-3 assimilation system for EOS-Terra support. GEOS-3 is the successor to the GEOS-1 system documented by Pfaendtner et al. . These data grids extend from 1000 to 0.2 hPa, have a horizontal resolution of 1° longitude by 1° latitude, and are produced four times daily.
 The United Kingdom Meteorological Office (UKMO) product generated for the Upper Atmosphere Research Satellite (UARS) project is another assimilation effort, described by Swinbank and O'Neil . The data used here extend from 1000 to 0.4 hPa, have a horizontal resolution of 3.75° longitude by 2.5° latitude, and are produced once per day.
 The third source of meteorological data used here is from the long-term assimilation performed by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). The procedures of the NCEP/NCAR reanalysis system are applied consistently to over 40 years of raw data, resulting in a data set which is useful for long-term studies (for further information, see Kalnay et al. ). These data extend from 1000 to 10 hPa, have a horizontal resolution of 2.5° longitude by 2.5° latitude, and are produced four times daily.
 To account for diabatic effects, heating rates were calculated from the UKMO analyses using the model described by Rosenfield et al. .
2.2. Ozone Data
 SOLVE consisted of three deployments: 2–14 December 1999; 10 January to 3 February 2000; and 26 February to 16 March 2000. During these periods, the NASA DC-8 and ER-2 aircraft flew numerous sorties out of Kiruna, Sweden.
 On board the ER-2, a dual beam UV-absorption photometer measured ozone volume mixing ratios at flight altitudes (above 18 km). Proffitt and McLaughlin  describe the instrument. These data are well-calibrated and of good accuracy (around 3%). And at one measurement per second on an aircraft moving at approximately 200 m/s, they have high spatial and temporal resolution. However, their coverage is limited to the actual position of the aircraft.
 In contrast, two lidar instruments on board the DC-8 measured profiles of ozone above the aircraft well into the stratosphere. The UV Differential Absorption Lidar (DIAL) measurements have a vertical resolution of approximately 750 m and are taken at least 5 min apart (giving a horizontal resolution of up to 70 km). DIAL profiles reach to 25 or 30 km. DIAL measures ozone number densities, and the DAO analyzed temperatures are used to convert these to volume mixing ratios. See Browell et al.  for further description of the instrument.
 The Airborne Raman Ozone, Temperature, and Aerosol Lidar (AROTEL) uses Rayleigh and Raman scattering to obtain temperature and ozone profiles with a vertical resolution of 0.5 to 1.5 km and which are taken at least 2 min apart (giving a horizontal resolution of up to 24 km). AROTEL profiles reach up to 35 to 40 km. Like DIAL, AROTEL obtains ozone number densities, but AROTEL uses its own temperature measurements to convert to volume mixing ratios (J. Burris, personal communication).
 These three aircraft-based instruments provide stratospheric ozone measurements of high resolution along their flight tracks which cut cross large areas of the Arctic between Greenland and Novaya Zemlya. They are limited to flight days within the three SOLVE deployment periods, however.
 Ozonesondes launched by the THESEO 2000 campaign, the Meteorological Service of Canada, the World Meteorological Organization network, Japan, and Russia measured profiles at a number of sites in the Arctic. Using an electrochemical concentration cell, these instruments take measurements with a vertical resolution between 60 and 150 m and typically reach up to around 30 km. Although the launch sites are geographically sparse, these profiles exist for nearly every day of the period examined here.
 PV was obtained from the meteorological analysis closest in time to each measurement by interpolating the gridded field bilinearly in the horizontal and using cubic spline interpolation in log-pressure for the vertical. The lidar instruments' profiles are a function of geometric height above the aircraft; the analyzed geopotential heights on pressure surfaces were converted to geometric heights and used to obtain the pressure of each measurement along the flight track. Modified PV [Lait, 1994] was used to avoid the strong vertical scaling exhibited by regular Ertel's PV. For consistency, the θ values were similarly interpolated from the meteorological analyses, even for instruments which measured temperature.
 A time-varying ozone composite was constructed on a grid in PV-θ space. The edges of the grid were chosen to be well-removed from the values typical of the area of interest (the Arctic lower stratosphere): 0 to 50 PV Units (One PVU being one 106 K m2/kg s) and 200 to 1000 K in θ. The grid coordinates were nondimensionalized to simplify the data weighting calculations.
 A reasonably long-lived trace gas is expected to be well-mixed along contours of PV on a surface of constant θ [Leovy et al., 1985], and in the absence of diabatic effects and chemical changes a simple composite made by averaging mixing ratios near a grid point should yield an accurate picture of a time-invariant trace gas distribution in PV-θ space. Such a composite should be constructed only over time periods short enough that diabatic effects can be neglected.
 But over the course of the 10 weeks examined here one cannot neglect diabatic effects or chemical ozone loss. Both effects appear as a change in ozone mixing ratio at a given point in PV-θ space. One must take into account this time-varying nature of the field when creating the PV-θ composite.
 Over periods of a few weeks (shorter than seasonal timescales), the ozone mixing ratio χ at fixed PV and θ values can be approximated as a linear change in time t:
To make the ozone PV-θ composite, constants a(PV, θ) and b(PV,θ) were computed by constructing a time series at each grid point of all the nearby ozone measurements. A linear least squares fit in time was applied to the measurements, which were weighted by
where σi is the estimated or quoted uncertainty in the ith measurement and di is a scaled nondimensional distance from the ith measurement to the grid point in PV-θ coordinates. A typical time series and fit for the ozonesonde data is shown in Figure 1.
 The results of the time fits are two fields a(PV, θ) and b(PV,θ), containing intercepts and slopes, respectively. An ozone field in PV-θ space can be reconstructed from a and b for any day. This reconstructed ozone grid can be mapped onto points in real space for which PV and θ values are known in order to obtain nominal values of ozone there. Figure 2, for example, shows ozonesonde data which has been mapped onto vertical profiles above the NASA DC-8 for comparison with the AROTEL data. The figure shows the comparison for the flight of 9 March, when the DC-8 flew back and forth across the vortex edge. The remapped sonde data generally compare well with the AROTEL measurements. Two properties of the reconstructed field stand out. First, its spatial resolution is much less than that of the original data. This is not surprising, considering the averaging process and the limited resolution of the meteorological analyses. Nevertheless, the reconstructed field does show the edge structure clearly. Second, the reconstructed ozonesonde data cover a much larger part of the flight than the actual AROTEL measurements, despite the fact that the raw sonde profiles are much more sparsely distributed over the Arctic region than the AROTEL profiles. The reconstruction process assumes that ozone values measured under (and averaged within) certain meteorological conditions will be typical of all ozone values in identical conditions, and maps them accordingly.
 In a similar way, one can use gridded three-dimensional fields of PV and θ to map the ozone composite onto the fields' grid points to obtain an ozone field covering a large area. After using climatological values to fill in regions above and below the reconstructed profiles, such a field can be integrated vertically, yielding a total ozone field that can be compared with TOMS measurements. A comparison for a typical day is shown in Figure 3. PV-θ reconstruction reproduces the morphology of the total ozone field fairly well, and the values themselves are reasonable. For lower total ozone amounts, the values from the reconstruction are higher than the TOMS measured values. Inspection of ozonesonde and reconstructed ozone profiles indicates that these differences are chiefly caused by uncertainties in the reconstructed values in the lowermost stratosphere/upper troposphere, where small variations in ozone mixing ratio can result in large variations in total ozone.
 Reconstructed fields can be used to determine ozone change rates by differencing the fields at the beginning and end of a time period, or by mapping the slopes from the least squares fits into real space. However, the change caused by diabatic descent of air in the polar vortex and the change caused by chemical destruction of ozone will be indistinguishable. A way is needed to account for the diabatic descent to enable the rate of chemical destruction to be determined. This analysis uses two methods for accounting for diabatic effects.
 To determine how much descent took place within the vortex over this period, air parcel trajectories were traced using an isentropic trajectory model with diabatic corrections (see Schoeberl et al. , but here the net diabatic heating rate is not balanced, as given by Schoeberl et al. ). Parcels were initialized at approximately equally spaced grid points on θ surfaces spaced 10 K apart from 400 to 600 K, and the trajectories were run both forward and backward between 10 January and 18 March using the UKMO meteorological data and heating rates from the Rosenfield model.
 To obtain descent rates within the vortex core, only those parcel trajectories which started out and ended up in the core of the vortex were retained. The vortex core was found by determining the PV value that marks the highest 10% all PV values on the (equidistant) grid points which lie poleward of 50°N on each theta surface. These PV values were used to delimit the core of the vortex on the beginning and ending dates; this practice was supported by inspection of contours of these values on maps of potential vorticity.
 For each of the starting θ surfaces, the parcels' ending θ values were subtracted to get the average descent over this period. Figure 4 shows the result. Parcels starting at 600 K in mid-January had descended by some 40 K, on average, by mid-March. Parcels in the lower stratosphere, between 400 and 500 K, descended roughly 15 to 20 K during the same time. To get the average diabatic descent as a function of initial potential temperature, two straight lines were fit to the data, meeting at 475 K.
 To determine ozone loss, ozone fields were reconstructed on 10 January and 17 March on pairs of potential temperature surfaces within the vortex core, the 17 March surfaces being adjusted upward to compensate for the descent of air. The ozone decline was calculated by differencing these two vertical profiles; this method will be referred to as the “vortex-core average descent” method below.
 The second method used to remove diabatic effects involved tracing the parcel trajectories of the ozone measurements themselves. If the trajectory model were perfect, then parcels started on 10 January with certain PV and θ coordinates would end on 18 March with different values of PV and θ. If these “diabatically adjusted” PV-θ coordinates are used in the linear time fits, then the slopes of those fits should reflect chemical loss alone. (Schoeberl et al.  uses a similar technique.) This method will be termed “diabatic coordinate adjustment” in the discussion which follows.
 Of course, trajectories of individual parcels cannot be traced accurately for such long periods, but Schoeberl and Sparling  indicate that reasonable results can be obtained using large ensembles of trajectories whose results are interpreted in a statistical sense.
4.1. Vortex-Core Average Descent Method
 To apply the vortex-core average descent method of determining loss, ozone measurements from the ER-2 in situ instrument, the DC-8 AROTEL and DIAL lidar instruments, and the THESEO 2000 ozonesondes were combined into a single PV-θ composite. Measurements from each instrument were thinned out until they were of approximately equal density in PV-θ space, so that no one instrument would dominate the analysis. The resulting composite was used to reconstruct ozone on potential temperature surfaces for 10 January and 17 March. The surfaces for 17 March were adjusted upwards to account for diabatic descent as determined by the fit in Figure 4. Reconstructed grid points of ozone in the core of the vortex were selected and area-averaged to obtain two vertical profiles, one at each end of the time period being examined.
Figure 5 shows these profiles. The difference between these curves, divided by the time period, is the average chemical ozone loss rate. The ozone loss rate calculated here peaks at 470 K with a value of 0.026 ppmv/d and decreased to near 0 at 550 to 650 K. Results are shown using the NCAR/NCEP Reanalysis; the UKMO analyses and DAO data produce similar curves with loss rates of 0.025 and 0.026, respectively, at 470 K.
 The profiles in Figure 5 extend down to 350 K and show the loss rates continuing to shrink below the 400 K level. The PV-θ technique is more suitable for use in the stratosphere, where (modified) PV and θ are at least quasi-conserved and quasi-orthogonal. Nevertheless, the technique seems to yield reasonable values for loss rates down into the very lowest part of the stratosphere and into the uppermost troposphere, and possible spurious trends arising from movement of the tropopause and its attendant sharp ozone gradient do not appear.
4.2. Diabatic Coordinate Adjustment Method
 To apply the diabatic coordinate adjustment method, measurements from the ozonesondes were used, since they were sparse enough that their trajectories could be traced easily. All days' sonde profiles were run forward to 18 March to obtain their diabatically adjusted PV and θ values on that date. They were also run backward to obtain their diabatically adjusted PV and θ values on 10 January. Parcels whose PV changed by more than 25% over this period were discarded to reduce the effects of parcels entering or leaving the vortex. The remaining measurements, with their adjusted PV-θ coordinates, were then used to construct a time-varying composite, and the slopes from the resulting time fits were obtained. Uncertainties in the slopes were also computed from the covariance matrices of the time fit coefficients (as shown by Meyer ).
 The loss rates were mapped onto vertical profiles in the vortex core; Figure 6 shows the area-weighted average of these profiles. Figure 6a shows the results for the forward trajectory run on 10 January. The loss rate peaks at 0.032 ± 0.007 ppmv/d at 460 K. This is larger than that computed from the vortex-core average descent method, but it peaks in about the same altitude. (Vortex-core average descent loss rates computed from the ozonesonde data alone had the same peak location and value as from the composite of all the instruments.) Figure 6b shows the results for the back trajectory run on 17 March; the loss rate peaks around 0.030 ± 0.008 ppmv/d at 440 K. The peak is about the same magnitude (indicating agreement between the forward and back trajectory runs), but it is located about 20 K lower in potential temperature.
 The back trajectory loss rates mapped to the 10 January profile are very similar to the forward trajectory rates for that date. Likewise, the forward trajectory results mapped to 17 March are similar to the back trajectory results for that date. That is, both trajectory runs show similar peak loss rates which descend in θ over the time period examined. Figure 7 shows both rates mapped onto 13 February profiles (the middle of the period). One difference between the two runs is that the forward trajectory profiles exhibit a small offset near the bottom of the profile (and are very nearly zero at the top), while the backward trajectory profiles show a small offset near the top of the profiles (and are very nearly zero at the bottom).
 A third set of trajectories was calculated in which the parcels were all traced to 13 February. To reach this date, measurements made earlier were run forward, and measurements made later were run backwards. Thus, the average length of a trajectory was reduced by approximately one-half. The results are in agreement with the others; at 450 K on 13 February, the average loss rate is 0.026 ± 0.005 ppmv/d.
Figure 8 shows the time fit slopes (from the backwards trajectory run) for the 440 K surface as a function of equivalent latitude [Butchart and Remsberg, 1986] for 13 February. The area-weighted average loss rate within the inner vortex region on the 440 K surface is 0.030 ± 0.009, the same as seen in the profile results. Expanding the average to include most of the vortex decreases the loss rate slightly to 0.028 ± 0.007 at 440 K.
 Results from the backwards trajectory run are similar within the vortex, but the change rates outside the vortex vary greatly between the two runs (from approximately −0.01 to +0.02 ppmv/d at 470 K). The near-zero loss rate shown in Figure 8 outside the vortex must be considered highly uncertain.
 From equation 1, the loss rate of total ozone OT becomes:
where W = 0.789 m s2/kg and ps is the surface pressure. We do not reconstruct ozone values in the lower troposphere, but fixing the (notional) ozone profile to zero at the surface (as is done to derive the total ozone values mapped in Figure 3) makes the second term vanish. (As a dynamical effect, the second term has no bearing on chemical ozone loss anyway.) Thus, integrating the time slopes yields that part of the time rate of change of total ozone which is caused by chemical destruction.
 Time fit slopes from the diabatically adjusted sonde data were mapped onto vertical profiles as a function of pressure. Loss rates from the back trajectory results were used because they were close to zero below 400 K, a region more heavily weighted in the integration. Any ozone increases (e.g., from the offsets near the top of the profiles) were zeroed out—only ozone destruction rates are of interest. These rate profiles were then integrated and area-averaged within the vortex core for each day between 10 January and 17 March.
Figure 9 shows the daily total ozone loss rates for the core of the vortex. The losses begin at approximately 0.8 DU/d and increase to 1.3 DU/d by 17 March. The loss rates' evolution is associated with a decrease in θ at the ozone loss peak and with a stronger shift in the PV values associated with the vortex core.
5. Discussion and Conclusions
5.1. Analysis Uncertainties
 The PV-θ analysis has several potential pitfalls. It depends on its constituent being long-lived enough to be well-mixed along contours of isentropic potential vorticity. In the middle stratosphere and above, where photochemistry dominates, the method is of limited applicability to ozone. This analysis has been confined to the lower stratosphere.
 When an ozone measurement is made near the vortex edge in the sunlight, where chlorine-driven photochemical destruction is likely to be enhanced, this measurement may not be typical of ozone values around a PV contour on a θ surface that intersects the measurement location. With enough additional measurements around that contour, PV-θ analysis will yield an averaged view of the ozone field which the ozone-depleted measurements will influence but not necessarily dominate. Poor sampling, however, may lead to the sunlit region being underrepresented or overrepresented in the average until the ozone-depleted air is mixed along the contour. This analysis relies on the time series fit to average out the sudden drops in ozone that might appear in such cases.
 To distinguish between diabatic effects and chemical destruction of ozone, this analysis uses diabatic trajectories of large numbers of parcels traced over about 10 weeks. Averaging the effects of large numbers of parcels might well compensate for the inaccuracy of individual parcel trajectories, but there remains the possibility of systematic artifacts of the meteorological analysis used or of the radiation model used to generate the heating rates.
 The diabatic heating rates have been verified in previous work [Rosenfield and Schoeberl, 2001] for the UKMO meteorological products, and they appear to be reasonable.
 Another approach would be to analyze a tracer such as N2O and test whether the diabatic trajectories reduce the apparent rate of change, which should be a purely diabatic effect. This has been attempted, and the results suggest that using diabatically adjusted trajectories tends to reduce the rates of change in the vortex core at altitudes higher than 500 K. However, the N2O measurements from SOLVE were sparse enough, and the uncertainties in the rates are consequently large enough to make these results inconclusive. That is, the differences between the uncorrected rate profiles and the diabatically corrected rate profiles are smaller than the uncertainties in either.
 Another effect which would complicate matters is mixing across the vortex boundary. Although the polar vortex is generally recognized as being isolated from the midlatitudes [Bowman, 1993; Schoeberl et al., 2002], it is not completely isolated—slow or weak mixing may occur over the course of a season, in addition to occasional major intrusion events such as one described by Plumb et al. . The PV-θ technique may still reconstruct ozone fields with some degree of fidelity in these circumstances, but untangling chemical destruction from mixing becomes problematic. In this analysis, the issue is addressed by excluding parcels whose diabatic trajectories involved a change of PV of more than 25%, but it is unclear whether this is sufficient given the limitations of tracing individual parcels. In other words, it is difficult to say whether a parcel has been excluded because it moved into or out of the vortex, or because its trajectory is simply not accurately traced.
 Inspection of the grid point trajectories used to determine descent rates shows only a few cases where trajectories which originated outside the vortex in January ended up inside the vortex in March: about 1.3% of the mid-March vortex parcels at 420–430 K for the back-trajectories only. For other theta levels and for the forward trajectory run, no such parcels were found. Schoeberl et al. , who used a more comprehensive trajectory modeling run, support the assertion that mixing into the vortex was negligible over most of this period.
 Toward the middle of March, as the vortex was breaking up, the effects of mixing are expected to increase. A sharper drop-off in ozone at the end of the time series can be seen in Figure 1, and it is difficult to separate the effects of mixing from those of chemical destruction in the increased sunlight. This analysis partially side-steps the issue by fitting a linear trend over the 10-week period, so that the sudden drop-off at the end does not influence the overall trend too strongly.
5.2. Other Techniques
 PV-θ analysis of diabatically adjusted sonde data gives an average ozone loss rate of around 0.03 ± 0.008 ppmv/d near 440 to 470 K. Strictly speaking, cumulative ozone loss should be estimated from a Lagrangian framework, following air parcels. But because the rates are derived from parcels whose coordinates have been corrected for diabatic effects, and because the vortex is fairly isolated, a rough estimate for the total loss can be obtained by multiplying the rate by the length of the time period: approximately 2.0 ppmv.
 Other techniques have been used to categorize ozone loss. Instead of placing all the data into a composite time-dependent field, the Match program [Rex et al., 1999] uses paired individual ozonesonde profiles to determine ozone loss. Match selects the pairs by tracing the trajectories of sonde-sampled air parcels until they intersect other sonde launches days later. By using small clusters of trajectories for each measurement, and by averaging differenced pairs together, Match tends to reduce the uncertainties associated with the trajectory calculations. Because Match uses changes in PV as a criterion in matching pairs of sonde launches, its ozone values are effectively categorized by PV in a way similar to PV-θ analysis. Instead of dealing with pairwise differences at discrete θ levels, though, the PV-θ technique has the effect of averaging all ozone measurements of similar PV and θ values. More data will tend to enter such an average at the cost of a higher dependence upon the assumption than ozone is well-mixed along an isentropic PV contour. Match results for SOLVE [Rex et al., 2002] are similar to those presented here, about 2.6 ppmv cumulative loss near 460 K.
 The vortex-averaged analysis of Schoeberl et al.  involves diabatic trajectory calculations initialized from massive numbers of ozone measurement locations, so that the inaccuracies associated with individual parcels are averaged out. The data which remain inside the vortex are fit to a quadratic curve at various theta levels to obtain ozone loss rates from December 1999 through mid-March 2000 (around 0.025 ppmv/d). Solar exposure is also used to discriminate between parcels in the core of the vortex and parcels from the edge region; excluding parcels near the sunlit edge is important for separating out parcels with higher loss rates which might be seen in January. Their analysis yields an ozone loss rate of approximately 0.025 ppmv/d.
 Another analysis that uses trajectory calculations to correct for diabatic effects has been performed by Swartz et al. . From stellar occultation measurements analyzed by applying a vortex-averaged descent correction and by tracing individual trajectories, they found an average daily loss rate of about 0.024 ppmv/d from 23 January to 4 March.
 The PV-θ technique with diabatic corrections may be thought of as a way of enhancing such trajectory analyses to produce a continuously evolving ozone field. The peak ozone loss rates produced here are somewhat less than Match's, but somewhat higher than that obtained by the Schoeberl trajectory analysis. The peak loss rates seem to be a little lower and broader in altitude in the latter results, as well, but this may be an artifact of the heavy smoothing done here.
 Ozone measurements from AROTEL, DIAL, the NOAA ER-2 instrument, and the THESEO 2000 ozonesondes have been combined using a PV-θ analysis technique which allows the ozone field to evolve in time. Realistic ozone fields have been obtained by mapping the ozone field from PV-θ coordinates back into real space. Diabatic effects have been estimated using modeled trajectories of large numbers of parcels. Estimates of chemical ozone loss in the lower stratosphere are found to peak at 0.030 ± 0.009 ppmv/d near 460 K in January, with this peak descending to 440 K in March. The loss rates decrease to near 0 at 550–600 K and below 400 K. The cumulative loss near 450 K is thus about 2 ppmv over the period. These results appear to be in broad agreement with other analyses.
 The author wishes to acknowledge the DC-8 and ER-2 pilots and the flight and ground crews who made the aircraft measurements possible under sometimes difficult conditions; the sonde launch personnel; the SOLVE logistics staff and the personnel of the Arena Arctica in Kiruna, Sweden; and SOLVE and THESEO 2000 management. This research was supported by the NASA's Atmospheric Chemistry Modeling and Analysis Program and the Upper Atmosphere Research Program.