Total Deformation and its Role in Heavy Precipitation Events Associated with Deformation-Dominant Flow Patterns

Transcription

1 ADVANCES IN ATMOSPHERIC SCIENCES VOL. 25 NO Tal Defmain and is Rle in Heavy Pecipiain Evens Assciaed wih Defmain-Dminan Flw Paens GAO Shuing 1 (påë) YANG Shuai 12 (fl R) XUE Ming 3 (Å ) and CUI Chunguang 4 (ws1) 1 Labay f Clud-Pecipiain Physics and Sevee Sms (LACS) Insiue f Amspheic Physics Chinese Academy f Sciences Beijing Gaduae Univesiy f Chinese Academy f Sciences Beijing Schl f Meelgy and Cene f Analysis and Pedicin f Sms Univesiy f Oklahma Nman Oklahma USA 4 Insiue f Heavy Rain China Meelgical Adminisain (CMA) Wuhan (Received 29 Augus 2006; evised 23 Januay 2007) ABSTRACT In his pape i is elucidaed ha he al defmain (TD) defined as he squae f he sum f squaed seching defmain and squaed sheaing defmain is an invaian independen f he cdinae sysem used. An idealized flw field is hen cnsuced demnsae he cnfluence effec f a nn-divegen and iainal defmain field n misue ansp. T exple he chaaceisics and le f TD ne heavy ainfall case ha ccued in he middle and lwe eaches f he Yangze Rive (MRYR) ve China assciaed wih a fn wih shea line is analyzed using he Weahe Reseach and Fecasing (WRF) mdel upu daa. I is fund ha igh befe he ccuence f pecipiain he effec f he cnfluence induced by defmain n misue ansp pvides a favable cndiin f pecipiain. Duing he pecipiain bh lcain and ienain f he zne f lage TD cincide wih he cnfluen shea line. The ainbands ae nealy paallel wih and lcaed lighly he suh f he znes f lage TD and he cnfluen shea line. The TD in he lwe psphee inceases in value as pecipiain pesiss. When TD appaches is maximal value he nex 6-hu pecipiain eaches is peak cespndingly. A endency equain f TD is deived. The analysis f linea celain and RMS diffeence beween individual ems in he al defmain equain and he sum f he ems shws ha he pessue gadien plays a maj le in deemining he lcal change f al defmain. Key wds: defmain cnfluence pecipiain equain DOI: /s y 1. Inducin Amng he basic vaiables ha descibe he amsphee namely empeaue pessue humidiy and wind velciy nly wind velciy is a vec. A he messcale whee he chaaceisic scale is less han he Rssby adius f defmain i is knwn ha he wind field deemines he mass field hugh gesphic adjusmen (Rssby ; Yeh 1957; Yeh and Li 1982; Zeng 1963abc). A he even smalle cnvecive sm scale he impance f wind field is even me eviden. I is knwn ha he envinmenal wind pfile has a sng cnl n he sm ypes (Weisman and Klemp 1982) and sm dynamics (e.g. Wale and Thpe 1979). The envinmenal heliciy defined as he d pduc f he envinmenal velciy and viciy vecs plays an impan le in he sm lngeviy and he - Cespnding auh: GAO Shuing gs@lasg.iap.ac.cn

2 12 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 ain chaaceisics f hundesms (e.g. Davies- Jnes 1984; Eling 1985; Lilly 1986ab; Degemeie e al. 1993; Lu and Ga 2003). The impance f he wind field has been ecgnized by many eseaches. Peessen (1956) shwed ha a 2D linea wind field culd be expessed as a cmbinain f anslain divegence defmain and viciy cmpnens. Ohe eseaches including Wiin-Nielsen (1973) and Nbuy (2002) have als discussed he abve ppeies f wind fields in sme deail. Tadiinally he divegence and viciy ae w quaniies ha have eceived ms aenin. The pgnsic equains f viciy and divegence deived fm he equains f min have been used exensively in he lieaue as well as in exbks f sudying dynamics f fluid flws and vaius amspheic phenmena (Wu and Tan 1989). The defmain has in cmpaisn eceived much less aenin excep in sudies f fngenesis. F ceain ypes f pecipiain sysems such as hse assciaed wih he easen China mei-yu fn he lagescale flw paen fen exhibis a dminan defmain paen a he lw levels while he divegence and viciy ae smeimes f smalle magniudes. F hese ypes f sysems i is impan undesand he le f defmain in he iggeing and mainenance f he pecipiain and gain insigh n he ime evluin f he defmain field. In secin 2 f his pape an idealized flw mdel is fis cnsuced demnsae he cnfluence effec f nn-divegen and iainal defmain n misue. In secin 3 i is shwn ha he al defmain is an invaian independen f he cdinae sysem used. A pgnsic equain f he al hiznal defmain is deived. In secin 4 ne heavy ainfall case assciaed wih a mei-yu fn in an alms eas-wes ienain ve easen China is numeically simulaed and analyzed. In secin 5 he defmain field and is le assciaed wih he heavy ainfall case ae diagnsed and analyzed using he Weahe Reseach and Fecasing (WRF) mdel upu daa. In secin 6 he elaive cnibuins al defmain f he ems in he al defmain equain ae analyzed f he ainfall case. Cnclusins ae given in secin An idealized flw field mdel A pue 2D defmain flw is nn-divegen and iainal. F his easn i by iself des n pduce veical lifing a he lw levels ceae cnvegence hugh he Ekman pumping effec. Bu defmain is impan in fngenesis. I inceases he hiznal empeaue gadien and heefe bacliniciy hugh advecin which als leads fngenesis. In addiin he defmain flw can play an impan le in advecing misue in a pecipiain egin. T illusae he le f a defmain-dminaed flw field ha is ypical f he flw paen assciaed wih he mei-yu fn an idealized flw field f he ypical saddle paen is cnsuced. Ou idealized flw field is cnsuced hugh a linea cmbinain f w funcins. Funcin 1 defines a vex (Luhe Whie pesnal cmmunicain 2006) whee Φ n (R R 0 )= V T (R) =V 0 ( Φ1 +Φ 2 2 2nR0 2n 1 R (2n 1)R 2n 0 ) + R2n n = This vex cnains w fee paamees n and R 0 whee n is an inege R 0 is a chaaceisic adius and R he adius fm he vex cene. This vex lks like a smhed vesin f he Rankine cmbined vex (Haasi and Lis 2005); in paicula i avids he singulaiy pin assciaed wih he Rankine cmbined vex a R = R 0 (Fig. 1). Ne ha hee V T is he angenial wind speed wih he vex V 0 he maximum value f V T a adius R 0 andr is he adius f he cnsuced high and lw ciculains. And funcin 2 specifies a pue defmain flw: { u = bx v = by whee b is a psiive cnsan. A linea cmbinain V 0 y i c l e v l i a n e g n a T R 0 Radial disance fm vex cene Fig. 1. Tangenial velciy deived fm he adiinal Rankine cmbined vex (slid line) and vex (dashed line) which lks like a smhed vesin f he Rankine cmbined vex.

3 NO. 1 GAO ET AL. 13 in p id G ake x = y = 60 km). In Eq. (1) α is a weigh deemined by 0 R ij >R 0 α = R ij 25 x R 1 <R ij R <R ij R 1 whee x is he gid spacing. R 0 = 1200 km R 1 = 900 km. Gid pin Fig. 2. Cnsuced idealized flw field wih w highs and w lws. f hem gives ( u v ) ( ) sin θ =αk(m)v T (R) cs θ ( ) bx +(1 α) (1) by whee K(m) = { 1 when m =1 3 1 when m =2 4 (b) whee m = deneheN. m quadan; an θ = y Y 0m x X 0m sin θ = y Y 0m R cs θ = x X 0m R y =(j 51) y x =(i 51) x whee he al gid pins ae R = R(x y) = (x X 0m ) 2 +(y Y 0m ) 2. (c) (X 0m Y 0m )= (X 01 Y 01 ) = (25 x 25 y) when m =1 (X 02 Y 02 )=( 25 x 25 y) when m =2 (X 03 Y 03 )=( 25 x 25 y) when m =3 (X 04 Y 04 ) = (25 x 25 y) when m =4 ae he fu cenes f cnsuced high and lw ciculains. The defmain cefficien b = The cene f he flw egin is a he igin f he cdinae sysem. The velciy is calculaed n a gid a a gid spacing f 60 km (i.e. we Fig. 3. Defmain (b) divegence and (c) viciy fields (10 5 s 1 ) f he idealized flw shwn in Fig. 1.

4 14 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 (b) in p id G (c) (d) in p id G Gid pin Gid pin Fig. 4. A 2D elaive humidiy field subjecing he advecin by he idealized defmain flw field a 0 hu (b) 12 hus (c) 24 hus and (d) 36 hus. The cnu inevals ae 0.1 and all cnus a ime ze have an eas-wes ienain. This idealized flw (Fig. 2) cnsiss f w highs (anicyclnes) and w lws (cyclnes) and an easwes cnfluence zne exiss beween he high-lw cuples he nh and he lw-high cuples he suh. In he cnfluence zne bh viciy and divegence ae acually small ze while defmain is lage (Fig. 3). The value f defmain is in he middle pa f he dmain (egin wih ange shading in Fig. 3a) while bh divegence and viciy ae ze in his egin (Figs. 3b and 3c). Ne ha he w ings f blue and ange in he divegence field ae he esuls f he uncain es in he finie diffeence calculain and he discninuiy beween he egins whee he flws ae defined by diffeen funcins. The same easn leads he w ings in viciy and defmain fields. F ypical mei-yu fnal sysems he hiznal empeaue gadien is usually weak and heefe he classical fngensis pcesses assciaed wih defmain flw ae less impan. An unifm backgund penial empeaue and an iniial backgund elaive misue field (ned as q) ae assumed as funcins f y. And q is specified as q = (y 1) whee y is he gid index in he y diecin. Subjec he advecin f his flw he islines f elaive humidiy afe 6 hus ae cncenaed disincly wads he cnfluence egin f he saddle field while he islines afe 12 hus becme even dense (Fig. 4b). Afe 36 hus he islines becme much me cncenaed (Fig. 4d) indicaing a buildup f sng misue gadien alng he cnfluence zne. In he case f hee dimensins veical min alng he cnfluence zne will cause he upwad ansp f he misue bugh in by he hiznal defmain flw. Ofen he misue gadien zne is n paallel he cnfluence zne. An example f such is when he iniial elaive humidiy (q) is specified by q = (x y) whee x is he gid index in he x diecin. Figue 5 shws he evluin f his humidiy field subjec he advecin f he same idealized flw. The cnus f elaive humidiy als becme me cncenaed as in he pevius case; meve he ienains f hese cnus becme me and me paallel he cnfluence zne (Fig. 5). Evenually he zne f sng misue gadien becmes paallel he cnfluence zne. In he eal amsphee his ype f saddle flw

5 NO. 1 GAO ET AL. 15 (b) in p id G (c) (d) in p id G Gid pin Gid pin Fig. 5. A 2D elaive humidiy field subjecing he advecin by he idealized defmain flw field a 0 hu (b) 12 hus (c) afe 24 hus and (d) 36 hus. The cnu inevals ae 0.1 and all cnus a ime ze have a suhwes-nheas ienain. is fen fund. Meve i is fen assciaed wih pecipiain. Since he viciy and divegence ae small in such a flw while he defmain is lage even in he absence f a disinc empeaue gadien heavy pecipiain can esul fm he cnfluence assciaed wih he defmain hugh he fcusing effec n misue. The ichness f misue in he cnfluence zne pvides a favable cndiin f mis cnvecin alhugh he acual iggeing f cnvecin is usually pvided by smehing else such as uppe-level lifing by a sh-wave ugh weak bu sill pesen lw-level cnvegence (Hxi e al. 1978; Maddx e al. 1978; Caacena e al. 1979; Maddx e al. 1980ab). These will be discussed in deail f w eal pecipiain cases in secins 4 and Tal defmain and is pedicin equain 3.1 Tal defmain In Peessen (1956) i is shwn ha a wdimensinal velciy field (u v) can be appximaed by a uncaed Tayl seies u = u 0 +(D + F )x/2 ( q)y/2 v = v 0 +( + q)x/2+(d F )y/2 (2a) (2b) whee u 0 and v 0 ae velciy cmpnens a he cdinae igin and ( u D = x + v ) ( v q = y x u ) y ( u F = x v ) ( v and = y x + u ) y which ae especively he divegence viciy seching defmain and sheaing defmain. The equain shws ha a 2D flw can be lcally expessed as a linea cmbinain f he abve fu quaniies. Tal defmain is usually defined as E = F (Peessen 1956; Keyse e al ; Nbuy 2002). We shw in he fllwing ha he magniude f al defmain is independen f he cdinae used he same as he divegence and viciy.

6 16 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 We ae he (x y) cdinae sysem aniclckwise by angle θ in a new cdinae sysem (x y ). The cdinae ansfm elains ae and x = x cs θ + y sin θ and y = y cs θ x sin θ. Theefe i can be shwn ha F = u x v y = ( ) ( ) u x v v y cs 2θ x + u y sin 2θ = F cs(2θ) sin(2θ) (3a) = v x + u y = ( ) ( ) u x v v y sin 2θ + x + u y cs 2θ = F sin(2θ)+ cs(2θ) (3b) Theefe E 2 = F = F whee pime denes he quaniy in he aed cdinae. This says ha he magniude f al defmain is independen f he cdinae sysem. F his easn he al defmain is a me meaningful quaniy analyze han he individual cmpnens f he defmain and i will be he pimay quaniy we examine in his pape. In he nex subsecin we will deive he al defmain equain. 3.2 Tal defmain equain The hiznal equains f min in he p- cdinae ae u + u u x + v u y + ω u p fv = g z x + F x v + u v x + v v y + ω v p + fu = g z y + F y. By he peain f [ F F x (4a) ] y (4b) + [ F y (4a) + ] x (4b) (4a) (4b) we bain he equain f al defmain E E = em1+em2+em3+em4+em5+em6 (5a) whee em1 = V E em2 = E h V em3 = em4 = F E uf + v E f y (5b) (5c) (5d) ( ) g 2 z x 2 g 2 z y 2 ( ) 2g 2 z E x y (5e) em5 = F ( ω u E x p ω ) v + y p ( ω u E y p + ω ) v (5f) x p em6 = F E ( Fx x F ) y + ( Fx y E y + F ) y. x (5g) Hee V is he 3D wind vec and h V is he hiznal divegence and ω = dp/d is he veical velciy in pessue cdinae. Fm Eq. (5a) we can see ha he lcal change f al defmain is caused by advecin (em1) hiznal divegence (em2) he em elaed β-effec (em3) he pessue gadien em (em4) he veical velciy cnibuins (em5) and he em elaed ficinal fce and/ ubulence mixing (em6). 3.3 The physical meaning f each em F he cnvenience f discussin we can chse u cdinae s ha he sheaing defmain is ze. We cnside a pue seching defmain field defined by u = αx and v = αy. The flw descibed by his se f equains in he egin clse he cdinae igin is he ypical flw paen assciaed wih a w-high and w-lw aangemen (see Fig. 2). F his flw u/ x > 0and v/ y < 0 and in he fis quadan u>0andv<0. Tem1 in Eq. (5a) epesens he advecin f al defmain. The sign f his em ( V E) is deemined by he angle beween he velciy vec and he gadien f al defmain. When he angle is less han 90 he pjecin f V n E is psiive s em1 is psiive; hewise he em is negaive.

7 NO. 1 GAO ET AL. 17 Tem2 epesens he change in al defmain due hiznal divegence. F a pue defmain field V h V = 0 s his em is ze. Tem3 is a em ha is elaed he β-effec he lngiudinal gadien f Cilis paamee f. Is sign is deemined by he ineacin beween u and f/ y unde he new cdinae (which makes =0) sysem. Tem4 epesens he effec f pessue fce. Unde he assumpin f a pue seching defmain flw paen i can be ewien as ( ) g 2 z x 2 g 2 z y 2. Is cnibuin he al defmain is deemined by he cmbinain f he shea in he x and y diecins f pessue fce (x and y epesen he new cdinae axis unde which he shea defmain is ze.). Tem5 cmbines he hiznal shea f veical velciy wih he veical shea f hiznal velciy in he new cdinae sysem. Unde he abve assumpin ( = 0) em5 can be ewien as ω u x p ω v y p. Is cnibuin he change f al defmain is deemined by he ineacin f signs f he cmpnens. 4. Analysis f he ainfall case in July 2003 ve China The le f viciy and divegence duing he ccuence and develpmen f enial ain evens has been invesigaed exensively in he lieaue (e.g. Hebe 1954; Sanley and Michael 1978ab; Liebmann e al. 1998; Davidsn e al. 1998; David and Andesn 2001) bu he le f al defmain befe he ccuence and duing he cuse f heavy ainfall has eceived much less aenin. Bluesein (1977) sudied he synpic-scale defmain elaed pical clud bands. Significan celains wee fund beween he clud bands and he ienain f he axis f dilaain f bjecively analyzed nndivegen winds a he lwe psphee. Bu sudies n he celains beween defmain and pecipiain ae few. F his easn ne heavy ainfall case assciaed wih he Eas China fn is seleced exple he chaaceisics and le f al defmain befe and duing he ainfall evens. The ienain f he ain band was alms eas-wes in he ainfall case. A heavy ainfall even assciaed wih a mei-yu fn ccued in he middle and lwe eaches f he Yangze Rive (MRYR) ve China fm 0000 UTC 4 July 1200 UTC 5 July The ainband was iened in he wes-suhwes eas-nheas diecin. The mei-yu fn fmed befe he nse f pecipiain and was mainained duing he cuse f pecipiain. Figue 6a shws ha a he 700-hPa level hee is a zne f high equivalen penial empeaue θ e ha clealy maks he mei-yu fnal zne ha seches in he nheas-suhwes ienain beween 27 N and 36 N. Alng his zne especially nea he nhen edge f his zne a line f sng cnfluence exiss ha is als a shea zne (Fig. 6b). This cnfluen shea zne is a esul f he lage-scale flw paen ha cnsiss f a subpical high lcaed in he nhwesen Pacific a mid--high laiude lw ceneed he nh a 48 N and 126 E and a geneal anicyclnic flw paen ve much f China nh f he Yanze Rive. This flw paen diffes fm he classical saddle ype defmain paen f he lack f anhe lw he suhwes and he vesize f he subpical high. The esul f his is he exisence f a significan amun f shea viciy alng he cnfluence zne. A he 200-hPa level he pecipiain egin is dminaed by a divegence flw alng he nheas edge f he Suh Asia high (n shwn). Theefe he lw-level cnfluence assciaed wih he defmain flw paen and he uppe-level divegence se up a favable ciculain paen f heavy mei-yu pecipiain. In de bain daa a highe spaial and empal esluins f he abve case and use he daa f a diagnsic sudy we pefmed a numeical simulain using he Advanced Reseach WRF mdel iniializing he mdel using he achived 1 1 NCEP/NCAR (Nainal Cene f Envinmenal Pedicin/Nainal Cenes f Amspheic Reseach) eal-ime glbal analyses daa. The Advanced Reseach WRF (ARW) dynamic ce uses cmpessible nn-hydsaic equains. I uses he 3d-de Runge-Kua ime-inegain scheme (Wicke and William 2002). F u simulains he physics pins used include he Feie micphysics scheme and he Kain-Fisch cumulus paameeizain scheme (Kain and Fisch 1990) he Medium- Range Fecas (MRF) bunday scheme (Hng and Pan 1996) Dudhia shwave adiain (Dudhia 1989) as well as he Rapid Radiaive Tansfe Mdel (RRTM) lngwave adiain scheme (Mlawe e al. 1997). The NCEP analyses a 6-hu inevals ae used as he bunday cndiins. The cene f he 27-km esluin mdel dmain is a 32 N and 117 E and has gids in he hiznal and 31 nnunifmly-spaced eain-fllwing levels in he ve-

8 18 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 (b) Fig. 6. The equivalen penial empeaue (K) and (b) seamline fields a he 700-hPa level a 0000 UTC 4 July (b) Fig. 7. Obseved and (b) simulaed 36-hu cumulaive ainfall (mm) ve he middle and lwe eaches f he Yangze Rive fm 0000 UTC 4 July 1200 UTC 5 July ical. The lage ime sep used is 120 s. The 36-hu inegain sas a 0000 UTC 4 July 2003 and upu a 20-minue inevals ae saved. Figues 7a and 7b shw he bseved and simulaed 36-hu cumulaive pecipiain beween 0000 UTC 4 July and 1200 UTC 5 July The simulaed and bseved maximum pecipiain cenes in MRYR ae lcaed especively a 32.5 N and E and a 32 Nand 120 E. The simulaed ainfall amun is simila he bseved ainfall amun [bh ae abu 110 mm (36 h) 1 ]. Due a lack f bsevainal daa ve he cean he simulaed pecipiain cann be validaed hee. N ae hee any pecipiain daa ve he Kean peninsula eihe. Ohewise he geneal pecipiain paens alng he Yangze Rive mach ahe well. Thus he simulaed daa will be used f

9 NO. 1 GAO ET AL Diagnsic analyses f al defmain and is elainship wih pecipiain (b) (c) Fig. 8. Tal defmain (b) divegence and (c) viciy (10 5 s 1 ) a he 700-hPa level a 0000 UTC 4 July The shaded aeas epesen values exceeding 6 2 and 6 especively f he pled fields. diagnsic analysis. T examine he pssible pgnsic value f he al defmain field as cmpaed he divegence and viciy fields hese hee fields ae pled in Fig. 8 a 700 hpa a 0000 UTC 4 July 2003 befe he nse f pecipiain. I can be seen fm he figue ha all he hee fields shw lage values alng a zne ha me less cincides wih he band f he lae 6-hu pecipiain. The magniude f abslue divegence is he smalles wih he maximum value being aund s 1 while ha f defmain is he lages exceeding s 1. The viciy maximum is abu s 1. This shws quaniaively f such ypical flw paens assciaed wih mei-yu fns ha al defmain is a dminan ppey f he flw me s han cnvegence and viciy. I is knwn ha cnvegence and viciy bh have impan les play in pecipiain sysems by pducing ascen via lw-level cnvegence fcing and by inducing lw-level cnvegence via he Ekman pumping effec especively. Pue defmain cnains n divegence viciy bu when i is he dminan ppey f he lw-level flw is effec cann be velked. In his case i plays an impan le in lw-level misue ansp by binging in mis ai fm he suh side f he main cnfluence zne. This siuain is simila ha f idealized defmain flw and he assciaed humidiy advecin cnsideed in secin 2. Unlike classical cld wam fns he hiznal empeaue gadien assciaed wih he mei-yu fns is n sng his can be seen fm Fig. 9a f he cuen case. Bu he gadien f misue is sng acss he fn and in he fnal zne (Fig. 9b). The zne f high elaively humidiy a he 700-hPa level is a esul f he lifing f misue by he lw-level cnfluen flw which als ansps misue hiznally in he zne and he hiznal flw is dminaed by he defmain. The esuls f his case shw ha he cnfluence assciaed wih he al defmain fcuses he misue in he cnfluence zne which pvides a favable cndiin f misue cnvecin. The cnvegence hugh weake elaive defmain is sill he ne ha igges he cnvecin via veical lifing bu he le f defmain in he misue ansp is als impan. Since lage values f al defmain ae pesen befe he nse f pecipiain i is believed have significan sense he pgnsis f pecipiain. Afe 0000 UTC 4 July 2003 pecipiain began ccu and he ainband fmed (Fig. 10) wihin he zne f lage al defmain (Fig. 11). Duing he

10 20 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 Fig. 9. Tempeaue (K dashed line) and elaively humidiy (% slid line) a he 700-hPa level a 0000 UTC 4 July especively. A maj band f lage al defmain exends fm 33 N a 1800 UTC 4 July 31.5 Na 2100 UTC 4 July and hee is a sligh incease in he al defmain duing his peid. Cmpaing Fig. 10 and Fig. 11 ne can see ha he lage value f al defmain pecedes he 6-hu cumulaive pecipiain maxima by 6 12 hus. The 6-hu pecipiain eaches is maximum f 30 mm (6h) 1 a 0600 UTC July 5 (Fig. 12a) wheeas he 6-hu mean al defmain (Fig. 12b) eaches is peak magniude f abu s 1 a 0000 UTC 5 July 6 hus ahead f he pecipiain maximum. The abve analysis indicaes ha he al defmain has a pedicive value f he pecipiain me han 6 hus in he fuue. Basednheabveanalysesnheainfallcase sme cnclusins ae dawn as fllws. Befe and duing he cuse f pecipiain bh he lcain and seching diecins f he band f lage al defmain and f he cnfluen shea line velap in he lwe psphee. The ainbands ae lcaed slighly hei suhwes and he seching diecin f he ainband is geneally he same as he lage-value zne f defmain. The value f al defmain in he lwe psphee inceases befe he pecipiain eaches is maximum inensiy and he ime lag f he lae is fen me han 6 hus. The magniudes f bh lw-level divegence and viciy ae smalle han ha f al defmain f he w ypical pecipiain cases examined suggesing ha he al defmain is a leas an impan pecus f heavy pecipiain f he ype analyzed hee. 6. The elaive cnibuins f he ems in he defmain equain Fig. 10. Time-laiude css secin f 6-hu cumulaive pecipiain (mm) alng 118 E fm 0000 UTC 4 July 1200 UTC 5 July cuse f pecipiain he al defmain maximum is lcaed slighly nh f he maximum pecipiain. Thei ends ae cnsisen wih each he and bh ppagae suhwad fm nh f 33 N 30 N. Tw pecipiain bands f me han 22 mm ccu beween 1700 UTC 4 July and 0000 UTC 5 July and beween 2300 UTC 4 July and 0800 UTC 5 July In he pevius secin we analyzed he lw-level defmain fields f he heavy ainfall case ha ccued ve China and discussed he lcain and ienain elaive he cnfluence zne and he bands f sng viciy and divegence. F he case he defmain is fund have lage abslue magniudes han eihe divegence viciy. The impance f he defmain field in hese sysems is eviden. Fuhe in secin 3 we deived he al defmain equain. In his secin using he WRF mdel upu we calculae he igh-hand-side ems f he al defmain equain Eq. (5a) excep f he ficin em f he ainfall case in de gain a bee undesanding f he pcesses cnibuing he ime evluin f al defmain. F he July 2003 case since he lages pecipiain appeas in he egin f N and E (Figs. 7a and 7b) his egin is chsen calculae he

11 NO. 1 GAO ET AL. 21 Fig. 11. Time-laiude css secin f al defmain (10 5 s 1 ) alng 118 E a he 700-hPa level fm 0000 UTC 4 July 1200 UTC 5 July The egins wih al defmain exceeding s 1 ae shaded ) s 0 ( 1 n i a m f e d l a T ) m ( m n i a i ip c e P Table 1. I can be seen ha Tem2 has a negaive celain cefficien wih he Sum wheeas he ems have psiive celains. Tem4 has he lages psiive celain cefficien f and he smalles RMS diffeence f s 2 amng all ems. Tem1 and Tem5 have mdeae psiive celain cefficiens (aund 0.5) and small RMS diffeences ( s 2 ). The abve analysis indicaes ha he pessue gadien em is a maj cnibu he lcal change f al defmain wheeas he veical velciy em and he advecin em als have cnsideable cnibuins. Since he effec f he pessue gadien em is dminan in he defmain-dminan flw paen whee he high-lw and lw-high especively cuple bh sides f he cnfluence zne he pessue gadien is n nly a fce igge and mainain his kind f flw paen bu i acceleaes he defmain flw. Meve he fcus f mass field wads he cnfluen zne caused by he advecin f defmain flw has sme psiive feedback he pessue gadien beween bh sides f he cnfluence zne. Theefe he pessue gadien fce has clse elain he change f lcal defmain. I is he basic and he dminan fac inducing he change f defmain-dminan flw paens. Als due he defmain-dminan flw paen he divegence is small. S he Tem2 has he smalles cnibuin he lcal change f defmain. I is eviden ha he advecin will change he lcal defmain. As f he veical velciy em as menined abve in secin 2 in he case f hee dimensins veical min alng he cnfluence zne will cause he upwad ansp f he misue bugh in by he hiznal defmain flw. I plays a le f adjusing he mass field and wind field namely he pessue and flw fields and heefe leads he change f lcal defmain. 7. Cnclusins Fig. 12. Time seies f 6-hu maximum cumulaive pecipiain (mm slid line) and he magniude f 6-hu ime-mean al defmain (10 5 s 1 dashed line) a 700 hpa a he cene f pecipiain a 32 N 119 E fm 0000 UTC UTC 5 July aea-mean f he ems in Eq. (5a) and he ime endency (Sum=Tem1 + Tem2+ +Tem5) fm 0000 UTC 4 July 1200 UTC 5 July The ime seies f hese ems ae pled (n shwn hee). T idenify he maj pcesses ha ae espnsible f he endency f al defmain he linea celain cefficiens and RMS diffeences beween he sum and Tems 1 hugh 5 ae calculaed and pesened in In his pape i has been shwn ha he al defmain is an invaian independen f he cdinae sysem i is expessed in. An idealized flw field was cnsuced demnsae he advecin effec n 2D misue fields by an essenially nn-divegen and iainal defmain flw ha is simila he flw paens assciaed wih ypical heavy pecipiain sysems ve easen China especially hse assciaed wih he mei-yu fn. One heavy ainfall case was examined exple he chaaceisics and le f al defmain befe and duing he heavy ainfall. Numeical simulain f he ainfall even was pefmed using he WRF mdel a a 27-km hiznal esluin and he mdel upus wee used f diagnsic analyses n he case.

12 22 TOTAL DEFORMATION AND ITS ROLE IN PRECIPITATION EVENTS VOL. 25 Table 1. Celain cefficiens and RMS diffeences beween individual ems in he al defmain equain and he sum f he ems f he July 2003 case. Tem Celain cefficien RMS (10 8 kg m 3 s 2 ) I was fund ha befe he nse f pecipiain he cnfluence effec assciaed wih he defmain and he ansp f misue by such a flw ses up a favable cndiin f heavy pecipiain. Duing he pecipiain peid bh he lcain and ienain f he band f lage al defmain and hse f he cnfluen shea line ae alms idenical in he lwe psphee. The pecipiain band is usually lcaed slighly he suh f he shea line. The value f al defmain in he lwe psphee inceases befe and duing he pecipiain. The al defmain usually eaches is maximum value abu 6 hus befe he pecipiain eaches is peak inensiy. Theefe he sudy n al defmain may be helpful f sudying pecipiain evens especially f he evens assciaed wih he mei-yu fn and wih defmain-dminan flw paens. T idenify he maj cnibus he change f al defmain he al defmain equain was deived in a simila way as he divegence and viciy equains wee. Calculains f individual ems in he equain shwed ha he pessue gadien em is he lages cnibu he lcal change f al defmain wheeas he veical velciy em and advecin ems als cnibue he change. In his pape nly ne heavy ainfall case was analyzed. T bain me geneal cnclusins me cases shuld be examined which is planned f he fuue. Daa f highe empal and spaial esluins shuld be used exple he elainship beween he al defmain and he pecipiain in me deail. Acknwledgemens. S. Ga and S. Yang wee supped by he Nainal Naual Science Fundain f China unde Gan Ns and and by he Olympic Pjec unde Gan N. KACX1-02. M. Xue acknwledges he supp fm he Chinese Academy f Sciences (Gan N ) which enabled he cllabain. REFERENCES Bluesein H. B. 1977: Synpic-scale defmain and pical bands. J. Ams. Sci Caacena F. R. A. Maddx L. R. Hxi and C. F. Chappell 1979: Mesanalysis f he big Thmpsn sm. Mn. Wea. Rev David J. S. and J. L. Andesn 2001: Is midlaiude cnvecin an acive passive playe in pducing glbal ciculain paens? J. Climae Davidsn N. E. K. Kuihaa T. Ka G. Mills and K. Pui 1998: Dynamics and pedicin f a messcale exeme ain even in he Baiu fn ve Kyushu Japan. Mn. Wea. Rev Davies-Jnes R. P. 1984: The igin f updaf ain in supecell sms. J. Ams. Sci Degemeie K. K. S. M. Lazaus and R. P. Davies- Jnes 1993: The influence f heliciy n numeically simulaed cnvecive sms. Mn. Wea. Rev Dudhia J. 1989: Numeical sudy f cnvecin bseved duing he wine mnsn expeimen using a messcale w-dimensinal mdel. J. Ams. Sci Eling D. 1985: Sme aspecs f heliciy in amsphee flws. Bei. Phys. Ams Haasi P. R. and R. Lis 2005: Pincipal cmpnen analysis f Dpple ada daa. Pa I: Gemeic cnnecins beween eigenvecs and he ce egin f amsphee vicies. J. Ams. Sci Hebe R. 1954: Rainfall and viciy advecin. J. Ams. Sci Hng S. Y. and H. L. Pan 1996: Nn-lcal bunday laye veical diffusin in a medium-ange fecas mdel. Mn. Wea. Rev Hxi L. R. J. M. Fisch and C. F. Chappell 1978: Reply. Mn. Wea. Rev Kain J. S. and J. M. Fisch 1990: A ne-dimensinal enaining/deaining plume mdel and is applicain in cnvecive paameeizain. J. Ams. Sci Keyse D. M. J. Pecnick and M. A. Shapi 1986: Diagnsis f he le f veical defmain in a wdimensinal pimiive equain mdel f uppe-level fngenesis. J. Ams. Sci Keyse D. J. M. Reede and J. R. Reed 1988: A genealizain f Peessen s fngenesis funcin and is elain he fcing f veical min. Mn. Wea. Rev Liebmann B. J. A. Maeng J. D. Glick V. E. Kusky I. C. Waine and O. Massamban 1998: A cmpaisn f ainfall uging lngwave adiain and divegence ve he Amazn Basin. J. Climae Lilly D. K. 1986a: The sucue enegeics and ppagain f ain cnvecive sms. Pa I: Enegy exchange wih he mean flw. J. Ams. Sci. 43

13 NO. 1 GAO ET AL Lilly D. K. 1986b: The sucue enegeics and ppagain f ain cnvecive sms. Pa II: Heliciy and sm sabiliy. J. Ams. Sci Lu H. and S. Ga 2003: On he heliciy and he heliciy equain. Aca Ameelgica Sinica (in Chinese) MaddxR.A.L.R.HxiC.F.ChappellandF.Caacena 1978: Cmpaisn f meelgical aspecs f he big Thmpsn and apid ciy flash flds. Mn. Wea. Rev Maddx R. A. F. Canva and L. R. Hxi 1980a: Meelgical chaaceisics f flash fld evens ve he wesen Unied Saes. Mn. Wea. Rev Maddx R. A. L. R. Hxi and C. F. Chappell 1980b: A sudy f nadic hundesm ineacins wih hemal bundaies. Mn. Wea. Rev Mlawe E. J. S. J. Taubman and P. D. Bwn 1997: Radiaive ansfe f inhmgeneus amsphee: RRTM a validaed celaed-k mdel f he lngwave. J. Gephys. Res Nbuy J. 2002: Lage-Scale Amsphee-Ocean Dynamics. Vl. I Cambidge Univesiy Pess Unied Kingdm 370pp. Peessen S. 1956: Weahe Analysis and Fecasing. Vl. I 2nd ed. McGaw-Hill New Yk 428pp. Rssby C. G. 1937: On he muual adjusmen f pessue and velciy disibuin in ceain simple cuen sysems I. J. Ma. Res Rssby C. G. 1938: On he muual adjusmen f pessue and velciy disibuin in ceain simple cuen sysems II. J. Ma. Res Sanley L. U. and G. Michael 1978a: The le f suface divegence and viciy in he life cycle f cnvecive ainfall. Pa I: Obsevan and analysis. J. Ams. Sci Sanley L. U. and G. Michael 1978b: The le f suface divegence and viciy in he life cycle f cnvecive ainfall. Pa II: Descipive mdel. J. Ams. Sci Wale F. and A. J. Thpe 1979: An evaluain f heies f sm min using bsevains f pical cnvecive sysems. Mn. Wea. Rev Weisman M. L. and J. B. Klemp 1982: The dependence f numeically simulaed cnvecive sms n veical wind shea and buyancy. Mn. Wea. Rev Wicke L. J. and J. S. William 2002: Time-spliing mehds f elasic mdels using fwad ime schemes. Mn. Wea. Rev Wiin-Nielsen A. 1973: Cmpendium f Meelgy. Vl. I WMO 364pp. Wu R. and Z. Tan 1989: Genealized viciy and penial viciy cnvesain law and applicain. Aca Meelgica Sinica (in Chinese) Yeh T. C. 1957: On he fmain f quasi-geshpic min in he amsphee. J. Mee. Sc. Japan (75h annivesay vlume) Yeh T. C. and M. Li 1982: On he chaaceisics f scales f he amspheic mins. J. Mee. Sc. Japan Zeng Q. 1963a: The effec f iginal disubance sucue n adapain and he applicain f bseved wind field. Aca Meelgica Sinica (in Chinese) Zeng Q. 1963b: The adapain and develpmen in amsphee. I. Aca Meelgica Sinica (in Chinese) Zeng Q. 1963c: The adapain and develpmen in amsphee. II. Aca Meelgica Sinica (in Chinese)