CHAPTER 1 INTRODUCTION. mainly because it has a highly skewed distribution in space and time. Rain-gauge

Transcription

1 CHAPTER 1 INTRODUCTION Prcipitation is on of th most difficult of all atmosphric variabls to masur, mainly bcaus it has a highly skwd distribution in spac and tim. Rain-gaug ntworks ar vry spars or vn nonavailabl ovr vast dsrts, mountains, and jungl aras and ovr ocans, which maks satllit-drivd rtrivals th only way to obtain rainfall stimats ovr th abov aras. Th accuracy of th satllit rmot snsing stimation largly dpnds on rtrival tchniqus, which ar always basd on som assumptions and nvr prfct. Among all kinds of prcipitation systms, tropical cyclons ar probably th most important bcaus thy occasionally caus major disastrs on human bing and thy may contribut larg prcnt of bnficial rainfall for agricultur in many rgions (Rodgrs t al. 000; 001). Thy ar also probably th most difficult kind to quantitativly stimat prcipitation bcaus thy usually dvlop and grow ovr ocan and during landfall high winds oftn compromis rain masurmnts in land. 1.1 Tropical Cyclons According to th dfinition givn by th National Hurrican Cntr (NHC), tropical cyclons ar warm-cor nonfrontal synoptic-scal cyclons. Thy originat ovr tropical or subtropical watrs, with organizd dp convction and a closd surfac wind

2 circulation about a wll-dfind cntr. Whn a maximum 10-minut avrag wind spd in th rang of 8 to 33 knots, th storm is calld a tropical dprssion. Whn th maximum 10-minut avrag winds rach 34 knots, it bcoms a tropical storm, and a tropical cyclon at 64 knots. A tropical cyclon is also calld a hurrican if it is ovr th North Atlantic Ocan or a typhoon if it is ovr th North Pacific Ocan. Th winds that swirl about th cntr dcras with hight, but typically fill th whol troposphr (Haurwitz 1935). Th innr cor rgion in a tropical cyclon contains th spiral bands of prcipitation, th ywall, and th y that diffrntiats tropical cyclons from any othr mtorological phnomna. Willoughby t al. (198, 1984) proposd that th storm s radar structur can b idntifid as th stationary band complx (SBC) that consistnts of an ywall, a principal rainband, conncting bands, and svral scondary rainbands outsid th ywall. Th ywall rgion is a quasi-circular ring of convction surrounding th circulation cntr. Onc formd, a tropical cyclon is maintaind by th xtraction of hat nrgy from ocan at high tmpratur and hat xport at th low tmpraturs of th uppr troposphr. Tropical cyclons ar an important sourc of rainfall for agricultur and othr watr applications ovr th rgions of subtropics and tropics. Climatological studis show that tropical cyclons contribut approximatly 7% and 4% of th total rainfall in th ntir domain of th North Pacific and North Atlantic, rspctivly, during tropical cyclon sason, with maximum rgional contributions of about 30% (Rodgrs t al. 000, 001). As a main nrgy sourc for th dvlopmnt and maintnanc of tropical cyclons, th rlas of latnt hat is dirctly rlatd to th tropical cyclon intnsity (Adlr and Rogrs 1977; Rodgrs and Adlr 1981; Rao and MacArthur 1994; Rodgrs t al. 1994a,b). Th surfac rain rat and th vrtical distribution of hydromtor profils

3 3 can b usd dirctly to stimat th latnt hat rlas. So th rainfall rat, ic watr contnt (IWC), and liquid watr (LWC) hav implications for tropical cyclon intnsity. High corrlations wr found btwn th futur tropical cyclon intnsity and satllitbasd 85-GHz ic-scattring signatur within o 1 radius of th cyclon cntr (Ccil and Zipsr, 1999) and rainfall rats within th o radius of th cntr of typhoons (Rao and MacArthur, 1994). Howvr, prdicting rainfall and intnsity associatd with tropical cyclons is a major oprational challng. Although track forcasts continu to improv, quantitativ prcipitation and intnsity forcasts hav shown littl skill (DMaria and Kaplan 1999). Accurat quantitativ rainfall and hydromtor contnt stimation, and thrfor latnt hating stimation, within tropical cyclons ovr ocan is a difficult problm bcaus thr ar no dirct masurmnts availabl. Rsarch aircraft can fly through th storm and provid prcipitation stimats from passiv and activ instrumnts. Th flight-lvl microphysics obsrvations rprsnt th limitd but important data sourc to hlp thos stimations. At th sam tim, th Tropical Rainfall Masuring Mission (TRMM, Simpson t al. 1988, 1996; Kummrow t al. 1998, 000) satllit provids both radar vrtical structur information and high rsolution passiv microwav obsrvations ovr Tropics. With th long priod of covrag ovr ocans, on of th TRMM goals is to obtain th four-dimnsional structur of latnt hating in th tropical atmosphr. TRMM can obtain about 700 ovrpasss of tropical cyclons ach yar, which is an important data sourc for study of this uniqu systm.

4 4 1. Background of Microwav Rmot Snsing 1..1 Ovrviw Microwav rmot snsing uss microwav radiation at wavlngths from about 1 mm to about 10 cm (or at frquncis from about 300 GHz to 3 GHz). On of th main attractions of th microwav band is th rlativ transparncy of clouds at ths wavlngths, so that som proprtis of th surfac and of th atmosphric column can b stimatd undr narly all-wathr condition. In contrast, th IR radiation could sriously b intrfrd with by vn thin clouds. Thr ar two typs of microwav rmot snsing: passiv and activ. Passiv microwav snsors, oftn rfrrd to as microwav radiomtrs, ar rcivrs that masur th radiation manating from th scn undr obsrvation. Activ microwav snsors, oftn rfrrd to as radar, provid thir own sourc of illumination and masur backscattring from cloud and prcipitation. Microwav radiation propagating in th atmosphr is absorbd by atmosphric gass and absorbd and scattrd by hydromtors. Both absorption and scattring rmov nrgy from a bam of radiation travrsing th mdium. Th bam of radiation is attnuatd, and w call this attnuation xtinction. Thus, xtinction is a rsult of absorption plus scattring. In th fild of radiativ transfr, it is customary to us a trm calld cross sction σ, analogous to th gomtrical ara of a particl, to dnot th amount of nrgy rmovd from th original bam by th particl. Whn th cross sction is associatd with a particl dimnsion, it units ar dnotd in trms of ara (m ). Thus, th xtinction cross sction σ, in units of ara, is th sum of th absorption and scattring cross sctions ( σ + σ ). Howvr, whn th cross sction is in rfrnc to a s unit mass, its units ar givn in ara pr mass (m /kg) and w call it mass xtinction cross

5 5 sction ( k ). But usually w call k mass xtinction cofficint ( k k + k, whr = a s ka and k s ar mass absorption cofficint and mass scattring cofficint). Furthrmor, whn th xtinction cross sction σ is multiplid by th particl numbr dnsity N (m -3 ), or whn th mass xtinction cofficint is multiplid by th dnsity (kg/m 3 ), th quantity is rfrrd to as th xtinction cofficint ( β ), whos units ar givn in trms of lngth (m -1 ), thn w hav β = N( D) σ ( D dd (1.1) ) whr D is th quivalnt sphrical particl diamtr and N(D) is th particl numbr concntration in diamtr intrval from D to D+dD. Emission is th procss by which som of th intrnal nrgy of a matrial is convrtd into radiant nrgy. Emission by a blackbody is th convrs of absorption. Th intnsity of radiation mittd by a blackbody with a physical tmpratur T is givn by Planck s Function B(T ) : hc Bλ ( T ) 5 / k ( hc B λ = λt 1) (1.) whr λ is wavlngth, c = m/s is th spd of light, h = J is Planck s -3 constant, and k B = J/K is Boltzmann s constant. In microwav rmot snsing of th atmosphr, th wavlngths of intrst ar quit long -- λ ~ 1 mm or longr. In th limit of larg wavlngth, ckb Bλ ( T ) T (1.3) 4 λ

6 6 in which cas blackbody mission is sn to b proportional to absolut tmpratur. This so-calld Rayligh-Jans approximation significantly simplifis som kinds of radiativ transfr calculations in th microwav band. Blackbody is th idalization of any ral objct, and th Planck s function is th thortical maximum possibl mission from any ral objct. Emissivity ε λ is dfind as th ration of what is mittd by an objct to what would b mittd if it wr a blackbody. Absorptivity a λ is dfind as th ration of what is absorbd by an objct to what would b absorbd if it wr a blackbody. Th rlationship btwn absorptivity and missivity is mbodid succinctly by Kirchhoff s Law, which stats that ε λ = a λ (1.4) Th microwav missivitis of natural surfac ar oftn considrably lss than unity and may in fact vary wildly from on scn to th nxt. In particular, th land surfac missivitis ar typically as larg as , whras ocan surfac missivitis may b as small as This variation in surfac missivity maks it much mor difficult to us microwav imagry for accuratly stimating surfac tmpratur, but gratly facilitats th dtrmination of othr surfac proprtis. Th microwav radiomtr masurs th radianc, which is usually convrtd into th quivalnt blackbody tmpratur or brightnss tmpratur T b by using th Planck s Function. A particularly convnint proprty of th microwav band is th validity of th Rayligh-Jans approximation, which allows us to work with brightnss tmpratur as a convnint stand-in for radiant intnsity. Bcaus of th proportionality btwn blackbody radianc and tmpratur in th microwav band, thr is a vry simpl rlationship btwn T, ε λ, and T b :

7 7 T b ε λ T (1.5) 1.. Passiv Microwav Rmot Snsing of Prcipitation Passiv microwav radiomtrs hav bn carrid on satllits for climatic-scal prcipitation obsrvations sinc 197 (Arkin and Ardanuy, 1989). Thy masurs radiancs that ar th intgratd ffct of absorption/mission and scattring through a prcipitating cloud along th snsor path viw. Considr th passag of radiation of wavlngth λ through a layr of atmosphric mdium with infinitsimal thicknss ds, masurd along th dirction of propagation. If th radiant intnsity is initially I, th chang of I ( di ) along ds can b writtn as: (1.6) di = di + di + di xt mit scat whr th dpltion du to xtinction (both absorption and scattring) is givn by di = β Ids (1.7) xt whr th xtinction cofficint is th sum of th absorption cofficint and scattring cofficint, i.., β = β + β. Th sourc du to mission is a s di = β ab( T ds (1.8) mit ) whr B(T) is th Planck s function. Th sourc du to th radiation from any dirction θ scattrd into th bam in th dirction of intrst θ is

8 8 β s di scat = p( θ, θ ) I( θ ) dω ds 4π 4π (1.9) whr th scattring phas function p ( θ, θ ) is rquird to satisfy th normalization condition 1 p ( θ, θ ) dω = 1 (1.10) 4π 4 π Th complt diffrntial form of th radiativ transfr quation can b writtn as β s di = β + β + θ θ θ ω Ids abds p(, ) I( ) d ds (1.11) 4π 4π This is th most gnral and complt form of th radiativ transfr quation. In th microwav band, bcaus of th Rayligh-Jans approximation th radiant intnsity I and th Planck s function B in (1.11) can b substitutd by T b and T. Th calculation of (1.11) is vry complx du to th xistnc of th scattring sourc trm (th last trm of (1.11) on th right hand sid), which rquirs a solution for th intnsity fild not just in on dirction along a on-dimnsional path but for all dirctions simultanously in thr-dimnsional spac. On would thrfor lik to b abl to nglct scattring (as a sourc, at last) whnvr possibl. So th qustion is, whn dos scattring mattr? Th scattring componnt of th radiativ transfr quation (1.11) dpnds on th local scattring cofficint and th scattring phas function. Ths in turn dpnd both on wavlngth and on th siz, phas, and numbr of particls. Th siz of a particl is th most important dfining charactristic. In gnral, particls that ar far smallr than th wavlngth will scattr only vry wakly.

9 9 A nondimnsional siz paramtr x is dfind as: πr x (1.1) λ whr r is th radius of a sphrical particl. Givn th valu of x, on can immdiatly dtrmin whthr scattring by th particl is likly to b significant and, if so, which broad scattring rgim Rayligh, Mi, or gomtric optics is most applicabl. Fig. 1.1 rprsnts how various combinations of particl typ and wavlngth rlat to ths rgims. From Fig. 1.1, w s that in th microwav band (1 mm < λ < 10 cm), th siz paramtrs of all atmosphric particls from small air molculs to larg hails ar in ngligibl scattring, Rayligh, or Mi rgims (Ptty 004). In th fild of th quantitativ prcipitation stimation using passiv microwav rmot snsing, basically thr ar two typs of algorithms basd on if th scattring ffct can b nglctd or not: mission-basd and scattring-basd (th profiling algorithm as mntiond latr is just th combination of ths two). Emission-basd algorithms ar basd on th downward-looking microwav radiomtr obsrvations on low frquncis. For frquncy lss than 19 GHz (wavlngth gratr than 1.55 cm), almost all prcipitation particls xcpt larg hails, which ar byond th considration of this study on tropical ocanic rainfall systms, ar in Rayligh scattring rgim according to Fig Th Mi thory givs th xtinction (absorption and scattring) cross sction for a sphr as a function of siz paramtr x and rlativ indx of rfraction m as follow: λ σ = (n + 1)( a + b ) (1.13) R π n= 1 n n

10 Figur 1.1. Rlationship btwn particl siz, radiation wavlngth and scattring bhavior for atmosphric particls. Diagonal dashd lins rprsnt rough boundaris btwn scattring rgims (rprintd with prmission from Ptty 004). 10

11 11 λ σ = ) (1.14) s (n + 1)( an + bn π n = 1 whr th cofficints a and b ar rfrrd to as Mi scattring cofficints and ar n n functions of x and m. (1.13) and (1.14) ar valid for both Rayligh and Mi scattring rgim. In particular, for Rayligh rgim (x is small nough), th scattring and absorption cross sction simplifis to: 16πr 4 m 1 σ s = x (1.15) 3 m + m 1 σ a = 4πr x Im{ } (1.16) m + W s that th absorption cross sction is proportional to r 3, whil th scattring cross sction is proportional to r 6. So for sufficintly small liquid particls (for liquid, m has a nonzro imaginary part), th scattring is insignificant. Thus, σ σ, and th mass a xtinction cofficint k can b xprssd as: k σ a = ρ(4/3) πr 3 6π m = Im{ ρλ m 1 } + (1.17) whr ρ is th dnsity of th particl. Not that thr is no dpndnc of k on th particl radius r. Thrfor, for radiation passing through a cloud of sufficintly small absorbing particls, th total absorption is proportional to th total mass path, rgardlss of th xact sizs of th constitunt particls. At low frquncis, this condition is quit valid for particls radius lss than 100 µ m in nonrainning clouds.

12 1 Th Mi thory-basd calculations by Wilhit t al. (1997) prsntd both xtinction and absorption cofficints for raindrops at 19 GHz for a Marshall-Palmr distribution of raindrops as a function of rain rat (s Fig. 1 of Wilhit t al. 1997). Thir rsults show how th xtinction is dfind by th rain rat and furthrmor how th xtinction at this frquncy is largly govrnd by absorption procsss sinc th scattring cofficint is almost an ordr of magnitud smallr than th absorption cofficint. Anothr important finding by Wilhit t al. (1977) is that th rain rat and absorption cofficints rprsnts similar momnts (although thy ar not thr momnts as in Rayligh approximation) of th raindrop siz distribution. Thus, although both th brightnss tmpratur and rain rat ar individually dpndnt on th drop siz distribution, th rlationship btwn th two should not b xcssivly dpndnt on th dtails of th particl siz distribution (s thir Fig. 5). Aftr nglcting scattring, it is straightforward in principl to driv th brightnss tmpratur associatd with upwlling radiation as a function of rain rat basd on (1.11). Emission from raindrops, whn viwd against a cold ocan background, incrass with incrasing optical dpth. This incrasd mission, masurd as an incrasd brightnss tmpratur, is thn associatd with th rain rat. Fig. 1. shows an xampl of th rlationship from th radiativ transfr simulation. Th calculatd brightnss tmpratur at 10.7 GHz is prsntd as a function of th modld rain rat. From Fig. 1., w s that th 10.7 GHz brightnss tmpratur incrass with rain rat incrasing up to 50 mm/hr without saturation. For lss than 10 GHz microwav channls, th saturation limit of rain rat will b vn largr. As will b mntiond in Chaptr, th Stppd Frquncy Microwav Radiomtr (SFMR) on th NOAA P3 aircraft has six frquncis

13 Figur 1.. Rlationship btwn nadir 10.7-GHz brightnss tmpratur and surfac rain rat ovr th tropical ocan using th modl dscribd by Kummrow and Winman 1998 (rprintd with prmission from McGaughy t al. 1996). 13

14 14 btwn 4.55 to 7. GHz. It has th ability to stimat vry havy rain rat using th mission-basd algorithm. For TRMM, mission-basd algorithms usually us 10 GHz channl to stimat larg rain rats and us 19 GHz channl to stimat smallr rain rats sinc 19 GHz is mor snsitiv to small rain rat valus but saturats for rain rat largr that 15-0 mm/hr. Fig. 1.3 shows th brightnss tmpratur - rain rat rlationships at 18, 37, and 85.6 GHz from th radiativ transfr modling for ovr land and ovr ocan. From Fig. 1.3, th brightnss tmpratur - rain rat rlationship ovr ocan for 18 GHz is complx. For rain rat lss than 15 mm/hr, Tb incrass as rain rat incrass. But for rain rat largr than 15-0 mm/hr, scattring by th larg ic crystals ovr rgions of havy rainfall confuss mattrs. Radiation mittd from th undrlying rain is scattrd downward by th ovrlying layr of ic particls and away from any instrumnt looking downward abov th cloud. This incras in scattring as rain rat incrass (or xactly ic watr path incrass) lads to a dcras in brightnss tmpratur. This is what th scattringbasd algorithm is basd on. Scattring-basd algorithms us microwav obsrvations at high frquncis (gratr than 37 GHz). For ths channls, th siz paramtrs for cloud and prcipitation particls ar usually btwn 1~6, so it is in Mi scattring rgim. Th scattring ffct of frozn hydromtors for ths channls is not ngligibl. Thus, th complt radiativ transfr quation (1.11) nds to b solvd including mission, absorption, and scattring ffcts of liquid, combind phas, and ic hydromtors. Th first of this kind of microwav radiativ transfr modl is prsntd by Wu and Winman (1984) and Kummrow and Winman (1988). Thir simulation rsults show that th prsnc of ic hydromtors markdly dprsss th brightnss tmpraturs at 37 and 86 GHz, which

15 Fig Brightnss tmpratur - rain rat rlationships at 18, 37, and 85.6 GHz from th radiativ transfr modling of Wu and Winman (1984). Th vrtical distribution of hydromtors was basd upon avragd radar rsults and assumd ic prcipitation abov and liquid prcipitation blow th frzing lvl (rprintd with prmission from Spncr t al. 1989). 15

16 16 is consistnt with satllit microwav radiomtr obsrvations. Fig. 1.3 also shows th dprssion of th calculatd brightnss tmpratur at 37 and 85.6 GHz as a function of th modld rain rat. In th simulation of Fig. 1.3, th amount of frozn hydromtors incrass with incrasing th rain rat. In fact, th dirct rlationship is btwn th total ic watr path (instad of rain rat) and th brightnss tmpratur dprssion. Unlik mission basd rtrivals, which ar not xcssivly snsitiv to particl siz distribution, scattring basd rtrivals ar vry snsitiv to particl siz distribution th particl siz distribution (PSD. In th following txt, th PSD will b usd to rprsnt both rain drop siz distribution and ic particl siz distribution). Fig. 1.4 dpicts th Mi scattring xtinction fficincy Q ( Q = σ / πr ) calculatd from (1.13) as a function of siz paramtr x for a sphr with m = This is rprsntativ valu for ic in th microwav band. Not that no imaginary part is assumd in m, so th ic particl is nonabsorbing, which mans Q = 0 and Q = Q s. Th ral valu of th imaginary part of a m for ic at frquncis from 37 ~ 85 GHz varis from to as tmpratur varis from 0 to o 70 C. But ths small valus do not bring much absorption thrfor do not chang th Q curv vry much. From Fig. 1.4a, w s that th rlationship btwn xtinction (scattring only hr) fficincy Q and siz paramtr is vry complx. Q starts at 0 for x = 0 and riss monotonically up to about x =.5 (for 85 GHz, it rprsnts ic particls with siz lss than 3 mm; for 37 GHz, it rprsnts ic particls with siz lss than 6 mm), whr Q achivs a maximum valu of about 5. In othr words, for this valu of x, th ic particl scattrs fiv tims as much radiation as on might surmis from its cross sctional ara alon. Thraftr, it xhibits an vndampning oscillation about a man valu of, which is th limiting valu of Q for larg x. At th othr nd of th rang, w compar Q (=Q s ) computd using th xact Mi

17 17 a b Figur 1.4. Th xtinction fficincy Q as a function of siz paramtr x for a nonabsorbing ic sphr with m=1.78, for various of x. (a) Dtail for x < 10; (b) Dtail for x < 3, comparing th Rayligh (small particl) approximation and xact Mi thory.

18 18 thory with that obtaind for th small-particl (Rayligh) limit (Fig. 1.4b). W can s that th agrmnt is quit good up to about x = 1.. Byond that point, Q incrass lss rapidly than th x 4 dpndnc prdictd by (1.15). So for x < 1., th xtinction cofficint β in (1.1) is proportional to D 6 as in Rayligh rgim. For 1. < x < 6, th rlation btwn β and particl diamtr D is not monotonically according to Fig. 1.4a. Th bulk paramtrs of prcipitation that w most concrn ar rain rat (R) and watr contnt (M) dfind as: = 3 N D) V ( D) D 0 R ( dd (1.18) M π = N( D) ρd dd (1.19) whr ρ is th dnsity of liquid or ic particls, and V(D) is th trminal fall vlocity of raindrops, which is approximatly proportional to D 0.5 to D 1 for raindrops and frozn hydromtors dpnding on thir sizs and habits, tc. (Rodgrs and Yau 1989; Pruppachr and Kltt, 1997). From (1.18) and (1.19), R is proportional to V(D)D 3 and M is proportional to a spcific PSD. 3 D. Thrfor w can not stimat R and M from β without knowing 1..3 Activ Microwav Rmot Snsing of Prcipitation As on of activ microwav rmot snsing instrumnts, radar has bcom on of th most important obsrvational tools of oprational mtorologists. Wathr radar, in wavlngths of -10 cm, allows th monitoring of rainfall with far mor dtail in both tim and spac than is possibl with convntional rain gaugs. Radar masurs th

19 19 backsattring of cloud and prcipitation particls. Following th dfinition of th xtinction cross sction in sction.1, th backscattring or radar cross sction σ b is o rlatd to th fraction of incidnt wav powr scattring backward ( 180 scattring angl). Th Mi quation yilding th solution for σ b is: λ n σ = ( 1) (n + 1)( a b ) (1.0) b π n= 1 n n whr th cofficints a and b ar as sam as thos in (1.13) and (1.14). For most n n wathr radars, almost all prcipitation hydromtors can b considrd small compard to th wavlngth, so th Rayligh approximation applis and in Rayligh rgim bcoms: σ b 5 6 π D m 1 σ b = (1.1) 4 λ m + Th radar rflctivity η (similar as xtinction cofficint β in (1.1)) is dfind as th sum of th singl particl backscattring cofficints pr unit volum. η is xprssd by: η = N ( D) σ ( D) dd (1.) 0 b For Rayligh scattring, η can b rplacd by th radar rflctivity factor, Z, dfind by: Z = 5 π 4 λ η m m 1 + = 6 N( D) D dd 0 (1.3)

20 0 Th standard radar systm dtrmins th watr quivalnt radar rflctivity factor (Z) by assuming that th complx indx of rfraction m is as sam as that for watr. So for ic particls, th radar rflctivity factor Zi is usually 7 db highr than radar masurd Z bcaus th diffrnc of th complx indx of rfraction btwn watr and ic (Rinhart 1997). For simplicity, w us Z as quivalnt radar rflctivity factor instad of Z in th folowing txt, and w will call both Z and dbz=10log10(z) as th radar rflctivity. Th advantag of a spacborn downlooking radar is to provid vrtical profils of radar rflctivitis, which ar rlatd to th vrtical distribution of rain rat and watr contnt, thraftr latnt hat rlas. From (3.1), howvr, w s that radar rflctivity is proportional to 6 D. Howvr, from (1.18) and (1.19), rain rat R is proportional to V(D)D 3 and watr contnt M is proportional to 3 D, so th invrsion from Z to R or M is impossibl without knowing N(D), th PSD. Th Z-R rlationship can b xprssd by b Z = ar (1.4) whr a and b ar constant for a spcific PSD. Th Z-M rlationship is similar as (1.4). Unfortunatly, PSD has a larg varibility for diffrnt nvironmnt conditions and prcipitation typs. Studis hav show that th rain PSD fluctuations limit th rain rat masurmnt accuracy to ~30-40% on avrag, if a singl climatological Z-R rlationship is usd (Chandraskar t al. 003). This accuracy could b improvd significantly if th Z-R rlationship is adjustd basd on prcipitation typ.

21 Bamfilling Problm of Spac-basd Microwav Obsrvations Th spac-basd radiomtr and radar obsrvations may provid accurat prcipitation masurmnts with narly global covrag. Howvr, on difficulty in rtriving rain rat and hydromtor contnt from spac-basd platform is corrcting for th so-calld bamfilling ffct. For spacd-basd microwav instrumnts, th foot print siz or fild of viw (FOV) is usually largr than th typical siz of rain clls. This implis that th rainfall within th FOV may not b uniformly sprad, spcially whn obsrving convctiv rainfall. Th bamfilling problm coms about bcaus th radiomtr or radar masurs a FOV ara avrag microwav brightnss tmpratur T b or radar rflctivity factor Z, whil th obsrvr dsirs an stimat of th FOV ara avrag rain rat R or watr contnt M. Th problm is that th formula rlating th point valu of T b or Z and th point valu of R or M is nonlinar, which can b s from Fig. 1. and (1.4). Hnc, straightforward insrtion of th masurd FOV T b or Z into th formula dos not lad to th FOV avrag R or M bcaus of th htrognity of rainfall within th FOV. Th magnitud of bamfilling rror for a spcific instrumnt is dpndnt on its footprint siz. Aircraft radar with a footprint siz lss than 1 km will almost hav no bamfilling problm bcaus th typical convctiv cll is largr than 1- km. An aircraft radiomtr would hav lss bamfilling rror than a satllit radiomtr bcaus th footprint siz of an aircraft radiomtr is typically much smallr than that of a satllit radiomtr. Radiomtrs at low frquncis would hav mor svr bamfilling problm than radiomtrs at high frquncis bcaus of th much largr footprint siz of lowfrquncy radiomtrs.

22 1.3 Invrsion Problm and PSD Issus From sction 1., w s that th a spcific PSD assumption is ndd for both radar-only and radiomtr-only prcipitation rtrivals, although th mission basd radiomtr-only algorithm is not vry snsitiv to PSD (Wilhit t al. 1977). In th quantitativ prcipitation stimation from rmot snsing obsrvations, th variability of PSD rprsnts on of th main difficultis surrounding th rtrival of prcipitation rats and hydromtor contnts. Obsrvations indicat a significant variability of PSD (Bringi t al. 003; Hymsfild t al 00b) in diffrnt rain typs, synoptic conditions, and go-locations, implying highly variabl Z-R, K-Z, Z-IWC, and Z-IWC rlations (K is th attnuation/xtinction cofficint β for radars). Th variation of Z-R, K-R, Z-LWC, and Z-IWC rlations in diffrnt rain typs has bn studid xtnsivly for many kinds of prcipitation systms including hurricans. Stout and Mullr (1968) summarizd that in radar rainfall stimats thr ar diffrncs on th ordr of 150% that can b attributd to diffrnt typs of rain or diffrnt synoptic conditions. Atlas t al. (1999) confirmd th systmatic variation of Z-R rlations btwn a squnc of rain typs in rainfall systms ovr th tropical ocans. Dlriu t al. (000) prsntd th K-R rlation variations among widsprad, thundrstorm, and th intnsiv long-lasting autumn rain vnts in Cvnns in Franc. Howvr, in hurricans, Jorgnsn and Willis (198) and Willis and Jorgnsn (1981) showd no obvious variation of Z-R and Z-LWC btwn stratiform and convctiv rain typs, whil Black (1990) gav vry diffrnt Z-IWC rlations for diffrnt rain typs. Houz t al. (199) rfrrd to th hurrican as a giant mixmastr that stirs and tnds to homogniz th prcipitation rgion lying just outsid th ywall. Qustions arising hr ar, In th spcial hurrican prcipitation nvironmnt, could w xpct a nar-indpndnc of

23 3 PSD in th rain rgion for diffrnt rain typs? How dos th PSD issu affct on th microwav prcipitation rtrival? Could PSD paramtrs b rtrivd along with hydromtor profils by combining radar and radiomtr obsrvations? It is vry important to undrstand th spcial PSD charactristics in hurricans, not only for rmot snsing rtrivals, but also for microphysics paramtrization in numrical modls, and improving our knowldg of cloud and prcipitation procsss. 1.4 Outlin In this vin, this rsarch compriss two main objctivs, which will addrss both mission-basd passiv microwav prcipitation rtrival and combind radar-radiomtr rtrival algorithms, and also addrss th PSD variations as a function of rain typs in tropical cyclons. In Chaptr, an mission-basd rain rat algorithm in hurricans from th Stppd Frquncy Microwav Radiomtr (SFMR) on th National Ocanic and Atmosphric Administration (NOAA) WP-3D aircraft is validatd by using simultanous obsrvations from two radars on th sam aircraft. Th DSD variability in convctiv and stratiform rgions ar invstigatd. Chaptr 3 will formulat a nw combind radarradiomtr algorithm to stimat PSD paramtrs and hydromtor profils in tropical cyclons, analyz th rror sourcs by doing snsitivity tsts, implmnt and apply this algorithm to aircraft data, validat it by using indpndnt aircraft in situ microphysics and radiomtr masurmnts, compar th rtrivals with radar-only and radiomtronly algorithms, and finally apply th combind algorithm to a TRMM hurrican cas.