Synthetic aperture radar imaging of ocean-bottom topography via tidal-curent interactions: theory and observations

Lab

T Q:

INT. J. REMOTE SENSING. 1985, VOL. 6 NO. 7 1179-1200

Synthetic aperture radar imaging of ocean-bottom topography via

tidal-current interactions: theory and observations

R. A. SHUCHMAN, D. R. LYZENGA and G. A. MEADOWS Radar Science Laboratory, Environmental Research Institute of Michigan, FO Box 8618, Ann Arbor, Michigan 4l07, U.S.A.

(Received 23 March 1984; infinalform 20 November 1984)

Abstract. A numerical model has been developed for the purpose of explaining and quantifying the relationship between the SEASAT synthetic aperture radar (SAR) signatures and the bottom topography of the ocean in the Southern Bight of the North Sea and Nantucket Shoals. The model uses environmental data (wind, current and depth changes), and radar system parameters (frequency, polarization, incidence angle and resolution cell size) as inputs and predicts SAR-observed backseatter changes over topographic changes in the ocean floor. The model results compare favourably with the actual SEASAT SAR-observed backscatter values. The comparisons between the model and the actual data are all within 15 dB except for one limiting geometry. The model suggests that for bottom features to be visible on SAR imagery, a moderate to high current velocity (04 rn/s or greater) and a low to moderate wind (between 15 and 7-5m/s) must be present.

1. Introduction

The SEASAT synthetic aperture radar (SAR) launched in 1978 by NASA,

collected ocean imagery during approximately 200 of the 1500 orbits it was in operation. Although this SAR system operated at L band (23.5 cm), a wavelength

which does not penetrate an appreciable distance into the water, the data from

SEASAT revealed many patterns that are apparently related to subsurface or bottom

features. An extensive study reported by Kasischke el al. (1983 a, b) examined all passes of SEASAT SAR imagery collected over non-frozen ocean regions for evidence

of bottom-related surface signatures. ¡n this study, the positions of the unidentified

patterns which were suspected to be bottom-induced were determined by identifying

known land areas or through the use of satellite ephemeris records. Hydrographic charts from these areas were examined to determine whether or not the patterns

occurred over a distinct bottom feature.

Of the some 200 orbits of SEASAT SAR imagery examined, approximately 80 per

cent were found to contain patterns on the imagery which could be correlated to a distinct bottom feature. Kasischkeet al. (1983 b) report on 35 test cases which were

rigorously examined and the surface patterns on the imagery compared with

hydrographic charts and ancillary data (environmental conditions coincident with the satellite overpass). These test cases are presented in table 1.

Some of the most dramatic and least expected features are those related to ocean-bottom transverse sand waves and longitudinal sand bars (occurrence of these features are indicated by the SWS symbol on table I). These SAR-observed features correspond very well to the local bottom bathymetric features and have been noted on SAR data of

1180 _{R. A. Shuchrnan et al.}

Table 1. Summary of SEASAT SAR imagery examined from bathymetric features (modified from Kasischke et al. 1983 b).

Study site (location)

Little Bahama

Bank-Grand Bahama Island

Great Bahama

Bank-Bimini

Great Bahama Ban

k-Southern Edge Tongue of the Ocean

Haití-Rochelois Bank

Bermuda Nantucket Shoals Cook Inlet, Alaska North Rona Rock Sula Sgier English Channel

North-east Atlantic

Bottom feature(s)t

k Bottom feature key: DWB, deep-water bank: DWR, deep-water ridge; DWS, deep-water shelf; DWSM, deep-water seamount; EB. edge of bank in the Caribbean; MB, mud bank; SI, shoal area surrounding an island: SWS, shallow water sandbank.

407 25 July 1978 12.46 ER 651 11 August 1978 12.26 EB 407 25 July 1978 12.4.6 EB 651 11 August 1978 12.26 EB 407 25 July 1978 12.46 EB 651 11 August 1978 12.26 EB 450 28 July 1978 06.23 EB. SWS 529 2August 1978 18.37 EB. SWS 694 14August 1978 07.37 EB, SWS 1024 6 September 1978 09.18 EB, SWS 1110 12 September 1978 09.43 EB, SWS 1153 15 September 1978 09.66 EB, SWS 1196 18 September 1978 10.09 EB, SWS 1239 21 September 1978 10.21 EB, SWS 1282 24 September 1978 10.34 EB, SWS 1325 27 September 1978 10.47 EB, SWS 1368 30 September 1978 11.00 ER, SWS 1411 3 October 1978 11.12 EB, SWS 492 31 July 1978 11.28 SI 1267 23 September 1978 14.20 SI 880 27 August 1978 12.25 SwS 289 17 July 1978 11.50 SWS, MB 762 19 August 1978 06.41 SI 762 19 August 1978 06.41 SI 762 19 August 1978 06.41 SWS, MB 957 1 September 1978 21.40 SwS 1430 4 October 1978 20.42 SWS 1473 8 October 1978 00.15 SWS 547 4 August 1978 06.15 DWB, DWR, DWS, DWSM 556 4 August 1978 21.35 DWB, DWR, DWS, DWSM 599 7 August 1978 21.43 DWB, DWR, DWS, DWSM 633 10August1978 06.29 DWB, DWR, DWS 642 10August1978 21.50 DWR, DWS, DWSM 719 16 August 1978 06.43 DWB. DWR, DWS 757 18 August 1978 22.40 DWB. DWR, DWS 762 19 August 1978 06.41 DWB. DWR. DWS 791 21 August 1978 07.24 DWB, DWR, DWS, DWSM 834 24August 1978 07.30 DWB, DWR, DWS 958 1 September 1978 23.54 DWB, DWR 1006 5 September 1978 08.15 DWB. DWR. DWS 1044 8 September 1978 00.18 DWB. DWR 1049 8 September 1978 08.27 DWB. DWR, DWS 1087 11 September 1978 00.30 DWB. DWR SEASAT revolution Date Time (G.M.T.)

SAR imagingofoce&n-boztom topography 1181 ocean regions of up to 50m in depth. Examination of environmental data (winds,

gravity waves, air/sea temperature, density stratification and currents) indicates these

SAR-observed features are only present when a tidal current (04 rn/s or greater) is

flowing over the bottom and wind conditions are moderate (less than 10 m/s).

This paper first reviews the mechanisms for SAR detection of ocean-surface

patterns This SAR imaging theory is then combined with a simplified hydrodynamic theory to describe the observation of subsurface features on the SEASAT SAR English

Channel and Nantucket Shoal data sets. Numerical results from this model are

compared with the actual SEASAT SAR data and found to yield satisfactory

agreement in most cases.

2. SAR imaging mechanisms

The patterns observed on SAR images of the ocean surface are the result of a

complex set ofimaging mechanisms including real modulations and effects due to the

motion of the surface. In addition, the detectability of any given surface pattern is

influenced by the variability of the background signal, which is due to speckle as well as random surface fluctuations.

Real modulations consist of scalar variations in the small-scale and large-scale

roughness, where the length scale depends on the radar wavelength. This real

modulation represents what a 'real aperture' imaging radar or scatterometer would

observe. Small-scale roughness influences the radar return through the Bragg scatter-ing mechanism, and possibly also through specular scatterscatter-ing (Kwoh and Lake 1983)

and 'wedge scattering' from cusped waves (Lyzenga et al. 1983). There is a general consensus within the radio-oceanography community that a BraggRice scattering theory adequately explains the L-hand backscatter values obtained from the ocean

surface at intermediate incidence angles (2Q-6O). That is, the radar cross section of the surface is proportional to the wave spectral density at the wavenumber

kb=2kosinû

(I)

where kb = 2ir/L and k0 = 2ir/Ä, L and i. being the wavelengths of the surface waves and

the radar, respectively, and 6 is the incidence angle (Wright 1966). Large-scale

roughness perturbations cause a change in the Bragg scattering due to a local tilting of

the surface as well as changes in the amount of specular reflection. For the casè of internal waves and bottom topographic features, the real modulations are a result of

interactions between wind-generated surface waves and the surface currents induced by the subsurface phenomena of interest, as described in §4.

Motion effects are also a primary contributor to SAR images of the ocean surface. Ordered motions of the sea surface, such as orbital velocities and accelerations due to

gravity and internal waves, can cause velocity bunching (i.e. periodic regions of

increased and decreased image intensity) in the images (Alpers et al. 1981) as wellas

degrading the azimuth resolution of the images. A second category of motions which

are random in nature also contribute to the SAR signatures of the ocean. Random

motions cause azimuth smearing or streaking of the images (Lyzenga and Shuchman 1983). Random motions on a scale smaller than the SAR resolution may be described in terms of the coherence time or life-time of the ocean scatterers. Recall that SAR. to

achieve its high resolution, observes the ocean for a period of time (the integration

time) to generate the synthetic antenna. A moving ocean surface results in

a

perturbation of the phase of the scatterers during this time interval and this results in an altered image (Jam 1978, Alpers and Rufenach 1979, Shuchman et al. 1981).

1182 R. A. Shuchinan et al.

The third factor which contributes to the detectability of SA R-observed signatures is the background signal variability. This variability is due to both speckle and large-scale surface variations which are unrelated to the phenomenon of interest. Speckle isa

result of coherent interference effects among scatterers which are randomly distributed within each resolution cell. The speckle size is a function of the spatial resolution. The

speckle intensity can be reduced by utilizing multilook processing (or non-coherent

addition) techniques during processing of the SAR signals (Porcello etal. 1976).

Random surface variations also contribute to the background variability in SAR ocean-surface images. These large-scale variations can be a result of a number of

oceanographic phenomena including gravity waves, either well organized or random

in nature, variable wind creating patchiness on the ocean surface, rain squalls and

mesoscale features such as ocean fronts (Shuchman 1982).

3. Data description

SEASAT data collected over shoal regions of the Southern Bight of the North Sea (English Channel) and east of Nantucket Island were selected for study. Four SEASAT revolutions provide SAR coverage of the Southern Bight region of the North Sea (see figure 1), while one pass was collected over Nantucket Shoals (see figure 2). The SAR swaths(l0Okm wide) are indicated as rectangles on the figures. As indicated on table 2 (a summary of SAR data collected over the two test sites), the satellite overpasses span the time from 19 August to 8 October 1978, representing late-summer conditions in the

Channel and Nantucket Shoal area. Note from table 2 and figure 1 that revolutions

957, 1430 and 1473 have generally the same orientation (i.e. radar look direction with

respect to the Channel), while revolution 762 represents the nearly orthogonal look direction. For the Nantucket Shoals data, the radar look direction relative to the subsurface features was similar to the English Channel overpass occurring during

revolution 762.

The English Channel test site is characterized by a series of longitudinal and

transverse sand waves which are situated in water depth varying from approximalely

Revs. t3O

NPosition of NOORD-hinder Light Vessd where weather data was coltected. & - Indicates Radar Look Direction

- Indicates Radar Look Direction

Figure 2. Distribution of sand shoals and sand waves on Nantucket Shoals and Nantucket Sound. Curved lines indicate crests of sand waves; based on sounding from U.S. coast and geodetic survey (from Uchupi 1968).

-

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>--

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-.

ZoD

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r °

-ç

'::---

c'

-

.

\,, S\ ',

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yc

'-¿J, 1S4..&P40 _{-s ?-'} -. .; I o(

5s'

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U ç

¿;:

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1iWi

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Table 2. SAR System and satellite parameters for study sites. Time over Incident target channel Satellite heading SAR look direction angle, nearfar

Revolution Date Node (G.M.T.) (T°) (T°) (degrees)

English Channel 762 19 August 1978 25O2 06-30 3330 63° 20-25-2 957 1 September 1978 17205 2140 223° 313° 196-249 1430 4 October 1978 172-76 0040 223° 313° l9-6--249 1473 8 October 1978 l7226 0015 223° 313° 196-249 Nantucket Shoals 880 27 August 1978 30585 12-34 334° 640 _194-24-8

SA R imaging of ocettn-bottom topography 1183

Indicates coverage of digital data for Rev. 880

1184 R.A.Shuchnan et al.

50 to 3 m. Bathymetric contour charts of the southern and northern ends of the study

sire are presented in figures 3 and 4, respectively. The sand waves are quite clearly identifiable as elongated arcuate features with closely spaced contours surrounding

them. Closely spaced contours indicate rapid depth changes.

Figure 5 is the SEASAT digital image of the Southern Bight of the North Sea

(English Channel) test site obtained on revolution 762. The image, processed at the Jet Propulsion Laboratory (JPL), represents a 100 km x 100 km scene with a resolution of 25m x 25 m. This image is not radiometrically or geometrically corrected. Figure 6 is a detailed comparison of the radar image and the bathymetric chart of the bottom in the

test area for revolution 762. From figure 6 it can be noted that the sand waves are

visible with stronger radar returns resulting in the down current side of their crest lines. The transverse sand waves are predominantly on the gentler slope of the asymmetrical

longitudinal sand waves (or banks) and their crest lines bend around to trend

increasingly more parallel to the longitudinal sand-wave axis. Kenyon (1981) reports that at the time of this image collection a current of l-2 rn/s was flowing 20° obliquely

to the longitudinal sand waves and parallel to the orthogonal of the transverse waes.

This current, as well as other values of interest for revolution 762, are indicated on figure 6. Kenyon (1981) further noted that analysis of widescan sonar records from

near South Falls (Caston 1979) has revealed additional transverse sand waves which are not seen on the image.

The longitudinal sandbanks are tidal-built sandbanks and are one of the two main depositional faces of the off-shore tidal environment in the English Channel, the other being the off-shore sand sheet faces (Kenyon ei aI. 1979). The longitudinal sandbanks

are the largest bedforms of the southern bight of the North Sea, and can, in extreme

cases, be as much as 120km long and 30 km wide. The tidal currents passing over these

SI .S

SI.

Figure 3. Bathymetric chart of the southern end of the study site (reconstructed from British Admiralty Chart 1406).

53.5

53°

52.5°

52°

1° 1.5° 2° 2.5 3° 3.5° 4° 4.5°

Figure 4. Bathymetric chart of the northern end of the study site (reconstructed from British Admiralty Chart 37160).

Figure 5. JPL digitally processed image of SEASAT revolution 762, 19August1978. SAR imaging of ocean-bottom topograph;' 1185

C

1186 _{R. A. Shuch/nan et al.}

sandbanks are usually very strong, running between 1 and 2m/s at peak flow as

indicated in figure 6.

The transverse sand wave, also found within the English Channel data, are large

flow-transverse bedforms coupled to oscillatory boundary-layer currents of the tidal

origin (Allan J 980). These transverse sand waves are considered giant ripples with heights up to an average of 10-15m and with wavelengths of several hundreds of

metres (Lohmann 1976).

The second test site utilized in this study was Nantucket Shoal. Figure 7 is a JPL-processed digital image of the Nantucket Shoal test area. The image characteristics are

similar to figure 5. A transect line that plots radar reflectivity versus water depth in metres is presented on the figure. Also note that the frontal boundaries and internal

waves are identified on the figure. The Nantucket test area is a shoal region composed of long ridges trending generally north-westsouth-east and rising to within 5m of the

surface. The Nantucket Shoal test site is similar to the English Channel test site in

respect to having both longitudinal and transverse sand waves. Shepard ei aI. (1934) and Uchupi (1968) describe the Nantucket Shoal region as an area of glacial morainic ridging reworked by tidal currents to form a series of sand shoals (longitudinal) and sand waves (transverse). Figure 2 from Uchupi (1968) shows the distribution of sand

shoals and sand waves on Nantucket Shoals and Nantucket Sound. The shoals run many tens of kilometres in length, while the transverse sand-wave crests are up to

10km long and average 10m in height. A typical wavelength for these transverse sand

waves is approximately 400m (Stewart and Jordan 1956). One of the authors has recently (October 1984) conducted a precision hydrographic study of the northern portion of Nantucket Shoals. The results of this resurvey indicate that although the fine-scale details of the shoal bathymetry change frequently, the gross features

(location and magnitude of major bathymetric features) do remain constant within the location accuracy obtainable from the SEASAT SAR.

Table 3 summarizes the environmental conditions present in the English Channel at

the time of the four SEASAT passes as well as the conditions present at Nantucket

Shoals for the one pass. It is unfortunate that only one pass was collected

over

Nantucket Shoals but this data set is well documented with respect to the

environ-mental condition at the time of the overpass. These data, combined with the four passes

of SAR data over the English Channel, appear to be sufficient to validate the

hydrodynamic/electromagnetic model.

4. Model description

A first-order hydrodynamic,/electromagnetic numerical modelling effort was un-dertaken in order to investigate the relationship between SAR-observed sand ridges,

environmental (wind, water depth, current speed, water temperature, etc.) and

SA R-system (frequency, polarization, resolution, incident angle, look direction,

etc.) parameters necessary to image these

features. A flow chart

for the

hydrodynamic/electromagnetic model is presented in figure 8. The environmental inputs include: wind speed (m/s) and direction (degrees); initial current (m/s) and

direction (degrees); and water depth on a grid basis (m). The SAR-system parameters include: wavelength (cm); polarization (either vertical or horizontal); incidence angle (degrees), radar look angle (degrees) and resolution (m). The model first calculates the

surface current as a function of the irregular topography (changing depth), and then

considers the interaction of the (Bragg) surface waves with this current.

r, /

Om .9 rn/s

-yr

- -.--i . s.

/

--.

-rn/s OUNKEROUE Figure 6.

Comparison of radar image and chart of the seabed east of Dover Straits (Depth in metres). (The dashed lines in the chart

are recommended

1188 R. A. Shuchman et al.

Figure 7. Numerous oceanic features observed off Nantucket Island, Massachusetts, on

SEASAT revolution 880, 27 August 1978.

one-dimensional flow profile over a bottom topographic feature. To provide an initial characterization of the hydrodynamic flow conditions, two dimensionless quantities were calculated. These two numbers from open channel hydrodynamic theory were the Froude Number (Fr = u/../(gd): the ratio of the flow velocity, u, to the shallow water

a Standard meteorological convention (i.e. direction from). b In all cases, the water column

was unstratified, and no rainfall or ocean swell was present.

Direction current is flowing towards (value is near South Falls sandbank).

d Average current value for

test area.

'1 kn=0SI rn/s. -'N.A. = not applicable.

Table 3.

Environmental data recorded at the time of satellite overpass.

Revolution

Visibility

of

Winde

subsurface speed and features

direction

Waterb temp. (°C)

Air _temp. (°C)

Wave _height (m)

Period of waves (s)

Currentc _{speed and} direction

Currentd _{speed and} direction

A typical _{water depth}

Froude

at feature

number

(m) Fr=u//(g

Reynolds number Re=ud/v

762 (English Channel) Very visible 40kn 146°(T) 16.4 17 05 1 14 kn _210°(T) 16 kn _224°(T) 76 008 386x 106 957 (English Channel) Very faint 200 kn 326°(T) 16.5 15 10 4 02 kn _210°(T) 02 kn 174°(T) 12.1 0.01 877 x l0 1430 _{(English Channel)} Very faint 210 kn 315°(T) 15.5 11 10 4 l3 kn 30°(T) 19 kn _45(T) 13.1 006 617 x 106 1473 (English Channel) Moderately visible 110 kn 15°(T) 153 15 0.5 3 12 kn _210°(T) 07 kn _218°(T) 108 006 470x jØ6 880 (Nantucket Shoals) Very visible 120 kn 260°(T) 200 195 05 5 N.A.1 10 kn _200°(T) 50 007 180x106

C

1190 _{R. A. Shuchrnan et al.}

Environmental and Radar System Inputs Calculate Change in Wave

Length (Kinematic) Conservation Equation)

t

Calculate Change in Wave Height Wave (Action)

Equation)

t

Compute Radar Cross Section

t

Incorporate Speckle Noise and Generate 2-D

Simulated Image

Figure 8. Flow chart for hydrodynamic/electromagnetic model.

depth) and the Reynolds number (Re = ud/y: the ratio of inertial to viscous forces

within the flow field where r is the kinematic viscosity). Calculated values (see table 3) for each of these dimensionless numbers indicate that the flow conditions present at the

time of the SEASAT overpasses were those characteristic of turbulent-subcritical flows.

Under these conditions, the tidal flow velocity, U0 approaching the bottom feature, is less than the shallow water gravity wave phase speed given by J(gí1). Hence, small waves can propagate upstream with a speed (/(gd) - U0). Therefore, neither standing waves nor a classic hydraulic jump should be anticipated to occur over these bottom

features. All SAR-sensed surface expressions in the vicinity of these topographic

features will,therefore, most likely be attributable to a modulation of the small-scale wave field by variations in the current flow rate.

Under the conditions of subcntical open channel flow, the free surface will deform downwards directly over the bottom feature, hence decreasing the local water depth.

Conversely, the free surface will deform upwards again over the trailing edge of the feature. In response to these free surface deformations, the flow will accelerate over the leading edge of the bottom feature and decelerate to the free system velocity, U0, over the trailing edge. These lateral flow velocity gradients will produce a corresponding straining of the surface wave field as described by the kinematic wave conservation equation.

For the long, linear bottom features considered in this study, the interaction of a tidal current with the bottom may be described in terms of a simple

quasi-one-dimensional model. Under this assumption, the component of the current parallel to

t

t

Current Profile as Calculate Bragg

Function of Changing Ocean Wave Depth

SAR imaging of ocean-bottom topography ₁₁₉₁ the ridge axis is constant, i.e. none of the water is assumed to flow around the shallow

feature. Thus only the perpendicular component vanes and this component can be

calculated simply by conservation of mass.

The interaction of surface gravity waves with a variable current has been described by Hughes (1978) and Phillips (1977, 1981), among others. This interaction is described by two equations. the kinematic (or wave) conservation equation, and the wave-action (or energy) equation. The former equation may be written as

êk/ôz + V(co + kV) = 0 (2)

where k is the wavenumber, w=.J(gk) is the radian frequency of the ocean surface wave and V is the current velocity. In the steadystate case, the first term (i.e. the time derivative) may be ignored. If the current variations are one dimensional,_{as asumed} above, the solution of this equation is simply

w+k1'=w0+k0Ç0

(3)

k70 (4)

where _{k and}k _{are the wavenumber components perpendicular and parallel to the}

ridge, respectively, and

k0, k0

are their values in the constant-current region away

from the ridge. These equations express the changes in the wavelength and direction of a wave entering a variable current.

In order to calculate the radar cross section using the Bragg scattering model, it is necessary to obtain the wave spectral density at the Bragg wavenumber_kbas given in equation (1). Therefore, at each point in the scene, equations(3)and (4) are first solved for

k0

and

k0,

that is, the initial wavelength and direction of the wave which becomes

the Bragg wave at the point considered. The second step is then to follow this _wave train through the current pattern and to compute the changes in wave amplitude or

spectral density along this path.

The changes in wave amplitude are described by the wave-action equation, which may be written (following Hughes 1978) as

+(V+ôw/3k)V4=ß4)(l -4)/4))

(5)

where4)= çli/w is the wave-action spectrum, /i(k) is the wave-height spectrum, ß is a

wave growth/relaxation parameter related to the wind speed and direction and

_{4, is}

the equilibrium spectrum for the given wind conditions. Large uncertainties exist with regard to the correct value of the wave growth/relaxation rate ß. Measurements of this parameter have been reviewed by Hughes (1978) and fit by the expression

ß =(cou/c)cos 0{00l + 0.016(u*/c)Jcos O} { I exp

_{[- 89(u/c_0.03)2]}}

₍₆₎ where u' is the friction velocity, c is the wave phase speed and O is the anglebetween the wind and wave propagation directions. This equation was used for calculating ß in the present study, assuming the friction velocity to be 1/30 of the wind speed reported in table3.

Equation (5) was solved numerically by following each wave train through the current pattern, beginning in an undisturbed region where the background _wave

spectral density was assumed to be given by Phillips' spectrum, i.e.

1192 R. A. Shuchthan et al.

where k0 is the initial wavenumber, as discussed above. At each point along the wave

path, the changes in wavelength and direction are computed from equations (3) and

(4), and the appropriate values are substituted in equation (5), which is then solved for the wave spectral density.

As an example, consider the case of a wave field being carried by a current over a ridge in the bottom. As the wave propagates into a region of increasing current (i e. as it approaches the ridge), it is elongated and the amplitude is decreased. After the wave passes the shallowest point, the current then decreases and the waves become shorter

and of higher amplitude. Neglecting wave growth/relaxation effects, the amplitude

would return to the original value resulting in only a dark band over the ridge.

However, if these wave growth/relaxation effects are present, the wave amplitude

relaxes towards the equilibrium value in the divergence region and overshoots' beyond

the initial value in the convergence region, resulting in regions of both lesser and

greater wave height or surface roughness than the background value.

The wave-height spectral densities obtained from this model were used to compute changes in the radar cross section of the surface, assuming a Bragg scattering model as described in §2. That is, the radar cross section is assumed to be proportional to l'(kb), where kb is the Bragg wavenumber. The effects of speckle are incorporated by choosing

a random number from the appropriate distribution function (see, for example,

Porcello et al. 1976) whose mean value is equal to the calculated radar cross section. This process is repeated for each resolution cell to form a two-dimensional image, or a one-dimensional plot through the feature.

5. Model results and erification

Quantitative results of the ERIM model were compared with a series of relative radar backscatter measurements made from digital and optical data from the four SEASAT SAR English Channel revolutions and one Nantucket Shoals orbit. The backscatter measurements were made at the output plane of the ERIM optical SAR

processor using an optical probe; thus, the effects of recording the radar data on film could be neglected. Recall the compressed SAR signals on processed output film are limited to approximately 18 dB, while the signal film in its uncompressed form retains the full dynamic range of the SEASAT system.

In addition to the optical measurement, the digital data for revolutions 762 and 880

were also analysed. The digital data were averaged to obtain backscatter values

representing the same area as the optical probe.

Three locations within the English Channel were selected for detailed study (i.e.

comparison with modelled results). The English Channel test sites included South Falls

and Sandettie Sand Banks (see figure 6 for location) and a series of transverse sand waves resting in approximately 32 m of water, the wave crests of which are aligned

perpendicularly to Sandettie Bank. The transverse sand waves have a wavelength of

approximately 400m and amplitude of 65m with the crests of the sand waves

approximately 25 m below the water surface.

The locations for detailed study of the Nantucket Shoals test area are indicated on figure 7 as the letters A and B. The letter A represents a sand shoal, while letter B is a region of transverse sand waves.

Figure 9 shows the optically generated 25 km quarter swath images for the four

revolutions of the English Channel and also indicates the location of an optical scan

made over the vicinity of South Falls (IA). Note the optical images confirm that the

N

I

REV. 762

SA R imaging of ocen-botiom topography

2A a) C i) C N REV. 1473 1193 REV. 1430 _{REV. 957}

Figure 9. SAR imagery of the English Channel showing the locations of backscatter

measurements made over South Falls and Sandettie Banks (azimuth is horizontal).

and not visible (or very faintly visible) on revolutions 1430 and 957. Also shown on the

figure are the locations of optical scans (2A) made over the Sandettie Bank. The

location of the transverse sand-wave measurement is indicated as the letter 3A. Recall

the SAR-system and environment parameters for these four revolutions are

sum-marized in table 3.

A simulated SAR image of South Falls revolution 762 is presented in figure 10. In

this figure the computer-generated grey map represents an area of 25 km x 25 km where each value (pixel) represents 20m x 20m. As presented on the legend of the

figure, each symbol on the grey map represents a 05dB signal level. Figure II

represents the idealized cross section of South Falls at the time of satellite overpass which was modelled. The reflectivity map presented in figure lO demonstrates the

capability of the model to provide a two-dimensional, simulated SAR image as output. Table 4 summarizes the modelled versus actual SAR backscatter values, for which

the change in the o value across the bottom feature is given. Both the optically and

digitally extracted backscatter values are presented in Table 4. These optical and digital values differed by less than 05 dB. Note that the table gives relative backscatter values, and thus the problem of absolute calibration is avoided.

a)

1194 R. A. Shuchnian et al. 2.5 Km (AilmtI,} O Tr -n fl -s.O T b.5 TO -7 0V -7fl T -i -7.5 10 V.3 1V 7 -IO (74 lA

iiI

ti 30.6 n

3Tmy

I 1000m 1.-j WiND 146e 4 knots SURFACE CURRENT L4 knots 20 (T) SEA LEVEL

Figure 11. Idealized cross section of South Falls, SEASAT revolution 762.

Figure lO. Modelled backscatter map for revolution 762 showing good visibility of South Falls.

VSAR

imaging of ocem-bozzom topography ₁₁₉₅ Table 4. _{Comparison between modelled and actual SAR backscatter values.}

f Indicates SEASAT SAR backscatter value was obtained from digital data. Note actual

measurements are relative backscatter; they have been normalized toaverage model value.

Examination of the South Falls case reveals a model prediction of backscatter

variations of 03 and 07dB for revolutions 957 and 1430, respectively. The SEASAT images for these revolutions showed very faint or invisible features near South Falls, and the optical measurements yielded no measurable change in radar cross section over the ridge. For revolution 1473, the model predicted_{a backscatter variation of 11 dB} over South Falls and the empirical measurements showed a variation of about 25dB

across the ridge. The image for this revolution shows a clearly identifiable feature corresponding to South Falls, although the feature is less distinct than _{in revolution}

762. The fact that the measured decrease in the radar return is larger in magnitude than the model result, while the measured increase is about the same, appears to indicate that the actual wind growth/relaxation effect was smaller than that incorporated in the model. It should be noted that there is a wide disparity in measurements of the wind growth/relative rate, and the mechanisms governing this process are not completely understood at the present time.

To validate the model further, the digital SAR data from revolution _{762 was}

compared in detail with the model results. Figure 12 represents a one-dimensional slice of model results compared with the actual SAR digital backscatter values of the same area. On the figures, the solid lines indicate the radar cross section calculated from the

model, while the dotted line is the relative radar cross section obtained from the digitally processed SEASAT SAR data. Comparisons between model and actual

values for the South Fall Bank and transverse waves corresponding to revolution 762

Revolution

Subsurface feature

EM model results (dB) _{backscatter values (dB)}Actual SEASAT SAR

Min. Max. Min. cc Max. e0 Aa0

762 South Falls

27

F3 40

24

14

38t

22

1.1 33 957 South Falls

02

01 03 0-0 0-0 00 1430 South Falls

04

03 07 00 00 00 1473 South Falls

06

05

II

F7

09 26 762 Transverse sand waves

24

F3 37

23

l-6 _3-9t 762 Sandettie 00 00 00

31

20

_51t

Sand Bank 957 Sandettie 00 01 01 OE2 01 03 Sand Bank 1430 Sandettie 0-0 00 ØØ 03 ₀₃ OE6 Sand Bank 1473 _Sandettie

05

_{04 09}

08

_{1-1 19} Sand Bank 880 Location A

09

08 17

09

15

24t

(longitudinal sand) 880 Location B 26 20 46

1-8

48

46t

(transverse sand waves)

1196 R. A.Shuchínan et al.

actual SAR values

- model results r.I SOUTH FALLS _\

/\

'--.' w - o-0; e CD

D'

TRANSVERSE SAND WAVES LJ

D

_Q'

e C, e e C.'. a.' 0.0 0.8 .6 2.4 DISTRNCE(K11) 3.2 91 2Ó.00 40 00 6000 80.00 100D0 20.00 DIS1flNE (KM)

Figure 12. Model versus actual back.scatter cross section for revolution 762 South Falls and transverse sand waves case. Note the model predicts no backscatter change for Sandettie Sand Bank.

environmental conditions are presented on the figure. The comparison between model and actual data is quite good for both South Falls and the transverse waves case. The model and actual SAR backscatter are within 10 dB of each other everywhere on the two graphs. The sharp peak in the transverse sand-wave case is predicted by the model, and is a result of wind direction with respect to the ridge and the current.

The hydrodynamic model predicted no change in radar cross section over the

Sandettie Sand Bank for the revolution 762 case, where the bank is aligned in the

cross-track direction. The fact that this feature was observed, with approximately a 5 dB

change in backscatter, appears to indicate an additional mechanism not incorporated

in the model, such as possible wave breaking or other non-linear effects. Modelled

results over the Sandettie test site for revolutions 957 and 1473 were in better

agreement with actual SAR values (to within 10dB).

The Nantucket Shoal test, using locations A and B as presented earlier, both produced favourable comparisons between the model and actual SAR backscatter

values. As indicated in table 4, both modelled test mean values agreed to within 0-2 dB of the actual SAR backscatter measurements.

SA R imaging of ocean-bottom topography 1197

Model limitations

The hydrodynamic/electromagnetic model was exercised for three locations within

the English Channel test site and two locations within the Nantucket Shoals area.

Table 4 summarized the comparison between the modelled and actual backscatter

values. As presented earlier, the modelled results compare favourably with the actual SEASAT SAR values.

The notable exception to the favourable comparison was the Sandettie Sand Bank

test site for revolution 762. Recall from figures 1, 5 and 6 that Sandettie Bank, as

imaged during orbit762,is aligned along the radar line of sight. The model used in this

study predicts no change in the component of the current along the direction of _the

bank, and therefore no change in the wave spectral density for wave propagating in this direction.

The apparent failure of the model for this feature may be due to several reasons, including the following: (i) the simple current model may not be adequate for this case, and there may actually be changes in the current along the ridge, (ii) the fact that the

ridge is not smooth, i.e. there are numerous transverse sand waves along the ridge which are actually responsible for the observed image variations and (iii) the radar

return is influenced by surface waves travelling in other directions, either through non-linear hydrodynamic effects or non-Bragg scattering mechanisms.

The model sensitivity to the relative current direction, topographic feature

orientation, wind direction and radar look direction is illustrated in figure 13. In figure

13 the change in backscatter (AirO) for the South Falls Bank (rev. 762)case is plotted as

the radar look direction is varied. Note from the figure that the model predicts a

maximum change in backscatter results when the radar is looking approximately

perpendicular to the ridge. Also note that the model predicts a very small backscatter change when the radar looks parallel to the ridge, as was the situation for the Sandettie Sand Bank case.

Summary and conclusions

A numerical modelling effort that included hydrodynamic and electromagnetic

effects has been undertaken for the purpose of explaining and quantifying SEASAT SAR backscatter signatures that relate to the bottom topography of the oceans. Large quantities of SEASAT SAR imagery have been reviewed revealing the existence of surface expressions of subsurface features on many passes of imagery. The most vivid of these cases are those surface expressions associated with shoal regions (50m and less

water depth) east of Nantucket Island and the Southern Bight of the North _Sea

(English Channel). Both these regions, characterized by shallow, subaqueous banks and sand waves, were studied as part of this modelling effort.

The hydrodynamic model developed and utilized within this study embodies the interactionof_{a tidal current with the bottom features and the interaction of the surface}

Bragg waves with the current variations. The hydrodynamic model utilizes as inputs

environmental data (wind, waves, currents, depth, tides and density stratification) coincident with the SAR data collection and predicts as output the change in the

small-scale roughness (i.e. Bragg wave amplitude) of the ocean surface.

The results from the hydrodynamic model were used in an SAR reflectivity model to generate SAR reflectivity grey maps of images showing varying degrees of bottom features. The results of the combined model were compared with actual SEASAT

imagery of the test sites and found to compare well in all cases, except for the case of a linear feature aligned in the SAR look direction.

The success of this model suggests that Bragg scattering is indeed the primary

scattering mechanism for the SEASAT SAR operating conditions, and that variations in surface reflectivity as observed by this sensor can be predicted to first order by linear hydrodynamic theory. The failure of the model in the aforementioned case appears to imply that either non-linear hydrodynamic effects or non-Bragg scattering effects can be important in certain situations, however.

Based upon the results of this investigation, the following conclusions can be made regarding the environmental conditions required for visibility of bottom topographic features in SAR imagery. These conditions may be stated as follows:

A tidal current of at least 040 rn/s (OE8Okn) must be present.

A wind of at least I rn/s (2kn), but not greater than 7.5 rn/s (l5kn) must be

present, with at least some component in the radar range direction.

These conclusions have been reached on the basis of the model as presently developed and as applied to relatively distinctive shallow bottom features in the English Channel

C 1198 R. A. Shuchrnan et al. 6 Looking -L to Ridge 5 Note: Ridge is oriented lS true 4 < 3 _{Rev. 762} Look Direction 2 Looki ng Along Ridge O 30 50 70 90 110 130 150 170 190 210

RADAR LOOK DIRECTION (DEGREES TRUE)

Figure 13. Maximum backscatter change versus look direction for South Falls as predicted by the model for conditions occurring during SEASAT revolution 762.

SAR imaging 'of ocean-bottom topography ₁₁₉₉ and Nantucket Shoals. The actual limits on the current and wind may be different for

other geographical locations, and could be further refined by_{more extensive model}

development and verification.

Acknowledgments

The work reported in this paper was performed at the Environmental_Research

Institute of Michigan (ERIM) under contract in part to four government agencies. The

agencies and the technical monitors include: Office of Naval Research (Mr. _Hans Dolezalek), Defense Mapping Agency/Naval Research Laboratory

(Dr. James

Hammack and Mr. Peter Mitchell), National Oceanic and Atmospheric tion (Mr. John W. Sherman, III) and the National Aeronautics and Space

Administra-tion (Drs. Lawrence McGoldrick and William Patzert). The contract numbers for

these funded research activities are: ONR Contract N000 14-81-C-2254, ONR (NASA) Contract N00014-8 1-C-0692 and NOAA/NASA SEASAT Announcement of Oppor-tunity Contract MO-A0l-78-00-4339.

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