1. Introduction
Through nearly a decade of studies beginning with the Winter Icing and Storms Projects (Rasmussen et al. 1992), a radar remote sensing capability has been sought to identify ice particles in glaciated and mixed-phase clouds and, specifically, to distinguish clouds of supercooled, 50–500-μm-diameter, drizzle-sized droplets from clouds of the various ice particles. The wavelength at Ka band (8.66 mm) is suitable for detection of these droplets, which are small compared to raindrops, snowflakes, and hail. Explicit identification of these droplets is the focal interest because they can present a particularly severe aircraft icing hazard when supercooled (Politovich 1996; Ashendon et al. 1996; Ashendon and Marwitz 1997, as summarized by Reinking et al. 1997b). Explicit identification of the differing ice particles is important as well because some types will themselves create hazards to aircraft, and because ice particles of differing growth characteristics, through vapor consumption and riming, can influence liquid water content, droplet size, and droplet lifetime in mixed phase clouds. Thus, there are advantages in differentiating among not only the pristine ice crystals of “regular” growth habits (the basic planar and columnar types) but also among the more spherical and irregular ice particles such as graupel and aggregates, and between all of these and drizzle droplets.
The results of the series of studies including this one show that dual-polarization Ka-band radar can be used to identify drizzle and the various ice hydrometeors in clouds and precipitation. However, selection of the polarization state is important. This is demonstrated through scattering calculations and measurements. Ensembles of ice crystals settle with the mean orientation of their major dimensions near horizontal, but the standard deviations of angles from this preferred orientation are variable and unpredictable (where, for example, 3° is minimal and 15° is substantial). Thus, the basic premise of this paper is that the best polarization states will be those that maximize the measured signals and differentiate the hydrometeors but are not very sensitive to the standard deviations of the orientation angle, and a linear or even better, an approximately linear polarization transmitted at a 45° slant is therefore a natural choice.
Any of several polarimetric measurands singularly or in combination demonstrate some sensitivity to particle type (Table 8.1 in Doviak and Zrnić 1993; Zrnić and Ryzhkov 1999). In this study, the radar polarization parameter measured for this purpose is the depolarization ratio (DR) a parameter influenced predominantly by hydrometeor type if the appropriate polarization state is used. DR is defined as the logarithm of the ratio of power returned in the “weak” channel to power returned in the “strong” channel when a polarized signal is transmitted, where these receiving channels are orthogonal. Hydrometeors of the various types will depolarize and backscatter the transmitted microwave radiation according to their aspect ratio (prolate or oblate shape), settling orientation, and bulk density, and the polarization state of transmitted radiation. The first three factors are determined by cloud properties, but the fourth, the polarization state, can be engineered.
The transmitted polarization state can be selected from a continuum of possible elliptical polarizations, where linear and circular define the limits. In general, linear polarization transmitted in the horizontal plane, and received in both the same, co-polar plane and the perpendicular (vertical), cross-polar plane, is most commonly employed for dual-polarization measurements. Circular polarization has also been investigated and utilized for various purposes. These studies include tracking of chaff fibers that are in some respects an extremely elongated representation of columnar crystals (Martner and Kropfli 1989) and an attempt at hydrometeor identification by Hendry and Antar (1984). Circular polarization applied to particle identification has been considered theoretically by Matrosov (1991) and Matrosov et al. (2001).
The transmitted polarization state determines the magnitude of the separation or isolation in DR of each category of hydrometeor. In selecting from the available continuum, the states nearer to optimal for this purpose would maximize the isolation, but only so much as allowed by practical, compromising limitations in radar performance that influence the measurement. Thus, it is appropriate to ask, how much separation in detected DR is sufficient for an explicit and deterministic measurement, and what polarizations can be transmitted to accomplish this? We define a deterministic measurement in the normal sense, as one that will estimate particle type directly by measuring one parameter, the values of which are uniquely defined by theory for the particular particle types. This estimate is made without relying on the use of a probabilistic approach, such as techniques involving neural networks, statistical decision theory, or fuzzy logic, which combine several parameters that only in combination will tend to uniquely identify a particle type (e.g., Liu and Chandrasekar 2000). The next question is this: Given that the more regular crystals can be most readily differentiated by this method, can the more spherical and irregular shapes of ice particles, with wide-ranging bulk densities, such as blocky columns, graupel, and aggregates also be differentiated among themselves and from drizzle droplets by measuring the same single parameter?
Several polarization states have now been investigated using NOAA/K, the Environmental Technology Laboratory's (ETL) cloud-sensing, selectable dual-polarization, scanning Doppler Ka-band (8.6-mm) radar (Kropfli et al. 1995; Kropfli and Kelly 1996). In the next section, the method for measuring the depolarization ratio is outlined for the NOAA/K technology, and our previous investigations are reviewed as some of the options for the appropriate polarization state are examined and required compromises are considered. The reasons are established for exploring a 45° slant, quasi-linear polarization state. The justification for the slight ellipticity that sets this state apart from a true linear one is examined. Then the scattering theory that is the foundation is presented.
To test the performance of this polarization state by measuring slant quasi-linear depolarization ratio (SLDR) at 45° (SLDR*-45) in the field, the radar was deployed for the Mount Washington Icing Sensors Project (MWISP) to categorize hydrometeors in clouds formed in the forcing of orographic and cyclonic circulations over the slopes of Mt. Washington, New Hampshire. MWISP was conducted in April 1999 (Ryerson et al. 2000). As the acronym indicates, the focus was on testing several state-of-the-art remote sensors for their capabilities in detecting and measuring cloud characteristics that cause aircraft icing. The radar site was midway up the west slope of the mountain. Supporting data on Hydrometeor types and atmospheric conditions were gathered at the Mount Washington Observatory (MWO) at the summit, from the radar site, and from an aircraft. The results of the polarization measurements made at MWISP are interpreted with verification from the supporting data.
2. Background
Spheres do not depolarize microwave radiation transmitted in a linear or circular state, so drizzle-sized droplets, which are nearly or truly spherical, show minimal or no depolarization. This is the limiting case for which DR → −∞ for the ideal antenna. However, when the transmitted signal is not linear or circular, but rather has some ellipticity, even spheres including drizzle will depolarize the signal to some degree and return a nonzero signal in the weak channel. For any polarization state, the value of DR for spheres will be a constant, independent of the elevation or azimuth angle at which the radar points at them.
In practice, DR has a lower limit that bounds the measurements in either channel and is established by the antenna polarization cancellation ratio (cross-talk) and receiver noise. No longer does DR → −∞ for the nondepolarizing targets; rather their DR is defined as the decibel value of the cross-talk. The weak channel signal is usually significantly (e.g., tens of decibels) weaker than the strong channel signal. If the reflectivity (the strong-channel signal) of a cloud is low, the orthogonal, weak-channel signal can easily drop below the receiver noise, irrespective of the phase and other properties of the cloud particles. In that case, spherical and shaped particles are not separable in DR. The DR of any particular particle type is not measurable as a unique signature at this limit. In contrast, some ellipticity in the transmission enhances the weak-channel return relative to that in the strong channel, so the DR value for spheres will be a unique, measurable value above the cross-talk limit. Since the reflectivity of a cloud of drizzle-sized droplets can be at least as low as −15 dBZ, the radar must be able to measure a much fainter weak-channel return in low-reflectivity clouds. This is what is needed to uniquely distinguish drizzle from all forms of ice. Matrosov and Kropfli (1993) predicted this advantage to the measurement of DR offered by some ellipticity, and it was experimentally demonstrated with an elliptical polarization achieved with our first PRP, for which the ability to detect and measure DR in low-reflectivity clouds at relatively long ranges was enhanced by a strengthened return in the weak channel (Matrosov et al. 1996; Reinking et al. 1997a,b). For the linear and circular polarization states, in clouds with more substantial reflectivities, the weak-channel return will place the DR of significantly nonspherical particles above the cross-talk, but spherical drizzle and quasi-spherical ice particles like graupel can produce weak-channel returns that still can be lower than receiver noise. Thus, unique identification of spherical droplets by default can fail. The positive effect of ellipticity is examined further with our scattering calculations.
For particles that are randomly oriented in the horizontal plane (and therefore randomly oriented with respect to the antenna's azimuth angle), depolarizations caused by nonspherical particles will be greater than those caused by spherical particles for linear, circular, and slightly elliptical polarizations. (An exception occurs for the case when all the nonspherical particles are aligned along the electric vector of the linear polarizations. In this case, which is conceivable in strong electric fields, nonspherical particles will be indistinguishable from spheres by their depolarization patterns.) Most ice particles will depolarize the signal significantly because they are nonspherical and settle with a preferred horizontal orientation, although the magnitude of depolarization by ice particles is somewhat diminished by the decrease in bulk density relative to that of solid ice, and both relative to the density of liquid water. Depending on the polarization state, in contrast to spherical droplets, the DR of some of the nonspherical ice particle types will show a dependence on radar elevation angle.
Unfortunately, DR for nonspherical hydrometeors also depends on the three-dimensional canting of the particles about their preferred horizontal orientation. Matrosov (1991) theoretically examined the potential for hydrometeor identification using the horizontal polarization (ε = 0), and a circular polarization (ε = 1). His calculations demonstrated the high sensitivity of the horizontal depolarization ratio, LDR, to variations in ice crystal settling orientations compared to that for CDR. This conclusion derives from considerations of the asymmetry of non-spherical ice particles, which imply that if a horizontally polarized incident electric field is aligned with one axis of the particles, there can be no orthogonally polarized backscatter, so theoretically LDR → −∞; however, when falling particles wobble, the resulting distribution of canting angles increases LDR (Doviak and Zrnić 1993). CDR is sensitive only to variation of canting in the plane perpendicular to the polarization plane (“front-to-back” canting, along the beam), not to variation of the canting in the polarization plane (“side-to-side” canting, across the beam), so the sensitivity to the variation of orientation, while not eliminated, is diminished (Matrosov et al. 2001). A linear polarization slanted at 45° is sensitive to both side-to-side and front-to-back canting, but substantially less sensitive than LDR. This is true because for predominantly horizontally oriented particles, the weak-channel returns maximize when the electric vector of incident radiation is slanted at 45°, and in the vicinity of a maximum, DR changes due to variations in canting are minimized. Thus, the use of SLDR-45 also diminishes the sensitivity to the variation of orientation.
Since differences in DR serve to separate the hydrometeors of different shapes, a polarization that produces a wider range in DR will result in larger separations. For both the horizontal and circular polarization states, the dynamic range in DR is theoretically infinite. In practice, the widest possible range in DR is that between 0 dB and the antenna cross-talk limit. This range is available to differentiate the signatures of the differing hydrometeors, although only particles with a rare combination of properties would cause complete depolarization, to 0 dB. Horizontal polarization is commonly used, but calculations presented later show that the functional dynamic range, that which can actually be utilized to measure DR to differentiate hydrometeors, is so much narrower than the available range for this state that the advantage of the latter is not realized. Although the dynamic range defined by the cross-talk limit is fixed, the magnitude of the effective or available dynamic range is state dependent. For particles randomly oriented in the horizontal plane, some ellipticity in the polarization reduces the available dynamic range to one bounded at its lower limit by the DR of spherical targets. This lower limit is above the antenna cross-talk limit, so the DR for spheres actually may be measured.
In practice, it is difficult to achieve true horizontal or circular polarization, and this is true of the PRP technology. This was demonstrated by our first attempt in manufacturing a PRP that produced an elliptical state (ψ = 79.5° instead of 90°, ε = 0.83 instead of 1.0, at β = 45°). The measurements of the corresponding elliptical depolarization ratio (EDR; Table 1) for specific hydrometeor types showed excellent agreement with scattering calculations. However, the available dynamic range of observable EDR values was, in terms of dB, less than half that allowed by the radar's antenna cross-talk, and the utilized range 25% narrower than the available range. This resulted in a narrow separation of hydrometeors for some types and restricted the differentiation of drizzle from some ice types including graupel and blocky columns (Matrosov et al. 1996; Reinking et al. 1997a,b). Reduction of both the available and utilized dynamic ranges can be minimized, however, by selecting a polarization state with an ellipticity that deviates only slightly from the true linear or circular state. This compromise can result in a wider utilized dynamic range than that possible with the linear state, and this allows greater distinction among the hydrometeor types (see section 4).
In summation, LDR is subject to the ambiguities imposed by poor weak-channel signal in low-reflectivity clouds, indistinguishable droplets versus quasi-spherical ice particles in the noise at the antenna cross-talk even with higher reflectivities, uncertainties due to variations in ice particle settling orientation that can be confused with differences in shape, and a restricted dynamic range in DR. The horizontal polarization state therefore is a poor selection for hydrometeor identification. This is demonstrated later by calculations and some measurements that build on those of Matrosov (1991) and Matrosov et al. (2001). The CDR, by comparison, demonstrates low sensitivity to variations in flutter in the orientation for columnar crystals, and shows substantial sensitivity for planar crystals only when the elevation angle exceeds about 50° (Fig. 1 in Matrosov et al. 2001). This relative insensitivity of CDR to orientation makes it a better candidate, but the ambiguity of identifying spherical droplets by default in the cross-talk, including the effects of poor return in the weak channel in low reflectivity clouds, must still be dealt with.
A linear polarization transmitted at a 45° slant from horizontal, and received at 45° and 135°, is simple to implement (the PRP technology is useful for research but is not required) and is the closest relative to the common horizontal linear polarization. For particles predominantly oriented in the horizontal, and for spheres, the slant-linear state is in effect similar to circular. This state is not commonly used, but is presently receiving consideration as a possible choice for the next Weather Surveillance Radar-1988 Doppler Next Generation Weather Radar (Brunkow et al. 1997; Doviak et al. 2000). A slight ellipticity is introduced by imperfection of the PRP used to transmit slant-linear polarization. The linear state with the added advantages of the slant and a slight ellipticity was explored in this study. The quantitative theory and analyses presented in following sections show that this slant-45° quasi-linear state provides depolarizations (measured as SLDR*-45, Table 1) that substantially overcome the issues present with LDR.
3. Radar measurements and supporting data from MWISP
The measurement methods for NOAA/K were as follows. NOAA/K is equipped to provide a selection of transmitted polarization states for testing by installing any of several rotatable PRPs. Each engineered PRP produces a specific, fixed phase shift in the transmitted signal. Measurements of DR (ψ, β) with NOAA/K are taken by (i) selecting a PRP and setting β for a specific polarization state, setting the radar's antenna at a specific azimuth, and scanning it from horizon through zenith toward the opposite horizon in the vertical plane of an elevation (RHI) scan through a sector as wide as 175°. Alternatively, the measurements are taken by (ii) fixing the radar's beam at a selected elevation and azimuth and rotating the PRP through 360°, to continuously change the polarization state over the range and limits defined by the particular PRP. Regardless of the phase shift of the particular PRP, at zero rotation the transmitted polarization state remains that of the base state, LDR ≡ DR (ψ, 0°), which is independent of the value of ψ and is measured in the returned signal according to Eq. (2). A true half-wave plate (HWP) would induce a 180° phase shift, and rotation would vary the transmitted state through a continuum of slants of linear polarization, including 1) horizontal as noted, 2) a linear polarization slanted at 45° from horizontal at rotation β = 22.5°, and 3) vertical polarization at β = 45°, to measure, respectively, LDR ≡ DR (180°, 0°), SLDR ≡ DR (180°, 22.5°), and VLDR ≡ DR (180°, 45°) by Eq. (2). In contrast, a true quarter wave plate (QWP) would induce a 90° phase shift, and rotation would vary the transmitted state from horizontal at β = 0°, through a continuum of states of increasing ellipticity with increasing rotation, to circular at β = 45°, to measure, respectively, LDR ≡ DR (90°, 0°), EDR ≡ DR (90°, 1°–44°), and CDR ≡ DR (90°, 45°; Table 1). When using any PRP that is not a true HWP or QWP, polarizations will be transmitted that will have an ellipticities of 0 < ε < 1 at all rotations except zero or 180°, where the horizontal linear base state is transmitted.
For this study, we recognized from experience that precision engineering of the PRP for an exact phase shift is difficult, so a true slant linear (ψ = 180°) was targeted with the expectation that there would be some ellipticity, which would be advantageous. The PRP manufactured for this research induces a phase shift of approximately 177.4°, according to calibrations with spherical hydrometeors (section 5). The cross-talk limit for the antenna of NOAA/K is approximately −36 dB, so the maximum available dynamic range in DR is approximately 36 dB. This is the dynamic range for linear and circular polarizations for this radar. Ellipticity reduces the dynamic range in which DR may be measured to a value above the cross-talk limit, for particles randomly oriented with respect to the azimuth angle. The previously tested PRP that induced a 79.5° phase shift (ε = 0.83) to measure EDR = DR (79.5°, 45°) reduced the dynamic range to 15 dB, which was too narrow (Matrosov et al. 1996; Reinking et al. 1997a,b). The slightly elliptical, 45° slant polarization state produced by our new PRP reduced the dynamic range by several decibels, but not nearly to the extent realized with the more elliptical polarization. This allowed for measurement of the depolarization of drizzle at a value above the cross-talk limit of the antenna. The ∼2.6° offset from ψ = 180° induces a slight ellipticity in the transmitted radiation, which is approximately 0.02, allowing for an uncertainly of a few tenths of a degree in the 177.4° phase shift, which was obtained by matching the calculations from the PRP equation (Matrosov et al. 2001, p. 481) for spheres to the measured −29 dB. A rotation of this PRP to 22.5° allows a 45° slant quasi-linear depolarization ratio, SLDR*-45 ≡ DR (177.4°, 22.5°) to be measured (Table 1). For spheres, and for nonspherical particles with a preferred horizontal orientation but randomly oriented with respect to their azimuthal angle (or equivalently, their vertical axis of rotation), the slight ellipticity of this transmitted polarization state increases the weak-channel return over that possible with either true linear or circular polarization. This enhances DR measurements in clouds of low reflectivity (Matrosov and Kropfli 1993) at a sacrifice of some of the dynamic range for particle type separation. Conversely, at zero rotation of this or any other PRP, the transmitted state is independent of ψ and remains the base state of the radar, where the full dynamic range is available at a sacrifice of sensitivity.
Propagation effects on the value of DR for our radar have been considered in Matrosov et al. 2001. In brief, propagation of the signals through a media of nonspherical particles to and from the radar resolution volume increases the apparent depolarization ratio measured by the radar over the DR unaffected by propagation. The propagation effects increase as the elevation angle decreases. The increase is greater for the more non-spherical particles, and it depends on particle concentration. The ice water contents are not very large (usually not exceeding a few tenths of a gram per cubic meter). The estimates in Matrosov et al. (2001) show that the apparent increase of DR due to propagation effects does not exceed about 2 dB, for particles with a wide range of aspect ratios (0.1–1.0) if the distance (radial range) is within about 10 km and elevation angles are above about 30°—which is the case for the measurements reported in this paper. Note that since propagation effects tend to increase DR monotonically, if significant, they could be recognized by analyzing the DR range patterns. Our experimental data collected in the various field campaigns including MWISP indicate that these effects are very modest for the short ranges and high elevation angles. The images of radar scans presented later in this paper do not indicate any significant propagation effects.
During MWISP, NOAA/K was operated to measure DR, reflectivity (Ze), radial velocity (Ve), and other basic radar parameters from a site midway up the west slope of Mount Washington, at 0.5-km altitude MSL, 4.1-km range west, and 1.1 km below the summit, where MWO is located. The radar equipped with the 177.4°-PRP was used to measure the depolarization of signals transmitted at the 45° slant, quasi-linear state. Measurement at the horizontal and intermediate states was also possible.
Many kinds of supporting data were gathered during MWISP (Reyerson et al. 2000). Some in situ samples of hydrometeors from the MWO and at the radar site are used as in situ truth in this study. At the radar site, falling ice particles were sampled on black velvet and photographed and/or noted in the radar's electronic logbook. Hydrometeor imaging data from the MWO were taken with a Cloud Particle Imager CPI; Lawson and Jensen 1998; Lawson et al. 1998) and a standard Particle Measuring Systems (PMS) laser two-dimensional grayscale cloud probe (2DGC) operated by the Cold Regions Research and Engineering Laboratory (CRREL). A few particle measurements from the National Aeronautics and Space Administration (NASA) Flenn Research Center Twin Otter cloud physics aircraft were also used. Some rawinsondes from the NCAR CLASS and profiles of cloud liquid water content measured with ATEK sondes released from the radar site were also valuable to this study (Hill 1989, 1994).
The polarization measurements will be examined after we present their basis in scattering calculations.
4. Scattering calculations
NOAA/K can obtain measurements of DR as a function of antenna elevation or pointing angle, χ, from the RHI scans. The scattering calculations presented here predict the DR signatures of ice crystals of the most common “regular” growth habits (Pruppacher and Klett 1997, 44–46), as a function of χ, for three polarization states, standard (horizontal) linear, 45° slant linear, and 45° slant quasi-linear obtained with a 177.4° phase shift PRP. Thus, respectively, the relationships LDR(χ), SLDR-45(χ), and SLDR*-45(χ) were calculated for a Ka-band radar with a −36 dB antenna cross-talk limit. The model for these scattering calculations is explained by Matrosov et al. (1996, 2001). Matrosov et al. (2001) present similar calculations for SLDR-45(χ), and SLDR*-45(χ), but from the somewhat different perspective of testing the possibility for measuring particle aspect ratio, so effects of varying bulk density and aspect ratio are incorporated. The following calculations incorporate median crystal sizes and bulk densities that are field-measured values recorded in the literature, as explained by Reinking et. al. (1997a).
a. Horizontal polarization
For reference, the calculations for the horizontal polarization state are presented first. Thus, LDR(χ) is shown in Figs. 1a and 1b for spheres (drizzle) and the regular types of ice crystals. Dimensions affect shape, so the columnar crystals are separated according as the length/diameter ratio, L/D, relating to the representative size measurements, is greater or smaller than 2. For LDR, the dynamic range available for separation of hydrometeor types is maximized. For this polarization state, spheres cause no depolarization, so the backscatter is that of radiation from the co-polar channel at all elevation angles, and the calculated signature of spheres (drizzle) equals the −36 dB cross-talk limit at all χ. Both the planar and columnar families of crystals tend to settle with their larger dimension near horizontal. Their shapes therefore appear very different when irradiated at zenith (χ = 90°) and near the horizon (χ < 45°). Consequently, the selectively shaped ice particles cause depolarizations that vary with elevation angle. Variations of settling orientation are determined by the three-dimensional canting angle variability from axis tilt and rotation; we characterize this by the standard deviation of the major particle dimension from the preferred horizontal settling position, σθ. Horizontal polarization excites only the dipole moment along the horizontal principal axis of the scattering hydrometeors when the settling position is truly horizontal; however, when particles flutter as they fall, LDR becomes more a function of σθ than particle shape.
LDR increases with χ for the columnar family and decreases with χ for the planar family. This difference is very evident, and the χ-dependencies differentiate each type from the constant value for spheres (Figs. 1a,b). However, of the available 36-dB dynamic range, only 19 dB is used, and at both low χ and near zenith, some of the crystals show little differentiation from spheres. This differentiation is as little as 1 dB for crystals with settling orientations of small standard deviation (σθ = 3°, Fig. 1a). The separation from drizzle is increased by 5 to 10 dB if the crystals have a much larger variation in settling orientation (σθ = 15°, Fig. 1b), but the LDR values for the various crystals becomes more overlapped and inseparable. The sensitivity to σθ applies to columnar crystals at χ < 35°, approximately, and to planar crystals at all χ. In examining the same issue by another approach, Sturniolo et al. (2000) show that for χ fixed at 15°, LDR values for long columns increase within a range of 18%–39%, depending on aspect ratio, when σθ is increased from 6° to 30° (only slightly more change occurs as σθ is increased to 90°, where alignment is almost random).
A consistently large separation of crystals from drizzle would suggest an advantage in using LDR to detect these droplets. This separation would be established only if the variations in crystal settling orientation were always large, but they are not. Sassen (1980), using a lidar, measured maximum planar crystal “wobbles” of only 3°, apparently in calm air. Thus, for these crystals, σθ was evidently of the order of only 1°. Mallmann et al. (1998) show both photographic and theoretical evidence of narrow and broad sun pillars that were due, respectively, to crystals with “nearly” horizontal and less horizontal orientations. The supporting calculations consider canting angles between 2° and 10°. Canting angles of 10°–25° were measured for individual, rimed columnar crystals by Kajikawa (1976). Zikumunda and Vali (1972) present a frequency distribution for measured canting angles of rimed columnar crystals with length-to-diameter axis ratios, L/D primarily in the range of 2 to 10. Their distribution shows that ∼40% of the crystals fell with less than a 5° cant, and ∼90% fell with less than a 15° cant, although canting angles were as large as 75° for a few crystals. The riming undoubtedly tended to induce imbalances, to increase the variations in settling motions over those of pristine crystals. The samples for these analyses were very small, so relating the results to crystal populations is difficult. Nevertheless, collectively, these measurements demonstrate that the deviations of the settling orientation from horizontal may frequently be small but may vary through a wide range, such that σθ might be expected to vary widely from case to case. Significant differences between calm and turbulent clouds or due to variations in riming can be theorized. Some aspects of the secondary motions of ice particles have been described (as summarized by Pruppacher and Klett 1997, 444–446), but σθ is as yet unpredictable. The lack of consistency and predictability of σθ confuse the hydrometeor identification using LDR. The large variation of LDR with σθ is therefore one key aspect of horizontal polarization that eliminates it from candidacy for the optimal transmitted polarization state.
b. 45° slant linear polarization
A 45° tilt of the transmitted signal's polarization plane enhances the cross-polar return of non-spherical particles because it excites dipole moments along both principal axes of the scattering hydrometeors that are settling with a generally horizontal orientation. These aspects of the potential improvement offered by a 45° slant linear polarization are illustrated in Figs. 2a and 2b. First, the difference between available and utilized dynamic range must be considered. SLDR-45 = DR (180°, 22.5°) utilizes 29 dB of its available 36 dB dynamic range to differentiate among the noted crystal types and drizzle, 10 dB more than utilized with LDR with the same available dynamic range. Second, to within 0.5 dB, the columnar crystal types become independent of the difference between 3° and 15° in σθ and are nearly independent of χ as well, although advantageously offset from drizzle by ∼11–12 dB. For the same difference in σθ, the SLDR-45 signatures of planar crystals shift by less than 2 dB at χ ≤ 60°; the shift above 60° becomes as large as 8 dB, but the differentiation at low angles and the slope of the planer crystal curves is so large that their identification should be unambiguous. Third, whereas some LDR values for crystals approach that for drizzle at both low and high χ, with SLDR-45, all of the crystal types are differentiated from drizzle by 10 dB or more at all χ ≤ 60°. This means that a radar with the 45°-slant linear polarization should be able to very effectively differentiate drizzle from planar and columnar crystals with only a fixed beam set at a low antenna elevation angle. This cannot be done with LDR.
Since spherical droplets do not depolarize any truly linear signal, their null signature would be SLDR-45 = LDR → −∞ dB without the antenna cross-talk limit of the radar. With that limit imposed, their signature will be at −36 dB for NOAA/K. This is a disadvantage for both SLDR-45 and LDR that can introduce some ambiguity because the null signal (a weak-channel, cross-polar return below the noise) might be interpreted either as droplets or simply insufficient return to make a distinction in clouds with low reflectivities, thus, for NOAA/K when the strong-channel reflectivity is above the noise level by less than 36 dB. This situation can be remedied in part by using a slightly elliptical polarization because it raises the weak-channel return.
c. 45° slant, quasi-linear polarization
For the SLDR*-45 = DR (177.4°, 22.5°), the calculations as a function of χ are presented in Figs. 3a and 3b. The key features of the truly linear SLDR-45 are retained but compressed into a dynamic range that is 7 dB narrower than allowed by the −36 dB cross-talk limit of the radar. In this case, all of the regular crystal types are differentiated from drizzle by 5 dB or more at all χ ≤ 60°. This difference is substantial and easily measured. The spheres, now depolarizing but at a constant value independent of χ due to the signal's ellipticity, define the lower limit of this range for this polarization state as ∼−29 dB. However, according to the calculations, SLDR*-45 utilizes more of its available dynamic range than LDR for both large and small variations in settling orientation (Figs. 3a,b vs Figs. 1a,b). Some 20–22 dB of the available 29 dB is utilized to differentiate among the noted crystals and drizzle; this is still 1–3 dB more than the range utilized in LDR with the broader available range. The range utilized for differentiating among crystals only is 17–22 dB in SLDR*-45, 4–5 dB more than that in LDR (both ranges depending on σθ).
For further perspective on the effect of crystal flutter, examine the curves for the crystals that exhibit the greatest dependency on σθ, the hexagonal plates (P1a). When σθ is changed from 3° to 15°, SLDR*-45 shifts by only −2 dB at χ = 0° and +4 dB at χ = 90°, but LDR shifts by +8 dB at χ = 0° and +9 dB at χ = 90°. For σθ = 15°, LDR provides a separation from drizzle of at least 6 dB in the worst case, which is better than the 3 dB for SLDR*-45. Thus, if σθ were always relatively large (e.g., 15°), LDR would provide the greatest differentiation from drizzle, but that condition cannot be reliably assumed. Also, LDR does not provide the greatest separation among crystals only. Therefore, measurement of SLDR*-45 is expected to be much more dependent on crystal shape and less on orientation than LDR and, therefore, much more consistent. As with SLDR-45, SLDR*-45 of the planar crystals exhibits a steep slope between χ of 0° and 90°, and the signature of each type of columns is nearly constant, showing an increase of only ∼1 dB with increasing χ, and well separated from the −29 dB signature of drizzle droplets, well above the antenna's cross-talk.
d. Summary of comparisons
Some of the comparisons of the three polarization states, as derived from Figs. 1–3, are summarized in Table 2. The tabulated parameters include 1) the available but rarely achievable effective dynamic range for each depolarization ratio, 2) the portions of that range that are actually functional and utilized for differentiating among the regular crystals and droplets and for differentiating among only the various crystal types, 3) an example of the shift in each DR due to the 12° change in σθ (from 3° to 15°), and finally, 4) the minimum difference between the DRs of droplets and crystals at χ ≤ 60°, where the best differentiation is achieved. The values in Table 2 and Figs. 1–3 show that SLDR*-45 should be quite superior to LDR due to its (i) relative insensitivity to σθ, (ii) wider utilized dynamic range for separation of hydrometeors, and (iii) invariant and sizable minimum difference between the DR values for regular ice particles and for droplets at χ ≤ 60°. From the same table and figures we see that the slant linear depolarization ratio, SLDR-45, would offer distinctions superior to both LDR and SLDR*-45, were it not for two factors that do not appear in the table. Spherical scatterers are still identified only by default at the DR value of the antenna cross-talk; and the weak-channel return of nonspherical scatters comprising clouds with a (strong-channel) reflectivity less than the absolute value of the cross-talk above the noise will by default have the same DR as spheres. Thus, for any true linear state, including SLDR-45 (or the circular state), unambiguous, deterministic identification of spherical droplets in low-reflectivity clouds will be difficult, and range sensitivity is reduced, relative to the results using SLDR*-45. Also, scatters with higher strong-channel reflectivity but are nearly spherical may also have a SLDR-45 that approximates that of spheres, due to a weak-channel return that is not measureable and by default is also in the noise.
Some ellipticity introduces a weak-channel return from drizzle and from ice particles with randomness in orientation in the horizontal plane (Matrosov and Kropfli 1993). This covers most atmospheric situations, so ellipticity will normally provide a strengthened weak-channel echo to enhance detection and differentiation of low-reflectivity clouds of drizzle and the other particles. Slight ellipticity, as in SLDR*-45, raises the weak-channel signal for spheres several decibels above the antenna cross talk limit and allows for a definitive, directly measurable cross-polar power. This also increases the radial range of minimum detectability of low-reflectivity cloud. Of course, the radial range is also a function of radar hardware (power, antenna size, etc.) and mode of operation (dwell time, pulse length, etc.). Once these basic radar parameters are set, and the dwell-time-dependent minimum detectable polarization difference needed to distinguish all ice from low-DR water droplets is determined, the ellipticity needed to generate this minimum difference can then be determined exactly through scattering calculations. However, with too much ellipticity, the dynamic range in DR can be decreased too much to allow effective distinction among the various particles, so a reasonable compromise is necessary.
From the scattering calculations, in summary, compared to horizontal polarization, the primary functions and advantages of the transmission at a slant are 1) to relatively immunize the measured depolarization ratio against unpredictable variations due to particle oscillations in around their preferred horizontal orientation, and 2) to substantially increase the effective dynamic range that is utilized to differentiate the DR signatures of drizzle and the various ice hydrometeors. The primary function and advantage of the added ellipticity is to increase weak-channel, cross-polar return such that the ratio for least depolarization (that for spherical droplets) is at an explicitly measurable level above the antenna cross-talk and need not be determined by default. Equivalently, this gains radial range sensitivity. The ellipticity in SLDR*-45 compromises the utilized dynamic range somewhat relative to SLDR-45, but does not reduce it to the range for LDR. Given these factors, results in particle identification from the measurement of SLDR*-45 should be superior to those using SLDR-45, and both should be far superior to those from measurements of LDR.
5. The measured signature of drizzle droplets
Measurement of the signature of drizzle and experimental calibration of the designed polarization state are intertwined because the actual phase shift of each PRP is determined by field observation of spherical particles (drizzle droplets). The calibration can be accomplished by measuring return signals in drizzle from fixed beam measurements and RHI scans. With the radar pointed at a fixed elevation angle, the PRP is continuously rotated through at least 180°, to determine DR at all rotations, but particularly at β = 0° and 22.5° corresponding, respectively, to the horizontal and slant-linear states. The RHI measurements calibrate the fixed value of DR in drizzle for a specific polarization; this is accomplished with the PRP rotated to a fixed position to establish the state.
Beginning with an exemplary RHI scan, the MWISP PRP was fixed at β = 22.5° to measure SLDR*-45 (Fig. 4a, top panel; 1232 UTC 07 April 99). This RHI shows a cloud with ice aloft, where SLDR*-45 up to about −16 dB was measured. Ice precipitating from the cloud melted to produce a highly depolarizing bright band, where SLDR*-45 ≈ −10 dB. The hydrometeors below the bright band showed very uniform and minimal depolarization at any χ, indicating drizzle, which was observed at the ground. The differentiation of ice from liquid is immediately evident, as it was in measurements using EDR (Reinking 1997a,b), but it is the quantitative increase in separation that is of interest here. The corresponding cloud (strong-channel) reflectivity, Ze, shown in the bottom panel of Fig. 4a, reveals the melting level but otherwise only hints at differentiation of these features. A plot of the function, SLDR*-45(χ), at constant altitude through the drizzle in Fig. 4a, is invariant at −29 ± 0.5 dB; this is curve in Fig. 5 labeled “drizzle.” Thus, the effective dynamic range and the signature of drizzle for this PRP configuration is indicated to be −29 dB.
A calibration of the other type, with a PRP rotation, in another MWISP drizzle situation is shown in Fig. 6a (1559 UTC 26 April 99). At β = 0° (as well as β = ±90°), the measurement is that of LDR = DR (ψ, 0°) and is independent of phase shift, ψ. At any intermediate rotation, DR depends on ψ, so rotation through β provides the measurements to determine the actual phase shift of this PRP. The smooth curve in Fig. 6a is the calculated DR = f(β) for ψ = 177.4° and the antenna cross-talk of 36 dB. Curves from measurements at three altitudes in the drizzle with the radar pointing vertically are also shown. Unlike the calibrations for our PRP with ψ = 79.5° that we used to measure EDR (Matrosov et al. 1996; Reinking et al. 1997b), a nearly exact fit between the calculations and measurements was not obtained. The departures of the experimental curves from the theoretical curves in Fig. 6a are explained subjectively as the result of internal microwave reflections in the PRP. The calibration is somewhat disappointing in this respect and significantly deviant from theory at some rotations. However, it does suffice. As the three samples indicate, the patterns are reproducible and symmetric around β = 0°. The minima in the measured curves indicate that LDR ≈ −36 or −37 dB. This provides a foundation for the calibration because it approximates the radar cross-talk limit, as it should. The curve for ψ = 177.4° approximates the best fit at the intersection of the experimental curves and the vertical line at β = 22.5°, where SLDR*-45 is measured as DR (177.4°, 22.5°) ≈ −28 ± 0.5 dB. A measured depolarization of ∼−26.5 dB at a rotation of −67.5°, or 22.5° from −90°, is indicated at the intersection with the vertical line at the left in Fig. 6a. This would fit a curve for ψ ≈ 153°; the calculated calibration curve for this ψ would not account for the −29 dB drizzle signature verified by the analysis in Fig. 5 of the RHI in Fig. 4a. Thus, the curve for 177.4° approximates the correct choice to define the calibration. The slight ellipticity induced by the 177.4° phase shift in the PRP at 22.5° rotation (for the 45° slant) is illustrated in Fig. 6b.
The calibrations from the separate RHI and rotating PRP measurements differ only by approximately 1 dB. They experimentally establish the effective or functional dynamic range for this PRP as 28.5 ± 1 dB (corresponding to the signature of drizzle) and the phase shift as approximately 177.4°. Therefore, SLDR*-45 = DR (177.4°, 22.5°) as calculated in Figs. 3a and 3b where the dynamic range is 29 dB should provide reasonable predictions of the depolarizations by the basic types of hydrometeors. This dynamic range in depolarization ratio is about 14 dB wider than it was for EDR with a 79.5° phase shift and ensures much greater separations among drizzle and the other hydrometeors.
The absence of a cross-polar power returned when measuring LDR, which is not readily discerned in the DR measurements because the effect occurs as a signal at the −36-dB cross-talk level, is evident in the measurements of cross-polar intensity, Icr, which is used to derive Pcr (in this case, the weak-channel echo) and DR. An inspection of considerable data shows that the noise threshold occurs approximately where Icr ≈ 0.015 V, and the DR measurement is clearly discernable when Icr > 0.03–0.04 V; this value offers a threshold to identify reliable measurements. In contrast, reflectivity, for example, is range dependent and less rigid in separating good and unreliable signals. Figure 7 shows a time series of (a) DR (β), and (b) the corresponding Icr and standard (copolar) reflectivity, Ze. This 6-min period includes the PRP spin in Fig. 6a that was used for calibration. These data are from a slightly longer range. From the beginning of the series, the pattern in DR that defines drizzle repeated itself as the rotating PRP cycled during approximately the first 3.5 min. Here, the minima in DR at −35 to −37 dB occurred where Icr is below the noise threshold, indicating no cross-polarized signal; these are the values for LDR. SLDR*-45 is represented by the secondary peaks, where DR was −27 to −29 dB, and Icr rose to easily measured values above 0.1 volt.
After about 3.5 min, DR became erratic (Fig. 7a). This occurred when Ze first dropped below about −25 dBZ, and Icr decreased to values mostly under ∼0.04 V. At this time, the cross-polar reflectivity (not shown) dropped to nearly −50 dBZ. In the time series, the decline in Icr for SLDR*-45 shows that there is a transition to a signal dominated by noise, whereas the Icr for LDR remains below the noise level and the signal is not reliably measurable. This supports the arguments in favor of having some ellipticity in the selected polarization state to gain a cross-polar signal even in low-reflectivity droplets.
6. Measured depolarization by regular planar and columnar crystals
a. Planar crystals
Planar crystals settling with a preferred horizontal orientation present a quasi-circular cross-section and therefore depolarize the signal minimally when observed near zenith, but appear as more linear objects and depolarize the signal substantially when observed near the horizons. The consequent χ-dependent “V” pattern in the depolarization signature is illustrated in the RHI scan in the top panel in Fig. 4b (1257 UTC 14 April 1999). Substantially branched, unrimed dendrites, the most common of planar crystals [crystal type P1e, Magono and Lee (1966) classification, in Pruppacher and Klett (1997, 44–46)], were observed on black velvet at the surface and noted in the radar's electronic log book; they were very similar but less rimed than crystals photographed 15–30 min later (Fig. 8a). These targets are broadest at zenith, where even their reflectivities reached a maximum, a signature unique to planar crystals (bottom panel, Fig. 4b). A constant-altitude sample of SLDR*-45(χ) at 1.4 km AGL (“dendrites,” Fig. 5) from the data in the RHI scan shows depolarization ratios of approximately −12 or −13 dB at χ = 20° (and equivalently in the “reflection” at 160°) and −27 dB at 90° (zenith). This measured curve closely approximates the calculated curves for dendrites, especially that in Fig. 3b.
Due to their simple structure, hexagonal plates (class P1a) are predicted to produce a “V” signature that is even more pronounced than that of dendrites. This is demonstrated by the measured curve labeled as such in Fig. 5, where the depolarization at low χ was some 3 dB greater than that caused by the dendrites. The presence of the plates early in the evolution of this layer cloud was confirmed by the very first of a set of PMS 2DC probe measurements obtained over the radar with the NASA aircraft (Fig. 8b). This cloud rapidly changed to dendrites and aggregates, and some sector crystals were already present at this time, just 6 min after the radar sample, but the sector type would have depolarized the signal only slightly less than plates.
Compare the curves for the plates and dendrites in Fig. 5 for χ near zenith. Whereas the plates show a depolarization nearly equivalent to spheres and drizzle at this elevation and closely approximate the calculated curve for σθ = 3° (Fig. 3a), those for dendrites show about 3 dB less depolarization at the same angles and more closely approximate that for σθ = 15°. This suggests that the dendrites exhibited considerable randomness in their settling orientation, whereas the plates did not. This effect is of no consequence to particle identification for χ < 60°, as a comparison of the measured and calculated curves demonstrates. In view of the previous discussion about the effects of σθ, the selection of SLDR*-45 over LDR is further supported.
b. Columnar crystals
Long regular columnar crystals with length-to-diameter ratios, L/D > 2, were observed simultaneously with the radar (Fig. 4c, 1404 UTC 17 April 1999) and the CPI at the MWO (Fig. 8c). The CPI images indicate a mix of hollow columns and sheaths (respectively, type classifications C1f and N1e) with L/D ∼ 4–5. A rawinsonde released at 1300 UTC from the radar site shows saturation from 0° to −8°C, which matches the growth regime for those crystal types. A constant-altitude plot from the RHI scan (“long columns” in Fig. 5) shows that SLDR*-45 increased by only ∼2 dB, from about −18 dB to about −16 dB, as χ was increased from 30° to 90°. The experimental curve has approximately the same slope and lies between those calculated for needles (or sheaths) and hollow columns (Figs. 3a or 3b), which are themselves separated by only 1.3 dB.
Blocky columns (L/D < 2, classification C1e) are more spherical than other types of pristine ice crystals, with the possible exception of bullets (C1c), so their depolarizations will be closer to that of spheres. Observed blocky columns depolarized the signal 6–8 dB less than the long columns, but 4–5 dB more than the nondepolarizing drizzle, as predicted in Figs. 3a,b and measured in RHI scans. The RHI scans showed a uniformity of SLDR*-45 with χ similar to that in Fig. 4c for the long columns, but in this case at −24 dB, as illustrated in Fig. 4d and the corresponding constant-altitude sample of SLDR*-45(χ) labeled “blocky columns” in Fig. 5 (1043 UTC 27 April 1999). The predicted slight slope toward increasing depolarization (less negative DR) between low χ and zenith seems to be reversed in the measurement but is within the measurement error. Nevertheless, the measured depolarization ratio equals that predicted within less than 1 dB. Photographs and CPI images from the same period verified the crystal type (Fig. 8d) and showed that L/D ∼ 2 in this case.
Larger crystal densities would shift the curves for the columnar and the planar crystals upward to greater depolarizations (Matrosov et al. 2001), so the good fits of the measurements of SLDR*-45(χ) to the calculations with either σθ suggest that the densities used for the calculations are reasonable selections (Fig. 3).
The depolarization caused by regular crystals will dominate any signature of small interstitial droplets, which are common to mixed phase clouds. PMS FSSP probe measurements confirmed that the droplets among the columns in Fig. 8d had diameters under 10 μm, so those of approximately the same magnifications in Fig. 8c reached the order of 15 μm. Aircraft are required to be designed to fly through droplets of such small sizes, which are generally not regarded as an icing hazard unless present in large concentrations producing very large liquid water contents.
7. Measured depolarization by aggregated and irregular quasi-spherical ice particles
a. Common aggregates
When crystals aggregate, the composite particles are usually more spherical than individual crystals. Sometimes they are elongated, but they are always more irregular. The more spherical aggregates predictably depolarize less than the individual crystals that comprise them, according to observations and calculations of EDR based on Rayleigh scattering (Matrosov et al. 1996). Such calculations can only approximate the effect because aggregates are normally too large to be precisely represented by the Rayleigh calculations for the Ka band (maximum dimension D ≤ 2 mm, approximately). Upon aggregation, general aspects of the DR(χ) of the individual crystals are nevertheless retained, although subdued. For example, the “V” signature of dendrites is suppressed but still evident because such clouds still contain some relatively pristine crystals. Likewise, spatial dendrites will present relatively spherical, non-Rayleigh targets to the radar, so the depolarization is expected to be diminished from that of pristine dendrites and less well described by calculations. To quantitatively describe the depolarizations by such particles, we go directly to the measurements.
Aggregates of dendrites and spatial dendrites with individual crystals as large as 3 to 5 mm were observed during MWISP (Fig. 9a). A characteristic distinct “V” signature in SLDR*-45 and a strong Ze near zenith to ∼8 dBZ were both evident in corresponding RHI scans (Fig. 10a), in spite of the irregularity and relative sphericity of the aggregates and the particles composing them. SLDR*-45(χ) (Fig. 11, “aggregates of dendrites,” 1508 UTC 15 April 1999) was nevertheless subdued at low elevation angles, by ∼6 dB at 30° compared to the signature of unaggregated dendrites, but tended to retain the signature of individual dendrites at zenith (−26 to −27 dB), although with more statistical variance in the signal. The effect is qualitatively the same as that for EDR shown for progressive aggregation in the Figs. 7a–c in Matrosov et al. (1996). That study and this one show that aggregates do depolarize the transmitted signal more than spheres, and this depolarization is somewhat predictable from Rayleigh scattering theory, despite their relatively large sizes.
b. Elongated aggregates
Extremely large (2–5 cm), non-Rayleigh, elongated aggregates formed on 27 April 1999 (1906 UTC; Fig. 9b). The settling motions of these crystals were analogous to those of drifting feathers; the long, albeit distorted axes were oriented horizontally on average but exhibited the glide-pitch oscillations observed in fall motion studies (Pruppacher and Klett 1997, p. 445). CPI images indicate that plates and very large dendrites dominated, but some columnar crystals also formed in the cloud (1902 UTC 27 April 1999, Fig. 9c). Earlier RHI scans revealed columns below about 0.9 km AGL. Thus, the aggregates at higher altitudes formed from the planar crystals, but probably collected some columnar crystals before falling to the surface at the radar or advecting to the summit as suggested by the depicted CPI sample. The effect on DR of the elongation of aggregates of dendrites, relative to that of more spherical aggregates of dendrites, was isolated from the effect of added columns by determining DR(χ) at an altitude above the columnar growth regime. The sample at 1.6 km AGL (“elongated aggregates” in Fig. 11) shows that elongation tends toward flattening the SLDR*-45(χ) curve by increasing the depolarization by several decibels at all antenna elevation angles, but more so near zenith. Consequently, the curve is distinctly different from that of more spherical aggregates, although Ze was similar (6–8 dBZ). The curve for elongated aggregates approached the values for long columns (Fig. 3, L/D > 2; and Fig. 5) but still maintained a weakened but defined “V” signature of about 5-dB depth as a distinguishing factor.
The addition of the columns in the lower part of the cloud did flatten the SLDR*45(χ) curve to a value of ∼18 dB, approximately matching the signature of pristine long columns. The aggregates were distinguished, however, by their much greater size and reflectivity (8–10 dBZ), compared to −3 to −14 dBZ in the cloud of long columns (Fig. 4c). Long columns also readily aggregate, but such a case with columns alone has not been identified in the measurements.
c. Conical, lump, and hexagonal graupel
Conical graupel (classification R4c) is quite spherical compared to most other types of ice particles because L/D ≈ 1, despite the defined shape. However, the conical form develops as a result of a preferred settling orientation, with the apex of the cone upward. RHI scans through a convective shower of particles positively identified as large conical graupel (Fig. 9d) provided signals in SLDR*-45 that were quite uniform with χ. From the scan in Fig. 10b, a constant-altitude plot shows that SLDR*-45(χ) was approximately −23 to −25 dB, clearly distinguishing it by 4 to 6 dB from the −29 dB signature of drizzle (“conical graupel” in Fig. 11).
The relatively strong reflectivity common for graupel (Ze ≈ 8 − 20 dBZ; Fig. 10b) also distinguished it from the weak reflectivity of drizzle (predominantly, Ze < 4 dBZ in Fig. 4a, more commonly less than 0 dB). The signature of conical graupel in SLDR*-45(χ) might be mistaken for blocky columns, except that the columns present a signature more uniform with χ throughout the cloud and, in general, have a low Ze that is comparable to drizzle (e.g., Ze < −4 dBZ predominantly; Fig. 10b).
Rotation of the PRP with the antenna pointed to zenith provided a comparison of LDR and SLDR*-45 for the conical graupel (Fig. 12). Here, SLDR*-45 was consistently −24 to −26 dB and separated by a readily measurable 3–5 dB from the −29 dB of spheres, whereas LDR varied between −33 and −35 dB, allowing a distinction of only 1–3 dB from the −36 dB representing spheres using the horizontal polarization state (Fig. 12a). This was true despite cross-polar intensities far above the measurable threshold of 0.03–0.04 V and strong reflectivities (∼14–19 dBZ; Fig. 12b). Thus, the 45° slant, quasi-linear polarization is also superior to LDR for distinction of such relatively spherical ice particles.
An RHI measurement of SLDR*-45(χ) through small, irregular, lump graupel or snow pellets (classification R4b) that was patchy within the cloud is included in Fig. 11. Where the lump graupel was clearly dominant, the depolarizations are approximately equal to those caused by the conical graupel. Some hexagonal plates were beginning to settle into the lower layer that was generating the graupel, and the depolarization values at the low angles in this RHI sample approximate those measured for a third, hexagonal variety of graupel (see next paragraph). Overall, the irregularity of SLDR*-45 of the lump and conical graupel with χ was in sharp contrast with the uniform signature caused by drizzle. The CPI captured images of this graupel that reached maximum sizes of about 0.8–1.0 mm (Fig. 9e). The smaller sizes, and very small concentrations discerned from the minimal fallout rate, contributed to reflectivities of approximately +2 to −4 dBZ, as low as those of drizzle. Therefore, a high reflectivity can reinforce differentiation by depolarization but cannot be expected for graupel occurring in very low concentrations.
Branched planar crystals without rime depolarize the incident signal minimally at zenith but very substantially at lower elevation angles (e.g., “dendrites”; Fig. 5). However, branched planar crystals that collected heavy rime, such that they reached the graupel stage (Fig. 9f; hexagonal graupel, classification R4a), caused some of the lowest levels of depolarization observed for ice particles. This hexagonal graupel maintained the distinguishing “V” signature of planar crystals in the RHI scans of SLDR*-45 (Fig. 10c), making it distinguishable from drizzle, although the depolarizations at low antenna elevations were greatly suppressed. For example, at an antenna elevation as low as 30°, SLDR* -45 was still a very distinguishable 2–4 dB above the −29 dB drizzle signature (“hexagonal graupel;” Figs. 10c and 11). The reflectivity of this graupel was +2 to +8 dBZ.
8. A test case for supercooled drizzle detection
On 14 April 1999, an aircraft icing alert would have been issued if based on algorithms derived from the radar's depolarization signature and cloud temperature measurements. The supporting data show that this alert would have been justified.
A 10 m s−1 upslope flow below ∼1.7 km AGL (relative to the radar site) generated a cloud with vertically integrated liquid water reaching 0.5–0.6 mm by 2000 UTC. A CLASS rawinsonde from the site at that time revealed an adiabatic saturated layer supercooled to −6°C at its base at ∼1.3 km AGL and to −11°C at the base of a capping inversion near 2.1 km AGL. The inversion, itself, was saturated to ∼2.5 km AGL at −11° to −10°C. This temperature regime is optimal for aircraft icing. The cloud above approximately 1.7 km, in cross-slope flow and comprised predominantly of non-precipitating planar crystals, dissipated quickly after 2000 UTC, leaving only the upslope cloud, which persistently engulfed the summit as MWO weather observers recorded “fog” and “riming.”
Large supercooled droplets, the drizzle-sized droplets that are most likely to be a very significant icing hazard, were consistently imaged with the 2DGC PMS probe at the summit (Fig. 13). The diameters of these drizzle drops were predominantly in the 50–250-μm range; the modal and median diameters were both ∼150 μm, and the median volume diameter was ∼185 μm. The droplet images indicate slight distortion due to some mismatch between the sampling rate and wind speed, but the droplets were very nearly spherical. These were engulfed with tiny cloud droplets, which accounted for the observation of fog. Together, these caused a reflectivity of only 0 to −10 dBZ (Fig. 10d), and the SLDR*-45 signature was clearly that of drizzle, independent of χ and measured as −29.5 dB (Fig. 10d, and “drizzle,” Fig. 11).
The surface temperature was near −1°C during this period, and small, extremely sparse, quasi-spherical ice pellets were collected at the radar site, indicating that some of the drizzle drops were freezing. A few such pellets, indicated by their irregular outline in Fig. 13, were imaged among the drizzle droplets by the 2DGC probe. However, a substantial icing rate of ∼5–6 g h−1 measured with a Rosemount icing probe at the summit and the distinct images of the large droplets confirmed that a hazard existed and was detected by the radar's polarization measurement.
9. Conclusions
Supercooled droplets of drizzle size are known to present a potentially severe aircraft icing hazard. An approximation to an optimal radar polarization state has been sought for differentiating among drizzle and the various types of ice particles. The functional dynamic range in depolarization ratio, DR, varies according to polarization state and determines the potential separation of signatures for ice crystals and drizzle. The optimization requires compromise due to trade-offs between signal power of the weak-channel return and the functional dynamic range, and it requires consideration of the effect of variations of particle settling orientation, which differs among the polarization states.
A 45° slant quasi-linear polarization state, for measurement of SLDR*-45, was considered a reasonable option because of its practical simplicity, direct relationship to the single-horizontal polarization of operational radars, the SLDR*-45 value for drizzle-sized droplets at a decibel level above the radar antenna's cross-talk, good “weak” or cross-channel sensitivity to low reflectivity clouds, relative insensitivity to variations in ice crystal canting angle, and a retained wide effective dynamic range that can be utilized for superior separation of hydrometeor types compared to that in LDR, for particles with a preferred horizontal orientation. These features are substantiated by our scattering calculations and measurements. Deterministic, measurable differentiation was achieved with this polarization, in that the MWISP measurements of SLDR*-45 differentiate among the crystals of the various regular planar and columnar growth habits and among the more irregular ice particles, and segregate drizzle from all of these ice particles. For droplets and the ice particles of regular growth habits, which can be quite accurately modeled, these measurements of SLDR*-45 show extremely good agreement with the theoretical scattering calculations that model the depolarization ratios, to within about ±1 to 2 dB. Thus, this and supporting previous studies in the series confirm that the depolarization of transmitted polarized radiation by the regular ice crystals and drizzle can be well predicted by theory and uniquely separated from one another in corresponding measurements in DR. The many measurements show that these results are repeatable.
Such pristine ice crystals do form regularly in clouds, but they usually transition to aggregated or rimed stages of snowflake or graupel development. Therefore the results showing good differentiation among the irregular type of particles are equally important. Also, the aggregates are consistently well distinguished from parent planar crystals. However, the signatures for some graupel in the irregular category do tend to overlap with some of the signatures of the regular columnar crystal types. This introduces some uncertainty in the deterministic identification of these selective particles with DR alone, although it is clear that the statistical variance of DR with elevation angle is large for graupel and small of the particle types, so this helps in making the distinction. There are some other uncertainties. The irregular particles collectively are not so accurately modeled, so no firm prediction of deterministic values for these particles is possible, although some estimates of the general effects on DR have been calculated. And for Ka-band radar, which is near optimal for detecting drizzle-sized droplets (Kropfli et al. 1995), some of the crystals of regular growth habits and the more spherical and irregular particles become too large for the depolarization to be strictly described by Rayleigh scattering. Even so, Matrosov et al. (1996) and this study show that such particles do cause depolarization values that are quantitatively related to DR from scattering by the same fundamental shapes of particles in the Rayleigh regime, and these depolarizations can be estimated by experimental measurements.
Overall, our experience with the observations has indicated that reasonable averaging of data will allow us to detect and distinguish ice particles having DR values about 2 dB different from the value expected and measured for water droplets. Both the 45° tilt and the slight ellipticity of the transmitted signal enhance the cross-polarized return for ice particles over that obtainable in horizontal LDR. The slight rather than large ellipticity is also important. The dynamic range for particle separation in DR reaches its minimum when ɛ = 0.5, so very elliptical states near this one are restricted, although they do result in comparable return signals in both receiving channels, maximizing the polarization sensitivity to low reflectivity clouds, especially clouds spherical drizzle, that is sacrificed with the true horizontal and circular states.
The signatures of crystals in horizontal LDR will resemble spheres (and be indistinguishable from drizzle) if the scatterers have a zero canting angle. Moreover the horizontal LDR signature will change significantly as the standard deviation of the canting angle is increased, thus creating a family of indistinguishable depolarizations for the several types of particles. This depolarization ratio is as strongly dependent on the three-dimensional crystal canting as it is on particle shape. LDR consequently becomes unpredictable because the variations in canting angle are unknown and unpredictable. SLDR*-45, by comparison, is very stable, so it will minimize the potential errors in identification due to unknown variations in canting angle while establishing wide separations in depolarization according to hydrometeor type. This and other important influences described in this paper show that the horizontal depolarization ratio, LDR, is a poor choice for the purpose. Introducing the 45° slant and measuring SLDR-45 has very significant advantages, and overall SLDR*-45 is a superior choice.
Is SLDR*-45 (ɛ ≈ 0.02) the optimal state? SLDR*-45 is a compromise between the very elliptical states and the true linear state, and indeed a very good selection. The new calculations by Matrosov et al. (2001) indicate that a state with ɛ = 0.97 would improve isolation of drizzle over SLDR*-45 by a few decibels. Thus, states as near to circular (e.g., ɛ = 0.92–0.97) as SLDR*-45 is near to linear should also be considered. The desired polarization state can be achieved without the use of a phase-retarding plate, by adjusting the phase difference between the transmitted components. The practical aspects of instrumentation hardware and associated effects on transmitted power differ for the circular and linear states. Such factors should be weighed, and simplicity may drive the selection where other differences are small. However, this study has demonstrated the capability for hydrometeor differentiation and the importance of the selection of the polarization state, and the results significantly narrow the field of possible candidates for the optimal state.
The practical application of short-range dual-polarization Ka-band radar to identify clouds with potential aircraft icing conditions by profiling the depolarization ratio is discussed by Reinking et al. (2000). Based on the results in this paper and from the previous decade of studies by ETL, an operational-grade dual-polarization radar is being designed for this purpose and will soon be built to operate unattended and continuously (Reinking et al. 2001). For simplicity, this radar will operate with a beam fixed at an elevation angle between 30° and 40°, where the distinction of droplets from the many ice types is substantial, but the angle is high enough to effectively profile the clouds overhead. The fixed beam allows for a long dwell time (1 min) that, combined with a large antenna (3 m) and long pulse length (1.5 μs), will significantly enhance sensitivity to approximately −55 to −60 dBZ at 10-km range. Thus, within this range, the radar will be able to measure the weak-channel reflectivity and therefore the depolarization ratio in clouds with strong-channel reflectivities as low as approximately −25 or −30 dBZ, to uniquely identify clouds of drizzle and even smaller droplets. Since horizontal homogeneity of just a few kilometers in the clouds is all that is needed for clear identifications in the RHI scanning mode, a temporal continuity of several minutes in the clouds should suffice to make identifications in the fixed beam mode. An option to alternate every 5 min between the tilted angle and zenith is being incorporated to enhance ice particle identification in DR with a second point from the DR-χ curves and to measure spectra of the vertical velocity. The velocity measurement opens the possibility for further particle differentiation by fallspeed. A selection will be made between the slant-quasi-linear state tested here with good results, and the quasi-circular option, which the new theory indicates could be slightly better. The full system will include a microwave radiometer, pointed at the same elevation angle(s) as the radar, to continuously measure the path-integrated cloud liquid water content. Hourly temperature profiles to determine supercooling of the liquid will be ingested from an operational numerical model, so both of these complements will enhance identification of an icing hazard. In all, the Ka-band radar itself is being designed to provide a continuous time series of the profile of the depolarization ratio, reflectivity structure, and optionally the vertical velocity structure of passing clouds within the depth of the troposphere.
Acknowledgments
This research is in response to requirements and funding by the Federal Aviation Administration (FAA). The views expressed are those of the authors and do not necessarily represent the official policy of the FAA. Partial support was provided by NOAA/ETL. The major effort of David Korn in data processing made these analyses possible. Marcia Politovich of NCAR provided excellent leadership of MWISP. The CLASS soundings provided by NCAR, and the hydrometeor imagery provided by Paul Lawson of Spec, Inc., Charles Ryerson of CRREL, and Dean Miller of NASA-Glen were also essential to the analyses. Bruce Bartram and Kurt Clark of NOAA/ETL engineered and operated the radar; Carroll Campbell and Jan Gibson developed an outstanding new radar data acquisition and display system that greatly enhanced the data from MWISP.
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Calculations of the horizontal depolarization ratio, LDR = DR (180°, 0°) (dB), as a function of antenna elevation angle χ (°) for spheres (drizzle droplets) and for basic ice crystal types, planar (plates, dendrites, thick plates), and columnar (needles, long hollow columns, blocky solid columns); for standard deviation of canting angle (a) σθ = 3° and (b) σθ = 15° [also indicated are Magono and Lee crystal (1966) classifications; experimental mean major axes dimensions, Dm and Lm; and assumed ice densities, ρ]
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Calculations, as in Fig. 1, of the SLDR-45 = DR (180°, 22.5°) (dB) for (a) σθ = 3° and (b) σθ = 15°.
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Calculations as in Fig. 1, of the SLDR*-45 = DR (177.4°, 22.5°) (dB) for (a) σθ = 3° and (b) σθ = 15°.
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Over-the-top RHI scans, from east (right, azimuth 86.4°) through zenith to west (left), observing clouds of drizzle and ice particles of three pristine, regular growth habits. Each part of this figure shows a pair of images where the top panel is the depolarization ratio, SLDR*-45 (dB, upper color scale), and the bottom panel is the corresponding radar equivalent reflectivity, Ze (dBZ, lower color scale). The color scale for SLDR*-45 is the same in each case: range −6 to −32 dB, center at −20 dB. The scale for Ze was varied according to cloud intensity. Radial lines indicate antenna elevation angle in increments of 30°. Range ring intervals are 1 km from the radar located at bottom center. The upper, steep west slope of Mount Washington is evident as the line of ground clutter in view at the right in each figure, between the 2.7 and 3.7 km range. The MWO is located at the 4.1-km range, just under the horizon beyond the upper end of the clutter. These figures define the signatures of the following hydrometeors: (a) a cloud with ice particles aloft, the bright band (melting layer) near 600 m AGL, and drizzle below (1232 UTC 7 Apr 1999); (b) pristine planar crystals: unrimed dendrites were predominant in surface samples at the radar (1257 UTC 14 Apr 1999); (c) a mix of regular long columns and sheaths (1404 UTC 17 Apr 1999); and (d) blocky columns comprising a weak-reflectivity cloud (1043 UTC 27 Apr 1999)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Measured curves of SLDR*-45 a function of radar antenna elevation angle, SLDR* -45(χ) (dB, °), for drizzle-sized droplets and several types ice particles of regular growth habits, as labeled. The curves SLDR*-45(χ) at χ > 90° approximate mirror images of those for χ < 90° (i.e., the measurement at χ = 150° is equivalent to that at χ = 30°, etc., such that either half of the curve can be compared to the calculations in Fig. 2). Valid signal strength was ensured by restricting cross-polar intensity to Icr > 0.04 volts, somewhat above the 0.015 V threshold. Each measurement is at a constant altitude h, as follows: (a) drizzle: h = 0.2 km AGL in Fig. 4a, 1232 UTC 7 Apr 1999; (b) hexagonal plates (classification P1a): h = 2.2 km AGL, 1442 UTC 15 Apr; (c) dendrites (P1e): h = 1.4 km AGL in Fig. 4b, 1257 UTC 14 Apr; (d) long columns (C1f + N1e): h = 0.3 km AGL in Fig. 4c, 1404 UTC 17 Apr; and (e) blocky columns (C1e): h = 0.4 km AGL in Fig. 4d, 1043 UTC 27 Apr
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
(a) DR (dB), as a function of the rotation angle, β, of the PRP used in MWISP (1559 UTC 26 Apr 1999). The antenna was pointed to zenith (χ = 90°), and the PRP was rotated through β at 1 rpm to produce the experimental measurements in drizzle at 3 altitudes above the radar. The smooth curve is that calculated for a PRP with a 177.4° phase shift. The triple intersection of the vertical line at rotation β = 22.5°, the calculated curve, and the experimental curves indicates that SLDR*-45 ≈ −28.5 dB in drizzle (spheres). The minimum values of the curves show LDR ≈ −36 or −37 dB in drizzle, at the cross-talk limit of the radar; (b) the polarization ellipse representing the PRP with the 177.4° phase shift, rotated to 22.5° to establish the 45° slant in the transmitted signal
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
(Continued)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Time series of radar parameters measured during PRP rotations in drizzle: (a) DR (β) (dB), where the pattern of LDR and SLDR* -45 are noted, and LDR is repeated once in each 90° rotation; (b) the corresponding cross-polar intensity, Icr (V), and reflectivity, Ze (dBZ), 1556–1602 UTC 26 Apr 1999
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Samples of regular ice crystals corresponding to radar measurements summarized in Fig. 5: (a) dendrites (class P1e; photographs at radar site, ∼1315–1327 UTC 14 Apr 1999); (b) hexagonal plates and a few sectors (P1a and P1c, NASA aircraft PMS 2DGC samples, 1448 UTC 15 Apr); (c) long columns and sheaths, with small interstitial droplets (N1e, N1d, L/D > 2, CPI images at MWO, 1359–1402 UTC 17 Apr); and (d) blocky columns (C1e, L/D ≤ 2 predominantly; photograph ∼1044 UTC, CPI image ∼1117 UTC 27 Apr)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Samples of irregular Ice particle corresponding to depolarization measurements in Figs. 10 and 11: (a) Unrimed and moderately rimed spatial dendrites from one aggregate, photographed at the radar site (∼1508 UTC 15 Apr 1999); (b) elongated aggregate of crystals mainly of dendritic structure, L ∼ 2.2 cm (∼1906 UTC 27 Apr); (c) a CPI image near the same time of an aggregate of thick plates with sector-like extensions (P1f) and an attached column (1902 UTC 27 Apr 1999); (d) photograph of conical graupel (∼2105 UTC 20 Apr); (e) CPI images of lump graupel and very small interstitial cloud droplets (∼1445–1446 UTC 15 Apr); (f) and photograph of heavily rimed branched planar crystals, or hexagonal graupel (∼1217 UTC 13 Apr)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Over-the-top RHI scans, from east (right, azimuth 86.4°) through zenith to west (left), through clouds with aggregated and irregular ice particles and a cloud of supercooled drizzle-sized droplets. The format is the same as in Fig. 4, with the top panel of each image pair showing the depolarization ratio, SLDR*-45 (dB, upper color scale) and the bottom panel showing corresponding radar equivalent reflectivity, Ze (dBZ, lower color scale). These figures show the signatures of the following hydrometeors: (a) common aggregates of dendrites (1508 UTC 15 Apr 1999); (b) conical graupel, with melting layer just above the surface (2110 UTC 20 Apr 1999); (c) hexagonal graupel (1211 UTC 13 Apr 2000); (d) large supercooled droplets (2010 UTC 14 Apr 1999)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Measured curves of SLDR*-45(χ) (dB, °) from RHI scans from constant-altitude samples through the supercooled drizzle-sized droplets and several types of the more irregular and spherical ice particles (Figs. 9 and 10). Valid signal strength was ensured by restricting cross-polar intensity to Icr > 0.04 volts. Each measurement is at a constant altitude h, as follows: (a) drizzle: h = 0.5 km AGL 2010 UTC 14 Apr 1999; (b) aggregates, quasi-spherical, of dendrites and spatial dendrites (1.0 km AGL, 1508 UTC 15 Apr 1999); (c) elongated aggregates, extremely large, of planar crystals (1.6 km AGL, 1902 UTC 27 Apr 1999); (d) conical graupel (1.5 km AGL, 2110 UTC 20 Apr 1999); (e) lump graupel (dotted line, 0.3 km AGL, 1442 UTC 15 Apr 1999); and (f) hexagonal graupel (0.4 km AGL, 1211 UTC 13 Apr 1999).
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
As in Fig. 7a: (a) DR(β) from fixed-elevation rotation of the PRP in conical graupel, 2 km AGL, 211145–211444 UTC 20 Apr 1999; (b) and corresponding cross-polar intensity (Icr) and main-channel reflectivity (Ze). (Compare to data from spin in drizzle, Fig. 7.)
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
PMS 2DGC images of drizzle-sized droplets, predominantly of 50–250-μm diameters (particles with smooth circumference and, commonly, a bright center or “doughnut” appearance) and rare ice pellets of similar size (less regular particles with ragged circumference), sampled at MWO, 1945–2015 UTC 14 Apr 1999; width of image volume is 800 μm. Appearance of nonsphericity of the droplets is due to a slight mismatch between the wind speed and data recording rate of the PMS probe
Citation: Journal of Atmospheric and Oceanic Technology 19, 3; 10.1175/1520-0426-19.3.296
Definitions
Comparisons of available vs functional or utilized dynamic ranges in three depolarization ratios (DR), corresponding shifts in DR due to two differing ice crystal canting angles, and minimum differentiation in DR of regular ice crystals from spherical droplets at χ ≤ 60°
