Lectue 13 Pinciples of active emote sensing: Rada sensing of clouds and pecipitation. Ojectives: 1. Rada asics. Main types of adas.. Basic antenna paametes. 3. Paticle ackscatteing and ada equation. 4. Sensing of pecipitation and clouds with adas (weathe adas, space adas: TRMM and CloudSat). Requied eading: S: 8.1, p.401-40, 5.7, 8..1, 8.., 8..3, 8.3 Tutoial and Quiz: http://www.met.tamu.edu/class/atmo151/tut/ada/adamain.html Additional/advanced eading: Online tutoial: Chapte 3: http://www.ccs.ncan.gc.ca/ccs/lean/tutoials/fundam/chapte3/chapte3_1_e.html CloudSat we site: http://cloudsat.atmos.colostate.edu/ TRMM we site: http://www.eoc.nasda.go.jp/trmm/index_e.htm http://tmm.gsfc.nasa.gov/ 1. Rada asics. Main types of adas. Rada is an active emote sensing system opeating at the micowave wavelength. Rada is a anging instument: (RAdio Detection And Ranging) Basic pinciples: The senso tansmits a micowave (adio) signal towads a taget and detects the ackscatteed adiation. The stength of the ackscatteed signal is measued to disciminate etween diffeent tagets and the time delay etween the tansmitted and eflected signals detemines the distance (o ange) to the taget. Two pimay advantages of adas: all-weathe and day /night imaging 1
Rada modes of opeation: Constant wave (CW) mode: continuous eam of electomagnetic adiation is tansmitted and eceived => povides infomation aout the path integated ackscatteing adiation Pulsed mode: tansmits shot pulses (typically 10-6 -10-8 s) and measues ackscatteing adiation (o echoes) as a function of the ange. Rada ange esolution: Conside a ada with pulse duation t p dv R R 1 R t-t p / => R = c ( t-t p /)/ t => R = ct/ t+t p / => R 1 = c ( t+t p /)/ Thus ada ange esolution is whee c is the speed of light. R 1 -R = ct p / = h/ [13.1] Polem: A police pulsed speed-measuing ada must e ale to esolve the etuns fom two cas sepaated y 10 m. Find the maximum pulse duation that can e used to pevent ovelapping of the etuns fom the two vehicles. Ignoe the Dopple effect. Solution: R 1 -R = 10 m thus t p = *10m/3*10 8 m/s = 6.67*10-7 s
Polaizing Rada has fou possile cominations of oth tansmit and eceive polaizations as follows: HH - fo hoizontal tansmit and hoizontal eceive, VV - fo vetical tansmit and vetical eceive, HV - fo hoizontal tansmit and vetical eceive, and VH - fo vetical tansmit and hoizontal eceive. Micowave ands commonly used in ada emote sensing: (see tale 3.3) Ka, K, and Ku ands: vey shot wavelengths used in ealy aione ada systems ut uncommon today. X-and: used extensively on aione systems fo militay teain mapping. C-and: common on many aione eseach systems (CCRS Convai-580 and NASA AiSAR) and spaceone systems (including ERS-1 and and RADARSAT). S-and: used on oad the Russian ALMAZ satellite. L-and: used onoad Ameican SEASAT and Japanese JERS-1 satellites and NASA aione system. P-and: longest ada wavelengths, used on NASA expeimental aione eseach system. Types of adas: Non-imaging: (altimetes and scatteometes) Altimetes (often nadi-looking) Opeation pinciple: tansmit shot micowave pulses and measue the ound tip time delay to tagets to detemine thei distance fom the senso; Applications: used on aicaft fo altitude detemination and on aicaft and satellites fo topogaphic mapping, sea suface height measuements fom which wind speed can e estimated Example: ERS altimete 3
Figue. 13.1 Reflection of an altimete pulse fom a flat suface. As the pulse advances, the illuminated aea gows apidly fom a point to a disk, as does the etuned powe. Eventually, an annulus is fomed and the geomety is such that the annulus aea emains constant as the diamete inceases. The etuned signal stength, which depends on the eflecting aea, gows apidly until the annulus is fomed, emains constant until the gowing annulus eaches the edge of the ada eam, whee it stats to diminish. t 0 t 0 +t p * t 0 =H/c t p *> t p t p is the duation of the pulse Example: TOPEX/Poseidon and Jason-1 ada altimete: sea suface height (deviation fom the mean in cm) 4
Scatteometes Opeation pinciple: tansmit micowave signal and measues the stength of the ackscatteing adiation (eflection); Applications: measuements of wind speed and wind diection ove the oceans. Goundased scatteometes ae used extensively to accuately measue the ackscatte fom vaious tagets in ode to chaacteize diffeent mateials and suface types. Example: NASA Quick Scatteomete (QuikSCAT): Rada: 13.4 gigahetz; 110-watt pulse at 189-hetz pulse epetition fequency (PRF) Antenna: 1-mete-diamete otating dish that poduces two spot eams, sweeping in a cicula patten QuikSCAT measuement capaility: 1,800-kilomete swath duing each oit povides appoximately 90-pecent coveage of Eath's oceans evey day. Wind-speed measuements of 3 to 0 m/s, with an accuacy of m/s; diection, with an accuacy of 0 degees. Wind vecto esolution of 5 km. 5
Imaging adas (see many examples elow): Non-imaging sensos take measuements in one linea dimension, as opposed to the twodimensional epesentation of imaging sensos: Side-looking viewing geomety of imaging ada systems: The platfom tavels fowad in the flight diection (A) with the nadi (B) diectly eneath the platfom. The micowave eam is tansmitted oliquely at ight angles to the diection of flight illuminating a swath (C). Range (D) efes to the acosstack dimension pependicula to the flight diection, while azimuth (E) efes to the along-tack dimension paallel to the flight diection.. Basic antenna paametes. Antenna is a stuctue which seves as a tansition etween wave popagating in fee space and the fluctuating voltages in the cicuit to which it is connected. Basic antenna paametes (in fee space): 1) Field patten: 3-D quantities involving the vaiation of EM field o EM powe as a function of the spheical coodinates θ and ϕ: powe patten P(θ, ϕ) (in W s -1 ) and nomalized powe patten: P n (θ, ϕ) = P(θ, ϕ) / P max (θ, ϕ) NOTE: the adiation patten of an antenna is analogous to the scatteed adiation patten y a paticle. 6
Figue 13. Antenna powe patten in pola coodinates and in ectangula coodinates. NOTE: same name : Majo loe=main loe = Main eam 7
Since the diffeence etween the powe tansmitted y an antenna, P t (in W), and the powe eceived fom ackscatteing is typically seveal odes of magnitude, the eceived signal is expessed in Deciels (db): P P( in db ) = 10 log [13.] P t ) Antenna gain is defined as the atio of the intensity at the peak of the tansmission patten, I p, to an isotopic intensity that is deived assuming that the total powe, P t (in W), is distiuted equally in all diection R is the ange. I p G = [13.3] P / 4πR t 3) Beam aea (o eam solid angle) (in s) is defined as Ω = ( θ, ϕ dω A P n ) 4π The eam aea is a solid angle though which all of the powe adiated y the antenna would steam if P(θ, ϕ) maintained its maximum value ove was zeo elsewhee => Powe adiated (in W) = P max (θ, ϕ) Ω A Ω A and [13.4] The eam aea can e appoximated y the poduct of the half-powe eamwidths (HPBW, see Fig.13.) in two pincipal planes whee Ω θ ϕ [13.5] A θ HP is θ of the HPBW and ϕ HP is the ϕ of the HPBW. HP HP 4) Effective apetue, A e, (in m ) is defined as whee is the wavelength (in m) = A Ω [13.6] e A 8
5) Diectivity, D, ( 1, dimensionless) is defined as the atio of the maximum powe to its aveage value: D = P max (θ, ϕ) / P av (θ, ϕ) Othe expessions fo the diectivity D = Ω A diectivity fom patten [13.7] Ae D = 4π diectivity fom apetue [13.8] Fiis tansmission fomula Conside a tansmitting antenna of effective apetue A et and eceiving antenna with effective apetue A e. The distance etween the antennas is R. If tansmitted powe P t is adiated y an isotopic souce, the powe eceived pe unit aea at the eceiving antenna if Pt F = [13.9] 4πR and the powe availale to the eceive is P = FA e [13.10] But the tansmitting antenna has an effective apetue A et and hence a diectivity D (fom Eq.[13.8]): Aet D = 4π Thus the powe availale to the eceive is D times geate 4πA P et = FAe D = FAe [13.11] Sustituting Eq.[13.9] into Eq.[13.11] gives o P A 4πA P = [13.1] t e et 4πR P Ae A = et [13.13] P R t 9
3. Paticle ackscatteing and ada equation. Recall Lectue 6 in which we intoduced the efficiencies (o efficiency factos), cosssections 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, σ d, is defined as the amount of incident adiation scatteed into the diection Θ pe unit of solid angle σ s σ d ( Θ) = P( Θ) [13.14] 4π whee P(Θ ) is the scatteing phase function Bistatic scatteing coss-section, σ i, is defined as σ 4πσ ( Θ) [13.15] i = d Backscatteing coss-section, σ, is defined as 0 σ 4πσ ( Θ= 180 ) [13.16] = d Using Eq.[13.14], Eq.[13.16] can e e-witten as 0 σ = P( Θ = 180 ) [13.17] σ s Recall that the incident intensity I i and scatteed intensity I s y a paticle elates as σ s P( Θ) I s ( Θ) = I i [13.18] R 4π whee R is the distance fom the paticle. Fo the ackscatteing case, we can wite σ ( 180 ) ( 180 ) = 0 0 s P Θ Fs Θ = = Fi [13.19] R 4π o F s Θ = 180 0 ) 4π R = F i ( σ [13.0] 10
Thus, the physical meaning of the ack-scatteing coss-section is the aea that, when multiplied y the incident flux, 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 and thus k = σ ( ) N( ) d [13.1] 1 0 k = ksp( Θ = 180 ) [13.] whee P(Θ ) is the scatteing phase function aveaged ove the size distiution. Small size paamete limit (Rayleigh limit): it can e shown fom Mie theoy (see S: 5.7.1) that π 5 6 σ = K D 4 [13.3] whee K = m m 1 + ; m if the efactive index of the paticle; and D is the paticle diamete. Rada 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 R. Suppose that the oject has the ackscatteing coss-section (called ada coss-section) σ. dv Ω A R σ 11
Using the Fiis tansmission fomula, we can find the powe intecepted y the oject P int as P Pt A ( y oject = et σ R [13.4] 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 = /4π (see Eq.[13.8]). And using the Fiis tansmission fomula, we can find the powe eceived y the antenna Pint ( y oject ) Ae P = [13.5] R 4π Sustituting Eq.[13.4] into Eq.[13.5], we otain P A σ = 4 called the ada equation [13.6] P 4πR t whee A =A et = A e is the effective apetue of antenna (same fo tansmitting and eceiving). 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 P A kdv = 4 [13.7] P 4πR Fom lida eam geomety, the illuminated volume can e appoximated as and using Eq.[13.1] fo k, we have t dv R θ HP ϕ h / [13.8] HP P A hθ HPϕ HP = σ ( ) N ( ) d P 4πR [13.9] t 1
Assuming that paticle ae in the Rayleigh limit and using Eq.[13.3], we have the aove equation can e e-witten as 4 P π A hθ HPϕ HP 6 = K D N ( D) dd 6 P 4 R t [13.30] K = C Z [13.31] R P whee facto C depends on the antenna chaacteistics; and 6 Z D N ( D) dd = is called the ada eflectivity facto. NOTE: Eq.[13.31] is often called the ada equation. We can elate the ackscatteing coefficient and ada eflectivity as k 5 5 5 = π 6 π 6 π σ ( D ) N ( D ) dd = K D N ( D) dd = K D N ( D) dd = 4 4 4 K Z [13.3] If paticle ae not in the Rayleigh limit and/o nonspheical (e.g., ice cystals), the effective ada eflectivity facto, Z e, is intoduced. In the moe geneal case, Eq.[13.31] 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): P R K = C Z exp( k ( ) d ) e R [13.33] whee k e is the extinction coefficient along the path. o 13
4. Sensing of pecipitation and clouds with adas Pinciple: use a elationship etween the ada eflectivity facto Z (o Z e ) and the ainfall ate, R (mm/hou) in the fom (called Z-R elationships) whee A and ae constants depending on the type of ains. Z = A R [13.34] Empiical Z-R elationships (R in (mm/h) and Z in (mm 6 m -3 )): Statifom ain: Oogaphic ain: Snow: 1.6 Z = 00R [13.35] 1.71 Z = 31 R [13.36] Z = 000 R [13.37] The powe etuned to a ada (see Eq.[13.31]) can e nomalized using Eq.[13.] : P P ( in dbz ) = 10 log [13.38] Pef whee P 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 ). National Weathe Sevice adas (http://ada.weathe.gov/) The National Weathe Sevice (NWS) Weathe Suveillance Radas (WSR) ae of thee types: WSR-57S, WSR-74C, and WSR-88D (D stands a Dopple ada) Rada Wavelength (cm) Dish Diamete (feet) Pulse (micosecond) WSR-57 10.3 1 0.5 o 4 WSR-74C 5.4 8 3 WSR-88D 11.1 8 1.57 o 4.5 14
dbz Rainate (in/h) 65 16+ 60 8.00 55 4.00 5.50 47 1.5 41 0.50 36 0.5 30 0.10 0 Tace Example of the WSR ada image fo Coloado fo Apil, 00. Space adas: TRMM ada and CloudSat ada. TRMM ada- fist ada in space (launched in 1997). 13.8 GHz, 4.3-km footpint, 50-m vetical esolution, 1.67 µs pulse duation, coss-tack scanning, 15-km swath, 15
CloudSat ada: Cloud Pofiling Rada (CPR): 94-GHz nadi-looking ada which measues the powe ackscatteed y clouds as a function of distance fom the ada; CPR System Chaacteistics Nominal Fequency Pulse Width PRF Minimum Detectale Z* Data Window Antenna Size Dynamic Range Integation Time Vetical Resolution Coss-tack Resolution Along-tack Resolution 94 GHz 3.3 µsec 4300 Hz -6 dbz 0-5 km 1.95 m 70 db 0.3 sec 500 m 1.4 km.5 km 16
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. NOTE: A good eview pape: Stephens et al., 00, The CloudSat mission and the A-Tain: A new dimension of spaceased osevations of clouds and pecipitation. BAMS, 1771-1790, 00. Figue 13.3 Topical stom, Aleto, ove the Gulf of Mexico. The collection of images eveals how CloudSat "sees" the stom diffeently fom othe weathe satellites and sensos. The NEXRAD stom detection ada is limited y distance, peventing it fom mapping all of the stom's pecipitation. The infaed image on the GOES-1 satellite can detect cloud cove ut cannot povide details eneath the stom's cloud tops. Data collected y CloudSat eveal the tue height and extent of the stom. Vey heavy ainfall (lack aows) was detected ove aout 400 kilometes of the satellite's tack. CloudSat also located a smalle thundestom (white aow) hidden unde the clouds. 17