PACS: Mj, Dp, Ta

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1 * )2)3) 2) 4) 4) ) (, ) 2) (, ) 3) (, ) 4) (, ) ( ; ),.,,, ;,,,.. :,, PACS: Mj, 42.8.Dp, Ta,, 4., , Mouche, :, HH VV, Mouche., Zhag 0 Wag, HH VV,., 0,,,,,, 30,.,, Toporkov 3, Johso 4 Soriao 5,,. Toporkov Johso HH VV ;, Toporkov,,,, Toporkov * ( : ) ( : ). yua yeli@sohu.com c 202 Chiese Physical Society

2 .,,., 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, { } W l (K) = 4K 3 exp 0.74g2 K 2 U9.5 4, K K C, 0, K > K C, (7), U 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)

3 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 (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 cos θ i si θ i B 52 S l (B 4 Z l + B 34 D l ) B 55 B 44, (3)

5 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),,,,

6 . Bragg,, Bragg. HH VV, ( 5 ),,. 2 VV-pol (a) HH-pol; (b) 3 VV-pol (a) HH-pol; (b) 3, ,. 3,, (25 < θ i < 45 ),,., HH, VV, HH VV ( 4 ).,, 4 6, (.3 GHz). 6 HH

7 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 ;,, ;,,

8 , 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 Chapro B, Collard F, Ardhum F 2005 J. Geophys. Res. 0 C Johaesse J A, Kudryavtsev V, Akimov D, Eldevik T, Wither N, Chapro B 2005 J. Geophys. Res. 0 C Kudryavtsev V, Akimov D, Johaesse J A, Chapro B 2005 J. Geophys. Res. 0 doi: 0.029/ 2004JC Crombie D D 955 Nature Barrick D E 977 Radio Sci Bass F G, Fuks I M, Kalmykov A I, Ostrovsky I E, Roseberg A D 968 IEEE Tras. Ateas Propagat Wright J W, Keller W C 97 Phys. Fluids Mouche A, Chapro B, Reul N, Collard F 2008 Waves Radom ad Complex Media Zhag Y H, Wag Y H, Guo X 200 Chi. Phys. B Wag Y H, Zhag Y M 20 IEEE Tras. Geosci. Remote Sesig Guo X, Wag R, Wag Y H, Wu Z S 2008 Acta Phys. Si (i Chiese),,, Toporkov J V, Brow G S 2000 IEEE Tras. Geosci. Remote Sesig Johso J T, Toporkov J V, Brow G S 200 IEEE Tras. Geosci. Remote Sesig Soriao G, Joelso M, Saillard M, Marseille P C 2006 IEEE Tras. Geosci. Remote Sesig Wag Y H, Zhag Y M, He M X, Zhao C F 202 IEEE Tras. Geosci. Remote Sesig Zavoroty V U, Voroovich A G 998 IEEE Tras. Ateas Propagat Voroovich A G, Zavoroty V U 998 Waves Radom Media 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 Smith B G 967 Joural of Geophysical Research Keller W C, Plat W J 994 J. Geophys. Res

9 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 , 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: Mj, 42.8.Dp, Ta * Project supported by the Youg Scietists Fud of the Natioal Natural Sciece Foudatio of Chia (Grat No ), ad the Specialized Research Fud for the Doctoral Program of Higher Educatio (Grat No ). yua yeli@sohu.com

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