RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER 1 61 Influence of Sea Surface Roughne on the Electromagnetic Wave Propagation in the Duct Environment Xiaofeng ZHAO, Sixun HUANG Intitute of Meteorology, PLA Univ. of Sci. & Tech., Nanjing 1111, China zxf_bet@16.com, huangxp@yahoo.com.cn Abtract. Thi paper deal with a tudy of the influence of ea urface roughne on the electromagnetic wave propagation in the duct environment. The problem of electromagnetic wave propagation i modeled by uing the parabolic equation method. The roughne of the ea urface i computed by modifying the mooth urface Frenel reflection coefficient to account for the reduction in the pecular reflection due to the roughne reulting from ea wind peed. The propagation model i olved by the mixed Fourier plit-tep algorithm. Numerical experiment indicate that wind-driven roughened ea urface ha an impact on the electromagnetic wave propagation in the duct environment, the trength i intenified along with the increment of ea wind peed /or the operating frequencie. In a fixed duct environment, however, proper dipoition of the tranmitter could reduce thee impact. Keyword Electromagnetic wave propagation, parabolic equation, ea wind peed, evaporation duct. 1. Introduction Ducted propagation over the ea urface can eriouly impact hipboard radar communication, which i extremely important in telecommunication for the Navy. The phyic of propagation i affected by ever-changing atmopheric condition by complex feature on the ea urface [1]. Numerou numerical method are available for predicting electromagnetic wave propagation uch a geometric optic, normal mode analyi, parabolic equation (PE) method, combination of the above [-5]. The mot popular approach of the mentioned above i PE which could be ued to predict electromagnetic wave propagation in a complex environment. Previouly, ue of the PE to invetigate propagation in an inhomogeneou atmophere over irregular terrain ha been publihed a lot [6-1]. However, the reearche of the propagation over the rough ea urface are very few. In 3, Guillet et al. employed PE to tudied low grazing angle propagation above rough urface [11]. In thi paper, we will employ Miller-Brown- Vegh model to tudy the influence of wind-driven roughne on the electromagnetic wave propagation in the evaporation duct environment. A detailed dicuion will be focued on different numerical value for variou important parameter, i.e. ea wind peed, evaporation duct height, operating frequency, antenna altitude. The remainder of thi paper i organized a follow. In ection, a imple decription of the electromagnetic wave propagation model i introduced. Section 3 contruct the relationhip between the rough ea urface the mooth ea urface through the reflection coefficient. Finally, a dicuion of imulation of different parameter i preented in ection 4.. The Electromagnetic Wave Propagation Model For many year now PE ha been ued to model electromagnetic wave propagation in a complex environment. PE can be derived from the wave equation under certain aumption, it ha the form [7], n x, z1u x, z u( x, z) u( x, z) ik k (1) z x where u repreent a calar component of the electric field for horizontal polarization or a calar component of the magnetic field for vertical polarization, k i the free-pace wave number, x i the range axi, z i the height axi, n i the index of refraction. Owing to n i very cloe to unity, for environmental input, modified refractivity M i ued to decribe the information of the atmopheric environment. M i defined by z 6 M( x, z) n( x, z) 1 1 () ae where a e i the radiu of the earth. The two mot popular approache to numerically olving PE are the ue of implicit finite difference the Fourier plit-tep algorithm. However, the latter i much
6 XIAOFENG ZHAO, SIXUN HUANG, INFLUENCE OF SEA SURFACE ROUGHNESS ON THE ELECTROMAGNETIC WAVE more numerically efficient [3], i adopted in our calculation. Generally, plit-tep PE olution to electromagnetic problem implemented either Dirichlet or Neumann boundary condition correponding to horizontally or vertically polarized propagation, repectively, over a perfectly conduct urface. In rough ea urface, however, the perfectly conduct urface aumption i not ufficient ue of a urface impedance i highly deirable. The impedance boundary condition i ( xz, ) ux (,) (3) z z 1 1 ik in where Γ i the Frenel reflection coefficient θ i the grazing angle meaured from the local urface tangent, i.e. the complement of the incidence angle. The mixed Fourier tranform introduced a a rigorou method to incorporate urface impedance into plit-tep olution of the parabolic equation wa decribed in detail in [4], a fat computation algorithm for the mixed Fourier tranform plit-tep olution of PE wa preented in [1]. 3. Sea Surface Roughne Modeling Uing the impedance boundary condition, the reflection coefficient Γ hould be determined. In term of the law of reflection, for a giving grazing angle θ, the mooth urface reflection coefficient Γ S for horizontal polarization vertical polarization could, repectively, be decribed a [13] in n co SH (5) in n co SV n in n in n co n co where n i the complex dielectric contant, defined by n (4) (6) i6. (7) Here, ε σ are the relative permittivity conductivity repectively, which are function of radio frequency recommended by International Radio Conulting Committee (CCIR), λ i the electromagnetic wave length. One approach to modeling ea urface roughne involve multiplying the mooth urface Frenel reflection coefficient by a roughne parameter, which ha been calculated by Ament [14] for a Gauian ditribution of height corrected by Miller et al. [15]. The rough urface reflection coefficient, Γ R, i taken a R S exp[ ( g) ] I[( g) ] (8) h in g (9) where I (x) i the modified Beel function J (ix), σ h i the tard deviation of the ea urface elevation determined from wind peed, μ (m/), by h.51. (1) A mentioned above, when modifying reflection coefficient uing the Miller-Brown-Vegh model, the reulting expreion for α ha a trong dependence on the local grazing angle θ which i, in general, a function of geometry, more importantly, atmopheric refractivity. Dockery Kuttler have pointed out that geometric optic (GO) could provide a qualified grazing angle etimate in the evaporation duct environment [1]. Therefore, GO will be adopted in our computation. 4. Numerical Experiment The purpoe of thi paper i to tudy the influence of ea urface roughne to the electromagnetic wave propagation in the evaporation duct environment. Firt, an evaporation duct model hould be elected. For thermally neutral condition in which the air ea temperature are equal, the modified refractivity M can be determined at any height z by the relationhip [16] M ( z) M().15z.15dln[( z z ) / z ] (11) where d i evaporation duct height, ln[ ] i the natural logarithm, z i momentum roughne length of 1.5 1-4 m. In the following, two experiment are performed. For every experiment, a Gauian antenna pattern i ued horizontal polarization i aumed. The elevation angle i deg the beamwidth i 1 deg. The detailed expreion of the Gauian antenna pattern could refer to [7]. Experiment 1: The evaporation duct height the antenna altitude are fixed at 3 m 1 m, repectively. Then, the propagation characteritic at different ea wind peed operating frequencie are invetigated. The ea wind peed are changeable, from m/ to 1 m/. Uing the PE/mixed Fourier plit-tep algorithm, the value of one-way propagation lo i computed. Here, the computation domain i fixed on [1 km m], the horizontal increment vertical increment are 5 m 1 m, repectively. The coverage diagram (db) for one-way propagation lo i hown in Fig. 1, in which the operating frequency i 8 MHz, Fig. 1(a) i for ea wind peed of m/, Fig. 1(b) i for 1 m/, Fig. 1(c) i the abolute difference of the above two figure.
RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER 1 63 Fig. 1. The coverage diagram (db) for one-way propagation lo. (a) i for m/; (b) i for 1m/, (c) i the abolute difference of (a) (b). Fig.. Comparion of propagation lo at antenna altitude (1 m) in a 3 m evaporation duct between mooth ea urface (ea wind peed of m/, olid line) rough ea urface (ea wind peed of 1 m/, dahed line). The operating frequency i 8 MHz. Fig. 3. Relative error at different operating frequencie different ea wind peed.
64 XIAOFENG ZHAO, SIXUN HUANG, INFLUENCE OF SEA SURFACE ROUGHNESS ON THE ELECTROMAGNETIC WAVE In order to analyze the influence of wind-driven roughne on the electromagnetic wave propagation, the value of propagation lo at the antenna altitude are elected to compute the relative error of the propagation lo between the mooth ea urface the rough ea urface. The relative error Λ i defined a 1 N u PLi PLi 1% (1) N P i1 Li where P L u i the value of propagation lo correponding to the wind-driven rough ea urface P L correponding to mooth urface, N i the number of dicrete point in the horizontal direction. The value of propagation lo along the horizontal ditance at the antenna altitude 1 m in Fig. 1(a) 1(b) are preented in Fig.. Uing equation (1), the relative error at different operating frequencie different ea wind peed are hown in Fig. 3. From Fig. 1-3, it i clearly een that, conidering the ea urface roughne, the electromagnetic propagation loe more energy than the mooth urface cae, the propagation loe are trengthening with the ditance. Fig. 3 how that with the increment of ea wind peed /or operating frequency, the relative error between mooth ea urface rough ea urface become larger larger. In 1 MHz 1 m/ cae, the relative error could even exceed 8.7%. However, when the ea wind peed i under 5 m/, the error could be limited within 1.%. Experiment : The operating frequency i fixed at 8 MHz. The relationhip between evaporation duct height antenna altitude will be tudied. The evaporation duct height are et at 1 m, m, 3 m. Within the duct, the antenna altitude are changeable, from 1 m to the duct height. Fig. 4 how the relative error between mooth urface cae (ea wind peed of m/) rough urface cae (ea wind peed of 1 m/). Fig. 4. Relative error between mooth urface cae (ea wind peed of m/) rough urface cae (ea wind peed of 1 m/) at different evaporation duct height different antenna altitude. From Fig. 4, we could ee the poition of antenna altitude within the duct ha great impact upon the propagation lo in the rough ea urface cae. The tronger the evaporation duct exit, the larger the relative error of propagation lo will be generated. In 1 m duct, the maximum error preent at tranmitter altitude of m, in m duct, the maximum error preent at 1 m, 5 m in 3 m evaporation duct. When the relative error reache the maximum value, it will have a tendency to decreaing with the increment of the antenna altitude. The above two experiment how that, in the evaporation duct environment, the electromagnetic wave propagation characteritic over the rough ea urface are different from that over the mooth ea urface. In general, the error enlarge with the increment of ea wind peed, operating frequencie evaporation duct height. At a fixed atmophere environment, proper dipoition of the tranmitter could reduce thee error. The minimum error value uually exit near the top of the duct. However, if the tranmitter i etting at the top of the duct, it i not in favor of increaing radar detecting ditance. In our imulation, the maximum ea wind peed i elected a 1 m/. In practical duct environment, the ea wind peed i uually below 1 m/ becaue larger wind peed i detructive to the generation of the evaporation duct. If the ea wind peed i not very large (under 5 m/), we could ignore the influence of the ea urface roughne to the electromagnetic wave propagation in the duct environment. 5. Concluion Thi paper ha invetigated the influence of the ea urface roughne on the electromagnetic wave propagation in the evaporation duct environment. Conidering the ea urface roughne, the impedance boundary condition wa ued, the Miller-Brown-Vegh model wa em-
RADIOENGINEERING, VOL. 19, NO. 4, DECEMBER 1 65 ployed to compute the wind-driven rough urface reflection coefficient. Two numerical experiment were performed in term of different ea wind peed, operating frequencie, evaporation duct height antenna altitude, preent a traightforward underting of the relationhip of thee parameter to the roughne influence on propagation characteritic. However, the Miller-Brown-Vegh model doen't take into account the influence of the urface geometry, which will be invetigated in our future work. Acknowledgement Thi work ha been upported by the National Natural Science Foundation of China, grant No. 47753, Refractivity etimation from radar ea clutter by incorporating regularization technique into data aimilation method. Reference [1] YAN, H. J., FU, Y., HONG, Z. J. Introduction to Modern Atmopheric Refraction. Shanghai: Science Educational Pre, 6. [] HE, G. Y., LU, C. C., HONG, J. C., DENG, H. Computation Meaurement of Electromagnetic Scattering. Peking: National Defence Indutry Pre, 6. [3] VALTR, P., PECHAC, P. Tropopheric refraction modeling uing ray-tracing parabolic equation. Radioengineering, 5, vol. 14, no. 4, p. 98-14. [4] KUTTLER, J. R., DOCKERY, G. D. Theoretical decription of the parabolic approximation/ Fourier plit-tep method of repreenting electromagnetic propagation in the tropophere. Radio Science, 1991, vol. 6, no., p. 381-393. [5] HITNEY, H. V. Hybrid ray optic parabolic equation method for radar propagation modelling. In Proc. IEE Int. Conf. Radar. Brighton (U.K.), 199, p. 58-61. [6] BARRIOS, A. E. Parabolic equation modelling in horizontally inhomogeneou environment. IEEE Tranaction on Antenna Propagation, 199, vol. 4, no. 7, p. 791-797. [7] BARRIOS, A. E. A terrain parabolic equation model for propagation in the tropophere. IEEE Tranaction on Antenna Propagation, 1994, vol. 4, no. 1, p. 9-98. [8] GRABNER, M, KVICERA, V. Clear-air propagation modelling uing parabolic equation method. Radioengineering, 3, vol. 1, no. 4, p. 5-54. [9] OZGUN, O. Recurive two-way parabolic equation approach for modelling terrain effect in tropopheric propagation. IEEE Tranaction on Antenna Propagation, 9, vol. 57, no. 9, p. 76-714. [1] VALTR, P., PECHAC, P., KVICERA, V., GRABNER, M. A terretrial multiple-receiver radio link experiment at 1.7 GHz comparion of reult with parabolic equation calculation. Radioengineering, 1, vol. 19, no. 1, p. 117-11. [11] GUILLET, N., FABBRO, V., BOURLIER, C., COMBES, P. F. Low grazing angle propagation above rough urface by the parabolic wave equation. In Geocience Remote Sening Sympoium, 3. [1] DOCKERY, G. D., KUTTLER, J. R. An improved impedanceboundary algorithm for Fourier plit-tep olution of the parabolic wave equation. IEEE Tranaction on Antenna Propagation, 1996, vol. 44, no. 1. p. 159-1599. [13] YANG, X. Q., ZHAO, J. S., WANG, Y. Electromagnetic Field Electromagnetic Wave. Peking: National Defence Indutry Pre,. [14] AMENT, W. S. Toward a theory of reflection by a rough urface. In Proc. IRE. 1953, vol. 41, p. 14-146. [15] MILLER, A. R., BROWN, R. M., VEGH, E. New derivation for rough urface reflection coefficient for the ditribution of eawave elevation. In IEE Proc, 1984, vol. 131, no., p. 114-116. [16] HITNEY, H. V., VIETH, R. Statitical aement of evaporation duct propagation. IEEE Tranaction on Antenna Propagation, 199, vol. 38, no. 6, p. 794-799. About Author... Xiaofeng ZHAO wa born in Jiangu, China. He received hi M.Sc. degree from PLA Univerity of Science Technology in 9. Now he i working toward hi Ph.D. at the Intitute of Meteorology of the ame univerity. Hi reearch interet include radiowave propagation modeling atmopheric refractivity inverion from radar ea clutter. Sixun HUANG wa born in Shanghai, China. He received hi M.Sc. degree in applied mathematic from Fundan Univerity in 1981. He i now a Profeor at the Intitute of Meteorology, PLA Univerity of Science Technology. Hi reearch interet are in the field of radiowave propagation modeling remote ening technologie.