Raindrop Size Spectrum in Deep Convective Regions of the Americas

: This study compared drop size distribution (DSD) measurements on the surface, the corresponding properties, and the precipitation modes among three deep convective regions within the Americas. The measurement compilation corresponded to two sites in the midlatitudes: the U.S. Southern Great Plains and Córdoba Province in subtropical South America, as well as to one site in the tropics: Manacapuru in central Amazonia; these are all areas where intense rain-producing systems contribute to the majority of rainfall in the Americas’ largest river basins. This compilation included two types of disdrometers (Parsivel and 2D-Video Disdrometer) that were used at the midlatitude sites and one type of disdrometer (Parsivel) that was deployed at the tropical site. The distributions of physical parameters (such as rain rate R , mass-weighted mean diameter D m , and normalized droplet concentration N w ) for the raindrop spectra without rainfall mode classiﬁcation seemed similar, except for the much broader N w distributions in Córdoba. The raindrop spectra were then classiﬁed into a light precipitation mode and a precipitation mode by using a cutoff at 0.5 mm h − 1 based on previous studies that characterized the full drop size spectra. These segregated rain modes are potentially unique relative to previously studied terrain-inﬂuenced sites. In the light precipitation and precipitation modes, the dominant higher frequency observed in a broad distribution of N w in both types of disdrometers and the identiﬁcation of shallow light precipitation in vertically pointing cloud radar data represent unique characteristics of the Córdoba site relative to the others. As a result, the co-variability between the physical parameters of the DSD indicates that the precipitation observed in Córdoba may confound existing methods of determining the rain type by using the drop size distribution. methodology, L.R.Z. L.R.Z., J.C.H.; L.R.Z.; L.R.Z.; investigation, L.R.Z. L.R.Z.; data L.R.Z., A.L., J.C.H.; writing—original L.R.Z.; writing—review L.R.Z., J.C.H., visualization, L.R.Z. S.W.N.;


Introduction
Clouds help to drive the atmospheric circulation from the global to the convective scale through diabatic heat release. In addition to heating and cooling due to radiative effects and the phase changes of water, clouds also moderate the global hydrological cycle through precipitation processes and vertical transportation of water [1][2][3]. The microphysical processes that modify a cloud's structure and lifetime and control a cloud's redistribution of heat and moisture are linked to the underlying thermodynamic conditions arising primarily from vertical air motions within and outside these cloud systems [4][5][6][7]. Understanding the connections between the kinematic and thermodynamic conditions that influence cloud dynamics, microphysics, and attendant rainfall production is essential from a hydrometeorological perspective. However, these intertwined processes that operate from the micro-to the meso-scale can be difficult to represent with fidelity in multi-scale atmospheric models [2,3,8,9].
Liquid drops and ice particles of diverse sizes are involved in cloud microphysics [4]. The drop size distribution (DSD) is a characteristic of liquid precipitation, and DSD obser-vations are of interest in applications beyond understanding microphysical processes in clouds. To illustrate this, for rainfall estimation with satellite-based methods or groundbased retrieval algorithms, DSDs are critical for determining the relations in the reflectivityrain rate [10][11][12][13][14] and improving dual-polarization rainfall retrievals [15][16][17][18]. Additionally, the characterization of DSDs in multi-scale models is vital for representing the processes of cloud dynamics and rainfall prediction in numerical simulations and forecasts [19][20][21][22]. It is also essential for broader studies of soil erosion due to rainfall and irrigation systems in agricultural engineering [23][24][25][26][27][28].
Various formulated mathematical models quantify the shape characteristics of the raindrop size distribution; for example, the exponential distribution N(D) = N 0 exp(−λD), where N(D) is the raindrop concentration per droplet diameter D (mm) interval per unit of volume (m −3 mm −1 ), N 0 (m −3 mm −1 ) is the intercept parameter, and λ (mm −1 ) is the slope parameter, as first formulated by Marshall and Palmer [29]. Moreover, the three-parameter gamma distribution N(D) = N 0 D µ exp(−λD), with N 0 (m −3 mm −1 ), µ (unitless), and λ (mm −1 ), was introduced by Ulbrich [30] and Willis [31], but had a disadvantage in that the three parameters are mathematical and not easily interpretable physical quantities. Hence, Testud et al. [32] proposed the normalization of raindrop distribution without an a priori assumption about the DSD shape and found a normalized intercept parameter N w proportional to LWC and (D −4 m ), where LWC is the water content of liquid precipitation (gm −3 ), and D m is the mass-weighted mean diameter (mm). Subsequently, the three physical quantities in this normalized gamma DSD are N w , D m , and µ, where N w represents the intercept parameter of an exponential distribution with the same LWC and D m , as well as shape parameter µ of 0 (Appendix A.).
Moreover, radar hydro-meteorology is dependent on the estimation of the raindrop size distribution (DSD) as a function of parameters of rain physics through the relationships of Z = aR b . Here, Z is the radar reflectivity factor (in linear units of mm 6 m −3 ), and R is the rain rate (mm h −1 ). The empirical quantities (a, b) depend on the variability of the DSD for different climatic regimes of rain due to differences in their dominant microphysical processes [30,[33][34][35][36][37]. The diverse Z − R relationships in the literature also imply different N w values depending on the microphysical processes and rainfall intensity occurring in varying climate regimes [30,32,36,38]. In DSDs from radars and disdrometers, Bringi et al. [36,39] analyzed the linear relation between N w (or log 10 N w ) and the median volume diameter (D 0 ) to classify surface rainfall at maritime and continental locations in two regimes. These analyses revealed microphysical differences in the stratiform and convective rain regimes that were attributed to different formation processes.
Consequently, Bringi et al. [36,39] introduced a convective-stratiform segregation criterion based on these two parameters for maritime and continental geographical locations. Subsequently, Thompson et al. [40] examined DSD observations in tropical oceanic rain at two locations. They showed DSD characteristics for stratiform tropical oceanic rain that were similar to those of [39], but found a larger N w with smaller D 0 in convective rain, in contrast to previous studies up to that point, which presented smaller N w with smaller D 0 for maritime continental locations [36,38,39,41,42].
In another study that used many disdrometer sites worldwide, Dolan et al. [38] used principal component analysis to examine the spatial-temporal variability in DSD datasets in twelve geographical locations from high latitudes to the tropics. They presented a conceptual model of the variability between N w and D 0 based on clustering of the dominant processes that modified the DSD shapes for different rainfall modes. All sites reported larger N w in the high latitudes and smaller N w in the midlatitudes. The two sites examined in the tropics reported an N w bimodality for convective and stratiform rain clusters and larger N w with smaller D 0 . Another global examination of DSD properties from Gatlin et al. [43] analyzed samples of large drops from eighteen geographical sites in various rainfall conditions, reporting maximum raindrop diameter values (D max ) of up to 9.0−9.7 mm for the validation of assumptions of D max in remote sensing retrieval algorithms. Furthermore, Thurai et al. [44] examined the effects of small drops by using a combined two-instrument raindrop size spectrum at two sites in the United States, and they showed precipitation and drizzle modes. At the same time, they showed higher values of N w due to the minimum raindrop diameter values (D min < 0.7 mm), which are generally undercounted by commonly used disdrometers, including those used in this study.
In spite of the disdrometer-based efforts to measure surface precipitation and improve precipitation representation worldwide, a literature review indicated that some climatic regimes have scarce disdrometer measurements [45][46][47], particularly in South America [48,49]. For example, the NASA Tropical Rainfall Measuring Mission-Large-Scale Biosphere-Atmosphere (TRMM-LBA) experiment conducted in 1999 in southwestern Amazonia [43,[50][51][52] and the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Green Ocean Amazon (GoAmazon) field campaign conducted in central Amazonia during 2014 and 2015 [53][54][55] collected DSD observations. Moreover, the DOE ARM Cloud, Aerosol, and Complex Terrain Interactions (CACTI) and Remote sensing of Electrification, Lightning, And Mesoscale/microscale Processes with Adaptive Ground Observations (RELAMPAGO) field campaigns conducted during the austral warm season of 2018-2019 collected disdrometer observations in west-central Argentina near the Sierras de Córdoba (SDC) [56,57]. This north-south-oriented mountain range east of the Andes in subtropical South America is known to frequently initiate deep convection [56][57][58][59][60][61]. In addition, measurements from the Integrated Precipitation and Hydrology Experiment (IPHEx), which was conducted in the Appalachian Mountains of North Carolina (USA), formed an extensive DSD database for midlatitude mountainous terrain [62]. However, mountainous regions worldwide likely have a range of orographically impacted precipitation processes that lead to substantial variability in the surface DSD characteristics.
The precipitation processes in subtropical South America may be unique compared to those of other climate regimes. Observations from the Precipitation Radar (PR) aboard the TRMM satellite showed that the deep convective regions in subtropical South America produce some of the most intense and organized convective systems on Earth [63,64].
Previous studies have compared the vertical and horizontal radar reflectivity echo structures of three deep convection regions in the Americas, including the Amazon and west-central Argentina, by examining an 11-year record of storms from the TRMM PR dataset [58,[65][66][67][68]. For example, Rasmussen et al. [66] suggested that organized convective systems bearing wide convective cores are more frequent near the SDC, which was where the RELAMPAGO-CACTI field campaign took place. As this frequent and organized convection moves to the east and northeast of the SDC, it presents similarities with the mesoscale convective system (MCS) structure of a leading line of cells followed by a stratiform rain region, which was observed in Central Oklahoma in the United States [69]. However, storms in the Great Plains do not interact significantly with surrounding topography, such as storms near the SDC, where terrain-induced flow modifications have led to the rapid organization of convection [58,59], which we hypothesize can be reflected in the differences in the variability of DSD parameters. Therefore, these MCSs of the wide convective core storm type are relatively infrequent in the Amazon compared to warmseason storms in subtropical South America and the Great Plains. Thus, Romatschke and Houze [65] and Rasmussen et al. [66] more commonly classified MCSs in the Amazon as storms with broader stratiform areas during the warm season than those of the midlatitude sites considered herein.
The purpose of this work is to leverage these recent disdrometer data collection efforts to compare the DSDs and DSD parameters among three deep convective regions in the Americas: the core site of the RELAMPAGO-CACTI field campaign near the SDC, the US Southern Great Plains site, and central tropical Amazonia during the GoAmazon field campaign. Casanovas et al. [70] described intra-site DSD variability across central Argentina during RELAMPAGO-CACTI, whereas this study compared the DSD characteristics across campaigns in the Americas for the first time. Section 2 outlines the data and methods, and Section 3 summarizes the results obtained from this comparison of the DSDs between the midlatitude sites (COR and SGP) and the tropical site (MAN). Section 4 discusses the more notorious variability of the DSD parameters affected by the complex terrain at COR relative to SGP and MAN, and potentially to previously studied orographically influenced sites. Furthermore, Section 5 presents the overall conclusions.

Locations of Sites and Field Experiments
The three sites in the Americas examined in this study spanned different climate regimes: humid subtropical grasslands for the US Southern Great Plains, an equatorial rainforest in Manacapuru, Brazil, and a humid subtropical climate near the complex terrain in Córdoba, Argentina. For reference, Figure 1 shows the three sites where intense rainproducing systems contribute to the majority of rainfall in their respective river basins: Mississippi, Amazon, and La Plata. Table 1 gives information on each site's location and coordinates, the source instruments, and the data collection period selected. For these sites, the ground-based measurements compiled from the ARM user facility correspond to the following field experiments.   [72,[75][76][77]. It is considered a crucial convective area in the tropics where moderately intense to weak convective systems cause significant rainfall throughout the austral summer [63,64,[78][79][80][81]. The ARM Mobile Facility (AMF1) and Mobile Aerosol Observing System (MAOS) were at the "T3" site near Manacapuru, which is on the Amazon River and is located 80 km west of the Manaus airport [53][54][55]82]. The ARM acronym for this site is MAO, but this study denotes it as MAN (MANacapuru). 3. In connection with the National Science Foundation (NSF)-led RELAMPAGO field campaign, the DOE ARM CACTI field campaign collected disdrometer observations in Villa Yacanto (see Figure 2). Both experiments took place in Córdoba, Argentina, near the SDC during the warm season of 2018-2019. Headwaters in the SDC form the Carcarañá River Basin, which flows into the Paraná River, a major river in the La Plata Basin, the third-largest basin in the Americas. These rivers are vital for socioeconomic activities and are highly influenced by frequent and intense, organized convection and the consequent severe weather impacts, including costly flooding disasters [67,[83][84][85][86][87]. Approximately 20 km to the east of the highest terrain of the SDC and 90 km southwest from Córdoba's capital city was located the ARM Mobile Facility-1 (AMF1) site [60,88,89]. The ARM acronym for this site is COR (CORdoba). Table 1. Disdrometer information for the three sites is presented with the corresponding campaign, location, coordinates, type of source instrument, and observation period. In addition, an overview of the data segregated by rain mode (Lpm: R < 0.5 mm h −1 , and Pm: R > 0.5 mm h −1 ) is presented with the respective numbers of rainy minutes, and the values of 10 log 10 R, D m , and log 10 N w corresponding to the highest frequencies of occurrence or peaks were determined subjectively.

Disdrometer Instrumentation and Data Analysis Methods
The ARM program's disdrometers have collected DSD spectra in sites where there might not be other routine disdrometer-based observations and precipitation because severe convective storms represent a fundamental contribution to the Americas' major river basins. For the observational periods and experiments examined here, between 2014 and 2019, the ARM program mainly deployed two types of disdrometers for long-term measurements of DSDs. These are a particle size velocity (PARSIVEL) laser-optical disdrometer and a two-dimensional video disdrometer, or 2D-video disdrometer (2DVD).
The OTT HydroMet PARSIVEL 2 , or PARSIVEL2 disdrometer (henceforth PARS), provides measurements of the raw particle size and fall speed distributions within a matrix (32 × 32) constructed from particle counts of uneven classes that are from 0.06 to 24 mm in diameter at OTT fall velocities from 0.050 s −1 to 20.80 m s −1 . For this study, the uniform bin width selected was 0.20 mm [90]. Some of the primary variables were the Lhermitte fall velocity (m s −1 ), surface precipitation as the rainfall rate (R), liquid water content (LWC), number concentration, and raindrop characteristic size as the median volume diameter (D 0 ) [52,91,92]. The PARS is known for its robustness and low maintenance requirements, as well as for being subject to error with larger raindrops and faster fall velocities when calculating the DSD parameters [38,93,94]. The ARM Parsivel2 Handbook [92] provides further information about other primary variables and expected uncertainty. In addition, the reports from the GoAmazon and CACTI field campaigns [60,95] and from recent studies that used ARM data [38,94] give more details about the deployment and standard corrections of PARS.
The raw output files of the 2D-video disdrometer (hereafter 2DVD) contain the dimensions of every drop observed by two scanning cameras and their respective matching systems, with an equivolumetric diameter from 0.20 (or finer grid resolution) to 10 mm [96,97]. Moreover, some of the constructed observables are the raindrop oblateness and fall speed, and the drop diameter is the center of the bin for drops for each 0.2 mm bin spacing [43,52,98]. The 2DVD requires frequent calibration and tends to underestimate small droplet concentrations [38,40,43,44]. However, it provides the most accurate concentration of large raindrops and characterization of raindrop shapes because there are fewer errors in the matching procedure [18,43,44,52,97]. More information on the 2DVD and its deployment are available in the ARM VDIS Instrument Handbook [98], the CACTI field campaign report [60], and previous studies that used ARM datasets [38,40,94]. Note that the sampling area of the 2DVD line-scan camera is 0.01 m 2 , while the PARS laser sheet images were over an area of 0.0054 m 2 [52,92,98].
Following the corrections applied in similar DSD studies [43,52,93,94], the raw dataset processing considered for each 1-min raindrop spectrum removed drop sizes D 0 with a diameter of less than 0.2 mm for being unreliable in these disdrometers [52,93,94]. Moreover, following Giangrande et al. [94], the dataset processing removed rain rates R lower than 0.1 mm h −1 and used at least 5 min of consecutive rain with a rate greater than 0.1 mm h −1 to reduce any noise in the 1-min DSD measurements. Previous studies found the above data processing method to be more accurate for moderate to large raindrops due to the disdrometer's resolution and the consequent tendency to underestimate the concentration of small raindrops [44,52,94].
Apart from the recent value-added ARM products-LDQUANTS (Laser Disdrometer Quantities) and VDISQUANTS (Video Disdrometer Quantities) [99], which provide quality control for some of the DSD properties-the filtering of the disdrometers' raw data to eliminate secondary or suspicious drops is left to the users, as their filtering requirements may vary (MJ Bartholomew 2020, personal communication).
Nonetheless, the precision in the DSD representation and the measurements of the drop size and fall velocity by the disdrometers can be significantly affected by strong winds during intense rainfall [100], especially for the PARS compared to the 2DVD [93]. So, the first stage of quality control is masking the drops that exceed the calculated Lhermitte fall velocity [92,101], v Lhermitte ± (threshold = 2 m s −1 ), to include light-precipitationmode droplets and to eliminate secondary or suspicious droplets from rain splashes and wind effects during heavy precipitation. Other standard filtering methods and thresholds (v Lhermitte ± 50%) [52,93,102] were extensively tested, but resulted in a detriment to the smaller drops [93], especially at the COR site. This modification in the criteria, including small drops, was independently verified with radar echoes at COR from precipitating clouds (see below). Therefore, the second stage of the quality control and processing of the data included retaining 1-min observations with at least 100 drops [38,40,94]. For the spectra that were retained in the second stage, following the criteria of previous studies that characterized the full drop size spectra [44], rain rates lower than 0.5 mm h −1 defined the "light precipitation mode" (Lpm), and rain rates greater than 0.5 mm h −1 defined the "precipitation mode" (Pm) [43,103,104].
Subsequently, the DSD parameters were calculated by using these data with a 0.20 mm binning, and they included the Lhermitte fall velocity v Lhermitte , mass-weighted mean diameter D m , mass standard deviation σ m , normalized intercept parameter N w , liquid water content LWC, and the median volume diameter D 0 [25,32,97,101,105,106]. Appendix A contains the DSD parameter relationships used in the data processing. Table 1 details the total number of minutes after the quality control was used in the calculations of the DSD parameters for each site, instrument, and rain mode. There was good agreement between these calculations and the corresponding nugget DSD parameters from the LDQUANTS and VDISQUANTS. However, our analysis does not show these comparisons.
The hydrological applications of light precipitation for the Córdoba region are important during the wet season, but even more critical during the dry season [104] (e.g., a sequence of days with persistent drizzle throughout the San Roque Lake region reported in 2018 [107]). Furthermore, Section 3.3 presents two case studies with a high-frequency occurrence of Lpm in order to enhance the characterization of the properties of drizzle and light rain. Here, the data collected by the Ka-band ARM Zenith-pointing Doppler cloud Radar (KAZR) [108] provided appropriate monitoring of the light precipitation mode in tandem with the disdrometer observations at the COR site (see Figure 2). It is worth noting that when averaging the 1-min Lpm PARS disdrometer observations with the 15-min sequence of KAZR measurements, the precipitation analysis should not be affected by the KAZR's small attenuation in light rain conditions [94,109].
In addition, collocated with the disdrometers, rain gauges, such as a tipping-bucket rain gauge (TBRG) [110] and a weighing-bucket precipitation gauge (WRG) [111], were used to make additional precipitation measurements. Neither the TBRG nor WRG was used to measure the DSDs or report relevant rain-rate errors in light and heavy precipitation, respectively, but they provided reliable total rain values [52,112]. As a further verification at the COR site, the TBRG 1-min rain-rate measurements [113] were compared with the corresponding PARS observations. Specifically, the TBRG and PARS showed a good agreement throughout the observational period of COR (correlation coefficient = 0.73, RMSE = 16.11 mm h −1 , n = 2948).

DSD Parameter Distributions
A comparison of the probability density functions (pdfs) of the rain rate-expressed as 10 log 10 R (in dBR with R units mm h −1 ), the mass-weighted mean diameter is expressed as D m (in mm), and the normalized intercept parameter is expressed as log 10 N w (in BN w , where N w in units of m −3 mm −1 )-is presented to examine the site-to-site variability. Appendix A reviews the definitions and formulas of these three parameters, which were given by Williams et al. [25,105]. Figures 3a, 4a and 5a show five lines: the non-segregated data are in violet/blue lines for COR, magenta/orange lines for SGP, and a green line for MAN. Otherwise, Figures 3b-d, 4b-d and 5b-d present two lines for the segregated data; the dashed line is for the light precipitation mode (Lpm) and the solid line is for the precipitation mode (Pm). Again, the PARS/2DVD datasets are indicated here by violet/blue lines for COR, magenta/orange lines for SGP, and green lines for MAN. The logarithmic dBR scale in Figure 3 provides a convenient comparison between Lpm and Pm in the rain-rate pdfs.
Considering all of the non-segregated rain observations, the pdfs of the rain rate in Figure 3a appear to be quite similar, particularly at the midlatitude sites. Concurrently, a lower (higher) frequency of observed values between 0-5 (10-15) dBR-corresponding with the rain-rate range of 1-3 (10-30) mm h −1 -was estimated at MAN. Despite the general agreement, slight differences existed between COR and SGP, where the COR site had higher (lower) frequencies in the range of 0-2.5 (10-15) dBR or 1-1.8 (10-30) mm h −1 . Figure 3b-d examine the 10 log 10 R rain-rate pdfs at each site, which were separated into the Lpm and Pm rainfall modes. Overall, when separated into modes, the rain-rate pdfs at each site appeared to show right-skewed distributions for the Lpm, indicating a higher frequency of heavier rain with the heavy right tail near the maximum rain-rate cutoff. On the other hand, the Pm had more gaussian left-skewed distributions towards the minimum rain-rate cutoff, as more frequent light rain was registered in this mode. The discrepancies between PARS and 2DVD in the rain rate for the two rainfall modes at the COR and SGP sites were minor. Table 1 compiles the 10 log 10 R statistics for the three sites.
At SGP and COR, the pdfs of the rain rate were similar between PARS and 2DVD for Lpm and Pm. However, the SGP observations of the rain rate revealed slightly higher frequencies than those of COR and MAN for Lpm, but very similar rain-rate distributions for Pm to those of the COR site (Figure 3b-d). On the other hand, the MAN Pm observations of the rain rate (Figure 3d) revealed slightly lower (higher) frequencies at 0-5 (10-15) dBR than those of the other two sites.  Figure 4a shows that the pdfs of D m without classification at the three sites were generally similar, but had some differences. The violet/blue D m distributions for COR were more skewed toward raindrop sizes of less than 1 mm. Thus, MAN and SGP showed their higher frequencies at diameters that were greater than 1 mm; both PARS distributions were similar and had higher frequencies near 1 mm than the slightly shifted SGP 2DVD distribution due to its peak near 1.3 mm.
Separating the D m distributions into precipitation modes, Figure 4b-d reveal comparable distributions across the three sites. For the Lpm, more notable differences were apparent between the COR site and the other two sites, including the PARS, which showed higher discrepancies with the 2DVD. The confined distribution of PARS at the COR site had the most frequent values of D m , which were around 0.45 mm, while the 2DVD presented a broader D m peak that extended between 0.40 and 0.64 mm; both sensors recorded peaks at the second bin, however. The SGP Lpm distributions showed D m peaks at 0.58 and 0.80 mm for PARS and at around 0.52 and 0.91 mm for the 2DVD. PARS showed higher frequencies of D m than the 2DVD, but the peaking in the third and fifth measurable size bins was similar for both instruments at the SGP site. The MAN Lpm distribution presented the most frequent D m values at 0.68 and 0.83 mm, as well as peaks in the fourth and fifth measurable size bins.
The PARS/2DVD Pm distributions of D m were comparable among the three sites, except for the much more left-skewed distributions at the COR site towards raindrop sizes of less than 1 mm-more precisely, near 0.63 mm (PARS) and around 0.55 and 0.80 mm (2DVD). The two disdrometers at COR and SGP showed good agreement, except for slight discrepancies at both ends of the spectrum. The SGP Pm distributions showed D m peaks around 1.20 mm for PARS and around 1.40 mm for the 2DVD. Again, both SGP disdrometers exhibited slight disagreement between 1 and 2 mm. The MAN distribution had its most frequent D m value near 1.15 mm, similarly to that of SGP. Table 1 summarizes these D m statistics. Overall, in comparing the PARS and 2DVD estimates of D m , larger interinstrument differences existed in light precipitation (Lpm) than in heavier precipitation (Pm), which could be due to the instruments' different resolutions and sampling areas, which could be amplified for small droplets.   Figure 5 displays the log 10 N w pdfs. The COR site had significant differences with respect to the SGP and MAN in the N w breadth distributions without segregation (Figure 5a), which included the PARS/2DVD discrepancies in this parameter across the spectrum.
For the DSDs with segregation, the PARS/2DVD Lpm observations at SGP (Figure 5c) showed relatively confined bimodal log 10 N w distributions with peaks around 3.70 and 4.45 (PARS) and 3.40 and 4.55 (2DVD), respectively. PARS showed somewhat higher frequencies of N w than those of the 2DVD at the SGP site. MAN (Figure 5d) also had a relatively confined but unimodal Lpm distribution with a peak near log 10 N w = 3.55. COR had broader bimodal Lpm N w distributions (Figure 5b), with peaks at 4.15 and 4.80 (PARS) and 4.0 and 5.20 (2DVD). PARS exposed a moderately higher frequency near log 10 N w = 4.80 than that of the 2DVD near log 10 N w = 5.20 at the COR site.
The Pm distributions were similarly confined at the SGP and MAN sites (Figure 5c discrepancies in the the normalized intercept parameter for Pm at the COR and SGP sites were minor compared to those for Lpm. Table 1 reviews these N w statistics.

Joint Distributions of DSD Parameters
To analyze the site-to-site co-variability of DSD parameters in the N w and D 0 space [114], Figures 6 and 7 show joint histograms of log 10 N w (in BN w , where N w is in units of m −3 mm −1 ) versus mean raindrop diameter D 0 (in mm), separated by the Lpm and Pm rainfall modes. Furthermore, Figure 8 displays the Pm joint histograms of liquid water content LWC as log 10 LWC (in BLWC, where LWC is in units of g m −3 ) versus the median raindrop diameter as log 10 D 0 (in BD 0 , where D 0 is in units of mm). These figures also include the convectivestratiform rainfall separator lines: log 10 N w = 1.6D 0 + 6.3 (taken from Bringi et al. [39]) is in green, log 10 N w = 3.85 is shown with red dashed lines, and log 10 LWC = 4.0D 0 − 0.9 is shown with gray dashed lines; the latter two were taken from Thompson et al. [40]. The colored/colored and dashed contours indicate the PARS/2DVD datasets.
All of the observations of N w -D 0 for Lpm at the three sites were below the segregation line that was taken from Bringi et al. [39] (Figure 6). They would thus be categorized as stratiform, even though the radar observations that we examined showed that this was likely precipitation formed by shallow clouds and drizzle. Considering the convectivestratiform segregation criteria from Thompson et al. [40], most of the Lpm observations would fall into the stratiform category; however, a minor fraction of the N w -D 0 observations above this segregation line would be classified as convective. Concerning the other sites, COR presented more variability in log 10 N w and a higher frequency of high values of log 10 N w around D 0 = 0.40 mm. The two disdrometers at COR and SGP showed good agreement, except for their discrepancies with the 2DVD in a fraction of the observations, which lower values of log 10 N w of around D 0 = 1-2 mm.    Figure 7 shows the co-variability of N w and D 0 for Pm. Most of these observations at the three sites were below the line from Bringi et al. [39]. However, each site showed a general inverse relationship between log 10 N w and D 0 , as shown by previous studies and as expected given the sites' locations in regions containing substantial amounts of deep convective precipitation [39][40][41]115]. The regions of the highest observed probability of N w and D 0 were close to each other at the SGP and MAN sites-near log 10 N w = 3.50 and D 0 = 1.10 mm-but the COR site peaked near log 10 N w = 4.25 and D 0 = 0.75 mm. Similarly to the results presented in the subsections above for Pm, the values of D 0 among the sites occupied consonant ranges, but were less consistent for N w . The primary difference among the sites stood out: The large variability of N w at COR extended to the observations in the N w -D 0 space, with frequencies of N w observations that were above 10 5 mm −1 m −3 in both the PARS and 2DVD distributions. Again, the two disdrometers at the COR and SGP sites presented good agreement, except for the 2DVD discrepancies, which included a minor fraction of the observations with medium values of log 10 N w that were around D 0 = 2-4 mm above the line from Bringi et al. [39].
In terms of the relationship between LWC and D 0 for Pm (Figure 8 and a singlevariable analysis that is not shown), the midlatitude sites had similar discrepancies for both the PARS and 2DVD instruments. The segregation line from Thompson et al. [40] divided the observations into two regions. Furthermore, the distribution of observations for MAN extended to higher values of both LWC and D 0 , which was also noted in tropical sites (Tokay and Short [116], Yuter and Houze [117], Thompson et al. [40], Dolan et al. [38]). However, this relationship did not appear as clearly as it did in the multi-site DSD composites shown by Dolan et al. [38]. This possibly indicated the sometimes continental nature of the convection observed in the Amazon Basin despite its moniker as the "Green Ocean", which has yielded a reputation of having maritime-like convective intensity characteristics [118].

Lpm Observations during CACTI
To visualize the temporal patterns of Lpm versus Pm at the COR site as a function of the diurnal cycle, Figure 9 shows the occurrence of precipitation during the period of observation with PARS as a function of the day versus the local time of day. The time from the early afternoon to the overnight hours was when the precipitation mode was prevalent, consistently with an afternoon-midnight maximum in the continental diurnal cycle [119,120]. However, Lpm tended to occur in several episodes that lasted several hours throughout the campaign. These Lpm episodes did not seem to have a strong likelihood of occurring at a particular time of day; however, they were more likely to occur during events when heavier precipitation also occurred. Because the synoptic forcing in this region strongly modulated heavy precipitation, it was suggested that the flow associated with synoptic systems-coupled with the orographic forcing-plays a role in generating Lpm precipitation, which would more likely tend to occur during the morning [62]. Table 2 shows the top 10 days with the highest frequency of Lpm observations throughout the COR campaign according to PARS. Considering the period from December 2018 to February 2019, four of these ten events occurred during the summer season. Interestingly, several days with high numbers of Lpm minutes occurred early in the CACTI campaign in late October (23)(24)(25) October; all appear in Table 2).
To explore the types of precipitating systems that contributed to the relatively high observed normalized size intercept values at the COR site, we present additional observations of the two days with the highest frequencies of Lpm occurrence in Table 2. Figures  10 and 11 provide ARM Ka-band Zenith-pointing Radar (KAZR) scans collected over the COR site to show the vertical structure of the radar echoes, as well as the corresponding DSD parameters observed by the PARS disdrometer. Figure 10 shows the case from 22 October 2018, where there were shallow precipitating clouds that were mostly below 2000 m above the site throughout much of the day, and were interrupted by deep convection that occurred between 06 and 12 UTC (03-09 local time). During these intense convective events, R exceeded 30 mm h −1 , D 0 exceeded 2 mm, and log 10 N w decreased to values of less than 3, which were consistent with convective precipitation [38]. Outside of the times with heavier precipitation, the rainfall was characterized by the shallow precipitation noted above, and much of it was classified as the Lpm. There were some weak convective generating cells that appeared to be present in these warm clouds that contained drizzle (also in the Doppler velocity, which is not shown). The values of log 10 N w in m −3 mm −1 exceeded 5 throughout much of the event, with D 0 hovering around 0.5 mm and the rain rate remaining below 0.5 mm h −1 . It is interesting to note that this precipitation did not have any connection with the echoes aloft. The KAZR had a minimum detectable reflectivity of better than −35 dBZ at 1 km. For these cases, the KZAR could not detect any of the falling precipitation particles that acted in the seeder-feeder precipitation growth process for the Lpm, as observed in the precipitation mechanisms in other mountain ranges, such as the southern Appalachian Mountains in the USA [62].
For the case that contained the second-highest number of daily Lpm-classified periods, Figure 11 presents a case where a shallow Lpm again exists between two deep convective core events. The first convective event occurred overnight near 0500 UTC or 0100 local time, with anvil clouds existing above 6 km for several hours and rain rates that were <2 mm h −1 , including some periods of Lpm near-surface precipitation. The next day, another afternoon convective event occurred near 1900 UTC or 1700 local time. Between these events, clouds, drizzle, and light precipitation with high log 10 N w and low D 0 values occurred for more than 12 h. These clouds appeared to be shallower and less convective in the reflectivity and Doppler velocity observations than the clouds of the 22 October 2018 case. Again, the lack of a meteorological echo above the shallow cloud layer supported the lack of a seeder-feeder precipitation mechanism. An investigation of other cases and those presented here seemed to suggest that the microphysical generation mechanism for these events is shallow orographic upslope forcing. These particular DSD structures alongside their radar-determined vertical structures help support the COR observations' certain uniqueness, especially regarding the shallow vertical structures and high N w values seen in both the Lpm and Pm rainfall modes in these cases. Rain rate (mm hr -1 ) R Figure 11. As in Figure 10, but for the period 00 UTC 23 Feb-00 UTC 24 February 2019.

Discussion
The results presented in Section 3 show the evaluation of a compilation of disdrometer datasets in order to compare DSDs and the DSD parameters among three sites in the Americas. Table 1 summarizes the log 10 N w peaks and most frequent values in the light precipitation mode (Lpm) and the precipitation mode (Pm), as described in Section 2.
Complementing the analysis performed earlier for the three sites ( Figure 6), the Lpm DSD parameters at the COR site included peak values of log 10 N w of around 4.15 and 4.80 for PARS and at 4.11 and 5.15 for the 2DVD. The SPG Lpm distributions had its most frequent log 10 N w values at 3.70 and 4.40 for PARS and 3.40 and 4.55 for the 2DVD. The MAN Lpm distribution had its most frequent log 10 N w values at 3.60 and 4.20.
More specifically, for Lpm (Figure 6), the COR observations exhibited similarly high values of log 10 N w compared to the group that was categorized as having weak convection in Dolan et al. [38] (4.71 for the midlatitudes). However, the relatively smaller mean raindrop sizes observed (D 0 ∼ 0.45-0.55 mm for PARS and 2DVD) and the almost low rain rate and liquid water content placed some of the Lpm observations in the group that represented vapor deposition in Dolan et al. [38] (D 0 ∼ 0.68 mm for the midlatitudes). Our investigation of these periods did not show the involvement of ice processes in the large majority of the Lpm cases.
The COR site also presented higher numbers of rainy minutes for all precipitation modes than those of the MAN site in the PARS measurements. However, these rainy minutes did not comprise light precipitation, which the disdrometers could miss because of their inclination to underestimate the DSD for tiny/small drops, including fog and drizzle [44,104]. Avoiding this underestimation and characterizing the full DSD spectrum would also require measurements with higher-resolution instruments, such as the CACTI and GoAmazon G-1 aircraft imaging probes or other optical sensors that were used in previous studies [44,104,121].
Further, by using meteorological data and model outputs for the total observation period of GoAmazon (from 1 January 2014 to 31 December 2015) at the MAN site, Marengo et al. [80] showed that this campaign took place during a relatively dry period. Nevertheless, despite the surprisingly high precipitation frequency observed in Villa Yacanto during CACTI, it is left to future work to climatologically determine if the COR site or the MAN site has a higher precipitation frequency.

Summary and Conclusions
This study presents a comparison of the variabilities of raindrop size distribution parameters among three deep convective regions in the Americas: the US Southern Great Plains and west-central Argentina in the midlatitudes and the central Amazon in the tropics. Considering the lack of drop size distribution studies in South America, data from Parsivel disdrometers (and 2DVD disdrometers, where available) were analyzed here to characterize the raindrop size spectra in these climatically and hydrologically important regions, which were the focus of intensive field campaign operations. In order to analyze the variability of the DSD parameters at the three sites, the probability density functions (pdfs) of the rain rate R, mass-weighted mean diameter D m , and normalized droplet concentration N w were presented. The results were segregated into a precipitation mode (Pm, R > 0.5 mm h −1 ) and a light precipitation mode (Lpm, R < 0.5 mm h −1 ) to elucidate the differences in the drop size distribution parameters and the driving physical precipitation processes.
The primary results of this paper are as follows: • The comparison of the DSDs in terms of pdfs showed that the rain-rate distributions were similar between the midlatitude COR and SGP sites and were less frequent than heavy rains at the tropical MAN site. At the COR site, more frequent precipitation was found, with a smaller median mass diameter and a broader range of normalized droplet concentration. • The two-dimensional histograms of the normalized droplet concentration N w revealed that COR exhibited a more considerable variability in the N w values for both the Pm and Lpm rainfall modes in comparison to SGP and MAN, and it had a higher frequency of high concentrations. These high concentrations of particle size distributions extended into the analysis of the N w -D 0 parameter space, where the high concentration numbers observed were associated with small D 0 values. However, the co-variability of LWC and D 0 appeared to be quite similar for the sites examined in the midlatitudes (COR and SGP), contrary to the co-variability at MAN, which appeared to be extended towards higher values of D 0 and LWC, which is a characteristic of tropical rainfall that was observed in previous studies and that is possibly related to enhanced collision-coalescence growth processes there [38,40,116,117]. • In examining cases with high N w and low D 0 values, these appeared to be associated with drizzle and light rain originating from shallow clouds. These warm clouds may be associated with periods of orographic upslope flow, but are not due to seederfeeder processes, as found in prior studies of light precipitation in complex terrain [62]. Additionally, while some studies have noted that warm clouds may occupy this portion of the N w -D 0 parameter space [62], which resembles both the weak convection and vapor deposition features from Dolan et al. [38] in the N w -D 0 phase space (Section 4), this region occupies the stratiform region according to disdrometerbased convective-stratiform separation techniques; it is recommended to use these with caution in orographically influenced environments, such as that of the COR site.
These unique precipitation characteristics at the COR site and their relationship with the thermodynamic and kinematic environment are likely impacted by the site's location in flows that are affected by the complex terrain, and they will be examined further in a future study. The results presented herein display the novel observations of precipitation processes that make the COR site potentially unique relative to previously studied orographically influenced sites. For future research, additional analysis of aircraft-based imaging probes, lidar measurements [122], soundings [123], the KAZR Doppler [108], and C- [124] and Kascanning [125] precipitation and cloud radar measurements will better characterize the microphysics of the rain processes in Lpm at the COR site, may also be considered.

Abbreviations
The following abbreviations are used in this manuscript: The terminal velocity of falling raindrops v Lhermitte (in m s −1 ), which was calculated following Lhermitte (1988 [126]) and was considered in the ARM Parsivel2 Handbook [92], is shown in the equation below. The mass-weighted mean diameter or mass spectrum mean diameter D m (in mm) corresponds to the first moment of the mass spectrum, as indicated by Williams et al. [25]. According to Williams et al. [25], the mass standard deviation σ m (in mm) is the square root of the second moment of the mass spectrum or the mass spectrum variance σ 2 m (in mm 2 ). The normalized intercept parameter N w (in m −3 mm −1 ), which is normalized with respect to D m , is proportional to the density of water ρ w and the liquid water content LWC [25,32,105]. The liquid water content LWC (in g m −3 ) for a gamma-shaped DSD, where ρ w is the density of water, is given by the equation below, which was indicated by Williams et al. [25]. As documented by Williams (2011) [105], the median raindrop diameter D 0 (in mm) represents the diameter that equally divides the total liquid water content into two equal portions and is given by the analytical solution of the integral equation below.