The effect of polar stratospheric clouds (PSCs) on ozone depletion during the 1999–2000 Arctic winter has been assessed using a coupled microphysical/photochemical model. Scenarios spanned a large range of denitrification levels, with up to 80% vortex-averaged denitrification and localized dehydration. PSC composition was varied, exploring sensitivity to heterogeneous reaction rates. PSC formation during February was critical in causing severe ozone depletion below 500 K. Heterogeneous chemistry on these PSCs was able to continuously reactivate the newly produced ClONO2. Only 30–40% vortex-averaged ozone loss would have occurred without this chlorine reactivation; with it, 21–32% more ozone loss is possible. During February (unlike earlier in the winter), chlorine reactivation and ozone loss were sensitive to heterogeneous chemistry: varying the reactivities altered ozone loss by 11%. An analysis of the critical temperatures for heterogeneous chemistry demonstrates the importance of temperatures near the nitric acid trihydrate condensation point, where many uncertainties influence heterogeneous reaction rates. Chlorine reactivation during February also prevented denitrification from enhancing ozone loss until March: 70% vortex-averaged denitrification only enhanced ozone depletion by 3% on 10 March. The mid-March vortex breakup probably limited the extent of ozone depletion; if the vortex had remained stable until 15 April, 16% ozone loss (out of a total 68% ozone loss) could be caused by 70% denitrification. Ozone loss intensifies nonlinearly with enhanced denitrification: in individual air parcels with 90% denitrification, 40% ozone loss in mid-April can be attributed to denitrification alone.
 Two ingredients are known to be important in causing ozone loss in the polar stratosphere: chorine activation and denitrification [e.g., Solomon, 1999]. Chlorine activation is responsible for converting inorganic chlorine from relatively inert forms, namely HCl and ClONO2, into active species such as ClO that rapidly and catalytically destroy ozone. Denitrification is the permanent removal of HNO3 from the stratosphere; otherwise, HNO3 causes deactivation of ClO during the polar springtime. Polar stratospheric clouds (PSCs) play a key role in both processes: the clouds provide the surfaces on which heterogeneous reactions activate chlorine, and, under the right circumstances, the cloud particles can sediment, causing HNO3 removal. Quantifying these processes is critical for understanding current and future ozone loss.
 Especially in the Arctic, models have not always been able to reproduce observations of ozone depletion. In many cases, ozone depletion is underpredicted by models [Becker et al., 1998, 2000; Deniel et al., 1998; Woyke et al., 1999], by as much as 50%. However, results have varied, particularly from year to year. Guirlet et al. , using the SLIMCAT model, found that the model underestimated ozone depletion in some years, but had good agreement for other winters. Sinnhuber et al.  found good model/measurement agreement with the SLIMCAT model for the 1999/2000 winter; they have suggested that the cold temperatures during that winter caused increased model denitrification, improving ozone results.
 Several studies have explored the sensitivity of chlorine activation and ozone depletion to PSC characteristics. One factor is denitrification, which is controlled by the PSC properties, and increases modeled ozone loss [Chipperfield and Pyle, 1998; Waibel et al., 1999; Becker et al., 2000; Tabazadeh et al., 2000]. On the other hand, chlorine activation is mostly insensitive to assumptions about the PSC composition. Only if PSCs persist into the springtime (when heterogeneous reactions are not saturated) do variations in their characteristics alter modeled ozone loss [Portmann et al., 1996; Carslaw et al., 1997]. Since PSCs generally are not present during the Arctic spring, denitrification is usually the dominant factor.
 The SOLVE campaign provided an unprecedented opportunity to study both ozone depletion and the PSC characteristics that led to this depletion. Unusually cold temperatures [Manney and Sabutis, 2000] promoted widespread PSC formation [Fahey et al., 2001] (E. V. Browell et al., Polar stratospheric cloud types, distributions, optical characteristics, and correlations with temperatures and gravity waves during the SOLVE campaign, submitted to Journal of Geophysical Research, 2002). In situ measurements show widespread denitrification [Popp et al., 2001] contributing to severe ozone depletion [Sinnhuber et al., 2000; Richard et al., 2001; Gao et al., 2001].
 We have previously used a detailed microphysical model to study the characteristics of the PSCs during the 1999–2000 winter [Drdla et al., 2002]. In this paper, the chemistry in these scenarios is explored. The wide range of denitrification levels in the work of Drdla et al.  allows for a more complete quantification of the relationship between denitrification and ozone loss. The scenarios also provide the opportunity to examine differences between NAT, NAD, and liquid-phase aerosols. Finally, several of the scenarios also yield dehydration, allowing its role in ozone depletion to be revisited [e.g., Chipperfield and Pyle, 1998].
 Another motivation for this study is that our understanding of PSC microphysics is continually improving. Previous modeling studies have assumed that ice formation leads to denitrification [e.g., Waibel et al., 1999; Sinnhuber et al., 2000]. However, this mechanism is unable to reproduce the extent of PSC formation and denitrification that were observed by the SOLVE campaign. Drdla et al.  tested scenarios that are more successful at capturing the observed characteristics of the 1999–2000 winter. The current study extends this research, by examining whether a model scenario with denitrification comparable to observations also produces realistic ozone loss.
 Following a description of the model and its initialization, the results will be divided into a section on chlorine activation and a section on ozone depletion. The chlorine activation discussion will focus on the sensitivity of chlorine chemistry to the heterogeneous reactivity by comparing scenarios with varying assumptions about PSC composition. The behavior during different phases of the winter will be quantified. The ozone depletion section begins by examining the effects of this chlorine activation on ozone. Finally, the role of denitrification on ozone depletion will be discussed, again by comparing different scenarios with a wide range of different denitrification levels.
2. Model Description
 The Integrated Microphysics and Chemistry on Trajectories (IMPACT) model used in this study calculates full PSC microphysics, heterogeneous chemistry, and gas-phase chemistry along trajectories. By doing simulations along a large set of trajectories, it is possible to calculate the winter-long, three-dimensional evolution of the stratospheric vortex.
 The model microphysics, discussed in more detail by Drdla et al. , determines the aerosol size distribution and composition based upon the temperature evolution. Multiple aerosol types (liquid, NAT, NAD, or ice) can be simultaneously present, with size bins to represent the size distribution of each particle type. The effects of condensation, evaporation, sedimentation, nucleation, freezing, and melting are all modeled. PSCs affect the chemistry both via heterogeneous chemistry and by removing condensed-phase species. The removal may be temporary, when HNO3 and H2O are sequestered in the PSC particles, or permanent, due to sedimentation causing denitrification and dehydration. The model sedimentation includes a calculation of the incoming particle flux from higher altitudes (causing renitrification and rehydration) as discussed by Drdla et al. .
 One feature of this model is the detailed treatment of heterogeneous chemistry. A comprehensive set of heterogeneous reactions has been included in the simulations (Table 1). At each time step, the heterogeneous reaction rates are calculated based on the simulated PSC particle types present and their size distribution, including size-dependent effects. Based on the available laboratory data, the sticking coefficients are dependent on temperature, relative humidity, and composition. Figure 1 provides typical values of some of the sticking coefficients.
Table 1. Heterogeneous Reactions Included in Model and the Value of the Sticking Coefficient or Method of Determining it for Each Particle Composition
 For ice and NAT particles, the reactions are explicitly treated as surface reactions, accounting for species surface coverage, as described by Tabazadeh and Turco . For SAT, the physical absorption model of Henson et al.  has been used.
 Reaction rates in liquid particles have been calculated from the available data on liquid-phase solubility, diffusion, and rate coefficients. For a typical reaction A + B (where B is the condensed-phase reactant), the sticking coefficient of the gas-phase reactant A, γA, can be determined from [e.g., Donaldson et al., 1997]:
αA is the mass accommodation coefficient of A, ωA is the mean molecular speed of A, R is the gas constant, T is the temperature, H*A is the effective Henry's law constant for A, DA is the diffusivity of A, kII is the liquid-phase reaction rate for A + B, and [B]c is the condensed phase concentration of B (= H*BpB at equilibrium, where pB is the partial pressure of B). f(r/l) is a size dependent factor [Hanson et al., 1994], based on the ratio of the particle radius, r, to the diffusoreactive length . Equation (1) is used for all liquid-phase reactions, except for N2O5 and BrONO2 hydrolyses (measurements of these reactions show nearly constant sticking coefficients, Table 1); the parameters used in equation (1) for all other reactions are listed in Table 2. Several of these parameters have only been determined for binary H2SO4/H2O solutions; in these cases the equilibrium binary solution composition [Tabazadeh et al., 1997b] is used. Otherwise, the ternary solution composition, as calculated by the microphysical model, is used to calculate the parameters.
Table 2. Values and Sources Used to Calculate Parameters Necessary for Liquid Solution Reactivities
 For reactions (R1) and (R2), the reaction-specific modifications to equation (1) of Hanson  have been included, except that the values of DHCl and H*HCl used here (Table 2) differ slightly from those used by Hanson . For reactions (R11) and (R12), the temperature and composition dependence of kII has not been measured. As done by Hendricks et al. , the single measurement of (R12) by Abbatt and Nowak  has been extrapolated, assuming the behavior of (R12) is comparable to (R5). For (R11), a diffusion-limited rate has been assumed, consistent with the data of Abbatt . Even with such a large assumed value for kII, this reaction is not important: reactions (R10) and (R12) are always much faster at removing HOBr and HBr, respectively.
 The gas-phase chemistry [Drdla et al., 1999] incorporates 58 species, grouped into 29 families. 188 gas-phase reactions (41 of which are photodissociations) are considered, using rates from the work of Sander et al. . Complete chorine and bromine chemistry is included; iodine chemistry is excluded. The solar flux for the photodissociation rates is determined from lookup tables [Pierson et al., 2000]; the tables provide solar flux as a function of wavelength based on pressure, overhead ozone column, zenith angle, and surface albedo. Total Ozone Mapping Spectrometer satellite measurements provided the total ozone column and surface albedo along each trajectory; climatological ozone profiles were used to estimate the fraction of the total ozone column above the trajectory.
 A set of 2905 winter-long, vortex-filling diabatic trajectories [Drdla et al., 2002] has been used to provide the dynamical forcing for the model. Each trajectory extended from 1 November 1999 to 15 April 2000, allowing the full impact of PSC processing on ozone depletion to be evaluated. In altitude, the trajectories spanned from the bottom of the vortex (based on the work of Nash et al. , the vortex typically could not be defined below 425 K) to above the highest level at which PSCs could possibly form (∼700 K). The trajectory ensemble was constructed to provide uniform coverage of the vortex and vortex edge region on 15 January; supplementary trajectories also ensured complete coverage on 15 March and 15 November.
 One limitation of the simulations is that no mixing occurs; each trajectory is modeled completely independently. As long as the vortex is stable, mixing of midlatitude air into the vortex is minimal, and even mixing among air parcels within the vortex is limited [Schoeberl et al., 1992]. However, in the 1999–2000 winter, the vortex began to break down in mid-March; the vortex area decreased by 75% between 10 and 20 March. Only a small area of the vortex was able to persist after the March breakup and remain stable into April. Despite the vortex breakup, the simulations have been extended to 15 April to allow the full effect of denitrification to be examined. The extensions can only be considered an extrapolation of what might have happened if the vortex had remained stable through mid-April (preventing any midlatitude air from mixing into the vortex) rather than a representation of the 1999–2000 winter.
 This paper will focus on vortex-averaged behavior. Given the trajectory-based approach, the vortex average is calculated by averaging over the trajectories present in the vortex. When examining the overall winter evolution (particularly Figures 3, 4, and 9), the average on each date and at each potential temperature level (using 25 K bins) is calculated by averaging the characteristics of all the trajectories located in the vortex for that date and level. For most of the winter (from 5 December to 10 March), more than 150 trajectories are present at each level.
 However, using such vortex averages, several factors are responsible for variations. Diabatic descent of trajectories through the fixed levels and transport of trajectories into or out of the vortex alter the specific set of trajectories, thus reproducing the effects of transport. This study is frequently interested in isolating the effects of chemistry on the trajectories. To do so, the analysis has focused on a fixed set of trajectories, specifically the 1455 trajectories that were inside the vortex on 1 March. Averages using this set of trajectories will be described as “fixed-vortex” averages. The effects of both vortex size changes and descent are eliminated in these averages.
 “Fixed-vortex” averages are also used to explore ozone loss at the end of the winter, providing an approximation of the vortex evolution if it had remained stable throughout the model duration, i.e., to 15 April. Only 10 trajectories were located in the small vortex remnant that persisted into April; this number is too small to provide meaningful statistics. The behavior of the trajectories has been examined, confirming that the ozone loss characteristics of the full set are comparable to the 10 vortex-remnant trajectories.
 Measurements made in November 1999, averaged at 25 K potential temperature intervals, were used to initialize the trajectories. CH4, N2O, SF6, CFCl3, and CF2Cl2 were initialized directly from in situ LACE measurements [Elkins et al., 1996] on the OMS balloon launched 19 November 1999. POAM [Bevilacqua, 1997; Hoppel et al., 2002] O3 profiles within the vortex for the whole month of November were averaged to provide initial O3 values. Constant profiles of H2O (5 ppmv) and H2SO4 (0.17 ppbv, all condensed) were assumed.
 Additional quantities of interest were derived from the measurements. The N2O–NOy correlation observed by MkIV data [Toon et al., 1999] on 3 December, 1999 was used to estimate the initial NOy profile. NOy was partitioned among the component nitrogen species, with initially 90% in HNO3, 5% in N2O5, and 2.5% in each of NO and NO2. The SF6, CFCl3, and CF2Cl2 data have been used to estimate the age of the air mass and thus total inorganic chlorine (Cly) and total inorganic bromine (Bry) [Montzka et al., 1996; Volk et al., 1997; Wamsley et al., 1998]. The Cly was distributed as 70% HCl and 30% ClONO2; the Bry, 9% HBr, 72% BrONO2, 18% BrO, and 1% HOBr. Following initialization, model chemistry dictates the partitioning of the nitrogen, chlorine, and bromine families.
 The resulting vertical profiles were used to initialize all of the trajectories, using each trajectory's potential temperature on 19 November. Since the discussion will focus on the end of the winter, Figure 2 shows initial profiles of several key species taking the effect of winter-long subsidence into account. The resulting profiles can be directly compared with profiles shown later in the paper (e.g., Figure 10).
2.2. Model Scenarios
Drdla et al.  compared the PSC characteristics, denitrification, and dehydration produced by a range of assumptions about PSC microphysics. 43 scenarios in all were considered, which differed mainly in the assumed freezing mechanism. Seven of these scenarios, demonstrating the variability of model chemistry, were selected for detailed examination in this study; the other 36 are only used to provide a more complete relationship between denitrification and ozone loss (e.g., Figure 11).
 The only difference between the simulations discussed here and those by Drdla et al.  is that, for this study, liquid particles have been prevented from sedimenting. As discussed by Drdla et al. , even in a scenario with only liquid-phase particles, some denitrification is possible due to sedimentation of those liquid particles. This liquid-phase sedimentation was explicitly turned off so that the “Liquid” scenario provides a baseline with no denitrification or dehydration. For consistent sulfate aerosol characteristics, all the other simulations were also performed with liquid particle sedimentation turned off. This change reduces denitrification levels relative to the simulations shown by Drdla et al. , but typically by only 5–10%.
 The seven main scenarios of this study are compared in Table 3. In the baseline scenario, “Liquid,” there is no freezing, forcing all aerosol to be liquid. All other scenarios include homogeneous freezing to form ice and one additional freezing process. The second process is necessary to form widespread solid-phase PSCs and thus widespread denitrification. The introduction of a second freezing process also decouples denitrification from ice formation: denitrification occurs without dehydration.
Table 3. Scenarios That are Examined in This Study
Freezing Type and Rate
NAT or NAD
All scenarios except “Liquid” include ice freezing, calculated using freezing rates from the work of Tabazadeh et al. . An additional freezing process to form NAD or NAT, as listed in the table, is also included. For heterogeneous freezing, the percent of particles that heterogeneously freeze, f, is specified (in all cases, using the “HetFrzB” assumptions discussed by Drdla et al. ). For homogeneous freezing, the rate k (cm−3 s−1) is specified. Vortex-averaged denitrification is provided for 450 K on 1 March.
Heterogeneous, f = 0.02%
Matches observed denitrification
Homogeneous, k = 107
Matches observed denitrification
Heterogeneous, f = 0.1%
Matches observed denitrification
Heterogeneous, f = 0.1%
Maximum simulated denitrification
Heterogeneous, f = 100%
Widespread NAT PSCs with large surface areas
Homogeneous, k = 109
Limited PSC formation in springtime with widespread SAT
 Three scenarios, “HetMatch,” “HomMatch,” and “NADMatch,” were selected because the extent of denitrification was comparable to the SOLVE measurements (i.e., ubiquitous denitrification in the vortex with typical denitrification levels of 60–70%). “HomMatch” and “HetMatch” both have NAT particle formation. In the former, a homogeneous freezing process is assumed, i.e., all particles are theoretically able to freeze, but the actual number of particles is controlled by the freezing rate, k. In the latter, heterogeneous freezing is assumed: a fixed percent of the particles are assumed to contain “special” nuclei that promote freezing. “NADMatch” has NAD particle formation by heterogeneous freezing.
 To demonstrate the effects of more intense denitrification, the “MaxDenit” scenario will be discussed. This scenario had the most extreme denitrification of all the cases considered.
 Finally, two scenarios have been included to demonstrate possible changes to heterogeneous chemistry. In “MaxNAT” all the available particles freeze and can grow as NAT, increasing the heterogeneous reactivity at temperatures just below the NAT condensation point. Reduced heterogeneous reactivity in the same temperature region is produced in the “MaxSAT” scenario. Two characteristics of “MaxSAT” are responsible for the low reactivity. First, a fast freezing rate causes most of the particles (more than 70% at 450 K) to freeze into SAT by the end of the winter, which suppresses liquid-phase heterogeneous reactions. Second, solid-phase PSCs are assumed to be NAD, preventing their formation until 2 K below the NAT frost point.
3. Model Results: Chlorine Evolution
 The overall level of active chlorine, ClOx, and the rate of HCl activation during the 1999–2000 winter are summarized in Figures 3 and 4. These figures are for the “Liquid” scenario, in which only liquid-phase PSCs are present, and no denitrification occurs. The chlorine species chemistry can be divided into three periods during the 1999–2000 winter: chlorine activation, chlorine reactivation, and chlorine recovery.
 During the first half of the winter, heterogeneous reactions convert chlorine from the inactive reservoirs, HCl and ClONO2, to the more reactive ClOx species. At most levels, the ClOx/Cly ratio is near its maximum value for the winter on 1 February; the period of the winter up until 1 February will therefore be labeled as the “chlorine activation” period. During the month of February, sufficient sunlight is available for chlorine to begin to recover. However, the continued presence of PSC temperatures in the lower stratosphere introduces continued chlorine activation that competes with chlorine recovery; the month of February is described in this study as a period of “chlorine reactivation.” Finally, in March the period of unequivocal “chlorine recovery” commences, as temperatures warm up enough for unimpeded conversion of ClOx to HCl and ClONO2 to proceed.
 PSCs, and the various microphysical scenarios, influence chlorine differently during each of these three periods. To demonstrate the effects, the discussion will focus on the fixed-vortex average evolution at 450 K.
3.1. Chlorine Activation
 Chlorine activation starts in December, with the onset of cold temperatures. Repeated exposures to cold temperatures through the winter enhance the activation, reaching a maximum at 450 K in the “Liquid” scenario of 75.5%, averaged over the whole vortex, on 29 January (Figure 3). However, the chlorine activation rate (Figures 4 and 5b) is not solely related to the minimum temperature. During the period of coldest temperatures, near 10 January, heterogeneous reaction rates are negligible. This is because the extent of chlorine activation during this period is limited by the availability of ClONO2 (Figure 5d) and other species that react with HCl. Averaged over the vortex, one-quarter of the inorganic chlorine remains present as HCl (Figure 5c) through early February; in individual air parcels, the HCl/Cly ratio ranges from 5 to 35% within the vortex. (A slight dip in gas-phase HCl around 10 January is caused by HCl temporary dissolution, but not reaction, in the dilute sulfate particles present at these very cold temperatures.)
 Analysis of the individual reactions that contribute to Figure 4 reveals that reaction with ClONO2, reaction (R2), dominates HCl activation at all levels of the stratosphere. Reaction with HOCl, reaction (R5) is also important, causing 40% of the HCl activation at most levels. However, the primary source of HOCl during the polar winter is ClONO2 hydrolysis (R1): therefore the availability of ClONO2 effectively controls the extent of heterogeneous HCl activation. The only other HCl reaction to play any role in the “Liquid” simulation is (R10), reaction with HOBr, but it is almost two orders of magnitude slower than (R2) or (R5). Without any gas-phase chemistry, the initial conditions (70% of Cly as HCl and 30% as ClONO2) would allow a chlorine activation level of 60% ClOx/Cly. 75.5% active chlorine, as reached on 29 January, indicates that during the early winter gas-phase chemistry does convert some of the ClOx back to ClONO2 and HOCl; the regenerated ClONO2 and HOCl rapidly react again with HCl, thus creating additional ClOx.
 The ratio of ClONO2 to HCl at the beginning of the winter is clearly a critical parameter in determining the extent of chlorine activation. Examination of the HCl evolution in the early winter suggests that the HCl initialization was at near-equilibrium levels but may have been slightly too low: during the first 15 days of the simulation, HCl levels increase, but by less than 0.1%. Any increase in initial HCl levels would serve to further limit the availability of ClONO2 and HOCl. Therefore, the key features of these simulations, that chlorine activation is limited by the availability of ClONO2 and HOCl and that HCl remains present through the winter, would not be affected by uncertainties in the initial HCl/Cly ratio.
 The early winter chlorine evolution is comparable in all of the scenarios considered (Figures 5a–5d), with remarkably similar ClOx/Cly levels in late January: among these seven simulations, ClOx/Cly only varies by 2.1% on 29 February. In simulations with widespread NAT particles (i.e., “MaxNAT”), chlorine activation occurs more rapidly in early December, but the situation reverses later in the month. Previous studies have also found little sensitivity of chlorine activation to the composition of the PSCs, despite the different reactivities of the various particle types. This insensitivity is another indication that the heterogeneous reactions saturate. The timescale for HCl and ClONO2 reaction can be as short as minutes; given PSCs that are present for multiple days, at least one of the available reactants is removed long before the evaporation of the PSC. Large variations in the heterogeneous reaction rates have no effect, as long as the reaction timescale remains faster than the PSC lifetimes.
 Another implication of the rapid reaction timescales is explored in more detail in Figure 6. Many papers have presented the sticking coefficients or heterogeneous reaction coefficients as a function of temperature, as shown in Figure 1 or Figure 6a, respectively. These figures suggest that the coldest temperatures are far more important for activating chlorine than more moderate temperatures: the sticking coefficients increase exponentially as temperatures cool (Figure 1). PSC surface areas are also largest at the cold temperatures, further accelerating the theoretical reactivity (Figure 6a).
 However, integrating the actual chlorine activation rates as a function of temperature in these model results reveals a very different picture. ClOx production is most efficient within a few degrees of the NAT condensation point; 29% of Cly is even activated at temperatures above the NAT condensation point. Two factors are limiting the role of the coldest temperatures. First, cold temperatures are rare (Figure 6c). Even though the 1999–2000 winter was unusually cold, the mode temperature was above the NAT condensation point. Second, and more importantly, the heterogeneous reactivity near the NAT condensation point is fast enough to allow all of the available ClONO2 (Figure 6d) and HOCl (not shown) to react; by the time the colder temperatures are reached, the necessary reactants are no longer present.
 In a scenario with large numbers of NAT particles (“MaxNAT”), the overall heterogeneous reactivity is increased by the large particle surface area just below the NAT condensation point. (The surface area increase enabled by NAT condensation more than compensates for the slight decrease in sticking coefficients on NAT relative to liquid solutions.) As a result, removal of ClONO2 and other reactants occurs more rapidly, further increasing the role played by moderately warm temperatures. 93% of the chlorine activation occurs above T − TNAT = −4 K. Overall, 70% of the chlorine is activated by NAT particles. Liquid particles are responsible for the remainder, primarily due to their role at temperatures above the NAT condensation point. But in the end, the chlorine activation at the end of February, i.e., Figure 5a, is nearly identical to the other simulations.
3.2. Chlorine Reactivation
 During the month of February, solar exposure is sufficient to initiate chlorine deactivation. With no denitrification, HNO3 begins to break down, releasing NO2. The reaction of HNO3 with OH is the most important HNO3 decomposition reaction in early spring; only one-third of the NO2 is produced by HNO3 photolysis. Almost all of the resultant NO2 rapidly reacts with and deactivates ClO:
 In addition, temperatures cold enough to permit PSC formation persisted into the month of February. At the end of January, heterogeneous reactions had essentially ceased because of the lack of reactants such as ClONO2 (Figure 5b). Now, however, the newly produced ClONO2 begins to react heterogeneously, reactivating chlorine and consuming HCl. One result is that ClOx levels remain nearly level during the month. Reactivation also strongly alters the HCl evolution (Figure 5c). Both ClONO2 and HOCl (the product of ClONO2 hydrolysis, (R1)) react with HCl, causing the lowest HCl levels of the winter (approaching zero in many air parcels) to be reached on 7 March, at the end of the last PSC event. Overall, for the “Liquid” scenario in Figure 5, 43% of the heterogeneous chlorine activation during the entire winter occurs after 1 February.
 Denitrification has a limited impact on chlorine levels during this period. Because of the decreased availability of NO2 in denitrified regions, less ClOx is deactivated to ClONO2, reducing ClONO2 levels (Figure 5d). However, active chlorine levels are not affected to a similar degree (Figure 5a): less ClONO2 reduces the extent of reactivation. The net effect is to cause only slightly more active chlorine to be present in denitrified scenarios. HCl levels (Figure 5c) are nearly flat during February in the “MaxDenit” scenario: gas-phase formation of HCl is closely balanced by the heterogeneous removal of HCl.
 A second factor has a greater influence on active chlorine levels in February than denitrification: the rate of the heterogeneous reactions. Figure 7 allows the heterogeneous reactions during the month of February to be compared with those earlier in the winter (Figure 6). Unlike earlier in the winter, the heterogeneous reactions in February are not saturated; the photochemistry is constantly reforming ClONO2 via reaction (R14). This is evident in Figure 7d where ClONO2 remains present at temperatures below the NAT condensation point.
 The “MaxNAT” scenario demonstrates the effect on chlorine of altering the heterogeneous reaction rates (since denitrification in this scenario is small, it has limited effect). ClOx levels are noticeably higher in “MaxNAT” than in “Liquid” because NAT formation allows slightly faster heterogeneous reactions at temperatures just below the NAT condensation point (Figures 5a and 5b). Overall, 41% more chlorine activation is possible after 1 February in the “MaxNAT” scenario; before 1 February, the “MaxNAT” net chlorine activation is only 7% faster than the “Liquid.” ClONO2 levels are correspondingly lower, especially at cold temperatures, where the reaction rates approach saturation. (The onset of saturation suggests that further increases in the reaction rates would have limited impact.) On 7 March, the ClOx/Cly level is 19% larger in the “MaxNAT” scenario than in the “Liquid;” this effect is more than twice as large as the 9.2% active chlorine enhancement caused by extensive denitrification in the “MaxDenit” scenario (Figure 5a).
 Another simulation, “MaxSAT,” experienced the opposite effect. In this case, since SAT and NAD control the heterogeneous chemistry, the chlorine activation rate is reduced in the critical temperature range, near the NAT condensation point. The overall chlorine activation rate is 8.8% less than for the “Liquid” scenario. Therefore, this simulation had the lowest ClOx levels of all the scenarios that were examined.
 In all scenarios other than “MaxNAT” and “MaxSAT,” liquid-phase reactions dominated heterogeneous chemistry, and therefore the reactivities were fairly similar to the “Liquid” scenario. A corollary of the small solid-phase particle concentrations necessary to get substantial denitrification is that most of the aerosol remains liquid throughout the winter. For f < 10% (heterogeneous freezing cases) or k < 108 (homogeneous freezing cases), liquid aerosol dominates the surface area and chemistry, especially in February. For each of “HetMatch,” “HomMatch,” “NADMatch,” and “MaxDenit” more than 99% of the chlorine reactivation occurred on liquid-phase particles. This is also true for most of the other 36 scenarios considered by Drdla et al. . Therefore, only denitrification levels produced variations in chlorine evolution and ozone depletion for most cases.
 To assess the impact of the February chlorine reactivation, it is possible to estimate what the evolution of the vortex would otherwise have been. The ClOx produced by heterogeneous reactions after 1 February has been subtracted from the modeled ClOx values (Figure 8a); an exponential decay (derived from the original simulation's decay rate in March) was assumed once ClOx/Cly fell below 30%. The resulting ClOx curve is realistic: active chlorine declines monotonically; the recovery of chlorine is faster in the absence of denitrification. Also, the “MaxNAT” and “MaxSAT” simulations now have very similar chlorine levels: the denitrification level (which coincidentally is very similar for these two scenarios) is controlling the chlorine evolution in the absence of the effects of heterogeneous chemistry. Comparison of the estimated ClOx values with the original model values (Figure 5a) reveals that chlorine recovers about two weeks earlier. The effect of this reduction in chlorine on ozone loss rates will be discussed in section 4.
 This discussion has focused on the 450 K level. PSC formation during February and March was concentrated in the lower stratosphere. No significant chlorine reactivation occurred at 500 K or higher. On the other hand, below 450 K, the frequency of PSCs increased, causing more extensive heterogeneous reactions at 425 K (this study does not extend below 425 K). These altitude variations are evident in both Figures 3 and 4, and will be discussed further in relationship to ozone profiles in section 4.
3.3. Chlorine Recovery
 Starting in March, rapid chlorine recovery is possible. If sufficient NOy is present, the fastest deactivation route is reaction (R14), producing ClONO2 and consuming all available NO2. Elevated ClONO2/Cly ratios (up to 68%) result in mid-March. ClONO2 then slowly decays back to typical values. In the “Liquid” scenario, chlorine recovery is possible before the vortex break up (about 15 March); mixing with midlatitude air is not necessary for chlorine deactivation.
 HCl recovers more slowly, and even by 15 April, HCl/Cly levels in the “Liquid” run are lower than usual for midlatitudes. The primary pathway for HCl production at 450 K is:
At 450 K, the rate of reaction (R16) can be as high as 80% of the rate of (R15), particularly in denitrified scenarios. At higher levels, e.g., 500 K, (R16) is faster than (R15) by as much as 150%. Reaction (R16) is a minor channel of the ClO + OH reaction; only during the last decade have accurate measurements of its branching ratio become available [e.g., Lipson et al., 1999]. Its role in chlorine deactivation in polar springtime (especially in the presence of denitrification) highlights the importance of accurate information on this reaction.
 For denitrified scenarios the evolution is very different. ClONO2 formation is prevented by the low nitrogen levels. Instead, chlorine recovery is dominated by formation of HCl by reactions (R15) and (R16). Since recovery to HCl is about four times slower than to ClONO2, high levels of active chlorine are maintained for longer. The simulations show high levels of active chlorine persisting past 15 March, when two-thirds of the vortex air mixes out to midlatitudes. At this point, the introduction of HNO3 by mixing processes (which are not part of these model calculations) is likely to rapidly deactivate the remaining chlorine. The model results in late March and April represent the maximum possible levels of active chlorine, demonstrating, for example, the possible effect of a more stable and persistent vortex.
4. Model Results: Ozone Depletion
 When sufficient sunlight is available, activated chlorine efficiently destroys ozone. Even in the “Liquid” scenario (Figure 9), ozone loss exceeds 50% in the lower stratosphere. Other simulations yielded even more ozone loss, especially in April (Figure 10). These results have been analyzed to quantify the influence of several of the factors that were discussed in section 3. First, the impact of the chlorine reactivation in February has been examined, both to estimate how much ozone loss can be attributed to the late winter PSCs and to examine how sensitive ozone loss is to variations in heterogeneous chemistry during that period. Second, the role of denitrification has been quantified.
4.1. The Influence of Late Winter PSCs on Ozone Depletion
 As evidenced by comparing Figures 5a and 8a, the chlorine reactivation on PSCs in February (and even as late as 7 March) delayed chlorine recovery in the lower stratosphere by at least two weeks. Since solar exposure accelerates rapidly during this period, this delay should have a dramatic impact on ozone loss.
 To examine the effect of reactivation, the ozone depletion corresponding to Figure 8a's nonreactivated chlorine levels has been estimated. The ozone loss rate was assumed to be linearly proportional to ClOx; accordingly, the ozone evolution has been estimated by decreasing the ozone loss rate according to the ratio of the nonreactivated ClOx curve (Figure 8a) to the initial ClOx curve (Figure 5a). This is likely to underestimate the impact, since one of the most important ozone-depleting reactions, ClO + ClO, has a quadratic dependence on active chlorine levels. Even so, the results (Figures 8b and 8c) show that at least 20% ozone loss can be attributed to chlorine reactivation in February. For most simulations, the ozone loss contribution is remarkably similar, ranging from 23.6% to 25.7%, despite large variations in denitrification—the only simulations outside this range are “MaxNAT” and “MaxSAT.”
 For the “MaxNAT” scenario, with its more efficient heterogeneous reactions, the effect of those reactions on ozone is even larger. Figure 5g shows that in early March ozone loss rates in the “MaxNAT” scenario are 75% faster than in the “Liquid” scenario, reaching 3.5%/day. Figure 8c estimates that 32.3% ozone loss is caused by chlorine reactivation, 8.7% more than for the “Liquid” scenario. “MaxSAT,” on the other hand, experienced the slowest chlorine reactivation rates with an estimated effect of the reactivation of only 21.1%.
 The impact of the chlorine reactivation rates can also be calculated by comparing the ozone loss calculations in the original simulations, thus avoiding the approximations used to determine Figure 8. Figure 11, as discussed more in the next section, shows the difference in ozone loss between each simulation and the baseline “Liquid” scenario. This “extra ozone loss” can be attributed to two main factors: denitrification and variability in heterogeneous reaction rates. The effect of denitrification can be quantified, as described by equation (2) in the next section. The remaining ozone enhancement is due to changes in the heterogeneous reactions. Comparison of the “MaxNAT” scenario and “Liquid” scenarios shows that a 41% increase in the heterogeneous reaction rates leads to 6.9% more ozone loss. Similarly, for the “MaxSAT” scenario, a 4.0% decrease in ozone loss is caused by a 8.8% decrease in the rates.
 Since the frequency of the late winter PSCs varied with altitude, their effect on ozone depletion is also altitude dependent. Without chlorine reactivation, the ozone loss profile in each scenario is nearly flat from 425 to 500 K (Figure 10b). Therefore PSC activity in February and March is responsible for a strong increase in ozone depletion confined to the lower stratosphere.
4.2. The Influence of Denitrification on Ozone Depletion
 The ozone evolution (Figure 5) and ozone profiles (Figure 10) provide a qualitative indication of the effectiveness of denitrification: increased ozone loss in the “MaxDenit” scenario relative to the “Liquid” scenario can be ascribed to denitrification. On the other hand, a comparison of “HetMatch,” “HomMatch,” and “NADMatch” at 450 K (all having similar denitrification levels), reveals fairly similar evolution. This indicates that the differences in PSC characteristics among these scenarios have little effect on ozone depletion; only their denitrification level appears relevant.
 A more detailed examination of the relationship between denitrification and vortex-averaged ozone loss has been conducted, using the full set of 43 scenarios discussed by Drdla et al. . For each scenario, the difference between that scenario's ozone loss at each potential temperature and the “Liquid” scenario ozone loss at the same level has been determined. This difference can be compared to the vortex-averaged denitrification at the same potential temperature in that scenario (Figure 11). Scenarios where factors other than denitrification are playing a role are highlighted, namely “MaxNAT” and “MaxSAT,” whose anomalous chlorine reactivation was discussed in the previous section.
 In early March, denitrification has little influence on ozone levels, especially in the lower vortex. Figure 11a shows that on 10 March, at most 10% more ozone loss occurs in the denitrified scenarios, primarily at 500 K. At lower levels, the effect is halved. This impact is smaller than the ∼25% ozone loss due to chlorine reactivation inferred from Figure 8c. It is smaller even than the change in ozone loss than can be effected by modifying heterogeneous chemistry (i.e., the 10.9% difference between the “MaxNAT” and “MaxSAT” scenarios).
 The weak denitrification signal on 10 March is another repercussion of the February chlorine reactivation. Denitrification affects ozone by slowing the rate of chlorine recovery, but recovery is only possible once heterogeneous reactions have ceased. Comparison of Figures 10b and 10c confirms that larger denitrification-induced ozone loss enhancements (i.e., ozone loss relative to the “Liquid” scenario) would have been possible on 10 March if reactivation had not occurred.
 For scenarios with little denitrification, ozone loss rates peak in early March. Figure 5g shows that for the “Liquid” scenario, ozone loss peaks at 2.0%/day on 8 March; the loss rate has halved by the middle of the month. Therefore, in the absence of denitrification, ozone loss is essentially complete by the time the vortex broke up in mid-March. A more stable vortex, persisting into April, would not have promoted more ozone loss.
 For denitrified scenarios, the situation is quite different. In the “MaxNAT” scenario, the ozone loss rate peaks (at 3.2%/day) on 18 March; even though active chlorine levels are lower than earlier in the month, the increased solar exposure is able to maintain fast ozone loss rates. Furthermore, the ozone loss rates decline fairly slowly and have not gone to zero even by the end of the simulation on 15 April.
 However, these calculations do not include any effects due to mixing. In the late winter, the weakening of the vortex would enhance the amount of midlatitude air that can mix in with vortex air parcels, lowering active chlorine levels and introducing sufficient NOy to rapidly deactivate the remaining active chlorine. Without these processes, the calculations extending into April can not accurately represent the evolution of the 1999–2000 winter. The simulations can still be used, though, to extrapolate what could occur if the vortex had persisted, or what might occur in the future if the Arctic vortex becomes more stable. In particular, the extended simulations provide an opportunity to investigate the full effect of denitrification on ozone depletion.
Figure 11 follows the fixed-vortex ozone depletion from 10 March to 15 April. Fits of the ozone–denitrification relationship are shown for each of four dates; in generating these fits, data from the scenarios with unusual chlorine reactivation, namely “MaxNAT” and “MaxSAT” have been excluded. Note that the ozone loss in the “Liquid” scenario also increases from 10 March to 15 April (i.e., Figures 10b and 10d), with a maximum of 9.8% more ozone loss at 425 K.
 The effect of denitrification on ozone loss increases constantly between 10 March and 15 April, especially for simulations with large levels of denitrification. But even for average denitrification exceeding 80%, the effect on ozone loss is limited to 30%. The fit determined for 15 April is only slightly nonlinear:
Both ΔO3 and ΔNOy are changes relative to the initial quantities, expressed in percent. Extrapolating this relationship to 100% denitrification would imply a maximum ozone loss enhancement of 34%.
 Individual trajectories, however, experienced ozone loss exceeding 95% in some scenarios, allowing better quantification of the effects of extreme denitrification. Examining individual trajectories also allows factors that moderate ozone loss to be identified. Figure 12 shows the impact of denitrification in individual trajectories from the “MaxDenit” scenario. In many trajectories, more than 50% ozone depletion is caused by denitrification alone, but ozone loss varies significantly at high denitrification levels. Investigation of individual trajectories reveals that most of the variability can be ascribed to two factors. First, a small number of trajectories experienced dehydration (those with dehydration greater than 15% are identified in Figure 12); by impeding PSC formation and thus chlorine reactivation in February and March, dehydration reduces ozone loss [e.g., Chipperfield and Pyle, 1998]. Second, for many points, extreme ozone loss in the baseline “Liquid” scenario limits the possible additional effect of denitrification (e.g., if the baseline loss is 70%, the additional effect of denitrification must be less than 30%). Points with total ozone loss exceeding 80% are identified in Figure 12. These points are preferentially at lower altitudes (where baseline ozone depletion is greatest); this explains the altitude dependence apparent in Figure 11b.
 The denitrification–ozone loss relationship for individual trajectories can be described by:
Points with extreme total ozone loss (>80%) or >15% dehydration were excluded in generating this fit. Examination of other scenarios with localized renitrification reveals that this equation is valid for ΔNOy values ranging from −25% (i.e., renitrified air) to 95%. Compared to equation (2), equation (3) demonstrates a much stronger relationship between denitrification and ozone loss at high denitrification levels, suggesting that extrapolating equation (2) past 80% denitrification is not appropriate. Given the dramatic effect on ozone loss of small increases in denitrification (e.g., from 80% to 90%), quantifying the factors that could enhance denitrification is important, especially in winters where the vortex persists into late springtime.
 The modeled ozone loss on 10 March can be compared with several measurements of ozone loss made during the 1999–2000 winter. In situ measurements of ozone loss were made by the ER-2 during late February and the first half of March [Gao et al., 2001; Richard et al., 2001]. Several characteristics of the model are consistent with the work of Gao et al. . 10–20% ozone depletion in January and February is evident both in the observations and the model results at 450 K. The onset of denitrification affecting ozone depletion is comparable: in the measurements, denitrification only begins to enhance ozone loss following 26 February. However, quantitative differences are also present. The total ozone loss at 450 K on 12 March derived by Richard et al. , 58 ± 4%, is slightly larger than in model simulations with appropriate denitrification levels: ozone loss in the “HetMatch,” “HomMatch,” and “NADMatch” scenarios is 51–52% on 12 March. The model ozone loss rates differ in the opposite direction: model values of 2–3.2%/day are larger than the 1.3–2%/day values quoted by both Richard et al.  and Gao et al. . A more detailed analysis is necessary to understand these differences, including a comparison between the available chlorine measurements and the model results. However, the model/measurement comparison appears better than in modeling studies of previous winters.
 In the model, the effect of denitrification only becomes important following the last ER-2 flight. Ozonesondes and the Global Ozone Monitoring Experiment satellite show 70% ozone loss in late March [Sinnhuber et al., 2000; Rex et al., 2002]. This increase in ozone depletion, relative to the ER-2 measurements, is consistent with the effect of denitrification in the model results. Both Sinnhuber et al.  and Rex et al.  show that ozone loss is confined to the lower stratosphere, also consistent with the model. However, as with the ER-2 comparison, the model values are slightly lower than observations. Another difference relative to these studies is that, based on their model results, Sinnhuber et al.  conclude that denitrification played a large role in the ozone depletion. However, our results would suggest only 15% ozone depletion can be attributed to denitrification; the remainder of the enhanced ozone loss is caused by heterogeneous chemistry late in the winter.
5. Summary and Conclusions
 This study has explored the impact of PSCs on chemistry, both through their role in heterogeneous chlorine activation, and through the effects of denitrification. A range of different scenarios for PSC formation have been compared, to assess the sensitivity of ozone depletion to uncertainties in our understanding of PSC microphysics. Two factors were found to be important in causing ozone loss during the 1999–2000 Arctic winter. First, continuing PSC formation during February and even early March allowed heterogeneous reactions to reactivate chlorine; the extent of this reactivation and thus the magnitude of ozone depletion were sensitive to the heterogeneous reaction rates. Second, denitrification can increase ozone loss, but only at the very end of the winter; the breakup of the vortex in mid-March 2000 limited the potential ozone loss due to denitrification.
 If PSC activity had ceased on 1 February, and no denitrification was present, ozone loss during the 1999–2000 winter would have been limited to a fairly uniform 30% from 425 to 500 K. As in previous studies, the magnitude of this ozone loss is not sensitive to the characteristics of the widespread PSCs that formed during December and January: a wide range of assumed PSC compositions (including liquid, NAD, and NAT) produced nearly identical chlorine activation at the end of February. The extent of chlorine activation was limited by the availability of ClONO2, rather than the reactivities of the available PSC surfaces.
 In actuality, continued PSC formation was possible during February and early March, and the chlorine reactivation during this period alone induced an additional 21–32% ozone loss at 450 K. Previous studies have also found that low temperatures persisting into March are a necessary ingredient for strong Arctic ozone loss [e.g., Guirlet et al., 2000]. The PSCs during this period were particularly effective because the increased solar exposure had begun to regenerate ClONO2, the critical reactant that had limited the extent of HCl activation earlier in the winter. Furthermore, these conditions caused the extent of chlorine activation to depend upon the characteristics of the PSCs and, more specifically, upon the heterogeneous reaction rates. Increasing the heterogeneous reactivity by 41% caused 19% more active chlorine and enhanced ozone loss by 6.9%; decreasing the reactivity by only 8.8% caused 4.3% less active chlorine and reduced ozone loss by 4.0%. In these simulations, the heterogeneous reactivity was altered by changing the PSC composition; equal magnitude effects could be expected by varying the assumed sticking coefficients or surface areas. Furthermore, the temperatures critical for this chlorine reactivation, from about 0 to 4 K below the NAT condensation point, are complex to model. Liquid aerosols are truly ternary in behavior: HNO3, H2SO4, and H2O are all condensed in significant quantities. Very few laboratory measurements of heterogeneous reaction rates have been made on ternary solutions, and the results of those studies differ. The characteristics of solid-phase PSCs depend strongly upon the assumed composition (NAD or NAT) and the formation mechanism. Therefore, more confidence in PSC reactivities is necessary to properly understand ozone depletion during Arctic winters where PSC formation persists into February and March.
 Denitrification also influences ozone depletion in these simulations, in contrast to the work of Portmann et al.  who conclude that denitrification is not important if chlorine reactivation occurs in the springtime. This is in part another symptom of the differences between Antarctic and Arctic ozone loss: the less extreme ozone loss in the Arctic allows many more factors to influence overall ozone depletion. However, denitrification only becomes important after the last PSC event (8 March at 450 K); up to 5 weeks are necessary for ozone loss to maximize if denitrification is severe. The vortex break up in mid-March during this winter therefore limited the effect of denitrification.
 Following the vortex breakup, the accuracy of these simulations in portraying the evolution of the 1999–2000 winter decreases because effects such as mixing are not included in the trajectory-based model. However, the ozone evolution does represent the possible effect if the vortex had remained stable until 15 April, the end of the simulations. A nonlinear relationship between ozone loss and denitrification is apparent on 15 April. 70% vortex-averaged denitrification, as observed during the 1999–2000 winter, can cause an additional 20% ozone loss. Analysis of individual trajectories suggests that ozone loss would accelerate rapidly if denitrification intensified: in the extreme of 95% denitrification, nearly 50% ozone loss can be caused by denitrification alone.
 The model ozone levels at the end of the winter appear to be slightly higher than observations [Sinnhuber et al., 2000; Richard et al., 2001; Gao et al., 2001; Rex et al., 2002]. However, further study is necessary to accurately compare the model with the wealth of available observations during SOLVE. Given the strong sensitivity of model results to heterogeneous reactivities, confirmation of the heterogeneous reaction rates appears particularly important. Furthermore, discrepancies in ozone depletion at higher levels in January (where the model predicts negligible ozone loss, compared to observations of some ozone loss) need to be understood. Finally, SOLVE in situ measurements of chlorine species, including HCl, ClONO2, ClO, and Cl2O2, will provide insights on many aspects of the chemistry which may result in revisions to model reaction rates.
 The study was specific to the 1999–2000 winter, and the large interannual variability in the Arctic limits the number of general conclusions that can be drawn from any one winter. Future studies will examine other recent winters, and also the Antarctic, to examine how well long-term variations in ozone loss can be modeled, and to further quantify the role of processes such as denitrification.
 We would like to thank the SOLVE science team for providing the data used to initialize these simulations, particularly G. Toon, R. Bevilacqua, and J. W. Elkins. A. Tabazadeh provided many useful comments. This research was funded by the NASA Atmospheric Chemistry Modeling and Analysis Program.