a. Disdrometer datasets

Recent campaigns by the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Program (Ackerman and Stokes 2003) and the National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM; Hou et al. 2014) ground validation (GV) program have greatly expanded DSD observations globally. We have compiled 12 disdrometer datasets from diverse locations and meteorological regimes, spanning from the tropics to the high latitudes, that are supported by polarimetric radar observations (Table 1). Two-dimensional video disdrometer (2DVD) datasets from tropical ocean (Manus Island, Papua New Guinea, and Gan Island, Maldives), tropical coastal (Darwin, Northern Territory, Australia), midlatitude continental [Southern Great Plains (SGP)], and high-latitude continental (Finland) locations were provided by the DOE ARM program. These datasets were collected in collaboration with several DOE field campaigns: Tropical Warm Pool–International Cloud Experiment (TWP-ICE) in 2006 (Darwin), ARM MJO Investigation Experiment (AMIE) in 2011 (Gan and Manus Islands), and Biogenic Aerosols—Effects on Clouds and Climate (BAECC) in a high-latitude boreal forest (Finland). Collocated disdrometer and polarimetric radar datasets from coastal orographic high-latitude, continental high-latitude, midlatitude orographic, and midlatitude continental locations were provided by five recent NASA GV experiments [Light Precipitation Validation Experiment (LPVEx): Finland; Midlatitude Continental Clouds and Convection Experiment (MC3E): Great Plains; Iowa Flood Studies (IFloodS): Iowa; Integrated Precipitation and Hydrology Experiment (IPHEx): southern Appalachian Mountains; and Olympic Mountains Experiment (OLYMPEX): Washington State). Additionally, a midlatitude coastal disdrometer dataset was collected at NASA Wallops Island, Virginia. The locations of the datasets are shown in Fig. 1, and a summary of the data and experiments is given in Table 1. These datasets ranged in length from six weeks (LPVEx) to five years (SGP) and sampled from 2080 raining minutes (~35 h; LPVEx) to 78 124 raining minutes (~1300 h; OLYMPEX).¹ While the NASA GV experiments deployed several instruments to sample spatial variability, all raining minutes from all described instruments are considered together for each campaign. Field campaign data from the same geographic location and/or time are grouped with corresponding longer-term datasets, resulting in eight datasets: IFloodS, SGP, IPHEx, Finland, tropical ocean, Darwin, OLYMPEX, and Wallops. For ease of discussion and analysis herein, data have been grouped by latitude (Fig. 1): high (≥45°), middle (23°–45°), and low (≤23°), based on the similarities between datasets in common latitude bands (not shown). This grouping results in approximately 90 000 raining minutes in the high and low latitudes and 150 000 min in the midlatitudes, with each band comprising both field experiments and long-term installations.

Table 1.

Description of disdrometer datasets used in this study. The *, +, #, and † denote datasets that were grouped because of cospatial/cotemporal or similar variability and will be referred to by the identifier name. The raining minutes presented are after the quality control described in the text.

• Download Figure
• Download figure as PowerPoint slide

(a) Locations of disdrometer observations used herein. See Table 1 for individual datasets that fit into the larger eight locations. (b) Distribution of raining minutes as a function of latitude band.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Most of the observations used are derived from a 2DVD (Schönhuber et al. 2008), which uses perpendicular lasers to image drops that fall through the square catchment area (100 cm²). During TWP-ICE, a Joss–Waldvogel impact disdrometer (JWD) was used (Joss and Waldvogel 1967). During OLYMPEX, five 2DVDs were deployed along with 13 automated Parsivel units (APU; Battaglia et al. 2010). During OLYMPEX, the 2DVDs were found to undersample the number of drops because of high drop concentrations in this complex orographic environment. For this reason, we opted to use the APU optical disdrometers for OLYMPEX.

Following the methodology in T15, 1-min data in every location were thresholded on the total number of drops (>100) and rain rate (>0.05 mm h⁻¹). This threshold removed on average 30% of the data but less than 1% of the total rainfall (the drop count threshold was responsible for the removal of most observations). These thresholds help prevent small sample sizes from skewing DSD estimates (Smith et al. 1993; Smith 2016). The 2DVDs directly measure liquid water content (LWC; g m⁻³) and rain rate R (mm h⁻¹), while an empirical fall speed relationship is used for the JWD and APUs to obtain LWC and R (Tokay et al. 2001). A “deadtime correction” (Sheppard and Joe 1994) was applied to the JWD data to account for recovery time of the instrument transducer following drop impacts (Williams et al. 2000). Although it would be ideal to have common platforms across all locations, the availability of these datasets necessitates using three different instruments. Despite different limitations of each instrument such as limited drop sizes (JWD), overestimates of drop size in heavy rain (Parsivels), and beam mismatch (2DVD), previous studies have analyzed the comparative performance of JWDs, 2DVDs, and Parsivels and generally found agreement in distribution fits and integrated parameters (e.g., Tokay et al. 2001; Thurai et al. 2011). We performed a sensitivity study (not shown) where analysis with collocated instruments (e.g., 2DVD and APU in OLYMPEX) confirms that the results presented herein do not significantly change based on instrument choice.

The mass spectrum can be derived directly from disdrometer measurements (Williams et al. 2014):

where N(D) is measured by the disdrometer as a function of the size bins and ρ_w is the density of water (g cm⁻³). The rain DSD can then be described by the mean mass diameter D_m, which is the first moment of the mass spectrum, and the mass standard deviation σ_m, the square root of the second moment, which represents the breadth of the mass spectrum. For more details of this formulation, see Williams et al. (2014).

Rain DSDs have often been described with a modified gamma distribution (Ulbrich 1983), which is nominally defined by an intercept, median size, and shape factor that describes the breadth and slope of the distribution. A special case of the four-parameter modified gamma distribution is the normalized gamma with three free parameters (Petty and Huang 2011). The normalized gamma distribution accounts for varying LWC (Willis 1984) and is described by the intercept parameter N_w (m⁻³ mm⁻¹; we will use logN_w for ease), median drop diameter D₀ (mm), and shape parameter μ:

where N_w (mm⁻¹ m⁻³) is defined as

Additionally, D_m is related to the median drop diameter through μ:

Although the assumption of a normalized gamma fit to the DSD may not fully capture the true spectrum of rain DSDs (Thurai et al. 2017), we employ it here to place our results in context with the wide body of previous literature that invoked this assumption.

Further details of the gamma distribution can be found in Bringi and Chandrasekar (2001). To derive the parameters of the normalized gamma DSD from each minute of disdrometer data, the Thurai et al. (2014) methodology was adopted, which fits the gamma parameters through a μ-search technique. For further information about DSD formulations and processing, see Bringi and Chandrasekar (2001), Thurai et al. (2014), and T15. Data were restricted to μ values in the range from −4 to 15 to ensure the gamma fit is a reasonable assumption. This screening process removed <1% of data points in our dataset.

Several datasets included times when frozen precipitation was present (e.g., LPVEx, OLYMPEX, SGP, and Finland). For the shorter GV field projects with multiple 2DVDs, instruments and dates were excluded from analysis when snow contamination was identified (LPVEx and OLYMPEX; A. Tokay and J. Zagrodnik 2016, personal communication). However, for the longer datasets (SGP and Finland), a more automated method was developed to discard snow-contaminated observations. A distinct population of data exhibited lower-than-expected R for a given LWC. Since R is fundamentally related to the fall speed and size of each drop, this indicates a population of particles with fall speeds lower than that of rain (e.g., snow; Yuter et al. 2006). Thus, any days that had 10 or more points that fell below R = 9.0 LWC^1.1 (determined subjectively based on the anomalous population and examination of those days against ASOS observations of snow) were excluded from the analysis to remove snow contamination.

b. PCA

PCA is a technique often used in atmospheric science to simplify the analysis of large and complex datasets. In essence, PCA uses linear regression to explain the main modes of variability of a dataset. Hence, the variability of a dataset is distilled into its most important components. PCA can be thought of as a type of pattern or cluster analysis that explains the covariance of parameters simultaneously. Additionally, PCA is empirical in that the results are based solely on the dataset. For example, in the BR03 study, convective and stratiform DSD were stratified based on rain rate. In PCA, such assumptions are unnecessary.

PCA results in a set of vectors [also called empirical orthogonal functions (EOFs)] forming an orthogonal set of basis vectors and are ordered by their ability to explain the variability in the dataset. The first EOF is the vector that explains the largest amount of variance. The second EOF is orthogonal to the first EOF and describes the largest fraction of the remaining variance after the variance from the first vector has been removed. This process continues until the collective EOFs explain all of the variance (including noise). For example, if there are six input parameters, there will be six resulting EOFs, which will collectively explain 100% of the variance in the sample dataset. In practice, some studies may concentrate on the first few leading EOFs, since successive EOFs may yield little additional physical interpretation. For these reasons, we only present the leading two EOFs for our analysis. A linear combination of the EOF vectors describes each point in the dataset, the coefficients of which are known as the principal components (PCs). The PCs can be thought of as a measure of the resemblance between a particular data point and an EOF vector.

To prepare the disdrometer data for PCA, we constructed M (number of attributes or quantities describing the DSD) arrays of length N (corresponding to the number of DSD data points). For the PCA analysis, we selected D_m, N_w, and σ_m to describe the DSD and the integral rain parameters R, LWC, and total number of drops N_t to describe the DSD variability. These parameters are selected because they are commonly used to describe precipitation, they can be easily calculated from disdrometer measurements, and they provide meaningful information toward understanding the physics of rainfall. We have chosen to use the mass spectrum width σ_m and the mean mass diameter D_m instead of the gamma shape parameter μ and the median drop diameter D₀ because the former two variables can be calculated from the disdrometer measurements without the need to assume a gamma distribution. We use N_w because it provides information about how the LWC is distributed across diameter space [Eq. (3)]. The covariance matrix among the six parameters for each latitude band and the global dataset are available in the online supplemental material (Fig. S1). The parameters of N_w, N_t, R, and LWC are lognormally distributed (e.g., Bringi and Chandrasekar 2001; T15) and are therefore included in the PCA in log form (logN_w, logN_t, logR, and logLWC). The data are normalized to standard anomalies of each characteristic quantity by subtracting the mean and dividing by the standard deviation. This was done to prevent quantities with large variances from dominating the EOFs, which could obscure scientifically relevant results. Additionally, deviations from the mean indicate when values are anomalously high or low, making simultaneous interpretation of multiple quantities easier. Once each quantity is standardized, the arrays are combined into a matrix of N rows × M columns. The PCA returns M orthogonal EOF vectors, with corresponding values of fractional variance explained, as well as N PC values (corresponding to each data point) for each EOF vector.

The orthogonality constraint imposed by PCA can cause problems in certain situations. First, information about a particular process may be included in multiple EOFs because physical processes are not necessarily orthogonal. Second, each PC series can have positive and negative values. Since the sign of each EOF is arbitrary, each mode of variability has exactly two opposite components. This can complicate the physical interpretation of PCA results since physical processes are not always linear and orthogonal. Nonetheless, PCA provides an objective lens through which we can look at a large disdrometer dataset to gain novel insights about precipitation formation processes.

a. Comparisons of datasets

We begin by examining the variability of DSDs across latitude bands projected in logN_w–D₀ space (Figs. 2a–c). The BR09 and T15 C-S separation lines are included for context. In all locations, the most frequent values are centered near D₀ = 1 mm, with the median logN_w higher in the high latitudes (3.8–4) and lower in the midlatitudes (3–3.5). The midlatitudes have broader ranges of D₀ and N_w compared to high and low latitudes. The characteristic bimodality in the tropics of logN_w is evident, which was noted by previous studies. The tropical distribution of logN_w peaks in terms of frequency of occurrence at 3.4 and also at 4, and these maxima correspond to convective and stratiform populations (Ulbrich and Atlas 2007; BR09; Thurai et al. 2010; Bringi et al. 2012; T15). Indeed, this distinction serves as the basis for the T15 C-S separation line. We find it curious that the tropical datasets exhibit such a distinct bimodality in logN_w and D₀ associated with C-S rain. This bimodality is lacking in other datasets such as the midlatitudes despite significant convective and stratiform precipitation components. In fact, the T15 line appears to cut through the mode of the logN_w–D₀ distribution in the high latitudes, suggesting this method is only appropriate for characterizing C-S precipitation within the tropical oceans. It is possible that the intense ice-based precipitation in the midlatitudes somehow disrupts the clear separation seen in the tropics, where ice processes are likely weaker or play a lesser role in overall precipitation. Thus, the oceanic convection is size limited (e.g., constrained D₀) but dependent on LWC, which directly drives logN_w [Eq. (3)]. Another striking feature of the tropics is the moderate density of points clustered around D₀ = 1.5 mm and logN_w = 4–5, a population that is not readily evident in the other locations. This is associated with a peak in LWC > 1 g m⁻³ at about D₀ = 1.7 (Fig. 2f). Again, the tropics have two distinct clusters in D₀–LWC space that have been noted in many previous studies (Tokay and Short 1996; Yuter and Houze 1997; T15) as being associated with convective (upper branch) and stratiform (lower branch) precipitation. The midlatitude datasets have a noticeable extension of large mean diameters for moderate LWC (Fig. 2e). The high latitudes rarely exceed 1 g m⁻³, with the most frequent values being 0.1–0.5 g m⁻³ (Fig. 2d). Interestingly, these median values are higher than the most frequent values in the other locations (Figs. 2d–f), which could be due to the atmospheric rivers affecting the OLYMPEX region (which dominate the high-latitude sample) bringing ample moisture to the domain (Houze et al. 2017).

• Download Figure
• Download figure as PowerPoint slide

Two-dimensional normalized frequency of occurrence as a function of latitude band for (a)–(c) logN_w–D₀ and (d)–(f) LWC–D₀. The BR09 and T15 C-S lines are presented with gray dashed and solid lines, respectively, in (a)–(c).

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

It is obvious from Fig. 2 that DSDs vary by location (individual locations shown in Figs. S2 and S3), and as in the case of C-S separation lines, there may be important underlying microphysical processes that are responsible for this variance. It is also clear that no one location fully captures the entire spectrum of global DSD variability. Given this regional DSD variability, we are motivated to ask, what are the primary modes of temporal and spatial DSD variability across the globe? Can different surface DSDs be explained and linked to the microphysical processes shaping them aloft? We explore these questions next.

b. PCA results

Figure 3 shows the first two primary EOFs associated with the DSD characteristic parameters (logN_w, D_m, σ_m, logLWC, logR, and logN_t). The standard anomaly associated with each parameter for each of the resulting EOFs is indicated. Importantly, despite some spread in the magnitude of the standard anomalies, every location shows the same modes of covariance in the first two EOFs. Although we present the aggregate of datasets in a given latitude band, this finding holds true for every individual dataset (Fig. S4). Again, we note that the sign of each PC is arbitrary and that mathematically the positive and negative modes are exact opposites. We have neglected the EOFs beyond EOF2, which collectively explain a much smaller amount of variability and may relate to measurement noise or higher-order temporal variability rather than underlying physical processes (Larsen and O’Dell 2016). It is important to note that the first two EOFs explain ~88% of the variability across all latitude bands (Table 2). The positive mode of EOF1 is associated with relatively high logLWC and logR, large logN_w, large D₀, and high σ_m. This EOF explains 57%–62% of the variability in each location and 58% globally (Table 2). EOF2, which explains 20%–31% of the variability (30% globally), is characterized by relatively large logN_t and logN_w and small D₀ and σ_m in the positive mode but relatively little variability in logLWC or logR.

• Download Figure
• Download figure as PowerPoint slide

The first two EOFs for each latitude band and the global dataset (black). Solid lines indicate the positive modes, and dashed lines indicate the negative modes (where the sign is arbitrary).

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Table 2.

Percent variance explained by the first two EOFs.

To equally compare resulting EOFs from different locations, each of which may or may not capture the full breadth of DSD variability, we normalize all data against the global dataset (i.e., all data combined) by subtracting the global mean and dividing by the standard deviation. All subsequent results are shown relative to this global normalization and global EOFs.

It is most useful to examine these orthogonal modes of variability by investigating data points that are most characteristic of each mode. This is accomplished by isolating points with the largest PC values, which represent where the points project most strongly onto an EOF. To this end, unless otherwise indicated, we select a threshold of |1.5| (σ_1.5) for all PCs. The selection of points that do not meet these criteria will be referred to as “ambiguous” because they bear resemblance to multiple EOFs. Here, we note that these threshold values are somewhat arbitrary and the high thresholds used herein have been selected to highlight differences between populations, but the overall results do not change with the prescribed threshold; larger values result in more distinct separation between opposing modes, while smaller values result in more overlap.

The distributions of PC1 and PC2 for each latitude band are shown in Fig. 4. The σ_1.5 thresholds are illustrated with dashed lines. While the bulk of points (~77%) are contained below the thresholds (by design), 23% of points meet one or more of these thresholds; in fact, there is a noticeable population with large absolute PC1 and PC2 values. Leveraging these PC distributions, we define six distinct groups. Illustrated by colored boxes in Fig. 4, these groups are positive PC1 but ambiguous PC2 (group 1; red), negative PC1 (group 2; green), positive PC2 but ambiguous PC1 (group 3; yellow), negative PC2 and ambiguous PC1 (group 4; blue), positive PC1 and positive PC2 (group 5; orange), and positive PC1 and negative PC2 (group 6; purple).

• Download Figure
• Download figure as PowerPoint slide

Frequency density of joint distributions of PC1 and PC2. Dashed red lines illustrate the σ_1.5 thresholds, and the dashed black lines indicate the 0 value for PC1 and PC2. Shaded boxes represent the six groups of points with similar characteristics based on PCA.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Already, clear latitudinal differences emerge from this PC-based grouping (Fig. 4). For example, the high latitudes have a large number of points in group 3 but few points in group 5, group 1, or group 6 at the σ_1.5 threshold. In contrast, the low latitudes have a number of points in both group 1 and group 5. The midlatitudes have the largest number of points in group 6 of any latitude band. The relative percentages of each group in each band is shown in the supplemental material (Fig. S5). We will probe the characteristics of each of these six populations in the next section to understand their potential origins from a microphysical perspective and possible implications.

c. DSD parameters

Here, we will cast the results of the PCA into different formulations and 2D distributions for physical interpretation and comparison with previous studies. For example, BR09 and T15 found distinct populations in logN_w–D₀ and LWC–D₀ space, which they attributed to convective and stratiform rainfall.

Mean gamma DSD, determined by inserting the mean values for N_w, D₀, and μ into Eq. (2) for each of the six groups identified above, contrasts the characteristic size distributions associated with the associated covariance among the DSD parameters (Fig. 5a). Figure 5b illustrates the normalized (section 2b) mean values of the different parameters for each of the six groups. For reference, the global mean values of LWC, R, N_t, σ_m, and the gamma parameters (logN_w, D₀, and μ) are annotated in Fig. 5a, and mean values of the gamma parameters are listed in Tables 3–5. Group 1 (red) is associated with R significantly larger than 4 mm h⁻¹ (the global mean), shape parameters μ < 4, and mean drop diameters D₀ > 1.1 mm, resulting in a broad size distribution. In contrast, group 2 (green) is characterized by narrow size distributions (Fig. 5a) and relatively low R and LWC (Fig. 5b). Both groups 4 (blue) and 6 (purple) have strong negative anomalies in μ (i.e., smaller than the global mean of 4), resulting in more exponential-type (broad) size distributions (Fig. 5a). While having anomalously large D₀ and low logN_w, group 6 also has anomalously high logR, logLWC, and drop concentrations (logN_t). Here, we recall that N_w is directly proportional to LWC but inversely proportional to D₀⁴ [Eq. (3)]. The resulting anomalously low logN_w is due to the exceptionally high D₀ anomalies even though the total number of drops and LWC are high. Group 3 has a high logN_w consistent with the smallest mean mass-weighted diameter, indicating a population of numerous small drops with little size dispersion. This population also has logLWC and logR values near the global mean. However, DSDs in group 5 (orange) have the highest anomalies of logR and logLWC, greatest total number of drops, and highest logN_w.

• Download Figure
• Download figure as PowerPoint slide

(a) Global characteristic size distributions using the mean values for each identified group. Global means of all data points are indicated. (b) Normalized mean values of parameters for the six groups.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Table 3.

Mean D₀ values for the six groups using the PC thresholds in Fig. 4.

Table 4.

Mean logN_w values for the six groups using the PC thresholds in Fig. 4.

Table 5.

Mean μ values for the six groups using the PC thresholds in Fig. 4.

These PCA-guided groups result in distinct clusters in 2D parameter space (Figs. 6 and 7). Again, we note that although we only display the aggregate results for the three latitude bands, these clusters are repeatable in every dataset considered (see Fig. S6). Perhaps most striking, but maybe not unexpected because of the orthogonality of the EOF analysis, is the distinction in logN_w–D₀ space (Figs. 6a–c). Group 1 (red) resides in the moderate to high D₀ and moderate to low logN_w, but it is clear this group contains the highest LWC observations in our dataset, along with group 5 (Figs. 7a–c). This population of points is associated with relatively low, even negative, values of μ (Figs. 6d–i), indicating broad size distributions (Fig. 5a). The surprising conformity of this cluster in the tropics to the robust C-S lines proposed by T15 and BR09 underpins group 1 as convective. Conversely, the points in group 2 (green) are confined to relatively small D₀ values and low logN_w because of the combined effect of low LWC and small D₀. The bulk of the population falls in the stratiform classification for both BR09 and T15 C-S in the tropics. Additionally, this cluster has generally high μ values (>6), indicating relatively narrow size distributions (Figs. 6d–f and 5a) or perhaps that a normalized gamma distribution is inadequate to describe the distribution of these particular samples (Thurai et al. 2017).

• Download Figure
• Download figure as PowerPoint slide

Two-dimensional distributions of each group in the (left) high-, (center) mid-, and (right) low-latitude bands for (a)–(c) logN_w–D₀, (d)–(f) μ–D₀, and (g)–(i) logN_w–μ space. The gray dots encompass the entire space for each dataset and represent the points that did not meet PC thresholds (ambiguous); red is group 1, green is group 2, yellow is group 3, blue is group 4, orange is group 5, and purple is group 6. Contours highlight smoothed Gaussian 1-σ points for each group. In (a)–(c), the solid black line is the T15 C-S separation line for the tropical oceans and the dashed black line is the BR09 C-S separation.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

• Download Figure
• Download figure as PowerPoint slide

As in Fig. 6, but for (a)–(c) LWC–D₀, (d)–(f) Z–R, and (g)–(i) R–μ space.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Group 3 (yellow) points are largely restricted to logN_w values larger than 4.5 because of a wide range of LWC but small D₀ (Figs. 7a–c), with the bulk of the population having small (<~1.0 mm) D₀ (Table 3). Group 3 points span nearly all μ (Figs. 6d–i and 7g–i), especially in the high latitudes, but the majority are larger than μ = 5 (Table 5). The group 3 population falls in the region of the spectrum that both BR09 and T15 attribute to weak, shallow radar echoes. Group 4 (blue) is associated with large D₀ (>1.5 mm, up to 3 mm) and low logN_w (<3.5, as low as 1), which is a function of both the large sizes and the relatively low LWC (Fig. 7). Group 4 has μ values generally <3, centered from around −1 to 0 (Figs. 6d–f; Tables 3–5).

The two groups with large absolute values of PC1 and PC2 (groups 5 and 6; orange and purple, respectively) have notable properties. Group 5 is more common in the tropics compared to the midlatitudes and high latitudes. Group 5 is characterized by the largest total number of drops and the largest LWC despite D₀ near the global mean of 1.13 mm. These points are exclusively above the BR09 and the T15 convective lines in the tropics. In contrast, the midlatitudes have the most points in group 6, which consist of relatively high LWC and moderate N_t but very large sizes, leading to low logN_w values (Fig. 6b). This group also has the lowest μ because of the large number of drops and large mean D₀.

d. Radar observations

We have demonstrated a distinct clustering of surface DSD parameters and speculated about possible physical processes producing these distributions. To further investigate the possible microphysical processes contributing to the DSDs in each of the six groups, we examined the vertical structure of radar echoes over specific disdrometer locations using polarimetric radar observations. In each case, range–height indicator (RHI) and/or plan position indicator (PPI) scans were used to geolocate the radar gates above the disdrometer locations, creating a vertical profile over the disdrometer. These vertical profiles were then time matched to the disdrometer PCA group classifications. This analysis provides an independent method to study the characteristics of each group because the radar and the disdrometer are separate measurements.

Mean reflectivity Z and differential reflectivity Z_dr profiles were created from RHI data for each disdrometer PCA group (Fig. 8). It should be noted that for the radar analysis in this section, the PC thresholds have been lowered for illustration purposes. That is, the matched radar–disdrometer times may not have many points that meet the σ_1.5 thresholds, since only 22% of points in the entire disdrometer database meet these thresholds. To make this problem tractable, we will focus on specific locations: OLYMPEX to represent the high latitudes; MC3E, IFloodS, and IPHEx for the midlatitudes; and Gan Island and Darwin for the tropics, all providing coincident polarimetric data over nearby disdrometers (Table 6). The disdrometer PC values spanning five minutes around the radar RHI time were averaged and used to assign the radar profiles to a particular group. Six RHI gates over each point are averaged, and RHI gate heights were interpolated to a common set of heights for comparison. To account for clutter at the lowest radar bins, the heights start at 0.2 km AGL. The analysis resulted in 1466 (midlatitude), 1336 (low latitude), and 3320 (high latitude) disdrometer/radar matches with precipitation (Table 6). Mean Z and Z_dr for each match were smoothed with a Gaussian filter in height. In each profile, the 0-dBZ echo-top height (ETH) was calculated and plotted against the reflectivity at 2.5 km (Figs. 8g–i) as an estimate of the mean intensity and depth of precipitation in each group. We recognize the complexities of linking vertical information to surface observations because of advection and point-to-volume comparisons, and these effects may dilute the signal in the analysis below. However, we have attempted to minimize these effects through spatial and temporal averaging of the radar and disdrometer data.

• Download Figure
• Download figure as PowerPoint slide

Vertical structure of (a)–(c) reflectivity and (d)–(f) differential reflectivity Z_dr for each of the six groups from coincident radar RHIs for the (left) high-, (center) mid-, and (right) low-latitude bands. (g)–(i) The mean reflectivity at 2.5 km as a function of the mean radar 0-dBZ echo-top height as a function of group determined by the surface disdrometer. Here, the low latitudes are composed from Darwin and Gan Island data; the midlatitudes from IFloodS, MC3E, and IPHEx data; and the high latitudes from OLYMPEX radar data. Note that the numbers composing each group indicated in the legends of (a)–(c) do not match those given in Table 6 because of the ambiguous points, which are not shown. PC thresholds of σ_1.0 were used for this analysis.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

Table 6.

Summary of the radar characteristics and disdrometer matches.

Although the systematic increase in ETH with decreasing latitude is evident (perhaps due to the annual mean tropopause height; Price and Rind 1993), there are clear trends within each group across latitudes (Fig. 8). Groups 1 and 6 have the highest mean reflectivity values (for all latitudes) throughout the depth of the column and significant ETH. Groups 2 and 3 have the lowest mean reflectivities and lowest ETH. Mean ETH in group 3 remains below 5 km in the high and midlatitudes, and mean reflectivities are below 20 dBZ in all latitude bands, suggesting a designation of shallow, weak warm rain showers for this group. Group 2 has similar mean Z and ETH values to group 3 and a relative maximum in Z_dr near the environmental freezing level (e.g., the radar brightband signature). We suggest that this group is likely associated with weak vertical motions indicative of stratiform precipitation, where particles grow by vapor deposition and aggregation and then melt as they fall below the 0°C level (Houze 1997) or are detrained from deep convection and continue to grow in mesoscale updrafts as they fall out (Rutledge and Houze 1987). These processes fundamentally limit the maximum drop diameters and rain rates (Yuter and Houze 2002). Group 4 has a very distinct signature, especially in the midlatitude samples. Group 4 has high ETH and modest peak reflectivities (<30 dBZ). At subfreezing temperatures, radar reflectivities increase toward the melting layer while Z_dr is slightly positive aloft and then decrease toward the melting layer, reaching a minimum near 0 dB just above the environmental melting layer. While this behavior is evident in all midlatitude Z_dr profiles, it is most notable in group 4. This is consistent with small-oriented ice crystals aloft (Kennedy and Rutledge 2011; evident by weak reflectivity and positive Z_dr) that begin to aggregate to form larger particles that increase reflectivity and decrease Z_dr to near zero (associated with very low bulk density and small degrees of oblateness). However, once these particles begin to melt, they produce a sharp increase in both reflectivity and Z_dr (e.g., the radar brightband signature). We postulate that group 4 is consistent with deposition–aggregation-driven stratiform precipitation. There were too few coincident RHIs in group 5 in the midlatitude samples (<20), so they are not shown. At Gan Island (OLYMPEX), the mean ETH for group 5 reaches 8 (5) km compared to the deeper groups 1 and 6, at ~9 (6) km. In both locations, Z values are larger than group 2 or group 3, particularly below the melting layer. In the low latitudes, Z_dr remains constant or increases slightly below the melting layer while Z increases, which is a signature of robust collision–coalescence in the warm layer (Kumjian and Prat 2014). The group 5 signature in OLYMPEX is associated with decreasing Z_dr in the shallow warm layer. This signature has been attributed to drop breakup (Kumjian and Prat 2014); however, this mechanism is unlikely in the OLYMPEX regime because of the short fall distance of drops and generally small drop sizes. Therefore, the physical processes underpinning group 5 in the high latitudes is unclear. The Z_dr profiles of group 6 exhibit increases below the melting layer, especially in the midlatitudes, which had the largest number of samples in this group. The high ETH and large reflectivities above the melting layer are consistent with strong convective vertical motions and are similar to the median convective vertical profiles of midlatitude convection illustrated in Carr et al. (2017). The larger Z throughout the column and warm-layer Z_dr values of group 6 are consistent with a signature of ice-based convection and melting below the 0°C layer. The increasing Z_dr and Z toward the surface suggest continued coalescence growth below the melting layer (Kumjian and Prat 2014).

To put these mean samples into a larger spatial context, we examined time–height series for several cases in each latitude band. The AMIE Gan and OLYMPEX experiments both employed high-temporal-resolution RHI scanning, so time–height series were created by averaging 30 gates in range at each disdrometer gate for each elevation over the disdrometer point. Time–height series for IFloodS and Darwin used PPI data by averaging 10 gates in the azimuthal direction and 30 gates in range over the disdrometer location for each elevation, similar to the quasi-vertical profile (QVP) method described by Ryzhkov et al. (2016) but averaged over a smaller area. Representative reflectivity time–height series for each latitude band for different groups are shown in Figs. 9–11.

• Download Figure
• Download figure as PowerPoint slide

Time–height cross sections constructed from (a) C-band polarimetric (CPOL) PPI data from Darwin and (e),(i) S-band polarimetric (SPOL) RHI data from Gan Island. Radar reflectivity is color contoured in (a), (d), (e), (h), (i), and (l), where (d), (h), and (l) represent a PPI at the time of the vertical line and the disdrometer location denoted by a black dot. The reflectivity scale is the same as the time–height, and the approximate scale of the PPI is given at the bottom. The start times of the PPIs/RHIs used to construct the time–height cross sections are illustrated by hatch marks along x = 0 in (a), (e), and (i). The disdrometer group classifications are shown as colored dots along the time series. (b),(f),(j) For reference, the disdrometer points are shown in logN_w–D₀ space. Below the reflectivity time–height in (a), (e), and (i) are (c),(g),(k) the PC values as a time series, with the PC thresholds indicated by dashed horizontal lines. Note: for illustration purposes, the PC σ threshold has been lowered to σ_1.0.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

• Download Figure
• Download figure as PowerPoint slide

As in Fig. 9, but time–height cross sections constructed from NASA polarimetric (NPOL) PPI data from IFloodS.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

• Download Figure
• Download figure as PowerPoint slide

As in Fig. 9, but time–height cross sections constructed from NPOL RHI data from OLYMPEX.

Citation: Journal of the Atmospheric Sciences 75, 5; 10.1175/JAS-D-17-0242.1

An example from Darwin on 16 January illustrates a region of stratiform precipitation followed by a convective cell passing near the disdrometer at 1205 UTC (Fig. 9a). The majority of the time series is classified as group 4 by the disdrometer during clearly stratiform precipitation, evidenced by a persistent bright band around 5 km. The passage of the convective core results in a brief classification of group 1. A second tropical example from Gan Island shows a widespread stratiform region with a continuous bright band evident at the environmental melting level (~5 km). As an embedded convective element passes by around 0420–0450 UTC (Fig. 9e), reflectivities are enhanced below the bright band, and the group switches from 1 to 5 as PC2 values increase (Fig. 9g). After this time, the PCA is ambiguous before switching to group 6 as the heavy stratiform precipitation sets in (Fig. 9e) and finally groups 4 and 2 as the stratiform echo weakens. This example is also illustrated in T15 and shows the transition from convective (groups 1 and 5) to stratiform (groups 2 and 4) precipitation. The last tropical example, also from Gan Island, shows what is termed “weak, shallow convection” by T15. Reflectivities are largely below 25 dBZ, and the echo top remains below the melting layer in an area of weak echoes (Fig. 9i). The disdrometer PCA shows small PC1 and positive PC2, mostly classified as groups 2 and 3.

The first example from IFloodS, representing the midlatitudes, shows the passage of an intense deep convective core, with peak reflectivities > 50- and 40-dBZ echoes reaching 10 km, followed by a fledgling stratiform region (Fig. 10a). As the core passes over the disdrometer, large PC1 values result in a group 1 classification, followed by a narrow band of group 6 on the back edge of the core, then group 4, and finally group 2 as the stratiform precipitation sets in after 1015 UTC. The second IFloodS example (Fig. 10e) shows a small, shallow convective cell passing around 1840 UTC, followed by a region of “lumpy stratiform” with a clear brightband signature but some enhanced reflectivity above the bright band between 1855 and 1955 UTC. The small convective cell with echo heights only reaching 6 km and reflectivities ~35 dBZ is associated with a limited number of group 5 identifications. Group 4 is identified where the bright band has strong reflectivities (>30 dBZ), and the most intense bright band with reflectivities approaching 40 dBZ is identified as group 6 and even some group 1. As the stratiform weakens after 1955 UTC, the disdrometer PCA identifies mostly group 2. The last example also illustrates a period of lumpy stratiform, with a clear brightband signature but enhanced reflectivity aloft (Fig. 10i). Group 1 is identified early in the time period but switches to group 6 as 30-dBZ reflectivities reach 6–8 km accompanied by large reflectivities in the bright band (>45 dBZ). As the bright band and reflectivities aloft weaken, the classification switches to group 4 and some group 2 (both identifying stratiform precipitation).

The last examples illustrate the unique coastal mountain high-latitude regime in OLYMPEX. Groups 1 and 6 are identified during a period of strong low-level reflectivities, upward of 40 dBZ below 3 km, the approximate height of the environmental melting layer during this time. In a 2-km-deep layer above the melting level, reflectivities are up to 35 dBZ, and echo tops are ~8 km (Fig. 11a). A contrasting example (Fig. 11e) illustrating mostly group 6 and some group 4 shows shallower echo tops (around 6 km) but similar strong reflectivities in the warm layer (below 2 km in this case) and some more intense periods with reflectivities above 45 dBZ (e.g., 1145 UTC). These intense periods are classified as group 6. In contrast to the first OLYMPEX example, reflectivities fall off near the surface. As the reflectivity aloft weakens after 1250 UTC, groups 4 and 2 are evident. Finally, a period of weak, shallow reflectivity is illustrated by the example in Fig. 11i. Echo tops are lower in comparison to the previous two cases (<4 km), and reflectivities are limited to <30 dBZ. The majority of these points are classified as group 3, similar to the weak, shallow echoes accompanying group 3 in the tropical example (Fig. 9g).

These specific examples serve to support our hypothesis that group 1 encompasses convection, with stronger reflectivities and deeper echoes (Figs. 9a,b, 10a, and 11a). The hypothesized stratiform nature of group 2 is also supported by these examples, as this group is generally identified by the disdrometer when radar echoes display a weak to moderate bright band and reflectivities remain below 30 dBZ (Figs. 9a, 10e, and 11i). Radar examples support the hypothesis that group 3 is associated with weak, shallow echoes (Figs. 9i, 11i), while group 4 appears to be associated with more intense stratiform precipitation, where brightband reflectivities are >35 dBZ (Figs. 9a,e, 10e,i, and 11e). According to the radar analysis, group 5 appears when reflectivities in the warm layer are significant (>30 dBZ), suggesting the presence of robust coalescence processes (Fig. 9e). Group 6 is generally associated with the most intense reflectivities, sometimes on the edge of a convective core (Fig. 10a), sometimes in strong, lumpy stratiform (Figs. 10e,i, and 11a,e), suggestive of larger melted ice particles.