Influence off evaporation ducts on radar sea return

J.P. Reilly, BEE, MSEG.D. Dockery, BSc, MSEE

Indexing terms: Radar, Clutter, Modelling, Radio-wave propagation

Abstract: Modelling of radar sea return is dis-cussed with consideration of propagation condi-tions. Both the intensity and propagationdirection of energy incident at the sea surface canbe significantly affected by the refractive conditionof the atmosphere. The paper describes and evalu-ates a model that incorporates both of theseeffects for the situation where the propagationconditions are characterised as evaporation ducts.Such ducts are the most persistent marine propa-gation environment on a worldwide basis for low-altitude propagation. It is shown that commonlyencountered evaporation ducts can profoundlyaffect sea returns.

1 Introduction

Probably the most extensively studied aspect of seareturn is the average reflectivity. Measurements of seareflectivity have been made since the early days of radar,using a variety of experimental devices, and taken undera variety of environmental and operational conditions.Such observations, supplemented with theoretical prin-ciples, have lead to a variety of empirical models whosepurpose is to predict average radar sea return given aknowledge of the pertinent variables related to the radar,the sea, and the method of observation. Despite attemptsto account for the relevant parameters in empiricalmodels, calculated predictions of clutter power frequentlydeviate significantly from measurements. We would liketo account for these deviations so as to improve ourability to predict the performance of existing radarsystems and to assist in the selection of design features inplanned systems.

In this paper we show that a significant source ofvariability in radar measurements may be traced tovariations in the atmospheric conditions affecting low-altitude radar propagation. We show that evaporationducts — a common marine phenomenon experienced ona worldwide basis — can profoundly affect radar propa-gation and, consequently, the associated sea clutter.

2 Existing sea reflectivity models

2.1 Comparison of modelsSeveral empirical models for calculating the averagevalue of sea reflectivity are compared below. The studiedmodels have been derived from publications by the

Paper 7149F (E15), first received 27th June and in revised form 27thNovember 1989The authors are with The Johns Hopkins University, Applied PhysicsLaboratory, Johns Hopkins Road, Laurel, MD 20707-6099, USA

Georgia Institute of Technology [1], the TechnologyService Corp. [2], Sittrop [3], and a hybrid model thatincludes work by Barton [4], summary data from Refer-ences 5 and 6 and features of the Georgia Institute ofTechnology model. The four models are referred to hereas GIT, TSC, SIT, and HYB, respectively. The GIT,TSC and HYB models are applicable over a broad fre-quency range, whereas the SIT model applies only to X-and Ku-bands. The GIT model is described in Appendix7.1 of this report, and the HYB model is described inAppendix 7.2.

Figs. 1 and 2 compare the models at radar frequenciesof 3 and 9.3 GHz, over the grazing angle range 0.1 to 10

1.0Grazing angle, i

Fig. 1 Comparison of sea clutter models at S-band, ha = 0.3 m (S « 2); , ha = 1.9 m (S a 5)

D.GIT; x,TSC; O, HYBVertical polarisation, upwind look direction, 3 GHz

10.0

-80.00.1 10.01.0

Grazing angle, 4>

Fig. 2 Comparison of sea clutter models at X-band

, ha = 0.3 m (S as 2); , ha = 1.9 m (S a 5)D, GIT; x, TSC; O, HYB; A, SITVertical polarisation, upwind look direction, 9.3 GHz

degrees. Curves are shown separately for sea conditionshaving average wave heights of 0.3 and 1.9 m(corresponding to sea states 2 and 5). These examplesapply to vertical polarisation and an upwind radarazimuth direction.

The TSC, HYB and SIT models are in reasonableagreement, especially with regard to the dependency of

80 IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

reflectivity on grazing angle. The GIT model, on theother hand, significantly deviates from the others at lowgrazing angles. In the GIT model, the reflectivity variesapproximately as i/̂ 4 at small grazing angles, whereas inthe other models the relationship is closer to \p2. It isworth examining the grazing angle dependency and theo-retical expectations for rough surface scattering in orderto gain insight into the possible role of propagationeffects in explaining these discrepancies.

2.2 Backscatter from the ocean surface in standardpropagation conditions

All of the mean clutter cross-section models mentionedabove are based to some extent on published measure-ments of clutter power. The GIT model, however, con-tains an analytical factor to account for the rapid falloffin clutter power that has been observed below a certaingrazing angle in some measurements (see, for example,Reference 7); these measurements generally exhibit the \j/*falloff described in previous section. The empiricalparameters in the HYB and TSC models were adjustedusing a more diverse set of measurements that greatlyreduce the falloff at small grazing angles.

A hypothesis put forward here is that the measureddata used to adjust empirical parameters in the GITmodel were collected during standard, nonducting propa-gation conditions; this hypothesis is addressed again inSection 3.1. The adjustment factors for incidence angle inthe GIT model have a dominant effect at small angles;this small-grazing-angle region will be referred to as the'interference region' for reasons that will become clear. Atutorial discussion of the 'classical interference effect' forclutter return at small angles is presented in Reference 8;a brief description of this effect is included below.

Fig. 3 (adapted from Reference 8) illustrates thegeneral relationship between the normalised backscatter

Large grazingangle region

Small grazingangle region(i/<4 slope)

Plateau region

't Grazing angle, \

Fig. 3 Idealised relationship between reflectivity and grazing angle forrough surface scattering

Diagram shows general relationship, but is not drawn to scale

reflectivity a0 and the grazing angle \jj. For angles lessthan a transition angle \j/t (to be defined later) the reflec-tivity varies approximately as i/f4 in accordance withtheoretical expectations [9]. As the grazing angle isincreased beyond \jtt, a plateau region is reached in whichthe reflectivity does not vary strongly with grazing angle.As the grazing angle is further increased, the reflectivity isgoverned by a 'near-vertical incidence' region in whichthe backscatter increases sharply with grazing angle.

The received clutter power Pc may be expressed as

Pc = - 4 (1)

where Ky is a constant which involves the various termsin the radar range equation (i.e. antenna gain, transmit

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

power etc.), a0 is the clutter cross-section per unit area, Ac

is the illuminated clutter area and R is the range from theradar.

In the plateau region, o0 is frequently represented asbeing proportional to if/. In this case, since Ac grows lin-early with range and since \j/ is proportional to R~l atmoderate ranges, the clutter power relationship in theplateau region is

PcccR (plateau region) (2)

On the other hand, o0 is sometimes taken to be constantin the plateau region, in which case the range power lawin eqn. 2 is —3, rather than —4.

In the region where \j/ < ij/c, a0 varies as R~4, and

P, o c I T 7 (interference region) (3)

Fig. 4 illustrates qualitatively the expected range depen-dence of received clutter power.

R"3 to R slope

slope

Range, logarithmic scale

Fig. 4 Range dependence of received clutter power for idealised roughsurface scattering (not to scale)

Critical range R, corresponds to grazing angle 4>, in Fig. 3

At small grazing angles the reflectivity behaviour canbe explained in terms of the backscatter from a reflectornear a smooth conducting surface. In this grazing inci-dence region, backscatter power is subjected to multipathinterference from combined direct and forward-scatteredrays from individual sea wave structures, as illustrated inFig. 5. The propagation factor | F |4, can be expressed in

Fig. 5 Rough surface backscatter with multipath effect

Equivalent scattering height he is roughly associated with the transitional range R,in Fig. 4 for idealised propagation conditions

this case as [8]

I) sin if/14 (4)

where he is the effective height of the scatterer, as illus-trated in Fig. 5. According to Reference 8, the falloff inclutter power changes from R~3 to /?~7 at the rangewhere | F | 4 = 1. The transitional grazing angle \j/t corre-sponding to this point is

sin \J/t = X/(4nhe) (5)

81

The transitional angle has also been related to averagewave height [1] by

sin <A, = X/{Kha) (6)

where K is a constant and ha is the average wave height.The experimental data examined by the authors of Refer-ence 1 show an average value of K = 6.3 for S- throughX-band, with some variation with radar wave length.

Table 1 : Transitional grazing angle for sea clutter

Sea

23456

ah, m

0.1240.2790.4960.7751.116

L1.25

7.003.111.751.120.78

tfjt at listed frequency,

SGHz 3.0 GHz

2.911.290.730.470.32

C

deg

X6.0 GHz 9.3 GHz

1.460.650.360.230.16

0.940.420.230.150.10

Combining eqns. 5 and 6 results in the relationship he =0.5ha. An alternative definition is given in Reference 10,where the value he = 0Jha was proposed.* In this paper,we will use an average of these two values to representthe effective scattering height of the sea:

0.6ft,, (7)

Although there is clearly some uncertainty in the defini-tion of he, the clutter calculations presented in this paperare relatively insensitive to its specific value over a ratherwide range. Table 1 evaluates \jtt using eqns. 5 and 7.

The clutter power range laws described above areexpected to occur in nonducting propagation conditions,such as the standard '4/3 earth' atmosphere. However,significant deviations from these ideal range laws areoften observed in experimental data. For example, rangelaw exponents as low as —4 have been observed in theregion where —7 is expected under the standard atmo-sphere assumption [11]. Although clutter measurementshave historically had many uncertainties with respect tothe measurement conditions, the presence of ducting ornear-ducting (superrefraction) conditions is the probablecause of high clutter levels at longer ranges. Indeed,certain clutter reflectivity data presented in Reference 11,applying to a period when ducting was present, can befitted to the grazing angle relationship i//lA. Measure-ments from the same area, but made later in the daywhen ducting was absent, provided a grazing angle fit ofabout i^38.

At this point, it is useful to differentiate between thegeometrical grazing angle that a straight line from theantenna makes with the surface tangent at a given range,and the angle that the incident energy makes with thesame surface tangent at that range. The former angle canbe calculated from geometry and is the angle used in thegrazing-angle relationships mentioned above. The latterdefinition, however, is the one that should be used todrive empirical models of reflectivity. In standardatmosphere-type conditions, the two definitions agreewhen an adjustment is made to the earth radius used inthe geometrical calculations. In more complicatedrefractive conditions, the directions of propagation at thesurface is substantially modified and cannot be deter-mined from geometry alone. Thus, without an indepen-

* This conclusion makes use of the relationship ha = yj(2n)oh, where ah

is the RMS wave height. The quantities cited in this paper may berelated to other sea indices by the following relationships: Hl/3 = l.6ha,where H1 / 3 is the 'significant' wave height; S = 3.6y/(ha), where S is thesea state index, and ha is the average wave height in metres.

dent method of estimating the propagation direction, onecannot deduce a grazing-angle law from clutter powermeasurements based on the apparent range law.Approaches for estimating the propagation grazing angleat each range are discussed in Section 3.2.

3 Sea clutter models including propagationeffects

3.1 Propagation conditions over the oceanThe influence of the atmosphere on radar propagation isfrequently accounted for using an equivalent earth radiusmodel. This depiction is justified if the vertical gradient ofthe microwave index of refraction is approximately con-stant, in which case refractive effects can be accounted forusing an earth radius multiplier [12]. The radius multi-plier k = 4/3 is often used and is referred to as a 'stan-dard atmosphere' condition. Despite this nomenclature,the constant refractivity gradient is exceptional for near-surface microwave propagation over the ocean.

As noted by Hitney et al. [13], low-altitude propaga-tion over the ocean may be subject to surface-based ductsand evaporation ducts. Surface-based ducts generallyarise due to temperature inversions which result when awarm, dry air mass lies above a cool, moist air mass.Evaporation ducts, on the other hand, are formed pri-marily by the rapid decrease in humidity with increasingaltitude just above the ocean's surface [14-16]. Thishumidity gradient is always present over the ocean, butthe altitude at which the humidity achieves the nominalambient value varies greatly. Table 2 lists data developed

Table 2: Average* duct heights for various global regions[from Reference 30]

Area descriptor

Northern AtlanticEastern AtlanticCanadian AtlanticWestern AtlanticMediterraneanPersian GulfIndian OceanTropicsNorthern Pacificworldwide average

Evap.ductheight, m

5.37.45.8

14.111.814.715-915.97.8

13.1

SFC-basedduct height,m

426486

118125202110

997485

OccurrenceSFC duct, %

1.32.84.19.8

13.445.513.413.66.28.0

* Averages for surface-based duct are conditioned on the presenceof that type of duct. In contrast, averages for evaporation ducts aretaken unconditionally.

from Reference 13 concerning average heights of evapo-ration ducts and surface-based ocean ducts for variousareas of the world. In this table, the average heights ofsurface-based ducts were determined conditioned on thefact that such a duct is present. A separate column in thetable lists the frequency of occurrence of the surface-based duct. The tabulated average heights for evapo-ration ducts, on the other hand, are takenunconditionally. Surface-based ducts can occur withrather large thicknesses but their frequency of occurrenceis much lower than that of evaporation ducts for mostareas of the world; the worldwide occurrence of surface-based ducts is only 8%. Evaporation ducts, on the otherhand, occur with much smaller thickness, but they arerelatively common. Thus, with regard to frequency ofoccurrence, the evaporation duct is usually the dominantpropagation mechanism affecting sea clutter data.

Fig. 6 illustrates three histograms of evaporation ductheights, as determined from the publication of Hitney et

82 IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

al. [13]. Additional duct height statistics have beenpublished by Anderson [17]. A duct height of zero metreson this scale indicates a constant refractivity gradientcorresponding to the 4/3 earth radius model. Fig. daapplies to worldwide conditions where the average duct

15

10

10 30 4020

Duct height, m

Histograms of evaporation duct heights (adapted from Refer-Fig. 6ence 13)a Worldwide annual average, hd= 13.1 mb Western Atlantic, hd = 14.1 mc Eastern Atlantic, hd = 7.4 m

height is 13.1 m. Fig. 6b applies to the Western Atlantic,which includes latitudes between 20° and 40°; in thisregion the average duct height is 14.1 m. Fig. 6c appliesto the Eastern Atlantic, which includes latitudes between40° and 60°; in this region, the average duct height is7.4 m. As a general rule, duct heights are smaller as onemoves from the tropics to higher latitudes. However,even in the Northern Atlantic (latitudes between 60° and70°), the average duct height is 5.3 m. As will be demon-strated subsequently, these average evaporation ducts arelarge enough to affect the grazing angles, propagationfactors and, ultimately, received clutter power.

The GIT reflectivity model is believed to representclutter under standard propagation conditions, since itgenerally reflects theoretical expectations of rough-surface scattering for a standard atmosphere at low-grazing angles. The other empirical models provide a fitto mean clutter cross-section measurements obtainedunder a variety of conditions. Considering the prevalenceof evaporation ducts in marine environments, it is likelythat those measurements have been averaged over avariety of propagation conditions that include ducting.

3.2 Grazing angle considerationsAs previously mentioned, propagation conditions canaffect significantly the grazing angle at the sea surface.Due to the sensitivity of the clutter cross section to if/, it

is desirable to account for distortions in the grazing anglein some way. In preparation for later descriptions ofmethods for incorporating propagation effects in cluttercalculations, this section gives a brief discussion ofgrazing-angle issues.

Fig. 7 presents grazing angles against range calculatedby a geometric optics (ray tracing) method for a 4/3 earth

1.0 cr

2> 0.1 =

0.01

z V ^ J ' '

-1! 1 1

:i i i i

M M 1 1

5=

^ —

\ 2

\4/3 earth

M i l l 1 1

1 1

hri = 3

- 2 0

- 1 0

4

(hd = 0

1 I

1 1

0 m

)

I |

-

-

_.LL

U

:

i10010

Range, km

Fig. 7 Grazing angles for various evaporation ducts determined fromgeometric optics

Antenna height = 23 m; duct height = 0 to 30 m

atmosphere, and for various evaporation ducts havingheights hd of 0 to 30 m; the antenna height is 23 m. Inthis figure, as well as elsewhere in this paper, the calcu-lations have been based on evaporation duct refractiveindex of refraction profiles defined in Reference 13 as

M{h) = M(0) + 0.125& - 0.125/id In (h/h0) (8)

where M is the modified index of refraction, h is heightabove the surface in metres, hd is duct height in metres,and h0 = 0.00015 m. Eqn. 8 applies to neutrally buoyantconditions. Once the gradient dM/dh reaches the stan-dard value of 0.118M units per metre, it is 'frozen' to thatvalue for higher altitudes.

For evaporation duct heights that are lower than theantenna height, geometric optics calculations will resultin a limiting range RL beyond which no rays strike thesurface; the last ray that reaches the surface will bereferred to as the limiting ray. This behaviour reflects thefact that geometric optics is too simplified to indicate thecoupling of energy into these ducts when the antenna isnot in the duct. When the duct height is greater than theantenna height, as with the hd = 30 m case, geometricoptics will generate one or more 'trapped' rays, and alimiting range R does not exist. With the exception of thehd = 30 m curve, the curves in Fig. 7 were cut off atapproximately RL.

The grazing angles for the various ducts shown in Fig.7 approach asymptotic minima, if/L, at RL. This observa-tion provides some justification for assuming that theenergy propagated beyond RL is also associated with theangle \f/L. This assumption is intuitive, for instance, forduct height and frequency combinations that result in thepropagation of a single waveguide mode with its associ-ated angle [18]. In the calculations presented in the nextsection, i//L is assumed at all ranges greater than RL. Thisassumption has yet to be verified experimentally or witha more rigorous analytic study.

Geometric optics results are frequency independentand correspond to propagation in the limit of very highfrequencies. As a result, even small ducting structures(such as a 2 m evaporation duct) have the maximumeffect on the calculated grazing angles. The accuracy ofthese angle estimates will depend on the size of the duct

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990 83

(or other refractive index structures) as well as the fre-quency. Although the frequencies at which the geometricoptics calculations become inaccurate for each ductheight have yet to be determined, angle estimates areexpected to be quite good for UHF frequencies andhigher. Future studies are expected to yield a betterunderstanding of this issue. The methods of estimatinggrazing angles and calculating propagation factor valuesare separately treated in the modelling approachesdescribed below.

3.3 Accounting for propagation effectsAs illustrated by the curves in Fig. 7, the propagationcondition can significantly affect the grazing angle.Accordingly, a simple method of incorporating propaga-tion effects into sea clutter calculations entails evaluatingthe GIT model with the grazing angles that result fromthe propagation conditions, rather than with the 4/3earth grazing angle. The rationale of the procedure restson the assumption that the GIT model accurately rep-resents grazing angle dependence at small angles. Fig. 8

- 2 0

- 4 0

- 6 0

E - 8 0 -

E

3 -ioo

I

-

I

I

I

I I

s= 0

I |

i i 111

^ H Y B

I I I I I

1

^ 2

I

"

—•4

|

I

- 2 0

— 10

I I I I I

h d =30m

I I I I I

I

--

|

I I I

h d = 3 0 m

I I I I I I I I100

Fig. 8 Sea reflectivity calculated using GIT model with grazing angleadjusted for propagation condition ha = 1.25 (S = 4)

a S-bandb X-band

shows the results of this procedure for S- and X-bandand a vertically polarised radar at a height of 23 m. Thefigure shows the GIT model evaluated at the grazingangles calculated for duct heights of 0, 2, 4, 10, 20 and30 m, and with an average wave height of 1.25 m (seastate 4). The zero duct height is the GIT model applyingto the standard 4/3 earth condition. The upper brokencurve is the HYB model. It can be seen in this examplethat a simple grazing-angle adjustment has a significantinfluence on the calculated reflectivity, bringing the GITmodel prediction closer to the HYB predictions. At lowersea states (e.g. ha = 0.25 m), however, the adjusted GITpredictions fall significantly below (20 dB or more) theHYB predictions. This effect will be evident in the resultspresented below.

While the method of adjustment described aboveappears to have practical advantages, the procedure failsto account for variation in the propagation factor —which can be as important as the variations in thegrazing angle. Fig. 9 provides examples of the two-waypropagation factor (i.e. power relative to free space) foran S-band and X-band radar and for several evaporationduct heights. The assumed altitude is 0.75 m, correspond-

84

ing to an average wave height of 1.25 m, as indicated byeqn. 7. The calculations have made use of refractive indexprofiles for the various ducts that were generated by eqn.8. The propagation factor calculations were made using

10

Range ,km

Fig. 9 Two-way propagation factor at S- and X-band for variousevaporation duct heights

Antenna height = 23 m; effective clutter height = 0.75 ma S-bandb X-band

the electromagnetic parabolic equation (EMPE) propa-gation model, which provides a complete solution of aparabolic approximation to the Helmholtz wave equa-tion [19, 20]. Alternative approaches for propagationmodelling have been used by others [21].

It is reasonable to expect that sea returns will respondto the propagation factor applicable to near-surface alti-tudes. Accordingly, a method that incorporates bothgrazing-angle and propagation factor effects is desirable.As we alluded to earlier, the methods described here usethe assumption that the GIT reflectivity calculationsapply to a standard atmosphere condition. The philos-ophy is to remove the 4/3 earth propagation factor fromthe GIT reflectivity values and to substitute the propaga-tion factor for the specific propagation condition of inter-est. This results in an adjusted reflectivity aop that iscalculated as follows:

a*M) = - ^ ^ (9)F*(^)

<JOM]/P) = &*{$p)Fp*{\ltp) (10)

In eqn. 9, ao{^/) is the reflectivity determined from theGIT model evaluated at the grazing angle \j/, and F*(\f/) isthe propagation factor for the 4/3 earth model, evaluatedat a range corresponding to the grazing angle ^. In eqn.10, Fp(i/jp) is the propagation factor for ducted propaga-tion, evaluated at a range where the grazing angle is \j/p.In our calculations, \\ip is determined by optical ray-tracedata, such as shown in Fig. 7. Beyond the limiting range,we assume that the grazing angle is equal to the asymp-totic values noted at the limiting range. aop(\j/p) is theadjusted reflectivity that accounts for variations in boththe grazing angle and the propagation factor.

The reflectivity calculation indicated by eqns. 9 and 10involves the ratio F*/F*, which causes the resultinganswer to be relatively insensitive to the precise heightthat is assumed for the clutter. This assertion can beunderstood by noting that at the low altitudes associatedwith effective clutter heights, F* and F£ have a similar

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

relative dependence on altitude, independent of the pro-pagation condition. For convenience, we shall refer to thecalculation method indicated by eqns. 9 and 10 as thereflectivity and propagation (REPROP) method.

E

*Em•o>?

>

ecti

etl

cc

Figa / i ,b />,

c / i (

%

E

• o

>?

ivit

Flee

t

cc

Fifia hb h

c h

- 20

- 40

-60

- 8 0

-100

ion120

1

—="

-

- a1

- 4 0

- 60

-80

-100

1201ZU

l 1

—

—

-—

-b1

— 2 0

-40

-60

-80

-100

T20.

1~ . _

-

-

-

_

- c1

1 1

1 I

Nh J —" d

1 1

1 1

hd-

1 1

1 1

Uh d =

1 1

T i 1 1 1 1

HYB

J.

T

I-

~T

I

""-^

I I I I I 11

-—

-

hd = 30m~

_1 H I 2 r M s l 1 O T 2 O M i l

10

Mill

HYB

2>

1 111110

1 1 111

HYB

•"i= 0

j .

^ ^

1 1 I I I

10

I

4

|

I

*— —" ^

4

|

Range, km

100

I II IIII

--

hd = 30 m ""

20

\ —10I I I I 11

100

I I I I I I

—hd = 30 m -

-

20\

10

—I I I I I I

100

. 10 Reflectivity at 3 GHz calculated by REPROP method= 0.25 m (S as 1.8)

= 1.25 m (S « 4.0)= 2.50 m (S » 5.7)

- 4 0

- 6 0

-80

-100

i o nIZU<5ft

— / u

- 4 0

-60

-80

1

--

__ a

1

1

—-

—-—

_ b

1

on— £X)

- 4 0

- 6 0

- 8 0

-100

1 on— 1/U

1

-

-

-

c

1

1 1

h(j

1 1

1 1

hd

1 1

1 1

hd = 0

1 I

1

|

1

= c

I

1•Ml

|

I I I II

HYB

**

I I I II10

Mill^ HYB

^ ^ ^ ^

Mill10

Mill^^ HYB

2 N

Mill10

Range , knr

I

h d =

\I

Ih

\ 4

I

I

4

I

I I I 111

___

30 m -

^. -

S^20\/l10 _

I I I I I II100

I M I N I

d = 30m- ^ —'

10 *•* ""

—

_I I I I I I I

100

I I I I I II= 30 m _

-

-

1 M 1 1 11100

|. 11 Reflectivity at 9 GHz calculated by REPROP method, = 0.25 m (S tsl.8), = 1.25 m (S « 4.0)„ = 2.50 m (S « 5.7)

Figs. 10 and 11 illustrate reflectivity values that aregenerated by using REPROP method. The antennaheight is assumed to be 23 m, and the polarisation is ver-tical. The curves have been arbitrarily terminated at thelesser of ij/L or 0.1°. Each figure includes separate plotsfor average wave heights of ha = 0.25, 1.25, and 2.5 m.The figures also list equivalent sea states (S) according tothe footnote in Section 2.2. These values correspond tosea states 1.8, 4.0 and 5.5, respectively. The results of theHYB model (upper dashed curve), and the unmodifiedGIT model (lower dashed curves labelled hd = 0) are alsoincluded for comparison.

Fig. 10 demonstrates that the reflectivity calculatedfrom the GIT model is significantly increased whenmodified for ducting effects, and that the increase is mostsignificant at distant ranges. Reflectivity calculated withthe REPROP method is generally less than the corre-sponding values calculated with only a grazing angleadjustment (Fig. 8). The HYB results shown on eachgraph make use of grazing angles from the 4/3 earthatmosphere. At the lowest sea states (part a in eachfigure), the predictions are well below the HYB curves. Athigher seat states (parts b and c), the reflectivity valuesapproach, and in some cases exceed, the HYB curves.

The HYB reflectivity values are typically used as anaverage over a variety of propagation conditions, whilethe GIT model values are thought to apply to standardatmosphere propagation conditions. If this conjecture istrue, then one would expect the REPROP curves to fallabove and below the HYB data. The trend in Fig. 10 iscertainly in that direction, but there is still considerabledifferences between the HYB and the REPROP curves atthe lowest sea states. These discrepancies are discussedfurther in Section 4.

40

0

- 4 0

- 8 0

-120

40

0

- 4 0

- 8 0

_ I ^

-

-

- ai i

^ i i i i

^ ^

M i l

I I I

\

I I I

I I

0

I I

I I I I I L

hd = 30m -

\ 20_

i^2 4 \ n

10

Range, km

Fig. 12 Relative clutter power calculated using REPROP cluttermodelha = 1.25 m (S « 4.0)a 3 GHzb 6 GHzc 9 GHz

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990 85

3.4 Received clutter powerThe rate of falloff of clutter power may be convenientlyexamined by calculating a normalised power (Pcn):

Pcn = PJPc(ref) (11)

where Pc is the absolute clutter power and Pc(ref) is thatdetermined under some reference set of conditions. Thenormalisation by Pc{ref) makes Pcn independent of radarspecific variables (such as transmit power and antennagain). For the comparison presented in this section, thereference condition is defined as the received clutterpower in a 4/3 earth atmosphere and at a range of 10 km.

The ratio given by eqn. 11 may be expressed alterna-tively as

<Top(ref)RVR?ef(12)

where aop(R, if/d) refers to the REPROP reflectivity deter-mined at range R, aop{ref) is the same variable corre-sponding to the reference condition (4/3 earth andR = 10 km) and Rref is the reference range (10 km).

Fig. 12 illustrates the range dependence of Pcn for theREPROP method at frequencies of 3, 6 and 9 GHz. Indi-vidual curves are shown for the 4/3 earth atmosphere,and for duct heights of 2, 4, 10, 20 and 30 m. The oscil-lations that are seen at the higher frequencies and ductheights are due to multimode interference effects thatarise because the larger ducts support more than onewaveguide mode. The depths of the nulls are not accu-rately represented due to the relatively coarse range stepsused in the calculations (20 steps per decade, equallyspaced on a logarithmic scale).

4 Discussion

The approach for predicting clutter levels in evaporationducting conditions presented here can potentially beapplied in grazing-angle regimes where the empiricalmodels are not advertised to work, i.e. below 0.1°. Thelower limit on the grazing angle that is intended to beused in the models is a result of the fact that the experi-mental observations on which they are based rarelyinclude such small angles. Thus, empirically speaking, theangular dependence of the reflectivity below 0.1° is anunknown. In most cases, these small angles correspond tolonger ranges and smaller reflectivity and propagationfactor values such that the clutter signal levels are quitelow. Nevertheless, an investigator should be aware of thespeculative nature of reflectivities corresponding to suchsmall grazing angles.

The REPROP method can potentially be applied tothe full frequency range over which the associated reflec-tivity models were originally intended. The range ofapplicability of the GIT model was given as 1 to100 GHz; the range of the data base [5, 6] used in theHYB model is 0.5 to 35 GHz. The REPROP method hasyet to be tested over such large frequency ranges. In prin-ciple, the REPROP method should be applicable forthese frequency ranges. However, although grazing anglesderived from geometric optics are sufficiently accurate,the EMPE propagation model has yet to be testedagainst other numerical procedures for frequencies above20 GHz. Also, propagation becomes increasingly sensi-tive to atmospheric microstructure as the frequency isincreased and, as a result, using the 'mean' refractivityprofile defined by eqn. 8 to represent the environmentmay be questionable for such high frequencies. The

9 GHz examples presented in this paper are expected tobe free of these complications, but calculations at muchhigher frequencies should be approached with caution.

It is likely that the unmodified GIT model under-predicts reflectivity at small grazing angles underenvironmental conditions that deviate from a standardatmosphere. The adjustments to the GIT model sug-gested in this paper tend to increase the reflectivityvalues, thus improving their agreement with those of theHYB model. But these adjustments generally fall short ofthe HYB predictions, particularly at low frequencies andsea states. At 3 GHz, for example, the REPROP curves ofFigs. 10 and 11 are well below the HYB results for rangesbeyond 1 km. At shorter ranges, however, both REPROPand HYB models nearly converge at a range consistentwith \J/t as defined in eqn. 6.

In Figs. 10a and lla, the discrepancies between theHYB model and the REPROP and GIT models occur atranges where propagation is not expected to be impor-tant; this is supported by the fact that the GIT andREPROP results are in agreement at these ranges for allof the duct heights considered. Thus, the discrepanciesarise from differences in the reflectivities provided by theGIT and HYB models at low sea states. An attempt toshed light on this issue using 3 GHz, vertically polarisedclutter measurements is described in Reference 22. Thatstudy suggests that the GIT model is providing thecorrect low sea state reflectivities, at least at 3 GHz.

The predictive capability of the REPROP cluttermodel has only begun to be validated using measuredsignal and environmental data. For the particular case ofS-band clutter behaviour in coastal environmental condi-tions, calculations using the REPROP model have beencompared with some experimental data [22]. Therefractive conditions during these tests varied substan-tially with range. As demonstrated in Reference 22, theREPROP model performed quite well in this particularinstance.

5 Acknowledgments

The authors acknowledge the contributions of S.A.Rudie, who developed and ran computer software insupport of this study. This work was supported by theNATO AAW Program Office under task 3-1-18.

6 References

1 HORST, M.M, DYER, F.B., and TULEY, M.T.: 'Radar sea cluttermodel'. Int. Conf. on Antennas and propagation, IEE Conf. Pub.169, Pt 2, 1978

2 FLETCHER, C: 'Clutter subroutine'. Technology Service Corp.,Silver Spring, MD, USA, Memorandum TSC-W84-01/cad, 17thAugust 1978

3 SITTROP, H.: 'Characteristics of clutter and targets at X- and Ku-band'. AGARD Conf. Proc. No. 197, 'New techniques and systemsin radar'. The Hague, The Netherlands, June 1977, pp. 28.1-28.27

4 BARTON, D.K.: 'Radars. Vol. 5' (The Raytheon Co., 1975)5 RIVERS, W., NATHANSON, F.E., and BLAKE, L.: 'Shipboard

surveillance radar environment study'. Technology Service Corp.,Silver Spring, MD, USA, Report TSC-W25-8, 25th April, 1977

6 NATHANSON, F.E.: 'Radar design principles' (McGraw-Hill, NewYork, 1969)

7 KATZIN, M.: 'On the mechanisms of radar sea clutter', Proc. IRE,1957, 45, (1), pp. 44-54

8 LONG, M.W.: 'Radar reflectivity of land and sea' (Artech House,1983)

9 PEAKE, W.H.: 'Theory of radar return from rough terrain'. 1959IRE Convention Record, 1959, 7, pp. 27-41

10 STEBEN, J.O., and URKOWITZ, H.: 'An improved model forsimulating radar sea return, including sea spikes', IEE Conf. Pub.281, Radar '87, 19th-21st October 1987, London, pp. 466-470

86 IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

11 DYER, F.B., GARY, M.J., and EWELL, G.W.: 'Some comments onthe characterization of radar sea return'. Proc. Int. IEEE Symp. onAntennas and Propagation, Atlanta, 1974, pp. 323-326

12 SCELLING, J.C., BURROWS, C.R., and FERRELL, E.B.: 'Ultra-short-wave propagation', Proc. IRE, 1933, 21, pp. 440-461

13 HITNEY, H.V., BARRIOS, A.E., and LINDEM, G.E.: 'Engineer'srefractive effects prediction system (EREPS). Revision 1.00, User'smanual'. Document AD 203443 Naval Ocean Systems Center, SanDiego, CA, July 1988

14 JESKE, H.: 'Die Ausbreitung elektromagnetischer Wellen im cm-bism-Band iiber dem Meer unter besonderer Beriicksichtigung dermeteorologicschen Bedingungen in der maritimen Grenzschicht'.Hamburger Geophysikalische Einzelschriften (De Gruyter,Hamburg, 1965)

15 GOSSARD, E.E.: 'The height distribution of refractive index struc-ture parameter in an atmosphere being modified by spatial tran-sition at its lower boundary', Radio ScL, 1978,13, (3), pp. 489-500

16 PAULUS, R.A.: 'Practical application of an evaporation ductmodel', Radio ScL, 1985, 20, (4), pp. 887-896

17 ANDERSON, K.D.: 'Radar measurements at 16.5 GHz in theoceanic evaporation duct', IEEE Trans., 1989, AP-37, (1), pp.100-106

18 BRECKHOVSKIKH, L.M.: 'Waves in layered media' (AcademicPress, New York, 1980), Chap. 5

19 DOCKERY, G.D.: 'Modeling electromagnetic wave propagation inthe troposphere using the parabolic equation', IEEE Trans., 1988,AP-36, (10), pp. 1464-1470

20 KO, H.W., SARI, J.W., and SKURA, J.P.: 'Anomalous microwavepropagation through atmospheric ducts', The Johns Hopkins APLTech. Dig., 1983,4, (2), pp. 12-16

21 BAUMGARTNER, G.B., HITNEY, H.V., and RAPPERT, R.A.:'Duct propagation modelling for the integrated-refractive predictionsystem (IREPS)', IEE Proc. F, Commun., Radar & Signal Process.,1983, 30, (7), pp. 630-642

22 DOCKERY, G.D.: 'A method for modelling sea surface clutter incomplicated propagation environments', IEE Proc. F, Radar &Signal Process., 1990, 37, (2), pp. 73-79

7 Appendix

7.1 GIT sea clutter model7.1.1 Frequency range = 1 to 10 GHz

(a) Reflectivity equations

aJLH) = 10 log [3.9 x l ( r 6 ^ 0 - 4 G f l G u G w ]

(b) Adjustment factors

Ga = fl*/(l + «4)

Gu = exp {0.25 cos <t>{\ - 2.8i/^-0-33}

Gw = [1-94KW/(1 + Kw/15.4)]«

(c) Definitions for adjustment factors

q = 1.93A"004

a = (14.4A + 5.5)^hJX

7.1.3 Auxiliary equations

ha = 4.52 x l O " 3 ^ 5

Vw = 3.16S08

7.7.4 Units and symbols

o0{H), GO{V) = reflectivity for H and V

polarisation (dB m2/m2)

ha = average wave height, m

k = radar wavelength, m

ijj = grazing angle, radians

Vw = wind velocity, m/s

0 = look direction relative

to wind direction, radians

7.2 Hybrid sea clutter modelThe hybrid (HYB) model largely conforms to the datathat were first published in Reference 6 and later elabo-rated on in Reference 5. The model defined here takesinto account the fact that these data have been averagedover all wind directions. A transitional grazing angle isbased on the definition in References 1 and 4. A polarisa-tion adjustment has been taken directly from Reference 1,which was developed as an empirical fit to the data inReference 6.

7.2.7 Mean reflectivity

ao(H) - 1.05 In (ha + 0.015) + 1.09 In (X)+ 1.27 In (il/ + 0.0001) + 9.70 (3 to 10 GHz)

ao{H) - 1.73 In (ha + 0.015) + 3.76 In (X)+ 2.46 In 0/f + 0.0001) + 22.2 (below 3 GHz)

where ao(H) and <JO(V) are the reflectivities evaluated at Hand V polarisations, respectively.

(b) Adjustment factors

Ga = a4/(l + a4)

Gu = exp {0.2 cos (j>{\ - 2.8«A)(/l + 0.015)-°-4}

Gw = [1.94KW/(1 + Kw/15.4)]«

(c) Definitions for adjustment factors

q = 1.1/(2 + 0.015)° 4

a = (14.4/1 + 5.5)ij/hJX

7.1.2 Frequency range = 10 to 100 GHz(a) Reflectivity equations

ao{H) = 10 log [5.78 x 10- 6 ^° - 5 4 7 G a G u GJ

°0(V) = <*o- 1-38 In (ha) + 3.43 In (A)

+ 1.31 In 0/0 + 18.55

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990

where oo is the mean reflectivity in units of dB m2/m2

and <ro(ref) is a reference reflectivity applying to S (seastate) = 5, I/J (grazing angle) = 0.1°, P (polarisation) = V,and <f> (look direction) = 0° (upwind). Kg, Ks, Kp, and Kd

are decibel adjustments for arbitrary values of S, ij/, P,and (j>.

7.2.2 Grazing angle adjustment (Kg): Define a refer-ence grazing angle \j/r, and a transitional angle \pt asfollows:

where ah is the RMS wave height.(a) for ij/t ^ \\ir

0 for \\i< ij/r

8 •A/'Ar ^or •Ar ^ •A ^ •Ar2̂0 log i/',/i/'r 4- 10 log \jj/\jjt for \j/t<\jj< 30°

(fc) for (A, < i/v

[0 for il/ ^tj/r

7.2.3 Sea state adjustment

Ks = 5(S - 5)

87

where S is the sea state. The relationship between seastate and average wave height is stated in Section 7.2.7.

7.2.4 Polarisation adjustment: With vertical polarisa-tion, the polarisation adjustment Kp is zero. With hori-zontal polarisation, Kp is based on the relationships inReference 1 as follows:

1.7 In (ha + 0.015) - 3.8 In X

- 2.5 In

1.1 In (ha + 0.015) - 1.1 In X

+ 0.0001 ) - 22.2 / < 3 GHz

- 1.3 In + 0.0001 J - 9.7 3

1.4 In (ha) - 3.4 In X

- 1 . 3 In ^ - 1 8 . 6

where ha is the average wave height in metres.

7.2.5 Wind direction adjustment

1.7 log y) (cos (/> -

10

where <p is the radar look angle with respect to the winddirection, defined such that (f> = 0 when looking upwind.

7.2.6 Reference reflectivity

[24.4 log/-65.2 / ^ 12.5°0{ref) = [3.25 log/-42.0 / > 12.5

7.2.7 Auxiliary equations

Vw = 3.2S08 (wind velocity)

oh = 0.03IS2 (RMS wave height)

ha = 0.08S2 (average wave height)

7.2.5 Units

a0: dB m2/m2

X, <TZ, ha: m

ij/: degrees

Vw: m/s

/ : G H z

Kg,Kp,Kd:dB

IEE PROCEEDINGS, Vol. 137, Pt. F, No. 2, APRIL 1990