171251 , 2

ADVISORY GROUP FOR AEROSPACE RESEARCH & DEVELOPMEI

AGARD CONFERENCE PROCEEDINGS No.77

on

Electromagnetics of the Sea

' .

i- I

T I B INTERACTION OF HF/VHF RADIO WAVES WITH THb: S A SURFACE AND I T S IMPLICATIONS

by

Donald E. Barrlak

T h e Ohio State University ana Colombus Laboratories T h e Electriaal Engineering Department

Colombus, Ohio 43210

Battelle Memorial Institute

C o l o m b u s , Ohio 43201

18

18

SOMMAIRE

Pour dtudier l ' in teract ion d e s ondes rad io B haute8 f rdquences avec la m e r , l 'auteur ana lyse l e s per turba t ions aux l imi t e s . I1 voit l ' influence de l 'agi ta t ion de l a m e r s u r la propa- gation des ondes t e r r e s t r e s 3 t r a v e r s l 'ockan c o m m e une augmentat ion de l ' impkdance effective B la surface. A l 'a ide du s p e c t r e d e s ondes de vent de Phi l l ips , il prockde 3 d e s es t imat ions quantitative6 de la ddperdit ion supplkmenta i re due B l 'd ta t de la m e r . 11 m o n t r e que la diffusion B p a r t i r de la m e r e s t due B l 'effet Bragg . 11 ext ra i t p a r dkrivation, puis examine, l ' in tensi tk e t le s p e c t r e du s ignal diffusk. I1 ana lyse enfin p lus i eu r s configurations bis ta t iquee de r a d a r u t i l i skes pour la m e s u r e d e s s p e c t r e s d e s ondes ocdaniques. Ces configurations impliquent d i v e r s e s conbinaieone de bateaux. de boudes, d 'avions, de sa te l l i t es e t de s ta t ions c6 t i8 re s . Il examine sous une f o r m e a s s e z dktail lke l e e possibi l i tds de r ea l i s a t ion de deux sys tkmes de c e gen re , e t conclut que le matdr i e l dont on d ispoee semble en p e r m e t t r e l e dkveloppement.

THE INTERACTION OF HF/VHF RADIO WAVES W I T H THE SEA SURFACE AND ITS IMPLICATIONS

Donald E. Barrick

The Electrical Engineering Department B a t t e l l e Memorial I n s t i t u t e The Ohio State University and Columbus Laboratories

Columbus, Ohio 43210 Columbus, Ohio 43201

SUMMARY

The in te rac t ion of HF and VHF radio waves with the sea is examined using a boundary per turbat ion analysis . crease i n the e f f e c t i v e surface impedance. s t a t e using the P h i l l i p s wind-wave spectrum. Both t h e sca t te red s igna l i n t e n s i t y and spectrum a r e derived and examined. radar configurations f o r measuring ocean-wave spectra are analyzed. of ships , buoys, a i r c r a f t , s a t e l l i t e s , and shore s t a t i o n s . The f e a s i b i l i t y of two such systems is e x a m - ined i n some d e t a i l , and t h e i r implementation appears possible with present-day hardware.

1. INTRODUCTION.

The e f f e c t of ocean roughness on ground-wave propagation across the ocean is seen a s an in- Quant i ta t ive est imetes a r e made of the added loss due t o sea

Sca t te r from the sea is shown t o a r i s e from the Bragg e f f e c t . Final ly , severa l b i s t a t i c

These involve various combinations

Winds blowing a t speeds grea te r than 10 knots over the ocean exc i te the longer and higher ocean waves. For example, a 10-knot wind can c r e a t e waves about 20 meters in length, while a 30-knot wind w i l l arouse waves about 200 meters long. meteorological condi t ions over the ocean, t h e remote sensing of the c h a r a c t e r i s t i c s of ocean waves with these lengths w i l l provide valuable data concerning the weather Over the sea.

Since wind speeds between these l i m i t s a r e highly ind ica t ive of the

Elementary physical p r inc ip les ind ica te t h a t electromagnetic waves whose wavelengths a r e compa- rab le t o the longer ocean wavelengths should i n t e r a c t s i g n i f i c a n t l y with these water waves. magnetic waves l i e i n the HF and VHF regions of the spectrum. in te rac t ion mechanism was discovered experimentally by Crombie i n 1955[ ly . He observed t h a t near-grazing backscat ter a t 13.56 MHz is Doppler-shifted by a d i s c r e t e increment above and below the c a r r i e r . v e l o c i t i e s required t o produce these s h i f t s a r e possessed only by ocean waves whose lengths a r e precisely one-half the electromagnetic wavelength and whose c r e s t l i n e s l i e perpendicular to , the transmission path. Hence, the mechanism was seen t o be Bragg s c a t t e r from ocean-wave t r a i n s moving toward and away from the radar i n much the same manner a s a set of t r a n s l a t i n g d i f f r a c t i o n grat ings. Crombie presents recent experimental observations of t h i s phenomenon and i n t e r p r e t s the two s p e c t r a l s h i f t s in terms of advancing and receding water waves a t a number of HF frequencies.

Quant i ta t ive theore t ica l es t imates of the in te rac t ion , however, lagged the measurements by

Such e lec t ro- These sus ic ions were confirmed and the

The

In an accompanying paper,

many years. surface, we a r e ab le t o pred ic t the magnitude of s c a t t e r and propagation across the sea a t HF and VHF. Both high-angle r e f l e c t i o n and s c a t t e r a s w e l l a s near-grazing propagation (i.e., ground-wave propagation) and s c a t t e r can and w i l l be analyzed i n t h i s manner here.

(i) i t s height, 5, above a mean plane i s small i n terms of the wavelength; ( i i ) i t s slopes ( i . e . , C aC/& and 6 conductingayand hence an impedance boundary condi t ion can be employed.

Now, however, applying the c l a s s i c a l boundary per turbat ion approach of Rice[2] t o a random

The sea surface a t HF/VHF is very amenable t o

= ac/ay) are small f o r these longer ocean waves; and ( i i i ) the ocean-water medium is hfghly

, analysis by t h i s technique because it s a t i s f i e s a l l of the necessary assumptions inherent i n the der ivat ion: - In the next sect ion, we show t h a t the ocean roughness can a f f e c t a v e r t i c a l l y polarized ground

Such an e f f e c t should be expected, s ince corrugations have long been used t o It is shown t h a t the

wave propagating above it. guide waves along the conducting surface of antennas, wires, and o ther s t ruc tures . random roughness changes the e f f e c t i v e surface impedance; t h i s corrected impedance can then be used i n any of t h e ground-wave treatments t o es t imate the f i e l d s t rength a t tenuat ion with dis tance, such curves based on the P h i l l i p s i so t ropic wind-wave spectrum.

We present

The subsequent sec t ion deals with s c a t t e r i n g of HF/VHF waves by the longer ocean waves. Both razing (ground-wave) incidence and the higher incidence angle regions a r e considered. An expression E?, the s c a t t e r i n g cross sec t ion per u n i t surface area is derived f o r the P h i l l i p s ocean wave-height

model. We a l s o obtain an expression f o r t h e sca t te red s i g n a l spectrum, t o the f i r s t order, and show the d i s c r e t e , Doppler-shifted frequencies measured by Crombie and others a r e predicted. The expressions a r e general and can be applied t o backscat ter a s w e l l as b i s t a t i c radio geometries.

In the f i n a l sect ion, w e discuss possible methods of sensing the ocean wave-height spectrum by Several have already suggested measuring the electromagnetic sca t te red s i g n a l and i ts Doppler spectrum.

the use of HF ionospherical ly propagated sea s c a t t e r a s a method of ocean-wave sensing[3]. We suggest nonionospheric techniques here involving combinations of sh ips , buoys, a i r c r a f t , and shore s t a t i o n s i n b i s t a t i c modes t o measure the ocean-wave spectrum. ava i lab le permit t h e reso lu t ion necessary t o s o r t out the presence and s t rengths of ocean waves of various lengths and d i rec t ions ; hence, such techniques can o f f e r a valuable input t o real-time global oceanography/meteorology.

2. GROUND-WAVE PROPAGATION ACROSS THE SEA.

2.1

The s i g n a l processing techniques cur ren t ly

Derivation of Ef fec t ive Surface Impedance of a S l i g h t l y Rough Surface.

Much a t t e n t i o n has been given t o rad ia t ion from a dipole above a smooth, f i n i t e l y conducting medium. r e s u l t s and reduced them t o a convenient graphical form f o r engineering calculat ions.

S ~ m m e r f e l d [ ~ ] f i r s t solved the problem f o r a planar i n t e r f s c e ; Norton[5] later in te rpre ted h i s Others, including

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van der Po1 and Bremmer[61 and FockI71, obtained asymptotic so lu t ions t o the problem of rad ia t ion above a smooth spher ica l ear th , and Norton generated curves t o f a c i l i t a t e the use of these r e su l t s [8 ] . review of t he subjec t by Wait[g] is recommended to the reader.

A thorough

Essent ia l ly , Wait[9] shows t h a t one can formulate the ground-wave r ad ia t ion and propagation problem i n terms of. t he impedance of the sur face normalized t o tha t of f r ee space, i .e. , A = Z /Z , where Z is the impedance of the sur face i n ohms, and Z Asand Z than unfty, and hence v e r t i c a l po lar iza t ion is favored f o r near-grazing o r ground-wave propagation.

120 rdl i s the impedance of f r e e space. Tfe & e n t i t i e s For the ea r th and sea , A i s much l e s s a r e functions of the grazing angle and a t e r i a l p roper t ies .

It was es tab l i shed by Norton[ 101 and Wise[11] tha t v e r t i c a l l y polarized waves propagating near grazing and near the sur face of the ground appear t o be gXided waves loca l ly , even though macroscopically they do not exh ib i t t h i s guided (or Zenneck-wave) nature. e f f ec t ive impedance of a s l i g h t l y rough surface, t r ea t ing the propagation f i e l d a t a mean planar i n t e r - face a s a l oca l ly guided wave.

F i r s t , w e write the expression f o r the planar f i e l d guided by a f l a t , smooth, highly conducting The geometry is shown i n Figure 1.

Hence, we s h a l l derive i n t h i s sec t ion the

surface. der iva t ion :

Jordan[12] can be consulted f o r t h i s straightforward

EZ EO e x p { i k , m x - ikoAZ - i w o t } ,

Ex - E o A e x p { i b m x - i k , A Z - iwt} ,

where Eo i s the .E-field amplitude constant, and k, is t he wavenumber i n f r ee space, i . e . , 2n/A, where A i s the wavelength. The normalized surface impedance a t grazing f o r a medium below the smooth in t e r f ace of complex permi t t iv i ty 61 and permeability can be wr i t t en a s

Included i n is the e f f e c t of conductivity, i.e., c l = E + i al/u0, where 6 is the r e a l d i e l e c t r i c constant of the medium and q i s i t s conductivity. q 4 mhos/meter, €1 €0 (80 + i7200), and A - 1.18 x lo-’ exp(-iT/4).

ri For sg!i water a t 10 MHz, f o r example, eri 80 &,

Now, w e wr i t e the t o t a l f i e l d above a s l i g h t l y rough surface (see Figure 2) a s follows:

CO

r-

Ex = AE(h,O,z) + Am, E(m + h,n,z) , m, n=-”

m -

m P

EZ = E(h,O,z) + Cmn E(m + h,n,z) , m, n=-m

where

E(m + h,n ,z ) = Eoexp[ia(h + m)x + iany + ib(m + h,n)z) ,

and

b(h + h,n) = ,hkz - a2(m + h)a - aana . The de f in i t i on of b above is such t h a t Equations (2) s a t i s f y the Helmholz wave equation. The

Cartesian components of t he H-field a r e not given here, but a r e readi ly determined from Maxwell’s equations.

I n the above equations, t he presence of roughness manifests i t s e l f a s the summation terms. AS the roughness height approaches zero, A then become iden t i ca l with Equations (2’f”thenecome iden t i ca l with Equations (1) f o r a guided wave over a smooth impedance boundary.

, B , Cmn, w i l l vanish, and b(h,O) + - h a ; Equations (2)

Also, Coo i s taken t o be iden t i ca l ly zero i n (2c). This choice is possible; what it r e a l l y means is t h a t a l l of t he remaining constants a r e normalized so t ha t the 0,O mode appearing i n (2c) is removed from t h e s m t i o n and grouped with the preceding term, E(h,O,z) with amplitude Eo. t he quided-wave portions of t he f i e l d appearing i n Equations (2) a r e a l l terms having the E(h,O,z) s t ruc ture . These are

Physically,

E: = (A + A001 E(h,O,z) , ( 4 a )

Whis is analogous t o the f a c t t h a t a spher ica l wave appears planar loca l lv , i .e. , wi th in the area of a Fresnel zone, but macroscopically it is spher ica l i n nature.

EG = BooE(h,O,z) , Y

G EZ = E(h,O,z) .

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The remaining portions of Equations (2) cons is t of modes generated by the roughness. These modes, t o be termed the sca t t e red f i e l d here, ac tua l ly include both propagating and evanescent modes.

The guided-wave portions of the perturbed f i e l d s a r e given by Equations (4). When one compares (4a) and (4c) with ( lb ) and ( l a ) f o r a smooth impedance boundary, one is lead t o def ine an "effective" o r average impedance guided-wave propagation across a roughened surface a s

- A = ( A + b o ) = A + ( b o ) (5)

i.e., the e f f ec t ive impedance cons is t s of t he constant impedance of a smooth in te r face plus (Aoo), which accounts f o r the roughness. be used, and the goal of t he ana lys i s w i l l be to derive an expression fo r (Aoo) . I f the roughness i s t o cont r ibu te t o the impedance, we expect t h i s average t o be nonzero. Physically, (5 ) says tha t the average wave f r o n t and polar iza t ion tilt a t t he sur face is

( E ~ ) / ( E ~ ) = a = A + (bo)

which i s another way of defining the e f f ec t ive sur face impedance.

The braces ( ) denote an average. This convenient de f in i t i on w i l l i n f a c t

G G ,

I n solving f o r bo, we expand the surface height i t s e l f i n a Fourier s e r i e s , va l id over a square of s i d e L :

03

G(X,Y) = 1 P(m,n) expEia(mx + ny)3 ( 6 ) m, n=-a

where a = 2n/L. We can a l s o w r i t e the sur face slopes ag/m( and ag/ay by d i f f e ren t i a t ing ( 6 ) .

We intend t o solve f o r bo by a standard perturbation approach. Equations ( 2 ) f o r the f i e l d s a r e t o be subs t i tu ted in to the Leontovich boundary condition a t the surface. This condition is:

- T - T Here, E and H a r e the t o t a l e l e c t r i c and magnetic f i e l d s above the sur face , a s given i n Equations ( 2 ) with z = 6. The quantity is the uni t normal to t h i s surface. It is expressible i n terms of the sur face slopes a s

The determination of bo proceeds by ordering the terms i n the r e su l t i ng s e r i e s i n order of smallness. The following quan t i t i e s a r e assumed t o be small, and hence serve a s perturbation parameters: (1) << 1 -- i .e. , roughness height is small com red t o wavelength; ( 2 ) << 1 -- i.e., t he sur face slopes a r e r e l a t i v e l y small; and (3) FI << 1 -- i .e. , the normalized impedance of the medium below the sur face is small.

A l l of the above conditions a r e s a t i s f i e d by the sea a t HF/VHF.

Sparing the a lgebra ic drudgery ( the d e t a i l s of which can be found i n Reference 13), the above procedure shows tha t t o the f i r s t order i n the perturbation parameters, b o = 0. To the second order,

where

D(myn) + b(m + h,n) A P ! ) + 11 .

The above expression f o r bo is va l id f o r de te rminis t ic , periodic surfaces a s we l l a s random rough surfaces. For example i f the sur face is s inusoida l i n the x-direction with period L, then A00 cons is t s of only two terms, t he ones f o r m = fl, n = 0. When Aoo is then added t o A , one has the e f f ec t ive sur face impedance of t h i s s inusoida l surface.

When the sur face i s random, a s i n the case of the sea , the P(m,n) a r e random var iab les . I n t h i s case, we a r e in t e re s t ed i n the average value of bo, and the P(m,n) a r e r e l a t ed t o the wave height spectrum of the surface, W(p,q) a s follows:

where p = am = 2w/L and q = an = 2 m / L . I f we then take the average of bo i n (8), use ( l o ) , and

18-4

s u b s t i t u t e bo) i n t o (5) we obtain: m m

where

b‘ =L,& - ( ~ + k , ) ~ - qa . ko

The de f in i t i on of W(p,q) follows t h a t of Rice[’], a s does most of t he nota t ion used here; t h i s is done t o f a c i l i t a t e reference t o h i s c l a s s i c perturbation treatment.

As a check on ( l l ) , i f w e permit A t o approach zero i n (12) we obta in F(p,q) = pa/b’, and

This r e s u l t was derived from an in t eg ra l equation technique by Feinbergf141. zero, Equation (13) becomes iden t i ca l t o tha t obtained by Rice[2] f o r a per fec t ly conducting surface.

To i n t e r p r e t the simpler form, (13), l e t us r e f e r t o Figure 3. t o r\ of the in t eg ra l i n t o two par t s , R The cont r ibu t ion R A the height spectrum lying wi th in the circle ceneered a t p / b = -1, q/ko = 0. s p a t i a l frequencies, o r waves, wi th in t h i s region, then the r e s i s t i v e cont r ibu t ion is zero; these s p a t i a l frequencies m u s t thus be less than 216. than A12 can cont r ibu te t o the r e s i s t i v e portion. From a study of s c a t t e r from t h i s type of s u r f a ~ e , f ~ ~ ’ ~ ~ ] it has been shown t h a t waves whose lengths a r e g rea t e r than 112 a r e responsible f o r s c a t t e r . Hence the in t e rp re t a t ion of the r e s i s t i v e portion becomes c l ea re r ; longer ocean waves whose wavenumbers l i e wi th in the c i r c l e a r e responsible f o r removal of energy from the guided wave and scatter of t h i s energy i n t o a l l d i rec t ions i n the upper hemisphere. This energy removal produces an increase i n the r e s i s t i v e term of t h e sur face impedance.

I f we allow A t o approach

We separate the cont r ibu t ion and -iX . comes e n t i r e l y from t h a t part of

I f there a r e no roughness

Physically, t h i s statement means tha t only ocean waves longe

On the o ther hand, i f there a r e no ocean waves whose lengths a r e g rea t e r than a half-wavelength (i.e., t h a t l i e outside the un i t c i r c l e ) , then the roughness cont r ibu t ion t o A is purely reac t ive ; i n addi t ion , it is always an inductive reactance. ( a t least t o the f i r s t o rder i n 166, the roughness he ight ) . Hence, t h i s higher-frequency roughness produces a perturbation on the loca l f i e l d a t the sur face t h a t e x i s t s only a t and near the region between the waves; s ince there a r e no sca t t e red propagating f i e l d s removing energy from the guided wave, t h i s e f f e c t should be evident only very near the surface. propagating, but evanescent.

2.2

Roughness waves of these sho r t e r lengths do not s c a t t e r

The perturbed modes i n t h i s case a r e not

Ef fec t ive Surface Impedance of the Sea Using the Ph i l l i p s Wind-Wave Spectrum.

The presence of roughness on the ocean is due t o winds blowing across the sea. The f u l l growth of the longer waves (20-200 meters) by winds (10-30 knots ) , however, requires severa l hours t o f u l l y develop. Af te r t he winds have ceased, the higher longer waves do not immediately abate. decrease i n amplitude only as they t r ave l t o o ther a reas of the ocean and a s they break a t t h e i r c r e s t s .

They

Thus, t he longer waves a t a given patch on the ocean o r ig ina t e from two sources: ( i ) winds which have blown across t h a t patch f o r the severa l hours p r io r t o the observation, and ( i i ) waves which have been developed a t o ther t i m e s and places and which may be considerably weaker i n magnitude than a t t h e i r o r ig ins ; these l a t t e r a r e ca l l ed s w e l l . Only i n the case of the former a r e there ava i lab le simple mathematical models r e l a t ing the wave heights t o t h e i r meteorological sources, the winds.

Hence the bes t we can do i n attempting t o estimate the e f f e c t of sea s t a t e on radio-wave propagation and s c a t t e r is t o use a simple wind-wave model and neglect the e f f e c t of swell . involved w i l l almost ce r t a in ly be one of overestimation. less than those due t o the recent, l oca l winds, s ince “swell” is ac tua l ly d iss ipa t ion . and should be t r ea t ed a s such.

The e r r o r Roughness heights due t o swell a r e bound t o be

Therefore, t he predictions of the e f f e c t s presented here represent l’worst-case” estimates, i n the process of

The Neumann-Pierson ocean-wave spectrum was suggested some f i f t e e n years ago[17], and predictions based on it can be found i n (13). oceanographers t o search f o r a more accurate model.

dependence of t he Neumann-Pierson model. cu tof f is much more pronounced than the a r t i f i c i a l exponential f ac to r attached t o the Neumann-Pierson spectrum. eing i so t rop ic

Ocean-wave data gathered i n recent year fl,powever, have led many Phi l l ips [18] and Munk have presented convi c ing

evidence t o show tha t the s p a t i a l spectrum should behave a s (pa + qa)’a, instead of the (pa + s a ) -ob

than the cosine-squared d i r e c t i o n a l i t y of ten assumed with the Neumann-Pierson model iY7B .

More important, however, measurements show t h a t the lower-end

Slope measurements by Cox and Munk[20] show t h a t the spectrum is c lose r

Hence, we employ the following spectrum[ 181 :

where B i den t i ca l ly zero fo r /&< g/Ua and a l s o i n the half-space from which the wind is coming.

0.005, g = 9 81 m s (acce lera t ion of grav i ty) , and U is the wind speed i n m / s . The spectrum is

18-5

We use (14) i n a numerical evaluation of Equation ll), and the r e s u l t s f o r the normalized r e s i s t i v e and reac t ive portions of e f f ec t ive sur face impedance a r e shown i n Figure 4. We divide the spectrum, (14), by two and in t eg ra t e over a l l p,q space, r a the r than only over the forward wind ha l f . This is necessary because a t a given in s t an t the sea p r o f i l e w i l l appear "frozen" t o a radio wave, end it w i l l not be possible t o t e l l from t h i s p r o f i l e whether the waves a r e moving forward o r backward. For the spectrum of Equation (14), the mean-square height i s ha = 1/2 B @/pa. only f o r G h " << 1, they can be used fo r frequencies up t o about 50 MHz with a wind speed of 25 knots. The conductivity of the sea is taken as U = 4 mhos/meter.

2.3 Basic Transmission Loss Across the Sea Using the Ph i l l i p s Wind-Wave Spectrum.

Since the curves a r e meaningful

- We can now employ the e f f ec t ive sur face impedance, A, accounting fo r roughness i n any of the

more-or-less standard techniques f o r ca lcu la t ing ground-wave ropagation. I n pa r t i cu la r , we employ a

Their program is modified to the extent t h a t i t w i l l accept the r e s i s t i v e and r eac t ive portions of the sur face impedance r a the r than the ground conductivity and d i e l e c t r i c constant; the output i s modified so t h a t i t p r in t s bas ic transmission loss as well as the o ther var iab les .

modified version of a FORTRAN I V program avai lab le from ESSA[ E 11 f o r propagation over a spher ica l ear th .

Basic transmission loss is a concept widely publicized by Norton[ZZ] i n the 1950's. Formally, i t is defined a s

(dec ibe ls )

where Pti is the power transmitted by an i so t rop ic r ad ia to r and P rad ia tor . I n a simple communication problem, one must merely su66ract out the free-space antenna gains ( i n dB) i n order t o determine the ove ra l l power loss. For example, the bas ic transmission loss between two points i n f r e e space separated by d is tance d is 10 L 0 g l ~ ( 4 n d / h ) ~ ; i f the same two points a r e located above a f l a t , pe r f ec t ly conducting ground plane, the 4 i s replaced by 2 i n the parentheses. The pres- en ta t ion of ground-wave a t tenuat ion in the form of basic transmission loss appears t o be more readi ly in t e rp re t ab le and usefu l than many of the ground-wave normalizations (e.g., un i ty electric dipole, 1 kW transmitted power, f i e l d s t rength one m i l e from the t ransmi t te r , e t c . ) .

is the power received by an i so t ropic

Figure 5 shows t h i s bas ic transmission loss between two points a t t he sur face of a per fec t ly smooth sea a s a function of range. 0 = 4 mhos/m ( typ ica l of the At l an t i c ) , and e f f ec t ive ea r th radius f ac to r of 4/3 (accounting fo r atmospheric r e f r a c t i v i t y i n an idea l ized manner). I n Figures 6-8, we show the added transmission loss due t o sea state. These curves were ca lcu la ted using the same program and subt rac t ing the r e s u l t s from those of Figure 5 f o r a smooth sea. located near t he surface.

These were computed from the program using a water conductivity

I n a l l these cases, the t ransmi t te r and receiver points a r e

Figures 9-11 show the bas ic transmission loss t o various points above the ea r th when the t rans- m i t t e r is located a t the surface. The f i r s t number a t each height-range gr id point i s the loss when the sea is per fec t ly smooth, while the second represents t he loss when the sea is f u l l y excited by a 25-knot wind. observes a drop i n s igna l of 2-3 dB and then a monotonic increase a s he moves out of the surface-wave region i n t o the lit, or space-wave region. not necessary, because the transmission loss becomes simply the inverse-distance r e l a t i o n given a f t e r Equation (15).

The "height-gain" e f f e c t is c l e a r l y i n evidence a s one moves upward a t a given range; one f i r s t

I n the lit region, such curves and computer programs a r e

One should observe from Figure 6 t h a t the added "loss" due t o sea roughness i n some cases is

Thus the negative, ind ica t ing an increase i n s igna l leve l . This e f f e c t is expected, because a t these lower frequencies, most of t he ocean wavelengths a r e s t i l l small compared t o the rad io wavelength. cont r ibu t ion t o the sur face impedance is almost e n t i r e l y reac t ive , r a the r than r e s i s t i v e . corrugations on an otherwise conducting sur face have long been known t o cont r ibu te t o i t s reactance, wi th a r e su l t i ng e f f e c t of "trapping", o r guiding the energy near the surface. WaitI9] discusses t h i s trapping mechanism. The e f f e c t here is not strong, however, because the r e s i s t i v e por t ion is already high due t o t h e f i n i t e water conductivity. Also, it should be noted by comparing the curves a t 10 MHz and 30 MHz (Figures 7.and 8) t h a t losses due t o sea s t a t e would seem t o be l e s s pronounced above about 15 MHz. This a r i s e s from the f a c t t h a t the simple increase i n impedance due t o water conductivity with frequency overshadows the increase due t o roughness.

Small

Again, it should be mentioned t h a t the curves presented here a r e based on the Ph i l l i p s i so t rop ic wind-wave spectrum. A s such, the losses a r e believed t o represent an upper l i m i t , because (i) it takes many hours f o r a s t rong wind t o f u l l y arouse the sea ; (ii) the length of ocean over which an in tense wind is blowing (termed "fetch") may be l e s s than the range between t ransmi t te r and rece iver ; and ( i i i ) the gent le r , ever-present s w e l l cont r ibu t ion t o roughness is neglected.

3.

3.1 Derivation of the Scattered Field Mode Coeff ic ien ts .

SCATTER OF A GROUND WAVE BY THE MOVING SEA SURFACE.

I n the preceding sec t ion , w e examined the s t ruc tu re of the ground wave propagating across a rough sea. We represented the e l e c t r i c f i e l d above the s l i g h t l y rough sur face by Equations (2) , and w e saw t h a t t he influence of the roughness on ground-wave propagation manifested i t s e l f i n the second- order bo term of the series of (2a). I n t h i s sec t ion , w e wish t o examine the remaining perturbed f i e l d coe f f i c i en t s Am, Bm, and C surface. of t h i s "scattered" f i e l d may not be propagating. i s imaginary, the modes a r e evanescent, o r nonpropagating. When m and n a r e s u f f i c i e n t l y small, however, t h a t b(h + m,n) is r e a l , the sca t t e red modes propagate u F a r d , away from the sur face , i n d i rec t ions

. The existence of these coe f f i c i en t s i s due t o the roughness on the The series r e p r e s e s plane-wave modal expansions of the "scattered" f i e l d , although the modes

When m and n a r e such tha t b(h + m,n), defined i n (3b),

18-6

r e l a t ed to m and n. (= an/ko) f a l l i n g ins ide the displaced un i t c i r c l e .

I n the wavenumber space of Figure 3, t h i s corresponds to p / h (= amlk,), q / b

We generalize the previous expansions a t t h i s point t o include time. The s l i g h t l y rough sur face var ies i n height with t i m e a s

m

~ ( x , y , t ) = 1 P(m,n,A)exp[ia(m + ny) + i w k t - j , (16) m,n, A=--

where w = 2n/T, T being the bas ic t i m e period of the Fourier expansion. defined i n (6) . passing over the surface a r e s t i l l represented a s i n Equations ( 2 ) , but with the added subscr ip t A (i .e. , A m p ... ,E(m + h,n,A,z)).

The remaining terms a r e a s The perturbed f i e l d s a r i s i n g from a v e r t i c a l l y polarized wave a t grazing incidence

In addi t ion , (3a) is expanded t o show t h i s t i m e dependence a s

E(m + h,n,k,z) = Eoexp{ia(h + m)x + iany + ib(m + h,n)z + i(wA - uo) t ] , (17) -iqt

where the time dependence of the incident f i e l d on the c a r r i e r WO is e

The so lu t ion of t he problem here then cons is t s of f inding A Bmk, and CmnA. This i s done

We again employ the Leon?%vlch, o r impedance, boundary The

i n the straightforward perturbation manner. condition given before Equation ( 7 ) , s ince t h i s condition i s f u l f i l l e d by sea water below UHF. assumptions involved in ' the perturbation parameters a r e a s given a f t e r Equation ( 7 ) . coef f ic ien ts* f o r a r b i t r a r y m, n, and k a r e of f i r s t -o rde r i n these perturbation parameters, and are :

The general

where

N B = -ian[l + + (1 - y)] + iam b - ,

and D(m,n) is a s given i n Equation (9).

Throughout t he der iva t ions of the above coe f f i c i en t s , only f i r s t -o rde r terms i n ko6, &, 6 , The second-order cor rec t ions have been derived b$ and A

fo r per fec t ly conducting sur faces , and these a r e complex i n general and d i f f i c u l t t o i n t e rp re t . When one reaches the point where the second-order terms a r e necessary t o cor rec t the above expressions, t he e n t i r e perturbation technique has been pushed t o the l i m i t of i t s expected va l id i ty .

t he perturbation parameters) were retained.

The f i r s t -o rde r coe f f i c i en t s of the sca t t e red f i e l d give pa r t i cu la r ly enlightening in te rpre- t a t ions of the in te rac t ion mechanism. The d i r ec t ion of propagation of the sca t te red m,n,k mode i s d i r e c t l y r e l a t ed t o the Fourier component of t he surface, and f o r propagation modes, t h i s d i r ec t ion i s the Bragg d i r ec t ion required by a periodic surface with wavenumbers am and an.

3.2 The Far-Field Sca t t e r from a Sea Surface Patch.

I n Equations (2) and (M), w e have modal, plane-wave expansion f o r the f i e l d s above a sur face of i n f i n i t e extent. We wish now t o apply the preceding r e s u l t s t o a patch of sea sur face of f i n i t e extent. I n pa r t i cu la r , l e t us choose a square patch of s i d e L. ab ly la rger than the wavelength, A, but considerably smaller than b, the d is tance from the patch t o the observation point. It is t h i s s i t u a t i o n which i s of i n t e r e s t here, i.e., X << L << &.

the patch center (See Figure 12), w e can employ the following equation f o r the sca t t e red magnetic f ie ld[24] :

I n most p rac t i ca l s i t ua t ions , L w i l l be consider-

When the sca t t e r ing patch is considerably smaller i n extent than b, the far-zone d is tance from

( 2 0 ) - where 2 and H i n the integrand a r e the f i e l d s evaluated a t Ehe surface element dS'. Here f$ is a un i t vector gointing i n the des i red observation d i rec t ion , i.e., i$ = sin-8 cos 8 area fncrement, dS', on the sur face of in tegra t ion .

cos cp x + s i n 8 s i n cp, 9 + S z, where the angles a r e a s defined i n Figure 12. The vector r"points from the o h g i n t o the loca l

The pertufsbation approach of the preceding sec t ion shows tha t the s l i g h t roughness produces a

i n the integrand evaluated on t h i s plane.

s ca t t e r ed E-field, E , whose three Cartesian components a r e represented by the three sumnations of Equations (2). At a l so makes it possible t o choose our sur face of in tegra t ion as $he 2, = 0 plane by wr i t ing 3 and H determined from 3 using Maxwell's equations.

Whe method of so lu t ion follows d i r e c t l y t h a t of RicetZ].

Then dS' = dxdy, and n = z ; 3 i s simpiy Also, w e restrict our i n t e r e s t a t t h i s point t o the cp,

The algebra is straightforward and hence omitted here.

7 3 component of H ( % , t ) , i.e., the sca t t e red H-field normal t o the s c a t t e r plane. Then the in t eg ra l becomes:

- i k s i n os cos cp, x - iko s i n BS s i n cpsy

X e dXdY , where f (m,n) is a f ac to r containing NA, NBy and fa", determined from (20).

cp

Equation (21) can be in tegra ted oirer the square patch t o give

i(w.8 - %)t Bs cos cp, - am - (kosin Bs cos 'p - am -

r G = L P(m,n,a)f (m,n) ' m,n,.t cp

(22b)

A s ye t , no s ta t is t ics have been introduced. Equation (22) can apply f o r a de te rminis t ic per iodic sur face with Fourier expansion coe f f i c i en t s E(m,n,.8) a s wel l a s t o a random surface. square H@ and average a t t h i s point t o obta in the sca t t e r ing c ross sec t ion per un i t area. However, s ince w e w i l l u l t imate ly be in t e re s t ed an expression va l id near grazing ( i . e . , B averaging process, and f i r s t study the e f f e c t of s c a t t e r above a plane w i t g nonzero sur face impedance, A.

3.3

We could

+ W2), we s h a l l defer the

Application of the Compensation Theorem t o Sca t te r .

King[25,26] has recent ly applied the Compensation Theorem t o the problem of rad ia t ion from a dipole above a plane with sur face impedance, A. r e rad ia t ion from a s c a t t e r i n g patch on the surface t o a far-zone point above a plane with e f f ec t ive sur face impedance, A.

We s h a l l apply i t i n the same manner t o our problem:

The reader i s re fer red t o King's papers f o r d e t a i l s on the technique.

The der iva t ion shows tha t the general rad ia t ion problem can be reduced to the following in t eg ra l equation (Equations (6) and (7 ) of King[26]):

where the indicated angles a r e shown i n Figure 13.

Here, €I$ ( the f i r s t term on the r i g h t s i d e of (23)) is the "unperturbed" $ component of the H-field a t the observation point, t he l g f t s i d e of (23) represents the "perturbed" 6' component of the H-field a t t he observation point, and H q ' i n the integrand i s the f i e l d a t dS, t he in t eg ra t ion point on the plane.

component of thg "perturbed" H-

The terms "perturbed" and "unperturbed" as used with the Compensation Theorem have d i f f e ren t meanings than used previously with the technique f o r s c a t t e r from a s l i g h t l y rough surface. "perturbed1I f i e l d here i s the unknown quantity, and i t s nature depends upon the sur face over which it propagates. Qe "unperturbed" so lu t ion t o the problem is presumed known. equation i n H

Analogous t o King[26], w e s e l e c t f o r our "unperturbed" f i e l d the far-zone HS component re rad ia ted from the sur face patch when the remainder of the sur face is per fec t ly cond%cting ( i . e . , A = 0) . This is given by Equation (22a) when we set A = 0 i n Equation (22b) f o r f (m,n).

cp

The

Thus (23) is an in t eg ra l t he des i red "perturbed" f i e l d .

c p '

Thus, the re rad ia ted H-field t o be used a s the unperturbed so lu t ion i n (23) is

where Gkrepresents Qp of (22b) but with A = 0. of t he location over t he per fec t ly conducting plane.

This expression i s doubled from tha t of (22a) because

Now, analogous t o King[26] w e def ine the "perturbed" o r unknown f i e l d a s equal t o the "unperturbed" f i e l d times a slowly varying a t tenuat ion function, i.e.,

H S ' = Hs F ' (d ,z ,a ) . c p c p

Then Equation (23) can be rewr i t ten as an in t eg ra l equation i n F ' , obtaining:

where G $ ( O ) is GC evaluated a t Us, cps and GG(cp1) is GC evaluated a t eS = n/2, cps f '91. cp cp

i8 -8

We now note t h a t f o r highly conducting surfaces where 1x1 << 1, tha t F ' is c lose t o uni ty and the above in t eg ra l is very near ly zero. z/d -+ 0) tha t the incident and r e f l ec t ed waves re rad ia ted by the patch cancel and only the Norton gurface wave remains. Therefore, t he in t eg ra l i n (26) is important only a t very s m a l l j r a z i n g angles, t yp ica l ly O0-O.S0 f o r sea wate: (i.e., below the Brewster angle). constant, and a l s o Gv(M) is near ly constant over the important region of in tegra t ion near ch. = 0, 0, n/2. Also, s i n 6 1 and cos 'f 1, so t h a t the in t eg ra l equation s impl i f ies t o

I t is only i n the v i c i n i t y of grazing ( i . e . , n/2 - 8

I n t h i s region, A i n the integrand is nearly a

The remaining so lu t ion t o (27) is performed by King[25,26]. Using an e l l i p t i c coordinate system a s a bas i s f o r the sur face in t eg ra l and performing a s t a t iona ry phase in tegra t ion i n the 'pi di rec t ion , t he r e s u l t is reduced t o an inhomogeneous Volterra in t eg ra l equation of the second kind. is then solved, and F ' is s h a m t o be iden t i ca l ly the Norton a t tenuat ion fac tor .

This

The point of t h i s sec t ion i s the following: polarized electromagnetic energy over an imperfect sur face does so i n a manner iden t i ca l t o a v e r t i c a l d ipole located on the same plane. Within the r e s t r i c t i o n s of the problem, therefore , a l l one must do i s evaluate Equation (22a) a t A = 0 (i.e., the per fec t ly conducting l imi t ) and multiply by 2F', the Norton a t tenuat ion fac tor .

a patch of sea sca t t e r ing or re rad ia t ing v e r t i c a l l y

the bas ic transmission loss derived and discussed previously, 2F' becomes 2F' = 2k,%1OLb In ter" 20, Of where Lbs 5 is defined and presented on those curves i n decibels. Hence the f i e l d sca t t e red by the patch of sea can be expressed a s

i L2eiko% F' GC o r a l t e r n a t e l y

HS(R,,t) cp = ko2mb c p y

where F ' is t he Norton a t tenuat ion function, Lb is the bas ic transmission loss derived i n the preceding sec t ion , and GC is G of (22b) evaluated a t A + 0.

3.4 Derivation of t he Average Scattered Signal Spectrum.

A t t h i s point, we a r e ready t o consider averaging over ensembles of surfaces whose Fourier

' p ' p

expansion coe f f i c i en t s P(m,n,a) a r e random var iab les . To thJs end, we form H$Ro , t , ) T ( R , , t2 ) from (28) , ( the star denotes complex conjugate) and avefjage t o obta in R ( T ) , where T = tl - t 2 .

s t a t i o n a r i t y i n the temporal sense so t ha t R ( 7 ) depends only on the d i f fe rence , 7, and not upon ti o r t 2 .

h i s implies

I n the above, the s i x summations have been reduced t o the t r i p l e i n t eg ra l by using the s t a t i s t i c a l independence of the Fourier coe f f i c i en t s and the de f in i t i on of the s p a t i a l and temporal sur face height spectrum:

s W ( p , q , w ) fo r m2 = -1, n2 = -nl , I"

Also, i n the merging of s e r i e s i n t o in t eg ra l s , we employ p = am, q = an, w = w a . Since a l l quan t i t i e s i n the integrand now apply t o a per fec t ly conducting surface, ah becomes ko, a s seen from a preceding section. The quantity f$(p,q) represents f (m,n) of (22b) evaluated f o r A + 0, am + p, an + q.

cp Equation (29) can be s impl i f ied fu r the r by employing an assumption we made e a r l i e r : the

s c a t t e r i n patch s i ze , L, is much g rea t e r than wavelength, so t h a t b L >> 1. Under these conditions, the [ s i n X/X]' functions i n the integrand become impulse functions :

eS COS 'p, - k, - p ) ~ L 7 - 2n 6[p - ko(s in Bs cos (4, - l ) ] ,

(kosin Os cos 'p - ko - p ) ~

with a similar expression f o r the o ther fac tor . t o give

These impulse functions permit in tegra t ion over p and q

18-9

Rather than t h e co r re l a t ion function of the sca t t e red s igna l , we a r e in te res ted i n i t s power dens i ty spectrum; t h i s is simply the Fourier transform of R'(T), where*

d r .

Making t h i s transformation, we ob ta in

X W[ko(sin es (p, - l), kosin es s i n cps, U - . We now simplify f b by noting tha t a s A + 0, NA + - i p = -ib (s in 8, cos ys - l ) , NB - - i q = s i n cp i b s i n and D(m,n) + 1. Carrying through the algebra, we a r r i v e a t the following

5 '

where & = he Eo. sca t t e r ing %8s sec t ion per un i t sur face area per radian/sec bandwidth by multiplying by 4rrRa/L2HzF'2 to ob t a i n

(33)

Now, the above r e s u l t can be converted to u(w), the range-independent b i s t a t i c

u(u) = *;(sin Bs - cos cps)a W [ b ( s i n ,8 cos 'p . To obta in 8, t he average b i s t a t i c s ca t t e r ing c ross sec t ion per un i t a r ea , w e in tegra te over a l l

- l), kosin es s i n qs , U) - WO]

frequencies t o obta in

u(cu)dw , o r

d' = sin os - cos cps)a W[ko(sin os cos cp, - l ) , kosin Os s i n cp,] , (34)

where i n (34) we have reduced the sur face height spatial-temporal spectrum W(p,q,cO) appearing i n (33) to the sur face height s p a t i a l spectrum, W(p,q).

Let us r e c a l l t h a t we have i n (33) and (34) the average sca t te red s igna l spectrum and b i s t a t i c cross sec t ion per un i t area of a sur face illuminated by a ground wave propagating along the x-direction and sca t t e r ing in to the d i r ec t ion Os, qS. The polar iza t ion (E-field d i r ec t ion ) re ta ined i n both the in- c ident and sca t t e r ing d i rec t ions is v e r t i c a l ( i . e . , lying i n the planes of incidence and s c a t t e r ) . The imperfect nature of the sur face i s taken i n t o account by the Norton a t tenuat ion f ac to r , F ' , appearing i n the equations. Thus, i f w e can find W(p,q) and W(p,q,w) fo r the sea surface, w e have expressions f o r the sca t t e r ing cross sec t ion and s igna l spectrum expressed d i r e c t l y i n terms of these surface-height spectra. Conversely, by measuring u(w) fo r various sca t t e r ing angles and frequencies, we might hope t o deduce estimates of t he ocean wave-height spectrum.

Equation (34) can be compared with previous r e s u l t s by Barrick and Peaket 3 [ 16] J [ 271 , where the incidence angle has not been taken a s grazing (i .e. , e i i s not n/2 a s we assume i n t h i s paper). ever, one should take note of t he d i f f e ren t normalization: w e normalize here by dividing by the total ground-wave f i e l d in t ens i ty , Eo o r &; over the sca t t e r ing patch. (8, # n/2) discussed i n the above references, the conventional normalization divides by the downcoming incident f i e l d . A t grazing the l a t t e r is one-half of Eo, the t o t a l ground-wave f i e l d . Hence, the r e s u l t s f o r 8 i n the above references have an added f ac to r of 4 present i n (34). be more d ive r s i ty than convention on how t o define sca t t e r ing cross sec t ions of sur face objec ts a t near- grazing angles, and one must be wary i n using o thers r e s u l t s because of the constant presence o r absence of fac tors 2, 4, and even 16 i n the de f in i t i ons .

H m -

I n the case of sky-wave c l u t t e r

Unfortunately there appears t o

F ina l ly , we c a l l a t t en t ion to the sca t t e r ing mechanism i n evidence i n Equations (33) and (34): Bragg s c a t t e r . b ( s i n 8, COS 'ps - l ) , q = kosin es s i n cps, as seen from the arguments of the wave-height spectrum in those equations. f o r a d i f f r a c t i o n gra t ing which i s t o s c a t t e r a wave a t grazing incidence along the x-axis i n t o d i rec t ions 8

3.5

The b i s t a t i c radar responds t o only those roughness waves with wavenumbers p =

These roughness wave c r e s t s a r e of prec ise ly the co r rec t length and or ien ta t ion d i r ec t ion

9 % 'ps*

First-Order Ocean Wave-Height Spatial-Temporal Spectrum.

To a f i r s t order, we can r e l a t e W(p,q) t o W(p,q,w) f o r the ocean. This i s possible because deep-water waves of a given length, L, t r a v e l a t a speed v

*It should be cautioned t h a t t he normalizations used here i n t h e de f in i t i ons of t he Fourier transforms do

= JgL/Zn, where g 9.81 m / s a is the acce l - W

not conform t o many used i n communication theory. Rice's workI21.

W e employ these i n order t o permit reference t o

18-10

e ra t ion of gravity. shown, however, t ha t t h i s r a t i o is always small, f o r when i t exceeds 0.14, wave c r e s t s tend t o be unstable and break, d i s s ipa t ing energy and reducing the height of the waves. temporal wavenumber, w, is r e l a t ed uniquely t o the s p a t i a l wavenumbers by the following d ispers ion equation:

This is cor rec t t o a f i r s t order i n the'waveheight/wavelength r a t i o . Studies have

Hence, t o t h i s f i r s t order, the

where the f s igns arise from ambiguity i n the d i r ec t ion of t r ave l of the ocean waves.

Therefore, Equation (16) f o r f i r s t -o rde r ocean waves may be rewr i t ten as follows: W

where wf is given i n (35).

t he Fourier transform, i.e., We can now determine W(p,q,w) by multiplying 6 ( x 1 , y l Y t l ) by 6(xa ,yz , t2) , averaging, and taking

m ipT + iqT + iU)T

X Y dT d7 dT , w'(P,q,U) = + ~ ~ ~ ~ 6 ~ X 1 , Y l y t ~ ~ 6 ~ x s , Y s , t s ~ ~ e X Y

where T = x1 - x2, T = y1 - ya, and T = tl - t,. Using the de f in i t i ons of t he s p a t i a l spectrum given i n (10); the spatial-Temporal spectrum then becomes:

w(P,q,w) = 2W+(P,q)6[W + "+I + 2W-(P,q)6[U + U)-I , (37)

where again the f s igns r e f e r t o the d i r ec t ion of motion of the waves, and U* is given i n (35).

wavenumbers) cons is t s of only two possible d i sc re t e temporal frequencies, w t o p and q through (35).

3.6

The above ind ica tes t h a t the spatial-temporal wave-height spectrum fo r a given p , q ( s p a t i a l and w-, which a r e r e l a t ed +

Radar Sca t t e r and the Ph i l l i p s I so t ropic Wind-Wave Spectrum.

Let us now combine Equation (33) f o r t he sca t t e red s igna l spectrum with (37) f o r the f i r e t - order spatial-temporal spectrum of the ocean. Recall t ha t (33) represents t he v e r t i c a l l y polarized signal sca t t e red i n a d i r ec t ion EIS, cps from a ground wave (ve r t i ca l ly polarized) per un i t area of sea per rad iadsecond bandwidth.

u(w) = 2n16(sin es - COS rps)2{w+[b(sin Os cos cp, - I) , b s i n Os s i n cp ]6(w + W+ - q,) +W_[k,(s in Qs COS (p, - I), b s i n Os s i n cps16(w + w - - Q)} .

S

(38)

Notice t h a t t h i s sca t te red s igna l spectrum cons is t s of two spikes centered a t ub, the c a r r i e r , but sh i f t ed by an amount

These Doppler s h i f t s correspond t o t h e ve loc i t i e s of ocean waves with the proper lengths f o r Bragg s c a t t e r , i.e., L = X/[sina 8, - 2 s i n Bs cos cps + 1]'/', where A = 2n/k,, i s the radio wavelengths.

l a rges t i n t he backscatter d iver t ion , where 8s -+ n/2, 'ps + n. water waves responsible f o r s ca t t e r ing becomes the sho r t e s t , i .e. , L = h / 2 .

The'frequency s h i f t , U*, is zero i n the forward d i rec t ion , where e -+ n/2, cp 0. I t is

Here, U* = f JZk,g, and'the lengths of the

For backscatter a t 10 MHz, f o r example, f* = w /2n = f0.322 Hz, and L = 15 meters. observation of such s h i f t s i n the received s igna l is e n t i r e l y possible with the processing techniques ava i lab le i n present day receivers. Here, of course, the + s ign i n f ront of the s h i f t a r i s e s from receding waves and the - s ign , from approaching waves. ocean waves approaching and receding from the radar.

The * I n f a c t , Crombie c l e a r l y observed these s h i f t s a s ea r ly a s 1955[11.

The s t rength of each spec t r a l l i n e gives a quant i ta t ive ind ica t ion of the s t rengths of

L e t us now spec ia l i ze these equations t o the case of backscatter (tis = n/2, 'ps = n) and employ the Ph i l l i p s model f o r an i so t ropic , wind-driven f u l l y developed sea. form f o r W(p,q), and using t h i s , we have the following pa r t i cu la r ly simple r e s u l t s :

Equation (14) gives the functional

U(W) = 2B[f+6(m - + JzgE) + f _ 6 ( ~ - (4, - Jpgk,)] , and (40)

(41) 8 = B = 0.005

I n Equation (401, (giving the s igna l spectrum), f+ and f - represent the f r ac t ion of spec t ra l energy i n the advancing and receding waves, with f+ + f - = 1.

un i t area. ti^^ (41) is va l id f o r the average b i s t a t i c scatter--as wel l a s backscatter--cross sec t ion per

Based on the Ph i l l i p s i so t rop ic wind-wave spectrum, it represents a very concise expresgion f o r

18-11

the s c a t t e r c ross section. c l u t t e r power received. a l s o by Fk~nk and Nierenberg1191. a t HF using v e r t i c a l polarization. on frequency, In su f f i c i en t data a r e ava i lab le a t HF t o deduce any c l e a r frequency dependence, but observations tend t o confirm a r e l a t ive1 weak frequency dependence. Had we used a Neumann-Pierson ocean- wave model, 8 would have varied a s ko- 'F, being -21 dB a t 10 MHz.

The quantity, 8 Expressed i n decibe

is commonly used i n radar systems ana lys i s t o estimate the j , Equation (41) becomes 8 -23 dB; t h i s r e s u l t has been noted

Values f o r ff between -20 dB and -30 dB have been reported fo r sea c l u t t e r A s ign i f i can t aspect of t h i s model f o r 8 i s i t s lack of dependence

L e t us r e c a l l what w e have i n Equation (41) and the Ph i l l i p s spectrum. We have a t bes t a crude estimate of f u l l y developed ocean roughness based on the wind above the surface. i s assumed to be i so t ropic , but i s iden t i ca l ly zero f o r wind speeds less than JglZk, meterslsecond a s discussed a f t e r Equation (14). ve loc i ty , and -23 dB f o r winds exceeding t h i s ve loc i ty . abrupt drop i n 8 with wind speed. overestimate of W(p,q) and hence, 8, because the model neglects swell and a l s o the f i n i t e fe tch over which a patch of ocean i s l i k e l y t o be f u l l y aroused.

3.7

The ocean-wave d i r ec t ion

Hence, 8 f o r backscatter would be iden t i ca l ly zero f o r winds below t h i s I n prac t ice , one would not expect t o observe t h i s

I n addi t ion , the wind-wave spectrum would appear t o represent an

The Received Power and Signal Spectrum.

I n (34) and (38) we have the backscattering c ross sec t ion per un i t area and i ts time spec t r a l These a r e r e l a t ed t o the received s igna l power through the radar range equation a s dens i ty f o r the sea.

follows :

where dP ((U) and dP ds. The quantity P i i s the transmitted power, G and G a r e the transmitt ing and receiving antenna ( f ree- space) gain functions i n the d i r ec t ion of the paTch, RT and RR a r e the d is tances , transmitter-to-patch and patch-to-receiver. t a rge t - to- rece iver path, respectively--the t a rge t being the patch of sea, d s . The quan t i t i e s U(w) and 8, as r e l a t ed to (34) and (38), m u s t be evaluated a t the b i s t a t i c angles e s , q s a t the patch.

following way:

a r e the amounts of power per rad ls and power received from a patch of sea of area R

R

Fi and Fk a re the Norton a t tenuat ion f ac to r s f o r the t ransmi t te r - to- ta rge t path and

The received power spec t r a l density, PR(w), i s r e l a t ed to the t o t a l average power i n the

= p PR(w)d(U (43) 'R 2 ,m

Equations (42) can a l t e r n a t e l y be expressed i n tenus of the bas ic transmission loss discussed i n Section I1 by t h e following equations:

yR o(w)ds , and dPR = " P ~ G ~ G ~ 8ds dPR((U) =

%T%R haQbTabR ,

where

and LbR being the bas ic transmission losses i n dec ibe ls over the t ransmi t te r - ta rge t and ta rge t - rece iver a z h s . Again, severa l of t he parameters i n the above equations may be functions of the b i s t a t i c angles a t t he patch, dS.

To obta in the t o t a l received s igna l power o r power spec t r a l dens i ty , one then in tegra tes over

I n such cases the in tegra t ions can a l l a reas of the sea. Frequently, however, such patches a re l imited i n extent by the use of a short-pulse (o r an equivalent time-coded) s igna l and f i n i t e antenna beamidths. o f t en be simplified.

4. MEASUREMENT OF THE OCEAN-WAVE SPECTRUM W I T H A BISTATIC RADAR.

4.1 General Considerations.

The simple r e l a t ionsh ip between the sca t t e red s igna l and the ocean wave-height s p a t i a l spectrum expressed i n (38) suggests p o s s i b i l i t i e s f o r quan t i t a t ive measurement of t he s t a t e of the sea surface. While oceanographers have devised severa l techniques f o r measuring the temporal wave-height spectrum of t h e sur face (fromwhich the nondirectional s p a t i a l spectrum may be obtained), very few p rac t i ca l and r e l i a b l e methods permit measurement of the d i r ec t iona l spatial spectrum, W(p,q). technique which can measure t h i s quantity should provide oceanographers with welcome knowledge about the nature of ocean waves.

Hence a new sensing

Where less d e t a i l about t he sur face spectrum is needed, t he use of HF radar i n conjunction with sh ips , a i r c r a f t , sa te l l i tes , o r o ther telemetry/relay devices could y i e ld frequent estimates of sea s t a t e . on a global bas i s . schemes s u f f e r se r ious def ic ienc ies i n t h i s respect. remote sensor w i l l prove t o be a workable so lu t ion t o t h i s problem.

A t present t he re a r e no operable sensors which provide such da ta , and most proposed We f e e l t ha t t he HF radar a s an ocean-surface

A study of Equation (38) shows t h a t severa l radar parameters appear i n the arguments of W(p,q) which might be exploited. va r i a t ion might l i e between 3 and 30 MHz since the more important, longer ocean waves have lenghts

By varying the frequency of operation, we change b. A su i t ab le range of

18-12

corresponding t o the radio wavelengths i n t h i s region. not impractical; ionosounders presently provide a continuous sweep over nearly a decade i n frequency. Probing the ocean with d i f f e ren t frequencies w i l l provide information about the lower-end cutoff of the spectrum, ind ica t ing whether o r not longer ocean waves a r e present.

A t HF, devices with such a range of operation a r e

The Doppler s h i f t i n frequency from the c a r r i e r i s contained i n the sca t t e red s igna l spectrum. By observing t h i s spectrum f o r a given transmitted frequency, one can obta in i n f o m t i o n about the d i r ec t iona l nature of W(p,q). area over which t h e in tegra t ion of (38) (as shown i n Equation (42a)) takes place, and the impulse functions uniquely r e l a t e the angles and arguments of W(p,q) t o the Doppler-frequency s h i f t of the received s igna l from the c a r r i e r .

The use of short-pulse s igna ls and t i m e delay a t the receiver defines an

F ina l ly , t he use of a s t a t iona ry t ransmi t te r and moving rece iver , such a s an a i r c r a f t o r s a t e l l i t e , provides another means of varying BS, cp , and the Doppler s h i f t t o various pa r t s of the i l luminated area. Several such schemes can be anagyzed by the use of Equations (38) and (42) along with the geometries involved i n the pa r t i cu la r b i s t a t i c arrangement. be considered and discussed here.

Two d i f f e ren t b i s t a t i c arrangements w i l l

A t microwave frequencies, backscatter radars tend t o be more p rac t i ca l than b i s t a t i c systems.

Unless one has a narrow antenna beamwidth so a s t o i l luminate a small angular patch of sea , A t HF, however, the implementation of a simple, s ta t ionary , backscatter radar t o measure W(p,q) i s d i f f i c u l t . one obtains no d i r e c t i o n a l i t y information about the sea. requi re antenna a r rays up t o a m i l e long. measurement of offshore waves approaching the beach. The requirement f o r operation over decade frequency ranges compounds the complexity and already consider- ab le expense involved i n e l ec t ron ic beam scanning with such a phased ar ray . single-wire antennas with (nearly) omnidirectional rad ia t ion pa t te rns a r e much more p rac t i ca l a t HF, recommending the use of b i s t a t i c configurations t o obta in d i r ec t iona l information.*

4.2 A B i s t a t i c Surface-Surface Configuration.

Narrow antenna beamwidths a t these frequencies, Such antennas must be land-based and a r e thus useful only fo r

Size precludes t h e i r use i n midocean appl ica t ions .

Hence, schemes involving shor t ,

We s h a l l examine here a b i s t a t i c radar configuration a s shown i n Figure 14. The t ransmi t t ing and receiving antennas we take t o be half-wave v e r t i c a l whips, located a d is tance d apa r t on (nearly) s ta t ionary sur face platforms. I n prac t ice , these may be sh ips , buoys, i s lands , shore s t a t ions , o r combinations of these. The spacing, d, should be l e s s than 200-300 km; otherwise the sea surface m y vary considerably s t a t i s t i c a l l y between these points.

We a l s o assume tha t the radar employs a short-pulse s igna l of duration T (or an equivalent time-coded s igna l ) . s igna l s a r r iv ing a t later times represent sea s c a t t e r or ig ina t ing from confocal e l l i p t i c a l annul i , a s shown shaded i n Figure 14. by d. Thus by observing the received s igna l spectrum f o r a given time delay, one can separate the scatter a r i s i n g from d i f f e ren t portions of the e l l i p t i c a l r ing. waves of t he proper Bragg length whose c r e s t l i n e s a r e tangent t o the e l l i p s e . Pos i t ive Doppler s h i f t s o r ig ina t e from waves moving across the e l l i p t i c a l r i ng toward the baseline, while negative s h i f t s a r e due t o motion away from the baseline. The g rea t e s t Ibppler s h i f t s a r e due t o the sho r t e r waves a t the ends of the e l l i p s e moving along the baseline, while the sho r t e s t s h i f t s a r e due t o waves crossing the e l l i p s e a t the midpoint, with motions perpendicular t o the baseline.

Defining td = d/c a s the t i m e delay f o r reception of the d i r e c t t ransmi t te r pulse,

The f o c i of the e l l i p s e s a r e the t ransmi t te r and receiver points separated

This s c a t t e r or ig ina tes from ocean

Nierenberg and M ~ n k ' ~ ~ ] have examined the arguments of W(p,q) i n (38) (with 8, = n/2 f o r surface-surface propagation). t he time-delay and Doppler observables and the p,q ocean-wave s p a t i a l wavenumbers. formation, l e t us normalize the observed Doppler frequency t o tha t f o r ocean-wave backscatter, i .e. , f = f /f where f = 1/2n- i s the Doppler s h i f t f o r backscatter. Since the observed Doppler d i f t fs @Latest foibbackscatter, 0 s fN 5 1. Nierenberg and Munk1281 then define a quant i ty K equal t o G; it is exac t ly equal t o t h e magnitude of the s p a t i a l wavenumber of the ocean waves producing the Bragg s c a t t e r a t a given point on the e l l i p s e divided by 2k,. backscatter (i.e., cps = n). The o ther radar observable, t i m e delay, i s a l s o normalized, dividing by the d i r e c t base l ine time delay, i.e., S = t/td. wavenumbers by dividing by 2 b , i.e., U = p / 2 b , V = q/2k,. Then the transformation of i n t e r e s t r e l a t e s K o r f (Doppler s h i f t ) and S(time delay) f o r a point on the e l l i p t i c a l annulus t o the ocean wavenumbers U and ! responsible f o r s ca t t e r . wave-height spectrum fo r a l l U , V i n t h i s range by observing K and S . formation. AS can be seen, t he re a r e no ocean wavenumbers tha t cannot be determined from some combination of t i m e delay and Doppler s h i f t . wavenumbers, p and q, between zero and i n f i n i t y ; one measures the shor te r wavenumbers by increasing the transmitted frequency.

They have numerically generated l i nes showing the transformation between To show t h i s t rans-

Hence, 0 K s 1, with K = 1 occurring f o r

Then 1 s S < a. We a l s o normalize the ocean s p a t i a l

Since 0 s tu(, (VI s 1, we would l i k e t o be ab le t o determine the ocean Figures 15 and 16 show t h i s t rans-

The normalized ocean wavenumbers, U and V can correspond t o any ac tua l

I n order t o show how the ac tua l received s igna l spectrum might look using t h i s system, we employ the Ph i l l i p s i so t rop ic ocean-wave mode; w e assupe t h a t a l l ocean waves which can s c a t t e r the radio waves are f u l l y aroused?. an e l l i p t i c a l annulus. The radar parameters se lec ted a r e the following. The antennas a r e v e r t i c a l ground- fed quarter-wave whips with equivalent free-space gains of 0.82. frequencies a r e considered: 5 and 10 MHz. The s igna l pulse length i s taken a s 'r = 12.5 p s , and we con- s i d e r t he e l l i p t i c a l annulus representing a delay td + T, i.e., one pulse length a f t e r the a r r i v a l of the d i r e c t pulse.

*An exception w i l l be discussed i n Section 4.3, i n which a single-element omnidirectional antenna can be

We employ Equation (44a) along with (40), (with f+ = f - = 1/2) in tegra t ing over

They a r e located 100 km apar t . Two

used on a moving s h i p t o obta in d i r ec t iona l information about the ocean waves.

mence, we ob ta in an upper l i m i t on sca t t e red power i n t h i s manner.

For t h i s configuration the in tegra t ion e s t Derforme 1 e l ? t i c s coordinates . where

18-13

- I

%TdpdB, an n tegra t ion over 8 between 0 and %, where p = 0.274, dp = 0.1352 f o r t he pulse length and time delay chosen.

= d/2 (coshp + cos e), = d/2 (coshp - cos e). Then in tegra t ion over the annulus represents

The in tegra t ion can be performed exactly because of the impulse functions, and we obtain:

where fdb is the backscatter Doppler s h i f t the s ide of t he e l l i p s e ; it i s f and %, t he ranges t o the par t og'the patch sca t t e r ing the frequency f.bTT:::eabra(nges a r e given i n terms of f a s

iven previously and f i s the Doppler s h i f t from waves a t

I = fdb&. The free-space g&ns a a r e functions of

I I f . .&-I ? r n

[l - ,/ 1 - (e)- 1 and \ = cosh p % = 2 cosh p X d

The bas ic transmission losses may then be determined from the r e s u l t s of Section 2.

The received spectrum defined i s (45) i n nonzero only f o r frequencies i n the range f I f - fdb , P lo ts of t h i s dimensionless quantity a t 5 and 10 MHz a r e shown i n Figures 17 and ld? Shown f,l

a l s o there a r e the ocean wavelengths, ocean-wave d i rec t ions with respect t o the baseline, a d wind speed required t o exc i te t he waves responsible f o r s c a t t e r a t the indicated Doppler s h i f t . The "ears" near the endpoints a r e due to s c a t t e r from the "stationary" regions of the e l l i p s e , v iz . , the s ides and ends. The heights observed f o r these "ears" w i l l depend upon the reso lu t ion of t he spec t r a l processor.

I n prac t ice , the received s igna l spectrum w i l l be lower than tha t shown i n Figures 17 and 18 f o r t he f u l l y developed wind-wave model. lower Doppler frequencies is l i k e l y t o be weaker because these longer ocean waves a r e l i ke ly t o be present l e s s of the t i m e .

This should be compared with a received s igna l power d i r e c t from the t ransmi t te r of about 3.2 X TO-' PT. Hence the sea-scattered s igna l i s down about 23 dB from the d i r e c t s igna l , which places no s t r ingen t demands on the receiver dynamic range.

The dashed curves show more typ ica l shapes; the s igna l a t the

The t o t a l sea-scattered power received from the e l l i p s e is approximately 1.5 X P a t 5 MHz.

4.3 A B i s t a t i c Surface- to-Surface Configuration.

Here we consider a b i s t a t i c radar a s shown i n Figure 19. The t ransmi t te r i s a quarter-wave v e r t i c a l whip on a buoy o r ship. (or equivalent coded s igna ls ) a r e employed. by the in t e r sec t ion of confocal spheroids with the ocean surface. t ransmi t te r and receiver points. The in t e r sec t ion curves a r e nonconfocal e l l i p ses . So a s not t o be bogged down i n mathematical d e t a i l s of nonconfocal e l l i p t i c a l s t r i p s , l e t us spec ia l i ze here to the s i t u a t i o n when the s a t e l l i t e is d i r e c t l y overhead, fo r then these s t r i p s become c i r c u l a r annul i .

The receiver i n t h i s case is a nonstationary s a t e l l i t e , and shor t pulses I n general, ocean areas of constant time delay a r e represented

The foc i of these spheroids a r e the

The pr inc ip le of operation with t h i s configuration is d i f f e ren t from tha t of the preceding system, i n tha t here we explo i t the motion of one of t he antennas to separa te the s c a t t e r from d i f f e r e n t pa r t s on the c i r cu la r ring. range-rate t o these points i s d i f f e ren t . s h i f t s due t o s a t e l l i t e motion from the Doppler s h i f t s due t o water-wave motion ( the mechanism used i n the preceding system).

The Doppler s h i f t from d i f f e ren t points on the r ing var ies because the S a t e l l i t e speeds a r e s u f f i c i e n t t h a t one can separa te Doppler

Let us assume s a t e l l i t e motion along the x-direction with the o r b i t a l plane coinciding with the The antenna on the s a t e l l i t e is assumed t o have x-z plane.

a free-space gain, G of a half-wave dipole, i .e. , 1.64. The gain of the quarter-wave transmitt ing antenna is, a s before, 0.82.R'We assume t h a t the s a t e l l i t e i s a t a l t i t u d e RR a 300 km and moving with ve loc i ty 8000 m / s . We se l ec t a pulse length 7 = 10 p s , yie ld ing a c l u t t e r r ing width of d% = 3 km. a l s o pick a time delay t - t = 50 PS, corresponding to RT = 15 km (td i s the time delay of the d i r e c t s igna l from the t ransmi t te r $0 the s a t e l l i t e ) . We a l s o s e l e c t the Ph i l l i p s i so t rop ic wind-wave spectrum as an example; it represents the most in tense sea-sca t te r s i t ua t ion . Employing Equations (42s) and (40) and employing the per t inent b i s t a t i c angles, 8 = 0, 'p = 0, we have the following f o r the received s igna l spectrum:

Again, w e employ frequencies of 5 t o 10 MHz.

Let u s

I n obtaining the above from (40), it is assumed f t o s a t e l l i t e motion (fdm a f,(%/\)v/c) is consiAerably l a rge r than fdb, the Doppler s h i f t due t o wave motion described i n the preceding sec t ion . A t 5 MHz, t h i s s h i f t fdm i s 6.67 Hz i n cont ras t with fdb = 0.228 Hz f o r the ocean-wave Doppler. ou ts ide t h i s range, the f i r s t -o rde r spectrum is zero.

= f - = 1/2. Also, fdm, the maximum Doppler s h i f t due

The above equation is va l id f o r the range -fdm S f - fo S fdm;

P lo ts of t h i s dimensionless quantity a r e shown i n Figures 20 and 21 a t 5 and 10 MHz. Shown a l so is the angular d i r ec t ion from the o r b i t a l plane t o the point on the r ing responsible f o r s c a t t e r a t a given frequency. 30 meters a t the two frequencies. d i r ec t iona l wave-height spectrum a t the wavenumbers p = ko cos 'p and q = k, s i n cp.

The ocean waves responsible f o r s c a t t e r a r e a l l of lengths L = 1 = 6 0 meters and They a l s o cross the r ing r ad ia l ly ; hence the angle cp gives us the

By varying the

18- 14

frequency (and hence b) and observing the s igna l spectrum (and hence (p), we can obtain the complete d i r ec t iona l spectrum of the surface.

I n the system of the l a s t sec t ion , ocean waves of many lengths were observed a t a given frequency; here, a given frequency permits observation of waves of only one wavelength--the radar wavelength.

The t o t a l received sea-scattered power f o r t h i s configuration is P a 2.5 X PT a t 5 MHz.

This compares t o the received s igna l d i r ec t from the buoy, which i s considergbly l e s s than 10'' pT , typ ica l ly of t he order t he n u l l of the pa t te rn of the v e r t i c a l whip transmitt ing antenna; t heo re t i ca l ly the d i r e c t component should drop t o zero, but p rac t i ca l ly , a drop of 20 dB from the main antenna lobe might be expected. lower the d i r e c t s igna l compared with the sea-scattered Signal, the b e t t e r , f o r the dynamic range and in te r fe rence problems w i l l be reduced.

PT. This reduced d i r e c t power occurs because the s a t e l l i t e overhead is i n

The

A problem which must be recognized i n connection with t h i s system a t lower HF frequencies i s It may be only a t nighttime tha t frequencies a s low a s 5 MHz can

The favored region f o r s a t e l l i t e reception w i l l occur when it i s c lose t o the the presence of the ionosphere. penetrate the ionosphere. overhead pos i t ion , s ince t h i s region o f fe r s the bes t chances f o r penetration and lowest a t tenuat ion by the ionosphere.

Several a l t e rna te s t o the s a t e l l i t e receiver could operate on the same moving Doppler pr inc ip le . A lower, slower f ly ing a i r c r a f t receiver could accomplish the same task a s the s a t e l l i t e . a l t e rna t ive would have the t ransmi t te r and receiver mounted on the same sh ip ; the s h i p ' s Doppler would be used t o resolve the sea s c a t t e r d i r ec t iona l ly . range a s the speeds of the ocean waves responsible fo r s c a t t e r , and both must be taken i n t o account i n the equations.

A second

However, t he s h i p ' s ve loc i ty w i l l l i e i n the same

The buoy/transmit, s a t e l l i t e / r e c e i v e configuration suggested could a l s o ba used rec iproca l ly . However, l a rge r t ransmi t te r powers should be ava i lab le from a buoy. I n addi t ion , the poss ib i l i t y of the s a t e l l i t e s e l ec t ing and in te r roga t ing a buoy, recording the s igna l , and then t ransmi t t ing i t t o ea r th f o r processing a t a more convenient point i n the o r b i t ind ica tes t h a t the arrangement here i s more des i rab le than i t s rec iproca l configuration.

5. SUMMARY AND CONCLUSIONS.

The longer ocean waves (i .e. , 20-200 meters) i n t e rac t s ign i f i can t ly and predictably with radio waves i n the HF/VHF region. The sca t t e r ing mechanism deduced theo re t i ca l ly and confirmed experimentally i s the Bragg e f f ec t . The theo re t i ca l bas i s f o r t h i s e f f e c t is developed and reviewed here. The problem i s analyzed using the boundary perturbation approach of Rice [21 along with a Leontovich boundary condition a t the surface. This approach is va l id a s long a s the ocean wave-height is small i n terms the radio wavelength and the sur face slopes of the longer ocean waves a r e small. Both of these conditions a r e met by ocean waves i n the HF and lower-VHF regions. I n addi t ion , the r e s t r i c t i o n s required fo r the appl ica t ion of the Leontovich boundary condition a r e e a s i l y s a t i s f i e d by ocean water a t these frequencies. As long a s the technique is not pushed beyond i ts intended l i m i t s , the r e s u l t s and in t e rp re t a t ion obtained therefrom w i l l be va l id .

Using the perturbation technique, we derive an expression f o r the e f f ec t ive sur face impedance of

We apply it t o the sea using a s l i g h t l y rough planar surface. It cons is t s of two parts: the impedance of the surface when it i s per fec t ly smooth, along with a second term due t o the presence of roughness. the Ph i l l i p s i so t rop ic ocean-wave spectrum f o r a model. Calculations show tha t a t 5-20 MHz, the change i n impedance due t o roughness can be a s much a s 100% of i ts unperturbed value fo r a smooth ocean-water surface. These e f f ec t ive sur face impedances a r e then used i n a standard ground-wave program t o determine curves of added transmission loss due t o sea s t a t e . The curves show tha t below about 2 MHz, ocean roughness can be neglected, but a t 15 MHz, the increase i n one-way loss can be a s much a s 15 dB a t 100 n m i .

Sca t t e r of HF/VHF waves from the sea is a l s o analyzed using the perturbation approach.

They a r e va l id i n the region near grazing (as w e l l

The random ocean sur face is considered a function of time as w e l l a s space, and expressions a r e derived f o r the b i s t a t i c s ca t t e r ed s igna l i n t ens i ty and spectrum. a s a t higher angles) f o r v e r t i c a l l y polarized waves. To a f i r s t order, water waves of a given length t r ave l a t a given speed; when t h i s r e s t r i c t i o n is used i n the ocean wave-height spec t rwn- the sca t te red s igna l from a patch of sea is shown t o cons i s t of two impulse functions, equid is tan t ,from. the c a r r i e r i n the frequency domain. These impulses represent ocean-wave t r a i n s of the required Bragg length moving a t the corresponding d i sc re t e ve loc i ty toward and away from the radar. observed over 15 years ago i n HF backscatter data from the sea. Furthermore, the use of the Ph i l l i p s i so t rop ic ocean-wave spectrum gives an upper l i m i t a t 4 (backscatter cross sec t ion per un i t a rea) of -23 dB, a value i n agreement with severa l measurements.

These impulse functions have been

The possible use of b i s t a t i c radar configurations f o r study of sea surface is explored. Two techniques a r e b r i e f l y analyzed: o ther using a s t a t iona ry surface t ransmi t te r and o rb i t i ng receiver. I n the f i r s t case, the observables a r e the processed s igna l spectrum and the time delay a t which it i s computed; these a r e then r e l a t ed s i m p t o the s p a t i a l wavenumbers of the d i r ec t iona l ocean wave-height spectrum. receiver motion permits d i r ec t iona l resolution of the ocean waves, and frequency va r i a t ion provides the magnitude of the ocean wavenumbers. a i r c r a f t , buoys, shore s t a t ions , and s a t e l l i t e s . Power requirements and antenna s i z e s a r e not design l imi ta t ions f o r t he b i s t a t i c configurations discussed, and the processing requirements f o r the received s igna l a r e within the s t a t e of the a r t . f o r monitoring the sea s t a t e and f o r de t a i l ed study of the nature of ocean waves.

one employing a s t a t iona ry sur face t ransmi t te r and receiver and the

I n the second system, the

Many var ia t ions of these systems a r e possible, employing sh ips ,

HF/VHF radars appear t o be one of the most promising systems both

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REFERENCES

Crombie, D. D. , "Doppler Spectrum of Sea Echo a t 13.56 Mc/s", Nature, Vol. 175, p. 681 (1955).

Rice, S. O., "Reflection of Electromagnetic Waves from S l igh t ly Rough Surfaces", i n Theory of Electro- magnetic Waves, M. Kline, Edi tor , p. 351, In te rsc ience Publishers, New York (1957); a l so Dover Publications, New York (1963).

Ward, J. F., "Power Spectra from Ocean Movements Measured Remotely by Ionospheric Radio Backscatter", Nature,.Vol. 223, p. 1325 (1969).

Sommerfeld, A., "The Propagation of Waves i n Wireless Telegraphy", Annalen der Physik, Vol. 28, p. 665 (1909).

Norton, K. A. , "The Propagation of Radio Waves over the Surface of the Earth and i n the Upper Atmosphere, Par t I - Ground Wave Propagation from Short Antennas", Proc. IRE, Vol. 24, p. 1367 (1936); 'I..., Par t I1 - The Propagation from Ver t ica l , Horizontal, and Loop Antennas over a Plane Earth of F i n i t e Conductivity", Proc. IRE, Vol. 25, p. 1203 (1937).

van der Pol, B. , and H. Bremer, "The Dif f rac t ion of Electromagnetic Waves from an E lec t r i ca l Point Source.Round a F in i t e ly Conducting Sphere", Philosophical Mag., Ser ies 7, Vol. 24, pp. 141-176, pp. 825-864; Vol. 25, pp. 817-834; Vol. 26, pp. 261-275 (1937, 1938, 1939).

Fock, V. A., "Diffraction of Radio Waves Around the Ear th ' s Surface", J. Phys. (USSR), Vol. 9, p. 256 (1945).

Norton, K . A., "The Calculation of Ground Wave Field In tens i ty over a F in i t e ly Conducting Spherical Earth", Proc. IRE, Vol. 29, p 623 (1941).

Wait, J. R., "Electromagnetic Surface Waves", i n Advances i n Radio Research, J. A. Saxton, Edi tor , Vol. 1, pp. 157-217, Academic Press, New York (1964).

Norton, K. A . , "The Physical Reali ty of Space and Surface Waves i n the Radiation Field of Ridio ' Antennas", Proc. IRE, Vol. 25, p. 1192 (1937).

Wise, W. H., "The Physical Reali ty of the Zenneck Surface Wave", Bel l System Tech. J . , Vol. 16, p. 35 (1937).

Jordan, E. C. , Electromagnetic Waves and Radiating Systems, Prentice-Hall, Englewood C l i f f s , New Jersey (1950).

Barrick, D. E. , "Theory of Ground-Wave Propagation Across a Rough Sea a t Dekameter Wavelengths", Research Report, Ba t t e l l e Memorial I n s t i t u t e , Columbus, Ohio (January 1970).

Feinberg, E. , "On the Propagation of Radio Waves Along an Imperfect Surface", J. Phys. (USSR), Vol. 8, p. 317 (1944).

Barrick, D. E., and W. H,. Peake, "Scattering from Surfaces wi th Different Roughness Scales: Analysis and In te rpre ta t ion" , Research Report, Ba t t e l l e Memorial I n s t i t u t e , Columbus, Ohio (November 1967), AD 662751; a l s o published under separa te cover by the ElectroScience Laboratory, Ohio S t a t e University, Columbus, Ohio (September 1967), N67-39091.

Barrick, D. E., and W . H. Peake, "A Review of Sca t te r ing from Surfaces with Different Roughness Scales", Radio Science, Vol. 3 (New Ser ies ) , p. 865 .(1968).

Kinsman, Blair, Wind Waves, Prentice-Hall, Englewood C l i f f s , New Jersey, pp. 386-403 (1965).

Phi l l i p s , 0. M., Dynamics of the Upper Ocean, Cambridge University Press, London, pp. 109-139 (1966).

Munk, W. H., and W. A. Nierenberg, "High Frequency Radar Sea Return and the Ph i l l i p s Saturation Constant", Nature, Vol. 224, p. 1285 (1969).

Cox, C., and W. Munk, "Measurement of the Roughness of t he Sea Surface from Photographs of the Sun's Glit ter", J. O p t . Soc. Am., Vol. 44, p. 838 (1954).

Berry, L. A., and M. E. Chrisman, "A FORTRAN Program f o r Calculation of Ground Wave Propagation Over Homogeneous Spherical Earth f o r Dipole Antennas", Report 9178, National Bureau of Standards, Boulder, Colorado (1966).

Norton, K. A., "Transmission Loss i n Radio Propagation: II", Report 5092, National Bureau of Standards, Boulder, Colorado (1957).

Norton, K. A., "Transmission Loss i n Radio Propagation", Proc. IRE, Vol,. 41, p. 146 (1953).

Ruck, G. T., D. E. Barrick, W . D. S tuar t , and C . K. Krichbaum, Radar Cross Section Handbook, Vol. 1, Plenum Press, New York, p. 53 0970).

King, R. J. , "An Introduction t o Electromagnetic Surface Wave Propagation", I E E E Trans. on Education, Vol. 11, p. 59 (1968).

King, R. J., "Electromagnetic Wave Propagation Over a Constant Impedance Plane", Radio Science, Vol. 4, p. 255 (1969).

18-16

27. Ruck, G . T . , D. E . Barrick, W . D. Stuart, and C . K . Krichbaum, Radar Cross Section Handbook, Vol. 2 , Plenum Press, New York, pp. 703-709 (1970).

28. Nierenberg, W . A . , and W . H . Munk, "Sea Spectra and Radar Scattering", Working Paper, 1969 JASON Summer Study, Boulder, Colorado,

z Free Spoce

propogatlon

--X

y-axis into page

Surface

Figure 1. Guided Wave Above a Planar Impedance Boundary.

Figure 2. Slightly Rough Surface Geometry.

Surface roughness in remainder of plane producas no scotter. This roughness contributes to XA , the effect& surfom reoctonce.

p/ko = roughness spatial wavenumber in x-direction normalized to radio wovenumkr

in y-direction normalized to rodio wovenumber

q/ko = roughness spatial wavenumkr

Spectrol region in which surfoca rcughness prodvas scatter. This region contributes to R ,, ,the effoctlve surface resirtam. It Is respmsible f a q/ko removal ond dissipotiin of energy from th gmund wove.

\

18-17

ko = free spoce rodio wovenudm = 2d.A = w /c

Propagation takes plow olong the x-direction

Figure 3. Effect of Varioua Regiom of S p t t a l Roughness Spectrum on Effective Surface Impedance.

0.06

0.05

18-18

0.01

0 I 2 5 10 20 50 100 200

Frequency, megahertz

Figure 4. Effective Surface Impodaoce, x, v8 Wind Speed and Frequency. pzlillips Isotropic Wave Spectrm.

F i g w e 5. msie T n n s m i s s h n Loss Across the 0cee.n BeWeen Poinu a t the Surface of Srmoth Spherie.1 Earth. Conductivity is 4 mhoslmeter and an Effective Earth Radius Factor of 413 is Assumd.

18-19

B

Range, kibtneters

Ftgure 6. Added TrBn&mission Lass Due to $ea S t a t e a t 3 ME. Antennas are Located Just Above sutfsce. Phill€p Isotropic ocesn-wave spaatrcm%.

.

Figure 7 . Added Transmission Los8 Due to S e a State a t €0 ME. Antennas are Located Just Abwe Surface. Phi l l ips Isotropic Ocean-Wave Spectrum.

18-20

Range, kilometers

Figure 8. Added Transmiasion Iasa Due to Sea State at 30 W e . Antennas are located Just Above Surface. Phil l ips Isotropic Ocean-Wave Spectrum.

Figure 9 . Basic Transmission Loss to Points at Various HeighLs and Ranges Above the Ocean at 3 W. Number is for Perfectly Smooth Sea, Second is for Sea State 5 (25 knot wind) using Fkill ips Ocenn-Wave Spectrum.

First

18-21

Figure 10. Basic Transmission Loss t o Points a t Various Heights and Ranges Above the Ocean a t 10 MHz. Number is f o r Per fec t ly Smooth Sea, Second is f o r Sea S t a t e 5 (25 knot wind) Using Ph i l l i p s Ocean-Wave Spectrum.

F i r s t

Figure 11. Basic Transmission Loss t o PoinLs al: Various Heights and Ranges Above the Ocean a t 30 MHz. Number is f o r Per fec t ly Smooth Sea, Second is f o r Sea S t a t e 5 (25 knot wind) Using Ph i l l i p s Ocean-Wave Spectrum.

F i r s t

18-22

I

ti KO , ci;FSwttering patch

Figure 12. Far-Zone Scatter Geometry.

Figure 13. Geometry for Compensation Theorem.

Constant 8 lines

r C o n s l u n t p-lines

I ' \ '!-Ornni -directional receiver Omni -directional transmitter

Figure 14. Bistatic Surface-to-Surface Radar.

18-23

4.00i-

-K - fN

Figure 15. Transformation between U (Normalized Spatial x-Wavenumber), and fN (Normalized Doppler Shift) and S (Normalized Time Delay) Radar Observables.

I

Normalized Doppler Shift , fN(or K= f:)

Figure 16. Transformation between V (Normalized Spatial y-Wavenumber), and fN (Normalized Doppler Shift) and S (Normalized Time Delay) Radar Observables.

18-24

- -

- I

I3 16 20 2 6 Wind speed(knots) 26 20 16 13 \ ; ; 1- responsible for waves -1-1

\ '.

\ \ . \ \k I

30m 42m 66m 1 1 2 m c Length o f Ocean __c 112m 66m 42m 30m b-1 waves scattering M

180° 1 3 3 ~ 112.5O 90" - Angle from - 90' 67.5' 47' 0'

- -

- I

2.0

1.5-

-

0 1.0-

x 0.8 - 0.7 - 0.6 - 0.5 - 0.4 -

0.3 -

' 0 0.9 -

0.2 -

\ '.

\ \ . \ \k I

- 1.84

propagation direction

* 0.0027 Hz w P,

I 1'- I \ /

\ / \

0 , l h I '-1 I I I 1 ' 1 I 1 -0.30 -0 .25 -0.20 -0.15 -0.10 -0.05 0 0.05 0.10 0.15 0.20 0.25 C

f - f o

Figure 17. Received Signal Spectrum a t 5 MHz f o r Sea Sca t t e r Configuration of Figure 14. Computed f o r Fully Aroused Ptrillips I so t ropic Ocean-Wave Spectrum. Expected Measurements from Non-Isotropic Sea.

Sol id Lines Were Dashed Curves Represent

I .5

I .c

0.t

0 .t - I 0 - 0.1

0.:

0.1!

0.1

18 -Wind speed (knots) -v 18 responsible for waves

15m 21m 33m 58m- Lengthofocean - 58117 33m

waves scattering dm Angle from -c9O0 67.5O 47.4 0" 180° ISo 1 1 2 5 O 90°--

propagation direction

- -

- - 0.953

0.0039 0.0039-

0.05 0.10 0.15 0.20 0.25 0.30 10

Figure 18. Received Signal Spectrum a t 10 MHz f o r Sea Sca t t e r Configuration of Figure 14. Computed f o r Fully Aroused Ph i l l i p s I so t ropic Ocean-Wave Spectrum. Expected Measurements from Non-Isotropic Sea.

Solid Lines Were Dashed Curves Represent

18-25

Figure 19. Bistatic Surface-to-Satellite, Radar.

0.07 0.06 I I I I I I I I I I I I

-7 -6 -5 -4 -3 - 2 -I 0 I 2 3 4 5 8

f-to

Figure 20. Received Signal Spectrum a t 5 MHz for Sea Scatter Configuration of Figure 19; Computed for Fully Aroused Phill ips Isotropic Ocean-Wave Spectrum.

Figure 21. Received Signal Spectrum a t 10 MHz for Sea Scatter Configuration of Figure 19; Computed for Fully Aroused Phill ips Isotropic Ocean-Wave Spectrum.