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 Ozone observations from ozonesondes, the lidars aboard the DC-8, in situ ozone measurements from the ER-2, and satellite ozone measurements from Polar Ozone and Aerosol Measurement III (POAM) were used to assess ozone loss during the Sage III Ozone Loss and Validation Experiment (SOLVE) and Third European Stratospheric Experiment on Ozone (THESEO) 1999–2000 Arctic campaign. Two methods of analysis were used. In the first method a simple regression analysis of the data time series is performed on the ozonesonde and POAM measurements within the vortex. In the second method the ozone measurements from all available ozone data were injected into a free-running diabatic trajectory model and were carried forward in time from 1 December to 15 March. Vortex ozone loss was then estimated by comparing the ozone values of those parcels initiated early in the campaign with those parcels injected later in the campaign. Despite the variety of observational techniques used during SOLVE, the measurements provide a fairly consistent picture. Over the whole vortex the largest ozone loss occurs between 550 and 400 K potential temperatures (∼23–16 km) with over 1.5 ppmv (∼55%) lost by 15 March, the end of the SOLVE mission period. An ozone loss rate of 0.04–0.05 ppmv/day was computed for 15 March. The total column loss was between 44 and 57 DU or 11–15%. Ozonesondes launched after 15 March suggest that an additional 0.5 ppmv or more ozone was lost between 15 March and 1 April.
 One of the challenges in assessing polar winter chemical ozone loss is untangling the effects of dynamics and chemistry. Dynamical descent of vortex air during the fall and winter will cause lower stratospheric ozone to increase. In contrast, heterogeneous chemical processing of vortex air will decrease ozone. In addition, air from midlatitudes will occasionally intrude into the vortex. Since stratospheric, midlatitude air below ∼23 km has generally a lower ozone concentration than the vortex interior in midwinter, the in-mixing of midlatitude air, like chemistry, can also decrease ozone amounts within the vortex.
 One approach to untangling dynamical and chemical processes in estimating ozone loss is to use simultaneous conservative tracer measurements. For example, Proffitt et al.  and Schoeberl et al.  used N2O measurements to estimate Arctic ozone loss during the late winter Airborne Arctic Stratospheric Expedition (1989). The idea is to tag ozone with a conservative tracer value and compare ozone amounts with similar conservative tracer value during the chemical loss period. The ozone-conservative tracer correlation shifts in the presence of chemical loss, and this method can be used to estimate and remove the meteorological effects. Pseudo tracers have also been used to separate chemistry from dynamics in estimating ozone loss. For example, Manney et al.  use potential vorticity (PV) as a pseudo tracer to estimate ozone loss from MLS data and lidar data, respectively, but this technique requires high quality PV computations and PV is not strictly conserved under diabatic processes. Sinnhuber et al.  use a passive ozone tracer in their chemical transport model and estimate ozone loss by comparing ozone observations with the passive tracer.
Plumb et al.  have pointed out that conservative tracer-ozone correlations should not be used over extended periods because when continuous mixing into the vortex interior occurs the tracer relationships are altered even if there is no chemistry. This can lead to incorrect estimations of vortex ozone loss and denitrification. To avoid this problem, Richard et al.  has computed the ozone loss during the Sage III Ozone Loss and Validation Experiment (SOLVE) 1999–2000 winter period using ozone and two conservative tracers.
 Unfortunately most ozone measurements are made without the simultaneous measurement of long-lived tracer fields (e.g., lidar ozone measurements, some satellite measurements, and ozonesondes). Thus we need to be able to estimate ozone loss without the use of long-lived tracers. In this paper, we use two techniques to estimate ozone loss during the SOLVE campaign (December 1999–March 2000). The first technique is to use a simple regression analysis of ozonesondes and Polar Ozone and Aerosol Measurement III (POAM) data [Lucke et al., 1999]. This analysis can be performed for two reasons. First, the SOLVE campaign was coordinated with the Third European Stratospheric Experiment on Ozone (THESEO) campaign so there were a significant number of ozonesondes launched within the polar vortex from November 1999 to April 2000. Meteorological analyses show that the vortex was cold and persistent with no major stratospheric warmings in the lower stratosphere [Manney and Sabutis, 2000]. Second, back trajectory calculations we have performed from 15 March to 20 December also show that there were no significant intrusions of midlatitude air into the vortex during the winter period. Because of this fortuitous isolation, a simple regression analysis of the ozone data should provide a reasonable assessment of the average vortex ozone loss over the winter period.
 The second technique we use to analyze the SOLVE ozone data employs a diabatic trajectory model. In order to compute the ozone loss, trajectories are initiated whenever a measurement is made. By comparing vortex air parcels initiated early in the integration period with measurements late in the period, ozone loss can be estimated. This new technique does not depend on any assumption about the accuracy of any individual parcel trajectory only that statistics of the air parcels not be systematically biased. This approach is unlike the Match technique [van der Gathen et al., 1995; Rex et al., 1999, 2002] which does depend on the accuracy of trajectory air mass predictions.
 Measurements of stratospheric ozone from five instruments were used in this study. The instruments are briefly described in this section, and their measurement parameters, such as vertical resolution and measurement error, are also given (see also Table 1).
Table 1. Ozone Measurement Parameters for the Instruments Considered in This Work
 Electrochemical Concentration Cell (ECC) ozonesondes are launched periodically on balloons and reach altitudes of up to 35 km [Komhyr et al., 1995]. They measure ozone by pumping air through potassium iodide (KI) solutions of different concentrations, contained in separate cathode and anode chambers. The solutions are buffered with potassium bromide. The presence of ozone causes I2 to be formed, which is then converted to I−, giving rise to an electrical current. ECC ozonesondes have been used in a number of comparison campaigns [Komhyr et al., 1995; Steinbrecht et al., 1999], giving a good indication of their measurement precision and accuracy as shown in Table 1 [Komhyr et al., 1995].
 POAM III [Lucke et al., 1999] is a nine-channel (354 to 1018 nm) solar occultation instrument designed to measure stratospheric profiles of ozone, NO2 and water vapor densities, aerosol extinction at five wavelengths, and temperature. POAM III was launched on the French Satellite Pour Observation de la Terre (SPOT) 4 satellite on 23 March 1998, into a Sun-synchronous polar orbit. The latitude of the POAM measurements varies slowly throughout the year between 55°N and 73°N and between 63°S and 88°S, with essentially identical coverage from year to year. The POAM Version 3 data algorithm validation has been performed using comparisons with the Halogen Occultation Experiment (HALOE) version 19 (O3, NO2, H2O and aerosol), Stratospheric Aerosol and Gas Experiment (SAGE) II version 6.0 (O3 and aerosols) and ozonesondes (O3). For O3, POAM generally agrees to within 5 to 8% with SAGE II, HALOE and ECC ozonesondes in the altitude range from 15 to 60 km. Somewhat larger disagreements (10–15%) are seen below 15 km.
 The NASA Langley airborne UV Differential Absorption Lidar (DIAL) system has been used to measure ozone, aerosol, and cloud profiles during four previous stratospheric ozone investigations, affording the opportunity for many comparisons with other ozone measuring instruments [Browell, 1989; Margitan et al., 1989; Browell et al., 1990, 1993, 1998; Grant et al., 1998]. This system uses two frequency-doubled Nd:YAG lasers to pump two high-conversion efficiency, frequency-doubled, tunable dye lasers. In stratospheric O3 investigations, the two frequency-doubled dye lasers are operated independently with one tuned to 301 nm for the O3 DIAL on-line wavelength and the other tuned to 311 nm for the off-line wavelength. All of the beams are transmitted in the zenith direction through a 40-cm-diameter fused silica window. The atmospheric backscattered laser returns are collected by a 36-cm telescope, optically separated, and directed on to different detectors.
 The UV Photometer used for in situ O3 measurements on the ER-2 is based on the design of Proffitt and McLaughlin . It uses a mercury lamp emitting radiation centered at 254 nm. Since it employs two absorption chambers, it can make measurements with a 1 s time constant.
 The NASA GSFC/LaRC Airborne Raman Ozone, Aerosol and Temperature Lidar was flown for the first time during the SOLVE mission. A detailed description of the instrument and all the measurements is currently in press (T. McGee, personal communication, 2001). The ozone measurement is made using the differential absorption technique: a XeCl excimer laser (200 mJ at 200 Hz) transmits 308 nm radiation, which is absorbed by ozone; and 355 nm from a Nd-YAG laser is used as the atmospheric reference. The beams are transmitted coaxially with the 16″ receiver telescope, and the return signals are separated using dichroic beam splitters and interference filters. All signals are photon counted. In order to ensure linearity over a dynamic range greater than 106, up to five separate detectors are used for each wavelength. The precision of the ozone measurement, as well as the vertical resolution, is variable depending on the altitude. The values in Table 1 are generally representative for nighttime measurements. During daytime (solar zenith angles ∼75°), the measurement upper altitude is generally limited to 26 km.
2.1. Vortex Ozone Regression Analysis
 For the POAM and ozonesonde time series regression analysis, we interpolate the ozone measurements onto vortex interior surfaces that are diabatically descending in time. The descent rates are determined from the ensemble average descent of parcels using the trajectory calculation discussed below. The data are first processed by selecting only observations within the vortex edge at 520 K as determined by the isentropic MPV gradient [Nash et al., 1996] (hereinafter referred to as the Nash algorithm). Figure 1 shows the ozonesonde and POAM equivalent latitude locations at 520 K relative to the vortex edge at 520 K. (For the definition of equivalent latitude, see Butchart and Remsberg ) No adjustment is made in these calculations for the drift of the ozonesonde balloon.
Figure 2a shows the ozonesonde data time series for those measurements within the vortex edge. The appearance of bands of high modified potential vorticity (MPV) [Lait, 1994] and ozone at upper levels demonstrates that even though the ozonesonde or POAM measurement can be within the vortex at 520 K the measurement can be outside of the vortex at higher altitudes due to the tilt of the vortex or the motion of the balloon. At these higher altitudes, the ozone mixing ratio outside the vortex is higher than inside the vortex. To reduce the amount of nonvortex observations, a second filter is applied to the data. First, the data are fit to a second-order polynomial along descending surfaces (shown as thin lines). The descending surfaces are computed from the diabatic descent of an ensemble of trajectory points that are inside the vortex from 1 December through 15 March. The details of this calculation are described below. If the observations deviate by more than 1 ppmv from the fit, that data point is removed. The result is shown in Figure 2b and indicates that this method does a reasonable job of eliminating additional outlying observations while still retaining the essential character of the time series. Both POAM and ozonesonde data are processed in the same way. The POAM data are not shown.
2.2. Trajectory Analysis
 In the trajectory method, we simply inject parcels when ozone measurements are made and continue to move the parcels diabatically until the end of the integration period. This method automatically accounts for the descent of the parcels and for entrainment or detrainment of material from the vortex. It is important to note that some of the parcel integrations will be up to 105 days long so we only expect that the distribution of the parcels will be accurate in a statistical sense. In other words, the loss amounts calculated using this technique should approximate the vortex average provided there are a sufficient number of parcels to represent the air mass characteristics. We have tested the fidelity of this approximation by comparing the 15 March 2000 difference between the temperature obtained by averaging the parcels within the vortex and the analyzed average vortex temperature. For the isentropic levels between 400 and 600 K, the temperature difference is <1° except at 400 K where it is 4.5 K. This means that using parcel averages reasonably approximates the vortex average except at 400 K; however, at 400 K, the vortex is fairly broken up so the “vortex average” is somewhat ambiguous.
 By comparing ozone amounts associated with different vortex parcels initiated at different times we can estimate the net loss ozone loss. The population of parcels examined at the end of the integration represents a different data set from data sets used in the ozonesonde and POAM regression analyses. For example, measurements made at the edge of the vortex are included in the simple regression analysis, but those measurements will probably not be included in the trajectory analysis since the vortex edge material erodes away during the winter. In other words, many edge measurements, represented as parcels, will end up in midlatitudes and thus not be included in the trajectory analysis.
 The trajectory integration begins on 1 December 1999 and is carried through to 15 March 2000. POAM and ozonesonde measurements were made over the whole winter period. The December period corresponds to the first SOLVE aircraft segment during which only DC-8 lidar and in situ ozone measurements were made. The DC-8 in situ measurements are below the region of interest and not used in this analysis. During the January and March segments of SOLVE, ER-2 in situ ozone measurements are added to the DC-8 measurements.
 The diabatic trajectory descent method has been generally validated using HALOE methane observations within the austral and boreal polar vortices [Rosenfield and Schoeberl, 2001]. We have also compared the trajectory descent estimates based upon the long-lived tracers measured by the ER-2 (E. Ray, private communication, 2001) during SOLVE. Best agreement with changes in SF6 between January and early March was obtained when the net diabatic heating was not globally balanced and linear interpolation of the heating rates between mandatory pressure levels was used. (Usually, spline interpolations are used in projecting the diabatic heating rates onto the parcel locations. However, when heating rates become very small, the spline methods can create unrealistic local minima.)
 Observations used to initiate a parcel trajectory were screened to remove any obviously bad measurements, and any data taken below the 330 K potential temperature (PT) surface were ignored. Trajectories were started at the position and PT of the measurement. For ozonesonde data, the drift in the balloon location is not recorded with the data so we compute the drift of the balloon using the wind observations recorded by the ozonesonde or using global meteorological analyses. With ozonesonde and ER-2 data, simultaneous measurements of pressure and temperature are used to compute PT. The UV Differential Absorption Lidar (DIAL) [Browell et al., 1998] and Airborne Ozone and Temperature Lidar (AROTEL) [McGee et al., 2001] and the POAM satellite measurement locations were interpolated from geometric coordinates to PT surfaces using the UK Met Office (UKMO) global analysis [Swinbank and O'Neill, 1994].
 The large amount of lidar data creates a problem with this analysis approach since a single flight of the DC-8 lidars creates more observational data than the entire winter set of ozonesondes. However, most of the lidar data has a high degree of horizontal correlation and thus the extra observations do not add information on the large-scale ozone changes. Thus we have thinned the lidar and ER-2 data sets using the distance that the horizontal autocorrelation falls to zero to provide an “equivalent ozonesonde” data set. Within the vortex, the autocorrelation distance is about 400 km for DIAL, 250 km for the ER-2 in situ measurements and 300 km for AROTEL although these numbers vary a little from flight to flight. The different autocorrelations arise from different post processing algorithms that include averaging of the data to increase the precision.
 After integrating the trajectory model forward from 1 December 1999 to 15 March 2000, over 200,000 observations have been inserted. Both measurements outside and inside the vortex are included in this analysis. Figure 3 shows the altitude and equivalent latitude distribution of the parcels on 15 March. It is apparent from the figure that many of the parcels have been shed from the vortex as might be expected from ongoing late winter vortex erosion.
 As mentioned above, ozone loss is computed by comparing the ozone concentration of parcels generated throughout the integration period. This Lagrangian approach to assessing ozone loss is very different from the Match technique [van der Gathen et al., 1995; Rex et al., 1999]. The Match technique calculates the difference between successive ozone measurements (usually ozonesondes) that are connected using a trajectory calculation. Thus the Match requires frequent ozonesonde launches, and an accurate forecast of the motion of the measured air mass. The technique described here does not rely on the accuracy of individual trajectories but on the accuracy of the ensemble that, from our test described above, appears to accurately represent vortex conditions.
3.1. Regression Analysis of Ozonesonde and POAM Data
 The ozone change using the regression analysis from 1 December 1999 to 15 March 2000 is shown in Figure 4. As mentioned above, the data are fit to each descending surface shown in the figure. By mapping the data fits to the descending surfaces, and assuming isolation of the vortex from midlatitudes, the loss shown in Figure 4 should entirely be a result of chemical processes. The standard deviation of the data fit will be discussed later.
 The ozonesonde and POAM data generally agree: the ozone change (loss) is largest in March, and the rate of this change is also largest during the February-March period. By 15 March vortex averaged loss amounts are between 55 and 65%. This loss decreases rapidly with altitude above 530 K. Prior to the main decrease period in February-March, the POAM series indicates some loss above 480 K during January. Below we discuss the January and March periods. The ozonesonde increase in ozone seen in the Figure 4a during the December period will be discussed in the summary section.
3.1.1. January Ozone Loss
Figure 5 shows the UKMO analyzed temperatures of the vortex during the SOLVE period. The most intense cold periods occurred in late December and January and at altitudes coincident with POAM ozone loss in January. Formation of PSCs in this period would enhance reactive chlorine levels, and thus it is plausible that there is some ozone loss occurring in January. Given our understanding of the photochemistry of polar ozone [Solomon, 1999], loss at this time would have to take place near the edge of the polar vortex where the solar illumination is the greatest. Midwinter ozone loss near the edge of the vortex has recently been derived for the Antarctic [Lee et al., 2000].
 To further investigate the possibility of edge loss, we have calculated the fraction of sunlight observed by air parcels at the 520 K potential temperature surface using trajectory calculations. The probability distribution functions (PDF) for equivalent latitude and solar exposure in these data are shown in Figure 6.
 Solar exposure was computed by performing a seven day reverse domain fill back trajectory calculation for each day of the SOLVE winter period [see Schoeberl and Newman, 1996], and then computing the amount of time each parcel encountered solar zenith angles less than 90°. The solar exposure map generated at 1° by 1° resolution is used to estimate the parcel solar exposure shown in Figure 6. Given our current understanding of the polar ozone loss processes and the observation of wide spread polar stratospheric cloud observations during December, solar exposure above zero means that some ozone loss should take place for those air parcels. The mobility of the Arctic vortex allows even high equivalent latitude parcels to have some exposure. Although the mean solar exposure for ozonesonde and POAM parcels is nearly the same, the POAM distribution is more skewed toward higher solar exposures (Figure 6b) while the ozonesonde PDF shown in Figure 6a is skewed in the other direction. This is not very surprising since POAM requires sunlight to make measurements, and during January 2000 the POAM measurements tended to be at lower equivalent latitudes near the edge of the vortex (as seen in Figure 1b). Since solar exposure will not be a linear indicator of ozone loss, the skew of the distribution is a more important factor than the mean. To check the sensitivity of the diagnosed ozone loss to solar exposure, we performed a series of experiments restricting the POAM measurements to higher equivalent latitudes in the period 1 December–15 February. The resultant PDF for >75° restriction is shown in Figure 6c. The restriction in equivalent latitude has the effect of also reducing the solar exposure as would expected from the arguments above.
Figure 7 summarizes the results of several experiments in which the equivalent latitude and solar exposure were restricted. The conclusion drawn from these experiments is that when the population of the POAM data is altered so that solar exposure is reduced, the data sets tend to show very little ozone loss. The ozonesonde data shows a different effect. Since the population is restricted to higher equivalent latitudes, the January increase in ozone seen in Figure 4a is reduced. Because the ozonesonde data set already has very low solar exposure, restricting the data set to high equivalent latitudes does not significantly alter the solar exposure of the population, but it does reduce the population of points near the edge of the vortex. This eliminates the occasional edge point that has high ozone (see Figure 2). This result shows that the increase in ozone seen in the ozonesonde analysis (Figure 4a) is probably due to inclusion of edge points, not the result of any real increase.
 We conclude from this analysis that ozone loss by mid-January is small and restricted to lower equivalent latitudes or parcels with larger solar exposure. We also conclude that the POAM and ozonesonde data tell the same story when the population of measurements are restricted to equivalent conditions. This conclusion is supported by the model calculations made during SOLVE (REPROBUS model group, private communication, 2000) [see Deniel et al., 1998] that also show that January ozone loss is confined to the illuminated edge of the vortex.
3.1.2. March Ozone Loss
Figure 8 compares the 15 March loss amounts between the POAM and ozonesonde series. The trajectory analysis is also shown, and will be discussed below. Column ozone change is also indicated in the caption. Generally there is good agreement between the data sets below 460 K. At higher altitudes the ozonesonde and POAM data sets show an offset of about 0.5 ppmv or more. The discrepancy arises from the trends in early winter where the ozonesonde data show increases in ozone while the POAM analysis shows a decrease (Figure 4). By 15 March the ozone loss rates (Figure 9) agree reasonably well with a rate of ∼0.04 ppmv/day. This is nearly the same rate as is seen during peak Antarctic ozone loss rate period [Wu and Dessler, 2001] and is what might be expected in a fully sunlit vortex which contains high levels of ClO as was observed during SOLVE [Santee et al., 2000].
 As noted above the 0.5 ppmv discrepancy between POAM and ozonesonde data in Figure 8 also arises from the sampling bias. High ozonesonde measurements amounts in mid-January (Figure 2b) push the January ozonesonde amounts above the POAM amounts. The second-order fit to the ozonesonde data becomes more parabolic with a peak in early January. As a result, the 1 December ozonesonde fit value is below the POAM fit value thus giving a smaller net ozone loss for the ozonesonde data. This effect also gives rise to the increase in ozone seen in Figure 4a. If the ozonesonde data sets are filtered to high equivalent latitudes, the January peak is reduced and the ozonesonde and POAM data are in closer agreement (Figure 7).
3.2. Trajectory Analysis
 As discussed in section 2.2 we use the trajectory model to compare all ozone measurements within the vortex. Figures 10a and 10b show the analysis for 15 March at two isentropic surfaces, 460 and 520 K. Although parcels exist at a continuum of PT values from 600 to 350 K, for simplicity, separate analyses are performed only for isentropic levels 20 K apart from 400 to 600 K. The data are selected for analysis by marking parcels within a ±2 K window of the target potential temperature within the vortex edge (see Figure 10). Usually the vortex edge from the Nash algorithm is used; however, visible in Figure 10 is a lobe of the main vortex that, on 15 March has separated from the main vortex toward the upper right of the figure. This lobe may contain midlatitudes air that has mixed in during the process of separation. The Nash algorithm, at some potential temperature surfaces, will place the edge around that lobe, so a higher PV edge value is used in those cases. A cursory examination of the data reveals that some ozone observations are quite far from the ensemble mean with the same age. These observations usually originate near the edge of the vortex where the chemical boundary and the MPV boundary do not exactly line up. To reduce the influence of these points, the data are filtered so that points 0.5 ppmv from the regression curve are rejected. Although this sounds like a severe rejection criterion only about 15% additional data are rejected using this criteria compared to a rejection criteria of 2 ppmv.
Figure 10 shows the mix of the data used. Generally, ozonesonde, AROTEL, and POAM data contribute at all altitudes. Dial makes a large contribution to the data below 500 K. Compared to the other data sets, the ER-2 makes a negligible contribution. Because of the variable number of parcels that exist with any given age, the regression analysis is performed by computing the daily averaged ozone amount. The daily averages are shown in Figure 10 (upper right) as small crosses (see caption for Figure 10). Once the daily averages are computed for a given PT value, a second-order polynomial is fit to the daily average data.
Figures 8 and 9 compare the trajectory computed 1 December-15 March loss amounts and 15 March loss rates with the ozonesonde and POAM regression analyses. Trajectory results are labeled BFT for Brute Force Trajectory. In general, there is good agreement between the three techniques. The trajectory analysis shows a somewhat lower loss amount in the main loss regions (below 520 K) than POAM, but produces about the same loss rate as the POAM and ozonesonde analysis. The difference in the loss amounts can probably be attributed to the sample population. In the trajectory scheme the number of parcels used in the analysis are those remaining within the vortex on 15 March. In contrast, the ozonesonde and POAM measurement population includes all of the points inside the vortex when the measurement is made. It is more likely that a parcel initiated deep within the vortex will still be within the vortex by 15 March. Thus the trajectory technique will not consider many of the POAM observations at the edge of the vortex since these will have been eroded to midlatitudes by 15 March.
4. Discussion and Summary
 The SOLVE winter period (1 December 1999–15 March 2000) was characterized by cold temperatures, an isolated Arctic stratospheric vortex and significant ozone loss. In this paper we have performed analyses using two methods: a simple regression analysis of ozonesonde POAM measurements within the vortex, and a trajectory analysis which includes both of those data sets as well as DC-8 lidar and ER-2 in situ ozone data. The high altitude balloon flights made from Kiruna were not used since the data from those platform were too small to influence the outcome. The trajectory analysis is a new approach where measurement trajectories are started whenever and wherever a measurement is made. At the end of the trajectory integration, all parcels remaining within the vortex are compared. The plot of ozone measurement amount versus age of the measurements shows the ozone change.
 By mid-January the POAM regression analysis reveals a small ozone loss that is not apparent in the ozonesonde regression analysis. The disagreement between the two analyses can be reduced by reselecting the POAM observations to reduce the solar exposure and the number of vortex edge measurements. Thus the likely source of the disagreement between POAM and ozonesonde analysis is (1) ozone loss at the edge of the vortex for parcels that have been exposed to sunlight and (2) the occasional high ozone value from an ozonesonde which is not completely inside the vortex. The fact that ozone loss may take place first at the edge of the vortex has already been suggested from Antarctic observations [Lee et al., 2000]. Thus, given a fairly symmetric nearly pole centered vortex as occurred during SOLVE, the development of edge loss is not a surprise. Chemical model calculations made during SOLVE also show that January loss is higher at the edge of the vortex than in the interior. Because the POAM instrument samples preferentially along the vortex edge in January 2000, the population of POAM measurement emphasizes edge ozone loss. The important point here is that ozone loss within the vortex in January during SOLVE was apparently nonuniform. Furthermore, since the edge is a barrier to mixing [Schoeberl et al., 1989; Bowman, 1993, 1996], ozone loss near the vortex edge would be very slowly communicated to the interior. Thus the nonuniform ozone loss in January, may give rise to persistent residual ozone variability, and this variability will result in uncertainty in ozone loss amount. In fact, DIAL measurements within the vortex interior on 13 March 2000 show a 1 ppmv variation range at 18 km over large regions.
 In mid-January 2000 our analysis found smaller ozone loss rates than the Match-derived loss rates of about 0.04–0.05 ppmv/day for the winters 1992, 1995, and 1996 [Rex et al., 1997, 1998, 1999]. However, our results do generally agree with the results from Match for the winter 2000 [Rex et al., 2002] with smaller ozone loss rates in January than in previous years.
 By the middle of March our analyses show ozone loss amounts between 1.5 and 2 ppmv (45–55%, respectively) for the winter period (Figure 8). POAM regression analyses show the higher ozone loss (2 ppmv), compared to the ozonesonde regression analyses and the trajectory calculation. This disagreement is small given the small number of ozonesonde measurements compared to POAM. However, the POAM regression analysis is sensitive to the selection of points near the edge of the vortex. To show this sensitivity, we have selected only POAM parcels from the trajectory analysis and performed a second-order regression analysis on the data subset. These are POAM initiated parcels that are still within the vortex by 15 March. Figure 11 shows that if only the POAM parcels remaining within the vortex are used then the ozone loss is 0.75 ppmv less than computed using the simple POAM regression analysis. Figure 12 shows the PDF of the 1–20 January equivalent latitudes for the POAM points used in the trajectory analysis. Figure 12 should be compared to Figure 6b. In Figure 6b the mean equivalent latitude for the POAM regression analysis is ∼70° where the mean equivalent latitude for the trajectory POAM points over the same period is ∼80°. The means that the POAM points used for the trajectory analysis (those remaining in the vortex at 15 March) were those with almost no solar exposure (compare Figures 6b and 6c to see the impact of restricting equivalent latitude has on solar exposure) and thus show very little ozone loss during this period.
 A number of other estimates of ozone loss within the December 1999-January 2000 polar vortex have been made. Santee et al.  computed ozone loss from late winter (February to mid-March) from the Microwave Limb Sounder (MLS) observations. They estimated a February vortex averaged 465 K loss rate of 0.04 ± 0.01 ppmv/day. This loss rate is comparable to our 15 March loss rate, but on the high side for February. From both ozonesonde and trajectory analysis we compute a mid-February 465 K vortex loss rate of ∼0.025 ppmv/day. Figure 13 shows the loss rate computed from the ozonesonde analysis. In mid-February, the loss rate maximizes near 500 K, and given the vertical weighting functions of the MLS data, their ozone loss rate is in agreement with this analysis to within their error bars.
Richard et al. , using ER-2 aircraft data, have also computed a loss rate between the beginning of January and the end of February and for the period from the end of February to mid-March. In agreement with our analysis they concluded that the January loss rates were small but by mid-March the loss rate was 0.05 ppmv/day. This is in good agreement with our calculations as well (Figures 9 and 13). Assuming the high loss rates, and applying them to a 38-day period Richard et al. obtain a loss amount of 2 ppmv. Our calculations suggest that this is an over estimate since the loss rates are changing rapidly over this period, and it is probably inappropriate to apply the highest loss rate to the last 38 days. However, in broad scope, the two computations are in agreement in both the loss rate and amount of loss.
 Ozone loss amounts have also been estimated independently by Rex et al.  using the Match technique applied to the ozonesonde data, and Hoppel et al.  using an analysis of the POAM data. All of these analysis use air mass descent estimates to try and remove the dynamical changes in ozone. Aside from the different analysis methods and data sets used, there at least two broad regions that create disagreement between these various estimates of ozone loss. The first comes from the starting date of the analyses. Many of the estimates start at 15 January 2000 while we start our analysis at 1 December 1999. Figure 4a shows that starting at 15 January will increase our 460 K ozonesonde loss estimate by about 0.25 ppmv and decrease our 460 K POAM loss estimate by about the same amount. This would bring the two estimates into near agreement (within the error bars) in Figure 8 (∼1.75 ppmv loss) and partially correct for edge loss. The second source of uncertainty is in the various estimates of the descent rate. The simplest way to estimate this sensitivity to descent rate is to look at the increase in ozone expected from descent. Using the mid-January vortex profile, and assuming a 50 K PT descent in the 500–400 K region over winter, the increase in ozone would be roughly 0.5 ppmv. From the long-lived tracer data the uncertainty in the net descent is about 20 K (E. Ray, personal communication, 2001) which means that descent uncertainty alone could account for 0.2 ppmv (∼10%) difference among the loss estimates. Thus it is not surprising that the various analysis techniques arrive at ozone loss numbers that differ to within 0.5 ppmv. We conclude that the various estimates of ozone loss are actually in fairly good agreement given the variety of techniques, the variety of estimates of descent, and the residual variability within the vortex ozone field.
 Ozonesondes continued to be launched into the vortex after 15 March and the ozonesonde regression analysis shown in Figure 4a extends to the end of March. By that time, nearly 70% of the ozone was lost (more than 2 ppmv) even though the vortex rapidly shrank in area during that period. Sinnhuber et al.  also show ozone loss amounts of 70% by the beginning of April using the Ny-Alesund ozonesondes. Their loss amounts are nearly 2.5 ppmv compared with ours which are just over 2.0 ppmv for the same period. The differences can be traced to our selection of the data within the vortex MPV edge. Some of the late March Ny-Alesund ozonesondes are outside the MPV edge as determined by the gradient, and are not included in our analysis. This is a period when the vortex is eroding rapidly and large fragments have broken off the main vortex. If we restrict our analysis to just Ny-Alesund observations and relax the edge criterion for March we obtain the Sinnhuber et al. values. However, it is not clear that the Sinnhuber et al. number represents a vortex average loss amount or an upper limit on that loss.
 We have also done a computation of the column ozone loss from December 1999 through 15 March 2000. This loss can be crudely compared with polar ozone changes from the Total Ozone Mapping Spectrometer (TOMS). Taking the 63°–90°N average of all the TOMS March data 1979–1990 and comparing that with the average in March 2000, we find that polar total ozone decreased by ∼61 Dobson Units (DU) compared to the pre-1990 average. The year-to-year variability prior to 1990 was about 26 DU peak to peak so this decrease is well beyond the pre-1990 fluctuation range. For example, in 1986, the March averaged polar temperatures were close to that observed during SOLVE and the March mean column ozone was 430 DU. The average column ozone for the SOLVE March period was 385 DU. Thus at least 45 DU could be plausibly assigned to chemistry, assuming, as a lower bound, that none of the loss in 1986 was chemical. From Figure 8, the chemical decrease is computed for winter 2000 will be between 44 (ozonesonde) and 57 DU (POAM), which is in reasonable agreement with this crude estimate.
 The authors wish to acknowledge the SOLVE and THESEO management, logistics personnel, and the staff at Arena Arctica, Kiruna, Sweden for excellent mission support. We would also like to thank the DC-8 and ER-2 aircraft managers, ground crew, and pilots for their superior performance during the SOLVE mission. This work was funded by NASA's Upper Atmosphere Research Program and the Earth Observing System Program Office.