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Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds

The properties of planar ice crystals settling horizontally have been investigated using a vertically-pointing Doppler lidar. Strong specular reflections were observed from their oriented basal facets, identified by comparison with a second lidar pointing 4deg from zenith. Analysis of 17 months of continuous high-resolution observations reveal that these pristine crystals are frequently observed in ice falling from mid-level mixed-phase layer clouds (85% of the time for layers at -15C). Detailed analysis of a case study indicates that the crystals are nucleated and grow rapidly within the supercooled layer, then fall out, forming well-defined layers of specular reflection. From the lidar alone the fraction of oriented crystals cannot be quantified, but polarimetric radar measurements confirmed that a substantial fraction of the crystal population was well oriented. As the crystals fall into subsaturated air, specular reflection is observed to switch off as the crystal faces become rounded and lose their faceted structure. Specular reflection in ice falling from supercooled layers colder than -22C was also observed, but was much less pronounced than at warmer temperatures: we suggest that in cold clouds it is the small droplets in the distribution that freeze into plates and produce specular reflection, whilst larger droplets freeze into complex polycrystals. The lidar Doppler measurements show that typical fall speeds for the oriented crystals are 0.3m/s, with a weak temperature correlation; the corresponding Reynolds number is Re~10, in agreement with light-pillar measurements. Coincident Doppler radar observations show no correlation between the specular enhancement and eddy dissipation rate, indicating that turbulence does not control crystal orientation in these clouds.


Introduction
It has been recognised for some time that single pristine ice crystals often fall with their major axes horizontal over a certain range of Reynolds number. Polarimetric radar measurements and in-situ sampling led Hogan et al. 2002), and they are poorly simulated in numerical weather models at present (Bodas-Salcedo et al. 2008).
Vertical lidar measurements are an alternative and powerful means of observing these pristine crystal populations. If the crystals are planar (and given the lack of active ice nuclei at temperatures warmer than −8 • C this is the case for many ice-producing supercooled layers, Pruppacher and Klett 1997) their basal facets will tend to orient in the horizontal plane, and strong 'mirrorlike' specular reflections are observed as the lidar beam is reflected directly back to the receiver (Platt 1978. Simultaneous measurements at vertical and at a few degrees from zenith allows reliable identification of oriented crystal populations from the large difference in backscatter observed at the two angles (Thomas et al. 1990). In this paper we apply this technique to identify layers of planar crystals, and investigate some of their characteristics using a vertically pointing Doppler lidar at the Chilbolton Observatory in Hampshire. This instrument has operated continuously since September 2006, and the extensive data set allows us to provide a much more thorough statistical investigation of the conditions in which these crystals occur than has previously been possible, as well as providing many fascinating case studies. These are (to the authors' knowledge) the first measurements of Doppler velocities from specularly reflecting crystals, and this new information provides valuable insight into the fall speeds and likely sizes of the crystals involved.
The article comprises a review of previous observations and theory on crystal orientation and specular reflection, followed by details of the instruments used, a case study of a supercooled layer cloud precipitating oriented pristine crystals, and a statistical analysis of 17 months of continuous lidar data. A brief discussion concludes the paper.

Review of previous observations and theory
Although the orientation of ice crystals as they fall is not yet fully understood, we can identify some general features. Very small crystals ∼ 10µm in diameter are affected by rotational Brownian motion (thermal noise) and have an approximately random orientation as they fall. Drag is produced as vorticity generated at the crystal surface diffuses away (Batchelor 1967), and orienting torques are weak (Katz 1998): these crystals are unlikely to produce significant specular reflection. As the crystals grow bigger and the Reynolds number Re = vD/ν k increases to ∼ 1 (D here is the diameter of the crystal, v its fall speed, and ν k the kinematic viscosity of the air), the time taken to fall a distance equal to the particle diameter t = D/v becomes comparable to the time taken for the vorticity generated at the crystal surface to diffuse that same distance t ≈ D 2 /ν k , and the vorticity is 'left behind' as it falls. Stable, symmetrical vortices are formed behind falling discs (Willmarth et al. 1964, Pitter et al. 1973; numerical experiments by Wang and Ji (1997) confirm that these standing eddies also form behind hexagonal plate and broad-branch ice crystal shapes. If the crystal is inclined at an angle to the horizontal plane the asymmetrical drag acts to reorient the plate into the horizontal position: this reorientation is stabilised by viscosity, so oscillations around the horizontal are damped, and the particle falls stably and steadily (Willmarth et al. 1964).
Measurements of natural ice crystals by Kajikawa (1992) confirm that horizontal orientation occurs for a variety of planar crystal types (all of the P1 and P2 types defined by Magono and Lee 1966). As the crystals grow even larger, the inertial forces are too strong to be damped, and the horizontal orientation becomes unstable: this initially affects the wake downstream producing a slow pitching motion, whilst at larger Reynolds number the vortices begin to QJRMS QJRMS 00: 1-26 (2009) shed fluid behind the falling crystal leading to more irregular tumbling motions (Willmarth et al. 1964, Kajikawa 1992. Circular discs fall steadily between 1 < Re < 100; for the natural ice crystals measured by Kajikawa the maximum Reynolds number for stable orientation was in the range Re 50-100, and depended on the crystal habit. Provided that enough crystals are falling in the preferred Reynolds number regime, and they have sufficient faceted surface, strong specular reflection is possible. We note that even branched and dendritic planar crystals typically have a faceted plate at their centre (eg. Bentley and Humphreys 1964) which may allow specular reflection to occur. Platt (1977) first observed layers of unusually strong backscatter in a mixed-phase altostratus cloud.
Model calculations (Platt 1978) for populations of ice discs with various flutter angles showed that specular reflection was able to explain the vertical lidar observations. To clinch the interpretation, Platt et al. (1978) made scanning observations in a thin mid-level ice cloud where very strong backscatter was observed at vertical with almost almost no depolarisation (specular reflection at normal incidence does not rotate the plane of polarised light); scanning the lidar 2 • away from vertical decreased the measured backscatter by an order of magnitude, and increased the depolarisation ratio to 25%. At the same time, a sub-sun (similar to a light pillar, see below) was reported by a research aircraft flying above, confirming the presence of specularly reflecting crystals.
Since then, a number of similar observations have been made. Sassen (1984) observed strong backscatter and low depolarisation in the ice falling beneath a supercooled liquid layer embedded in a deep orographic cloud. Platt et al. (1987) identified layers of ice cloud with anomalously large backscatter and low depolarisation (integrated through the layer). Similarly, Hogan and Illingworth (2003) used integrated backscatter measurements to identify regions of strong specular reflection, and found it to occur exclusively between −10 and −20 • C for 20 days of lidar data. Thomas et al. (1990) Thomas et al. (1990) Accumulated mid-latitude Present in approximately 50% of cloud at all heights cirrus cases from 3 years most of the observations clustered around 9 km altitude Young et al. (2000) 8 mid-latitude case studies Observed 20% of time in layers −10 > Tm > −20 • C, mid-level, mixed-phase did not occur at other temperatures Hogan and Illingworth (2003) 20 days continuous data Observed 18% of time in cloud layers at 4 km, not observed at cirrus altitudes Noel and Sassen (2005) 6 cirrus cases Observed 22% of time for T > −20 • C, 35% in cold clouds T < −30 • C Hu (2007) 1 month of CALIPSO data Half of all optically thick ice cloud profiles affected Chepfer et al. (1999) 3 months POLDER data 37-50% of all ice-only cloud show specular glint Noel and Chepfer et al. (2004) POLDER, 31 ice cloud cases 80% of ice-only cloud showed specular glint of the amount of faceted surface on the crystal, and distribution of crystal orientations is required, and these quantities are not well constrained at present. As an example, to produce a backscatter of 10 −4 m −1 sr −1 only requires a concentration of ∼ 1m −3 ice discs 500µm in diameter if they are all perfectly aligned. However in practice a distribution of crystal orientations must always exist, and the above observations show that it will be much wider than the lidar field of view (66µrad for our monostatic Doppler lidar). This means that the true planar crystal population is much larger (1000× larger for a uniform 2 • flutter), and only a small fraction of the crystals are reflecting the lidar beam back to the receiver at any one time. Likewise, if only part of the crystal surface is faceted, a correspondingly larger crystal population is required. Linking crystal concentrations to observed backscatter values is therefore very difficult.
In addition to lidar measurements, passive measurements of radiances from space can also be affected as sunlight glints off oriented crystals: Chepfer et al. (1999) analysed 30 days of POLDER data and found that this happened in at least 40% of ice cloud. Note this instrument has a much wider field of view than lidar (6.7km pixel size). Noel and Chepfer (2004) looked at 31 ice cloud cases, and found 80% were affected by a specular reflection. Looking at the change in radiance around the glint direction and comparing to simulated reflectances, they estimated around 10% of crystals were horizontally oriented on average. Most recently, Bréon and Dubrulle (2004) used a crystal orientation model, combined with radiative transfer calculations and estimated that the fraction of oriented crystals was typically only 1%. Clouds containing supercooled liquid were excluded from these studies by detection of the rainbow scattering pattern from spherical liquid droplets.
Finally, Sassen (1980) took photographs of light pillars produced by artificial lights during snowfall. These optical phenomena are produced by oriented crystals between the light source and observer, which reflect the light from their horizontal facets, producing a pillar of light apparently extending vertically from the light source.
Any crystal wobble produces a spreading out of the pillar, as rays of light out of the plane formed by the light pillar, the light source and the observer are also reflected (to the observer), leading to a finite pillar width. By measuring this pillar width, Sassen estimated the characteristic wobble of the crystals in the snowfall, with observed values in the range 0.5-3 • . Correlating this width with the mean QJRMS QJRMS 00: 1-26 (2009)

Instruments and method
The key instrument in this study is a newly developed Full Doppler spectra are also recorded once per minute by both radars when cloud is present; the integration time for these spectra is 1 second.
A key parameter in this study is the lidar 'colour ratio' which we define as the ratio of the lidar backscatter measured by the 905nm ceilometer to that measured by the 1.5µm Doppler lidar: Colour ratio [dB] = 10 log 10 β 905nm β 1.5µm Under conditions where there is no specular reflection we expect this ratio to be greater than 0dB for ice particles, since the imaginary component of the refractive index of ice is 3 orders of magnitude larger at 1.5µm compared to 905nm (n = 4.7 × 10 −4 vs. n = 4.3 × 10 −7 , Warren 1984). This results in significant absorption of photons as they travel through the ice crystal, and a corresponding reduction in the backscatter † . As a guide to the magnitude of this effect, consider a ray of light as it undergoes a series of internal reflections through the ice crystal and back to the lidar telescope. According to the Beer-Lambert rule, its intensity will be reduced by a factor exp(−4πn x/λ), † We note that the attenuation of the lidar beam as it passes through a unit volume of cloud depends only the extinction of the ice particles within the cloud, which should be the same at both wavelengths (equal to twice the projected area of the crystals per units volume of air, assuming geometric optics). As a result the ratio of the measured attenuated backscatters should be identical to the ratio of the true (unattenuated) backscatters, provided that the ice cloud sampled by the two lidar beams is the same (ie. it is horizontally homogeneous on scales of a few hundred metres). We have neglected attenuation by aerosol particles, and multiple scattering between ice crystals. so for a total path length of x = 200µm, the backscatter at λ = 1.5µm is reduced by 3.4dB, whilst light at the ceilometer wavelength is essentially unaffected. We conclude that this differential absorption is likely to be significant for ice crystals in the atmosphere which are typically a few hundred microns to a few millimetres in size, and expect positive colour ratios > 0dB. This effect could in principle be used to measure crystal size in ice clouds, and will be explored in a separate publication.
To check the analysis above is correct, we have col-  figure 1 shows the histogram of the measured colour ratio in the ice-phase regions. It is apparent that the absorption effect is significant, with 95% of the data corresponding to colour ratios between +3 and +12 dB (ie. backscatter at 1.5µm reduced by a factor 2 to 16).
Almost no data were observed with colour ratios < 0dB -the 1% of pixels that were, revealed themselves on closer inspection to be isolated points resulting from occasional artefacts recorded by the ceilometer.
These off-vertical measurements contrast sharply with our observations with the 1.5µm Doppler lidar pointing directly vertical. In such cases we frequently observe colour ratios < 0 dB, in some cases as low as −25 dB (ie. 300× more backscatter at vertical). We conclude that these negative colour ratios must correspond to cases where the ice crystals are highly aligned in the horizontal, ie. the specular reflection from the horizontal crystal facets produces a strong signal in the vertical Doppler lidar data which is not present in the off-vertical ceilometer data, leading to the negative colour ratios. In what follows we will use this condition to identify regions of cloud where specular reflection is occurring (negative colour ratios) and where it is not (positive colour ratios). to break up allowing an unobscured view of the mixedphase cloud above: figure 2 shows the time series from the ceilometer and Doppler lidar for the period 01-10 UTC.
The off-zenith ceilometer clearly picks out the location of the thin supercooled liquid water layers, with a well defined primary liquid layer at the top (3800-4100m altitude), and intermittent secondary liquid layers embedded in the 1-2km deep ice fall streaks. The concentration of ice crystals is much lower than the concentration of cloud droplets, and so the backscatter is an order of magnitude smaller in the ice virga than in the supercooled liquid layer; the fall streak structure of the sedimenting ice crystals is clearly visible here. In the lowest 1km weak returns from the boundary-layer aerosol are visible in the lidar time series; the radar meanwhile is insensitive to these tiny aerosol particles.
The 0Z sounding from Herstmonceux (125km east of Chilbolton) is shown in figure 3, and the water-saturated layers at 3800-4100m and 2500-2700m seem to be consistent with the ceilometer imagery. The temperature at the top of the uppermost liquid layer was −15 • C; a slight temperature inversion was present at cloud top, and the air above was much drier. Wind speeds were relatively light; directional shear was observed in the ice virga, and is also apparent from the shape of the fall streaks in the radar time series, figure 2).
Data from the vertically-pointing Doppler lidar are also shown in figure 2, and it is immediately apparent that the backscatter in the ice virga is typically one order of magnitude (10 dB) larger than that recorded by the ceilometer, in spite of the increased absorption at 1.5µm.
This convinces us that oriented planar crystals are present in significant numbers in the virga. These crystals must be nucleated in the primary supercooled layer, growing by deposition in the vapour-rich conditions. The temperature in this water-saturated layer was between −12.5 and −15 • C leading to a large supersaturation over ice (see   To get an estimate of the terminal velocities of the oriented ice crystals, we have isolated areas with colour ratio < 0dB and calculated the mean lidar Doppler velocity over the 9 hour period. By averaging over several hours we expect to remove the mesoscale air motions observed in the detailed time series and obtain approximate values for the still-air velocities of the crystals. We estimate this to be −0.23ms −1 . Sassen's (1980) light pillar data indicated that there is likely to be a Reynolds number (Re ≈ 8) where the crystal flutter is minimised, and we expect that these crystals will provide the strongest weighting to the Doppler velocity measurements. Heymsfield and Kajikawa (1987) measured the fall velocity of planar ice crystals collected at the ground in northern Japan (1 km above sea level), and formulated velocity-diameter relationships from those observations. Using the pressure correction method of Beard (1980) we have used this data to calculate the ranges of Reynolds number and crystal diameter corresponding to a fall speed of 0.23ms −1 for various assumed crystal habits: these values are tabulated in (III).
We find Re ≈ 4, D ≈ 400µm for the most compact habit (hexagonal plates) increasing to Re ≈ 11, D ≈ 1200µm for the most open (stellar crystals). This range of Reynolds numbers is broadly consistent with Sassen's observations, but may be more robust since we are measuring velocities directly rather than median crystal diameters at the ground (this may be significant since the distribution of crystal orientations is not the same for all crystal diameters). Our observations are also consistent with Kajikawa's (1992) observations since the Reynolds numbers estimated here are smaller than the critical values where the fall motion becomes unstable.  = −15dB), decreasing steadily at lower altitudes. The backscatter profiles in the supercooled liquid are well matched, with slightly higher returns from the ceilometer due to the difference in backscatter to extinction ratio between the two wavelengths (see appendix A). This is evidence that the lidars are well calibrated, and that the attenuation through the ice virga is the same for both lidar beams, despite the enormous difference in backscatter.
The regions near cloud base with positive colour ratios (≈ +4 dB) are noted with interest. The fall off in lidar and radar backscatter in this region indicates that it is subsaturated with respect to ice. In these conditions evaporation tends to proceed from crystal edges since this is where the molecules are most weakly bound. If the subsaturation is very slight, evaporation occurs slowly in discrete layers, allowing the crystal to maintain its faceted structure (Hallett et al. 2001). If the crystal falls into drier air however, multiple steps form at the edges (Mason 1971) and the evaporation rate becomes limited by the diffusion of the molecules through the air, leading to strong vapour gradients at the edges and corners (Nelson 1998, Westbrook et al. 2008, producing smooth, rounded crystals (Nelson 1998). Rounding also appears to be more favourable at warmer temperatures (Hallett et al. 2001).
Given these results it seems clear that the regions of positive colour ratios are cloud where evaporating crystals have lost their faceted surfaces and become rounded, so specular reflection can no longer occur ‡ . This is consistent with calculations by Mishchenko et al. (1997) who showed that flat-faced discs could produce strong specular reflection, whilst thin oblate spheroids (ie. slightly rounded faces) could not.
An alternative explanation might be that the crystals have evaporated to the point where the crystals are too small to be horizontally oriented (tens of microns in diameter, see section 2). However, given that the radar and lidar Doppler velocities in this region are consistent with crystals several hundred microns in size, we discount this idea. ‡ This idea also appears to explain the vertical lidar observations of two mid-level clouds by Uchino et al. (1988) who were puzzled when they found that that whilst the returns from the middle of their clouds were characteristic of specular reflection (very high backscatter, very low depolarisation ratios), the returns from the base of the virga were characteristic of normal ice cloud (much lower backscatter, depolarisation ratios increased to ≈ 30%), and that this was co-located with a rapid decrease in relative humidity with respect to ice.
Identification of these regions where specular reflection is 'switched off' may therefore be a useful observational tool to determine if the crystals are evaporating in layers or losing their shape. The latter case is also evidence that the whole crystal surface is close to ice saturation (Nelson 1998), and that the crystal evaporation rates are governed by the standard electrostatic approximation (Mason 1971, Westbrook et al. 2008. To investigate the initial growth of the ice at the top the cloud we have averaged the vertical 94-GHz radar Doppler velocity and reflectivity over the whole period corresponding to this velocity is rather sensitive to the assumed habit, ranging from 800µm for hexagonal plates to 3500µm assuming stellars (Heymsfield and Kajikawa 1987). We note that over the depth of the supercooled layer the reflectivity increases by about 6dB, which corresponds to a doubling of the average crystal mass over that distance (since reflectivity is, to first order, proportional to mass 2 ) whilst Ryan et al. (1976) observed crystal masses to increase by a factor of ten between 50 and 150 seconds of growth. The comparison is not so clear-cut because of non-Rayleigh scattering effects and sedimentation, but the implication is that the crystals are not simply nucleated at cloud top and grow whilst steadily falling falling through the water saturated layer, but are also mixed through the layer as the air is gently turned over, smoothing out some of the reflectivity structure. It may be that crystals are also nucleated throughout the depth of the liquid layer rather than only at the top, which would have a similar effect.
Below 3800m there appears to be relatively little change in reflectivity or velocity, suggesting little growth is occuring -presumably the relative humidity falls off sharply to near ice saturation here (there is some evidence for this in the radiosonde profile, figure 3). in a 1km thick layer with droplets ascending at 1ms −1 ; our example is much thinner and more weakly forced, and our estimated liquid water path is an order of magnitude smaller.  . We also note that the exact crystal habit is quite sensitive to the growth temperature, and given the range of temperatures spanned by the supercooled layer, it is quite likely a range of planar habits develop simultaneously, and are then sorted as they fall. The very largest values of Z DR (≈ 3dB) seem to be found only close to the very top of the cloud: presumably these are small platelike crystals in the early stages of growth, with a volume fraction close to unity (see figure 9); the crystals lower down will likely have been growing for longer, developing tenuous branches, perhaps aggregating, and will therefore will have a lower volume fraction and lower Z DR . The observation of strong differential reflectivity even at the very base of the virga where the crystals are evaporating is further evidence that the lack of specular reflection in the evaporation zone is due to the crystals becoming rounded (whilst still maintaining their horizontal orientation) rather than their orientation being disrupted, for example by turbulence associated with evaporating cooling.

17 months of statistics
We now present a statistical analysis of specular reflection from 17 months of continuous observations. A number of the studies cited in section 2 have calculated statistics on the occurrence of specular reflection, as summarised in We identify cloud as range gates where the backscatter is greater than 5 × 10 −7 m −1 sr −1 from both lidars.
The presence of supercooled liquid droplets is inferred by backscatter from the off-vertical ceilometer exceeding 10 −4 m −1 sr −1 and this range gate is flagged and removed.
The backscatter from the three range gates below this are also removed from the analysis since these may also contain liquid, and all the data from range gates above is also discarded since liquid cloud may well have significant structure on the scale of hundreds of metres and as a result there may be some differential attenuation between the zenith and off-zenith lidar beams, which could perhaps lead to an ambiguous interpretation of colour ratios measured from ice cloud above. The remaining ice cloud QJRMS  Figure 10. Percentage of ice cloud which is identified as containing specularly reflecting ice crystals, binned as a function of temperature. A distinct peak is apparent close to −15 • C, where 40% of ice cloud measured by both lidars is observed to be influenced by specular reflection. At temperatures colder than −30 • C this fraction is only 10%. These figures are likely underestimates, and the dashed line shows the fraction of cloud affected if all colour ratios < +3dB are counted (see text). The total number of ice pixels in each temperature bin ranged from 3 × 10 4 in the coldest bin, to 1.5 × 10 5 in the warmest.
is divided into data with colour ratios < 0 dB (specular reflection) and data with colour ratios > 0 dB ('normal' ice cloud). Note that the lidar signal is attenuated even in

Occurrence by temperature
Using the method described above we have calculated the fraction of cloud that is observed by both lidars and which is identified as containing specularly reflecting ice crystals. Overall we find that of the 1.55 × 10 6 ice cloud pixels analysed, 26% were affected by specular reflection.
Breaking this fraction down as a function of temperature reveals further insight, as shown by the horizontal bars in figure 10 -it is apparent that most of the specular reflection is concentrated at temperatures warmer than −25 • C, with a maximum in the region of −15 • C where over 40% of ice cloud observed is affected by specular reflection. These observations seem consistent with the expectation that planar monocrystals typically grow in the temperature range −9 to −22 • C (Pruppacher and Klett 1997). There is no obvious 'gap' corresponding to the window of column/needle growth between −3 and −8 • C, but since there are few ice nuclei at these warm temperatures anyway, the specular in this region is likely planar crystals formed at colder temperatures sedimenting in from above. The maximum occurrence around −15 • C seems sensible, since thin planar crystals are well known to grow in this temperature region.
At temperatures between −30 and −40 • C only around 10% of cloud is affected by specular reflection.
This is a significantly smaller fraction than observed in cirrus clouds by Thomas et al. (1990), although their scanning lidar arrangement may be a more sensitive tool to detect weak specular reflection, since such a setup is not complicated by differential absorption effects (see below). Figure 11 shows the observed distribution of lidar colour ratios as a function of temperature. The lack of bimodality around the 0dB mark suggests that in fact specular reflection is likely to be occurring weakly in some of the cloud where we measure positive colour ratios. This is a result of the increased absorption at 1.5µm compared to 905nm as discussed in section 2.
Specifically, this would correspond to cases where the specular reflection component of the backscatter is of comparable magnitude to the backscatter from the other ice particles in the cloud, and the overall colour ratio is positive (our off-zenith measurements indicated that ice particles which are not affected by specular reflection yield colour ratios in the range +3 to +12dB).
The distinction between specular and non-specular ice is most obvious at the mid-level temperatures between −10 and −20 • C, where a long straight tail extending out to −20dB is apparently distinct from a more bell shaped distribution for normal ice cloud, with the two curves intercepting at approximately +3dB. At temperatures colder than −30 • C the distribution is much narrower with relatively few colour ratios < 0dB, and the magnitude of the specular reflection (as characterised by the colour ratio) in these cold clouds is much weaker than at We note that if it were assumed that all values less than +3dB in fact corresponded to some specular reflection occurring in the lidar sample, the overall fraction of ice cloud affected would rise from 26% to 40%. The occurence by temperature following this assumption is shown by the dashed line in figure 10. Our estimates of the frequency of specular reflection should therefore be considered as lower bounds on the true occurence, and this emphasises the large fraction of cloud in which specular reflection is possible, especially at the mid-levels. In the subsections that follow we will use the 0 dB threshold to identify cloud as specular or not, ie. where the effect is strong enough to be measureable without ambiguity.

Fall speeds
Applying the method of identification above, we can use the Doppler velocity measurements from the vertical lidar to study how fast the oriented crystals fall. The frequency distribution of Doppler velocities for all cloud affected by specular reflection is shown in figure 12, which also where the fall orientation is stable and the fall speeds are relatively slow. The corresponding Reynolds numbers for various assumed crystal habits have been calculated using Heymsfield and Kajikawa's (1987) relationships. Segregation of the data by colour ratio (not shown for brevity) shows a slight decrease at the most extreme colour ratios (10-20%); however this decrease is much smaller than the variation between the different assumed crystal habits (Re ≈ 5 for hexagonal plates vs Re ≈ 20 assuming stellars). In any case it seems that the specular backscatter and Doppler velocity is weighted to crystals falling with Re ∼ 10, with a factor of 2 uncertainty. This is consistent with Sassen's light pillar observations, and the case study in section 4.
Plotting the Doppler velocity distribution for specular crystals as a function of temperature yields figure 13.
The average particle fall speed for normal ice cloud was calculated by Westbrook and Illingworth (2009) and was found to increase systematically with temperature from the influence of larger particles and broader size spectra at warm temperatures. In contrast to this, the velocity distribution for specularly reflecting crystals shows a rather weaker variation with temperature, with average crystal fall speeds increasing from 0.25ms −1 at −35 • C, to 0.3ms −1 at −15 • C; there appears to be a slight broadening of the distribution for the warmest clouds, with an average velocity of 0.4ms −1 at −5 • C. Possibly this corresponds to planar crystals formed at the mid-levels which thicken as they fall into air temperatures characteristic of columnar growth, increasing their weight relative to their drag, and allowing them to sediment more quickly for a given Reynolds number. As in section 4 the mean Doppler velocities and implied crystal Reynolds numbers are lower than the maximum stable values found by Kajikawa (1992) for all assumed crystal types.

Crystal alignment
The correlation between turbulent air motion and colour ratio measurements has also been investigated, to determine whether the horizontal orientation of the ice crystals is affected by the turbulent eddies. The eddy dissipation rate ε was estimated as described in section 4, and the results were binned by colour ratio and dissipation rate.
The resulting mean and standard deviation of log 10 is shown in figure 14, and we observe that there is essentially no correlation between colour ratio and turbulence.
There is a hint that the standard deviation is slightly lower for the most extreme colour ratios; however this is because there are very few samples here. These statistics are consistent with the case study in section 4. Klett (1995) and Bréon and Dubrulle (2004) performed theoretical calculations of the influence on turbulence on crystal orientation, and these also indicate that for the observed levels of ε, crystals can be oriented to well within 1 • of horizontal. Our observed range of ε values are consistent with other ice cloud observations (eg. Gultepe andStarr 1995, Bouniol et al. 2003). We note that the bulk of our values are an order of magnitude lower than in Klett's calculation for 'weak' turbulence, and suggest that in most stratiform clouds, the ability of turbulent eddies to influence the air flow on the scales relevant to ice crystals is probably minimal.
The lack of correlation observed above leads us to believe that the colour ratio is primarily sensitive to the fraction of ice particles which are pristine planar crystals with Re close to 10.

Supercooled layers
As mentioned in section 3, it is our experience that super- with specular ice crystals precipitating out. To investigate this behaviour in more detail, figure 16 shows the distribution of colour ratios measured in the specular ice, as a function of supercooled layer temperature. This distribution demonstrates that specular reflection is strongest in the ice falling from supercooled layers which lie between −10 and −20 • C (where the droplets will freeze into planar monocrystals eg. Ryan et al. 1976 Klett 1997), and one may hypothesise that the observed specular reflection is the result of Parry-oriented columns (major axis horizontal, prism face horizontal), rather than plates; such a case has been documented by Sassen and Takano (2000). However observations of the associated Parry arc are very rare, and Sassen and Benson (2001) have argued that in general only planar ice crystals will produce specular reflection.
Perhaps a more likely explaination of our observations is that planar crystal growth is occurring at colder temperatures than expected. Planar crystals have been observed to grow at cold temperatures in a number of studies. Aufm Kampe et al. (1951) grew mainly platelike polycrystals from a supercooled water cloud in a cold chamber at −22 • C and −29 • C, along with a smaller fraction of simple plates and columns. Hallett (2002,2004)  We suggest therefore that our observed specular reflection in cold clouds is the result of small cloud droplets freezing into simple (thick) plates which produce specular reflection, whilst the larger droplets in the droplet distribution freeze into irregular polycrystals.
Whereas in clouds warmer than −20 • C the vast majority of cloud droplets will freeze as monocrystals irrespective of droplet size, for colder clouds an increasing fraction of the droplets frozen will be polycrystalline, and incapable of producing specular reflection.
We note that although on average specular reflection in cold clouds is much weaker, there are still individual cases where it is large (≈ −10dB) -these may be examples where the droplets are particularly small. For the low liquid water content stratiform clouds which dominate our observations, we anticipate there may be a stronger weighting towards smaller droplets (and therefore more single crystals) than in more convective-type clouds. Note that the droplets in Heymsfield et al. 's (1991) altocumulus layer with specular reflection in the virga below had a mean diameter of only ≈ 10µm.

Layers of planar crystals
Our observations (eg. section 3) indicate that specular crystals form widespread layers stretching over many QJRMS QJRMS 00: 1-26 (2009) kilometres; this also fits in with previous lidar observations (Platt 1977 we observed layers from ∼ 1 km up to more than 100 km in extent. This large variability is also consistent with Korolev et al.'s observations. The depth of the specular layers has also been characterised -we estimate a mean depth of 600m, approximately independent of temperature. This figure is a convolution of the true layer depth and the extinction of the lidar beam in optically thick clouds, and is likely an underestimate. 5.6 Backscatter and radar reflectivity Figure 18 shows distributions of attenuated backscatter recorded from each lidar, with separate bars indicating specular and normal ice cloud. The data from the vertically pointing 1.5µm lidar shows that the backscatter from clouds affected by specular reflection is typically a factor of 5dB larger than that recorded for normal clouds. From the 905nm data we observe the opposite, ie. clouds where specular reflection is present typically have a backscatter which is typically around 5dB lower than that recorded in normal ice cloud. This suggests that cloud where specular reflection is occurring may tend to be optically thinner than average. However, the interpretation of this result is subtle since the lidar is attenuated as it passes through the cloud, and our experience suggests that specular reflection is rarely observed at cloud base (because the crystal facets become rounded as they evaporate), which may bias the statistics towards lower values of off-zenith backscatter.
Radar reflectivities have been measured from the 35GHz cloud radar at Chilbolton, and data were analysed for the 7 month period June 2007 to January 2008. Figure   19 shows the distribution of radar reflectivity measured in ice clouds which are also observed by both lidars, and it appears that the reflectivity distribution in clouds which are affected by specular reflection (black bars) is almost identical to the reflectivity distribution for all ice cloud (grey lines). The suggestion then is that the ice water content in cloud where there is specular reflection is representative of the complete subset of ice cloud observed by both lidars. A case study of a long-lived supercooled layer with planar ice crystals precipitating below was presented as a typical scenario where strong specular reflection is likely to be observed, and the backscatter at vertical was a factor of 30 (15dB) larger than observed off-zenith. Simultaneous polarimetric radar measurements confirmed that the general crystal population was well oriented with values of Z DR typically ≈ 2dB. Observations at the base of the ice virga reveal that specular reflection does not occur in this region, even though the Z DR measurements show that the crystals are still well oriented, and this is evidence that the crystals are evaporating rapidly and becoming rounded in shape. This may be a useful observational technique to identify whether crystals are evaporating layer-by-layer at small subsaturations, or whether the evaporation rate is rapid and uncontrolled in drier air (Nelson 1998, Hallett et al. 2001. High temporal resolution Doppler radar measurements reveal that there was appreciable convective overturning at cloud top due to radiative cooling of the liquid layer to space, and this turbulence extended down into the ice virga. Despite this turbulent air motion ( ≈ 3 × 10 −4 m 2 s −3 ), strong specular reflection was still observed in this region of virga, indicating that turbulence does not have a strong effect on crystal orientation in stratiform clouds. This is backed up by the lack of correlation between the measured colour ratio and in section 5.3.
Lidar Doppler measurements indicate that these horizontally oriented crystals fall slowly, with a mean velocity of ≈ 0.3ms −1 and a weak temperature dependence, in contrast to normal ice cloud where the observed sedimentation velocities in warm clouds are twice as fast as those at −40 • C. Using velocity-diameter relationships, we estimate that the most strongly oriented planar crystals have a Reynolds number in the region of Re ∼ 10 with a factor of 2 uncertainty. This value is consistent with previous measurements of light pillars by Sassen (1980 Finally, whilst we have observed that specular reflection is strong in many cases, we see from figure 11 that in the majority of cloud it occurs at a relatively weak level with colour ratios close to 0 dB, and indeed at all temperatures the modal colour ratio is positive (ie. no specular reflection). This lends support to the in-situ observations of Korolev et al. (2000) which indicate that most ice particles in thick stratiform clouds are 'irregular', probably a mixture of complex polycrystals and aggregated particles (Stoelinga et al. 2007), but with few planar monocrystals mixed in. The important exception to this rule appears to be thin supercooled layer clouds, particularly those in the range −10 to −20 • C, which our measurements indicate are a prolific source of pristine planar monocrystals. have amplitude E 0 . Resolving the incident wave along the spheroid's major and minor axes the amplitudes are: E 0 − along major axis 1 (parallel to H) (2) E 0 / √ 2 − along major axis 2 (⊥ to H) E 0 / √ 2 − along minor axis (4) inducing dipole moments: E 0 α major − in the H channel (5) 0.5E 0 (α major + α minor ) − in the V channel (6) where α i=major,minor are the polarisabilities: The geometric factors L i for spheroids are detailed in Bohren and Huffman (1983); the permittivity of the air ice mixture is calculated using Maxwell-Garnett's rule for spherical inclusions (see Bohren and Huffman) -this prescription depends only on the volume fraction of ice in the mixture f v = (volume of ice)/(volume of spheroid).
The differential reflectivity is then simply: Z DR = 10 log 10 4 α major α major + α minor 2 (8) which is maximised for thin plates of solid ice (f v = 1) at Z DR = 3.6dB. Hogan et al. (2002) have performed more extensive calculations of this parameter for 0 • elevation.