## 1. Background and motivation

The majority of the world’s rainfall occurs in the tropics, particularly over the warm pool spanning the equatorial Indian and west Pacific Oceans. Attributing rainfall to certain cloud types (i.e., shallow, congestus, or deep convection, stratiform rain, or a mixture thereof) is of critical importance for diagnosing the resulting vertical distribution of latent heating (Johnson et al. 1999; Schumacher et al. 2004), which can drive convergence and vertical motion (Matsuno 1966; Yanai et al. 1973; Zhang and Hagos 2009). Toward this end, identifying dominant modes of tropical, oceanic rain variability is important because this is still a major source of uncertainty in ground-based, shipborne, and spaceborne radar rainfall estimation (Munchak et al. 2012). For example, many studies have thoroughly detailed why and how cloud microphysical processes and vertical motions differ during convective (C) and stratiform (S) rain, which lead to characteristically different drop size distributions (DSDs) in each rain type (Williams et al. 1995; Tokay and Short 1996; Houze 1997; Tokay et al. 1999; Atlas et al. 1999, 2000; Bringi et al. 2003, hereafter BR03; Houze 2004; Bringi et al. 2009, hereafter BR09; Thurai et al. 2010, hereafter TH10; Schumacher et al. 2015; Zhu et al. 2015). There is also a region where (or time period when) active convective updrafts might be decaying into stratiform precipitation (Biggerstaff and Houze 1993; Braun and Houze 1994; Williams et al. 1995; Uijlenhoet et al. 2003; Sharma et al. 2009). These resulting DSDs lie between convective and stratiform. Additionally, marked differences exist between continental and maritime DSDs, both of which produce convective and stratiform rain of varying intensities, efficiencies, and integral rain parameters, based on differences in updraft intensity and subcloud processes (Twomey 1977; Ulbrich and Atlas 1978; Zipser and LeMone 1980; Zipser 2003; Ulbrich and Atlas 2007; Minor et al. 2011; Wilson et al. 2013; Kumjian and Prat 2014).

The primary goal of this study is to investigate DSDs of equatorial, oceanic rainfall, which are less often studied because of their remote location, despite their contribution to the global hydrologic cycle. To do so, we take advantage of two long-term 2D video disdrometer (2DVD) datasets over the equatorial Indian and west Pacific Oceans, at Gan (3.5-month record) and Manus (18-month record) Islands, respectively (Fig. 1). BR03 identified maritime and continental convective DSD “clusters,” as well as a linear variation of stratiform rain in the normalized gamma number concentration and median volume diameter [*N*_{w}(*D*_{0})] plane, which can be measured by disdrometers or derived from dual-polarization radar data. Their work involved DSD quantities from selected rain events in Florida, coastal Australia, Austria, Puerto Rico, Brazil, Kwajalein, Colorado, Papua New Guinea, and the South China Sea, as well as a mean of many west Pacific warm pool events. A separation line between convective and stratiform rain was determined by BR09 using the Darwin, Australia, datasets. DSDs were considered convective (stratiform) if *N*_{w} was greater (less) than a naturally emerging separator line: log_{10}*D*_{0} + 6.3. This partitioning method was found to be consistent with data from selected rain events in BR03 and with more data from Darwin by TH10 and Penide et al. (2013). TH10 also found agreement between the DSD-based *N*_{w}(*D*_{0}) C/S partitioning method and the widely used Steiner et al. (1995) radar reflectivity-based partitioning algorithm using data from Darwin. This radar method identifies convective cores based on a reflectivity threshold and whether localized regions of reflectivity stand out relative to the smoothed, background reflectivity field, which can be modified for particular regions and radar data resolutions (Yuter and Houze 1997, 1998).

The classification and rain attribution of shallow, weak cumulus convection are critical, because this cloud type is ubiquitous across the warm pool (Johnson et al. 1999; Rauber et al. 2007; Jakob and Schumacher 2008; Barnes and Houze 2013), where the atmosphere is conditionally unstable below the equivalent potential temperature *θ*_{e} minimum (Lilly 1960). However, this relatively shallow and weak oceanic convection is not dominant in coastal or continental boundary layers, which likely explains its underrepresentation in BR03, BR09, and TH10, which consist of data mostly from midlatitude and subtropical land locations near oceans. Shallow, maritime, tropical convective clouds moisten the lower troposphere (Nitta and Esbensen 1974; Lin and Johnson 1996; Johnson and Lin 1997; Johnson et al. 1999) and may play an important role in Madden–Julian oscillation (MJO) evolution (Kemball-Cook and Weare 2001; Kiladis et al. 2005; Benedict and Randall 2007; Seo et al. 2014; Ruppert and Johnson 2015; Barnes et al. 2015). However, they are difficult to detect and track because of limited vertical, horizontal, and temporal resolution and the minimum detectable signals of many remote sensing platforms (Schumacher and Houze 2003; Jakob and Schumacher 2008; Funk and Schumacher 2013; Ruppert and Johnson 2015). The “stretched building block” hypothesis by Mapes et al. (2006) explains how stratiform clouds and all three major convective cloud types (shallow, congestus, and deep) are usually present over relatively large areas of the tropics, but some become more dominant than others during certain phases of the MJO. This is also consistent with recent MJO observational studies in the equatorial Indian and west Pacific Oceans (Riley et al. 2011; Barnes and Houze 2013; Zuluaga and Houze 2013; Powell and Houze 2013; Rowe and Houze 2014; Xu and Rutledge 2014, 2015; Barnes et al. 2015).

Current DSD partitioning methods have not comprehensively considered tropical, oceanic convection. In fact, close inspection of Okinawa warm, shallow, convection DSD from TH10, Darwin maritime convection data from BR03, Darwin premonsoon-season data from BR09, and Darwin wet-season data from Bringi and Chandrasekar (2001, hereafter BC01) reveals that weak, shallow, maritime convection does not uniformly lie on the convective side of the subtropical, continental BR09 separator line. In contrast to continental convection, these maritime convective storms are characteristic of warm rain processes [i.e., condensation and collision–coalescence at temperatures > 0°C (Pruppacher and Klett 1997; Cotton et al. 2011)]. These processes result in high *N*_{w} but relatively low *D*_{0}. The inclusion of continental convection (~hailstorms) in BR09 caused their separator line to be sloped downward toward low *N*_{w} and large *D*_{0} (BR03). These more intense continental storms containing vigorous mixed-phase processes and much evaporation are common over tropical land but rare over tropical oceans (Kumjian and Prat 2014; Rowe and Houze 2014). Therefore, the remote oceanic, tropical DSD of interest in the current study might warrant a different C/S separation method than the subtropical, continental BR09 line. The current study’s primary goal is to analyze the C/S DSD variability and radar characteristics of a long-term tropical, equatorial, maritime dataset not available in previous studies.

The secondary goal of this study is to utilize the DSD measurements to form single-polarization radar-based rainfall estimation equations for these oceanic, tropical rain regimes. Many power-law equations have been developed to relate radar reflectivity [*Z*_{h} (dB*Z*) or *z* (mm^{6} m^{−3})] to rainfall rate *R* (mm h^{−1}) for characteristic modes of DSD variability in particular regions based on the cloud microphysical processes encountered there (Battan 1973; Ulbrich and Atlas 1978; Atlas et al. 1984; Ulbrich and Atlas 1998; Steiner et al. 2004; Ryzhkov et al. 2005). The current study intends to build upon many previous rainfall-estimation-focused studies that used shorter-time-record DSD data from various instruments in the equatorial Atlantic Ocean (Cunning and Sax 1977; Austin and Geotis 1979; Hudlow 1979), the west Pacific Ocean (Tokay and Short 1996; Yuter and Houze 1997; Atlas et al. 1999; Tokay et al. 1999; Atlas et al. 2000; Atlas and Ulbrich 2000; Ulbrich and Atlas 2002), and other coastal, subtropical locations (Keenan et al. 2001; BR03, BR09, Bringi et al. 2011, 2012; TH10). The equatorial Indian Ocean has been relatively less studied.

Following this introduction, Section 2 describes the measurement systems and data processing involved in this study. Section 3 compares distributions of DSD *R*, *z*, number concentration, drop diameters, and liquid water content from the two equatorial (Indian and west Pacific) sites, which are shown to be similar. Radar data are used in section 4 to investigate the storm characteristics associated with each mode of DSD variability observed at Gan Island. Section 5 elaborates on a physically based separation found between convective and stratiform precipitation using DSD number concentration. We also quantify the sensitivity of C/S rain statistics to this separation method. New *R*(*z*) equations for all, convective, and stratiform rain are presented for the equatorial Indian and west Pacific Ocean sites. The potential sensitivity of rainfall statistics to different *R*(*z*) equations is discussed in section 6. Conclusions are found in section 7.

## 2. Data and methods

### a. Domain and radar data

Figure 1 shows Gan and Manus Islands, as well as other locations of tropical, oceanic DSD research, such as Kwajalein and the domains of the 1974 Global Atmospheric Research Program (GARP) Atmospheric Tropical Experiment (GATE; Hudlow 1979), the 1992–93 Tropical Ocean Global Atmosphere Coupled Atmosphere–Ocean Response Experiment (TOGA-COARE; Webster and Lukas 1992), and the Mirai Indian Ocean Cruise for the Study of MJO-Convective Onset (MISMO; Yoneyama et al. 2008). The Manus Island 2DVD has been operational since December 2011 (the data record examined herein is from 2 December 2011 to 21 April 2013; no continuous radar data are available at Manus). An identical 2DVD was operating on Gan Island 8 km away (141° radial) from the NCAR S-band dual-polarization (S-Pol) radar (Addu Atoll) during the 2011–12 Dynamics of the MJO field campaign (DYNAMO; Fig. 1; Yoneyama et al. 2013; Johnson and Ciesielski 2013). The Gan 2DVD and S-Pol radar operated simultaneously from 1 October 2011 to 16 January 2012; the Gan 2DVD record continues to 2 February 2012. Island conditions are considered to be similar to the surrounding ocean (Johnson and Ciesielski 2013).

Zuluaga and Houze (2013) describe the S-Pol radar deployment during DYNAMO and subsequent postprocessing. S-Pol vertical cross section, or range height indicator (RHI), scans were collected directly over the Gan Island disdrometer every 15 min. Low-level plan position indicator (PPI) scans also captured the horizontal distribution of precipitation at the same time as the vertical cross sections. Radar scans were manually investigated. We use the horizontal reflectivity *Z*_{h} (dB*Z*), differential reflectivity *Z*_{dr} (positive for oblate, negative for prolate, and near zero for spherical or tumbling hydrometeors), and the correlation coefficient *ρ*_{hυ} [a scalar quantity, decreases from unity because of the presence of non-Rayleigh scatterers and as hydrometeors in the same radar gate become less similar, either in phase, shape, and/or orientation; see Straka et al. (2000), BC01, and Kumjian (2013)]. Radar brightband identification caused by melting snow is much more reliable with dual-polarization radar variables than with radar reflectivity alone (e.g., Brandes and Ikeda 2004; Thompson et al. 2014). The radar bright band is an indicator of stratiform rain type.

Unfortunately, we cannot analyze radar statistics of convective, stratiform, or total rainfall occurrence/accumulation over the disdrometer from PPI, RHI, or gridded horizontal reflectivity scans for a variety of reasons. The radar was blocked to the west, rendering echoes at low levels in this direction untrustworthy. The radar was also prohibitively close to the disdrometer, which placed the 2DVD within the “cone of silence” of gridded PPI radar reflectivity fields in the lower 3 km. Additionally, RHIs were not conducted south or west of the disdrometer location and were contaminated by ground clutter surrounding the disdrometer below 1 km. Therefore, horizontal reflectivity gradients and echo evolution cannot be assessed with either the PPI or RHI radar data within a 10-km radius surrounding the 2DVD, as specified by the Steiner et al. (1995) and Yuter and Houze (1998) radar-based C/S partitioning methods. Select RHIs were manually investigated over the disdrometer, but quantitative rainfall estimation above the 2DVD for all RHIs could not be conducted for statistical comparison with the 2DVD. Last, there is no established way to automatically classify C/S echoes with RHI or PPI polar coordinate radar data.

### b. 2DVD data

Schönhuber et al. (2008) described the third-generation 2DVD in detail. The Department of Energy’s Atmospheric Radiation Measurement Program (ARM) 2DVDs at Gan and Manus Islands provide 1-min drop count and drop number density^{1} measurements across fifty 0.2-mm-wide-diameter bins ranging from 0.0–0.2 to 9.8–10.0 mm (http://www.archive.arm.gov/discovery/). Only 1-min DSD data with at least 100 total drops and *R* > 0.05 mm h^{−1} during at least a 3-min consecutive raining period were analyzed. These thresholds prevent DSDs composed of only a few small drops from skewing the analysis (P. L. Smith and V. N. Bringi 2012, personal communication) and are consistent with our intent to focus on raining DSD. The 18-month Manus Island time series provided 27 179 one-minute raining DSD data points, while Gan Island had 4446 points over 3.5 months. No smoothing or averaging was performed. Besides the spatial sampling issues of a 100 cm^{2} area on the ground and some missed data during high winds, the chief 2DVD instrument error is the underestimation of small drops, so we ignored data from the first size bin centered on 0.1 mm, as suggested by Tokay et al. (2013). The 2DVDs directly sense integral^{2} rain parameters, such as liquid water content LWC (g m^{−3}) and rain rate *R* (mm h^{−1}), the latter equivalent to the flux of water across the catchment area (100 cm^{2}) given each drop’s measured fall speed. In contrast, Joss–Waldvogel impact disdrometers (JWDs) require drop count correction and calibration algorithms (Tokay et al. 2001, 2005, 2013), used to have worse small-drop detection capability, and must rely on an empirical fall speed relation based on drop diameter to calculate *R* and LWC (Gunn and Kinzer 1949; Atlas et al. 1973), which introduces additional error, as described by Salles and Creutin (2003).

*D*

_{0}(mm)]. DSDs naturally exhibit a gamma-shaped distribution (Ulbrich 1983), which can be normalized so DSDs of varying LWC can be easily compared (Willis 1984). For this reason, Lee et al. (2004) stated that normalized gamma DSD methods may produce more evident distinction between C/S rain types. Thurai et al. (2014) detailed the “

*μ*search” method used in the current study to determine the normalized gamma DSD generalized number concentration

^{3}or intercept parameter

*N*

_{w}(mm

^{−1}m

^{−3}) and shape parameter

*μ*, from which

*D*

_{0}is estimated. These parameters are related by

*ρ*

_{w}is the density of water, 1 g cm

^{−3}(BC01). This

*μ*-search technique is more accurate than the often-used method of moments because it takes more DSD information into account and iteratively seeks the gamma parameters that most likely describe the distribution of interest through minimization of cost functions (Smith and Kliche 2005; Kliche et al. 2008). For simplicity, log

_{10}

*N*

_{w}is analyzed in the current study as in BR03.

### c. Simulated radar variables

Surface disdrometer DSD data can be integrated to determine how a radar would sample that volume of rain and to calibrate radar-based rainfall estimates (Waterman 1971; Mishchenko et al. 1996). It is necessary to compute radar reflectivity *Z*_{h} [(dB*Z*) or more often the linear version *z* (mm^{6} m^{−3}) because of its larger dynamic range] based on theoretical, electromagnetic scattering calculations from the raw DSD number density data rather than using the simplified *z* ~ *D*^{6} calculation for spheres, which ignores the effects of drop oblateness and fall behavior. Radar reflectivity was simulated assuming rain drops were liquid, had a zero mean canting angle with a standard deviation about the mean up to 7.5° (Huang et al. 2008), and followed the Thurai et al. (2007) drop shape model. Drops were considered to be 20°C and viewed at a nearly horizontal (1°) incident angle at S band (11 cm; e.g., S-Pol). Since *Z*_{h} should be independent of wavelength for Rayleigh scatterers, S-band *R*(*z*) equations can be applied to C- and X-band data. We use orthogonal linear regression to derive all power-law equations, including *R*(*z*), because it minimizes error in both the *R* and *z* directions perpendicular to the best-fit line, so *R*(*z*) and *z*(*R*) are equivalent.

## 3. Drop size distribution observations

To investigate DSD variability at Gan and Manus Islands, *D*_{MAX}, *D*_{0}, log_{10}*N*_{w}, and LWC histograms normalized by the length of each dataset are shown in Fig. 2. Table 1 shows that the Gan and Manus Island datasets exhibit similar variances, means, standard deviations, minima, maxima, and 5th and 95th percentiles of *D*_{MAX}, *D*_{0}, LWC, and log_{10}*N*_{w} (Table 1). Most *D*_{MAX} values at both locations are between 1.0 and 3.6 mm. The LWC values are near ~0.03–0.1 g m^{−3}, but some values exceed 5 g m^{−3}, indicative of strong cumulonimbus clouds (Cotton et al. 2011).The *D*_{0} values are small (0.8–1 mm), but large *D*_{0} values >1.6 mm are observed. Potentially related to the issue of small drop detection by older instruments, many previous tropical oceanic DSD studies except Bringi et al. (2012) list slightly higher mean *D*_{0} (Table 2). The LWC, *D*_{MAX}, and *D*_{0} are slightly higher at Manus compared to Gan Island, with slightly lower log_{10}*N*_{w}, which is also evident in Fig. 2. Despite these minimal differences and being separated by the Maritime Continent, DSD distributions at Manus and Gan Islands still appear very similar, suggesting that the cloud microphysical processes in these two regions are analogous or nearly equivalent. Many studies have shown similar cloud population intensity, morphology, and radar echo evolution over each tropical ocean basin associated with the ITCZ and MJO (Short et al. 1997; LeMone et al. 1998; DeMott and Rutledge 1998a,b; Rickenbach and Rutledge 1998; Zuluaga and Houze 2013; Barnes and Houze 2013; Xu and Rutledge 2014, 2015; Guy and Jorgensen 2014; Rowe and Houze 2014).

Histograms normalized by record length for Manus and Gan 2DVD DSD (a) max diameter *D*_{MAX} (mm), (b) median diameter *D*_{0} (mm), (c) number concentration log_{10}*N*_{w} (unitless), and (d) liquid water content LWC (g m^{−3}, binned on a log_{10} scale).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Histograms normalized by record length for Manus and Gan 2DVD DSD (a) max diameter *D*_{MAX} (mm), (b) median diameter *D*_{0} (mm), (c) number concentration log_{10}*N*_{w} (unitless), and (d) liquid water content LWC (g m^{−3}, binned on a log_{10} scale).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Histograms normalized by record length for Manus and Gan 2DVD DSD (a) max diameter *D*_{MAX} (mm), (b) median diameter *D*_{0} (mm), (c) number concentration log_{10}*N*_{w} (unitless), and (d) liquid water content LWC (g m^{−3}, binned on a log_{10} scale).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Variance (var), mean, standard deviation, min, max, and 5th and 95th percentiles of integral rain parameters at Manus (27 142 points) and Gan (4446 points) Islands: DSD max diameter *D*_{MAX} (mm); median diameter *D*_{0} (mm); liquid water content LWC (g m^{−3}); number concentration log_{10}*N*_{w} (unitless).

Mean values of median diameter *D*_{0} (mm) and number concentration log_{10}*N*_{w} (unitless) from previous studies of all, convective, and stratiform rain in tropical, maritime locations.

The mean log_{10}*N*_{w} for both sites is about 3.7 (Table 1 and Fig. 2), which is close to the Marshall and Palmer (1948) exponential DSD concentration, log_{10}(8000) m^{−3} mm^{−1} = 3.9, as well as to the mean values listed in Table 2 found by BC01, Illingworth and Blackman (2002), TH10, Islam et al. (2012), and Penide et al. (2013). The mean log_{10}*N*_{w} lies between bimodal distribution peaks at about 3.25 and 4.1, which are nearly one standard deviation (*σ*) from the mean and almost 2*σ* from each other. These bimodal log_{10}*N*_{w} peaks correspond to an order-of-magnitude difference in number concentration (*N*_{w}). Bimodal log_{10}*N*_{w} probability distribution function (PDF) peaks at other maritime locations were also found by Ulbrich and Atlas (2007), BR09, TH10, and Bringi et al. (2012) corresponding to maritime stratiform and convective populations (Table 2). Tokay and Short (1996) and Testud et al. (2001) also documented two C/S modes with higher number concentration, LWC, and DSD slope (*λ* for exponential DSD) for a given rain rate in convection compared to stratiform. This reflects the fact that stratiform rain has been affected by aggregation above and in the melting layer, which shifts mass to larger size bins, reduces number concentration, and also flattens the DSD slope (Lo and Passarelli 1982). In accordance with these previous studies, we suggest that a physically based distinction between convective and stratiform rain produced the log_{10}*N*_{w} bimodality observed in Fig. 2 for Gan and Manus Islands.

BR03 and BR09 plotted log_{10}*N*_{w} against *D*_{0} to distinguish different modes of raining DSD variability. They found a sloped separator line at log_{10}*D*_{0} + 6.3, where convective storms existed to the right of (above) the separator line. They considered mostly strong coastal tropical, coastal subtropical, and continental midlatitude convection. Stratiform rain was nearly always situated to the left of (below) their separation line, with decaying convection, or convection transitioning into stratiform rain, extending into the high log_{10}*N*_{w}, low *D*_{0} quadrant. TH10 investigated maritime convection and stratiform rain and found them separated by the same BR09 line, but with variations in log_{10}*N*_{w} playing a significant role. They also presented weak, maritime convective DSD sample means of several thousand data points from Okinawa, Japan, that were just below the BR09 line at high log_{10}*N*_{w} but relatively low *D*_{0}, suggestive of maritime, warm rain processes.

Figure 3 shows log_{10}*N*_{w} and *D*_{0} smoothed 2D histograms for Gan and Manus Islands. The relatively sharp cutoff of data in the lowest *N*_{w}(*D*_{0}) quadrant is due to necessary rain rate and total drop number data quality thresholds. The Manus samples are more numerous and more evenly spread but distributed in similar spatial orientations compared to the Gan samples, as suggested by the histograms of individual parameters in Fig. 2. A large proportion of data exists near log_{10}*N*_{w} = 3.2 and *D*_{0} = 1.0 mm (Gan) and 0.9 mm (Manus), corresponding to stratiform rain in BR03, BR09, and TH10. A secondary peak occurs near log_{10}*N*_{w} = 4.1 and *D*_{0} = 0.7–1.1 mm, similar to the shallow, weak, convective Okinawa data from TH10. These two frequent modes of variability appear to be separated by a nearly horizontally oriented area of lower frequency of occurrence somewhere between log_{10}*N*_{w} = 3.7 and 3.9. Figure 3 shows that a very small fraction of the Manus and Gan Island data points would be classified as convective by the BR09 separator line, which does not seem to fall between any natural breaks in this tropical, maritime *N*_{w}(*D*_{0}) distribution. Although Barnes and Houze (2014) and Rowe and Houze (2014) show radar observations of graupel and small hail aloft in storms during DYNAMO in the central Indian Ocean, which result in high *D*_{0} and low log_{10}*N*_{w}, these vigorous convective processes are not frequent over the warm pool and certainly not to the same magnitude as the midlatitude and subtropical continental convection considered when forming the BR09 separation line. Instead, a new convective/stratiform separator line at log_{10}

Gan and Manus Island *N*_{w}(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the original subtropical, continental BR09 log_{10}*D*_{0} + 6.3 and updated tropical, oceanic C/S log_{10}*N*_{w} = 3.85 separation lines. Gan (Manus) Island: 130 (100) bins in each direction; 13 (8) bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island *N*_{w}(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the original subtropical, continental BR09 log_{10}*D*_{0} + 6.3 and updated tropical, oceanic C/S log_{10}*N*_{w} = 3.85 separation lines. Gan (Manus) Island: 130 (100) bins in each direction; 13 (8) bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island *N*_{w}(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the original subtropical, continental BR09 log_{10}*D*_{0} + 6.3 and updated tropical, oceanic C/S log_{10}*N*_{w} = 3.85 separation lines. Gan (Manus) Island: 130 (100) bins in each direction; 13 (8) bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

It is worth pointing out that the log_{10}*D*_{0}) distributions for the Gan and Manus Islands also exhibit two modes of variability on either side of this separator line (Fig. 4), each oriented in the same direction of increasing LWC for increasing *D*_{0} when both variables are plotted on a logarithmic scale [illustrating the LWC ~ *N*_{w}(*D*_{0}), the LWC(*D*_{0}) distributions at each location also appear very spatially correlated, except that the Gan Island dataset has fewer total data points so that the contoured 2D histogram clusters are not as well organized as for Manus Island. The 2D histograms of LWC(*D*_{MAX}) also exhibit two modes of variability, similar to LWC(*D*_{0}).

Gan and Manus Island LWC(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the updated tropical, oceanic C/S rain LWC^{SEP} separation line, which is equivalent to log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island LWC(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the updated tropical, oceanic C/S rain LWC^{SEP} separation line, which is equivalent to log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island LWC(*D*_{0}) smoothed 2D histograms contoured by frequency of occurrence with the updated tropical, oceanic C/S rain LWC^{SEP} separation line, which is equivalent to log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Using Figs. 3 and 4 as references, the next section is devoted to 1) explaining why these two frequency peaks, in both the *N*_{w}(*D*_{0}) and LWC(*D*_{0}) spaces, actually correspond to stratiform and convective tropical, oceanic rain and 2) justifying the placement of the new log_{10}

## 4. Radar observations

The entire DYNAMO S-Pol RHI dataset was examined to find times when the radar indicated rain over the disdrometer and the disdrometer also recorded data. This resulted in 372 analyzed case studies of S-Pol vertical cross section radar scans with coincident Gan Island 2DVD data. Analyzing sequences of paired observations helped elucidate the evolution of DSD spectra with respect to the horizontal and vertical evolution of radar echoes above and around the disdrometer. These case studies reveal why a separation line at log_{10}*N*_{w}(*D*_{0}) and LWC(*D*_{0}) parameter spaces and, thus, the full intensity and organizational spectrum between stratiform and tropical, maritime convective rain. Note that the 0°C level was consistently between 4.5 and 5.1 km AGL (550–600 hPa) during these DYNAMO case studies. Residual ground clutter (identifiable by low *ρ*_{hυ} and negative/variable *Z*_{dr}) contaminates radar data near the disdrometer (varying from case to case depending on atmospheric refraction of the radar beam downward).

### a. Case 1: Strong, widespread convection

Figure 5 shows an example of widespread, deep convection. The S-Pol radar horizontal (PPI) and vertical (RHI) cross sections over the Gan disdrometer, 8 km away at 141° azimuth, show a large area of *Z*_{h} > 50 dB*Z* over the disdrometer and extending up to 5.5 km AGL. The differential reflectivity over the disdrometer is over 2 dB, indicating the presence of large, horizontally oriented raindrops (BC01). High *Z*_{dr} of this same magnitude and low *ρ*_{hυ} to 0.93 near 5 km AGL indicates some melting, but in a disrupted fashion because of strong convection. A horizontally elongated, stable, stratiform rain radar bright band is not evident. As this deep convection passed over the disdrometer, log_{10}*N*_{w} and *D*_{0} were both relatively high, between 4.3 and 4.6 and 1.4 and 1.7 mm, respectively. The LWC was correspondingly high, with values approaching 5 g m^{−3}, and rain rates were between 30 and 100 mm h^{−1}. The BR09 method would have classified this example as convection.

Case study 1 of widespread deep convection at 2130 UTC 23 Dec 2011 with S-Pol radar PPI and RHI of reflectivity *Z*_{h}, differential reflectivity *Z*_{dr}, and the correlation coefficient *ρ*_{hυ}. Range rings at 8 and 25 km; Gan Island 2DVD along the black arrow at 8-km range denoted by the caret on RHI in this direction. The *N*_{w}(*D*_{0}), LWC(*D*_{0}), and *R* time series are plotted throughout 2117–2130 UTC, where time increases as the colored markers go from blue to red. The log_{10}^{SEP} line are plotted to differentiate convection above and stratiform rain below.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 1 of widespread deep convection at 2130 UTC 23 Dec 2011 with S-Pol radar PPI and RHI of reflectivity *Z*_{h}, differential reflectivity *Z*_{dr}, and the correlation coefficient *ρ*_{hυ}. Range rings at 8 and 25 km; Gan Island 2DVD along the black arrow at 8-km range denoted by the caret on RHI in this direction. The *N*_{w}(*D*_{0}), LWC(*D*_{0}), and *R* time series are plotted throughout 2117–2130 UTC, where time increases as the colored markers go from blue to red. The log_{10}^{SEP} line are plotted to differentiate convection above and stratiform rain below.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 1 of widespread deep convection at 2130 UTC 23 Dec 2011 with S-Pol radar PPI and RHI of reflectivity *Z*_{h}, differential reflectivity *Z*_{dr}, and the correlation coefficient *ρ*_{hυ}. Range rings at 8 and 25 km; Gan Island 2DVD along the black arrow at 8-km range denoted by the caret on RHI in this direction. The *N*_{w}(*D*_{0}), LWC(*D*_{0}), and *R* time series are plotted throughout 2117–2130 UTC, where time increases as the colored markers go from blue to red. The log_{10}^{SEP} line are plotted to differentiate convection above and stratiform rain below.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### b. Case 2: Strong, isolated convection

Figure 6 shows another case of strong convection with near-surface reflectivity exceeding 45 dB*Z*, but associated with an isolated cell. The *Z*_{dr} is above 1 dB below 2 km, and *ρ*_{hυ} is above 0.99 throughout the entirety of the echo, meaning there is no established melting layer. The number concentration (log_{10}*N*_{w}) is slightly lower than the widespread deep convective case in Fig. 5, between 4.0 and 4.2. Since *N*_{w} is proportional to LWC by Eq. (1), it is not surprising that LWC for this case is also slightly lower, near 2–4 g m^{−3}, while rain rates were between 30 and 50 mm h^{−1}. However, the median drop diameters of these DSDs are slightly higher than case 1, exceeding 1.5 mm. Both the widespread and isolated strong convective cases are near the upper, right-hand edge of the *N*_{w}(*D*_{0}) and LWC(*D*_{0}) 2D histograms (Figs. 3 and 4). The BR09 method would have classified this example as convection.

Case study 2: as in Fig. 5, but for isolated strong convection at 2145 UTC 17 Dec 2011, with 2DVD data spanning 2137–2146 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 2: as in Fig. 5, but for isolated strong convection at 2145 UTC 17 Dec 2011, with 2DVD data spanning 2137–2146 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 2: as in Fig. 5, but for isolated strong convection at 2145 UTC 17 Dec 2011, with 2DVD data spanning 2137–2146 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### c. Case 3: Weak, widespread convection

Weaker convection was frequently observed according to DSD and radar observations. This type of weakly forced, weakly organized convection tended to decay rapidly. Figure 7 is an example of localized enhancements of reflectivity extending from the surface upward that, according to radar vertical cross sections, do not even reach the 0°C level (4.5–5.1 km AGL or 600–550 hPa throughout the field campaign). Therefore, these warm rain DSDs could not have been influenced by vapor deposition, aggregation, or melting. This case is thus convective in nature, driven by surface buoyancy. The *Z*_{dr} is near zero, and *ρ*_{hυ} is near unity throughout most of this shallow echo except for the leading edge at the beginning of the time series (storm propagated southeast over the 2DVD). For more than 45 min after this initial radar scan, the log_{10}*N*_{w} remained relatively high near 4.6–4.8, while *D*_{0} was near 1 mm, consistent with the lower radar reflectivities seen in this example compared to stronger convection. LWC was still near 0.5–1 g m^{−3} on the top side of the LWC^{SEP} line with rain rates between 5 and 15 mm h^{−1}. DSDs in both parameter spaces were indicative of belonging to the upper mode of each bimodal distribution shown in the previous section. These DSDs lie directly on the BR09 separation line (not shown).

Case study 3: as in Fig. 5, but for widespread, shallow convection at 0900 UTC 08 Dec 2011, with 2DVD data spanning 0903–0930 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 3: as in Fig. 5, but for widespread, shallow convection at 0900 UTC 08 Dec 2011, with 2DVD data spanning 0903–0930 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 3: as in Fig. 5, but for widespread, shallow convection at 0900 UTC 08 Dec 2011, with 2DVD data spanning 0903–0930 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### d. Case 4: Weaker, isolated convection

An example of even weaker, shallower convection in Fig. 8 shows the same high log_{10}*N*_{w} near 4.5 as the weak, widespread convection in case 3, but with *D*_{0} as low as 0.6 mm. The LWC is correspondingly lower between 0.1 and 0.5 g m^{−3}, with *R* between 1 and 5 mm h^{−1}. These radar echoes are also smaller in horizontal area. Radar reflectivity is mostly between 20 and 30 dB*Z*, with some localized areas above 35 dB*Z*. The vertical elongation of these echoes upward, but only to 4 km AGL, and the lack of any radar signatures of melting, aggregation, or ice aloft signifies that these echoes are convective in origin, driven by buoyancy within the moist marine boundary layer. The continental, subtropical BR09 separation would have classified these DSD as stratiform.

Case study 4: as in Fig. 5, but for shallow convection at 2115 UTC 14 Dec 2011, with 2DVD data spanning 2114–2122 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 4: as in Fig. 5, but for shallow convection at 2115 UTC 14 Dec 2011, with 2DVD data spanning 2114–2122 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 4: as in Fig. 5, but for shallow convection at 2115 UTC 14 Dec 2011, with 2DVD data spanning 2114–2122 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### e. Case 5: Weaker, shallower convection

At the highest log_{10}*N*_{w} but lowest *D*_{0} end of the spectrum, light rain with echo tops below 2 km AGL was observed in several cases akin to Fig. 9. The shallow cloud depth, confined below the trade wind inversion in this case, likely played a role in limiting drop growth. The maximum diameters from these DSDs ranged from 0.83 to 1.98 mm, with an average maximum diameter of only 1.32 mm. Median drop diameters were 0.5–0.75 mm. These light rain DSDs account for the extension of the *N*_{w}(*D*_{0}) 2D histogram in Fig. 3 up and to the far left of the diagram, which also lies on the stratiform side of the BR09 separation line. The radar characteristics and inferred low-level heating profile of this precipitation warrant its classification as convection, albeit weak. The *Z*_{h} remained below 30 dB*Z*, horizontal *Z*_{h} gradients were weak, *Z*_{dr} remained near zero, and *ρ*_{hυ} was near unity, except for obvious ground clutter where *ρ*_{hυ} < 0.75 and *Z*_{dr} < 0.5 dB. As expected, rain rate was fairly low, ranging between 0.3 and 10 mm h^{−1}.

Case study 5: as in Fig. 5, but for light rain at 0745 UTC 23 Nov 2011, with 2DVD data spanning 0730–0810 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 5: as in Fig. 5, but for light rain at 0745 UTC 23 Nov 2011, with 2DVD data spanning 0730–0810 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 5: as in Fig. 5, but for light rain at 0745 UTC 23 Nov 2011, with 2DVD data spanning 0730–0810 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### f. Case 6: Moderate stratiform

Moderate stratiform rain exhibits much different radar and DSD characteristics than convection (Houze 1997). For instance, stratiform rain in Fig. 10 has rain rates in the same ranges as the preceding weak convection (<10 mm h^{−1}), similarly low LWC between 0.1 and 0.5 g m^{−3}, but *D*_{0} > 1 mm and log_{10}*N*_{w} between 3.6 and 3.85. The same *R* and LWC were apparently achieved with much lower log_{10}*N*_{w}, slightly greater surface *Z*_{h}, and greater *D*_{0}. This suggests that these DSDs exhibit different covariances between the integral rain parameters compared to convection (Atlas et al. 1973). The LWC(*D*_{0}) and *N*_{w}(*D*_{0}) points are on the stratiform side of the separation lines. Throughout inspection of all 372 radar–2DVD case studies, stratiform rain with a clear radar bright band was observed to approach, but stay below the log_{10}*N*_{w}(*D*_{0}) ranges are not as region dependent as convection.

Case study 6: as in Fig. 5, but for stratiform rain at 2031 UTC 22 Nov 2011, with 2DVD data spanning 2021–2055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 6: as in Fig. 5, but for stratiform rain at 2031 UTC 22 Nov 2011, with 2DVD data spanning 2021–2055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 6: as in Fig. 5, but for stratiform rain at 2031 UTC 22 Nov 2011, with 2DVD data spanning 2021–2055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### g. Case 7: Weak stratiform

Widespread, weaker stratiform rain (Fig. 11) exhibited brightband signatures but with even lower surface log_{10}*N*_{w} near 3.3 and *D*_{0} < 1 mm, consistent with lower surface *Z*_{h}. The LWC(*D*_{0}) samples during this time were on the lower side of the LWC^{SEP} line, with *R* only ranging from 0.1 to 0.3 mm h^{−1}. These samples were nearly coincident with the main frequency of occurrence maxima observed in Figs. 3 and 4. This mode of precipitation is obviously more frequently observed than the upper mode of LWC(*D*_{0}) and *N*_{w}(*D*_{0}) variability associated with convection, most likely because stratiform rain lasts longer and covers a wider area. This is consistent with previous tropical rainfall studies that report stratiform rain being more commonly observed per unit area and per unit time than convection, even though convection is responsible for more accumulated rainfall (e.g., Cheng and Houze 1979; Tokay and Short 1996; Zuluaga and Houze 2013; Xu and Rutledge 2014). The BR09 method would have classified these echoes as stratiform.

Case study 7: as in Fig. 5, but for weak stratiform rain at 1045 UTC 26 Oct 2011, with 2DVD data spanning 1035–1055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 7: as in Fig. 5, but for weak stratiform rain at 1045 UTC 26 Oct 2011, with 2DVD data spanning 1035–1055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 7: as in Fig. 5, but for weak stratiform rain at 1045 UTC 26 Oct 2011, with 2DVD data spanning 1035–1055 UTC. Time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### h. Case 8: Gradual transition from embedded convection to stratiform

The last two case studies demonstrate convection transitioning to stratiform rain. Figure 12 begins with convection embedded in a widespread, long-lived stratiform rain region. Low-level reflectivity exceeds 45 dB*Z*. The convective updrafts and precipitation growth processes appear to have disrupted the bright band locally above the disdrometer. The log_{10}*N*_{w} during this first scan of the series was well above the new separation line at 4.3, while *D*_{0} was nearly 1.5 mm, *R* was near 30 mm h^{−1}, and LWC was just over 1 g m^{−3}. The second set of radar scans show that the convection decayed over a 30-min period and the region of high reflectivity descended to the ground. The bright band also started to become more established and uniform during this time. However, there were still areas of enhanced reflectivity aloft, which were vertically elongated above the high-reflectivity fall streak. The DSDs remained on the upper portion of the *N*_{w}(*D*_{0}) and LWC(*D*_{0}) distributions, but were approaching each separation line. Likewise, rain rates were 10 mm h^{−1}.

Case study 8: as in Fig. 5, but for a transition from a leading convection line to strong stratiform rain at 0430, 0500, 0530, and 0600 UTC 24 Oct 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0420–0625 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 8: as in Fig. 5, but for a transition from a leading convection line to strong stratiform rain at 0430, 0500, 0530, and 0600 UTC 24 Oct 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0420–0625 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 8: as in Fig. 5, but for a transition from a leading convection line to strong stratiform rain at 0430, 0500, 0530, and 0600 UTC 24 Oct 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0420–0625 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

By the time of the third radar scan 30 min later, 1 h after strong convection passed over the disdrometer, the radar echoes were more horizontally uniform, many portions of the radar bright band showed *ρ*_{hυ} below 0.93, DSD had crossed the LWC(*D*_{0}) and *N*_{w}(*D*_{0}) separation lines, and rain rates decreased to 3 mm h^{−1}. The fourth radar scan shows an invigoration of the radar bright band to above 45 dB*Z* over a +15-km-wide area near 4.5 km AGL. A deep portion of the radar bright band exhibited *ρ*_{hυ} < 0.83 and *Z*_{dr} > 2 dB. These polarimetric data are consistent with the expectation of large rain drops at the surface (Tokay et al. 1999; Brandes et al. 2004), which was verified by observations of *D*_{0} near 1.9 mm at this time. Near-surface *Z*_{dr} was 0.5–1 dB, and surface rain rates were just under 10 mm h^{−1}. The layer of near-zero *Z*_{dr} just above the bright band and increasing *Z*_{dr} with altitude toward echo top above the disdrometer suggest pristine ice crystal growth near cloud top and subsequent aggregation above the melting layer (Ryzhkov et al. 2005; Kennedy and Rutledge 2011; Thompson et al. 2014). Braun and Houze (1994) highlight the role of vapor deposition aloft in producing strong stratiform bright bands. In addition, the aggregation process can concentrate LWC into fewer, but larger drops, which is supported by the trends observed in these DSD parameters from radar scans 2–4: lower LWC near 0.3 g m^{−3}, greater *D*_{0}, and lower log_{10}*N*_{w} near 3.2 compared to scans 2 and 3. This “zig–zag” migration through integral rain parameter spaces during a C/S transition was also noted by Tokay and Short (1996) and Atlas et al. (1999). The further decrease in surface *D*_{0}, LWC, *R*, *Z*_{h}, and even log_{10}*N*_{w} toward the end of this DSD sample period was associated with much lighter stratiform rain and a weaker bright band (not shown with radar, similar to case 7).

### i. Case 9: Abrupt transition from leading convection to stratiform

A different but commonly observed transition from a leading convective line to a trailing stratiform region is illustrated in Fig. 13. The DSD and radar echoes begin in a similar fashion as the previous case, with only faint, disrupted signatures of melting in *ρ*_{hυ} aloft and high log_{10}*N*_{w}, LWC, and *D*_{0} above each separation line. Rain rates reached 20 mm h^{−1} with surface *Z*_{h} just above 40 dB*Z* over the disdrometer. Radar echoes 15 min later in the second panel of the series look very similar to the decaying convection observed in the previous case study, with a fall streak of high reflectivity extending toward the ground and some lingering heterogeneity in the reflectivity pattern above discontinuous polarimetric signatures of melting near 5 km AGL. The DSD did not vary much between these two radar scans. Then, over the course of only five minutes, DSD shifted to the lower side of the log_{10}^{SEP} lines, and rain rates decreased to around 5 mm h^{−1}. The third set of RHIs just after the transition show more horizontally homogeneous reflectivity patterns above the melting layer with increased *Z*_{dr}, *Z*_{h}, and reduced *ρ*_{hυ} in the melting layer, suggesting more dominant stratiform rain processes throughout the column. The number concentration and LWC rapidly decreased as *D*_{0} increased, consistent with the effects of snowflake aggregation aloft. The near-zero *Z*_{dr} layer above the bright band also supports this hypothesis.

Case study 9: as in Fig. 5, but for a transition from convection embedded in stratiform rain to strong stratiform rain at 0300, 0315, 0330, and 0415 UTC 23 Nov 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0302–0420 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 9: as in Fig. 5, but for a transition from convection embedded in stratiform rain to strong stratiform rain at 0300, 0315, 0330, and 0415 UTC 23 Nov 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0302–0420 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Case study 9: as in Fig. 5, but for a transition from convection embedded in stratiform rain to strong stratiform rain at 0300, 0315, 0330, and 0415 UTC 23 Nov 2011 (corresponding to label numbers 1–4, respectively), with 2DVD data spanning 0302–0420 UTC. Numbers 1–4 correspond to callout points in the 2DVD data based on the time of the radar scans, where time increases as the colored markers go from blue to red.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

This abrupt C/S transition was also reported as a number concentration jump by Waldvogel (1974), Tokay and Short (1996), and Braun and Houze (1994). According to the 372 case radar–2DVD case studies examined, while stratiform cases always exhibited lower log_{10}*N*_{w} than convection, the evolution between C/S rain was not usually as quick as this example. It is also interesting that *D*_{0} and LWC vary in the same direction, or slope, as rain intensity varies within both stratiform and convective scenes, but the transition between the two rain types follows a different *D*_{0} and LWC covariance not predicted by Eq. (1) (evidenced in both Figs. 12 and 13).

The DSD remained relatively constant in time until 45 min later in the fourth radar data example, when a strong radar bright band >50 dB*Z* developed above the disdrometer and led to *Z*_{dr} > 1 dB between 0 and 4 km AGL. The correlation *ρ*_{hυ} was below 0.93, and *Z*_{dr} exceeded 3 dB over a relatively deep brightband depth compared to previous radar scans. Tokay et al. (1999) and Brandes et al. (2004) explained how surface *D*_{0} often increases as brightband reflectivity and depth increase. Despite the intense stratiform bright band aloft, surface rain rates were still limited to about 9 mm h^{−1}.

### j. Discussion

Convection was observed to rapidly evolve and decay, sometimes over very small spatial scales such that only a small portion of the convective radar echo actually went over the disdrometer. The resulting DSDs observed at the surface were therefore sometimes difficult to attribute to particular convective radar echoes because of the S-Pol’s 15-min update time. DSDs in the intermediate time periods between convective updrafts or before and after their passage over the disdrometer were usually quite scattered. Likely because of drop size sorting in the turbulent cloud edge, the first and last few minutes of a convective DSD event sometimes exhibited very low number concentrations but very high *D*_{0}. For these reasons, Gunn and Marshall (1955) recount that rain usually begins with a few large drops, with moderate *Z*_{h} but only small rain rates. Despite these understandable fluctuations associated with convection, the cases with clear convective precipitation over the disdrometer were uniformly above the log_{10}*N*_{w}(*D*_{0}) parameter space. Stratiform rain DSD were more stable and slowly evolving. These stratiform radar echoes did not produce DSD above log_{10}_{10}

Yuter and Houze (2002) make an important point that, even if DSD separation methods can delineate C/S populations (as we demonstrate for this rain regime), a huge hurdle still remains if radar algorithms cannot. Radar observations in this section suggest that reflectivity texture-based algorithms and dual-polarization radar-based melting layer detection algorithms should be able to distinguish most types of tropical, oceanic rain consistently with this DSD-based approach. TH10 demonstrate this clearly for stratiform rain and strong convection using the BR09 DSD and Steiner et al. (1995) radar-based methods. However, light convective rain in Fig. 7 would be difficult to classify as convection using traditional radar-based techniques because of weak horizontal reflectivity gradients, overall low *Z*_{h}, and low echo-top heights. Another challenge for radar C/S algorithms is to detect convection embedded within stratiform rain (e.g., Fig. 12), especially if the convective echoes are shallow and exist below the radar bright band. Observations in this section showed that fall streaks within stratiform rain, associated with a relatively high surface rain rate up to 10 mm h^{−1} and *Z*_{h} up to 40 dB*Z*, were often the result of recently decayed convective activity (Yuter and Houze 1997, 1998). In Figs. 12 and 13, the DSDs settled down to the stratiform *N*_{w}(*D*_{0}) and LWC(*D*_{0}) mode after the fall streak ended and once the reflectivity was more horizontally homogeneous above the bright band, as suggested by the Williams et al. (1995) vertically pointing radar classification method.

## 5. DSD-based convective/stratiform rain classification

In addition to analyzing 2DVD–radar case studies, we also explore a mathematical way to test which line, between log_{10}*R*(*z*) equations is used in a self-consistency test to see when the 2DVD total, convective, and stratiform accumulated rainfall converged with *R*(*z*)_{C} and *R*(*z*)_{S} estimates. C/S *R*(*z*) equations were iteratively formed with C/S *R* and *z* data as the partitioning line varied. The errors between the Gan 2DVD *R* and C/S *R*(*z*) did not minimize for any particular separation line. However, this goal was achieved between log_{10}*R*, as seen in Table 3. The log_{10}

Sensitivity of rain statistics to log_{10}*N*_{w} partitioning methods by comparing to Manus and Gan Island convective and stratiform 2DVD rain fractions and the percent difference between all, convective, and stratiform rain accumulations according to the 2DVD vs *R*(*z*)_{C} and *R*(*z*)_{S} calculations. These tests were run for convective/stratiform rain partitioning methods ranging from log_{10}

Table 3 also shows the variability in C/S rain fraction and frequency of occurrence estimates as the separation line varied. Moving the line from log_{10}*N*_{w} = 3.9 to 3.7 accounted for a 6% decrease (increase) in convective (stratiform) rain fraction and a 10% decrease (increase) in convective (stratiform) rain frequency of occurrence at both locations. The case studies motivated log_{10}_{10}*N*_{w} window of uncertainty in rainfall estimates as a result of this separation technique. This window corresponds to 3% (2%) of total rainfall accumulation and 5% (4%) of rain occurrences.

The resulting Manus Island *R*(*z*)_{C} and *R*(*z*)_{S} equations according to the log_{10}*D*_{0}, *D*_{MAX}, log_{10}*N*_{w}, and LWC for each C/S Manus Island population are shown in Table 5. By design, log_{10}*N*_{w} is higher for convection than stratiform rain. The *D*_{0} and *D*_{MAX} 5%–95% ranges for each C/S population overlap substantially. However, there is a slight indication of higher *D*_{0} in stratiform rain but higher *D*_{MAX} for convection, potentially because of the lack of vigorous riming processes in tropical, maritime convection. The LWC is understandably much greater in convection (95% value of 2.88 g m^{−3}) than stratiform (mostly below 0.33 g m^{−3}).

The *R*(*z*) equations from GATE (Hudlow 1979), TOGA COARE (Tokay and Short 1996), and MISMO (Yoneyama et al. 2008) field experiments, as well as new tropical, oceanic rain relationships derived from Manus and Gan Island 2DVD data (see domain in Fig. 1).

Mean, minimum, 5th percentile, 95th percentile, and maximum integral rain parameters for convective and stratiform DSD at Manus Island: max diameter *D*_{MAX} (mm); median diameter *D*_{0} (mm); liquid water content LWC (g m^{−3}); number concentration log_{10}*N*_{w} (unitless).

The C/S rain statistics using log_{10}*Z*_{h} associated with these oceanic echoes compared to land-based convection (Schumacher and Houze 2003). Section 2 explains why radar scanning geometry relative to the disdrometer prevented testing of this hypothesis in the current study.

Convective and stratiform rainfall accumulation and frequency of occurrence fractions according to Manus and Gan Island 2DVD rain rate *R* (mm h^{−1}) and log_{10}

Table 6 quantifies that, at both locations, about 30% of accumulated rainfall is due to rain with *R* < 10 mm h^{−1}, which accounts for 87% of all rain occurrences. If a simple rule, such as classifying convection as any point with *R* > 10 mm h^{−1}, were applied, the resulting, erroneous C/S rain fraction would be 87/13, and the erroneous C/S rain frequency fraction would be 71/29. Rain accumulation from this weak (*R* < 10 mm h^{−1}) subset has equal volume contributions (14% of total rain volume each) from convective and stratiform DSD. If *R*(*z*)_{C} and *R*(*z*)_{S} are used on simulated reflectivity, and a single *R*(*z*)_{ALL} equation is used to treat these convective DSD with *R* < 10 mm h^{−1} (14% of total rainfall at Manus Island), the estimated percentage of rainfall due to weak convection decreases to 11%. If a stratiform *R*(*z*)_{S} is used in this context, in the case of a misclassification of weak, shallow convection as stratiform, the percentage of rain due to this population decreases further to 8%. If the lightly raining, convective DSD are treated with the appropriate *R*(*z*)_{C} equation developed herein, their contribution to total rainfall is preserved. Similar results are found at Gan.

These statistics also show that almost two-thirds of the total raining occurrences come from stratiform rain <10 mm h^{−1} (58% of all rain), while one-third of occurrences originate from convection <10 mm h^{−1} (30% of all rain volume). The remaining 12% of occurrences are from convection with *R* > 10 mm h^{−1}. Johnson et al. (1999) also found that shallow, trade wind cumulus clouds were much more abundant than cumulus congestus and deep convection during TOGA-COARE, even though more rain fell from the latter, more intense elements. According to the Manus and Gan Island datasets, only 18%–21% of the convective rain volume is from samples with *R* < 10 mm h^{−1}, while 72%–75% of stratiform rain volume is due to these weak rain rates. Consistent with Johnson et al. (1999), 70% of all convective occurrences and 98% of all stratiform rain occurrences exhibited *R* < 10 mm h^{−1}. Results are similar when C/S DSDs are thresholded by 40 dB*Z*.

Figure 14 illustrates the statistics from Table 6. The *N*_{w}(*D*_{0}) and LWC(*D*_{0}) distributions have been colored by radar reflectivity and rain rate to show that a majority of both the convective and stratiform samples have rain rates less than 10 mm h^{−1} and *Z*_{h} < 40 dB*Z*. For example, stratiform rain (below the new dashed separation lines) is mainly limited to below 40 dB*Z* and below 10 mm h^{−1} near the surface, consistent with Tokay et al. (2001), Tokay and Short (1996), and others. It is interesting that the BR09 classification (solid separation line) is nearly synonymous with a 40-dB*Z* or 10 mm h^{−1} threshold for these tropical, maritime datasets. While convection undoubtedly appears to exceed these thresholds and stratiform rain does not, the BR09 classification is too conservative for the weak, oceanic convection frequently observed at the Manus and Gan Islands as in Figs. 7, 8, and 9. Convection (above the new dashed separation lines) apparently manifests itself across the entire range of *R* and *Z*_{h} values (well below 10 mm h^{−1} and 40 dB*Z*), which was also shown by Bell and Suhasini (1994) and Zuidema et al. (2012). Thus, a major accomplishment of this study has been to modify the *N*_{w}(*D*_{0}) BR09 C/S separation methodology to properly distinguish both strong and shallow weak maritime convection from stratiform rain in tropical, oceanic regions.

Manus Island LWC(*D*_{0}) and *N*_{w}(*D*_{0}) scatterplots color coded by 2DVD rain rate *R* and reflectivity *Z*_{h}, with the original subtropical, continental BR09 and updated tropical, oceanic C/S log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island LWC(*D*_{0}) and *N*_{w}(*D*_{0}) scatterplots color coded by 2DVD rain rate *R* and reflectivity *Z*_{h}, with the original subtropical, continental BR09 and updated tropical, oceanic C/S log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island LWC(*D*_{0}) and *N*_{w}(*D*_{0}) scatterplots color coded by 2DVD rain rate *R* and reflectivity *Z*_{h}, with the original subtropical, continental BR09 and updated tropical, oceanic C/S log_{10}

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

## 6. Implications for radar applications

### a. C/S R(z) variability

Figure 14 also illustrates that convection has higher *R* and *Z*_{h} for a given *D*_{0} than stratiform rain. The same *D*_{0} can lead to a variety of reflectivities and rain rates depending on the number concentration. A physical interpretation is that higher *N*_{w} (during convection) for a given *D*_{0} (which overlap between C/S rain) leads to greater LWC. The need to constrain *R*(*z*) variability motivates radar classification of C/S echoes as well as formation and application of separate *R*(*z*) equations for each rain type. Exploration of other integral rain parameter spaces further affirms that C/S modes of DSD variability exist within the Manus and Gan Island datasets. Figure 15 shows that *R*(*D*_{0}), *R*(LWC), *z*(LWC), and *R*(*λ*) distributions consistently exhibit two populations that can be separated by log_{10}*R*(*D*_{0}) space is more distinct than that presented by Atlas et al. (2000). Convective rain achieves the same *R* as stratiform, but with lower *D*_{0}, higher log10*N*_{w}, and higher LWC. The overlapping *z* ranges between C and S rain reflect the fact that each of these DSD modes carry characteristically different LWC amounts for a given reflectivity (Table 5). The exponential DSD slope (*λ*) is flattened, or decreased, in stratiform precipitation associated with the aggregation of smaller crystals into larger snowflakes above the melting level (Lo and Passarelli 1982). Higher slope values are achieved during convection when new particles are formed via condensation, collision, and coalescence, also shown by Tokay and Short (1996). Orthogonal linear regression was used to relate *z*(LWC) and *R*(*λ*) in C/S/all rain, which are presented in Table 7. The green all-data lines in Fig. 15 compromise a significant amount of DSD covariance described by each C/S best-fit line.

Manus Island (a) *R*(*D*_{0}), (b) *R*(LWC), (c) *z*(LWC), and (d) *R*(*λ*) partitioned by the log_{10}*z*(LWC) and *R*(*λ*) regression lines are superimposed in (c) and (d), respectively, for the entire DSD dataset (green) and each convective and stratiform population [black lines represent convective (stratiform) relationship on top (bottom) overlaying red (blue) points]. Similar distributions are observed at Gan Island.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island (a) *R*(*D*_{0}), (b) *R*(LWC), (c) *z*(LWC), and (d) *R*(*λ*) partitioned by the log_{10}*z*(LWC) and *R*(*λ*) regression lines are superimposed in (c) and (d), respectively, for the entire DSD dataset (green) and each convective and stratiform population [black lines represent convective (stratiform) relationship on top (bottom) overlaying red (blue) points]. Similar distributions are observed at Gan Island.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island (a) *R*(*D*_{0}), (b) *R*(LWC), (c) *z*(LWC), and (d) *R*(*λ*) partitioned by the log_{10}*z*(LWC) and *R*(*λ*) regression lines are superimposed in (c) and (d), respectively, for the entire DSD dataset (green) and each convective and stratiform population [black lines represent convective (stratiform) relationship on top (bottom) overlaying red (blue) points]. Similar distributions are observed at Gan Island.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island best-fit equations for rain rate *R* (mm h^{−1}) as a function of exponential DSD slope parameter *λ* (mm^{−1}) and radar reflectivity *z* (mm^{6} m^{−3}) as a function of liquid water content LWC (g m^{−3}) for convective rain, stratiform rain, and all rain.

To investigate whether the aforementioned C/S DSD variability can account for any *R*(*z*) variability during actual raining events, *R*(*z*) distributions for all nine 2DVD–radar case studies are shown in Fig. 16. The *R*(*z*)_{C}, *R*(*z*)_{ALL}, and *R*(*z*)_{S} from Table 4 are shown for reference, with *R*(*z*)_{C} consistently yielding higher rain rates for a given *Z*_{h} than *R*(*z*)_{S}. The *R*(*z*) data from widespread, as well as isolated, strong convection (cases 1 and 2) were in the high *Z*_{h}, high *R* spectrum aligned with *R*(*z*)_{C} and therefore also *R*(*z*)_{ALL}, since they converge there. Case 3 exhibited shallow, weaker convection below 5 km and had lower *Z*_{h} with correspondingly lower *R*, most in line with *R*(*z*)_{C} and well above *R*(*z*)_{ALL}. The isolated, weak convection below 4 km in case 4 had much lower *R* (<10 mm h^{−1}) but was aligned with *R*(*z*)_{C} rather than *R*(*z*)_{S}. Even though warm rain processes in case 5 barely reached 3 km, the rain rates were slightly higher than in case 4 and also on the convective *R*(*z*)_{C} line. In contrast, moderate stratiform rain rates at nearly the same intensity as the weakest, shallowest convective rain example hovered on the stratiform *R*(*z*)_{S} line, just below 10 mm h^{−1}. Even lower rain rates in case 7 during weak stratiform rain were along *R*(*z*)_{S} [in the region where *R*(*z*)_{ALL} converges to *R*(*z*)_{S}]. Cases 8 and 9 showed transitions between embedded and leading convection, respectively, to heavy stratiform rain. Both cases showed migrations from *R*(*z*)_{C}, across *R*(*z*)_{ALL}, and to *R*(*z*)_{S}, with case 8’s DSD after the fourth radar vertical cross section being more consistent with the weak stratiform rain from case 7.

The *R*(*z*) for case studies 1–9, where time increases as the colored markers go from blue to red. Lines represent the *R*(*z*)_{C} (upper), *R*(*z*)_{ALL} (middle), and *R*(*z*)_{S} (lower) best-fit equations shown.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

The *R*(*z*) for case studies 1–9, where time increases as the colored markers go from blue to red. Lines represent the *R*(*z*)_{C} (upper), *R*(*z*)_{ALL} (middle), and *R*(*z*)_{S} (lower) best-fit equations shown.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

The *R*(*z*) for case studies 1–9, where time increases as the colored markers go from blue to red. Lines represent the *R*(*z*)_{C} (upper), *R*(*z*)_{ALL} (middle), and *R*(*z*)_{S} (lower) best-fit equations shown.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Besides demonstrating consistency between the radar case study conclusions and the DSD partitioning method, another important result of these *R*(*z*) case studies is that the *R*(*z*)_{ALL} equation fit to the entire DSD dataset is hardly ever a “best fit” to individual cases of rain. The only exception is during the strongest convection or weakest stratiform rain, because *R*(*z*)_{ALL} converges to either *R*(*z*)_{C} or *R*(*z*)_{S} at either endpoint. If an appropriate C/S partitioning method can be used, we believe this motivates formation and use of separate C/S *R*(*z*) equations, because *R*(*z*)_{ALL} lies between these two major modes of DSD variability (i.e., convective and stratiform rain).

Returning to the similarity observed between Manus and Gan Island DSD variability, Fig. 17 shows simulated radar reflectivity as a function of 2DVD rain rate for both locations. The *R*(*z*)_{ALL} lines for each location are plotted together, illustrating that the similar distributions yield nearly identical *R*(*z*)_{ALL} equations: *R*(*z*)_{ALL} = 0.019*z*^{0.729} for Gan Island and *R*(*z*)_{ALL} = 0.020*z*^{0.721} for Manus, which are equivalent to *z*(*R*)_{ALL} = 228*R*^{1.37} at Gan and *z*(*R*)_{ALL} = 216*R*^{1.39} at Manus. We move forward with the Manus Island equations (in Table 4), since they are based on 7 times as many points but appear to represent the same *R*(*z*) variability observed at Gan Island. For instance, the second panel in Fig. 17 shows a histogram of the orthogonal distances between each (*z, R*) point and the Manus Island best-fit line. When normalized by the length of each dataset, the histograms are nearly equivalent. Both locations have the same percentage of *R*(*z*) points scattered in each distance increment about the Manus Island best-fit line.

(a) Gan and Manus Island 2DVD *Z*_{h} and *R* with linear regression best-fit lines for each location. (b) Normalized histograms of the orthogonal distance from each (*z*, *R*) point at each location to the Manus Island best-fit line. Distances are in logarithmic *R*(*z*) units in both directions.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

(a) Gan and Manus Island 2DVD *Z*_{h} and *R* with linear regression best-fit lines for each location. (b) Normalized histograms of the orthogonal distance from each (*z*, *R*) point at each location to the Manus Island best-fit line. Distances are in logarithmic *R*(*z*) units in both directions.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

(a) Gan and Manus Island 2DVD *Z*_{h} and *R* with linear regression best-fit lines for each location. (b) Normalized histograms of the orthogonal distance from each (*z*, *R*) point at each location to the Manus Island best-fit line. Distances are in logarithmic *R*(*z*) units in both directions.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

To examine these *R*(*z*) distributions further, 2D histograms of *R*(*z*) contoured by frequency of occurrence for both locations appear in Figs. 18a and 18b. A majority of the points lie below the *R*(*z*)_{ALL} line for *Z*_{h} < 30–40 dB*Z*, with indication of another high density region of points above the line as *Z*_{h} > 25 dB*Z*. Figures 18c and 18d use Manus Island data and the log_{10}*R*(*z*)_{ALL} line lies between the convective and stratiform modes in a region of lower frequency of occurrence exhibiting moderate *Z*_{h} and *R* ranges.

Gan and Manus Island *R*(*z*) smoothed 2D histograms contoured by frequency of occurrence with linear regression best-fit line from Manus Island. Gan Island: 180 bins in each direction and 6-bin Gaussian filter width. Manus Island number of bins in each direction: all = 280, convective = 200, stratiform = 235; 10-bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island *R*(*z*) smoothed 2D histograms contoured by frequency of occurrence with linear regression best-fit line from Manus Island. Gan Island: 180 bins in each direction and 6-bin Gaussian filter width. Manus Island number of bins in each direction: all = 280, convective = 200, stratiform = 235; 10-bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Gan and Manus Island *R*(*z*) smoothed 2D histograms contoured by frequency of occurrence with linear regression best-fit line from Manus Island. Gan Island: 180 bins in each direction and 6-bin Gaussian filter width. Manus Island number of bins in each direction: all = 280, convective = 200, stratiform = 235; 10-bin Gaussian filter width.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Figure 19 more clearly demonstrates that C/S DSD variability in log_{10}*N*_{w} explains most of the *R*(*z*) variability in these tropical, oceanic data. The *R*(*z*) distribution is colored by median drop diameter and number concentration using the fuller Manus Island dataset (similar results found for Gan Island; not shown), akin to the rain parameter diagram of Ulbrich and Atlas (1978, 1998) and Steiner et al. (2004). Low log_{10}*N*_{w} ranges ≤3.85 only exist in the lower (stratiform) mode of the *R*(*z*) distribution in Fig. 18. Likewise, high log_{10}*N*_{w} ranges >3.85 are only experienced in the upper (convective) *R*(*z*) mode. Sauvageot and Lacaux (1995), Tokay et al. (1999), Testud et al. (2001), Morrison et al. (2009), TH10, and Bringi et al. (2012) also suggested that number concentration explained more rain variability over the tropical warm pool than variations in median drop diameter. This corresponds to concentration-controlled DSD variability, as opposed to size controlled or a combination thereof, described mathematically by Steiner et al. (2004). For instance, the two main *R*(*z*) modes of variability in this dataset (Fig. 18) share nearly the entire range of median drop diameter *D*_{0} but have mutually exclusive number concentration (log_{10}*N*_{w}) ranges, which is consistent with Table 1, Table 5, and Figs. 3 and 4.

Manus Island *R*(*z*) color coded by (a) *D*_{0} and (b) log_{10}*N*_{w} plotted with C/S *R*(*z*).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island *R*(*z*) color coded by (a) *D*_{0} and (b) log_{10}*N*_{w} plotted with C/S *R*(*z*).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island *R*(*z*) color coded by (a) *D*_{0} and (b) log_{10}*N*_{w} plotted with C/S *R*(*z*).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

### b. Radar-based C/S rainfall estimation

It is obvious from Figs. 16 and 18 how *R*(*z*)_{C} and even *R*(*z*)_{ALL} would overestimate stratiform rain if applied in the wrong context, and likewise how *R*(*z*)_{S} and *R*(*z*)_{ALL} would underestimate convective rain in many cases. Table 8 assesses the impacts of applying either a combination of *R*(*z*)_{C} and *R*(*z*)_{S} or *R*(*z*)_{ALL} to the long-term simulated 2DVD radar reflectivity dataset. A 3% overestimation of total rain, 4% overestimation of convective rain, and only −0.01% underestimation of stratiform rain is encountered when using *R*(*z*)_{C} and *R*(*z*)_{S} for each distribution at Manus Is. compared to 2DVD *R* estimates. If the *R*(*z*)_{ALL} equation is used only on the shallow, weak convective population, as in the case of uncertain C/S partitioning of this population, and separate *R*(*z*)_{C} and *R*(*z*)_{S} equations are used appropriately in all other instances, the total, convective, and stratiform rain accumulation errors are nearly zero. However, the percentage of rainfall by weak convection <10 mm h^{−1} is underestimated at 11% instead of 14% as indicated by the 2DVD (Table 6). If the *R*(*z*)_{S} equation is used on weak, shallow convection, as in the case of a misclassification, the total rainfall is underestimated by 3%, convective rainfall amounts are underestimated by 4%, and stratiform rainfall is still well reproduced. The percentage of total rainfall due to weak, convection is further underestimated to 9% compared to 2DVD *R* or using *R*(*z*)_{C} appropriately (Table 6). Using a simple *R* > 10 mm h^{−1} threshold to denote convection and applying C/S *R*(*z*) from this basis results in small total and convective rainfall errors, but a 17% overestimation of stratiform rainfall, which results in ±3% errors in S/C rain fraction. Therefore, using the individual C/S *R*(*z*) relationships with inaccurate C/S partitioning method will produce misleading results. If radar-based C/S partitioning confidence is low, *R*(*z*)_{ALL} should be used.

Manus Island total, convective, and stratiform rainfall accumulation and C/S fraction of total rain. Estimates are from 2DVD rain rate *R* and various methods applied to 2DVD simulated *z*. Percent differences between 2DVD *R* and other *R* estimates are given. Percent differences between rain fractions are simply differences between fractions.

While the error in total rainfall accumulation is slightly lower (and negative) when using *R*(*z*)_{ALL} compared to the C/S *R*(*z*) method (−2.7%), this is overshadowed by vast over- and underestimations of stratiform (+59%) and convective (−15%) rain accumulation. Since *R*(*z*) is a power-law equation, and the underestimation of high rain rates outweighs the underestimation of relatively lower rain rates, total rainfall is ultimately underestimated in this case. Similar to results by Testud et al. (2001), *R*(*z*)_{C}, *R*(*z*)_{S}, and *R*(*z*)_{ALL} explain 98.5%, 96.4%, and 93.9% of the total variance in each respective population. Therefore, in addition to minimizing errors in C/S rain accumulation, using separate C/S *R*(*z*) relations for each rain population can also help explain more total variance than a single *R*(*z*)_{ALL}.

The errors associated with using *R*(*z*)_{ALL} have been quantified. For instance, even on these long-term Manus and Gan Island datasets, using the *R*(*z*)_{ALL} equation on the entire dataset yields a ±10% difference in stratiform and convective rainfall fraction, respectively, compared to 2DVD *R* and C/S *R*(*z*) estimates in Table 6. Differences in rainfall fraction estimates due to using *R*(*z*)_{ALL} are expected to be higher for individual case studies when averaging over shorter time periods. Therefore, ±10% is considered to be the minimum error expected when estimating rainfall fraction caused by using *R*(*z*)_{ALL} instead of distinguishing and treating C/S populations separately. Using *R*(*z*)_{C} and *R*(*z*)_{S} only produces a ±0.6% difference from 2DVD percentages of C/S rain fraction. When *R*(*z*)_{ALL} or *R*(*z*)_{S} are used for weak, shallow convection, and C/S *R*(*z*) equations are used appropriately for the rest of the dataset, the C/S fractions of the resulting total rainfall from these methods hardly differ from 2DVD C/S fraction estimates and are of opposite sign than using C/S *R*(*z*). However, Table 6 illustrates that the fraction of shallow, weak convective rain decreases from 14% to 11% using *R*(*z*)_{ALL} and to 8% using *R*(*z*)_{S} in this context.

We also consider the impact of using TOGA COARE and MISMO *R*(*z*) relationships from Table 4 in Fig. 17 and Table 8, since these equations were formed with DSD in the equatorial west Pacific and Indian Oceans, respectively (Fig. 1). Although not plotted, the GATE and new *R*(*z*)_{ALL} equations are also very similar (Table 4). The TOGA COARE C/S relationships yield slightly different rainfall statistics than the new *R*(*z*)_{C} and *R*(*z*)_{S} relationships. Total rainfall and convective rainfall have similar errors as using the new C/S relationships, because the *R*(*z*)_{C} equations are nearly equivalent in Fig. 20 and Table 4. However, stratiform rain is strongly overestimated by the Tokay and Short (1996) *R*(*z*)_{S} compared to 2DVD *R*, because their *R*(*z*)_{S} has a lower slope. This leads to a ±1.3 difference in S/C rainfall fraction compared to the 2DVD. Since Manus Island and TOGA-COARE are both in the western Pacific, this difference is most likely due to Tokay and Short’s (1996) use of impact JWD disdrometers with less accurate small-drop detection, the nonnormalized^{4} gamma DSD number concentration *N*_{0}, a probability matching method to find *R*(*z*), different DSD data processing techniques, and/or resulting differences in C/S partitioning methods (^{9}*R*^{−4.9}).

Manus Island *R*(*z*) scatterplots and regression lines for (a) the entire dataset, (b) the dataset partitioned into convective and stratiform populations according to the updated log_{10}*R*(*z*) equations in Table 4 from MISMO, TOGA COARE, and the current study are plotted.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island *R*(*z*) scatterplots and regression lines for (a) the entire dataset, (b) the dataset partitioned into convective and stratiform populations according to the updated log_{10}*R*(*z*) equations in Table 4 from MISMO, TOGA COARE, and the current study are plotted.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Manus Island *R*(*z*) scatterplots and regression lines for (a) the entire dataset, (b) the dataset partitioned into convective and stratiform populations according to the updated log_{10}*R*(*z*) equations in Table 4 from MISMO, TOGA COARE, and the current study are plotted.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

The MISMO relationship from JWD data is similar to *R*(*z*)_{ALL} in Fig. 20, except that it leans toward the convective DSD more than stratiform at the lower end of the *R*(*z*) spectrum. This is because of this relationship’s reliance on mostly convective DSD samples from only 6 weeks of data leading up to the active MJO, according to Yoneyama et al. (2008) and Masaki Katsumata (2006, personal communication). Thus, using the MISMO *R*(*z*)_{ALL} leads to an 11% overestimation (underestimation) of stratiform (convective) rain fraction compared to 2DVD *R* estimates (i.e., yielding a C/S rain fraction closer to 70/30). The errors on total, convective, and stratiform rainfall accumulation using the MISMO *R*(*z*) compared to 2DVD estimates are relatively small for total rain accumulation, but are −13% for convective rain and +58% for stratiform rain.

Finally, we discuss the choice of *R*(*z*) relationships relative to MJO evolution. DeWitt et al. (2013) described a central Indian Ocean evolution of aerosol loading as a function of MJO, which could impact the resultant DSDs. Similarly, Xu and Rutledge (2014) and Virts and Houze (2015) observed increased storm intensity and lightning activity leading up to the heaviest rain-producing phases of the MJO, which could also be related to DSD variability. However, it appears that the same *R*(*z*)_{C}, *R*(*z*)_{S}, and *R*(*z*)_{ALL} relationships are applicable during all phases of the MJO, because the LWC(*D*_{0}) and *N*_{w}(*D*_{0}) covariance, as well as the log_{10}*R*(*z*), should not be directly related to MJO phase. According to the long-term DSD datasets, it appears that only one version of the *R*(*z*)_{S}, *R*(*z*)_{C}, and *R*(*z*)_{ALL} equations is necessary for this tropical, oceanic rain regime. Furthermore, it would be inappropriate to partition *R*(*z*)_{ALL} by MJO phase because we have shown that the spread in *R*(*z*) can be succinctly explained by mutually exclusive *N*_{w} differences between C and S rain, both of which are present during all phases of the MJO according to both Manus and Gan DSD datasets and other studies in these tropical ocean basins.

## 7. Conclusions

This study documented tropical, maritime DSD variability captured by the Gan and Manus Island 2DVDs with 3.5- and 18-month records in the equatorial Indian and west Pacific Oceans, respectively. The spectra of integral rain parameters and separation between convective (C) and stratiform (S) rain were similar at each location, suggesting that cloud microphysical and dynamical properties are also similar at these locations. Both are open ocean locations with characteristically warm sea surface temperatures and influenced by similar large-scale forcing, such as the ITCZ and MJO. DSDs were characterized by high number concentrations (*N*_{w}) and small-to-medium drop diameters (95% of *D*_{0} < 1.7 mm; *D*_{MAX} < 4 mm) compared to continental DSDs. These DSDs were consistent with maritime, warm rain processes, such as condensation and coalescence, as well as some riming growth in more intense convection. In contrast, stratiform rain had an order of magnitude lower log_{10}*N _{w}* compared to convection, consistent with aggregation above the melting level.

The conceptual model in Fig. 21 illustrates the dominant cloud microphysical processes giving rise to Manus and Gan Island DSDs in various quadrants of the *N*_{w}(*D*_{0}) space. Arrows indicate how intensifying stratiform and convective rain (i.e., higher reflectivity, higher rain rate, greater brightband intensity, or higher echo-top height) attain higher liquid water content and median raindrop diameters but maintain over an order of magnitude different *N _{w}* between C and S precipitation. Compared to weaker, shallower warm rain convection, stronger, deeper convection has higher

*D*

_{0}, consistent with deeper cloud depths. Stronger updrafts in these convective clouds promote higher liquid water contents, which also promote larger particle sizes.

Conceptual model of dominant microphysical processes (dark green) in the *N*_{w}(*D*_{0}) space. The background is a grayscale smoothed contoured frequency 2D histogram showing darker (more frequent) DSD pairs from Manus Island 2DVD. Distinctions are made between maritime convection (red) and stratiform rain (blue) on either side of the updated log_{10}*R*, radar reflectivity *Z*_{h}, bright band, or echo-top height), the median drop diameter *D*_{0} and liquid water content LWC increase with much smaller variation in number concentration log_{10}*N*_{w} for either convective or stratiform rain. Thus, the red and blue arrows generally point in the direction of more intense convection and more intense stratiform precipitation by these metrics, respectively.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Conceptual model of dominant microphysical processes (dark green) in the *N*_{w}(*D*_{0}) space. The background is a grayscale smoothed contoured frequency 2D histogram showing darker (more frequent) DSD pairs from Manus Island 2DVD. Distinctions are made between maritime convection (red) and stratiform rain (blue) on either side of the updated log_{10}*R*, radar reflectivity *Z*_{h}, bright band, or echo-top height), the median drop diameter *D*_{0} and liquid water content LWC increase with much smaller variation in number concentration log_{10}*N*_{w} for either convective or stratiform rain. Thus, the red and blue arrows generally point in the direction of more intense convection and more intense stratiform precipitation by these metrics, respectively.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

Conceptual model of dominant microphysical processes (dark green) in the *N*_{w}(*D*_{0}) space. The background is a grayscale smoothed contoured frequency 2D histogram showing darker (more frequent) DSD pairs from Manus Island 2DVD. Distinctions are made between maritime convection (red) and stratiform rain (blue) on either side of the updated log_{10}*R*, radar reflectivity *Z*_{h}, bright band, or echo-top height), the median drop diameter *D*_{0} and liquid water content LWC increase with much smaller variation in number concentration log_{10}*N*_{w} for either convective or stratiform rain. Thus, the red and blue arrows generally point in the direction of more intense convection and more intense stratiform precipitation by these metrics, respectively.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0206.1

The log_{10}*R*(*z*) self-consistency test. While a separation line may not appear physically satisfying at first, evaluation of radar echo and DSD evolution from all 372 case studies, previous observational studies, and theoretical evidence of number-controlled DSDs (Steiner et al. 2004) support our conclusion that number concentration is the most discerning feature between stratiform rain DSD and convective, maritime, tropical rain DSD. The new separation line is more applicable for tropical, oceanic rain regimes where weak convection (*R* < 10 mm h^{−1} and usually *Z*_{h} < 35 dB*Z*) is ubiquitous. Weak, shallow convection by these metrics made up about 14% of rain volume and 30% of rain occurrences at the equatorial Indian and west Pacific sites. We offer evidence for increased convective rain fraction and frequency estimates compared to previous tropical, oceanic studies because our high-resolution DSD dataset and corresponding C/S partitioning algorithm provide better detection and treatment of this rain type. For instance, the DSD data yielded a long-term average 41/59 C/S rainfall frequency ratio and an 81/19 C/S rain fraction.

This long-term stratiform/convective rainfall fraction was found to vary by ±10%, respectively, when a single *R*(*z*)_{ALL} equation was used to calculate *R* compared to the directly sensed 2DVD *R*. In contrast, the 2DVD rain fraction estimate was recreated within ±0.6% when using *R*(*z*)_{C} and *R*(*z*)_{S} applied to the convective and stratiform rain populations, respectively. Use of separate C/S equations also minimized errors in convective and stratiform rain accumulation and statistically explained more *R* variance. Current radar-based C/S echo partitioning algorithms should be able to mimic the DSD-based classification technique with sufficient spatial and temporal resolution and tuning for the tropical, oceanic precipitation regime. However, current radar-based C/S partitioning has considerable uncertainty in shallow, weak convection and convective elements embedded in stratiform rain. The benefits of using C/S *R*(*z*) equations will not be realized if the partitioning is incorrect. If a confident echo identification cannot be made, the best alternative is *R*(*z*)_{ALL}. A paired, statistical comparison between 2DVD and radar C/S classifications and rain rate would help quantify the uncertainty involved in application of different *R*(*z*) relationships to real radar data but is not possible with the given datasets (explained in section 2).

This long-term, high-spatiotemporal-resolution dataset has provided new, comprehensive insights regarding tropical drop size distributions and rainfall variability since these types of data are not typically available in remote oceanic regions. Furthermore, characterizing and reducing the uncertainty associated with radar-based rainfall estimates is an important step toward confidently addressing more fundamental questions about tropical atmospheric dynamics and the contribution of freshwater into the oceans.

## Acknowledgments

This research was funded by the NSF Graduate Research Fellowship Award DGE-1321845, NSF Award AGS-1063928, and DOE/ASR Award DE#SC0007016. We acknowledge DOE/ARM for supplying the long-term Manus and Gan Island 2DVD datasets. Thanks are given to Paul Hein and G. J. Huang for data management and processing (CSU). We appreciate conversations with Nick Guy (University of Wyoming), Robert Houze, Angela Rowe, and Scott Powell (University of Washington), Courtney Schumacher (TAMU), Scott Collis (Argonne National Laboratory), Christopher Williams (CIRES), as well as Elizabeth Barnes, Richard Johnson, John Peters, and Doug Stoltz (CSU). We are also particularly grateful to V. N. Bringi (CSU) for his insightful comments regarding this work. We also thank Michael Dixon, Bob Rilling, John Hubbert, and Scott Ellis (NCAR) for discussions concerning DYNAMO S-Pol radar data. We thank Chidong Zhang, Kunio Yoneyama, and Chuck Long for their leadership in the DYNAMO, CINDY, and AMIE projects, respectively. Three reviews helped improve the content and organization of this manuscript.

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