Continued Development of a Cloud Droplet Formation. Parameterization for Global Climate Models

Transcription

1 Contnued Develoment of a Cloud Drolet Formaton Parameterzaton for Global Clmate Models Chrstos Fountouks 1 and * Athanasos Nenes 1, 1 School of Chemcal and Bomolecular Engneerng School of Earth and Atmosherc Scences Georga Insttute of Technology Atlanta, GA 3033 * Corresondng author.

2 Abstract Ths study resents contnued develoment of the Nenes and Senfeld (003) cloud drolet actvaton arameterzaton. Frst, we exanded the formulaton to ) allow for a lognormal reresentaton of aerosol sze dstrbuton, and, ) nclude a sze-deendant mass transfer coeffcent for the growth of water drolets to accommodate the effect of sze (and otentally organc flms) on the drolet growth rate. The erformance of the new scheme s evaluated by comarng the arameterzed cloud drolet number concentraton wth that of a detaled numercal actvaton cloud arcel model. The resultng modfed arameterzaton robustly and closely tracks the arcel model smulatons, even for low values of the accommodaton coeffcent (average error 4.1±1.3%). The modfcatons to nclude the effect of accommodaton coeffcent do not ncrease the comutatonal cost but substantally mroves the arameterzaton erformance. Ths work offers a robust, comutatonally effcent and frst-rncles aroach for drectly lnkng comlex chemcal effects (e.g., surface tenson deresson, changes n water vaor accommodaton, solute contrbuton from artal solublty) on aerosol actvaton wthn a global clmate modelng framework.

3 1. Introducton Of the most uncertan of anthroogenc clmate forcngs s the effect of aerosols on clouds (IPCC, 001). Calculaton of cloud roertes from recursor aerosol n general crculaton models (GCMs) has often reled on emrcal (henomenologcal) correlatons (e.g. Boucher and Lohmann, 1995; Gultee and Isaac, 1996), whch are subject to sgnfcant uncertanty. To address ths lmtaton, frst-rncle aroaches (e.g., Ghan et al., 1997; Lohmann et al., 1999) have been roosed, whch requre settng u a cloud drolet number balance n each GCM grd cell; rocesses such as the actvaton of aerosol nto cloud drolets, evaoraton, and collson/coalescence affect drolet number concentraton. Exlctly resolvng each of these rocesses s far beyond anythng comutatonally feasble for GCMs, so, a rognostc GCM estmate of the aerosol ndrect effect must rely on arameterzatons of aerosol-cloud nteractons. The chemcal comlexty and heterogenety of global aerosol can have an mortant effect on actvaton and must be ncluded n aerosol-cloud nteracton studes (e.g., Nenes et al., 001; Rssman et al., 00; Lance et al., 004). Incororatng such comlexty nto extant arameterzatons s not a trval task. For examle, the resence of surface actve seces may facltate the actvaton of cloud condensaton nucle (CCN) nto cloud drolets (Facchn et al., 1999). The nfluence of surfactants deends on ther concentraton (e.g., Shulman et al., 1996; Charlson et al., 001) whch vares consderably wth CCN dry sze (e.g., Charlson et al., 001; Rssman et al., 004). Because of ths, an exlct relatonsh between the crtcal suersaturaton, s c (the suersaturaton requred to actvate a CCN nto cloud drolet) and the crtcal dameter, D c s not ossble (L et al., 1998; Rssman et al., 004), and becomes challengng to 3

4 ncororate nto mechanstc arameterzatons (Rssman et al., 004). Furthermore, the drolet growth rate may be nfluenced by the resence of organc flms (Fengold and Chuang, 00; Chuang, 003; Nenes et al., 00; Medna and Nenes, 004; Lance et al., 004) and slghtly soluble substances (Shantz et al., 003; Shulman et al., 1996) both of whch could have an mact on cloud drolet number (Nenes et al., 00). One of the most comrehensve arameterzatons develoed to date s by Nenes and Senfeld (003) (hereafter referred to as NS ). NS can treat nternally or externally mxed aerosol wth sze-varyng comoston and can nclude the deresson of surface tenson from the resence of surfactants, nsoluble seces and slghtly soluble seces wthn a framework n whch mnmal amount of emrcal nformaton s used (e.g., of all 00 cases tested by NS, only 0% requred a correlaton derved from a numercal arcel model). Deste the sgnfcant mrovement n drolet number redcton comared to other arameterzatons, NS may underestmate the drolet number concentraton, and cannot, as most other mechanstc arameterzatons, exlctly consder the otental delays n drolet growth from the resence of flm formng comounds. Furthermore, NS emloys a sectonal reresentaton of aerosol sze, whch may mose an unnecessary comutatonal burden for global clmate models usng lognormal aerosol sze dstrbutons. These shortcomngs are addressed n ths study. The research resented here extends the NS arameterzaton by ) rovdng a formulaton of the arameterzaton for a lognormal descrton of the aerosol sze dstrbuton, and, ) ncludng exlct sze-deendence of water vaor dffusvty. The latter overcomes the underredcton tendency of the orgnal formulaton, and, allows to 4

5 exlctly nclude the effect of organcs that may affect the condensatonal growth of CCN.. The NS arameterzaton NS s based on a generalzed sectonal reresentaton of aerosol sze and comoston (nternally or externally mxed), wth sze-varyng comoston. The NS methodology nvolves two stes: The frst nvolves calculaton of CCN concentraton as a functon of suersaturaton (the CCN sectrum ) usng the arorate form of Köhler theory (e.g., Senfeld and Pands, 1998). In the second ste, the CCN sectrum s ncluded wthn the dynamcal framework of an adabatc arcel wth a constant udraft velocty (or coolng rate), to comute the mum suersaturaton, s, acheved durng the cloud arcel ascent. Calculaton of s s based on a balance between water vaor avalablty from coolng and water vaor deleton from the condensatonal growth of the CCN. CCN wth s c s wll then be actvated nto drolets. NS ntroduce the concet of oulaton slttng to obtan an analytcal exresson for the water vaor condensaton rate; an ntegro-dfferental equaton s ths way reduced to an algebrac equaton whch can be numercally solved. Poulaton slttng entals dvson of the CCN nto two searate oulatons: those whch have a sze close to ther crtcal dameter (the dameter a CCN must grow to before exerencng unstable growth), and those that do not. As a result of ths aroach, knetc lmtatons on drolet growth are exlctly consdered, and, (comared wth other mechanstc arameterzatons), the relance on emrcal nformaton or correlatons s sgnfcantly reduced. A comarson of NS wth extant arameterzatons s done n Nenes and Senfeld (003) and wll not be reeated here. 5

6 3. NS formulaton for lognormal aerosol The sectonal reresentaton of aerosol sze and comoston gves the most general descrton of aerosol sze dstrbuton. However, f such a reresentaton s not avalable n a host model, t may be unnecessarly costly to mlement. Instead, a formulaton usng a lognormal descrton of the aerosol may be referred and s derved here. 3.1 Reresentaton of the CCN sectrum Usng the nomenclature of Nenes and Senfeld (003), sze dstrbutons, n d (D ), are taken to be of the sngle or multle lognormal form, n d ( D ) dn d ln D = m n N ln ( D = / Dg =, ) ex 1 π lnσ ln σ (1) where D s artcle dameter, N s the aerosol number concentraton, D g, s the geometrc mean dameter of mode, σ s the geometrc standard devaton for mode, and n m s the number of modes n the dstrbuton. If the chemcal comoston of an aerosol mode does not vary wth sze, then n d (D ) can be maed to suersaturaton sace and the crtcal suersaturaton dstrbuton, n s (s), can be obtaned as follows: where dn dn d ln D s n ( s) = = () ds d ln D ds dn d ln D n m = N ln ( D = / D g, ) ex 1 π lnσ ln σ (3) The crtcal suersaturaton of a artcle wth dameter D s 6

7 3 / A s = (4) B 3 D where 4σM A = w and ρ w B νρ M s w = (Senfeld and Pands, 1998), ρ s s the solute densty, ρ M w s M s the solute molecular weght, ν s the number of ons resultng from the dssocaton of one solute molecule. From Equaton (4) we obtan, d ln D ds = (5) 3s and D D g sg = s / 3 (6) Substtuton of Equatons (1), (3), (5) and (6) nto () yelds the crtcal suersaturaton dstrbuton, s n ( s) n m = / 3 N ln ( s = g, / s) ex 1 3s π lnσ ln σ (7) where s g, s the crtcal suersaturaton of a artcle wth dameter D g,. From Equaton (7), the CCN sectrum (concentraton of artcles wth s c s), F s (s), s gven by F s ( s / s) s n m = s N ln g, ( s) = n ( s) ds = erfc lnσ (8) If the mum arcel suersaturaton, s, s known, the actvated drolet number, N d, can be calculated from Equaton (8), as s N d = F ( s ) (9) 7

8 3. Calculatng s and drolet number concentraton The mum suersaturaton, s, s calculated from an equaton that exresses the water vaor balance (Nenes and Senfeld, 003): av πγρ w Gs I(0, s ) = 0 (10) where, gm wl gm a M a M wl a =, γ = + (11) s c RT RT M c RT w and V s the cloud arcel udraft velocty, ρ w s the densty of water, T s the arcel temerature, M w s the molecular weght of water, L s the latent heat of condensaton of water, s s the water vaor ressure, c s the heat caacty of ar, s the ambent ressure and R s the unversal gas constant. G n Equaton (10) s gven by G = ρ RT * ' D M v w v w 1 Lρ w[( LM + k w ' a / RT ) 1] T (1) where * v s the saturaton vaor ressure of water, D v s the dffusvty of water vaor n ar and k a s the thermal conductvty of ar. The quantty I(0,s ) n Equaton (1) s defned as, S G 1/ I(0, s ) = [ D ( τ ) + ( s s( τ ) )] n( s) ds (13) av 0 D (τ) denotes the sze of a CCN when t s exosed to s = s c ; τ s the tme needed (above cloud base) to develo the suersaturaton needed for ts actvaton. A common assumton (e.g., used by Ghan et al., 1993) s that CCN nstantaneously actvate,.e., D (τ) s equal to the CCN crtcal dameter, D c =8M w σ/3rτρ w s, (where σ s the drolet 8

9 surface tenson at the ont of actvaton). Evaluaton of I(0,s ) and substtuton nto Equaton (10) results n an algebrac equaton that can be solved for s. 3.3 Calculaton of Integral I(0,s ) We can aroxmate I(0,s ) by emloyng the oulaton slttng concet of NS: I( 0, s ) = I1(0, s art ) + I ( s art, s ) (14) where s art s the arttonng crtcal suersaturaton (Nenes and Senfeld, 003), that defnes the boundary between the CCN oulatons. In Equaton (14), I 1 (0,s art ) reresents the growth of CCN for whch D ( τ ) << G t τ sdt, or those that exerence sgnfcant growth beyond the ont where they are exosed to s > s c. I (s art,s ) exresses the growth of CCN that do not strctly actvate, or do not exerence sgnfcant growth beyond ther crtcal dameter for whch we assume D ( τ ) >> G t τ sdt. Wth these smlfcatons, I 1 (0, s art ) and I (s art, s ) (usng Equaton 8) become, I (0, s 1 art ) = S art 0 G av 1/ ( s s ) 1/ 3s N ln ex π lnσ ln σ [( s s) ] / 3 g, / ds (15) I ( s art where s g, s gven by, s ) = S S art A 3s 3s N ln ex π lnσ ln σ [( s s) ] / 3 g, / ds (16) s g, 3 4A ρ wm = (17) 7νρ M D s w s 3, g M s s the solute molecular weght, ν s the effectve Van t Hoff factor and ρ s s the densty of the solute and A=4M w σ/rτρ w. Equaton (17) assumes that the CCN are comletely 9

10 soluble; arorate modfcatons should be used f the CCN contan a slghtly soluble (Laaksonen et al., 1998), nsoluble (e.g., Senfeld and Pands, 1998) or surfactant fracton (Rssman et al., 004). The ntegraton of Equatons (15) and (16) can be done wth the hel of the ( ) ln s g, / s transformaton coeffcent u =, and by aroxmatng 3 lnσ s 1 g, Equaton (15) wth 1, s s, g 1 s 1/ n I (0, s 1 art N ) = G av 1/ s erfc u ( ) art 1 s s g, 9ln σ ex erfc u art 3lnσ + (18) I AN 9ln σ 3lnσ ( s art, s ) = ex erf u art erf u 3s g, 8 3lnσ (19) where u art ( s / s ) ln g, art =, 3 lnσ ( s g / s ) ln, u = (0) 3 lnσ It should be noted that the ntegrals n equatons (18) through (0) bears some smlarty wth the formulatons of Abdul-Razzak et al. (1998); ths smlarty arses from the usage of lognormal dstrbutons. However, our formulatons are dstnctly dfferent, as, ) they arse from the alcaton of oulaton slttng and thus use the ntegrals n a dstnct manner, and, ) lack the ost-ntegraton modfcatons aled by Abdul-Razzak et al. (1998). 3.4 Usng the arameterzaton The rocedure for usng the modal formulaton s smlar to the sectonal aerosol formulaton (Nenes and Senfeld, 003). Fgure 1 dslays the soluton algorthm for the 10

11 lognormal aerosol formulaton.. s art s calculated usng the descrmnant crteron, or the sgn of the quantty = s 4 16A αv 9G. exresses the extent of knetc lmtatons throughout the drolet oulaton; = 0 marks a boundary between two drolet growth regmes, one where most CCN are free from knetc lmtatons ( > 0) and one n whch knetc lmtatons are domnant ( < 0). When > 0, s art s gven by an analytcal exresson as s art 1 16A av = s Gs 1/ 1/ ; when < 0, s art s determned by an emrcal correlaton, s art = s 10 mn 3 7 A s 0.384,1.0. After determnng s art, Equatons (18) and (19) are substtuted nto Equaton (10), and solved for s usng the bsecton method. The number of drolets s comuted from Equaton (9). An evaluaton of the modal formulaton s rovded n secton Includng sze-deendant growth knetcs nto NS In develong the sectonal and modal formulatons of NS, we have assumed that the dffusvty of water vaor onto the drolets, D v, s ndeendent of ther sze. Although a good aroxmaton for water drolets larger than 10µm (Senfeld and Pands, 1998), t substantally decreases for smaller and otentally multcomonent dros (Senfeld and Pands, 1998). As a result, water vaor condensaton n the ntal stages of cloud formaton s overestmated and the stronger cometton for water vaor bases the arcel suersaturaton low. Ths results n an underestmaton of cloud drolet concentraton, whch worsens f the resence of flm-formng comounds further medes the growth rate. It s mortant to note that other mechanstc arameterzatons (e.g., Ghan et al., 11

12 1993; Abdul-Razzak et al., 1998; Rssman et al., 004) also neglect sze-deendence of the dffusvty coeffcent and also tend to underestmate N d (Nenes and Senfeld, 003). Sze effects on water vaor dffusvty can be ntroduced by the followng relatonsh (Fukuta and Walter, 1970), D ' v Dv = (1) Dv πm w 1+ a D RT c where a c s the accommodaton coeffcent, a fundamental arameter that exresses the robablty of a water vaor molecule remanng n the drolet hase uon collson (Senfeld and Pands, 1998), a c number of molecules enterng the lqud hase = number of molecular collsons wth the drolet surface For ure water, a c ranges between 0.1 and 0.3 (L et al., 001) but an aged atmosherc drolet tends to have a lower accommodaton coeffcent, tycally between 0.04 and 0.06 (Pruacher and Klett, 000; Shaw and Lamb, 1999; Conant et al., 004). The resence of organc flms can further decrease the accommodaton coeffcent; although stll controversal, there are ndcatons that such comounds exst n the atmoshere (e.g., Chuang, 003). For tycal drolet szes, D v deends strongly on a c (Equaton 1). For a value of a c close to unty, the dfference between D v and D v s less than 5% for artcles larger than 1 µm and less than 5% for drolet dameters larger than 5µm. However, D v becomes sgnfcantly lower than D v f a c <1 (Senfeld and Pands, 1998). Therefore, ntroducng the deendence of D v on sze and a c s mortant to elmnate bases n drolet actvaton. 1

13 The thermal conductvty of ar, k a (Equaton 1), also has a deendence on sze, whch s rather weak for the drolet szes of nterest. Smulatons (not shown here) confrm that ntroducng a sze-deendant thermal conductvty s not necessary. 4.1 Imlementng sze-deendant D v nto NS Equaton (1) could be substtuted nto Equaton (1) n order to account for the szedeendence on D v. However, n such a case, Equaton (13) becomes mractcal n ts mlementaton. An alternate aroach s needed. Two aroaches can be used to ntroduce correctons to D v : ) usng an average value for the dffusvty, D v,ave, for those CCN that actvate, and, ) calculatng ' D v for each CCN secton. We choose to adot the frst aroach because t can be used n both sectonal and modal formulatons of the NS arameterzaton (whle the second aroach cannot), and, the second aroach adds uon the comutatonal burden. A secton-secfc D v method has also been develoed (Mng et al., n revew). For smlcty, we adot a szeaveraged dffuson coeffcent, D v,ave, D, bg ' DvdD D, low Dv, ave = D (), bg dd where D,bg and D,low are the uer and lower sze bounds used for calculatng the average. Substtutng Equaton (1) nto () and ntegratng yelds: D D + B v, bg D ( ) v, ave = D, bg D, low B ln (3) D D, bg, low D, low + B D, low 13

14 where B = D a c v π M RT w 1/. In dervng Equaton (3), we assume that a c remans constant throughout the actvaton rocess. If D,bg and D,low and a c are known, Equaton (3) can be used to calculate D v,ave, and substtuted nto the G term (Equaton 13) of NS. a c s usually constraned from observatons (e.g., Chuang et al., 003; Conant et al., 004). What remans s the determnaton of the D,bg and D,low. 4. Determnaton of D,bg and D,low We have evaluated two methods for calculatng D,bg and D,low : Emrcal determnaton of D,bg and D,low. A set of numercal arcel model smulatons were used to determne D,bg and D,low that, after substtuton nto Equaton (3) (and subsequently nto NS), would gve a arameterzed N d n agreement wth the numercal arcel redctons. Publshed lterature suggests values for a c as low as 10-5 (e.g., Chuang, 003) durng the ntal stages of artcle growth; f true, such CCN would exerence a slow growth hase (wth a very low a c ) followed by a fast growth hase wth much hgher a c. Smulatons wth the Nenes et al. (1998) arcel model (not shown) suggests that CCN wth a constant a c ~ 10-3 exerences roughly the same growth as a flm-breakng CCN wth a slow-growth hase a c ~ 10-5 and a rad-growth hase a c ~ Therefore, a c s assumed to vary between and 1.0. D,bg and D,low were determned for the wde set of condtons and a c lsted n Table 1. Otmzaton crtera were the mnmzaton of error and standard devaton between arameterzed and arcel model N d. The otmum D,bg was found to be 5 µm, whle the 14

15 otmum D,low was found to vary wth a c ; a correlaton that relates the otmum D,low and a c was then derved, where D,low s gven n µm { a,5.0} D, low = mn c (4) From Equaton (4), a c ncreases wth decreasng D,low. Ths s exected; for large a c, small CCN exerence less knetc lmtatons, and therefore can actvate nto drolets (Nenes et al., 001). As a result, a wder range of CCN szes need to be consdered n the calculaton of D v,ave, so D,low should decrease. When a c decreases, only the largest of CCN (wth low s c ) have enough tme to actvate; hence a narrow range of CCN szes can contrbute to drolet number concentraton, thus ncreasng D,low. Theoretcal determnaton of D,bg and D,low. D,bg and D,low may also be determned usng theoretcal arguments. One can be derved from the equaton that descrbes the dffusonal growth of a drolet from tme τ (when the arcel suersaturaton s equal to the CCN crtcal suersaturaton, s c ), to the tme of mum suersaturaton, t (Nenes and Senfeld, 003), D = D t ( τ ) + G s dt (5) τ D (τ), lke n Equaton (13), s assumed to be equal to the crtcal dameter D c =8M w σ/3rτρ w s c, whle the suersaturaton ntegral n Equaton (5) can be evaluated usng the lower bound of Twomey (1959): t τ s dt 1 [ s av s( τ ) ] (6) 15

16 where s(τ) s the arcel suersaturaton at tme τ. Substtutng Equaton (6) nto (5), we eventually obtan D [ s s ] A G = + c,mn 3s, (7) c,mn av where s c,mn s the crtcal suersaturaton of the largest CCN that exceeds ts crtcal dameter. Equaton (7) can be used as an estmate for the uer lmt D,bg. The lower lmt, D,low, can be estmated by the smallest CCN that can theoretcally actvate: A = (8) 3s D, low It s notable that n ths method, D,bg deends on a c as oosed to the emrcal method where D,low deends on a c. Assessment of D,bg and D,low calculaton methods Both methods of calculatng D v,ave were ntroduced nto the NS arameterzaton; N d redctons were then comared wth arcel model smulatons. The comarsons were done for the actvaton of sngle mode lognormal aerosol wth D,g rangng between 0.05 to 0.5µm, σ between 1.1 to.5, and for udraft condtons rangng between V = 0.1 to 3.0 ms -1. Ambent P and T were set to 800 mbar and 83 K, resectvely. Fgure shows the arameterzed drolet number concentraton (usng the two dfferent methods of estmatng D v,ave ) aganst the arcel model smulatons. The 1:1 lne reresents a erfect agreement between the arameterzaton and the arcel model. Results are resented for two values of the accommodaton coeffcent (a c = 0.04, a c = 0.1). An average error of 6% (±1%) was observed for the theoretcal method, whch slghtly undererforms aganst 16

17 the emrcal method (average error=%, ±0.9%). We thus choose to use the emrcal method untl an alternate theoretcal crteron s derved. 5. Evaluaton of modfed NS arameterzaton 5.1 Method The sectonal formulaton of the arameterzaton, as well as the dffusvty modfcaton were assessed for ther ablty to reroduce smulatons from the adabatc cloud arcel model of Nenes et al., (001) over a large range of aerosol sze dstrbutons and udraft veloctes. The detaled numercal arcel model used n ths study has been wdely used and recently evaluated wth n-stu data (Conant et al., 004). Table shows all the smulaton sets used for the evaluaton of the arameterzaton. Both sngle and tr-modal aerosols were consdered, for number concentratons and mode dameters characterstc of troosherc aerosol. For trmodal aerosol, we have selected four of the Whtby (1978) trmodal reresentatons, namely the marne, clean contnental, average background, and urban aerosol reresentatons (Table 3). The udraft veloctes used n our evaluaton ranges between 0.1 and 3.0 m s -1 ; together wth the wde range of aerosol number concentratons consdered, s vares from 0.01% to over 1%, coverng the clmatcally mortant range of cloud drolet formaton condtons. 5. Evaluaton of the modal formulaton Evaluaton of the modal formulaton s done by comarng ts redctons of N d wth those of the sectonal arameterzaton. We consder the actvaton of lognormal aerosol, so both formulatons should gve the same drolet number (rovded the dscretzaton error of the sectonal formulaton s nsgnfcant). Ths s shown n Fgure 3, whch dects the arameterzed N d, usng the sectonal vs. the modal formulaton. Cases 17

18 consdered were for a sngle mode lognormal aerosol wth D,g rangng between 0.05 to 0.75µm, σ rangng between 1.1 to.5, and for udraft condtons rangng between V = 0.1 to 3.0 ms -1. The sectonal formulaton used 00 sectons for dscretzng the lognormal dstrbuton. Regardless of actvaton condtons, the arameterzaton wth modal formulaton s as robust as the arameterzaton wth the sectonal reresentaton (average error 1%, standard devaton 0.3%). Therefore, for lognormal aerosol, both formulatons can be nterchanged wthout any loss n accuracy. The advantage of usng the lognormal dstrbuton s that t s smler to mlement and, more than two orders of magntute faster on a Pentum PC, than the sectonal formulaton (wth 00 sectons). 5.3 Evaluaton of arameterzaton wth modfed dffusvty Fgure 4 dslays the drolet number concentraton as redcted by NS and by the (Nenes et al., (001)) arcel model for the aerosol condtons of Table 3. The arameterzed drolet number concentratons closely follow the arcel model smulatons; however, there s a tendency for underestmaton, whch s not sgnfcant for a c =1.0, but worsens as a c decreases (Fgure 5). Ths roblem s resolved by substtutng D v n the G term of Equaton (17) wth the modfed dffusvty, D v,ave. Fgures 6 and 7 dslay the drolet number concentraton from the modfed arameterzaton aganst the arcel model redctons for the sngle mode (Fgure 6) and trmodal (Fgure 7) aerosol of Table. Results are resented for a c = 0.04 and a c = It s clear that the modfed arameterzaton catures the arcel model smulatons much better than the orgnal NS, even for low values of a c. The overestmaton (average error 4.1±1.3%) observed n Fgure 7 for marne aerosol s caused by the fact that the descrmnant for these aerosol s close to zero, at the transton between the knetcally lmted ( >0) and knetcally free 18

19 ( <0) regmes. Under such condtons, the exresson for calculatng s art s least accurate. Nevertheless, the modfed dffusvty remarkably mroves the erformance of the arameterzaton, even for such challengng aerosol as those wth flm formng comounds. It should also be noted that the modfcatons ose neglgble comutatonal burden, as oosed to emloyng a more exensve algorthm (e.g., a secton-secfc D v ). 6. Summary The aerosol actvaton arameterzaton develoed by Nenes and Senfeld (003) was arorately modfed to ) allow for a lognormal reresentaton of aerosol sze dstrbuton, and, ) nclude a sze-deendant mass transfer coeffcent for the growth of water drolets (whch exlctly ncludes the accommodaton coeffcent). To address ths, an average value of the water vaor dffusvty s ntroduced n the arameterzaton. Two methods were exlored for determnng the uer and lower bound of the drolet dameter needed for calculatng the average water vaor dffusvty. The most accurate emloys an emrcal correlaton derved from numercal arcel smulaton. Predctons of the modfed NS arameterzaton are comared aganst detaled cloud arcel actvaton model smulatons for a wde varety of aerosol actvaton condtons. The modfed NS arameterzaton closely tracks the arcel model smulatons, even for low values of the accommodaton coeffcent, wthout any ncrease n comutatonal cost. Ths work offers a much needed rgorous and comutatonally nexensve framework for drectly lnkng comlex chemcal effects on aerosol actvaton n global clmate models. 19

20 Acknowledgements Ths research was suorted by a NASA EOS-IDS, a NASA New Investgator Award, and by Georga Insttute of Technology faculty startu funds. 0

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