The temperature and shape of ice particles in polar mesospheric clouds (PMCs) were determined using observations near 3 μm wavelength from the Solar Occultation for Ice Experiment (SOFIE). The resulting ice temperatures are 5–20 K colder than the current SOFIE temperatures retrieved from CO2 transmission measurements. Particle shape is described using oblate spheroids, and the axial ratios determined in this study are slightly more spherical than previous results obtained using SOFIE observations assuming constant temperature (1.9 at the altitude of peak mass density compared to 2.3 previously). Using ice temperatures in an equilibrium PMC model results in ice mass densities that are much higher than observed. SOFIE observations indicate that the amount of H2O that can enter the ice phase is related to ice concentration, suggesting that ice nucleation plays an important role in determining PMC formation and variability. This result may also imply that the neglect of transient phenomena in the equilibrium PMC model may be a large source of error. SOFIE observations do not support the existence of amorphous ice particles near the summer mesopause but rather indicate that cubic ice is ubiquitous.
 Polar mesospheric clouds (PMCs) consist of ice particles which form near the polar summer mesopause. Solar Occultation for Ice Experiment (SOFIE) observations were used to simultaneously determine vertical profiles of the temperature and shape of mesospheric ice particles. The observations were also used to examine whether PMC particles are crystalline or amorphous. SOFIE was launched in April 2007 onboard the Aeronomy of Ice in the Mesosphere (AIM) satellite [Russell et al., 2009] to measure temperature (T), five gaseous species (O3, H2O, CO2, CH4, and NO), PMCs, and meteoric smoke [Gordley et al., 2009; Hervig et al., 2009a, 2009b]. The SOFIE field-of-view (FOV) subtends ∼1.6 km vertically and the tangent point sample volume length is ∼290 km along the line-of-sight (LOS). Observations are taken continuously at latitudes from 65° to 82°S (spacecraft sunset) and 65° to 82°N (sunrise). Each day SOFIE observes 15 sunsets (and 15 sunrises) at virtually the same latitude. This work uses version 1.022 SOFIE results, which are available online (http://www/sofie.gats-inc.com). SOFIE measurements are used to determine a variety of ice properties including mass density, particle shape, effective radius, and the parameters of a Gaussian size distribution as described in the work of Hervig et al. [2009a]. SOFIE ice extinction measurements have a precision of 5 × 10 −8 km−1 [Gordley et al., 2009].
 The primary SOFIE temperature product is retrieved from atmospheric transmissions measured within the 4.3 μm CO2 band. The temperature retrievals require treatment of non-local thermodynamic equilibrium (NON-LTE) effects, which reduce the temperatures by about 10 K near the summer mesopause compared to ignoring non-LTE effects. The temperature measurements are expected to have a precision of ∼0.2 K; however, comparisons with independent measurements suggest that V1.022 SOFIE CO2 temperatures contain a warm bias of 5–10 K near the polar summer mesopause [Hervig et al., 2009c]. This warm bias may be due in part to inherent measurement effects and/or retrieval deficiencies. Recent studies of the effects of diurnal tides on temperatures and PMCs indicate that temperatures are generally ∼5 K warmer at the SOFIE measurement local time (∼23 h) compared to other times [Stevens et al., 2010]. It is also possible that a warm bias is due to the relatively large SOFIE sample volume combined with fine scale variability. Lidar observations indicate that temperatures near the summer mesopause can vary by over 30 K within periods of less than 4 h [Höffner and Lübken, 2007], and Baumgarten et al.  indicate temperature gradients of up to 3 K km−1 derived from the structure within PMC layers. Hypothetical temperature variability along the SOFIE LOS, consistent with Höffner and Lübken, is shown in Figure 1. Because the measured CO2 transmission is an average over the LOS, the retrieved average temperature would be biased warm with respect to the regions cold enough to form ice.
 In contrast, the temperature associated only with ice particles should generally be below the frost point temperature (Tice). Petilina and Zasetsky  derived the temperatures of mesospheric ice particles using infrared (IR) solar occultation measurements from the Atmospheric Chemistry Experiment (ACE) instrument. They found that ice temperatures were significantly colder than associated temperatures derived from gaseous absorption. This occurs in part because the signal due only to ice is unaffected by interstitial warm regions along the LOS and thus is more representative of the specific conditions associated with ice.
 The present study was motivated by the recent derivation of mesospheric ice particle temperature (iceT) by Petilina and Zasetsky . The underlying principal is that the OH stretch peak in ice absorption (2.7–3.5 μm wavelength) changes width and position as a function of temperature. This behavior is captured in the ice refractive index data of Clapp et al. , which were measured for temperatures from 130 to 210 K (10 K intervals) and wavelengths from 2.5 to 12.5 μm. The Clapp et al. data represent cubic ice (Ic) for T < ∼150 K and hexagonal (Ih) ice for higher T, although the refractive index for Ic and Ih are thought to be identical [Warren, 1984].
 The wavelength dependence of IR extinction is dependent on ice particle shape in addition to temperature. This work treated nonspherical particles as randomly oriented oblate spheroids and computed extinction cross sections using the T-matrix method of Mishchenko and Travis . Axial ratio (AR) denotes the ratio of horizontal (equatorial) to rotational (polar) axes of a spheroid as defined in the work of Mishchenko and Travis, where AR > 1 corresponds to oblate spheroids. The size of nonspherical particles is defined as the radius of an equivalent-volume sphere. SOFIE ice extinctions were modeled assuming oblate spheroids using refractive indices from the work of Clapp et al. , including convolution over the SOFIE relative spectral response and the solar source function.
 Modeled ice extinctions within the OH stretch region show that the extinction peak is broader and shifted toward lower wavelengths at warmer temperatures (Figure 2). Of the SOFIE wavelengths relevant to this study (see Figure 2), the best candidates are bands 8 (2.939 μm), 9 (3.064 μm), and 10 (3.186 μm), due to the high signal-to-noise and lack of gaseous interference at the altitudes of interest. IR ice extinctions are also retrieved from bands 11 (3.384 μm) and 12 (3.479 μm); however, the results are currently not precise enough due to inadequate removal of gaseous interference and also due to the relatively lower ice signals compared to bands 8–10. The wavelength dependence of IR extinction is independent of particle size for typical PMC particle radii (<100 nm), as demonstrated in the work of Hervig et al. [2009a]. The model calculations used in this work therefore assumed a single Gaussian size distribution with a median radius of 30 nm and width of 12 nm. Considering other size distributions within the typical range for PMCs does not alter the results presented here. Including SOFIE wavelengths shorter than ∼2.5 μm would complicate this effort because the wavelength dependence of extinction is strongly dependent on particle size. Note that modeled extinctions considering other ice refractive indices [e.g., Toon et al., 1994] are generally consistent with results using Clapp et al., and that the Clapp et al. data were used alone because they capture the temperature dependence in a consistent set of indices.
 The sensitivity of SOFIE IR extinctions to ice temperature and AR is demonstrated in greater detail by the model results shown in Figure 3. Temperature dependence of the extinction ratios becomes somewhat asymptotic for T > 150 K, and this behavior continues to warmer temperatures. The majority of SOFIE observations, however, are consistent with T < 150 K, as demonstrated in Figure 4 where Northern Hemisphere (NH) observations at 84 km are compared to model results for a range of temperatures and AR. Examining SOFIE observations for altitudes from 80 to 90 km leads to the same conclusion. We therefore considered only temperatures ≤150 K in the inversions presented here and realize that this approach may cause a small fraction of the results to be erroneous. SOFIE observations in Figure 4 are identified as ice or non-ice according the method in the work of Hervig et al. [2009a]. Note that the majority of SOFIE results that are outside the modeled range for ice are from non-ice observations. Some observations identified as ice are not consistent with the modeled range for ice in Figure 4. These instances are attributed to the use of observations at only two wavelengths and model results for only one temperature by the Hervig et al. [2009a] method, as opposed to three wavelengths and a range of model temperatures as in Figure 4.
 While Petilina and Zasetsky  determined iceT for fixed particle shapes, we find that a combination of three SOFIE wavelengths is sufficient to simultaneously determine both iceT and AR. In the iceT/AR retrievals, all combinations of iceT and AR are found that can explain a given extinction ratio, for multiple ratios formed using bands 8–10. The solution is taken as the unique pair of iceT and AR from the range of possible solutions. The Clapp et al. indices do not cover T < 130 K, and the modeled extinction ratios were extrapolated linearly to 120 K (Figure 3) for use in the retrievals. While the basis for this extrapolation is debatable, we find that most SOFIE observations are consistent with T > 130 K (Figure 4) and thus conclude that the extrapolation to lower temperature has only a minor effect on the results.
 Uncertainties in retrieved iceT and AR were determined using a Monte Carlo approach with the SOFIE noise (5 × 10−8 km−1) randomly applied to synthetic bands 8–10 measurements. Random uncertainties are determined as the standard deviation of 500 random samples. Systematic errors were taken as the difference between the known solution and the average solution, and the total uncertainty is the root sum square of the random and systematic components (Figure 5). There are cases where the applied random errors give synthetic measurements that fall outside the range of modeled extinction ratios. These cases do not yield a solution and lead to small systematic uncertainties. Uncertainties determined as a function of band 9 extinction indicate total uncertainties in iceT of <9 K for low extinction and <1 K for high extinction (Figure 5). These estimates are slightly lower than that of Petilina and Zasetsky , who determined iceT errors of ∼12 K for the ACE application. One explanation for this difference is that Petilina and Zasetsky fixed particle shape and carried the resulting effects in their iceT error budget, whereas the present study simultaneously determines particle shape. The uncertainty in retrieved AR ranges from <50% at low extinction to <5% when extinctions are high (Figure 5).
3. Ice Temperature and Shape Results
 SOFIE observations in the NH during 2008 were used to retrieve vertical profiles of iceT and AR for this work. Results from the other PMC season observed thus far lead to similar concussions. These retrievals used only measurements with bands 8–10 extinctions greater than 10−7 km−1 (twice the noise), consistent with the ice identification threshold used by Hervig et al. [2009a]. Example profiles of retrieved iceT and AR are shown in Figure 6. In this example, iceT is 5–12 K colder than the CO2 temperatures and always below the frost point (Figure 6a). The axial ratios retrieved in this work are similar to but slightly more spherical than results obtained from the same observations using the method of Hervig et al. [2009a] (Figure 6b). In this study, Tice was determined using Murphy and Koop  (MK05) saturation vapor pressures and observed total water (gas plus ice phase). Total water was used for this purpose in order to approximate the conditions that lead to PMC growth, as suggested in the work of Hervig et al. [2009c].
 Probability distributions of iceT and CO2 temperature, for all altitudes where ice was observed, indicate that iceT is always <150 K with a median value that is ∼10 K lower than the median CO2 temperature (Figure 7a). While the absence of iceT > 150 K results from a limit in the inversions (see section 2), this limit is rarely encountered (e.g., Figure 4) and the dominance of iceT < 150 K is thus considered a physical result. iceT is almost always below the frost point, in contrast to the V1.022 CO2 temperatures which are below Tice roughly half the time when ice is observed (Figure 7b). Note that Espy and Jutt  calculated that PMC particles should be ∼5 K warmer than the surrounding air temperature. This finding is in contradiction to the current SOFIE results which show iceT < T, unless the SOFIE V1.022 CO2 temperatures contain a warm bias of greater than the 5–10 K that is currently suspected.
Figure 8a shows time series of CO2 temperature and Tice at the mesopause compared to the lowest iceT observed in a profile. Note that the average iceT remains fairly constant and always less than Tice during the season, while the CO2 temperatures can be greater than Tice at times when ice is present. Although the SOFIE V1.022 CO2 temperatures are warmer than the temperature climatology based on falling sphere (FS) observations [Lübken, 1999], SOFIE iceT are slightly colder than the FS results (Figure 8a). The average iceT remains low and fairly constant throughout the season, even at the start or end of summer when air temperatures are higher. This occurs because the average iceT at summer's start or end is due only to a small number of observed clouds, whereas the average air temperatures are from a mix of cold (cloudy) and warm (clear-sky) conditions. The current results suggest that mesospheric ice particles are slightly more spherical than results obtained with the same data but using the approach of Hervig et al. [2009a] (Figure 8b). The average AR for 1 June to 20 August 2008 at the altitude of peak ice mass density (Zmax) was 1.9 for using the present approach compared to 2.3 for using the method of Hervig et al. [2009a] with the same observations.
 Average profiles of iceT and CO2 temperature are compared to the FS climatology in Figure 9a. While individual iceT profiles exhibit vertical variability (e.g., Figure 6a), the average profile is fairly constant. Near 88 km the average iceT is close the FS values, where the V1.022 CO2 temperatures are up to 10 K warmer. The July-average AR determined according to the present study are slightly lower than values determined from the same observations according to Hervig et al. [2009a] at all altitudes (Figure 9b). Hervig et al. [2009a] report AR retrieved from SOFIE bands 9 and 10, using ice refractive indices for constant temperature (145 K). Because the current study accounts for temperature dependence, the AR reported here may be more reliable.
4. Relationships Between PMCs and iceT
Hervig et al. [2009c] reported relationships between PMCs, temperature, and water vapor using SOFIE observations from the NH in 2008. It was shown that the ice mass density and column ice water content (IWC) are well correlated with temperature, with a steeper dependence during the warming phase of summer when water vapor is highest. They also employed a zero-dimensional (0-D) thermodynamic equilibrium model using MK05 saturation vapor pressures with V1.022 SOFIE CO2 temperatures and water vapor. The reported model - SOFIE differences for July 2008 were 16% in gas phase equivalent ice mass density (Qice) at 0.005 hPa, 36% in IWC, and −0.1 km in Zmax. Using iceT from this work with MK05 vapor pressures and SOFIE water vapor in the 0-D model, we find that the model overestimates observed Qice at 0.005 hPa by 91%, overestimates IWC by 290%, and underestimates Zmax by 1.8 km. The dramatic increases in Qice and IWC are due to lower iceT compared to the V1.022 CO2 temperatures and also because the 0-D model assigns all H2O in excess of saturation to the ice phase. For example, using iceT in the 0-D model results in more than 90% of the water vapor being assigned to the ice phase at 0.005 hPa, on average. The lower Zmax is due to much colder iceT at lower altitudes (see Figures 6 and 9). These differences may be due to unrealistically low ice temperatures or result from the neglect of transient phenomena (such as nucleation) in the 0-D model.
 Because the SOFIE V1.022 CO2 temperatures are believed to be biased warm and since iceT appears to be more consistent with expected PMC temperatures, the changes reported here may indicate that the 0-D model inherently overestimates Qice. This possibility was discussed in the work of Hervig et al. [2009c], in relation to 0-D model results using the FS temperatures which nearly doubled the modeled Qice. There is theoretical evidence that the amount of H2O that can be converted to ice is limited by the number of ice particles nucleated, which should be close to the ice concentration (N) because coagulation is considered unimportant in PMCs [Rapp and Thomas, 2006]. This possibility was explored using observed ice concentrations from SOFIE [Hervig et al., 2009a] in conjunction with observed water vapor (Qgas) and Qice. For this purpose, the extent of dehydration (D) was defined as the ratio of Qice over the total water (Qtot = Qice + Qgas), D = Qice/Qtot. Examining D versus N for time series at 0.005 hPa and for July-average profiles reveals that D is always less than ∼0.4 and greatest when ice concentrations are high (Figure 10). The time-dependent results at 0.005 hPa in Figure 10 were fit according to
for N in cm−3. It is apparent in Figure 10 that the relationship between N and D is similar over time at one pressure and over altitude. The extent that the dehydration–ice concentration relationship may be universal was further examined by using observed ice concentration profiles (Figure 11a) with (1) to determine D versus altitude. Recall that (1) was derived from time-dependent observations at 0.005 hPa. The results show that the observed dehydration versus altitude can be predicted from observed concentrations with (1), with the main discrepancy at altitudes above ∼87 km where the predicted D is lower than observed. Above ∼86 km, SOFIE ice concentration retrievals are often absent and/or increasingly uncertain [Hervig et al., 2009a]. The observed relationship between D and ice concentration suggests that PMC formation and variability are related to ice nucleation. This conclusion does not eliminate temperature or humidity as controlling variables because ice nucleation depends on these quantities but rather points to ice nucleation as a specific pathway in determining PMC formation and variability.
 It is prudent here to consider the effects of spatial nonuniformity in PMCs within the SOFIE sample volume. Because the SOFIE inversions assume that PMCs are spherically symmetric, the retrieved PMC extinctions can be biased low by approximately the fraction of the sample volume that is occupied by cloud (CF). Because this bias translates directly to both the retrieved N and Qice, this effect may be important in interpreting the relationship between N and D. Note, however, that two competing factors exist. First, concentration is strongly dependent on particle size, and particle size is immune to PMC nonuniformity because it is derived from the ratio of simultaneously measured extinctions which are impacted identically by nonuniformity [Gordley et al., 2009]. As a result, the effect of cloud nonuniformity on N will not be the same as in Qice. The second factor is that retrieved water vapor may be impacted by PMC nonuniformity because the dehydration associated with PMCs could be equally nonuniform. In this case, the sample volume average water vapor would be biased high with respect to the local value associated with PMCs, and this effect would compete against a low bias in Qice in the denominator of D. Finally, the impact of cloud nonuniformity was examined using coincident Cloud Imaging and Particle Size (CIPS) PMC images [McClintock et al., 2009], which view the SOFIE sample volume from the AIM satellite within ∼6 min time of each SOFIE observation. CF was determined from CIPS data for comparison with SOFIE. The results indicate that neither N or Qice are correlated with CF, and we conclude that the observed correlation between N and D is not an artifact of PMC nonuniformity.
5. The Phase of Mesospheric Ice
 While the conditions associated with PMCs are generally thought to favor cubic ice (Ic), it has been suggested that PMCs may originate as amorphous ice (Ia) through homogeneous nucleation at temperatures below ∼130 K [Zasetsky et al., 2009; Murray and Jensen, 2010]. Ia is expected to crystallize into Ic within minutes at 140 K, but this process may require days at 120 K [Jenniskens et al., 1997]. Murray and Jensen therefore suggested that both Ia and Ic may be present in mesospheric ice clouds, with Ia more likely at altitudes near the mesopause where temperatures are lowest (e.g., Figure 9a).
 The possibility of amorphous ice was examined by comparing SOFIE observations with modeled extinctions based on the Ia refractive indices from Hudgins et al. , Leger et al. , and Mukai and Kraetschmer . The Hudgins et al. indices are available for wavelengths from 2.5 to 200 μm and temperatures from 10 to 140 K, and it was suspected that the Ia ice samples were transforming into Ic for T > ∼100 K. The Leger et al. indices were measured for 77 K and wavelengths from 2.5 to 80 μm, and the Mukai and Kraetschmer indices for 23 K and wavelengths from 2.5 to 15 μm. SOFIE observations within the IR (bands 8–10) were used for this purpose because there is no dependence on particle size [Hervig et al., 2009a], and these observations offer the greatest signal to noise. SOFIE observations during the coldest portion of the PMC season (1 June to 20 August) and from 81 to 91 km altitude are compared to modeled extinction ratios for cubic and amorphous ice considering various temperatures and AR in Figure 12. These results used all SOFIE observations when the bands 8–10 extinctions were greater than the noise. The comparison of observed and modeled band 10/8 versus band 9/8 extinction ratios (Figure 12a) shows that most observations are consistent with predictions for Ic. Including error bars in Figure 12a does not alter this conclusion (they were excluded for visual clarity). Recall that the optical signature for cubic and hexagonal ICE are considered to be identical [Warren, 1984], and that although we identify Ic, Ih cannot be ruled out. A few observations are consistent with predictions for Ia based on the Leger et al. indices, and model results based on the Hudgins et al. or Mukai and Kraetschmer indices are similar but generally farther from the observations. Probability distributions of the observed band 9/8 (Figure 12b) and band 10/8 (Figure 12c) extinction ratios indicate that very few observations are consistent with amorphous ice, even when taking the extinction ratios separately.
 Potential amorphous ice observations were identified as those where the bands 8–10 extinctions were above the noise and the combined band 9/8 and band 10/8 extinction ratios were close to any of the Ia model predictions (e.g., Figure 12a). For this purpose, the distance from a SOFIE observation (band 10/8 versus band 9/8 extinction ratio) to a line which fits all modeled Ia results was required to be less than 0.25. The observations are found to be consistent with amorphous ice less than 5% of the time at altitudes below ∼91 km (Figure 13). In contrast, the Ic detection probability peaks at ∼80% between 80 and 90 km (where air temperatures are lowest) (Figure 13). While most observations are clearly consistent with Ic, the remaining extinction ratios appear to be somewhat randomly distributed (Figure 12a), suggesting that identification of Ia in the observations may be accidental. The conclusion that amorphous ice is not observed by SOFIE near the polar summer mesopause is not considered to be a by-product of errors in the amorphous ice refractive indices because model results based on indices from three references are generally consistent.
 The possibility that Ia particles are below the SOFIE detection limit was explored with guidance from the results of Murray and Jensen , which suggest effective radii from 2 to 15 nm and concentrations (N) from 10 to 105 cm−3. Extinction at 3.064 μm (band 9) was calculated using the Ia refractive index from the work of Leger et al.  assuming monodisperse spherical particles (Figure 14). These results indicate that for N > 102 cm−3, populations with radii >4 nm should be detected by SOFIE and that 2 nm particles would be detected if N > 600 cm−3. Because the model predictions of Ia radii and concentration in the work of Murray and Jensen  allow both detectable and undetectable populations, the SOFIE results presented here do not definitively confirm or deny the existence of amorphous ice near the summer mesopause. Note that Murray and Jensen did not simulate the transition from Ia to Ic and that their Ia concentrations are therefore an upper limit. It is possible that Ia nucleates but is a transient phase due to rapid transformation into Ic. While SOFIE observations place constraints on the size and concentration of Ia particles that could be observed, the detection of transient Ia populations is a statistical problem that is not easily bounded.
 SOFIE observations near the polar summer mesopause have been used to derive vertical profiles of ice particle temperature and shape simultaneously. The results show that ice temperatures are 5–20 K colder than the current V1.022 SOFIE temperatures determined from CO2 transmissions. The particle axial ratios from this work are similar to but slightly more spherical than those derived from SOFIE according to the method of Hervig et al. [2009a]. SOFIE observations indicate that the amount of H2O that can enter the ice phase is related to ice concentration, leading to the suggestion that ice nucleation plays an important role in determining PMC formation and variability. Using ice temperatures in an equilibrium PMC model results in large overestimates of predicted ice mass densities. These results indicate that the equilibrium assumption ignores some important processes, with ice nucleation as a candidate because ice growth is apparently limited by the number of particles nucleated. Finally, SOFIE observations are consistent with the presence of cubic ice but suggest that amorphous ice is either absent or cannot be detected.
 This work was supported by the NASA/AIM mission funded by NASA's Small Explorers Program under contract NAS5-03132. We thank the AIM and SOFIE teams for years of dedication and service.