Identification of Hydrometeors with Elliptical and Linear Polarization Ka-Band Radar

Roger F. Reinking NOAA/ERL/Environmental Technology Laboratory, Boulder, Colorado

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Sergey Y. Matrosov Cooperative Institute for Research in the Environmental Sciences, University of Colorado, and NOAA/ERL/Environmental Technology Laboratory, Boulder, Colorado

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Roelof T. Bruintjes Research Applications Program, National Center for Atmospheric Research, Boulder, Colorado

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Brooks E. Martner NOAA/ERL/Environmental Technology Laboratory, Boulder, Colorado

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Abstract

Polarimetric radar can be used to identify various types of hydrometeors. Ice crystals of the varied growth habits depolarize and backscatter millimeter-wavelength radiation according to crystal aspect ratio, bulk density, and orientation, and the polarization state of the incident radiation. In this paper model calculations of the depolarization caused by various crystal types are extended from previous work, and Ka-band (8.66 mm) radar measurements of linear and elliptical depolarization ratios (LDR and EDR) from various ice hydrometeors are presented. The measurements for regular crystals are related to the models. Drizzle drops, which are quasi-spherical, serve as a reference. Signature discrimination in cloud systems with more than one type of hydrometeor is addressed.

The model calculations illustrate the interplay of the parameters that control depolarization. They predict that in the depolarization signatures, crystals of the various basic planar and columnar habits should generally be most separable, one habit group from another and, to a degree, within each group when they occur in common, mature size distributions. It is verified in this and related papers that measurements of depolarization with a Ka-band dual-polarization radar provide good estimates of hydrometeor identity to separately distinguish drizzle, pristine crystals of various growth habits, graupel, and aggregates in winter storm clouds that have reasonable horizontal homogeneity over short distances (∼10–20 km). Characterization of the mix of two or three hydrometeor types is also possible, once the individual types are identified in some part of the cloud. Quantitative agreement between the measurements and the models, supported by snow crystal samples, was much better for EDR than for LDR; that is, EDR enabled more specific hydrometeor identification. However, LDR provided indications of randomness of crystal orientation and a wider decibel gap differentiating graupel from drizzle.

Corresponding author address: Dr. Roger F. Reinking, Environmental Technology Laboratory, NOAA/ERL/ETL, R/E/ET6, 325 Broadway, Boulder, CO 80303-3328.

rreinking@etl.noaa.gov

Abstract

Polarimetric radar can be used to identify various types of hydrometeors. Ice crystals of the varied growth habits depolarize and backscatter millimeter-wavelength radiation according to crystal aspect ratio, bulk density, and orientation, and the polarization state of the incident radiation. In this paper model calculations of the depolarization caused by various crystal types are extended from previous work, and Ka-band (8.66 mm) radar measurements of linear and elliptical depolarization ratios (LDR and EDR) from various ice hydrometeors are presented. The measurements for regular crystals are related to the models. Drizzle drops, which are quasi-spherical, serve as a reference. Signature discrimination in cloud systems with more than one type of hydrometeor is addressed.

The model calculations illustrate the interplay of the parameters that control depolarization. They predict that in the depolarization signatures, crystals of the various basic planar and columnar habits should generally be most separable, one habit group from another and, to a degree, within each group when they occur in common, mature size distributions. It is verified in this and related papers that measurements of depolarization with a Ka-band dual-polarization radar provide good estimates of hydrometeor identity to separately distinguish drizzle, pristine crystals of various growth habits, graupel, and aggregates in winter storm clouds that have reasonable horizontal homogeneity over short distances (∼10–20 km). Characterization of the mix of two or three hydrometeor types is also possible, once the individual types are identified in some part of the cloud. Quantitative agreement between the measurements and the models, supported by snow crystal samples, was much better for EDR than for LDR; that is, EDR enabled more specific hydrometeor identification. However, LDR provided indications of randomness of crystal orientation and a wider decibel gap differentiating graupel from drizzle.

Corresponding author address: Dr. Roger F. Reinking, Environmental Technology Laboratory, NOAA/ERL/ETL, R/E/ET6, 325 Broadway, Boulder, CO 80303-3328.

rreinking@etl.noaa.gov

Introduction

Applications in aircraft icing, climate effects, precipitation prediction, precipitation enhancement, and water resources make it essential to monitor and characterize clouds that produce or fail to produce ice crystals. Radar can provide some of the appropriate measurements if more observables than basic reflectivity and Doppler velocity are used. Polarimetric radar offers some solutions. Recent developments in radar polarization measurement capabilities and applied theory together make it feasible to identify hydrometeor types as they form and grow within clouds. Ice crystals of the various growth habits depolarize and backscatter millimeter-wavelength radiation according to crystal aspect ratio, bulk density, and orientation, and the polarization state of the incident radiation (Matrosov 1991a; Vivekanandan et al. 1994; Kropfli et al. 1995; Reinking et al. 1996). The effect is measured as a depolarization ratio.

In this paper, building on depolarization modeling studies by Matrosov (1991a,b) and Matrosov et al. (1996), some linear depolarization model calculations are refined to apply to the radar that was used and to represent very typical ice crystal size distributions. Also, elliptical depolarization model calculations are added to represent the same typical size distributions and some nontypical size distributions that represent conceivable worst-case scenarios for crystal habit discrimination. These models provide the foundation of the present study, which emphasizes experimental measurements. These measurements were taken with a selectable dual-polarization Ka-band radar that induced a 79.5° phase shift with a phase-retarding plate (PRP) to create the polarized signal. The dual-polarization capability is described as “selectable” because the transmitted polarization state can be chosen from or varied through a continuum of ellipticity between horizontal linear and near circular, with the hardware configuration used to obtain the measurements.

The primary goal of this work is to determine reliable depolarization signatures that identify various hydrometeor types. Reliable signatures are defined as those measurements that are repeatable and compatible with the model predictions. The capability to discriminate among ice crystals of various basic growth habits is verified by correlating the radar data with field samples of snow crystals and the modeled depolarizations. Drizzle is used as a reference. Evidence is presented indicating that graupel can be quantitatively discriminated from drizzle, as well as the other hydrometeors. Signature discrimination in cloud systems with more than one type of hydrometeor is described from two case studies.

The reported measurements were made in shallow winter upslope storm clouds. These clouds serve well as laboratories for polarization radar studies to identify individual types of snow crystals. The upslope storms of interest form in moist advection over rising terrain on the High Plains immediately east of Colorado’s Rocky Mountains (Reinking and Boatman 1986). The clouds are often capped by a temperature inversion and therefore develop in confined volumes extending from near the ground upward to 1–3 km above ground level (AGL). This structure can confine the temperature regimes and therefore isolate the temperature-dependent growth habits by which crystals can develop. This structure also allows radar observations to be made at very close range.

Background

The radar

The National Oceanic and Atmospheric Administration (NOAA)/Environmental Technology Laboratory Ka-band (8.66 mm) cloud-sensing Doppler radar, with an offset Cassegrain antenna and selectable dual polarization (Martner and Kropfli 1993; Kropfli et al. 1995), was one of several state-of-the-art atmospheric remote sensors deployed for the Winter Icing and Storms Project (WISP) field campaigns in 1993 and 1994. The radar was located on the High Plains, near Platteville, Colorado, in 1993 and near Erie, Colorado, in 1994. WISP used the specialized instruments to detect microphysical and dynamic features of upslope storms relevant to the formation and depletion of supercooled liquid water, as is necessary for forecasting aircraft icing conditions (Rasmussen et al. 1992). Observations of ice hydrometeors and their effects on glaciation of the supercooled water were part of this investigation.

The Ka-band radar’s sensitivity to cloud particles (about −30 dBZ at 10 km), Doppler velocity precision (∼5 cm s−1), fine spatial resolution (37.5-m or 0.25-μs pulse width and 0.5° beamwidth), agile polarization capability, and relative insensitivity to ground clutter make it ideal for winter storm measurements (Kropfli et al. 1995). The polarization agility is provided by the PRP. The PRP resolves the transmitted beam into two components, retards the phase of one relative to the other, and then reunites the two components (Shurcliff 1962). A 90° phase-shift PRP produces circular polarization from incident horizontal polarization when its “slow” axis is rotated 45° from horizontal. In practice, when the phase shift differs somewhat from 90°, all of the polarizations produced by the PRP will be elliptical (except for 0° and multiples of 90° for which the polarization will remain horizontal linear). The largest ellipticity coefficient (or most circular polarization state possible) is then produced at multiples of 45° rotation. The PRP either can be rotated at constant speed at selected, fixed radar elevation angles (β) to vary the transmitted polarization state, or it can be fixed at a selected polarization state for scanning. Orthogonal polarization components of the backscattered waves are received and recorded simultaneously.

In the 1993 WISP instrument test (WISPIT) and WISP-94, at the radar operator’s discretion, polarizations were either fixed for range–height indicator (RHI) scans or cycled through the available continuum of polarization states, between horizontal linear and near-circular elliptical, at multiple, fixed elevation angles (e.g., 7.5°, 45°, and 90°) while rotating the PRP continuously. A true quarter-wave PRP was designed to induce a 90° phase shift. The result of manufacturing was somewhat different. Calibrations show that the PRP used in WISP induces a phase shift of 78° ± 2°, and comparisons of experimental data with models derived from Rayleigh scattering theory indicate that the actual shift is about 79.5° (Matrosov et al. 1996).

Although the optimal, “tuned” polarization states (linear and circular) provide the maximum dynamic range in depolarization ratios, they are not ideal for monitoring low-reflectivity clouds (Matrosov 1991b). These polarizations produce the minimal return signal in the receiving cross-polarized channel and therefore can make such clouds invisible in this channel. A proper choice of elliptical polarization intermediate between the linear and circular limiting states increases the signal level in the orthogonal channel relative to the main channel, making polarization studies possible in relatively low-reflectivity clouds. This means that the Ka-band radar, with a provision for a continuum of polarization states and an elliptical limit that is near but not circular, should provide exceptional information from which to infer hydrometeor particle type, particularly in winter storms that are commonly of low reflectivity. Thus, the PRP with a 79.5° rather than 90° phase shift has benefits.

Depolarization models and measurements

Horizontal linear and circular depolarization ratios (LDR and CDR, respectively) are the limiting values of the elliptical depolarization ratio (EDR). A preliminary basis for interpreting the Ka-band radar measurements was provided by applying Rayleigh scattering theory to derive models of radar polarization parameters that characterize cloud ice crystal backscattering in terms of the elevation-angle dependency of LDR and CDR (Matrosov 1991a). It was shown that scattering ice crystals of basic planar and columnar habits should be distinguishable in the measurements. Effects of bulk densities and settling orientations of the hydrometeors were accounted for in these models.

In the WISP projects, the first polarization measurements were obtained in upslope clouds with 1) planar ice crystals in large and small concentrations, 2) small and large aggregates of planar crystals, 3) columnar crystals, 4) graupel, 5) drizzle, and 6) raindrops. From these data, Reinking et al. (1993) and Reiking et al. (1995a) provided initial experimental evidence that the various ice hydrometeors and drizzle could indeed be identified and distinguished by using measurements from the polarization-agile Ka-band radar and matching them to the early model calculations. It was found that the progression from individual planar crystals (dendrites) to aggregates of dendrites could be monitored in the radar’s depolarization signature; the quantitative difference is noted by Kropfli et al. (1995).

The model considered by Matrosov (1991a) treated selected simple ice crystals. For example, the planar family was identified by hexagonal plates, which provide only an approximation to branched planar crystals. The theory was extended, specifically, to the elliptical polarizations provided with the 79.5° PRP used in WISP (Matrosov et al. 1996). This was accomplished by explicitly modeling families of planar and columnar crystals and aggregates of dendrites through a more detailed accounting of shape, size, and bulk density effects. This enabled the investigators to solidify the model’s potential for verification with the radar measurements, which they demonstrated for dendrites and aggregates of dendrites. To establish a reference, they verified the match of theory and measurements for drizzle, which serves as a calibration because of droplet sphericity. With this model for guidance, Reinking et al. (1995b) provided initial analyses of measurements that separated and identified thick plates; they likewise identified needlelike crystals with another PRP and a corresponding model.

In this paper, the prior theoretical linear and more habit-specific elliptical depolarization calculations are improved and extended; these calculations are intercompared with more in-depth analyses of the data from Reinking et al. (1993), Reiking et al. (1995a), and Reinking et al. (1995b) to identify specific types of hydrometeors with the Ka-band radar. Some companion analyses of these data have been examined for applications to precipitation enhancement (Reinking et al. 1996). Some of the measurements were taken in clouds with mixed types of hydrometeors, and the influence of the mix versus the individual hydrometeor types on the depolarization is demonstrated. The verification of the models and measurements is assisted by actual snow crystal samples taken in situ, at the surface near or at the radar sites, some with a microphysics van provided by the National Center for Atmospheric Research. The theoretical models are compared to measurements at fixed altitudes in clouds, rather than at fixed radar range, so as to minimize gradients due to hydrometeor development that occur primarily in the vertical. With this approach, compared to one using a constant range that ignores those vertical gradients, the signal will be relatively more attenuated by liquid water at the greater ranges (lower elevation angles) on the constant altitude plane. This effect has not significantly impeded crystal identification.

Essentials and extensions of the depolarization models

Hydrometeors depolarize the backscattered signal according to their aspect ratio, bulk density, and settling orientation, and the polarization state of the transmitted signal. For most snow crystals of regular growth habits, the aspect ratio increases with size, so this parameter combines shape and size effects. EDR is specified as the logarithmic ratio of the radar echo received in the copolarized channel to the radar echo received in the cross-polarized channel, so
i1520-0450-36-4-322-e1
where P is power. In (1), LDR and CDR define the limiting extremes of EDR, values of LDR will be positive (opposite convention) because Pco > Pcr and values of CDR will be negative because Pco < Pcr. This form of (1) is most convenient for addressing depolarization ratios from the continuum of elliptical polarization states provided by the rotating PRP.

LDR corresponds to a 0° rotation and CDR to a 45° rotation of a quarter-wave PRP. For a PRP detuned from the 90° phase shift, the most circular polarization state possible still occurs at 45° rotation and is represented by EDP45. For this state and the PRP that induces a 79.5° phase shift, the ellipticity of the transmitted signal is ϵ = tan(79.5°/2) = 0.832. Spheres are the reference hydrometeor shape; the corresponding EDR45 ≈ −14.8 dB and is independent of radar elevation angle β. Nonspherical hydrometeors with preferred orientations will produce depolarizations that change systematically with β or with changes in the ellipticity of the transmitted signal that occur with PRP rotation at fixed β.

For a given polarization state, the magnitude of variation of the depolarization ratio (LDR or EDR45) with β decreases with increasing random deviation from the preferred hydrometeor orientations. This is accounted for by the standard deviation of the crystal major dimension from horizontal orientation σθ, where θ is the angle of deviation. (Specifically, θ is distributed as a truncated Gaussian, with the mean canting angle vertical, in a spherical coordinate system where the azimuthal angle ϕ is uniformly distributed and randomly oriented.) Calculations (Matrosov 1991a) show that for both planar and columnar crystals and a given polarization state the variation of depolarization ratio with β decreases and the distinctions among different habits become increasingly less separated with increasing random deviation from the preferred horizontal crystal settling orientations. However, even for orientations with a standard deviation of σθ = 45°, the curves for the individual basic crystal habits can be differentiated, at least as theoretically modeled. None of the models consider the possible effects of cloud electrification on crystal orientation.

The LDR–β and CDR–β relationships computed by Matrosov (1991a) illustrate the effects of σθ, but do not account for channel cross talk in radar receivers. The cross talk (specifically, the integrated cancellation ratio) is a measure of channel isolation. The cross talk limits the detectable depolarization ratio to about ±35 dB for the Ka-band radar; the effect of this is accounted for in the later theoretical calculations (Matrosov et al. 1996) and in this paper.

In this paper some LDR measurements are considered, but emphasis is placed on EDR45 measurements. This is done because the models indicate that EDR45 is several times less sensitive than LDR to σθ. Therefore, use of EDR45 should enable a more specific identification. The computations discussed in the remainder of this section show us what to expect from the measurements and illustrate the influences of the parameters affecting depolarization.

Figure 1 shows revised LDR–β relationships from the model for (a) σθ = 3° and (b) σθ = 10°, with the cross talk accounted for. Similarly, Fig. 2 shows selected EDR45β curves for the 79.5° PRP. The EDR45 values for σθ = 3° and σθ = 10° differ by only about 1–2 dB, so only curves for σθ = 3° are presented here. However, for a given ice crystal type, this difference in σθ causes LDR to differ by as much as 7.5 dB, with the exception that values for the individual planar crystal types (dendrites, hexagonal plates, etc.) are nearly equal to each other at high elevation angles.

The crystal classifications indicated in Figs. 1 and 2 are those of Magono and Lee (1966). The size distribution medians of the crystal major dimensions, diameter Do or length Lo, are noted; crystal aspect ratio is designated a/b, where a is the short axis and b is the long axis. Some assumed size distributions provide the basis for the computations of Matrosov et al. (1996). However, crystal habits represented by mature size distributions actually measured in nature seem to offer the most definitive differentiability in depolarizations. A mature size distribution is one in which crystals of very large as well as very small sizes are present in a cloud, such that a full range of potential crystal growth is represented. Therefore, the LDR and EDR45 relationships in Figs. 1 and 2, for several basic growth habits (needles, hollow columns, hexagonal plates, and dendrites), are based on median sizes taken from distributions measured from a 14 042-crystal sample from Sierra Nevada snowfall (Reinking 1974). Full-size ranges are represented by these distributions. The thick plates are based on measurements from a small sample taken in WISP (see section 7). Blocky, solid columns were not part of the samples, but the computations were added to illustrate a realistic contrast. These models are calculated from full distributions represented by the median sizes; the aspect ratios and bulk densities noted in this paper correspond only to the median-sized crystals and therefore only approximately represent the distributions.

For both LDR and EDR45, the computations in Figs. 1 and 2 predict that the signal depolarizations by planar and columnar crystal groups should be readily separable. Also, the specific crystal habits within each group should be separable insofar as bulk densities and aspect ratios are sufficiently different. Larger densities cause greater depolarizations, thus moving the depolarization ratio nearer zero (Matrosov et al. 1996). The greater dynamic range in LDR than EDR45 results in somewhat greater differences in the LDR values that separate the varied growth habits. However, EDR45 is also predicted to provide significant separation of the crystal types for most sizes and growth habits noted. In practice, of course, maximum differentiation among the various crystal types presumes reasonably homogeneous cloud layers with isolation of individual growth habits.

In LDR and EDR45, for fixed σθ, the depolarizations by the hexagonal plates (a/b ≈ 0.08), solid columns (0.70), hollow columns (0.32), and elementary needles (0.08) are individually unique and differentiable, at least in theory. Dendrites (a/b ≈ 0.04) and thick plates (0.28) are likewise each differentiable from the other crystal types; however, due to a coincidence of opposite and compensating effects of significantly differing densities and aspect ratios, they are not significantly differentiable from each other in theory but should be differentiable in field measurements if supplemental information on their differing cloud nucleation temperatures can be provided.

In LDR, the slope of the curves for the planar types is positive with increasing β, whereas that for the columnar types is negative; this contrast offers an advantage in the differentiation of the basic habit groups. This advantage does not exist in EDR45 with the 79.5° PRP, for which values monotonically become more negative (depolarization decreases) from lower elevation angles toward zenith (β = 90°) for each planar and columnar crystal type (Fig. 2). This advantage for LDR is offset by the influence of σθ. The models (Fig. 1a vs Fig. 1b) predict that, for LDR, a realistic change in σθ will confuse differentiation of the more specific crystal habits within a habit group. For the same change, EDR45 is hardly affected.

In all, the patterns of the LDR–β and EDR45β in Figs. 1 and 2 make it easy to visualize the effect of populations of natural ice crystals in their settling orientations, which present geometric cross sections and induce corresponding depolarizations at zenith that are different from those at lower pointing angles. The depolarizations calculated here, with application of median sizes of representative mature size distributions, indicate good potential for separate identification of most of the basic habits in field measurements.

For contrast, Figs. 3a,b show some worst-case scenarios in EDR45 that are conceivable if crystals of different habits within the individual groups (planar and columnar) were to occur with size distributions similar to those during the first few minutes of growth; also, the case of differing sizes/aspect ratios and densities that have offsetting effects on the depolarization is reiterated for direct comparison. Most of these depolarization curves are for crystals of the same median dimension, 250 μm, with some important exceptions.

In Fig. 3a, depolarizations due to 250-μm hexagonal plates and 250-μm dendrites differ, though only slightly (by less than 0.3 dB), because of the small density difference and equal aspect ratios (a/b ≈ 0.09 in both cases); thus, either maturing plates or early-growth dendrites could produce nearly the same signature.

Likewise, in Fig. 3b, the depolarization curve for solid columns 250 μm in length (a/b ≈ 0.66) is separated by less than 0.2 dB from hollow columns (a/b ≈ 0.61) of equal length; the density difference δρ is less than 0.05 g cm−3. The shape effects dominate when density differences are small (e.g., δρ < 0.1 g cm−3). Contrarily, the effect of significantly different crystal densities can compensate for the effect of large size and aspect ratio differences, as in the case of dendrites (ρ ≈ 0.4 g cm−3) versus thick plates (ρ ≈ 0.9 g cm−3) discussed earlier. (The thick plate and dendrite curves are repeated in Fig. 3a.)

With the depolarization data alone, the noted, paired crystal types are almost inseparable, even in theory. Such pairing is not expected to occur commonly in any given cloud because the basic crystal growth habits produce reasonably unique size distributions (Fig. 2) and are very temperature dependent.

The depolarizations induced by some same-size crystals are substantially differentiable; for example, 250-μm hexagonal plates (a/b ≈ 0.09) should be readily differentiable from the 250-μm thick plates (a/b ≈ 0.28). Dendrites of significantly differing size (e.g., 250 μm vs 2000 μm) can also be separated, since the large variation in dendrite depolarization is strongly governed by bulk density, which substantially decreases with growth. Depolarizations from dendrites decrease with increasing crystal size (EDR45 becomes more negative), but depolarizations from hexagonal plates increase with increasing size (EDR45 moves toward 0); to visualize this, compare the curves for 100-μm hexagonal plates (a/b ≈ 0.14) and 250-μm hexagonal plates (a/b ≈ 0.09) in Fig. 3a. The effect of the hexagonal plates is opposite because they are of constant density and change only their aspect ratio with growth.

These scenarios illustrate the interplay of the parameters that control depolarization.

Drizzle as a reference

Spheres do not depolarize the incident radiation. Drizzle drops tend to be small enough to be nearly spherical, so they offer an experimental calibration. This calibration, presented by Matrosov et al. (1996), shows excellent agreement between polarization measurements and the theory-based model at all polarization states between LDR and EDR45 for the 79.5° PRP. For drizzle observed with the Ka-band radar, the measurements show, at the linear polarization extreme EDR = LDR ≈ +35 dB, the limit imposed by the radar’s channel cross talk; at the other elliptical polarization extreme EDR = EDR45 ≈ −14.8 dB, the measurements show the theoretical value for spheres.

This experimental result is repeatable, as shown in Fig. 4, by additional samples from a PRP rotation in drizzle, where each cycle in the depolarization ratio represents a 45° rotation of the PRP. Many such samples were obtained. The most positive values in Fig. 4 correspond to LDR and the most negative to EDR45. The EDR45 again agrees with the model, and LDR matches the cross-talk limit, with values of −14.7 ± 0.5 dB and +34.6 ± 0.9 dB, respectively (these values are expressed as the mean, with tolerances equal to the maximum deviation measured in the sample). For these measurements at β = 30°, where the oblateness of ice crystals would be evident, spheres are indicated. Equivalent data taken 5 min later at β = 90° also agree with a value of 35.3 ± 3 dB in LDR and a value of −15 ± 0.2 dB in EDR45. Thus, the measured values were independent of elevation angle, verifying the presence of spheres. The theory and data for drizzle provide the reference depolarization values in EDR45 and LDR for data from other types of hydrometeors.

Branched planar crystals

The branched planar crystals present large targets that appear very oblate at low β and near circular (i.e., like spheres) at β = 90°. They are ideal for demonstrating the effect of crystal shape and linked parameters on depolarization. A snowfall of nearly pristine dendrites (types P1d, P1e, and P1f) presented the greatest measured decibel range in EDR45 as a function of β among the various crystal types observed so far. Indeed, the dendrites, settling with approximately horizontal orientation, presented a sufficient target to enhance reflectivity at zenith over that at lower β in RHI scans. The reflectivity of this 11 March 1993 snowfall ranged from approximately −3 to +5 dBZ; this is a strong target for the Ka-band radar. A project radiosonde launched at 2057 UTC indicated a 1-km depth of cloud colder than −12°C with a top near −16°C, which is appropriate for the generation of dendrites; cloud base was near −7°C.

Matrosov et al. (1996) presented a radar image of the EDR field from an RHI scan through the dendrites, corresponding experimental and modeled curves of EDR45 versus β, and a correlated snow crystal sample that provided verification of the model in situ. Dendrites of some 1000–4000 μm were sampled. The modeled curve for 1500-μm dendrites agrees with the measured curve to within about 0.6 dB; a best-fit curve for a distribution of crystals with a median size of approximately 2000 μm is suggested. This median size is approximately equal to that measured for the mature distribution of dendrites represented in Fig. 2.

Figure 5 shows another RHI sample from a different altitude in the same cloud. In this case, modeled curves are superimposed for dendritic crystals with aspect ratios of 0.038 and 0.035 and densities of 0.51 g cm−3 and 0.45 g cm−3, which correspond to diameters of 1500 and 2000 μm, respectively. Corresponding PRP rotations through the snowfall of dendrites were made 2–8 min later at fixed radar elevations of 90°, 30°, and 10° (Fig. 6). At these three elevations, respectively, EDR45 repeatedly reached −15.0 ± 0.5 dB, −8.6 ± 0.3 dB, and −7.8 ± 0.8 dB. These values match within 0.5 dB the modeled values for 2000-μm dendrites (−14.6, −8.3, and −6.8 dB at β = 90°, 30°, and 10°, respectively). The fixed-polarization RHI samples, presented by Matrosov et al. (1996) and here, and the fixed-elevation, rotating PRP data all show the predicted well-defined pattern of EDR45 as a function of β. As with the drizzle, the several illustrated dendrite samples and many others not shown demonstrate repeatable close agreement between theory and observations.

The agreement between the measurements in Fig. 6 and the model follow, but not so precisely, for LDR. The measured LDR values for dendrites were +27.6 ± 1.4 dB, +24.0 ± 3.0 dB, and +20.0 ± 1.3 dB at β = 90°, 30°, and 10°, respectively. LDR was much more variable from sample to sample (peak to peak in Fig. 6) than EDR45. At β = 90°, the measured LDR was about 7 dB more depolarized than that measured for drizzle (∼+35 dB, Fig. 4). LDR increased with β, so the general slope of the curve set by the experimental PRP data clearly identifies the crystals as planar. The measured values are about 5–8 dB less depolarized than the theoretical values for dendrites, and 2–5 dB less than the theoretical values for hexagonal plates, with σθ = 3° (Fig. 1a). However, for σθ = 10° (Fig. 1b) the modeled values for dendrites are 21.3, 23.2, and 30 dB at β = 90°, 30°, and 10°, respectively; the measured values differ by +3.4, −0.8, and +2.3 dB from this model. The measurements at β = 90° and 10° are actually closer to the model values for the hexagonal plates. The agreement between model and experiment is not as good as that in EDR45, but it does suggest that the population of dendrites had a randomness of orientation on the order of 10°.

In summation, the parameter EDR45 combined with the temperature measurements provided the specific crystal habit identification, but LDR provided the estimate of randomness of orientation. This indicates that the information in the measurements can be enhanced by obtaining both measurements with the rotating PRP.

Graupel versus drizzle

A convective graupel shower passed directly over the radar on 8 February 1994. Conical graupel was observed but not photographed at the ground about 20 km upwind before the shower reached the radar; irregular graupel with occasional hints of conical structure was observed and photographed at the radar site (Fig. 7). Of the latter, approximate diameters were 1–4 mm (mean size, 2 mm) for 17 graupel particles sampled. At this time, graupel clearly dominated the precipitation, although the samples included some significantly smaller (∼0.2 mm) plates from a cloud layer below the altitudes studied here.

Figure 8 shows the elliptical depolarization in both an RHI scan in drizzle, which serves as a reference, and an RHI scan through the graupel shower. For the drizzle, the RHI indicates EDR45 ≈ −14.4 ± 0.3 dB, which to within a few tenths matches the −14.8-dB theoretical value for spheres. Truly spherical particles of any density will fall on the limiting −14.8-dB line. Thus, shape and preferred orientation are responsible for shifting signatures away from this line toward greater depolarizations. Conical graupel is shaped like a space capsule and settles with the blunt end down—that is, it is oriented. Conceivably, this shape and orientation would cause it to appear spherical at β = 90° and slightly less than spherical at low elevation angles, despite a tendency for such graupel to grow with a 1:1 axis ratio (Pruppacher and Klett 1978, p. 50). A population of irregular or conical graupel, oscillating or tumbling to produce more nearly random orientation, would be expected to produce depolarizations with minimal dependence on elevation angle. In comparison, the model of Matrosov et al. (1996) shows that prolate, low-density aggregates with a 0.3 aspect ratio will have an elevation-angle dependency with a range of only 0.6 dB; the model curve is much flatter than that for oblate particles of the same aspect ratio.

A graupel population may have as great a tendency toward a mix of prolate and oblate shapes as any hydrometeor. The depolarization by graupel has yet to be modeled; the sizes up to 4 mm take it beyond the Rayleigh scattering regime. However, experimentally, for the graupel and β between 30° and 150°, the measured EDR45 ≈ −13.8 ± 0.3 dB for the sample in Fig. 8. Thus, the graupel depolarization was nearly invariant with β, suggesting an effect of randomness in orientation of irregularly shaped particles, which would flatten the depolarization curves but not drive them to equality with the EDR45β constant for spheres. Several drizzle and graupel RHIs were examined. The graupel depolarized the transmitted radiation up to 1.2 dB more than drizzle.

Figure 9 shows measurements from PRP spins in graupel at β = 45° and 90°, and also at an altitude of 1 km AGL. These data contain additional information. The values of EDR45 are consistent with the RHIs at −13.8 ± 0.3 dB. One LDR value from graupel reached the antenna limit of approximately 35 dB, but all others fell short by 2–5 dB (and more in other samples), whereas LDR in drizzle consistently reached 33–35 dB. For the graupel data in Fig. 9, LDR ≈ 32.1 ± 4.6 dB. The LDR values were again less consistent than those of the EDR45. Although this variability would complicate specific ice particle identification using LDR, the larger difference from 35 dB may offer an advantage in graupel–drizzle distinction, since the EDR45 values differ by only a decibel or two.

Graupel depolarization needs to be measured in more cases to determine the repeatability of these results. Cloud temperature and evidence of a melting layer (bright band) used with the polarization data can also help to distinguish the quasi-spherical ice particles from drizzle. In this case, the air was subfreezing, so there was no melting layer.

Thick plates and graupel

Here, the depolarizations due to thick plates and graupel occurring both separately and mixed are examined. The RHI scan in Fig. 10a shows a deep shower with 0–6-dBZ reflectivities and an underlying layer cloud with reflectivities of −10 to −20 dBZ. This scan also shows three distinct depolarization zones, labeled “1,” “2,” and “3” in Fig. 10b. A strong dependence of EDR45 on β is evident in a shallow cloud layer composed of thick plates (zone 1). These thick plates (crystal type C1g) were the simplest ice crystals monitored with the radar. They formed at −18° to −20°C, according to a concurrent local sounding, and in accord with standard crystal habit dependence on temperature. The shower aloft was producing graupel; here (zone 2), EDR45 is quite uniform and independent of β, with predominant depolarizations between −13.5 and −14.5 dB, in accord with the measurements reported in the preceding section (these data were taken from the same 8 February 1994 shower, but 15–20 min earlier). Figure 10c shows a crystal sample from the zone of the mix (zone 3), where graupel fell through the layer of thick plates and scavenged them.

The measured dependency of EDR45 on β in the thick-plate cloud and in the graupel–plate mix is shown in Fig. 11. A curve exemplifying planar crystals is evident where the thick plates prevailed (β < 90°); the depolarization increases by about 6.5 dB between β = 90° and 20°. In the graupel-dominant mix, the influence of the plates is still indicated, but the difference between 90° and 160° (equivalently, 20° elevation) is only about 2 dB, due to depolarization reduction (curve flattening) caused by the graupel.

The median and mean diameters of the thick plates were approximately equal at b = 254 μm (45 samples); the mean axis ratio was a/b = 0.28 ± 0.08 (12 samples). Given this axis ratio, Fig. 12 compares the experimental depolarization data from zone 1 with the model EDR45 curves for crystals with σθ = 3° and 23°. Measured cloud-top depolarizations from 0.77 km AGL had a large variance, but they agree well with the model for σθ = 3°—that is, for minimal random variation in crystal orientation from the horizontal. Lower in the cloud body (0.70 and 0.50 km AGL), the measured curves are flattened slightly, as if by greater randomness in the orientation. Here, agreement is good with the model for σθ = 23° at high β, but with σθ = 3° at low β. Even with this curiosity, the offset from the theoretical values is only about 1 dB in either scenario. No rotating PRP data, and therefore no LDR data, were obtained from the thick plates.

Columns with other hydrometeors

Model and previous measurements

Columnar crystals, which settle with their long axes approximately horizontal, depolarize a radar beam pointed to zenith as randomly oriented, very nonspherical objects; thus, they are expected to depolarize the incident beam more than the planar crystal types for horizontal linear and circular (or near-circular) polarizations. At low radar elevation angles, these crystals depolarize the signal as highly nonspherical objects when irradiated edge-on but as spherical objects when irradiated end-on; here, they are expected to depolarize the signal less than the planar crystal types (Figs. 1 and 2).

Reinking et al. (1995b) have obtained depolarization measurements (EDR45) in deep clouds that explicitly identify needlelike crystals (type N1a). Those measurements demonstrate that columnar crystals can be detected and clearly separated from the planar types, drizzle, and other hydrometeors, at least when they occur as the dominant hydrometeor and the polarizations used to detect them are closer to circular than that provided by the 79.5° PRP. Those measurements were obtained in another project, with a 95° PRP, and are the subject of a separate study.

When depolarization is measured using a 79.5° PRP, the result is that the difference in EDR45 between zenith and low elevation angles is predicted to be relatively subtle but still potentially measurable for the columnar habits. Theoretically, EDR45 for the various columnar crystals randomly oriented in the horizontal plane changes by about 2.5 dB between zenith and 0° (Fig. 2). Appropriately, the predicted depolarizations for all elevation angles are substantially greater than the −14.8-dB value for spheres.

As LDR is calculated, the result is qualitatively the same in that the difference in depolarization between zenith and low elevation angles is also predicted to be less for the columnar habits than the planar ones; however, this difference, about 6–9 dB (Figs. 1a,b), is of significantly greater magnitude than those for EDR45. Furthermore, whereas LDR decreases monotonically with increasing β for planar crystals, it increases monotonically for columnar crystals. Given these two factors, LDR would be expected to offer a significant advantage in identifying columnar crystals and distinguishing them from planar types. However, as discussed in section 3, this advantage is expected to be confounded by the effect of random deviations in crystal orientation from the horizontal, which is greatly magnified in LDR. For example, a change in σθ from 3° to 10° (Fig. 1a vs Fig. 1b) shifts curves for columns by about 6 dB.

The layered cloud

The WISP climatology produced columnar crystals only in microphysically complex situations during the Ka-band radar observations. Using the 79.5° PRP, a few measurements in clouds with some columnar crystals were nevertheless obtained. Observations on 25 February 1994 offered a possible opportunity to measure depolarization from columnar and planar crystals simultaneously. Between 0540 and 0640 UTC, the radar monitored a cloud system about 3.5 km deep. Two solid cloud layers were separated by clear air and low-reflectivity wispy cloud layers and fallstreaks (Fig. 13a). A 0600 UTC sounding (Fig. 14) from a location 30 km east of the radar site showed one major and one minor inversion aloft capping the two main cloud layers near 1.5 and 3.4 km AGL. The range of temperatures through the shallow layers was appropriate for nucleation of a suite of different crystal habits: temperatures were suitable for nucleation of planar crystals in cloud between the surface and 1.3 km AGL (−10° to −16°C), columnar crystals between 1.3 and 2.5 km AGL (−5° to −10°C), and planar crystals above that (−10° to −15°C). However, a minimum in crystal growth rate occurs in the −9° to −12°C temperature regime (Ryan et al. 1976), so the habit transition through −10°C can result in relatively isometric crystals (a/b nearer unity) such as blocky columns; these tend to be superior rimers and graupel embryos at smaller sizes than plates, dendrites, or needle crystals due to their higher terminal velocities (Fukuta et al. 1982; Bruintjes et al. 1987). The upper cloud layer occurred over the radar site even though the air was not saturated over the sounding site. Within the radar’s field of view, the upper layer was quite tilted and had bases as low as 1.7 km, indicating temperatures as warm as −6°C (toward azimuth 42° in Fig. 13a).

Snow crystals sampled during the radar observations between 0540 and 0640 UTC show the suite of ice types produced (Fig. 15): 600–1000-μm graupel, indicating heavy riming in some part of the cloud (Figs. 15a,g); graupel with needlelike protrusions, indicating secondary growth while falling through the columnar temperature regime (Figs. 15b,f); columnar crystals, including 700–1500-μm sheaths or needles and bundles of needles (N1a,b,c; Figs. 15c,d,e,g); and, finally, planar crystals, predominantly 2000-μm stellars and dendrites (P2a,b,c; Figs. 15d,f,g), and 800-μm crystals with sectorlike branches (P1b, Fig. 15e). The indicated snow crystal sizes are taken from only a few samples and therefore are only very approximate representations of the actual distributions. Notably, most of the columnar and planar crystals were completely unrimed, indicating that they did not form in the same layer as the graupel.

The EDR45 measurements

The pattern in the 15 RHIs inspected clearly defined distinct differences among the depolarizations within the upper, middle, and lower clouds, as shown in the RHI sample from 0551 UTC in Fig. 13b. The EDR45 shows a perceptible, but slight, dependence on β in the upper layer, a less subtle dependence on β in the intervening wispy cloud, and a strong dependence on β in the lower layer. The EDR45 values in the upper cloud are offset from −14.8 dB for spherical hydrometeors. The reflectivity in the lower cloud was only −4 to +2 dBZ, and that in the upper layer was larger (2–8 dBZ). The measurements at 30° and higher in the upper cloud were within the 6-km range. Within the lower cloud, the depolarization signatures remained very strong out through the maximum range of the scan (12.5 km). Vertically, the demarcations in depolarization among the layers were quite abrupt; that is, there was no gradual decay of signal along the beam.

Figure 16 shows EDR45 versus β plotted for several altitudes from the 0551 UTC RHI. Table 1 lists the average values of EDR45 and LDR measured in the PRP rotations that followed the noted RHI by 6–14 min; the variances (±) are maximum deviations, as before. Trends with increasing altitude can be noted. This figure and table are the basis of the following discussion.

Within the upper layer, at 2.8 km AGL, EDR45 was −13.9 dB at both 45° and 90° elevation, and LDR was +30.6 and +31.7 dB at 45° and 90°, respectively. These were essentially independent of elevation angle, showed some depolarization (as opposed to spheres), and were equal to the values obtained for graupel (section 6). These values are from the PRP rotations (Table 1). Through 2.8–3.0 km AGL, the RHI hints at an elevation-angle dependency, with an EDR45 difference between 90° and 45° ranging from 0.2 to 0.8 dB (e.g., it was about 0.5 dB at 2.8 km AGL in Fig. 16). The theoretical curve for blocky solid columns with a/b = 0.7 in Fig. 2 indicates a difference of 0.6 dB between a depolarization of −13.7 dB at 90° and −13.1 dB at 45°. The temperatures of −10° to −12°C were appropriate for nucleation of the slow-growing, fast-riming, nearly isometric crystals such as blocky columns in much of this cloud layer. In unrelated field sampling, Bruintjes et al. (1987) found blocky columns that formed around −10°C.

The occurrence of nearly isometric, rapidly riming crystals and the consequent formation of graupel in only the upper layer explains the separate formation of long columns and planar crystals, without significant riming, at appropriate temperatures in the middle and lower cloud layers. These factors may also explain the relatively larger reflectivity of the upper layer, which is apparently due to the sizes and concentrations of a combination of blocky columns, graupel, and the water drops that were being collected as rime. The graupel particles that actually precipitated, however, were insufficient to suppress the other crystal depolarization signatures while falling through the lower cloud layer. This observation corroborates the reflectivity RHI (Fig. 13a) that shows only weak reflectivity fallstreaks interspersed with clear air below the upper cloud layer.

In the lower cloud layer, the RHI scans clearly showed the dominant EDR45 signature of planar crystals (Fig. 13b, and 0.5 and 0.9 km AGL curves in Fig. 16). At approximately 0.7 km AGL and lower altitudes, EDR45 changed most dramatically between β = 90° and 45° to reach a very high depolarization at the lowest elevation angles (∼−5.5 dB at 5°); this is accounted for by the sampled sector-branched crystals (Fig. 15e), which are similar to plates and therefore depolarize more like plates than the sampled stellars and dendrites (Fig. 2). The observed range of temperatures supports this range of habit development within the lower layer. EDR45 reached about −13.9 to −14.5 dB at zenith in several low-altitude samples from the RHI and in the rotating PRP measurements (Table 1), compared to the expected −14.6 dB for these habits (e.g., as in Figs. 2 and 5).

With increasing altitude (contrary to the effect of aggregation described by Reinking et al. 1993), above 0.7 km AGL, the EDR45β curves flatten as the overlying regimes appropriate for columnar crystal nucleation are reached (Fig. 16). According to the temperature sounding (Fig. 14), the RHI sample for 1.3 km AGL is at the base of the columnar-crystal-producing regime. Near this altitude, the columnar crystals would have attained their greatest sizes (smallest aspect ratios, a/b) and provided their strongest depolarizations. EDR45 measured at 1.3 km AGL (Fig. 16) was approximately −13.2 dB at 90° and −11.8 dB at 45° elevation; at 1.4 km AGL, for example, the respective depolarizations were similar (about−13.4 and −11.2 dB). Depolarizations of the same magnitudes were measured at the same altitudes in the subsequent PRP rotations (Table 1). Theoretically, 700-μm needles with a density of 0.5 g cm−3, in an approximation representative of those sampled, would produce depolarizations of −11.9 dB at 90° and −11.3 dB at 45° (Fig. 2); these values match within 0.1 dB those from Fig. 5 in Matrosov et al. (1996) for needles with a density of 0.6 g cm−3 and a median size of 1000 μm, which more closely approximate the sizes observed.

Thus, the observed depolarization, as represented by the 1.3-km AGL curve in Fig. 16, is offset from the curve for 2.8 km AGL, similar to model curves in Fig. 2 indicating that needles would be offset from blocky columns. The magnitudes of the observed values at β = 45° are comparable to the theory for needles, but those for β = 90° are about 1.4 dB less depolarized than the theory. The measured values at 1.3-km altitude do show a dependence on β that was appropriately intermediate to depolarizations due to the planar crystals in the lower layer and the blocky columns deduced as the source of graupel in the upper cloud layer (Fig. 16 and Table 1). However, this slope of the EDR45β curve for 1.3 km AGL is slightly greater than that theoretically expected for columnar crystals (but much less than expected for planar crystals). This slope persisted with reasonable consistency up through 2.5 km AGL (Fig. 16), through the entire long-column nucleation regime, although the curves above about 1.5 km generally became erratic due to weak and spatially intermittent cloud. If 1) this slope had been influenced by added planar crystals (which could have nucleated at the temperatures of highest cloud tops), or if 2) the midlevel depolarizations were not due to columns at all, but rather to planar crystals whose signatures were partially suppressed by graupel, depolarization signatures of the planar types should have been measured above the columnar nucleation layer; such evidence was not found. If planar crystals and graupel coexisted and precipitated together from the upper layer, why then would the signature suppression by graupel decrease from the upper layer downward into the midlevels? This could only occur if new crystals nucleated and became dominant at the midlevels; however, according to the temperature structure, the new crystals had to be columnar. Despite all of these good arguments, the magnitudes and slopes of the EDR45β curves, together with those of the LDR–β relationships in the next section, hint at a mix of some planar crystals dominated by columns at the middle cloud levels.

Clearly, varied mixes of hydrometeor types occurred throughout the depths of the observed cloud layers, so “pure” depolarization signatures were not measured. Despite the lack of pure signatures, however, the EDR45 theoretical and measured values are sufficiently similar to deduce, with the help of the temperature sounding and the sampled crystals, that the depolarizations from blocky columns and needles were detected and reasonably quantified within this less than simple cloud system.

The LDR measurements

As with the measurements of other crystals in other clouds, LDR was more variant and less definitive than EDR45. For columnar crystals, the LDR is predicted to decrease by about 3 dB from β = 45° to β = 90°; in opposition, the LDR for planar crystals is predicted to increase by about 6 dB for the same increase in β (Figs. 1a,b). A comparison of LDR values in Table 1 and theoretical curves in Figs. 1a,b leads to the following results.

In the observed planar crystal layer, at 0.5 km AGL (Table 1), LDR appropriately increased with β, but by only about 60% of the predicted increment (∼3.5 dB). The curve defined by LDR at 45° and 90° elevation does intersect the theoretical curve for dendrites with σθ = 10° and agrees with the modeled values to within about 1.5 dB. This is good agreement and consistent with the findings on branched planar crystals (section 5).

At 0.9 km AGL, where the planar crystals were less prominent but still dominant according to the EDR45 data in Fig. 16, the increase in LDR with β was minimal (∼1.2 dB) and well within the range of maximum deviations. The near-zero slope of the LDR–β relationship as measured commits neither to planar nor columnar crystals. With LDR near 30 dB, the indicated depolarization is separated from the model for σθ = 10° by about +6 dB at β = 45° and +1 dB at β = 90° (Table 1 vs Fig. 1b), whereas for σθ = 3° the separation is about −0.3 dB at 45° and −4 dB at 90°. In all, neither the magnitudes nor the slope of the curve defined by the data provide a good fit to the planar crystal models.

Noncommittal differences in LDR between 45° and 90° carry into the long-column-producing layer. Increases rather than the expected decreases with elevation angle are suggested, but slopes of the curves defined by the data are zero within the measured maximum deviations (Table 1, 1.3–1.5 km AGL). In this layer the magnitudes of LDR were in the range of 24.3–29.2 dB; these values are intermediate to those predicted for planar and columnar types if σθ = 3° (Fig. 1a) and closest to the magnitude predicted for planar crystals if σθ = 10° (Fig. 1b). This is inconsistent with temperatures measured in this cloud layer and the crystal types sampled at the ground.

In the upper cloud layer, the LDR magnitudes, near 30 dB, were consistently among the largest (Table 1, 2.8 and 3.0 km AGL) and generally differentiable from those measured in the lower layers where the other crystal types prevailed. This case of least depolarization fits graupel, which were the most spherical particles observed in this case. However, the measured LDR values are not differentiable from those measured at 0.9 km, where the planar crystal depolarizations in EDR45 were dominant but degraded by the mix of other hydrometeors also falling through that altitude. It may require explicit modeling of the mix to explain this similarity. The 30-dB values indicate 4–6 dB less depolarization than would be caused by blocky columns (Figs. 1a,b), suggesting that graupel dominated the upper layer. The credibility of this deduction is tainted by the lack of distinction from the crystals of the mix at the lower altitude. In all, the measured LDR–β relationships do not commit to curves that would clearly identify either planar or columnar crystals except in the planar-dominant regime at 0.5 km AGL.

Conclusions

Models of depolarizations caused by snow crystals and corresponding measurements made with a selectable-dual-polarization Ka-band radar have been examined and compared. Snow crystal samples provide “truth” for most of the measurements. The theoretical calculations relate depolarization ratios for horizontal-linear and elliptical polarization states to radar elevation angle. Effects of ice crystal aspect ratio, bulk density, and randomness of settling orientation have been considered; possible electrical effects on orientation have not been considered. The elliptical polarization state applied was that for a 79.5° phase shift induced by the phase-retarding plate in the transmitted radiation. The models, extended from previous works, predict that planar crystals and columnar crystals should be readily differentiable as groups, especially when occurring in common, mature size distributions and singularly or dominantly within some portion of a cloud system. Within either the planar or columnar crystal group, many of the individual basic habits are also predicted to be separable because the depolarizations they cause should differ by several decibels.

Contrarily, some worst-case scenarios with less than mature size distributions were also examined. Here, the calculated depolarizations induced by some of the individual habits within either group tend to cluster in the models for size distributions with similar median size, aspect ratio, and density. Also, the calculated curves show that depolarizations for some differing crystal types superimpose when the crystals reach mature growth, according as aspect ratio and density interact. Complementary information on cloud temperature structure, indicating which habits can be nucleated, can help to discriminate among such nonunique depolarization signatures.

Experimental depolarization data have been presented for drizzle, dendrites, thick plates, graupel, thick plates mixed with graupel, and a comparatively complex case with evidence of blocky columns, graupel, needles, sectors, and dendrites. Reinking et al. (1995b) have presented other data for needles, and Matrosov et al. (1996) have additionally presented data for aggregates of dendrites. The point-measurement snow crystal samples at ground level could not precisely represent the radar measurement volumes, but they quite accurately identified crystal types and, with cloud-temperature profiles, linked those types to generating cloud layers. Collectively, the data have verified that measurements of depolarization with a Ka-band radar provide good estimates of the identity of a dominant or singularly occurring hydrometeor type; such measurements can also characterize the mix of two hydrometeor types, once the depolarizations from individual types are identified in generating layers of the cloud. Of course, this has been most readily accomplished with cloud layers that were reasonably stratified or otherwise horizontally homogeneous on scales on the order of 10 km or longer. Knowledge of the depolarization gradients, temperature structure, and the context provided by the reflectivity of the cloud have assisted in deciphering hydrometeor type in the more complex situations.

The elliptical depolarization ratio EDR45, which corresponds to 45° rotation of the 79.5° PRP used in the radar for this study, provided measurements in close agreement with theory. However, the models predict that the signatures of columnar crystals, as defined by the variation of the EDR with radar elevation angle, will be subtle compared to those for planar types for the 79.5° PRP. The measurements show that differentiation of columnar types from graupel or within the nucleation zones leading to mixes of crystal types can be difficult without a phase shift nearer to circular.

The depolarization of the elliptically polarized radar signals caused by graupel was distinguishably different from the signature of nondepolarizing drizzle in multiple samples and is compatible with theoretical concepts. However, the repeatability of this small difference needs to be established through more observations. Additional differentiating information may come from the spatial or temporal variance of the depolarization ratio, with drizzle exhibiting the lesser variance.

Matrosov et al. (1996) compared the use of linear, circular, and elliptical depolarizations, and further comparisons have been made here. LDR is on the order of five- to eightfold more sensitive than EDR45 to collective signal-degrading influences such as low-reflectivity cloud and randomness in settling crystal orientation (i.e., crystal canting angle and aspect ratio relative to the radar beam). LDR may also be influenced by limitations of the fine-angle sampling in rotations of the PRP used in these studies, although EDR45 values were essentially the same when measured either with the rotating PRP or in RHIs. The net result is that LDR was found to fluctuate more and provide less definitive identification of crystal types than its elliptical counterpart. For pristine dendrites, EDR45 combined with the temperature measurements provided the specific crystal habit identification, whereas LDR indicated only that the crystals were planar. LDR, however, did provide an estimate of the randomness of orientation of these crystals, which was on the order of 10° in the observations. This indicates that the information in the measurements can be enhanced by obtaining both LDR and EDR45 measurements with the rotating PRP. As with EDR45, the LDR measurements also clearly differentiated graupel and crystals with regular growth habits from spherical drizzle. However, the LDR measurements did not clearly differentiate dominant columnar or planar crystals when complexities of ice hydrometeor mixes occurred. Also, the theoretical computations have a number of adjustable parameters, and imprecise or incomplete representations here may also influence the fits to the measurements.

In summation, according to the models, for a fixed polarization state, measurements of the depolarization ratio as a function of radar elevation angle will separate ice crystal types according to their physics, at least where clouds are reasonably homogeneous horizontally. Measurements of EDR45 quantitatively support the models. The rotating PRP offers additional opportunity for crystal type discrimination by rapidly varying the transmitted polarization state for alternating measurements of EDR45 and LDR. However, measurements of EDR45 have provided the greater differentiation among hydrometeor types. Repeatability of the results has been demonstrated for selected cases. Dual-polarization radar provides the means to follow the microphysical transitions that not only determine the ice crystal habits generated, but also crystal aggregation and graupel-forming processes. The kind of information derived from the reported models and experiments will help to define the presence, nature, and evolution of cloud ice and drizzle.

Acknowledgments

Robert Kropfli was instrumental in technically and fiscally facilitating the development of the polarization technology. Bruce Bartram and Kurt Clark engineered and operated the radar and received the NOAA Bronze Medal for their innovations; Michelle Ryan processed the radar data. This work was funded by the Winter Icing and Storms Program of the Federal Aviation Administration’s Aviation Weather Development Program through a subcontract with the National Center for Atmospheric Research. Drs. Roy Rasmussen and Marcia Politovich directed WISP. The views expressed are those of the authors and do not necessarily represent the official position of the U.S. government.

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Fig. 1.
Fig. 1.

Modeled LDR (dB; ϵ = 0) as a function of radar elevation angle β (°) for ice crystals of basic regular growth habits with median sizes measured in nature and randomness of orientation for (a) σθ = ±3° and (b) σθ = ±10°. Spherical droplets would be represented by a horizontal line at +35 dB, the cross-talk limit of the radar antenna.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 2.
Fig. 2.

Elliptical depolarization ratio EDR45 as a function of radar elevation angle β for ice crystals of basic growth habits with median sizes measured in nature; EDR45 = −14.8 dB for spherical hydrometeors. Based on the model of Matrosov et al. (1996) for the 79.5° PRP (ϵ = 0.832); σθ = ±3°.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 3.
Fig. 3.

Examples of conceivable but unlikely worst-case coincidence of EDR45β relationships for ice crystals of basic growth habits and equal size, or with offsetting effects of density and aspect ratio; (a) planar crystals and (b) columnar crystals. Model as in Fig. 2.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 4.
Fig. 4.

Time series of EDR from a complete rotation of the 79.5° PRP at β = 30° in drizzle (6 April 1993). Time equates to plate rotation angle, with maximum to minimum EDR represented in each 45° of rotation. Positive limits correspond to LDR; negative limits correspond to EDR45.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 5.
Fig. 5.

Experimental EDR45 vs β from a 175° over-the-top RHI through dendrites (1 km AGL at 2057 UTC 11 March 1993) and modeled curves for dendrites with median sizes of 1500 (a/b ≈ 0.038, ρ ≈ 0.51 g cm−3) and 2000 μm (a/b ≈ 0.035, ρ ≈ 0.45 g cm−3).

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 6.
Fig. 6.

Time series of EDR from PRP rotation (as in Fig. 4) for dendrites; (a) β = 90°, (b) β = 30°, and (c) β = 10° (11 March 1993).

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 7.
Fig. 7.

Photographs of graupel sampled at the radar site at 2100–2111 UTC 8 February 1994; particles are 1.7 and 3.2 mm (1-mm scale divisions).

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 8.
Fig. 8.

EDR45 vs β from RHI scans through drizzle (2114 UTC 6 April 1993) and graupel (2100 UTC 8 February 1994).

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 9.
Fig. 9.

Time series of EDR from PRP rotation (as in Fig. 4), in graupel, for (a) β = 45° and (b) β = 90° (8 February 1994). There is no significant variation with elevation and angle, but LDR and EDR45 are measurably offset from the limiting values for spheres.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 10.
Fig. 10.

Over-the-top RHI of (a) Ze (dBZ) and (b) EDR45 (dB) at 2039 UTC 8 February 1994; 2-km range rings. Three distinct depolarization zones are indicated. (c) Photograph of thick plates (∼200–300 μm) scavenged by graupel (∼ 1.5 mm × 1.0 mm) from cloud zone 2.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 10.
Fig. 10.

(Continued )

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 11.
Fig. 11.

EDR45 vs β for thick plates (left half) and graupel–thick-plate mix (right half) from RHI measured as graupel shower reached the radar (center); 0.5 km AGL at 2047 UTC 8 February 1994.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 12.
Fig. 12.

Thick-plate model depolarizations with crystal axis ratio and σθ specified, and measured EDR45 as a function of β for three sampling altitudes.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 13.
Fig. 13.

(a) RHI scan of Ze at 0551 UTC 25 February 1994 (scale is 8 to −20 dBZ, with 3-km range rings); (b) corresponding EDR45 (scale of −4 to −16 dB). Azimuth 42° is to the right in the figure.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 14.
Fig. 14.

Sounding of temperature and dewpoint (°C) approximately 30 km from the radar at 0600 UTC 25 February 1994. Vertical scales are in kilometers at mean sea level and millibars (subtract 1.5 km for altitude AGL); the ground level is indicated by the base of the sounding.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 15.
Fig. 15.

Photographs of snow crystals sampled at the radar site between 0550 and 0640 UTC 25 February 1994. Scale represents 1 mm.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Fig. 16.
Fig. 16.

EDR45 vs β for indicated altitudes AGL within the cloud system depicted in Fig. 13. Altitude 2.8 km AGL (dashed) was within the upper cloud layer, where formation of blocky columns and graupel was indicated; 1.3 km AGL (solid) was near the top of the lowest layer and at the base of the needle or sheath crystal-nucleation regime of the middle clouds; 0.9 and 0.5 km AGL (dotted) were within the planar crystal-nucleation regime of the lowest layer.

Citation: Journal of Applied Meteorology 36, 4; 10.1175/1520-0450(1997)036<0322:IOHWEA>2.0.CO;2

Table 1.

Averages of EDR45 and LDR measured in layered cloud with the rotating PRP at 0557–0605 UTC 25 February 1994.

Table 1.
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  • Bruintjes, R. T., A. J. Heymsfield, and T. W. Krauss, 1987: An examination of double-plate ice crystals and the initiation of precipitation in continental cumulus clouds. J. Atmos. Sci.,44, 1331–1349.

  • Fukuta, N., M. W. Kowa, and N. H. Gong, 1982: Determination of ice-crystal growth parameters in a new supercooled cloud tunnel. Preprints, Conf. on Cloud Physics, Chicago, IL, Amer. Meteor. Soc., 325–328.

  • Kropfli, R. A., and Coauthors, 1995: Cloud physics studies with 8-mm-wavelength radar. Atmos. Res.,35, 299–313.

  • Magono, C., and C. W. Lee, 1966: Meteorological classification of natural snow crystals. J. Fac. Sci., Hokkaido Univ. Ser. 7,2, 321–335.

  • Martner, B. E., and R. A. Kropfli, 1993: Observations of multilayered clouds using Ka-band radar. Proc. 31st Aerospace Sciences Meeting and Exhibit, Reno, NV, Amer. Inst. Aeronautics and Astronautics, 1–8.

  • Matrosov, S. Y., 1991a: Theoretical study of radar polarization parameters obtained from cirrus clouds. J. Atmos. Sci.,48, 1062–1070.

  • ——, 1991b: Prospects for the measurement of ice-cloud particle shape and orientation with elliptically polarized radar signals. Radio Sci.,26, 847–856.

  • ——, R. F. Reinking, R. A. Kropfli, and B. W. Bartram, 1996: Estimation of ice hydrometeors types and shapes from radar polarization measurements. J. Atmos. Oceanic Technol.,13, 85–96.

  • Pruppacher, H. R., and J. D. Klett, 1978: Microphysics of Clouds and Precipitation. D. Reidel, 714 pp.

  • Rasmussen, R., and Coauthors, 1992: Winter Icing and Storms Project (WISP). Bull. Amer. Meteor. Soc.,73, 951–974.

  • Reinking, R. F., 1974: Empirical assessment of accretion microphysics. Dissertation Abstracts International, Vol. 35, No. 3, Xerox University Microfilms, 365 pp.

  • ——, and J. F. Boatman, 1986: Upslope precipitation events. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., 437–471.

  • ——, B. W. Orr, B. B. Stankov, and C. A. Davis, 1993: NOAA Ka-band cloud-sensing radar measurements during WISPIT. Preprints, Fifth Int. Conf. on Aviation Weather Systems, Vienna, VA, Amer. Meteor. Soc., 130–134.

  • ——, S. Y. Matrosov, B. E. Martner, R. A. Kropfli, and B. W. Bartram, 1995a: Hydrometeor identification with millimeter-wave dual-polarization radar. Preprints, Conf. on Cloud Physics, Dallas, TX, Amer. Meteor. Soc., 47–49.

  • ——, ——, R. T. Bruintjes, B. E. Martner, and R. A. Kropfli, 1995b: Further comparison of experimental and theoretical radar polarization signatures due to ice-hydrometeor growth habit. Preprints, 27th Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 47–49.

  • ——, ——, and ——, 1996: Hydrometeor identification with elliptical polarization radar: Applications for glaciogenic cloud seeding. J. Wea. Modif.,28, 6–18.

  • Ryan, B. F., E. R. Wishart, and D. E. Shaw, 1976: The growth rates and densitites of ice crystals between −3°C and −21°C. J. Atmos. Sci.,33, 842–851.

  • Shurcliff, W. A., 1962: Polarized Light. Harvard University Press, 208 pp.

  • Vivekanandan, J., V. Bringi, M. Hagan, and P. Meischner, 1994: Polarimetric radar studies of atmospheric ice particles. IEEE Trans. Geosci. Remote Sens.,32, 1–10.

  • Fig. 1.

    Modeled LDR (dB; ϵ = 0) as a function of radar elevation angle β (°) for ice crystals of basic regular growth habits with median sizes measured in nature and randomness of orientation for (a) σθ = ±3° and (b) σθ = ±10°. Spherical droplets would be represented by a horizontal line at +35 dB, the cross-talk limit of the radar antenna.

  • Fig. 2.

    Elliptical depolarization ratio EDR45 as a function of radar elevation angle β for ice crystals of basic growth habits with median sizes measured in nature; EDR45 = −14.8 dB for spherical hydrometeors. Based on the model of Matrosov et al. (1996) for the 79.5° PRP (ϵ = 0.832); σθ = ±3°.

  • Fig. 3.

    Examples of conceivable but unlikely worst-case coincidence of EDR45β relationships for ice crystals of basic growth habits and equal size, or with offsetting effects of density and aspect ratio; (a) planar crystals and (b) columnar crystals. Model as in Fig. 2.

  • Fig. 4.

    Time series of EDR from a complete rotation of the 79.5° PRP at β = 30° in drizzle (6 April 1993). Time equates to plate rotation angle, with maximum to minimum EDR represented in each 45° of rotation. Positive limits correspond to LDR; negative limits correspond to EDR45.

  • Fig. 5.

    Experimental EDR45 vs β from a 175° over-the-top RHI through dendrites (1 km AGL at 2057 UTC 11 March 1993) and modeled curves for dendrites with median sizes of 1500 (a/b ≈ 0.038, ρ ≈ 0.51 g cm−3) and 2000 μm (a/b ≈ 0.035, ρ ≈ 0.45 g cm−3).

  • Fig. 6.

    Time series of EDR from PRP rotation (as in Fig. 4) for dendrites; (a) β = 90°, (b) β = 30°, and (c) β = 10° (11 March 1993).

  • Fig. 7.

    Photographs of graupel sampled at the radar site at 2100–2111 UTC 8 February 1994; particles are 1.7 and 3.2 mm (1-mm scale divisions).

  • Fig. 8.

    EDR45 vs β from RHI scans through drizzle (2114 UTC 6 April 1993) and graupel (2100 UTC 8 February 1994).

  • Fig. 9.

    Time series of EDR from PRP rotation (as in Fig. 4), in graupel, for (a) β = 45° and (b) β = 90° (8 February 1994). There is no significant variation with elevation and angle, but LDR and EDR45 are measurably offset from the limiting values for spheres.

  • Fig. 10.

    Over-the-top RHI of (a) Ze (dBZ) and (b) EDR45 (dB) at 2039 UTC 8 February 1994; 2-km range rings. Three distinct depolarization zones are indicated. (c) Photograph of thick plates (∼200–300 μm) scavenged by graupel (∼ 1.5 mm × 1.0 mm) from cloud zone 2.

  • Fig. 10.

    (Continued )

  • Fig. 11.

    EDR45 vs β for thick plates (left half) and graupel–thick-plate mix (right half) from RHI measured as graupel shower reached the radar (center); 0.5 km AGL at 2047 UTC 8 February 1994.

  • Fig. 12.

    Thick-plate model depolarizations with crystal axis ratio and σθ specified, and measured EDR45 as a function of β for three sampling altitudes.

  • Fig. 13.

    (a) RHI scan of Ze at 0551 UTC 25 February 1994 (scale is 8 to −20 dBZ, with 3-km range rings); (b) corresponding EDR45 (scale of −4 to −16 dB). Azimuth 42° is to the right in the figure.

  • Fig. 14.

    Sounding of temperature and dewpoint (°C) approximately 30 km from the radar at 0600 UTC 25 February 1994. Vertical scales are in kilometers at mean sea level and millibars (subtract 1.5 km for altitude AGL); the ground level is indicated by the base of the sounding.

  • Fig. 15.

    Photographs of snow crystals sampled at the radar site between 0550 and 0640 UTC 25 February 1994. Scale represents 1 mm.

  • Fig. 16.

    EDR45 vs β for indicated altitudes AGL within the cloud system depicted in Fig. 13. Altitude 2.8 km AGL (dashed) was within the upper cloud layer, where formation of blocky columns and graupel was indicated; 1.3 km AGL (solid) was near the top of the lowest layer and at the base of the needle or sheath crystal-nucleation regime of the middle clouds; 0.9 and 0.5 km AGL (dotted) were within the planar crystal-nucleation regime of the lowest layer.

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