Applications of radars: Sensing of clouds and precipitation.

Transcription

1 Lectue 1 Applications of adas: Sensing of clouds and pecipitation. Ojectives: 1. aticle ackscatteing and ada equation.. Sensing of pecipitation and clouds with adas (weathe adas, space adas: TMM and CloudSat). equied eading: G:.7, 8..1, 8.., 8..3, 8.3 Additional/advanced eading: CloudSat we site: TMM we site: aticle ackscatteing and ada equation. ecall Lectue 9 in which we intoduced intoduce the efficiencies (o efficiency factos), coss-sections and volume coefficients fo extinction, scatteing and asoption. Let s intoduce ackscatteing chaacteistics needed in active emote sensing (ada and lidas) Diffeential scatteing coss-section, d, is defined as the amount of incident adiation scatteed into the diection Θ pe unit of solid angle s d ( Θ) = ( Θ) [1.1] π whee (Θ ) is the scatteing phase function Bistatic scatteing coss-section, i, is defined as π ( Θ) [1.] i = d Backscatteing coss-section,, is defined as 0 π ( Θ= 180 ) [1.3] = d 1

2 Using Eq.[1.1], Eq.[1.3] can e e-witten as 0 = ( Θ = 180 ) [1.] s ecall that the incident intensity I i and scatteed intensity I s y a paticle elates as s ( Θ) I s ( Θ) = I i [1.] π whee is the distance fom the paticle. Fo the ackscatteing case, we can wite ( 180 ) ( 180 ) = 0 0 s Θ Fs Θ = = Fi [1.6] π o F s Θ = ) π = F i ( [1.7] Thus, the physical meaning of the ack-scatteing coss-section is the aea that, when multiplied y the incident flux density, gives the total powe adiated y an isotopic souce such that it adiates the same powe in the ackwad diection as the scattee. Fo the paticle nume size distiution N(), the ackscatteing volume coefficient, κ, is k = ( ) N( ) d [1.8] 1 and thus 0 k = ks( Θ = 180 ) [1.9] whee (Θ ) is the scatteing phase function aveaged ove the size distiution. Small size paamete limit (ayleigh limit): it can e shown fom Mie theoy (see G.7.1) that π 6 = K D [1.10] whee K = m m 1 + ; m if the efactive index of the paticle; and D is the paticle diamete.

3 ada equation Conside a tansmitting ada with an antenna of effective apetue A et and pulse duation t p (o length h=ct p ). The ada illuminates an oject (e.g., a cloud) at the distance. Suppose that the oject has the ackscatteing coss-section (called ada coss-section). dv Ω A Using the Fiis tansmission fomula, we can find the powe intecepted y the oject int as t A ( y oject = et [1.11] int ) Using that the scatteing oject can e consideed as an isotopic souce such that it adiates the same powe in the ackwad diection, it has diectivity D=1 and effective apetue A e = /π (see Eq.[0.8]). And using the Fiis tansmission fomula, we can find the powe eceived y the antenna int ( y oject ) Ae = [1.1] π Sustituting Eq.[1.11] into Eq.[1.1], we otain A = [1.13] π t whee A =A et = A e is the effective apetue of antenna (same fo tansmitting and eceiving). Eq.[1.13] is called the ada equation. 3

4 If the oject is a cloud with size distiution N() and the volume ackscatteing coefficient k. The powe ackscatteed y the volume dv and eceived y lida can e expessed as A kdv = [1.1] π Fom lida eam geomety, the illuminated volume can e appoximated as and using Eq.[1.8] fo k, we have t t dv θ H ϕ h / [1.1] H A hθ Hϕ H = ( ) N ( d π [1.16] ) Assuming that paticle ae in the ayleigh limit and using Eq.[1.10], we have the aove equation can e e-witten as π A hθ Hϕ H 6 = K D N ( D) dd 6 t [1.17] K = C Z [1.18] whee facto C depends on the antenna chaacteistics; and 6 Z D N ( D) dd = is called the ada eflectivity facto. Eq.[1.18] is often called the ada equation. We can elate the ackscatteing coefficient and ada eflectivity as k = π 6 π 6 π ( D) N ( D) dd = K D N ( D) dd = K D N ( D) dd = K Z [1.19] If paticle ae not in the ayleigh limit and/o nonspheical (e.g., ice cystals), the effective ada eflectivity facto, Z e, is intoduced.

5 In the moe geneal case, Eq.[1.18] must e coected to account fo the attenuation along the path to and fom the scatteed volume (a cloud) (i.e., attenuation may aise fom asoption y atmospheic gases, asoption y cloud dops and pecipitation): K = C Z exp( k ( ) d ) e [1.0] whee k e is the extinction coefficient along the path. o. Sensing of pecipitation and clouds with adas ecipitation fom ada: use a elationship etween the ada eflectivity facto Z (o Z e ) and the ainfall ate, (mm/hou) in the fom (called Z- elationships) whee A and ae constants depending on the type of ains. Z = A [1.1] Empiical Z- elationships ( in (mm/h) and Z in (mm 6 m -3 )): Statifom ain: Oogaphic ain: Snow: 1.6 Z = 00 [1.] 1.71 Z = 31 [1.3] Z = 000 [1.] The powe etuned to a ada (see Eq.[1.18]) can e nomalized using Eq.[0.] : ( in dbz ) = 10 log [1.] ef whee ef is the efeence powe which is often taken to e that powe which would e etuned if each m 3 of the atmosphee contained one dop with D= 1 mm (Z = 1 mm 6 m -3 ).

6 National Weathe Sevice adas The National Weathe Sevice (NWS) Weathe Suveillance adas (WS) ae of thee types: WS-7S, WS-7C, and WS-88D (D stands a Dopple ada (see Lectue ); ada Wavelength (cm) Dish Diamete (feet) ulse (micosecond) WS o WS-7C. 8 3 WS-88D o. dbz ainate (in/h) Tace Example of the WS ada image fo Coloado fo Apil, 00. 6

7 Space adas: TMM ada and CloudSat ada TMM ada- fist ada in space (launched in 1997) GHz,.3-km footpint, 0-m vetical esolution, 1.67 µs pulse duation, coss-tack scanning, 1-km swath, CloudSat ada: (will e launched in Apil 00) The pimay science ojectives: Quantitatively evaluate the epesentation of clouds and cloud pocesses in gloal atmospheic ciculation models, leading to impovements in oth weathe foecasting and climate pediction; Quantitatively evaluate the elationship etween the vetical pofiles of cloud liquid wate and ice content and the adiative heating y clouds. 7

8 Cloud ofiling ada (C): 9-GHz nadi-looking ada which measues the powe ackscatteed y clouds as a function of distance fom the ada; sensitivity defined y a minimum detectale eflectivity facto of -30 dbz, alongtack sampling of km, a dynamic ange of 70 db, 00 m vetical esolution and caliation accuacy of 1. db. 8