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This study investigates Bragg scatter signatures in dual-polarization radar observations, which are defined by low differential reflectivity values, as a proxy for convective boundary layer (CBL) depth. Using data from the WSR-88D in Twin Lakes, Oklahoma (KTLX), local minima in quasi-vertical profiles of are found to provide a reasonable estimate of CBL depth when compared with depth estimates from upper-air soundings from Norman, Oklahoma (KOUN), during 2014. The 243 Bragg scatter and upper-air sounding CBL depth estimates have a correlation of 0.90 and an RMSE of 254 m. Using Bragg scatter as a proxy for CBL depth was expanded to other seasons and locations—performing well in Wilmington, Ohio; Fairbanks, Alaska; Tucson, Arizona; Minneapolis, Minnesota; Albany, New York; Portland, Oregon; and Tampa, Florida—showing its potential usefulness in monitoring CBL depth throughout the year in a variety of geographic locations and meteorological conditions.

The mean axis ratio (length/width) and the degree of orientation of cloud ice particles are retrieved from radar differential reflectivity (ZDR) and the copolar correlation coefficient (ρhv) measured with the S-band WSR-88D radar. Hardware differential phases and amplifications in the polarimetric channels affect measured ZDR and ρhv and are taken into consideration in the retrieval procedure. The retrieval is performed for particles in shapes of hexagonal prisms, which are closer to shapes of real cloud particles than frequently used spheroids. The median retrieved axis ratio for prisms is larger than that for spheroids. The statistical 1σ retrieval errors caused by fluctuations of radar returns are about 40% in areas of signal-to-noise ratios stronger than 10 dB. The values of the degree of orientation lie in an interval from 2° to 23°, which points to significant perturbations in the orientations of ice particles most likely caused by the wind field.

Clear-air Bragg scatter (CABS) is a refractivity gradient return generated by turbulent eddies that operational Weather Surveillance Radar-1988 Doppler (WSR-88D) systems can detect. The randomly oriented nature of the eddies results in a differential reflectivity (ZDR) value near 0 dB, and thus CABS can be used as an assessment of ZDR calibration in the absence of excessive contamination from precipitation or biota. An automated algorithm to estimate ZDR bias from CABS was developed by the Radar Operations Center and can be used to assess the calibration quality of the dual-polarized WSR-88D fleet. This technique supplements existing ZDR bias assessment tools, especially the use of other external targets, such as light rain and dry snow.The estimates of ZDR bias from CABS using a 1700–1900 UTC time window were compared to estimates from the light rain and dry snow methods. Output from the automated CABS algorithm had approximately the same amount of bias reported as the light rain and dry snow estimates (within ±0.1 dB). As the 1700–1900 UTC time window appeared too restrictive, a modified version of the algorithm was tested to detect CABS diurnally on a volume-by-volume basis (continuous monitoring). Continuous monitoring resulted in a two- to fourfold increase in the number of days with CABS detections. Results suggest estimates from CABS are viable for many sites throughout the year and provide an important addition to existing bias estimation techniques.

This study analyzes radar observations of evaporation in rain and investigates its impact on surface rainfall and atmospheric cooling rates. A 1D model is used to examine the impact of raindrop evaporation on the evolution of the initial raindrop size distribution (DSD), the resulting reflectivity (Z), and differential reflectivity (ZDR) and surface rain rates. Raindrop evaporation leads to a decrease of Z and an increase of ZDR toward the surface because of the depletion of small raindrops that evaporate first and thus enhance the mean raindrop size. The latter effect, however, can be reduced because of the increasing temperature toward the surface and may even lead to a decrease of ZDR toward the surface. Two events with significant rain evaporation, observed simultaneously by a polarimetric X-band radar and a K-band Micro Rain Radar (MRR), offer quite detailed insight into the evaporation process. During the first event, which exhibits an initial ZDR > 1.5 dB in the upper rain column, raindrops undergo relatively weak evaporation as deduced from the decrease of the small raindrop fraction observed by the MRR. The second event is characterized by a lower initial ZDR < 0.5 dB with all raindrops evaporating before reaching the ground. A retrieval scheme for estimating the evaporation-related cooling rate and surface precipitation from polarimetric radar observations below the bright band is derived based on MRR observations. The algorithm is then used to simulate polarimetric X-band radar observations, which might mitigate uncertainties in the surface rainfall retrievals due to evaporation at far distances from the radars and in the case of beam blocking.

The Ministry of Land, Infrastructure and Transport (MOLIT) of South Korea operates two S-band dual-polarimetric radars, as of 2013, to manage water resources through quantitative rainfall estimations at the surface level. However, the radar measurements suffer from range ambiguity. In this study, an algorithm based on fuzzy logic is developed to identify range overlaid echoes using seven inputs: standard deviations of differential reflectivity SD(ZDR), differential propagation phase SD(ϕDP), correlation coefficient SD(ρHV) and spectrum width SD(συ), mean of ρHV and συ, and difference of ϕDP from the system offset ΔϕDP. An examination of the algorithm’s performance shows that these echoes can be well identified and that echoes strongly affected by second trip are highlighted by high probabilities, over 0.6; echoes weakly affected have probabilities from 0.4 to 0.6; and those with low probabilities, below 0.4, are assigned as echoes without range ambiguity. A quantitative analysis of a limited number of cases using the usual skill scores shows that when the probability of 0.4 is considered as a threshold for identifying the range overlaid echoes, they can be identified with a probability of detection of 90%, a false alarm rate of 6%, and a critical success index of 84%.

The effect of ship motion on shipborne polarimetric radar measurements is considered at C band. Calculations are carried out by (i) varying the “effective” mean canting angle and (ii) separately examining the elevation dependence. Scattering from a single oblate hydrometeor is considered at first. Equations are derived (i) to convert the measured differential reflectivity for nonzero mean canting angles to those for zero mean canting angle and (ii) to do the corresponding corrections for nonzero elevation angles. Scattering calculations are also performed using the T-matrix method with measured drop size distributions as input. Dependence on mean volume diameter is examined as well as variations of the four main polarimetric parameters. The results show that as long as the ship movement is limited to a roll of less than about 10°–15°, the effects are tolerable. Furthermore, the results from the scattering simulations have been used to provide equations for correction factors that can be applied to compensate for the “apparent” nonzero canting angles and nonzero elevation angles, so that drop size distribution parameters and rainfall rates can be estimated without any bias.

The conventional technique for calibrating Zdr using natural scatterers is based on vertical-looking observations. In some operational weather radar, this method is not applicable because of mechanical constraints that prohibit vertical measurement or choices in the scanning strategies. A technique for calibrating Zdr based on properties of rain returns is proposed and analyzed. The technique is based on an examination of properties of differential reflectivity measurements collected at increasing elevations. Differential reflectivity observed in rain decreases with increasing elevation due to the increasing view angle. Using the hypothesis of uniform microphysical profiles below the bright band, deviations of the profile of differential reflectivity with elevation with respect to the theoretical profile can be used to detect and quantify the presence of a bias on differential reflectivity. To apply this concept in the presence of a nonuniform microphysical profile, the contribution of vertical changes in microphysics to Zdr variation in height is also accounted for. An error parameter associated with the estimated Zdr bias can be used as a quality indicator of the bias estimation; it allows definition of a criterion based on a threshold of root-mean-square error that permits acceptance or rejection of a Zdr bias estimation obtained with the proposed method. The technique is demonstrated using data collected by an operational weather radar at Arpa Piemonte (Italy) and evaluated using independent disdrometer measurement. Results show that under certain conditions discussed in the paper, this method can provide Zdr calibration within an accuracy of 0.1 dB.

A calibration procedure of differential reflectivity on the Weather Surveillance Radar-1988 Doppler (WSR-88D) is described. It has been tested on NOAA's modified WSR-88D research and development polarimetric radar and is directly applicable to radars that simultaneously transmit and receive waves having horizontal and vertical polarization.

In this paper, the attenuation-correction methodology presented in Part I is applied to radar measurements observed by the multiparameter radar at the X-band wavelength (MP-X) of the National Research Institute for Earth Science and Disaster Prevention (NIED), and is evaluated by comparison with scattering simulations using ground-based disdrometer data. Further, effects of attenuation on the estimation of rainfall amounts and drop size distribution parameters are also investigated. The joint variability of the corrected reflectivity and differential reflectivity show good agreement with scattering simulations. In addition, specific attenuation and differential attenuation, which are derived in the correction procedure, show good agreement with scattering simulations. In addition, a composite rainfall-rate algorithm is proposed and evaluated by comparison with eight gauges. The radar-rainfall estimates from the uncorrected (or observed) ZH produce severe underestimation, even at short ranges from the radar and for stratiform rain events. On the contrary, the reflectivity-based rainfall estimates from the attenuation-corrected ZH does not show such severe underestimation and does show better agreement with rain gauge measurements. More accurate rainfall amounts can be obtained from a simple composite algorithm based on specific differential phase KDP, with the R(ZH_cor) estimates being used for low rainfall rates (KDP ≤ 0.3° km−1 or ZH_cor ≤ 35 dBZ). This improvement in accuracy of rainfall estimation based on KDP is a result of the insensitivity of the rainfall algorithm to natural variations of drop size distributions (DSDs). The ZH, ZDR, and KDP data are also used to infer the parameters (median volume diameter D0 and normalized intercept parameter Nw) of a normalized gamma DSD. The retrieval of D0 and Nw from the corrected radar data show good agreement with those from disdrometer data in terms of the respective relative frequency histograms. The results of this study demonstrate that high-quality hydrometeorological information on rain events such as rainfall amounts and DSDs can be derived from X-band polarimetric radars.

Techniques for the absolute calibration of radar reflectivity Z and differential reflectivity ZDR measured with dual-polarization weather radars are examined herein. Calibration of Z is based on the idea of self-consistency among Z, ZDR, and the specific differential phase KDP in rain. Extensive spatial and temporal averaging is used to derive the average values of ZDR and KDP for each 1 dB step in Z. Such averaging substantially reduces the standard error of the KDP estimate so the technique can be used for a wide range of rain intensities, including light rain. In this paper, the performance of different consistency relations is analyzed and a new self-consistency methodology is suggested. The proposed scheme substantially reduces the impact of variability in the drop size distribution and raindrop shape on the quality of the Z calibration. The new calibration technique was tested on a large polarimetric dataset obtained during the Joint Polarization Experiment in Oklahoma and yielded an accuracy of Z calibration within 1 dB. Absolute calibration of ZDR is performed using solar measurements at orthogonal polarizations and polarimetric properties of natural targets like light rain and dry aggregated snow that are probed at high elevation angles. Because vertical sounding is prohibited for operational Weather Surveillance Radar-1988 Doppler (WSR-88D) radars because of mechanical constraints, the existing methodology for ZDR calibration is modified for nonzenith elevation angles. It is shown that the required 0.1–0.2-dB accuracy of the ZDR calibration is potentially achievable.

Error characteristics of rainfall measurements were studied using six collocated Joss–Waldvogel (JW) disdrometers that are located at NASA’s Wallops Flight Facility. The six disdrometer means of rain rate R, reflectivity Z, and differential reflectivity ZDR, for a given minute were considered as a reference. The maximum deviations of R, Z, and ZDR from the mean in a rain event were 0.6 mm h−1, 1.3 dB, and 0.05 dB, respectively. Rainfall statistics were then examined between disdrometer pairs. The root-mean-square (rms) difference of R, Z, and ZDR between paired disdrometers in a rain event were as high as 3.2 mm h−1, 3.7 dB, and 0.3 dB, respectively. The rms difference of R and ZDR were even higher when the disdrometer observations were stratified based on reflectivity intervals. The differences in disdrometer rainfall measurements have a potential impact when the disdrometers are considered as calibration tools for vertically pointing and scanning radars. The differences between the disdrometer measurements also result in differences in coefficients and exponents of the derived relations between radar parameters and rain rate. Among the four different relations between radar parameters and rain rate, the absolute difference in rain rate |ΔR| from two different JW disdrometers was highest in R(ZH, ZDR) and lowest in R(KDP, ZDR). The other two relations were R(Z) and R(KDP). The |ΔR| increases with increasing horizontally polarized reflectivity ZH, and differential specific phase KDP in both single- and dual-parameter rainfall estimators, while the |ΔR| increases with decreasing ZDR in dual-parameter rainfall estimators. Several sources of JW disdrometer malfunctions were also presented. The hardware problems were the leading cause for the malfunction of the JW disdrometers, as identified by the manufacturer. A single JW disdrometer could have inherent measurement errors that can only be identified in the presence of collocated (preferably two) rain-measuring instruments.

While radars measure several quantities closely coupled to the rainfall rate, for frequencies less than 15 GHz, estimates of the rainwater content W are traditionally computed from the radar reflectivity factor Z or the rate of attenuation A--quantities only weakly related to W. Consequently, instantaneous point estimates of W using Z and A are often erroneous. A more natural, alternative parameter for estimating W at these frequencies is the specific polarization propagation differential phase shift phi(sub DP), which is a measure of the change in the difference between phases of vertically (V) and horizontally (H) polarized waves with increasing distance from a radar. It is now well known that W is nearly linearly related to phi(sub DP) divided by (1 - reversed R), where reversed R is the mass-weighted mean axis ratio of the raindrops. Unfortunately, such relations are not widely used in part because measurements of phi(sub DP) are scarce but also because one must determine reversed R. In this work it is shown that this parameter can be estimated using the differential reflectivity (Z(sub H)/Z(sub V) at 3 GHz. An alternative technique is suggested for higher frequencies when the differential reflectivity becomes degraded by attenuation. While theory indicates that it should be possible using phi(sub DP) to estimate W quite accurately, measurement errors increase the uncertainty to +/- 18%-35% depending on reversed R. While far from ideal, it appears that these estimates are likely to be considerably more accurate than those deduced using currently available methods.

Combined measurements of differential reflectivity and cross-correlation coefficient between linear copolar components of weather radar returns have been obtained with a noncoherent X-band polarimetric meteorological radar. In examining these data, special attention is devoted to the problem of discrimination between liquid and solid hydrometeors and to identification of the areas of strong ground-clutter contamination. Furthermore, polarization parameters of backscattered signals are used to locate updrafts.

A differential reflectivity radar technique for observing hailstorms is demonstrated using measurements obtained during the 13 June 1984 Denver hailstorm. The hail regions of the storm are identified with the differential reflectivity hail signal. Histograms of ZH and ZDR are generated for different heights in the hail regions and the relative variation of these parameters is also determined. It is observed that due to melting, the mean values of ZH and ZDR increase with decreasing height below the 0°C level (which is around 2.6 km above ground level). Furthermore, at the lower levels ZDR varies between −1 and +2 dB and ZH is generally greater than 50 dBZ. The value of ZH peaks at around 60 dBZ or more when ZDR is in the range −0.5 to 0 dB and 1.5 to 2 dB at 1.5 km and 2 km below the 0°C level, respectively. These and other features of ZH and ZDR are interpreted in terms of the size, shape and fall behavior of the hailstones using the dual wavelength ratio and the linear depolarization ratio rada...

Two radars of different characteristics were used on a clear night in early summer to investigate the nature of the clear air echoes. It is deduced that most of the echoes on this evening were due to insects rather than atmospheric turbulence or birds 1) by the magnitude of differential reflectivity; 2) by the lack of characteristic bird wing beat signature; 3) by the inability to recognize birds using a collimated spotlight; 4) by the strength of the signal return; and 5) by the migration schedules of birds in central Illinois. The CHILL radar measured differential reflectivity, and showed that, at low levels, the insects were flying with a common heading. At higher levels, the differential reflectivity showed no preferential heading of the insects, but was still greater than for atmospheric turbulence. It is proposed that differential reflectivity provides a means of differentiating between echoes due to atmospheric turbulence and insects.

Calculations have been made of the radar backscattering, differential reflectivity, and circular depolarization ratio of large oblate spheroids composed of spongy ice. Results are compatible with laboratory measurements by earlier investigators. As expected, scattering of 10-cm radiation depends to an important extent on the size, water content, and axial ratios of the spheroids. Observations of differential reflectivities close to zero in hailstorms can be explained, as was done by V. N. Bringi and his associates, as resulting from the irregular shapes and tumbling of hailstones. But such observations could also be explained by size-distributed oblate spheroids with equivalent diameters greater than about 3.5 cm, falling with vertical symmetry axes.

Backscatter amplitude ratios are defined for horizontal and vertical polarizations. These new parameters of linear polarization provide not only a coherent interpretation of the magnitude of the cross-correlation function between horizontally and vertically copolarized backscattered signals (ρL) but also give new meaning and applications for differential reflectivity (ζ). In particular, it is demonstrated that ρL and ζ can be used to determine the mean and variance of the amplitude ratios. In rain these quantities can be transformed into estimates of the mean and variance of drop axis ratios. This information can potentially improve polarization estimates of rainfall, provided ρL is measured accurately. Amplitude ratios also appear to be useful for investigating melting processes. Measurements indicate the presence of prolate-like scatterers even where ζ is greater than unity in some bright bands. It is hypothesized that this scattering from apparent prolates is, at least in part, a result of the...

The differential reflectivity (ZDR) measures the mean shape of hydrometeors and provides an estimate of the mean size of raindrops Observations of ZDR for rain may be combined with the conventional radar reflectivity factor (Z) and fitted to any two-parameter raindrop size distribution and this information used to derive more accurate rainfall rates. In such work the precise shape of raindrops is a critical parameter. Recently available data suggest that large raindrops are more oblate than previously believed. These new shapes support the idea that ZDR values above 3.5 dB can be attributed to rain. Average values of ZDR as a function of Z obtained in heavy rain by the Chilbolton radar agree very closely with those predicted using the new shapes. Statistics are also presented of the natural variability of raindrop spectra in heavy rain. Analytic expressions are proposed for computing rainfall rate from Z and ZDR.

This paper presents an analysis of the accuracy of rain rate estimates from data observed with a radar that has alternating horizontal and vertical polarization. Theoretical accuracies of rain rates from the reflectivity, the differential reflectivity and the differential propagation phase shift are considered via-a-vis the drop size distribution (DSD) variability, using a computer simulation procedure. First measurements of the differential propagation phase shift have been provided by the National Severe Storms Laboratory's dual-polarized radar, in addition to the reflectivity and the differential reflectivity. An examination of the radar data has revealed factors that could affect the rain rate estimates to a greater extent than the often contended DSD variability in the case of differential reflectivity method. Errors caused by sidelobe contamination significantly affect the differential phase shift data, so that a large spatial scale averaging is required to obtain reasonably accurate rain r...

Use of the lognormal form of raindrop size distributions in simulations of differential reflectivity (ZDR) measurements is investigated. Using two remotely measured variables and an empirical relation, the three parameters of the lognormal distribution can be deduced and the spectrum integrated to obtain rain rate. This is demonstrated by a simulation of the ZDR method using ground-based drop size distributions. Drop axis ratio and sampling time effects are also investigated and results compared to those obtained using a gamma distribution. It is shown that the lognormal representation is easily adaptable for use in the ZDR method. Using our dataset, we show that the lognormal size distribution provides lower average absolute deviations of theoretically determined rain rates from actual ones (10.7%) than those obtained using either the exponential (41.0%) or gamma distributions (11.8%).

Multiple parameter radar measurements (dual frequency hail signal DFR-HS or differential reflectivity ZDR) can be strongly affected by the mismatch of the antenna illumination functions at the two wavelengths or polarizations. The resulting instrumental error can be estimated, with some approximations, from the independently measured reflectivity at one wavelength or polarization by using the actual radar illumination functions. This objective estimation of the antenna-induced error is made in some real cases and its possible conseqences on the data analysis are discussed.

Processing of simultaneous measurements of differential polarization parameters (differential reflectivity, ZDR, and differential phase shift, ϕDP) and Doppler spectral moments is discussed. It is shown how ZDR and ϕDP modulate the Doppler signal and what effects they have on the autocovariance at lag 1 if a sequence of alternately polarized fields (linear horizontal, H, and vertical, V) is transmitted. A scheme to overcome these effects is proposed and demonstrated on recorded time series data from a radar with polarization diversity.

A perturbation method is applied to spheroidal oscillating drops to determine the effect of fundamental axisymmetric oscillations on the power spectra and polarimetric measurements. It is shown that vibration magnitudes that produce less than 10% change in equilibrium axial ratios are insufficient to produce measurable changes in the differential reflectivity or differential phase constant, yet they can lead to a detectable increase in sidebands of the power spectra. Larger oscillations do produce measurable effects on the polarimetric variables.