1. Introduction

Estimation of the mass-weighted mean drop diameter D_mass to within ±0.5-mm accuracy from the Dual-Frequency Precipitation Radar (DPR) on board National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM) Core Observatory is one of the level 1 science requirements of the GPM mission (Skofronick-Jackson et al. 2017). The GPM DPR algorithm adopted a normalized gamma raindrop size distribution (DSD) defined by D_mass, the normalized intercept parameter N_W, and the shape parameter μ (Seto et al. 2013). The shape parameter is assumed to be constant with μ = 2 for the combined radar–radiometer algorithm (Grecu et al. 2016) and μ = 3 for the DPR algorithm (Iguchi et al. 2017). The accuracy of the DPR-derived D_mass and N_W is evaluated through direct comparison of ground-based radar products following volumetric footprint matching.

The GPM ground validation team routinely processes a select subset of 70+ National Weather Service (NWS) dual-polarization radars as well as several research radars over the United States with an addition of several tropical and high-latitude oceanic sites for all GPM core satellite overpasses (Pippitt et al. 2015). This labor-intensive, quality-controlled dataset includes D_mass and N_W and is produced using the Validation Network architecture (Schwaller and Morris 2011). The D_mass and N_W are derived from dual-polarized radar measurements of horizontal reflectivity Z_H and differential reflectivity Z_DR through empirical D_mass(Z_DR) and N_W(Z_H, D_mass) relationships. In turn, the empirical relationships are based on combined analysis of two-dimensional video disdrometer (2DVD) data obtained during six different GPM field campaigns (Tokay et al. 2020).

From the perspective of ground validation traceability, it is important to evaluate the accuracy of the ground-based-radar-derived DSD. Historically, the radar-derived products are often evaluated through comparative studies with surface measurements, which are considered as a reference. For the radar rainfall estimate, there are numerous studies in the literature on quantitative analysis of radar-estimated and gauge-measured rainfall (Cifelli et al. 2011; Giangrande et al. 2014a). For radar-derived DSD, however, there are a limited number of studies where radar-estimated and disdrometer-measured DSD parameters have been compared (Brandes et al. 2004, hereinafter B04; Thurai et al. 2012, hereinafter T12). This is mainly due to the unavailability of such datasets; however, they have recently become more plentiful through NASA GPM and the U.S. Department of Energy Atmospheric Radiation Measurement Program’s (Giangrande et al. 2014b) field studies.

Both B04 and T12 were event-based studies in which a single 2DVD was 38 and 15 km from S- and C-band polarimetric radars, respectively. Both studies derived empirical relationships between radar observables of Z_H and Z_DR and constrained gamma DSD parameters of median volume diameter D₀ and N_W using simulated and disdrometer-based size distributions and prescribed drop shapes. Comparative studies are subject to measurement errors from both radars and disdrometers, as well as the time–height ambiguity and significant sampling volume differences. Measurement errors can be mitigated by calibrating radar and disdrometer while the time–height ambiguity depends on the characteristics of precipitation and the experimental setup. Both B04 and T12 selected relatively uniform stratiform events where the radar pixel was approximately 350 and 250 m above ground, respectively. B04 and T12 showed good agreement between radar-derived and disdrometer-calculated D₀ and log(N_W). A key to their success in estimating D₀ and log(N_W) was the good agreement between radar-measured and disdrometer-calculated Z_H and Z_DR.

One of the main causes of the discrepancy between disdrometer- and radar-measured or disdrometer- and radar-derived parameters is the vertical variability of precipitation. As the distance between the disdrometer and radar measurement increases, the radar pulse volumes and the vertical variability of hydrometeors increases and becomes more complicated in the presence of mixed or frozen particles at the radar pixel height. The radar measurements are also vulnerable to surface clutter. Despite the error sources listed above, there is merit in quantifying the differences between disdrometer and radar measurements at various disdrometer-radar distances, different climate regimes, and various weather systems. Comparative studies provide a realistic range of differences between the two platforms for measured and derived parameters.

This study is dedicated exclusively to the quantification of observed differences in DSD parameters between radar and disdrometer platforms. The dataset used in this study had several diverse features. The precipitation systems were originated both over the land and over the ocean. Both frontal and orographic lifting initiated the precipitation formation. Airmass thunderstorms and mesoscale convective systems provided abundant precipitation. The rest of the paper is organized as follows: Section 2 summarizes the database used in this study. Section 3 describes the mathematical form of the relationships between the DSD parameters of D_mass and N_W and dual-polarization radar observables of Z_H and Z_DR with the derivation methods using disdrometer datasets. Section 4 presents a comparative study of the disdrometer-calculated and radar-measured radar parameters of Z_H and Z_DR as well as disdrometer-calculated and radar-estimated D_mass and N_W. A dedicated section 4c describes the fraction of the radar-based Z_H and Z_DR pairs that were outside the envelope of the disdrometer observations. Conclusions are presented in section 5.

2. Database

The database was constructed from coincident NASA’s S-band polarimetic radar (NPOL) and 2DVD observations during three GPM ground validation (GV) field campaigns: the Iowa Flood Studies (IFloodS), the Integrated Precipitation and Hydrology Experiment (IPHEx), and the Olympic Mountain Experiment (OLYMPEx). Figure 1 depicts the position of the 2DVDs with respect to the NPOL during these field campaigns, and Table 1 lists the location and duration of the field campaigns as well as the number of 2DVDs and their sampling size.

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Position of the 2DVDs with respect to NPOL radar during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The 50- and 100-km rings of the NPOL radar are also shown.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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Table 1.

List of the field campaigns, their coordinates as based on the NPOL site, the duration of database, and the number of 2DVD sites and matched sample size between 2DVD and NPOL. The sample size after adopting a 0.5 ≤ D_mass ≤ 4.0 mm interval is also given in parentheses.

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Considering the NPOL database, Z_DR was calibrated by vertical profiles of natural precipitation targets (Gorgucci et al. 1999). Absolute Z_H calibration was then determined via self-consistency of the polarimetric variables (Ryzhkov et al. 2005) and the stability of the calibration was monitored using the relative calibration adjustment (Silberstein et al. 2008; Wolff et al. 2015). After labor-intensive quality control of NPOL data for ground clutter and nonmeteorological echo removal and subsequent calibration (Pippitt et al. 2015), the radar data were ready for analyses. Nine radar pixels, one directly above the 2DVDs and eight neighboring pixels, were identified and extracted for this study. It should be noted that it is not feasible to totally avoid ground clutter, especially when it is embedded with meteorological echo. In these cases, clutter cannot be completely removed because high quality control thresholds would remove too much real echo. In addition, higher radar elevation beams can intersect the bright band, especially at far distances. For this study, the comparison of radar observables of Z_H and Z_DR and derived DSD parameters of D_mass and log(N_W) are shown for NPOL gates directly above the 2DVDs. A comparative study using the neighboring eight radar pixels did not significantly alter the findings of this study.

Considering the 2DVD database, a “rain” threshold was considered as the occurrence of a minimum of 10 drops and minimum rain rate of 0.01 mm h⁻¹ in 1-min observations. For this study, the average DSD is calculated for three consecutive rainy minutes centered at the radar scan time. A study using 5-, 7-, and 9-min DSD average did not significantly alter the findings of this study. Very light rain was eliminated from the coincident dataset by setting a Z_H threshold of 5 dB to both the NPOL and 2DVD datasets. The Z_DR was also bounded by a maximum of 4 dB to be consistent with the conditions of the derived D_mass(Z_DR) relationship. The initial sample sizes that were given in Table 1 reflect the coincident database after the Z_H and Z_DR thresholds were applied. The D_mass(Z_DR) relationship has an additional bound on D_mass as being greater than 0.5 mm and less than 4.0 mm. The resultant samples after these additional thresholds on D_mass were applied to the comparison of DSD parameters and the resultant sample sizes are shown in Table 1 in parenthesis.

In the presence of abundant rainfall and six 2DVD units, IFloodS provided a richer sample of coincident datasets with respect to the other two experiments. During OLYMPEx, rain was also abundant (Zagrodnik et al. 2018) but the coincident sample size was substantially lower with the availability of only three 2DVD units. Despite the fact that five 2DVD units were available during IPHEx, sample sizes were limited as a result of the fewer rain events than during IFloodS and OLYMPEx.

Cumulative distributions of rain rate (RR), D_mass, and log(N_W) showed the diverse nature of rainfall between the three field campaigns (Fig. 2). Light rain (RR < 1 mm h⁻¹) occurred the most during IFloodS, while heavy rain (RR ≥ 10 mm h⁻¹) was most frequently observed during IPHEx (Fig. 2a). The mean RR was substantially higher during IPHEx, while median and maximum RR were distinctly lower during IFloodS and OLYMPEx, respectively (Table 2). These statistics were based on the 3-min-average 2DVD RR that coincides with the radar scan time. The datasets were diverse in terms of population of small (D < 1 mm), midsize (1 ≤ D < 3mm), and large (D ≥ 3 mm) drops. The OLYMPEx dataset consists of mostly small–midsize raindrops resulting in the highest occurrence of D_mass < 1.2 mm and log(N_W) ≥ 3.5 (Figs. 2b,c). For the purpose of this study, we considered D_mass of 1.2 mm as a characteristic size such that the DSD samples dominated by small drops have D_mass < 1.2 mm. Similarly, log(N_W) of 3.5 is the characteristic value above which represents the samples with abundant number of raindrops. Both D_mass and log(N_W) characteristic values are subjective and are determined through examining the cumulative distributions of these parameters from six different field studies (Tokay et al. 2020). IPHEx had substantially more samples at 1.2 ≤ D_mass < 2.1 mm range and IFloodS had the highest number of samples at log(N_W) < 3.5 among the three field campaigns. The lowest mean and median D_mass and the highest mean and median log(N_W) were also observed during OLYMPEx. The similarities in the distribution of rain rate and diversities in the distribution of DSD parameters between the IFloodS and OLYMPEx demonstrate the common observation that the similar rain rates can result from completely different contributions of small, medium, and large drops. This was emphasized when rainfall from convective and stratiform clouds was examined in tropical systems (Tokay and Short 1996; Thompson et al. 2015).

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Cumulative distributions of (a) rain rate, (b) mass-weighted drop diameter, and (c) logarithmic normalized intercept parameter of three different 2DVD datasets.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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Table 2.

Mean, median, and maximum of rain rate R, mass-weighted drop diameter D_mass, and logarithmic normalized intercept parameter log(N_W) for three different 2DVD datasets that were used in this study.

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3. Method

Reflectivities Z_H and Z_DR were measured by NPOL and were calculated from size and fall velocity measurements of the 2DVD. Although 2DVD was also capable of measuring drop axis ratios, this study used the laboratory-based observed axis ratios following Andsager et al. (1999) for drops up to 6 mm and equilibrium drop shapes (Beard and Chuang 1987) for drops larger than 6 mm; Z_H and Z_DR were derived for S-band wavelength (NPOL’s operational frequency) following Rayleigh–Gans theory (Tokay et al. 2002). The Z_DR is the ratio of reflectivity at horizontal polarization Z_H to reflectivity at vertical polarization Z_V. The reflectivity at horizontal and vertical polarization is expressed as a function of wavelength λ, dielectric constant of water |K_water|², and shape factors S_H,V as follows:

$Z_{H,V}={\displaystyle \frac{{\lambda }^4}{{\pi }^5{\left|K_{\text{water}}\right|}^2}}{\displaystyle {\int }_{D_{\min }}^{D_{\max }}{S}_{H,V}\left(D,r\right)D^{6}N\left(D\right)\hspace{0.17em}dD},$(3)

where the shape factors are a function of drop axis ratio r. Drop diameter D_mass is the ratio of the fourth moment to the third moment of size distribution and is expressed in millimeters. It is calculated from 2DVD size and fall velocity measurements as

$D_{\text{mass}}={\displaystyle \frac{{\displaystyle {\int }_{D_{\min }}^{D_{\max }}{D}^{4}N\left(D\right)\hspace{0.17em}dD}}{{\displaystyle {\int }_{D_{\min }}^{D_{\max }}{D}^{3}N\left(D\right)\hspace{0.17em}dD}}}.$(4)

The D_mass is also calculated from NPOL Z_DR measurements through a third-order polynominal as

$D_{\text{mass}}=a{Z}_{\text{DR}}^3+b{Z}_{\text{DR}}^2+c{Z}_{\text{DR}}+d,$(5)

where Z_DR is in decibels and the a, b, c, and d coefficients are derived from 2DVD datasets for each field campaign (Table 3). Since the 2DVD datasets in each field campaign may not have sufficient sample size at high Z_DR intervals, a generic D_mass(Z_DR) relationship was derived combining all available 2DVD datasets from six different field campaigns to determine D_mass at these ranges. The three additional 2DVD datasets that are not used in this study were collected during the Midlatitude Continental Convective Clouds Experiment in northern Oklahoma, and long-term (more than a year) field studies at the NASA Goddard Space Flight Center Wallops Flight Facility in Wallops Island, Virginia, and the NASA Marshall Space Flight Center in Huntsville, Alabama (Tokay et al. 2020).

Table 3.

The coefficients of the D_mass–Z_DR relationship and the maximum Z_DR range for the three different 2DVD datasets and the combined dataset, which includes three additional field campaigns.

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4. NPOL–2DVD comparisons

The level of agreement between NPOL-measured and 2DVD-calculated Z_H and Z_DR is related to the agreement between NPOL-derived and 2DVD-calculated D_mass and N_W. Midsize to large drops are the main contributors to the Z_H (Adirosi et al. 2015) and because of its power-weighted nature, Z_DR is very sensitive to the presence of a few large drops that have the lowest axis ratios (Tokay et al. 2020). The presence or absence of a few large drops could therefore result in noticeably different 2DVD-calculated Z_H and Z_DR values. Both parameters are therefore heavily affected by the differences in sampling volumes of NPOL and 2DVD.

The sampling volume of NWS operational radars can exceed that of the 2DVD by a factor of 10⁷ or more at a distance of 30 km (Cao et al. 2008). The disdrometer sampling volume is a multiplicative function of sampling cross section, fall velocity that corresponds to the characteristic size, and sampling interval (Campos and Zawadzki 2000). The cross section of the 2DVD is nominally 0.01 m², and the integration period was 180 s in this study. If mean or median drop size is the characteristic size, the sampling size is less than 15 m³ among the three field campaigns. If maximum drop size is the characteristic size, the sampling volume is less than 18 m³. The sampling volume of the radar depends on the beamwidth, range gate size, and the distance from radar. The beamwidth of NPOL was 0.98° in all three field campaigns, and the range gate was 150 m during IFloodS and 125 m during IPHEx and OLYMPEx. Table 4 lists the 2DVD-NPOL distances as well as NPOL elevation angles and beam heights. For IFloodS, the NPOL sampling volume is 3 378 908 m³ at its closest distance of 5 km and 1 550 794 368 m³ at its farthest distance of 106 km. The NPOL sampling volumes were within this range for the other two field campaigns. The differences in sampling volume ranged from 10⁵ to 10⁷ orders of magnitude at distances from 5 to 106 km from the radar. The beam heights were calculated on the basis of a 4/3 Earth radius model under standard atmospheric conditions. The possible pitfalls of this model were presented by Zeng et al. (2014) and are beyond the scope of this study. For the sites that are located at higher elevations than the NPOL, the distance of the beam height to the ground is less than what was reported in Table 4. During IPHEX, the farthest three sites (SN36, SN37, and SN38) were 380, 732, and 1072 m higher elevation than the NPOL.

Table 4.

NPOL elevation angle based on first (label 1st) or second (label 2nd) elevation, beam height at the 2DVD sites, and NPOL–2DVD distance during IFloodS, IPHEx, and OLYMPEx.

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The time–height ambiguity is another source of disagreement between disdrometer and radar measurements. The vertical variability of the DSD results in a nonuniform profile of Z_H and Z_DR between the altitude of the radar scan and the ground. For fast moving storms, there is a time lag between the radar scan time and disdrometer observations especially at far distances. These factors are best investigated through collocated vertically pointing radars and disdrometers (Tokay et al. 2009).

Because NPOL is a transportable facility and not situated on a tower (the antenna feed horn is ~8 m above ground level at an elevation angle of 0°), the first elevation angle is often subject to ground clutter. The second elevation is therefore selected to compare 2DVD and NPOL variables except at the farthest distances during IFloodS and OLYMPEx. It should also be added that no corrections for height-dependent drop fall-speed time lags or vertical wind shear/direction impacts on drop trajectories were applied. Based on the environmental conditions, the bright band was not a factor for this study.

a. Z_H and Z_DR

Good agreement was evident between 2DVD-calculated and NPOL-measured Z_H. During IFloodS, the NPOL bias relative to the 2DVD observations ranged from as high as −1.48 dB to +0.50 dB (Table 5). Note that the negative bias shows the underestimation of the NPOL variable while the overestimation of the NPOL variable is depicted with a positive bias. The absolute bias increased with range, spanning values from 3.28 dB at 15 km to 4.66 dB at 69 km range, but was lower at the farthest distance where the vertical distance between the NPOL pixel and 2DVD was less than the closer sites because of the use of first elevation angle (Table 4). While there was large scatter around the 1:1 line (Fig. 3a), the majority of the observations were aligned along the 1:1 line (Fig. 4a). Several outliers are visible in the figures. Among those, a couple of outliers at the SN37 site had Z_H of 2DVD that was higher than 50 dB and Z_H of NPOL that was less than 20 dB (Fig. 3a).

Table 5.

Comparison of 2DVD-calculated and NPOL-measured Z_H (dBZ) during IFloodS, IPHEx, and OLYMPEx. Considering Z_H of 2DVD as a reference, bias and absolute bias are presented at each 2DVD site for each field campaign. The sample sizes are also given.

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Scatter diagram of 2DVD-calculated and NPOL-measured Z_H during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The colors represent the specific 2DVD site during each field campaign.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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A 2D density plot of 2DVD-calculated and NPOL-measured Z_H during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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During IPHEx, the NPOL underestimated Z_H with noticeably high biases of −2.73 and −2.33 dB at the two farthest sites (SN37 and SN38) at ranges greater than 100 km and in higher terrain. The corresponding absolute biases in these two sites, 6.80 and 7.10 dB, were the highest among three field campaigns. A relatively small sample of high Z_H in the 2DVD resulted in this high bias and they were not event specific (Fig. 3b). Among those, one sample at SN37 had Z_H of 2DVD that was higher than 50 dB and Z_H of NPOL that was less than 20 dB. These samples were not visible in the frequency diagram where most of the observations lay on the 1:1 line (Fig. 4b). This demonstrates the importance of both scatter and 2D density diagrams.

During OLYMPEx, the NPOL overestimated Z_H for all three sites but the bias at the farthest site (SN38) was at least one-half of its value of the closest two sites (SN35 and SN36) (Table 5). The absolute bias increased from 3.70 to 4.39 dB between the closest two distances but was 3.96 dB at the farthest distance. The NPOL beam height was 145 m lower at the SN38 site than at the SN35 site because of the differences in elevation angles (Table 4). The SN38 site was also only 8.4 km farther from NPOL than the SN36 site. Important was that the majority of the observations were aligned with the 1:1 line (Fig. 4c) and the scatter about the 1:1 line was considerably less pronounced, with relatively fewer outliers than the other two field campaigns. Two of the outliers at the SN35 site had Z_H of 2DVD that was less than 10 dB and Z_H of NPOL that was around 35 dB (Fig. 3c).

There were considerable differences between 2DVD-calculated and NPOL-measured Z_DR. The Z_DR biases were positive, indicating an overestimation by NPOL relative to the 2DVD, at all sites during all three field campaigns, but were drastically different in magnitude between the sites (Table 6). The Z_DR bias at its closest 2DVD-NPOL distance was the highest, 0.6 dB, among all sites during IFloodS. The rest of the five sites had low Z_DR bias (<±0.1 dB). The high bias at the closest site was attributed to surface clutter, which also played a role at the closest 2DVD-NPOL distance during IPHEx. Both sites were less than 10 km of distance from NPOL in respective field campaigns. High Z_DR biases were also present at the two farthest sites, which were located at higher elevation, during IPHEx. High biases were mainly driven by the samples of NPOL Z_DR that were greater than 2 dB and 2DVD Z_DR that were less than 0.5 dB (Fig. 5). The wide scatter on both side of the 1:1 line, on the other hand, reflected the combination of low bias (<0.1 dB) and considerably higher absolute bias (0.27–0.35 dB) in Z_DR at total of eight sites in three field campaigns (Figs. 5 and 6). This highlights that the low bias itself can mislead for the evaluation of the level of agreement.

Table 6.

Comparison of 2DVD-calculated and NPOL-measured Z_DR (dB) during IFloodS, IPHEx, and OLYMPEx. Considering Z_DR of 2DVD as a reference, bias and absolute bias are presented at each 2DVD site for each field campaign.

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As in Fig. 3, but for Z_DR.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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As in Fig. 4, but for Z_DR.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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b. D_mass and N_W

NPOL-based D_mass is derived from Z_DR and the comparison of D_mass between 2DVD and NPOL had similar statistics as for Z_DR. The D_mass bias was very high—0.32 mm—at the closest NPOL–2DVD distance and was low (≤0.05 mm) for the other five sites during IFloodS (Table 7). The D_mass biases were also low at all sites except for the two farthest sites (SN37, SN38) where time–height ambiguity was significant during IPHEx. The differences in beam height played a role in determining the D_mass bias. During OLYMPEx, D_mass bias was very low at SN35 site but the absolute biases in D_mass were about the same at SN35 and SN38 sites. Although SN38 site was farthest away from NPOL, the radar beam height was the closest to the ground since the first rather than the second beam was used at SN38 site in this study (Table 4). The absolute bias in D_mass remained less than 0.4 mm at the sites where biases were equal to or less than 0.1 mm during the three field campaigns. The absolute bias in D_mass was as high as 0.62 mm at the SN37 site during IPHEx where bias was also the highest—0.34 mm—among the field campaigns. The positive bias in D_mass indicates that the mass-weighted size spectrum is shifted toward smaller sizes in 2DVD. This means that the normalized size spectrum will have more small drops and/or a lack of large drops, resulting in lower D_mass.

Table 7.

Comparison of 2DVD-calculated and NPOL-estimated D_mass (mm) during IFloodS, IPHEx, and OLYMPEx. Considering D_mass of 2DVD as a reference, bias and absolute bias are presented at each 2DVD site for each field campaign. The sample sizes are also given.

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On closer examination, the scatter and 2D density diagrams of 2DVD-calculated and NPOL-estimated D_mass revealed wide scatter from 1:1 line especially during IFloodS (Fig. 7). At the same time, a majority of the observations aligned on the 1:1 line during IFloodS, while they diverge from the 1:1 line biased toward NPOL and 2DVD D_mass during IPHEx, and OLYMPEx, respectively (Fig. 8). There were no site-specific outliers in each field campaign except a small cluster of outliers were visible at NPOL-estimated D_mass that are greater than 3 mm during OLYMPEx (Fig. 7c). The scatter diagram also showed five samples of 2DVD-calculated D_mass that were larger than 3.6 mm during IFloodS (Fig. 7a). These samples were underestimated by NPOL with no range dependency.

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Scatter diagram of 2DVD-calculated and NPOL-estimated D_mass during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The colors represent the specific 2DVD site during each field campaign.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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A 2D density plot of 2DVD-calculated and NPOL-estimated D_mass during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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N_W is a function of both Z_H and D_mass and the log(N_W) statistics followed somewhat similar trends as D_mass. Absolute biases of log(N_W) were less than 1 except the nearest 2DVD site (SN25) during IFloodS, the farthest two sites (SN37 and SN38) during IPHEx and the middle site (SN36) during OLYMPEx (Table 8). The log(N_W) bias was near 0.6 and negative at the nearest site where ground clutter was the factor during IFloodS. The negative and high biases were also present at two farthest sites during IPHEx. The biases were relatively low during OLYMPEx where the highest bias—0.27—was at the closest site (SN35). N_W is related to the peak of the number of drops per given volume per size interval and the drop counts per volume typically decreases with size. The negative bias therefore indicates fewer drops per volume in NPOL and the vice versa is true for positive bias.

Table 8.

Comparison of 2DVD-calculated and NPOL-estimated log(N_W) during IFloodS, IPHEx, and OLYMPEx. Considering log(N_W) of 2DVD as a reference, bias and absolute bias are presented at each 2DVD site for each field campaign.

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The order of magnitude of log(N_W) was substantially higher and was at the limits of the GPM GV DSD retrieval algorithm for NPOL-derived log(N_W). The vast majority of the 2DVD observations, on the other hand, were within values log(N_W) of 2–4.5 (Figs. 9 and 10). Following Eq. (7), high Z_H and low D_mass results in high log(N_W). The unlikely combination of Z_H of 45 dB and D_mass of 1.4 mm, for instance, corresponds to log(N_W) of 5. The combination of Z_H of 30 dB and D_mass of 3.1 mm, on the other hand, results in log(N_W) of 1. Although these pairs do not exist in the 2DVD database, they exist in the NPOL database since D_mass is the derived quantity. It is therefore expected that the estimation of log(N_W) is poorer than the estimation of D_mass.

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As in Fig. 7, but for log(N_W).

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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As in Fig. 8, but for log(N_W).

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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c. Outliers

The diagram of Z_H/Z_DR fields, which have been previously used for determining hail by radar (Aydin et al. 1986), precipitation segments (e.g., stratiform rain vs thunderstorm core), and precipitation type (e.g., continental vs tropical) by disdrometer (Zhang et al. 2006; Kumjian 2013), shows the major differences in radar and disdrometer observations. Cao et al. (2008) who overlaid 2DVD and dual-polarization-radar-based Z_H/Z_DR fields, marked the high Z_DR region observed by radar only. This region is attributed to the leading edge of convection with large drops and relatively low drop concentrations. As noted by Kumjian (2013), Z_DR varies with drop size and shape and a few large drops can result in very high Z_DR values (>2.5 dB). Z_H, on the other hand, is directly proportional to the particle concentration and may have moderate values (25–30 dB). Given the fact that the sample volume of the disdrometers is much smaller than the radar, the relatively infrequent big drops may not be caught by the disdrometer.

The 2DVD observations from three field sites were merged to determine the boundaries of the envelope of the Z_H/Z_DR field (Fig. 11a). The envelope was wide in both Z_H and Z_DR space. At Z_H of 40 dB, Z_DR ranged from 0.3 to 3.8 dB. Similarly, at Z_DR of 1 dB, Z_H ranged from 15 to 50 dB. The majority of the observations fell in much narrower range centering at Z_H of 20 dB and Z_DR of 0.2 dB (Fig. 11b). The NPOL Z_H/Z_DR observations outside the 2DVD Z_H/Z_DR envelope mostly occurred at moderate-to-high Z_DR and low-to-moderate Z_H regime (Regime I) (Fig. 11c). The IPHEx radar data had the highest percentage, 15%, of observations with respect to IFloodS and OLYMPEx in this regime (Table 9). The low Z_DR and high Z_H regime (Regime II), on the other hand, had 2% or less of the observations in a given field campaign. None of the two regimes corresponded to a particular segment of the storms. There was no correlation between the leading edge of the convective events and Regime I as previously reported by Cao et al. (2008).

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(a) Envelope of 2DVD-calculated Z_H and Z_DR. The 2DVD database is from the three field campaigns listed in Table 1. (b) A 2D density plot of 2DVD-calculated Z_H and Z_DR. (c) NPOL-measured Z_H and Z_DR fields outside the 2DVD Z_H and Z_DR envelope. Regimes and I and II denote high Z_DR–low Z_H fields and low Z_DR–high Z_H fields, respectively. (d) The Z_H/Z_DR matrix. The matrix consists of 60 Z_H columns and 40 Z_DR rows where Z_H ranged from 0 to 60 dB with 1-dB bin width and Z_DR ranged from 0 to 4 dB with 0.1-dB bin width. Regimes I and II are shaded in blue.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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Table 9.

Comparison of 2DVD-calculated and NPOL-measured/estimated Z_H, Z_DR, D_mass, and log(N_W) before and after removal of the Z_H–Z_DR pairs outside the 2DVD Z_H–Z_DR envelope during IFloodS, IPHEx, and OLYMPEx. The bias and absolute bias statistics are given before (italics) and after (boldface) the removal of Regime I and II clusters. The reduction in sample size and its partitioning after removal of Regime I and II are also given.

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The combined Regimes I and II consist of 15% of the observations during IPHEx, 5% and 5.5% higher than the OLYMPEx and IFloodS, respectively. The recalculated bias and absolute bias after eliminating observations in these two regimes was noticeably less for Z_DR and log(N_W) and marginally less for Z_H and D_mass (Table 9). The reduction in absolute bias was 0.35 and 0.12 dB for Z_H and Z_DR and 0.05 mm and 0.14 for D_mass, and log(N_W), respectively, during IPHEx.

The majority of the Regime-I samples occurred with Z_H of less than 30 dB, with a slight bias toward the 2DVD observations (Fig. 12a). The Regime-II samples occurred with Z_H of higher than 30 dB, with no significant bias. The observations for Regimes I and II were very distinct in Z_DR (Fig. 12b). Almost all of the Regime-I observations occurred in a narrow zone where Z_DR-2DVD was less than 0.6 dB and Z_DR-NPOL was above 0.2 dB. The Regime-II observations, on the other hand, were mainly observed at Z_DR-NPOL less than 0.4 dB and Z_DR-2DVD less than 1 dB. Regime I corresponded to the overestimation of D_mass and underestimation of log(N_W) by NPOL, and the vice versa is true for Regime II (Figs. 12c,d). Observations for both Regime I and Regime II fell into the envelope of the rest of the observations in D_mass but were at the edge of the observations in log(N_W). The reduction of dynamic range of NPOL-estimated log(N_W) resulting from the absence of Regime I was significant.

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Scatter diagram of 2DVD-calculated and NPOL-measured (a) Z_H and (b) Z_DR and 2DVD-calculated and NPOL-estimated (c) D_mass and (d) log(N_W). Regimes I and II were marked with red and blue circles, respectively.

Citation: Journal of Applied Meteorology and Climatology 59, 3; 10.1175/JAMC-D-18-0339.1

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A key question relates to the origin of Regimes I and II in NPOL observations. The 2DVD is widely used as a reference instrument for DSD measurements (Tokay et al. 2013). The underestimation of small drops has been recognized and recently investigated through field studies where 2DVD was collocated with a Meteorological Particle Spectrometer (Thurai and Bringi 2018). In this study, we tested three DSDs that had abundant small drops and maximum drop diameter of 2.9 mm or less. These DSDs had Z_DR of 0.43–0.55 dB, very similar to Regime-II Z_DR values. The corresponding Z_H ranged between 29.1 and 35.7 dB. Considering that 0.9 mm is the smallest drop size where 2DVD has the correct drop number counts, we reassigned drop concentration for the first size bins, 0.1–0.7 mm, extending the slope of the distribution such that the modified DSDs had essentially an exponential distribution. While total concentration drastically increased before and after the modified DSD, the increase in Z_H was less than 0.1 dB. This exercise showed that Regime II was not related to underestimation of small drops by 2DVD. Given the fact that the radar samples much greater volume than the disdrometer, it is feasible that the disdrometer may not sample less-frequent large drops. We artificially added a single drop at 1-, 2-, and 3-mm diameter larger than the observed D_max of the three samples mentioned above. The presence of the additional drop enhanced Z_H and Z_DR as much as 6 and 2.3 dB, respectively, but it did not cross over to Regime I or II. It was also evident that NPOL observations in Regimes I and II were present regardless of 2DVD site distance to radar throughout field campaigns. Since this study was based on NPOL measurements, we questioned whether Regimes I and II exist in operational radars. Indeed, Regime I and Regime II do exist in NWS dual-polarization radars. To differentiate these unrealistic DSDs in radar observations, a matrix of Z_H/Z_DR was created following Fig. 11c and is shown in Fig. 11d.

5. Conclusions

This study was motivated by the fact that the dual-polarization radar-based N_W and D_mass are required products for the validation of GPM DPR N_W and D_mass estimates. More specifically, the evaluation of the ground-radar-based D_mass is a requirement for the GPM GV program because it is a NASA level 1 science requirement for the GPM mission. Algorithm developers seek information on possible shortcomings of both ground- and spaceborne radar DSD estimates. A comparative study of radar-measured and disdrometer-calculated Z_H and Z_DR is the basis but is also a difficult task for evaluating radar-derived DSD parameters. Previous studies carefully selected and examined the agreement between disdrometer/radar Z_H and Z_DR pairs at optimum radar-disdrometer distance (15–40 km at S-band) (B04; T12), which is shorter for higher-frequency radars. This study included one or two optimum sites in each field campaign, but the ground clutter was a factor at the lowest elevation angle due to the site of NPOL antenna at the top of the container rather than on a tower. Using the second-lowest elevation, the NPOL beam height was 369 m above the ground at a distance of 15.2 km. This is comparable to the previous studies as being the best-case scenario. For most of the field studies including radar-estimated and gauge-measured rainfall comparative studies (Giangrande and Ryzhkov 2008; Cunha et al. 2013), the logistics did not allow deployment of the in situ devices near the radar site. Having the 2DVDs at various ranges from the NPOL radar (Fig. 1) enabled this study to quantify the level of agreement with distance.

As the best-case scenario, the absolute biases of Z_H and Z_DR were relatively low, ranging from 3.3 to 3.7 and from 0.27 to 0.32 dB, respectively at the shortest distance (15–20 km from the radar) in the absence of surface clutter for the three field campaigns. The corresponding absolute biases of D_mass and log(N_W) were 0.31–0.36 mm and 0.34–0.98, respectively. The absolute bias in Z_H increased with distance but was relatively low at the farthest distance during IFloodS and OLYMPEx where the first elevation rather than the second elevation was used for the comparative study. Specifically, the absolute biases of Z_H were about the same at 47.4 and 106.1 km distances from radar but the difference in the NPOL beam height was only 129 m because of the choice of first versus second elevation angles during IFloodS. This highlights the importance of time–height ambiguity.

During IPHEx, the absolute biases of Z_H were higher at a given distance than during the other two field campaigns. This could be result of higher occurrence of heavy rain where size sorting is significant. Two of the 2DVDs (SN37 and SN38) were deployed in mountainous terrain to determine the role of orography in DSD characteristics. These two 2DVDs were over 100 km from NPOL with radar beam height 3.2 and 2.5 km above the ground after accounting the height difference between NPOL and the two sites. Considering the greater time–height ambiguity and greater difference in sampling volumes between 2DVD and NPOL observations, the agreement in Z_H was poor at these two sites and they do not serve as a validation site for evaluating dual-polarization radar DSD retrieval algorithm.

A closer look at the NPOL-measured and 2DVD-calculated Z_H and Z_DR fields revealed two regimes. These regimes coincided with either under or overestimated NPOL-derived log(N_W). The combined Regimes I and II covered a considerable amount of the total observation, 9%–15%, of the coincident NPOL/2DVD database. When these regimes were removed from the database, the absolute biases were noticeably reduced for Z_H, Z_DR, D_mass, and log(N_W).

The 2DVD, a reference instrument, underestimates the concentration of small drops (Thurai and Bringi 2018) but the addition of small drops does not correspond to either Regime I or Regime II. The implication of these nonrealistic DSD in NPOL observations could be significant for radar rainfall estimation. Hydrologists rely on radar rainfall estimates for flood forecasting and the majority of the comparative studies use rain gauges as a reference (Cunha et al. 2013). The accuracy of Z_H/Z_DR couples should therefore independently be evaluated prior to radar rainfall estimation. The envelope of Z_H/Z_DR presented here could be used a reference in these studies.

Reflectivities Z_H and Z_DR are vital radar measurements for radar rainfall mapping. The study presented here showed the presence of surface clutter at radar distances of less than 15 km even after labor-intensive radar quality control. The quality control had to be relaxed; otherwise true precipitation would be removed along with the clutter. The best agreement between point 2DVD and areal NPOL Z_H and Z_DR was mostly at the second elevation of the radar except for the farthest sites during IFloodS and OLYMPEx. These factors play an important role in radar rainfall and DSD parameter mapping, both of which are used to direct comparison with the GPM satellite estimates.

There are parallel efforts in comparing ground-based and DPR-based rainfall (Petracca et al. 2018) and DSD parameters over Italy and the United States (D’Adderio et al. 2018; Petersen et al. 2020). One significant aspect of the comparison process is the careful DPR to ground-based geometric volume matching that has been implemented in the Validation Network software. The similar measurement type (radar) and closer spatial and temporal scales matched (Schwaller and Morris 2011) combined with an intrinsically large number of coincident samples should help to firmly establish (in a statistical sense) the degree to which the space-based estimates of the DSD converge with ground-based estimates toward demonstrating attainment of GPM level 1 science requirements that pertain to the DSD.