5.2 QUANTITATIVE PRECIPITATION IN SIMULATED DEEP CONVECTION: SENSITIVITY TO THE HAIL/GRAUPEL CATEGORY

Matthew S. Gilmore*1,3, Jerry M. Straka2, and Erik N. Rasmussen1,3 1 Cooperative Institute for Mesoscale Meteorological Studies, Univ. of Oklahoma, Norman, OK 2 School of Meteorology, Univ. of Oklahoma, Norman, OK 3NOAA/National Severe Storms Laboratory (NSSL), Boulder, CO

* 1. INTRODUCTION at an instant in time can be found using, nnxoxx= l , —3 m .) Thus, each distribution is a function of rx and nox. In order to improve warm season flood forecasting, Notice that within LFO-3, both hail and graupel are efforts are underway to couple rainfall output from represented by a single category called “hail/graupel”. cloud-scale atmospheric models to hydrological models. This means that one must artificially choose a constant However, before such efforts can bear fruit, the variation r and n a priori to represent both types of particles. in rainfall due to the uncertainties inherent in h oh microphysical parameterizations must be assessed. Herein, hail and graupel are individually defined as Understanding these microphysical sensitivities is a those particles in the hail/graupel distribution that are major focus of the U.S. Weather Research Program greater than or less than 5 mm, respectively. (Droegemeier et al. 2000). Here, we will demonstrate large model sensitivity in 3. EXPERIMENTAL DESIGN rainfall and hailfall due to variations in microphysical input specifications that describe the hail/graupel The Straka Atmospheric Model (Johnson et al. distribution. The 3-class ice microphysical package 1993; Straka and Anderson 1993; Carpenter et al. 1998) used in our study (hereafter, LFO-3) is very similar to is the three-dimensional, non-hydrostatic cloud model that presented by Lin et al. (1983). LFO-3 is a prime used for the simulations. Grid spacing of Dz = 500 and candidate for study since Lin et al (1983) schemes are Dx = Dy = 1000 m are used in a 90 x 90 x 22 km3 routinely used in forecast models such as the Advanced domain. Regional Prediction Model (Xue et al. 2001) and the Weather Research and Forecasting Model (Michalakes 3.1. Initial Conditions et al. 2000). We hope that our investigation will motivate an exploration of how such uncertainties The model is initialized with the idealized should be treated in cloud scale and hydrological temperature and moisture profile described in Weisman forecast models. and Klemp (1984; hereafter WK84). Environmental CAPE is 2200 J kg-1. The vertical wind shear profile is 2. REVIEW OF THE ICE MICROPHYSICS SCHEME represented by a half-circle hodograph that traces an arc length of 50 m s-1 over the lowest 5 km AGL. LFO-3 predicts a single moment, bulk mixing ratio, (Results using a 30 m s-1 arc length hodograph are for each precipitating class. The negligibly precipitating omitted here for the sake of brevity.) Above z = 5 km particles (cloud ice and cloud water) are mono- AGL, the wind speed is held constant at the z = 5 km dispersed. The faster precipitating particles (rain, snow, value. An axially symmetric thermal bubble with and hail/graupel) are defined by inverse-exponential maximum temperature excess of +1°C is used to initiate size distributions wherein the most numerous particles convection (e.g., Klemp and Wilhelmson 1978). (n) are found at the smallest diameter sizes (D). -1 —4 nDxoxxx()=- nexp( Dl ) (m ), (1) 3.2. Microphysics treatments wherein x is r (rain), s (snow), or h (hail). The mean size of each distribution is equal to the slope parameter, The sensitivity experiments were designed by 14/ varying the bulk particle density and intercept parameter lrxxxox= qn/ ( pr) (m), (2) [] constants for the hail/graupel category. There are wherein rx is the species particle density, nox is the numerous in situ observations motivating these —3 intercept parameter, r is the local air density, and qx is experiments. Graupel density varies from 50 to 890 kg m —3 the species mixing ratio. (The total number of particles and hail density varies from 700 to 900 kg m in observed storms (Pruppacher and Klett 1978). Also, noh varies from 103 to 105 for hail and is as high as 1010 for graupel (Dennis et al. 1971; Federer and Waldvogel * Corresponding author address: Matthew S. Gilmore, 1975; Spahn 1976; Knight et al. 1982). Combinations NOAA/NSSL, 325 Broadway N/C/MRD, Boulder, CO over a range of the observed values were chosen and 80305-3328; e-mail: [email protected] are shown in Table 1. In addition, a warm-rain simulation (ice processes turned off; hereafter referred Graupel Hail 8 to as WR) was performed for reference. 10 a) b) 25 The N3r9 and N8r4 cases allow the greatest 20 r9 number of hail and graupel particles, respectively, with N3 other cases having intermediate amounts (Fig. 1a). )

) 9 Mass is distributed over a smaller range and is weighted 6 15 r

-1 N4 -1 10 toward the smallest-sized particles for the N8r4 case r9 Rain 10 N5 (m s r4 t (not shown). Both a smaller particle density and a mm N4 V larger intercept parameter conspire to give a smaller -3 5 N6r4 mass-weighted mean terminal fall velocity (V ) over all t 4 N8r4 ranges of water content (Fig. 1b). 10 Snow 0 5 10 15 Water Content (g m-3) Table 1. Parameters used to define the inverse-exponential distributions for the hail/graupel category. The rain and snow (Number dm 2 parameters are held constant. Rain and snow have particle 10 densities of 100 and 1000 kg m—3 and intercepts of 8x106 and 3x106 —4 m , respectively. The treatments are labeled as Narb wherein a is N8 Rain N6 N5 Snow a —4 N4 N4 N3 the exponent in the slope intercept parameter, 4x10 m , and b is r r r r r r 4 4 9 4 9 the first digit in particle density, b00 kg m—3. N5r4 and N7r4 cases 9 were also performed but are omitted here due to redundancy. 010203040

Simulation noh Bulk Particle Diameter (mm) (m—4) Particle Fig. 1. a) Size distribution for water content 10 g m—3 and b) Mass-

Density weighted mean terminal fall velocity (Vt) as a function of water (kg m—3) content for each species (z=4.5 km AGL).

N3r9 4x103 900 4 a) N3r9 N4r9 4x10 900 38 5 N5r9 4x10 900 24 N4r4 4x104 400 20 14 24 32 N6r4 4x106 400 38 8 8 14 8 N8r4 4x10 400 31 30 30 40 20 12 24 16 32 42 44 4. RESULTS AND DISCUSSION 8 8 54 49 47 Compared to the N3r9 storms, the N8r4 storms 29 q'min=0.00 -4.47 -4.83 -4.88 have stronger and wider updrafts, warmer minimum 10 km temperatures in the low-level outflow, smaller gradients in precipitation, and more precipitation spreading farther b) N8r4 downstream (Fig. 2). The N8r4 right-moving supercell 25 also experiences less southward movement by 56 27 approximately 15 km (Fig. 2b); apparently due to a 39 52 weaker cold pool. Evolutions for other cases fall 55 34 27 between these two. 42 36 21 36 The maximum updraft speed increases gradually 25 39 from a hail-weighted distribution to a graupel-weighted 45 58 61 distribution (Fig 3). This is due to increasing latent heat 62 release and a warmer updraft above z = 4 km AGL (Fig. 30 4a). As one marches from N3r9 to N8r4, low-level q'min=0.00 -2.18 -2.93 -3.52 downdrafts weaken (not shown), the minimum 10 km Fig. 2. Evolution in midlevel storm structure depicted at 30, 60, 90, temperature within the cold pool warms (z £ 1 km AGL and 120 min for cases a) N3r9 and b) N8r4. Total precipitation in Fig. 4b), and the minimum temperature decreases mixing ratio at z=4.75 km AGL is contoured at 2 g kg—1 intervals near the melting level and rises in altitude (2 £ z £ 4 km beginning at 0.1 g kg—1. Regions of updraft > 5 m s—1 at z = 4.75 AGL in Fig. 4b). In addition, the amount of time-average km AGL are shaded with the updraft maxima located by dots and rain decreases at low levels while the amount of labeled in m s—1. The surface gust front (—0.5°C perturbation graupel/hail at upper levels (and its prevalent altitude) potential temperature, q’) is denoted by a thick barbed line. The increases (Fig. 5a). The average amounts of snow, surface q’ (°C) minimum is also shown. 9 a) Max q' r r9 65 N3 4 N4 r 4 4 r r N8r4 N4 60 N6r4 N6 N8 N4r4 N5 55 N5r9 Warm r N4r9 Rain 9 ) 10

-1 50 N3r9 45 WR w (m s 40 8 35 30 01530456075 90 105 120 Time (min) Fig. 3. Time series of maximum updraft in the domain. 6 cloud ice, cloud water, and rain (z > 5 km) also decrease as one marches from N3r9 to N8r4 (Fig. 5). These kinematical and microphysical changes 4 occur due to changes in the hail/graupel Vt and those 246 810 growth rate equations that are a function of hail/graupel z (km) r h and noh. The deposition rate of hail/graupel and all b) Min q' accretion rates by hail/graupel are larger in N8r4 versus 4 4 N3r9 (Fig. 6). This helps explain the warmer and faster r 4 N8 r updrafts in the graupel-weighted cases. The increased N6 r4 rate by which hail/graupel accretes snow, cloud ice, N4 cloud water, and rain also explains their reduced amounts in the graupel-weighted cases (Fig. 5). 2 However, the increased sublimation and melting rates outside the updraft, along with much slower Vt, results in much less precipitation reaching ground in 9 4 N3r r N8r4 compared to N3r9 (27 Tg versus 78 Tg; Table 2). 9 0 N4r r4 N8 N6 Also, the maximum precipitation depth accumulation in -3 -2 -1 0 N8r4 is about three times less than N3r9 (21 versus 57 q' ( K) mm; not shown). Fig. Additional experiments (not shown here) 4. Time-averaged altitude profiles of a) maximum domain q' and b) demonstrate that the model's accumulated precipitation minimum domain q' for the 6 ice-microphysical parameterizations is less sensitive to, but in the same direction as, and the warm rain parameterization (thin black line). The average e q u i v a l e n t m a g n i t u d e c h a n g e s i n t h e i n t e r c e p t was computed using model data sampled every 3 minutes from t=0 to t=120 minutes.

a) q & q b) q c) q and q d) total q 14 r h s c i

12 N8 r 4

4 r N8 r N 4 10 6r N8 N6 4 4 r N4 r N4 4 6 N3 WR r 9 N4 r N4 N r N4 r N3 4 4 9 4 r r N5 r N r9 8 9 9 5 9 r N r N5 9 N4 4r 9 5 N4 N 9 r r r r 9 9 N3 4

z (km) 6 N N6 8r r4 4 N 3 r 4 9 WR WR 2

0 .05.10 .15 .20 .25 .30 .05 .10 .035 .05.10 .15 .20 .25 .30 Average Water Content (g m-3 ) Fig. 5. Plots of temporally- and spatially- averaged water content (g m—3) as a function of altitude for the 7 cases in the study. Cases are shown in terms of a) rain and hail/graupel, b) snow, c) cloud water and cloud ice, and d) total water. Temporal averaging was performed upon data output with 3 min frequency from t=0 to t=120 min. Spatial averaging was performed horizontally with every point in the 90 x 90 km grid. Arrows show the direction of change from N3r9 to N8r4. ( T altitude). ahigher at found was greater actual LPstormsstoremost oftheirwatermassin are shown. Those processes labeled with non-bold and bold lettering refer to sinks and sources for hail/graupel, respectively. hail/graupel, respectively. for and sources sinks to refer andboldlettering labeledwith non-bold processes Those shown. are repeated withweakershear(30ms accumulated precipitationwhenourexperimentswere we havealsofoundafactorofthreedifferencein between cases(McCumberetal.1991).However, did notshowsuchlargeprecipitation-falldifferences squall lines(albeit,withasmallerrangeofintercepts) supercells. Apreviousstudyofsimulatedtropical from thefactthatlargehailismoreprolificin accumulated precipitationbetweencasesmightresult parameter forrainorsnow. Fi few precipitation (LP)supercell"(Moller etal.1994).Too bears anyresemblanceto theso-called"low- uncertainty cannotbediscounted. hodograph) andthereforethemicrophysical si ( t he WK84 environmental sounding for cases a) N3 a) for cases sounding environmental he WK84 qhacw qhdpv able 2. Ground-accumulated precipitation mass by t =2hours. t by mass precipitation Ground-accumulated able 2. nce cloud ice of 1 of cloud g kg ice nce g. 6. Production and loss rates as a function of hail/graupel mixing ratio for z = 6.25 km altitude (except for for (except altitude km z = 6.25 for ratio hail/graupel mixing of as afunction rates andloss Production 6. g. amRi 61 61 0 56.17 56.17 Warm Rain Simulation Production and Loss Rates (kg kg-1s-1) 10 10 10 10 10 10 10 We warnthereaderthatlargedifferencesin The readermaywonderwhether theN8 N3 N8 N6 N4 N5 N4 in situ ), a , -8 -7 -6 -5 -4 -3 - qhaci 2 r r r r r r 02 9 4 4 4 9 9 10% supersaturation with respect to ice was assumed. The dotted line for linefor dotted The assumed. was ice to respect with supersaturation 10% a) N3

, observations existtoevaluate whether qhacr QHDPV hail/graupelsublimation QHSBV QHACS QHACI QHACR hail/graupelmeltingtorain QHMLR QHACW r 9 , and — oa anHail Rain Total Accumulated Mass(tera 75 74 10.096 67.49 77.59 72 72 ~0 27.21 17x10 0.035 48.64 0.015 0.569 27.21 64.83 48.64 66.61 70.53 64.86 66.63 71.10 1

qhacs hail/graupel deposition hail/graupel accretingsnow hail/graupel accretingcloudice hail/graupel accretingrain hail/graupel accretingcloudwater wa s not present in any of the simulations at the reference altitude of z = 6.25 km AGL (however, that amount that and (however, km z = 6.25 of AGL altitude reference the at simulations the of inany present not ) were computed 46810 246810 Key -1

assuming a mixing ratio 1gkg of amixing assuming r arc length Hail/Graupel MixingRatio(gkg QHACI QHM 9 and b) N8 9 andb) g r rams)

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=1.1) r 4. Only those rates that change with hail/graupel intercept and/or density and/or intercept with hail/graupel change that rates those Only 4. b) N8 graupel versusanothericespecies.Also,N8 6. Agreement #NA67RJ0150. provided bytheNSSLunderNOAA-OUCooperative ATM-9617318. Partialfundingforthisresearchwas Science FoundationundergrantsATM-0003869and 5. prescription ofhail/graupelinterceptanddensity. microphysics schemesthatdonotrequirearbitrary motivating theuseofmoresophisticatedice these sensitivitiesisanimportantfirststepin forecasting isquestionable.However,understanding scheme inwarmseasoncloud-scaleprecipitation hail/graupel distribution.Therefore,theutilityofthis factor ofthreeduetouncertaintiesinspecifyingthe simulated withLFO-3microphysicscanvarybya accumulation beneathdeepconvectivestorms within asinglespeciesthathasfixed because hailandgraupelinLFO-3arerepresented observed withLPsupercells.Thislimitationarises incapable ofsimulatinglargehailstonesthatareoften

References areavailableupon request. REFERENCES This researchwassupportedbytheNational ACKNOWLEDGMENTS We haveshownthattheprecipitation r 4 — qhaci 1

fo r

t -1 indicates that the production rate was hypothetical was rate production that the indicates he accreted particles. For hail/graupel deposition For particles. he accreted ) qhmlr , valid for for = z , valid

QHACR r h and

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=1.1) 3 km AGL) in AGL) km 3 n oh . on rates r 4 is