Radar Scattering from a Diffuse Vegetation Layer Over a Smooth Surface

Home , Charles Elachi, Nader Engheta

212 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-20, NO. 2,.APRIL 1982 Radar Scattering from a Diffuse Vegetation Layer Over a Smooth Surface

NADER ENGHETA, STUDENT MEMBER, IEEE, AND CHARLES ELACHI, MEMBER, IEEE

Abstract-A simple model is presented for the oblique backscatter and bistatic scatter from a smooth surface overlain by a diffuse layer. Only single scattering in the diffuse layer is taken into account. The model analysis shows that the combination of volume scattering and oblique reflection at the surface may increase appreciably the waves scattering. The scattering strongly depends on the properties of the smooth surface. These results support some of the observations made with the Seasat spaceborne imaging radar over flooded regions with heavy vegetation cover.

1. INTRODUCTION IN A RECENT PAPER, MacDonald et al. [5] reported that in their analysis of Seasat SAR data, they observed anomalous tonal variations in areas having relatively uniform and homo- geneous vegetation canopy. They found that under certain conditions, the radar waves penetrate the vegetation canopy, and that high return is observed in region with standing surface water. Fig. 1 shows an example of a Seasat SAR image which illustrates this effect. In this paper, we present a simple theoretical model which shows that the presence of a diffuse vegetation layer over a 0 10 20 KM smooth surface could, in some cases, increase appreciably the Fig. 1. Seasat radar image of the east-central area in Arkansas acquired backscattering cross section at oblique angles. In the absence on July 24, 1978. Arrows indicate anomalous radar returns. They all correspond to areas of standing water covered partially or fully by a of any vegetation layer, the backscattering cross section from vegetation canopy. The three arrows in the upper left of the image a smooth surface is nul at oblique angles. If a layer of scat- (near Conway) indicate large swamp areas with a discontinuous de- terer covers the smooth surface, the combination of scattering ciduous forest canopy (about 85 percent cover). Most of the other arrows indicate axbow lakes or abandoned meanders along the in the layer and reflection at the surface could lead to oblique Arkansas river (courtesy of H. MacDonald). backscatter larger than if the layer is by itself. Another way of viewing this effect was given by MacDonald et al. [5S . As the wave penetrates the layer, its amplitude and phase are cover be represented by a uniform layer of particles small rela- modified randomly. When this wave interacts with the smooth tive to the wavelength. In the case of the Seasat SAR, the surface, the effect is similar to the case of the plane wave with radar wavelength was 24 cm. a randomly rough surface. In Section 11, we present the general theoretical formulation The problem of scattering from a scattering layer using the for the backscatter with linear polarization. In Section 111, we Dyson equation and the first-order normalization method was discuss the special case of small scattering particles. In Sections investigated by Fung [3]. In this paper, we present a very IV and V, we consider the case of circular polarization. Fi- simple model which seems to explain the effect observed ex- nally, in Section VI, we discuss the case of bistatic scattering. perimentally and gives an approximate solution for the back- In all our analysis we neglect multiple scattering in the diffuse scattering of linear and circular waves and the bistatic scatter- layer. ing of linear waves. It is assumed that the vegetation layer 11. FORMULATION OF THE BACKSCATTERING CROSS Manuscript received April 14, 1981; revised September 22,1981. This SECTION FOR LINEAR POLARIZATION paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Con- There are four possible combinations of single scattering and tract NAS7-100, sponsored by the National Aeronautics and Space reflection which can lead to a backward return of the incident Administration. wave. These four cases are illustrated in Fig. 2. The backscat- N. Engheta is with the California Institute of Technology, Pasadena, CA 91125. tering cross sections for the four cases are given by C. Elachi is with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109. al = a(O, 0) e '

*,- e 7S peel. Ol . P,P,7,," ..V. a) (b) (c) (d1) Fig. 2. Different ray tracing configurations which contribute to the backscatter signal as a result of reflection at the interface and/or scattering from the particles in the diffuse layer.

u2= Ra(G, H - 0)e-(1+a2) dence, i.e., horizontal polarization, and

-Ra(H- 0, 0)e (al +c2) 2 u(O, - 0) = 4HTa2 P (koa)4 cos2 (20) (5) EP+ 2 '= R2a(II - 0, H2 when the electric vector is in the of ver- where plane incidence, i.e., tical polarization. In the above expressions, ep is the relative R Fresnel power reflection coefficient at the surface dielectric constant of the particles and ko = 2H/X. with an incidence anigle equal to 0; The backscattering cross section is then given by [from (2)] a(k, ?y) bistatic scattering cross section with incoming angle Q and scattering angle 'y; e ot~~~e 2,1 L= E = o sinha + 2R +R'e (6a) °z1 round-trip loss in the layer above the scattering t HH element; °2 round-trip loss in the layer between the scattering when the electric vector is perpendicular to the plane of inci- element and the surface. dence, and

The backscattering cross section for a typical particle is a sinh a[1 + 2R11 cos2 20 si +R 2e-2

4 oz = aOn = [o(0,0) + 2Ru(0, - 0)eC 2 (6b) t n=1 when the electric vector is in the plane of incidence. In the - - + 0, H e 2 (1 ) R2a(ri 0) 2]e-1 above expressions, R is the Fresnel power reflection coeffi- Because the scattering element has equal probability to be at cient which is given by Jordan and Balmain [4]. The loss any location in the layer, then by integrating over the thick- coefficient y is equal to the absorption loss (the scattering ness of the scattering layer we get loss is negligible when X >> a) in m1 and is given by [2]

1.8H 3 Ep2M + - E a(O, 0) Ma(6, rl 0)ihsinh a (7) Ut xp (epl + 2)2 + Cp2 where ePI, e,P2 are the real and imaginary part of the particles + R2u(H - 0,H- 0)ee2 sinh a (2) relative dielectric constant, M is the mass density of the scattering layer in g/m3, p is the density of the particles in where a = 'yL/cos 0, is the loss per unit length, and L is the y g/cm3, and X is the wavelength in cm. layer thickness. = The behavior of A St /a0e' sinh a as a function of the III. SPECIAL CASE OF SMALL SPHERICAL PARTICLES observation geometry and the relative dielectric constant e is illustrated in Fig. 3. A represents the additional factor which The most simple case is when the scattering particles size is results from the presence of a reflecting surface below the much X = smaller than the wavelength (i.e., > 4Ha, a particles scattering layer. size). In this case, the scattering is given by [ 1 ] In the case of a thick layer, yL >> 1 and A = 1, the presence of the reflecting surface has no effect. This is due to the fact O, - 0) = = p (r- (0 0) 0 =4HIa2 2 (koa)4 (3) that almost no energy penetrates through the layer and get re- flected by the surface. and Another special case is when L = 0 (i.e., low density scattering negligible absorption). Then 1 layer, a(0, Hl - 0) = 4Hla2 P (koa)4 (4) CP+ 2 AHH =(I +R1)2 (8a) when the electric vector is perpendicular to the plane of inci- Avv = 1 + 2RI cos2 20 +R2 . (8b) 214 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-20, NO. 2, APRIL 1982

k I\ Iu

vv YL=1 AHH YL = I 2- 2 Fig. 4. Geometry for circularly polarized wave.

E = Oa Fig. 4) 1- I C=3 Ei =E, ± iEH (11)

where ± corresponds to the right and left circular polarization,

0 30 46 60 S0 0 30 45 S0 so0 respectively. The scattered field from the particle is equal to 0 0

Fig. 3. Plots of the additional factors AHHandA vv for different values Es = S1 (0)Evev ± iS2 (0)EHeH (12) of ac (losses in the diffuse layer) and e (dielectric constant of the flat interface). These plots correspond to the case of linear polarization. and after reflection

Er = Si (0)Rr1Evee +iS2(0)RIEHeH (13) In the limit of a perfectly reflecting surface (such as a water where the prime corresponds to the amplitude reflection co- layer) then efficient (R =R2). For a circularly polarized incident wave AHH 4 (9a) EH = EU = EO. Then Avv = 2(1 + cos2 20). (9b) Er = (SI(0)R lev + iS2(0)RIeH)Eo (14) Thus the backscattering cross section is increased by 3 to 6 dB which is an elliptically polarized return. An elliptically polar- due to the presence of the totally reflecting surface. ized wabve can be subdivided into two circularly polarized

Fig. 3 shows A vv and AHH as a function of the incidence waves. Therefore, we get angle. We considered the cases of c = 3, 9, and oo (perfectly - S2(0)RI 2 = S1(0)R' reflecting surface) and yL 0 and 1. It is clear that for small 9RR = ALL = (1 5a) yL (i.e., appreciable penetration in the vegetation layer), the surface interface can play an appreciable role. For instance, in SI(0)R' +S2(0)RI the case of the Seasat radar configuration (HH, 200 incidence 9RL gLR 2 (15b) angle), the change in the surface dielectric constant from e = 3 to = leads to an increase in the backscatter by 4/1.2 = 3.3 The same expressions apply to the configuration in Fig. 2(c). (i.e., 5.2 dB). This is qualitatively consistant with the Seasat In the case of scattering and double reflection (Fig. 2(d)), SAR observations over swampy and flooded regions with following the same steps as above and remembering that the vegetation cover (Fig. 1). scattering at the particle is backward not bistatic, then we find that IV. FORMULATION OF THE BACKSCATTERING CROSS SECTION FOR CIRCULAR POLARIZATION URR = ALL - IO 2 (16a) The four backscatter configurations are the same as in Fig. 2. For the configuration where only scattering occurs (Fig. 2(a)), R +R11 U~ LR 2CT (16b) we have (neglecting absorption loss for the time being) U9RL

9RL =- LR U9 (lOa) Therefore, the total backscattering cross section is given by

ALL RR 0 (l Ob) =X, [2 Sj(O)RII S2(0)RI e-c where the subscript L and R refers to right and left circular polarization. us next in Let consider the configuration Fig. 2(b) (i.e., R- sinha e2je( R12 e (17a) scattering and reflection). The incident wave is given by (see ENGHETA AND ELACHI: RADAR SCATTERING FROM VEGETATION 215

=0O ARR 7 =0 tA RL ARR =ALL = 4. 4-1 e= I0 as expected. Another special case is when yL = 0 and RI, = R1 = 1, -l1,R( = 1). Then 2- 2- e=9 (RI=

8=9 e=3 ARL =ALR = 2 + (1 + cos 20)2

D 30 46 6o 0 30 46 6i0 - cos ALL =ARR = (1 20)2 ALL=ARR 2

For the case of large e, the direct polarization factor (ARL = ALR) varies from 4 at normal incidence to 2 at grazing inci- YL = 1 7L =1 RL dence. The depolarized factor varies from zero at normal in- 2-t 2 cidence to 2 at grazing incidence.

VI. BISTATIC SCATTERING 8=3 The approach used in the previous sections to derive the 8=9 8=3 0 backscattering cross section can also be used to derive the

60 cross section. that the > 30 46 60 90 30 46 90 bistatic scattering Assuming incoming 0 0 and outgoing waves are in the same plane, and that only single Fig. 5. Plots of ARR and ARL for. the different values of oc and e. scattering is accounted for, the different ray tracing possibili- These plots correspond to the case of circular polarization. ties are shown in Fig. 6. For scattering particles that are non- directional, the scattering cross section for the four configurations in 6 are [ sinh a +2 + Fig. given by, respectively, S1(0)R S2 (0)RL2i -o =+j2 e l 1 = RL LR U(0,q) Ca2 = u(0, HI--)R(O) + Ro +2 sinha e 288e- (17b) a3 = a( - 0, q)R(0)

V. CASE OF SMALL SPHERICAL PARTICLES U4 = O(H - 0, Hl - k)R(0)R(Ob). In the case of small spherical particles we have The scattering cross section is then equal to

S1(0) =-\ cos 20 at = U(0, )[1 +R(0)R(q)] + u(0, II - 4)[R(0) +R(Q)] S2(0)= X where the effect of losses in the diffuse layer has been neglected and the particles are assumed to be symmetric. The additional and the backscattering cross section is equal to factor due to the interface is then

= L = Uoe~2ot [I{RI cos 20 + RI12 Ut RR LL 2 A=

sinha - R + aRI e1a = 1 + R(0)R(O) + [R(0) + R(4)] u(0, H )/ca(0, 0). a_ R2 This shows that the interface does increase the bistatic cross section. It can be very large if a(0, 1 - /) is much larger than E = sinh a [ cos a EZZ aoe_ IR' 20-2 R11 sinh a RL LR a(0, O). Using the data given by Barrick [2, fig. 3-7], we give the following examples to illustrate this point. For a = 3X/fI + eRj ;R1 2 -2c] then

a(0, 150) , 250 we = In Fig. 5, plotted ARR =ALL ERR ai/ao sinh ate' and a(0, 30) ARL = ALR = -RL 9/a0 sinh aexe for different cases. In the case of direct polarized return (i.e., ERL and ILR), A repre- for vertical polarization, and sents the presence additional factor which results from the of a(25, 155) the reflecting surface. In the case of depolarized return (i.e., =3500 25) ERR and ELL), A represents the total factor relative to the a(255 polarized return without the reflecting surface. for horizontal polarization. One special case is whenyL >> 1. Then In the case of isotropic scattering by the particles, A becomes

ARL =ALR = 1 A = [1 + R(0)] [1 + R()]. 216 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. GE-20, NO. 2, APRIL 1982

(a) (b) (c) (d) Fig. 6. Different ray tracing configurations which contribute to the scattered signal (bistatic) as a result of reflection at the interface and/ or scattering from the particles in the diffuse layer.

VI. CONCLUSION At present he is working towards the Ph.D. degree at the California Institute of Technology If the electromagnetic energy is not appreciably absorbed or in electromagnetic theory and wave propaga- scattered by the diffuse layer, the bottom interface will play tion. He has been a Research Assistant at the an California Institute of Technology, Pasadena, important role in oblique backscattering even if it is per- since 1979. He has also been part time asso- fectly smooth. This effect is also important in bistatic scatter- ciated with the Jet Propulsion Laboratory, ing. In the case of the Seasat radar data shown in Fig. 1, the since July 1980, investigating theoretical prob- theory presented in this paper verifies the observation by lems related to remote sensing. Mr. is a member of APS. MacDonald et al. [5] that the presence of a water interface Engheta (due to flooding) below the vegetation canopy will increase the surface scattering at oblique angles. We also presented how this effect depends on the polarization of the wave and its incidence angle. The theory presented here is based on simple ray tracing and single scattering. In a future paper, we will present the Charles Elachi (M'71) was born in Rayak, Lebanon, on April 18, 1947. He received the "Ingenieur" degree in radioelectricity with honors and case of multiple scattering and a rough interface surface. the "Prix de Houille Blanche" from the Polytechnic Institute of Gren- oble, Grenoble, France, in 1968, and the B.S. degree in physics from REFERENCES the University of Grenoble in 1968. He received the M.S. and Ph.D. [1] D. E. Barrick, Radar Cross Section Handbook, vol. 1, G. T. Ruck, degrees in electrical engineering and business economics from the Cali- Ed. New York: Plenum Press, 1970, ch. 3. fornia Institute ofTechnology, Pasadena, in 1969 and 1971, respectively. [2] L. J. Battan, Radar Observation of the Atmosphere. Chicago, IL: He has worked at the Physical Spectrometry Laboratory, University Univ. of Chicago Press, 1973. of Grenoble, on plasma in microwave cavities. He was a Teaching Assis- [3] A. K. Fung, "Scattering from a vegetation layer," IEEE Trans. tant at Caltech in 1969. In 1970 he joined the Space Sciences Division, Geosci. Electron., vol. GE-17, pp. 1-6, 1979. Jet Propulsion Laboratory, Pasadena, where he is presently Leader of [4] E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radi- the Radar Remote Sensing Team, which is involved in investigating atingSystems. Englewood Cliffs, NJ: Prentice Hall, 1968. spacecraft-borne scientific experiments for planetary and Earth studies [5] H. C. MacDonald, W. P. Waite, and J. S. Demarcke, "Use of Seasat using coherent radar techniques. Since 1980, he has been the Manager satellite radar imagery for the detection of standing water beneath for Radar Development which covers all aspects of the radar remote forest vegetation," presented at the Amer. Soc. of Photogram- sensing program at JPL. He is the principal investigator on the Shuttle metry, Ann. Tech. Meet., Niagara Falls, NY, 1980. Imaging Radar. He is also involved in studying theoretical electro- * magnetic problems related to scattering from natural terrain, remote sensing, stratified media, space-time periodic media, and DFB lasers. Nader Engheta (S'80) was born in Tehran, Iran, on October 8, 1955. He has 130 papers, patents, reports, and conference presentations in He received the B.S. degree (honors) in electrical engineering from the above fields. the University of Tehran in 1978. He entered the California Institute In 1973, Dr. Elachi was the first recipient of the R. W. P. King award. of Technology in September 1978 and received the M.S. degree in elec- In 1980, he received the Autometric Award of the American Photo- trical engineering in June 1979. grammetric Society. He is a member of AAAS and Sigma Xi.