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  • View in gallery

    Classification of precipitation types in MC3E. Asterisks and circles represent convective and stratiform precipitation, respectively. The solid line represents Eq. (4) and demarcates different precipitation types. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    Three different DSD groups from (a),(b) event 6 and (c) event 17 (see Table 2 for the event numbers). Each group is composed of DSDs with approximately the same LWC values and different wind speed values. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    Parameters (left) and (right) as a function of wind speed. The solid lines represent the fitted lines to the data with the correlation coefficient values provided in the legends. Data (symbols) are from the same rainfall events presented in Fig. 2: (a),(b) Fig. 2a; (c),(d) Fig. 2b; and (e),(f) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    Parameters (a) and (b) as a function of wind speed for all of the DSD groups. Each line represents the fitted line to the V and V data for a DSD group. Solid, dashed, and dotted lines denote decreasing, increasing, and no-trend cases, respectively. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    Typical normalized DSDs: (left) marked lines represent measured data and solid lines represent lines fit to the data and (right) marked lines represent lines fit to each of the DSD data in a given DSD group. Data (symbols) are from the same rainfall events presented in Fig. 2: (a),(b) Fig. 2a; (c),(d) Fig. 2b; and (e),(f) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    DSD slope as a function of wind speed. The solid lines represent the lines fit to the data with the correlation coefficient values provided in the legends. Data (symbols) are from the same rainfall events presented in Fig. 2: (a) Fig. 2a, (b) Fig. 2b, and (c) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

  • View in gallery

    DSD slope as a function of wind speed for all of the DSD groups. Each line represents the line fit to the mV data for a DSD group. Rainfall data are obtained by (a) 2DVD and (b) Parsivel disdrometers. Solid, dashed, and dotted lines denote decreasing, increasing, and no-trend cases, respectively.

  • View in gallery

    Regime diagram for the binary raindrop collision outcomes adopted from Testik (2009). Vertical dashed arrows are used to illustrate the shift of the raindrop collision outcome predictions from coalescence and bounce regimes to breakup regime for a hypothetical increase of the collisional Weber number values due to wind.

  • View in gallery

    Horizontal raindrop speeds calculated using Eq. (11) from z = 200 m to z = 1 m (disdrometer level) for different drop diameters and selected wind speeds at 1 m elevation (shown next to the solid lines).

  • View in gallery

    Flowchart outlining the analysis procedure that was used to identify the breakup mode(s) that controls the DSD shape evolution.

  • View in gallery

    Spontaneous Weber number values (solid circles) calculated for typical DSDs measured by the 2DVD. Dashed lines represent the critical spontaneous Weber number of 6, and stars represent the spontaneous Weber number value for the largest raindrop retrieved from the MRR measurements but not observed by the 2DVD measurements.

  • View in gallery

    The average of the five largest spontaneous Weber numbers of the DSD spectrum for all of the analyzed 2DVD DSDs plotted against the corresponding wind speeds calculated at the disdrometer level.

  • View in gallery

    Retrieved DSDs from MRR measurements at the height of 1015 m for the entire MC3E field campaign.

  • View in gallery

    Histogram of the number of the DSD spectra for the ratio of the collision period and the travel time of the hypothetical raindrops from an elevation of 1015 m to the disdrometer level .

  • View in gallery

    Collision outcome predictions shown on the p regime diagram for the collisions between a hypothetical raindrop and each of the raindrops in the associated DSD. Predictions are for the same four selected DSDs used in Fig. 11. Percentages of the total predictions that fall into each region of the diagram are provided in the legend.

  • View in gallery

    Histogram of the percentages of the total DSD spectra for the breakup percentages of the total predictions for a given spectrum.

  • View in gallery

    DSDs retrieved by MRR at different elevations as an example of (a) counterclockwise and (b) clockwise rotation of DSDs. (c) Collision outcome predictions (symbols) for the collisions between a 4-mm raindrop and raindrops of different sizes ranging from 0.1 to 4 mm shown on Testik (2009) regime diagram.

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Wind Effects on the Shape of Raindrop Size Distribution

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  • 1 Department of Civil and Environmental Engineering, The University of Texas at San Antonio, San Antonio, Texas
  • 2 Impact Forecasting, Aon Benfield, Chicago, Illinois
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Abstract

The wind effects on the shape of drop size distribution (DSD) and the driving microphysical processes for the DSD shape evolution were investigated using the dataset from the Midlatitude Continental Convective Clouds Experiment (MC3E). The quality-controlled DSD spectra from MC3E were grouped for each of the rainfall events by considering the precipitation type (stratiform vs convective) and liquid water content for the analysis. The DSD parameters (e.g., mass-weighted mean diameter) and the fitted DSD slopes for these grouped spectra showed statistically significant trends with varying wind speed. Increasing wind speeds were observed to modify the DSD shapes by increasing the number of small drops and decreasing the number of large drops, indicating that the raindrop breakup process governs the DSD shape evolution. Both spontaneous and collisional raindrop breakup modes were analyzed to elucidate the process responsible for the DSD shape evolution with varying wind speed. The analysis revealed that the collisional breakup process controls the wind-induced DSD shape. The findings of this study are of importance in DSD parameterizations that are essential to a wide variety of applications such as radar rainfall retrievals and hydrologic models.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Dr. Firat Y. Testik, firat.testik@utsa.edu

Abstract

The wind effects on the shape of drop size distribution (DSD) and the driving microphysical processes for the DSD shape evolution were investigated using the dataset from the Midlatitude Continental Convective Clouds Experiment (MC3E). The quality-controlled DSD spectra from MC3E were grouped for each of the rainfall events by considering the precipitation type (stratiform vs convective) and liquid water content for the analysis. The DSD parameters (e.g., mass-weighted mean diameter) and the fitted DSD slopes for these grouped spectra showed statistically significant trends with varying wind speed. Increasing wind speeds were observed to modify the DSD shapes by increasing the number of small drops and decreasing the number of large drops, indicating that the raindrop breakup process governs the DSD shape evolution. Both spontaneous and collisional raindrop breakup modes were analyzed to elucidate the process responsible for the DSD shape evolution with varying wind speed. The analysis revealed that the collisional breakup process controls the wind-induced DSD shape. The findings of this study are of importance in DSD parameterizations that are essential to a wide variety of applications such as radar rainfall retrievals and hydrologic models.

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Corresponding author e-mail: Dr. Firat Y. Testik, firat.testik@utsa.edu

1. Introduction

Information about drop size distribution (DSD) has been essential to a wide variety of applications, including rainfall retrievals using remote sensing (e.g., ground-based and spaceborne weather radars) and hydrologic and climate modeling (e.g., Bringi and Chandrasekar 2001; Testik and Barros 2007; Testik and Gebremichael 2010). In these applications, DSDs are typically represented using mathematical distribution functions, including exponential (Marshall and Palmer 1948), Gaussian (Maguire and Avery 1994), lognormal (Feingold and Levin 1986), and gamma functions (Ulbrich 1983). These distribution functions are used with the assumption that a static shape is maintained from the cloud level to the ground level. In reality, however, the DSDs are shaped by a number of physical processes, such as drop breakup/coalescence, local updraft/downdraft, and evaporation/condensation through the air column (Testik and Barros 2007). Therefore, a generalized representation of DSDs using a specific distribution function along with the assumption of static DSD shapes presents an accuracy challenge relevant to quantitative analysis and modeling (e.g., Brandes et al. 2004; Adirosi et al. 2014). There have been a number of studies over the past few decades as part of a long, but much needed, pursuit of developing an advanced understanding for the fundamental processes and mechanisms that drive the DSD variations [see Testik and Barros (2007); McFarquhar (2010), and references therein]. In this study, we investigated the effects of horizontal wind, an important but rather overlooked environmental agent, on the DSD shape variations and the governing microphysical processes.

There are two aspects of wind-driven rain that are closely related to our study: wind-induced horizontal drift of raindrops and DSD modulations. The few studies on the horizontal drift of raindrops have been driven by applications such as surface radar rainfall estimation (Collier 1999; Lack and Fox 2007) and rain splash detachment of soil (Erpul et al. 2002). Relevant to our study, horizontal drift of raindrops is considered to have an effect on the microphysical processes that govern the DSD evolution. We incorporated raindrop horizontal drift into our analysis by use of the equation derived by Pedersen and Hasholt (1995), which is included in section 4 of this article. Previous studies reported distinct DSD characteristics during tropical cyclones and hurricanes (e.g., Ulbrich and Lee 2002; Maeso et al. 2005), which are associated with strong winds and typically heavy rains, without delving into the governing microphysics. These studies reported high concentrations of raindrops in the small size spectrum of the DSDs with the absence of raindrops that were larger than approximately 4 mm in equivalent volume diameter (i.e., the diameter of a sphere with the same volume as the raindrop). Among such studies, Tokay et al. (2008) and Friedrich et al. (2013b) used a Joss–Waldvogel disdrometer and a precipitation imaging probe, respectively. Tokay et al. (2008) documented a maximum-observed raindrop diameter of 4.11 mm and a mass-weighted mean diameter of 1.68 mm for the combined statistics of four tropical cyclones. Although larger raindrops (up to approximately 5 mm in diameter) were observed by Friedrich et al. (2013b) during Hurricane Ike in 2008, the majority of the observed raindrops were less than 3 mm, displaying consistency with the observations of Tokay et al. and others. Schuur et al. (2001) and Friedrich et al. (2013a) also reported high concentrations of small-sized drops for severe thunderstorms. Friedrich et al. (2013a) reported an increase in the number of small-sized drops with an increase in wind speed and the standard deviation of the wind speed during such events. They related the observed high concentration of the small-sized drops to the raindrop breakup and evaporation processes. Though Friedrich et al. did not show any evidence to support this hypothesis, raindrop breakup and coalescence processes are the usual suspects for DSD modulations toward an increased number of smaller and larger drop sizes, respectively (see Testik and Barros 2007). Indeed, DSD modulations caused by drop breakup and coalescence processes in the absence of wind have been demonstrated by various numerical studies over the past few decades (e.g., Srivastava 1967, 1971; List and McFarquhar 1990; Prat et al. 2012). Moreover, recently using a network of optical disdrometers, Jameson et al. (2015) reported that the spatial pair correlations associated with the small drops increased in convective rains, but not in stratiform rains. Jameson et al. interpreted this observed spatial pair correlation behavior as the likely reflection of raindrop breakup discussed in Larsen et al. (2014).

Two different modes of raindrop breakups (spontaneous breakup induced by aerodynamic forcing and collisional breakup) are considered to have a controlling role on the DSD modulations/evolution. Though the relative contributions of the two breakup modes have long been a subject of debate in the absence of direct observations, collisional breakup has been widely assumed to be the dominant breakup mode in shaping DSDs. Recently, when theoretically analyzing the fragmentation products of noninteracting, isolated drops, Villermaux and Bossa (2009) argued that the spontaneous breakup of raindrops determines the DSD and its evolution from cloud to ground level, undermining the importance of collisional breakup. This controversial conclusion involved the major assumption that the exponential DSD by Marshall and Palmer (1948) is sufficient in representing the variability and transient nature of natural rainfall. The conclusion made by Villermaux and Bossa was argued against by Barros et al. (2010) on the basis that their aforementioned assumption was questionable, including that there was missing physics-based support for their mathematical analysis. Furthermore, McFarquhar (2010) noted that the analysis from Villermaux and Bossa did not consider the collision rates between raindrops of varying size, supporting the role of collisional breakup and coalescence as the two main factors that control DSD evolution. Nevertheless, the investigation from Villermaux and Bossa certainly provoked the need to revisit the debate on the relative importance of the breakup modes on the DSDs.

In our investigation we probed into the DSD modulations due to wind with a goal of identifying the controlling microphysical processes. Therefore, it was central to our study to elucidate whether one of the breakup modes, spontaneous or collisional breakup, dominates over the other one in DSD modulations (e.g., McTaggart-Cowan and List 1975; Villermaux and Bossa 2009; McFarquhar 2010) or if both of the breakup modes modulate the DSD collectively (e.g., Kobayashi and Adachi 2001). Rainfall data from the Midlatitude Continental Convective Clouds Experiment (MC3E; Petersen and Jensen 2012) were utilized for the analysis presented here. The spontaneous breakup model of Villermaux and Bossa (2009) and the collisional breakup model of Testik (2009), which are briefly described later in section 4, provided the quantitative means for our analysis.

This article is organized as follows. A description of the MC3E field campaign and the utilized datasets is provided in section 2. The impact of the horizontal wind on the DSD shapes and parameters is elucidated in section 3, which is followed by a detailed discussion on the governing microphysics in section 4. Finally, conclusions are provided in section 5.

2. Data

The analysis presented in this article utilizes data from the MC3E field campaign (Petersen and Jensen 2012) that was conducted in central Oklahoma between April and June 2011. This field campaign aimed to provide a comprehensive visualization of the three-dimensional meteorological environment through a multitude of airborne, spaceborne, and ground-based instruments (Jensen et al. 2016). The datasets utilized in this study are from ground-based instruments, including a two-dimensional video disdrometer (2DVD; MC3E instrument identification sn35; Kruger and Krajewski 2002), a Parsivel disdrometer (MC3E instrument identification apu01; Loffler-Mang and Joss 2000) in support of the 2DVD measurements, a wind speed anemometer (R.M. Young Wind Monitor), a temperature sensor (Campbell Scientific, Inc. Model HMP45C), and a micro rain radar (MRR; Peters et al. 2002, 2005) that is capable of retrieving DSDs up to thousands of meters above the ground level. Geographic locations of these instruments are provided in Table 1. Note that although all of these instruments were not collocated, they were, however, positioned close enough (within a circle of approximately 0.8 km in radius) for the purposes of our analysis. All of the rainfall events observed by the 2DVD during the MC3E are tabulated in Table 2.

Table 1.

Geographical locations of the utilized instruments in MC3E.

Table 1.
Table 2.

Rainfall events during MC3E. Variable Rmax is the maximum rainfall rate for the given rainfall event.

Table 2.

The datasets (and relevant parameters) utilized in this study include DSDs for 1-min time intervals, DSD parameters of mass-weighted mean diameter [Eq. (1)] and normalized intercept parameter [Eq. (2)], liquid water contents (LWC), measured raindrop characteristics (e.g., diameter and fall speed), horizontal wind speeds V, and air temperatures. The horizontal wind speeds were measured using an anemometer that was 10 m above the ground and the vertical wind speeds were ignored in the absence of measurements. Therefore, hereafter, the terms “wind speed” and “wind velocity” refer to the “horizontal wind speed” and “horizontal wind velocity,” respectively. The DSD datasets and raindrop parameters were from three different types of instruments: 2DVD, Parsivel disdrometer, and MRR. The quality of the raw data was improved by the removal of raindrop measurements with (i) diameters larger than 10 mm and (ii) fall speeds deviating more than ±50% from terminal speed predictions by Gunn and Kinzer (1949) [similar to Tokay et al. (2001)]. Moreover, DSDs with less than 10 drops or those that correspond to rainfall rates that are less than 0.01 mm h−1 were excluded from the dataset. Parameters (mm) and (mm−1 m−3) are representative parameters for a given DSD and were used to investigate the wind impact on the DSD shape as presented in section 3. The values of these parameters were calculated using the following two relationships that are independent of a specific distribution function (Testud et al. 2001):
e1
e2
Here is the DSD (mm−1 m−3); D is the raindrop diameter (mm); and are the minimum and maximum raindrop diameters (mm) for a given DSD, respectively; is the water density (g m−3); and is the LWC (g m−3) as calculated using the following relationship:
e3
MC3E rainfall events were classified as convective and stratiform precipitations for analysis purposes. There are various well-accepted convective/stratiform precipitation classification methodologies (e.g., Steiner et al. 1995; Williams et al. 1995; Bringi et al. 2009; Thurai et al. 2010). Among these methodologies, the methodology by Tokay and Short (1996), which utilizes only disdrometer measurements and does not rely on radar measurements, was used in our analysis. The methodology by Tokay and Short is based upon an empirical formula that was developed using over 7600 DSD measurements from tropical oceanic rainfall and assuming gamma distributions for the measured DSDs. For an in-depth analysis with more accurate precipitation classifications for the MC3E rainfall events, one may benefit from comparing the classifications based upon this methodology with the overlying precipitation feature structures using the ground-based radar data available for the MC3E field campaign. In Fig. 1, the classifications of MC3E rainfall events are presented. In this figure, the solid line represents the empirical formula from Tokay and Short, which is provided in Eq. (4) below. This line demarcates the convective (above the line) and stratiform (below the line) precipitation events:
e4
where is the intercept parameter (mm−1−μ m−3), is the rain rate (mm h−1; obtained from disdrometer measurements in this study), and is the gamma distribution shape parameter. In our calculations, values were calculated from the measured DSDs using Eq. (5) [see chapter 7.1.4 in Bringi and Chandrasekar (2001)]:
e5
Here is the gamma function. To estimate the values, the mass spectrum parameters and the standard deviation of the mass-weighted mean diameter were used to avoid possible fitting errors (Williams et al. 2014; Thurai et al. 2014) due to the correlation between and parameters (see Chandrasekar and Bringi 1987; Moisseev and Chandrasekar 2007). The empirical formulation in Eq. (6), which is derived from more than 5100 DSD samples from the MC3E field campaign using the methodology by Williams et al. (2014) and Thurai et al. (2014), was used for estimating the values. This empirical formulation was provided in a presentation by Williams and also confirmed by the present authors:
e6
Fig. 1.
Fig. 1.

Classification of precipitation types in MC3E. Asterisks and circles represent convective and stratiform precipitation, respectively. The solid line represents Eq. (4) and demarcates different precipitation types. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

3. Analysis and results

The first step of our analysis was to explore the impact of wind on DSD shape using the 2DVD DSD data from the MC3E field campaign. To avoid potential large measurement errors associated with light rainfall events, only the DSD data from rainfall events with LWC values larger than 0.2 g m−3 were included in the analyses. This selected threshold LWC value corresponds to the rain rate of approximately 2.54 mm h−1, which is classified as the lower bound of the moderate rainfall intensity (OFCM 2005). The DSDs that were included in our analysis were then grouped (25 groups in total) in an attempt to isolate wind effects on the DSD modulations (see Fig. 2 for a sample of grouped DSDs). The criteria in grouping the DSDs were (i) the DSDs should be from the same rainfall event (see Table 2) with same precipitation type (i.e., convective or stratiform rainfall as classified in section 2) and (ii) the corresponding LWC values should be close (i.e., the difference between the maximum and minimum LWC values in a group was less than 10% of the maximum LWC value in the group). In addition, the DSD count had to be larger than three in order to constitute a group. The first criterion was set as an attempt to filter out the effects of cloud-level processes on the DSD shape. The second criterion was set because LWC and DSD are correlated [see Eq. (3)] and different LWC values may mask the effect of wind on the DSDs as illustrated in Figs. 2a and 2b. The grouped DSDs in Figs. 2a and 2b were from the same rainfall event (event 6 in Table 2) and had similar wind speeds but different LWC values. As can be seen in these graphs, the number of large drops increases with the increase of LWC value, indicating that LWC is a factor to consider in isolating wind effects on DSD modulations. When examined individually, each of the graphs in Fig. 2 (i.e., with LWC value being approximately the same) suggests that as the wind speed increases, the number of small drops increases and the number of large drops decreases. This figure clearly shows the effect of wind speed on DSD shaping.

Fig. 2.
Fig. 2.

Three different DSD groups from (a),(b) event 6 and (c) event 17 (see Table 2 for the event numbers). Each group is composed of DSDs with approximately the same LWC values and different wind speed values. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

To further demonstrate the wind effects on DSD shaping, the parameters and , which characterize the shape of a DSD, were used in the subsequent statistical analysis. The and values for each of the measured DSDs were first calculated from Eqs. (1)(3). The correlations between each of these two parameters and the wind speed were then investigated for all of the DSD groups. Linear lines were fit via least squares regressions to show the dependency of and on wind speed. Three pairs of sample plots that show this dependency are presented in Fig. 3. These plots are for the same DSD data presented in Fig. 2. As can be clearly seen in Fig. 3, the and values have strong decreasing and increasing trends, respectively, with increasing wind speeds. To quantify the correlation between the selected DSD parameters and the wind speed, Pearson correlation coefficient ρ values, which are calculated to be rather high, are also provided in this figure. Parameters and have opposing trends with the wind speed as expected [see Eqs. (1)(3)]. The fitted least squares lines for V and V data for all of the DSD groups are plotted in Fig. 4. In this figure, solid, dashed, and dotted lines represent decreasing trends, increasing trends, and no-trend cases, respectively. A no-trend case is defined here as a case where the absolute value of ρ is less than 0.2, a value below which the correlation between the parameters can be assumed to be negligible. Our analysis for the entire DSD groups showed that approximately 70%, 20%, and 10% of the DSD groups fall under the decreasing trend, increasing trend, and no-trend cases for , respectively, and approximately 20%, 70%, and 10% of the DSD groups fall under the decreasing trend, increasing trend, and no-trend cases for , respectively. This finding indicates that wind has a pronounced effect in shaping DSDs. In particular, DSDs are shaped toward an increased number of smaller drops and decreased number of larger drops with increased wind speed.

Fig. 3.
Fig. 3.

Parameters (left) and (right) as a function of wind speed. The solid lines represent the fitted lines to the data with the correlation coefficient values provided in the legends. Data (symbols) are from the same rainfall events presented in Fig. 2: (a),(b) Fig. 2a; (c),(d) Fig. 2b; and (e),(f) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 4.
Fig. 4.

Parameters (a) and (b) as a function of wind speed for all of the DSD groups. Each line represents the fitted line to the V and V data for a DSD group. Solid, dashed, and dotted lines denote decreasing, increasing, and no-trend cases, respectively. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

The hypothesis that wind speed alters the DSD by increasing and decreasing the drop concentration on the left side (i.e., small-sized end) and right side (i.e., large-sized end) of the DSD, respectively, was further examined through the slopes of the measured DSDs. Given the accuracy limitations of 2DVD measurements for small drops (Thurai et al. 2014), DSD slopes were analyzed only for raindrops that are larger than or equal to 0.5 mm in equivalent volume diameter. In analyzing the DSD slopes, and values for each of the measured DSDs were first normalized using the corresponding and values, and then linear lines were fit to the normalized DSDs using least squares regressions. Typical normalized DSDs along with the fitted lines are presented in Fig. 5. For each of the DSD groups, the correlation between the slopes of the drop size distributions m and the corresponding wind speeds were investigated by fitting linear least squares regression lines to the mV data (see Fig. 6). These fitted lines for all of the DSD groups are plotted in Fig. 7 to visualize the mV trends. In this figure, lines that were fitted to both 2DVD measurements (Fig. 7a) and Parsivel measurements (Fig. 7b), with the purpose of providing support to 2DVD measurements, are presented. Approximately 70%, 10%, and 20% of all of the DSD groups from 2DVD measurements showed DSD slope changes with wind that can be classified as a decreasing trend, increasing trend, and no trend, respectively. Similarly, approximately 70% of all of the DSD groups from Parsivel measurements show decreasing trends for mV data (71% decreasing trend, 24% increasing trend, and 5% no trend). This finding clearly demonstrates that wind drives a clockwise DSD rotation through microphysical processes that are responsible for an increased number of small drops and decreased number of large drops (i.e., raindrop breakup).

Fig. 5.
Fig. 5.

Typical normalized DSDs: (left) marked lines represent measured data and solid lines represent lines fit to the data and (right) marked lines represent lines fit to each of the DSD data in a given DSD group. Data (symbols) are from the same rainfall events presented in Fig. 2: (a),(b) Fig. 2a; (c),(d) Fig. 2b; and (e),(f) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 6.
Fig. 6.

DSD slope as a function of wind speed. The solid lines represent the lines fit to the data with the correlation coefficient values provided in the legends. Data (symbols) are from the same rainfall events presented in Fig. 2: (a) Fig. 2a, (b) Fig. 2b, and (c) Fig. 2c. Rainfall data used in this figure are from 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 7.
Fig. 7.

DSD slope as a function of wind speed for all of the DSD groups. Each line represents the line fit to the mV data for a DSD group. Rainfall data are obtained by (a) 2DVD and (b) Parsivel disdrometers. Solid, dashed, and dotted lines denote decreasing, increasing, and no-trend cases, respectively.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

4. Governing microphysics: Spontaneous versus collisional breakup

In this section, the underlying microphysical process for the wind-induced DSD modulation (i.e., raindrop breakup) is elucidated with the specific goal of identifying the controlling breakup mode: spontaneous breakup and/or collisional breakup.

Villermaux and Bossa (2009) provided a criterion for the occurrence of spontaneous breakup in terms of the spontaneous Weber number of the raindrop, which is expressed as follows:
e7
Here is the magnitude of the relative raindrop velocity with respect to the air motion, and and are the air density and surface tension of water, respectively. Please note that both density and surface tension are functions of temperature. According to Villermaux and Bossa, spontaneous breakup occurs when the value is larger than a critical value (henceforth, referred to as the critical spontaneous Weber number ), which is found to be 6.
In order for the collisional breakup to occur, two raindrops must collide (which is governed by the collision rate) and the outcome of the collision should be breakup (among the three possible collision outcomes: bounce, coalescence, and breakup; Testik and Barros 2007). The collision rate of an individual raindrop with an equivalent volume diameter in a raindrop size distribution can be calculated using the following equation (Rogers 1989):
e8
Here CR is the collision rate and is the collision kernel. In the absence of turbulence, can be parameterized as (Rogers 1989; Wang et al. 1998):
e9
Here is the magnitude of the velocity difference between two falling raindrops with diameters and , respectively, and is the collision efficiency for the two raindrops. Note that the value of can be approximated as unity if the sizes of the two colliding drops are relatively large [i.e., larger than approximately 0.2 mm in diameter, which are classified as Class II and III raindrops by Testik and Barros (2007); see Rogers (1989); Czys and Tang (1995); Testik and Barros (2007)]. Therefore, we approximated as unity in our analysis.
Testik (2009) developed a regime diagram to determine the raindrop collision outcomes in terms of bounce, coalescence, and breakup. This regime diagram is based upon the values of the collisional Weber number [Eq. (10a)], and the diameter ratio of the two colliding drops p [Eq. (10b)] (Testik 2009; Testik et al. 2011), which are defined as follows:
e10a
e10b
Here is the magnitude of the velocity difference between the two colliding drops with diameters of and , where . The regime diagram of Testik (2009) is provided in Fig. 8. The two regime separation curves (solid lines) are defined by the balance between the collision kinetic energy (CKE) and the surface energy of the colliding drops (SE1 for the larger drop and SE2 for the smaller drop; i.e., CKE/SE1 = 1 defines the upper separation curve and CKE/SE2 = 1 defines the lower separation curve in Fig. 8). The two curves delineate the diagram into three regions for bounce, coalescence, and breakup. The occurrence of the collision outcomes is predicted based upon the region in which and p values fall in the diagram.
Fig. 8.
Fig. 8.

Regime diagram for the binary raindrop collision outcomes adopted from Testik (2009). Vertical dashed arrows are used to illustrate the shift of the raindrop collision outcome predictions from coalescence and bounce regimes to breakup regime for a hypothetical increase of the collisional Weber number values due to wind.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

The spontaneous Weber number [Eq. (7)], collision rate [Eqs. (8), (9)] and collisional Weber number [Eq. (10)] are all functions of the raindrop’s relative speed (i.e., magnitude of the velocity difference) with respect to either the air motion or another raindrop. Consequently, wind effects on the relative speed of a raindrop will influence the values of all of these quantities, affecting the relevant microphysical process. In all of our calculations in this study, whenever vertical raindrop speed measurements were not available, vertical raindrop speeds were assumed to be equal to the terminal values in still air. Note that recent studies reported the presence of super- and subterminal raindrops (e.g., Testik et al. 2006; Montero-Martinez et al. 2009; Thurai et al. 2013). For calculating the horizontal raindrop speed υ, we used the formulation by Pedersen and Hasholt (1995) that is provided in Eq. (11). This formulation provides predictions of the horizontal raindrop speed at different elevations h and wind speeds V:
e11
Here, is the drag coefficient, which is a function of the raindrop diameter. Sample horizontal raindrop speed calculations are demonstrated in Fig. 9. These calculations were performed by solving Eq. (11) numerically from 200 m elevation down to the disdrometer level (assumed to be 1 m from the ground based upon visual inspection of the available field setup photos) for selected surface wind speeds. In our calculations, we assumed a log-law wind speed u profile (Powell et al. 2003) of from z = 200 m to the disdrometer level (i.e., z = 1 m). Here, z is the elevation, is the surface roughness length [assumed as 0.03 m in our calculations, which corresponds to the open terrain classification of Wieringa (1992), based upon a visual inspection of the upstream of the experimental site], k is the von Kármán coefficient with a value of 0.4, and is the friction velocity that can be calculated using the log-law wind profile with the given profile parameter values and the wind speed value measured at z = 10 m elevation. The starting elevation of 200 m was sufficiently high for horizontal raindrop speed calculations to be independent of the starting elevation (Pedersen and Hasholt 1995). In our subsequent analysis, these horizontal raindrop speeds at the disdrometer level were then used to compute the relative raindrop speeds used in Eqs. (7)(10). Please note that, in the absence of wind profile information, the log-law profile is deemed to be a suitable profile for our analysis. The log-law profile is typically a preferred representation of the wind profile in the lower part of the planetary boundary layer (e.g., Counihan 1975; Powell et al. 2003). To evaluate the sensitivity of our results to the selected canonical wind profile, we conducted the following analysis in the remainder of this article also for the power-law wind profile [ from z = 200 m to the disdrometer level, where is the wind speed at 10 m elevation; see, e.g., Davenport (1960) for the power-law profile] and a hybrid wind speed profile that is a combination of the log-law and power-law profiles [i.e., from z = 200 m to z = 10 m, and with = 0.005 m and k = 0.4 from z = 10 m to the disdrometer level] as suggested by Pedersen and Hasholt (1995). The analyses using these three different wind speed profiles indicated that the findings of our study results are not sensitive to the selected wind speed profile. Therefore, only the results obtained by using the log-law wind profile are presented in this article.
Fig. 9.
Fig. 9.

Horizontal raindrop speeds calculated using Eq. (11) from z = 200 m to z = 1 m (disdrometer level) for different drop diameters and selected wind speeds at 1 m elevation (shown next to the solid lines).

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Figure 9 and Eqs. (7)(10) lead to the following two conclusions:

  1. Figure 9 shows that, for a raindrop of a given size, the relative raindrop speed with respect to the air motion increases for increasing wind speeds. For example, the difference between the horizontal raindrop speed and wind speed increases from 0.78 to 4.68 m s−1 for a 2 mm raindrop when the wind speed increases from 2 to 12 m s−1. Equation (7) implies that an increase in the relative raindrop speed increases the spontaneous Weber number value. Consequently, for higher wind speeds, one would expect a larger number of raindrops to experience the spontaneous breakup.
  2. Figure 9 shows that, for two raindrops of different sizes, the magnitude of the velocity difference between the raindrops increases with increasing wind speeds. For example, the difference between the horizontal speeds of a 1- and a 5-mm drop increases from 0.60 to 3.57 m s−1 when the wind speed increases from 2 to 12 m s−1. Equations (8)(10) imply that an increase in the relative raindrop speeds increases both the collision rate and the collisional Weber number. Consequently, with higher wind speeds, one would expect a larger number of binary raindrop collisions and more energetic collisions that would favor a tendency toward the breakup regime as illustrated by the vertical arrows in Fig. 8.

The commonality of these two conclusions is that higher wind speeds are associated with a larger number of raindrop breakups. This finding supports our discussion of an increased number of smaller raindrops resulting from increasing wind speeds (see Figs. 27). The remaining question is which of the raindrop breakup modes controls the DSD shaping procedure. In the absence of direct observational capabilities to answer this question, we followed an analysis procedure that is outlined in Fig. 10. Both of the possible control scenarios were analyzed as follows.

Fig. 10.
Fig. 10.

Flowchart outlining the analysis procedure that was used to identify the breakup mode(s) that controls the DSD shape evolution.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

a. Scenario 1: Spontaneous breakup controls

Here, we evaluate the following hypothesis: spontaneous breakup controls the DSD shape. The underlying physical reasoning for this hypothesis is that wind increases the value of a raindrop to a value that is larger than or equal to the value [6 from Villermaux and Bossa (2009)] and/or wind decreases the value, leading to a large number of spontaneous breakups that shape the DSD. For this evaluation, values for all of the raindrops measured by the 2DVD are calculated using Eq. (7). Figure 11 shows the calculated values as a function of the raindrop diameter for four typical DSD spectra. In Fig. 11, solid circles represent the calculated values from the 2DVD measurements, stars represent the calculated values for the largest raindrops that were observed in MRR measurements but not in 2DVD measurements (discussed later), and the solid horizontal lines represent the value of 6 (Villermaux and Bossa 2009). As can be seen in Fig. 11d and later in Fig. 12, there are a small number of raindrops with values that are larger than the value of 6. There may be several different reasons for this observation, including raindrop measurement artifacts and the embedded assumptions in the analysis from Villermaux and Bossa for the derivation of the value. Nevertheless, the accuracy of the value does not impede our analysis and is beyond the scope of this article.

Fig. 11.
Fig. 11.

Spontaneous Weber number values (solid circles) calculated for typical DSDs measured by the 2DVD. Dashed lines represent the critical spontaneous Weber number of 6, and stars represent the spontaneous Weber number value for the largest raindrop retrieved from the MRR measurements but not observed by the 2DVD measurements.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 12.
Fig. 12.

The average of the five largest spontaneous Weber numbers of the DSD spectrum for all of the analyzed 2DVD DSDs plotted against the corresponding wind speeds calculated at the disdrometer level.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

In our evaluation we used the average of the five largest spontaneous Weber numbers from each of the DSD spectra measured by the 2DVD. The calculated values for the significant majority of the DSD measurements were less than the value (see Fig. 12), indicating that either spontaneous raindrop breakup was absent and evolution of the DSD was not controlled by the spontaneous breakup or spontaneous breakups had already led to a quasi-steady DSD. If a quasi-steady DSD formed because of spontaneous breakups, one would expect that all of the values were close to the value of 6. This is, however, clearly not the case, as observed in Figs. 11 and 12. Then, the only remaining possibility for our hypothesis stated above to hold true is that the value correlates with the wind speed. For example, one may argue that increased wind speed may induce increased wind shear, which may amplify the instabilities that lead to spontaneous raindrop breakup, resulting in values that are less than 6 and correlate with wind speed. Since, for a quasi-steady DSD formed by spontaneous breakups, values can only be smaller than (but should be close to) the values, if a correlation between and wind speed exists, a correlation between and the wind speed should also exist. Nevertheless, it can be seen from Fig. 12 that there is practically no correlation between and V. The value of ρ is only about 0.2, indicating that almost no correlation exists between the two variables. A strong correlation between two variables usually has a ρ of 0.7 or above. Therefore, it is concluded that the hypothesized control of the DSD evolution by the spontaneous breakup does not hold true for the MC3E observations.

b. Scenario 2: Collisional breakup controls

Here, we evaluate the following hypothesis: collisional breakup controls the DSD shape. For this evaluation, both the rate and outcome of binary raindrop collisions were investigated within the context of DSD shape modification. The largest raindrop sizes retrieved from the MRR measurements aloft (at the height of 1015 m), but not observed by the 2DVD at the disdrometer level, were utilized in investigating the collision rate and outcome (i.e., breakup, coalescence, and bounce). In the following discussion, the largest raindrop of a DSD retrieved by the MRR, which potentially existed aloft but was not observed at the disdrometer level, is referred to as the hypothetical raindrop. Note that Das et al. (2010) report that the MRR and the Joss–Waldvogel disdrometer provide similar DSD spectra at the large raindrop size bins. All of the DSDs retrieved from MRR measurements at the height of 1015 m during MC3E are presented in Fig. 13. For each of the 1-min DSD measurements by the 2DVD at the disdrometer level, the corresponding hypothetical raindrop at the same time was determined using these retrieved DSDs from MRR measurements. There is clearly a time lag for the DSDs aloft to reach the disdrometer level, and the 2DVD DSD measurements do not correspond to the retrieved MRR DSDs. Nevertheless, considering the short travel time [~O(minutes)] of the raindrops from 1015 m to the disdrometer level, the DSD aloft retrieved at the same time as the 2DVD measurements would be representative for our purposes. In determining the size of the hypothetical raindrop, since the measurement volumes of the MRR and 2DVD are different, a conversion factor was applied to match their measurement volumes (see Peters et al. 2002). The size of the hypothetical raindrop was deemed to be equal to the largest bin size in the MRR DSD with a drop count of no less than one. The majority (73%) of the hypothetical raindrops had diameters larger than the largest diameter of the 2DVD-measured raindrops, and only 10% of the hypothetical raindrops had values larger than the value of 6. This observation is consistent with the wind-induced evolution of the DSDs discussed in section 3 and hints at the rare presence, if any, of spontaneous breakup for the MRR measurement elevations. Therefore, it supports the collisional breakup-controlled DSD hypothesis.

Fig. 13.
Fig. 13.

Retrieved DSDs from MRR measurements at the height of 1015 m for the entire MC3E field campaign.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

To ascertain the collisional breakup-controlled DSD hypothesis, the rate and outcomes of collisions between the hypothetical raindrop (from MRR measurements) associated with a given 2DVD DSD measurement and all of the raindrops observed in that particular 2DVD DSD were calculated using Eqs. (8)(10) and the regime diagram by Testik (2009). This analysis was to demonstrate that nonexistence of the hypothetical raindrops at the disdrometer level might be due to collisional breakup. In these calculations, the fall velocity of the hypothetical raindrops was estimated by assuming terminal speed [predicted by Gunn and Kinzer (1949)] in the vertical direction and speed predictions of Eq. (11) in the horizontal direction. There are apparent error sources (e.g., accuracy of the hypothetical drop size and velocity) in this analysis that may be problematic for quantitative purposes, yet are acceptable for the following qualitative analysis performed in this study. In Fig. 14, a histogram of the number of the DSD spectra for the ratio of the collision period (inverse of the collision rate) and the travel time of the hypothetical drops from 1015 m to the disdrometer level is shown. This histogram shows that values are larger than values for most (89%) of the hypothetical raindrops, indicating that these hypothetical raindrops would have experienced at least one collision throughout their fall. To investigate the outcomes of these collisions, and p values for the collision of each of the hypothetical raindrops with each of the raindrops in the associated DSDs were calculated and the collision outcomes were determined using the regime diagram. Figure 15 shows the outcomes of such collisions for four selected DSD spectra that are identical to those presented in Fig. 11. As can be seen in this figure, the majority of the calculated data points fall in the breakup region (region II) of the regime diagram. For example, 93.0% of the total predictions fall into region II in Fig. 15a. It is important to note that predictions that fall into region I (referred to as the coalescence region) include both coalescence and neck breakup predictions whereas predictions that fall into region II include only breakup predictions. This means that the total number of raindrop breakup predictions is certainly larger than the number of breakup predictions presented in region II. For a conservative estimation, the breakup percentage of the total predictions for a given spectrum is defined as the breakup percentage from region II only. These conservative estimations serve sufficiently for the scope of our discussion in this study. For a more detailed analysis, one may also include the neck breakup predictions from region I in the total number of breakup predictions. This detailed analysis, however, would require predictions of the collision angle between the raindrops. The importance of the collision angle in determining the collision outcome has been noted by several investigations (e.g., List and Whelpdale 1969; Beard et al. 2001), and recently Testik et al. (2011) showed how the collision angle determines the collision outcome in region I (i.e., coalescence or neck breakup). In Fig. 16, a histogram is presented that shows the values. This histogram presents a clear dominancy of breakup predictions for the hypothetical raindrops. This qualitative analysis conducted for the hypothetical raindrops is representative for other such large raindrops that potentially existed aloft but were absent at the disdrometer level. These findings indicate that wind-induced clockwise DSD rotation is driven by collisional breakup.

Fig. 14.
Fig. 14.

Histogram of the number of the DSD spectra for the ratio of the collision period and the travel time of the hypothetical raindrops from an elevation of 1015 m to the disdrometer level .

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 15.
Fig. 15.

Collision outcome predictions shown on the p regime diagram for the collisions between a hypothetical raindrop and each of the raindrops in the associated DSD. Predictions are for the same four selected DSDs used in Fig. 11. Percentages of the total predictions that fall into each region of the diagram are provided in the legend.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Fig. 16.
Fig. 16.

Histogram of the percentages of the total DSD spectra for the breakup percentages of the total predictions for a given spectrum.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

Although our analysis in section 3 showed that the majority of the DSDs experienced a wind-induced clockwise rotation, there was still a notable amount of DSD observations that showed wind-induced evolution with no trend or a reverse trend (i.e., counterclockwise rotation). This phenomenon was most likely related to the favored collision outcome, coalescence or breakup, for a given DSD. While a breakup-favored DSD experiences a breakup-dominated DSD evolution (i.e., clockwise DSD rotation with an increase in the number of small drops and a decrease in the number of large drops due to the breakup process), a coalescence-favored DSD experiences a coalescence-dominated DSD evolution (i.e., counterclockwise DSD rotation with a decrease in the number of small drops and an increase in the number of large drops due to the coalescence process). Typical coalescence-favored DSDs in the MC3E campaign were the DSDs aloft with a high concentration of small drops. An example of such a DSD behavior (i.e., counterclockwise rotation of coalescence-favored DSDs) from MRR retrievals at different heights is presented in Fig. 17a. In addition, an example of clockwise DSD rotation from MRR retrievals at different heights is presented in Fig. 17b for comparison purposes. To explain the counterclockwise DSD rotation observation, we considered the collisions of a 4-mm drop (a typical large drop size) with drops of different sizes varying from 0.1 to 4 mm. The predicted outcomes of these collisions are illustrated in the collision regime diagram presented in Fig. 17c. In these calculations, drops were assumed to fall at terminal speeds following Gunn and Kinzer (1949). Figure 17c shows that as the size of the smaller of the colliding drops decreases, collision outcome predictions exhibit a tendency for a coalescence prediction (region I of the diagram), explaining the association of the coalescence-favored DSD with the DSDs that have a high concentration of smaller drops.

Fig. 17.
Fig. 17.

DSDs retrieved by MRR at different elevations as an example of (a) counterclockwise and (b) clockwise rotation of DSDs. (c) Collision outcome predictions (symbols) for the collisions between a 4-mm raindrop and raindrops of different sizes ranging from 0.1 to 4 mm shown on Testik (2009) regime diagram.

Citation: Journal of Hydrometeorology 18, 5; 10.1175/JHM-D-16-0211.1

5. Conclusions

This study elucidated the wind-induced DSD shape evolution and relevant microphysics using datasets from the MC3E field campaign. It was demonstrated that increasing wind speeds have a statistically significant effect of increasing the number of small drops and decreasing the number of large drops. Such clockwise DSD rotations with increasing wind speeds were observed for approximately 70% of the entire DSD groups. It is apparent that the raindrop breakup process, which is expected to intensify with an increase in wind speeds, was responsible for the observed clockwise DSD rotations. Nevertheless, there has been a lack of general consensus on the dominancy of the two raindrop breakup modes, spontaneous and collisional, on the DSD shape modulations. Therefore, each of the breakup modes was evaluated to identify the breakup mode that controls the DSD shape modulations. This evaluation involved a rather untraditional multifaceted analysis (as outlined in Fig. 10) of the DSD data both aloft from the MRR measurements and at the disdrometer level from the 2DVD measurements. It was concluded that the collisional raindrop breakup was the controlling breakup mode for the observed wind-induced DSD shape evolution. There was also a portion (approximately 30%) of the DSD observations that showed either counterclockwise rotation or no rotation due to wind effects. It is discussed that such DSD shape modulations were associated with the coalescence-favored DSDs, which have a high concentration of smaller raindrops.

We expect turbulence to have an important role in the evolution of rain structure. In contrast to the wide body of literature on the turbulence effects on cloud droplets (e.g., Pinsky and Khain 1996; Khain et al. 2007; Seifert et al. 2010; Grabowski and Wang 2013), turbulence effects on the larger-sized, faster-falling, and widely dispersed raindrops have yet to be studied in greater detail. Given the state of knowledge in this aspect of the problem, we did not consider the potential effects of turbulence on the DSD evolution and relevant physical processes. In particular, turbulence effects on the processes that regulate the raindrop fall speed may have sizable impacts on the DSD evolution as altered raindrop fall speeds would result in altered collision frequencies and outcomes. There may be a number of such processes. For example, Beard and Jameson (1983) studied the turbulence effects on the raindrop canting. It is clear that changes in the orientation of a large raindrop that is not spherical would be associated with changes in the aerodynamic drag force acting on the drop, leading to an alteration of the fall speed. Another example of potential turbulence effects may be related to the preferential sweeping process (e.g., Wang and Maxey 1993; Aliseda et al. 2002; Frankel et al. 2016), which is the accumulation of small particles on the downward side of the turbulent eddies, resulting in enhanced fall/settling speeds. Incorporating such considerations of turbulence effects into our analysis is a complex task and is out of the scope of our study. Nevertheless, it is evident that the response of different size raindrops to different turbulent scales would create a wide spectrum of raindrop fall speeds and trajectories. Under such conditions, we would expect turbulence has an important role in enhancing the collision-induced rain structure evolution.

To the best of our knowledge, our study is the first study that takes a significant step in considering the effects of horizontal wind on the vertical evolution of rain structure. The findings of our study show the importance of incorporating the wind effects in DSD parameterizations and the critical role of binary raindrop collisions in the DSD shape evolution. DSDs have vital practical significance in numerous applications. For example, radar rainfall estimations rely on the accurate parameterizations of the DSDs (Bringi and Chandrasekar 2001). Although it is yet to be investigated, the wind-induced errors in radar rainfall retrievals are likely to be significant. Our findings warrant detailed future studies that investigate both wind effects on the DSDs and the propagation of these effects in the broad range of applications that implement DSD information.

Acknowledgments

This research was supported with funds provided by the National Science Foundation under Grants AGS-1612681 and AGS-1144846 to the first author (F.Y.T.). The second author was a graduate student under the guidance of F.Y.T.

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