Retrieval of three-dimensional distribution of rainfall parameters for rain attenuation correction using multi-parameter radar

Transcription

1 Retieval of thee-dimensional distibution of ainfall paametes fo ain attenuation coection using multi-paamete ada Dong-Soon Kim 1, Dong-In Lee 1, Masayuki Maki 2 and Ji-Young Gu 1 1 Depatment of Envionmental Atmospheic Sciences, Pukyong National Univesity, Busan, Koea 2 National Reseach Institute fo Eath Science and Disaste Pevention, Tsukuba, Japan

2 1. Intoduction The most common dual-polaimetic ada measuements : 1) The Reflectivity factos at and V polaization (Z, Z V, mm 6 m -3 ) 2) The Diffeential eflectivity facto (Z DR ) 3) The Popagation diffeential phase shift (Φ) Advantages of specific diffeential phase K 1) Independence of eceive and tansmitte calibations 2) No affection by attenuation 3) Immune to beam blockage 4) No bias by gound clutte cancelles ) Insensitive to vaiations in dop size distibution 6) Little bias by the pesence of hail 7) an be used to detect anomalous popagation

3 oect ainfall attenuation of ada paametes : Essential to especially fo X-band weathe ada. Pak. S. G et al.(2)

4 Seveal attenuation coection algoithms using diffeential popagation phase have been poposed. (A =az b, A = αk ) Bingi et al. 199 : Gamma RSD paametes (N, D, n) Linea Φ with fixed α Ryzhkov and Znic 199 (fo S-band) : Empiical linea Φ with aveage α Testud et al. 2 : Standad ZPI α is fixed a pioi : Does not account fo tempeatue and dop shape effects. N constant assumption Bing and handaseka 21 (fo -band): Iteative ZPI (Nea eal-time ) α is estimated optimally Accounts fo dop shape and tempeatue effects N constant assumption Pak et al. 2 (fo X-band) : Iteative ZPI α is estimated optimally

5 These studies use the elationship A =αk whee A the specific attenuation, K the specific diffeential phase. α (e.g..7~.6 db/deg. at X-band : Jameson 1992, aey et al 2, Pak et al. 24)) is vaiable along the ange in a pecipitation system, because the coefficient α depends on the tempeatue and aindop size distibution (DSD). This study poposes ae etieve ange pofile of optimum α descibes impoved ain attenuation coection algoithms fo ada eflectivity (Z ) and diffeential eflectivity (Z DR ) using measued diffeential popagation phase (Φ ).

6 2. Methodology [ Basic Equations ] The coection of ada eflectivity fo attenuation Z e ( ) = Z m ( )exp{.46 A ( s) ds} (1a) Z Ve ( ) = Z Vm ( )exp{.46 A V ( s) ds} (1b) Specific attenuation A (in dbkm -1 ) A ( ) = a[ Z ( )] b (2) And a linea elation between A and K (in km -1 ) is assumed with coefficient constant A ( ) = αk ( ) (3)

7 Specific attenuation A() Assuming Zm ( ) A( i ) A( ) = b i ( b i ) Z ( ) + A( ).46bZ ( s) ds m i b i m (4) A( ) = αk ( ) () Integation both sides of Eq.(2) with espect to ange fom to i, and ecalling that α 1 αk ( s) ds = ( Φ ( 1 ) Φ ( )) = 2 2 α ΔΦ (6) A( ) = I( Zm ( ; ) 1 b ) [ 1 exp{.23αbδφ ( ; 1 )}] [ 1 exp{.23αbδφ ( ; )}] I( ; ) 1 ( 1) (7a) I( ; ) =.46 bz ( s) ds b m (7b)

8 [ Pocedues ] 1. Assumptions b in Eq. (7).78 (Testud et al. 2) 2. Estimate A fom Eq.(7) using an assumed α 3. alculate Φ of Eq.(8b) using estimated A and calculate Eo of Eq.(8a) j = ) Φ, α) 4. Repeat the steps 2 and 3 fo α =.1 ~ 1.1 ( =.). Select optimum α which minimizes the Eo of Eq.(8a) 6. oect ain attenuation of Z by optimum A by N Eo = Φ Φ Δα α =.1 ~ 1.1 ( =.) Path-length ( ~ i ) : 3 km (ovelap 1. km) fil ( j ( A( s, α) (, α ) = 2 ds ( ) 1 α j Δα (8a) (8b) Z ( ) = Z m ( )exp{.46 A ( s) ds} (9) 7. oect ain attenuation of Z V (Z Vm =Z m /Z DRm ) as in the same pocedue of Z 8. alculate Z DR Z DR ( ) = Z Z V ( ) ( ) (1)

9 N Eo = Φ Φ j = fil ( j ) Φ ( j, α) A( s, α) (, α ) = 2 ds ( ) 1 α (8a) (8b) 1e+ 1e+4 Eo of Φ 1e+3 α opt =.26 1e+2 1e Ray 294 at 1:9 LST 11.Sep. 21 α (db/deg) Minimizes the Eo point

10 α =.1~1.1 (Δα :.) b =.78 Estimate A fom Eq.(7a) and (7b) using an assumed α b Zm ( )1 [ exp{.23α bδφ( ; 1 )}] A( ) = ( 1 I( ; ) 1 exp{.23α bδφ ( ; )} I( ; ) = b m 1 I( ; ).46 bz ( s) ds [ ] ) Select optimum α which minimizes the Eo of (8a) A, Φ c alculate Φ of (8b) using estimated A, and calculate Eo of (8a) Eo= Φ Φ i j= fil ( ) Φ j 1 (, α) A( s, α) (, α ) = 2 ds ( 1 ) α j (7a) (7b) (8a) (8b) Path-length = 3 km (Ovelap 1. km) oect ain attenuation of Z by optimum A Z ( ) = Z m ( )exp{.46 A ( s) ds} (9) oect ain attenuation of Z V (Z Vm =Z m /Z DRm ) as in the same pocedue of Z Z alculate Z DR ( ) Z ( )/ Z ( ) (1) DR = V

11 Unfolding of Φ (d) Φ Φ ( deg) φ' ( ) w φ ( )/ w = 1:9 LST 11 Sep. 21 (2. ) dp j j k dp j k j k k= 1 k= 1 (d) Φ (1) Φ ( deg) j-3 j-2 j-1 φ ( j-3 ) φ ( j-2 ) φ ( j-1 ) w j-3 =1 w j-2 =2 w j-1 =4 1 alculate φ ( j ) fom Eq.(1) 2 φ ( j )-φ ( j ) φ ( j )+18-φ ( j ) φ ( j )=φ ( j ) 3 φ ( j )-φ ( j ) φ ( j )+18-φ ( j ) φ ( j )=φ ( j )+18 4 alculate fom to max

12 FIR (Finite Impulse Response) Filteing 2 Φ ( deg) Φ (degee) Φ ( deg) Φ _Fil. Φ _Ob (d) Φ fil :19 LST 9 Aug. 23 (2.1 )

13 3. Results Location of MP-X Rada

14 NIED MP-X Rada Specifications Fequency Antenna type Scanning ange (speed) : AZ EL Antenna gain Beam-width Tansmission tube Peak powe Pulse width Pulse epetition fequency Polaization Dopple pocessing Noise figue Obsevation ange Obsevation paametes Gz 2.1m diamete paabolic antenna 36 ( 36 deg/s) -2 ~ + 92 ( 18 deg/s) 41.6 db 1.3 deg Magneton kw. μs 1,8 z oizontal, Vetical PPP, FFT 2.3 db 8 km Z, V D, W, Z DR, ρ hv, Φ, K

15 2 Z(dBZ) Z(dBZ) V (a) Z (b) Z V db Φ ( deg) (c) Z DR (d) il Φ f Fig. 1. Range-Azimuth images of polaimetic vaiables obseved at an elevation angle of 2.1, at 4:19 LST 9 Aug. 23: (a) Z, (b) Z V, (c) Z DR, (d) Φ fil

16 2 α α V (a) α Η (b) αv A 1 2 A V (c) A (d) A V α Fig. 2. Range-Azimuth images of (a), (b) V, (c) A and (d) A V at an elevation angle of 2.1, at 4:19 LST 9 Aug. 23. α

17 2 Z(dBZ) Z(dBZ) V (a) Z _ (b) ZV_ db Φ ( deg) (c) Z DR_ (d) Φ _ Fig. 3. Range-Azimuth images of coected polaimetic vaiables at an elevation angle of 2.1, at 4:19 LST 9 Aug. 23: (a) Z _, (b) Z V_, (c) Z DR_ and (d) Φ _

18 (a) 8 (b) Z _ Z _R (α =.36) Z (Measued) 1 8 Φ (degee) Z (dbz) 6 4 A 6 4 A (dbkm -1 ) 8 6 Φ _ Φ _R (α =.36) Φ fil (Measued) (a) 8 6 (b) Z _ 1 8 Φ (degee) Z (dbz) 4 Z _R (α =.36) Z (Measued) A 6 4 A (dbkm -1 ) Φ _ Φ _R (α =.36) Φ fil (Measued) Fig. 4. Range pofiles of polaimetic vaiables along azimuth angle of 21 and 33 at 4:19 LST 9 Aug. 23: (a) Φ, (b) Z and A 2

19 Fig.. Scatte plots of K and A vs. Z at 4:19 LST 9 Aug. 23: (a) and (c) compaisons with the coected data fo attenuation, (b) and (d) compaisons the measued Z _m.

20 Fig. 6. Scatte plots of Z and Z DR vs. Z at 4:19 LST 9 Aug. 23: (a) and (c) compaisons with the coected data fo attenuation, (b) and (d) compaisons the measued Z _m.

21 Fig. 1. Same as Fig. 6. except fo (a) A vs. K and (b) Z _ vs. Z _.

22 4. Summay and Discussion Impoved ain attenuation coection algoithms fo Z and Z DR, which extend the selfconsistent method with bette accuacy and obustness, have been intoduced. In the pesent study, ange pofiles of optimum α with 1. km esolution ae obtained to estimate specific attenuation. The optimum was distibuted ove a wide ange fom.16 to.76 db/deg. Reconstucted Φ using the optimum α shows good ageement with measued Φ. This means the validity of the coection of method Z and Z DR. The coected data K -Z, A -Z, Z DR -Z and Z -Z elations also show simila featue with theoetical values : A =.21K 1.22, Z =1.1Z oected Z and Z DR can be used to moe accuate estimation of ainfall paametes such as ain ate, hydometeo type, and DSD. Rainfall estimation based on K, Z and Z DR Estimation of aindop size distibution paametes Median volume diamete D Intecept paamete N W of a nomalized gamma dop size distibution