TMCnet News
The Impact of Raindrop Collisional Processes on the Polarimetric Radar Variables [Journal of the Atmospheric Sciences](Journal of the Atmospheric Sciences Via Acquire Media NewsEdge) ABSTRACT The impact of the collisional warm-rain microphysical processes on the polarimetric radar variables is quantified using a coupled microphysics-electromagnetic scattering model. A one-dimensional bin-microphysical rain shaft model that resolves explicitly the evolution of the drop size distribution (DSD) under the influence of collisional coalescence and breakup, drop settling, and aerodynamic breakup is coupled with electromagnetic scattering calculations that simulate vertical profiles of the polarimetric radar variables: reflectivity factor at horizontal polarization ZH, differential reflectivity ZDR, and specific differential phase KDP. The polarimetric radar fingerprint of each individual microphysical process is quantified as a function of the shape of the initial DSD and for different values of nominal rainfall rate. Results indicate that individual microphysical processes (collisional processes, evaporation) display a distinctive signature and evolve within specific areas of ZH -ZDR and ZDR -KDP space. Furthermore, a comparison of the resulting simulated vertical profiles of the polarimetric variables with radar and disdrometer observations suggests that bin-microphysical parameterizations of drop breakup most frequently used are overly aggressive for the largest rainfall rates, resulting in very "tropical" DSDs heavily skewed toward smaller drops. 1. Introduction As raindrops descend toward the surface, the evolution of their distribution of sizes is governed by a number of microphysical processes. These processes include sedi- mentation or size sorting, evaporation, aerodynamic and collisional breakup, and coalescence. Understanding the physics governing the evolution of the drop size distri- bution (DSD) is important because changes of the DSD affect the mass flux or rainfall rate experienced at the surface. Further, understanding how these processes af- fect radar measurements is critical for optimizing remote quantitative precipitation estimates as well as studies of precipitation microphysics using remote sensing. Another major impetus for understanding the evolu- tion of raindrop size spectra is that storm dynamics can be strongly influenced by precipitation microphysics (Srivastava 1985, 1987; Markowski et al. 2002; Gilmore etal.2004; Dawson et al.2010; VanWeverberg etal. 2011; Bryan and Morrison 2012; Morrison et al. 2012). This is because processes like precipitation loading, evaporation of raindrops, and melting of hailstones generate negative buoyancy that can affect storm behavior and evolution via downdraft and cold pool production. Thus, providing the best approximation to the physics governing precipitation processes is crucial for storm-scale modeling. Model simulations of convective storms have been found to be quite sensitive to microphysical parameterizations, in- cluding warm-rain processes (Ferrier et al. 1995; Morrison etal. 2009; Dawson et al. 2010; Bryan and Morrison2012). As an example, Morrison et al. (2012) found large sensi- tivity to the drop breakup parameterization, including its substantial effects on storm characteristics such as cold pool strength, propagation speed, and precipitation accu- mulation. Though these parameterizations are based on kernels and efficiencies developed from laboratory and bin model studies, there still exists considerable uncer- tainty (Morrison et al. 2012). The processes that are the subject of the present study are the collisional processes of coalescence and breakup. There has been much experimental work in the labora- tory with colliding drop pairs (McTaggart-Cowan and List 1975; Low and List 1982a, hereafter LL82a; Ochs et al. 1995; Barros et al. 2008; among others) and, more recently, direct numerical simulation of colliding drops (Schlottke et al. 2010). These studies have been in- strumental in leading to the determination of collision efficiencies between drop pairs of various sizes and the development of coalescence and breakup kernels used in model parameterizations (Low and List 1982b, hereafter LL82b; Feingold et al. 1988; Beard and Ochs 1995; McFarquhar 2004; Prat et al. 2012). Analytic and nu- merical models of the evolution of raindrop spectra un- dergoing these processes have also been widely studied (List and Gillespie 1976; Valdez and Young 1985; Brown 1987,1988,1993,1997;Listetal.1987;Tzivionetal.1989; List and McFarquhar 1990; Hu and Srivastava 1995; Seifert et al. 2005; Prat and Barros 2007a,b, 2009; Prat et al. 2012), as have numerical methods for efficiently and accurately solving the stochastic collection and breakup equation (Bleck 1970; Bott 1998, 2000, 2001; Prat and Barros 2007b; Jacobson 2011). In contrast to the extensive modeling and laboratory studies mentioned above, there has been relatively little work in validating these models and kernels in nature. The emergence of dual-polarization radar offers added information regarding the evolution of the shape of the DSD. The variables available from polarimetric radar measurements that will be discussed in this study are radar reflectivity factor at horizontal polarization ZH, differen- tial reflectivity ZDR, specific differential phase KDP,and the copolar correlation coefficient rhy. A detailed de- scription of these polarimetric variables may be found in various textbooks (e.g., Doviak and Zrnic^ 1993; Bringi and Chandrasekar 2001) or review articles (e.g., Herzegh and Jameson 1992; Zrni^c and Ryzhkov 1999; Ryzhkov et al. 2005; Kumjian 2013a,b,c). Briefly, ZH is strongly dependent on the equivalent volume diameter D of par- ticles; it is proportional to D6 for particles that are elec- tromagnetically small compared to the radar wavelength. In addition, ZH depends on the concentration of particles in the radar sampling volume. In rain, ZH generally in- creases for increasingly heavy rainfall rates and varies from near 0 dBZ or less in light drizzle to .50 dBZ in extremely heavy downpours. The reflectivity-weighted shape of particles in the radar sampling volume is measured by ZDR, where values of 0 dB indicate spherical or randomly oriented hydrometeors and increasing magnitudes of positive or negative values indicate increasing particle anisotropy. In rain, values vary from 0 dB in drizzle to 4-5 dB in heavy continental rain at S band (and up to 6 dB or more at C band). Although ZDR is independent of particle concentration, it does depend on the shape of the DSD. The accumulated phase lag between the horizontally and vertically polarized waves per unit radial distance is given by KDP and thus measures the concentration of anisotropic particles within the sampling volume. It is dependent on particle concentration, shape, size, and composition but is not affected by spherical or randomly oriented particles. Values of KDP vary from 08 km21 in drizzle to .48 km21 (at S band) in very heavy rain. It is also inversely proportional to the radar wavelength, so shorter wavelengths like C and X band will produce proportionally larger KDP values for the same sampled rainfall. In rain, rhy is near unity, except for heavy continental rain at C band, in which values may drop as low as 0.93 owing to resonance scattering effects by large raindrops. These polarimetric variables are affected by changes in the distribution of sizes and shapes of particles and thus can provide information about the physical pro- cesses acting on the precipitation. Such new information may be used to validate microphysical models of rain physics as well as to "fingerprint" the dominant ongoing processes in precipitation. Studies along these lines have investigated the other warm-rain processes of evapora- tion (Kumjian and Ryzhkov 2010) and size sorting of raindrops (Kumjian and Ryzhkov 2012). Thus, one of the objectives of this study is to quantify the impact of coalescence and breakup of raindrops on the dual- polarization radar variables, thereby determining the microphysical fingerprints of the processes in polari- metric radar data. To do this, we use the one-dimensional version of an explicit bin-microphysical model (Prat and Barros 2007a,b; Prat et al. 2012) coupled with T-matrix electro- magnetic scattering calculations (e.g., Waterman 1969; Mishchenko 2000) and the polarimetric radar oper- ator of Ryzhkov et al. (2011). Though idealized and operating within a simplified (one dimensional) frame- work, this type of modeling approach allows for efficient exploration of parameter space and isolation of partic- ular processes. Results of the coupled microphysics- scattering model are compared to disdrometer and radar observations. The next section briefly describes the models used in this study. Section 3 presents the modeling results, and section 4 compares these theoretical results with observations. Section 5 provides a discussion of the results, and a summary of conclusions is presented in section 6. 2. Models a. Microphysical model This work uses the one-dimensional version of a bin- spectral model from Prat et al. (2012) that resolves ex- plicitly the evolution of the DSD under the influence of microphysical processes throughout the rain column. The column is 3 km deep with a vertical grid spacing of 10 m. Simulations are allowed to run for 1 h, integrated at a time step of 1 s. The discretization of the stochastic collection-breakup equation is achieved using a number and mass conservative scheme (Prat and Barros 2007b). The raindrop spectrum is divided into 40 bin categories with diameters ranging from 0.1 to 7.0 mm. The dis- cretization grid is irregular: geometric (grid parameter s 5 2) for the lower diameter range (d # 0.8 mm) and regular (Dd 5 0.2 mm) in the higher diameter range (d . 0.8 mm) to minimize numerical diffusion in the higher diameter range (Prat and Barros 2007b). The rain rate is given by RR(z, t) 5 p/6^in5bi1n540 Ni(z, t)di3 Vi(z), where Ni(z, t) is the total number density of drops in the ith class size, Vi(z) is the drop fall velocity for a drop of the ith bin (Best 1950), and di is the equi- volume drop diameter of drops in the ith bin. An ex- ploration of the effect of the raindrop fall speed parameterization on the collisional processes will be the subject of a companion study. The model uses a selection of coalescence-breakup kernels found in the literature. In this work, the co- alescence kernel Ecoal is taken from Seifert et al. (2005). It combines the LL82a expression in the large diameter drop range (d . 0.06 cm) and the Beard and Ochs (1995) expression in the small diameter drop range (d , 0.03 cm). The fragment distribution function kijk is de- rived from the parameterization proposed by McFarquhar (2004). The collisional breakup parameterization in- cludes the three types of breakups (filament, sheet, disc) identified by McTaggart-Cowan and List (1975). The occurrence and number of resulting fragments from a drop-drop interaction is provided by LL82b. The spontaneous (aerodynamic) breakup of large drops (kth class size) is also accounted for, and the expression for the probability of breakup Pk and the resulting distri- bution function nik is given by Srivastava (1971). Note that evaporation is excluded in this study but was treated separately in Kumjian and Ryzhkov (2010). The interested reader will refer to the following ref- erences for the discretization of the stochastic collection and stochastic breakup equations (SCE/SBE), kernel formulations, and the one-dimensional Lagrangian implementation (Prat and Barros 2007a,b). b. Electromagnetic scattering model Output from the microphysical model is converted into profiles of the polarimetric radar variables using electromagnetic scattering calculations. Raindrops are assumed to consist of pure liquid water at a temperature of 208C. Note that the complex relative permittivity of liquid water is a function of both radar wavelength and temperature; we perform calculations for S-, C-, and X-band radar wavelengths (10.97, 5.4, and 3.2 cm, re- spectively). Though temperature can also affect the scattering results, we maintain a constant drop temper- ature to isolate the impact of the microphysical pro- cesses. A realistic model of drop temperature and its impact on vertical profiles of polarimetric variables is beyond the scope of the present study and will be the subject of future work. Raindrops are treated as oblate spheroids, using the corrected diameter-shape relation of Brandes et al. (2004). We assume a mean canting angle of 08 (i.e., on average, the symmetry axis of the drops is aligned with the vertical) and a 2D Gaussian distribution of canting angles with rms width of 108,followingRyzhkov et al. (2002, 2011). Complex scattering amplitudes for forward and backward scattering at horizontal and vertical polariza- tions are calculated using a T-matrix code (e.g., Waterman 1969; Mishchenko 2000). The polarimetric radar variables are computed following Ryzhkov (2001) and Ryzhkov et al. (2011), with DSDs explicitly predicted by the mi- crophysical model. Artifacts observed in polarimetric ra- dar data such as attenuation, differential attenuation, or depolarization effects (e.g., Kumjian 2013c)arenotcon- sideredinthisstudy. 3. Results In the first simulation, a Marshall-Palmer DSD aloft is allowed to run for 1 h (the DSD aloft is steady in time). The evolution of the vertical profiles of the polarimetric radar variables in the 3-km domain is investigated. The simulated profiles of ZH, ZDR, KDP, and rainfall rate are shown in Fig. 1 at six different times. The simulation considers drop settling, coalescence, collisional breakup, and aerodynamic breakup-collectively what we will call "full physics." The initial transient differential sedi- mentation (size sorting) is clearly seen in the large ver- tical gradients (i.e., much larger than the typical variability in vertical profiles) of all variables in the first 5 min of the simulation, including a large increase in ZDR and large decreases in ZH, KDP, and rainfall rate toward the bottom of the descending rain shaft. These results are in agreement with the various size sorting models in Kumjian and Ryzhkov (2012). After 1 h of simulation, and well after steady state has been achieved, the vertical profiles exhibit changes over the domain that are much smaller in magnitude. Note that the profiles achieve steadystateafter about28min ofsimulation time for the DSD initialized aloft. Heavier (lighter) rainfall rates achieve steady state faster (slower), as described in Prat and Barros (2009). Although the time necessary to achieve steady state highlights the transient nature of most rain events observed (Prat and Barros 2009), a steady-state (or near-steady) situation will allow for assessing the impact of the different microphysical mechanisms on the shape of the DSD and the derived polarimetric variables. Next, we allow or disallow certain processes, allowing the evolution of the DSD to be governed by individual processes. Doing so enables us to study the impact of each individual process on the resulting DSD and vertical profiles of the radar variables. In this way, the polarimetric fingerprint of each process may be quanti- fied. Figures 2a-d show the vertical profiles for the rain shaft undergoing only aerodynamic breakup. Decreases toward the ground in the ZH, ZDR, and KDP profiles are evident. Such decreases arise from the spontaneous breakup of the largest drops (.5 mm), as shown in Fig. 2e by the decreased number concentration in the tail of the surface DSD after an hour of simulation. Collisional breakup (Figs. 2f-j) reveals a similar fingerprint of ZH, ZDR,andKDP decreasing toward the ground. However, the decreases are much larger in magnitude because more of the drop spectrum is affected by collisions and sub- sequent breakup. There is a noticeable decrease in number concentration of drops larger than about 3 mm in diameter (Fig. 2j). Also note in Fig. 2j the large shift of mass from larger drop size bins to the smallest drop sizes. This is a result of the breakup of large drops creating numerous smaller drop fragments (LL82a; LL82b; Beard and Ochs 1995). If instead we consider coalescence only, the opposite fingerprint to that of breakup is revealed (Figs. 2k-o): increases in ZH, ZDR, and KDP toward the ground as mass from smaller drops is shifted to larger sizes. Note that the magnitudes of these increases are small because only the smallest drops (,1 mm) are significantly de- pleted (Fig. 2o). The full-physics simulation (Figs. 2p-t) demonstrates the fingerprint expected from the in- teraction of all collisional processes for this initial DSD and rainfall rate, which is a decrease in ZH and ZDR toward the ground. Note that KDP first decreases aloft before starting to increase again toward the ground. Such nonmonotonic behavior arises because large drops aloft first breakup, decreasing KDP. Then, drops with sizes from ;0.6 to 1.7 mm are depleted by coalescence, contributing to an increase in concentration of drops with sizes from ;1.7 to 3.1 mm, which increases KDP. Note that because mass is strictly conserved in the model, RR is constant in height for the steady-state shaft. Next, we investigate the sensitivity of the polarimetric fingerprints to the initial DSD aloft (Fig. 3). For each case, a nominal rainfall rate aloft of 20 mm h21 is pre- scribed, but with varying DSD shape parameters. After an hour of evolution, the resulting steady-state DSD at the ground is quite similar, irrespective of the initial DSD aloft. This is in agreement with Prat and Barros (2009). The most notable differences are with the concentration of larger drops .4 mm (cf. the right side of the final DSDs in Figs. 3a and 3d). However, the re- sulting polarimetric fingerprint is determined by the evolution of the shape of the DSD, which can be thought of as a combination of three effects: a decrease in the concentration of large drops (which tends to shift the median diameter to smaller values), a decrease in the number of small drops (which tends to shift the median diameter to larger values), and an increase in the num- ber of medium-sized drops, which tends to draw in the median diameter from larger or smaller sizes. For the smallest initial drop sizes (Fig. 3d), a shift in mass of small and large drops to the medium-sized drops leads to the largest increase in ZDR and an increase in KDP to- ward the ground. Note that the variability of changes in ZDR is larger than of changes in KDP. Because KDP is dependent on the concentration of drops, it is more strongly weighted by the medium-sized drops (1-3 mm), which increase by about the same amount in each case. (The very tiniest drops, which are nearly spherical, contribute very little to KDP.) In contrast, ZDR is independent of number concentration but is reflectivity weighted, making ZDR especially sensitive to changes in the large-drop tail of the distribution. Thus, the overall changes in height of ZDR depend on (i) the decreasing contribution of large drops to the total ZH, which would tend to decrease ZDR; (ii) the increasing contribution of medium-sized drops to the total ZH, which could have a positive or negative effect on ZDR depending on the initial shape of the DSD; and (iii) the decreasing contribution of small drops to the total ZH, which would tend to increase ZDR values. These considerations imply that for DSDs with initially large concentrations of big drops (i.e., large initial ZDR), ZDR should decrease when collisional processes are dominant. To quantify this effect, we next perform simulations for a wide variety of initial DSDs, rainfall rates, and for the three weather radar frequencies (S, C, and X bands). In addition to the Marshall-Palmer DSDs with varying rainfall rates (1, 2, 5, 10, 20, 50, 100mm h21), we make use of normalized-gamma DSDs (Testud et al. 2001) for a similar range of rainfall rates and for shape parameters of 21, 0, 2, and 5, with varying normalized intercept parameter and median volume diameter D0 values. These simulations include full physics, which herein means settling and all collisional processes. The changes in ZH and ZDR over the 3-km domain for given initial values of ZH and ZDR aloft are presented in Fig. 4. In general, increasing values of ZH aloft lead to de- creasing changes in ZH and ZDR over the rain shaft, eventually leading to a reversal of the sign of the change (Figs. 4a,b). Similarly, larger initial ZDR aloft generally means more negative changes in ZH and ZDR (Figs. 4c,d), as anticipated by the arguments presented above. The reversal in sign of the changes in ZH occurs between about 1.0 and 1.5 dB in ZDR (Fig. 4c) whereas the re- versal in sign of DZDR occurs between 0.7 and 1.0 dB (Fig. 4d). Notice that the initial ZDR aloft is better cor- related to the resulting change over the rain shaft than the initial ZH aloft. This is because ZDR is better related to the shape and slope of the DSD than ZH. The strati- fication of points especially evident in Fig. 4a is by rainfall rate. This demonstrates that rainfall rate is not a good predictor of the evolution of the DSD within the rain shaft; rather, the initial shape of the DSD observed by the initial ZDR aloft is best (Figs. 4c,d). There is not much of a distinction among the different radar wavelengths in terms of the initial ZH and result- ing change in ZH (Fig. 4a), though there are slightly larger decreases in ZH possible at C and X bands com- pared to S band. The C-band simulations reveal the largest range of initial ZDR and also largest range of changes possible in ZDR (Figs. 4b-d), owing to the strong sensitivity of ZDR to big drops (5-6 mm in di- ameter) at C band that is a result of resonance scattering effects. Also note the divergence of the scatter of DZH for initial ZDR values larger than about 2 dB (Fig. 4c); in particular, the X-band points reveal a much larger de- crease in ZH compared to C band for a given initial ZDR. This is because larger raindrops (.3 mm) are non- Rayleigh scatterers at X band and contribute more to the observed ZH than the same raindrops do at S band. Thus, their breakup leads to larger overall reductions in ZH at X band than at S band. Despite the changes in the radar variables, rainfall rate does not change over the domain in the steady-state simulations. This is because of two factors: (i) mass is explicitly conserved because of the mass and number conservative discretization scheme used in the microphysical model (Prat and Barros 2007a, b), and (ii) there are compensating changes in the flux of mass as mass is redistributed from the tails of the distri- bution to the middle (i.e., increases in RR owing to small drops being collected by larger drops is offset by de- creases in RR as larger drops break up into smaller drops). Figure 5 displays the same simulations in terms of their polarimetric fingerprints (changes over the 3-km domain). From Fig. 5a, it is clear that for the range of DSDs and rainfall rates tested, the sign of the change in ZH and ZDR over the 3-km rain shaft can be either positive or negative (i.e., increases or decreases are possible). Similarly, the sign of KDP can be positive or negative (Fig. 5b). When both ZH and ZDR (KDP)de- crease toward the ground, the signal from drop breakup is dominant. Likewise, increases in both ZH and ZDR (KDP) toward the ground signify a dominance of the coalescence fingerprint. Because of the aforemen- tioned difference in changeover points for where DZH and DZDR reverse signs, there is a limited range of conditions at which DZH maybepositiveandDZDR (or DKDP) negative. These could indicate the fingerprint of a "balance" between coalescence and breakup. In- triguingly, the signal for evaporation [an increase in ZDR and decrease in ZH and KDP, documented pre- viously in Kumjian and Ryzhkov (2010)] does not overlap with the signal from coalescence-breakup simulations (Fig. 5a). Similarly, there is no overlap in the collisional processes and evaporation in the DZDR- DKDP phase space (Fig. 5b). Note also that the signal from size sorting is similar to that of evaporation, but larger in magnitude (Kumjian and Ryzhkov 2012), and thus also distinguishable from the fingerprints attrib- uted to the collisional processes. Comparing the different wavelengths, we see the largest differences for the decreases in ZH and ZDR (Fig. 5a, bottom left). Though decreases in ZH are larger at X band and C band relative to S band, the C-band simulations reveal the largest changes in ZDR. This is likely owing to the resonance scattering effect at C band for large drops, which makes this frequency more sen- sitive to changes in the large-drop end of the DSD. In contrast, there is little distinction between the ZH-ZDR fingerprints at different wavelengths when both ZH and ZDR increase (i.e., coalescence-dominated cases). The DZDR-DKDP space (Fig. 5b) reveals larger scatter, but demonstrates that the largest KDP increases are expected at X band and the largest KDP decreases expected at C band. Thus, though the polarimetric fingerprints of the collisional processes at a given wavelength may be different from those at other wavelengths, the breakup and coalescence processes have a polarimetric finger- print distinct from that of evaporation and size sorting. This may allow for accurate diagnoses of the physical process dominating the signal in radar observations, particularly those made with radars operating at dif- ferent frequencies. 4. Comparison to observations In this section, the results of our idealized simulations are compared to polarimetric radar and 2D video disdrometer observations. a. Polarimetric radar observations Owing to a relative lack of evaporation, warm, humid tropical environments provide a desirable natural labora- tory for studying warm-rain collisional processes. We use S-band data from the National Center for Atmo- spheric Research (NCAR) dual-wavelength polar- imetric SPolKa (herein "SPol") radar that was collected during the Dynamics of the Madden-Julian Oscillation (DYNAMO)/Atmospheric Radiation Measurement Pro- gram Madden-Julien Oscillation (MJO) Investigation Experiment (ARM-AMIE), which took place in the cen- tral Indian Ocean in late 2011 into early 2012 [for details, see Yoneyama et al. (2013)].Thesedatahavegone through an extensive quality control process at NCAR, including calibration and correction for attenuation and differential attenuation. A number of stratiform and convective rain cases that were observed during DYNAMO/ARM-AMIE are used in this study (14, 16, 28, and 31 October; 15, 16, and 17 November; 10 and 22 December 2011). Here, a "strati- form" case is loosely defined as one containing a well- defined, horizontally homogeneous melting layer bright band, whereas "convective" cases are those with a cellu- lar, isolated appearance and a lack of a well-defined melting-layer bright band. As will be shown, the parti- tioning of stratiform and convective does not matter for our purposes. The idea is to explore a range of rainfall rates and initial DSDs for comparison with the simula- tions rather than to simulate specific events. The initial ZH aloft in these cases varies from ,20 dBZ in the weakest stratiform case to .50 dBZ in the stronger con- vective cases. The median ZH and ZDR vertical profiles in the 0.5-3.5-km-AGL layer were taken over 1-km-range windows, with rhy $ 0.98 used as a threshold to ensure the precipitation was pure rain and that the data did not suffer from any contamination from ground clutter, the melting layer bright band, or nonuniform beamfilling. Changes in ZH and ZDR over the 3-km layer are plotted in Fig. 6 along with the simulations presented earlier (these include the wide range of initial DSD shapes and rainfall rates-i.e., those shown in Figs. 4 and 5). There is good agreement between the observations and the simulations over a range of initial ZDR values (Fig. 6a)in that DSDs characterized by smaller drops initially (i.e., smaller initial ZDR) tend to lead to increases in ZDR over the rain shaft. We note two discrepancies between the microphysical fingerprints in the simulations and the observations (Fig. 6b). First, in the breakup-dominant quadrant (negative DZH and negative DZDR, or bottom left), the observed decreases in ZDR generally are smaller for a given de- crease in ZH than predicted by the model. This may signify that the simulations are too aggressive in their treatment of drop breakup. In the coalescence- dominant quadrant (positive DZH and positive DZDR, top right), we see substantially larger increases in ZH and ZDR than predicted by the model. It is not clear how much of this is attributable to more efficient co- alescence in the observations than in the simulations, additional drop growth by collection of cloud water droplets, or the possible role of vertical air motions (note that many of these points are from the convective cases). In particular, some of the differences observed could be explained by the relative simplification of the column model configuration. Accurate measurements of the air motion could be incorporated dynamically into the model to account for updrafts and/or downdrafts (e.g., Prat et al. 2008). Also note that overaggressive breakup in the simulations may place a limit on the amount of coalescence possible, thus limiting the max- imum increases in ZH and ZDR. The SPol observations reveal that both the fingerprint for coalescence and the fingerprint for breakup are possible in either convective or stratiform rainfall; the physics of drop collisions does not care whether the system is characterized as convective or stratiform. Rather, the initial shape of the DSD (observed mainly through the initial ZDR aloft) is the primary indicator of the subsequent behavior of the rain shaft. The rainfall rate (or initial ZH aloft) is of secondary importance, similar in stratification to the simulations. In the tropical DYNAMO/ARM-AMIE dataset, much of the convec- tive rain data reveal the coalescence fingerprint. This primarily is because of the initially small drops aloft. More continental convection, in which large drops are formed aloft via melting of hail and graupel, are ex- pected to produce more breakup signatures. Likewise, a variety of stratiform cases reveal fingerprints for breakup, coalescence, and (sometimes) evaporation. The next comparison uses data from the C-band Scan- ning ARM Precipitation Radar (CSAPR) and features the stratiform region of a mesoscale convective system observed on 20 May 2011 during the Midlatitude Conti- nental Convective Clouds Experiment (MC3E). These data have been corrected for attenuation and differential attenuation. Also, the case was selected because of a lack of significant differential propagation phase FDP in the rain region, implying that differential attenuation should be minimized. Again, median vertical profiles are con- structed from the RHI scans, though here 5-km windows are used to smooth out noisy fluctuations in the data. The "pure rain" segments were selected based on the vertical profile of rhy $ 0.98, as before. As such, the vertical depth of the profiles varies as a function of range from the radar (and all are less than 3 km in depth). To make compari- sons with the 3-km rain shaft simulations, a least squares linear1 fit was applied to the average vertical profiles in each 5-km window. Using the slope of ZH and ZDR,the change in these variables over a 3-km distance is com- puted. Note that a linear slope assumption may introduce an overestimation of the magnitudes of the changes over the profiles. However, when the same technique was ap- plied to the SPol data as a sanity check, the changes based on the slope of the linear fit were in good accord with the observed actual 3-km changes. The resulting comparison between the radar data and simulated C-band results are shown in Fig. 7. Despite having some overlap, there are numerous points in the radar data showing larger increases in ZDR (Fig. 7a)than the simulations. Note that many (but not all) of these points are associated with the fingerprint for evaporation or size sorting (Fig. 7b). Evaporation is expected to play a larger role in this continental case compared to the tropical SPol cases, so the results are not surprising. Other points reveal larger increases in ZH and ZDR than pre- dicted by model simulations (Fig. 7b), which could in- dicate more efficient coalescence or less efficient breakup in real rainfall situations. Both SPol and CSAPR data from two very different climatological regions reveal similar comparisons with the simulations, including suggestions that the simula- tions are too aggressive with drop breakup and/or less efficient at coalescence than what is observed. These data also demonstrate that it is an oversimplification to assert that convective or stratiform rainfall always exhibits one fingerprint or the other. Similarly, such statements based on rainfall rate or initial ZH alone also are unwarranted. For example, consider a rainfall rate of 50 mm h21,which would by nearly any standard be considered convective in nature. If the initial DSD is skewed toward smaller drops (i.e., more "tropical" rain), the expected fingerprint based on simulations and observations is an increase in ZDR toward the ground, indicating a dominance of drop coalescence. On the other hand, a more continental convective storm with a rainfall rate of 50 mm h21 and larger initial ZDR is expected to produce the breakup fingerprint. Thus, stratiform and convective partitioning does not matter for determining the expected behavior of microphysical processes in the rain shaft; what matters most is the initial shape of the DSD aloft and whether it is skewed toward smaller or larger drops, which is mea- surable using ZDR. This has implications for rainfall es- timation algorithms such as vertical profiles of reflectivity (VPR) techniques that treat the rain physics of convective and stratiform precipitation differently. Prat and Barros (2009) have shown that governance of the evolution of ZH in the rain shaft and the resulting DSD at the ground transitions from a DSD-dependent regime to a rainfall-rate-dependent regime for large nominal rainfall rates prescribed aloft. Specifically, for rainfall rates in ex- cess of 30 mm h21, DSDs would converge to the same ZH- rainfall rate space. Whereas ZH and KDP were found to behave similarly in our study, ZDR displays contrasting behavior, indicating that the initial DSD remains an im- portant factor on its subsequent evolution. Thus, com- bined use of ZH and ZDR should better characterize the microphysical structure and evolution of the rain shaft. More detailed analyses over a wider range of pre- cipitation intensities, environmental conditions, and ini- tial values of ZDR aloft should be conducted to investigate the possible contributions of (i) measurement errors and/or problems with the representativeness of the lin- early extrapolated radar profiles in the CSAPR case, (ii) limitations of the coalescence-breakup parameteri- zations, (iii) simplifications induced by the idealized column model to the simulation-observation discrep- ancies, and/or (iv) limitations due to the transient nature of most rain events observed. b. 2D video disdrometer observations For Marshall-Palmer DSDs with different rainfall rates, we compute the ZH and ZDR at every height level and at every time and plot them in ZH-ZDR space (Fig. 8). In Figs. 8a and 8b, the full-physics simulations are shown in the black markers, whereas we isolate colli- sional breakup only (Fig. 8a) and coalescence only (Fig. 8b) as shown in the colored markers. The initial tran- sient effects of differential sedimentation are evident by the high-ZDR, low-ZH points. As the DSD evolves, the ZH-ZDR points progress to the right and down in Fig. 8, until the steady-state (equilibrium) DSD is achieved. We can compare the resulting ZH-ZDR pairs to pub- lished observations of many thousands of DSDs mea- sured with a 2D video disdrometer. The best-fit curves for the relation between ZH and ZDR in rain are shown for two locations: Oklahoma (Cao et al. 2008, solid blue line) and Florida (Zhang et al. 2006, dashed blue line). As expected, the more tropical environment of Florida results in lower ZDR for a given ZH than the more continental Oklahoma environment, particularly for heavier rain. Long-term observations of this sort exhibit quite a bit of scatter, which is represented by the dotted blue curves depicting the envelope of observations from Florida in Brandes et al. (2004). Of note is that simulations for rainfall rates higher than about 10 mm h21 have resulting ZDR values below both the Florida and Oklahoma relations for a given ZH. This demonstrates that the simulations produce DSDs characterized by smaller drops than in the disdrometer- based observations (i.e., a lower ZDR for a given ZH). Note that for the heaviest rainfall rate of 100 mm h21, the final ZH-ZDR points lie outside the envelope of observations from Brandes et al. (2004). Because the breakup of drops is dominant at heavier rainfall rates in the model (Prat and Barros 2009), the results suggest that the breakup of drops may be too aggressive in the sim- ulations. Evaporation becomes decreasingly important with higher rainfall rates (Hu and Srivastava 1995), so it is unlikely that evaporation (which would increase ZDR)is playing a significant role in the discrepancy. The dominance of breakup is especially evident when we compare the full-physics runs to the coalescence-only simulations (Fig. 8b), as there is a large separation be- tween the final ZH-ZDR points for heavier rainfall rates. In contrast to the full-physics and breakup-only simu- lations, the coalescence-only runs (Fig. 8b) produce final ZH-ZDR values in much better agreement with the ob- served ZH-ZDR relations. 5. Discussion While the combination of a microphysical and elec- tromagnetic model allowed us to determine un- ambiguously the impact of selected microphysical processes on the dual-polarization variables, additional insight has been provided on the physical parameteriza- tion of these processes. The observations presented herein suggesting that the breakup is overaggressive are consistent with some previous laboratory and numerical work. For example, Hu and Srivastava (1995) found that the modeled equilibrium DSD slope was far steeper than observed equilibrium DSDs, and thus suggested that the Low and List (LL; LL82a; LL82b) breakup parameteri- zation might greatly overestimate the number of frag- ments produced during breakup. This is echoed in the more recent laboratory work of Barros et al. (2008),who report systematic overestimations of the number of drop fragments produced in breakup events, particularly for the fragment diameter range 0.5-1.0 mm. Such an en- hancement of the small-drop end of the DSD steepens the DSD slope, contributing to a decrease in ZDR. Using direct numerical simulations of drop collisions, Straub et al. (2010) reported that, under stationary conditions, their equilibrium DSD featured many more large drops than the LL parameterization. Additionally, they found more drops larger than 2.8 mm in diameter than the McFarquhar (2004) modification to the LL parameteri- zation. In this case, the Straub et al. (2010) parameteri- zation would be expected to produce larger ZDR for their equilibrium DSD compared to the LL and McFarquhar (2004) parameterizations. An overestimation of the number concentration of small drops has ramifications for modeling of convective storms. Small drops evaporate more rapidly than larger drops owing to their larger surface-area-to-volume ratio (e.g., Pruppacher and Klett 1997). So, small-drop- dominated DSDs have a large evaporative potential. Overestimating the number of small drops (and/or slope of the DSD) in numerical models would then exaggerate negative buoyancy production. Thus, improving the parameterization of drop breakup has important impli- cations for modeling of cold pool generation and sub- sequent storm behavior and evolution (e.g., Morrison et al. 2012). The results of this study may also be useful for quan- titative precipitation estimation (QPE). Typically, QPE techniques based on VPR assume that ZH increases to- ward the ground in heavy convective rain. The recent study of Cao et al. (2013) found that this was the case for rainfall rates in excess of 18 mm h21; for lower rainfall rates and stratiform precipitation, they found that the ZH profile decreases toward the ground. The argument is that coalescence and/or accretion growth is dominant in convective precipitation, whereas evaporation and/or breakup dominate in stratiform precipitation. This ap- proach, based on observations and a conceptualized mi- crophysics model, disagrees with rain shaft model simulations of the collisional processes, wherein equilib- rium DSDs resulting from heavier rainfall rates are asso- ciated with the dominance of breakup and thus decreasing ZH toward the ground (Prat and Barros 2009). Addition- ally, the present study has shown that ZH can decrease or increase toward the ground when collisional processes are acting, depending on the DSD shape and rainfall rate. Thus, it is important to consider the vertical profiles of ZH and ZDR to more effectively diagnose the dominant physical processes governing the evolution of the vertical structure of precipitation. In particular, the initial ZDR aloft seems to be the best predictor of the behavior of the vertical profiles of ZH and ZDR. By considering the profiles of both ZH and ZDR, cases where evaporation may or may not be occurring can be identified and quantitative pre- cipitation estimates adjusted accordingly. For example, the microphysics model results suggest that the collisional processes themselves do not significantly alter the rainfall rate, whereas evaporation (which depletes rainwater mass into water vapor) does [e.g., see Fig. 11 in Kumjian and Ryzhkov (2010)]. So, using polarimetry to distinguish be- tween cases of evaporation or the collisional processes, both of which can cause decreases in ZH, can be quite useful for QPE and hydrometeorological applications. 6. Summary We have explored the impact of the warm-rain colli- sional processes on the resulting vertical profiles of the polarimetric radar variables. This was accomplished by employing an explicit microphysical model describing the warm-rain processes of drop settling, coalescence, colli- sional breakup, and aerodynamic breakup in a 1D rain shaft. This microphysics model was coupled to an elec- tromagnetic scattering model for raindrops. The coupled electromagnetic-microphysical model was used to de- termine the time-varying vertical profiles of ZH, ZDR,and KDP at S, C, and X bands. The polarimetric "fingerprint" of each process (acting in isolation and in combination) was quantified. The results demonstrate that the initial ZDR aloft is a better predictor than ZH or rainfall rate for the sub- sequent changes in ZH and ZDR over the 3-km domain. For initial ZDR values less than about 1.0 dB aloft, the ZH and ZDR increase toward the ground, indicating the dominance of coalescence. For larger ZDR values aloft, the simulations predict decreases in ZH and ZDR toward the ground as the breakup processes dominate. Changes in ZDR are largest in magnitude at C band, suggesting that C-band radars may be best able to observe these fingerprints in nature. The fingerprints for the collisional processes depend on the rainfall rate and initial DSD aloft and even display some variability between different radar wavelengths. However, they do not overlap with the signatures for evaporation and size sorting (i.e., increases in ZDR and decreases in ZH and KDP toward the ground), suggesting that a distinction between the dominant ongoing pro- cesses may be made using polarimetric radar data. The simulations were compared to disdrometer and polarimetric radar observations. These comparisons suggest that the breakup kernels employed (LL82b; McFarquhar 2004) may be too aggressive, and the co- alescence parameterizations used (LL82a; Beard and Ochs 1995) may be too weak, especially for the higher rainfall rates, producing erroneously large concentra- tions of small raindrops. This is manifested as very low ZDR for a given ZH value, or rain that has very "tropi- cal" characteristics. Indeed, simulated ZDR values for the highest rainfall rates considered lie outside the bounds of published disdrometer observations from Florida. In contrast, the "coalescence only" simulations produce resulting ZH-ZDR pairs that are in better agreement with the disdrometer data, though data from SPol in a tropical environment indicate that coalescence fingerprints can be substantially larger than predicted by the model. Therefore, because of the unequivocal de- pendency between selected microphysical processes and the polarimetric radar variables, real-time rainfall field observations could be of great help to improve micro- physical parameterizations of drop-drop interactions via inverse problem modeling techniques. Dual- polarization radar observations for different storm types could be used as "real laboratory" experiments to develop and improve parameterizations. Future work will investigate newer breakup kernels that lessen the efficiency of breakup and the number of fragments produced from breakup events as well as the observed variability of microphysical fingerprints in a larger number of different environmental conditions, rainfall intensities, and initial DSD shapes. Acknowledgments. SPolKa radar data were collected as part of DYNAMO/ARM-AMIE, which was spon- sored by NSF, NOAA, ONR, DOE, NASA, and JAMSTEC. The involvement of the NSF-sponsored NCAR Earth Observing Laboratory (EOL) is ac- knowledged. Scott Ellis and Bob Rilling (NCAR-EOL) are thanked for providing access to the SPolKa data, which are archived at the DYNAMO Data Archive Center maintained by NCAR EOL. The authors also would like to thank Dr. Scott Collis (Argonne National Laboratory) for providing the CSAPR data. Support for this work for the first author comes from Grant ER#65459 from the Department of Energy Atmo- spheric System Research program and from the National Center for Atmospheric Research (NCAR) Advanced Study Program. The second author is sup- ported by the NOAA/NCDC Climate Data Records and Science Stewardship Program through the Cooperative Institute for Climate and Satellites-North Carolina under the Agreement NA09NES4400006. We would also like to thank Dr. Hugh Morrison (NCAR MMM), Dr. Angela Rowe (University of Washington), and two additional anonymous reviewers who provided a constructive review of the manuscript. 1 Other options, such as a parabolic or polynomial fit, are pos- sible as well. However, the linear fit was deemed sufficiently rep- resentative for the vast majority of the profiles used. REFERENCES Barros, A. P., O. P. Prat, P. Shrestha, F. Y. Testik, and L. F. Bliven, 2008: Revisiting Low and List (1982): Evaluation of raindrop collision parameterizations using laboratory observations and modeling. J. Atmos. Sci., 65, 2983-2993, doi:10.1175/ 2008JAS2630.1. Beard, K. V., and H. T. Ochs, 1995: Collisions between small pre- cipitation drops. Part II: Formulas for coalescence, temporary coalescence, and satellites. J. Atmos. Sci., 52, 3977-3996, doi:10.1175/1520-0469(1995)052,3977:CBSPDP.2.0.CO;2. Best, A. C., 1950: Empirical formulae for the terminal velocity of water drops falling through the atmosphere. Quart. J. Roy. Meteor. Soc., 76, 302-311, doi:10.1002/qj.49707632905. Bleck, R., 1970: A fast, approximate method for integrating the stochastic coalescence equation. J. Geophys. Res., 75, 5165- 5171, doi:10.1029/JC075i027p05165. Bott, A., 1998: A flux method for the numerical solution of the stochastic collection equation. J. Atmos. Sci., 55, 2284-2293, doi:10.1175/1520-0469(1998)055,2284:AFMFTN.2.0.CO;2. -, 2000: A flux method for the numerical solution of the sto- chastic collection equation: Extension to two-dimensional particle distributions. J. Atmos. Sci., 57, 284-294, doi:10.1175/ 1520-0469(2000)057,0284:AFMFTN.2.0.CO;2. -, 2001: A new method for the solution of the stochastic collec- tion equation in cloud models with spectral aerosol and cloud drop microphysics. Atmos. Res., 59-60, 361-372, doi:10.1016/ S0169-8095(01)00125-9. Brandes, E. A., G. Zhang, and J. Vivekanandan, 2004: Drop size distribution retrieval with polarimetric radar: Model and application. J. Appl. Meteor., 43, 461-475, doi:10.1175/ 1520-0450(2004)043,0461:DSDRWP.2.0.CO;2;Cor- rigendum,44,186,doi:10.1175/1520-0450(2005)44,186: C.2.0.CO;2. Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar. 1st ed. Cambridge University Press, 636 pp. Brown, P. S., 1987: Parameterization of drop-spectrum evolution due to coalescence and breakup. J. Atmos. Sci., 44, 242-249, doi:10.1175/1520-0469(1987)044,0242:PODSED.2.0.CO;2. -, 1988: The effects of filament, sheet, and disk breakup upon the drop spectrum. J. Atmos. Sci., 45, 712-718, doi:10.1175/ 1520-0469(1988)045,0712:TEOFSA.2.0.CO;2. -, 1993: Analysis and parameterization of the combined coalescence, breakup, and evaporation processes. J. Atmos. Sci., 50, 2940-2951, doi:10.1175/1520-0469(1993)050,2940: AAPOTC.2.0.CO;2. -, 1997: Mass conservation considerations in analytic re- presentation of raindrop fragment distributions. J. Atmos. Sci., 54, 1675-1687, doi:10.1175/1520-0469(1997)054,1675: MCCIAR.2.0.CO;2. Bryan, G. H., and H. Morrison, 2012: Sensitivity of a simulated squall line to horizontal resolution and parameterization of microphysics. Mon. Wea. Rev., 140, 202-225, doi:10.1175/ MWR-D-11-00046.1. Cao,Q.,G.Zhang,E. A.Brandes,T.J.Schuur,A.V.Ryzhkov,and K. Ikeda, 2008: Analysis of video disdrometer and polar- imetric radar data to characterize rain microphysics in Okla- homa. J. Appl. Meteor. Climatol., 47, 2238-2255, doi:10.1175/ 2008JAMC1732.1. -, Y. Hong, J. Gourley, Y. Qi, J. Zhang, Y. Wen, and P.-E. Kirstetter, 2013: Statistical and physical analysis of the vertical structure of precipitation in the mountainous west region of the United States using 111 years of spaceborne observations from TRMM precipitation radar. J. Appl. Meteor. Climatol., 52, 408- 424, doi:10.1175/JAMC-D-12-095.1. Dawson, D. T., M. Xue, J. A. Milbrandt, and M. K. Yau, 2010: Comparison of evaporation and cold pool development be- tween single-moment and multimoment bulk microphysics schemes in idealized simulations of tornadic thunderstorms. Mon. Wea. Rev., 138, 1152-1171, doi:10.1175/2009MWR2956.1. Doviak, R. J., and D. S. Zrni^c, 1993: Doppler Radar and Weather Observations. 2nd ed. Academic Press, 562 pp. Feingold, G., S. Tzivion, and Z. Leviv, 1988: Evolution of raindrop spectra. Part I: Solution to the stochastic collection/breakup equation using the method of moments. J. Atmos. Sci., 45, 3387- 3399, doi:10.1175/1520-0469(1988)045,3387:EORSPI.2.0.CO;2. Ferrier, B. S., W.-K. Tao, and J. Simpson, 1995: A double-moment multiple-phase four-class bulk ice scheme. Part II: Simulations of convective storms in different large-scale environments and comparisons with other bulk parameterizations. J. Atmos. Sci., 52, 1001-1033, doi:10.1175/1520-0469(1995)052,1001: ADMMPF.2.0.CO;2. Gilmore, M. S., J. M. Straka, and E. N. Rasmussen, 2004: Pre- cipitation and evolution sensitivity in simulated deep convec- tive storms: Comparisons between liquid-only and simple ice and liquidphase microphysics. Mon. Wea. Rev., 132,1897-1916, doi:10.1175/1520-0493(2004)132,1897:PAESIS.2.0.CO;2. Herzegh, P. H., and A. R. Jameson, 1992: Observing precipitation through dual-polarization radar measurements. Bull. Amer. Me- teor. Soc., 73, 1365-1374, doi:10.1175/1520-0477(1992)073,1365: OPTDPR.2.0.CO;2. Hu, Z., and R. C. Srivastava, 1995: Evolution of raindrop size dis- tribution by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 1761-1783, doi:10.1175/ 1520-0469(1995)052,1761:EORSDB.2.0.CO;2. Jacobson, M. Z., 2011: Numerical solution to drop coalescence/ breakup with a volume-conserving, positive-definite, and unconditionally stable scheme. J. Atmos. Sci., 68, 334-346, doi:10.1175/2010JAS3605.1. Kumjian, M. R., 2013a: Principles and applications of dual- polarization weather radar. Part I: Description of the polarimetric radar variables. J. Oper. Meteor., 1, 226-242, doi:10.15191/nwajom.2013.0119. -, 2013b: Principles and applications of dual-polarization weather radar. Part II: Warm- and cold-season applications. J. Oper. Meteor., 1, 243-264, doi:10.15191/nwajom.2013.0120. -, 2013c: Principles and applications of dual-polarization weather radar. Part III: Artifacts. J. Oper. Meteor., 1, 265- 274, doi:10.15191/nwajom.2013.0121. -, and A. V. Ryzhkov, 2010: The impact of evaporation on polarimetric characteristics of rain: Theoretical model and practical implications. J. Appl. Meteor. Climatol., 49, 1247- 1267, doi:10.1175/2010JAMC2243.1. -, and -, 2012: The impact of size sorting on the polarimetric radar variables. J. Atmos. Sci., 69, 2042-2060, doi:10.1175/ JAS-D-11-0125.1. List, R., and J. R. Gillespie, 1976: Evolution of raindrop spectra with collision-induced breakup. J. Atmos. Sci., 33, 2007-2013, doi:10.1175/1520-0469(1976)033,2007:EORSWC.2.0.CO;2. -, and G. M. McFarquhar, 1990: The evolution of three-peak raindrop size distributions in one-dimensional shaft models. Part I: Single-pulse rain. J. Atmos. Sci., 47, 2996-3006, doi:10.1175/1520-0469(1990)047,2996:TEOTPR.2.0.CO;2. -, N. R. Donaldson, and R. E. Stewart, 1987: Temporal evolution of drop spectra to collisional equilibrium in steady and pulsating rain. J. Atmos. Sci., 44, 362-372, doi:10.1175/ 1520-0469(1987)044,0362:TEODST.2.0.CO;2. Low, T. B., and R. List, 1982a: Collision, coalescence, and breakup of raindrops. Part I: Experimentally established coalescence efficiencies and fragment size distributions in breakup. J. Atmos. Sci., 39, 1591-1606, doi:10.1175/ 1520-0469(1982)039,1591:CCABOR.2.0.CO;2. -, and -, 1982b: Collision, coalescence, and breakup of raindrops. Part II: Parameterization of fragment size distributions. J. Atmos. Sci., 39, 1607-1619, doi:10.1175/ 1520-0469(1982)039,1607:CCABOR.2.0.CO;2. Markowski, P. M., J. M. Straka, and E. N. Rasmussen, 2002: Direct surface thermodynamic observations within the rear-flank downdrafts of nontornadic and tornadic supercells. Mon. Wea. Rev., 130, 1692-1721, doi:10.1175/1520-0493(2002)130,1692: DSTOWT.2.0.CO;2. McFarquhar, G. M., 2004: A new representation of collision- induced breakup of raindrops and its implications for the shapes of raindrop size distributions. J. Atmos. Sci., 61, 777-794, doi:10.1175/1520-0469(2004)061,0777: ANROCB.2.0.CO;2. McTaggart-Cowan, J. D., and R.List, 1975: Collision and breakup of water drops at terminal velocity. J. Atmos. Sci., 32, 1401-1411, doi:10.1175/1520-0469(1975)032,1401:CABOWD.2.0.CO;2. Mishchenko, M. I., 2000: Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation. Appl. Opt., 39, 1026-1031, doi:10.1364/AO.39.001026. Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 991-1007, doi:10.1175/2008MWR2556.1. -, S. A. Tessendorf, K. Ikeda, and G. Thompson, 2012: Sensi- tivity of a simulated midlatitude squall line to parameteriza- tion of raindrop breakup. Mon. Wea. Rev., 140, 2437-2460, doi:10.1175/MWR-D-11-00283.1. Ochs,H.T.,K.V.Beard,R.R.Czys,N.F.Laird,D.E.Schaufelberger, and D. J. Holdridge, 1995: Collisions between small pre- cipitation drops. Part I: Laboratory measurements of bounce, coalescence, and temporary coalescence. J. Atmos. Sci., 52, 2258-2275, doi:10.1175/1520-0469(1995)052,2258: CBSPDP.2.0.CO;2. Prat, O. P., and A. P. Barros, 2007a: Exploring the use of a column model for the characterization of microphysical processes in warm rain: Results from a homogeneous rainshaft model. Adv. Geosci., 10, 145-152, doi:10.5194/adgeo-10-145-2007. -, and -, 2007b: A robust numerical solution of the sto- chastic collection-breakup equation for warm rain. J. Appl. Meteor. Climatol., 46, 1480-1497, doi:10.1175/JAM2544.1. -, and -, 2009: Exploring the transient behavior of Z-R relationships: Implications for radar rainfall estimation. J. Appl. Meteor. Climatol., 48, 2127-2143, doi:10.1175/ 2009JAMC2165.1. -, -, and C. R. Williams, 2008: An intercomparison of model simulations and VPR estimates of the vertical structure of warm stratiform rainfall during TWP-ICE. J. Appl. Meteor. Climatol., 47, 2797-2815, doi:10.1175/2008JAMC1801.1. -, -, and F. Y. Testik, 2012: On the influence of raindrop collision outcomes on equilibrium drop size distributions. J. Atmos. Sci., 69, 1534-1546, doi:10.1175/JAS-D-11-0192.1. Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds and Precipitation. 2nd ed. Kluwer Academic Publishers, 954 pp. Ryzhkov, A. V., 2001: Interpretation of polarimetric radar co- variance matrix for meteorological scatterers: Theoretical analysis. J. Atmos. Oceanic Technol., 18, 315-328, doi:10.1175/ 1520-0426(2001)018,0315:IOPRCM.2.0.CO;2. -, D. S. Zrni^c, J. C. Hubbert, V. N. Bringi, J. Vivekanandan, and E. A. Brandes, 2002: Polarimetric radar observations and interpretation of co-cross-polar correlation coefficients. J. Atmos. Oceanic Technol., 19, 340-354, doi:10.1175/ 1520-0426-19.3.340. -, T. J. Schuur, D. W. Burgess, P. L. Heinselman, S. E. Giangrande, and D. S. Zrni^c, 2005: The Joint Polarization Experiment: Polarimetric rainfall measurements and hy- drometeor classification. Bull. Amer. Meteor. Soc., 86, 809- 824, doi:10.1175/BAMS-86-6-809. -, M. Pinsky, A. Pokrovsky, and A. Khain, 2011: Polarimetric radar observation operator for a cloud model with spectral microphysics. J. Appl. Meteor. Climatol., 50, 873-894, doi:10.1175/2010JAMC2363.1. Schlottke, J., W. Straub, K. D. Beheng, H. Gomaa, and B. Weigand, 2010: Numerical investigation of collision-induced breakup of raindrops. Part I: Methodology and dependencies on collision energy and eccentricity. J. Atmos. Sci., 67, 557-575, doi:10.1175/ 2009JAS3174.1. Seifert, A., A. P. Khain, U. Blahak,and K.D. Beheng, 2005: Possible effects of collisional breakup on mixed-phase deep convection simulated by a spectral (bin) cloud model. J. Atmos. Sci., 62, 1917-1931, doi:10.1175/JAS3432.1. Srivastava, R. C., 1971: Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci., 28, 410-415, doi:10.1175/1520-0469(1971)028,0410:SDORGB.2.0.CO;2. -, 1985: A simple model of evaporatively driven downdraft: Application to microburst downdraft. J. Atmos. Sci., 42, 1004- 1023, doi:10.1175/1520-0469(1985)042,1004:ASMOED.2.0. CO;2. -, 1987: A model of intense downdrafts driven by the melting and evaporation of precipitation. J. Atmos. Sci., 44, 1752-1774, doi:10.1175/1520-0469(1987)044,1752:AMOIDD.2.0.CO;2. Straub, W., K. D. Beheng, A. Seifert, J. Schlottke, and B. Weigand, 2010: Numerical investigation of collision-induced breakup of raindrops. Part II: Parameterizations of coalescence efficien- cies and fragment size distributions. J. Atmos. Sci., 67, 576- 588, doi:10.1175/2009JAS3175.1. Testud,J.,S.Oury,R.A.Black,P.Almayenc,andX.Dou, 2001: The concept of "normalized" distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor., 40, 1118-1140, doi:10.1175/ 1520-0450(2001)040,1118:TCONDT.2.0.CO;2. Tzivion, S., G. Feingold, and Z. Levin, 1989: The evolution of rain- drop spectra. Part II: Collisional collection/breakup and evap- oration in a rainshaft. J. Atmos. Sci., 46, 3312-3328, doi:10.1175/ 1520-0469(1989)046,3312:TEORSP.2.0.CO;2. Valdez, M. P., and K. C. Young, 1985: Number fluxes in equilibrium raindrop populations: A Markov chain analysis. J. Atmos. Sci., 42, 1024-1036, doi:10.1175/1520-0469(1985)042,1024: NFIERP.2.0.CO;2. Van Weverberg, K., N. P. M. van Lipzig, and L. Delobbe, 2011: The impact of size distribution assumptions in a bulk one-moment microphysics scheme on simulated surface precipitation and storm dynamics during a low-topped supercell case in Belgium. Mon. Wea. Rev., 139, 1131-1147, doi:10.1175/2010MWR3481.1. Waterman, P. C., 1969: Scattering by dielectric obstacles. Alta Freq., 38, 348-352. Yoneyama, K., C. Zhang, and C. N. Long, 2013: Tracking pulses of the Madden-Julian Oscillation. Bull. Amer. Meteor. Soc., 94, 1871-1891, doi:10.1175/BAMS-D-12-00157.1. Zhang, G., J. Sun, and E. A. Brandes, 2006: Improving parame- terization of rain microphysics with disdrometer and radar observations. J. Atmos. Sci., 63, 1273-1290, doi:10.1175/ JAS3680.1. Zrni^c, D. S., and A. V. Ryzhkov, 1999: Polarimetry for weather surveillance radars. Bull. Amer. Meteor. Soc., 80, 389-406, doi:10.1175/1520-0477(1999)080,0389:PFWSR.2.0.CO;2. MATTHEW R. KUMJIAN* Advanced Study Program, National Center for Atmospheric Research,1 Boulder, Colorado OLIVIER P. PRAT Cooperative Institute for Climate and Satellites, North Carolina State University, and NOAA/National Climatic Data Center, Asheville, North Carolina (Manuscript received 10 November 2013, in final form 7 March 2014) * Current affiliation: Department of Meteorology, The Pennsyl- vania State University, University Park, Pennsylvania. 1 The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Dr. Matthew R. Kumjian, De- partment of Meteorology, The Pennsylvania State University, 513 Walker Building, University Park, PA 16802. E-mail: [email protected] (c) 2014 American Meteorological Society |