Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain

Polarization lidar observations ofbackscatter phase matrices from

oriented ice crystals and rain

Matthew Hayman,1,∗ Scott Spuler,1 and Bruce Morley1

1National Center for Atmospheric Research, Earth Observing Lab, Boulder, CO, 80307, USA∗[email protected]

Abstract: Oriented particles can exhibit different polarization propertiesthan randomly oriented particles. These properties cannot be resolved byconventional polarization lidar systems and are capable of corrupting theinterpretation of depolarization ratio measurements. Additionally, the typi-cal characteristics of backscatter phase matrices from atmospheric orientedparticles are not well established. The National Center for AtmosphericResearch High Spectral Resolution Lidar was outfitted in spring of 2012to measure the backscatter phase matrix, allowing it to fully characterizethe polarization properties of oriented particles. The lidar data analyzedhere considers operation at 4◦, 22◦ and 32◦ off zenith in Boulder, CO,USA (40.0◦N,105.2◦W). The HSRL has primarily observed oriented icecrystal signatures at lidar tilt angles near 32◦ off zenith which correspondsto an expected peak in backscatter from horizontally oriented plates. Themaximum occurrence frequency of oriented ice crystals is measured at 5km, where 2% of clouds produced significant oriented ice signatures by ex-hibiting diattenuation in their scattering matrices. The HSRL also observedoriented particle characteristics of rain at all three tilt angles. Orientedsignatures in rain are common at all three tilt angles. As many as 70% ofall rain observations made at 22◦ off zenith exhibited oriented signatures.The oriented rain signatures exhibit significant linear diattenuation andretardance.

© 2014 Optical Society of America

OCIS codes: (010.3640) Lidar; (010.1350) Backscattering; (010.1615) Clouds; (010.2940) Icecrystal phenomena.

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#209739 - $15.00 USD Received 8 Apr 2014; revised 24 Jun 2014; accepted 25 Jun 2014; published 3 Jul 2014(C) 2014 OSA 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016976 | OPTICS EXPRESS 16976

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1. Introduction

Conventional polarization lidar instruments perform two polarization measurements [1–4]. Onedetection channel corresponds to the original transmitted polarization state (the parallel chan-nel), and the second channel corresponds to the polarization orthogonal to the original trans-mitted state (the perpendicular channel). The polarization properties of the scattering volumeare subsequently described as the depolarization ratio written

δ =N⊥N‖

, (1)

where N⊥ is the background subtracted signal on the perpendicular channel and N‖ is the back-ground subtracted signal on the parallel channel.

It should be observed, however, that the depolarization ratio is not necessarily a completedescription of the polarization properties of the scattering volume. For a theoretically completedescription, we generally use the backscatter phase matrix, a sixteen element Mueller matrixcapable of representing all polarization effects exhibited by scattering volumes.

In most cases, polarization lidar data is interpreted by assuming the scattering volume con-sists of randomly oriented particles. A volume consisting of randomly oriented particles is


macroscopically isotropic which means the backscatter phase matrix is rotationally invari-ant [5]. This property combined with reciprocity gives a backscatter phase matrix of randomlyoriented particles with three degrees of freedom and the form [5, 6]:

F(π) = β

⎡⎢⎢⎣

1 0 0 f14

0 1−d 0 00 0 d−1 0f14 0 0 2d−1

⎤⎥⎥⎦ . (2)

The scalar β is the volume backscatter coefficient and d is the depolarization of the volume.The f14 element is the result of circular diattenuation (also called circular dichroism) in theindividual particle scattering properties. This term is commonly ignored and is zero if the par-ticles are axially symmetric (therefore each particle has f14 = 0) or their mirror particles existin equal numbers (a mirror particle would have an f14 element opposite the original particleand therefore cancels the term in the ensemble matrix) [7]. Measurements of this term reportedin [5] as well as this work suggest this element is typically zero in atmospheric scattering pro-cesses. This means that the most commonly assumed atmospheric backscatter phase matrix hastwo degrees of freedom.

The relationship between the depolarization ratio δ and d depends on the ellipticity of thepolarization lidar state (generally linear or circular polarizations), but assuming f14 is zero, theirrelationship is monotonic, invertible and fully defined. Because the medium is macroscopicallyisotropic, direction of incidence is omitted from the backscatter phase matrix argument andonly the scattering angle is needed to describe the scattering geometry (π for backscattering).

While there is often good argument for the assumption of random orientation, there areknown cases where particles in the atmosphere exhibit preferential orientation. In the mostgeneral interpretation, the backscatter phase matrix has ten degrees of freedom. Making no as-sumptions about the orientation or symmetries but assuming reciprocity applies, the scatteringmatrix is given by [7]

F(ϕ)(�ki,−�ki) = R(ϕ)F(�ki,−�ki)R(ϕ) = β

⎡⎢⎢⎢⎣

1 f (ϕ)12 f (ϕ)13 f (ϕ)14

f (ϕ)12 f (ϕ)22 f (ϕ)23 f (ϕ)24

− f (ϕ)13 − f (ϕ)23 f (ϕ)33 f (ϕ)34

f (ϕ)14 f (ϕ)24 − f (ϕ)34 f (ϕ)44

⎤⎥⎥⎥⎦ , (3)

where R(ϕ) is a Mueller rotation matrix of angle ϕ . The superscript (ϕ) denotes that the matrixelements are from the matrix with ten unique elements. The rotation term allows that the matrixhas some linear coordinate basis given by the angle ϕ , that would set one or more matrixelement to zero (thus ϕ represents one of the ten degrees of freedom in the matrix). Whenwe cannot assume randomly oriented particles, the scattering medium is not macroscopicallyisotropic so the backscatter phase matrix is a function of the direction of incidence,�ki.

Rotating the matrix F(ϕ)(�ki,−�ki) by the angle −ϕ allows us to obtain the matrix in its basecoordinates F(�ki,−�ki). Note the rotation angle ϕ is dictated by the angle between the instru-ment’s polarization coordinate basis and the s-polarization of the orientation plane (most oftenassumed to be the horizontal plane in atmospheric scattering). In this work we assume that theparticles under interrogation are not optically active. Beyond the presence of strong magneticfields in the ionosphere or lightning there seems to be little argument for this polarization effectin optical atmospheric scattering. From these assumptions we obtain the form of the scattering


matrix in its base coordinates as [5]

F(�ki,−�ki) = β

⎡⎢⎢⎣

1 f12 0 f14

f12 f22 0 00 0 f33 f34

f14 0 − f34 f44

⎤⎥⎥⎦ , (4)

where there are now six degrees of freedom (we report seven matrix elements, but reciprocityreduces the number of degrees of freedom to six [8]).

When the scattering volume is described by Eq. (4), the depolarization ratio is not sufficientto accurately determine the polarization properties of the scattering volume, and the measuredvalue of the depolarization ratio depends on the degree-of-polarization (DOP), linear polar-ization angle and ellipticity of the polarization state used to interrogate the volume [9]. Forpolarized incident light (DOP = 1), the depolarization ratio is generally given by

δ =1+2 f14 sin2χ + f44 sin2 2χ − cos2 2χ

(f22 cos2 2ψ − f33 sin2 2ψ

)

1+2 f12 cos2χ cos2ψ − f44 sin2 2χ + cos2 2χ(

f22 cos2 2ψ − f33 sin2 2ψ) , (5)

where ψ is the linear angle and χ is the ellipticity angle of the lidar’s polarization state. For lin-ear depolarization lidar χ = 0 or π

2 and for circular depolarization lidar χ =±π4 . The value of

ψ is generally not specified in linear depolarization lidar. Linear depolarization ratio measure-ments of oriented particles depend on four scattering matrix terms (β , f12, f22 and f33) whilecircular depolarization ratios depend on three terms (β , f14 and f44). Observations reportedhere and by [5] indicate that f14 is typically zero, thereby reducing the dependency of circulardepolarization to two matrix elements [10].

Figure 1 considers two cases of oriented scatterers and the possible linear depolarization ra-tios (χ = 0) as a function of the lidar’s linear polarization angle, ψ . The red case uses scatteringmatrix measurements of oriented ice crystals and the blue case is calculated using scatteringmatrix measurements of oriented rain drops. The oriented ice crystals analyzed for this plotproduce linear depolarization ratios between approximately 0.15 and 0.25 depending on thelidar’s linear polarization state. The depolarization ratio of this instance of rain may be any-where between 0.1 and 0.6 depending on the linear polarization state, ψ , used to interrogatethe volume. Thus, the presence of oriented particles can contribute significant ambiguity todepolarization ratio measurements.

It should be noted that the presence of oriented particles is necessary but not sufficient togive ambiguous depolarization ratio measurements. To observe the matrix described in Eq. (4),three conditions must be met:

1. A subpopulation of the particles must have a non-uniform orientation distribution.

2. The particles’ orientation distribution must not exhibit rotational symmetry about theobserving instrument’s line of sight.

3. The backscatter from the oriented population cannot be significantly diluted by randomlyoriented populations [11].

Thus, vertically or nadir directed lidar observing high backscatter specular reflections from hor-izontally oriented plates satisfy conditions (1.) and (3.), but because the orientation distributionexhibits rotational symmetry about the vertical (therefore lidar line-of-sight), condition (2.) isnot satisfied. The depolarization ratio is still sufficient for describing polarization properties ofthe volume though the signal is dominated by oriented plates. If the lidar is tilted, or the parti-cles exhibit azimuthal orientation, conditions (1.) and (2.) are met, but significant backscatter


Fig. 1. Example of measured depolarization ratio as a function of linear polarization anglefor rain (blue) and oriented ice crystals (red). The matrices used for this simulation wereobtained from an observation of oriented ice crystals on June 24, 2012 and rain on July 9,2012 over Boulder, CO, USA (40.0◦N,105.2◦W).

from randomly oriented particles, also in the volume, could prevent any significant observationof the oriented scattering matrix terms (condition (3.) may not be satisfied).

It has been noted in [12, 13] that horizontally oriented plates have strong backscatter crosssections at lidar tilt angles near 32.5◦. It is most likely that conditions (2.) and (3.) are satisfiedby oriented plates when the lidar is tilted at this angle. Oriented columns are expected to exhibita similar backscatter peak for lidar tilt angles near 57.5◦ but practical limitations prevent usfrom operating the lidar at such a large tilt angle.

In the spring of 2012, the National Center for Atmospheric Research (NCAR) High SpectralResolution Lidar (HSRL) was modified to measure the full backscatter phase matrix of orientedparticles [14]. The instrument uses temporally varying transmitted and measured polarizationstates at a wavelength of 532 nm to reconstruct the ten element backscatter phase matrix de-scribed by Eq. (3). After obtaining the ten element matrix, it is reduced to the form in Eq. (4) byapplying a linear rotation that best reflects the expected block diagonal form in Eq. (4). Becausethe HSRL performs a polarimetrically complete measurement, it cannot exclusively operate inthe eigen states of of mirrors, beamsplitters, etc (a technique common to many conventionalpolarization lidar). All independent polarization terms are accounted for including partial po-larization of the laser, mirror retardance/diatenuation and imperfect polarization analyzers. Thedetails of the measurement as well as a complete list of all 30 calibration terms are providedin [14].

Observations of full scattering matrices reported in [5] suggest that preferential azimuthalorientation over western Siberia appears to the be the rule, more than the exception. Morethan 90% of observed ice clouds had non-zero f12 scattering matrix elements ( f12 = 0 when thevolume is composed of randomly oriented particles). The question as to whether this orientationbehavior is common in other regions remains uninvestigated.

The results presented in [5] represent the only polarimetrically complete observations ofbackscatter polarization properties from oriented particles found in the atmosphere. As a result,


the general impact of oriented particles on depolarization lidar data remains largely unquanti-fied. Further, optimization and development of new polarimetic lidar techniques will inevitablyrequire some a priori information about the scattering matrices common in the atmosphere. Theintent of this work is to provide some additional insight into observed polarization propertiesof oriented particles in the atmosphere, though these observations are limited to brief periodsat one geographical location (Boulder, Colorado, USA, 40.0◦N,105.2◦W).

2. Observations

We filter for oriented particles in HSRL measurements by resolving non-zero off diagonalterms, f12 and f34, of the scattering matrix. The f12 element is the linear diattenuation ofthe scattering matrix and describes the particles’ preference for scattering one linear polar-ization over its orthogonal state [9]. The f34 element is most closely associated with retardancewhich generally transforms the ellipticity of the backscattered radiation. The scattering matrixis recorded as the set of ten scattering matrix elements, F(ϕ)(�ki,−�ki) in Eq. (3), to account forlinear rotation [14]. This matrix is then reduced to the seven element form shown in Eq. (4)by applying the necessary Mueller matrix rotations. The reduced matrix data is analyzed forstatistically significant deviation from zero in the f12 and f34 terms by awarding an orientationindex value based on the computed signal-to-noise. The orientation index is bounded betweenzero and one by using the definitions

O12 = erf

( | f12|σ12

√2

), (6)

and

O34 = erf

( | f34|σ34

√2

), (7)

where erf is the error function or Gauss error function and σ jk is the standard deviation of thejk element of the scattering matrix. These functions provide a bounded scale for assessing thelikelihood that a scattering volume has statistically significant oriented scattering terms.

The NCAR HSRL has operated at tilt angles of 4◦ (as close to vertical as possible with this in-strument), 22◦ and 32◦. The observational periods analyzed in this work and their durations areshown in Table 1. All observations were made in Boulder, Colorado, USA (40.0◦N,105.2◦W).Observations during summer and late fall 2012 at 22◦ and 32◦ tilt are analyzed, while anal-ysis of near zenith operation (4◦) is limited to late summer 2013. The selection of these datasets for analysis is based on the lidar’s operational status, data set duration, and quality of dataand calibrations. The number of observation days at 4◦ off zenith are substantially less than thespecified duration. This is because the lidar had several days in late August and early Septemberwhere the transmit laser was not locked to the iodine absorption line in the molecular receiverchannel, so retrieval of the backscatter ratio was not possible.

Table 1. HSRL Data Sets Analyzed

Start Date End Date Observation Days Tilt AngleJune 13, 2012 July 9, 2012 24 32◦July 11, 2012 Sept. 2, 2012 54 22◦Nov. 16, 2012 Dec. 9, 2012 24 22◦Dec. 12, 2012 Dec. 22, 2012 13 32◦Aug. 17, 2013 Sept. 25, 2013 25 4◦


Figure 2 shows a clear case of oriented ice observation on December 18, 2012. The topplot shows the particle linear depolarization. The plots have been filtered to highlight cloudscattering by removing signals that have a backscatter ratio less than 2, where backscatter ra-tio is computed as the total backscatter divided by the molecular backscatter. The depolariz-ation ratio is calculated based on the measured f44 element which reflects the HSRL’s originalconfiguration that measured circular depolarization. The results are reported as an equivalentlinear depolarization ratio. The bottom plot shows the resulting maximum orientation index,max(O12,O34). In this case the oriented particles are exclusively identified by non-zero f12 el-ements. For oriented ice crystals, the f34 element is not typically large enough for the HSRL toresolve a non-zero value, which is consistent with findings in [5].

Oriented ice crystals are observed just below or in very close proximity to liquid water clouds(determined by their low depolarization). This observation, like most oriented ice crystal ob-servations seen by HSRL during this field test, appears to be a case of ice virga precipitatingout of liquid water or mixed phase clouds, which is qualitatively similar to observations ofhorizontally oriented plates reported in [15].

Fig. 2. A case of oriented ice crystal observations from December 18, 2012, Boulder, CO,USA (40.0◦N,105.2◦W) where the lidar is tilted 32◦ off zenith. The top plot shows theequivalent particle linear depolarization ratio (calculated using the f44 element). The bot-tom panel shows the orientation index used as a metric for identifying regions containingoriented particles. Water or mixed phase clouds are precipitating ice virga. Oriented parti-cles are observed in this virga at 2 and 3 km, just below the liquid cloud base.

Figure 3 shows observation of oriented rain drops which occur when drag forces cause theotherwise round drops to flatten along the vertical direction [16, 17]. In this case, it is a combi-nation of f34 and f12 that allows the oriented drops to be identified.

During the summer of 2012 several forest fires were burning in Colorado and their smoke


Fig. 3. A case of oriented rain observations from July 17, 2012, Boulder, CO, USA(40.0◦N,105.2◦W) where the lidar is tilted 22◦ off zenith. The top plot shows the equivalentparticle linear depolarization ratio (calculated using the f44 element). The bottom panelshows the orientation index used as a metric for identifying regions containing orientedparticles. Large rain drops flatten as they fall and have strong oriented particle polarizationsignatures.

frequently appears in the lidar profiles. The smoke can have a backscatter ratio exceeding 2(the criteria previously used to filter for clouds) so we have added an additional criteria tothe processed data sets shown below. A scattering volume is only counted as a cloud if thebackscatter ratio is greater than 2 and

BSR ≥−10 f44 −2, (8)

where BSR is the measured backscatter ratio and f44 is the scattering matrix element fromEq. (4) which is bounded between values of -1 and 1. This additional criteria avoids includingsmoke in orientation frequency statistics.

Figure 4 shows the total time of cloud observations for each lidar tilt angle as a function ofaltitude. Figure 5 shows the frequency at which those clouds produced statistically significantoriented scattering matrices as a function of altitude. The observation frequency is determinedby the time of oriented particle observation (time where O12 > 0.4 or O34 > 0.4) divided bythe total time of cloud observations (where backscatter ratio is greater than 2 and satisfying Eq.(8)). We selected an orientation index threshold of 0.4 to focus this analysis on clear cases oforiented particles. All data is analyzed in 40 second integrations at 30 m range resolution. Theobservations made in summer are shown as solid lines, while the late fall/winter observationsare dashed lines. The frequent oriented particle signatures seen below 3 km during the summerare caused by rain.


Observations of oriented ice crystals conforming to Eq. (4) are quite rare, with a maximumfrequency just under 2% of all cloud observations between 5 and 6 km when the lidar wasdirected 32◦ off zenith. Those observations are easily identified in several data sets as clearf12 signatures in ice falling out of mixed phase clouds (similar to Fig. 2). In a small numberof cases, oriented ice crystal signatures are seen at other tilt angles or higher altitudes. Theseare typically associated with the tops of convective storms but do not have a clear consistentstructure that makes them stand out as a real atmospheric effect. It is difficult to determine if thesignatures seen in convective storms represent false positives or actual preferential orientationof ice crystals at the cloud tops.

Fig. 4. Total time of cloud observation for each data set. The range resolution is 0.03 km.

In late fall 2012, no oriented particles were identified when the lidar was tilted at 22◦ offzenith. Cirrus clouds were frequently present in this data and no convective storms were ob-served during this time. There were no convective storms when the lidar operated at 32◦ offzenith during December 2012, but there were two days where oriented ice crystals were clearlyidentified (one is the example shown in Fig. 2). The conditions under which oriented ice crys-tals were observed in the winter were similar to those in the summer (ice precipitating out ofliquid or mixed phase clouds), but the ice crystals were observed at lower altitudes.

Figure 6 shows a histogram of measured f44 vs. f33 for all cloud observations when the lidarwas tilted 32◦ off zenith in June/July 2012. The green line shows the expected relationship

f44 = 1−2 f22 = 1+2 f33 (9)

for randomly oriented particles. Note from Eq. (2) that f22 = − f33 and there is no distinctionbetween F and F(ϕ) when the volume consists of randomly oriented particles. Figure 6 showsthat most clouds conform to the relationship in Eq. (9). This indicates that the HSRL matrixobservations are consistent with fundamental scattering theory, and therefore reliable measuresof the scattering matrix. There is a sizable population that does not fall on the green line. Thatspur above the green line corresponds to rain observations. The oriented ice crystal observationswith significant nonzero f12 elements are still scattered about green dashed line. Thus, testing


Fig. 5. Fraction of cloud observations where clouds have oriented scattering matrices. Therange resolution is 0.03 km. There are no oriented scattering matrix observations in Novem-ber and December 2012 when the lidar is tilted at 22◦.

the relationship described by Eq. (9) does not appear to be a good method for identifyingscattering effects of oriented ice crystals.

A unique feature of high spectral resolution lidar is its ability to separately measure molecu-lar and total (aerosol and molecular) backscatter [18]. This allows for a straight forward com-putation of atmospheric extinction with relatively few assumptions. The extinction propertiesof oriented ice crystals did not appear to be significantly different from spatially and tempo-rally close randomly oriented ice. For example, the virga in Fig. 2 demonstrated no resolvabledifference in extinction between instances with high and low orientation index.

Altitude integrated histograms of randomly oriented clouds and rain, oriented rain and ori-ented ice crystals are shown in Fig. 7. The rain observations exhibit a higher extinction at 32◦off zenith than 22◦ or 4◦. This is unexpected, since flattened rain drops should have a largerprojected area when the lidar is directed vertically. It is possible this is the result of differentrain size distributions between the observational periods. Because we could not identify signif-icant oriented populations at tilt angles other than 32◦, it is not clear whether or not oriented icecrystals significantly change extinction as a function of lidar tilt angle.

Histograms of the oriented particle matrix elements as a function of altitude were created forthree of the five data sets considered here. The November/December 2012 data was omitted dueto the relatively few cases of oriented particles observed. The histograms for June/July 2012 at32◦, July/August 2012 at 22◦ and August/September 2013 at 4◦ are shown in Figs. 8, 9 and10 respectively. In interpreting these plots, oriented ice crystals are attributed to occurrencesabove 3 km and rain is below 3 km. Also the data presented in these plots has been filteredfor only those cases where the particles are determined to be oriented based on an orientationindex greater than 0.4. Note that f14 is not reported as this term shows no statistically significantdeviation from zero in any of the analyzed observations.

As mentioned previously, oriented ice crystals only appear to produce clear, statistically sig-nificant oriented scattering matrices when the lidar is tilted near 32◦ off zenith. It’s notable thatthe ice crystals tend to form at the same altitudes. This is likely because plate formation at sizes


Fig. 6. Histogram of f44 vs f33 of all cloud observations from June/July 2012 when the lidaroperated at 32◦ off zenith. The green line shows the expected relationship for randomlyoriented particles given by Eq. (9). The color bar is log10 of the number of cloud events (40second integration at 30 m resolution) recorded in each bin.

known to orient (approximate diameter larger than 100μm [19]) occur in a relatively narrowtemperature range [20–22]. Analysis of CALIPSO data by [23, 24] found that observations oforiented plates were consistently bounded between −30◦C and −10◦C. In [24] it is reportedthat oriented ice crystal observations by CALIPSO were typically near an altitude of 5 km atBoulder’s latitude of 40◦N.

Oriented ice crystals tend to be most easily identified by their non-zero f12 elements, or lineardiattenuation. The f34 element associated with retardance is generally not resolvable with icecrystals. Additionally, the diagonal matrix terms tend to closely approximate the relationshipin Eq. (9). As part of that relationship f22 = − f33 which is more or less reflected in Fig. 8.Oriented scattering matrices are only consistently and clearly observed from ice crystals whenthe lidar is tilted at 32◦ off zenith. While some instances of oriented ice crystals appear at othertilt angles, it is not clear if they are the result of poor filtering or actual instances of orientedparticles.

In contrast to oriented ice crystals, rain appears to be best described by the scattering matrixin Eq. (4) for all three lidar tilt angles. Even at 4◦, rainfall still produces a significant (thoughreduced) population of oriented particles. Rain produces both significant linear diattenuation( f12) and retardance ( f34) though there does not appear to be an obvious functional relationshipbetween the two parameters. Also, oriented rain does not typically conform to the relationshipin Eq. (9), a fact clearly visible in Fig. 6. It is notable that in most cases | f22| > | f33|. Thisis probably because the depolarizing characteristics of the rain are relatively small, where thesmaller | f33| is caused by retardance.

At 4◦ off zenith, the oriented signatures of rain are significantly weaker and less frequentthan the other two tilt angles but still common enough that it is never practical to assume thematrix in Eq. (2) when observing polarization properties of rain.

It is not entirely clear why rain still produces an oriented scattering matrix at 4◦. One possi-


Fig. 7. Altitude integrated histograms for extinction of randomly oriented clouds and rain(top), oriented rain (middle) and oriented ice crystals (bottom). The histograms are sepa-rated according to lidar tilt angle with summer observations at 32◦ (blue), 22◦ (green) and4◦ (red) off zenith.

bility is that 4◦ tilt is still sufficient for rain to satisfy condition (2.). Alternately it is possiblethat winds are shifting the mean canting angle of the rain.

Before reduction to its seven element form, the linear diattenuation elements have the rela-tionship

tan2ϕ =f (ϕ)13

f (ϕ)12

. (10)

A cursory analysis of the angle ϕ in rain indicates that the orienting effect at 4◦ is consistentlyin the same direction. This suggests that the oriented scattering matrix of rain is probably dueto the 4◦ tilt of the lidar. This analysis does not completely rule out wind, as it is possible thewind direction during rain fall was always the same over the August/September 2013 observa-tional period. However radar observations have indicated the mean canting angle of rain is notexpected to deviate by more than 1−2◦ [25], which suggests that the lidar tilt angle is the moresignificant term.

3. Conclusion

The presence of oriented particles has the potential to render conventional polarization lidarmeasurements ambiguous. Only with information about the scattering matrix elements com-mon in the atmosphere, is it possible to assess the magnitude of such depolarization ratio ambi-guities. Further, such scattering matrix observations allow us to determine common cases whereoriented particles significantly contribute to the backscatter light.


Fig. 8. Histograms of measured matrix elements for scattering matrices conforming to Eq.(4) (instances of high orientation index). Observations here are from June and July 2012when the lidar was tilted 32◦ off zenith. Oriented ice crystals are seen at approximately 5km, while oriented rain is below 3 km. The color bar is the same for all plots and is log10 ofthe fraction of total observations where rain or clouds were observed to have the specifiedelement value.

The NCAR HSRL has observed the full backscatter matrix of clouds and aerosols over Boul-der, Colorado, USA (40.0◦N,105.2◦W) at three tilt angles. These observations have been an-alyzed to report information about the types of scattering matrices that are typical for atmo-spheric observations.

We have described how the presence of oriented particles in a scattering volume is not suf-ficient to produce an oriented scattering matrix. Two additional criteria are required, a breakin rotational symmetry along the lidar line-of-sight, and sufficient backscatter from the ori-ented population to be observable over a randomly oriented sub population. Observations bythe NCAR HSRL have shown clear cases where ice crystals and rain drops satisfy all three cri-teria to produce a statistically significant oriented backscatter phase matrix. In circumstanceswhere the oriented particle backscatter is not observable (does not satisfy all three criteria),there is no issue in using conventional polarization lidar to interrogate the volume.

In this work we have shown observed statistics on scattering matrix elements for lidar opera-tion at 4◦, 22◦, and 32◦ off zenith. Oriented ice crystals are most visible where the lidar is tilted32◦ and are identified by significant linear diattenuation signatures ( f12). Their backscatter ma-trix diagonals, however, typically conform to the relationship expected for randomly orientedparticles, and they do not appear to exhibit significant retarding effects ( f34). The instances oforiented ice crystals that were clearly visible were those of ice virga precipitating out of wa-ter or mixed phase clouds, which is similar to observations of oriented plates reported in [15].


Fig. 9. Histograms of measured matrix elements for scattering matrices conforming to Eq.(4) (instances of high orientation index). Observations here are from July and August 2012when the lidar was tilted 22◦ off zenith. Oriented rain below 3 km is the only major con-tributor to oriented particle signatures. The color bar is the same for all plots and is log10 ofthe fraction of total observations where rain or clouds were observed to have the specifiedelement value.

These precipitating oriented ice crystals were observed in both summer and late fall, thoughthe ice crystals formed at lower altitudes in the late fall. We found that clouds produce scatte-ring matrices conforming to Eq. (4) in less than 2% of cloud observations made by HSRL. Itshould be noted that this analysis focused on cases of clearly oriented particles and instancesof smaller oriented populations are not likely to be counted as “oriented” in this analysis. Ourintent is not to definitively determine where particles orient, but rather, where their scatteringproperties cannot be approximated by Eq. (2).

To our knowledge, the NCAR HSRL is the first lidar instrument to fully observe the opticalpolarization properties of rain. The backscatter matrices of rain in the data analyzed here com-monly have the form of oriented particles, even at the smallest lidar tilt angle of 4◦. The highlyambiguous depolarization ratio expected from these scatterers is perhaps somewhat mitigatedby the fact that lidar is not commonly used to interrogate rain (though not all together absentfrom polarization lidar studies [1]). It should be emphasized that one should never assume raincan be accurately described using the linear depolarization ratio. Circular depolarization ratiomeasurements can be used, but they should be qualified to make clear that the scattering matrixhas the form in Eq. (4). Additionally, our observations of rain suggest a potential use of moreadvanced lidar polarimetry in characterization of precipitation. Thus, more complete polariza-tion lidar may be a useful tool in characterizing raindrop evaporation, coalescence and liquidwater content.


Fig. 10. Histograms of measured matrix elements for scattering matrices conforming to Eq.(4) (instances of high orientation index). Observations here are from August and September2013 when the lidar was tilted 4◦ off zenith. Oriented rain below 3 km is the only majorcontributor to oriented particle signatures. The color bar is the same for all plots and islog10 of the fraction of total observations where rain or clouds were observed to have thespecified element value.

Acknowledgments

The National Center for Atmospheric Research is sponsored by the National Science Founda-tion.


Documents

Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain