1. Introduction
Regions of convective and stratiform precipitation are known to differ considerably in terms of 1) microphysical composition and associated precipitation rates (e.g., Houghton 1968); 2) thermodynamic properties including diabatic heating rates, perturbations to the altitude of the environmental melting (or freezing) level, and related storm divergence profiles (e.g., Johnson 1984; Houze 1989; Mapes and Houze 1993); and 3) their relative frequency of occurrence across the globe (e.g., Schumacher and Houze 2003). Recognition of these differences has motivated several previous studies to develop methods that objectively identify convective and stratiform precipitation in radar and satellite observations in order to enable improvements in our understanding of their differences and associated physical and dynamical processes (e.g., Adler and Negri 1988; Williams and Ecklund 1995; Steiner et al. 1995; DeMott et al. 1995; Anagnostou and Kummerow 1997; Hong et al. 1999; Anagnostou 2004; Bringi et al. 2009; Yang et al. 2013).
One of the most well-known and utilized schemes for convective-stratiform classification using ground-based radar observations is the Steiner et al. (1995) method, hereafter referred to as SHY. SHY employs a three-step procedure to distinguish between convective and stratiform precipitation using observations at the lowest elevation in a radar volume. First, any value of the radar reflectivity factor at horizontal polarization (
Many studies have built upon the SHY procedure by incorporating vertical information in the classification to improve its performance, particularly in cases where convection is weak, stratiform precipitation is intense, or convective regions are strongly tilted in the vertical (thereby inadvertently decoupling convective precipitation at low altitudes from its source aloft). Biggerstaff and Listemaa (2000) added a step to compute the vertical lapse rate of 
While the aforementioned studies incorporated vertical storm information in the SHY procedure, the primary classification between convective and stratiform precipitation in SHY-based algorithms and similar approaches is completed using a single low-altitude map of 
In this study, we introduce a method for classifying radar echo using three-dimensional high-resolution composites of radar observations from the Next Generation Weather Radar (NEXRAD) Weather Surveillance Radar-1988 Doppler (WSR-88D) network (Crum and Alberty 1993). We call this method the Storm Labeling in Three Dimensions (SL3D) algorithm. The SL3D algorithm uses the vertical depth and echo-top altitude of 
2. Radar data
The radar data used in this study are three-dimensional composites of NEXRAD WSR-88D observations, where the volume data from individual radars are provided by the National Centers for Environmental Information (NCEI; National Weather Service 1991). Radar composites are created following the methods outlined in Homeyer (2014) and updated in Homeyer and Kumjian (2015). In short, observations from each radar are binned in space and time at 5-min intervals in a volume with 0.02° (~2 km) latitude–longitude grid spacing and 1-km grid spacing in the vertical. For binning, observations are weighted out to 300 km in range and within 5 min of the composite time using a Gaussian function. Grid volumes with large cumulative bin weights (i.e., the sum weight of all observations contributing to a grid volume) and a high fraction of echo detection in contributing radar scans are retained for analysis. The largest weights are given to observations closest to a radar location and closest in time to that of the composite. The time-binning component is the only difference from the procedure outlined in Homeyer and Kumjian (2015); hence, no interpolation is performed on the individual radar scans in time or space. Each composite contains up to four polarimetric variables for analysis: 
The polarimetric variables from NEXRAD radars provide information on the size, shape and/or orientation, concentration, and phase of precipitable hydrometeors. For example, 
The 
3. SL3D algorithm
The storm classification algorithm used in this study (SL3D) stratifies radar echo into five categories: convection, convective updraft, precipitating stratiform, nonprecipitating stratiform, and ice-only anvil. In summary, the objective of the SL3D convective classification is to identify precipitation that is directly generated by convective motions (i.e., strong vertical motion or “updrafts”). Precipitating (nonprecipitating) stratiform encompasses any mixed-phase cloud that does not contain convective updrafts and is (is not) precipitating. Anvil is considered to be ice-only cloud resulting from upper-tropospheric detrainment of ice crystals by convection or advected from a convectively generated stratiform region. More detailed descriptions of the classification categories are defined in their corresponding sections below and a summary of the criteria applied to the radar observations is presented in Table 1. It is important to note that the convection classification occurs first and is incrementally followed by the stratiform (precipitating and nonprecipitating) and anvil classifications. Convective echo cannot be relabeled as stratiform or anvil. Similarly, echo identified as stratiform cannot be relabeled as anvil. Once the precipitating and nonprecipitating echo regions are identified, echo may be identified as convective updraft within 12 km of any echo classified as convection if one of several conditions are met; these conditions are outlined below.
The criteria used for classification into the five SL3D categories, where 
SL3D incorporates information from the atmospheric environment. Namely, the altitude of the 0°C level (i.e., the melting level) is used, which we obtain from radiosonde observations for the cases presented in this study. While it is possible to couple melting-layer identification algorithms to SL3D using the radar observations alone (e.g., Giangrande et al. 2008), it is outside the scope of this study to evaluate and determine the sensitivity to each method. Since any objective classification is prone to error, it is the authors’ preference to limit such error sources for the SL3D algorithm and specify the altitude of the melting level.
a. Convection and stratiform
As outlined in the introduction, there are distinct microphysical and thermodynamic differences between convective and stratiform precipitation. Convective precipitation occurs when strong, deep mesoscale uplift and/or positive buoyancy leads to the development and growth of cloud particles. As the droplets are lofted into the middle troposphere, they freeze and grow rapidly by the collection and glaciation of additional supercooled liquid water (e.g., Churchill and Houze 1984). These updrafts can loft precipitable particles into the upper troposphere and thereby result in deep, vertically erect columns of high-
Stratiform precipitation results from weak mesoscale ascent at altitudes typically above the freezing level that leads to the formation, growth, and fallout of ice crystals to lower altitudes. Upper-level detrainment from deep convection is often a common source of ice crystals in stratiform regions. Ice crystals can also be actively generated in the stratiform region above the melting level (e.g., Braun and Houze 1994). The falling ice crystals in a stratiform system aggregate, which leads to moderate rates of precipitation (relative to that in convection). If the aggregates descend below the melting level, they are often visible in radar observations as a shallow layer of elevated 
While the vertical structures of convective and stratiform systems are distinct, their column-maximum 
The SL3D convective classification is internally partitioned into three steps to better identify convection of varying extent and intensity. Radar echo in each grid square that meets any of the following three criteria is labeled as convection: 1) 
Criterion 1 uses 
Once convective regions are identified using the three criteria outlined above, we apply two quality control techniques that modify the classification. Any single convective grid point that is adjacent only to nonconvective grid points is removed, as it is expected to be false or inconclusive based on the classification criteria. Once the single-point classifications are removed, any grid points immediately adjacent to remaining convective echo are also classified as convective if their column-maximum 
Grid points that do not meet the convective criteria undergo possible stratiform classification. The stratiform classification in SL3D is split into two mutually exclusive categories: 1) precipitating stratiform and 2) nonprecipitating stratiform. While vertical velocities in stratiform regions are typically an order of magnitude smaller than those in convection, considerable differences in vertical velocities between precipitating and nonprecipitating stratiform clouds have also been documented. For instance, Schumacher et al. (2015) found that mean vertical velocities in the tropics from the near surface to 10 km ranged from −0.1 to 0.2 m s−1 for stratiform and from 0.1 to 0.9 m s−1 for convection. The full spectra of vertical velocity measurements varied from about −2 to 2 m s−1 for stratiform and from −5 to 18 m s−1 for convection. For nonprecipitating cloud (their transitional anvil), the mean vertical velocities were weaker than stratiform and varied from −0.05 to 0.05 m s−1, with minima and maxima ranging from about −1.25 to 1.5 m s−1 (Schumacher et al. 2015). The nonprecipitating stratiform region encompasses the transition between precipitating stratiform and ice-only anvil, where some stratiform growth (i.e., aggregation) has occurred but does not lead to precipitation. Ideally, regions categorized as precipitating stratiform include only those observations with nonconvective precipitation at the surface. However, since radar coverage is limited near the surface, data at 3 km are used to draw the primary distinction between precipitating and nonprecipitating echoes. The 3-km height is the lowest altitude with near-uniform coverage in the NEXRAD WSR-88D network. When available, data below 3 km are used to identify additional regions of weak precipitation. The 3-km analysis level is also used in the SHY algorithm for comparisons with SL3D in section 5 below.
Precipitating stratiform is defined as that with 
As briefly outlined above, we specify the melting-level altitude in SL3D to assist with echo classification. While some unique radar features can be used to help identify stratiform regions (e.g., 
b. Anvil
In previous studies, anvil regions have commonly been separated into modes thought to be representative of unique physical and/or dynamic regimes. For example, Frederick and Schumacher (2008) stratified anvil into mixed-phase and ice-only cloud due to important differences in radiative properties between the two categories. The SL3D anvil classification is designed to identify nonprecipitating ice-only cloud above the melting level resulting from convective detrainment in the upper troposphere (mixed-phase nonprecipitating clouds are categorized as nonprecipitating stratiform). To accomplish this, we identify regions as anvil if radar echo (
c. Convective updraft
Following the convection, stratiform, and anvil classification, radar echo is evaluated to determine whether or not signatures indicative of strong convective updrafts are present. To identify convective updrafts, the SL3D algorithm searches for three well-known radar signatures: 1) weak-echo regions [WERs; bounded or unbounded, e.g., Browning and Donaldson (1963); Musil et al. (1986); Calhoun et al. (2013)], 2) 
For radar composites that include the full suite of polarimetric variables, updraft classifications also include 
Snyder et al. (2015) have recently developed an algorithm for objectively identifying 
SL3D updrafts are identified by locating 
Finally, following identification of WERs, 
4. Example SL3D classifications and convective updraft validation
To demonstrate the application of the SL3D classification, we show a simple dual-polarization case in Fig. 1 that contains a large supercell storm in north Texas at 0055 UTC 18 May 2013. The melting level for this case is ~4.75 km. Figure 1a shows a 3-km constant-altitude map of 
Maps of (a) ZH at 3-km altitude, (b) column-maximum ZH, and (c) SL3D classification for a supercell located in northeast TX at 0055 UTC 18 May 2013. The thick line labeled A–B in (a) and shown in each map shows the location of the vertical cross sections in Fig. 2.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
The SL3D classification shows that the precipitating portion of the supercell is largely identified as convection, with a broad convective updraft near the location of the hook echo. To determine what physical characteristics are contributing to the SL3D classification of the supercell, we present a vertical cross section of the polarimetric variables in Fig. 2 along a path that bisects the storm’s hook echo and updraft region (the A–B line in each map in Fig. 1). The vertical sections reveal that both a deep (up to 8 km in altitude) bounded WER and 
Vertical cross sections of (a) ZH, (b) ZDR, and (c) KDP following the thick line in Fig. 1, from A (left) to B (right). The thick colored line at the base of each cross section shows the corresponding SL3D classification.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
While the example using WSR-88D observations in Figs. 1 and 2 is encouraging, validation of the performance of the echo-based updraft algorithm is desired to establish confidence in its use. To achieve such validation, we include examples of SL3D application to two multi-Doppler radar cases, which provide measurements of the three-dimensional wind fields within storms. The vertical velocities were retrieved using variational integration of the continuity equation (O’Brien 1970). Figure 3 presents application of the SL3D algorithm to a supercell storm at 0030 UTC 30 June 2000 that was observed during the Severe Thunderstorm Electrification and Precipitation Study (STEPS; Lang and Rutledge 2002; Lang et al. 2004). Since this case includes only single-polarization radar observations (i.e., 
Maps of (a) ZH at 3-km altitude, (b) column-maximum ZH, (c) the SL3D classification, and (d) dual-Doppler-derived mean vertical velocity in the vertical column from a storm observed during STEPS at 0030 UTC 30 Jun 2000. The black lines denote the SL3D updraft classifications using WER identification alone.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
A second validation case is provided in Fig. 4. For this case, dual-Doppler radar observations are taken from a storm in northeast Colorado (Basarab et al. 2015; Basarab 2015) observed at 2230 UTC 6 June 2012 during the Deep Convective Clouds and Chemistry (DC3) experiment (Barth et al. 2015). In contrast to the STEPS storm, this DC3 case includes dual-polarization observations that allow for validation of the entire three-step updraft identification algorithm in SL3D. For this case, the updraft identified in both SL3D and the Doppler wind field is displaced to the south of the most intense precipitation (Figs. 4a and 4f). Although the updraft region is displaced, the updraft location in the dual-Doppler wind field and SL3D classification are nearly coincident. The WER is once again visible by comparing the 3-km and column-maximum 
Maps of (a) ZH at 3-km altitude, (b) column-maximum ZH, (c) ZDR at 5-km altitude, (d) KDP at 5-km altitude, (e) the SL3D classification, and (f) the maximum dual-Doppler-derived vertical velocity at 2230 UTC 6 Jun 2012. The black lines denote the SL3D updraft classifications using WER identification alone and the white lines denote the SL3D updraft classifications using polarimetric variables alone.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
5. Comparisons of SL3D with traditional methods
As outlined in the introduction, traditional radar echo classification methods like the SHY algorithm are designed for precipitation estimation and use a single low-altitude map of 
Figures 5a–c show maps of column-maximum 
Maps of (a) column-maximum ZH, (b) SL3D classification, (c) SHY classification, and (bottom) a vertical cross section of ZH following the thick line labeled A–B in (a) for a collection of deep quasi-linear convective storms over OK and southeast KS at 0125 UTC 14 May 2009. The thick colored lines at the base of the cross section show the corresponding SL3D and SHY classifications.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
Figure 6 shows application of the SL3D algorithm to a case containing multiple discrete supercell storms and a mesoscale convective system (MCS) over central and northeastern Oklahoma, respectively, at 2325 UTC 23 May 2011. The melting level for this case is ~4.25 km. This case demonstrates the performance of the SL3D classification for a wide variety of convective organizations and intensities. Only single-polarization observations are available, such that updrafts are classified using WER identification alone. Both SL3D and SHY produce reasonable convective classifications within the MCS, again with noticeably larger convective regions in the SL3D classification. The differences in the scales of convective classifications between SL3D and SHY are largest in the supercell storms, which is a reflection of the dependence of SL3D on the depth of the intense reflectivity column. For the WER-only updraft classification in SL3D, this case demonstrates that unless the convection is sufficiently intense, few, if any, updraft regions are identified using the WER method alone. In particular, each supercell has a clearly defined updraft, demonstrating the robustness of the WER classification method in supercell storms, which (as discussed in section 3c) typically contain large bounded WERs. The MCS in the northeastern portion of the domain, however, shows little to no area classified as convective updraft.
Maps of (a) column-maximum ZH, (b) ZH at 3-km altitude, (c) SL3D classification, and (d) SHY classification for a collection of supercell storms and an MCS over OK at 2325 UTC 23 May 2011. The white ellipse in (a) encloses weaker convection that is discussed in the text.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
The cases presented thus far are largely limited to intense and/or extreme storms located in the U.S. Great Plains. To demonstrate the success of SL3D in other regions and environments, we include three additional cases here and a fourth in section 6 below. First, Fig. 7 shows observations centered over southeast Texas during the landfall of Tropical Storm Bill at 0000 UTC 17 June 2015. Additional weaker convection and stratiform rain is included in the northwestern portion of the domain and moderately intense convection in the eastern portion of the domain. The melting level for this case is ~4.75 km; however, a pronounced increase in the melting-level height is noted by the height of the bright band within Tropical Storm Bill (line A–B; Fig. 7). While differences similar to those outlined in previous cases can be observed here, we focus our attention on differences within the tropical storm and in the broad area of weak convection surrounded by stratiform rain in the northwest portion of the domain. Specifically, the vertical cross section labeled A–B in Fig. 7a bisects Tropical Storm Bill, while the cross section labeled C–D bisects the weaker convection.
Maps of (a) column-maximum ZH, (b) SL3D classification, (c) SHY classification, and (bottom) vertical cross sections of ZH following the thick lines labeled A–B and C–D in (a) for Tropical Storm Bill in southeast TX and additional nearby precipitation in AR, LA, OK, and TX at 0000 UTC 17 Jun 2015. The thick colored lines at the base of each cross section show the corresponding SL3D and SHY classifications.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
For Tropical Storm Bill, a deep convective tower is observed to be reaching altitudes in excess of 17 km near the center of the storm, followed by a large region of weak-to-moderate stratiform rain radially outward. Both the SL3D and SHY classifications correctly identify the convective region near the center of the storm, with the SL3D convective classification extending farther toward the center. The displacement of the SL3D classification relative to that from SHY corresponds to the extension of higher reflectivity aloft, capturing the weaker precipitation just below the high-reflectivity column. Radially outward from the convective region, however, is a region with larger differences between the SL3D and SHY classifications. Namely, there is a region of intense stratiform rain classified by SHY as convective. Though overrepresentation of convection by the SHY algorithm is rare, such false classification is due to the absolute 
Additional differences between the SL3D and SHY classifications are observed in the cross section through the weaker convection in Fig. 7 (labeled C–D). This cross section demonstrates the SL3D classification capturing the horizontal extent of higher reflectivity in the weaker storms while the SHY algorithm classifies smaller regions that appear to be primarily limited to exceedances of the 43-dBZ 
Further examples of improvements in the classification of weaker convection can be found in storms from the Southeast and Northeast regions of the United States (Figs. 8 and 9, respectively). The melting level for the Southeast case is ~4.5 km and for the Northeast case it is ~4.25 km. For the Southeast case, there are two lines of convection: one translating northwest to southeast across the Florida panhandle and the other translating southwest to northeast across central Georgia. For both convective lines, SL3D convective classifications are both more numerous and slightly broader in horizontal extent. We present a cross section in Fig. 8 through one of the convective regions that is broad in the SL3D classification and marginally present in the SHY classification. In this cross section, two weak-to-moderate convective cells are apparent on the southern end of the storm and reach altitudes at and slightly above the melting level. While SL3D identifies both of these convective regions well, SHY misses the deeper of the two, which has lower column-maximum 
Maps of (a) column-maximum ZH, (b) SL3D classification, (c) SHY classification, and (bottom) a vertical cross section of ZH following the thick line labeled A–B for an MCS located over AL, FL, and GA at 0000 UTC 24 Jul 2013. The thick colored lines at the base of the cross section show the corresponding SL3D and SHY classifications.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
As in Fig. 8, but for scattered weak convection and an MCS located primarily over NY and PA at 2300 UTC 25 Jun 2014.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
6. Importance of the polarimetric updraft classification
As outlined in section 3c and demonstrated using multiple cases in this study, convective updraft identification using single-polarization radar observations with the SL3D algorithm is limited to the existence of WERs in 
Figures 10 and 11 demonstrate the importance of identifying both 
Maps of (a) column-maximum ZH, (b) ZDR at 5-km altitude, (c) KDP at 5-km altitude, (d) SL3D classification, (e) SL3D classification with ZDR-only updraft classification, and (f) SL3D classification with KDP-only updraft classification for an MCS located in northern IN and OH at 0330 UTC 13 Jun 2013. The thick lines on each map show the locations of the vertical cross sections in Fig. 11.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
Vertical cross sections of (a) ZH, (b) ZDR, and (c) KDP along the line in Fig. 10, from A (left) to B (right). The thick horizontal line in each cross section represents the altitude of the environmental melting level and the thick colored line at the base of each cross section shows the corresponding SL3D classification.
Citation: Monthly Weather Review 145, 3; 10.1175/MWR-D-16-0089.1
7. Limitations of the SL3D algorithm
Although we have presented several successful applications of the SL3D algorithm, there are some limitations of the method worth discussing here. While the WER updraft classification performs well in strong supercell storms and is able to identify the core updraft region (e.g., Fig. 3), more quantitative validation is required. Additionally, there are cases where false WER-based updraft classifications are revealed in the SL3D classification. Such false WERs are typically associated with deep convection containing narrow regions of precipitation, leading to updraft classifications on both upstream and downstream sides of the storm. In reality, most updrafts are limited in space to one side of a storm (e.g., Jorgensen et al. 1997; Lang and Rutledge 2008; and Figs. 3 and 4 here). Examples of this error can be seen for the 14 May 2009 case in Fig. 5. It should be noted, however, that such WER errors typically account for ≪1% of the total classified area (determined by analyzing updraft classifications in several additional cases not shown here). Thus, we expect false WER identifications to be negligible in most (if not all) cases.
While the convective classification in SL3D performs well in most cases, there are times where some stratiform rain is falsely classified as convection. The thresholds used in the convective classification here were chosen in order to minimize such errors using many case studies of the NEXRAD WSR-88D composite observations. These errors depend strongly on the intensity of stratiform rain and the melting-level altitude (which may be modified significantly within a storm). Future studies are needed to examine the probability of detection and false alarm rate of the convective classification for weak convection.
Finally, there are important limitations of the SL3D algorithm related to the characteristics of the radar dataset it is applied to. Since the SL3D classifications require substantial vertical information to be successful, it may not be appropriate to apply the algorithm to data from a single NEXRAD WSR-88D because of both a lack of vertical coverage and resolution degradation at larger distances from the radar. However, the SL3D algorithm can be applied to any gridded volumetric radar dataset so long as the vertical resolution of the dataset is sufficient (≤1-km grid spacing) and the depth of the volume spans altitudes from 3 to 10 km (as required by the classification categories). In addition, one potential issue for application of the SL3D algorithm related to grid resolution is the sensitivity of the convective classification to the melting-level altitude. Namely, for datasets with vertical resolution that meets or exceeds the uncertainty in the altitude of the melting level used, the 
8. Summary and discussion
This study introduced a new storm classification algorithm for single- and dual-polarization radar observations that leverages three-dimensional information of a volumetric dataset: the SL3D algorithm. Several cases of varying intensity, complexity, and regionality were presented to demonstrate the performance of the algorithm. Comparisons between the SL3D algorithm and a traditional storm classification method (Steiner et al. 1995) revealed that convective regions were commonly larger in scale when using the SL3D classification. This difference was shown to commonly be the result of including echo-top information in the classification and is dependent on the degree of vertical tilt of convection. For cases of less intense convection that traditional methods were unable to detect, the SL3D algorithm was successful in their identification (e.g., see Figs. 7–9). Both the increased frequency of identifying convection and the larger convective regions may have an important impact on the latent heating budget of convective systems (e.g., Houze 1989), especially for latent heat retrievals utilizing two-dimensional methods to aid in the discrimination of echo (e.g., Tao et al. 1993, 2001).
In addition, we introduced a novel three-part convective updraft identification method that leverages both single- and dual-polarization radar information and enables identification of updrafts within storms of varying intensity and complexity. For single-polarization radar, we employed a WER identification method, which was shown to perform well in supercell storms but was unable to routinely identify updrafts in cases with alternative convective organization. For dual-polarization radar observations, the addition of 
Since SL3D enables the classification of radar echo into five dynamically and physically based categories, it allows for targeted research on individual elements of a storm. For example, previous convective transport studies have found that 
Acknowledgments
We thank two anonymous reviewers and M. Kumjian at The Pennsylvania State University for providing constructive comments on the manuscript. We would also like to thank Brett Basarab from Colorado State University for providing the DC3 dual-Doppler data. MS and GLM were supported by the National Science Foundation (NSF) under Grant AGS-1432930. CRH was supported by the NSF under Grant AGS-1522910.
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