Explicit Forecasts of Winter Precipitation Using an ...u0758091/MPschemes/Thompson2004.pdfaircraft icing. To accomplish this goal, the bulk, mixed-phase microphysical parameterization

FEBRUARY 2004 519T H O M P S O N E T A L .

q 2004 American Meteorological Society

Explicit Forecasts of Winter Precipitation Using an Improved Bulk MicrophysicsScheme. Part I: Description and Sensitivity Analysis

GREGORY THOMPSON, ROY M. RASMUSSEN, AND KEVIN MANNING

National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 26 December 2002, in final form 19 September 2003)

ABSTRACT

This study evaluates the sensitivity of winter precipitation to numerous aspects of a bulk, mixed-phase mi-crophysical parameterization found in three widely used mesoscale models [the fifth-generation PennsylvaniaState University–National Center for Atmospheric Research Mesoscale Model (MM5), the Rapid Update Cycle(RUC), and the Weather Research and Forecast (WRF) model]. Sensitivities of the microphysics to primary iceinitiation, autoconversion, cloud condensation nuclei (CCN) spectra, treatment of graupel, and parameters con-trolling the snow and rain size distributions are tested. The sensitivity tests are performed by simulating variouscloud depths (with different cloud-top temperatures) using flow over an idealized two-dimensional mountain.The height and width of the two-dimensional barrier are designed to reproduce an updraft pattern with extentand magnitude consistent with documented freezing-drizzle cases. By increasing the moisture profile to saturationat low temperatures, a deep, precipitating snow cloud is also simulated. Upon testing the primary sensitivitiesof the microphysics scheme in two dimensions as reported in the present study, the MM5 with the modifiedscheme will be tested in multiple case studies and the results will be compared to observations in a forthcomingcompanion paper, Part II.

The key results of this study are 1) the choice of ice initiation schemes is relatively unimportant for deepprecipitating snow clouds but more important for shallow warm clouds having cloud-top temperature greaterthan 2138C, 2) the assumed snow size distribution and associated snow diffusional growth along with theassumed graupel size distribution and method of transforming rimed snow into graupel have major impacts onthe mass of cloud water and formation of freezing drizzle, and 3) a proper simulation of drizzle using a single-moment scheme and exponential size distribution requires an increase in the rain intercept parameter, therebyreducing rain terminal velocities to values more characteristic of drizzle.

1. Introduction

Numerical weather prediction of winter precipitationhas been consistently improving over the past two de-cades, though there are still occasional ‘‘bust’’ forecasts.Advancing technology allows increasingly sophisticatedphysics to be incorporated into numerical models ofincreasing resolution. The representation of cloud mi-crostructure and resulting hydrometeor evolution is noexception, using either explicit bin-resolving cloudmodels (Young 1974; Hall 1980; Kogan 1991; Feingoldet al. 1988, 1994; Geresdi 1998; Rasmussen et al. 2002)or bulk microphysical parameterizations (Lin et al.1983; Rutledge and Hobbs 1983, 1984; Cotton et al.1986; Ferrier 1994; Kong and Yau 1997; Reisner et al.1998). Bin models prognose multiple variables for spe-cific intervals of each hydrometeor species size spec-trum and are therefore extremely expensive in terms ofcomputer time and memory. For this reason, bin models

Corresponding author address: Gregory Thompson, NCAR-RAP,P.O. Box 3000, Boulder, CO 80301-3000.E-mail: [email protected]

are not yet viable for real-time NWP efforts, thoughcontinued technological advances are likely to changethis in the future. Alternatively, models designed forreal-time applications utilize bulk microphysical param-eterizations that reduce the number of prognostic var-iables by assuming hydrometeor size spectra follow aprescribed exponential (Kessler 1969) or gamma dis-tribution (Verlinde et al. 1990; Walko et al. 1995).

Development and testing of bulk microphysicalschemes tend to conform to one or two of the followingscenarios: 1) clouds produced by deep convection (Linet al. 1983; Murakami 1990; Ferrier 1994; Walko et al.1995; Meyers et al. 1997; Swann 1998), 2) clouds as-sociated with cold and/or warm fronts (Rutledge andHobbs 1983, 1984; Reisner et al. 1998; Tremblay et al.2001), or 3) clouds produced by orographic lift (Cottonet al. 1986; Meyers and Cotton 1992; Meyers et al.1992). In the first two scenarios above, there tends tobe tropospheric deep and strong ascent (vertical veloc-ities ;1–10 m s21), while the third scenario generallyinvolves weaker lift by comparison (;0.3–1 m s21) butequally cold cloud tops (temperature ,2408C).

In general, relatively deep and cold cloud system sim-

520 VOLUME 132M O N T H L Y W E A T H E R R E V I E W

ulations have abundant ice and snow that may masksubtle dependencies of a microphysical parameteriza-tion to produce supercooled liquid water. In many ways,simulations of deep precipitating storm systems are‘‘forgiving’’ of subtle sensitivities within a microphysicsscheme since there is abundant lift and abundant pre-cipitation. Where quantitative precipitation forecasts areconcerned, these sensitivities are relatively unimportant.However, in the aircraft operations arena, for example,they are critical to predicting whether airframe icingoccurs or not. If the simulated cloud is composed pri-marily of snow, then liquid water is depleted, in whichcase little or no aircraft icing is predicted to occur. Incontrast, the absence of ice and snow typically leads todevelopment of supercooled cloud liquid water, orworse, supercooled drizzle (Cober et al. 2001).

The ultimate goal of the research reported in thispaper is to improve explicit, real-time forecasts of su-percooled liquid water and hence improve forecasts ofaircraft icing. To accomplish this goal, the bulk, mixed-phase microphysical parameterization described in Reis-ner et al. (1998, hereafter RRB) is rigorously tested andimproved. Each modification to RRB is discussed insection 2. Sensitivity tests are performed similar to Ras-mussen et al. (2002, hereafter RG) using idealized flowover a two-dimensional barrier, and the scheme is tunedto results of the bin model of the aforementioned study.However, to ensure the model is not overly tuned toproduce liquid instead of ice, we also perform tests ofdeeper and colder cloud systems. The implementationdetails are found in section 3, while section 4 containsthe results of numerous 2D sensitivity experiments. Sec-tion 5 provides conclusions and a discussion of related,future topics. Most of the bulk microphysical studiesmentioned earlier used a single case study for their test.In a forthcoming companion paper, Part II, the finalscheme is tested on multiple case studies involvingcloud systems of various temperatures/depths from anumber of field projects from different geographical re-gions of the United States.

2. Description of the bulk microphysicsparameterization

The bulk microphysical parameterization used in thisstudy is an upgraded version of the scheme presentedin RRB. Although it is available in three widely usedmesoscale models, its development and testing are pri-marily performed using the fifth-generation Pennsyl-vania State University–National Center for AtmosphericResearch (PSU–NCAR) Mesoscale Model (MM5), withresults propagated to the Rapid Update Cycle (RUC; cf.Benjamin et al. 2004) and Weather Research and Fore-casting (WRF) models. In RRB, this scheme is describedas ‘‘option 4’’ (referred to as ‘‘Reisner2’’ by MM5 users)and is currently the most complex microphysics optionavailable in the MM5 code distributed to the user com-munity. Option 4 is a bulk, mixed-phase microphysics

scheme with prognostic variables for the mixing ratiosof cloud water (qc), rain (qr), cloud ice (qi), snow (qs),and graupel (qg), plus the number concentration of ice(Ni). To date, the version described in RRB as ‘‘option5,’’ which additionally prognoses number concentra-tions of graupel and snow, is not widely available andis therefore not considered in this study. Furthermore,the additional computational cost of option 5 inhibitsits use for real-time applications as desired for the RUCand WRF models. Improvements and modifications toRRB are discussed below, while a number of additional,relatively minor alterations and corrections are includedin the appendix.

a. Initiation of cloud ice

The nucleation of cloud ice due to deposition andcondensation freezing previously used a relationship de-scribed in Fletcher (1962) as follows:

25N 5 10 exp[0.6(T 2 T)],i,Fletcher 0 (1)

where To 5 273.15 K, T is the ambient temperature (K),and Ni is the number of ice crystals initiated (L21). Asmentioned in RRB, this relationship produces errone-ously high concentrations of ice particles at very lowtemperatures; thus, ice number concentration was thres-holded at the value attained when T 5 246 K. For thecurrent study, the Fletcher curve is replaced by a similarrelationship determined by Cooper (1986) based on di-rect ice crystal measurements and given by

N 5 0.005 exp[0.304(T 2 T)].i,Cooper 0 (2)

Similar to the low-temperature cutoff mentioned above,the number of ice crystals initiated is prevented fromexceeding the value attained when T 5 233 K. Bothrelationships are tested in sensitivity experiments dis-cussed later as well as an alternate methodology for iceinitiation described in Meyers et al. (1992) and givenby

N 5 exp(20.639 1 0.1296S ),i,Meyers i (3)

where Si is the supersaturation (percent) with respect toice. A depiction of these three relationships is found inFig. 1 and reveals an order of magnitude or greaterdifference among them for temperatures between 258and 2158C but nearly the same concentration of icenear 2258C. The schemes again differ by nearly anorder of magnitude below approximately 2508C. Notein Fig. 1 that the line shown for Ni,Meyers assumes max-imum possible Si (i.e., water saturation).

A related, fundamental shift in ice initiation pertainsto the necessary conditions to nucleate ice. Previously,ice was allowed to initiate by Eq. (1) as soon as icesaturation was attained for all temperatures less than08C. In the current scheme, ice does not form by Eq.(2) until the air is saturated with respect to water andT , 258C or until the water vapor mixing ratio exceeds5% supersaturation with respect to ice. However, as in


FIG. 1. Ice nucleation by deposition and condensation freezing asa function of temperature given by Fletcher (1962), Cooper (1986),and Meyers et al. (1992) at water saturation. Note that the variabilityexceeds an order of magnitude at relatively high temperatures.

RRB, ice continues to be formed by freezing of clouddroplets (T , 258C) and by a secondary ice-nucleationmethod, commonly referred to as rime-splinter ice pro-duction, based on work by Hallet and Mossop (1974).

b. Autoconversion

The collision and coalescence of cloud droplets toform raindrops is parameterized by autoconverting be-tween the mixing ratios of the two hydrometeor species,qc and qr, following Kessler (1969) and given by

dqr 5 aH(q 2 q ), (4)c codt

where a 5 1 3 1023 s21 is a time constant, H is aHeaviside function, and qco 5 0.35 3 1023 is a thresholdvalue. Previously, the threshold used in RRB was 0.53 1023 but is reduced based on results by RG. Besidestesting the old and revised thresholds, an additional sen-sitivity test is performed with qco 5 0.1 3 1023.

As an alternative to the Kessler autoconversionscheme, the methodology described by Berry (1968) isalso evaluated using the relationship

2dQ Qr c5 , (5)dt 0.0266 Nb2 1 1 21 2D Qb c

where Qr is the rain water content (g m23), Db 5 0.3is the dispersion factor, Nb is cloud droplet concentration(cm23), and Qc is the cloud water content (g m23).

In another, alternative autoconversion scheme, Walko

et al. (1995) adapted a Berry and Reinhardt (1974) pa-rameterization using the relationship1

122 20 4 20.52.7 3 10 q 3 10 D (1 1 y) 2 0.4c mean[ ]16dqr 5 ,

dt 3.76 21/6 21[0.5 3 10 D (1 1 y) 2 7.5]meanr qa c

(6)

where y represents a gamma distribution shape param-eter, ra and rw are the density of air and water (kg m23),respectively, and Dmean is the mean diameter (m) of clouddroplets computed from cloud water mixing ratio (qc)and concentration (Nc) using

1/36r qa cD 5 . (7)mean 1 2pr Nw c

In our application of Eq. (6), y is set to 3, and both thenumerator and denominator must be positive. Substi-tuting various droplet concentrations of 50, 100, 200,and 500 cm23 into Eqs. (6) and (7), we compute min-imum cloud water mixing ratios of 0.171, 0.343, 0.686,and 1.71 g kg21, respectively, before cloud water con-verts to rain. Hence, Eq. (6) simplifies to a form similarto the Kessler autoconversion scheme with constant Nc,but the rates of rain conversion tend to be lower usingEq. (6) compared to Eq. (4). Nonetheless, this alterationis desireable because of its physical basis and for other/future modeling studies where Nc could be prognosed.

c. Treatment of graupel

In RRB, the size distribution of graupel assumed anexponential form [N(D) 5 No,g e ] with a constant2l Dg

intercept parameter (No,g 5 4 3 106 m24), whereas, inthe current study, the distribution is altered in two ways.First, the distribution assumes the following generalizedgamma form

(y21) 2l DgN(D) 5 N D e ,o,g (8)

where0.2pr Ng o,g

l 5 1.32 and (9)g 1 2rqg

0.92prgN 5 2.38 (10)o,g 1 2rqg

replace the slope and intercept parameters of the ex-ponential distribution, y 5 2, and rg 5 400 kg m23 isthe density of graupel. Second, No,g depends on qg sim-ilar to the RRB approach for determining No,s as a func-tion of qs. Whereas the RRB study used observations

1 This equation corrects three errors found in Walko et al. [1995,Eqs. (74)–(76)] and one error found in Berry and Reinhardt [1974,Eq. (16)].


FIG. 2. Contours of (a) PSDEP (kg kg21 s21) as a function of mixingratio and temperature, (b) PSACW (kg kg21 s21) as a function ofsnow and cloud water mixing ratio, and (c) the ratio of PSDEP/PSACW at T 5 2108C. Note in (c) that depositional growth generallyexceeds riming growth until cloud liquid water increases to appre-ciable amounts typically associated with drizzle or rain formation.

by Sekhon and Srivastava (1970) to derive No,s 5 f (qs),we derive Eq. (10) using observations from Brown andSwann (1997). Note that because No,g → ` as qg → 0,we limit the magnitude of No,g such that it cannot exceeda fixed maximum value (5 3 107 m24) while also im-posing a lower limit of 1 3 104 m24.

Besides the modification to the shape of the graupeldistribution, the conversion of rimed snow into graupelis altered from the RRB study. In RRB, Eq. (A.43)contains the model time step, Dt, potentially requiringtuning when the time step is adjusted. In the currentstudy, we follow the treatment found in Murakami(1990) and evaluate the larger of two terms: depositionalgrowth (PSDEP) and riming growth (PSACW) of snow,computed as in Rutledge and Hobbs (1983) using

PSDEP

4(S 2 1)Ni o,s5A 1 B

b 5sG 1 1 21/2 2 2 0.65 a rs1/33 1 0.44S , (11)c 2 b /215/21 2 sl m ls s

and

rpa q E N G(b 1 3)s c sc o,s sPSACW 5 , (12)b 13s4 ls

respectively, where A and B are thermodynamic termsgiven in Pruppacher and Klett (1978), Sc 5 0.6 is theSchmidt number, as 5 11.72 m s21 and bs 5 0.41(12b )s

are constants in the snow fall speed relation, Esc is thecollection efficiency between snow and cloud water, ls

is the slope of the snow size distribution (m21) and mis the dynamic viscosity of air (kg m21 s21). If riminggrowth exceeds depositional growth, then graupel in-creases at the rate given by PSACW, otherwise snowincreases at this rate. To illustrate the relative contri-butions by these two terms, Fig. 2 presents PSDEP con-tours as a function of snow mixing ratio and temperature(Fig. 2a), PSACW contours as a function of snow andcloud water mixing ratios (Fig. 2b), and the ratio of thetwo at T 5 2108C (Fig. 2c). In general, riming growthdoes not exceed depositional growth until cloud liquidwater exceeds 0.1 g kg21. Rutledge and Hobbs (1984)required a threshold snow mixing ratio of 0.1 g kg21

and a cloud water mixing ratio threshold of 0.5 g kg21

before producing graupel. These thresholds approxi-mately correspond to PSDEP/PSACW 5 0.2 curveshown in Fig. 2c, implying that riming growth mustexceed depositional growth by a factor of 5 before rimedsnow transitions to the graupel category.

d. Intercept parameter of the snow size distribution

RRB determined that a fixed snow intercept parameterled to the depletion of too much cloud water, therefore

motivating the mass-dependent No,s relationship usedpreviously in MM5. Similarly, Swann (1998) utilizedsnow and graupel intercept parameters that dependedon mixing ratio in a single-moment microphysics


FIG. 3. PSDEP (solid) and snow size distribution intercept param-eter (No,s dotted) vs temperature using the new temperature-dependentNo,s (thick lines/dots) given by Eq. (13) and original mass-dependentNo,s (thin lines/dots) relationship given by Reisner et al. (1998). In(a), the snow mixing ratio varies between 0.002 and 0.2 g kg21 asin a typical, shallow, mixed-phase cloud, and depositional growth islower at relatively high temperatures using the new scheme ratherthan the old scheme. In (b), the snow mixing ratio varies between0.05 and 0.5 g kg21 as in a typical, deep, precipitating snow cloud,and depositional growth is always larger using the new scheme ratherthan the old.

scheme; however, he speculated that a temperature orheight dependence may improve the scheme to matchresults from a double-moment scheme. By analyzing 37particle-size spectra from aircraft flights through frontalclouds at virtually all temperatures aloft, Houze et al.(1979) found that mean particle diameter increased withincreasing temperature, and, more importantly, No andl decreased with increasing temperature as a result ofgrowth by aggregation. Thus, we decided to implementan explicit temperature-dependent No,s into the schemeusing the curve for total precipitation water content 0.03# M , 0.3 in Fig. 7 of Houze et al. (1979), resultingin the following relationship:

8 6N 5 min{2 3 10 , 2 3 10o,s

3 exp[20.12 min(20.001, T 2 T )]}, (13)o

where To 5 273.15 K, and T is the ambient temperature(K). Considering that this version of the microphysicscode lacks a snow aggregate species, perhaps a tem-perature-dependent No,s is the simplest way to param-eterize this effect. Alternatively, the addition of an ag-gregate species and associated prognostic equationscould be developed.

The largest impact of the new relationship for No,s

pertains to depositional growth of snow [PSDEP; Eq.(11)], which is illustrated in Fig. 3. In Fig. 3a, the ver-tical profile of snow mixing ratio varies from 0.002 to0.2 g kg21, corresponding to a hypothetical, shallow,mixed-phase cloud. Note that the maximum No,s exceedsthe old value by an order of magnitude at low temper-atures; thus, the depositional growth is larger at tem-peratures , 2208C using the new method. However, inrelatively warm air (T . 2208C), the intercept param-eter is less using the new method, and therefore de-positional growth is reduced. On the other hand, whenthe vertical profile of snow mixing ratio more closelymimics a deep snow cloud with qs ranging from 0.05to 0.5 g kg21 (corresponding to Fig. 3b), then PSDEPis always larger using the temperature-dependent rela-tionship over the mass-dependent No,s.

Whereas the maximum depositional growth of a sin-gle ice crystal generally peaks around T 5 2148C (see,e.g., Wallace and Hobbs 1977 or Young 1993), Figs. 2aand 3 represent the aggregate effect of depositionalgrowth on an entire snow size distribution. The verybroad minimum centered at 2358C in Fig. 2a and max-imum at approximately 2208C in Fig. 3 are a result ofthe increase in No,s with decreasing temperature [Eq.(13)]. In other words, a population of large numbers ofsmall snow crystals at T 5 2308C grows nearly asrapidly by deposition as a reduced number of largercrystals at higher temperatures.

e. Intercept parameter of the rain size distribution

Unlike the intercept parameter for snow, previous stud-ies do not support a temperature-dependent rain size dis-

tribution. Instead, it is quite reasonable to assume thatwater drops undergo a gradual transition from cloud drop-let sizes (diameter less than approximately 50 mm)through drizzle drops (diameter approximately 50–500mm) on their way to becoming raindrops. However, near-ly all single-moment bulk microphysics schemes simplymake an abrupt transition from cloud water to rain withthe associated Marshall–Palmer size distribution and in-tercept parameter of 8 3 106 m24. Thus liquid dropsundergo a transition from nonsettling (most bulk micro-physics schemes do not sediment cloud droplets) to typ-


FIG. 4. Mass-weighted terminal velocity vs mixing ratio for hy-drometeor species: snow, graupel, and rain at 900 hPa and T 5 258C.The dashed line labeled ‘‘orig. rain’’ indicates the terminal velocityfor rain using a constant value of No,r 5 8 3 106 m24, while thesolid, thick line labeled ‘‘new rain’’ uses the new mass-dependentrelationship in Eq. (14) (tested in sensitivity test RONV).

ical rain terminal velocities of 1–4 m s21 instantaneously.This leaves little time for water drops to interact as drizzledrops with other microphysical species such as snow,graupel, and cloud water. Instead, raindrops race to hitthe earth as precipitation and rarely remain suspendedwithin gentle stratiform updrafts. With these consider-ations in mind, we alter the rain size distribution via theintercept parameter to replicate a drizzle transition where-by the size distribution of rain consists primarily of driz-zle-size drops for very low rain mixing ratios. On theother hand, when rain mixing ratio increases, the interceptparameter decreases, thus broadening the rain distributionand replicating the original formulation. The followingfunction encapsulates the transition of the intercept pa-rameter from drizzle to rain:

N 2 N 4(q 2 q )1,r 2,r ro rN 5 tanho,r 1 2 [ ]2 qro

N 1 N1,r 2,r1 , (14)2

where N1,r 5 1 3 1010 m24 is an upper-intercept limit,N2,r 5 8 3 106 m24 is a lower-intercept limit, and qro

5 1 3 1024 is essentially the transition value betweenthe two limits. The terminal velocity that results whenNo,r spans this range is shown in Fig. 4 (labeled as ‘‘newrain’’) along with the curve for the original terminalvelocity using the previously fixed value of No,r andcurves for terminal velocities of snow and graupel. Thegraph shows the primary result of a varying No,r is thatsmall qr (theoretically more common of drizzle ratherthan rain) produce a terminal velocity between 0.2 and2 m s21, whereas large rain mixing ratios produce ter-

minal velocities between 2 and 8 m s21. According toYoung (1993), the former velocities correspond to dropswith diameters between 50 and 200 mm, while the lattervelocities correspond to drops with diameters between200 mm and 1 mm. Results of sensitivity tests for thisand all other alterations are presented in section 4.

3. Approach

As discussed in the introduction, a primary goal ofthis study is to reproduce the results found by RG usinga bulk microphysics parameterization in place of thecomputationally demanding detailed model. To accom-plish this, a two-dimensional version of the PSU–NCARMesoscale Model is configured nearly identically to theRG study. The MM5 domain is 120 points wide, spaced10 km apart, by 39 sp vertical levels, with effectivespacing of 40 m at the surface stretching to a constant900 m from 5 km to the model top at 100 hPa. Flowof 15 m s21 impinges upon a bell-shaped mountain 1 kmhigh with a 100-km half-width. The initial temperatureand moisture profiles (thick solid lines shown in Fig.5a) are modified slightly from the RG study in order tovary the moisture in a realistic manner to create cloudsof varying depths and temperatures. The temperatureand moisture profiles below the barrier height are iden-tical in the two studies, but the inversion between 1 and3 km is slightly warmer (18–28C) and drier in this studycompared to the inversion found in RG (thick, dashedlines in Fig. 5a represent the temperature and moistureprofiles used in RG). Furthermore, the temperature pro-file above the inversion differs significantly from theRG sounding but is not important for comparison pur-poses since the simulated cloud resides within and belowthe inversion. Previously, the lapse rate above the in-version was absolutely stable whereas the new lapse rateis conditionally unstable. This alteration allows forvarying the depth of saturation to simulate a deep pre-cipitating snow cloud as well as the relatively warmcloud top as in the RG study. Alternatively, we couldhave used the RG sounding while increasing the mois-ture to saturation, but this would have created an un-realistic profile for a deep precipitating snow cloud. Asexpected, there are minor differences between the sim-ulation using the new sounding and a simulation usingthe RG sounding. The new sounding results in a slightlywarmer and shallower cloud: cloud-top temperature(CTT) reaches 2138C using the modified sounding ver-sus CTT 5 2148C using the original RG sounding.

Table 1 presents the simulation experiments per-formed using the new sounding discussed above. Asshown, sensitivities of the microphysics to primary iceinitiation, autoconversion, and continental and maritimecloud condensation nuclei (CCN) spectra, treatment ofgraupel, and parameters controlling the snow and rainsize distributions are tested. The code used in the sim-ulation referred to throughout as ‘‘CONTROL’’ includesCooper ice initiation given by Eq. (2), whereas the


FIG. 5. Initial soundings used in MM5 2D idealized-flow sensitivity tests. The soundings produce clouds with: (a) CTT 5 2138C, (b)CTT 5 2258C, (c) CTT 5 2608C, and (d) seeder–feeder cloud system. Wind barbs are plotted at every model s level, with a full barbrepresenting 5 m s21.

Fletcher and Meyers ice initiation schemes are tested insensitivity experiments referred to as ‘‘Fletcher’’ and‘‘Meyers,’’ respectively. CONTROL also uses the Kes-sler autoconversion scheme of Eq. (4) with cloud watermixing ratio threshold set to 0.35 3 1023, whereas thethreshold is lowered in an experiment called ‘‘Kessler1’’and then raised in experiment ‘‘Kessler5.’’ To test fur-ther the sensitivity to autoconversion, the Berry schemeof Eq. (5) is used in an experiment called ‘‘Berry’’ andthe Berry and Reinhardt scheme of Eq. (6) is run asexperiment ‘‘BandR.’’ Autoconversion and CCN spec-tra are linked via the relationship between cloud watermixing ratio and concentration [Eq. (7)]. Therefore, in

association with the BandR simulation, the number con-centration of cloud droplets (set to 100 cm23 in CON-TROL) is decreased to 50 cm23 in the ‘‘Maritime’’ ex-periment, then increased to 200 cm23 in ‘‘Continental1’’and increased again to 500 cm23 in ‘‘Continental2.’’CONTROL uses the gamma size distribution for grau-pel, whereas an experiment called ‘‘Graupel1’’ uses theoriginal exponential distribution and constant No,g as inRRB. Furthermore, CONTROL requires riming growthof snow to exceed depositional growth before convert-ing rimed snow into graupel, but Graupel1 uses the RRBformulation (containing the time step dependency) forthis conversion process. Then, in a sensitivity experi-


TABLE 1. Summary of sensitivity experiments with alterations from CONTROL listed under brief description.

Experimentname Brief description

CTT 52138C

CTT 52258C

CTT 52608C

Seeder–feeder

CONTROL Cooper ice initiation [Eq. (2)], Kessler autoconversion [Eq. (4); qco 50.35 3 1023], Nc 5 100 cm23, No,g 5 f (qg) [Eq. (10)], Murakamirimed snow-to-graupel conversion, No,s 5 f (qs), and No,r 5 8 3 106

m24.

3 3 3 3

Fletcher Fletcher ice initiation [Eq. (1)]. 3 3Meyers Meyers ice initiation [Eq. (3)]. 3 3Kessler1 Kessler autoconversion [Eq. (4); qco 5 0.1 3 1023]. 3Kessler5 Kessler autoconversion [Eq. (4); qco 5 0.5 3 1023]. 3Berry Berry autoconversion [Eq. (5)]. 3BandR Berry and Reinhardt autoconversion [Eq. (6)]. 3Maritime* Maritime CCN spectra, Nc 5 50 cm23. 3Continental1* Continental CCN spectra, Nc 5 200 cm23. 3Continental2* Polluted continental CCN spectra, Nc 5 500 cm23. 3Graupel1 Original exponential distribution, No,g 5 4 3 106 m24, and original

Reisner rimed snow-to-graupel conversion.3 3 3 3

Graupel2 Riming growth of snow must be 3 times larger than depositionalgrowth before creating graupel.

3 3 3 3

Version2 Combine Fletcher, Kessler5, and Graupel1. 3 3SON Constant No,s 5 2 3 107 m24. 3 3 3 3SONV No,s 5 f (T ) [Eq. (13)]. 3 3 3 3RON1 Constant No,r 5 1 3 1010 m24. 3RONV1 No,r 5 f (qr) [Eq. (14)]. 3Final Combine BandR (Nc 5 100 cm23), Graupel2, SONV, and RONV. 3 3 3 3

* Combines code used in BandR, and all ice physics are disabled.1 Combines code used in SONV.

ment called ‘‘Graupel2,’’ the gamma distribution is re-introduced, but the riming growth must exceed depo-sitional growth of snow by a factor of 3 before con-verting rimed snow to graupel. In RRB and CONTROL,the intercept parameter of snow is a function of snowmixing ratio, while a constant value is tested in ‘‘SON,’’followed by a test using the temperature-dependent re-lationship of Eq. (13) in experiment ‘‘SONV.’’ Next,the intercept parameter for rain is constant in CON-TROL but increased for experiment ‘‘RON’’ and alteredto depend on rain mixing ratio by Eq. (14) in experiment‘‘RONV.’’ Last, a sensitivity simulation combiningmodifications used in BandR (with Nc 5 100 cm23),Graupel2, SONV, and RONV is performed in the ex-periment called ‘‘Final.’’ This combination representsthe final bulk microphysics parameterization and is whatwe recommend for general use by modelers using thisscheme, particularly MM5, RUC, and WRF real-timeapplications.

Besides CONTROL and the 17 sensitivity experi-ments that used the temperature and moisture profilesshown in Fig. 5a, additional simulations are performedwith the same temperature profile but with moistureincreased to saturation to various temperatures, thus pro-ducing cloud systems extending to the 2258 and 2608Clevels (Figs. 5b and 5c, respectively). Last, the moisturein the 2608C cloud-top temperature sounding is de-creased to 38C dewpoint below saturation between 1and 3 km to simulate a seeder–feeder cloud system (Fig.5d).

4. Sensitivity tests

a. CONTROL experiment

During the initial 30 min, a small cloud composedof water forms approximately two-thirds of the wayup the barrier. This liquid cloud grows horizontally andvertically while a small amount of cloud ice is initiatednear cloud top. Cloud water and cloud ice continue toincrease during the first two hours of the simulation,with vertical growth to 2 km (approximately 2138C).Cloud ice rapidly grows by deposition to form snowthat sediments and precipitates. Once snow forms, itaccretes cloud water and rimes, thus increasing themass of snow but also creating a comparable amountof graupel. The formation of graupel triggers ice mul-tiplication (within the temperature range 238 to 288C),which increases the background value of ice numberconcentration from 0.05 to 0.7 L21. These new ice crys-tals form directly within the liquid portion of the cloudand rapidly grow to snow sizes and accrete more cloudwater. As snow and graupel continue to increase inmass, cloud water slowly depletes. Two hours into theCONTROL simulation, the cloud water peaks at 0.364g kg21 , just crossing the threshold quantity for auto-conversion to the rain category (essentially becomingfreezing drizzle). Thereafter, cloud water decreases asglaciation dominates, while snow and graupel precip-itate in nearly equal proportions. A snapshot of themicrophysical species: cloud water, cloud ice, snow,rain, and graupel at 3 h, along with a plot of precip-itation type and amount at hours 3 and 4 are shown in


FIG. 6. Vertical cross sections from experiment CONTROL at 3 h using CTT 5 2138C sounding (Fig. 5a): (a) cloud liquid water (g kg21),(b) snow mixing ratio (g kg21; shaded) with number concentration of ice (contours at 25, 50, 100, . . . m23), (c) rain mixing ratio (g kg21),and (d) graupel mixing ratio (g kg21). Also, precipitation accumulation since initial time vs distance at 3 h (dashed line) and 4 h (solid line)segregated by (e) rain (mm) and (f ) snow and graupel (mm).

Fig. 6, while 3-h domain-maximum values of all hy-drometeor species are listed in Table 2, along with 6-h simulation maxima shown in parentheses. The thirdvalue found in square brackets in each column is thermse (L2 norm) computed as the square root of thesum (over all grid points) of squared differences be-tween the bulk and bin models at 3 h.

b. Bin model

To compare directly between results of the bulk ver-sus the bin models, we performed a new bin-modelsimulation using the CTT 5 2138C sounding. Whilethe bin model is capable of depleting ice nuclei, thebulk model is not; so, for proper comparison, we dis-


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abled ice nuclei depletion (as in RG simulation 10). Inthis manner, both the bin and bulk schemes initiate newice crystals as the number concentration falls below theprescribed Cooper amount [Eq. (2) and Fig. 1]. As dis-cussed in RG and graphically shown here in Fig. 7 andTable 2, this has important consequences to the resultingcloud water, rain, snow, and graupel amounts. The newbin-model simulation contains 4 times as much frozenhydrometeors (snow and graupel) and approximatelyone-half as much liquid compared to results shown inRG with ice nuclei depletion active. The sensitivity ex-periments described below illustrate the key modifica-tions to the bulk scheme that bring the simulation intocloser agreement with results of this new bin-modelsimulation.

c. Ice initiation: Meyers and Fletcher experiments

To illustrate the sensitivity of the microphysics pa-rameterization to primary ice initiation, the model ismodified to use the ice nucleation schemes of Meyerset al. (1992) and Fletcher (1962). The experiment calledMeyers produces at least an order of magnitude moreice crystals throughout the cloud compared to CON-TROL. The increase in ice number produces the antic-ipated result of less cloud water (;16%) and 14% moresnow (Table 2). The Fletcher experiment, on the otherhand, produces an order of magnitude reduction in icenumber concentration at cloud top than CONTROL, re-sulting in marginally more cloud liquid water.

d. Autoconversion: Kessler1, Kessler5, Berry, andBandR experiments

The next series of tests involves the treatment of con-verting cloud water to the rain category by autocon-version using Kessler’s methodology in Eq. (4), the Ber-ry scheme in Eq. (5), and the Berry and Reinhardtscheme in Eq. (6). The Kessler autoconversion thresholdis 0.35 3 1023 in CONTROL, 0.1 3 1023 in Kessler1,and 0.5 3 1023 in Kessler5. Not unexpectedly, Kessler1produces far less cloud water (maximum 0.133 g kg21),a lot more rain, and less graupel than CONTROL, ascloud water is readily converted to rain that precipitatesquickly onto the ground. Kessler5 is hardly differentfrom CONTROL since the updraft produced by this flowregime is only strong enough to produce a limitedamount of cloud water that is depleted by snow and ice.The Berry experiment produces drastically smalleramounts of cloud water mixing ratio (maximum 0.067g kg21), much more rain (accumulation ø 0.4 mm), andslightly less snow/graupel than CONTROL. The BandRexperiment nearly matches CONTROL except for aslight increase in maximum cloud water and less rainbecause of its low autoconversion rate (when comparedto the Kessler rate).

To see the true sensitivities of these autoconversionschemes, one needs to disable all the ice species/inter-


FIG. 7. Vertical cross sections at 3 h from the experiment using Rasmussen et al. (2002) bin microphysics model and CTT 5 2138Csounding (Fig. 5a); otherwise same as Fig. 6.

actions and simulate the warm-rain process by itself.Results from this suite of tests with ice physics disabledproduces the results shown in Fig. 8a. The same trendas mentioned above occurs with Kessler1 and Berry,showing very aggressive rain production initiating fromthe lowest cloud water amounts. CONTROL is next (notshown), followed by Kessler5, then BandR. It is alsoclear from this figure that BandR has the slowest rateof cloud water to rain conversion of all the experiments.

e. CCN spectra: Maritime, Continental1, andContinental2 experiments

The sensitivity of the microphysics to CCN spectrais addressed using three simulations with various clouddroplet concentrations (Nc, a proxy variable for CCNspectra). Since the Kessler (1969) autoconversionscheme does not include the effects of Nc, these testsare combined with the Berry and Reinhardt (1974) au-


FIG. 8. Time series of cloud water (qc—left abscissa; solid lines)and rain (qr—right abscissa; dashed lines) mixing ratios (g kg21)from the set of (a) autoconversion and (b) CCN spectra experiments.

toconversion method discussed above in experimentBandR. Whereas CONTROL used Nc 5 100 cm23, theMaritime experiment uses Nc 5 50 cm23, Continental1uses Nc 5 200 cm23, and Continental2 uses Nc 5 500cm23. Like the previous test above, we disable all icephysics to prevent water depletion by ice and to compareagainst results of RG. As expected, the Maritime ex-periment produces the least cloud water and the mostrain, while Continental2 produces the greatest cloud wa-ter mixing ratio and no rain (Fig. 8b). Direct compar-isons to results by RG are found below (section 4i).

f. Treatment of graupel: Graupel1 and Graupel2experiments

The treatment of graupel has major impacts on amixed-phase simulation such as this one. Besides theassumed graupel size distribution, the treatment of snow

riming and subsequent conversion to graupel is also im-portant. In experiment Graupel1, the original exponentialor Marshall–Palmer size distribution employed by RRBreplaces Eqs. (8)–(10). Furthermore, the conversion ofrimed snow to graupel is altered from the new meth-odology discussed in section 2 back to its original for-mulation as specified in RRB. Results of this test reveala 14% reduction of cloud water, a 30% increase in snow,and 51% less graupel. Graupel is reduced primarily be-cause its intercept parameter is constant and relativelylow in Graupel1; therefore, depositional growth of grau-pel is reduced from that of CONTROL. Instead of grow-ing graupel, deposition onto snow dominates, as evi-denced by the accumulated precipitation plot (Fig. 9f)showing snow dominating between the third and fourthhour. None of the results discussed thus far matches thoseof RG, where the primary precipitation was rain with asmall amount of snow.

In the experiment called Graupel2, riming growth ofsnow must exceed depositional growth by a factor of 3before rimed snow is transferred to the graupel category,whereas CONTROL required a unity ratio. The differ-ence between these two threshold ratios is shown in Fig.2c, with CONTROL represented by the 1.0 curve andGraupel2 represented approximately halfway betweenthe 0.2 and 0.4 curves. Results of this test reveal nograupel but 73% more snow, 18% less cloud water, and34% less cloud ice than CONTROL (see Table 2). Thedecrease in cloud ice is due to the lack of ice multipli-cation, a direct consequence of eliminating graupel sinceriming growth does not attain the new threshold re-quirement. Similar to Graupel1, snow mass increasesdue to deposition at the expense of cloud water.

g. Version2 experiment

As discussed in section 2, a significant number of mod-ifications have been made to the MM5 microphysicsscheme since RRB. In an experiment referred to as Ver-sion2, the code is modified to approximate RRB; how-ever, an exact match is not possible because of bug fixes.In its simplest form, the modifications to CONTROLcombine three of the sensitivity experiments above:Fletcher, Kessler5, and Graupel1. Not surprisingly, theresulting hydrometeor amounts (Table 2) are very similarto the Graupel1 experiment since little sensitivity wasnoted between CONTROL and Fletcher or Kessler5.

h. Snow intercept parameter: SON and SONVexperiments

In sensitivity experiment SON, No,s is set constant toits maximum value, 2.0 3 107 m24. This simulationproduces only 9% more snow but no other discernibledifferences in resulting hydrometeor mixing ratios ver-sus CONTROL. This is logical because the relativelysmall mixing ratio of snow produced by this shallowcloud is insufficient to reduce No,s in CONTROL (es-


FIG. 9. Vertical cross sections from experiment Graupel1 at 3 h using CTT 5 2138C sounding (Fig. 5a); otherwise same as Fig. 6.

sentially No,s is constant in CONTROL); however, theimpacts of this sensitivity test are apparent in the deeperand colder cloud systems discussed later.

In experiment SONV, No,s depends on temperature viaEq. (13) replacing the RRB mass-dependent relation-ship, resulting in significant differences versus CON-TROL. The maximum cloud water mixing ratio realizedin this test is 0.397 g kg21, with an order of magnitudeless snow, 22% less graupel, and dramatically increased

rain (nearly half of the precipitation is freezing drizzle)compared to CONTROL. This result (shown in Fig. 10)compares favorably to the RG study except for the largeramounts of graupel in this simulation. The dramaticdecrease in snow mixing ratio is due to a reduced de-positional growth of snow (recall Fig. 3a) because thesnow size distribution is shifted toward large sizes atrelatively high temperatures (and the slope of the dis-tribution decreases).


FIG. 10. Vertical cross sections from experiment SONV at 3 h using CTT 5 2138C sounding (Fig. 5a); otherwise same as Fig. 6.

i. Rain intercept parameter: RON and RONVexperiments

Similar to the previous modifications to the interceptparameter of snow, the intercept parameter of rain, No,s

is altered from 8.0 3 106 m24 in CONTROL to 1.0 31010 m24 in the sensitivity experiment referred to asRON. Testing this parameter without significant rain ismeaningless, so this experiment also combines the mod-ifications of SONV, whose simulation produces the most

rainwater. From the discussion in section 2e and Fig. 4,note that the impact of this change to No,r alters theterminal velocity of rain from approximately 2 to 0.5m s21 (for the amount of rain produced in SONV). Theresulting cloud water at 3 h shown in Fig. 11a is 4%less than the cloud water produced in SONV (Fig. 10)because rain falls more slowly in RON, thus accretingmore cloud water. Accordingly, the resulting rain ac-cumulation is ;50% greater in RON (Fig. 11e), and theamount of rain suspended within the cloud is an order


FIG. 11. Vertical cross sections from experiment RON at 3 h using CTT 5 2138C sounding (Fig. 5a); otherwise same as Fig. 6.

of magnitude larger (;0.07 g kg21; Fig. 11c). The sus-pended rain mixing ratio is significantly increased inthis simulation as compared to SONV because of thelower terminal velocity of raindrops.

In the experiment referred to as RONV, No,r variesbetween the values used in experiments RON and CON-TROL according to Eq. (14). As shown in Table 2, theresulting mixing ratios are essentially identical com-pared to RON because the rain mixing ratio does notincrease sufficiently to impact (decrease) No,r.

To see the ramifications of a variable intercept pa-rameter, we repeated the RONV experiment without anyice microphysics active, thus allowing higher cloud wa-ter and rain mixing ratios to develop. Furthermore, weaim to reproduce results by RG in association with CCNspectra sensitivities duplicated here in Fig. 12a. Notethat while using a maritime CCN spectrum, their cloudwater increased to ;0.4 g kg21 before the onset of rain(drizzle) at approximately 1 h. When RG switched to acontinental CCN spectrum, their cloud water rose to


FIG. 12. Time series of cloud water (qc—left abscissa; solid lines)and rain (qr—right abscissa; dashed lines) mixing ratios (g kg21)using maritime and continental CCN spectra: (a) identical to Fig. 6of Rasmussen et al. (2002) provided for comparison and (b) resultswhen No,r depends on rain mixing ratio as in experiment RONV.

;0.7 g kg21 and required 3 h before producing rain. Ineither case, the rain mixing ratio rapidly increased toapproximately 0.1 g kg21 then remained nearly constant.When the RG sounding is used in an all-warm versionof the bulk model using the code in experiment BandR(recall section 4d), the resulting cloud water mixingratios are in reasonable agreement with results by RG,but the rain mixing ratios are a factor of 10 too low (cf.Fig. 8b to Fig. 12a). This is due to the large terminalvelocity of rain (;3 m s21) when the intercept parameteris set constant at its classical value (8 3 106 m24);hence, rain is rapidly precipitating to the ground andnot remaining suspended aloft like drizzle, as it is inthe RG study. When the intercept parameter is alteredto depend on mixing ratio, an experiment combiningthe all-warm BandR and RONV codes produces resultsin closer agreement to RG as shown in Fig. 12b.

j. Final experiment

Finally, in the last sensitivity simulation, the codemodifications of BandR (with Nc 5 100 cm23), Grau-pel2, SONV, and RONV combine to produce the ex-periment called Final. Results of this test (see Fig. 13and Table 2) show a slight increase in cloud water (5%),a sharp decrease in rainwater (73%), significantly moresnow (nearly an order of magnitude), and less graupel(14%) compared to RONV. Changes to the liquid por-tion are primarily due to swapping the autoconversionscheme, while the balance between snow and graupelis primarily due to the higher threshold for producinggraupel in the Graupel2 portion of the code.

More important than comparing Final to RONV isthe comparison of the Final experiment to the bin model(recall Fig. 7). While individual mixing ratios of eachmicrophysical species do not perfectly agree, the bal-ance of liquid and frozen species matches more closelythan any other experiment. This is confirmed by thermse values found in Table 2 as well as visual inspectionof Figs. 7a–f and 13a–f.

k. Deeper/colder cloud systems

Besides testing a shallow cloud with cloud-top tem-perature of 2138C, tests are performed with deeper andcolder cloud systems. In the remainder of this section,the temperature profile remains the same as before, butthe moisture profile is altered to produce cloud systemsof various depths and temperatures. Furthermore, a sub-set of the sensitivity studies (see Table 1) are repeatedto reveal responses due to both cloud depth/temperatureas well as the treatment of certain aspects of the mi-crophysical parameterization. There is little reason toperform the full suite of tests because a few of theprevious tests require sufficient cloud water or rain toexist, which, as will soon be shown, is lacking in thesedeeper/colder clouds.

1) CTT 5 2258C

The first test moistens the profile to ice saturationfrom the barrier height to the altitude of the 2208C level(recall Fig. 5b). The resulting cloud (reaching T 52258C) is primarily composed of ice and snow withvery low cloud water mixing ratio (Fig. 14 and Table3). Except for a brief time early in the cloud evolution,the reduced cloud water does not rime snow sufficientlyto convert into graupel, and the principal precipitationtype at the ground is snow.

Tests were conducted using the Meyers and Fletchersensitivity simulations, but the results (not shown) werenegligibly different from CONTROL except for the ex-pected differences in number concentration of ice dueto the temperature within the cloud. The resulting snowwas no different than CONTROL because there wereroughly equivalent ice number concentrations at cloudtop using all three schemes (recall Fig. 1).


FIG. 13. Vertical cross sections from experiment Final at 3 h using CTT 5 2138C sounding (Fig. 5a); otherwise same as Fig. 6.

Repeating the Graupel1 test using the original, ex-ponential size distribution along with the original con-version of rimed snow to graupel produces 9% lesscloud water, 5% less snow, and much more graupelcompared to CONTROL (see Table 3). The Graupel2test with more restrictive rimed snow to graupel con-version eliminates the very small quantity of graupelpreviously found in CONTROL.

When the Fletcher, Kessler5, and Graupel1 experi-ments are combined to create the Version2 test, the re-

sults replicate the sensitivity found in the warmercloud—namely, results of Version2 are negligibly dif-ferent from Graupel1.

Repeating the SON test results in a third as muchcloud water and 28% more snow versus CONTROL plus15% more snow accumulation. This is expected sinceNo,s 5 2 3 107 m24 causes snow to grow quicker thanthe RRB mass-dependent relationship that decreases No,s

as the snow mass increases in the deeper cloud system.Finally, in SONV with its temperature-dependent No,s,


FIG. 14. Vertical cross sections from experiment CONTROL at 3 h using CTT 5 2258C sounding (Fig. 5b); otherwise same as Fig. 6,except the scale of the abscissa is increased.

results show a 17% increase in cloud water and 22% in-crease in snow over CONTROL, with a slightly morenarrow precipitation imprint on the barrier (Fig. 15 andTable 3). The higher amounts of cloud water and snowresult in a trace amount of graupel. While the maximumcloud water mixing ratio (0.324 g kg21) nearly attains thatof the CONTROL simulation for the shallow cloud, thiswater cloud rapidly glaciates to produce a realistic time

evolution of the cloud. Not surprisingly, combining theSONV test with Graupel2, RONV, and BandR to re-createthe Final experiment nearly eliminates all graupel.

2) CTT 5 2608C

Increasing the depth of the cloud to either the 2408or 2608C level produces two orders of magnitude more


TABLE 3. As in Table 2, domain-maximum hydrometeor quantities from 2D sensitivity simulations of various cloud depths andtemperatures.

Cloud system qc (g kg21) qi (31023 g kg21) Ni (L21) qr (g kg21) qs (g kg21) qg (g kg21)

CONTROLCTT 5 2258CCTT 5 2608CSeeder–feeder

0.114 (0.240)0.109 (0.240)0.308 (0.383)

0.64 (3.5)34 (49)35 (46)

5.8 (40)1120 (1190)1110 (1190)

0.000 (0.000)0.000 (0.000)0.000 (0.004)

0.177 (0.182)0.205 (0.215)0.160 (0.186)

0.000 (0.029)0.000 (0.028)0.040 (0.049)

FletcherCTT 5 2608C 0.109 (0.241) 15 (16) 124 (145) 0.000 (0.000) 0.207 (0.219) 0.000 (0.028)

MeyersCTT 5 2608C 0.110 (0.226) 2.6 (10) 26 (104) 0.000 (0.000) 0.199 (0.206) 0.000 (0.026)

Graupel1CTT 5 2258CCTT 5 2608CSeeder–feeder

0.104 (0.226)0.100 (0.226)0.314 (0.383)

0.63 (3.5)34 (49)35 (46)

5.8 (40)1110 (1190)1130 (1190)

0.000 (0.000)0.000 (0.000)0.000 (0.004)

0.168 (0.173)0.195 (0.204)0.173 (0.182)

0.011 (0.012)0.012 (0.014)0.012 (0.021)

Graupel2CTT 5 2258CCTT 5 2608CSeeder–feeder

0.114 (0.225)0.109 (0.225)0.276 (0.370)

0.64 (3.5)34 (49)35 (46)

5.5 (40)1120 (1190)1130 (1190)

0.000 (0.000)0.000 (0.000)0.000 (0.017)

0.177 (0.181)0.205 (0.215)0.174 (0.185)

0.000 (0.000)0.000 (0.000)0.000 (0.002)

Version2CTT 5 2258C 0.102 (0.225) 1.4 (13) 13 (123) 0.000 (0.000) 0.167 (0.173) 0.011 (0.012)

SONCTT 5 2258CCTT 5 2608CSeeder–feeder

0.031 (0.240)0.028 (0.240)0.306 (0.383)

0.64 (3.5)34 (39)35 (46)

6.2 (41)1140 (1190)1130 (1190)

0.000 (0.000)0.000 (0.000)0.000 (0.004)

0.227 (0.265)0.269 (0.296)0.264 (0.265)

0.000 (0.031)0.000 (0.030)0.043 (0.055)

SONVCTT 5 2258CCTT 5 2608CSeeder–feeder

0.133 (0.324)0.119 (0.328)0.336 (0.400)

0.57 (3.4)33 (47)34 (44)

5.5 (39)1150 (1200)1110 (1190)

0.000 (0.000)0.000 (0.000)0.001 (0.008)

0.216 (0.222)0.258 (0.293)0.186 (0.219)

0.009 (0.040)0.006 (0.041)0.056 (0.058)

FinalCTT 5 2258CCTT 5 2608CSeeder–feeder

0.125 (0.288)0.113 (0.288)0.328 (0.429)

0.57 (3.4)33 (47)34 (44)

5.5 (39)1110 (1190)1110 (1190)

0.000 (0.000)0.000 (0.000)0.004 (0.006)

0.215 (0.221)0.257 (0.291)0.207 (0.213)

0.000 (0.000)0.000 (0.011)0.014 (0.044)

cloud ice (mass and number concentration), a very smalldecrease in cloud water (;4%), and somewhat largerincrease in snow mixing ratio (;16%) and snow pre-cipitation for all the tests in a nearly uniform manner(Table 3). An exception is the SON sensitivity experi-ment that produces about 11% less cloud water whenthe cloud increases depth from the 2258C to the 2608Clevel. Results of the SONV experiment (shown in Fig.16 and Table 3) also reveal an 11% decrease in cloudwater mixing ratio between the two cloud depths, butSONV maintains a low liquid-water cloud whereas SONnearly eliminates all traces of cloud water. The Finalexperiment produces the same sensitivity found in the2258C cloud simulation and nearly eliminates the smallamount of graupel.

3) SEEDER–FEEDER CLOUD SYSTEM

Using the same sounding as the CTT 5 2608C testand altering the moisture between 1 and 3 km by de-creasing the dewpoint temperature 38C below ice sat-uration produces a classic seeder–feeder-type cloud sys-tem. Between 0 and 2 h, the two clouds remain distinct,

with an entirely ice and snow cloud at high levels anda mixed-phase cloud similar to the original, relativelywarm, and mostly water cloud adjacent to the barrier.As time progresses though, the snow formed in the up-per cloud falls and reaches the lower cloud, causing themostly water cloud to glaciate.

The individual sensitivity experiments nearly dupli-cate the sensitivities shown in the last section, but theamount of cloud water in the shallow, low-level cloudadjacent to the barrier is greater than the CTT 5 2608Ctest, as this cloud initially grows independent of theupper ice/snow cloud. However, because the upper clouddoes begin to interact with the lower cloud after 2 h,the cloud water is depleted more rapidly in the seeder–feeder cloud than in the original CTT 5 2138C cloud.As expected, the seeder–feeder simulation looks nearlyidentical to the CTT 5 2608C simulation beyond 4 h.SONV and Final attain the highest cloud water mixingratio of all experiments, consistent with the other clouddepths and temperatures. In fact, the Final simulationproduces a minute amount of freezing drizzle just priorto glaciation by the upper cloud (Fig. 17).


FIG. 15. Vertical cross sections from experiment SONV at 3 h using CTT 5 2258C sounding (Fig. 5b); otherwise same as Fig. 14.

5. Conclusions

In summary, the bulk, mixed-phase microphysicalparameterization described in Reisner et al. (1998) wasrigorously tested using sensitivity experiments withidealized flow over a two-dimensional barrier. Im-provements to the bulk scheme were made in order toreproduce results of the bin microphysics model ofRasmussen et al. (2002). Key improvements are thefollowing:

• primary ice nucleation using Eq. (2), as in Cooper(1986), replaces the Fletcher (1962) curve;

• autoconversion using Eq. (6), as in Walko et al.(1995), replaces the Kessler (1969) scheme;

• a generalized gamma distribution for graupel usingEq. (8) replaces the exponential distribution; the as-sociated intercept parameter depends on mixing ratiousing Eq. (10) instead of remaining constant; and rim-ing growth of snow must exceed depositional growth


FIG. 16. Vertical cross sections from experiment SONV at 3 h using CTT 5 2608C sounding (Fig. 5c); otherwise same as Fig. 14.

of snow by a factor of 3 before rimed snow transfersinto the graupel category;

• the intercept parameter of the snow size distributiondepends on temperature using Eq. (13) replacing themixing ratio dependency;

• the intercept parameter for the rain size distributiondepends on rain mixing ratio, thereby simulating thefall velocity of drizzle drops as well as raindrops.

Tests of three ice initiation schemes producing anorder of magnitude different numbers of ice crystalsrevealed little sensitivity when simulating deep and coldcloud systems having cloud-top temperatures less than2258C but more sensitivity when simulating relativelywarm cloud systems (the most sensitivity was seen attemperatures between 08 and 2108C). In particular, theMeyers et al. (1992) scheme, which produced the most


FIG. 17. Vertical cross sections from experiment Final at 3 h using seeder–feeder sounding (Fig. 5d); otherwise same as Fig. 13, exceptthe scale of the abscissa is increased.

ice crystals, depleted the most cloud water as expected.For this reason and since Cooper (1986) directly mea-sured ice crystal concentrations, we chose to use theCooper curve to initiate ice by deposition nucleation forthe final microphysics code.

A series of tests using simplistic, commonly usedautoconversion methods to convert cloud water to therain category showed the anticipated result of increasing(decreasing) cloud water (drizzle) content with increas-

ing cloud droplet concentration (a proxy variable forCCN). One exception was the Kessler (1969) schemesince it converts cloud water to rain based on attaininga threshold cloud water content and contains no depen-dence on droplet concentration. In the end, we chose touse the Walko et al. (1995) adaptation of a Berry andReinhardt (1974) autoconversion scheme since it rep-resents the fundamental process of drizzle formation asa function of CCN. In cases where the CCN spectrum


is known, we advise modelers to set an appropriate valuefor Nc, otherwise we advise setting Nc 5 100 cm23 forgeneral use as a compromise between maritime and con-tinental CCN spectra. In the future, we intend to presetthe value of Nc based on surface characteristics (prox-imity to land/sea/ice/urban regions) and/or boundarylayer depth and advect this quantity to allow for inho-mogeneous CCN spectra. Also in the future, we plan totest a scheme proposed by Khairoutdinov and Kogan(2000) with more sophisticated treatment for convertingcloud water to rain.

In the next series of sensitivity experiments, two as-pects pertaining to the treatment of graupel were tested,and the balance of cloud water, snow, and graupel wasfound to be very sensitive. First, the assumed size dis-tribution was altered from an exponential distributionto a generalized gamma distribution. When an expo-nential distribution was used, the simulations producedmore graupel and did not compare as favorably to resultsby the bin model as when a gamma distribution wasused, primarily due to depositional growth by smallgraupel particles. Second, the conversion of rimed snowto graupel was altered to eliminate a dependence onmodel time step. The final code now consists of a com-bination of ideas by Murakami (1990) and Rutledge andHobbs (1984) whereby rimed snow does not convert tograupel until the riming growth rate is 3 times largerthan the depositional growth rate of snow. This require-ment produced results in closer agreement to the binmodel, but it still lacks a solid physical basis. In thefuture, we anticipate analyzing aircraft data from theImprovement of Microphysical Parameterizationsthrough Observational Verification Experiments (IM-PROVE) field projects (Stoelinga et al. 2004) to attempta more physical consideration of graupel initiation fromrimed snow.

Of the numerous sensitivity experiments, the seriestesting the intercept parameter of the snow size distri-bution caused the largest change in cloud water andresulting formation of freezing drizzle. When the inter-cept parameter was altered from a dependence on massto a dependence on temperature following observed databy Houze et al. (1979), the maximum cloud water mix-ing ratio increased from 0.18 to 0.39 g kg21 (using theoriginal RG sounding, while much less sensitivity wasfound in the CTT 5 2138C sounding). The increase ledto the formation of rain, essentially freezing drizzle, thatcorrelated well with the results of the bin model. How-ever, since the rain intercept parameter was set ratherlow for the extremely low rain precipitation rate, therain resulting from experiment SONV quickly fell tothe ground. Therefore, a final modification was to makethe rain distribution’s intercept parameter a function ofthe rain mixing ratio in order to simulate the lowerterminal velocities associated with drizzle. This type oftreatment is lacking in nearly all bulk microphysicalparameterizations. The results from this simulation gave

the best agreement with the bin model and is the rec-ommended configuration of the scheme.

Besides the set of 3D simulations of various winterstorm systems reported in the forthcoming companionpaper, we intend to simulate a number of the cases fromthe IMPROVE-1/2 observation campaigns. The IM-PROVE project collected an immense amount of in situand remote measurements of cloud microphysical datafor the primary purpose of improving numerical models’bulk representation of microphysics.

Acknowledgments. The authors wish to thank BillHall, Istvan Geresdi, John Brown, Stewart Cober, MattGarvert, Brain Colle, Mark Stoelinga, Guenther Zaengl,Marcia Politovich, and Gerhard Kramm for their valu-able contributions to this work. This research is in re-sponse to requirements and funding by the Federal Avi-ation Administration. The views expressed are those ofthe authors and do not necessarily represent the officialpolicy or position of the FAA.

APPENDIX

Corrections and Additions to Reisner et al. (1998)

Besides the major changes discussed in section 2, thefollowing list contains corrections and minor additionsto Reisner et al. (1998):

• Eq. (A.7): The term Picns should be positive, not neg-ative.

• Eq. (A.29): Ni should be divided by r (in numerator).• Eq. (A.36): A9 should state r (in numerator).2Ls

• Eqs. (A.36) and (A.62): is missing (also missing1/3S c

in Rutledge and Hobbs 1983); appears correctly herein Eq. (11).

• Eq. (A.42): ri should be rw (in numerator).• Eq. (A.48): s should be r s.U U U Ur

• Eq. (A.58): L f should be multiplied by r (in denom-inator).

• Eq. (A.61): r should be omitted.• Appendix B: m, dynamic viscosity of air, should have

units of kg m21 s21.• Eq. (A.6): Production of graupel by graupel accreting

rain, Pgacr, using Eq. (A.13) of Rutledge and Hobbs(1983) is added.

• Appendix B and Eq. (A.29): mso 5 4.4 3 10211 kgconflicts with a minimum radius for snow of 75 mmstated below Eq. (A.29). Using 75-mm minimum ra-dius of snow produces mso 5 1.77 3 10210 kg.

• Eqs. (A.36) and (A.57): Latent heat effects reduce theamount of depositional growth of snow or graupel.Previously the effect was ignored, but now it has beenincluded following Cotton and Anthes [1989, Eqs.(4)–(37)].

• Eq. (A.19): Formulas for computing saturation mixingratios of water and ice are replaced using the poly-nomial estimates of Flatau et al. (1992).

• Eqs. (A.43), (A.46), (A.59), and (A.61): In place of


constant efficiencies (1.0), efficiencies for collisionsbetween cloud water and snow, graupel, and rain uti-lize a Stokes number relationship.

• Previously, any rimed snow in the appropriate tem-perature range triggered ice multiplication. Now, fol-lowing Hobbs and Rangno (1998), graupel is requiredinstead of rimed snow.

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Explicit Forecasts of Winter Precipitation Using an ...u0758091/MPschemes/Thompson2004.pdfaircraft icing. To accomplish this goal, the bulk, mixed-phase microphysical parameterization