RETRIEVAL OF VERTICAL RAIN RATE PROFILE BY DUAL-FREQUENCY RADAR DATA

Transcription

1 P5R.8 RETRIEVAL OF VERTICAL RAIN RATE PROFILE BY DUAL-FREQUENCY RADAR DATA Koyuu Iwanami 1 Yohei Chono 2 Toshio Haimaya 2 Jacques Testud 3 Masayuki Maki 1 Ryohei Misumi 1 Sang-Goon Pak 1 1: National Reseach Institute fo Eath Science and Disaste Pevention (NIED) Tsukuba Japan 2: Hokkaido Univesity Sappoo Japan 3: NOVIMET Vélizy Fance 1. INTRODUCTION Based on the success of the TRMM mission GPM (Global Pecipitation Measuement) mission was poposed. A dual-fequency pecipitation ada (DPR) on the coe satellite of GPM is expected to play a significant ole in the mission (Iguchi 23). Testud (24) descibed that thee wee two appoaches that is diffeential (Iguchi and Meneghini 1995) and integal (Meneghini and Nakamua 199) techniques in dual-fequency algoithm fo the etieval of ain ate pofile. In this study etieval algoithm of vetical ain ate pofile by dual-fequency ada was poposed in line with integal appoach and applied to the NIED gound-based ada data. 2. ALGORITHM The developed etieval algoithm of vetical ain ate pofile by dual-fequency ada uses a mutual constaint that expesses the consistency of the along path attenuations ove a common segment sampled at the two fequencies and the assumption that N is constant along the pofile (Testud 24). 2.1 Relationships between DSD Moments The invese model consists of thee elationships between two of eflectivity facto Z in mm 6 m -3 specific attenuation A in dbkm -1 and ain ate R in mmh -1 nomalized by the nomalized intecept paamete N of DSD (dop size distibution) of ain in the poposed algoithm. N is defined as 4 4 LWC N = 4 (1) πρ D w whee LWC is the liquid wate content ρ w is the density of liquid wate and D m is the mean volume diamete (atio of the fouth to the thid moment of the DSD). N epesents the intecept paamete N of the exponential distibution with the same LWC and D m whateve the shape of the DSD (Testud et al. 21). It was shown in Testud et al. (2) that quasi-univesal elationships wee established Coesponding autho addess: Koyuu Iwanami National Reseach Institute fo Eath Science and Disaste Pevention (NIED) Tsukuba 35-6 Japan; iwanami@bosai.go.jp m between any couple of integal paametes of the DSD afte the nomalization by N and the elationships might be satisfactoily appoximated by powe laws. The following epesentations wee used as the invese model fo the etieval: ( 1 b) b A = an Z (2) ( 1 d ) d R = cn Z (3) ( 1 f ) f R = en A (4) whee a b c d e and f ae the coefficients dependent on the tempeatue. These coefficients at X- Ka- and W-band wee deived fom Z and A calculated by the T-Matix method (Mishchenko et al. 2 22) and R using DSD data. DSD data wee measued by ORS (Optical Raindop Spectomete) and the RD-69 disdometes at seveal sites in Japan fom 1996 to 23. The calculation was done on the conditions of 15 C tempeatue axis atio by Andsage et al. (1999) teminal velocity appoximated by Atlas and Ulbich (1977) of aindop. The coefficients in the elationships (2) to (4) wee deived by the least squae fitting fom scatte plots such as Fig. 1. It was found that uncetainty of the elationships could be deceased by the nomalization compaing top with bottom panels in Fig. 1. Heeafte the combination of X- and Ka-band ada data will be consideed because the effect of moment of DSD stongly appeaed at W-band. The diffeences of the coefficients with DSD obsevation sites wee small. 2.2 Retieval Algoithm The appaent (attenuated) ada eflectivity Z a can be epesented by the equivalent ada eflectivity Z e and specific attenuation A as Za() = Ze()exp.46 A() u du (5) whee is the ange fom the ada. Hitschfeld and Bodan (1954) showed the solution of (5) is b A ( n) Za( i) A ( i ) = (6) b Z ( ) + A( ) I( ) whee a n n i n n b I ( ) = i n.46 b Za( udu ). This means that the specific attenuation pofile A( i ) along segment [ n ] is the function of the pofile Z a ( i ) and the value of A at the fa bound n. Hee it was assumed that N was constant along i (7)

2 FIG. 1. Scatte plots of elationships between A and Z (left) R and Z (cente) and R and A (ight) befoe (top) and afte (bottom) the nomalization by N at Ka-band. Each paamete was calculated by T-matix method using obseved DSD data. the segment [ n ]. Testud et al. (21) demonstated that the vaiability of N was essential fom event to event and this vaiability was much moe modeate within one paticula event afte sepaating convective and statifom ain. Then N in the segment [ n ] can be expessed as whee ( bq) 1 exp.46 N = ai( ) n n 1 ( 1 b) Q = A( u) du. (9) Ou etieval algoithm by dual-fequency ada utilizes a mutual constaint that expesses the consistency of the along path attenuations ove a common segment sampled at the two fequencies (Testud 24) which can be expessed as n ( 1 q) q 2 = 1 (8) n A ( udu ) pn A( udu ) (1) whee [ n ] epesent a common inteval of data sampled by the two fequencies and ( 1 q) q 2 = (11) A pn A 1 is the powe low elationship elating the specific attenuations at two fequencies. Subscipt 1 and 2 indicates the lowe and highe fequency espectively. The coefficients p and q wee also deived fom T-Matix calculation using DSD data. Figue 2 shows scatte plots of elationship between specific attenuations at the X- and Ka-band befoe and afte the nomalization by the N. The etieval pocedue depicted in Fig. 3 is as FIG. 2. Scatte plots of elationships between specific attenuations A at Ka- and X-band befoe (top) and afte (bottom) the nomalization by N. Values of A wee calculated by T-matix method using obseved DSD data.

3 follows. Subscipt X and Ka shows X- and Ka-band espectively. (i) Fist specific attenuation A X ( n ) at the fa bound n at X-band is assumed and the vetical pofile A X ( i ) is calculated by the obseved pofile of Z ax ( i ) though (6). (ii) Q X is calculated fom pofile A X ( i ) then N X is deived fom Q X and Z ax ( i ). (iii) A Ka ( n ) at the fa bound n at Ka-band is assumed and the vetical pofile A Ka ( i ) is calculated by the obseved pofile of Z aka ( i ) in the same way as (i). (iv) N Ka is calculated as in (ii). (v) A Ka ( n ) which makes N Ka equal to N X is deived by compaing them in (ii) and (iv). So fa a set of A Ka ( n ) and N fo one A X ( n ) can be detemined. (vi) A set of A X ( i ) and A Ka ( i ) calculated fom A X ( n ) and A Ka ( n ) with N in (v) is estimated by the mutual constaint of (1) and the best set of A X ( n ) A Ka ( n ) and N is selected. (vii) Rain ate pofile R( i ) is calculated fom the A( n ) and N by (4). Two pofiles of R X ( i ) and R Ka ( i ) can be available fom the A X ( i ) and A Ka ( i ) espectively. by the model calculations befoe its application to obseved ada data. The test pofiles of appaent eflectivity facto Z a ( i ) at X- and Ka-band wee made by calculated eflectivity facto Z e ( i ) and specific attenuation A( i ) fom assumed pofiles of ain ate R O ( i ) and N. Then ain ate pofiles wee etieved fom the test data of appaent eflectivity facto pofiles. The value of ain ate on the gound suface R O () and N was set to 7.6 mmh -1 and m -4 espectively. Thee pofiles of R O ( i ) which was constant inceasing and deceasing with height wee assumed. Figue 4 indicates the etieval esults fo thee types of ain ate pofiles. Left panels show the Z a ( i ) at X- and Ka-band and ight panels show model R O ( i ) etieved R X ( i ) and R Ka ( i ) togethe with R MP ( i ) calculated by Z-R elationship (Z=2R 1.6 ) using Z ax ( i ). A X ( n ) A Ka ( n ) Z ax ( i ) (6) Z aka ( i ) A X ( i ) A Ka ( i ) (8) N X (=) N Ka A X ( n ) A Ka ( n ) N (1) A X ( n ) A Ka ( n ) N (6) A X ( i ) A Ka ( i ) 3. RESULTS (4) 3.1 Model Calculations R( i ) FIG. 3. Schematic chat of the poposed algoithm. Numbes in paentheses indicate equations in text. In ode to veify the developed ain ate etieval algoithm by dual-fequency ada data it was tested FIG. 4. Left panels show the pofile of appaent eflectivity facto Z a ( i ) at X- (blue) and Ka-band (ed) calculated fom model pofile of ain ate R O ( i ) (black line) in the ight panels and N. Right panels indicates etieval esults of ain ate pofiles of R X ( i ) (blue dots) and R Ka ( i ) (ed dots) togethe with R MP ( i ) estimated by Z-R elationship (geen dots) fo thee model pofiles of R O ( i ). Although the etieved ain ate pofiles had tendency to slightly undeestimate they could estimate model pofiles accuately and wee much

4 bette than by Z-R elationship. The maximum etieved eos at the highest level (3 m) wee 5 and 11 % fo R X and R Ka fo the model pofile inceasing with height. Fo the model pofiles constant and inceasing with height R Ka could etieve moe accuately than R X in the lowe altitude (that is nea the ada) but vice vesa in the highe altitude. It was possible to eplace (i) and (ii) with (iii) and (iv) in the ode of etieval pocedue descibed in the pevious section but the etieval eos became lage. The accuate data nea the gound suface could not obtained by gound-based adas because of the hadwae limitation and gound clutte. In the case without data nea the gound suface it was also possible to etieve ain ate pofile with small eo by assuming constant ain ate of measued value on the gound in the ange of no data. 3.2 Application to Obseved Data The poposed algoithm was applied to the obseved data. A field expeiment named Vetically Pointing Measuements Tsukuba 21 (VPM_ TKB1) was caied out by using the gound-based tiple-band multipaamete ada system (Iwanami et al. 21) at the NIED (36.12N 14.9E) in Tsukuba Japan duing June 12 to July Thee adas MP-X and MP-Ka/W continuously measued vetical pofiles by PPI scans of 9 degee elevation. The ange esolution was 1 m fo MP-X and 5 m fo MP-Ka/W adas and the numbe of pulse integation was 256. The etieval algoithm was applied to one minute aveage ada data afte Ka-band data wee set to 1 m esolution data. Rain ate data by disdomete RD-69 on the gound wee also used fo the etieval. Figue 5 shows time height coss sections of the obseved Z ax (top) Z aka (middle) and etieved ain ate (bottom) fom 11:43 to 11:51 JST on June It was found that easonable ain ate pofiles wee deived but fo 11:43. Z ax 1/6/21 Z aka 1/6/21 R x 1/6/21 4. DISCUSSIONS It was assumed that N is constant along the segment [ n ] in this algoithm. Sensitivity tests fo N vaiations by 1 5 % and one ode with height wee made. Calculations wee made fo the same thee ain ate pofiles as in Fig. 4 and Z a ( i ) wee made fo two cases that N in the height ange uppe than 15 m (N H ) was lage and smalle than that below 15 m (N L ). Results fo the constant ain ate pofile in case of N H > N L and N H < N L wee shown in Fig. 6 and 7 espectively. In case of N H > N L etieved ain ate pofiles undeestimated (Fig. 6) on the othe hand oveestimated in uppe level and undeestimated in lowe level in case of N H < N L (Fig. 7). The eos of etieved ain ate in the highe levels wee less than about 1 15 and 5 % fo N vaiations by 1 5 % and one ode espectively. The effect of the FIG. 5. Time height coss sections of the obseved Z ax (top) Z aka (middle) and etieved ain ate (bottom) fom 11:43 to 11:51 JST on June N vaiations on the etieval esults wee not lage. Retieval eos in case of N H > N L wee lage than N H < N L by about 5 %. It was also found that the etieval eo could be suppessed by the application of the etieval fo each segment if the height of N

5 FIG. 6. Same as Fig. 4 but fo only the constant ain ate pofile with height in case of N H > N L. Only the model (black line) and etieved R X ( i ) (blue dots) ain ate pofiles ae shown in the ight panels. change was known (figues not shown). This suggests that the segmentation of the ay like the ZPHI algoithm (Testud et al. 2) may impove the poposed etieval algoithm. 5. SUMMARY Retieval algoithm of vetical ain ate pofile by dual-fequency ada was developed and applied to the NIED gound-based ada data. The algoithm uses a mutual constaint that expesses the consistency of the along path attenuations ove a common segment sampled at the two fequencies and the assumption that N is constant along the pofile (Testud 24). Relationships between two of eflectivity facto specific attenuation and ain ate nomalized by the nomalized intecept paamete N (Testud et al. 21) at X- Ka- and W-band wee obtained by T-Matix calculations using DSD data measued with disdometes at seveal sites in Japan. Uncetainty of the elationships could be deceased by the nomalization although the effect of moment of DSD stongly appeaed at W-band. FIG. 7. Same as Fig. 6 but fo in case of N H < N L. The poposed algoithm was tested by model calculations. The test pofiles of appaent eflectivity facto wee made by calculated eflectivity facto and specific attenuation fom assumed pofiles of ain ate and N. Then ain ate pofiles wee etieved fom the test data of appaent eflectivity facto pofiles. The etieved eos wee less than 5 % and lage at highe altitude because of the accumulated eo of attenuation estimation but esults wee much bette than by Z-R elationship. Sensitivity tests fo N vaiations by 1 5 % and one ode with height wee also made and eos of etieved ain ate wee less than about 1 15 and 5 % espectively. If the height of N change was known the etieval eo could be suppessed. In the case without data nea the gound suface it was possible to etieve ain ate pofile with small eo by assuming constant ain ate in the ange of no data by measued ain ate on the gound. The poposed algoithm was applied to the data obseved by the NIED X- and Ka-band adas in Tsukuba city Japan in June 21 and easonable ain ate pofiles wee deived. It is necessay to calibate ada eflectivity well to etieve ain ate accuately. ACKNOWLEDGEMENTS

6 This wok has been patly suppoted by CREST (Coe Reseach fo Evolutional Science and Technology) of JST (Japan Science and Technology Copoation) entitled GSMaP: Global Satellite Mapping of Pecipitation. The authos thank D. Akihio Hashimoto fom AESTO (Advanced Eath Science and Technology Oganization) Japan fo his poviding DSD data measued by the Optical Raindop Spectomete and those analysis pogams. REFERENCES Andsage K. K. V. Bead and N. F. Laid 1999: Laboatoy measuements of axis atios fo lage aindops. J. Atmos. Sci Atlas D. and C. W. Wlbich 1977: Path- and aea-integated ainfall measuement by micowave attenuation in the 1-3 cm band. J. Appl. Meteo Hitschfeld W. and J. Bodan 1954: Eos inheent in ada measuement of ainfall at attenuating wavelengths. J. Meteo Iguchi T. 23: Spacebone pecipitation adas in TRMM and GPM. Poc. 31 st Conf. Rada Meteo Iguchi T. and R. Meneghini 1995: Diffeential equations fo dual-fequency ada etuns. Poc. 27 th Conf. Rada Meteo Iwanami K. R. Misumi M. Maki T. Wakayama K. Hata and S. Watanabe 21: Development of a multipaamete ada system on mobile platfom. Poc. 3 th Inten l Conf. Rada Meteo Meneghini R. and K. Nakamua 199: Range pofiling of the ain ate by an aibone weathe ada. Remote Sensing Envion Mishchenko M. I. J. W. Hovenie and L. D. Tavis 2: Light Scatteing by Nonspheical Paticles. Academic Pess. 69pp. Mishchenko M. I. L. D. Tavis and A. A. Lacis 22: Scatteing Absoption and Emission of Light by Small Paticles. Cambidge Univ. Pess. 445pp. Testud J. 24: Pecipitation measuements fom space. Weathe Rada Spinge Testud J. E. Le Boua E. Obligis and M. Ali-Mehenni 2: The ain pofile algoithm applied to polaimetic weathe ada. J. Atmos. Ocean. Tech Testud J. S. Ouy R. A. Black P. Amayenc and X. Dou 21: The concept of nomalized distibution to descibe aindop specta: A tool fo cloud physics and cloud emote sensing. J. Appl. Meteo