Interannual variations of early winter Antarctic polar stratospheric cloud formation and nitric acid observed by CALIOP and MLS

We use satellite-borne measurements collected over the last decade (2006–2015) from the Aura Microwave Limb Sounder (MLS) and the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) to investigate the nitric acid distribution and the properties of polar stratospheric clouds (PSCs) in the early winter Antarctic vortex. Frequently, at the very start of the winter, we find that synoptic-scale depletion of HNO3 can be detected in the inner vortex before the first lidar detection of geophysically associated PSCs. The generation of “sub-visible” PSCs can be explained as arising from the development of a solid particle population with low number densities and large particle sizes. Assumed to be composed of nitric acid trihydrate (NAT), the sub-visible PSCs form at ambient temperatures well above the ice frost point, but also above the temperature at which supercooled ternary solution (STS) grows out of the background supercooled binary solution (SBS) distribution. The temperature regime of their formation, inferred from the simultaneous uptake of ambient HNO3 into NAT and their Lagrangian temperature histories, is at a depression of a few kelvin with respect to the NAT existence threshold, TNAT. Therefore, their nucleation requires a considerable supersaturation of HNO3 over NAT, and is consistent with a recently described heterogeneous nucleation process on solid foreign nuclei immersed in liquid aerosol. We make a detailed investigation of the comparative limits of detection of PSCs and the resulting sequestration of HNO3 imposed by lidar, mid-infrared, and microwave techniques. We find that the temperature history of air parcels, in addition to the local ambient temperature, is an important factor in the relative frequency of formation of liquid/solid PSCs. We conclude that the initiation of NAT nucleation and the subsequent development of large NAT particles capable of sedimentation and denitrification in the early winter do not emanate from an ice-seeding process. Finally, we investigate the patterns of interannual variability and compare the relative formation frequency of liquid and solid PSCs in the Antarctic lower polar stratosphere using the results of a cluster analysis to synthesize the combined CALIOP and MLS measurements into a relatively small number of interrelated categories.

to control the heterogeneous nucleation rate in the ZOMM model: nucleation barrier, nucleation strength, and compatibility factor. These were adjusted with consideration of the detection thresholds applied to the model results (Engel et al., 2013;Hoyle et al., 2013), to replicate successfully the CALIOP backscatter observations for a representative orbit. The tuned model was then used to facilitate intercomparisons with the CALIOP observations during December 2009 and to verify the model results for a few case studies in the Arctic (Engel et al., 2013;Hoyle et al., 2013). However, the low visibility of the NAT 5 PSCs, as we indicated in L12 ::::::::::::::::: Lambert et al. (2012) , poses a detection challenge for lidar backscatter techniques, even though the accompanying HNO 3 sequestration in NAT can be substantial and detectable by other instruments as a decrease in the gas-phase HNO 3 .
In situ measurements of NAT particles on a synoptic scale, with a large-particle mode of around 15 µm diameter, from the Forward Scattering Spectrometer Probe (FSSP) (Molleker et al., 2014), and observations of their attendant denitrification 10 (Woiwode et al., 2014), were reported during the Arctic RECONCILE (reconciliation of essential process parameters for an enhanced predictability of Arctic stratospheric ozone) campaign (von Hobe et al., 2013). In order to resolve discrepancies involving implied condensed HNO 3 above that available from the gas phase (including additional HNO 3 brought down by renitrification) and growth/sedimentation rates that are not commensurate with back trajectories, those authors hypothesized that the particles are non-compact or highly aspherical or NAT-coated ice. Grooß et al. (2014) coupled a saturation-dependent 15 parameterization of the ZOMM heterogeneous NAT scheme with the Chemical Lagrangian Model of the Stratosphere (CLaMS) and determined that derived PSC properties were in better agreement with CALIOP data than for simulations using a constant rate NAT nucleation, thus confirming the results of Hoyle et al. (2013). Furthermore, Grooß et al. (2014) compared their simulations to the Arctic in situ aerosol size distributions from FSSP in January 2010 and found that the observed large NAT particles (exceeding 15 µm diameter) were not present in the co-located simulations. However, the CLaMS simulations did lead to an overestimation of their actual size. Zhu et al. (2015) also found that particles with diameters of 20 µm were produced with their homogeneous nucleation scheme, which does not require that there are special nuclei only available under certain 25 conditions.
PSC formation processes at play in the Arctic are clearly applicable to the Antarctic, and the recent observations from REC-ONCILE add support to the conclusions of our previous work (L12) :::::::::::::::::: (Lambert et al., 2012) , which highlighted the appearance of synoptic-scale large-particle NAT in the early Antarctic winter of 2008. Obviously, the hypotheses concerning the origin and microphysical characteristics of these so-called "NAT rocks" will be a challenge to validate without further in situ observations. 30 However, the decade-long record of overlapping spaceborne CALIOP and MLS measurements presents an opportunity to develop improved algorithms for the extraction of information on PSCs and to apply new-found knowledge to the understanding of their current and future role in ozone depletion.
In section 2 we review the satellite instruments and atmospheric measurements used in our analyses. The temperature history of an air parcel and the relation to heterogeneous nucleation of NAT is explored. We introduce a compact alternative visual-35 ization to the standard graphical representation of satellite orbit plots that enables easier comprehension of several parameters plotted at multiple atmospheric levels and spanning many days of observations. In section 3 we investigate the limits of detection of equilibrium STS and STS/NAT mixtures separately for lidar backscatter, mid-infrared extinction and uptake of HNO 3 from the gas phase. We also investigate STS and NAT PSCs in terms of the distributions in a 3-parameter space of HNO 3 , backscatter and temperature. We compare these with the CALIOP PSC classification scheme, which uses fixed regions within 5 a 2-parameter discrimination domain (depolarization vs total backscatter). In section 4 we show orbit transects and time-series of colocated CALIOP and MLS data. These are used to investigate the relative formation of liquid/solid PSCs and the resulting denitrification and renitrification. In section 5 the early stages of formation of Antarctic PSCs at 68-21 hPa in 2009 are examined using CALIOP PSC types and Lagrangian temperature history, with the inference of an initial population of sub-visible solid-particle NAT clouds superseded by a predominantly liquid STS composition over a period of about a week. Finally, the 10 interannual variability of the early Antarctic PSC seasons from 2006-2015 is discussed in section 6.

Datasets and methodology
The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) dual-wavelength elastic backscatter lidar (Winker et al., 2009)  We derive collocated meteorological data from the Goddard Earth Observing System Data Assimilation System (GEOS-5 DAS). The 6-hourly synoptic gridded data products (Rienecker et al., 2008) of temperatures and winds are supplied on a 540 by 361 longitude-latitude grid. The GEOS-5 data are interpolated in location and time to the MLS along-track data. Parcel temperature histories are obtained from the MLS Lagrangian Trajectory Diagnostic (LTD) dataset (Livesey et al., 2015), which 25 consists of 15-day forward and reverse trajectories launched from a curtain of points along the Aura MLS observation track.
The advection calculations are based on Manney et al. (1994), with wind fields and diabatic heating rates taken from the 3-hourly Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) dataset (Bosilovich et al., 2015).
Advances in both the GEOS-5 model and the assimilation system, including GPS Radio Occultation datasets, are included in MERRA-2. The integration uses a fourth-order Runge-Kutta scheme with a 5 minute time-step, and saved trajectory locations 30 and temperatures are output every 30 minutes. The MLS Derived Meteorological Products (DMPs)  are used where necessary to identify measurement locations that lie within the Antarctic vortex based on the potential vorticity field, sP V < −1.4, scaled in "vorticity units" (Manney et al., 1994).

CALIOP PSC data
We use the CALIOP Level-1b v3 standard data product to extract information on PSCs (as documented in L12 :::::::::::::::::: Lambert et al. (2012) ) at a 50 km horizontal by 0.5 km vertical resolution. We also use a recently released Level 2 operational dataset L2PSCMask (v1 Polar Stratospheric Cloud Mask Product) produced by the CALIPSO science team. The Level-2 operational data consist of nighttime only data and contain profiles of PSC presence, composition, optical properties, and meteorological information 5 along the CALIPSO orbit tracks at 5 km horizontal by 180 m vertical resolution.
We have determined that the v1 L2PSCMask operational product has an incorrect separation of the MIX1 and MIX2 classifications and does not follow the boundary specification given by Pitts et al. (2009) since it failed to include in MIX1 those observations with a total scattering ratio less than 1.25. Separation of PSCs into the MIX1 and MIX2 classes is somewhat arbitrary, but provides useful information on the NAT number densities . 10 The following three-step algorithm (using the Scientific Data Set variable names supplied with the CALIPSO Hierarchical Data Files (HDF) files) has been applied to generate the correct MIX1 and MIX2 classes:

MLS gas-phase constituents
The Microwave Limb Sounder measures thermal emission at millimeter and sub-millimeter wavelengths from the Earth's limb (Waters et al., 2006) along the forward direction of the Aura spacecraft flight track, with a vertical scan from the surface to 90 km every 24.7 s. Each orbit consists of 240 scans spaced at 1.5 • (165 km) along-track, with a total of almost 3500 20 profiles per day and a latitudinal coverage of 82 • S to 82 • N. The Level-1 limb radiance measurements are inverted using 2-D optimal estimation  to produce Level-2 profiles of atmospheric temperature and composition. Validation of the MLS H 2 O and HNO 3 data products and error estimations are discussed in detail by Read et al. (2007),  and Santee et al. (2007). Here we use the MLS version 4 (v4) data (Livesey et al., 2016) with single-profile precisions (accuracies) of 4-15 % (4-7 %) for H 2 O and 0.6 ppbv (1-2 ppbv) for HNO 3 .

Temperature history and relation to NAT nucleation and growth processes
In this work we frequently apply a convenient temperature coordinate transformation, T − T ICE , by using MLS H 2 O to calculate the ice frost point, in order to remove height-related variations due to changes in the H 2 O partial pressure (L12 and P13) :::::::::::::::::::::::::::::::: (Lambert et al., 2012;Pitts et al., 2013) . As in L12 ::::::::::::::::: Lambert et al. (2012) we quantify the duration of exposure of an air parcel to low temperatures by defining the temperature threshold exposure (TTE) as the total integrated time the air par- 30 cel is subject to synoptic-scale temperatures below the chosen threshold. We use a threshold of T ICE + 4 K (approximately T NAT − 3.5 K) to demonstrate empirically the correlation of TTE with the uptake of HNO 3 by NAT PSCs. The temperature history follows a diabatic back-trajectory for up to 15 days obtained from the MLS LTD dataset (Livesey et al., 2015). The TTE is the total time (in days) that an air parcel has been exposed to temperatures below T ICE +4 K since the last time the temperature fell below T NAT and remained below T NAT consistently, i.e. any number of episodes of cooling below T ICE + 4 K are 5 accumulated providing that the air parcel has remained consistently below T NAT . conditions, T NAT is also lowered by about 3 K. TTE is a remarkably good indicator of the geographical extent of the HNO 3 depletion in the vortex (L12) :::::::::::::::::: (Lambert et al., 2012) . Here, we explore the correspondence of TTE with NAT nucleation and growth processes.
According to the development of NAT along a sample trajectory shown by Hoyle et al. (2013) in their Figure 1, substantial nucleation begins only for temperatures below T NAT − 4 K. We investigate the temperature-time domain of the nucleation 15 process in Figure 1, for both (a) early season unperturbed and (b) late season denitrified atmospheres, and calculate the resulting NAT number densities using the heterogeneous nucleation scheme given in Hoyle et al. The figure serves to illustrate the general properties of NAT cloud formation, but in reality the temperature-time path is important for the modeling of specific clouds.
The nucleation rate is a strong function of temperature, and the nucleated NAT shows an almost step-like transition over a narrow temperature range. In contrast, the variation of NAT density with exposure time is more gradual because the nucleation 20 rate at a fixed temperature (i.e. fixed supersaturation) depends only on the integration over time. Exposure to temperatures of T NAT − 2.2 K and above produces negligible NAT densities (< 10 −6 cm −3 ), even for time durations exceeding a month, whereas exposures of ∼ one day to temperatures near T NAT − 4 K produces NAT densities three orders of magnitude greater (∼ 10 −3 cm −3 ). At lower temperatures, the NAT saturation ratio is limited by uptake of HNO 3 from the gas phase by STS (Luo et al., 2003), causing the curvature of the NAT density contours below T NAT − 4.5 K. Denitrification has little effect on 25 the sharp temperature transition, but at lower temperatures where STS forms there is a visible decrease in the NAT number density generated for the same time duration. At nucleation, the NAT particle sizes are small and no larger than the progenitor aerosol particle (SBS or STS). Hence, considerable growth of the NAT particles is required before they can be detected using remote sensing techniques. TTE can be viewed as a proxy for the time elapsed since nucleation occurred, i.e. as a measure of the effective growth-time of the NAT particles. The NAT volume density increases gradually through sequestration of HNO 3 30 from the ambient gas phase, and the particles may not achieve their much larger equilibrium size until several days following nucleation. Figure 2a shows typical orbit tracks of the MLS HNO 3 distribution mapped onto a polar stereographic projection for ascending and descending orbits at 32 hPa. Each colored square is centered at the corresponding MLS profile latitude/longitude retrieval location. The along-track spacing is 1.5 • (distance between centers of the squares). Note that the dimensions of the squares are not related to the MLS along-track (several hundred km for HNO 3 ) or across-track (about 10 km) resolutions. Orbit numbering 5 (0 is the day start orbit) is shown around the 60 • S latitude circle. The color scheme indicates contrasting colors either side of 10 ppbv. Over the 10-day period (26 May to 5 June 2009, Figure 2a and b), the HNO 3 values decrease and the area with values < 10 ppbv is seen to increase and move eastward. Such "satellite data orbit plots" are commonly used, but they do not scale up easily for viewing multiple quantities and pressure levels over periods of the order of a month; e.g. to track the evolution of four parameters over twenty days at four distinct atmospheric levels requires the digestion of 320 images. 10 We present an alternative scheme, designed to improve the data visualization, with some similarities to the familiar Hovmöller diagram, but with the abscissa following selected sections of the satellite orbit track rather than running along a zonal or meridional circle. Figure 2c shows the same data as in Figure 2a, but replotted as a time-ordered sequence of the along-track points. The MLS orbit tracks are unfolded along the abscissa as a function of the along-track angle (1.5 • is the angular spacing), where the along-track angle of 30 • corresponds to the closest approach of the orbit to the South Pole (at about latitude 82 • S).

15
Also shown for convenience are the along-track distances (in km), and the corresponding latitudes and solar zenith angles. The MLS measurement time (hours since start of day at 0UT) is on the ordinate. The orbit numbers are given next to the right hand ordinate. Again the dimensions of the squares are not related to the MLS orbital track spacing or the MLS measurement time (each complete vertical atmospheric profile is accumulated over about 25 s). The main purpose of this compact visual representation (i.e. a sparse "raster" image) is that it enables the "raw" daily observations to be stacked into a longer time-series without 20 involving gridding onto a map projection. Note that there is a geographical data void (within 8 • of the pole, see Figure 2a and b) that is not apparent in the raster representation. MLS looks forward in the along-track direction, so it never actually looks into the 8 • polar cap, nor does CALIOP with its nadir view. While the low HNO 3 in the vortex rotates eastward in the orbit track plot, this motion translates into a time displacement in the raster plot. The ascending/descending tracks do not intersect in the raster plot and the terminator is always on the rightmost side (a feature that could be potentially useful for examining 25 diurnal species such as ClO).

Detection and classification of PSCs
Improvements in modeling capabilities drive a commensurate need for a thorough evaluation of the observational aspects of PSC research, such as biases in temperature analyses, derived air parcel temperature histories along trajectories and instrument measurement biases and uncertainties. This is highlighted in a specific example shown by Hoyle et al. (2013) in the Arctic Hoyle et al. noted the prolonged exposure time (80h) resulting in sedimentation of NAT as a potential cause of the lack of coincident lidar signal from CALIOP in the L2PSCMask product. However, we have determined that smoothing of the CALIOP L2PSCMask data using a 5x5 median filter to improve signal to noise does in fact indicate the presence of PSCs. In Figure 3, we compare the along-track cross-sections of the MLS HNO 3 , CALIOP L2PSCMask, and the smoothed total and perpendicular backscatter ratios. Additionally, inspection of the MLS gas-phase HNO 3 identifies a coincident decrease also consistent with the location of the CALIOP PSCs (note that the ZOMM model HNO 3 is not shown by Hoyle et al.).

5
3.1 Modeled uptake of HNO 3 , lidar backscatter and infrared extinction in PSCs We model the microphysics of representative STS and NAT particle distributions according to the methodology given in Pitts et al. (2009) and L12 :::::::::::::::::: Lambert et al. (2012) . For the lidar scattering calculations, Mie theory is used for liquid spherical particles and the T-matrix (Mishchenko and Travis, 1998) for solid NAT particles. As we noted in L12 :::::::::::::::::: Lambert et al. (2012) , the NAT particle shape is an open issue, and we continue here to use a range of spheroidal shapes to illustrate the lidar sensitivity to NAT. 10 Real refractive indices at 532 nm were assumed to be 1.43 for STS and 1.50 for NAT, with zero imaginary refractive indices for both particle types. For the mid-infrared region, complex refractive indices were obtained from the tabulations given by Myhre et al. (2005) for STS and Toon et al. (1994) for NAT.
Existence temperatures of the PSC types are calculated using equilibrium thermodynamics and are dependent on the ambient partial pressures of H 2 O in the case of the ice frost point, T ICE (Murphy and Koop, 2005), and also HNO 3 for T NAT (Hanson 15 and Mauersberger, 1988) and STS (Carlsaw et al., 1995). Errors in the calculations of these reference temperatures arising from uncertainties in the MLS H 2 O and HNO 3 data are estimated to be ≤ 0.5 K for T ICE and ≤ 0.7 K for T NAT in the pressure range 70-20 hPa.
SBS particles grow by condensation on cooling, first by uptake of H 2 O from the gas phase and then, at sufficiently low temperatures, uptake of HNO 3 occurs, forming STS at a few kelvin below the NAT point close to T STS ∼ T NAT − 3.5 K 20 (Carslaw et al., 1997;Drdla et al., 2003). In the polar stratosphere, NAT is thermodynamically stable at temperatures below T NAT ∼ T ICE + 7 K, although the NAT nucleation process is still not understood in detail.
The PSC detection limits for lidar backscatter and infrared extinction are dependent on the background aerosol loading in addition to measurement noise. Under conditions of high quiescent background aerosol loadings (e.g. at times perturbed by volcanic aerosol), a higher threshold is required to discriminate PSCs from the background. The thresholds also depend on 25 vertical and horizontal averaging both along-track and across-track. In the case of MLS, the across-track averaging (i.e. the 240 GHz antenna beam width at the tangent point) is around 8 km, the vertical field of view for HNO 3 is a few km and the along-track sampling is over several hundred km. We have investigated coarser averaging of the lidar data in the along-track and vertical directions to achieve better signal-to-noise. However, the across-track averaging of CALIOP is only about 0.09 km, and as a result the sampling volumes of limb sounding instruments are three or more orders of magnitude larger. The nominal 30 sampling volumes that demonstrate the much larger limb sounder sampling are shown in Table 1.
For illustration here we use typical threshold levels appropriate for the CALIOP Level-1b v3 lidar data gridded with a 50 km by 0.5 km resolution (L12) :::::::::::::::::: (Lambert et al., 2012) : total backscatter ratio, R T = 1.25 (STS type threshold), and perpendicular backscatter, β ⊥ = 2.5 × 10 −6 km −1 sr −1 (MIX type threshold). For a mid-infrared limb sounder operating in the window-region near 12 µm at 46 hPa we use an extinction threshold, k ext = 5 × 10 −5 km −1 . This value is based on measurements by the Improved Stratosphere and Mesosphere Sounder (Lambert et al., 1996)  aerosol extinction is modeled adequately by a log-normal distribution with the stated threshold being at least three standard deviations higher than the mean of the extinction distribution. For the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument, Spang and Remedios (2003) determined a cloud-index parameter (CI) with a threshold for PSC detection of CI < 4.5, and Höpfner et al. (2006b) indicated this corresponds to a volume density detection limit of 0.2-0.4 µm 3 cm −3 . Finally, the threshold level for detection of the gas-phase removal resulting from the ambient HNO 3 uptake in 10 STS is taken to be 1 ppbv, slightly higher than the 0.6 ppbv MLS measurement uncertainty. volume are well modeled (Carlsaw et al., 1994), as is the uptake of HNO 3 from the gas phase (L12) :::::::::::::::::: (Lambert et al., 2012) .

Equilibrium STS
Uptake of HNO 3 from the gas phase varies rapidly (50, 10, 1 %) over a narrow temperature range (T −T ICE = 2.3, 3.1, 3.9 K), and the maximum temperature derivative (−6.7 ppbv / K) is at T − T ICE = 2.9 K. The theoretical residual gas-phase HNO 3 , accounting for the uptake in STS, is shown in Figure 4b as a function of the total backscatter and 12 µm infrared extinction.
In a scatter plot, the observations of HNO 3 and backscatter (or extinction) in the presence of STS are expected to lie beneath 20 the theoretical curve, and this is investigated in Section 3.2. Figure 4c shows that the infrared extinction is marginally more sensitive to STS than the lidar backscatter, since the corresponding threshold equivalent condensed HNO 3 contents of STS are 0.65 and 0.84 ppbv for the two measurement approaches, respectively.
The large-particle example shown in Figure 5a is for a NAT particle distribution with a number density N NAT = 0.001 cm −3 and effective radius R eff = 6.5 µm. Note that in this example the uptake of HNO 3 follows the NAT equilibrium curve until the 10 saturation point is reached and the condensed HNO 3 equals the volume in the assumed NAT particle distribution (plateau region with 4 ppbv condensed HNO 3 ). No further uptake of HNO 3 occurs until the temperature decreases sufficiently to allow growth of STS. This example is a crude, but not unrealistic, snapshot of a possible STS/NAT mixture at a particular time because the growth of NAT is kinetically limited (Voigt et al., 2005). A high number density of NAT nuclei would ultimately lead to a NAT distribution with smaller particle sizes than a low number density since the available HNO 3 is spread over a large number of 15 particles (Jensen et al., 2002). Once nucleated, a NAT particle will continue to grow, providing there is sufficient HNO 3 and H 2 O available and T < T NAT , such that the HNO 3 vapor pressure over NAT is supersaturated, until it attains its equilibrium size (reaching a radius of tens of microns). Gravitational sedimentation may cause the NAT particles to descend into a region of lower HNO 3 and/or rising temperature, causing evaporation rather than growth. The Wegener-Bergeron-Findeisen process will cause sequestration of HNO 3 by NAT in a mixed phase STS/NAT cloud at the expense of the HNO 3 in the liquid STS (Voigt 20 et al., 2005). However, if the STS forms quickly by rapid cooling, then the uptake of ambient HNO 3 can be predominantly into STS rather than into NAT. Growth of NAT is therefore retarded at these low temperatures of a few K above the frost point (Voigt et al., 2005).
The lidar detection of NAT (back scattering in visible spectrum) is sensitive to the asphericity parameter, whereas the infrared extinction (dependent mainly on emission and therefore particle volume) is not. Hence, there are four lidar total backscatter 25 curves corresponding to each aspect ratio in Figure 5a, but only a single infrared extinction curve is plotted representative of all four. Likewise, the inferred uptake of HNO 3 by STS/NAT as measured by microwave observations is also insensitive to particle shape (in addition, the aerosol emission is negligible in the microwave region and has no effect on the gas measurements). In the absence of an actual PSC detection, the observed reduction in gas-phase HNO 3 is an indirect detection method of PSC activity (L12) :::::::::::::::::: (Lambert et al., 2012) , since either the HNO 3 is condensed into NAT PSCs below the detection threshold of the lidar or 30 the NAT particles were so large they sedimented and the missing gas-phase HNO 3 is the result of permanent denitrification.
The theoretical condensed HNO 3 in NAT at a fixed temperature of T − T ICE = 5 K is shown in Figure 5b as a function of the NAT number density. At this temperature, the STS contribution to the backscatter, infrared extinction and HNO 3 uptake is negligible (see Figure 4) and we may safely concentrate on the properties of the NAT particles alone. The temperature is about 2.5 K below the NAT existence temperature and about 2 K above the temperature at which substantial uptake of 35 HNO 3 into STS occurs. The red diamond symbol marks the detection threshold for 1 ppbv of HNO 3 condensed in NAT (or equivalently a 1 ppbv uptake of HNO 3 from the gas phase) and corresponds to a NAT number density of 2.45 × 10 −4 cm −3 .
In Figure 5c we show the total lidar backscatter and infrared extinction as a function of the NAT number density. The total backscatter detection threshold (1.25) for the four particle aspect ratios corresponds to NAT number densities ranging from 4.9 to 8.4 × 10 −4 cm −3 compared to 1.4 × 10 −4 cm −3 for the infrared extinction threshold (k ext = 5 × 10 −5 km −1 ). For this 5 large particle radius example, uptake of HNO 3 and infrared detections are more sensitive than the lidar total backscatter. The perpendicular backscatter coefficient (Figure 5d) is more sensitive than the total backscatter to the presence of non-spherical NAT (resulting in the detection of lower number densities ranging from 1.2 to 3.6 × 10 −4 cm −3 , except for the 0.8 aspect ratio, which shows less sensitivity. Hence, operation of a lidar with an orthogonal polarization channel can substantially improve the detection threshold for non-spherical NAT for some aspect ratios. The infrared detection is shown to be more sensitive for the 10 large particle range, except for an aspect ratio of 0.95 for which the sensitivities are comparable.

Intercomparisons of PSC detection techniques
The sensitivity of different techniques employed to detect PSCs over a wide range of number densities and effective radii is illustrated with Figure 6. Selected detection limits for CALIOP lidar, infrared limb emission and inferred detection by the measured uptake of HNO 3 from the gas phase or the in situ aerosol detection of condensed HNO 3 in NAT are shown. Again, 15 the calculations are for a temperature T − T ICE = 5 K, since the purpose of the comparison is to show the potentially large variation in lidar backscatter response to NAT PSCs of differing asphericities. The lines in Figure 6 mark the detection limits for the various techniques and indicate the lowest NAT number density (N NAT ) that can be detected for a given NAT effective radius (R eff ); i.e. any combination of (N NAT , R eff ) lying below a given line is below the detection limit for that particular technique. The gray shading indicates the region that is below the detection threshold for any of the techniques assuming 20 the given variation in NAT aspect ratio. The solid (dashed) purple-blue lines correspond to the detection thresholds for total backscatter (perpendicular backscatter) for different aspect ratios. As expected from the previous section, the perpendicular backscatter is in general more sensitive to the presence of low number density NAT than is the total backscatter ratio. However, there is substantial variation in the sensitivity to the particle aspect ratio, . The sensitivity curves for infrared extinction (yellow) and lidar perpendicular backscatter are similar for the = 0.95 case for R eff ≥ 4, whereas for = 0.8 the lidar is much less 25 sensitive. For low number density / large particle NAT (bottom-right of Figure 6), the uptake of HNO 3 from the gas phase (red) can still be quite substantial (1 ppbv) and is independent of the particle asphericity. The extremes of the lidar sensitivity to small NAT (R eff < 1 µm) (ranging over an order of magnitude in particle number density) are seen to be reversed for large NAT (R eff > 5 µm); i.e. the lidar technique is more sensitive to small NAT with an aspect ratio of 0.80 than 0.95 and vice versa for large NAT. Except for the aspect ratio of 0.95, the detection limits for infrared emission and the uptake of 1 ppbv HNO 3 30 from the gas phase become more sensitive than the lidar limit for large NAT with R eff > 2.5 and R eff > 5µm, respectively.
The near coincidence of the green dashed line and red solid line shows that a NAT volume density of 0.2 µm 3 cm −3 (limit of detection for MIPAS given by Höpfner et al. (2006b)) is approximately equivalent to 1 ppbv of condensed HNO 3 . This threshold is consistent with a previous study by Hopfner (2004) ::::::::::::: Höpfner (2004) that showed that large particle, small number density NAT can be detected by MIPAS. The specific case studied was for a particle distribution with a 7 µm mode radius and number density 2.9 × 10 −4 cm −3 , which we estimate to be equivalent to a 12 µm extinction of 1.9 × 10 −4 km −1 (practically independent of the particle aspect ratio in the infrared region).

25
The black-white dashed line shows the theoretical lower limit of detection as a locus of points (δ, 1 − 1/R T ) for the chosen perpendicular backscatter threshold, β ⊥ = 2.5×10 −6 km −1 sr −1 , calculated for a typical polar atmosphere from the expression where the molecular depolarization δ m is 0.0036, the molecular perpendicular backscatter component, β m ⊥ is β T m δm 1+δm , the total Rayleigh scattering (both polarizations) is β T m , and the fractional depolarization range is δ = 0 . . . 1. This low detection 30 limit is not strictly attained in practice because of additional spatial coherence constraints that are imposed to reduce false positives to less than 0.1% (L12) :::::::::::::::::: (Lambert et al., 2012) . The coherence constraint results in the distribution of points in the None class appearing to the right side of the black-white dashed line. All the other imposed class boundaries are sharp, although this does not imply that the distinction between these PSC types is definitive. For example, as noted in P13 :::::::::::::: Pitts et al. (2013) , the ICE "arm" close to the LIQ class (normalized backscatter 0.7-0.85) is intersected by the MIX2/ICE boundary. Better separation between the MIX2 and ICE classes based on allowing for the seasonal variation in the location of the ice "arm" associated with denitrification was discussed in P13 :::::::::::::: Pitts et al. (2013) . Overall, the classification using the 2-D regions of the 5 depolarization vs normalized backscatter provides very good discrimination between STS and solid-particle PSCs.
Row 2: Gas-phase HNO 3 vs T − T ICE : In L12 and P13 ::::::::::::::::::::: Lambert et al. (2012) and :::::::::::::: Pitts et al. (2013) , we demonstrated that the uptake of HNO 3 vs temperature, classified according to CALIOP PSC types, is in good agreement with expected temperature existence regimes for STS, NAT and ice, except for an apparent ∼1 K bias with respect to the GEOS-5 temperatures. This is consistent with comparisons (not shown) 10 of coincident independent temperatures obtained from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) GPS Radio Occultation data, which indicate up to a 0.7 K cold bias in GEOS-5 in the 2009 Antarctic lower stratosphere. The LIQ class follows the theoretical equilibrium uptake of HNO 3 by STS (blue lines from 2 to 24 ppbv in 2 ppbv steps), and the MIX1 and MIX2 classes show significant non-equilibrium behaviour, along with two discernible branches following the STS and the NAT (green line) equilibrium curves. The ICE class is a compact and roughly symmetric 15 distribution, located at the lowest temperatures and lowest HNO 3 gas-phase amounts. The leading edge of the HNO 3 gas-phase distribution for the None class follows the STS uptake curve. Also visible is a separate highly denitrified branch (HNO 3 < 5 ppbv) extending to beyond 10 K above the ice frost point.

Row 3: Total backscatter (R T ) vs T − T ICE :
This row shows the temperature domains corresponding to the various CALIOP PSC classes (the region of highest backscat- 20 ter, R T > 10, is not shown). The blue lines indicate the theoretical STS backscatter vs T −T ICE for gas-phase HNO 3 increasing from 2 to 24 ppbv in 2 ppbv steps. Note that the current depolarization/backscatter classification scheme does not use temperature as a discriminant. Backscatter vs temperature is only used in the CALIOP classification scheme to determine daily detection thresholds ). The LIQ class shows a rapid increase in total backscatter near T − T ICE = 3.5 K (i.e. T STS is located at point the blue curves join the abscissa). There is a thin tail which does not reach out as far as T NAT (located 25 at the intersection of the two red-black dashed curves). The envelope of the theoretical STS curves (bounded by total HNO 3 values of 16-18 pbbv) is a reasonable description of the distribution, but at the lowest temperatures and highest expected backscatter (>6) the region is unpopulated. This may be because such conditions are favorable for freezing of STS to form ice (Koop et al., 1995). The MIX1 class shows a tail with very low backscatter extending from T STS out to beyond T NAT and consistent with N NAT ≤ 0.001 cm −3 . At temperatures below T STS the backscatter increases, but remains below values of about 3, 30 and the distribution is consistent with N NAT ≤ 0.01 cm −3 . The MIX2 class also shows a tail beyond T NAT and is consistent with the largest N NAT ranging up to slightly above 0.01 cm −3 , except at the lowest temperatures below T −T ICE = 1 K, where the backscatter increases rapidly. The demarcation between the MIX2 and ICE classes at R T = 5 is somewhat arbitrary and leads to NAT/ice mis-classification in this transition region. This effect is ameliorated by the use of a successive averaging scheme , since ice can generally be detected at a higher spatial resolution than is shown here. At the highest 35 backscatter values there is an apparent trend in the ICE class towards higher minimum temperatures. The None class shows a narrow distribution consistent with the chosen total backscatter threshold of 1.25.
Row 4: Gas-phase HNO 3 vs total backscatter (R T ): The blue lines indicate the theoretical STS HNO 3 vs backscatter curves. These show an almost linear decrease in HNO 3 with increasing backscatter. For the LIQ class the regions R T <2 with high HNO 3 and R T >6 with low HNO 3 are not fully 5 populated when compared to the theoretical curves. For low backscatter this is likely to indicate STS containing less than 0.8 ppbv of HNO 3 , which cannot be detected. For high backscatter this may suggest the result of freezing of STS to ice (see Row 3 discussion). The LIQ class also shows a bulge in the PDF around R T = 4 to 6 that reaches the theoretical curve for total HNO 3 =22 ppbv. Since the None class indicates that the maximum HNO 3 is 18.5 ppbv, the ∼3.5 ppbv excess HNO 3 in the LIQ PDF may have arisen from the formation of additional HNO 3 produced from heterogeneous reactions occurring on the liquid 10 particles and released into the gas phase or by renitrification from evaporation of sedimenting NAT clouds (see Section 4.2).
The None class also indicates totally denitrified regions (consistent with the noise floor of the MLS measurements) with insufficient HNO 3 to form any kind of non-ice PSCs. Note that the data in this row are independent of the suspected GEOS-5 temperature bias.

Evaluation of CALIOP and MLS colocated measurements 15
Although simultaneous colocated measurements of PSCs and gas constituents are obviously to be preferred over spatially and temporally decorrelated measurements, the availability of such measurements from MLS and CALIOP cannot be expected to provide full closure to the questions of PSC formation. Careful consideration of the details of PSC formation is required to reconcile the pieces of information garnered from the different measurement techniques. In this regard the ultimate aim would seem to be Lagrangian measurements following the full life-cycle of PSC evolution. However, further unresolved issues have 20 emerged from the long-duration stratospheric balloon flights by Ward et al. (2014), who describe measurements of the NAT nucleation rate that show much larger spatial inhomogeneities in NAT occurrence than anticipated.

MLS and CALIOP orbit transects
We have selected some views from the combined MLS and CALIOP data record to illustrate how the interpretation of the morphology of PSCs and gas-phase HNO 3 in along-track transects is governed not only by the local ambient temperature, 25 but also by the underlying temperature histories. Here we use the CALIOP Level 2 v1 PSC Mask dataset and also apply postprocessing to generate coarser horizontal/vertical bins for a better comparison at the scale of the MLS along-track and vertical resolution. Each averaging bin is the size of the MLS along-track separation (165 km) and the height between the mid-points of the pressure levels (2.7 km) for the MLS HNO 3 data product. Note that in this section we use the L2PSCMask data class name STS instead of LIQ. than that in the L2PSCMask composition plot, and the composition speckle can be seen as "blocky" regions in the LS_index.
Several contour lines are superposed on the orbit transects: The black/white quasi-horizontal labeled contours show a sample of the MLS pressure levels (HNO 3 is retrieved at 6-levels/decade change in pressure). The green and blue contours represent temperatures corresponding to the T NAT threshold (using GEOS-5 and MLS HNO 3 , H 2 O) and T ICE + 2 K, respectively. The 10 blue temperature contour encompasses an expected HNO 3 uptake of about 50% from the gas-phase into STS (see Figure 4a).
The yellow contour is the HNO 3 12 ppbv contour, and the red contour encloses the area with TTE ≥ 3 days.  Another orbit track (9, not shown) on the same day shows smaller HNO 3 uptake with no coincident PSC detections.
Case 2: 25 May 2009 / 2009d145 / 6: MLS HNO 3 shows a substantial region of HNO 3 uptake over 1500 km and suggests a combination of uptake in two separate regions, one located centrally within the local temperature minimum (blue contour, T ICE + 2 K) and another offset extending to the right edge of the T NAT contour (green). The temperature history (red contour) is the key to this rather apparent asymmetry of the HNO 3 distribution with respect to the T NAT contour, since the TTE clearly shows substantial STS class (with multi-class speckle), but only in the right half of the minimum local temperature region.
The left half is the area with the largest TTE values (red contour). The L2PSC_Mask shows MIX1/MIX2 class pixels below and to the left of the large STS cloud and also in the regions outside of the TTE and T NAT contours. We also note that 35 although the minimum temperatures along a number of the back trajectories passed below the frost point within two days of the MLS/CALIOP observations, no ice PSCs were detected.
Examination of the overlaps between the high TTE values (red contour) and local temperature minima (blue contour) in the cases discussed above reveals a correspondence with HNO 3 uptake, but a frequent lack of coincident PSC detections. The local temperatures are just as low (and sufficient for STS formation) as in the areas outside the overlaps, but the STS class 5 is not seen at all, whereas the TTE increases substantially. The corresponding detailed time histories of the temperatures at 32 hPa are shown in Figure 8d and reveal that the remarkable asymmetries in the along-track location of HNO 3 uptake with respect to the local temperature minimum distribution can be understood in terms of the different rates of cooling of particular air parcels. This indicates that in the regions where slow cooling forms NAT first (marked by long white arrows in cases 2 and 4), HNO 3 is sequestered into NAT, and therefore STS cannot grow. In contrast, there are regions where fast cooling occurs and 10 STS forms without prior NAT formation (marked by short white arrows in cases 2 and 4). The NAT exists as large particle / low number density clouds (sedimenting, sub-visible MIX1) that contain enough condensed HNO 3 to be detectable through MLS gas-phase depletion, but have low lidar backscatter and are invisible to CALIOP. Alternatively, it could be argued that the NAT particles grew so large further upstream that they were effectively removed to lower altitudes through sedimentation at the time of the orbit crossing observations, leaving behind a permanently denitrified air mass detected by MLS but without coincident 15 CALIOP PSC detections. However, further averaging of CALIOP backscatter (as discussed in Section 3) on 27 May, shown in Figure 9, does indicate a considerably larger area of solid particle detections (MIX1 class), associated with the high TTE region, and so it appears that we are dealing with the limit of the L2PSCMask detection range. Sedimentation of large NAT is suggested by the 2-4 km region of solid particle detections lying below the high TTE region.

20
The Antarctic gas-phase HNO 3 distribution shown in Figure 10 provides a record of the effects of the formation and dissipation of PSCs and is displayed as the daily areal coverage for equivalent latitudes less than 60 • S, for isentropic levels from 340 to 500 K. The white solid lines indicate low, median and high values of the HNO 3 probability density function. The minimum HNO 3 mixing ratios (i.e. the colored region below the 10th percentile white line) indicate that PSCs can lead to a complete removal of the available ambient HNO 3 from the gas phase. As shown in L12 :::::::::::::::::: Lambert et al. (2012) , the spread of HNO 3 25 mixing ratios in totally denitrified regions is compatible with the MLS precision. The temperature decrease starts from the upper levels of the vortex and descends over time, resulting in PSCs and HNO 3 uptake developing later at the lower levels. The maximum HNO 3 mixing ratios (i.e. the colored region above the 90th percentile white-line) indicate episodes of renitrification at the lower levels arising from the sedimentation of PSCs. As the NAT particles fall through lower levels, they may pass into regions where they are less thermodynamically stable. In these cases the evaporative release of HNO 3 from the condensed 30 phase increases the gas-phase values, and this is detected as a rise in the HNO 3 measured by MLS at the lower levels. The process is seen quite clearly in the increasing time lag between the appearance of anomalously large HNO 3 values above the 90th percentile at 420 K (mid-May) compared to 340 K (mid-June). This process acts to raise the NAT temperature existence threshold at the lower levels because of the enhanced gas-phase HNO 3 and therefore increases the likelihood of occurrence of NAT. Heterogeneous chemical reactions on the PSC particles involving ClONO 2 and N 2 O 5 produce additional HNO 3 , which remains in the condensed phase until the PSC dissipates . Therefore, an increase in gas-phase HNO 3 at a given level may arise from the evaporation either of sedimenting PSCs from above, or from extant PSCs that release the excess HNO 3 formed as a product of heterogeneous reactions. As the Antarctic winter progresses and the temperatures at the lower levels decrease, the redistributed HNO 3 is itself subject to further uptake into STS/NAT, resulting in potential further 5 denitrification and consequent removal of HNO 3 from a larger vertical range of the lower stratosphere.

Timeseries of PSC formation and Lagrangian temperature history
In this section we examine the formation of PSCs and the Lagrangian temperature history during the early 2009 Antarctic PSC season. Figure 11 shows presumably due to renitrification from evaporating NAT PSCs that have sedimented from a higher level. The combined data at 32 hPa indicate that, in the early period, the CALIOP L2PSCMask is not detecting PSCs, since there is a persistent area of daily HNO 3 depletion that is not matched by corresponding PSC detections, but is consistent with the temperature history. We use the term sub-visible PSCs to refer to these cases (i.e. significant depletion of gas-phase HNO 3 , but without detection by CALIOP). 30 We examine the variation of MLS HNO 3 with TTE for sub-visible PSCs in the period 2009d135-2009d144 (15)(16)(17)(18)(19)(20)(21)(22)(23)(24) in more detail in Figure 12. The scatter plot of the gas-phase HNO 3 values shows a range of ∼4 ppbv (from ∼14 to ∼18 ppbv) for low TTE, and as TTE increases beyond ∼1 day, the HNO 3 decreases. A highly simplified microphysical model has been used to calculate the uptake of HNO 3 from the gas phase. Growth of NAT by vapor deposition has been calculated in the manner outlined by Toon et al. (1989) and following the simplifications introduced by Carslaw et al. (2002). Here, we ignore sedimentation and calculate the growth of monodisperse NAT in a constant temperature atmosphere (T ICE + 4 K) for two different initial NAT densities (5 × 10 −4 and 5 × 10 −5 cm −3 ) and two initial total HNO 3 values that encompass the observed range (14 and 18 ppbv). The NAT growth model is initialized with a 0.1 µm radius at the nucleation time (TTE=0), and the 5 subsequent time evolution of the gas-phase HNO 3 is plotted as colored curves indicating the NAT particle radius. These two curves practically bound the MLS observations of the distribution of gas-phase HNO 3 as a function of TTE. As is well known, low NAT number densities produce large NAT particles (Jensen et al., 2002), which take several days to reach thermodynamic equilibrium (the uptake curves bottom out after 15 days or more). Backscatter calculations for NAT with characteristics of the upper curve (assuming = 0.9) show that the backscatter (perpendicular or total) is below the CALIOP threshold of detection 10 along the entire time evolution. For the lower curve, the higher NAT number density limits the particle growth to a much smaller radius, and backscatter calculations suggest that the NAT particles should be detectable after 0.8 days following nucleation for the perpendicular backscatter threshold and after 1.3 days for the total backscatter threshold. The details of the scattering calculations depend on assumptions about the underlying particle characteristics, for which we lack definitive knowledge.
However, observationally we repeatedly see large depletions of HNO 3 without accompanying particle detections, which can 15 be accounted for qualitatively by a NAT population characterized by low number densities/large radii.

Interannual variations in the early Antarctic PSC season
In this section we investigate the interannual variability of Antarctic PSCs and HNO 3 over the past decade and again make use of the geolocated raster plot format discussed in Section 2.4. Figure 13 shows  Figure 16) indicates that for the southern hemisphere, the 30 cold pool temperatures and the polar vortex are highly concentric. We have also investigated the daily scatter of temperature vs vorticity in the ERA-Interim reanalysis data (not shown here), and find that the annular region 60 • S to 82 • S (visible to Aura and CALIOP) describes adquately ::::::::: adequately the state of the region poleward of 82 • S (not sampled by Aura or CALIOP).
The start of the PSC season appears to display two modes (see Figures 13b and 15b), with some years having larger coverage of solid PSCs (2007, 2011 and 2014) than others, which show larger coverage of liquid PSCs (2008, 2009, 2010 and 2015). We identify the presence of sub-visible PSCs by a delay between the onset of gas-phase HNO 3 depletion (see Figures 13a and 15a) and the geophysically associated detection of PSCs (see Figures 13b and 15b). Table 2 lists the day number of the initial onset of HNO 3 depletion, the first day of detection of PSCs by CALIOP, the presence of sub-visible PSCs, and the predominant 5 PSC class (solid or liquid) for the first few days following detection. Sub-visible clouds are present in five out of the seven years with MLS and CALIOP overlap during the critical time period when uptake of gas-phase HNO 3 is first detected. The time lag between the observed depletion of gas-phase HNO 3 and the detection of PSCs varies and is largest in 2009 and 2014. We infer that the sub-visible PSCs are composed of NAT because the expected uptake of HNO 3 is negligible for STS at the associated ambient temperatures (see Figure 14b). In 2015 there is a notable period of several days (148-153) without 10 many PSC detections (see Figures 13b and 15b), although HNO 3 is still consistently low (see Figure 13a), probably indicating sedimentation of NAT and permanent denitrification. However, since Woiwode et al. (2014) have reported the presence of NAT with larger apparent sizes compared to compact spherical particles and with concomitant reduced settling rates, we must also consider the possibility that the NAT radius grew larger and subsequently evolved into sub-visible NAT. since, for the cases where CALIOP detects no cloud, about 60% correspond to cloudy scenes for MIPAS. Therefore, these MIPAS/CALIOP comparisons support our conclusion that CALIOP is not sensitive to low number density, large particle NAT. 20 The goal of describing the interannual variability of PSC seasons within the context of a decadal climatology can be met by synthesizing the CALIOP and MLS observations, consisting of the 4-variable data set (HNO 3 , TTE, T −T ICE and LS_index), into a number of characteristic groups or clusters and thereby capturing the major characteristics of PSC formation. Simple partitioning obtained by setting a single threshold boundary on each of the four variables would result in 16 different PSC groups (some of which may be empty). Such a large number of groupings would complicate interpretation, and so a more 25 parsimonious scheme is desirable to enforce a reduction in the number of groups. Cluster analysis (CA) is a well-established tool for unsupervised exploration of a data set (Jain, 2010). Ideally members of the same cluster (identified by their proximity to the cluster centroid) will naturally exhibit similar intrinsic properties and display low within-cluster variance, whereas the differences amongst the members of one cluster to another will display high between-cluster variance. We used a K-means centroid algorithm with a Euclidian distance metric to partition the 4-variable data set after performing zero mean and unit 30 variance normalization. K-means analyses were performed for a varying number of imposed clusters (K=2 to K=20), and the gap-statistic (Tibshirani et al., 2001) was used to assess the optimal number of clusters by comparison with uniformly random data and an uncorrelated data set obtained by randomly reordering the measurement times of the four variables. A steep rise in the gap-statistic was observed over the range K=2 to K=7, followed by a flattened plateau region out to K=20 (not shown). The clusterings obtained for K=6 are shown in Table 3 and Figure 16 for all the years 2006-2015. The K=6 case was chosen because the clusters fell practically into two sets (a,b) of three groups, corresponding to predominantly liquid (Figure 16a, LS_index > 0) and predominantly solid (Figure 16b, LS_index < 0) PSCs. No particular improvement was observed for the K=7 case.
The LS_index vs day number scatter plot indicates that there is some cross-over of liquid/solid PSCs present in both the a1 and a2 groups. The groups are presented superposed as a scatter plot on the thermodynamic HNO 3 vs T − T ICE diagram and show clearly that the two sets (a,b) are associated with the STS and NAT equilibrium branches. As in previous analyses, the 5 NAT population exhibits considerable non-equilibrium effects (L12, P13), :::::::::::::::::::::::::::::::: (Lambert et al., 2012;Pitts et al., 2013) , : with the temperature distribution extending to temperatures as low as the STS branch. No correction has been made for the suspected temperature bias in the meteorological temperature data (Section 3.2).
The stereographic map projections in Figure 16 show the PSC groups with higher temperatures (a3, b2, b3) extending to lower latitudes, reflecting the general outward radial increase of the polar temperature distribution. However, in particular, 10 group b3 displays similarities to a circumpolar NAT belt (Tabazadeh et al., 2001;Höpfner et al., 2006a)), although it is notable that this group also includes CALIOP detections at temperatures apparently higher than the NAT existence threshold T NAT = T ICE + 7 K. The b3 group temperature history (HNO 3 vs TTE) also shows little exposure to low temperatures. These may result from the inability of the gridded synoptic reanalysis data to capture accurately the local temperature minima. Another possibility is that the NAT particles may survive for a time before fully melting as they are advected downstream (L12)
Compelling evidence of the differences in the formation of liquid and solid PSCs can be deduced from comparisons of the temperature history of the groups. For the case of moderate gas-phase HNO 3 depletion, the occurrence of liquid PSCs (a3) shows a steep fall off in the TTE distribution beyond ∼1 day. In contrast, the occurrence of solid PSCs (b2) extends to TTE ∼ several days and also shows a trend of declining HNO 3 with increasing TTE that can be explained by reference to the NAT 20 growth curves modeled in Figure 12. For the case of large gas-phase HNO 3 depletion, the b1 group shows a peak around TTE=6 days, and very few of these solid PSCs formed at TTE < 2 days. This is also a consequence of the microphysics of NAT growth since it requires ∼days for the NAT particles to grow sufficiently to substantially deplete the gas-phase HNO 3 .
Permanent denitrification caused by sedimentation of large NAT is the likely cause of the fall off in the occurrence of PSCs in the b1 group at large TTE. In contrast, there exists a substantial occurrence of liquid PSCs at all values of TTE in groups a1 25 and a2, as expected since the growth/evaporation of STS is a faster process dependent on the instantaneous temperature.
The total number of coincident MLS and CALIOP observations over the 10-year time span is ∼2 × 10 4 , and the mean (standard deviation) of the relative number of observations (in percent) for group a is 55 (8) and for group b is 45 (11). Therefore liquid PSCs (group a) are the dominant form and solid PSCs (group b) have slightly more variability. The corresponding breakdown of the mean and standard deviation for the individual groups is given in Table 3. 30 The observations in each cluster obtained from the decadal climatology were sub-divided to produce data for the individual PSC seasons. The results are shown in the pie charts in Figure 15 to provide a convenient summary of the interannual variations.

Conclusions
A decade of MLS and CALIOP satellite measurements from 2006 to 2015 over the Antarctic polar vortex were used to investigate the early season development of PSCs and the gas-phase HNO 3 distribution in the lower stratosphere. We developed 5 a compact visual representation of the daily orbit tracks that allows a time-series to be constructed from the montage of a few hundred separate daily images, consisting of a combination of different days/pressure levels/species, and displayed on a single page.
Lidar properties were calculated for the STS and NAT components of PSCs. We reviewed the capabilities of spaceborne instruments (lidar, mid-infrared, microwave) applied to the detection of PSCs and uptake of HNO 3 and used the results to 10 investigate the generation of large particle / low number density NAT at temperatures above the ice frost point, which results in sub-visible PSCs that can be detected through the gas-phase uptake of HNO 3 . The presence of sub-visible PSCs was found in over half of the years examined.
In this work we have demonstrated that the early initiation of NAT nucleation in the Antarctic vortex takes place frequently at temperatures above the ice frost point and often before cooling produces liquid PSCs. A consistent picture emerges, with HNO 3 15 depletion occurring in the inner vortex, usually before any associated PSC development is detected by CALIOP. We conclude that an ice-seeding process is not essential for the initiation of NAT nucleation or subsequent development of large-scale NAT growth in the early winter.
We used detailed measurements in the CALIOP and MLS along-track transects to illustrate that the formation of PSCs is governed not only by the local ambient temperature, but is also shaped in large measure by the underlying temperature histories.

20
A cluster analysis method was used to organize the combined CALIOP and MLS data into a manageable form to guide an investigation of the decadal climatology and facilitate ready comparison of the patterns of interannual variability. The temperature distribution of the groups was used to compare the relative frequency of formation of liquid and solid PSCs in the Antarctic lower polar stratosphere.
Acknowledgements. We gratefully acknowledge members of the teams associated with the CALIOP and MLS instruments, and the GEOS-     month. An air parcel (containing the requisite background aerosol embedded with foreign nuclei) exposed to a temperature of T −TNAT = −4 K for one day will generate 0.0012 cm −3 of nucleated NAT particles. (b): as for (a) except for a denitrified atmosphere with 5 ppbv total HNO3. Each orbit is numbered sequentially. The square symbols denote the latitude and longitude locations of the MLS vertical profiles. The size of the squares is not representative of the along-track or across-track resolutions. HNO3 volume mixing ratio at 32 hPa is given by the color bar.
(c): The same data points are shown as a temporal raster plot. The ordinate is the time of day in hours (UT) and the abscissa is the geodetic along-track angle. The squares denote the time of day of the MLS measurement and the measurement location with respect to the closest 5 approach of the orbit track to the South Pole. Each orbit is numbered along the right ordinate. Also shown are the along-track distance, the latitude and the solar zenith angle. The size of the squares is not representative of the MLS integration time or the along-track resolution.   and correspondence to the uptake of HNO3 in STS. Figure 6. Intercomparison of the sensitivity of various PSC detection techniques to a range of NAT number densities and effective radii at a temperature of T − TICE = 5 K, for an ambient pressure of 46 hPa, 5 ppmv H2O, and 12 ppbv total HNO3. The purple-blue lines indicate the limits of detection for lidar with total backscatter (solid) and orthogonal channel (dashed) for a range of aspect ratios (EPS). The red (green) line indicates the sensitivity of an in situ sampling instrument to 1 ppb of condensed HNO3 in NAT (aerosol density, 0.2 µm 3 cm −3 ) or the equivalent uptake from the gas phase (e.g. by a microwave limb sounder). Yellow/orange lines indicate the sensitivities in the mid-infrared for a limb sounder at two wavelengths. NAT PSCs with particle distribution characteristics lying within the gray shaded region are undetectable by any of the above techniques, with the assumed horizontal and vertical averaging scales given in the text. identified in the text. Blue (green) lines are theoretical calculations for total HNO3 from 2 to 24 ppbv in 2 ppbv steps for STS (NAT) equilibrium. Red-black dashed lines are theoretical calculations for equilibrium NAT with number densities 0.001 cm −3 (bottom curve) and 0.01 cm −3 (top curve) and 14 ppbv total HNO3. The lower limit of detection, given by the black-white dashed line, is described in the text.         Thermodynamic diagrams indicate for reference the theoretical HNO3 uptake by STS (blue-black dashed line) and by NAT (green-black dashed line). The scatter plots show the MLS HNO3 vs temperature relative to the ice frost point colored by the corresponding LS_index obtained from CALIOP. Column a (b) shows the data in three groups a1-a3, (b1-b3), which are seen to be predominantly liquid (solid) PSC detections according to the LS_index. The colored contours ((a1-purple, a2-dark-blue, a3-light-blue), (b1-red, b2-orange, b3-yellow)) 5 contain 95% of the corresponding cluster members. The maps show the geographic distribution of the members of each of the clusters and are color-coded by the LS_index (inset color bar). A 2-D view (HNO3 vs TTE) is provided of the cluster densities (purple-yellow shading indicates low to high density) and the accompanying colored solid lines represent the normalized 1-D histogram of the TTE values. The cluster densities are also displayed as a 2-D view of LS_index vs day number.