# Ice Hydrometeor Shape Estimations Using Polarimetric Operational and Research Radar Measurements

## Abstract

**:**

_{e}, differential reflectivity, Z

_{DR}, and copolar correlation coefficient ρ

_{hv}, which are available from radar systems operating in either simultaneous or alternate transmutation of horizontally and vertically polarized signals. DR-r relations were developed for retrieving aspect ratios and their sensitivity to different assumptions and model uncertainties were discussed. To account for changing particle bulk density, which is a major contributor to the retrieval uncertainty, an approach is suggested to tune the DR-r relations using reflectivity-based estimates of characteristic hydrometeor size. The analyzed events include moderate snowfall observed by an operational S-band weather radar and a precipitating ice cloud observed by a scanning K

_{a}-band cloud radar at an Arctic location. Uncertainties of the retrievals are discussed.

## 1. Introduction

_{e}, differential reflectivity, Z

_{DR}, specific differential phase K

_{DP}, and copolar correlation coefficient, ρ

_{hv}. As an output, these algorithms prescribe different dominant hydrometeor types/species for cloud and precipitation particles filling the radar resolution volume. Typical ice hydrometeor species that are routinely identified using radar measurements are hail, graupel, aggregated snow, and ice crystals. Quantitative information on ice particle shapes, however, is not typically provided by the HID algorithms.

_{a}-band scanning radar measurements [13]. While this radar did not directly measure CDR, CDR values were reconstructed from linear polarization basis measurements as in [14]. Radar-based retrievals of particle aspect ratios in these studies agreed generally well with concurrent in-situ measurements when appropriate particle density assumptions were made.

_{DR}and ρ

_{hv}observations by radars operating in the simultaneous transmission-simultaneous reception (STSR) mode, which precludes direct measurements of depolarization. Later, weather radar Z

_{DR}and ρ

_{hv}measurements were applied to infer aspect ratios of ice cloud hydrometeors assuming the solid ice hexagonal particles, which are characteristic of single plates or solid columns [12]. Moreover, depending on particle shapes, observed polarimetric variables also depend on particle bulk density, so density assumptions are essential for aspect ratio retrievals from depolarization [9] or combined Z

_{DR}and ρ

_{hv}measurements [17]. For the soft spheroidal particle model, the particle bulk density assumption is, in essence, equivalent to an assumption of the complex dielectric constant of the ice-air mixture which dry hydrometeors are made of. Without the density assumption, only a polarizability parameter of the particles can be estimated [17]. The objective of this study was to extend depolarization-based ice hydrometeor shape retrievals to evaluate the spatial variability of their aspect ratios with approximate accounting for the effects of changing particle density.

## 2. Models and Methods

_{10}[(Z

_{dr}+ 1 − 2 Z

_{dr}

^{0.5}ρ

_{hv})/(Z

_{dr}+ 1 + 2 Z

_{dr}

^{0.5}ρ

_{hv})]

_{dr}is differential reflectivity in the linear scale (i.e., logarithmic scale Z

_{DR}= 10 log

_{10}(Z

_{dr}). For STSR measurements, DR depends on the transmitter phase shift between h and v polarized signals (φ

_{t}), which often is not known. It has been shown [16] that this dependence is usually rather weak. While being only a proxy for cthe ircular depolarization ratio, the DR parameter has important advantages over real depolarization measurements. It does not depend on propagation phase shift as true CDR [18]. DR estimates are available in all radar resolution volumes where directly measured co-polarized signals are reliably measured. The real depolarization measurements, on the other hand, are only available when weak depolarized echoes are reliably measured, which greatly diminishes radar coverage for depolarization ratios compared to reflectivity [10]. DR estimates, in essence, combine the information contained in Z

_{DR}and ρ

_{hv}for more convenient retrievals of particle aspect ratios.

_{dr}and ρ

_{hv}for spheroidal ice particles in the STSR measurement mode are given in [15,16]. To model aspect ratio (r)-DR relations for particle populations, it was assumed that the particle size distribution (PSD), as a function of particle major dimension, D, is described by the gamma-function:

_{o}exp[−(3.67 + μ)D/D

_{mv}]

_{o}, μ are the intercept and width parameters (note that DR is immune to changes in N

_{o}), and D

_{mv}is the median volume particle size, which represents the characteristic PSD size. Due to aerodynamic forcing, falling particles tend to be oriented with their major dimensions in the horizontal plane, so it was assumed that the mean canting angle θ is zero. Particle wobbling around the preferential horizontal orientation was described by the Gaussian distribution with respect to θ with the standard deviation σ

_{θ}.

^{b}

^{b}are empirical coefficients. The corresponding bulk density was calculated by dividing particle mass by the spheroidal volume and it was capped by the solid ice density maximum value of 0.916 g cm

^{−3}. A minimum value of 0.01 g cm

^{−3}was assumed when the use of m-D relations for larger particles resulted in values less than 0.01 g cm

^{−3}. Depending on the bulk density, the particle dielectric constant was calculated using the Maxwell–Garnet mixing rule for air-solid ice mixtures.

_{t}= 90° (i.e., circular polarization is transmitted), the exponential particle size distribution (i.e., μ = 0) and moderate particle wobbling (σ

_{θ}= 20°). The antenna polarization isolation, which is characterized by the minimal value of measurable LDR, was assumed to be −27 dB. This value is typical for many research and operational radars, including the ones used in previous studies [13]. The coefficients in the m-D relation were assumed to be a = 0.0053 and

^{b}= 2.1 (m is in grams, D is in cm). These coefficients were found to be suitable for low-to-moderately rimed snowflakes [22]. They also practically coincide with coefficients found independently [23] based on a large dataset of in situ measurements. DR for particles with r < 0.1 were not modeled. Such low aspect ratios are typically associated with single pristine crystals (e.g., dendrites, hexagonal plates).

_{mv}. Since ice hydrometeor scattering at S-band is generally in the Rayleigh regime, this variability is due to changing particle density, as it is proportional (for a given value of particle aspect ratio) to D

^{b−3}. Denser particles of the same shape cause stronger depolarization of observed radar echoes. For given particle shapes, PSD type and the m-D relation, D

_{mv}can be considered as a proxy for an ensemble averaged particle density, so it can be possible to account for the density effect on DR through the changes in D

_{mv}. Independent information on particle characteristic size, however, from the sources other than radar measurements (e.g., in situ microphysical observations) is usually unavailable, except for special research radar deployments with additional sensors.

_{mv}[24]. The second radar frequency measurements, however, are also rarely available. Another practical way to estimate D

_{mv}from single-wavelength radar measurements is through the use of empirical relations between D

_{mv}and radar reflectivity Z

_{e}[25]. As shown in [26], there are relatively strong statistical relations between Z

_{e}and PSD size parameters. These relations are akin to widely used relations between ice water content (IWC) and Z

_{e}. One reason that reflectivity is relatively strongly correlated to both IWC and D

_{mv}is that there is statistical correspondence between these two cloud/precipitation microphysical parameters. The corresponding correlation coefficients between D

_{mv}and radar reflectivity Z

_{e}are around 0.85 [26]. An average D

_{mv}-Z

_{e}relation obtained from the Global Precipitation Measurement (GPM) Cold Season Precipitation Experiment (GCPEX) dataset in that study can be approximated for S-band frequencies in the following way:

_{mv}= 0.095 Z

_{e}

^{0.31}

_{mv}is in cm and Z

_{e}is in mm

^{6}m

^{−3}. As found from modeling using in-situ PSDs, the data scatter around the best power-law fit size parameter—Reflectivity relation is on average around 50% [26].

_{mv}values from (4), relations of the type shown in Figure 1 can be used for retrievals of ice hydrometeor aspect ratios from DR estimates derived from radar measurements. In addition to the variability due to D

_{mv}(i.e., due to particle bulk density), which can be considered as a dominant source of changes in the r-DR relations, these relations are also sensitive to other radar configuration and particle microphysical parameters, such as α, φ

_{t}, μ, σ

_{θ}, and the coefficients in the m-D relations. Figure 2 illustrates corresponding sensitivities.

_{t}(curve 4 vs. curve 1 in Figure 2) from 90° (i.e., circular polarized signals are transmitted) to 0° (i.e., 45° slant linearly polarized signals are transmitted) result in the variability of particle aspect ratios of an order of only few hundredths. This is, in part, due to the fact that DR remains a good proxy for CDR corrected for propagation phase shift even though φ

_{t}can change rather significantly [16]. A similarly small variability is caused by changes in the radar elevation angle α from 10° to 20° (curve 3 vs. curve 1 in Figure 2). Note that 20° is the largest elevation angle used with the Weather Surveillance Radar-1988 Doppler (WSR-88D) operational weather radar network. Unlike the transmission phase shift φ

_{t}, which is often unknown, the radar elevation angle for each scan is known, so the r-DR relations can be easily adjusted for each value of α.

_{DR}, which is another radar variable sensitive to particle shapes. For the same value of the particle wobbling parameter σ

_{θ}, there is a one-to-one correspondence between DR and Z

_{DR}. This correspondence, however, changes with σ

_{θ}, as shown in Figure 3 where modeling results of this correspondence are depicted for two sets of assumptions, which differ only by values of σ

_{θ}. Compared to r-DR relations, there is a much stronger variability in the r-Z

_{DR}relations caused by uncertainties in σ

_{θ}. This point is illustrated in Figure 4, where both relation types are shown for different assumed values of σ

_{θ}. The relative insensitivity of DR to particle orientations/wobbling makes depolarization-based estimates of particle aspect ratios more robust compared to potential differential reflectivity-based aspect ratio estimates.

_{mv}values from reflectivity measurements [26] could be as large as a factor of 2, it can be expected that errors of particle aspect ratio retrievals from depolarization ratio estimates could be at least 0.2 or so. This precludes the effective use of the depolarization-based method suggested here for quantitatively estimating shapes of very non-spherical ice particles such as single pristine crystals (e.g., dendrites, hexagonal plates). High depolarization ratio values (e.g., DR > −15 dB) can be indicative about the presence of such crystals in a radar resolution volume as a dominant hydrometeor type. The use of this method for estimating general shape of ice hydrometeors (as expressed by aspect ratios) of irregular ice particle, however, could be rather robust and useful for different applications when general information about particle shape is needed (e.g., polarimetric radar QPE and microphysical modeling studies).

## 3. Results of Retrievals

#### 3.1. Examples of the Retrievals Using Operational Weather Radars

_{hv}(very high DR). Particle aspect ratio retrievals were performed with the assumptions, which were used to generate the modeling results shown in Figure 1, except that the actual radar beam elevation angle of 4.6° was accounted for. Retrieval results, however, are not very sensitive to the changes in the radar elevation angle in the range 0°–20° as compared to influencing factors affecting bulk density (e.g., m-D relation coefficients, a PSD shape), which is a major factor defining radar variables [27].

_{DR}values. At further radar ranges there is a tendency for more spherical particles. These ranges correspond to higher altitudes above the ground (e.g., at the 4.6° elevation the center of the radar beam is at an altitude of about 3.2 km above the ground for a 40 km range). An exception for this general tendency is a region at about 50 km to the south-east from the radar site, where locally higher values of Z

_{DR}and lower ρ

_{hv}values result in higher DR, which indicates rather non-spherical particles. Radiosonde sounding from the location in Chanhassen, MN (not shown) indicated that during radar measurements, temperatures at altitudes of about 3.2 km above ground were approximately −15 °C, which corresponds to a temperature regime favorable for the growth of dendritic crystals with low aspect ratios [28]. This might explain the transition between dominant shapes happening at radar ranges of around 40–50 km. Measurements at longer ranges, however, should be treated with some caution, as lower signal-to-noise ratios (SNRs) can cause biases in observed polarimetric variables [29]. To avoid very low SNRs, data points were considered only if reflectivities were greater than −10 dBZ.

_{DR}and low ρ

_{hv}values observed in these areas are indicative of dendritic-type pristine crystals being a dominant hydrometeor habit. According to the radiosonde soundings, the −15 °C level for this measurement time was at about 4 km above the ground (i.e., at approximately a 50 km range from the radar site). Note also that reflectivities across these areas vary very significantly, which results in a large dynamic range of particle median volume size estimates (e.g., from about 1 mm to approximately 4 mm). Almost everywhere else in the depicted scan particles are more spherical with aspect ratios of about 0.4–0.9 which are characteristic of irregular hydrometeor shapes. As for the event shown in Figure 5, the particle mean aspect ratio data in Figure 6 at further radar ranges (and thus at higher altitudes) are near 0.9–1.0 and rather noisy, which might be, in part, due to low SNR values and the influence of particle tumbling.

_{DR}biases will cause uncertainties in DR calculations and thus influence aspect ratio retrievals. Modeling with the DR Estimator (1) indicates that for a 0.1 dB Z

_{DR}bias and typical values of ρ

_{hv}(e.g., 0.85 < ρ

_{hv}< 0.995), errors in DR estimates are generally less than about 0.5 dB for smaller Z

_{DR}values (e.g., 0.2 dB < Z

_{DR}< 1.5 dB). For larger Z

_{DR}values, these errors generally diminish. The data in Figure 1 suggest that such DR errors can correspond to an additional uncertainty of aspect ratio retrievals of the order of several hundredths.

#### 3.2. An Example of the Retrievals Using a Research Cloud Radar

_{a}-band (~35 GHz) radar polarimetric measurements at the U.S. Department of Energy’s (DOE) Atmospheric Radiation Measurement (ARM) Program mobile facility in Oliktok Point (70.495° N, 149.886° W), Alaska [13]. The Scanning ARM Cloud Radar (SACR) used for these retrievals transmits horizontally and vertically polarized signals alternatively, which alleviates cross-coupling effects in the differential reflectivity data, and measures horizontal-vertical polarization linear depolarization ratio (LDR) directly, thus allowing estimations of DR, which, in this case, is the proxy of true CDR without unwanted effects of the propagation phase shift [14].

_{e}-D

_{mv}relation obtained specifically for the K

_{a}-band frequencies from the large in situ microphysical dataset [26]. It was assumed that the particle size distribution for the event time shown in Figure 7 had an exponential form as it was indicated by closely collocated in time in situ measurements using Video Ice Particle Sampler (VIPS), which was launched on a tethered balloon near the radar site [13]. The VIPS instrument provides quantitative information on particle size distributions and shapes. As seen from Figure 7d, estimated D

_{mv}values were generally smaller than about 1.5 mm in the larger area of observations and around 0.8–1 mm in the vicinity of the radar site. This agrees well with VIPS estimates of D

_{mv}≈ 0.08 mm which were obtained near the radar site at a balloon altitude of about 0.5 km at around the time of radar observations shown in Figure 7.

_{mv}values were generally less than 1.5 mm. At these reflectivity levels, non-Rayleigh scattering effects at K

_{a}-band are expected to be rather small [32]. For larger particle populations, however, these effects could be substantial and need to be accounted for in the retrievals. Especially important accounting for non-Rayleigh effects would be for the retrievals at W-band (~94 GHz) cloud radar frequencies [6]. Signal attenuation at W-band frequencies, however, is usually much more severe compared to lower frequencies [33], so sensible retrievals often could be available only for closer ranges.

## 4. Conclusions

_{mv}) representing the whole particle size distribution allows for implicit accounting for the density information in the radar-based aspect ratio retrievals. DR-r relations used in the retrievals were derived as a function of D

_{mv}. The mass-size (m-D) relations, which are representative for unrimed and low-to-moderately rimed atmospheric ice particles, were used in these derivations.

_{mv}estimates used in the aspect ratio retrievals were obtained from the reflectivity measurements. These estimates are based on a relatively high correlation between D

_{mv}and Z

_{e}, which was demonstrated using a wide range of in situ observations in precipitating ice clouds [26].

_{a}-band cloud radar observations in a precipitating ice cloud at Oliktok Point indicated a range gradient of particle dominant shapes. The retrieved aspect ratios near the radar site were around 0.4, which is in good agreement with in-situ sampling results. Overall, it can be concluded that in spite of uncertainties in the aspect ratio retrievals, which could be as high as 0.2 or so, the DR-based approach of estimating particle shapes is rather robust and can provide quantitative information on dominant ice hydrometeor shapes.

## Funding

## Conflicts of Interest

## References

- Vivekanandan, J.; Zrnic, D.S.; Ellis, S.M.; Oye, R.; Ryzhkov, A.V.; Straka, J. Cloud microphysics retrievals using S-band dual-polarization radar measurements. Bull. Am. Meteorol. Soc.
**1999**, 80, 381–388. [Google Scholar] [CrossRef] - Keenan, T. Hydrometeor classification with a C-band polarimetric radar. Aust. Meteorol. Mag.
**2003**, 52, 23–31. [Google Scholar] - Dolan, B.; Rutledge, S.A. A theory-based hydrometeor identification algorithm for X-band polarimetric radars. J. Atmos. Ocean. Technol.
**2009**, 26, 2071–2088. [Google Scholar] [CrossRef] [Green Version] - Hogan, R.L.; Tian, L.; Brown, P.R.A.; Westbrook, C.D.; Heymsfield, A.J.; Eastment, J.D. Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation. J. Appl. Meteorol. Climatol.
**2012**, 51, 655–671. [Google Scholar] [CrossRef] [Green Version] - Jensen, A.A.; Harrington, J.Y.; Morrison, H.; Milbrandt, J.A. Predicting ice shape evolution in a bulk microphysics model. J. Atmos. Sci.
**2017**, 74, 2081–2104. [Google Scholar] [CrossRef] - Kokhanovsky, A.; Macke, A. The dependence of the radiative characteristics of optically thick media on the shape of particles. J. Quant. Spectrosc. Radiat. Transf.
**1999**, 63, 393–407. [Google Scholar] [CrossRef] - Bukovcic, P.; Ryzhkov, A.; Zrnic´, D.; Zhang, G. Polarimetric radar relations for quantification of snow based on disdrometer data. J. Appl. Meteorol. Climatol.
**2018**, 57, 103–120. [Google Scholar] [CrossRef] - Matrosov, S.Y. Theoretical study of radar polarization parameters obtained from cirrus clouds. J. Atmos. Sci.
**1991**, 48, 1062–1070. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Reinking, R.F.; Kropfli, R.A.; Martner, B.E.; Bartram, B.W. On the use of radar depolarization ratios for estimating shapes of ice hydrometeors in winter clouds. J. Appl. Meteorol.
**2001**, 40, 479–490. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Mace, G.G.; Marchand, R.; Shupe, M.D.; Hallar, A.G.; McCubbin, I.B. Observations of Ice crystal habits with a scanning polarimetric W-band radar at slant linear depolarization ratio mode. J. Atmos. Ocean. Technol.
**2012**, 29, 989–1008. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Reinking, R.F.; Djalalova, I.V. Inferring fall altitudes of pristine dendritic crystals from polarimetric radar data. J. Atmos. Sci.
**2005**, 62, 241–250. [Google Scholar] [CrossRef] [Green Version] - Melnikov, V. Parameters of cloud ice particles retrieved from radar data. J. Atmos. Ocean. Technol.
**2017**, 34, 717–728. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Schmitt, C.G.; Maahn, M.; de Boer, G. Atmospheric ice particle shape estimates from polarimetric radar measurements and in situ observations. J. Atmos. Ocean. Technol.
**2017**, 34, 2569–2587. [Google Scholar] [CrossRef] - Jameson, A.R. Relations among linear and circular polarization parameters measured in canted hydrometeors. J. Atmos. Ocean. Technol.
**1987**, 4, 634–645. [Google Scholar] [CrossRef] [Green Version] - Melnikov, V.; Matrosov, S.Y. Estimations of aspect ratios of ice cloud particles with the WSR-88D radar. In Proceedings of the 36th Conference on Radar Meteorology, Breckenridge, CO, USA, 16–20 September 2013; American Meteorological Society: Washington, DC, USA, 2013; p. 245. Available online: https://ams.confex.com/ams/36Radar/webprogram/Paper228291.html (accessed on 21 October 2017).
- Ryzhkov, A.; Matrosov, S.Y.; Melnikov, V.; Zrnic, D.; Zhang, P.; Cao, Q.; Knight, M.; Simmer, C.; Troemel, S. Estimation of depolarization ratio using weather radars with simultaneous transmission /reception. J. Appl. Meteorol. Climatol.
**2017**, 56, 1797–1816. [Google Scholar] [CrossRef] - Myagkov, A.; Seifert, P.; Wandinger, U.; Bühl, J.; Engelmann, R. Relationship between temperature and apparent shape of pristine ice crystals derived from polarimetric cloud radar observations during the ACCEPT campaign. Atmos. Meas. Tech.
**2016**, 9, 3739–3754. [Google Scholar] [CrossRef] [Green Version] - Matrosov, S.Y. Depolarization estimates from linear H and V measurements with radar radars operating in simultaneous transmission-simultaneous receiving mode. J. Atmos. Ocean. Technol.
**2004**, 21, 574–583. [Google Scholar] [CrossRef] - Moisseev, D.N.; Lautaportti, S.; Tyynela, J.; Lim, S. Dual-polarization radar signatures in snowstorms: Role of snowflake aggregation. J. Geophys. Res.
**2015**, 120, 12644–12655. [Google Scholar] [CrossRef] [Green Version] - Reinking, R.F.; Matrosov, S.Y.; Kropfli, R.A.; Bartram, B.W. Evaluation of a slant 45° slant quasi-liner radar polarization for distinguishing drizzle droplets, pristine ice crystals, and less regular ice particles. J. Atmos. Ocean. Technol.
**2002**, 19, 296–321. [Google Scholar] [CrossRef] - Marchand, R.; Mace, G.G.; Hallar, A.G.; McCubbin, I.B.; Matrosov, S.Y.; Shupe, M.D. Enhanced radar backscattering due to oriented ice particles at 95 GHz during Storm-VEx. J. Atmos. Ocean. Technol.
**2013**, 30, 2336–2351. [Google Scholar] [CrossRef] - Von Lerber, A.; Moisseev, D.; Bliven, L.F.; Petersen, W.; Harri, A.M.; Chandrasekar, V. Microphysical properties of snow and their link to Ze-S relations during BAECC 2014. J. Appl. Meteorol. Climatol.
**2017**, 56, 1561–1582. [Google Scholar] [CrossRef] - Heymsfield, A.J.; Schmitt, C.; Bansemer, A. Ice cloud particle size distributions and pressure-dependent terminal velocities from in situ observations at temperatures from 0° to −86 °C. J. Atmos. Sci.
**2013**, 70, 4123–4154. [Google Scholar] [CrossRef] - Matrosov, S.Y. A dual-wavelength radar method to measure snowfall rate. J. Appl. Meteorol.
**1998**, 37, 1510–1521. [Google Scholar] [CrossRef] - Matrosov, S. Variability of microphysical parameters in high-altitude ice clouds: Results of the remote sensing method. J. Appl. Meteorol.
**1997**, 36, 633–648. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Heymsfield, A.J. Empirical relations between size parameters of ice hydrometeor populations and radar reflectivity. J. Appl. Meteorol. Climatol.
**2017**, 56, 2479–2488. [Google Scholar] [CrossRef] - Matrosov, S.Y.; Campbell, C.; Kingsmill, D.; Sukovich, E. Assessing snowfall rates from X-band radar reflectivity measurements. J. Atmos. Ocean. Technol.
**2009**, 26, 2324–2339. [Google Scholar] [CrossRef] [Green Version] - Kennedy, P.C.; Rutledge, S.A. S-band dual-polarization radar observations of winter storms. J. Appl. Meteorol. Climatol.
**2011**, 50, 844–858. [Google Scholar] [CrossRef] - Bringi, V.N.; Chandrasekar, V. Polarimetric Doppler Weather Radar; Cambridge University Press: Cambridge, UK, 2001; 636p. [Google Scholar]
- Matrosov, S.Y.; Shupe, M.D.; Djalalova, I.V. Snowfall retrievals using millimeter-wavelength cloud radars. J. Appl. Meteorol. Climatol.
**2008**, 47, 769–777. [Google Scholar] [CrossRef] [Green Version] - Atmospheric Radiation Measurement (ARM) User Facility. Ka-Band Scanning ARM Cloud Radar (KASACRPPIVH); 2016-10-20 to 2016-10-21, ARM Mobile Facility (OLI) Oliktok Point, Alaska, AMF3 (M1); Isom, B., Bharadwaj, N., Lindenmaier, I., Nelson, D., Hardin, J., Matthews, A., Eds.; ARM Data Center: Oak Ridge, TN, USA, 2018. [Google Scholar]
- Matrosov, S.Y.; Maahn, M.; de Boer, G. Observational and modeling study of ice hydrometeor radar dual-wavelength ratios. J. Appl. Meteorol. Climatol.
**2019**, 58, 2005–2017. [Google Scholar] [CrossRef] - Sassen, K.; Matrosov, S.; Campbell, J. CloudSat spaceborne 94 GHz radar bright band in the melting layer: An attenuation driven upside-down lidar analog. Geophys. Res. Lett.
**2007**, 34, L16818. [Google Scholar] [CrossRef]

**Figure 1.**r-DR relations for different values of median volume particle size, D

_{mv}, assuming that the radar elevation angle α = 10°, transmission phase shift φ

_{t}=90°, the standard deviation of particle wobbling σ

_{θ}= 20°, and m = 0.0053D

^{2.1}mass-size relation (m is in grams, D is in cm).

**Figure 2.**r-DR relations assuming D

_{mv}= 0.1 cm and different assumptions for the radar elevation angle α, transmission phase shift φ

_{t}, the standard deviation of particle wobbling σ

_{θ}, and the coefficients in the particle mass-size relation.

**Figure 3.**r-DR relations assuming D

_{mv}= 0.1 cm and different assumptions for the radar elevation angle α, the transmission phase shift φt, the standard deviation of particle wobbling σ

_{θ}, and the coefficients in particle mass-size relation. Different color segments correspond to results of modeling with different D

_{mv}values (i.e., 0.05, 0.1, 0.2, 0.3 and 0.5 cm).

**Figure 4.**r-DR (lower X-axis, black curves) and r-Z

_{DR}(upper X-axis, red curves) relations for different particle wobbling parameters σ

_{θ}.

**Figure 5.**Measurements of horizontal polarization reflectivity (

**a**), differential reflectivity (

**b**), copolar correlation coefficient (

**c**), estimates of depolarization ratio (

**e**) and retrievals of particle median volume size (

**d**) and aspect ratio (

**f**) corresponding to a KDLH radar scan at 4.5° on 5 March 2013 at 19:27 UTC.

**Figure 6.**Measurements of horizontal polarization reflectivity (

**a**), differential reflectivity (

**b**), copolar correlation coefficient (

**c**), estimates of depolarization ratio (

**e**) and retrievals of particle median volume size (

**d**) and aspect ratio (

**f**) corresponding to a KDLH radar scan at 4.5° on 20 February 2014 at 19:31 UTC.

**Figure 7.**Measurements of horizontal polarization reflectivity (

**a**), differential reflectivity (

**b**), copolar correlation coefficient (

**c**), estimates of depolarization ratio (

**e**) and retrievals of particle median volume size (

**d**) and aspect ratio (

**f**) corresponding to a KDLH radar scan at 5° on 21 October 2016 at 00:52 UTC.

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Matrosov, S.Y.
Ice Hydrometeor Shape Estimations Using Polarimetric Operational and Research Radar Measurements. *Atmosphere* **2020**, *11*, 97.
https://doi.org/10.3390/atmos11010097

**AMA Style**

Matrosov SY.
Ice Hydrometeor Shape Estimations Using Polarimetric Operational and Research Radar Measurements. *Atmosphere*. 2020; 11(1):97.
https://doi.org/10.3390/atmos11010097

**Chicago/Turabian Style**

Matrosov, Sergey Y.
2020. "Ice Hydrometeor Shape Estimations Using Polarimetric Operational and Research Radar Measurements" *Atmosphere* 11, no. 1: 97.
https://doi.org/10.3390/atmos11010097