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  • View in gallery

    Probability distributions of (a) rain rate, (b) mass-weighted drop diameter, and (c) logarithmic normalized intercept parameter of six different 2DVD datasets. The UAH and WFF sites are referred to as MSFC-UAH and GSFC-WFF in the text, respectively. The vertical dashed line represents the characteristic value of (a) rain rate (1 mm h−1) that separates light rain from moderate rain, (b) drop diameter (1.2 mm) that separates the samples of small vs medium/large drops dominance, and (c) drop count [3.5 log(NW)] that separates the samples when large number of drops were present or absent.

  • View in gallery

    Cumulative distributions of (a) rain rate, (b) mass-weighted drop diameter, and (c) logarithmic normalized intercept parameter of three different P2 datasets. The vertical dashed lines are as in Fig. 1.

  • View in gallery

    (a) The Dmass(ZDR) relationships for six different 2DVD datasets and the combined ALL dataset, (b) the difference in Dmass between site-specific and ALL Dmass(ZDR) relationship (c) NW(Dmass, ZH) relationships for six different 2DVD and ALL datasets at ZH of 30 dBZ. The UAH and WFF sites are referred to as MSFC-UAH and GSFC-WFF in the text, respectively.

  • View in gallery

    A flowchart of the GPM ground validation DSD retrieval algorithm. * For Dmass, the field campaign specific Dmass(ZDR) relationship is used until maximum ZDR listed in Table 3.

  • View in gallery

    ALL database NW(Dmass, ZH) relationship at six different ZH ranging from 10 to 60 dBZ (solid lines). The 2DVD observations during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx (colored circles indicate ZH).

  • View in gallery

    A 2D density plot of measured and estimated Dmass based on 2DVD database during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The 2DVD-calculated ZDR is used to estimate Dmass following Eq. (5) and Table 3.

  • View in gallery

    A 2D density plot of measured and estimated log(NW) based on 2DVD database during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The 2DVD-calculated Dmass and ZDR are used to estimate log(NW) following Eq. (6).

  • View in gallery

    Mean Dmass for a given ZDR interval (circles) and SIFT-based fits (lines) for (a) P2-based IFloodS and KWAJ and (b) OLYMPEx and KWAJ datasets. (c) The difference in Dmass as a function of ZDR based on KWAJ and IFloodS and on KWAJ and OLYMPEx Dmass(ZDR) relationships.

  • View in gallery

    Mean Dmass for a given ZDR interval (circles) and SIFT-based fits (lines) for 2DVD and P2 datasets during (a) IFloodS, and (b) OLYMPEx. (c) The difference in Dmass as a function of ZDR based on 2DVD- and P2-based Dmass(ZDR) relationships during IFloodS and during OLYMPEx.

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Development and Evaluation of the Raindrop Size Distribution Parameters for the NASA Global Precipitation Measurement Mission Ground Validation Program

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  • 1 Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, and NASA Goddard Space Flight Center, Greenbelt, Maryland
  • 2 Department of Physics and Earth Science, University of Ferrara, and Institute of Atmospheric Sciences and Climate, National Research Council, Rome, Italy
  • 3 Wallops Flight Facility, NASA Goddard Space Flight Center, Wallops Island, Virginia
  • 4 NASA Marshall Space Flight Center, Huntsville, Alabama
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Abstract

The National Aeronautics and Space Administration Global Precipitation Measurement (GPM) mission ground validation program uses dual-polarization radar moments to estimate raindrop size distribution (DSD) parameters, the mass-weighted mean drop diameter Dmass, and normalized intercept parameter NW, to validate the GPM Core Observatory–derived DSD parameters. The disdrometer-based Dmass and NW are derived through empirical relationships between Dmass and differential reflectivity ZDR, and between NW, reflectivity ZH, and Dmass. This study employs large datasets collected from two-dimensional video disdrometers (2DVD) during six different field studies to derive the requisite empirical relationships. The uncertainty of the derived Dmass(ZDR) relationship is evaluated through comparisons of 2DVD-calculated and ZDR-estimated Dmass, where ZDR is calculated directly from 2DVD observations. Similarly, the uncertainty of the NW(ZH, Dmass) relationship is evaluated through 2DVD-calculated and Dmass and ZH-estimated NW, where Dmass and ZH are directly calculated from 2DVD observations. This study also presents the sensitivity of Dmass(ZDR) relationships to climate regime and to disdrometer type after developing three additional Dmass(ZDR) relationships from second-generation Particle Size Velocity (PARSIVEL2) disdrometer (P2) observations collected in the Pacific Northwest, in Iowa, and at Kwajalein Atoll in the tropical Pacific Ocean. The application of P2-derived Dmass(ZDR) relationship based on precipitation in the northwestern United States to P2 observations collected over the tropical ocean resulted in the highest error among comparisons of the three datasets.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Global Precipitation Measurement (GPM) special collection.

Corresponding author: Ali Tokay, tokay@umbc.edu

Abstract

The National Aeronautics and Space Administration Global Precipitation Measurement (GPM) mission ground validation program uses dual-polarization radar moments to estimate raindrop size distribution (DSD) parameters, the mass-weighted mean drop diameter Dmass, and normalized intercept parameter NW, to validate the GPM Core Observatory–derived DSD parameters. The disdrometer-based Dmass and NW are derived through empirical relationships between Dmass and differential reflectivity ZDR, and between NW, reflectivity ZH, and Dmass. This study employs large datasets collected from two-dimensional video disdrometers (2DVD) during six different field studies to derive the requisite empirical relationships. The uncertainty of the derived Dmass(ZDR) relationship is evaluated through comparisons of 2DVD-calculated and ZDR-estimated Dmass, where ZDR is calculated directly from 2DVD observations. Similarly, the uncertainty of the NW(ZH, Dmass) relationship is evaluated through 2DVD-calculated and Dmass and ZH-estimated NW, where Dmass and ZH are directly calculated from 2DVD observations. This study also presents the sensitivity of Dmass(ZDR) relationships to climate regime and to disdrometer type after developing three additional Dmass(ZDR) relationships from second-generation Particle Size Velocity (PARSIVEL2) disdrometer (P2) observations collected in the Pacific Northwest, in Iowa, and at Kwajalein Atoll in the tropical Pacific Ocean. The application of P2-derived Dmass(ZDR) relationship based on precipitation in the northwestern United States to P2 observations collected over the tropical ocean resulted in the highest error among comparisons of the three datasets.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Global Precipitation Measurement (GPM) special collection.

Corresponding author: Ali Tokay, tokay@umbc.edu

1. Introduction

One of four level-1 science requirements specified by the National Aeronautics and Space Administration (NASA) for rain products collected by the NASA–Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM) mission core satellite states that measurements from the Core Observatory shall estimate the mass-weighted mean drop diameter Dmass of precipitation particle size distributions to within ±0.5 mm (Skofronick-Jackson et al. 2017). Mass-weighted drop diameter is one of three parameters in the normalized gamma raindrop size distribution (DSD). This version of the gamma DSD has been adopted in the GPM Dual-Frequency Precipitation Radar (DPR) algorithm (Seto et al. 2013). The normalized intercept parameter NW and the shape parameter μ are the other two parameters, the latter of which is assumed constant at μ = 2 for the combined radar–radiometer algorithm (Grecu et al. 2016), and at μ = 3 for the DPR algorithm (Iguchi et al. 2017).

The parameters of the gamma DSD are often obtained from dual-polarization radar measurements following empirical relationships (Adirosi et al. 2014). The empirical relationships are derived from disdrometer measurements or simulated DSDs and have a wide range of variability due to the differences in the source of the dataset, the various physical assumptions related to the DSD, the mathematical form of the relationship as well as the natural variability of precipitation. A majority of the previous work has relied on the median volume diameter D0 rather than Dmass as a parameter of gamma DSD. For example, Bringi et al. (2004) derived D0 and NW from horizontally polarized reflectivity ZH and differential reflectivity ZDR utilizing simulated size distributions with combinations of observed and equilibrium axis ratios of raindrops (Andsager et al. 1999; Beard and Chuang 1987) for S-band radar. The coefficients and mathematical form of the relationships were different for different ZDR intervals. Brandes et al. (2004) derived a third-order polynomial D0(ZDR) relationship, which was applicable for ZDR between 0.3 and 3 dB. They used a two-dimensional video disdrometer (2DVD) database from NASA’s Tropical Rainfall Measurement Mission field campaign in east-central Florida with a polynomial form of axis ratio–drop size relationship (Brandes et al. 2002). Cao et al. (2008) conducted a follow-up study using a different 2DVD database resulting in different coefficients for D0(ZDR) relationship.

Thurai et al. (2012) presented a case-based study where a fourth-order polynomial for D0(ZDR) relationship was derived using 2DVD observations from a widespread stratiform event in Huntsville, Alabama. Unlike the aforementioned studies, their D0(ZDR) relationship was derived for C-band radar and D0 was expressed as a function of ZH and ZDR for D0 less than 1 mm. Thurai et al. included a derivation of NW from ZH and D0 and found a reasonable agreement between the radar-derived and disdrometer-calculated values of D0 and NW.

The NASA GPM ground validation team routinely processes select National Weather Service (NWS) dual-polarization radars as well as several research radars over the United States and elsewhere for each GPM core satellite overpass (Pippitt et al. 2015). The labor-intensive quality control of the radar data aims to create a high-quality dataset, known as the GPM Validation Network (VN; Schwaller and Morris 2011). There are currently 78 radar sites in the VN: 62 continental U.S., 9 Brazilian, 2 Alaskan, and 5 tropical sites, which provide samples of widely varying precipitation regimes. The GPM Ground Validation (GV) program compares VN-derived Dmass and NW with the corresponding estimates of these quantities obtained from the GPM DPR. This is done by approximately matching in space and time the scattering volumes of the spaceborne and ground-based radars.

From a ground validation point of view, disdrometer measurements represent point measurements providing distributions of gamma DSD parameters including their expected ranges, means, and standard deviations in different precipitation regimes (e.g., tropics vs midlatitudes, oceanic vs continental, topographically uniform vs orographically complex). A direct comparison of the estimates of DSD parameters between the DPR and ground-based dual-polarimetric radars relies on the upscaling of radar measurements to DPR footprint scales and the use of empirical relationships designed to estimate Dmass and NW as modeled functions of radar-observed ZDR and ZH (D’Adderio et al. 2018).

This paper focuses exclusively on the methodology and testing employed to develop 2DVD-based parametric relationships for Dmass and NW based on ZDR and ZH. These relationships are currently used in the radar-based VN software architecture. The resulting radar-based estimates of Dmass and NW can eventually be compared to the estimates of these parameters made by DPR, though this is not attempted in the current study. A separate study describes the satellite to VN radar network matching statistics (Petersen et al. 2020). This study also employs Particle Size Velocity (PARSIVEL) disdrometer (P2) measurements to evaluate the utility of the empirical Dmass(ZDR) relationship for several climate regimes. This study is organized as follows: Section 2 summarizes the database used in this study including probability distributions of rain rate, Dmass, and log(NW) derived from the 2DVD (Schönhuber et al. 2008) and P2 (Löffler-Mang and Joss 2002). Section 3 describes the mathematical form of the relationships between the DSD parameters of Dmass and NW and dual-polarization radar observables of ZH and ZDR. The accuracy of these relationships is evaluated through comparison of the DSD parameters estimated by 2DVDs from three field campaigns in section 4. Section 5 is reserved for two sensitivity studies. First, the sensitivity of the derived Dmass(ZDR) relationship is tested among three sites consisting of a tropical site and two midlatitude sites. Second, the sensitivity of the Dmass(ZDR) relationship to the disdrometer type is presented by comparing collocated 2DVD and P2 observations from two different field campaigns. Conclusions are presented in section 6.

2. Database

The 2DVD was the primary instrument used in this study to derive the relationships between the radar observables and gamma DSD parameters. The datasets included four GPM field campaigns: the Midlatitude Continental Convective Clouds experiment (MC3E) (Jensen et al. 2016); the Iowa Flood Studies (IFloodS) (Seo et al. 2018); the Integrated Precipitation and Hydrology Experiment (IPHEx) (Duan et al. 2015); the Olympic Mountain Experiment (OLYMPEx) (Houze et al. 2017); and extended (longer than 1 year) data collections made at two NASA facilities: Marshall Space Flight Center, University of Alabama at Huntsville (MSFC-UAH), and NASA Goddard Space Flight Center Wallops Flight Facility (GSFC-WFF). These datasets represent a range of midlatitude meteorological regimes including midcontinental deep convection (MC3E), flood-producing frontal and mesoscale convective systems (IFloodS), warm-season Appalachian area orographic enhancements from valley to mountain (IPHEx), West Coast cold-season orographic enhancements from ocean to mountain (OLYMPEx), as well as a year-long sampling of midlatitude continental inland (MSFC-UAH) and coastal mid-Atlantic region precipitation (GSFC-WFF).

The raw 2DVD output is in the form of an ASCII daily file where each row contains information on individual particles including their equivalent diameter, fall velocity, oblateness, the sampling cross section, maximum height and width, and position of the particle in both planes, as well as a time stamp in milliseconds. The standard data processing of 2DVD observations includes construction of 1-min drop counts and DSD outputs at a 0.2-mm-diameter interval after applying a terminal fall velocity-based threshold to eliminate splash drops (Tokay et al. 2013). In this study, several additional thresholds were applied to the 2DVD datasets. The thresholds for processing any given 1-min period were set at the minimum occurrence of 100 drops and a minimum rain rate of 0.1 mm h−1 in each 1-min observation. This eliminates 16%–34% of the data depending on the field campaigns. To eliminate outliers, the calculated Dmass and S-band ZDR were limited to maximum values of 4 mm and 4 dB, respectively. These two thresholds in Dmass and ZDR eliminated less than 1% of the data regardless of field campaign. Considering the level-1 requirements for Dmass to be estimated within ±0.5-mm accuracy, the uncertainty in 2DVD measurement capability at drop sizes below ~0.5–0.7 mm (Tokay et al. 2013), and the intrinsic uncertainty associated with using polarimetric radar to retrieve very small drop sizes, the estimation of Dmass was further limited to minimum value of 0.5 mm. In that regard, Bringi et al. (2012) recognized that the statistical fluctuations in radar measurements resulted in negative values of ZDR and D0 was 0.45 mm at ZDR of −0.25 dB for D0(ZDR) relationship presented in their study. Each dataset consists of three to seven 2DVDs and the combined 2DVD dataset provided over 204 300 one-minute samples (Table 1). The sample size is determined by the duration of data collection, number of instruments, and frequency of rain. Field campaigns typically last 2 months and multiple sites are required to collect a large enough sample to represent the seasonal climate of the region. The use of five and seven 2DVDs in each field campaign led to the collection of over 9400 and 8300 samples despite dry periods of a week or longer during both IPHEx, and MC3E, respectively. Abundant rainfall, on the other hand, led to the collection of over 60 100 samples using only three 2DVDs during OLYMPEx. Data collection over a year at five separate 2DVD sites led to the most extensive database with over 74 400 samples being collected by the GSFC-WFF network.

Table 1.

List of the field campaigns, their coordinates, duration of database, and number and sample size of the 2DVD and P2. The number of P2 available during field campaigns could exceed the number of units used in this study. For the comparative study between 2DVD and P2, a subset of P2 is used as shown in parentheses.

Table 1.

The P2 data collected at Kwajalein (KWAJ) atoll served as a tropical-oceanic dataset. A multiyear dataset from this site was used for a comparative study with IFloodS and OLYMPEx. All P2 data were collected at 10-s resolution and integrated to 1 min. Standard processing of the P2 data includes the same terminal fall velocity threshold as used for 2DVD to eliminate the secondary drops and the use of modeled fall velocity versus drop diameter relationship, as opposed to the measured fall velocities (Tokay et al. 2013). The total number of 1-min samples from these three sites are listed in Table 1. Coincident database when both a 2DVD and P2 were operational and reported rainfall were used to determine the sensitivity of the empirical relationships to disdrometer type for the IFloodS and OLYMPEx data discussed in section 5. Table 1 also lists the number of 2DVD and P2 instruments and the sample size for each field campaign. It should be noted that we used a subset of available P2 data from IFloodS and OLYMPEx as shown in parentheses in Table 1.

The collective DSD datasets used in this study contain a diverse population of small (less than 1 mm in diameter), midsize (1–3 mm in diameter) and large (larger than 3 mm in diameter) drops (Tokay et al. 2013). The rich OLYMPEx dataset consists of mostly small to midsize raindrops resulting in relatively low mean and maximum rain rates (Table 2). The distribution of rain intensity shows more frequent sampling of light rain (less than 1 mm h−1) and the least frequent of heavy rain (higher than 10 mm h−1) as previously observed in the literature (Tokay et al. 2002, 2013). Cumulative distributions of rain occurrence measured by the 2DVD indicate that heavy rain occurred less than 5% of the time at all six sites, while the ratio of the occurrence of light to moderate rain (1–10 mm h−1) varied from site to site (Fig. 1a). The ratio compares the occurrence of light versus moderate rain such that the higher the ratio is the most frequent light rain occurs. The ratio was the highest at GSFC-WFF and the lowest at MC3E. The median rain rates were also the lowest and the highest at GSFC-WFF and MC3E, respectively (Table 2).

Table 2.

Mean, median, and maximum of rain rate R, mass-weighted drop diameter Dmass, and logarithmic normalized intercept parameter log(NW) for six different 2DVD and three different P2 datasets that were used in this study.

Table 2.
Fig. 1.
Fig. 1.

Probability distributions of (a) rain rate, (b) mass-weighted drop diameter, and (c) logarithmic normalized intercept parameter of six different 2DVD datasets. The UAH and WFF sites are referred to as MSFC-UAH and GSFC-WFF in the text, respectively. The vertical dashed line represents the characteristic value of (a) rain rate (1 mm h−1) that separates light rain from moderate rain, (b) drop diameter (1.2 mm) that separates the samples of small vs medium/large drops dominance, and (c) drop count [3.5 log(NW)] that separates the samples when large number of drops were present or absent.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

The mass-weighted mean drop diameter is often used as a defining characteristic of the DSD. For example, the presence of a large number of small drops and a relative lack of large drops will result in a lower Dmass for a given reflectivity (Tokay et al. 2008). Considering the DSD database examined in this study, we selected Dmass of 1.2 mm (Fig. 1b) as a threshold to illustrate DSDs characterized by small versus large drops. The corresponding median values of the Dmass observed in each field data collection then reflected the dominance of small drops measured in the OLYMPEx and GSFC-WFF datasets, and the presence of more numerous large drops in the MC3E dataset (reflected in the ensemble statistics shown in Table 2).

The normalized intercept parameter is a function of the number of drops and its value ranges over three orders of magnitude. Because of this large variation, it is common to use the logarithmic value of NW, log(NW). For a given DSD, the number of small drops typically exceeds the number of middle and large drops by an order of magnitude or larger (e.g., Tokay et al. 2016, 2017). The differences in cumulative distribution of log(NW) between the sites therefore reflect the presence or absence of an abundant number of small drops. Selecting log(NW) of 3.5 as a threshold, MC3E and OLYMPEx received the least and the most contribution from small drops, respectively (Fig. 1c). While GSFC-WFF and OLYMPEx had nearly identical cumulative distributions of Dmass, they were drastically different for the cumulative distributions of log(NW). The presence of an abundant supply of small drops due to orographic enhancement played a key role on high log(NW) during OLYMPEx (Zagrodnik et al. 2018). The median value of log(NW) was therefore the highest during OLYMPEx compared to the other five field campaigns (Table 2).

Precipitation in the tropics forms primarily over the oceans and is characterized by the presence of a large number of small drops (Thompson et al. 2015). Thompson et al. presented the statistics of D0 and log(NW) derived from 2DVD observations from Gan and Manus Islands located in the Indian and western Pacific Oceans, respectively. Their D0 and log(NW) statistics were in a good agreement with KWAJ P2 statistics despite the differences in disdrometer type. The median values of Dmass and log(NW) that were observed by the KWAJ P2 were low and high, respectively, relative to the values observed during IFloodS (Table 2).

The cumulative distributions of P2-based rain rates showed that about 35% of the observations fell into the light rain category at all P2 sites but heavy rain contributed nearly 8% to the observation at KWAJ (Fig. 2a). The ratio of light to moderate rain was therefore relatively higher in KWAJ than at the two midlatitude sites OLYMPEx, and IFloodS. An interesting feature was that the OLYMPEx median Dmass was lower and median log(NW) was higher than the values at KWAJ. The storms at both sites originated primarily over ocean but orographic enhancement resulted in a substantially higher number of small drops during OLYMPEx (Figs. 2b,c).

Fig. 2.
Fig. 2.

Cumulative distributions of (a) rain rate, (b) mass-weighted drop diameter, and (c) logarithmic normalized intercept parameter of three different P2 datasets. The vertical dashed lines are as in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

3. Methodology

As stated earlier, the GPM DPR algorithm adopted the normalized gamma distribution (Seto et al. 2013) as follows:
N(D)=NWf(μ)(DDmass)μexp[(4+μ)DDmass],
where D is the equivalent volume diameter in mm and f(μ) is given as a function of the shape parameter μ:
f(μ)=6256(4+μ)4+μΓ(4+μ),
where Γ refers to the complete gamma function. The shape parameter (unitless), Dmass (mm) and NW (mm−1 m−3) are the three parameters of the normalized gamma distribution. The mass-weighted mean drop diameter is the ratio of the fourth moment to the third moment of the size distribution, while the normalized intercept parameter is related to the liquid water content W (g m−3) and Dmass and is given as
NW=44103WπρWDmass4,
where ρw is the density of water (g cm−3). Both Eqs. (1) and (3) are based on the complete gamma function where the minimum and maximum drop sizes are assumed zero and infinity, respectively. In reality, the minimum and maximum diameter are determined by what is observed during the sampling period. The incomplete gamma function accounts for the observed minimum and maximum drop size and is therefore more realistic than the complete gamma function. The complete gamma function is subject to errors in calculating rain parameters especially when the maximum drop diameter is less than 3 mm in diameter (Adirosi et al. 2015).
In this study, both DSD parameters (Dmass and NW) and radar observables (ZH and ZDR) are directly calculated from disdrometer measurements. Differential reflectivity is the ratio of reflectivity at horizontal polarization ZH to reflectivity at vertical polarization ZV. The horizontally and vertically polarized radar reflectivities, ZH,V, in the Rayleigh regime are expressed as a function of the shape factors, SH,V, and multiplicative factors equal to the sixth moment of the drop diameter and the number concentration N(D):
ZH,V=DminDmaxSH,V(r,m)D6N(D)dD.
The shape factors are functions of the refractive index of water m and the axis ratio r of the raindrops and both refractive index and axis ratio are unitless. This study used the measured axis ratios of Andsager et al. (1999) for drops up to 6 mm and equilibrium drop shapes (Beard and Chuang 1987) for drops larger than 6 mm. ZH,V and ZDR are derived for S-band wavelength following Rayleigh–Gans theory (Seliga and Bringi 1976). In Eq. (4), ZH,V is expressed in linear units of mm6 m−3 but it is also used in logarithmic units of decibels dBZ; ZDR, on the other hand, is always expressed in logarithmic units (dB) and is given by
ZDR=10log10(ZHZV),
where ZH,V are in linear units. A third-order polynomial with sequential intensity filtering technique (SIFT; Lee and Zawadski 2005) was employed to derive the Dmass(ZDR) relationship as follows:
Dmass=aZDR3+bZDR2+cZDR+d,
where ZDR units are dB and where the coefficients a, b, c, and d, are listed in Table 3 for each of the six different datasets and the combined dataset. Polynomials represent the observations better than power-law relationships when the observations have a large scatter of the retrieved parameter (Dmass in this case) for a given observed parameter (ZDR in this case). The uncertainty in the relationship has been evaluated by calculating bias and absolute bias between the fitted and observed data. A comparative study of fourth- and third-order polynomial Dmass(ZDR) relationships showed that there is insignificant improvement for the higher-order polynomial over the range of ZDR and Dmass values considered.
Table 3.

The coefficients of the Dmass(ZDR) relationship and their valid maximum ZDR range for the six different 2DVD datasets and the combined dataset.

Table 3.

The linear least squares method is weighted to the regions where the highest percentage of data occur. For rainfall, the highest number of cases occur in light rain (rain rate < 1 mm h−1), which mostly corresponds to Dmass ≤ 1.0 mm and ZDR ≤ 0.5 dB. Higher biases due to reduced sample numbers are expected for the population of heavy rain (>10 mm h−1) samples, which corresponds to high ZDR and Dmass values. A nonlinear least squares fit, on the other hand, is weighted toward the less frequently sampled heavy rain and causes high biases for the low rain rates samples (Tokay et al. 2001). The SIFT method is used to mitigate these sensitivities to both light and heavy rain. In SIFT, the mean values of the retrieved variable are first calculated for a prescribed interval of the observed variable. This study used an interval of 0.1 dB for ZDR and the mean values of Dmass were calculated for ZDR between 0 and 4 dB as long as at least 10 samples were present in a given interval. The linear least squares method was then applied to the Dmass(ZDR) pairs. The mean value of the highest ZDR bin that had sufficient samples to be included in linear squares fit is shown in Table 3. The number of samples that were not included in determining Dmass(ZDR) relationships was less than 1% in all field campaigns.

No significant differences were observed between the Dmass(ZDR) relationships in the six different datasets except that Dmass(ZDR) from OLYMPEx had significantly lower Dmass for ZDR greater than 1.5 dB (Fig. 3a). The differences in DmassDmass) observed by combining ALL campaign specific datasets into a single Dmass(ZDR) relationship were therefore most significant for OLYMPEx (Fig. 3b). Here, the presence of an abundant number of small and midsize drops caused by orographic enhancement was the driving force for the differences in the Dmass(ZDR) relationships. The OLYMPEx data also had the lowest ZDR maximum for SIFT due to the absence of large drops.

Fig. 3.
Fig. 3.

(a) The Dmass(ZDR) relationships for six different 2DVD datasets and the combined ALL dataset, (b) the difference in Dmass between site-specific and ALL Dmass(ZDR) relationship (c) NW(Dmass, ZH) relationships for six different 2DVD and ALL datasets at ZH of 30 dBZ. The UAH and WFF sites are referred to as MSFC-UAH and GSFC-WFF in the text, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

Figure 4 presents the flowchart for the GPM-GV DSD retrieval algorithm, which was developed for mapping Dmass and log(NW) over the VN. The ground-based radar ZH and ZDR observations are the input and minimum and maximum values of ZDR, Dmass, and log(NW) are set to determine whether or not Dmass and NW are to be set to missing. The VN processing is primarily applied to the selected NWS operational radar network and therefore employs the ALL Dmass(ZDR) relationship listed in Table 3. For observations in individual field campaigns, on the other hand, campaign-specific Dmass(ZDR) relationships are used up to the maximum ZDR values listed in Table 3. For ZDR observations exceeding those noted in Table 3, the ALL Dmass(ZDR) relationship is used.

Fig. 4.
Fig. 4.

A flowchart of the GPM ground validation DSD retrieval algorithm. * For Dmass, the field campaign specific Dmass(ZDR) relationship is used until maximum ZDR listed in Table 3.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

The normalized intercept parameter is calculated as a function of ZH and Dmass similar to the Eq. (A.21) in Bringi et al. (2004):
NW=αZHDmassβ,
where ZH is in mm6 m−3, Dmass is in mm, and α and β are the empirical coefficient and exponent, respectively. Since Dmass is expressed as a function of ZDR, NW is therefore a function of both ZH and ZDR. The SIFT method was applied by computing mean values of NW and Dmass for 1-dB ZH intervals between 0 and 60 dB, as long as 10 or more samples were present at each interval. The average ZH value was converted back to linear units and linear least squares fitting was applied to the triples (NW, Dmass, and ZH) to obtain the coefficients a and b in Eq. (7). For the six datasets utilized in this study, the coefficients and exponents were nearly identical resulting in overlaid curves in log(NW) versus Dmass space at ZH of 30 dB (Fig. 3c). As in the case of Dmass, the GPM-GV DSD retrieval algorithm uses the ALL NW(ZH, Dmass) relationship, with α coefficient a of 35.30 and exponent β of −7.20. This relationship is valid for the entire ZH range in radar observations.

The ALL NW(ZH, Dmass) relationship is plotted over 2DVD observations of IFloodS, IPHEx, and OLYMPEx for ZH between 10 and 60 dB (Fig. 5). The results are similar for the other four sites listed in Table 1. Consistency between log(NW) and Dmass was evident for a given ZH for these three field campaigns. High log(NW) (>5), which generally represents the larger drop concentrations, occurred at a ZH of ~20 dB and Dmass of 0.5 mm in all three-field campaigns. Low log(NW) (<2), on the other hand, corresponded to Dmass higher than 2.5 mm and ZH greater than 35 dB. High Dmass values (>3.5 mm) corresponded to ZH greater than 50 dB but the vice versa is not the true. These high ZH values were also observed at Dmass as low as 2 mm during IFloodS and IPHEx.

Fig. 5.
Fig. 5.

ALL database NW(Dmass, ZH) relationship at six different ZH ranging from 10 to 60 dBZ (solid lines). The 2DVD observations during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx (colored circles indicate ZH).

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

The inverse relationship between log(NW) and Dmass is of particular importance. When ZDR is 0.1 dB, small drops dominate the DSD and large drops are absent. In these cases, Dmass can still be 0.5 mm or higher (Fig. 3a) but log(NW) is greater than 6 at 30 dBZ (Fig. 3c). For such a high log(NW), the population of small drops should be abundant but the 2DVD observations suggest that this is an unrealistic DSD. There was not a single 2DVD observation for log(NW) greater than 6 (Fig. 5). Hence it was determined that the GPM-GV DSD retrieval algorithms should eliminate noisy ZDR samples and unphysical values of log(NW) by eliminating values of log(NW) below 0.5 and above 6.

4. Evaluation of Dmass and NW retrievals

The accuracy of the Dmass(ZDR) relationships was evaluated by comparing the Dmass that was calculated from the 2DVDs to that retrieved from Eq. (5) employing the 2DVD-based ZDR. The field campaign specific coefficients listed in Table 3 were used to derive Dmass from Eq. (5). Bias and absolute bias are the quantitative measures of the evaluation where bias is defined as the estimated value minus observed quantity. A negative bias therefore refers to underestimation with respect to the observed value. The 2D density diagram, which merges 2DVD observations in a field campaign, shows the distribution of the observations with respect to a 1:1 line. The majority of the observations fall just off the 1:1 line leaning toward measured Dmass during IFloodS, IPHEx, and OLYMPEx (Fig. 6) as well as for MC3E, MSFC-UAH, and GSFC-WFF (not shown). This results in a very slight underestimation bias of Dmass of −0.07 mm or less (Table 4). The absolute bias, which is a measure of random error in the parametric representation, was 0.12–0.13 mm for Dmass, indicating that the derived Dmass(ZDR) relationships represented the observed data well. Interestingly, the ALL Dmass(ZDR) relationship resulted in either the same or lower bias and absolute bias in Dmass as opposed to the campaign specific Dmass(ZDR) relationship during IFloodS, IPHEx, and OLYMPEx (Table 4).

Fig. 6.
Fig. 6.

A 2D density plot of measured and estimated Dmass based on 2DVD database during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The 2DVD-calculated ZDR is used to estimate Dmass following Eq. (5) and Table 3.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

Table 4.

Performance of the Dmass(ZDR) and NW(ZH, Dmass) relationships during IFloodS, IPHEx, and OLYMPEx. Considering 2DVD-calculated Dmass and log(NW) as a reference, bias and absolute bias of these two DSD parameters were presented for the combined 2DVD dataset for each field campaign. The sample sizes were also given.

Table 4.

The accuracy of the NW(ZH, Dmass) relationship was evaluated in a similar manner through comparisons of NW, which were either directly calculated from 2DVD or retrieved from Eq. (6) using 2DVD-based ZH and Dmass. Since the GPM-GV DSD retrieval algorithm uses the ALL relationship, the ALL NW(ZH, Dmass) relationship was used for all field campaign datasets (Fig. 7). The majority of the observations were just off the 1:1 line leaning toward estimated log(NW) with a bias of equal to or less than 0.05 (Table 4). This trend was also true for the other sites, MC3E, MSFC-UAH, and GSFC-WFF (not shown). The absolute bias was 0.06–0.07 for log(NW), indicating that the NW(ZH, Dmass) relationships represented the observed database quite well.

Fig. 7.
Fig. 7.

A 2D density plot of measured and estimated log(NW) based on 2DVD database during (a) IFloodS, (b) IPHEx, and (c) OLYMPEx. The 2DVD-calculated Dmass and ZDR are used to estimate log(NW) following Eq. (6).

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

5. Sensitivity studies

a. Climate regime

All of the 2DVD data were obtained from midlatitude sites. KWAJ (8.8°N, 163.7°E), in the Marshall Islands, is a tropical oceanic site where P2 observations were available over a 3-yr period. To determine the sensitivity of the Dmass(ZDR) relationship to climate regimes, P2 observations from KWAJ and two midlatitude field campaigns were employed and a Dmass(ZDR) relationship was derived following the SIFT method for all four datasets. P2 also outputs precipitation phase and only rainy minutes were used in this study.

Through analysis of P2 data, it was seen that there were a few samples where ZDR was high and Dmass was low in midlatitude sites. Since the number of samples are generally low at high ZDR values, the mean Dmass that was calculated at high ZDR was almost invariant with increasing ZDR when SIFT was applied. A close look at these samples revealed that there were one or two large drops (>4.0 mm in diameter) in a single or two adjacent bins with no drops in the previous four or more adjacent size bins. This was never observed in any of the 2DVD data. The fall velocities of these questionable drops were within the expected range for their sizes and there was no compelling evidence for possible dripping or two drops falling crossing the laser beam at the same time. These suspicious drops were removed from the P2 database and are subject to further investigation.

The Dmass(ZDR) relationship derived from IFloodS and KWAJ P2 database were in good agreement throughout the ZDR range (Fig. 8a). Table 5 presents the coefficients of the Dmass(ZDR) relationships for IFloodS, OLYMPEx, and KWAJ following Eq. (5). For ZDR between 1 and 2 dB, the differences in Dmass between the IFloodS and KWAJ Dmass(ZDR) relationships were only 0.04 mm (Fig. 8c). The IFloodS Dmass(ZDR) relationship underestimated Dmass by only 0.03 mm when KWAJ P2 database was used (Table 6). The absolute biases were 0.12 and 0.09 mm when IFloodS or KWAJ Dmass(ZDR) relationships were used for IFloodS P2, and KWAJ P2 databases, respectively.

Fig. 8.
Fig. 8.

Mean Dmass for a given ZDR interval (circles) and SIFT-based fits (lines) for (a) P2-based IFloodS and KWAJ and (b) OLYMPEx and KWAJ datasets. (c) The difference in Dmass as a function of ZDR based on KWAJ and IFloodS and on KWAJ and OLYMPEx Dmass(ZDR) relationships.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

Table 5.

The coefficients of the Dmass(ZDR) relationship and the maximum ZDR range for three different P2 datasets. The sample sizes were also given.

Table 5.
Table 6.

Sensitivity of the Dmass estimation to the climate regimes. The bias and absolute bias in Dmass were presented when KWAJ and IFloodS (or OLYMPEx) Dmass(ZDR) relationships were tested for KWAJ and IFloodS (or OLYMPEx) P2 databases.

Table 6.

There were significant differences between OLYMPEx and KWAJ-based Dmass(ZDR) relationships (Fig. 8b). The difference in Dmass based on OLYMPEx and KWAJ Dmass(ZDR) relationships increased from 0.17 mm at ZDR of 1 dB to 0.43 mm at ZDR of 2 dB (Fig. 8c). The OLYMPEx Dmass(ZDR) relationship underestimated Dmass by 0.13 mm when KWAJ P2 database was used (Table 6). The bias was also relatively high, 0.10 mm when KWAJ Dmass(ZDR) relationship was used for OLYMPEx P2 database. The absolute biases were not drastically different when Dmass(ZDR) relationship derived from one experiment was used for another experiment database. The highest absolute bias, 0.15 mm was observed when OLYMPEx Dmass(ZDR) relationship was used for KWAJ P2 database but this was only 0.03 mm higher than the absolute bias when IFloodS Dmass(ZDR) relationship was used for IFloodS database.

b. Disdrometer type

Before we present the analysis of the comparative study between 2DVD and P2 observations, we need to point out that both 2DVD and P2 under sample small drops less than 0.7 mm in diameter. In fact, the P2 manufacturer left empty the first two size bins and these two channels corresponds to the drop sizes less than 0.25 mm. Thurai and Bringi (2018) were able to construct an accurate representation of DSD by using collocated measurements from a 2DVD and from a Meteorological Particle Spectrometer (MPS). MPS is designed to measure drizzle size drops, which are used to fill in the small-drop portion of the DSD that is underestimated by the 2DVD.

The sensitivity of the Dmass(ZDR) relationship to the disdrometer type was determined by reanalyzing the relationships for the collocated P2 and 2DVD observations from IFloodS and OLYMPEx. The subset where both disdrometers reported rainfall was employed to derive Dmass(ZDR) relationships after combining all available data in each field campaign and applying the same criterion for the minimum and maximum Dmass and ZDR bounds. The IFloodS and OLYMPEx had six and three collocated sites, respectively, but the latter one had nearly 4.5 times more samples due to abundant rainfall (Table 7).

Table 7.

The coefficients of the Dmass(ZDR) relationship and the maximum ZDR range for two different 2DVD and P2 datasets, which consist of coincident observations. The sample sizes were also given.

Table 7.

The agreement was good between the 2DVD- and P2-based Dmass(ZDR) relationships for both field campaigns where the difference in Dmass exceeded 0.2 mm only when ZDR was greater than 1.6 dB for OLYMPEx and 2.6 dB for IFloodS (Fig. 9). The quantization of the P2 raw drop counts could partially explain the differences in Dmass at high ZDR. To demonstrate the quantization effect, one of the OLYMPEx samples that had one drop at its twenty-first bin was considered as a test case. The midsize diameter at twenty-first bin is 5.5 mm with 1.0 mm bin width as opposed to 0.2-mm bin width in 2DVD. The calculated Dmass and ZDR from P2 test sample were 2.43 mm and 2.54 dB, respectively. If the exact size of the large drop was 5.0 mm (the lower edge of the bin in P2), Dmass and ZDR would be 2.30 mm and 2.41 dB, respectively. If the drop diameter would be 6.0 mm (the higher end of the bin in P2), Dmass and ZDR were 2.66 mm and 2.76 dB, respectively.

Fig. 9.
Fig. 9.

Mean Dmass for a given ZDR interval (circles) and SIFT-based fits (lines) for 2DVD and P2 datasets during (a) IFloodS, and (b) OLYMPEx. (c) The difference in Dmass as a function of ZDR based on 2DVD- and P2-based Dmass(ZDR) relationships during IFloodS and during OLYMPEx.

Citation: Journal of Atmospheric and Oceanic Technology 37, 1; 10.1175/JTECH-D-18-0071.1

The number of samples with large drops determines the extent of the validity of the SIFT-based Dmass(ZDR) relationship. Recall that a minimum of 10 samples are required to calculate mean Dmass for a given ZDR interval. The P2 registered more large drops than the 2DVD resulting in larger sample sizes of high ZDR in both field campaigns. The maximum ZDR interval was therefore higher for the P2 than for the 2DVD (Table 7). Quantization could play a role on the presence of more large drops in P2. Application of the P2-based Dmass(ZDR) relationship on the 2DVD database gave underestimates of Dmass while application of the 2DVD-based Dmass(ZDR) relationship on the P2 database overestimated Dmass (Table 8). For the eight different combinations in both field campaigns, the absolute bias in Dmass was the highest, 0.13 mm, during IFloodS when P2-based Dmass(ZDR) relationship was used for 2DVD database.

Table 8.

Sensitivity of the Dmass estimation to the disdrometer type. The bias and absolute bias in Dmass were presented when 2DVD and P2 Dmass(ZDR) relationships were tested for both 2DVD and P2 databases during IFloodS and OLYMPEx.

Table 8.

6. Conclusions

This study presents the methodology used by the GPM ground-validation team to develop Dmass(ZDR) and NW(ZH, Dmass) relationships for ground-based radar retrievals. The methodology is empirical and utilizes disdrometer datasets collected at six midlatitude sites and one tropical site. More emphasis was given to the retrieval of Dmass because its accuracy is tied to the level-1 requirements of the GPM mission. The sensitivity of the Dmass(ZDR) relationships to climate regime and disdrometer type was also presented. The uncertainty of the empirical relationships is shown by the two-dimensional distribution histogram of the retrieved and observed variables. The empirical fits perform better for narrow and unskewed distributions of the retrieved variable for a given value of the observed variable. Considering the Dmass(ZDR) relationship, the SIFT method using a third-order polynomial performed well with an absolute bias of 0.12–0.13 mm in Dmass during IFloodS, IPHEx, and OLYMPEx field campaigns. The absolute bias of log(NW), on the other hand, was 0.06–0.07 for the same three field campaigns in the NW(ZH, Dmass) relationship.

The 2DVD database from six sites was used to derive empirical relationships in estimating Dmass and NW. Although all six locations were at midlatitudes, there were noticeable differences in the coefficients of the Dmass(ZDR) relationships due to the differences in climate regimes. Orographic enhancement played a key role in the presence of abundant small drops and low concentrations of large drops resulting in lower Dmass at high ZDR during OLYMPEx in contrast to the other five sites. A few large drops resulted in large ZDR due its sensitivity to the drop shape, while Dmass remained relatively low due to its sensitivity to the concentration of large drops.

At KWAJ, a tropical oceanic site, large concentrations of small drops were also present while large drops were rare. The maximum ZDR interval was therefore considerably lower at KWAJ than the two midlatitude sites in Table 5. A P2-based comparison of Dmass(ZDR) relationships between KWAJ, IFloodS, and OLYMPEx revealed that the use of the OLYMPEx-based relationship for the KWAJ database resulted in the highest absolute bias, 0.15 mm in Dmass. The lower absolute bias in Dmass when the IFloodS-based relationship was used for the KWAJ database did not necessarily indicate a similar size spectrum from small to large drops though. The probability distribution of log(NW) in Fig. 1, for instance, showed a significant difference between IFloodS and KWAJ, which can be attributed to large number of small drops at the KWAJ site relative to the IFloodS site. Comparison between the 2DVD and P2 measurements showed that the absolute bias in Dmass was relatively high, 0.12–0.13 mm, when the P2-based Dmass(ZDR) relationship was applied to the 2DVD databases obtained during OLYMPEx and IFloodS. The differences in Dmass due to the differences between P2- and 2DVD-based Dmass(ZDR) relationships exceeded 0.2 mm at ZDR greater than 1.6 and 2.6 dB during OLYMPEx and IFloodS, respectively. These high ZDR regimes receive significant contributions from large drops where the quantization due to binned P2 raw data plays a role. Although we were unable to quantify this effect, the underestimation of small drops by both 2DVD (Thurai and Bringi 2018) and P2 (Park et al. 2017) results in higher Dmass and lower NW estimates than the actual values.

This study incorporated six 2DVD and three P2 datasets from seven different sites. While these sites exhibit diversity in terms of climate regime, other climate zones are worthy to expand this study further. New datasets from semiarid climate zone of southwestern United States and mountainous South Korea are becoming available and can be added to the validation of the derived Dmass(ZDR) relationship presented in this study. The sensitivity of NW(ZH, Dmass) relationships to different climate zones and disdrometer type can also be considered as a future study.

This study recognized the sensitivity of ZDR to the drop shape but did not investigate the impact of the deviations from mean drops shape in ZDR and therefore Dmass(ZDR) relationship. Gorgucci et al. (2002) derived D0(ZDR) and Dmass(ZDR) relationships using the same mean axis ratio versus drop diameter relationship presented in this study but they also presented the sensitivity of the coefficients of D0(ZH, ZDR) relationship to the drop shape.

The empirical relationships developed herein between the VN and DPR is used for direct comparison of DSD parameters (Petersen et al. 2020). One significant aspect of the VN comparison process is the careful geographic space-to-ground-based radar volume matching that occurs in the VN software. The matched spatial and temporal scales (Schwaller and Morris 2011) combined with an intrinsically large number of coincident samples help to firmly establish the degree to which the space-based estimates of the DSD converge with ground-based estimates. This is toward demonstrating attainment of GPM level-1 science requirements that pertain to the DSD.

Acknowledgments

The 2DVD and P2 MC3E, IFloodS, IPHEx, and OLYMPEx field campaign datasets are available through NASA Global Hydrology Resource Center (through https://ghrc.nsstc.nasa.gov/home/field-campaigns/XXX, where XXX refers to field campaign). Discussions with Robert Meneghini of NASA Goddard Space Flight Center improved the presentation of the manuscript. Special thanks to all of the 2DVD/P2 and NPOL engineers, technicians, and scientists based at NASA Wallops Flight Facility. This manuscript was funded under NASA Precipitation Measuring Mission NNX16AD45G led by Ramesh Kakar of NASA Headquarters. WAP and DBW acknowledge support from the GPM and PMM programs.

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