# Polarization Weather Radar Development from 1970–1995: Personal Reflections

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Brief Overview of Electromagnetics in Dual-Polarization Radar and Related Topics

**h•E**where

_{s}**h**describes the effective antenna “height” defined as

**h**= λ G

^{1/2}

**e**and

_{h}**E**is the backscattered wave from the particle [5]. The wavelength is λ, G is the gain, and

_{s}**e**is the unit vector which describes the radiated polarization state. In general,

_{h}**e**could be elliptically polarized (described by the ellipticity angle τ and orientation angle Φ of the ellipse) but most common is the linear antenna polarization state (defined by convention when the antenna is radiating with τ = 0 and

_{h}`Φ`= 0, 90° corresponding to H and V polarizations, respectively). The 2 × 2 scattering matrix

**S**describes the interaction between the wave incident on the particle and the wave that is scattered back,

**E**=

_{s}**S E**[6]. Thus, the voltage equation takes the bilinear form V =

_{inc}**h**•[

**S E**] and the received power is

_{inc}**[**

`|`h•**S E**]

_{inc}**[7]. From the expression for the received power, the generalized form of the radar cross-section takes the more familiar form σ(**

`|`^{2}**e**,

_{h}**e**) = 4π

_{inc}**•[**

`|`e_{h}**S e**]

_{inc}**where the unit polarization vector for the antenna is**

`|`^{2}**e**and that of the incident wave is

_{h}**e**. Note that the copolar radar cross-section is defined when

_{inc}**e**=

_{h}**e**whereas for cross-pol

_{inc}**e**is orthogonal to

_{h}**e**. From [2], for a sphere whose scattering matrix is for simplicity given by Shh = Svv = 1, Shv=0, the σ

_{inc}_{co}= 4π(2cos

^{2}τ

_{inc}− 1)

^{2}and σ

_{cx}= 4π(4cos

^{2}τ

_{inc}sin

^{2}τ

_{inc}).

_{co}/σ

_{cx}) or Elliptical Depolarization Ratio (EDR) turns to be −14 dB independent of elevation angle and forms a reference against which to compare the elevation angle dependence of EDR for other types of ice crystals, e.g., branched planar dendrites or irregular graupel. RHI scans in horizontally homogeneous winter precipitation showed dramatic swings of (8 dB) in EDR for plate-like crystals with elevation angle from 0 to 90 whereas irregular graupel showed EDR about 1 dB higher than for drizzle with no elevation angle dependence.

**T**) which enters into the voltage form of the radar range equation as V =

**h**•[

**T**] where superscript (t) is the matrix transpose. This complicates the separation of backscatter from propagation effects such as differential attenuation and differential phase shift which causes depolarization of the transmitted wave even at long wavelengths (S-band). In [15], McCormick and Hendry showed that when propagation effects dominate the signal returns then a complex plane plot of what they term as W/W

^{t}ST_{2}(W is the complex correlation and W

_{2}is the power in the main signal channel) as a function of increasing range can be used to measure differential attenuation and differential phase (as path averages over homogeneous sections). From these complex plane plots they were able to determine the anisotropy of the propagation medium and the first measurements in rain and snow were at K

_{u}-band and later at X-band in [16], which, additionally, used “slow” switching between right-hand and left-hand circular polarizations. Some years later Hendry confided to one of the authors (V.N.B) that one personal highlight of their K

_{u}-band measurements in snow was the recognition that the particles responsible for the circular depolarization ratio (i.e., the larger nonspherical aggregates with large variance of shapes) were different from those that contributed most to the differential propagation phase (i.e., horizontally oriented plate-like ice crystals). As described in the Canadian work, a principal conclusion was that raindrops form a highly oriented anisotropic propagation medium with symmetry axis near vertical. They also determined that differential phase shift due to oriented ice crystals aloft in thunderstorms could reveal changes that correlate with lightning discharges [17]. Later, using real-time displays of differential propagation phase shifts based on polarization agile (H, V)-basis data, the aforementioned changes could be easily identified by rapid RHI scans through thunderstorm cores aloft. There the differential propagation phase would decrease with range as electrostatic fields oriented the crystals vertically. The lightning discharge that followed relaxed the crystals into horizontal orientation and the differential phase would start increasing with range [18,19]; the process repeated at regular intervals. One of the authors (V.N.B) witnessed this repetitive “charge” and “discharge” phenomena by observing real-time displays on the Colorado State University-University of Chicago and Illinois State Water Survey (CSU-CHILL) radar RHI scans with chief engineer David Brunkow and it was a thrilling moment to see electromagnetic theory at work in nature and to observe it so easily.

_{DR}). In [25] the ARC radar data were “corrected” and re-analyzed to show that combined use of reflectivity, Z

_{DR}and to some extent the “degree of orientation” could identify hail and rain-hail mixtures.

_{DP}) and rain rate. From this relation and the Marshal Palmer R(Z) relation, D.Z. quickly computed the differential phase along some radials of reflectivity. The results indicated that the differential propagation phase could easily reach 180° in strong convective rain. The voltage in the intended LHC port can be simply expressed as V

_{L}= cos (K

_{DP}•r) where r is the range to the resolution volume [2]. Since it is assumed that two-way differential propagation phase (defined as 2K

_{DP}•r) reaches 180° or K

_{DP}•r reaches 90°, the LHC port receives no signal whereas the returned signal would be terminated at the RHC port. Recognizing that this “artificial” loss in the return signal would be devastating, D.Z. wrote a memo about this loss to Dr. Vernon Derr, the director of the Environmental Research Laboratories (National Severe Storms Laboratory is one of these laboratories), who informed the National Weather Service (NWS). The transmit polarization was soon changed to linear horizontal. This issue raised awareness among the NWS personnel about the impact of radar polarimetry.

## 3. Ohio State-Illinois Water Survey Collaboration

_{0}) and median volume diameter (D

_{0}) of an assumed exponential drop size distribution. At that time T.S. and V.N.B. were aware of (1) the wind-tunnel data of [46], which gave a simple linear expression for drop axis ratio (b/a) versus D in the form b/a = 1 − βD and (2) the conclusions in [47] that rain drops formed an anisotropic propagation medium with high degree of orientation. T.S. suggested a simplistic view of Rayleigh scattering by oblates arguing that an H-polarized wave would induce an electric dipole moment and related radar cross-section varying as a

^{6}(a being the major axis) whereas a V-polarized wave induced moment and related cross-section as b

^{6}(b the minor axis). Thus, small deviations in axis ratio would be amplified if the ratio (b/a)

^{6}were considered. A colleague suggested we use Gans’ method, as in [48], for scattering by oblate spheroids. Subsequently, the differential reflectivity technique for estimating R was presented by V.N.B. at an URSI conference in Boulder in 1974 followed by [49] where Z

_{DR}versus D

_{0}and log(Z

_{h}/N

_{0}) versus D

_{0}were given on the same plot to emphasize the retrieval of (N

_{0}, D

_{0}) and hence R. T.S. also included two block diagrams to measure Z

_{DR}. The first was based on polarization agility or pulse-to-pulse switching between H and V polarizations and sequential reception of the H and V polarized components of the backscattered wave via the same receiver. The second was polarization diversity, whereby the transmitted wave was fixed at slant linear 45° polarization and simultaneous reception of the H and V-polarized components were made via two receivers. T.S. knew from his prior research on wave propagation in the ionosphere at Penn State that receivers could be built that measure small differential amplitude (and differential phase shifts) very accurately, hence the assumption in [49] was made that Z

_{DR}could be measured to within 0.2–0.5 dB.

_{0}could be related to D

_{0}which together with differential reflectivity might provide better accuracy in estimation of R. The simple formula in [43] for coherent wave propagation was used along with T-matrix calculations for the forward scatter amplitudes. However, at that time an algorithm to estimate ΔΦ using pulse-to-pulse switching data was not available (that appeared later in a conference paper by Mueller) [53].

_{DR}. In the mid-1950s, Gene had already worked on drop shapes and scattering by spheroids, which appears to have played a role in his enthusiasm. The CHILL antenna had a feed/OMT for dual-pol capability but unused as yet. The feed/OMT was sent to OSU where the E/H-plane patterns were measured at the Electroscience Laboratory. The feed was a dual-mode Potter horn that gave well-matched E/H-plane patterns and the OMT had good port-to-port isolation. The antenna engineering staff indicated the feed was good for our application. It might be of interest to know that T.S. consulted with the famous antenna expert John Kraus (inventor of the helical antenna and Big Ear Radio Telescope, who was retired but still at OSU at that time) about dual-polarization radar measurements and Kraus’ response was “to keep it simple”. In retrospect, this was sound advice as there is no simpler concept than the two systems for measuring Z

_{DR}outlined by T.S. in [49]. In the summer of 1977 and during the waning days of the Severe Environmental Storms and Mesoscale Experiment (SESAME) project in Oklahoma (OK), the first “slow”-switched Z

_{DR}data in rain were obtained which showed that it could be measured and fell in the range predicted from theory [11]. In 1981, the first high-power switchable ferrite circulator (from an NSF grant awarded to Ohio State) was installed on the CHILL radar enabling measurement of “fast”-switched Z

_{DR}. Seliga and Mueller presented these data in 1982 at a URSI conference in the UK.

_{DR}, CDR, and specific differential phase in terms of, respectively, the reflectivity-weighted mean axis ratio, the mean and variance of the latter, and the product of W (rain water content) and the deviation of the mass-weighted mean axis ratio from unity were published in [54,55]. The axis ratio distributions from Jones’ [56] camera data which are extreme and not supported by later drop shape studies were used. Nevertheless, the interpretations are, in essence, applicable given the pdf of axis ratios. Assuming a linear relation of the form b/a = 1 − βD, the Z

_{DR}and specific differential phase were related to the ratio of 7

^{th}to 6

^{th}moments of the drop size distribution (DSD), and to the product of W, β, and the ratio of the 4

^{th}to 3

^{rd}moments (caveat is that β from Jones’ data is too low and biased to mean drop axis ratios closer to sphericity) [54,55].

## 4. Ohio State and Appleton Laboratory Collaboration

_{DR}measurements. A surplus air-surveillance S-band radar had been installed on the 25 m reflector antenna at Chilbolton, UK, for studies of rain attenuation along slant paths as part of radiowave propagation experiments. It was recognized that the parameters of the DSD were needed to estimate attenuation (which could then be scaled to K

_{u}-band) so the decision was taken by Martin Hall and the chief engineer, Steve Cherry, to build a motor-driven rotary vane switch integrated with a turnstile polarizer coupled to a scalar feed as one unit. A small NATO grant enabled collaboration between Appleton and OSU. In 1978, Martin and Steve came to OSU with time series of power samples at H and V polarizations with antenna stationary and from a single movable range gate. OSU was tasked with deriving the statistics of the normalized amplitude ratio of the H and V signals (the radar was incoherent) as a function of the correlation between the pulse pairs in the simpler case of uncorrelated sequence of (H,V)-pairs. An article on the bivariate chi distribution presented sufficient information to obtain the pdf of the normalized amplitude ratio with the correlation coefficient as a parameter. The agreement between theory and time-series analysis was unexpectedly good especially for correlation coefficients close to 1. The analysis was written up in a conference paper which was presented at a URSI conference organized by Profs. Riedler and Randeu in Graz, Austria [57]. At that conference, McCormick wrote down a formula for Z

_{DR}in terms of the elements of the coherency matrix at circular polarization [58]. As mentioned earlier, [24] derived the same after “correcting” for differential propagation shift in rain (see, also) [59].

_{DR}and the “optimal” estimator for Z

_{DR}starting from the 4 × 4 correlation matrix of the complex voltages. The expressions for mean and variance of Z

_{DR}were adapted from [60,61] resulting in the article [62].

## 5. Rutherford-Appleton Laboratory/Chilbolton Radar

_{DR}[12]. It included detection of ice (graupel) melting to rain in convection, snow aggregates melting to rain in stratiform events (with bright-band), and the spatial variability of the DSD parameters (N

_{0}, D

_{0}). This and the table of particle type classification based on (Z

_{H}, Z

_{DR}) were largely responsible for rapid acceleration of polarization agile radar development in the US [63] and in Europe (initially France, then Russia, Italy, and Germany, see Section 8). In 1982, an URSI Commission F symposium on Multiple-Parameter Radar Measurements of Precipitation [64] was held in Bournemouth, UK, with Martin Hall as the Symposium Chair. Seventy-nine attendees from 15 countries participated in ushering a new chapter in weather radar polarimetry. Subsequently, the conference papers were published in a Special Issue of Radio Science in 1984, edited by Martin Hall [65].

_{H}and Z

_{DR}with height in stratiform rain with bright-band. A layer of positive Z

_{DR}up to 4 dB at −10 °C was inferred to be caused by horizontally oriented plates (−10 °C being a growth region of dendritic crystals by vapor deposition). At lower heights to −5 °C, aggregation was inferred by increasing Z

_{H}(larger maximum sizes) but lower Z

_{DR}(lower bulk density and irregular shapes). The peak in Z

_{DR}(around 1.3 dB) due to partially melting snow was located near the base of bright-band just prior to the rapid transition to fully melted smaller rain drops. Another important example (which they termed as a “rare” occurrence) was a narrow column of high Z

_{H}and Z

_{DR}extending to 1.5 km above the melting level in convection and interpreted as supercooled rain drops carried up in the updraft. The above two examples, just based on (Z

_{H}, Z

_{DR}), inspired substantial research on the microphysical origins of the full complement of polarimetric signatures in winter storms and in positive Z

_{DR}columns in convective storms that is still ongoing.

_{H}, Z

_{DR})-pairs in rain and a rain–ice separation boundary was identified [67]. Data pairs that fell outside the rain area were inferred to be graupel/hail depending on the Z

_{H}values. This led to defining the quantitative HDR hail signature in [68] but, more importantly, to defining two-dimensional membership functions for rain in fuzzy-logic schemes [69,70,71].

_{DR}estimation of D

_{0}and subsequently much research has been done to establish this on a firmer basis including wind-tunnel measurements [74] and 2D-video disdrometer measurements [75] as well as the numerical prediction of equilibrium shapes [76]. A curve fitting approach using available axis ratio data from a variety of somewhat uncertain experimental and laboratory results (perhaps with compensating errors) has since been widely used [77].

_{DR}in the ice region of a stratiform rain event with aircraft-mounted particle imaging probes was published [78] which largely corroborated the inferences in [66]. Large positive Z

_{DR}were found in layers of “plate-like” crystals with low Z

_{H}, but when mixed with larger snow aggregates they found a “masking” effect, i.e., Z

_{DR}tended to 0 dB as Z

_{H}increased due to aggregation [78]. The shapes of snow aggregates (which dominates the Z

_{DR}) are highly irregular with effective permittivity much lower than solid ice, both of which cause Z

_{DR}to be close to 0 dB. Their paper spurred substantial polarimetric applications in winter precipitation using S, C, and X-band systems.

_{H}, Z

_{DR}) signatures in isolated echoes from initial stage (low concentration of large drops formed by coalescence processes) to vigorous updraft stage where positive Z

_{DR}columns extend to about −10 °C; this indicates lofting of rain into the cold part of the cloud [79]. They also describe the dissipating stage where (Z

_{H}, Z

_{DR}) in the rainshaft are consistent with exponential DSDs. The ultragiant aerosol hypothesis in [80] and a simple coalescence growth model was used to predict the (Z

_{H}, Z

_{DR}) [81]. The evolution from initial echo stage where low concentrations of large drops formed via coalescence was compared with radar measurements and found to be in good agreement [81].

_{H}, which is the difference between the peak value of Z

_{H}in the bright-band (BB) and the rain below, was given in [82]. The mode of ΔZ

_{H}was about 10 dB which occurred with large LDR values of about −15 dB indicating wet snow. In contrast, in stratiform rain with weak embedded convection the ΔZ

_{H}≈ 0 dB with lower LDR < −20 dB indicative of more compact rimed snow or graupel melting (with weak or no BB signature) to form rain. The engineering modifications to the Chilbolton radar circa 1994 are described in [83], which includes Doppler velocity and differential phase with all variables displayed in real-time.

## 6. Colorado State-NCAR-Ohio State/Penn State Collaboration

_{DR}errors in the presence of even modest spatial gradients of Z

_{H}[84,85]. At the suggestion of Thomas Seliga, the support struts were rotated by 45° in late 1986, which resulted in much better Z

_{DR}data quality in the presence of gradients [86].

_{DR}hail signature in strong convective storms was published in 1984 [87]. In a two-part series of articles [88,89], Part 1 used the detailed melting model of graupel [90] together with T-matrix (and two-layer T-matrix) scattering calculations, CP2 radar measurements, and aircraft data to show good agreement in the vertical profiles of Z

_{H}, Z

_{DR}and LDR between radar and model in two convective cases. This was perhaps the first such coupling of microphysical model output to EM scattering model specifically for melting graupel (the “dry” graupel size distribution aloft and sounding for the melting model were initialized with aircraft data). In the Part 2 article [89], CP2 radar data were used to compare the spatial distribution of Z

_{DR}, LDR, and dual-wavelength signatures in several hail storms. They showed very good spatial overlap of the signatures as well as consistency with scattering model predictions. The vertical structure of dual-wavelength hail signatures (>5 dB) above 0 °C level, enhanced LDR (> −20 dB), due to wet hail aloft and prominent Z

_{DR}hail signatures below the melting level demonstrated the value of combining polarimetric and dual-wavelength radar data.

_{H}, Z

_{DR}and differential phase more realistically (depending on wavelength, spectral width, number of sample pairs, and pulse repetition time as compared to simply assuming ad hoc Gaussian errors for the radar variables. The goal was to understand, using simulations, the error structure of polarimetric radar estimation of rain rate using different algorithms based on [Z

_{H}, Z

_{DR}, K

_{DP}] [92]. For disdrometer simulations, the DSD was modelled as the product of N

_{T}and the pdf (D) where N

_{T}is the total number of drops per unit volume assumed to be Poisson distributed and the pdf (D) was assumed to be the gamma pdf [93]. This form involves “double” random variables so the mean and variance of moments of the DSD, and correlation between moments, involved random sums over random number of total drop counts and random drop sizes. In [93], simulations of disdrometer-induced fluctuations in Z-R were compared with simulations of radar Z fluctuations with R (with full range of expected physical variations included). They showed quantitatively that disdrometer Z-R correlations would be much higher relative to radar-based Z-R correlations under ideal conditions [93]. A three-part series of papers followed on the error structure of radar and disdrometer measurements of rainfall using Z

_{DR}, X-band specific attenuation, and differential propagation phase [94,95,96].

_{H}and positive Z

_{DR}) were ubiquitous as were positive Z

_{DR}columns extending to −10 °C in more vigorous convective updrafts. It was David Johnson who alerted V.N.B. (via Roy Rasmussen) to look for positive Z

_{DR}in early echoes (with warm cloud bases) and their evolution based on his ultragiant aerosol hypothesis. The freezing of supercooled rain as inferred from the disappearance of the positive Z

_{DR}columns was almost always followed by a lightning discharge which was monitored in real time by Steve Goodman from NASA/Marshall to his great excitement. Dusan Zrnic happened to visit the CP2 radar during MIST and he, too, was greatly impressed by the real-time observations of positive Z

_{DR}column evolution. The time evolution of an isolated microburst-producing storm was described in [97] from early echo stage to vigorous growth stage to heavy precipitation loading by small wet hail in the dissipating stage along with cloud photos of the evolution on which contours of Z

_{H}were overlaid (true to the Fujita style of analysis and hand-drawn graphics by Roger). In a landmark article, the same storm was analyzed using triple Doppler synthesis in addition to Z

_{DR}, specific attenuation at X-band (A

_{x}), and dual-wavelength ratio (DWR) hail signatures from early echo to dissipating stage [98]. The time–height cross-sections of multiple radar observables (Z

_{H}, Z

_{DR}, A

_{x}, DWR, and updraft speeds) gave an excellent opportunity to synthesize the “bulk” microphysical evolution of the storm. The co-authors, Harold Orville and Fred Kopp of SDSM&T, used their two-dimensional time-dependent cloud model initialized with the morning sounding to compare with the radar observations [98]. By and large, the model microphysical evolution was consistent with radar observations during the vigorous growth and microburst-producing phases.

_{DR}columns extending several km above the 0 °C level and the enhanced LDR “cap” at the column top signifying mixed phase region (supercooled rain and wet ice) which can rapidly evolve into severe hailstorms were reviewed in [101]. They also showed the vertical structure of dual-wavelength and LDR signatures in a hailstorm and discuss the different scattering aspects, i.e., non-Rayleigh scattering at X-band versus depolarization due to wet, non-spherical hail.

_{H}, Z

_{DR}, A

_{x}, LDR], and in situ microphysical and electric field mill data were used to study the evolution of thunderstorm cells [102]. The mixed phase region inferred by overlapping enhanced LDR “cap” and a core of enhanced specific attenuation on top of positive Z

_{DR}columns (at about −10 °C) was validated by aircraft penetrations. Storm electrification was positively correlated with the first appearance of the mixed phase signatures aloft [103].

_{DR}columns. An enhanced LDR “cap” area on top of the positive Z

_{DR}column was interpreted as a region of large drops mixed with partially frozen and frozen hydrometeors, consistent with [101]. A positive K

_{DP}column on the western fringe of the main updraft was hypothesized to be the result of copious numbers of small drops (1–2 mm) shed by wet hailstones. Swaths of large hail at the surface (inferred from LDR signatures) and positive Z

_{DR}at 3.5 km AGL suggested that potential frozen drop embryos were favorably located for growth into large hailstones.

## 7. National Severe Storms Laboratory

_{DR}. At slow antenna scan speeds, it was possible to acquire data from tens of kilometers in range.

_{DR}) in the “fast”-switched mode accounting for correlation between all the samples in the H,V sequences (a generalization) of [62]), (2) where they related the zero-lag correlation coefficient |ρ

_{hv}(0)|to physical properties of the scatterers, and (3) computed the var (Z

_{DR}) in the mode where slant linear 45° polarization is transmitted with simultaneous reception of H and V-polarized components of the elliptically polarized backscattered electric field (suggested) in [49]. In this case, the 2 × 2 coherency matrix has 2 power terms and one complex correlation which by definition is at zero lag or ρ

_{hv}. The var (Z

_{DR}) in this mode involves the term 1 − |ρ

_{hv}|

^{2}which implies that if |ρ

_{hv}|

^{2}is sufficiently close to 1, then the var (Z

_{DR}) will reduce correspondingly. They estimated that |ρ

_{hv}|

^{2}due to raindrop shape variations (e.g., oscillations) or drop canting would be 0.99 or larger. Any decorrelation due to mixture of particle types such as rain-hail or wet snow shapes or tornado debris or even ground clutter would lower |ρ

_{hv}|

^{2}pointing to its utility as a useful radar measureable.

_{dp}) based on two estimators of which the better one was given by [53] and used in polarization agile “fast”-switched radars. The derivation for the var (Φ

_{dp}) is complicated but the end result is that it can be measured with standard deviation of a few degrees. In both [108,109] the authors drew on important works concerning pulse pair estimators of Doppler velocities [110,111,112,113] to obtain the statistics of the polarimetric variables (Z

_{DR}, Φ

_{dp}). In [109] they define ΔΦ as the range derivative of Φ

_{dp}and show that rain rate (R) derived from ΔΦ is less sensitive to DSD variations than Z–R relations. In a follow-up article, the field of ΔΦ from sector PPI scans were used to illustrate the range of values and their spatial variability [26]. Later, the specific differential phase (K

_{DP}) was defined as one-half the range derivative of Φ

_{dp}to be consistent with the radiowave propagation literature. In 1986, M.S. departed but details of algorithms used for mean Doppler velocity, differential phase, and correlation coefficient were contained in the notes of M.S. and D.Z. Soon thereafter, D.Z. assembled these notes into a Cooperative Institute for Mesoscale Meteorological Studies (CIMMS) report [114], which was widely distributed in the US and overseas with the aim of accelerating dual-polarization research. The specific algorithms for Doppler spectral width and the decoupling of mean Doppler velocity from Φ

_{dp}were given in [115]. For the record, NSSL produced reports many of which are on its Web site.

_{DP}) were approximately related to the fourth moment of the DSD from which linear relations of the form A = α K

_{DP}were formulated. In a similar manner, they also formulated a linear relation between specific differential attenuation between H and V polarized waves (A

_{DP}) and K

_{DP}. Simulations based on gamma DSDs were used to show the accuracy of these linear relations [117]. The latter article also provided experimental data from the polarimetric dual-wavelength CP2 radar by collecting time-series data in heavier rainfall from which X-band PIA was shown to be highly correlated with S-band Φ

_{dp}. After range filtering they showed that specific attenuation (Ax) was linearly related to S-band K

_{DP}which confirmed the theoretical predictions. The straightforward correction of measured reflectivity and differential reflectivity, which are strongly attenuated due to propagation in rain, invigorated the use of polarimetric X-band weather radars (and network of X-bands) in the next two decades.

_{H}, Z

_{DR}, K

_{DP}] in a hailstorm [118]. They made a keen inference that in a precipitation shaft composed of rain-hail mixtures, the hailstones due to tumbling or irregular shapes could be considered “isotropic” thus not contributing to the Re(f

_{h}–

_{v}) whereas the highly oriented oblate rain drops were the main contributors to Re(f

_{h}–fv). This follows from coherent addition of the forward scattered waves from the rain and hail. Thus, hail was “transparent” to K

_{DP}and this permitted the estimation of the rain water content in the precipitation shaft. RHI scans through the main precipitation shaft showed the height profiles of K

_{DP}as well as the separation of hail and rain amounts [118]. The descent of the hail and heavy rain to the surface (precipitation loading in the downdraft) was reflected by a lowering (or depression) of the height of the K

_{DP}column. They also described examples of interesting positive K

_{DP}above the 0 °C level, which was interpreted as possible supercooled drops lofted upwards in the updraft [118]. Substantial research in the next two decades on this topic followed, especially in tornadic supercells.

_{dp}and noting locations where there were localized deviations from the usual monotonic range profiles. Comparing the measured δ (≈5°) with a forward scattering model they were able to infer 10 mm wet aggregates at the base of the bright-band. For Rayleigh scattering the δ≈0 so the onset of non-Rayleigh scattering at S-band is about 10 mm or so for wet ice. The “dip” in the correlation coefficient was largely ascribed to non-zero values of δ as opposed to variance of shapes occurring at the base of the bright-band. The statistics of one estimator of |ρ

_{hv}(0)| was given in the Appendix of [120] in the form of plots of the standard deviation and bias versus number of (H,V)-pairs with Doppler spectrum width as a parameter. The standard deviation varied from 0.03–0.06, which was considered sufficient for detection of hail and bright-band. The statistics of |ρ

_{hv}(0)| under low signal-to-noise ratio (SNR), non-Gaussian spectra and both simultaneous and alternate sampling can be found in [121]. They found that simultaneous sampling (slant 45° transmit with simultaneous reception of H and V) gave much lower standard deviation in the range 0.003–0.006.

_{H}, Z

_{DR}, K

_{DP}, ρ

_{hv}] were not yet implemented on CIM radar or any other S-band radar in the US. Hence, a number of scientists in the US visited NSSL to collaborate with D.Z. on “slow” scanning time-series data which were unique at that time. They included V.N.B., V. Chandrasekar, and John Hubbert (from Colorado State) and K. Aydin from Penn State. One example was a hailstorm with supercell characteristics that was moving in the direction of the CIM radar. V.N.B., K.A., and the technician Mike Schmidt barely made it on time to start the radar as the leading edge of the storm approached. There was only time to set up RHI scans on the fly (i.e., “blind”) without knowing where the storm core was located. The intense hailstorm with golf ball-sized hail and intense rain rate went overhead and lightning brought the radar “down” after 30 min of data collection. Polarimetric data analysis from this hail storm, and based on the range of values of the four radar variables and scattering simulations, a schematic of three vertical cross-sections depicting hydrometeor classification for three periods were shown in [122]. The classification showed the varying height of the mixed-phase or melting level; light, medium, and intense rain rates; large hail; rain-hail mixture; graupel; oriented ice crystals and bright-band along with single Doppler-based up and down drafts. While subjective, the schematic synthesized much of the knowledge available at that time in terms of self-consistency of the radar variables, scattering calculations, and melting models. D.Z. constructed a classification Table with input from NSSL staff (Burgess and Doviak) and other scientists which was included in Chapter 8 (2

^{nd}edition) of [123].

## 8. France, Russia, Italy, and Germany

_{H}, Z

_{DR}) signatures in hail with a hail pad network is [128]. Specifically, they showed the time variation of Z

_{H}and Z

_{DR}over periods ranging from 6–30 minutes over the hail pad locations. From the hail pad data, the total number per m

^{2}and maximum size of hail were estimated for the duration of each event. They found negative Z

_{DR}values in the range −0.4 to −1 dB with Z

_{H}peaks of 60 dBZ during the very heavy hail intensity. For less intense hail events, the peak Z

_{H}was about 54 dBZ with Z

_{DR}in the range 0.6–2 dB. The correlation between maximum hail size and Z

_{H}alone was low at 0.68 but when Z

_{DR}was included the correlation improved to 0.86.

_{DR}measurements using a high0power switchable ferrite circulator and a single logarithmic receiver [129]. The transmit pulse sequence was either alternating [HVHV...] or the sequence [HHVV…]. The second sequence was used to estimate the correlation at zero lag from 1-lag estimators but from amplitude samples from the output of a logarithmic receiver. They show (Z

_{H}, Z

_{DR}] data from summertime convection near the St. Petersburg area collected in 1990 and largely confirm the prior inferences on positive Z

_{DR}columns extending, in one example, a staggering 8 km above the melting layer. They estimated severe differential attenuation at X-band at 0.3–0.4 dB/km, which is about a factor of 10 larger than predicted in [117]. Features such as positive Z

_{DR}layers aloft in winter stratiform cold rain events, the peak in Z

_{DR}at the base of the bright-band, and a “dip” in the zero lag correlation coefficient were consistent with prior results [129]. They also report on the expected values of the latter coefficient to distinguish between ground clutter and precipitation echoes.

_{DR}measurements using a high-power switchable ferrite circulator but the ferrite circulator limited the isolation to 20–25 dB or so. The radar was installed near Florence in 1990 as part of a real-time integrated Arno River flood forecasting system. The first operational dual-pol radars (network of three) appears to have been for the Emilia Romagna weather service and they are still operational (1991–present). These C-band dual-pol systems featured dual-offset Cassegrain reflector antennas for simultaneously achieving excellent side lobes and cross-pol performance with polarization agility capability using high power ferrite circulator switches.

_{dp}to derive K

_{DP}and δ

_{DR}was large in the range 3–4 dB with low Z

_{H}(10–20 dBZ) and then flew into a region of rimed dendrites and aggregates of dendrites where the Z

_{DR}was reduced (<0.5 dB) with higher Z

_{H}(30 dBZ) confirming the earlier results in [78] but with a better suite of optical array probes and cloud water measurements. The particle images were analyzed and classified manually into pristine crystals, rimed crystals, and aggregates, and quantitative frequency of occurrences of these types were calculated which confirmed the radar inferences.

_{H}and large Z

_{DR}(4–5 dB) consistent with active coalescence processes whereas in the heavier precipitation within the convective line the Z

_{H}was about 60–65 dBZ with large Z

_{DR}values of up to 7 dB. These large Z

_{DR}values occur at C-band due to resonant scattering of 6–7 mm drop sizes. The vertical profiles of [Z

_{H}, Z

_{DR}, K

_{DP,}and δ] showed values consistent with two-layer T-matrix calculations of water-coated hail, especially the measurements of large backscatter differential phase shift (δ) of 10–20°. The precipitation shaft was inferred to contain heavy rain and small melting hail with water torus (<10 mm).

## 9. Conclusions

_{H}, Z

_{DR}, K

_{DP}] in some “optimized” form. We seem to have also come full circle in QPE to using specific attenuation alone as an operational algorithm for the WSR-88D (the specific attenuation being a by-product from constrained attenuation-correction algorithms using Φ

_{dp}).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AMS | American Meteorological Society |

ARC | Alberta Research Council |

CIM | Cimarron, Oklahoma |

CIMMS | Cooperative Institute for Mesoscale Meteorological Studies |

CSU-CHILL | Colorado State University-University of Chicago and Illinois State Water Survey |

DDA | Discrete Dipole Approximation |

DFVLR | German Aerospace Research Establishment |

DWR | Dual-Wavelength Ratio |

EDR | Elliptical Depolarization Ratio |

EM | Electromagnetics |

HDR | Hail Detection |

LHC | Left Hand Circular |

MIST | Microburst and Severe Thunderstorm (Project) |

NCAR | National Center for Atmospheric Research |

NEXRAD | Next Generation Weather Radar |

NOAA | National Oceanic and Atmospheric Administration |

NSF | National Science Foundation |

NSSL | National Severe Storms Laboratory |

NWS | National Weather Service |

OMT | Orthomode Transducer |

OSU | Ohio State University |

PIA | Path Integrated Attenuation |

PPI | Plan Position Indicator |

RAL | Rutherford Appleton Laboratory |

RHC | Right Hand Circular |

RHI | Range Height Indicator |

SDSM&T | South Dakota School of Mines and Technology |

SESAME | Severe Environmental Storms and Mesoscale Experiment |

UND | University of North Dakota |

URSI | International Union of Radio Science |

WSR-88D | Weather Surveillance Radar 88 Doppler |

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**MDPI and ACS Style**

Bringi, V.; Zrnic, D. Polarization Weather Radar Development from 1970–1995: Personal Reflections. *Atmosphere* **2019**, *10*, 714.
https://doi.org/10.3390/atmos10110714

**AMA Style**

Bringi V, Zrnic D. Polarization Weather Radar Development from 1970–1995: Personal Reflections. *Atmosphere*. 2019; 10(11):714.
https://doi.org/10.3390/atmos10110714

**Chicago/Turabian Style**

Bringi, Viswanathan, and Dusan Zrnic. 2019. "Polarization Weather Radar Development from 1970–1995: Personal Reflections" *Atmosphere* 10, no. 11: 714.
https://doi.org/10.3390/atmos10110714