Sensitivity of a Simulated Midlatitude Squall Line to Parameterization of Raindrop Breakup

AUGUST 2012 M O R R I S O N E T A L . 2437

HUGH MORRISON,SARAH A. TESSENDORF,KYOKO IKEDA, AND GREGORY THOMPSON National Center for Atmospheric Research,* Boulder, Colorado

(Manuscript received 14 October 2011, in ﬁnal form 3 February 2012)

ABSTRACT

This paper describes idealized simulations of a squall line observed on 20 June 2007, in central Oklahoma. Results are compared with measurements from dual-polarization radar and surface disdrometer. The baseline model configuration qualitatively reproduces key storm features, but underpredicts precipitation rates and generally overpredicts median volume raindrop diameter. The sensitivity of model simulations to parameterization of raindrop breakup is tested under different low-level (0–2.5 km) environmental vertical wind shears. Storm characteristics exhibit considerable sensitivity to the parameterization of breakup, especially for moderate (0.0048 s21) shear. Simulations with more efficient breakup tend to have higher domain-mean precipitation rates under both moderate and higher (0.0064 s21) shear, despite the smaller mean drop size and hence lower mass-weighted fall speed and higher evaporation rate for a given rainwater content. In these runs, higher evaporation leads to stronger cold pools, faster propagation, larger storm size, greater updraft mass flux (but weaker convective updrafts at mid- and upper levels), and greater total condensation that com- pensates for the increased evaporation to give more surface precipitation. The impact of drop breakup on mass-weighted fall speed is also important and leads to a nonmonotonic response of storm characteristics (surface precipitation, cold pool strength, etc.) to changes in breakup efficiency under moderate wind shear. In contrast, the response is generally monotonic at higher wind shear. Interactions between drop breakup, convective dynamics, cold pool intensity, and low-level environmental wind shear are also described in the context of ‘‘Rotunno–Klemp–Weisman (RKW) theory,’’ which addresses how density currents evolve in sheared environments.

1. Introduction and active updraft cell generation along the gust front, a transition zone of lighter precipitation and a low-level Squall lines are linear systems of organized deep con- radar reﬂectivity minimum between the convective and vection, or mesoscale convective systems (MCSs). They stratiform regions, followed by a region of moderate are common in both midlatitude and tropical environ- precipitation in the trailing stratiform region. ments and have been extensively studied (e.g., Fujita Cloud-system-resolving models (CSRMs) utilizing a 1955; Zipser 1969; Ogura and Chen 1977; LeMone et al. horizontal grid spacing of order 1 km are well suited 1984; Houze 1989; Biggerstaff and Houze 1991, 1993). for simulating squall lines and other MCSs because These studies have suggested several common mor- they can explicitly resolve the mesoscale and deep phological features described by the conceptual model convective-scale dynamics. Understanding the be- of Biggerstaff and Houze (1991, see Fig. 18 therein). havior of such simulations is important since regional Mature squall lines typically contain an upshear-tilted, numerical weather prediction (NWP) models are now multicellular convective region with heavy precipitation commonly run at CSRM scale for convective-scale forecasting (e.g., Kain et al. 2008; Lean et al. 2008; * The National Center for Atmospheric Research is sponsored Weisman et al. 2008). Furthermore, CSRMs have been by the National Science Foundation. employed as smaller-scale models embedded within larger- scale general circulation models (GCMs; i.e., the multiscale modeling framework or ‘‘superparameterization,’’ pri- Corresponding author address: Hugh Morrison, National Center for Atmospheric Research, 3090 Center Green Dr., Boulder, CO marily to improve the representation of deep convec- 80301. tion; e.g., Grabowski 2001; Randall et al. 2003; Tao et al. E-mail: [email protected] 2009).

DOI: 10.1175/MWR-D-11-00283.1

Ó 2012 American Meteorological Society 2438 MONTHLY WEATHER REVIEW VOLUME 140

The parameterization of cloud microphysics remains consistent with a decrease in mean drop size as breakup a major challenge for simulating squall lines using efficiency is increased, leading to reduced fall speed CSRMs. Microphysical processes directly impact buoy- and increased evaporation. MM11 concluded that con- ancy, and hence convection, through condensate loading straining the parameterization of raindrop breakup is and latent heating or cooling due to phase changes. needed to reduce uncertainty of two-moment micro- Several studies have investigated the sensitivity of squall physics schemes,1 which is important since these schemes lines to representation of microphysics using bulk mi- are expected to be widely used in NWP and climate crophysics schemes (e.g., Fovell and Ogura 1988; models in the coming years. In this study, we extend the McCumber et al. 1991; Tao et al. 1995; Ferrier et al. work of MM11 and van Weverberg et al. (2012) to test 1995; Liu et al. 1997; Morrison et al. 2009; Bryan and systematically the sensitivity of a simulated squall line to Morrison 2012; van Weverberg et al. 2012). Parame- drop breakup. terization of rain microphysics has been identified as Environmental wind shear plays a critical role in the a critical aspect given the impact of rain evaporation on organization and structure of squall lines (e.g., Thorpe cold pool evolution (Ferrier et al. 1995; Morrison et al. et al. 1982; Nicholls et al. 1988; Weisman et al. 1988; 2009; Bryan and Morrison 2012; van Weverberg et al. Fovell and Ogura 1989; Szeto and Cho 1994; Robe and 2012). Morrison et al. (2009), Bryan and Morrison Emanuel 2001; Weisman and Rotunno 2004; James et al. (2012), and van Weverberg et al. (2012) investigated 2005; Bryan et al. 2006; Takemi 2007). Therefore we test sensitivity to using either a one-moment (predicting sensitivity of the simulated squall line to drop breakup mass mixing ratio only) or two-moment scheme (pre- over a range of different low-level vertical shears. In- dicting both mass and number mixing ratio) represen- teractions between drop breakup, cold pools, and storm tation of rain, with all other microphysical processes dynamics under varying strength of low-level shear can treated identically. Differences in the rain drop size also be viewed in the context of Rotunno–Klemp– distributions (DSDs) between the one- and two-moment Weisman (RKW) theory, which explains how density schemes led to reduced evaporation, enhanced surface currents evolve in a sheared environment (Rotunno precipitation in the trailing stratiform region, and weaker et al. 1988; Weisman and Rotunno 2004). This theory cold pools (especially well behind the surface gust front) postulates that maximum system intensity is attained using the two-moment schemes, with an overall improve- when the vorticity generated by cold pools is in approx- ment compared to observations (Bryan and Morrison imate balance with the low-level vertical environmental 2012). Similar impacts using one-moment versus two- shear, leading to the deepest lifting of environmental air. moment schemes have also been described for other Hence, changes in cold pool intensity or shear that move types of deep convection (Milbrandt and Yau 2006; the system away from optimal balance may result in Mansell and Wicker 2008; Luo et al. 2010; Dawson et al. weakening of the system. The simulations described in 2010), sometimes, but not always, leading to an im- this paper provide a backdrop for analysis of interactions proved comparison with observations when utilizing between cold pool evolution and low-level shear and two-moment schemes. hence assessment of RKW theory. Despite sensitivity to representation of rain DSDs, The overall goals of this study are 1) to develop a there has been little testing of specific processes, such as well-characterized midlatitude squall-line case study by raindrop breakup, that influence the DSDs in squall-line synthesizing a suite of observations, 2) to assess model simulations using two-moment schemes. An exception is performance against these observations, and 3) to quan- van Weverberg et al. (2012), who found that differing tify sensitivity of the model to the treatment of raindrop treatments of breakup led to large differences in maxi- breakup under different low-level environmental wind mum accumulated precipitation using two different two- shears, with interactions between microphysics, cold pool moment schemes. More systematic testing of sensitivity evolution, and storm dynamics analyzed in the context to drop breakup for a supercell storm was performed by of RKW theory. In this paper, the impacts of raindrop Morrison and Milbrandt (2011, hereafter MM11). They breakup on three-dimensional CSRM simulations of a found that evaporation and hence cold pool character- squall line are described. While this study focuses largely istics were highly sensitive to the parameterization of on sensitivity of the simulated storm to raindrop breakup, breakup; minimum perturbation potential temperature the comparison with observations demonstrates the varied by up to 7 K after 2 h of integration using various drop breakup formulations proposed in the literature. In these simulations, more efficient breakup parameteri- 1 Note that since breakup impacts number concentration but not zations led to reduced surface precipitation and stronger bulk mass of rain, it is parameterized in two-moment but not one- cold pools (see Table 2 in MM11). These impacts are moment schemes. AUGUST 2012 M O R R I S O N E T A L . 2439

FIG. 1. Radar reﬂectivity mosaic at 0600 UTC 20 Jun 2007 illustrating the large extent of the MCS. The KOUN radar domain (150-km radius) is indicated by the circle, with the locations of the two disdrometers shown by boxes.

model’s ability to reproduce overall storm features and was the subject of a previous study on electrification by provides observational constraints on the simulated rain Lang et al. (2010). Southeasterly low-level flow had set up DSDs. The analysis focuses on several key squall-line on 19 June, advecting moisture northward from the Gulf properties, including surface precipitation, cold pool of Mexico into the south-central plains to the east of a characteristics, radar reflectivity, and dynamical struc- dryline across eastern New Mexico. Extremely moist and ture, with an emphasis on interactions between the mi- unstable conditions prevailed over Oklahoma and Texas, crophysics, thermodynamics, and dynamics, and how with surface dew point temperatures exceeding 258C these interactions respond to different parameteriza- and a convective available potential energy (CAPE) of tions of breakup. The combination of disdrometer, ra- 4113 J kg21 shown by the sounding at 0000 UTC 20 June dar, and other measurements for this case affords an in Fig. 2 (calculated using 110-hPa mixed layer parcels). opportunity to address this issue by providing robust The observational infrastructure in central Oklahoma observational constraints on the modeled DSDs. for this case included two two-dimensional video disdrometers (2DVDs; Kruger and Krajewski 2002), a dual-polarization S-band Weather Surveillance Radar- 2. Case description and observations 1988 Doppler (WSR-88D) radar at KOUN, and a high- The 20 June 2007 squall line in central Oklahoma was resolution network of surface observations from the part of a large MCS (Fig. 1) that resulted from three Oklahoma Mesonet. The Oklahoma Mesonet (Brock separate convective systems that formed during the af- et al. 1995; McPherson et al. 2007) provided surface ternoon of 19 June 2007 and merged together later measurements every 5 min, such as temperature, hu- that evening. The first storms developed by 1700 UTC midity, wind, and precipitation, at more than 100 sites in 19 June in northwestern Kansas along a stationary front. the state of Oklahoma. The 2DVDs were deployed This cluster of storms moved southeastward toward within the KOUN radar domain during the 2007 wet Oklahoma and merged with another set of storms that season: one operated and owned by NCAR (17 km to formed by 2100 UTC in northern Oklahoma, forming the the east of KOUN) and the other by the University of portion of the squall line that passed over the Norman, Oklahoma (OU; 65 km to the southwest of KOUN). Oklahoma (KOUN), dual-polarization radar domain The radar, mesonet, and disdrometer measurements (Fig. 1) that is the focus of the present study. This storm were used to derive rain-rate and DSD parameters for 2440 MONTHLY WEATHER REVIEW VOLUME 140

FIG. 2. Thermodynamic sounding from Norman, OK (KOUN), at 0000 UTC 20 Jun 2007, approximately 6 h prior to the passage of the storm. Red and green lines show observations, with gray lines showing vertically smoothed proﬁles used for initial conditions in the model. Half and full ﬂags on the wind barbs represent wind speeds of 2.5 and 5 m s21, respectively. comparison with the model. A more detailed description been neglected for simplicity. Given that the focus of of the methodology for processing and analyzing these this paper is on treatment of microphysics, its parame- measurements is provided in the appendix. terization is described in more detail below.

3. Model description and setup b. Description of the microphysics scheme a. Model description The two-moment bulk cloud microphysics scheme used here predicts mass and number mixing ratios of five Simulations were conducted using the compressible, hydrometeor species: cloud droplets, cloud ice, snow, nonhydrostatic Advanced Research Weather Research rain, and hail.2 This scheme is based on the parameter- and Forecasting model (WRF) version 3.1 (Skamarock ization of Morrison et al. (2005), and subsequently im- et al. 2008). The governing equations are solved using plemented, with modifications, into WRF (Morrison a time-split integration with third-order Runge–Kutta et al. 2009). The hydrometeor size distributions N(D) scheme. Horizontal and vertical turbulent diffusion are are treated using gamma functions such as calculated using a 1.5-order TKE scheme (Skamarock et al. 2008). Horizontal and vertical advection is calculated using positive definite fifth- and third-order dis- cretization schemes, respectively. The upper and lower 2 The Morrison scheme available in WRF has a switch to rep- boundaries are free slip with zero vertical velocity. resent the rimed ice category as either graupel or hail. In this study, Surface fluxes are set to zero and radiative transfer has all simulations utilized settings representing rimed ice as hail. AUGUST 2012 M O R R I S O N E T A L . 2441

m 2lD N(D) 5 N0D e , (1) where D is the particle diameter; and N0, m, and l are the intercept, shape, and slope parameters, respectively. For all precipitation species as well as cloud ice, we assume that m 5 0 (i.e., an inverse exponential distribution). For cloud droplets, m is a function of the predicted droplet number concentration following the observations of

Martin et al. (1994). Since the scheme is two moment, N0 and l are free parameters that are determined from the predicted mass and number mixing ratios for each species: cNG(m 1 4) 1/d FIG. 3. Rain self-collection efﬁciency Ec as a function of number- l 5 , (2) weighted mean drop radius Dr for the various drop breakup pa- qG(m 1 1) rameterizations.

Nlm11 N 5 , (3) E 5 1, D , D 0 G(m 1 1) c r th Ec 5 2 2 exp[2300(Dr 2 Dth)], Dr $ Dth, (4) where G is the Euler gamma function and the parameters c and d are given by the assumed power-law mass– where Dth is the threshold Dr at which breakup occurs. diameter (m–D) relationship of the hydrometeors for For the baseline model configuration, Dth 5 300 mm. each species, where m 5 cDd. Here, all particles are Sensitivity to drop breakup was tested using different assumed to be spheres for simplicity, with a bulk particle formulations described in the literature: Ziegler [1985, density for the various ice species following Reisner hereafter Z85, his Eq. (18)] and Seifert [2008, hereafter et al. (1998), except hail, for which the bulk density is S08, his Eq. (A13)]. Specific parameter settings in these equal to 900 kg m23 following Lin et al. (1983). Other formulations are fairly arbitrary, although S08 showed details of the parameterization, including formulations their scheme produced reasonable results (in conjunc- for the various microphysical process rates, are given by tion with parameterized rain evaporation and spectral Morrison et al. (2009) and references therein. For sim- shape parameter) in a one-dimensional rainshaft model plicity, here we have assumed a constant cloud droplet when compared to a detailed bin microphysics model. concentration of 250 cm23. A description of the calcu- Nonetheless, there is considerable uncertainty in these lation of radar reflectivity from simulated hydrometeor formulations and they produce large differences in Ec as fields is given by Morrison et al. (2009). a function of Dr (Fig. 3). A key difference between these The parameterization of raindrop breakup, which is formulations is that S08 and Z85 give a weaker re- the focus of this paper, follows from a modified version duction of Ec with increasing Dr compared to BASE; Ec of the Verlinde and Cotton (1993, hereafter VC93) pa- values are greater than zero for Z85 for all values of Dr rameterization in the baseline model configuration and hence Z85 has less efficient breakup overall. Addi- (BASE).3 As in most other drop breakup schemes, tional sensitivity tests were also performed using the VC93 represents collisional drop breakup by modifying modified VC93 scheme as in BASE, but with Dth varied between 105 and 510 mm (BREAK1, BREAK2, and the bulk collection efficiency for rain self-collection Ec. BREAK3). These tests allow us to isolate changes to Breakup leads to a decrease of Ec as a function of mean a single parameter in the breakup scheme and more drop size Dr (equal to 1/l for the assumed exponential systematically investigate sensitivity to the efficiency of DSD). Negative values of Ec can occur when Dr is large, implying a net source of drop number from the com- drop breakup. While values of Dth of a few hundred mm bined effects of drop breakup and self-collection. The are small compared to sizes of large drops (greater than ;0.8 mm) that were observed to undergo breakup after formulation for Ec in the baseline scheme is given by colliding with smaller drops (Barros et al. 2008), it

should be kept in mind that Dth represents a number- weighted mean drop size; the DSDs extend to drop sizes 3 Drop breakup using the modiﬁed VC93 formulation is included in the Morrison scheme in WRFV3.2 and subsequent versions. larger than Dth. As shown in Fig. 3, BREAK1 gives Breakup in previous versions was treated implicitly by limiting rain more efﬁcient breakup (lower Ec) relative to BASE, l to a minimum value of 20 cm21. S08, or Z85. BREAK2 and BREAK3 produce less 2442 MONTHLY WEATHER REVIEW VOLUME 140

TABLE 1. List of the main simulations described in the text (shear indicates the speciﬁed 0–2.5-km environmental vertical wind shear).

Name Description Shear (s21)

BASE Baseline model conﬁguration (modiﬁed VC93 breakup parameterization, Dth 5 300 mm) 0.048 S08 Breakup parameterization of S08 0.048 Z85 Breakup parameterization of Z85 0.048

BREAK1 Modified VC93 breakup parameterization, Dth 5 105 mm 0.048 BREAK2 Modified VC93 breakup parameterization, Dth 5 405 mm 0.048 BREAK3 Modified VC93 breakup parameterization, Dth 5 510 mm 0.048 BASEF As in BASE, but for Vm and VN independent of mean drop size 0.048 BREAK1F As in BREAK1, but for Vm and VN independent of mean drop size 0.048 BREAK2F As in BREAK2, but for Vm and VN independent of mean drop size 0.048 BREAK3F As in BREAK3, but for Vm and VN independent of mean drop size 0.048 BASEH As in BASE, but for higher shear 0.064 BREAK1H As in BREAK1, but for higher shear 0.064 BREAK2H As in BREAK2, but for higher shear 0.064 BREAK3H As in BREAK3, but for higher shear 0.064

efficient breakup (greater Ec) than S08 or Z85 at rela- pool perturbation potential temperature u9 linearly de- tively small Dr, but more efficient breakup for Dr . 0.6– creases with height, from 25 K at 0 km to 0 K at 4.5 km, 0.8 mm. To separate the impact of drop breakup on rain and is inserted at 0 # x # 300 km (where x is the dis- sedimentation from that on other processes, additional tance along the x direction between 0 and 612 km). The simulations were performed with the rain mass- and initial cold pool extends across the domain in the y di- number-weighted fall speeds independent of mean drop rection. The magnitude of the lowest-level initial u9 is size and hence breakup (see section 4c). A summary of similar to or somewhat smaller than that of the cold pool the main simulations described herein is given in Table 1. that subsequently develops with the squall line. Random u perturbations with maximum amplitude of 60.05 K are c. Experimental design applied between 275 , x , 300 km and within the lowest We use an idealized model setup similar to Bryan and 4.5 km to initiate motion in the y direction. Morrison (2012). Given the length of the observed The environmental sounding for all simulations is squall line (several hundred kilometers; see Fig. 1), only based on observations from Norman, Oklahoma, at a portion is simulated using periodic lateral boundaries 0000 UTC 20 June 2007 (Fig. 2), about 6 h prior to pas- in the along-line (y) direction. Open boundary condi- sage of the storm at this location. The initial u and water tions are used in the across-line (x) direction. Simula- vapor mixing ratio qy from the sounding are vertically tions are integrated for 8 h. The domain size is 612 km 3 smoothed using a 1.25-km running average (gray lines in 128 km in the horizontal with the model lid at 20 km. A Fig. 2). For simplicity, we idealize the vertical wind shear Rayleigh damper with damping coefficient of 0.003 s21 profile to give moderate unidirectional shear (in the x is used in the upper 5 km to damp waves in the strato- direction) of 0.0048 s21 between 0 and 2.5 km, corre- sphere. Horizontal and vertical grid spacings are 1 km sponding to a 12 m s21 difference in horizontal wind and approximately 250 m, respectively. Previous studies between these levels, with zero wind above. This is have documented sensitivity of squall-line simulations somewhat stronger than the observed low-level shear to grid spacing (Bryan et al. 2003; Bryan and Morrison from the 0000 UTC sounding, which is nearly unidirec- 2012). While Bryan and Morrison (2012) found some tional at low levels, but with a difference in wind speed differences in quantities like surface precipitation and of only about 6–8 m s21 between the near-surface and updraft mass fluxes as the horizontal grid spacing was 2.5 km (Fig. 2). Simulations with weaker low-level envi- decreased from 1 km to 250 m, these runs were qualita- ronmental shear closer to that observed by the sounding tively similar and microphysical sensitivities were rela- are unable to sustain a squall line (see section 4e). While tively unaffected by grid spacing. Thus, we acknowledge this is perhaps suggestive of the model’s inability to model resolution as a potential source of uncertainty, but simulate a squall line under realistic conditions, it is noted perform simulations at 1-km horizontal grid spacing, that the shear at the time of storm passage (;6hprior which allows us to perform many more experiments than to its passage) may have been stronger than observed at would be possible using higher resolution. 000 UTC. Wind speed of the environment in the y direc- Convection is initiated by inserting a cold pool in part tion is set to zero. Sensitivity to the low-level vertical shear of the domain at the start of the integrations, similar to is tested, given its uncertainty and importance in storm the approach of Weisman et al. (1997). The initial cold structure and evolution. All of the breakup tests described AUGUST 2012 M O R R I S O N E T A L . 2443

FIG. 4. Horizontal cross section of reflectivity from the BASE FIG. 5. Vertical cross section of line-averaged reflectivity from the simulation at simulation time (a) 4, (b) 6, and (c) 8 h. Values are BASE simulation at simulation time (a) 4, (b) 6, and (c) 8 h. interpolated to a height of 1.13 km for comparison with observed radar reflectivity in Fig. 6. sections of reflectivity averaged in the y direction along above were run with either low (0.0032 s21), baseline, or the leading edge of the storm (defined by the lowest high (0.0064 s21) vertical shear between 0 and 2.5 km (see level 21Ku9 isotherm) are shown in Fig. 5. Convection Table 1). These results are detailed in section 4e. is initiated along the initial cold pool edge within the first Given initiation of the storm using an idealized linear 20 min. A region of stratiform precipitation develops cold pool, we focus mostly on comparing the simulated after about 3–4 h, and the storm reaches a quasi-steady and observed storms several hours after their formation, mature state after roughly 6 h, although the region of when they have a similar width (perpendicular to the stratiform precipitation continues to widen over time. line) and exhibit clear convective, transition, and trailing The model reproduces the overall observed reflectivity stratiform regions. This allows for a more robust analysis structure (Fig. 6), with a well-defined convective line, that is less influenced by initial conditions. However, we transition region, and trailing stratiform region charac- note that comparison of the idealized modeled storm teristic of midlatitude squall lines (e.g., Biggerstaff and with specific times and locations of the observed storm is Houze 1991). The simulated line-averaged reflectivity inevitably somewhat subjective, and this should be kept vertical structure also has similar features as observed; in mind when interpreting results. however, the observed 35-dBZ contour of the convective line reached 8 km at the mature stage of the MCS, 4. Results compared to only 6 km in the model, and the convective line had reflectivity greater than 45 dBZ up to 6 km in a. Comparison of baseline simulation and the observed convective line, but only up to 4 km in the observations model. The observed bright band was not very well de- Evolution of the reflectivity structure is shown for the fined, and was centered at 3.5 km, while it has higher BASE at a height of 1.13 km (Fig. 4). Vertical cross reflectivity in the model and is centered around 4 km. 2444 MONTHLY WEATHER REVIEW VOLUME 140

FIG. 6. Observed (a),(c),(e) horizontal and (b),(d),(f) line-averaged vertical cross sections of gridded reﬂectivity from KOUN at (top to bottom) three different times. The dashed lines in (a),(c),(e) indicate the region over which line-average vertical cross sections were calculated. North is notated in the horizontal cross sections for reference since they are displayed using the rotated Cartesian grid domain.

These differences may be due in part to large uncer- (Fig. 7), despite the low bias in reflectivity. The model also tainty in the calculation of brightband reflectivity from produces a sharp decrease of D0 with height that is not model hydrometeor fields. The simulated reflectivity seen in the radar retrievals. This is consistent with exces- above (below) the bright band is also higher (lower) sive drop size sorting during sedimentation, which is a than observed in the stratiform region. The across-line known problem in two-moment schemes that assume extent of the squall line was observed to be about exponential DSDs (Wacker and Seifert 2001; Milbrandt 190 km at this stage in its evolution, which is similar to and McTaggart-Cowan 2010; Mansell 2010). This issue the modeled extent of 170 km for BASE at 8 h. is further explored with a sensitivity test in which the Comparison of BASE with radar-retrieved and number-weighted raindrop fall speed, which is applied to disdrometer-derived raindrop D0 indicates that the model the sedimentation of rain number mixing ratio, is set equal produces values that are consistently too large within the to the mass-weighted fall speed applied to sedimenta- stratiform region by about a factor of 2 near the surface tion of mass mixing ratio. This test prevents size sorting AUGUST 2012 M O R R I S O N E T A L . 2445

FIG. 7. Vertical cross section of line-averaged raindrop median volume diameter D0 from (a) the BASE simulation at 8 h and (b) radar retrieval at 0750 UTC. (c) Comparison of disdrometer- derived D0 and line-averaged D0 from various simulations at the lowest model level. OBS1 and OBS2 indicate D0 from disdrometer assuming exponential and gamma DSDs, respectively. from occurring altogether, and produces a nearly constant D0 with height in the stratiform region (not shown). These results therefore provide evidence that excessive size sorting may indeed be responsible for the unrealistic vertical profiles of D0, although without size sorting the model still produces values of D0 that are too large. We note that allowing m to vary from an exponential distribution (m 5 0) can improve the treatment of size sorting in two-moment schemes (Milbrandt FIG. 8. Comparison of (a) line-averaged and (b) probability density function (PDF) of modeled and radar-retrieved pre- and McTaggart-Cowan 2010). However, disdrometer cipitation rates. Modeled precipitation rates are between 7 and 8 h observations indicate that the DSDs did not deviate and interpolated to a height of 1.13 km, and radar values are from greatly from exponential in the stratiform region for 0750 UTC at the same height. this storm, with fitted values of m having considerable variability but generally ranging between 0 and 2 (with Modeled values of D0 that are too large imply that the a tendency for larger m with lighter precipitation in the low bias of stratiform reflectivity below the melting level transition region). That said, DSDs above the surface is primarily a result of too little rainwater as opposed to were not measured and may have deviated more sub- mean drop sizes that are too small. This is further sug- stantially from exponential. Further investigation of gested by large underprediction of modeled pre- this issue is beyond the scope of this paper and left for cipitation rates (at a height of 1.13 km) compared to future work. radar retrievals (Fig. 8a). BASE produces a peak 2446 MONTHLY WEATHER REVIEW VOLUME 140

FIG. 9. Scatterplot of N0 vs rainwater content (RWC) for simulations using various drop breakup schemes. Modeled values (height ;125 m, t 5 8 h) are shown by green 1’s (red diamonds) for rain rates , 10 mm h21,(.10 mm h21), overlaid with disdrometer values shown by blue triangles (squares) for rain rates , 10 mm h21 (.10 mm h21). Best-fit lines using the least squares method are shown for 20 Jun (solid) and modeled values (dotted). precipitation rate in the convective region about 40% as two regions of relatively higher frequency in the ob- large as that from radar, while precipitation rates in the served PDF correspond to the large region of stratiform stratiform region are 4–8 times smaller. A probability rain and sharply peaked region of convective rain with density function (PDF) of precipitation rate (Fig. 8b) high precipitation rates; these regions are less distinct in shows modeled values to be nearly exponential, while the simulations. radar rates show significant deviations from exponential, b. Sensitivity to parameterization of raindrop with relatively greater frequency of occurrence near 3–5 breakup and 40–80 mm h21 and lower frequency at moderate rates. Here, the PDF is normalized to the total number Additional simulations were performed to test sensi- of points with rain rates greater than 1 mm h21. These tivity of the squall line to parameterization of raindrop AUGUST 2012 M O R R I S O N E T A L . 2447 breakup, as described in section 3b and summarized in Table 1. First, we describe tests using the S08 and Z85 breakup parameterizations. S08 and Z85 also treat breakup by reducing rain self-collection efficiency Ec similar to the modified VC93 formulation in BASE ex- pressed by (4), but these schemes produce large differences in Ec (see Fig. 3). Different breakup formulations produce widely varying rain DSD parameters (Fig. 9), corresponding with large differences in their impact on

Ec. Of the three schemes that were tested (BASE, S08, and Z85), Z85 produces the least efficient drop breakup overall and therefore the smallest values of N0 for a given rainwater content RWC especially for RWC . 0.1 g m23. BASE and S08 produce similar mean relationships between N0 and RWC, although BASE produces a somewhat greater spread for a given RWC. Thus, overall breakup efficiency appears to be similar between BASE FIG. 10. Scatterplot of disdrometer N0 vs rainwater content and S08, with less efficient breakup (larger Ec)inBASE (RWC) for 15 convective systems during the 2007 season (red dots), compared to S08 at smaller Dr compensated by more ef- overlaid with values for 20 Jun shown by blue triangles (squares) for ficient breakup in BASE for Dr . 0.6 mm (see Fig. 3). rain rates , 10 mm h21 (.10 mm h21). Best-fit lines using the least Simulations using any of the three breakup formulations squares method are shown for the disdrometer (solid) and seasonal underpredict N0 by one to two orders of magnitude for values (dotted). a given RWC compared to disdrometer. Since D0 is pro- 21/4 portional to N0 ,thisbiasofN0 corresponds to values of D that are too large relative to disdrometer and radar u 2 u 0 B [ g 1 0:61(q 2 q ) 2 q . (6) retrievals. There is a close correspondence between the u y y h N0–RWC relationship for this case and the 2007 seasonal observations collected in deep convective systems (com- Here g is acceleration of gravity, qh is the hydrometeor prising 15 cases; Fig. 10). Thus, it appears that the 20 June mass mixing ratio, and overbars denote the model’s base case provides a representative sample of DSD charac- state. For our analysis, C is averaged over the region teristics, and the model biases cannot be explained by 30 km behind the surface gust front. anomalous characteristics for this particular case. Overall, the three breakup parameterizations produce Time series of various quantities are shown in Fig. 11 fairly similar results. Domain-mean surface precipita- for BASE, S08, and Z85. This analysis includes domain- tion during the mature phase of the storm (from 6 to 8 h) mean surface precipitation rate, total condensation rate, differs by about 10% among the simulations, although total evaporation rate, precipitation efficiency (defined earlier differences exceed 100% (between ;3 and 5 h). as total condensation rate divided by surface pre- These differences can be partially explained by precipi- cipitation rate), average lowest-level u9 within the cold tation efficiency, which is highest in Z85 owing to the pool, fraction of the domain at the lowest level with cold larger mean drop size and hence fall speed, and lowest pool, ratio of cold pool intensity (C) to the difference in BASE. There are no consistent differences in total in the 0 and 2.5 km horizontal wind (DU), and mean condensation, evaporation, cold pool area and strength, propagation speed of the surface gust. (Hereafter, ‘‘total’’ propagation speed, or updraft characteristics between refers to vertically integrated and domain-averaged the simulations. quantities.) Throughout this paper, the cold pool is de- These results broadly suggest limited sensitivity of the fined by the region with u9# 22K. storm to drop breakup for the three schemes that were Here, C is defined using (e.g., Weisman and Rotunno tested. However, there is much greater sensitivity using 2004; Bryan et al. 2006) the modified VC93 scheme as in BASE, but varying the ð size threshold for breakup Dth. Here, Dth is varied be- H tween 105 and 510 mm, compared to 300 mm for BASE C2 5 2 (2B) dz, (5) 0 (see Table 1). Setting Dth to 105 mm (BREAK1) produces values of N0 that are similar to observations for where H is the cold pool depth (defined as the height of RWC greater than about 0.1 g m23 (Fig. 9). BREAK1 the level of neutral buoyancy), and B is buoyancy: also gives more realistic values of D0 than BASE when 2448 MONTHLY WEATHER REVIEW VOLUME 140

FIG. 11. Time series of (a) domain-mean surface precipitation rate, (b) total condensation rate, (c) total evaporation rate, (d) domain-mean precipitation efﬁciency, (e) mean lowest-level u9 within the cold pool, (f) cold pool area, (g) ratio cold pool intensity and difference in 2.5- and 0-km wind C/DU, and (h) propagation speed for the BASE, S08, and Z85 simulations. compared to disdrometer, although values are still surface precipitation with more efﬁcient drop breakup somewhat too large in the trailing stratiform region (Fig. 12a; in contrast with peak surface precipitation rates

(Fig.7c).IncreasingDth to 405 mm (BREAK2) and as described below). This is unexpected, since more efﬁ- 510 mm (BREAK3) results in progressively smaller N0 cient breakup leads to higher evaporation rates and lower (larger D0) for a given RWC, and increases the bias of mass-weighted fall speeds for a given RWC. Overall, N0 (and D0) relative to observations (Figs. 7c and 9). there is a close correspondence between rain evapora- Time series of various quantities (as in Fig. 11) are tion and surface precipitation in these simulations (Figs. shown in Fig. 12 for BREAK1, BASE, BREAK2, and 12a,c), with larger domain-mean precipitation rates oc- BREAK3. These simulations have considerably more curring with larger total evaporation rates. For example, spread than BASE, S08, and Z85, especially before 7 h. BREAK1 has by far the largest domain-mean precipita- In general, there is a tendency for greater domain-mean tion rates (especially before 6 h), despite the fact that it AUGUST 2012 M O R R I S O N E T A L . 2449

FIG. 12. As in Fig. 11, but for the BREAK1, BASE, BREAK2, and BREAK3 simulations. produces relatively small drops and hence lower mass- positive feedback that can enhance the sensitivity of weighted fall speeds and higher evaporation for a given modeled convective storm features to microphysical RWC. We propose the following chain of interactions to processes. van Weverberg et al. (2012) also found in- explain this counterintuitive result. First, larger evapora- creases in total condensation (latent heating) with stronger tion rates lead to greater cold pool intensity (Figs. 12e–g) cold pools in two-dimensional squall-line simulations, and hence faster propagation of the surface gust front although they reported less sensitivity of surface pre- (Fig. 12h), yielding a wider storm over time. A larger cipitation because of compensating changes in precip- storm results in greater domain-mean updraft mass flux itation efficiency. and hence total condensation (Fig. 12b), which compen- Horizontal cross sections of reflectivity at 8 h and a sates for the higher evaporation rates and leads to the height of 1.13 km for BREAK1, BREAK2, and BREAK3 increased domain-mean surface precipitation. Further- (Fig. 13) reflect storm propagation that is about a factor of more, greater condensation implies more condensed wa- 2slowerinBREAK2thanBREAK1(Fig.12h),leadingto ter is available for evaporation, leading to even stronger a relatively narrow storm. At this time, the storm simulated cold pools, faster propagation, etc. This represents a in BREAK1 is approximately twice as wide as that in 2450 MONTHLY WEATHER REVIEW VOLUME 140

FIG. 13. Horizontal cross section of reﬂectivity from the (a) BREAK1, (b) BREAK2, and (c) BREAK3 simulations at 8 h and interpolated to a height of 1.13 km.

BREAK2. Between 5 and 7 h, the storm in BREAK2 BREAK1 and higher reflectivity in BREAK2 and loses its linear organization and becomes highly asym- BREAK3. While more efficient breakup in BREAK1 metric in the y direction, before reorganizing as a improves comparison of the DSD parameters (N0 and contiguous line after ;7 h. While width and organiza- D0) with disdrometer and radar compared to the other tion are the most apparent differences in terms of overall simulations, it leads to an even greater low bias of low- structure, other notable differences include relatively level reflectivity in the stratiform region compared to weak low-level reflectivity in the stratiform region in radar (cf. Figs. 6a,c,e and 13). AUGUST 2012 M O R R I S O N E T A L . 2451

21 FIG. 14. Vertical profiles of (a) domain-mean updraft mass flux (conditionally sampled for w . 0ms ), (b) mean convective updraft mass flux (conditionally sampled for w . 2ms21), and (c) fraction of the domain with convective updrafts, for the BREAK1, BASE, BREAK2, and BREAK3 simulations. Values are averaged between 7 and 8 h.

Plots of line-average precipitation at a height of over the domain (not shown). BREAK2 and BREAK3 1.13 km indicate sensitivity of peak precipitation rates to tend to produce the strongest peak updrafts, while drop breakup (Fig. 8a), consistent with van Weverberg BREAK1 tends to have the weakest, although there is et al. (2012). In contrast with domain-mean precipitation, considerable variability. PDFs of updraft velocity at a peak precipitation rates increase with a reduction in drop height of ;7.5 km (Fig. 15) also show that BREAK2 breakup efﬁciency as a result of the increase in mean drop tends to have relatively more strong updrafts (w . 10– size and hence mass-weighted fall speed. PDFs of pre- 15 m s21) and fewer weak updrafts (w , 5ms21), with cipitation rate show relatively more instances of low- the opposite for BREAK1. precipitation rates in BREAK1, but fewer at middle and Interestingly, the modeled storm exhibits a clear 21 high rates (greater than about 10 mm h ), especially nonmonotonic sensitivity to Dth. For BREAK1, BASE, compared to BREAK2 (Fig. 8b). and BREAK2, the increase in Dth generally results BREAK2 has a much smaller domain-mean updraft in less domain-mean surface precipitation, smaller and mass ﬂux than the other simulations (Fig. 14a), which is weaker cold pools, slower propagation, and narrower consistent with its relatively small storm area (Fig. 13). storms as described above. However, a further increase

However, it has stronger convective updrafts above in Dth from BREAK2 to BREAK3 has the opposite ;4.5 km (Fig. 14b). Here convective updrafts are de- effects; results from BREAK3 are remarkably similar to 21 ﬁned using a threshold vertical velocity w of 2 m s , BASE (as well as S08 and Z85). Increasing Dth beyond although overall results are not sensitive to this thresh- the value in BREAK3 produces relatively limited change old. The fraction of convective updrafts is also relatively in results compared to BREAK3 (not shown). Thus, small in BREAK2 below 8 km, but larger above this BREAK2 produces the lowest surface precipitation rate height (Fig. 14c), implying that updrafts tend to reach and weakest cold pool of any simulation, despite the fact higher levels in this simulation. This presents an overall that it lies in the middle range of breakup efﬁciencies picture of fewer and/or smaller but stronger and more that were tested. To explore robustness of this result, we upright updrafts in BREAK2 compared to the other runs. performed additional simulations with small changes to

Conversely, BREAK1 has the greatest domain-mean Dth in the vicinity of the value set for BREAK2. These updraft mass ﬂux below 5 km, but a relatively small frac- simulations, with Dth set to either 380 or 430 mm, are tion of convective updrafts above 8 km. These differences similar to BREAK2 (not shown). Thus, the nonmonotonic are generally consistent with peak vertical velocities response appears to be robust. 2452 MONTHLY WEATHER REVIEW VOLUME 140

Hence, a key question is what explains the nonmonotonic response of the modeled storm to parameterization of drop breakup? Additional sensitivity tests with modiﬁcations to the rain fall speed help to address this question. In the model, the mass- and number-weighted fall speeds are given by

aG(b 1 4) V 5 , (7) m 6lb aG(b 1 1) V 5 , (8) N lb where a and b are parameters in the power-law fall speed–size relation (see Morrison 2012). In these tests, l is formulated to be independent of the pre-

dicted mean drop size for calculation of Vm and VN, and therefore is not impacted directly by drop breakup (for all other processes, the model-predicted values of l are used). Thus, instead of using (2) to calculate l FIG. 15. Probability density functions of updraft vertical velocity for (7) and (8), it is diagnosed as a function of RWC for the BREAK1, BASE, BREAK2, and BREAK3 simulations following: from 7 to 8 h and a height ;7.5 km. l 5 2:6 3 103RWC20:015, (9) This nonmonotonic response of the storm to drop breakup also likely explains greater sensitivity to vary- where l and RWC have units of m21 and g m23,respec- ing Dth than using the different breakup formulations tively. The l–RWC relationship in (9) produces values of (BASE, S08, and Z85). In terms of overall drop breakup l between BREAK1 and the disdrometer observations efficiency, BREAK2 lies between BASE, S08, and Z85, for a given RWC; however, the specific formulation of l as indicated by the N0–RWC relationships in Fig. 9, yet it from (9) is less important than the fact that the same produces a much lower domain-mean surface precipita- l–RWC relationship is used in all of these sensitivity tests tion rate, weaker cold pool, and slower propagation than for calculating Vm and VN. As in section 4b, these simula- any of these simulations. On the other hand, BREAK3 tions are performed with Dth 5 105, 300, 405, and 510 mm and Z85 have similarly inefficient drop breakup overall (BREAK1F, BASEF, BREAK2F, and BREAK3F, re-

(as again suggested by the N0–RWC relationships), yet spectively; see Table 1), along with baseline (moderate) both simulations produce similar storm characteristics low-level environmental wind shear. compared to BASE and S08. Thus, BREAK2 happens to With Vm and VN independent of the predicted mean lie in a region of parameter space that produces distinctly drop size and hence breakup, quantities such as surface different storm characteristics from BASE, S08, Z85, and precipitation rate, total evaporation and condensation, BREAK3. Additional sensitivity tests are described in cold pool intensity, propagation speed (Fig. 16), and section 4c that show this nonmonotonic behavior is related storm width and structure (not shown) exhibit a gener- to the impact of drop breakup on mean rain fall speed. ally monotonic response to Dth, especially before 6 h, in contrast with results described in section 4b. In these c. Impact of changes in raindrop fall speed runs, progressively less efficient drop breakup generally While the results in section 4b suggest that differences leads to reduced evaporation, weaker cold pools, slower in evaporation and hence cold pool evolution and storm propagation, narrower storms, reduced condensation, dynamics are critical in explaining sensitivity of the and reduced surface precipitation, with no evidence for simulated storm to drop breakup, the nonmonotonic a strongly nonmonotonic response, although BASEF response to drop breakup suggests that additional fac- and BREAK2F are similar. Additional simulations with tors are also important. In other words, if evaporation Dth . 510 mm give results similar to BREAK3F. Thus, was the only controlling process, progressively more we conclude that changes in rain fall speed play a critical efficient drop breakup and hence smaller mean drop role in the nonmonotonic response when fall speed size and greater evaporation (for a given RWC) would is fully coupled to drop size and hence breakup. Spe- lead one to expect a monotonic sensitivity to breakup. cific mechanisms explaining the impact of changes in fall AUGUST 2012 M O R R I S O N E T A L . 2453

FIG. 16. As in Fig. 11, but for the BREAK1F, BASEF, BREAK2F, and BREAK3F simulations with raindrop mass- and number-weighted fall speeds independent of mean drop size. speed on the response to breakup are unclear but appear support ‘‘RKW theory’’ (Rotunno et al. 1988; Weisman to be related to complex interactions between sedi- and Rotunno 2004). According to this theory, an optimal mentation and loading of rainwater, evaporation, cold state for system intensity occurs when the vorticity as- pool dynamics, and environmental wind shear. The im- sociated with low-level environmental shear is approx- portance of environmental wind shear is further sup- imately balanced by the cold pool’s circulation (i.e., ported by tests described in section 4c; simulations with when C/DU ; 1), leading to the deepest lifting of envi- increased low-level shear also produce a monotonic ronmental air (all else being equal) and upright con- sensitivity to breakup. Further work is needed to inves- vective cells. All simulations here give C/DU . 1 (Fig. tigate these interactions systematically. 12g), leading to an upshear-tilted convective structure. However, BREAK1, with the highest evaporation rates, d. Implications for RKW theory produces the strongest cold pool and hence largest C/ Close correspondence between the convective strength DU, especially before 6 h. Consistent with RKW theory, and cold pool intensity in these simulations broadly there are fewer strong updrafts (w . 10–15 m s21), 2454 MONTHLY WEATHER REVIEW VOLUME 140 weaker convective mass flux above ;5 km, and shal- drop breakup for the parameter range tested here. Large lower, more tilted convective updrafts (i.e., relatively sensitivity of the organization and structure of squall low convective updraft fraction above 8 km) in this sim- lines to shear is expected and has been well documented ulation. The opposite occurs in simulations with less in previous modeling studies (e.g., Thorpe et al. 1982; evaporation and relatively smaller C/DU (closer to unity), Nicholls et al. 1988; Weisman et al. 1988; Fovell and in particular BREAK2. Ogura 1989; Szeto and Cho 1994; Robe and Emanuel While the simulations in a less optimal state (i.e., C/DU 2001; Weisman and Rotunno 2004; James et al. 2005; farther from unity) with high evaporation rates produce Bryan et al. 2006; Takemi 2007). Despite large sensi- relatively weaker convective updrafts, other measures tivity of storm structure, there is limited impact of shear show an increase in storm intensity. In particular, storm on the rain DSD characteristics, such as the N0–RWC size, domain-mean updraft mass flux, total condensation relationship (not shown). rate, and mean surface precipitation are all greater in the Higher shear simulations exhibit similar relationships simulations with higher evaporation and larger C/DU, between total evaporation, cold pool intensity, propa- because of the interactions between microphysics, cold gation speed, total condensation, and domain-mean pool evolution, storm size, and total condensation dis- surface precipitation as in the baseline shear simula- cussed in section 4b. In a multimodel assessment of RKW tions, although overall sensitivity to breakup is smaller. theory applied to squall lines, Bryan et al. (2006) also These results again highlight the dominant control of reported greater total condensation in simulations with interactions between microphysics, cold pool evolution, relatively less optimal conditions. However, in contrast and dynamics on the response of domain-mean surface to our results, they found that total surface precipitation precipitation to drop breakup, rather than the direct was lower in these simulations. impact of raindrop size on precipitation. Thus, despite its tendency to produce the smallest mean drop size, and e. Sensitivity to vertical wind shear hence lowest fall speed and highest evaporation rate Given the importance of interactions between micro- for a given RWC, BREAK1H produces the highest physics, cold pool evolution, propagation speed, and domain-mean precipitation rate for the high shear runs storm dynamics, low-level vertical wind shear is expected (Fig. 17a). This is consistent with the interactions between to play an important role in the response of the storm to microphysics, cold pool evolution, and storm dynamics drop breakup. This idea is broadly consistent with the described in section 4b. importance of shear on squall-line intensity and structure An important difference from the baseline shear sim- in previous squall-line simulations (e.g., Weisman and ulations is that the response to drop breakup under higher Rotunno 2004) and encapsulated by RKW theory. To shear is monotonic; that is, various storm characteristics explore this issue, simulations with varying Dth,asde- tend to have a monotonic change as Dth is increased (Fig. scribed in previous subsections for baseline (moderate) 17). This qualitative difference in the response, depend- shear, were performed with the 0–2.5-km shear either de- ing on shear, further supports our suggestion that the creased from 0.048 (DU 5 12 m s21) to 0.0032 s21 (DU 5 nonmonotonic response under baseline shear depends on 8ms21) or increased to 0.0064 s21 (DU 5 16 m s21). interactions between drop sedimentation, evaporation, Regardless of the breakup parameterization, all simula- cold pool dynamics, and environmental shear. tions with the weaker shear failed to produce a long-lived squall line, with initial convection dissipating within the 5. Summary and conclusions first few hours and only weak, isolated convective cells remaining. This paper describes a series of idealized 3D simula- Simulations with higher shear (BREAK1H, BASEH, tions of a squall line observed on 20 June 2007 over BREAK2H, and BREAK3H; see Table 1) produce central Oklahoma. The baseline model configuration long-lived squall lines (Fig. 17), but give results that are reproduced key qualitative storm features, including a substantially different than with baseline shear (cf. Figs. leading edge of high reflectivity, a wide region of trailing 17 and 12). In particular, the higher shear simulations stratiform precipitation, and a transition region of low produce more precipitation, especially before 6 h, and reflectivity between the stratiform and convective regions. stronger cold pools than those with baseline shear. De- However, quantitatively the model exhibited a low bias of spite the stronger cold pools, the increase in cold pool reflectivity in the stratiform region even though raindrop intensity C is not enough to compensate for the larger median volume diameter was too large compared to radar DU, and hence C/DU is smaller (i.e., closer to unity) at retrievals and disdrometer measurements, indicating too high shear compared to baseline shear, mainly after 4– little rainwater. It also underpredicted precipitation rates 5 h. Overall, there is greater sensitivity to shear than in the convective region by a factor of roughly 2.5, and AUGUST 2012 M O R R I S O N E T A L . 2455

FIG. 17. As in Fig. 11, but for the BREAK1H, BASEH, BREAK2H, and BREAK3H simulations with higher vertical wind shear.

in the stratiform region by a factor of 4–8. Reasons for such as the N0–RWC relationship, were insensitive to en- the large underprediction of precipitation are unclear, vironmental shear. Simulations with BASE, S08, and Z85 but could be due to uncertainties in the environmental produced values of rain N0 that were too small by one–two conditions (e.g., sounding) or model configuration (mi- orders of magnitude for a given RWC, with a correspond- crophysics or other aspects). Further work based on ing large bias in mean drop size. Thus, these formula- longer-term statistical comparisons with observations is tions appear to produce breakup efficiencies that are too needed to determine if this bias is a consistent feature of weak, although we cannot rule out DSD biases resulting the microphysics scheme. from other processes such as excessive size sorting, which Different formulations for drop breakup from the is a known problem in two-moment schemes with expo- literature (BASE, S08, and Z85), as well as varying nential DSDs (Wacker and Seifert 2001; Milbrandt and threshold mean drop size Dth for breakup using the McTaggart-Cowan 2010; Mansell 2010). A sensitivity test modified VC93 formulation, were tested under different with mass-weighted raindrop fall speed applied to sedi- 0–2.5 km vertical wind shears. Rain DSD characteristics, mentation of both the rain number and mass mixing 2456 MONTHLY WEATHER REVIEW VOLUME 140 ratios, thereby preventing size sorting from occurring on mass- and number-weighted fall speeds, which was altogether, suggested that excessive size sorting may have found to be critical in explaining the nonmonotonic re- indeed been responsible for an unrealistic decrease of D0 sponse of storm characteristics to drop breakup under with height in the stratiform region in the baseline sim- baseline wind shear. For higher wind shear, the response ulation. However, without size sorting the model still was monotonic; more efficient breakup generally led to produced mean drop sizes that were too large compared progressively greater evaporation, stronger cold pools, to radar retrievals. Decreasing Dth from 300 mminBASE faster propagation, and more surface precipitation. Under to 105 mm in BREAK1 improved comparison of the weaker shear (0.0032 s21), a squall line could not be DSD parameters with observations. Gao et al. (2011) maintained using any of the breakup schemes. Our sim- also found an overprediction of mean drop size (ZDR) ulations used only a single thermodynamic profile from using their two-moment scheme, and improvement of a midlatitude, continental environment. Future work DSD characteristics by increasing the breakup efficiency. should evaluate the generality of these findings for However, more efficient breakup in BREAK1 tended to other conditions, such as tropical maritime environ- degrade other aspects such as maximum (line averaged) ments with lower CAPE and significantly higher low- surface precipitation and reflectivity structure. These re- level relative humidities. sults suggest that the primary model biases of low surface Overall, interactions between microphysics (evapo- precipitation and low-level reflectivity within the strati- ration in particular), cold pool intensity, and low-level form region were not a result of misrepresentation of the environmental wind shear in the simulations broadly rain DSDs and hence breakup. support RKW theory (Rotunno et al. 1988; Weisman We note that other aspects of the treatment of rain et al. 1988). Simulations with relatively strong cold pools DSDs may also be important. For example, the param- and C/DU farthest from unity (and hence farthest from eterization of DSD shape or width (i.e., m for the gamma ‘‘optimal’’ vorticity balance, which occurs when C/DU ; DSD) impacts processes such as rain evaporation and 1) had weaker, more tilted convective updrafts at mid sedimentation, and size sorting in particular (Milbrandt and upper-levels that tended not to penetrate as high and McTaggart-Cowan 2010), but we leave this as a as the more intense, upright updrafts in simulations subject for future work. Disdrometer observations can with weaker cold pools, consistent with RKW theory. also provide useful constraints on the parameterization However, other measures of storm strength, including of m (e.g., Cao et al. 2008), and we plan to pursue such domain-mean surface precipitation, overall storm size efforts in a follow-up study. We note, however, that and hence mean updraft mass flux, and total conden- existing observationally based parameterizations of m sation, were significantly greater in the simulations have relied upon surface disdrometer measurements; with stronger cold pools and larger C/DU,especially observational characterization of rain DSDs above the earlier in the simulations. Bryan et al. (2006) also found surface are needed to test the generality of these pa- greater total condensation in less optimal conditions rameterizations. in their multimodel study, but surface precipitation A key finding of this study is that the response of was larger in simulations with a more optimal balance. domain-mean surface precipitation to drop breakup by A possible explanation for the contrasting results is our varying Dth was mostly controlled by interactions be- use of a relatively sophisticated microphysics scheme tween the microphysics, cold pool characteristics, and that includes both liquid and ice hydrometeors; most dynamics, rather than direct impacts of breakup on drop previous numerical evaluations of RKW theory (e.g., size and precipitation as one might have expected. Thus, Weisman et al. 1988; Weisman and Rotunno 2004; simulations with more efficient breakup tended to have Bryan et al. 2006) used liquid-only schemes (e.g., Kessler higher domain-mean precipitation rates (but lower peak 1969), which are known to have difficulty simulating precipitation rates), despite the smaller mean drop realistic stratiform precipitation (e.g., Fovell and Ogura size and hence lower fall speed and higher evaporation 1988). Our simulations produced large stratiform re- rate for a given RWC, under both baseline moderate gions that contributed significantly to the total con- (0.0048 s21) and high (0.0064 s21) low-level environ- densation, evaporation, and cold pool evolution, and mental wind shears. We propose that this counterintui- appeared to be critical in driving the aforementioned tive result occurred because higher evaporation led to interactions between microphysics, cold pool evolu- stronger cold pools, faster propagation, larger storm tion, and dynamics that largely control the response of area, greater domain-mean updraft mass flux, and the domain-mean surface precipitation rate to changes greater total condensation that compensated for higher in microphysics. We also note that Bryan et al. (2006) evaporation to give more, not less, precipitation. This assessed RKW theory by modifying low-level envi- picture is complicated by the impact of drop breakup ronmental shear but not cold pool intensity, while we AUGUST 2012 M O R R I S O N E T A L . 2457 performed tests with changes to drop breakup that b. Radar analysis procedures impacted cold pool intensity. Further work is needed The KOUN radar data were cleaned up and gridded to investigate more systematically the microphysical prior to the analysis. Ground clutter and nonmeteorological context of RKW theory in squall lines across a greater data were omitted by removing data that had a correlation range of shears. coefficient (rhv) less than 0.85. The correlation coefficient is a polarimetric radar variable that indicates the level of Acknowledgments. This work was supported by the correlation between the horizontal and vertical polar- USWRP Short-Term Explicit Prediction (STEP) pro- ized backscattered power in a sample volume, and can gram at NCAR. HM was partially supported by the be a good indicator of nonmeteorological targets when NOAA Grant NA08OAR4310543, U.S. DOE ARM there is low correlation in the sample volume (i.e., hy- DE-FG02-08ER64574, and the NSF Science and Tech- drometeor classification categories are typically associ- nology Center for Multiscale Modeling of Atmospheric ated with r . 0.85; Straka et al. 2000; Schuur et al. Processes (CMMAP), managed by Colorado State Uni- hv 2003; Liu and Chandrasekar 2000; Park et al. 2009). This versity under Cooperative Agreement ATM-0425247. procedure also removed spurious data due to second trip We thank E. Brandes for discussion and guidance in echo contamination. Second trip echoes (radar echoes processing the disdrometer measurements, as well as received from a previous pulse volume after the next M. Weisman for comments on the manuscript. KOUN pulse has been transmitted) were triggered by the ex- radar is operated by NSSL and data was provided by Terry tensive and intense squall line that extended to the Schuur (CIMMS). Mike Dixon (NCAR) provided guid- southwest (and outside) of the KOUN radar domain. ance on the radar and mesonet data processing. Oklahoma Radar-derived variables (rain rate and D , see discus- Mesonet data are a cooperative venture between Okla- 0 sion below) were calculated from the radar data in polar homa State University and The University of Oklahoma coordinates after the data were cleaned up. Finally, the and supported by the taxpayers of Oklahoma. equivalent radar reflectivity (ZH), retrieved rain rate, and D0 were gridded to a Cartesian coordinate system APPENDIX with 0.5-km spacing using linear interpolation. To compare with the model simulation results, the gridded data were rotated by 558 to place the majority of Description of the Observations the convective line perpendicular to the x axis. Line- a. Disdrometer observations averaged calculations of ZH, D0, and retrieved rain rate (taken at 1.13 km AGL) were then performed to rep- Detailed descriptions of the two-dimensional video resent an average cross section of the squall line. This disdrometer (2DVD) and processing techniques can be was done using a 50-km-wide slab of data 25–75 km east found in Kruger and Krajewski (2002), Brandes et al. of the radar (on the rotated grid) to avoid influence of (2007), and Cao et al. (2008). The 2DVD has two high- the cone of silence. Choosing other locations to define resolution cameras orthogonal to one another and re- the slab for cross-section averaging (e.g., west of the cords silhouette images of raindrops falling through a radar) was tested and did not impact overall results or 10 cm 3 10 cm measurement area from which equiva- conclusions. lent volume diameter, oblateness, and terminal velocity of each raindrop are derived. In this study, the dis- c. Methodology for radar rain rate and D retrievals drometer data were quality controlled by ignoring any 0 particles whose measured terminal velocity significantly Numerous studies have shown that dual-polarization deviated from the wind tunnel raindrop terminal veloc- radar methods to compute rain rates perform better ity.Thedatawerethensortedinto41sizebinsof0.2-mm compared to calculating rain rates from ZH alone, be- width and having central diameters of 0.1–8.1 mm to de- cause dual-polarization radar measurements are sensi- termine 1-min DSDs. The parameters of the gamma dis- tive to particle size, shape, orientation, phase, and bulk tribution were computed from the second, fourth, and density (e.g., Goddard and Cherry 1984; Ryzhkov and sixth moments of the drop distributions following the Zrnic´ 1995; Brandes et al. 2002; Brandes et al. 2003). In moment-fitting approach of Ulbrich and Atlas (1998). For this study, following the technique of Brandes et al. (2002) the exponential distribution, the DSD parameters (such as and Brandes et al. (2003), radar-based rain rates were

N0 in Figs. 9 and 10) were calculated from the third and computed from three combinations of dual-polarization sixth moments. The disdrometer-derived raindrop median radar variables: 1) ZH and differential reflectivity (ZDR), volume diameter D0 (Fig. 7c) was calculated directly from 2) specific differential phase (KDP) and ZDR, and 3) KDP either the fitted gamma or exponential DSDs. alone. This technique starts by utilizing rain DSDs from 2458 MONTHLY WEATHER REVIEW VOLUME 140 disdrometer observations to compute ZH,ZDR, and KDP 2010) have documented that a potential bias in ZDR in as described by Zhang et al. (2001). Power-law rain- rain may exist even below the melting level from cross fall estimators (one for each of the combinations of coupling in SHV measurements compared to alternating dual-polarization radar variables listed above) are then transmit systems, which may affect polarimetric-derived determined by the least squares method with the dis- rainfall rates and D0. However, given the good agree- drometer measurements of rain rate as the dependent ment between the hybrid radar and mesonet rain rates variable. The three power-law rainfall estimators used in and between the radar-derived and disdrometer D0,it this study come from more than 4300 one-minute DSDs does not appear that a ZDR bias negatively affected re- collected by the 2DVDs in Oklahoma during stratiform trievals of these quantities in this study. and convective rain events during the summer seasons of 2005–07. REFERENCES To generate a single rain-rate field for each radar scan Barros, A. P., O. P. Prat, and P. Shrestha, 2008: Revisiting Low and based on the three rain-rate estimators, a decision-making List (1982): Evaluation of raindrop collision parameteriza- algorithm (referred to as ‘‘hybrid’’ rain-rate algorithm tions using laboratory observations and modeling. J. Atmos. hereafter) was used on a gate-by-gate basis. The hybrid Sci., 65, 2983–2993. Biggerstaff, M. I., and R. A. 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