The freezing processes that may lead to the formation of solid phase polar stratospheric clouds (PSCs) have been examined to assess their winter-long effects, especially denitrification, in a coupled microphysical/photochemical model. Trajectory simulations spanned from November 1999 to April 2000, using a large set of trajectories which provided representative coverage of the entire Arctic vortex through the period of PSC formation and ozone depletion. A freezing process occurring at temperatures above the ice frost point is shown to be necessary to explain both the occurrence of solid phase PSCs early in the winter and denitrification, especially without dehydration. If freezing only occurs below the ice frost point the primary contributor to denitrification is actually sedimentation of liquid phase PSC particles. The mechanism of a second freezing process, occurring above the ice frost point, can not yet be conclusively determined. Of the cases considered, heterogeneous freezing of the aerosol to form nitric acid trihydrate (NAT) particles best reproduced solid phase PSC formation and observations of widespread denitrification with limited dehydration. The simulations constrain the number of frozen particles to be near either 0.02% or 1% of the total aerosol number; values in between 0.02% and 1% produce more intense denitrification than observed, demonstrating that small changes in the number of frozen particles could exacerbate denitrification. However, this result was contingent upon assuming that the heterogeneous nuclei remain active, producing PSCs, throughout the winter. An idealized homogeneous freezing process was also able to produce NAT PSCs and denitrification (rates of 106–107 cm−3 s−1 compared favorably with data) but differed from observations in one key aspect: denitrification was more frequently accompanied by dehydration. Nitric acid dihydrate (NAD) particles were less effective than NAT at denitrification, but heterogeneous freezing of 0.1% of the aerosol yielded results marginally consistent with measurements. An important limitation, however, of all the scenarios considered is that they produced more intense and more widespread dehydration than was observed. This suggests that model minimum temperatures (from UK Meteorological Office analyses) were too cold by 1 to 3 K.
 Two decades of studying polar stratospheric clouds (PSCs) since the seminal work of McCormick et al.  have revealed that this label in fact encompasses several distinct categories of cloud. Based on satellite measurements [Poole and McCormick, 1988], Turco et al.  first coined the labels type I and type II PSCs. At the coldest temperatures, type II PSCs are observed with characteristics generally consistent with water ice clouds. At warmer temperatures, up to 7 K above the ice frost point, type I PSCs are observed. type I PSCs are formed by condensation of HNO3, but the exact composition can vary. At least two subcategories of type I PSCs exist, as first identified by Browell et al. . The lidar depolarization of some clouds, labeled type Ia PSCs, clearly indicates the presence of solid particles, whereas other clouds, labeled type Ib PSCs, appear to consist only of liquid particles [Arnold et al., 1992; Drdla et al., 1994]. The two categories of type I PSC have been observed at similar temperatures; the environmental factors that determine whether liquid or solid particles occur have not been resolved. One critical process is clearly the freezing of the background sulphate aerosols: freezing is necessary to produce solid phase PSCs, but the observed presence of liquid particles dictates that the freezing is not ubiquitous. This study has focused on the role of freezing in influencing the characteristics and effects of PSCs.
 Sulphate aerosols do not readily freeze, even though the particles are supercooled throughout the stratosphere. Binary H2SO4/H2O solutions, of which sulphate aerosols are composed, only freeze at temperatures several degrees below the ice frost point (∼185 K in the stratosphere). Several laboratories have investigated the freezing properties of such solutions [Middlebrook et al., 1993; Koop et al., 1995, 1998, 2000; Bertram et al., 1996; Chang et al., 1999], and the corresponding freezing rates have been derived [Tabazadeh et al., 1997a, 1997b, 2000]. The extent to which this freezing mechanism may contribute to PSC formation and effects such as denitrification has not been established. A full assessment requires consideration of many factors, including stratospheric temperatures, cooling rates and the microphysics by which the frozen particles grow and sediment.
 Other factors could potentially introduce alternative freezing pathways for stratospheric particles. Cold aerosols are not binary solutions, but ternary HNO3/H2SO4/H2O solutions (thus leading to the existence of liquid phase PSCs). The presence of HNO3 introduces the potential for additional homogeneous freezing pathways, leading to direct formation of HNO3-containing solids such as nitric acid trihydrate (NAT) and nitric acid dihydrate (NAD). Whether this occurs under stratospheric conditions is uncertain. Some studies have concluded that the HNO3 content does promote freezing [Molina et al., 1993; Beyer et al., 1994; Song, 1994; Iraci et al., 1995; Bertram and Sloan, 1998a, 1998b; Salcedo et al., 2001] but others have found no freezing until below the ice frost point [Koop et al., 1995, 2000].
 Also, the background stratospheric aerosol is not composed uniquely of pure H2SO4/H2O droplets. Many compounds have been identified, both internally and externally mixed with the sulphate particles. Key impurities include soot and meteoritic debris; trace quantities of many exotic compounds have been observed [Murphy et al., 1998]. It has been well established that aerosol impurities can act as heterogeneous nuclei in the atmosphere and promote freezing; the formation of cirrus clouds in the troposphere is an important example. Whether this may also be responsible for PSC formation depends upon the effectiveness of the specific compounds that are present in the stratosphere. Laboratory studies have tested the most important compounds, with primarily negative results [Beyer et al., 1994; Koop et al., 1995; Biermann et al., 1996]. One exception is amorphous silica, which has been found to promote freezing [Bogdan and Kulmala, 1999]. Furthermore, the difficulty in identifying every trace compound, including ones that may only be present in one out of a thousand or more particles, makes it hard to definitively exclude the possibility of heterogeneous freezing.
 Although the homogeneous and heterogeneous freezing processes are superficially similar, potentially both producing frozen particles at similar temperatures, key differences can be identified. Heterogeneous freezing can only occur in those particles that contain the nucleating compound. Therefore a fixed supply of “freezable” particles is available at the start of the winter; if those particles are removed (i.e., sediment out as PSC particles), they can not be replaced. PSCs at the end of the winter should have smaller frozen particle concentrations (possibly even no frozen particles) than those early in the winter. This seasonal evolution will be a primary factor determining PSC characteristics. For homogeneous freezing, on the other hand, all the liquid particles are theoretically able to freeze, although the volume dependence of the freezing rate favors larger particles. Therefore running out of frozen particles is very unlikely. The key factor influencing PSCs will instead be the recent temperature history: the homogeneous freezing rate is both directly and indirectly (via the aerosol composition) dependent on temperature.
 More laboratory data are necessary to understand these potential freezing processes. In particular, only laboratory data can provide the parameters, such as freezing rates as a function of composition, necessary for accurate modeling. However, modeling studies can, in the meantime, provide guidance by testing the impact of various processes in the stratosphere. For example, testing established freezing processes, in particular homogeneous freezing to form ice, is necessary to determine whether the formation mechanism is consistent with observed PSCs. More hypothetical processes can be tested to determine whether they can even play a role: how rapid does homogeneous freezing need to be to promote PSC formation? At what concentration do heterogeneous nuclei become important? How different are the PSCs created by heterogeneous or homogeneous freezing, and can these differences be exploited to further our understanding of observed PSCs?
 The most important benchmark for evaluating the significance of PSCs is their effect on ozone depletion. Two important links between PSCs and ozone have been identified: chlorine activation and denitrification. First, PSCs provide a surface for heterogeneous reactions which convert chlorine from inactive, reservoir species (HCl and ClONO2) to active forms such as ClO that rapidly react with ozone. Second, sedimentation of PSC particles permanently removes HNO3 from the stratosphere; the resultant denitrification allows ClO to remain active for longer, thus intensifying the ozone loss. Laboratory and modeling studies have shown that overall chlorine activation is often not sensitive to particle composition, despite known differences in the reactivities of the various PSC compounds. Denitrification, on the other hand, is associated with solid phase particles, and should be highly sensitive to assumptions about freezing. Waibel et al.  have studied the freezing processes that could have contributed to one HNO3 profile; further sensitivity tests, incorporating more observations, can further constrain the possible mechanisms by which denitrification occurs.
 This study was designed to investigate the potential importance of various freezing processes, focussing on the large-scale influence of the PSCs. A coupled microphysical/chemical model allowed the simulations both to accurately examine the details of PSC formation and to directly relate the resultant PSCs to the net ozone loss; a companion paper [Drdla and Schoeberl, 2002] discusses the ozone loss results. A range of scenarios were developed to examine each freezing process under a range of assumptions. In order to assess the overall effect, the simulations spanned the Arctic vortex for an entire winter, allowing quantities such as overall denitrification and ozone loss to be determined. The 1999/2000 Arctic winter was chosen as a sample winter. The results from the Stratospheric Aerosol and Gas Experiment (SAGE) III Ozone Loss and Validation Experiment (SOLVE) provide extensive information about the PSC characteristics during the 1999/2000 winter, allowing evaluation of the model scenarios. In addition, the cold temperatures during this winter provided conditions under which widespread freezing can occur and the effects of PSCs can be readily identified.
 We begin by discussing the characteristics of the 1999/2000 winter because the temperature and its evolution determined the scope of the modeling study. Also the PSC evolution observed by SOLVE observations is introduced, with a focus on the broad characteristics that are most useful for evaluating the model scenarios. The following section describes the methodology used for this study, including how the trajectory data set was generated, the initialization conditions, and the characteristics of the various scenarios.
 The main body of the paper presents the microphysical characteristics of the various runs. The runs are compared based on the PSC characteristics, denitrification, and dehydration. Special attention is paid to the conditions necessary for severe denitrification, because of its role in ozone depletion. Each potential freezing process is discussed separately: homogeneous freezing to form ice, homogeneous freezing to form NAT, heterogeneous freezing to form NAT, and freezing to form NAD.
2. Characteristics of the 1999/2000 Arctic Winter
2.1. Temperature Evolution
 The temperatures during the period of interest, namely, the 1999/2000 winter, are the most important factor controlling PSCs. The large interannual variability in temperature (among other factors) invalidates the concept of a “typical” Arctic winter. Winter 1999/2000 is an interesting winter because of the prolonged period of cold temperatures: Figure 1 shows the minimum temperatures in the UKMO analysis. The contour lines emphasize the regions in which the minimum temperature is cold enough for PSCs to possibly exist. The temperature at which NAT is stable (assuming 5 ppmv H2O and 10 ppbv HNO3) is used as an indicator for type I PSCs; since NAT is the most stable form of condensed HNO3, its condensation point represents the warmest temperature at which PSCs could potentially form. Note, however, that observations have shown that often type I PSCs do not form until temperatures are several degrees colder than the NAT condensation point: it is a necessary, but not sufficient, condition for PSC formation. Similarly, the temperature at which water ice becomes stable (the ice frost point) is used to indicate the region in which type II PSCs could possibly be present. The pressure dependence of both the NAT condensation point and the ice frost point cause these values to not coincide with a single temperature across all vertical levels.
 Temperatures were sufficiently cold for PSC formation continuously from 14 November 1999 to 15 March 2000; 500 K is, on average, near the center of the PSC layer, but the region of cold temperatures clearly descends during the winter. Between December and February the potential temperature of PSC formation decreases by 50–100 K. This corresponds to an altitude decrease of more than 5 km. The coldest period of the winter occurred in late December and early January. Not only were temperatures cold enough for type I PSCs in a deep layer but also temperatures were below the ice frost point, implying that type II PSCs could possibly form. The coldest temperature all winter was 184 K on 8 January at 500 K potential temperature; at this point the temperature was 3.5 K below the ice frost point.
 Unfortunately, during the 1999/2000 winter the temperatures reported by the various meteorological analyses differed noticeably. Figure 1 shows the minimum temperatures from the UK Meteorological Office (UKMO) analysis, as used in this study. However, the UKMO minimum temperatures tend to be colder than other analyses of the December–January period, that is, during the coldest period of the winter (P. Newman, private communication, 2001). For example, the minimum temperature in the Climate Prediction Center analysis is only 1 K below the ice frost point. Minimum temperatures in the Goddard Data Assimilation Office analysis and the National Centers for Environmental Prediction reanalysis are also nearly 2 K warmer than UKMO during this period. In the past, however, the UKMO analysis has had a warm bias; a 1.7 K warm bias was identified for the 1994/1995 winter [Pullen and Jones, 1997]. Uncertainties in the temperature are important in assessing the likelihood of type II PSC formation during the winter, potentially resulting in both quantitative and qualitative changes to model simulations. The effects of this uncertainty will be discussed as relevant in section 4.
2.2. SOLVE Observations
 Measurements made during the 1999/2000 winter as part of the SOLVE campaign provide an opportunity to evaluate the model scenarios. Because of this study's interest in large-scale, average features, an exact comparison between the model results and the measurements is not appropriate; future studies will focus on detailed model-measurement comparisons. Rather, the measurements have been used in qualitative or order-of-magnitude comparisons in order to identify model scenarios that are clearly inconsistent with the data.
 Three measurement criteria have been used in this study. First, DC-8 lidar measurements show that solid phase PSCs were present as early as 5 December. Second, ER-2 measurements of NOy show that most of the air in the vortex at ER-2 levels was denitrified; the typical denitrification level was 70%. Third, combining ER-2 measurements of water with the NOy data reveals that almost all of the denitrification occurred without dehydration. Several other measurement criteria were also considered, for example, the duration of PSCs into March or the concentrations of frozen particles. However, these criteria did not help to further limit the model scenarios or were less robust indicators than the three that have been chosen.
 SOLVE data clearly showed that solid phase particles were repeatedly present during the winter. The Differential Absorption Lidar (DIAL) on board the DC-8 [Browell et al., 1998] regularly observed depolarizing PSCs: this depolarization can only be produced by nonspherical, and thus solid phase, particles. The lidar data set was examined to identify when and where PSCs occurred, using the PSC criteria of Toon et al. : aerosol scattering ratio greater than 2 in the infrared and greater than 1.2 in the visible. For these PSC events the maximum depolarization (in infrared or visible) has been determined, as shown in Figure 2. The maximum depolarization frequently exceeds 30%, the depolarization cutoff used to identify type Ia PSCs by Browell et al. . On almost all dates the maximum depolarization exceeds 2%, which was the cutoff used by Toon et al.  to identify several categories of nonspherical PSCs.
 Of particular interest in Figure 2 are the PSCs observed early in December: depolarizing clouds were observed as early as 5 December. The December PSCs were all large scale (250 to 750 km in extent) with little vertical structure, indicating that they were most likely produced by synoptic scale cooling rather than localized, lee wave-type events. The existence of PSCs even earlier than 5 December can not be excluded based on this data set: the DC-8 only made two flights before 5 December, neither of which targeted cold temperatures in the vortex.
 Another important characteristic of this winter is the widespread denitrification that was observed by the NOy instrument [Fahey et al., 1989; Popp et al., 2001] on the ER-2. NOy, or odd nitrogen, is a chemical family that during polar winter consists almost exclusively of HNO3; ClONO2, NO, NO2, and N2O5 are small contributors. Denitrification can be identified by comparing the measured NOy level with the expected level, NOy*, as determined from prewinter N2O-NOy measurements [Fahey et al., 1989]: any difference is ascribed to denitrification. We have calculated NOy* by combining the N2O-NOy correlation observed by the MkIV balloon [Toon et al., 1999] on 3 December 1999 with ER-2 measurements of N2O, using the unified N2O data set [Hurst et al., 2002]. One significant source of uncertainty in determining denitrification from the SOLVE ER-2 data is estimating the actual NOy content in the presence of PSCs: the NOy inlet oversamples particles, and therefore overestimates NOy if HNO3-containing particles are present [Fahey et al., 1989; Fahey et al., 2001]. PSCs were present in 30% of the ER-2 data set. For these cases, we have estimated the condensed HNO3 and its enhancement factor, as described by Drdla et al. , in order to derive the actual total NOy, including gas phase and condensed phase contributions. Figure 3a shows the distribution of measured denitrification levels, comparing the distributions determined if PSC events are excluded or included in the data set. While the details of the distributions differ, the gross characteristics important for this study are similar: the majority of the air parcels were denitrified, with 70% being the most common level of denitrification. The distribution including all data points is used in this study in order to avoid a statistical bias, especially because several of the rehydration events, discussed later in this section, occurred in the presence of PSCs.
 The ER-2 NOy measurements also provide valuable information about the size and concentration of large, HNO3-containing particles [Fahey et al., 2001], showing small (<10−3 cm−3 s−1) concentrations of very large (5–10 μm radius) particles. This study has chosen not to use this information to constrain the model simulations. Extracting particle size distributions from the NOy data is complex and has only been done for limited time periods. More research is necessary to understand how to meaningfully compare these simulations with the available size distribution data.
 Water vapor measurements were also made on board the ER-2, which showed that despite the widespread denitrification, dehydration was very limited. For this study we have used water vapor measurements from the Jet Propulsion Laboratory laser hygrometer [May, 1998]. To identify dehydration, an expected H2O mixing ratio, labeled H2O* by analogy to NOy, was developed by correlating the ER-2 measurements of H2O and N2O, after excluding the hydration events identified by Herman et al. . This is a simplified approach, since total hydrogen (which includes H2 and CH4) is a better tracer than water alone. However, comparison of this technique with the results of the detailed analysis by Herman et al.  confirms that it is able to identify the dehydration and rehydration events described there. Five percent or larger changes in H2O can be identified using this method.
 A comparison of the water and NOy measurements (Figure 3b), confirms that most of the denitrification was observed without dehydration, comparable to previous Arctic winters [Fahey et al., 1990]. Of the air parcels with more than 50% denitrification, 98.5% had dehydration of less than 5%, 1.3% had more than 5% dehydration, and 0.2% were rehydrated. This is an important model diagnostic, because models frequently couple denitrification and dehydration. The diagnostic focuses on air parcels that are strongly (i.e., more than 50%) denitrified to make it useful specifically for identifying freezing processes. As will be discussed in section 4.1, liquid particles alone can cause denitrification of up to 40%; in these simulations, higher levels of denitrification are always caused by solid phase particles.
 The ER-2 observations of denitrification and dehydration were made between 20 January and 12 March; flight level was generally between 425 and 450 K. These measurements have been compared with the characteristics of the model air parcels located in the vortex, between 412.5 and 487.5 K, on 1 February 2000. The single model date of 1 February was chosen to provide a date within the ER-2 sampling period which is after the occurrence of most model denitrification and dehydration.
3. Modeling Approach
3.1. IMPACT Model Description
 The Integrated Microphysics and Aerosol Chemistry on Trajectories (IMPACT) model [Drdla, 1996] was used for this study. It is a trajectory model in which the Lagrangian evolution of an individual parcel is calculated as the air parcel circulates through the atmosphere. The IMPACT model simulates the PSC microphysics, heterogeneous chemistry, and gas phase chemistry.
 The model microphysics calculates the evolution of the multiple particle types that may be present in a PSC. The particle types considered in this study include liquid sulphate aerosols (binary solutions or ternary solutions, depending on the temperature), heterogeneous nuclei, frozen sulphuric acid tetrahydrate (SAT), solid phase type I PSCs, and water ice type II PSCs. In most scenarios, the solid phase type I PSC particles are assumed to be composed of NAT, but sensitivity tests have also been performed with NAD particles. In this study, only one of NAD or NAT is present in any given scenario. However, all the other particle compositions may be simultaneously present.
 The particles are simulated using multiple size bins, with 51 geometrically spaced bins ranging from 0.001 to 100 μm radius. The processes simulated include condensation, evaporation, sedimentation, nucleation, freezing, and melting. Growth of NAD, NAT, and water ice are calculated using standard growth equations [i.e., Toon et al., 1989]. Vapor pressures of these three compounds are taken from Worsnop et al. , Hanson and Mauersberger , and Marti and Mauersberger , respectively. The equilibrium composition of ternary solutions is calculated from Carslaw et al. . Model liquid phase particles grow toward this equilibrium composition at a rate limited by gas phase diffusion of HNO3 and H2O; competition of liquid particles with solid ones for HNO3 and H2O will also affect the composition. Fall velocities for sedimentation are from Pruppacher and Klett  and include nonsphericity effects for solid particles.
 The nucleation of a compound from the gas phase onto a solid substrate is calculated using standard heterogeneous nucleation equations [Pruppacher and Klett, 1997; Toon et al., 1989]. The m factor in these equations expresses the compatibility between two compounds, and thus the ability of one compound to serve as a nucleus for another; mNAT → Ice, for example, refers to the ability of water ice to nucleate onto NAT. In heterogeneous nucleation theory, m is defined as the cosine of the contact angle between a liquid compound and a substrate; however, for solid phase compounds the compatibility of the crystal lattices is a better description. Tables 1 and 2 show values that are assumed for m.
Table 1. Symbols for Key Model Parameters and the Value Used for the Parameters (or Range of Values for Parameters That Vary)
Description of Parameter
Nucleation compatibility of ice on SAT
mSAT → Ice
Nucleation compatibility of ice on NAT
mNAT → Ice
Nucleation compatibility of NAT on SAT
0.75 or 0.99
HNO3 accommodation coefficient on liquid solution
HNO3 accommodation coefficient on NAT
H2O accommodation coefficient on ice
Homogeneous freezing rate, cm−3 s−1
Fraction of aerosol containing heterogeneous nuclei
NAT saturation ratio above which freezing occurs (homogeneous or heterogeneous, as appropriate)
For parameters that were varied in a scenario, the default value is in boldface, and the full range tested is shown in parentheses. For scenarios with ice freezing, the freezing rates are determined based on Tabazadeh et al.  unless otherwise mentioned. N/A, not applicable.
 Multiple freezing processes have been considered in this study, alone and in combination. The details of the freezing processes are discussed in section 3.4. All frozen particles are tagged according to their formation mechanism, allowing the role of each individual freezing process to be determined. Upon freezing, sulphuric acid is assumed to all be converted into SAT. PSC evaporation causes the release of a SAT particle, which the model continues to monitor. SAT melts, restoring the initial sulphate aerosol, at the SAT melting point.
 The model also includes a full calculation of heterogenous and gas phase chemistry. Fifty eight species are considered, grouped into 29 families, which interact via 188 gas phase reactions (41 of which are photodissociations) and 13 heterogeneous reactions. The rates of all gas phase reactions are from JPL00-3. Drdla and Schoeberl  discuss the chemistry in greater detail.
3.2. Trajectory Data Set
 For this study a large data set of long-term trajectories has been used as the model's dynamical input. This ensemble of trajectories was generated to provide horizontal and vertical coverage of the whole vortex throughout the winter, thus allowing the three-dimensional evolution of the vortex to be examined. Similar sets of trajectories have been used in previous studies to represent the overall behavior of the Arctic vortex [Newman et al., 1993; Lutman et al., 1994, 1997] or other regions of the stratosphere [Fairlie et al., 1999; Pierce et al., 1999; Schoeberl et al., 1998, 2000]. No mixing or other interaction among the trajectories is taken into account in the simulations.
 We have chosen to use diabatic trajectories derived from UKMO analyses. The Goddard Space Flight Center's fast trajectory model [Schoeberl et al., 1993, 2000] was used to calculate the trajectories, incorporating diabatic descent based on calculated radiative heating rates [Rosenfield et al., 1994]. A start date of 1 November 1999 (19991101) was chosen in order to start the trajectories before the earliest possible PSC event (on 14 November 1999). All trajectories extended until 15 April 2000, allowing the full impact of PSC processing on ozone depletion to be evaluated. However, the vortex began to break down in mid March, and temperatures became too warm for further PSC formation. Therefore this study focuses on the vortex evolution up until 10 March.
 Given the focus on PSCs in this study, the trajectory data set was designed to provide representative sampling of the vortex during the period of peak PSC formation. The UKMO analysis on 15 January 2000 (20000115) was examined to determine the horizontal extent of the vortex using the Nash definition of the vortex edge [Nash et al., 1996]. The outermost vortex edge definition was used as a boundary, to encompass all of the vortex edge region as well as the vortex core. This analysis was performed on multiple potential temperature surfaces, spaced every 25 K from 450 to 700 K, to provide the vertical extent; 700 K was chosen as an upper boundary to cover the full vertical region in which PSCs may have formed during the winter (Figure 1). The vortex could not be clearly identified below 450 K, imposing a lower boundary to the analysis.
 Having identified the vortex region on 20000115, trajectories were initialized to fill it both horizontally and vertically. On each potential temperature surface, trajectories were placed throughout the vortex using a regularly spaced 450 km grid (Figure 4). Each point was randomly placed vertically in the 25-K-deep layer. This procedure produced 2395 points in total, filling the vortex from 437.5 to 712.5 K. For each point the backtrajectory to 19991101 and the forward trajectory to 20000415 were calculated and spliced together to create a 167-day-long trajectory spanning the winter.
 Two supplemental sets of trajectories were also created to ensure complete coverage of the vortex even at the beginning and end of the winter. For example, some midlatitude air can become entrained in the vortex during the winter; other air parcels that are initially in the vortex can mix out. The supplemental sets were designed to incorporate such air parcels. First, the vortex extent was determined on 15 March 2000 (20000315). Then the 2000315 positions of the primary set of trajectories (those initialized from the 20000115 analyses) were mapped out. Each grid point, using the same 450 km × 450 km × 25 K grid as initially, was checked to determine whether a trajectory was located near that point. (“Near” was defined as being anywhere within a box 50% larger than the grid box, i.e., 675 km × 675 km × 37.5 K.) If no existing trajectory was found, a new trajectory was generated for that location. This procedure was repeated for 19991115. An additional 510 trajectories were created, providing a total of 2905.
 Particle sedimentation is an important aspect of this study. Knowledge of the vertical structure is necessary to properly investigate sedimentation: not only does sedimentation remove particles from a layer, it also adds particles which are descending from higher levels. Both components are necessary to calculate the net flux of particles, HNO3, and H2O through a layer. Interactions between trajectories are not included in these simulations, so a different approach was necessary to provide continuous information on the vertical PSC structure along each trajectory.
 To determine the flux of particles into an air parcel, each trajectory point is modeled using a column rather than a single air parcel. The temperature profile in the column is determined at each trajectory location from the UKMO analysis. Additional, “surrogate,” model levels are spaced every 25 K in this column; these levels are forced to follow the motions of the true trajectory. The number of levels depends upon the trajectory altitude: enough levels are used to extend past the maximum PSC altitude at any point along the trajectory. Full PSC evolution is calculated on each of these surrogate levels solely to determine whether the particles ever sediment to the level of interest; sedimentation is the only interaction between the model levels. These surrogate levels are distinct from the proper trajectories that are being independently simulated at a given altitude. Only the true trajectories are used to provide the vertical profile information shown in this paper.
 This column-type approach is a simplification of the actual three-dimensional problem and ignores the effects of vertical wind shear. Wind shear should transport particles in or out of the column; on average, this factor is unlikely to introduce any systematic errors. Wind shear will also generally cause the air at higher levels to flow through air pools more rapidly than is treated by the column; the extent to which this affects the particle characteristics is unknown. However, uncertainties due to using a simplified column are likely to be no larger than the inherent uncertainties in trajectory modeling.
 Each trajectory was initialized in November based on its potential temperature. A single stratospheric profile, intended to be representative of the vortex as a whole, was constructed using available measurements. For this study, only the NOy, H2O, and H2SO4 profiles are important; initialization of the other species is discussed by Drdla and Schoeberl .
 NOy was initialized from a profile of N2O, combined with a N2O-NOy correlation. The N2O profile was measured by the in situ LACE instrument [Elkins et al., 1996] on the OMS balloon, launched 19 November 1999. The N2O-NOy correlation was that observed by the MkIV instrument [Toon et al., 1999] on a balloon launched 3 December 1999. This procedure was chosen instead of directly using the MkIV NOy profile for consistency with other chemical species in the model, most of which were initialized using data from the 19 November balloon launch. The resultant NOy profile is shown in Figure 5, both initially and on 1 February, after diabatic descent. NOy was partitioned among the component nitrogen species, initially with 90% in HNO3, 5% in N2O5, and 2.5% in each of NO and NO2; however, following initialization the model chemistry dictated the partitioning of these species.
 Constant profiles of H2O (5 ppmv) and H2SO4 (0.17 ppbv, all condensed) were assumed; both values are consistent with in situ ER-2 observations, and the water profile is also consistent with Polar Ozone and Aerosol Measurement profiles. The sulphate aerosol size distribution was assumed to be lognormal, using a number density of 106 mg air−1 and a distribution width of 1.52. For an air mass at 50 hPa and 210 K, this yields 8.8 cm−3 particles with mode radius 0.08 μm and a total surface area of 1 μm2 cm−3.
3.4. Description of Scenarios
 Several different scenarios have been considered in this study, each one consisting of a different set of assumptions about the microphysics controlling PSC characteristics. The primary differences between the different scenarios are the freezing processes that are allowed to occur (Table 2).
 The first model run, “Liquid,” has no freezing whatsoever; all particles remain liquid throughout the entire winter. Some denitrification occurred even in this scenario due to the sedimentation of the liquid particles; the impact of particle freezing has been assessed relative to this baseline level of denitrification.
 The first freezing process to be evaluated, in the “IceFrz” scenario, was homogeneous freezing below the ice frost point, or “ice freezing.” The freezing rates for this process were calculated according to Tabazadeh et al. . Freezing produces type II PSC ice particles (with NAT and SAT impurities) which can evaporate to yield first NAT particles, and eventually SAT. Based on laboratory and theoretical data [Iraci et al., 1995; MacKenzie et al., 1995], SAT is assumed to be a poor heterogeneous nucleus for NAT condensation (mNAT = 0.75). (This threshold prevents nucleation of solid phase PSCs unless the NAT supersaturation ratio exceeds 100. In the presence of liquid particles, such high supersaturations are precluded by liquid phase uptake of HNO3; therefore, mNAT = 0.75 effectively suppresses NAT formation on previously formed SAT particles.) A few sensitivity tests explored the limits of ice freezing by varying the trajectory temperatures or changing how the ice freezing rate was calculated. More details are provided in Table 2 and section 4.2.
 Next an additional homogeneous freezing process, occurring at warmer temperatures, was included. This second freezing process directly produces NAT particles and thus is referred to as “NAT freezing.” A simplified approach was taken to calculating the homogeneous freezing rate: whenever the saturation of HNO3 over NAT exceeded a critical value Scrit, freezing occurred at a fixed rate k. The resultant NAT particles are also assumed to serve as nuclei for ice condensation if temperatures become sufficiently cold. The main scenario, labeled “HomFrz,” assumed a freezing rate of k = 107 cm−3 s−1, which is the “HomFrz” value that best matched the SOLVE data. Sensitivity tests explored variations of this parameter.
 In the fourth set of model runs, “HetFrzA,” the NAT freezing process was assumed to be heterogeneous; ice freezing remained homogeneous exactly as in “IceFrz.” The percentage of particles containing heterogeneous nuclei ranged from 0.001% to 10% (default 0.02%). The subsequent evolution of these NAT particles is identical to the “HomFrz” scenario. In particular, the SAT cores that are released upon PSC evaporation are assumed to be poor nuclei for subsequent PSCs (mNAT = 0.75) in both scenarios. But unlike the “HomFrz” case, during these subsequent PSCs, there is no remaining pathway for frozen particle formation. None of the liquid particles contain a nucleus that allows freezing; all the particles with nuclei have been deactivated into inert SAT particles. This limited ability to form PSCs is a logical consequence of available laboratory data, but has a severe impact on PSC evolution.
 The fifth set of tests, “HetFrzB,” again explored heterogeneous freezing with one difference: the SAT particles were assumed to be good nuclei for NAT (mNAT = 0.99). Therefore every time the air mass cools, any existing solid (SAT) particles will be transformed into NAT particles at a low supersaturation ratio (SNAT ≈ 4). This scenario is consistent with the “preactivation” observed by Zhang et al.  but also implicitly covers many other potential variations in the heterogeneous freezing process, all of which could lead to heterogeneous nuclei remaining “active” throughout the winter. These possibilities include sulphate remaining liquid (either by forming a slurry, or by initially freezing then remelting [i.e., Koop and Carslaw, 1996; Iraci et al., 1998; Martin et al., 1998]) or the heterogeneous nuclei may be externally mixed (i.e., separate particles), rather than internally mixed, with the ambient sulphate aerosol. Although the details of the microphysics would differ in these cases, they share a key characteristic with the “HetFrzB” scenario: a proscribed number of particles are available to form NAT PSCs and they remain active throughout the winter.
 All of the scenarios considered so far assumed that the composition of solid phase HNO3 is nitric acid trihydrate. In the final tests, the dihydrate, NAD, was instead assumed to be present. Both homogeneous freezing, “NADHomFrz,” and heterogeneous freezing, “NADHetFrzB,” scenarios were considered. The parameters governing NAD condensation (other than vapor pressure and density) were assumed to be identical to the NAT parameters listed in Tables 1 and 2. The NAD saturation ratio, instead of NAT, was used to determine the critical saturation ratio (Scrit) above which freezing occurred.
4. Model Results
4.1. Liquid Phase PSCs Only: “Liquid” Scenario
 In the absence of any assumed freezing processes, the evolution of the aerosol during the 1999/2000 winter is straightforward. Widespread PSC formation is predicted, as shown in Figures 6a and 7a, but only several degrees below the NAT condensation point, where ternary solutions become possible. PSC coverage at 475 K maximizes at 46% (on 12 January). The PSCs clearly descend during the winter: the strongest PSC formation descends from 500 to 425 K (or lower), corresponding to more than 5 km of descent. This descent is almost exclusively due to temperature variations (see Figure 1). Therefore care must be exercised when interpreting a descent in PSC altitude as an indication of denitrification or dehydration; variations in temperature can have a much larger effect.
 Typically, liquid phase particles are too small for any significant sedimentation: even when the particles grow, the condensed mass is distributed across all the available particles, limiting the size of any individual particle. However, under the unusual circumstances of this scenario sedimentation becomes possible. As temperatures below the ice frost point are reached, liquid particles grow sufficiently to yield slow but noticeable denitrification (Figure 8). More than 10% denitrification, averaged over the vortex, is possible from 450 to 500 K (Figure 9a); the maximum denitrification in an individual air parcel is 37%. Although this process occurs almost exclusively below the ice frost point, the associated dehydration is at most 0.5%. As will be shown in the following sections, the role of liquids in denitrification is limited to occasions where no freezing has occurred. If solid phase particles are present, their preferential growth prevents the liquid particles from reaching the sizes necessary for significant sedimentation.
 The purpose of this run is purely to provide a baseline against which to assess the role of freezing. Its characteristics are clearly incompatible with the SOLVE observations: no solid phase PSCs ever form, and denitrification is far less, both in extent and severity, than observed.
4.2. Homogeneous Freezing to Form Ice: “Icefrz” Scenario
 The first freezing process tested in this study was homogeneous freezing below the ice frost point, since it is generally accepted that this process does occur. Figure 6b shows that type II PSCs are produced, but only during the coldest period of the winter. Freezing first occurs only when temperatures reach 3 K below the ice frost point, which for this winter was not until 8 January. Because the horizontal extent of these PSCs is limited to the very coldest regions, they are present in at most 2% of the vortex at any one time; a maximum of 10% of the vortex (at 475 K) is ever exposed to ice particles. In the rest of the vortex, liquid PSCs form and evolve just as in the “Liquid” scenario.
 The type II PSCs are efficient at dehydration. The particle concentrations are small (typically 5 × 10−3, maximum 5 × 10−2 cm−3) but the particles grow to reach average radii in excess of 20 μm; typically 30% dehydration (maximum 39%) results. The low frequency of ice formation, however, limits the vortex-wide average dehydration to only 3%. On the other hand, the ice particles are inefficient at directly causing denitrification. Most of the HNO3 is condensed in the liquid, ternary solution particles that are simultaneously present. The slow gas phase transfer of this HNO3 to the ice particles limits type-II-caused denitrification to less than 0.4%, vortex averaged.
 More important for denitrification are the NAT PSCs that are formed when ice particles are warmed above the ice frost point (Figures 6b and 7b). Particle concentrations in these clouds are also small (at most 0.015 cm−3), in fact even smaller than in the ice clouds because most of the ice particles sedimented out of the stratosphere. The particles are able to grow to average sizes of 5 μm, causing efficient denitrification in air parcels where temperatures remain cold for a few days; 89% denitrification occurs in individual air parcels (Figures 9b and 10). However, the limited extent of the PSCs constrains NAT particles to a vortex average 1.9% denitrification; overall, this contribution is small relative to the widespread liquid particles (Figures 8b and 9a). The impact of the NAT particles is also limited by their short duration: NAT PSCs were only present from 8 to 23 January.
Figure 10 shows the relationship between denitrification and dehydration by comparing the severity of denitrification and dehydration in individual air parcels at ER-2 levels. Almost all trajectories that were exposed to frozen particles in the “IceFrz” scenario experienced dehydration; only in the more strongly dehydrated air parcels is severe denitrification also evident. In other words, denitrification is strongly linked with dehydration in this scenario, because a single freezing process is responsible for both phenomena. Those air parcels that did not experience freezing behave identically to the “Liquid” scenario: moderate denitrification (<40%) with no dehydration.
 Comparing the results of this simulation with the SOLVE data set shows it to be deficient in several ways. First, the earliest occurrence of solid phase particles is on 8 January, 1 month later than was observed. Second, the extent of PSC processing is much less than observed: only 3.1% of the vortex at ER-2 levels is more than 50% denitrified, compared to an observed 75.3% (Table 3 and Figure 9b). Third, 100% of those denitrified air parcels are dehydrated (by 20–40%), which is far more extensive than observed.
Table 3. Denitrification Statistics for All Simulationsa
Percent of All Trajectories With >50% Denitrification
Percent of the Denitrified Trajectories With >5% Dehydration
Statistics were determined for 1 February, based on all trajectories in the vortex between 412.5 and 487.5 K (261 trajectories total). Boldface highlights the key scenarios, as shown in Figures 6–8. N/A, not applicable.
k = 102
k = 103
k = 104
k = 105
k = 106
k = 107
k = 108
k = 109
f = 0.001%
f = 0.01%
f = 0.1%
f = 1%
f = 10%
f = 0.001%
f = 0.01%
f = 0.02%
f = 0.03%
f = 0.1%
f = 0.3%
f = 1%
f = 10%
k = 102
k = 104
k = 105
k = 106
k = 107
k = 108
k = 109
f = 0.001%
f = 0.01%
f = 0.03%
f = 0.1%
f = 0.3%
f = 1%
f = 10%
 Denitrification by ice that has evaporated to yield NAT is much less important than in an analogous scenario considered by Waibel et al. . One difference is that Waibel et al.  were trying to simulate a single profile from the 1994/1995 winter; our simulations do produce localized denitrification, but not the widespread denitrification that was observed during SOLVE. Also, our simulation uses the latest laboratory data to calculate the ice freezing rate; Waibel et al.  assumed that freezing occurred more readily, specifically that 5 × 10−3 cm−3 particles froze at Sice = −1.5 K (about 1.5 K warmer than the “IceFrz” threshold). Finally, this simulation incorporates a full kinetic calculation of the growth of NAT particles, slowing NAT growth relative to the equilibrium assumed by Waibel et al. . Therefore these simulations do not support the conclusion of Waibel et al.  that NAT particles produced by ice freezing cause enough denitrification to explain observations.
 Several model uncertainties that could contribute to model/measurement discrepancies have been considered. For example, if temperatures were in fact colder than in the model, freezing would be more widespread. However, a sensitivity test in which all temperatures were decreased by 1 K, “IceFrzCold” (Table 3 and Figure 9), does not improve the comparison: PSCs still form too late and produce limited denitrification, all with dehydration. In addition, the UKMO analysis used in this study has generally colder temperatures than other analyses of the 1999/2000 winter (section 2.1); these temperatures effectively provide an upper limit on the possible extent of homogeneous freezing to ice during the 1999/2000 winter. Using temperatures that are 1 K warmer, which still results in minimum temperatures lower than other analyses, limits freezing to 0.4% of the vortex; further warming would eliminate all ice formation.
 Uncertainties in the freezing rate are another potential source of discrepancies. However, tests with significantly different freezing rate assumptions all yield denitrification that is coupled with dehydration (Table 3). Thus a robust feature of any scenario in which freezing occurs solely below the ice frost point appears to be coupled denitrification and dehydration. To resolve these discrepancies with the measurements, an additional freezing mechanism, that occurs above the ice frost point and directly produces type I PSCs, must be introduced.
4.3. Homogeneous Freezing to Form NAT: “Homfrz” Scenario
 One potential mechanism for creating more frozen particles is a second homogeneous freezing process, comparable in mechanism to ice freezing, but occurring at warmer temperatures. In these sensitivity tests, we have primarily explored variations of the assumed freezing rate for such a process. Other factors (i.e., αNAT and Scrit) that will also have a strong effect on the extent and influence of this freezing process have generally been set to make this process as effective as possible. The description focuses on the case where k = 107 cm−3 s−1 because, based on the SOLVE comparisons, it is the most realistic.
Figures 6c and 7c show the evolution of PSCs with this freezing process. Since freezing begins as soon as SNAT > 2 (∼1 K below the NAT condensation point), PSCs are already apparent on 19 November. Figure 7c shows that up to 67% of the vortex at 475 K may contain NAT PSCs at one time. Liquid PSC formation is completely suppressed. Because air circulates through the cold regions, 100% of the vortex below 550 K has been processed by solid phase PSCs by 1 February. The denitrification associated with this processing reduces the frequency of PSC formation late in the winter.
 The characteristics of the NAT PSCs vary during the winter (Figure 11) and even vary substantially among PSCs present at any one point in time. Particle freezing continues, accumulating particles with time, until NAT equilibrium is reached. This leads to maximum concentrations during the coldest period of the winter, namely, late December and January: concentrations are nearly 2 orders of magnitude larger than during the rest of the winter. The variability at any point reflects the range of air temperature histories that parcels in the vortex have experienced.
 The large particle concentrations in December and January are conducive to denitrification. Figure 8c shows that strong denitrification occurs throughout this period; the denitrification is clearly faster and more widespread (vertically and in time) than in either the “IceFrz” or “Liquid” scenarios. Since denitrification starts in December, some air parcels are 70% denitrified by 15 December. By 1 February, many air parcels have experienced 70% denitrification (Figure 13b). This denitrification is almost exclusively due to NAT PSCs: liquid PSCs have been suppressed, and, as in the “IceFrz” scenario, type II PSCs are a small contributor (causing at most 1.5% denitrification).
 The widespread NAT PSCs also dramatically influence type II PSC formation, increasing the extent of dehydration. Ice is assumed to readily nucleate on NAT [Tolbert and Middlebrook, 1990; Middlebrook et al., 1992], so type II PSCs can form almost as soon as temperatures fall below the ice frost point (26 December). The resulting ice clouds are 3 times more prevalent than in the “IceFrz” scenario, occupying up to 6% of the vortex. This type II PSC formation mechanism effectively suppresses the homogeneous ice freezing mechanism detailed in section 4.2: the high supersaturations necessary for ice freezing no longer occur. The ice clouds cause widespread dehydration (Figure 10): 41% of the vortex at 475 K is dehydrated. Again, denitrification and dehydration are coupled because essentially only one freezing process is occurring; in the “HomFrz” case, however, this one process is a NAT freezing process, rather than ice freezing as in “IceFrz.”
 In sensitivity tests the assumed freezing rate has been varied from 102 to 109 cm−3 s−1. The primary effect of a slower assumed freezing rate is to decrease the number of frozen particles. However, a decreased concentration tends to increase the size of the particles (Figure 12a) because the same mass of HNO3 is distributed over fewer particles. These two factors combine to yield a nonlinear relationship between the concentration and denitrification rate (Figure 12b). For small concentrations, too few particles are present for effective denitrification; the particles are removed by sedimentation before they take up a significant amount of the available HNO3. At the other extreme, the particles in the cloud are too small to sediment rapidly. Maximum denitrification rates at 475 K occur for particle concentrations between 10−2 and 10−3 cm−3 s−1. This effect, whereby intermediate particle concentrations are most effective at denitrification, has also been noted in idealized simulations [Jensen et al., 2002].
 The resultant sensitivity of overall denitrification to the freezing rate is shown in Figure 13. The most extreme denitrification at 475 K is caused by freezing rates of 104–105 cm−3 s−1, which produce particle concentrations near the maximum in denitrification rates. Faster rates become more effective at higher levels; k = 107 cm−3 s−1 causes maximum denitrification at 525 K.
 A comparison of these scenarios with the SOLVE data shows that “HomFrz” is much more successful at capturing aspects of the observations than “IceFrz.” PSC formation tends to start in November or early December. As the freezing rate is decreased, however, PSC onset is delayed: the freezing rate becomes slow enough that 1 to 2 days of cold temperatures are necessary for enough NAT particles to accumulate, allowing 1% of the HNO3 to condense (which is the criterion for identifying a PSC in Figures 6 and 7). For k = 104 cm−3 s−1 the onset of PSCs is 6 December; for k = 103 cm−3 s−1, liquid PSCs occur first, and frozen PSCs first form on 14 December, more than a week later than the SOLVE observations. Therefore the PSC onset criterion suggests that the freezing rate is at least k = 104 cm−3 s−1.
Figure 13 shows that a NAT homogeneous freezing process causes strong denitrification. In fact, for moderate freezing rates (k = 104–105 cm−3 s−1), denitrification is too intense, relative to the SOLVE observations: the denitrification frequency peaks at 90%, compared to the measured maximum at 70%. Slower freezing rates (i.e., k = 103 cm−3 s−1) limit the severity of the denitrification but also cause many air parcels to experience no denitrification. Instead, agreement with the SOLVE data is found for faster freezing rates, k = 106–107 cm−3 s−1; k = 107 cm−3 s−1 matches the overall shape of the denitrification distribution well. According to this scenario, the observed denitrification was less than the maximum possible because particles were limited to small sizes that do not sediment efficiently.
 However, in all of these simulations, dehydration is too widespread (Figure 10 and Table 3). Unlike the “IceFrz” scenarios, denitrification without dehydration is possible but is much less common than in the SOLVE measurements. The cold temperatures in the UKMO analysis could be responsible. If the minimum model temperatures were about 3 K higher, most of the type II PSCs would be eliminated in the “HomFrz” scenario, greatly reducing the extent of dehydration. The characteristics of the NAT PSCs would not necessarily be affected, since they require only prolonged periods of moderately cold temperatures, rather than the extreme cold necessary for ice formation. Without a clearer understanding of the minimum temperatures in January, the “HomFrz” scenario (with k ≈ 107 cm−3 s−1) can not be ruled out.
4.4. Heterogeneous Freezing to Form Single PSCs: “HetFrzA” Scenario
 Another possible mechanism for inducing freezing above the ice frost point is heterogeneous freezing, in which inclusions, or nuclei, in the particles allow freezing to occur at temperatures warmer than otherwise possible. To evaluate this process, 0.1% of the aerosol was assumed to contain heterogeneous nuclei. In the first set of tests, the subsequent microphysics of the frozen particles was identical to the “HomFrz” scenario.
Figures 6d and 7d show that NAT PSCs initially form as efficiently as in the “HomFrz” scenario, with clouds occurring as soon as temperatures fall below the NAT condensation point. Later in the winter, however, the frequency of NAT PSCs falls off. Maximum PSC coverage (at 475 K, 39%) is reached in late December. During January, when peak coverages are reached in the “HomFrz” scenario, the “HetFrzA” coverage falls off noticeably. By the end of the winter, NAT PSC formation is rare and liquid PSCs dominate.
 These characteristics are caused by a few key assumptions about the nature of the heterogeneous nuclei and the freezing process. The “HetFrzA” scenario assumes that there is a limited number of nuclei capable of inducing aerosols to freeze; this freezing causes a NAT PSC to form the first time an air parcel cools. All nuclei are consumed in this process. The next time temperatures in an air parcel cool, no nuclei are present in liquid particles to induce freezing. At the same time, nuclei in the previously frozen particles have been effectively deactivated. They are now contained in frozen SAT particles, but NAT is prevented from condensing on SAT because the structures of the two crystals are incompatible (expressed by mNAT = 0.75) [Iraci et al., 1995]. Therefore Figure 7d corresponds to a map of air parcels that are cooling for the first time.
 This scenario is able to reproduce the December PSC formation observed by SOLVE, even for variations in f from 10% to 0.001%. However, the reduction in PSCs during the middle and late winter limits denitrification to levels much less than observed (Figure 14). Although some air parcels experience denitrification in excess of 90%, their number is limited. Most trajectories experience no denitrification; a large fraction are renitrified, demonstrating that individual PSC events tend to only redistribute NOy a few kilometers lower. Finally, of the few air parcels that are strongly denitrified, a large fraction is also dehydrated. In this scenario the duration of the PSCs is too limited to explain the SOLVE observations.
4.5. Heterogeneous Freezing to Form Recurring PSCs: “HetFrzB” Scenario
 In the “HetFrzA” scenario the role of heterogeneous freezing was seriously limited by the assumption that each heterogeneous nucleus caused only one PSC to form. If, however, each nucleus can remain active, producing a PSC every time an air parcels cools below the NAT condensation point, heterogeneous freezing has the potential to be much more effective. This possibility was explored in the “HetFrzB” scenario, by allowing NAT to nucleate on the SAT cores that are produced by sulphate freezing (mNAT = 0.9).
 As shown in Figures 6e and 7e, this scenario has extensive PSC formation through December and January, comparable to “HomFrz.” The extent of PSC coverage in January is much greater than in “HetFrzA,” maximizing at 67% at 475 K, matching the “HomFrz” scenario. The strong denitrification (Figure 8) is also comparable to the “HomFrz” scenario.
 Beyond these superficial similarities, however, many differences between “HomFrz” and “HetFrzB” can be identified. Figure 11 shows that in “HetFrzB,” PSC concentrations decrease through the winter from the initial, maximum values. This reflects the gradual removal, by sedimentation, of the particles containing heterogeneous nuclei. Once the nuclei are lost, they can not be replenished, so PSC concentrations will inevitably decline with time. “HomFrz” PSC concentrations, on the other hand, initially increase with maximum values in mid January.
 Another difference is in the type II PSCs, which are less frequent in “HetFrzB” than in “HomFrz.” The cause is directly related to the concentrations discussed in the previous paragraph. In “HomFrz,” ice is able to form on the numerous NAT particles present when the ice frost point is reached. However, in “HetFrzB,” NAT concentrations are minimal at the ice frost point; the coldest air parcels, in particular, have had sufficient exposure for virtually all of the NAT particles to have sedimented. Therefore ice only forms at high supersaturations, where homogeneous freezing to form ice becomes possible, as in “IceFrz.” The characteristics of the type II PSCs in “HetFrzB” are very similar to those in the “IceFrz” scenario; the same is true of “HetFrzA.”
 Varying the assumed number of heterogeneous nuclei has effects comparable to varying the freezing rate in the “HomFrz” scenario (Figure 12): particle concentration and average radius are inversely related, causing the denitrification rate to maximize for concentrations near 10−2–10−3 cm−3 s−1. Average particle radii for the “HetFrzB” scenario tend to be slightly larger than for “HomFrz” because all the particles have had a long time to grow, resulting in a narrower distribution of large particles. The continuous supply of particles in “HomFrz” constantly introduces new, small particles, producing a broad size distribution and decreasing the average particle size. However, for large particle concentrations in Figure 12a the comparison between “HomFrz” and “HetFrzB” is complicated by the more extensive denitrification that has occurred in “HetFrzB.”
 In comparison with the SOLVE measurements, all of the “HetFrzB” cases considered are able to produce solid phase PSCs in early December. Even for the smallest value of f considered, 0.001%, some PSCs are present during the period of the SOLVE lidar measurements.
 The denitrification criterion shows that for f = 0.02%, denitrification maximizes at 70%, agreeing well with the measurements; the f = 0.02% case was highlighted for this reason. However, Figure 12 shows that f = 0.02% does not have the maximum denitrification rate. Figure 15 confirms this; increasing the number of frozen particles, i.e., f = 0.1%, results in many air parcels with 80–90% denitrification. But further increases in f decrease the efficiency of denitrification. For f = 10%, 70% denitrification is widespread, matching the SOLVE measurements almost as well as the f = 0.02% case. Therefore two distinct values of f are equally able to reproduce the measured denitrification distribution: f = 0.02% or f = 1%.
 Of the scenarios considered, “HetFrzB” has dehydration most similar to the observations. Table 3 shows that denitrification without dehydration is common. In addition, Figure 10 reveals that dehydration is primarily associated with air parcels experiencing ∼70% denitrification. In contrast, dehydration in the “HomFrz” scenario is less discriminating, often occurring in air parcels with moderate or little denitrification. The more limited dehydration in “HetFrzB” is a result of the reduced frequency of type II PSCs. In addition, two independent freezing mechanisms are effective in this scenario. One, heterogeneous freezing, produces exclusively NAT particles, and the other, homogeneous freezing, produces exclusively ice particles. Denitrification and dehydration are decoupled (except, of course, that both are promoted by cold temperatures).
 Despite these improvements, “HetFrzB” still has more dehydration than the measurements; 13–15% of denitrified air parcels are dehydrated, 10 times more than observed. Model dehydration levels reach 40%, whereas observations are limited to less than 10%. The freezing process that caused this dehydration is homogeneous freezing below the ice frost point; modifying the NAT freezing process can only increase the extent of dehydration (as in “HomFrz”), not decrease it. Although errors in the ice freezing rate could be responsible, the model temperatures are a more likely explanation. Warmer temperatures, more consistent with analyses other than UKMO, would reduce the extent of type II PSCs. For example, in the “IceFrzWarm” scenario (see section 4.2), temperatures were increased by 1 K. As a result, dehydration was restricted to 2% of the vortex, with maximum dehydration in an individual air parcel of 26%. Similar changes would be expected in the “HetFrzB” scenario and would improve agreement with measurements. The temperature modifications necessary would be smaller than required to “fix” dehydration in the “HomFrz” scenario.
 Overall, two values of f explain the observed measurements equally well: f = 0.02% and f = 1%. The primary difference between the characteristics of these two simulations is the NAT particle concentration. The initial 50-fold difference in concentration is magnified during the course of the winter. For f = 0.02%, most of the particles are removed in a PSC event; the small concentrations cause large particles, which are efficiently removed by sedimentation. However, for f = 1%, PSC concentrations are nearly constant during the winter because only a fraction of the particles is removed by sedimentation. Future research will investigate whether SOLVE measurements of PSC concentration can discriminate between these two cases.
4.6. NAD Freezing
 In all of the model runs discussed up until now, the composition of solid phase type I PSCs was assumed to be NAT, the most stable HNO3 compound. However, laboratory studies have suggested that metastable NAD formation may be kinetically favored. Several of the model runs were redone assuming NAD composition in order to assess how sensitive PSC characteristics are to the particle composition. NAD was directly substituted for NAT in the model scenario; all the parameters in Table 1 were set to the same values as in the analogous NAT simulation. The freezing thresholds were established using NAD saturation ratios, so freezing occurred whenever SNAD exceeded 2. The discussion focuses on the “NADHetFrzB” scenario, but “NADHomFrz” runs were also carried out (Figures 12 and 16 and Table 3).
 Because NAD only forms at temperatures several degrees colder than the NAT condensation point, NAD particles are more limited in extent, Figures 6f and 7f. In general, the vortex coverage is 10% less than in the analogous NAT run. Liquid PSC formation is correspondingly more frequent. However, the characteristics of individual PSCs tend to be similar to the NAT case: particle concentrations are similar, and particle sizes are only about 20% smaller (Figure 12).
 The NAD particles are able to produce denitrification, but the extent and severity of the denitrification is less. For “NADHetFrzB,” the maximum denitrification in an individual air parcel is 89%, compared to 96% in the comparable NAT simulation, and the overall average denitrification is less (Figure 16). A comparison of the denitrification distributions with the SOLVE measurements is less favourable than for the best NAT simulations: distributions tend to be broader, with more air parcels that experience little or moderate denitrification. The “NADHomFrz” scenarios in particular are unable to produce widespread, severe denitrification. However, the best “NADHetFrzB” scenario, for f = 0.1%, is able to reproduce the most basic qualitative characteristic of the measurements: the greatest number of air parcels experienced 70% denitrification.
 “NADHetFrzB” is also marginally consistent with the other SOLVE criteria. The first PSCs occur on 8 December for f = 0.1% and 30 November for f = 1%. The denitrification/dehydration statistics (Table 3) are no worse than for the analogous NAT simulations. Therefore, although the NAT simulations provide somewhat better agreement with the observations, the NAD simulations, in particular “NADHetFrzB” with f = 0.1%, can not be excluded. A more exact comparison between the model and measurements, accounting for uncertainties in each and for differences in the regions being sampled, would be necessary to discriminate between the NAD and NAT cases.
5. Summary and Conclusions
 This study has examined several mechanisms by which freezing may occur in the Arctic stratosphere, using the 1999–2000 winter as a representative cold Arctic winter. The freezing method affects whether and when type I NAT (or NAD) PSCs and type II PSCs can form. The most important effects of the resultant frozen particles have been discussed, namely, denitrification and dehydration. For the uncertain freezing processes, key parameters have been varied to estimate at what point the freezing process becomes effective. Comparisons with specific SOLVE measurements have identified which scenarios are incompatible with observations.
 To reproduce any of the key characteristics of the observed PSCs requires a freezing process that occurs above the ice frost point. Simulations including only freezing below the ice frost point, as advocated, for example, by Koop et al.  and Waibel et al. , produced very limited solid phase PSCs: observations of solid phase PSCs in early December, of extensive denitrification, and of denitrification without dehydration can not be explained. Several uncertainties in ice freezing were explored but were unable to substantially improve model agreement with measurements. For example, colder temperatures in the model cannot explain the discrepancies: cooling by much more than 1 K would be necessary, but the UKMO analysis used for the model temperatures was already colder than other analyses of the 1999/2000 winter. Even with extreme variations in the assumed ice freezing rate, PSC formation was insufficient, and denitrification was invariably associated with dehydration.
 Substantial model improvements were effected by introducing a second freezing process, occurring at warmer temperatures, in addition to ice freezing. Both an idealized homogeneous freezing mechanism and a heterogeneous one were tested, with a range of assumptions about the number of frozen particles and their composition. For homogeneous freezing the concentration was controlled by varying the assumed freezing rate k; for heterogeneous freezing the concentration was controlled by varying the fraction of particles assumed to contain a heterogeneous nucleus f. In all cases, varying the concentration controlled not only the extent of PSC formation but also the particle sizes and the net denitrification. Both NAD and NAT were examined.
 Several scenarios were able to explain two of the SOLVE observations used as criteria in this study: PSC formation in early December and the extent of denitrification. For homogeneous freezing to form NAT (the “HomFrz” scenario), best agreement was found for a freezing rate of k = 106–107 cm−3 s−1. For heterogeneous freezing to form NAT (the “HetFrzB” scenario), best agreement was found for two distinct values of f, either ∼0.02% or ∼1%; intermediate values of f overpredict denitrification. For NAD formation, only heterogeneous freezing was able to explain the data, if f = 0.1%, and the comparison with measurements was less favorable than for the NAT scenarios. However, for any heterogeneous freezing mechanism to effectively denitrify, it must be assumed that the heterogeneous nuclei remain active throughout the winter, instead of becoming deactivated by a SAT coating after formation of the first PSC.
 All of the scenarios overpredicted dehydration, and thus were not able to fully reproduce the third measurement criterion, denitrification with very little dehydration. Heterogeneous freezing (either to NAT or NAD) caused the least dehydration, but further reductions are only possible by reducing the homogeneous freezing of ice (calculated using the already limited freezing of Tabazadeh et al. ). Uncertainties in the model temperatures are more likely to be the culprit. Increasing the model's minimum temperatures by 1–2 K would improve dehydration in heterogeneous scenarios; ∼2 K further warming could possibly improve the homogeneous freezing scenarios. Only the minimum model temperatures, in particular temperature excursions below the ice frost point, would need to be modified; the resultant temperatures would all fall within the range of minimum temperatures produced by various analyses of the 1999/2000 winter. An analysis of measured, synoptic scale type II PSCs would help to constrain ice formation mechanisms and address the specifics of how dehydration occurs.
 Several differences between a homogeneous and heterogeneous freezing process were apparent in the simulations, and could possibly be exploited in further analysis. For homogeneous freezing, the strongest NAT PSCs occur during the longest periods of exposure to cold temperatures, as the frozen particle concentration accumulates. On the other hand, the concentrations and extent of heterogeneously formed PSCs decrease steadily through the winter. Therefore a comparison of PSC concentrations at the beginning of and near the end of a cold period would discriminate between the two possibilities. Also, PSC characteristics below the ice frost point differ: the heterogeneous freezing cases tended to have negligible NAT PSC concentrations, whereas homogeneous freezing produced large numbers of particles. This distinction also affects the ease with which type II PSCs can form: for homogeneous freezing, type II PSCs are found to form easily (by nucleating on the existing NAT particles), but for heterogeneous freezing, substantial ice supercooling is generally required before ice can freeze out of the liquid sulphate particles.
 Most of these diagnostics require detailed PSC information during the coldest period of the winter. Unfortunately, SOLVE observations were not made in late December or early January. Extrapolating backwards from the first SOLVE in situ measurements, on 20 January, is problematic. In all simulations, PSC concentrations decreased by more than order of magnitude during the month of January. Model denitrification rates on 20 January are 5 times slower than they had been 1 to 2 weeks earlier. More research is necessary to understand how the intense PSC processing in the middle of the winter is related to the PSCs observed later.
 The assumed NAT freezing processes examined in this study were responsible for nearly all the denitrification that occurred. Therefore a better understanding of such freezing processes is clearly necessary to improve our understanding of denitrification. In particular, these simulations show that even more intense denitrification than observed was theoretically possible during the 1999/2000 winter. For example, if heterogeneous freezing is responsible for NAT PSCs, year-to-year variability in the number of nuclei may be possible. Long-term trends in nuclei concentration could lead to more intense denitrification in future winters, even if temperatures are similar. Or, alternatively, denitrification could be mitigated by variations in the population of heterogeneous nuclei.
 The NAT freezing processes included in the simulations were speculative and were treated in a simplified manner; in particular, the temperature dependence of freezing was treated crudely. Recent research [Salcedo et al., 2001; Tabazadeh et al., 2001] has elucidated a mechanism for homogeneous freezing above the ice frost point; the complex temperature dependence could lead to PSC evolution different from that found in this study. Future simulations with the IMPACT model will examine the effects of such freezing in more detail. The existence of heterogeneous nuclei is uncertain. However, given that nucleus concentrations smaller than 10−2 cm−3 are sufficient to effect substantial denitrification, even relatively rare compounds could be important. Even if heterogeneous nuclei are identified, more details about the mechanism by which they are effective need to be known, in particular to understand whether the nuclei can remain effective throughout the winter.
 The denitrification in these simulations is intense and widespread enough to have an impact on ozone depletion. Drdla and Schoeberl  describe the chemistry that accompanied the microphysical evolution described here and quantify the impact of PSC formation on ozone depletion.
 This study is 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 observed variability in PSC characteristics, denitrification, and dehydration can be reproduced by the various microphysical scenarios. Even for the 1999/2000 winter, the extensive PSC measurements provide the opportunity for more detailed model/measurement comparisons. Research is ongoing to identify characteristics specific to the freezing mechanism which can be identified in the available measurements. An eventual understanding of the mechanism by which solid phase PSCs form is necessary to anticipate how denitrification, dehydration, and ozone loss may respond to future stratospheric conditions.
 We are grateful to Joan Rosenfield for providing the heating rate calculations. We would also like to thank the SOLVE science team for their efforts obtaining the data and their cooperation in sharing it, in particular David Fahey, Bob Herman, Paul Newman, M. J. Mahoney, and Geoff Toon. This research was funded by the NASA Atmospheric Chemistry Modeling and Analysis Program.