* )2)3) 2) 4) 4) ) (, 26607 ) 2) (, 26606 ) 3) (, 00049 ) 4) (, 266003 ) ( 20 8 22 ; 20 0 2 ),.,,, ;,,,.. :,, PACS: 42.68.Mj, 42.8.Dp, 92.60.Ta,, 4., 5 7. 9, Mouche, :, HH VV, Mouche., Zhag 0 Wag, HH VV,., 0,,,,,, 30,.,, Toporkov 3, Johso 4 Soriao 5,,. Toporkov Johso HH VV ;, Toporkov,,,, Toporkov * ( : 40906088) ( : 2008042302). E-mail: yua yeli@sohu.com c 202 Chiese Physical Society http://wulixb.iphy.ac.c 2423-
.,,., Wag 6,., Wag,. Zavorot 7,,., Zavorot. ( ),,.,,. 2,,, 7 Z(x, t) = Z l (x, t) + Z s (x, t), () Z l (x, t) Z s (x, t)., Z s (x, t) : 2k i cos θ i Z s (x, t).0, (2), k i θ i. Z l (x, t) Z s (x, t), W (K) W (K) = W l (K) + W s (K), (3) W l (K) W s (K), W (K), K K C, W l (K) = 0, K > K C, 0, K K C, W s (K) = W (K), K > K C, (4) K C K Bragg /6, K Bragg /3, K Bragg (θ i ) = 2k i si θ i Bragg 8.,., 3 : Z l (x, t) = ξ(k, t) exp(jk x), (5) j =,,ξ(k, t) t, ξ(k, t) = 2π {γ Wl (K ) 2 K exp jω(k )t + γ Wl ( K ) } expjω( K )t, (6) γ,. ω(k ) = g K., W l (K) P-M 3, { } 0.008 W l (K) = 4K 3 exp 0.74g2 K 2 U9.5 4, K K C, 0, K > K C, (7), U 9.5 9.5 m.,, S l (x, t) D l (x, t) V xl (x, t) V zl (x, t), S l (x, t) = jk ξ(k, t) exp(jk x), (8) D l (x, t) = K ξ(k 2, t) exp(jk x), (9) V xl (x, t) = ω ξ(k, t) exp(jk x), (0) 2423-2
V zl (x, t) = jω ξ(k, t) exp(jk x). () P (Z l, S l, D l ) P (Z l, S l, D l, V xl, V zl ) (Z l, S l, D l ) (Z l, S l, D l, V xl, V zl ). Z l, S l, D l,v xl V zl, P (Z l, S l, D l ) = = P (Z l, S l, D l, V xl, V zl ) = (2π) 3/2 N exp 2 U T N U (2π) 3/2 N exp (2π) 5/2 M exp A Zl 2 + 2A 3 D l Z l + A 22 Sl 2 + A 33 Dl 2 2 N 2 XT M X, (2) = (2π) 5/2 M exp{ B Zl 2 + B 22 Sl 2 + 2B 3 Z l D l + B 33 Dl 2 + 2B 4 Z l V xl + 2B 34 D l V xl + B 44 V 2 xl + 2B 25 S l V zl + B 55 V 2 zl/(2 M )}, (3), U T, X T N, M U T = Z l, S l, D l, (4) σ Z 2 l 0 σz 2 l D l N = 0 σ S 2 l 0, (5) σz 2 l D l 0 σd 2 l X T = Z l, S l, D l, V xl, V zl, (6) σ Z 2 l 0 σz 2 l D l σz 2 l V xl 0 0 σ S 2 l 0 0 σ 2 S l V zl M = σ Z 2 l D l 0 σd 2 l σd 2 l V xl 0, σ Z 2 l V xl 0 σd 2 l V xl σv 2 xl 0 0 σs 2 l V zl 0 0 σv 2 zl (7) U T X T U X, N M N M. (2) A ij N ij ; (3) B ij M m ij. 3, 9 σ pp (θ i ) = σ pp (θ i )P (S l)ds l, (8) θ i. P (S l).,, (8) σ pp (θ i ) = σ 0 pp(θ i )C pp Sh P (Z l, S l, D l )dz l ds l dd l, (9), σpp(θ 0 i ), Sh, C pp, σpp(θ 0 i ) C pp 8 σpp(θ 0 i ) = 4k3 i cos4 θ i α pp W s (2k i si θ i ), (20) ε 2 ε si 2 θ i + ε cos θ i 4 ε 2 ε si 2 θ i a +, HH-Pol, ε cos θ i b 4 C pp (θ i, r x ) = ε ε 2 ε si 2 (2) θ i + ε 2 ε cos θ i 4 ε ε 2 ε si 2 θ i a, VV-Pol. + ε 2 ε cos θ i b 4 2423-3
(20) (2) ε r cos θ i + ε r si θ, HH-pol, 2 α pp = (ε r )ε r ( + si 2 θ i ) si2 θ i ε r cos θ i +, VV-pol, ε r si θ 2 ) πτ a = 2 H() /3 (τ) exp( jτ + j5π, 2 ( j π b = 3 si 2 θ i 2τ ( 3jτ cos2 θ i )H () /3 (τ) + 3tH() /3 (τ) exp jτ + j 5π ), 2 τ = 3 k cos 3 θ i i ε r x si 2, r x = ( + S2 l )3/2, θ i D l H () /3 (τ) /3, ε, ε 2 Debye 20., (9) Sh 2 Sh = h(cot(θ i ) S l ) ( 2 erfc Zl ) Λ, (22) 2σZl 0, S l cot(θ i ), hcot(θ i ) S l =, S l < cot(θ i ), Λ = exp( v2 ) v πerfc(v) 2v, π v = cot θ i 2σSl, σ 2 Z l σ 2 S l. (2) (9). 4 f Dpp δf pq,, f Dpp δf pq 22 f Dpp = fσ pq σ pq, (23) δf 2 pp = f 2 σ pq σ pq f Dpp 2, (24),, f = k i π (V zl cos θ i + V xl si θ i ), σ pq = σ 0 ppc pp Sh. (23) (24) f Dpp = fσ0 pp(θ i )C ppsh P (Z l, S l, D l, V xl, V zl )dz l ds l dd l dv zl dv xl, (25) σ pp δf 2 pp = f 2 σ 0 pp(θ i )C ppsh P (Z l, S l, D l, V xl, V zl )dz l ds l dd l dv zl dv xl σ pp f Dpp 2. (26) (3) (25) (26), V xl, V zl, f Dpp 4 M π = σ λσ pp B44 B pp(θ 0 i ) C pp Sh Ψ α β dz l ds l dd l, (27) 55 δfpp 2 8 M π = σ λ 2 σ pp B44 B pp(θ 0 i ) C pp Sh Ψ α γ dz l ds l dd l, (28) 55 (B4 Z l + B 34 D l ) 2 α = exp β = 2 M B 44 + (B 25S l ) 2 2 M B 55 B 4 Z l + B 34 D l B 25 S l si θ i + cos θ i B 44 B 55 γ = si 2 θ i M B 44 + (B 4Z l + B 34 D l ) 2 B 2 44, (29), (30) + cos 2 θ i M B 55 + (B 52S l ) 2 B 2 55 + 2 cos θ i si θ i B 52 S l (B 4 Z l + B 34 D l ) B 55 B 44, (3) 2423-4
Ψ = Acta Phys. Si. Vol. 6, No. 2 (202) 2423 (2π) 5/2 M exp B Zl 2 + B 22 Sl 2 + 2B 3 Z l D l + B 33 Dl 2. (32) 2 M Bragg, f Dpp = f Dpp + f Bragg, (33) Bragg 3 f Bragg = gkbragg (θ i ). 2π 5 Toportov 3 MOMI, (.3 GHz)., (θ i 25 ),, : (a) U 9.5 = 5 m/s; (b) U 9.5 = 7 m/s, (θ i 25 )., θ i > 25,,. 2 7 m/s,, (a) (b), (.3 GHz). 2 : Total ; Tilt ; Cur+shadow ; Cur ; Noe ; Bragg Bragg ; Numerical 6. 2, 6,., 2, HH, ;, VV., HH. 9 HH VV, Kirchhoff,., 2,,,., 2 θ i > 80,. : ), ; 2),,,, 2423-5
. Bragg,, Bragg. HH VV, ( 5 ),,. 2 VV-pol (a) HH-pol; (b) 3 VV-pol (a) HH-pol; (b) 3, 2. 3 6,. 3,, (25 < θ i < 45 ),,., HH, VV, HH VV ( 4 ).,, 4 6, (.3 GHz). 6 HH 2423-6
5 40 < θ i < 75, VV,. 7, HH VV, 6. 7, HH VV,,,, ( ).,,,,.,,,. 7, 6 6, (a) HH-pol; (b) VV-pol, ;,., VV,,,, VV ;,,.,,,,.,, :,, HH VV ;,, ;,, 2423-7
, HH,, VV ;,,, HH VV, HH VV,.,. Johso J T, Burkholder R J, Toporkov J V, yzega D R, Plat W J 2009 IEEE Tras. Geosci. Remote Sesig 47 64 2 Chapro B, Collard F, Ardhum F 2005 J. Geophys. Res. 0 C07008 3 Johaesse J A, Kudryavtsev V, Akimov D, Eldevik T, Wither N, Chapro B 2005 J. Geophys. Res. 0 C0707 4 Kudryavtsev V, Akimov D, Johaesse J A, Chapro B 2005 J. Geophys. Res. 0 doi: 0.029/ 2004JC002505 5 Crombie D D 955 Nature 75 68 6 Barrick D E 977 Radio Sci. 2 45 7 Bass F G, Fuks I M, Kalmykov A I, Ostrovsky I E, Roseberg A D 968 IEEE Tras. Ateas Propagat. 6 560 8 Wright J W, Keller W C 97 Phys. Fluids 4 466 9 Mouche A, Chapro B, Reul N, Collard F 2008 Waves Radom ad Complex Media 8 85 0 Zhag Y H, Wag Y H, Guo X 200 Chi. Phys. B 9 05403 Wag Y H, Zhag Y M 20 IEEE Tras. Geosci. Remote Sesig 49 07 2 Guo X, Wag R, Wag Y H, Wu Z S 2008 Acta Phys. Si. 57 3464 (i Chiese),,, 2008 57 3464 3 Toporkov J V, Brow G S 2000 IEEE Tras. Geosci. Remote Sesig 38 66 4 Johso J T, Toporkov J V, Brow G S 200 IEEE Tras. Geosci. Remote Sesig 39 24 5 Soriao G, Joelso M, Saillard M, Marseille P C 2006 IEEE Tras. Geosci. Remote Sesig 44 2430 6 Wag Y H, Zhag Y M, He M X, Zhao C F 202 IEEE Tras. Geosci. Remote Sesig 50 04 7 Zavoroty V U, Voroovich A G 998 IEEE Tras. Ateas Propagat 46 84 8 Voroovich A G, Zavoroty V U 998 Waves Radom Media 8 4 9 Ulaby F T, Moore R K, Fug A K 982 Microwave Remote Sesig. Vol. II (Readig, MA: Addisio- Wesbey) 20 Klei A, Swift C T 977 IEEE Tras. Ateas Propagat 25 04 2 Smith B G 967 Joural of Geophysical Research 72 4059 22 Keller W C, Plat W J 994 J. Geophys. Res. 99 975 2423-8
Ivestigatio o Doppler spectra of microwave scatterig from sea surface Jiag We-Zheg )2)3) Yua Ye-i 2) Wag Yu-Hua 4) Zhag Ya-Mi 4) ) ( Istitute of Oceaology, Chiese Academy of Scieces, Qigdao 26607, Chia ) 2) ( The First Istitute of Oceaography, SOA, Qigdao 26606, Chia ) 3) ( Graduate School, Chiese Academy of Scieces, Beijig 00049, Chia ) 4) ( College of Iformatio Sciece.& Egieerig, Ocea Uiversity of Chia, Qigdao 266003, Chia ) ( Received 22 August 20; revised mauscript received 2 October 20 ) Abstract Based o the composite surface scatterig model, the aalytical formulas for Doppler shift ad badwidth of radar echoes retur from time-varyig sea surface are derived. I our derivatios, the iflueces of the tilt modulatio, the shadow ad the curvature of large-scale udulatig waves are all take ito accout for achievig more reasoable results. Comparisos betwee the theoretical results ad direct umerical simulatios demostrate that the aalytical formulas ca sigificatly improve the simulated results. Ad the effects of the tilt modulatio, the shadow ad the curvature o Doppler spectral properties are discussed i detail. From the simulated results, it is foud that the predicted Doppler shifts are always larger i HH-polarizatio tha i VV-polarizatio due to the tilt modulatio of large-scale waves. I additio, at low-grazig agles, the shadow of large-scale waves results i a rapid icrease of the predicted Doppler shift, ad o the cotrary maks the badwidth arrower. Keywords: time-varyig sea surface, electromagetic scatterig, Doppler spectra PACS: 42.68.Mj, 42.8.Dp, 92.60.Ta * Project supported by the Youg Scietists Fud of the Natioal Natural Sciece Foudatio of Chia (Grat No. 40906088), ad the Specialized Research Fud for the Doctoral Program of Higher Educatio (Grat No. 2008042302). E-mail: yua yeli@sohu.com 2423-9