Electromagnetic Waves Propagation above Rough Surface - PIERS

PIERS ONLINE, VOL. 4, NO. 7, 2008

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Electromagnetic Waves Propagation above Rough Surface: Application to Natural Surfaces O. Benhmammouch, L. Vaitilingom A. Khenchaf, and N. Caouren Laboratoire E3 I2 -EA3876 ENSIETA, Ecole Nationale Supérieure des Ingénieurs des Etudes et Techniques de l’Armement 2 rue Franois Verny 29806, Brest cedex 9, France

Abstract— In this paper, roughness effects, in electromagnetic wave propagation above natural surfaces, are introduced using a new method based on surface generation and a roughness parameter. Different surfaces are characterized by the means of permittivity. Finally some results are presented for different surfaces (ground, sea, snow cover) and frequencies (UHF-band, X-band). 1. INTRODUCTION

Electromagnetic wave propagation above rough surfaces requires a good understanding of various interaction phenomena of the wave with the propagation medium. Numerous methods are able to predict the electromagnetic wave propagation in the troposphere. Tow kinds of methods are developed in literature, exacts methods (Mode theory [1]) and asymptotic methods (geometrical optic [2], parabolic equation [3, 4]), the most popular method is the parabolic equation. In this paper a model based on this equation has been implemented to provide a tool for electromagnetic wave propagation prediction. A new method, based on surface generation, is introduced for a better taking into account of the surface’s roughness. To conclude, the surface’s roughness effects, on electromagnetic wave propagation, are demonstrated threw examples where some results of simulations are showed for different configurations and different surfaces. 2. ELECTROMAGNETIC PROPAGATION METHODS

The parabolic wave equation is widely used for predicting electromagnetic wave propagation in the troposphere. To obtain this equation, some simplifications are introduced on the conventional elliptical equations propagation to obtain a parabolic equation [3, 14]. To solve this equation we use the Split Step Fourier method [3, 14, 15]. In order to take into account the reflection of waves by the surface, an image propagation domain is introduced below the propagation domain (method of image source) (Figure 1). To satisfy Summerfield radiation conditions, towards infinity, an absorption area is added beyond maximum height, in this area the field is multiplied by an attenuation function, quick decrease towards zero.

Figure 1: Image source method and attenuation function.


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3. PROPAGATION MEDIUM AND SURFACE CHARACTERIZATION

In our work, we are interested on electromagnetic wave propagation in the troposphere, the lowest layer of Earth’s atmosphere (The mean average depth of the troposphere is about 11 km). The refraction index n is the most influent parameter in the electromagnetic wave propagation in the troposphere. It can be calculated using Smith-Weintraub model [18]: n = 1 + 7.76 · 10−5 P/T + 0.373 e/T 2 , where P is the atmospheric pressure, T is the temperature in Kelvin and e is the partial pressure of vapour. To calculate the scattering properties for different kinds of surfaces, the understanding of the their dielectric proprieties is essential. These proprieties are function of complex permittivity ε = ε0 − jε00 where ε0 represents electrical propagation capacity and ε00 represents electrical loss. For maritime surface, we use Debye model [5] to calculate ε as a function of temperature T , salinity S of the surface and frequency of incident wave in X-band for a temperature between 0 ◦ C and 40 ◦ C and salinity rate between 4 ppt and 35 ppt (Figure 2).

Figure 2: Debye model: (a) Real part of permittivity, (b) Imaginary part of permittivity.

In the case of snowy surface, we use Ozawa & Kuroiwa model [8]. The complexity of terrestrial surface impose the use of semi-empirical models like Topp model [7] or Dobson-Peplinsky model [6]. Topp quantifies permittivity of the ground in function of humidity rate for low frequency (20 MHz– 1 GHz) (Figure 3). For higher frequencies, we use Dobson-Peplinsky model.

Figure 3: Topp model: (a) Real part of permittivity, (b) Imaginary part of permittivity.


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(b)

humidity rate of 30%, temperature=20 humidity rate of 30%, temperature= 5 humidity rate of 50%, temperature=20

, clay rate =10%, sand rate of 10%. , clay rate =10%, sand rate of 10%. , clay rate =0 %, sand rate of 10%.

Figure 4: Dobson-Peplinsky model.

U10 =5 m/s U10 =10 m/s U10 =20 m/s

Figure 5: (a) Elfouhaily spectrum, (b) Sea profile for different wind speed. 4. ROUGH SURFACES

Accurate modelling of electromagnetic wave propagation over irregular terrain is crucial for the prediction of radar performance. To observe the influence of this type of terrain, we introduce a new method which consists on generating surface using a spectrum. Once the surface created, the electromagnetic wave is propagated using the method introduced by Mac Arthur and Bebbington [11]. In literature, we find a method which consists on an introduction of a roughness parameter (Ament [16] (1953), Miller et al. [17] (1984)). In our method this parameter is used to model the


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influence of the low roughness that cannot be introduced in surface generation because of mesh limitation. To generate a sea surface we use Elfouhaily spectrum [9] and a Monte-Carlo simulation [10]. This spectrum given in function of wind’s speed and one-dimensional fetch. To modeless terrestrial and snowy clutter, we employ Gaussian spectrum [13]. If we study this spectrum, we notice that the parameter σ (standard deviation) acts on vertical roughness whereas the parameter L (correlation length) acts on horizontal roughness (Figure 6).

L=0.1 m, σ = 1 m L=1 m, σ = 1 m L=1 m, σ = 0.5 m

Figure 6: (a) Gaussian spectrum, (b) Ground profile for different length correlation and standard deviation.

Figure 7: Propagation above staircase represented terrain.

For modelling electromagnetic wave propagation above sea or terrestrial surface, we use the method introduced by Mac Arthur and Bebbington [11]. The terrain is modelled with successive horizontal segments as shown in Figure 7. If the terrain goes up, the field is propagated with the SSF method and the part of field which is in the obstacle is set to zero. If terrain goes down the field is merely propagated by means of SSF method. 5. NUMERICAL RESULTS

In this section, the numerical results are presented. These results are computed for different surfaces type, source’s heights and different atmospheric conditions. The simulations are used to show the


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influence of natural surface’s geometry and constitution in electromagnetic waves propagation. The results obtained coherent whit those presented by Sevgi [19]. In Figure 8, path loss is illustrated for a terrestrial surface in UHF-band (500 MHz) the source is placed at 70 m height (a, b). The classical method consists on introduction of roughness effects using a coefficient. We can see that the new method allows a better taking into account of the surface roughness. Indeed, the interference lobes are less extended in the results obtained by the new method.

( a)

( b)

Figure 8: Path loss for a terrestrial surface, (a) Classical method, (b) Our method for 500 MHz.

In Figure 9, path loss is illustrated for a sea surface in X-band (10 GHz) a source placed at 30 m height and a wind speed of 15 m/s. The new method allows a better of the surface’s geometry, the perturbations due to roughness are more perceptible.

( a)

( b)

Figure 9: Path loss for 10 GHz and a sea surface, (a) Classical method, (b) Our method. 6. CONCLUSION AND PERSPECTIVES

The main purpose of this paper was the simulation of electromagnetic wave propagation, above rough natural surfaces. An original method, for a better taking into account of the surface’s roughness, was introduced. This method is based on generation of surfaces and the use of a roughness parameter to model small roughness. The results presented show an amelioration of propagation loss computation, the effects of the surface’s roughness are more perceptible in the results obtained with the new method. An evolution of our work will be the implementation of this method in a tri-dimensional propagation domain in presence of different types of natural surfaces. This generalisation will require an adaptation of the propagation equation, the surface generation and roughness parameter. Another evolution can be the adaptation of Fresnel’s reflection parameter


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to a bistatic radar configuration. This amelioration will be tested for a bi-dimensional domain and extended to a tri-dimensional. REFERENCES

1. Durand, J. C., “Optique géométrique et diagramme de portée Radar en atmosphère satandard,” Revue Technique Thomson, Vol. 20–21, No. 1, Mars 1989. 2. Fournier, M., “Méthodes d’évaluation de l’effet des conduits d’évaporation à la surface de la mer,” AGARD Meeting, ‘Multi Mechanism Propagation Paths’, Neuilly sur Seine, France, Octobre 1993. 3. Craig, K. H. and M. F. Levy, “Parabolic equation modelling of the effect of multipath and ducting on radar systems,” IEE Proc., Vol. 138, No. 2, 153–162, April 1991. 4. Douchin, N., S. Bolioli, F. Christophe, and P. Combes, “Etude théorique de la caractérisation radioélectrique du conduit d’évaporation,” 49th Proc. Symposium Int. Agard Remote Sensing of the Propagation Environment, CESME-Izmir, Turkey, December 1991. 5. Khenchaf, A., “Bistatic scattering and depolarization by randomly rough surfaces: Application to the natural rough surfaces in x-band,” Waves in Random Media, Vol. 11, 61–89, 2001. 6. Dobson, M. C., F. T. Ulaby, M. T. Hallikainen, and M. A. El-Rayes, “Microwave dielectric behavior of wet soil — Part II — Dielectric mixing models”, IEEE Trans. GRS, Vol. 23, No. 1, 35–46, 1985. 7. Topp, G. C., J. L. Davis, and A. P. Annan, “Electromagnetic determination of soil water content: Measurements in coaxial transmission lines,” Water Ressources Research, Vol. 16, No. 3, 574–582, 1980. 8. Ozawa, Y. and D. Kuroiwa, “Dielectric properties of ice, snow and supercooled water microwave propagation in snowy districts,” Monograph Ser. Res. Inst. Appl. Electricity, No. 6, 31–71, ed. Y. Asami, Hokkaido University, Sapporo, 1958. 9. Elfohaily, T., B. Chapron, K. Katsaros, and D. Vansdermark, “A unified directional spectrum for long and short wind-driven waves,” MTS/IEEE Conference Proceedings Oceans’97, Vol. 102, No. C7, 15781–15796, July 15, 1997. 10. Bein, G. P., “Monte carlo computer techniques for one-dimensional random media,” IEEE Transactions on Antennas and Propagation, Vol. 21, No. 1, 83–88, January 1973. 11. Mac Arthur, R. J. and D. H. O. Bebbington, “Diffraction over simple terrain obstacles by the method of parabolic equation,” ICAP91, IEE Conf. Pub., No. 333, 2824–2827, 1991. 12. Klein, L. and C. Swift, “An improved model for the dielectric constant of sea water at microwave frequencies,” IEEE Journal of Oceanic Engineering, Vol. 2, No. 1, 104–111, Januaray 1977. 13. Brown, G., “Backscattering from a Gaussian-distributed perfectly conducting rough surface,” IEEE Transactions on Antennas and Propagation, Vol. 26, No. 3, 472–482, May 1978. 14. Dockery, G. D., “Modelling electromagnetic wave propagation in the troposphere using the parabolic equation,” IEEE Transactions on Antennas and Propagation, Vol. 36, 1464–1470, 1989. 15. Ko, H. W., J. W. Sari, M. E. Thomas, P. J. Herchenroder, and P. J. Martone, “Anomalous propagation and radar coverage through inhomogeneous atmospheres,” AGARD CP-346, 25.1– 25.14, 1984. 16. Miller, A. R. and R. M. E. Brown, “New derivation for the rough surface reflection coefficient and for the distribution of seawave elevations,” IEE Proc. IRE, Vol. 131, Part H, 114–116, 1984. 17. Ament, W. S., “Toward a theory of reflection by a rough surface,” Proc. IRE, Vol. 41, 142–146, 1953. 18. Smith, E. K. and S. Weintraub, “The constants in the equation for atmospheric refractive index at the radio frequencies,” Proc. IRE, Vol. 41, 1035–1037, 1953. 19. Sevgi, L. and C ¸ . Uluisik, “A matlab-based visualization package for planar arrays of isotropic radiators,” IEEE Antennas and Propagation Magazine, Vol. 47, No. 1, 156–163, February 2005.