In situ Multiangle Spectrometer Probe (MASP) particle measurements have been analyzed to determine the typical behavior of sulfate particles during the SAGE III Ozone Loss and Validation Experiment (SOLVE) campaign. The study has explored variations in the total particle concentration measured by MASP. A new analysis method has been developed in which increases of the MASP concentration can be interpreted as growth of small particles (those which are smaller than 0.2 μm in radius at midlatitudes). The method also allows all of the MASP measurements made during the SOLVE campaign to be incorporated in a single analysis. At all levels of the stratosphere, the total MASP concentration (and therefore aerosol growth) varies continuously with temperature. This behavior is well-reproduced by assuming that the sulfate aerosols are liquid solutions, but cannot be reproduced if the aerosol is assumed to be frozen. At sufficiently cold temperatures, larger increases in the MASP concentration are consistently seen; the observed onset temperature for this growth is in good agreement with model expectations for liquid ternary solutions. Liquid-like behavior is apparent for all measurements made in the Arctic during SOLVE, both inside and outside the vortex, and even at the coldest temperatures sampled during the campaign. At the levels with the coldest measured temperatures, which cause maximum particle sizes and thus the greatest total MASP concentrations, 90% of the particles grow as liquids. Therefore, the freezing that occurred during the 1999–2000 Arctic winter was selective, with most of the particles remaining liquid even in the presence of a small number of frozen particles.
 A critical process that can occur during the polar stratospheric winter is freezing of the aerosol particles. Although at midlatitudes stratospheric aerosol is made up of supercooled liquid particles, polar stratospheric clouds (PSCs) containing frozen particles are observed during the winter [e.g., Browell et al., 1990]. These frozen particles are the primary cause of dehydration and denitrification [Drdla et al., 2002]. The freezing process should also alter the composition of the sulfate in the particles, converting it from liquid sulfuric acid to a frozen form, such as sulfuric acid tetrahydrate (SAT) or sulfuric acid hemihexahydrate (SAH) [Zhang et al., 1993]. Even after the PSCs evaporate, these frozen particles will remain present: SAT is thermodynamically more stable than liquid sulfate throughout most of the stratosphere. Only if temperatures approach 215 K is SAT predicted to melt [Middlebrook et al., 1993; Zhang et al., 1993]. Therefore PSC processing can fundamentally alter the aerosol characteristics for the remainder of the winter. Aerosol measurements demonstrating the presence of frozen particles would provide information about the extent of freezing earlier in the winter.
 In particular, the concentration of frozen particles is an indication of whether freezing is selective. Few frozen particles implies that freezing is highly selective and thus this is the process that controls the number of large PSC particles. Alternatively, many particles may freeze, leading to large frozen particle concentrations; in this case, another process (e.g., nucleation) limits the number of large PSC particles. Given the importance of large PSC particles in denitrification [Fahey et al., 2001; Drdla et al., 2002] understanding what process(es) control the particle formation and number is critical.
 Laboratory and theoretical data cannot yet address this issue. Available data show that homogeneous freezing of sulfuric acid particles is possible below the ice frost point [Tabazadeh et al., 2000; Koop et al., 2000], causing a small number of the largest particles to preferentially freeze. However, on the synoptic scale temperatures cold enough to allow this process are too rare to explain observed solid-phase PSCs during the 1999–2000 Arctic winter [Drdla et al., 2002].
 Freezing is possible in mesoscale lee-wave events, where the local temperatures can briefly fall below the ice frost point [Carslaw et al., 1998; 1999]. Studies of lee-wave PSCs show that most of the particles are activated and grow as ice [Carslaw et al., 1998; Wirth et al., 1999]. The fate of the sulfate in the particles is less certain. To explain the subsequent nitric acid trihydrate (NAT) particle evolution, Carslaw et al.  and Wirth et al.  assume that the sulfuric acid does not freeze along with the ice: instead, it persists as a liquid layer on the outside of the ice particles. Other studies have assumed that all the sulfuric acid is converted to SAT [Rivière et al., 2000]. If sulfate is frozen by lee waves, their overall effect on PSC evolution is much larger: cumulative lee-wave processing can cause more than 40% of the vortex to contain SAT [Carslaw et al., 1999].
 Establishing whether the sulfate particles are liquid or solid is important for understanding the subsequent evolution of the vortex. PSC formation depends on the phase of the background aerosol. If liquids are present, HNO3 condensation to form ternary solutions will compete with the growth of solid-phase NAT, reducing the size of the NAT particles. On the other hand, if only SAT is present, PSC formation may become very difficult [e.g., Tolbert, 1996], since HNO3 does not readily condense on SAT. Deliquescence of the SAT particles may allow PSC formation [Koop and Carslaw, 1996], but whether this process can occur is uncertain. The laboratory data of Iraci et al.  support this mechanism, but the data of Martin et al.  show it to be slow; Martin et al.  also demonstrate that such deliquescence is inefficient in denitrified situations.
 The phase of the sulfate particles will also affect heterogeneous chemistry. Even when PSCs are not present, liquid particles control the partitioning of nitrogen species through the heterogeneous hydrolysis of N2O5 [Fahey et al., 1993]. This reaction is more than 10 times less efficient on SAT than on liquid particles [DeMore et al., 1997]: widespread freezing would alter the relative concentrations of HNO3, NO, and NO2, which in turn can affect ozone levels.
 Measurements made during the SAGE III Ozone Loss and Validation Experiment (SOLVE) provide clear evidence for the presence of solid-phase nitric acid particles. In situ NOy measurements revealed the presence of very large (1–10 μm radius), nitric-acid-containing particles [Fahey et al., 2001]; such large sizes can only be attained by solid-phase particles. Satellite measurements frequently observed PSCs containing similarly large particles [Strawa et al., 2002]. Lidar measurements were generally depolarized [Drdla et al., 2002]. However, these measurements are all particularly sensitive to the characteristics of the largest particles [e.g., Steele and Turco, 1997; Toon et al., 2000], even if those particles only represent a minuscule fraction of all the particles present. Furthermore, the particles observed by Fahey et al.  had very small concentrations, typically less than 10−3 cm−3, compared to total aerosol concentrations exceeding 5 cm−3. Other types of measurements need to be analyzed to investigate the characteristics of the smaller particles — the majority of the particles — that are also present. Of particular interest is whether these particles froze at the same time as the larger particles.
 The Multiangle Aerosol Spectrometer Probe (MASP) instrument on the ER-2 aircraft provided in situ size distributions of particles greater than 0.2 μm radius during the SOLVE campaign. The measurements were made at ambient conditions, and therefore showed the particle growth due to uptake of H2O and HNO3 as the temperature cooled. The MASP size range included the large particles seen by Fahey et al. , causing the MASP total volume to be dominated by the large frozen particles when they were present. Therefore, although the total volume has been used in the past to identify liquid particles [Drdla et al., 1994; Dye et al., 1996; Del Negro et al., 1997], during SOLVE its use is complicated by the combined presence of both liquid-phase and solid-phase growth.
 This study has instead focused on the total concentration of particles observed by MASP. In general, several factors can influence the MASP concentration. However, the analysis described in section 4 enables measurements with similar characteristics, in particular similar sulfate aerosol loading, to be easily compared. The remaining variations in concentration predominantly reflect growth of small particles, in particular those particles that are smaller than 0.2 μm radius at midlatitude conditions. Large, frozen particles are a negligible and constant contribution to the MASP total concentration, resulting in a small impact on the analysis. A further advantage of using the concentration is the increased accuracy: the uncertainty of the MASP concentration is ±25%, compared to ±60% for volume [Baumgardner et al., 1992]. The measurements are discussed in greater detail in section 2. Equilibrium model calculations that have been used to assess the data are described in section 3.
 In order to provide a systematic analysis of the overall state of the stratospheric aerosol, it is important to include as many observations as possible. Previous studies [e.g., Drdla et al., 1994; Dye et al., 1996; Del Negro et al., 1997] of in situ particle measurements, however, have only examined sections of individual flights, typically restricted to portions of the flight at cruise altitude with limited changes in atmospheric composition. As a result only a fraction of the available data has been quantitatively analyzed. For this study, the new method of presenting the MASP measurements (section 4) allows the complete data set to be studied simultaneously.
Section 5 discusses the findings. The aerosol growth has been compared with model calculations to determine which PSC composition is most consistent with the overall behavior. Anomalous points have been identified, taking into account measurement uncertainties, to determine whether there is evidence for localized freezing events. Finally, a determination of the percentage of particles that behave as liquid has been attempted.
2. Measurement Descriptions
 The measurements used for this study were made on 12 ER-2 flights between 14 January 2000 and 12 March 2000. The campaign was based out of Kiruna, Sweden, allowing the majority of the flights to be made within the polar vortex. Frozen particles are likely to be present on these flights. Large solid-phase nitric-acid-containing particles [Fahey et al., 2001] were seen on most flights, as indicated in Figure 1. The coldest temperatures of the winter were experienced on about 10 January, before the first ER-2 flights [Drdla et al., 2002]. Any SAT particles produced during this period of cold temperatures should persist until temperatures exceed the SAT melting point (∼215 K). Figure 1 shows the fraction of the vortex in which melting may have occurred since 10 January, based on the temperature evolution of a set of vortex-filling diabatic trajectories derived from the UKMO analysis [Drdla et al., 2002]. Even by the end of the campaign, most of the vortex should still contain frozen particles, if any were ever able to form.
 This study focuses on measurements made by the Multiangle Spectrometer Probe (MASP) [Baumgardner et al., 1995]. MASP is an optical counter that measures particles by detecting the scattered light produced when individual particles pass through a low-intensity laser beam; the technique is similar to the Forward Scattering Spectrometer Probe (FSSP). The probe is designed to sample the particles with minimal perturbation to the airflow, and thus measures particles at ambient conditions. Both the forward-scattered and backward-scattered light are collected; the data used in this study are derived solely from the more intense forward-scattered light.
 Determining the concentration primarily requires counting the number of particles that pass through the laser beam. The primary source of uncertainty in the concentration is knowledge of the sample volume [Baumgardner et al., 1992], yielding an uncertainty of ±25%. The intensity of the forward-scattered light is related to the particle size; using Mie theory and assuming a refractive index (1.44 in this study) allows the size distribution to be measured. Particles smaller than 0.15 μm radius produce too little scatter to be detected by the probe and are therefore do not contribute to the total MASP concentration. Even particles smaller than 0.2 μm radius do not appear to be efficiently detected, so all particles identified as being smaller than 0.2 μm have been excluded from the analysis. This modification effectively sets a slightly larger scatter signal to be the lower detection limit of the instrument. Accordingly, the discussion will treat 0.2 μm as the lower size limit of the MASP concentration measurement; the change in total concentration is in all cases much smaller than the 25% measurement uncertainty. The MASP data set has also been filtered to remove a small number of data points that appear to be contaminated by sunlight. If the instrument happens to be pointing toward the Sun, sunlight can scatter into the detectors, causing artificially large concentrations [Baumgardner et al., 1995]. A comparison of aircraft heading with the solar position allows such time periods to be identified and removed from the data set.
 A second particle-sizing instrument is also part of the ER-2 payload, namely the Focused Cavity Aerosol Spectrometer (FCAS) [Jónsson et al., 1995]. Unlike MASP, FCAS does not sample particles under ambient conditions. Instead, particles are heated to 34°C inside the instrument, causing volatile components (in particular HNO3 and H2O) to evaporate. The primary compound that remains is H2SO4 in a very concentrated solution. These particles are counted and sized, yielding the number of particles, their sulfate content, and the size distribution. Particles larger than 0.04 μm radius are sampled, which includes almost all stratospheric aerosol particles.
 FCAS data have been used to provide initial sulfate aerosol size distributions for the model calculations described in section 3. For this study, the typical characteristics of the aerosol at a given level were of most interest. Analysis of the data revealed that the sulfate aerosol characteristics are strongly correlated with N2O, a standard stratospheric tracer. Several instruments on board the ER-2 measured N2O; a unified data set incorporating all these measurements has been developed and was used in this study [Hurst et al., 2002].
 For the standard model calculations, averaged FCAS size distributions at each N2O level were determined by normalizing all the measurements to a constant 68.5 wt % aerosol composition, binning according to N2O, and then averaging. Averaged size distributions at select N2O levels are shown in Figure 2. The data demonstrate systematic variations in aerosol number and volume (i.e., sulfate mass). The total FCAS number is highest at low values of N2O. However, for MASP-sized (>0.2 μm) particles, the lowest values are found at low N2O levels, which is especially apparent in the volume plot. Variability at a given N2O level is smaller than the variation between N2O levels: for the 170 ppbv N2O level, the shaded region in Figure 2 shows the one standard deviation variability.
 To test the sensitivity to the assumed size distribution, model results were additionally calculated assuming a monomodal lognormal size distribution. This simplified size distribution was constrained to match the FCAS total number and volume at each N2O level, assuming a distribution width of 1.52, consistent with past Arctic measurements [Wilson et al., 1992].
 An important value in this analysis is the NAT condensation temperature, TNAT. Measurements of temperature (T, K), pressure (p, hPa), water vapour mixing ratio ([H2O]), and nitric acid mixing ratio ([HNO3]) are necessary to calculate TNAT. T and p were measured by the Meteorological Measurement System (MMS) on board the ER-2, with accuracies of ±0.3 K and ±0.3 hPa, respectively [Gaines et al., 1992]; these values translate into uncertainties in TNAT of ±0.03 K and ±0.04 K. Measurements of water vapour were provided by the Jet Propulsion Laboratory Hygrometer [May, 1998], accuracy ±6% or ±0.3 K in TNAT. Although measurements of HNO3 were provided during SOLVE by the CIMS instrument (McKinney et al., manuscript in preparation), these measurements were available for less than half of the flights of interest. Therefore, HNO3 was instead estimated from measurements of NOy [Fahey et al., 1989; Fahey et al., 2001; Popp et al., 2001].
 The NOy “a” channel measures all the gas-phase compounds that contribute to NOy (HNO3, ClONO2, NO2, NO, and N2O5 are the most important during SOLVE) as well as condensed-phase HNO3 in particles up to about 1 μm radius [Fahey et al., 1989], with an accuracy of ±10%. Photochemical model calculations with the Integrated MicroPhysical and Aerosol Chemistry on Trajectory (IMPACT) model [Drdla et al., 2002] simulated the evolution along backtrajectories for multiple points along each ER-2 flight; these model results were used to estimate the fraction of NOy present as HNO3. For most of the SOLVE data, HNO3 is 85 to 99.96% of NOy. An accuracy of ±10%, bracketing this range of HNO3 fractions, has been assumed for the model calculations. Therefore, if no condensed-phase HNO3 is present, the NOy measurements can provide HNO3 with an accuracy of ±14%; varying HNO3 by ±14% alters the calculated value of TNAT by ±0.25 K. Therefore, under typical conditions the aggregate accuracy of T−TNAT is ±0.49 K.
 Under conditions where HNO3 may have condensed, however, interpreting the NOy data is more complicated. Particulate HNO3 is enhanced relative to the gas-phase by a factor that is a function of pressure, temperature, and particle size. For typical ER-2 cruise conditions between 50 and 100 hPa, the enhancement factor increases with size, up to about 30 for particles greater than 10 μm radius [Fahey et al., 1989]. For the standard calculations, we have assumed that the condensed-phase HNO3 in the “a” channel is only due to liquid-phase (ternary solution) HNO3. Using FCAS sulfate aerosol data and assuming equilibrium, the partitioning of HNO3 and the liquid-phase enhancement in the NOy instrument can be determined. An iterative calculation has been performed to determine the actual NOy necessary to match the measured values using these assumptions. The calculation introduces uncertainties due to the enhancement factor (known to ±30% [Fahey et al., 1989]) and in calculating the ternary solution composition. Recent revisions to the enhancement factors have not been included in this analysis [Dhaniyala et al., 2002], but the modifications are within the assumed ±30% uncertainty. A complete calculation of the uncertainty's propagation has been performed, taking into account the effect of uncertainties in T, p, and [H2O] on the modeled ternary solution composition, and also incorporating uncertainties in ternary solution models, by comparing the results of different models. All the uncertainties have been propagated through the HNO3 calculation. The HNO3 uncertainty maximizes at about ±50%, which alone causes an uncertainty in T−TNAT of +1/−0.5 K. Under these extreme conditions, the aggregate accuracy of T−TNAT is +1/−0.56 K. 4.5% of the SOLVE data have significant (>5%) condensed-phase HNO3 according to this analysis, exclusively at colder temperatures.
 One concern with this calculation, however, is that assuming a liquid-phase composition may bias the resultant behavior to artificially look like that of liquid particles. To address this concern, a second calculation of the HNO3 budget has been done, in which it is assumed that all the aerosol can grow into small, equilibrium NAT particles (instead of liquid particles). This scenario has the maximum possible HNO3 condensation, and therefore the lowest total HNO3. Results from this calculation will also be presented in section 5.
 Another assumption made in determining the available HNO3 is to ignore the HNO3 content of any large solid-phase particles that may be present. Fahey et al.  have presented measurements from the same NOy instrument that show that large HNO3-containing particles were present during SOLVE. The study of Fahey et al. , however, was based upon a second, “b,” channel of the NOy instrument. The “b” channel inlet samples particles of all sizes whereas large (>1 μm radius) particles are aerodynamically prevented from entering the inlet of the “a” channel used in our analysis. The two channels also differ somewhat in enhancement factors due to the locations of the inlet openings on the particle separator body [Dhaniyala et al., 2002]. The large sizes and small concentrations of the solid particles discussed by Fahey et al.  limit the rate at which HNO3 can condense to or evaporate from them. Therefore, their HNO3 content is not at equilibrium with the smaller particles of interest here, minimizing the influence of that HNO3 on the small particles. Furthermore, the large fall velocities of the particles imply that these particles did not originate within the air mass of interest [Fahey et al., 2001]. Accordingly, any additional HNO3 evident in the “b” channel data (which would be indicative of large particles (>1 μm)) has been ignored in this study.
 This study has used a slightly revised definition of the NAT condensation point, which we will label the “isentropic TNAT,” as opposed to the more common “isobaric TNAT.” By definition, TNAT is the temperature to which an air parcel must be cooled (or warmed) for the HNO3 partial pressure to exactly equal the HNO3 vapour pressure over NAT; i.e., for the NAT saturation to be unity. Hanson and Mauersberger  provided the equations which describe the HNO3 vapour pressure:
This equation is solved for given values of [H2O] and [HNO3]. Traditionally, the ambient pressure is used to provide a value for p; equation (1) can then be solved to yield TNAT. However, this implicitly assumes that the pressure, p, remains constant as the air is cooled (warmed) to reach TNAT, i.e., that cooling occurs isobarically.
 However, stratospheric air actually cools isentropically: the potential temperature remains constant, which requires pressure and temperature to vary simultaneously. Therefore, the pressure p in equation (1) is itself a function of TNAT; the relationship between them is:
where pi and Ti are the initial pressure and temperature in the air parcel of interest, R is the gas constant, and Cp is the heat capacity of air. Equations (1) and (2) can be solved simultaneously using a Newton-Raphson iterative technique: the resultant value is the isentropic value of TNAT, which more realistically represents the temperature at which NAT can theoretically condense.
 To provide a concrete example, consider a stratospheric air mass at 210 K, 50 hPa, with 5 ppmv of H2O and 10 ppbv of HNO3. The “isobaric” value of TNAT that would be calculated using equation (1) alone is 195.7 K. To cool toward this temperature, the air mass must rise, decreasing the pressure to 39.1 hPa by the time a temperature of 195.7 K is reached. Therefore, NAT cannot actually condense at the predetermined condensation point: because of the new pressure, the isobaric TNAT has decreased to 194.4 K. The “isentropic” value of TNAT for this same air parcel, however, is 194.2 K — this is the temperature at which NAT saturation will in fact be reached, and is a constant value for that air parcel (as long as motions remain isentropic). An analogous isentropic ice frost point can be defined, with the same advantages relative to the isobaric value for stratospheric applications.
3. Model Description
 Equilibrium model calculations have been used to assess how various particle types should behave under the measured conditions. Compositions considered include binary H2SO4/H2O liquids [Tabazadeh et al., 1997], ternary liquids [Carslaw et al., 1994], SAT, NAT [Hanson and Mauersberger, 1988], and NAD [Worsnop et al., 1993]. For each composition, the model determined the aerosol size distribution at equilibrium, assuming that all the particles are able to grow. For liquids, all particles are assumed to have the same composition (the Kelvin effect is not important for the particle sizes of interest); therefore, the volume of each particle increases in proportion to its initial volume. For solids (NAD and NAT), condensation (and thus volume changes) were assumed to be proportional to particle surface area, causing the size distribution to become narrower as the particles grow. From the resultant model size distributions, the number of particles larger than 0.2 μm (the MASP minimum radius) was determined.
 Although the assumptions that all particles will grow and that equilibrium exists are reasonable for liquid particles, they may not apply to NAD and NAT. Assuming all particles can grow will produce the maximum concentration of particles in the MASP range, so the model values serve as an upper limit. Non-equilibrium would cause extensive variability between air masses, since the temperature history would determine how much condensation has occurred. Therefore, NAT or NAD particles may produce a range of concentrations scattered near or below the idealized model values.
 The size distribution on a given N2O surface is determined from FCAS data, as shown in Figure 2. However, the concentrations determined by FCAS are systematically much smaller than the MASP concentrations. A more detailed analysis suggests that the problem is not in the modeling approach, in uncertainties in the FCAS size distributions, or even due to differences in how the instruments determine particle sizes. Rather, it appears at this point that there are underlying discrepancies between the FCAS and MASP measurements. For this study, the relative changes in MASP concentration are of most interest, rather than the absolute values. Therefore, we have opted to scale the FCAS data on each N2O surface to match the MASP concentrations at warm temperatures (T > TNAT). The relative changes in the model concentrations as the temperature cools can then be directly compared with the MASP measured values. The necessary scale factors (listed in Table 1) have been applied uniformly across the entire size distribution. Note that this study has arbitrarily chosen to increase FCAS values to match the MASP data; given that the cause of the discrepancy is unknown, it would be equally valid to decrease the MASP concentrations to values comparable to the FCAS measurements. The choice to use the former approach, in which the MASP concentration is not altered, does not imply that the FCAS measurements are less accurate.
Numbers do not include data from 14 January; number in parentheses provides number of additional data points provided by flight of 14 January.
 At cold temperatures (when HNO3 limits the particle growth) a complication arises in how to apply the scaling factor. The underlying issue is whether the H2SO4 to HNO3 ratio should be affected by the scaling process; the answer depends upon the implicitly assumed cause of the concentration discrepancy.
 If the sulfate particle concentration is increased, the H2SO4 to HNO3 ratio also increases. At cold temperatures, particle growth is determined by the available HNO3. If this HNO3 is distributed among a larger number of particles, the growth of each particle is limited (whether the assumed composition is liquid ternary solution, NAD, or NAT) relative to a baseline simulation, in which no scaling factors are imposed. The smallest particles do not grow larger than 0.2 μm, at least not within the temperature range experienced during SOLVE, decreasing the maximum model concentration. This approach would be appropriate if the FCAS/MASP concentration discrepancy were caused by some form of undersampling in the FCAS instrument.
 At the other extreme, however, the possibility that the MASP instrument is overcounting particles must also be considered. In that case, the baseline simulation (using observed FCAS values) simulation would accurately represent the H2SO4 to HNO3 ratio and the resulting particle evolution. In particular, a larger fraction of the available particles would grow to sizes larger than 0.2 μm at the coldest temperatures. Technically, the MASP measurements should be decreased by a scale factor to permit model/measurement comparisons. However, in a relative sense this is equivalent to increasing the model output by the scale factor: the relative number increase between any two temperatures of interest is identical in the two cases. The latter approach, increasing the model output by the scale factor, has been chosen here, which allows the range of model results to be compared in one graph without any need to also vary the measurement points.
 The best way to handle the scaling issue cannot be resolved until a detailed intercomparison of the FCAS and MASP data sets is possible, which may ultimately require an instrument comparison in a controlled laboratory environment. In the meantime, the range of possibilities has been considered to be a modeling uncertainty; section 5 will discuss the implications of this uncertainty on the data analysis.
 Uncertainties in the ternary solution model have also been considered. The ternary solution composition has been calculated with four different models of the HNO3/H2SO4/H2O system: Carslaw et al. , Tabazadeh et al. , Luo et al. , and Taleb et al. . Carslaw et al.'s  model has been used as the default model, and is the source for calculations unless otherwise stated. The other models have been used to assess the uncertainty in the models: the range of compositions predicted by the four models is assumed to represent the uncertainty in our knowledge of the ternary solution characteristics.
 Values of [H2O] and [HNO3] had to be assumed at each N2O surface for the model calculations. H2O was set to 5 ppmv. HNO3 was set to be 95% of NOy*, the expected level of NOy as a function of N2O in the absence of denitrification; MkIV balloon [Toon et al., 1999] measurements on 2 December 1999 (i.e., in the early winter Arctic vortex) provided the NOy* relationship. The simulated air mass was cooled isentropically at 450 K potential temperature. Exceptions to these assumed values will be explicitly noted. As discussed in the next section, the coordinates used in the analysis remove most of the variability caused by changes in the model's assumed HNO3, H2O, or potential temperature. In other words, using different input values for the model calculations would not substantially change the results. Instead, the analysis coordinates essentially assimilate all the available information on the actual measurements of H2O, HNO3, and potential temperature into the measurement points; the associated uncertainties in these parameters are therefore also incorporated into the measurement uncertainties.
4. Analysis Methodology
 The utility of the MASP instrument is that it measures increases in particle size, in particular the growth due to PSC formation. Previous studies have all focused on changes in aerosol volume, which is directly related to the particle size. However, for the MASP concentration used here, the relationship to particle growth is less obvious. In PSC events, the total particle concentration does not change: the concentrations measured by other particle instruments, such as FCAS and the condensation nuclei (CN) counter [Wilson et al., 1990] do not increase in PSCs (in fact, particle losses in the inlets of these two instrument cause slight decreases). The MASP instrument, though, only detects a portion of the available particles, namely those larger than 0.2 μm radius. At midlatitudes, and especially during nonvolcanic conditions, most of the stratospheric sulfate aerosol is smaller than 0.2 μm radius and undetectable by MASP. As these particles grow, they can increase in size past 0.2 μm, thus increasing the number of particles in the MASP size range.
 A scatterplot (Figure 3) of the total MASP concentration compared to the local temperature reveals that the concentration is indeed largest at the coldest temperatures sampled during SOLVE. However, at a given temperature, for example 195 K, the observed concentration varies over more than an order of magnitude. The first step in this study was to identify the factors contributing to this variability, in order to determine an appropriate method to analyze the available data.
 This variability is also present in the MASP volume measurements. To avoid complications, past studies [e.g., Drdla et al., 1994; Dye et al., 1996] have tended to limit their focus to a section of a single flight, selecting a portion of the flight where the characteristics of the sampled air remain relatively constant. Valuable insights have been gained with such an approach, but it is inherently limited. First, it depends upon the air mass characteristics remaining stable for a long enough period of time to provide sufficient measurements. Second, the temperature must vary over a meaningful temperature range during that period. A third shortcoming is that the variability that does inevitably occur during the flight segment of interest is difficult to quantify: how much variability is too much? How much of the data scatter can be attributed to variations in the air mass?
 To understand the factors that influence the MASP data, we have started by using an equilibrium model to simulate the characteristics of an air mass with a fixed population of liquid sulfuric acid aerosol particles. The assumed monomodal lognormal size distribution is shown in Figure 4. The 0.2 μm radius lower limit of the MASP instrument is shown as a vertical line in the figure.
 Simply by varying the temperature and pressure of the air parcel, the aerosol size distribution, and thus the concentration that would be measured by MASP, can be altered. Assuming that all of the particles remain liquid (and thus consist of H2SO4/H2O binary solutions or HNO3/H2SO4/H2O ternary solutions), all of the possible size distribution variations can be described as a combination of two factors: the composition of the aerosol and the air density of the parcel.
 The air density is a factor because aerosol particles respond to pressure and temperature variations in the same manner as air molecules: the particles become more closely spaced (larger concentration per volume) as the pressure increases (or temperature decreases). The resultant change in the size distribution is shown in Figure 4: the entire distribution magnifies or shrinks vertically. A typical solution is to express the particle concentration relative to the mass of air, i.e., (mg air)−1. Although the natural unit of the MASP concentration is volume-based, i.e., cm−3, the conversion is straightforward, requiring only measurements of the temperature and pressure. The conversion does not affect the accuracy of the concentration measurement (±25%), given the much smaller uncertainties in the temperature and pressure measurements (±0.15% and ±0.6%). At 210 K and 50 hPa, 1 cm−3 is equivalent to 12.1 (mg air)−1.
 The second factor is the aerosol composition. As conditions change, sulfuric acid absorbs and releases water and nitric acid, causing the size of an individual aerosol particle to increase or decrease. For particles larger than 0.2 μm, the Kelvin factor plays a small role, and therefore all sulfuric acid particles have the same equilibrium composition. The result is that all of the particles grow or shrink together. In Figure 4, this is seen as a translation of the entire distribution along the horizontal axis; the shape of the distribution is not affected. Although the total particle number does not change, the number of particles in the MASP size range does vary: this is why the MASP concentration provides information on the particle composition.
 The cases in Figure 4 were carefully selected to modify air density and composition independently; typically, a pressure or temperature change will cause both air density and composition to be altered. However, the resultant change in size distribution can always be interpreted as the combined effect of these two factors. Several factors in addition to T and p also affect the aerosol composition, in particular [H2O] and [HNO3]. These composition variations are also simply reflected as a horizontal shift of the size distribution in Figure 4. So, for a fixed collection of liquid particles all possible changes caused by air mass variability can be understood as a combination of two influences: the air density and the particle composition.
 As already mentioned, compensating for air density variations is straightforward: simply express the concentration in units of (mg air)−1 instead of cm−3. However, particle composition variations are more complex. For ternary solutions, at least four independent factors will affect the composition: T, p, [H2O], [HNO3]. These same four factors also control NAD and NAT condensation. Temperature is the dominant contributor; our approach is to summarize the influence of p, [H2O], and [HNO3] using the NAT condensation temperature, TNAT.
Figure 5 shows the MASP concentration as a function of temperature predicted by an equilibrium model for a fixed sulfate distribution, with varying levels of [H2O] and [HNO3]. Plotting the data against absolute temperature produces substantial variability. However, the same data plotted as temperature relative to the NAT condensation point (T−TNAT) is much more compact. For both ternary solutions and NAD, the differences between the different curves is reduced from as much as 4 K to less than 0.5 K. The behavior of the two compounds is much easier to distinguish. This technique is equally effective for NAT (equilibrium NAT growth, of course, always initiates at T−TNAT = 0), and even for other PSC compositions (i.e., binary solutions and SAT) and for variations in potential temperature. Although T−TNAT is particularly useful for examining cumulative particle concentrations and onset temperatures, it is less useful for examining the volume: changes in volume due to [HNO3], for example, are not removed by modifying the temperature coordinate.
 The one disadvantage of using T−TNAT is the increased uncertainty associated with calculating TNAT, as discussed in section 2. However, the uncertainty is in all cases less than the 4 K spread in the growth onset temperatures shown in Figure 5a. Therefore as long as sufficient measurements are available, T−TNAT is more useful than T for analyzing stratospheric particle growth. Other studies have used T−TNAT to compare liquid-phase and solid-phase PSC growth [e.g., Larsen et al., 1997; Hayashida et al., 2000], but have not demonstrated that this variable is effective for PSC compositions other than NAT. T−Tice (where Tice is the ice frost point) has also been used [e.g., Voigt et al., 2000]. However, if Figure 5b is replotted using T−Tice the results are less compact: T−Tice can account for variations in [H2O] but is unable to remove the effects of variability in [HNO3].
 The discussion so far has assumed a single, constant size distribution of sulfate aerosol, which is not valid in the stratosphere (Figure 2). Since the FCAS size distributions are nearly constant for a given N2O mixing ratio, sulfate variability can be accounted for by binning the data according to N2O. Therefore, we expect that most of the factors contributing to variations in the MASP concentration (expressed in (mg air)−1), can be accounted for using T−TNAT and binning by N2O. Any remaining changes in concentration when using these coordinates can be attributed to aerosol growth. Therefore, increases in concentration are synonymous with growth.
5.1. Detailed Model/Measurement Comparison at One N2O Level (170 ± 10 ppbv)
Figure 6 demonstrates that this analysis method is indeed effective in creating a data set with greatly reduced scatter. Measurements were made on this N2O surface (170 ± 10 ppbv) on all of the SOLVE flights. This analysis reveals strong flight-to-flight consistency in the data set. For example, the dramatic increase in concentration for T−TNAT < −4 K is reproduced on four separate flights. This consistency provides strong confidence in the robustness of this growth feature. Combining measurements from all the flights also permits analyses that would not otherwise be possible. For example, the coldest conditions in Figure 6 were observed on the flight of 5 March. But the aircraft was ascending during this period, causing conditions to vary substantially across the PSC event. The other points in Figure 6 from this flight were measured more than half an hour earlier; some of the points were narrow features isolated from other PSC activity. Previous approaches would have been unable to quantitatively examine this interesting PSC event. However, measurements from other flights are able to place the 5 March data in context and demonstrate that they are all consistent with the same growth mechanism, occurring across a wide temperature range. Finally, since all the available data has been incorporated in one figure, the bias in the data set has been minimized: measurements from filaments or the vortex edge, and at levels below ER-2 cruise altitude (typically only sampled during aircraft ascents and descents) are all included.
 The majority of the measurement points lie along a smooth curve, indicating that the particles grew continuously across the range of sampled temperatures. At temperatures above the NAT condensation point the growth is gradual. Still, the increase in concentration from T−TNAT = 5 K to T−TNAT = 0 K exceeds 25% and therefore cannot be attributed to measurement uncertainty. For temperatures more than 3 K below the NAT condensation point, growth accelerates rapidly but smoothly. Concentrations at the coldest temperatures are more than 10 times larger than the concentrations at the NAT condensation point.
 The smooth growth is inconsistent with the modeled behavior of solid-phase particles, as shown by the model curves in Figure 6. SAT particles would not grow at all: SAT growth can only occur via condensation of H2SO4, all of which is already in the condensed phase. Growth due to nucleation of NAT or NAD on the SAT particles would occur at temperatures warmer than the observed acceleration in growth (assuming equilibrium, as in Figure 6). Furthermore, the onset of growth for both NAT and NAD is an abrupt transition. No condensation is possible above their respective condensation points; at temperatures below the condensation point, the HNO3 vapour pressure decreases rapidly, allowing a large fraction of the HNO3 to condense even with only 1 K of cooling.
 Even considering nonequilibrium effects, NAD and NAT cannot be reconciled with the observed growth. If the particles observed at the coldest temperatures were NAD or NAT, they would remain stable at warmer temperatures, with almost no change in particle size. However, even with the hundreds of observations shown in Figure 6, large particle concentrations are never seen at T−TNAT > −4 K. Non-equilibrium would also introduce variability (i.e., a recently cooled air parcel might have no HNO3 condensation, but another air parcel at the same temperature that had been cold for days could be near equilibrium). The limited scatter in the observations, however, indicates that the particles are actually very near equilibrium. Equilibrium is consistent with the number of particles that do grow at the coldest temperatures: the large concentration implies large surface areas, facilitating rapid condensation and evaporation as conditions change.
 Liquid, ternary solutions are able to reproduce the observed behavior. At temperatures near the NAT condensation point, the gradual growth is consistent with uptake of water by binary sulfuric acid solutions — this gradual deliquescence of liquid-phase particles eliminates the abrupt transitions seen for solid-phase particles. At colder temperatures, ternary solution growth accelerates due to HNO3 condensation; the observed rapid growth, maximizing near T−TNAT = −4 K, is well reproduced by the model. The largest discrepancies between the measurements and the ternary liquid model are apparent at the coldest observed temperatures (T−TNAT ≈ 5 K), where the measurement points all exceed the model values. Under these conditions, the model results are limited by the assumed total particle concentration; the model growth levels off because all of the available particles have grown into the MASP size range. There is a hint in the measurements of a similar plateau, but at a higher level: the coldest measurement points, spanning about 1 K in T−TNAT, all have very similar concentrations. However, the uncertainty in T−TNAT (see Figure 7) is larger than 1 K, so the similarity with the model may only be coincidental. Reasons for the different maximum concentrations will be discussed below.
Figure 7 explores the uncertainties in the measurements and in the modeling of ternary solutions. A critical uncertainty in the measurement analysis is determining the available HNO3, necessary to calculate T−TNAT. To derive HNO3 from the NOy measurements at cold temperatures, it is necessary to make assumptions about how HNO3 condenses (section 2). In the standard TNAT calculations, HNO3 was assumed to condense as liquid, which may potentially bias the analysis. Figure 7 shows the same measurement points, but assumes the presence of NAT in the HNO3 calculation, thus producing an alternate TNAT. T−TNAT is increased by 1.5 K or more; the scatter in the data also increases. However, the primary trends in the data remain unaffected: a variation with temperature is apparent under all conditions, with more rapid, but not abrupt, growth at colder temperatures. The strong growth is still at temperatures much lower than TNAT, and large concentrations are never observed to persist to warmer temperatures. Therefore, this alternate TNAT calculation does not improve the agreement of the solid-phase model calculations with the measurements. On the other hand, it worsens the comparison with liquid ternary behavior. The rapid growth is at temperatures warmer than predicted by any ternary solution model. The increase (by a factor of two) in horizontal scatter also suggests that this calculation is less effective at capturing the data's variability. Therefore, the initial calculation, in which the HNO3 is derived assuming liquid-phase HNO3 condensation, appears to be the most appropriate.
 The error bars in Figure 7 indicate the aggregate error in the measurements. Almost all of the scatter in the data falls within the vertical ±25% uncertainty of the MASP concentration, indicating that the precision of the MASP measurement is the limiting factor in this analysis. The uncertainty in temperature maximizes for T−TNAT ≈ −4.5 K. However, the scatter in the measurements under these conditions is only about ±0.2 K, much less than the +1, −0.56 K data uncertainty.
 Some model uncertainties are also quantified in Figure 7. Several ternary solution composition models have been used to calculate the growth curves; the range encompassed by these different calculations is shown in light gray. The greatest difference is in the onset temperature for growth, with about 0.5 K variability. The standard calculations, using the model of Carslaw et al. , are in closest agreement with the measurements, but all the model results fall within the measurement uncertainty.
 The largest variability in the model results is at the coldest temperatures, where uncertainties in the sulfate aerosol size distribution are most evident. In all cases, the model results are scaled to match the measurements above the NAT condensation point, to bypass discrepancies between the FCAS and MASP concentrations (see section 3); this forces the effect of sulfate uncertainties to be apparent only at cold temperatures. Decreases in the model concentration (the lower limit of the sulfate distribution range) are apparent if the FCAS/MASP scaling factors (Table 2) are applied to the FCAS size distributions, in which case the particle growth becomes limited by the availability of HNO3. The resultant concentrations are too low relative to the measurements, even taking into account the measurement error bars. Better agreement at the coldest temperatures is evident at the upper limit of the model uncertainty range, which represents a model calculation using a simplified lognormal size distribution. Since the FCAS measurements show deviations from lognormal distributions, the simpler distribution is included primarily to demonstrate how the scaling process amplifies small changes in the size distribution at the coldest temperatures. If the causes for the MASP/FCAS concentration discrepancies are resolved, the model uncertainties at the coldest temperatures will be significantly reduced. On the other hand, these uncertainties are not a significant factor at temperatures above −4.5 K, and therefore do not impact model/measurement comparisons for the majority of the measurement points.
Table 2. MASP Concentrations and Inferred Percentages of Particles That Are Liquid
N2O Level, ±10 ppbv
N5, Average Concentration at T − TNAT = 5 ± 1.5 K, (mg air)−1
N0, Average Concentration at T − TNAT = 0 ± 0.5 K, (mg air)−1
Nmax, Concentration at Minimum T − TNAT, (mg air)−1
(Nmax − N5)/Nmax × 100, Percent of MASP Particles That Were Liquid
(Nmax − N5)/Ntot × 100, Percent of Total Particles That Were Measured and Liquid
(Ntot − Nmax)/Ntot × 100, Percent of Total Particles That Were Possibly Liquid (Including Those Not Measured)
This number was inferred by multiplying the FCAS concentration by the scale factor used to increase the FCAS concentration (both provided in Table 1). The positive uncertainty applied to this value is +25% (uncertainty of particle measurement); the minimum of the uncertainty range is set to be the unscaled FCAS measurement, less 25%. These uncertainties have been propagated to the derived percentages.
550 (+140, −470)
0.17 (+0.19, −0.12)
99.8 (+0.1, −0.2)
460 (+110, −380)
0.18 (+0.24, −0.19)
99.6 (+0.2, −0.4)
460 (+110, −380)
0.46 (+0.56, −0.43)
99.1 (+0.3, −0.8)
390 (+100, −310)
2.8 (+2.4, −1.2)
98.8 (+0.4, −1.0)
380 (+90, −300)
50 (+42, −18)
98.4 (+0.6, −1.3)
330 (+80, −270)
48 (+40, −17)
97.0 (+1.1, −2.5)
270 (+70, −210)
87 (+72, −32)
95.9 (+1.4, −3.3)
230 (+60, −170)
113 (+91, −41)
94.2 (+2.0, −4.6)
200 (+50, −150)
45 (+35, −17)
93.0 (+2.5, −5.4)
190 (+50, −140)
22 (+18, −10)
92.3 (+2.7, −6.0)
190 (+50, −140)
6.2 (+6.1, −4.4)
92.0 (+2.8, −6.2)
210 (+50, −150)
9.9 (+8.3, −5.1)
93.4 (+2.3, −5.0)
5.2. Examination of the Complete MASP Data Set: Overall Aerosol Characteristics
 The discussion in section 5.1 focused on data from the 170 ± 10 ppbv N2O surface because the cold temperatures observed at that level enabled a large range of MASP concentrations to be sampled. An overview of all the N2O levels, Figure 8, demonstrates that similar behavior was observed at the other levels. The primary difference at other levels is that the sampled temperatures were not always cold enough to cause ternary solution formation, as summarized in Table 1.
5.2.1. Anomalous Data on 14 January
 The most pronounced discrepancy in the data set is the behavior on 14 January. The measured concentrations on this flight are all much lower than observed under similar conditions on any other flight. Given that this flight occurred shortly after the coldest temperatures of the winter, it is tempting to ascribe the anomalous behavior to the widespread presence of frozen particles. The low concentrations would then indicate that the majority of the SAT particles were smaller than 0.2 μm; since SAT does not grow, the low concentrations would persist even as the temperature is decreased (i.e., the SAT curve shown in Figure 6). The observed range of temperatures on this flight was too small to effectively discriminate between solid and liquid particles based on temperature alone.
 However, examination of other available data shows that freezing is very unlikely to explain the measurements on 14 January. This data was collected during a transit flight from Westover, Massachusetts to Kiruna, Sweden, which sampled midlatitude air almost exclusively. Temperatures for the first 2 hours of the flight exceeded the SAT melting point (calculated based on the data of Zhang et al.  to be near 214 K). This data is at temperatures too warm to be shown in Figure 8, but the MASP concentrations are as low as at colder temperatures, and in particular are significantly lower than observations at similar temperatures on other dates. Furthermore, backtrajectories for the data shown in Figure 8 (L. R. Lait, personal communication) show that most of the air masses along the entire flight had been at temperatures above the SAT melting point within the last 2 days. Therefore, frozen SAT particles should not be present, especially for the air masses sampled at T−TNAT > 0.
 The low concentrations on 14 January also cannot be attributed to differences between air masses inside and outside of the vortex. Measurements outside the vortex were made during two other flights, namely 27 January and 11 March. On these occasions, the MASP concentrations outside of the vortex are consistent with the majority of the SOLVE data; most of the 27 January and 11 March data in Figures 8i and 8j are extravortex, and clearly do not agree with the 14 January points. Furthermore, FCAS measurements on all three flights are comparable, both in total particle concentration and in sulfate mass; CN measurements also do not show any anomalies on the 14th. Therefore, the low MASP concentrations on 14 January are difficult to explain, either by the presence of frozen particles or by the fact the air came from midlatitudes. The data from this flight have been excluded from the remaining analyses, in particular the data averages in Table 2. The number of points excluded is provided in Table 1.
5.2.2. Anomalous Data on Other Flights
 Even excluding 14 January, some scatter is evident in the data set: individual anomalous points could indicate occasional presence of air masses with a different aerosol composition. The overall scatter in the data does exceed the 25% uncertainty of the MASP concentration measurements. However, all the outliers are at most 10% past the uncertainty limits.
 One possible source of additional scatter is nonequilibrium particle compositions due to recent, rapid temperature changes. Such a mechanism would produce the greatest scatter at cold temperatures, where small temperature changes cause larger changes in particle size. However, much of the scatter is at temperatures above the NAT condensation point. This explanation therefore seems less likely.
 In an individual air mass containing exclusively SAT particles, the MASP concentration would decrease to values near the flat SAT model line shown in Figure 6, since SAT particles are smaller than their liquid counterparts below T−TNAT ≈ 5 K. Throughout most of the temperature range, the resulting size difference is too small to be distinguished from 40% measurement scatter. But for points with T−TNAT < −3.5 K, the absence of aerosol growth would cause concentrations smaller than observed at any time in the data set. 431 observations (13% of the measurements) were made at T−TNAT < −3.5 K. Especially given that frozen particles are most likely at cold temperatures, the large number of observations without significant concentrations of SAT particles (section 5.3 quantifies this concentration) suggests that such air parcels are rare.
 The data set also argues against NAT or NAD condensation on a large number of particles. Individual points with numerous NAT or NAD particles would be apparent in the data set as an increase in concentration, and should be able to occur at any temperature below the NAT (or NAD) condensation point. The majority of the points lying above the 25% uncertainty region in Figure 8 occur above the NAT condensation point and therefore cannot represent growth of solid-phase HNO3. Below the NAT condensation point, scatter above the 25% uncertainty region is also observed. Although the possibility that these points reflect growth of a different compound cannot be positively excluded, it is unlikely given that the frequency and magnitude of such points do not increase below the NAT condensation point. Furthermore, dramatic increases in concentration are only seen below T−TNAT = −3 K. Even if NAT or NAD only nucleated below T−TNAT = −3 K, the growth would persist to warmer temperatures; growth only at cold temperatures is not consistent with these particle compositions.
 Given the strong overall consistency with liquid growth and a possible explanation for increased scatter, these small anomalies are insufficient to prove that large numbers of SAT, NAT, or NAD particles were present. However, small numbers of such solid-phase particles cannot be excluded. Growth of the largest particles would not affect the MASP concentration; nongrowth of the smallest particles would also be undetectable. These possibilities will be discussed in more detail in section 5.3.
5.2.3. Comparison of Overall Behavior With Liquid Growth
 At nearly every N2O level, a wide range of temperatures was sampled, allowing changes in concentration as a function of temperature to be examined for evidence of aerosol growth. The average concentrations at T−TNAT = 0 K and T−TNAT = 5 K are compared in Table 2. In all cases (except N2O = 50 ± 10 ppbv) the concentration increases by more than 25%, the measurement uncertainty, as the temperature cools over this 5 K interval. Therefore, the overall behavior of the concentration is consistent with liquid particles. The exception is at the 50 ppbv N2O surface, where the temperature range is too small for this test to be applied.
 At colder temperatures, the concentration continues to rise, again in agreement with the expected behavior of liquid particles. At most levels, the temperatures fell more than 3.5 K below the NAT frost point, causing dramatic increases in concentration. The onset temperature for this growth is very consistent at all levels; the temperature scatter is less than half of that expected from the uncertainty in calculating T−TNAT. In all cases, the onset temperature agrees with that predicted for the growth of ternary solutions. Only ternary solution model calculations are shown in Figure 8 because the other possible PSC compositions are unable to reproduce these characteristics. The behavior of SAT, NAT, and NAD, and the comparison with the data are analogous at all levels to those shown in Figures 6 and 7 for the 170 ppbv surface.
 This overall analysis of the SOLVE data shows that the average behavior of the aerosol, throughout SOLVE, is most consistent with liquid particles, not just at the temperatures where ternary solution PSCs form, but also at warmer temperatures.
5.3. Estimating the Fraction of Particles That Are Liquid
 Two classes of particles can be distinguished in the MASP measurements. The largest particles, those that are larger than 0.2 μm even at warm temperatures, are a constant contributor to the measurements, no matter how their size may increase. Therefore, this analysis provides no information on their growth behavior or on their possible composition. The average particle concentration at T−TNAT = 5 ± 1.5 K, labeled N5, has been used to provide the typical concentration of these particles at each N2O surface; observations within this temperature range were made at every N2O level (Table 2).
 The increases in MASP concentration past this baseline value, N5, provide the particles whose growth can be characterized as liquid-like. The minimum temperature yields the maximum possible growth, so the particle concentration at the minimum value of T−TNAT, Nmax in Table 2, was used to provide the maximum concentration increase. The difference between Nmax and N5 provides a measure of the number of particles measured by MASP which grew as liquids.
Table 2 provides the percentage of the particles measured by MASP represented by this difference, Nmax−N5. However, at most N2O levels the minimum temperature was not low enough to expect that all the particles present grew into the MASP size range. Only at the two N2O levels with the lowest temperatures, 170 ppbv and 190 ppbv, did the conditions reach the point where the model concentration maximizes; the hint of a plateau in the measurements could indicate that all of the available particles grew into the MASP size range. Even at these levels, it is possible that some number of nongrowing particles (either SAT particles or nonsulfate particles) remain at small sizes. In general, quantifying the number of particles that were never seen in the MASP measurements is the greatest difficulty in determining the fraction of particles that are liquid.
 Ideally, other particle measurements on the ER-2 could provide the total particle concentration; the FCAS instrument can measure particles as small as 0.04 μm, and the CN counter, particles to 4 nm radius. The average concentrations measured by these instruments are shown in Table 1. However, whenever T−TNAT falls below −4 K, the measured MASP concentration exceeds both of these other measurements. This discrepancy is related to the previously discussed FCAS/MASP concentration discrepancy at warm temperatures, which necessitated scaling the model calculations (section 3). Applying the model scale factors to the total FCAS concentration does provide total concentrations more consistent with the maximum MASP concentrations at 170 and 190 ppbv N2O. Therefore, the product of the FCAS concentration and the previously determined scale factors has been used to provide an approximate total particle concentration, Ntot. Large uncertainties have been assigned to this total concentration to reflect that this empirical correction does not have a physical basis. The minimum of the uncertainty range is taken to be the actual FCAS concentration, less a 25% uncertainty. A 25% uncertainty has also been assumed at the large end of the uncertainty range. As previously mentioned, the choice to increase the FCAS measurements, instead of decreasing the MASP measurements, is arbitrary and does not imply that the FCAS measurements are the source of the discrepancy.
 A conservative estimate of the fraction of particles that are liquid can be determined by comparing the number of measured liquid particles, Nmax−N5, with the assumed total, Ntot. At 190 ppbv N2O, at least 70% of the total particles were liquid, even taking into account the large uncertainties; the results are consistent with all particles being liquid. The liquid fractions are almost as large at 170 ppbv. The decrease in the liquid particle fraction at higher and lower levels is associated with the more limited temperature ranges sampled at these levels: even if all the particles were liquid at these levels, the MASP instrument could not have observed them. Still, roughly half of the aerosol particles are identified as liquid through a broad region of the stratosphere.
 A second estimate of the liquid particle fraction can be made by extrapolating the observed behavior to smaller particle sizes. For most freezing mechanisms, large particles are the most likely to freeze: the likelihood of forming a freezing germ is proportional to the particle volume. Liquid behavior for particles of a given size implies that those particles were too small to freeze; smaller sulfate particles would be even less likely to freeze, and can be assumed to also be liquids. Therefore, for a volume-dependent freezing process and assuming that all the particles are composed of sulfate, the liquid behavior seen in the MASP size implies that smaller particles were also unable to freeze. In other words, the liquid composition of the smallest particles in the MASP range can be extrapolated to all the smaller, unmeasured particles which are even less likely to freeze. Under these assumptions, more than 90% of the particles at all levels are liquid (last column of Table 2), with little sensitivity to the assumed number of total particles.
 One scenario under which freezing may not be volume-dependent, however, is for very rapid cooling such as that produced by lee waves. Meilinger et al.  and Tsias et al.  describe how the extreme nonequilibrium conditions possible in lee waves can cause unusually large amounts of nitric acid to be present in the smallest particles. The composition of these particles may be better suited to cause freezing, despite the small volumes of the particles. Therefore, the extrapolated liquid particle fractions in the last column of Table 2 are not necessarily applicable for lee-wave-type freezing, and cannot be used to constrain the characteristics of such freezing. To date, however, case studies of lee-wave clouds have invoked more traditional freezing mechanisms [Carslaw et al., 1998; Tsias et al., 1999; Wirth et al., 1999].
 This study has introduced a new method of examining the growth of particles near the mode in the stratospheric aerosol size distribution. Although these particles represent the majority of the aerosol, their behavior can easily be hidden by the preferential growth of a few large particles. Variations in the MASP total concentration provide information specifically on the growth of those particles that are smaller than 0.2 μm radius at typical stratospheric conditions. A coordinate system appropriate for examining these measurements has been developed, which allows analysis of the complete SOLVE data set, including measurements in regions of high variability (e.g., filaments, vortex edge, aircraft altitude changes). Depending upon the range of temperatures sampled, MASP concentration measurements can potentially observe the growth of the majority of the sulfate aerosol, with more accuracy than volume measurements.
 Analysis of the SOLVE data set reveals that the overall behavior of the aerosol, throughout the stratosphere, is fully consistent with that expected for liquid sulfuric acid solutions. Liquid-like growth was observed from temperatures 5 K above the NAT condensation point to temperatures 6 K below it. Through most of this temperature range, the growth can be attributed primarily to uptake of H2O, but at temperatures more than 3.5 K below the NAT condensation point, rapid growth was evident as HNO3 condensed to form supercooled ternary solutions. The temperature at which HNO3 caused accelerated growth was in good agreement with models; the 1 K bias inferred from backscatter sonde data by Rosen et al.  is not supported by these measurements. The observed growth cannot be explained by solid-phase particles, whether composed of SAT, NAT, or NAD. Even examining individual points, there is no evidence for the occasional presence of large numbers of solid-phase particles.
 During the SOLVE campaign, temperatures fell more than 4.5 K below the NAT condensation point for N2O values between 120 and 200 ppbv. Dramatic increases in concentration were consistently observed by MASP at T−TNAT < −4.5 K, indicating that a large fraction of the aerosol was liquid. At 190 ppbv N2O, temperatures were cold enough to demonstrate that more than 90% of all the particles present were liquid.
 Quantifying the percent of particles that were liquid at other N2O values is difficult. This is partly due to uncertainties in relating the MASP concentration to the total particle concentration. Furthermore, the temperatures did not always provide the opportunity to examine the behavior of the smaller particles. However, the available data is consistent with more than 90% of the aerosol being liquid at all stratospheric levels. In particular, such large liquid percentages can be inferred if one assumes that the freezing processes are volume-dependent (valid for synoptic-scale cooling) and if most of the stratospheric aerosol contains sulfate.
 This analysis provides a view of the particle behavior that complements the other particle measurements available on the ER-2. The growth of the largest 5–10% of the particles is not detected by the total MASP concentration; other measurements are dominated by the largest particles. Measurements from the NOy instrument's “b” channel show the presence of large HNO3-containing particles, but with concentrations much less than 10−2 cm−3 [Fahey et al., 2001]. The MASP volume measurements and size distributions also show that small concentrations of particles grew to large sizes. The selective growth responsible for the small numbers of large particles is one characteristic that identifies these as solid particles. This study, by showing that the smaller particles have remained liquid, provides evidence that the freezing process producing the large particles is selective, and therefore may control the number of solid particles.
 The selective freezing implied by this study is consistent with slow cooling rates, especially for homogeneous freezing processes. For synoptic scale temperature variations, the slow cooling rates allow a small number of frozen particles to effectively remove the supersaturated vapour that is driving the process; further freezing is inhibited. Winter-long simulations [Drdla et al., 2002] investigating homogeneous freezing below the ice frost point [Tabazadeh et al., 2000] show that a small fraction of the aerosol freezes, even though very low temperatures are reached. The NAT and NAD homogeneous freezing mechanisms discussed by Tabazadeh et al.  also produce a very small number of frozen particles. Small frozen particle concentrations are possible for a heterogeneous freezing mechanism: the number of frozen particles is constrained by the number of particles that contain appropriate foreign material.
 These conclusions are in agreement with several previous studies in the Arctic that have shown evidence for liquid-phase particles even in the presence of solid-phase nitric acid. Shibata et al.  and Shibata  demonstrate that their lidar observations are best explained by extensive liquid particles which reduce the depolarization even in Type Ia PSCs. In an analysis of extensive lidar measurements from 1989, Toon et al.  frequently inferred that the clouds were a mixture of liquid- and solid-phase particles. In situ impactor measurements by Iwasaka et al.  show the simultaneous presence of both liquid and solid HNO3-containing particles. This study extends the earlier work by showing that such behavior is widespread throughout the vortex, and not just isolated to specific PSC observations, even in a winter with severe denitrification [Popp et al., 2001]. Comparable studies in the Antarctic are necessary to determine whether particles can remain liquid even in the colder temperatures experienced in the southern hemisphere.
 The widespread presence of liquid aerosol during SOLVE suggests that in general the majority of the aerosol should be treated as a liquid solution throughout the winter, at least in the Arctic. PSCs, even Type Ia PSCs, probably contain a mix of particle types. A small number may be frozen, causing denitrification and contributing an alternative surface for heterogeneous reactions. However, liquid aerosol is simultaneously present. Liquid-phase HNO3 condensation, which is clearly occurring based on these measurements, can compete with solid-phase particles, limiting their growth. The simultaneous presence of two particle compositions can complicate satellite analyses that need to explicitly assume that only PSC type is present [e.g., Santee et al., 1998]. The particles also provide a constant surface for liquid-phase reactions; the surface area due to liquid aerosols may exceed the contribution due to solid aerosols. The common assumption that all particles in PSCs have the same composition needs to be reexamined.
 We would like to thank the SOLVE science team for their efforts in obtaining the data and their cooperation in sharing it, in particular D. Fahey, R. Herman, L. R. Lait, and G. Toon. L. Iraci provided many insightful comments. This research was funded by the NASA Atmospheric Chemistry Modeling and Analysis Program. JBG gratefully acknowledges the National Research Council for funding his research associateship at NASA Ames.