Characteristic of EM-wave anomalous propagation in marine evaporation duct

Zhao Xiao-long Tianshui Normal Univ.

College of Physics and Information Science Tianshui, China

xlzhao76@163.com

Huang Ji-ying Xidian Univ.

School of Science Xi´an, China

jyhuang@xidian.edu.cn

Abstract—Based on the atmospheric modified refractivity, the difference between the evaporation duct and the standard atmosphere is analyzed. The propagation path and the transmission loss of the EM waves are calculated respectively by ray-tracing technique and Fourier split-step method of the parabolic equation in standard atmosphere and evaporation duct. The simulation results show that evaporation duct can trap some radio rays to extend the propagation distance of EM wave and result in the appearance of radar blind zone. The characteristic of the EM wave anomalous propagation in marine evaporation duct can help to improve the radar over-the-horizon detection performance.

Keywords-evaporation duct; modified refractivity; ray-tracing; parabolic equation

I. INTRODUCTION

Marine evaporation duct is a nearly permanent propagation mechanism due to the abrupt changes in the vertical temperature and humidity profiles just above the large ocean surface. Its existence greatly strengthens or degrades the capability of the naval Radar, Communication, and Electronic Support Measures (ESM) system. As early as the 1980s, the US navy has begun to develop and use IREPS to forecast atmospheric refraction effects and EREPS to assess the effects on Radar, Communications and Electronic Warfare. In recent years, many research institutes of China have also carried out successfully some experimental measurement to investigate the characteristics of the environment and radio-wave propagation in marine evaporation duct. In October 1997, a exploring atmospheric duct experiment made by China Research Institute of Radio Propagation (CRIRP) had been performed On East sea and South sea of China at longitude 115°-120° during one month. The measured data show that: the occurrence probability of evaporation duct at experimental sea area is generally about 80 percent; the annual average height of evaporation duct is generally about 7-15 m, nearly up to 25-40 m in March, April, September and November; the air-sea surface usually is a unstable layer at high-latitude areas when the evaporation duct exists and nearly neutral at low-latitude areas (e.g. [1]). Based on the characteristic parameter of the atmospheric duct-modified refractivity, the ray-tracing technique and the parabolic equation by Fourier split-step method were introduced to analyze the anomalous propagation of electromagnetic wave in marine evaporation duct.

II. FORMATION OF ATMOSPHERIC DUCT

Actually, the tropospheric atmosphere is non-uniform medium and its composition, pressure, temperature and humidity obviously vary with the height. The horizontal variety is usually negligible with comparison to the vertical. The refractive index of the lower atmosphere ranges from 1.00025 to 1.0004 and approximately equal to 1. The refractivity can be defined as the following:

5 6

277.6 3.73 10 ( 1) 10

P eN n

T T� � � � � � � (1)

Where, n is the refractive index, P is atmosphere pressure, eis vapor pressure, T is temperature.

If the Earth's surface is assumed to a plane, the propagation path of radio waves can be equivalent to some bending rays. The modified refractivity is introduced as:

610 0.157e

zM N N

a� � � �� z (2)

Where, ae is the radius of the earth and equal to 6370km, z is the height above the surface. Due to the non-uniform atmosphere, the propagation path of EM waves is not a straight line, but bends towards the Earth. If the curvature of radio rays is greater than the curvature of the Earth’s surface, an inequality is satisfied by:

0dM

dz� (3)

Where the minimum value of the modified refractivity corresponds with the height of the atmosphere duct. Equation (3) implies that the phenomenon of the atmosphere duct will appear within a certain height near the surface. The duct height can be predicted by different kinds of atmosphere layer or sounding data (e.g. [2], [3]).

III. MODIFIED REFRACTIVITY PROFILE

Based on the boundary layer theory of atmospheric science and the median-scale mode of numerical simulation, the modified refractivity near the sea surface is given by:

� � � �0 00.125 0.125M z M z z z� � �

___________________________________ 978-1-4244-4076-4/09/$25.00 ©2009 IEEE

0

0.125z

z

zd L dzd zL

�

� � �� �

� � �� �

� (4)

Where, z is the vertical height above the sea, z0 is the roughness height and equal to 0.00015m, d is the height of evaporation duct, L is Monin-Obukhov length, M(z0) is 339 M-unit at z0, � is a function of stability parameter z/L and is respectively equal to, less than and great than 1 at neutral, unstable and stable layer. Using the relationship recommended by Jeske (e.g. [2]), the modified refractivity profile of the stable, unstable and neutral stratification is plotted by Figure 1. The reference model recommended by ITU-R P.853-3 (e.g. [4]) divides standard atmosphere into seven continuous layers according to temperature with height. The modified refractivity of standard atmosphere below the height of 11km near the surface is plotted by Figure 2 on the basis of equation (1) and equation (2).

270 280 290 300 310 320 330 340

0

10

20

30

40

Hei

ght

Z /

m

Modified refractivity /M unit

Neutral layer Stable layer Unstable layer

Fig 1. Modified refractivity of evaporation duct

317 318 319 320 321 322 323 324 325

0

10

20

30

40

50

modified refractivity

Hei

ght

/m

Modified refractivity /M unit

Fig 2. Modified refractivity of standard atmosphere A comparison between Figure 1 and Figure 2 shows that

the modified refractivity of evaporation duct is obviously different from that of standard atmosphere. The M of standard atmosphere is nearly linear, and the M of evaporation duct rapidly decreases at tens of meters near the surface. For different atmosphere conditions, the strength �M of the evaporation duct is the greatest at unstable layer and the least at neutral layer.

IV. RAY-TRACING TECHNIQUE

Most of the electromagnetic problem are very difficult to solve strictly Maxwell's equations or the wave equation for analytical solutions. It can be concluded from Fermat principle

that Ray theory is a one-level approximation of Wave theory when the refractive index of the medium doesn’t vary dramatically at the length of one wavelength. Therefore, Ray-tracing technique of geometrical optics can be used to describe the high-frequency wave propagation. The radio ray geometry is shown by Figure 3. It depicts the ray bending under the influence of the refractive index. In Figure 3, Re is the radar watching range, R0 is the real range, xs is the surface range between the transmitter and the target, h0 is the antenna height, hT is the target height, �0 the initial elevation angle, �0 is the real elevation angle, �0 is the error of elevation angle, n0 and nTis respectively the refractive index at the height of transmitter and target.

Fig 3. Geometry of ray propagation

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

Range ( km )

Hei

ght (

m )

Fig 4 Ray propagation in standard atmosphere

0 0.5 1 1.5 2 2.5 3

x 105

0

10

20

30

40

50

Range ( m )

Hei

ght (

m )

Fig 5. Ray propagation in evaporation duct By the Ray equation of the Geometrical optics, a

relationship between the ray length and the target coordinates is given as in [5]:

2

2 2

0 0 0

( )( )

[ ( )( )] [ ( )( ) ]edR n h a h

dh n h a h n h a h �

�� �

� � � (5)

2 2

0 0

( )( )

( ) ( )e

S

dR n h a h

dx n h a a h 0�

��

� (6)

Where �0 is cos(�0). Equation 5 and equation 6 can be used to determine the watching range of the target Re, real height hand ground distance xs for radar.

When the initial elevation angle �0 ranges from -5� to 5�,Figure 4 depicts the propagation of the radio ray at standard atmosphere with a transmitter height of 30m. Figure 5 depicts the propagation of the radio ray at neutral layer of evaporation duct with a transmitter height of 30m and duct height of 30m. we can conclude from Figure 4 and Figure 5 that the propagating rays and the reflected ray in standard atmosphere seem always some straight lines and don’t be bent by refraction; some rays with small initial elevation angle are trapped in the evaporation duct and are reflected more and more times, and some rays with high elevation angle propagate through the top of the duct layer and result in the leakage of electromagnetic energy.

V. FOURIER SPLIT-STEP METHOD

For the approximately horizontal radio propagation with small elevated angle in evaporation duct environment, the parabolic equation derived from Helmholtz equations is a proper choice. The parabolic equation can be used to solve satisfactorily the propagation problem in non-uniform atmosphere and has favorable stability (e.g. [6]). The expression of the parabolic equation is given by:

2 2 2 22 1z x

e

zu ik u k n u

a� � � � � � �

� � �� �

0 (7)

Equation (7) neglects the backscattering and is applicable to analyze the long-distance propagation for horizontal direction. By Fourier split-step method, the solution of the equation (7) can be expressed as:

� � � �� �, exp , /u x x z i xm x z k� � � � 2

� � � �� �� �1 2exp / 2 ,F i xp k F u x z� � �� (8) When Electromagnetic waves propagate in the atmosphere,

the attenuation due to the spherical wave diffusion with propagation distance is defined as free space transmission loss, and the attenuation by the absorption, scattering, diffraction and reflection of the radio wave is known as medium transmission loss. According to EM wave theory, the basic transmission loss is given by:

� �420 log( )b

rL A

�

�� � dB (9)

Where, A is attenuation factor, r is a distance between the transmitter and the receiver, � is wavelength. The attenuation factor A is transmission loss relative to free space and it is a effective parameter to calculate the echo power. Based on the parabolic equation (7), the attenuation factor in evaporation duct is determined as in [7]:

� �,A x u x z� (10)

Fig 6. The space distribution of transmission loss in standard atmosphere

Fig 7. The space distribution of transmission loss in evaporation duct

When the radio frequency is 10GHz, the antenna height is 5m, the duct height is 30m, and the elevation angle is 0.35�, the basic transmission loss can be calculated by equation (7)-equation (10) and the pseudo-color map of the transmission loss is used to simulate the anomalous propagation in evaporation duct. Figure 6 and Figure 7 is respectively the pseudo-color map at standard atmosphere and at neutral layer of evaporation duct with the duct height 30m. we can conclude from Figure 6 and Figure 7 that the propagating rays and the reflected ray in standard atmosphere also seem some straight lines and there are obviously no bending rays by refraction; some rays are trapped in the evaporation duct and reflected more times than in standard atmosphere, and some rays propagate through the top of the duct layer and result in the leakage of electromagnetic energy. The conclusions above agree very well with that of ray-tracing. The pseudo-color map of the transmission loss can not only describe the radio propagation path, but also explain the space distribution of the electromagnetic energy along the path. Up to now, the latter isn’t able to be carried out by ray-tracing technique.

VI. CONCLUSIONS

From Figure 4, Figure 5, Figure 6 and Figure 7, we can see that the radio propagation at standard atmosphere is obviously different from that in evaporation duct. Some rays are trapped in evaporation duct and reflected more times. Due to the refraction of the evaporation duct, radar blind zone does not only exist at the top of the duct, but also appear at the horizon near the surface. This is to say, the evaporation duct help radar

to broaden the space coverage and extend the radar detecting capability for marine target. Therefore, the simulation of the anomalous propagation path and the transmission loss by ray-tracing technique and the parabolic equation can evaluate effectively the radar detection performance in marine evaporation duct.

ACKNOWLEDGMENT

This work was supported by ‘QingLan’Talent Engineering Funds by Tianshui Normal University and the Science Research Department of Tianshui Normal University (Grant TSB0817).

REFERENCES

[1] C.G. Liu, J.Y. Huang and C.Y. Jiang, “The occurrence of tropospheric ducts over the south-eastern coast of China,” Chinese Journal of Radio Science, vol. 17, pp. 509-513, Oct,2002.

[2] F.S. Dai, “The refractivity models in the marine atmospheric surface layer and their applications in the evaporation duct analysis,” Chinese Journal of Radio Science, vol. 13, pp. 280-286, Sep, 1998.

[3] Z.Y. Yao, et al, “The analysis on characteristics of atmospheric duct and its effects on the propagation of electromagnetic wave,” Acta Meteorologica Sinica, vol. 58, pp. 605-616, Oct, 2000.

[4] Radio-wave Propagation ITU-R Recommendations, Volume 2000, P Series-Part 1,2.

[5] S.J. Orfanidis, (2004) Electromagnetic Waves and Antennas, [Online]. Available: www.ece.rutgers.edu/~orfanidi/ewa, pp. 169-193

[6] G.D. Dockery., “Modeling electromagnetic wave propagation in the troposphere using the parabolic equation,” IEEE Trans on Antenna and Propagation, vol. 36, pp. 1464-1470,1988.

[7] K.H. Craig, etc “Parabolic equation modeling of the effects of multipath and ducting on radar systems,” IEE proceedings-F, vol. 138, pp. 153-162, 1991.

[8] C.G. Liu, J.Y. Huang, et al, “Characteritics of the lower atmospheric duct in China,” Journal of XiDian University, vol. 29, pp. 119-122,