AD-AiS4 922 THE USE OF THE GLISTENING SURFACE CONCEPT IN ROUGH i/iSURFRCE SCATTERING(U) ROME AIR DEVELOPMENT CENTER

LS F GRIFFISS AFB NV R J PAPA ET AL. JUL 84 RDC-TR-84-i59UNCLASSIFIED F/G 17/9 NL

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RADC-TR-84-159In-House ReportJuly 1984

THE USE OF THE GLISTENING SURFACECONCEPT IN ROUGH SURFACE SCATTERING

Lfl

Robert J. PapaJohn F. LennonRichard L. Taylor

APPROVED FOR PUBLIC RELEASE DISTRIBUTION UNLIMITED

DT.-*SELECJUN 12 1985

'If G-- ROME AIR DEVELOPMENT CENTER

Air Force Systems Command- ., Griffiss Air Force Base, NY 13441

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PHILIPP BLACKSMITHChief, EM Techniques BranchElectromagnetic Sciences Division

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The Use of the Glistening Surface (Contd) 61102F 2305 J4 0712. PERSONAL AUTHOR(S)

Papa, Robert J.; Lennon, John F.; Taylor, Richard L.13. TYPE OF REPORT 13b TIME COVERED 114 DATE OF REPORT lYr.. fo.. DayI 15. PAGE COUNT

In-House FRoM 6183 TOLL 1984 July 3516 SUPPLEMENTARY NOTATION

17 COSATI CODES Is ISUBJECT TE RMS ICon tnue on m -ite'e if neceana and identify by block niumber)

FIELD GROUP SUB GR "- Radar clutter)Physic, 20 14 Terrain scattering)Det 17 09 Radar multipath.19 ABSTRACT 'Continue on ,eere f ne har-. and identif by block nunlberI

, Calculations of diffuse power scattered from a rough surface have typically used theconcept of a glistening surface over which a centerline-varying surface cross section isintegrated. The usual form of that surface is derived for relatively smooth surfaces and

* - contains several other constraints that are not always evident. In this report, we willaddress the limitations on this definition and several alternative forms that are less re-

- .strictive. We will compare them with a more realistic solution in which the azimuthal.* variation in the surface cross section is taken into account and the integration is across

the entire signal footprint on the surface.The standard scattering surface dimensions are determined under constraints on both

the antenna heights and the surface width. In the report, we analyze the effect of remov-ing those constraints. In addition, we consider a second formulation in which one of theantenna terminals of the bistatic system is considered to be sufficiently distant so that itis treated as being at infinity. We examine the different boundary values for the (Contd)

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Block 11 (Contd)

Concept in Rough Surface Scattering

Block 19 (Contd)

..... glistening surface based on these different assumptions and compare the resultant

scattered power levels with the azimuthally varying cross section results.*'" One of the most important conclusions is that the use of the centerline normalized

cross section models can lead to calculated diffuse power levels that are in disagr -411twith the results for the more exact solution in which both the azimuthal variation in 'is accounted for and the integration is always across the entire radar footprint ratherthan a calculated glistening surface width. ~,~. ,

tLZ~~f.:e /L7?

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Av~'lnx~/o~'Contents

1. INTRODUCTION 5

1.1 Background 61.2 Scope 7

2. GLISTENING SURFACE DETERMINATION 7

3. CALCULATED SURFACES 14

4. ANALYSIS 23

5. DIFFUSE SCATTERED POWER 25

6. CONCLUSION 32

REFERENCES 35

Illustrations

1. Schematic Representation of Rough Surface Scattering 7

2. Antenna Power Patterns 8

3. Standard Glistening Surface Representations 10* 4. Glistening Surface With Receive Antenna at Infinity 12

5. Glistening Surface Dimensions, Smooth Surface, Large Separation 15

6. (listening Surface Dimensions, Smooth Surface, IntermediateSeparation 15 I

[3

6°

Illustrations

7. Glistening Surface Dimensions, Smooth Surface, Short Separation 16

8. Glistening Surface Dimensions, Slightly Rougher Surface, LargeSeparation 17

9. Glistening Surface Dimensions, Slightly Rougher Surface, IntermediateSeparation 17

10. Glistening Surface Dimensions, Rough Surface, Large Separation 18

11. Glistening Surface Dimensions, Rough Surface, IntermediateSeparation 19

12. Glistening Surface Dimensions, Rough Surface, Short Separation 19

13. Glistening Surface Dimensions, Very Rough Surface, Large Separation 20

14. Glistening Surface Dimensions, Very Rough Surface, IntermediateSeparation 21

15. Glistening Surface Dimensions, Very Rough Surface, Short Separation 22

16. Diffuse Power as a Function of Separation, Smooth Surface,* Azimuthal Variation for av 27

17. Diffuse Power as a Function of Separation, Smooth Surface,Standard Definition Glistening Surface 27

18. Diffuse Power as a Function of Separation, Smooth Surface,Alternate Definition Glistening Surface 28

19. Diffuse Power as a Function of Separation, Smooth Surface,Standard Glistening Surface Definition Without Height Constraints 28

20. Centerline Variation of aOat a Separation of 10km 29

21. Centerline Variation of aoat a Separation of 50km 30

22. Centerline Variation of co at a Separation of 90km 31

Tables

1. Summary of Scattering Model Cases 26

* 4

- - = : r , rbr..% = - . .- --- , -v -~ .v' -. -' r .'% ~ ~ ' r z - W S - .c 4 t-, : - .. .. . . :

I

%

The Use of the Glistening Surface Conceptin Rough Surface Scattering

1. INTRODUICTION'

The scattering of electromagnetic waves from rough terrains depends on the

characteristics of the rough surface. 1,,,,,6The rough surface may be de-

fined in terms of the statistical distribution of heights, their degree of correlation

22

(T is the surface correlation length), the variance of heights r, and the complex

dielectric constant associated with a particular type of terrain. A number of the-

(Received for publication 24 July 1984)

1. Papa, R.J., and Lennon, J. F. (1980) Electromagnetic scattering from roughsurfaces based on statistical characterization of the terrain, InternationalRadio Science Symposium (USRI), Quebec, Canada.

2. Papa, R.J., Lennon, J.F., and Taylor, R.L. (1980) Electromagpetic WaveScattering From Rough Terrain, RADC-TR-80-300, AD A098939.Li 3. Papa, R.J., Lennon, J. F., and Taylor, R. L. (1982) The Need for an ExpandedDefinition of Glistening Surface, RADC-TR-82-271, AD A130431.

* 4. Papa, R.J., and Lennon, J. F. (1983) Investigation of backscatter from an un-

even, rough surface, International Radio Science Symposium (URSI), Houston,Texas.

5. Papa, R.J., Lennon, J.F., and Taylor, R.L. (1982) Further Considerationsin Models of Rough Surface Scattering, RADC-TR-82-326, AD A130424.

6. Papa, R.J., Lennon J. F., and Taylor, R. L. (1983) Multipath effects on anazimuthal monopulse system, Trans. IEEE on Aerospace and ElectronicSystems, 585-597.

p 5

retical models describing rough surface scattering 7 ' 8 ' 9 relate these parameters

to the normalized radar cross section of the rough surface. In these models, the

surface area contributing to the scattering process (glistening surface) is defined

in different forms. This report contains an analysis of different definitions of glis-

tening surface and the constraints on their use for analyzing a bistatic radar sys-

tem scattering signals from terrain. Three distinct situations will be discussed.

The first is the case where both antennas are at finite heights and a finite sep-

aration. Three subcases are discussed that depend upon the relation between the

dimensions of the glistening surface and the antenna heights. Second, there is the

case where one antenna is considered to be at infinity. Finally, there is the com-

plete solution in which the azimuthally varying cross section is integrated over the

entire signal footprint. This solution is used as a basis for comparison with the

other results that have the more simplistic a0 values in their integrations.

1. 1 Background

In previous reports, 1, 2, 3, 4, 5, 6 we have explained that RADC/EEC has a

continuing interest in improving the modeling of the scattering from rough surfaces.

The investigations are devoted to two main topics: the characterization of the sur-

face and the electromagnetic wave scattering. The models in those studies are

based upon physical optics. A geometrical representation of scattering from a

surface is shown in Figure 1. In the studies of this present report, the azimuthal

and elevation patterns shown in Figure 2 correspond to the antenna located at the

higher altitude. The lower antenna has an isotropic pattern, and the other system

parameters are typical of those of the earlier reports.

The results of these investigations have implications for estimating radar sys-

tem performance. It was shown earlier 5 that extended definitions of the glistening

surface can give much more accurate diffuse power estimates than those given by

the conventional radar engineering approach formulated by Barton and Ward. 10

7. Beckmann, P., and Spizzichino, A. (1963) The Scattering of ElectromagneticWaves From Rough Surfaces, Macmillan Co., New York.

8. Ruck, G.T., Barrick, D.F., Stuart, W.D., and Krichbaum, C.K. (1970)

Radar Cross Section Handbook, 2, Plenum Press, New York.

9. Long, N.W. (1975) Radar Reflectivity of Land and Sea, Lexington Books,Lexington, Mass.

10. Barton, D. K., and Ward, H. R. (1969) Handbook of Radar Measurement,-Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

.

6.

PULSED RADAR BEACON DIRECT SIGNALMONOPULSE RECEIVER

.'MULTI PATH

ROUGH TERRAIN

Figure 1. Schematic Representation of Rough Surface Scattering

1.2 Scope

The report discusses the basic limitations of the definitions and modifications

that can be introduced when it is desired to apply the glistening surface models to

cases that are not consistent with the original assumptions contained in the theory.The results obtained using different models are compared and discussed.

2. (;I,ISTIENIN(; SIRFACE DETERMINATION

In studies of scattering from rough surfaces, investigators have made wide

use of the concept of glistening surface. The glistening surface is defined as that

part of the rough surface that reflects a significant amount of the transmitted en-

ergy into the receiver for a given set of antenna positions.Beckmann and Spizzichino 7 have derived a number of equations describing the

boundaries of the glistening surface and the associated normalized rough surface

scattering cross section. The different forms apply to a number of sets of condi-

tions and configurations of the antennas. The form that has received wide usage

is the one where it has been assumed that both the transmitting antenna height,tf A ' and the receiver height, H are small compared to the separation, d, be-

tween them (definition 1). There are a number of additional assumptions in the

derivation of this result, and, since it has been applied extensively, it is worth

examining the implications of these assumptions for the range of validity of the

equations.

We begin by listing some general assumptions in their formalism. These in-

clude the following:

(1 ) It is assumed that the normalized rough surface scattering cross section

or' is derived under the conditions of physical optics;

(2) It is assumed that the surface heights can be described by a bivariate

Gaussian or exponential statistical distribution; and

7

0

-1 - A7I'flT1AL J~DIF, T RLNCL.

-30- ELETVATION.]

zhi -40-

-50

-60 -80 -60 -40 -2 0 0 20 40 600 1AZIMUTH ANGLE (0EG)

0

-10-A:!IMVTHAL

-20- S:M FATTEAUN

-30ELEVATION0

ANLE IS 0

S-40-

.50

-60

-700 -60 -40 -20o 0 20 40 60 S0AZIM1UTH ANGLE (0(G)

0

-10 7EN

-20

-30

zS-50

-60AUUis

-70-6 -40 -20 0 20 40 60

VERTICAL ANGLE (DEG)

Figure 2. A zimsuthal Plane Monopulse andIvaluation Plane A ntenna P owe r Patterns

T'

(3) It is assumed that the Rayleigh roughness parameter

Z= [(27ra/A)(cosOi + cos 0s)

is much greater than one,

where a = standard deviation in surface height,

X = wavelength,

Oi angle of incidence,

and

s= scattering angle (elevation).

The derivation of the boundary of the glistening surface then proceeds by con-

sidering the linear bisector of the angle, 4TPR, in Figure 3. This bisector makes

an angle, 4 J3, with the vertical z-axis.

This angle /3 is related to the electromagnetics of the scattering:

V

tan )3 XV'

"here

xy x y

and Vx, Vy, v z

are direction cosines of the difference vector k = k. - k and k i and k are the

incident and reflected em wave vectors, respectively. If we define a roughness

factor, Tan )3 = (26 /T) where a is the standard deviation of the surface heights and

T is the surface correlation length, then we can express the normalized rough sur-

face cross section a0 as:

70 expI-tanI/tanf3lo (Bivariate exponential surface)

and

CO expl-tan)/3/tan 2 flo (Bivariate Gaussian surface)

Thus, frorii the electromagnetics, we define the glistening surface as the region

: .- .:. -. .

z

TT

0 X2/ x

GLISTENING SURFACE/d -7

General Conditions for Arbitrary Point P on the Boundary

BoundaryI I 'ooad(AilEdPInts

[3 or 1< 113 PO which is equivalent to the region for which the scattered power is

(I(L~Ia to (Jrgreater than lI/e of its maximum.

Intder the condition that ff and 11 "<d, the x-axial distances from the two an-A T

titias to the ends of the glistening surface are (Figure )

I 'I' \ 1 , cot2f/l aInd I'. - R, D - II' cot2 t

Nwxt, hv oxfressing the direction cosines of this bisector as a linear combina-

ion of the dirct ion ,osines of the lines 11T and PH, and using the normalization

(otv!it ion 00i the direct ion cosines, it is possible to derive the equation for the

E (N 2~ I)21 A

This is not a convenient form for general application because iterative procedures

have to be used to solve for the width. However, we can use it here to evaluate

the effects in some specific instances. This will allow us to see how including the

complete ainmuthal angular dependence affects the extent of the glistening surface

idth.

The results for roughness levels where '/o < 7r/4 are not surprising. The

,ith values usinQ the assumptions of the standard definition are small compared

a. ith the suparations (xl,X 2) Indeed, the iterated solutions including the complete

;i.outhal dependence are indistinguishable from the classical values. For larger

u,, T1ht,.s ,, though, wher(,- the widths are nonzero even at the antenna positions,

\ii. xected to see considerable differences. Figure 13, Figure 14, and Figure 15

th, sts for a 102 l 2 and T = 2 m at the three separations. This

1.,i,,sis t f13 72. -50 . ltven in these cases where the widths reach the or-

, 1.F , zieV(2 : t ill0terc;, the 2/3 standard and the iterated solutions are virtual-0

t1 ethnti, l1 at tie t v.o louer separations, and for the 9km case they are similar

.pt oV distatines less than twice the respective antenna heights. It is interest-

1. t,, 1,tc, t!iit, :at those distances, the standard width values exceed the iterated

t -, i ta ins no assumptions on the relative smallness of the heights

an P..i, lth.40. 'Ilhii i.-is consistent with the results found when the height restriction

W. c t-i s ia'ue 11). These figures also show that the modified (d-- )

c. suits ar s i: ilar to and even wider than the other values.

These dis ussions of the various width calculations have shown a number of

intece'stin patterns. For larger roughness values, the standard 2 /30 definition is

in oiiod aIreenient a ith the more complicated solutions of the less restrictive def-

initioits. This hold.-s true even for cases where the basic concepts implicit in the

,hfinlition have been violated (/3o > 45"), At smaller roughnesses (T = 200rn,.- )00 , thuere is less arecement with the alternative definitions, particularly at

tl. siiorter separations k here the 2)3 surface vanishes (1 I, >d). There, the

61t---) oeliniit ion ,as a finite, relatively s nall surface. It should be noted that if

th. i1 an! i.. onstraints are nelected, the surface generated by the standard

,-fiiition rlol tlueSi conditions is the same as the alternative result. This serves

t,) o. i' tiLat, for thOSe conditions, the assumiptions implicit in the 1 1 and I. 2

Ph'ter ,!itation have been violated as a result of the short separation distance. The

:lt rtativc re'sult is still valid even though the separation is not particularlv infi-

it- , c) l)at .d -Aiti tIe 55i.-n. or 90km cases.

I-h1 point to eiT hasiizc het'e is that there is a clear distinction in the calcula-

ti,I, )I t!he t,.o (i eisions of the glistening surface and that the basic, simple def-

itit can he os;ed ti) ive surfaces that agree with the more complicated formal-

24

-1

fact that, for this roughness, 1.1 and I., are small in the first definitit)ii. li

introduces the additional complication that near either end of the sur!'a: t-, th.-

dition that flA< x 1 , or IT< x 2 is not satisfied. The question is a hat el!# t y%-

lating the condition has on the width of the surface. To resolve this, t, , tie

results for a revised definition where the restriction is not included. I h,,- .idth

values are shown in the figures as crosses ('). At D = 3(1 NNU and 1) = , NI,

we see that the widths are only minimally altered b% that assui: itl i: i'., ,,

the distance has exceeded tw.'ce the height, the two surfaces are eii\ :,It.

D [ 5 NMlI, the shapes are similar near the transmitter andI shO , A ,,,1 Ii::, r,, o

only when x, < UT, in which region the two widths are decreasiny i,.

%. N %IL)Y IN*

The discussions of these ficTures have pointed out hoa incrteas nL tu , I ,WVt..>

affects the first Beckmann and Spizzichino 7 definition results. As tan ftit[1 and L, decrease and the height to x-axis ratio condition is no longer satisi( t

along the entire surface. From Figure 10, it is clear that, as the rou}lhnes.t con-

tinues to increase, 1 and 1 -0-o. When 420o- 90', the entire geoiitetric formal-

ism breaks down. At even smaller angles, the condition that v < x 1 , x0 is becor -

ing questionable. For instance, in Figure 12 we see that, even for 0 300,

there are points at which v is one-half the corresponding x distance.

This raises two questions. Tile first is how relaxing the v constraint affects

the width. The second is what the considerations are when j3 > 7r/4. In the two0

preceding width derivations, the assumption that v is small simplified the angular

component relationships. If we remove that condition, we can follow the same

procedures as before, but the result is more complex. \We arrive at a form:

x' [ 2 y2/ 2-7- / + IfIT TTAN2o

1, 2 /11 T/Q2~ ~~~~, Il \~' xt:~)/2

where

*) ,)

2 Tr

and

2-----------------------------------------*

I I I I I I i I I IO

/c

I- (1 OD

< N"4 T1

0

1.4

0

L) in

z ~I

cra csj

tr~tr

7 r22

0)

Cd

z Cd

z Cz

z - -

0 OD

o4LO -4-

< 1. ..T T b .)

ol UU

cr 0

o-.zz

212

0

Z)ca

C)

*1dC)

Cd

-4

C)

u

0EnzOz z

No CY

LU CZolU LL)C

< cr Ar tz 41

i i -

20

i~o1500 2

HAz 101 M 2 O - - -STANDARD GS DEFINITION

HT = 1220 M T = OM ALTERNATIVE GS DEFINITIONd =55318M Wx STANDARD GS (HtX)

1000

500-

00 1 2 3 4 5 6 7 8

X. (KM)

Figure 11. Glistening Surface Dimensions for Both Definitions, Inter-mediate Antenna Separation, Rough Surface (al/T =.33)

1500

I~ 20 2 --- TANAR GS DEFINITION

MT - 1220 M T z IOM ALTERNATIVE GS DEFINITIONd r 8987 M Wx STANDARD GS (H.*'X)

1000-

y (M)

500

00 I 2 3 4 5 6 78

X, (KM)

Figure 12. Glistening Surface Dimensions for Both Definitions, ShortAntenna Separation, Rough Surface (al/T =.33)

- 0

u~,J.

cnOD0 C/)

COOz (1

1-44

ou- x- o U2

~ ~N o

(ni N -S.41- NC

ZZ l I>0

cr cr 2Z< .4 rcro 0 r

0

C-

* II I I I I0 0 o

if) .. 0-

T K- P_ T Kr TP. - k -% -j -.

25

HA • 101 M --- STANDARD GS DEFINITIONHT - 1220 M ALTERNATIVE GS DEFINITIONd ' 92382M - -

20 4 r 10 M2

T ' 200 M

Y IM) i i I I

0 O 20 30 40 50 60 70

X, (KM)

Figure 8. Glistening Surface Dimensions for Both Definitions, LargeAnTenna Separation, Slightly Rougher Surface (or/T = . 015)

HA 11 -M GS DEFINITION

HT •1220 M ./ ALTERNATIVE GS DEFINITIONd

=55318 M/

20 az 2 I0 M

2

T -200 M /

15 "

YAy IM) / /

10

0 4

0 10 20 30 40 50 60 70

X (KM)

SFigure 8. Glistening Surface Dimensions for Both Definitions, Inter-mediate Antenna Separation, Slightly Rougher Surface (aT /T 015)

17

HA IIM--TADR G EINTONT!2MATRAIV SDFNTO' ... .~~ ~~~~ ~~~ *55318M" '" -'- " " ". . . "" '. .

.. . . .20 q . . . .I.0. .

.5 I I I I I I

- ALTERNATIVE GS DEFINITION HA 101 MHT= 1220 Md 8987 M

T z 500 M

- y (KM)

2

* 0

-1 0 1 2 3 4 5 6 7

X, (KM)

Figure 7. Glistening Surface Dimensions for the Alternative Definition, ShortAntenna Separation, Smooth Surface (alT = . 006)

.- Figure 8 and Figure 9 show the same comparisons for the case where2 2" a 10 m and T = 200m. This is a slightly rougher surface than before, but the

- - condition that h < x 1 and h 2< x 2 is still valid over the extent of the glistening sur-

faces. As before, Figure 8 shows the results at D = 50 NMI, and Figure 9, at

D = 30 NAII. The 5 NMI result isn't shown since the first definition again results

*" - in a nonexistent surface. The surface for the second definition is determined by

* . the first condition and is a small finite region, as was the case in Figure 7. The

second criterion of the second definition applies at D = 30 NMI and D = 50 NMI,

* and we have continuously increasing widths as x 1 increases. Since L 1 and L 2 are

smaller in these instances, the first definition surfaces are longer and the agree-

ment between the two models is quite reasonable for over half the separations.

Again, the condition that y< x 1,x 2 is satisfied for the first definition.

Figure 10, Figure 11, and Figure 12 show the comparisons for a much rougher

- surface at the three selected separations. Here a 2 = lom 2 and T = 10m. For

these conditions, the surface of the second definition is always controlled by the

second condition on 16, and hence continues to increase in width as x 1 increases.

At all three separations, the two surfaces are quite similar. This is related to the

16

-A.--

25

HA - 101 M STANDARD GS DEFINITIONHT - 1220 M - ALTERNATIVE GS DEFINITIONd - 92382M (4) HA . X1,2

2 0 " 10 N

2 0 M1

T • 500 M

15

y (M)

10

5

00 10 20 30 40 50 60 70

X, (KM)

Figure 5. Glistening Surface Dimensions for Both Definitions,Large Antenna Separation, Smooth Surface (a/T . 006)

25 I o ,

HA - 101 M --- STANDARD GS DEFINITIONHT - 1220 M ALTERNATIVE GS DEFINITIONd '55318 M

20 -" a2 IOM

2

,""T - 500 M

15

y M)

REEI

to

5

00 10 20 30 40 50 60 70

X, (KM)

Figure 6. Glistening Surface Dimensions for Both Definitions,Intermediate Antenna Separation, Smooth Surface (WIT = .006)

S15

0i

• -..• " .:..- .- -i "- ......-i -.- .-i'- .i. .'. .-.. , -. "..- .-i -...K -i

Note that in this derivation, tile assumption that y<<x 1 , x 2 is still required.

This formulation allows us to consider all x 1 , x 2 values such that 4 2flo < 900 or

" o< 45%qo/T < 0.5. Before addressing the width assumptions, we can look at

some results for the various definitions to clarify the situation discussed so far.

3. t1. IA'I'EI) SII{F ES

In Figure 5 through 15, we will consider three values of and will vary the

.-. separation of the antennas from 5 NMI to 30 NMI and then to 50 NMI. This offers

us the opportunity to analyze a wide range of conditions. For these cases, the

heights are fixed at 11A - 101 m and 1IT = 1220 M. This corresponds to heights

that we have used in earlier studies, and the implications of those values will be

discussed. For this comparison, we consider that the heights are less than the

* s eparation, y < d, and y < x1 . x,. We will examine the question of height to x

and x., ratio. F rom the point of view of the second definition, the selected condi-

* tions have d (except possibly the cases where d = 5 NMI).

In I- igure 5, we show both sets of results for the boundary of the glistening

* surface for the case where a2 = 10 m 2 and T = 500 m. The roughness is sufficient-

lv small so that the respective antenna heights are always less than the x-dis-

tances. At this separation, 50 NAI, the surface given by the first definition ex-

tends for half the total distance. The surface obtained from the second definition

is in reasonably good agreement out to about xI = 30km. However, since the an-

- gle j7< 11o, the surface continues to grow indefinitely rather than being cut off,

and would have to be terminated by a radar horizon condition. Thus, there is a

considerable difference in the surfaces close to the receive antenna.

Figure 6 shows the same case for a separation of 30 NMI. As in the preced-

ing figure, the second definition leads to a continuously growing width. In contrast,

for the first definition, the I1 and L2 values are almost equivalent to D, and that

surface extends only over a short distance near the transmitter. Thus, over most

of the separation, the two definitions lead to drastically different results for the

predicted glistening surface width,

Figure 7 shows the result for the same conditions when the antenna separation

has been reduced to 5 NINiI. At that distance, the standard definition results in the

combined I. and I. values exceeding D so that there is no glistening surface. For1 '2

the second case, if we consider that 1) = 5 NMI is sufficient to satisfy the condition

that )--,then $Y2 -8 0 . Thus, the first condition on 16 applies rather than the se-

cond, and we obtain a glistening surface of finite extent that is relatively short in

lenc'th and width, a trend consistent with the nonexistent surface result of the first

definition.

14

(0

V -2, 0 < 6 < V +2P

0 <6 7r/2

- T-< ai < 7r

These angular limits are equivalent to:

S HA cosacot6

y = HA sinctcot6

It should be noted that the form for Eq. (2) presented here is not the same as the7

equation given in Section 12. 4 of Beckmann and Spizzichino for the case where

the transmitter is very far from the receiver. There, the squaring of the sum of

sine terms has been omitted.

The difficulty with this approach is that the constraints initially are in terms

of angular relations rather than the straightforward (x1 , y) conditions of the pre-

ceding case. One of the questions addressed in this report is whether it is rea-

sonable to adopt this more complicated formulism for cases where the height HT

becomes relatively large. The alternative to be considered is the magnitude of

the error of the first result when the original assumptions are no longer strictly

valid. Associated with this is the reexamination of the (xjy) boundary values

when those constraints have been relaxed.

To carry out this analysis, we consider the two coordinate limits separately.

If we look at the x1 coordinates of the glistening surface (bounded by LlO L 2 ), we

see that, as long as 6 is small, all such points satisfy the assumption that

x1 ... A and x2 IT. As # increases, though, some points near the ends of the

surface may not satisfy this assumption. The next point is that, if we remove

that constraint, "e can derive a new expression for the width of the glistening sur-

face that does not require tIA <' X 1 and HIT<<X 2 . The result is:

x1 _X\ i . s. )2 TAN 2 o- [si)'( o os 2 "

-d o /J cos Y TA cos COS

* where

HA HTTAN Y and TAN Y = I .

1 2 x 2

* 13

4

Thus, the transmit. .i is assumed to be located very far from the receiver (see

Figure 4).

zR

HA

GLISTENING SURFACE

xP

Figure 4. Geometrical Representation of Glistening Surface for SystemWith One Antenna at Infinity

Hfere again, thle equation for the boundary of the glistening surface can be de-

rived by considering the direction cosines of thle linear bisector of the angle -1 13P'T.

This line makes an angle 6i with the z-axis. By expressing the direction cosines

of the bisector as a linear combijtation of the direction cosines of lines PT and PR,

setting thle angle fl equal to 11 , and using the normalization condition for the direc-

tion cosines, we can derive the following equation for the boundary of the glistening

surface:

2 cosce 7 - J- T A'YN (2)or coso -/ 0jcosy cosd)J

%%heru the angles~ ot, Y, and 6 are defined in I-igure 4. F or thle boundarv. ci and 6

are confined to tile followinv interv-als:

F. 12

[0o

I - z-. .- . . . . . ... .*.*.*

y-coordinate of the boundary of the glistening surface:

y s I +12Itan290 - (H A ") 1 /2 (

For this result, several additional assumptions have been required. These in-

clude:

(4) The y-coordinates of the glistening surface boundary are less than x and

x 2 that is

Y<<xl, x 2

where

x x-coordinate of point on glistening surface boundary,

and

x9 =d -x (see Figure 3);

(5) The angsle 01n is small; and

(6) The antenna height, IfA. and the receiver height, FIT , are small compared

to x and x2 , that is,

If A" xI and IfT"I x2.

The effects of these limiting assumptions will be discussed in detail, but first we

wish to introduce an alternative definition that Beckmann and Spizzichino 7 derive

for slightly different constraints. In this new case, definition 2, assumptions (1)

through (3) are still valid, but assumptions (4) through (6) have been replaced by

an alternative set of assumptions. For this case, we have:

and/or

1T

11 .

a .*..:- .

.-

'., - -< .I r is used ill tilt applicaltion of tin- cordititons of the

5. L SE SC VirrYutE R It

\\ e have discussed the assumptions and limitations of various glistening sur-

face dimensions for different conditions. To continue our analvsis, we turn to the

question of how using these different concepts affects the calculated diffuse power

scattered from the surface under those conditions.

The basic formalism for the standard calculation is discussed in earlier re-

ports. , 2, 3 %%e use the centerline a' value in the model and assume it applies

across the entire width. In their discussion of the second definition, Beckmann

and Spizzichino represent the power as a constant term times the integrated area

of the surface. In our interpretation of the power scattered by the surface gener-

ated by that definition, we again make use of the centerline a 0 distribution and mul-

* tiply it by the associated width at that point.

In both of these cases, the variation of aowith azimuthal angle has been ne-

glected. In order to evaluate the results of the calculations, we carried out the

complete analysis in which the actual azimuthal variation of a 0 is included and the

power is integrated over the radar footprint for the entire separation rather than

the glistening surface. The details of this solution can be found in Papa et al.

The distinctive features of these models are summarized in Table 1.9 2

Results for the case 0 10m 2 and T = 500m for the exact azimuthally vary-

ing a model are shown in Figure 16. The diffuse scattered power in this figure

is shown as a function of the separation between the two antennas. For analytical

purposes, it should be recalled that the three locations at which glistening sur-

faces have been examined correspond to 9 kin, 55 kin, and 92nkm. The largest

amounts of diffuse scattered power occur at short separations. The power drops

sharply out to a distance of 15ki and then tapers off more gradually, decreasing

to a level four orders of magnitude below the original levels by a separation of

55 in.

Ln I igure 17, the standard definition (2f3 ) results are shown for the sameo

roughness factor. At separations less than 52 kin, the glistening surface does not

exist under this definition, so there is no diffuse power. At greater separations,

the power is insensitive to separation.

* igure 183 shows the corresponding variation for diffuse scattered power when

the second definition W-d-) is used in the calculation. For separations greater

than 55kin, the two results are similar, with the second case exceeding the first

by about a factor of two. At shorter separations, though, this definition does not

25

o° . A

Table 1. Summary of Scattering Model Cases

Case Properties

Definition 1 Centerline a 0

HA, HT<< X1 0 X2

y << X1 , X 2

Definition 1A Constraint on HA I HT removed

Definition 1B Constraint removed on HA, HT, and Y

Definition 2 Centerline a'

Separation infinite and/or height of one

antenna infinite

Standard of a0 includes azimuthal variation

Comparison Integration over entire radar footprint

preclude the existence of a glistening surface. Thus, diffuse power is scattered

at a fairly constant level until the separation decreases to less than 15km. There,

the power curves show a dip followed by a return to the original levels. Given the

similarity in results at larger separations, the question arises as to how the power

for the two definitions would agree if the L 1 and L 2 conditions on the original defi-

nition surface were relaxed. The scattered power for that case is shown in Fig-

ure 19. It is clear that, for separations less than 55km, this extended length case

gives power levels consistent with those of the (d-.- ) definition.

Before continuing with general discussions of the models and comparing the

results with the more exact case we can use our calculated glistening surface

shapes at the three specific separations to interpret the results for the two defini-

tions of glistening surface.

. At 55km, the two results are slightly further apart in power than at 92 km,

but, in both instances, the agreement is quite close. This is significant in terms

. •of the depicted surfaces in Figure 6 and Figure 5. In both instances, the differ-

ence in dimensions is considerable, particularly at 55km. To place this in per-

spective, we have constructed the curves representing the variation in centerline

a) across the antenna separations as a function of roughness for the three dis-

tances discussed in the report. Figure 20 shows the variation for D = 5NAII, Fig-

ure 21 is fo-" 1) 30 N7dL, and tFigure 22 corresponds to D r 50 NI. In these fig-

ures, ce see that, as the rouahness decreases, the value of ao begins to be con-

2 6

o ,

%I

RANGE (N MI)

5 10 15 20 25 30 35 40 45 50

HAc IOIMHT= 1220 M

10- r2= 1o M2

0

U,.0

i0 -14

10 30 50 70 90

RANGE (KM)

Figure 16. Diffuse Scattered Power as a Function of Antenna Separation,Azimuthal Varying ac Calculation, Smooth Surface (O/T = .006)

RANGE (N MI)

5 10 15 20 25 30 35 40 45 5010- 4- IiI

HA: 101IMHT= 1220 M

0 =2 10 M.2

W T: 50OM

0

'

_U-

( 0 -100

* 10 30 50 70 90

RANGE (KM)

.r 17. Diffuse Scatt ,rcff l'o %,r as a FIunction of Antenna Separation, Stan-

dard (istening Surfac(, Calculation, Smooth Surface (a /T = 006)

27* .-

0.

RANGE (N MI)

65 10 1I5 2 0 25 3 0 35 40 45 50

-. HAm 101IMHTx 1220 M

.10810MT 50

0

C 1030 09

RAG (M

10 30 15 2 5 0 3570 45 90

Fiue1. Dfue ctee o e a ucino Antnn Sep raton

9 10. 15210 0 3 4 5 5

0

0 30 500 90

00

01

iO~~-- I i 'j7J I

105

1031

T= 158 M0 d= 10 KM

u 0- 2 = 1.0LiLi. 102

~N-

0 -0

0 10

Z-2 100.

2 1 .0 0.

I0-2

0 2 4 6 8 10

RANGE (KM)

I-.. '. n.rlin Variation of of Go for I)ifferent Roughness Levels, ShortA , iiia , aati(Jn (1) Pl) kin)

0,

o2=0.01T= 158 M

105-- d 55 KM

z 2=0.10

o 0

0

w

-.100

0

00

0 10210 05

03

o20.01

Tc 158 M

105.-dc 90KM

0

Cl,

0c-,

0

00

z

10'

0 020 30 40 50

RANGE (KM)

Figure 22. Centerline Variation of cro for Different flouglneSS Levels, IalargeAntenna Separation (D =90 kin)

* 31

-7.. 41

fined to a narrow region near the specular point and the peak value becomes sharp-

ly higher than for the uniformly distributed cobehavior at larger roughness condi-

tions. The case of interest here is that for a/T = 006. At 55km, we see that, by

the end of the classical 2flo surface, aOhas dropped to less than half its peak and

continues to fall beyond that point. The result is that the two definitions have simi-

lar power levels despite the disparity in surface. At 92 km, similar results occur.

There, the 200 surface is considerably longer than at 55km, so the agreement in

power levels is even closer. At 9km, the 2 o surface is nonexistent and the alter-

native surface is the finite ovoid shown. The ao variation is not significant in that

instance. It should be pointed out, though, that the power for the relaxed length

case does agree at that separation. Since the two surface widths are similar at

that separation, if and L are not imposed that result is to be expected.

Now that we have analyzed the behavior of the diffuse scattered power as given

by the two glistening surface definitions, we compare those results with the calcu-

lated power when the azimuthal variation in aOis included in the calculation. The

comparisons show that beyond 55 km, where results exist for the two definitions,

the result of not including azimuthal covariations is to overestimate the diffuse

scattered power by at least two orders of magnitude (20dB). At shorter separa-

tions, we can compare only the second definition solution. We see that the neglect

of azimuthal variation gives the result that the power stays relatively constant,

while in the. correct solution, the value gradually increases. At 15km, there is a

further discrepancy. There, the azimuthal solution rises sharply while the center-

line model shows a decrease in power. It should be noted that the solution of Fig-

ur(. 1) also shows a similar pattern at that separation, which is associated with a

decrease in the calculated width.

.0. (:4C (:.1 . I( )ON

The conclusion is, first, that the use of centerline ao models can lead to cal-

culated diffuse power levels that are in disagreement with the results for the model

in which both the azimuthal variation in aois taken into account, and the integra-

tion is always across the extent of the radar footprint rather than the calculated

glistening surface width.

Secondly, by careful consideration of the length constraints, the basic defini-

tion width determination can be used as well as more complicated forms.

*Thirdly, even when the assumptions limiting the width have been violated, the

results obtained using the basic definition are still quite reasonable. Thus, there

.' is no real justification for introducing the more complicated formalisms for the

* 32

. ....

dttt'rnination of tIit, glistenitI g surfact width tha Id) n)11o nztfill th, I iI) itDi,)ll if II-

posvd by the original simplifying assumptions.

I

,

I 33

I

' . - . ( . - . . . ( , ° -- ." . .- .. -. • ..- .

References

1. Papa, R.J., and Lennon, J.F. (1980) Electromagnetic scattering from roughsurfaces based on statistical characterization of the terrain, InternationalRadio Science Symposium (USRI), Quebec, Canada.

2. Papa, R.J., Lennon, J. F., and Taylor, R.L. (1980) Electromagnetic WaveScattering From Rough Terrain, RADC-TR-80-300, AD A098939.

3. Papa, R.J., Lennon, J.F., and Taylor, R.L. (1982) The Need for an Ex-panded Definition of Glistening Surface, RADC-TR-82-271, AD A130431.

4. Papa, R.J., and Lennon, J. F. (1983) Investigation of backscatter from anuneven, rough surface, International Radio Science Symposium (URSI),Houston, Texas.

5. Papa, R.J., Lennon, J.F., and Taylor, R.L. (1982) Further Considerationsin Mdcls of' Rough Surface Scattering, RADC-TR-82-326, AD A130424.

fi. Papa, R.J., Lennon, J.F., and Taylor, R.L. (1983) Multipath effects on anazimuthal monopulse system, Trans. IEEE on Aerospace and ElectronicSystems, 585-597.

7. Becknmann, 1., and Spizzichino, A. (1963) The Scattering of ElectromagneticWaves From Rough Surfaces, Macmillan Co., New York.

8. Ruck, G.T., Barrick, D.E., Stuart, W.D., and Krichbaum, C.K. (1970)Radar Cross Section Handbook, 2, Plenum Press, New York.

Long, N.W. (1!975) Radar Reflectivity of Land and Sea, Lexington Books,Lexington, Miss.

10. Barton, 1). K., and Ward, 11. R. (1969) Handbook of Radar Measurement,Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

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