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Wave direction estimates in coastal waters using radar
Coastal Engineering, 3 (1980) 249--267 O Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
249
WAVE DIRECTION ESTIMATES IN COASTAL WATERS USING RADAR
A.D. HEATHERSHAW, M.W.L. BLACKLEY and P.J. HARDCASTLE
Institute o f Oceanographic Sciences, Taunton, TA 1 2DW (Great Britain) (Received March 6, 1979; revised version accepted November 12, 1979)
ABSTRACT Heathershaw, A.D., Blackley, M.W.L. and Hardcastle, P.J., 1980. Wave direction estimates in coastal waters using radar. Coastal Eng., 3: 249--267. This paper describes the use of a conventional X-band radar in determining wave direction characteristics in coastal waters. It is shown that under suitable environmental conditions it is possible to determine a mean wave direction to within an estimated ± 2° and to observe wave refraction and diffraction processes in the vicinity o f harbours and on open coastlines. It is also shown that the radar may be used to estimate wave periods and the use o f the radar in determining the "annual" wave direction characteristics for a specific location is discussed. Examples of radar imagery are given together with technical details of the radar installations and equipment. Experience in the use of the radar at different sites and on different range settings suggests that the o p t i m u m height for the scanner, in this particular application, is in the range 15--20 m above mean sea level. Observations with the radar have been made simultaneously with measurements of the wave height, wave period and wind speed. It has thus been possible to establish some lower limits for the detection of swell waves by radar. In particular it has been found that about 80% of the waves not seen by the radar occur at wind speeds of less than 5 m s-1 and have significant wave heights of less than 1 m. These results are discussed in relation to the mechanism of wind wave generation and Bragg scattering from the sea surface. INTRODUCTION
Estimates o f wave direction are frequently required in m a n y coastal engineering problems. Semi-empirical methods of calculating littoral drift require this information as do studies in harbour design and location. In addition, this t y p e of information may assist in the planning o f ship and boat operations. In this article the use of radar to study wave direction in the vicinity of a large tidal harbour is described. Comparisons are also made with similar observations on an open coast. It is shown that despite a number o f obvious limitations, radar can provide a simple and effective means of studying wave direction in coastal waters, and under certain conditions can also provide information on wave period.
250 EQUIPMENT AND METHODS B e t w e e n O c t o b e r 1 9 7 6 and N o v e m b e r 1977 t h e I n s t i t u t e o f O c e a n o g r a p h i c Sciences o p e r a t e d a r a d a r i n s t a l l a t i o n at t h e end o f t h e s o u t h e r n b r e a k w a t e r at Port T a l b o t , S o u t h Wales (Fig. 1). T h e p u r p o s e o f t h e s e o b s e r v a t i o n s was to o b t a i n i n f o r m a t i o n on wave d i r e c t i o n t o b e used in c o n n e c t i o n w i t h b e a c h e r o s i o n studies o n t h e f o r e s h o r e near P o r t T a l b o t (Carr et al., 1977). A similar i n s t a l l a t i o n h a d b e e n o p e r a t e d p r e v i o u s l y b y t h e I n s t i t u t e in S t a r t Bay, D e v o n (Fig. 1) b e t w e e n A u g u s t 1 9 7 2 a n d J u n e 1974.
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Fig. 1. Location map showing the positions of the radar installation at Port Talbot and in Start Bay. The positions of wave recorders in relation to the radar at Port Talbot are also shown. Previous w o r k (e.g. O u d s h o o r n , 1 9 6 1 ) has established t h a t f o r a r a d a r t o be used in this p a r t i c u l a r a p p l i c a t i o n it is n e c e s s a r y f o r it t o o p e r a t e in t h e 3 c m or 8 m m b a n d (see f u r t h e r discussion), w i t h a pulse length o f less t h a n 0.1 Us a n d a h o r i z o n t a l aerial b e a m w i d t h o f 1 ° or less. T h e s e f a c t o r s a f f e c t t h e resolution a n d d e t e r m i n e t h e s h o r t e s t sea w a v e l e n g t h t h a t can be resolved. Because o f c o s t a n d w a v e l e n g t h c o n s i d e r a t i o n s , a 3.2 c m ( X - b a n d ) D e c c a T y p e 9 1 9 River R a d a r was selected. T h e s c a n n e r has a h o r i z o n t a l b e a m w i d t h o f 0.8 ° and r o t a t e s at 28 r p m . T h e r a d a r n o r m a l l y has a t r a n s m i t t e d pulse length o f 0.05 .us on d i s p l a y ranges u p t o 2 k m . M o d i f i c a t i o n s a l l o w e d this pulse length t o b e used u p t o t h e 8 k m range. T h e pulse r e p e t i t i o n r a t e is 3 4 0 0 per
251 second with a peak pow er of 3 kW and mean power o f 0.5 W. This gives a range resolving p o w e r of a b o u t 8 m and angular resolving power of 14 m at 1 km range. Although the o p t i m u m height for the scanner has n o t been determined, it has been f o u n d th at t he minimum for successful operation is about 10 m above mean sea level (MSL). As the height is raised so t h e reflection o f signals f r o m distant waves increases. However, experience with a similar radar installation at Mumbles in 1975 (Fig. 1) has shown that 50 m above MSL is t oo high f o r a radar o f this t y p e and results in a complete loss of the radar image. Experience with the radar at Port Talbot suggests that the o p t i m u m height for the scanner is probably in t he range 15--20 m above MSL. Details o f the installation at Port Talbot are shown schematically in Fig. 2. The radar aerial was m o u n t e d on a 6 m tubular-steel t ow er bolted to a concrete base, giving it a height above MSL of a pp roxi m at el y 14 m. In Start Bay a smaller tower was used t o m o u n t the aerial on the edge of a cliff at a height o f a p p r o x imately 16 m above MSL. In bot h cases the recording e q u i p m e n t was located nearby in a small hut. Radar Scanner steel tower
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Fig. 2. Schematic diagram of the radar :installation at Port Talbot showing the relative height of the scanner with respect to High and Low Water Springs (HWS and LWS) and Mean Sea Level (MSL). An Autocamera Mk 3 instrumentation camera was fitted and so arranged as to automatically phot ogr a ph one complete sweep of the display tube every three hours. B o th radar and camera were operated from 24 volt lead-acid batteries which needed recharging m ont hl y. For collecting information on nearshore wave direction characteristics at Port Talbot, the radar was operated on a 2 km range. However, at Start Bay the o p p o r t u n i t y was taken to experiment with different ranges: 1.6 km was used f o r nearshore wave direction and a 4.0 km range was used for investigating wave refraction effects. At b o t h sites wave recorders were located near the radar installations. At
252 Port Talbot a single cabled-in frequency-modulated (FM), seabed-pressure wave recorder was used and located approximately 1.5 km from the radar (see Fig. 1). In Start Bay, a similar type of recorder was used, one on either side of the radar, at distances of 2.8 and 1.2 km N and S respectively. It has thus been possible to compare the radar pictures with wave data collected at or about the same time. Information on the local wind speed (W) and direction at both sites was also available for these analyses. BRAGG RESONANT SCATTERING AND THE RELATION BETWEEN RADAR IMAGES AND SEA WAVES During the past t w e n t y years or so there have been considerable theoretical and technical developments in the use of radar to study the sea's surface. It is beyond the scope o f this paper to review this work in full. However, excellent summaries of recent developments in this field may be found, for example, in papers by Plant {1977), Graf et al. {1977), Elachi and Brown (1977), Elachi (1978) and Wright (1978). To explain how radar images sea waves it is necessary to consider two related aspects of the interaction between electromagnetic waves and the waves which form on the sea-surface. These are: (a) the mechanism whereby radar signals are reflected from the sea's surface; and (b) the relation between radar images of the waves and the waves themselves. Crombie (1955) observed discrete lines in the frequency spectrum of high frequency (10 MHz) radar signals scattered from the sea-surface and correctly hypothesized that these occurred as a result of a resonant interaction with surface gravity waves whose wavelength was precisely one half of the electromagnetic wavelength, that is about 15 m. This p h e n o m e n o n was demonstrated conclusively in laboratory experiments by Wright (1966) using microwave radar, although in this case the resonant interaction was with much shorter wavelengths. It is now generally believed (see e.g., Plant, 1977) that this mechanism, Bragg resonant scattering, is the means whereby coherent radar returns are obtained from the sea-surface. Bragg resonant scattering from an equally spaced array of point scatterers (Fig. 3) occurs when the path length differences are an integral number of half wavelengths of the radar. If the wavelength of the radar is LR then the distance L between scatterers will therefore be given by:
nLR
L-2sin0,n=l,
2 .....
(1)
where 0 is the angle of incidence (Fig. 3). For an X-band radar used at low grazing angles (i.e. 0 -* 90 °, and for the first-order Bragg scattering, i.e. n = 1, LR ~ 3.2 cm and therefore L = 1.6 cm. This suggests that the scatterers are
253
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Fig. 3. Schematic diagram showing (a) the Bragg scattering mechanism for capillary waves superimposed on a long period swell and (b) the azimuthal dependence of the radar return. e is the angle of incidence and ~ the azimuth of the radar beam.
small wavelets or capillary waves of wavelengths L ~" 1.6 cm. The first point (a) therefore is that at low grazing angles coherent radar returns from the sea surface are almost certainly provided b y a Bragg scattering mechanism. The a m o u n t o f energy in a radar signal reflected from the sea-surface is usually measured (see Guinard et al., 1971; Daley, 1973) in terms of a scattering coefficient a0 (sometimes referred to as the normalized radar scattering cross section) defined by: Oo
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where R incident Early ied with
4 n R 2 (Ps/Pi)
(2)
is the range to the scattering surface, Ps and ~ are the scattered and powers, respectively, and A is the area illuminated b y the radar. work with radar concentrated on determining the w a y in which a0 varsea-surface roughness and wind speed (W). In particular the earlier,
254 a n d m o r e r e c e n t w o r k ( J o n e s e t al., 1 9 7 7 ) , h a s s h o w n t h a t f o r a g i v e n p o l a r i z a t i o n o f t h e r a d a r s i g n a l a n d a n g l e o f i n c i d e n c e 0, o0 e x h i b i t s a c o m p l e x p o w e r - l a w d e p e n d e n c e . F o r e x a m p l e i t h a s b e e n s h o w n ( s e e G u i n a r d e t al., 1 9 7 1 ) t h a t f o r a n a n g l e o f i n c i d e n c e o f 3 0 °, o0 v a r i e s as W 3 f o r W < 5 m s -1 and W 1/2 f o r W > 5 m s -1 . I n n e i t h e r t h e e a r l y n o r m o r e r e c e n t w o r k d o l o c a l v a r i a t i o n s in t h e s c a t t e r i n g c r o s s s e c t i o n a0 a p p e a r t o h a v e b e e n e x t e n s i v e l y studied. N
Range 2 km Waves: Height
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Fig. 4. Typical radar images of the sea-surface in the vicinity of Port Talbot. Note that waves have been detected arriving well inshore at the beach and that there is considerable wave diffraction inside the harbour. Values of the significant wave height (Hs) and zero crossing period (Tz), at the time the radar images were recorded, are also shown.
255
However, it is precisely these variations which lead us to point (b); that is the relation between the radar image (see Figs. 4 and 5) and the sea-surface itself. The radar image is a two-dimensional presentation o f local variations in the scattering cross section (o0) of the sea-surface and, as pointed out by Elachi and Brown (1977) and Plant (1977), there are at least three modulating mechanisms which might lead to a localization of Bragg scatterers on swell waves and perhaps explain how radar images these features. These are: (1) tilt modulation in which the angle of incidence o f the radar wave with the capillary wave varies according to its position on the longer period swell wave;
Range 1-6 km
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(~ Fig. 5. Typical radar images obtained from the Start Bay radar installation showing the two dominant directions of wave approach (a) from the NE and (b) from the SE.. Note that on the larger range setting (b) it is possible to see the effects of wave refraction.
256
(2) a roughness modulation in which the wavelength of the capillary wave varies according to position on the swell wave; (3) modulation effects due to the orbital velocity of the swell waves which lead to doppler shift effects and defocussing of the image. In addition there will be some modulation of the capillary waves by tidal currents and in practice we may expect the reflected signal to exhibit all these modulation effects although Bragg scattering provides the fundamental resonant interaction between the radar signal and the capillary waves on the sea's surface. The importance of tilt modulation in the case of a horizontally polarised radar at low grazing angle (which is the type used here) has been demonstrated by Guinard et al. (1971) who showed that the reflected signal levels could only be explained theoretically by introducing a tilting of the sea-surface, in other words by introducing swell in an ad hoc manner. It is worth noting that this is a requirement which arises without the need to explain the radar images of the sea waves. Recent laboratory work by Lee (1977) has shown t h a t capillary waves tend to become localised on the crests of swell waves, their amplitude reaching a m a x i m u m in this position, with virtually no radar signal being reflected from the troughs where the capillary wave amplitude is greatly diminished. Earlier evidence for this was provided by Keller and Wright (1975). This mechanism would certainly explain our observations (Figs. 4 and 5b) where it is clear t h a t the radar successfully images the waves from behind as well as from in front thereby discounting localisation of capillary waves 6n the forward facing slopes. However, it is likely that the mechanism is considerably more complex than this and as pointed out by Elachi and Brown (1977), radar imagery of the ocean is a comparatively new field of research and much more work is required before the content of the radar image is fully understood. In the light of this evidence, therefore, it does n o t seem unreasonable to assume that the radar images the wave crests. However, it should be borne in mind t h a t Bragg resonant scattering will be strongest from those parts of the wave field where the radar beam is parallel to the direction of ripple propagation (Fig. 3) and that the radar system imposes a filter which is not only frequency dependent, that is it selects capillary wavelengths given by eq. 1, but t h a t it also has a directional dependence. Since the direction of ripple propagation and that of the underlying swell may be different, it is clear that the latter may be very complex and, in the absence of more precise information on the directional characteristics of the swell waves and capillary waves, may n o t be determinable. Despite these uncertainties however, it appears in practice (Figs. 4 and 5) that the directional response is approximately cosine so that, referring to Fig. 3, the wave-like pattern is most clearly revealed when the radar beam is parallel to the direction of wave propagation (i.e. ~ = 0 ° or + 180 ° ) with the least coherent image being obtained when the radar beam is parallel to the wave crests (i.e. ~ = + 90°).
257 INTERPRETATION OF RADAR IMAGES
Typical radar images of the sea-surface from the Port Talbot and Start Bay sites are shown in Figs. 4 and 5. For the Port Talbot site values of the significant wave height (Hs), zero crossing period (Tz), mean wave direction, wind direction and wind speed, are also shown. Wave direction was measured from the radar images with a protractor. It is interesting to note in these pictures the presence of considerable wave diffraction inside the harbour and that waves have been detected arriving well inshore at the beach to the north of the tidal harbour; the radar is thus able to "see" the backs as well as the fronts of the waves. However, it should be noted that the radar does not see the waves when the radar beam is parallel with the wave crests. For a good radar image of the sea-surface to be obtained using a low-grazing angle microwave radar, it is necessary that small wavelets or capillary waves having wavelengths comparable with that of the radar, be superimposed on wave and swell trains (see previous discussion). Wavelets are usually generated by local winds and there is thus the possibility that swell may be present and yet remain undetected by the radar. In fact, in this work we have found that during periods of calm or settled weather, swell in excess of 1 m with periods o f about 10s could on occasions be measured on a wave recorder and yet n o t be observed on the radar (see later discussion). However, these are comparatively rare events. Whether the radar will detect swell waves or not is therefore governed by the presence of capillary waves on the underlying swell. A detailed analysis of the radar images from the Port Talbot site has shown that on 952 occasions when waves were measured on the wave recorder (see Fig. 1) a wave pattern could n o t be detected on the radar for some 24.26% of the time (231 occasions). Observations during periods of rain were excluded from this analysis. The annual wind and wave climate for the area (see Figs. 6 and 7) shows that for 25% of the time significant wave heights (/-its) and wind speeds (W) are less than 0.25 m and 4 m s -1 respectively. However, it is wrong to think of these as lower limits to the detection of sea waves by radar in this particular application. Firstly there is no clear " c u t - o f f " in terms of wind speed and wave height and clearly there is some danger in using a single fractile estimate in this manner because it does not indicate how those waves which were not detected by the radar were distributed in terms of wave height and wind speed. Therefore we have attempted to look directly at the correlation between the observed waves and the meteorological data. Figure 8 shows the results of this analysis and indicates that there is a progressive increase in the number o f waves n o t detected by the radar as both windspeed and wave height decrease to zero so that of the waves not detected by the radar some 80% had significant wave heights less than 1 m and occurred at wind speeds of less than 5 m s-1.
258 20Offshol e
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Fig. 6. Percentage exceedance curve for significant wave height (Hs) measured at Port Talbot over a period o f 1 year (after F o r t n u m and Hardcastle, 1979). Fig. 7. Annual s u m m a r y of w i n d speed and direction characteristics at Port Talbot.
The fairly rapid increase in the number of waves not detected by the radar at wind speeds less than about 5--7 m s -1 may occur as a result of the scattering cross section a0 changing to a higher power-law dependence at lower wind speeds in the manner described b y Guinard et al. ( 1 9 7 1 ) (see previous discussion). Details o f the wave conditions at Port Talbot during those periods when radar observations were made are shown in Fig. 9. This shows the expected bias o f the radar towards higher waves, by virtue of their being associated with higher winds, and also suggests that wave steepness may be important in determining whether they will reflect radar signals or not. In Fig. 9 lines of constant wave steepness have been plotted to include shallow-water effects, where the steepness s has been taken as the ratio of significant wave height Hs to the wavelength L which in terms o f the zero crossing period Tz may be expressed as: s = T z [ ( g L / 2 ~ ) Hstanh (2n h / L ) ] ,/2
(3)
Here g is the acceleration due to gravity and h the mean depth which for these calculations has been taken as 12 m. For deep water waves this reduces to the usual expression (see Battjes, 1972) s = 2n H s / g Tz 2 .
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Fig. 9. Scatter plot of measured significant wave heights (Hs) and zero crossing periods (Tz) for the data shown in Fig. 8. Solid contours represent the recorded waves and broken contours represent those waves "seen" by the radar. Curves indicating wave steepness and calculated using eq. 3 are also shown. D u e t o shoaling e f f e c t s t h e m e a s u r e d w a v e heights s h o w n in Figs. 6, 8 a n d 9 s h o u l d b e increased b y a b o u t 10% t o o b t a i n the heights o f the waves seaward o f t h e radar; h o w e v e r this c o r r e c t i o n is c o n s i d e r e d s u f f i c i e n t l y small t o be n e g l e c t e d in this case. T w o m e t h o d s o f a n a l y z i n g t h e r a d a r images f o r w a v e d i r e c t i o n h a v e b e e n e m p l o y e d in this s t u d y . T h e first o f t h e s e enables r a p i d i n t e r p r e t a t i o n t o be carried o u t . E a c h f r a m e o f the d e v e l o p e d film was v i e w e d o n an enlarger a n d t h e angle b e t w e e n the d o m i n a n t w a v e c r e s t d i r e c t i o n (at a p o i n t a p p r o x i m a t e l y 1 k m s e a w a r d o f t h e radar) and a h e a d e r m a r k m e a s u r e d w i t h a p r o t r a c t o r t o w i t h i n an e s t i m a t e d + 5 ° , or b e t t e r , d e t e r m i n e d b y r e p e a t e d m e a s u r e m e n t w i t h d i f f e r e n t o p e r a t o r s . T h e m e a s u r e m e n t on a n y o n e i m a g e can be rep e a t e d several t i m e s t o o b t a i n a n average direction. T h e s e c o n d m e t h o d , w h i c h is less subjective t h a n t h e first, and w h i c h pror i d e s useful a d d i t i o n a l data, consists o f dividing a s e c t i o n o f an enlarged image i n t o 50 e l e m e n t s (Fig. 10); a line is t h e n d r a w n in e a c h square c o r r e s p o n d i n g t o t h e o r i e n t a t i o n o f an a c t u a l wave c r e s t w h e r e o n l y o n e is p r e s e n t and well d e f i n e d , or t h e e s t i m a t e d m e a n o r i e n t a t i o n o f a w a v e c r e s t w h e r e o n e or m o r e c o m p l e t e or i n c o m p l e t e images are p r e s e n t . T h e p o s i t i o n c o o r d i n a t e s o f t h e s e
261
P o s i t iq Radar
id
Fig. 10. 2 × 1 k m grid used in determining wave direction c h a r a c t e r i s t i c s at P o r t T a l b o t . The lines in each s q u a r e are e x a m p l e s o f f i t t e d o r actual wave crests.
lines are then recorded using a D-MAC digitising table and the mean of the 50 uniformly distributed direction estimates calculated together with the standard deviation, skewness and kurtosis. This procedure was carried out 23 times on the same image by different operators and the results of such an analysis are shown in Table I. This method has been tested with three different operators who have been found to agree to within _+ 3 ° on mean direction. This method can of course only be applied where it is known t h a t a single mean direction for the waves is applicable (i.e. there is no refraction or diffraction within the area of the grid). The results in Table I suggest t h a t this is the case for the particular record shown, with the 50 estimates of wave direction being distributed r a n d o m l y about each mean giving in most cases skewness and kurtosis values close to 0 and 3 respectively, i.e. the values for a Gaussian distribution. The variation of wave direction in each grid element (which to some extent is a combination o f actual variation and h u m a n error) is indicated by the standard deviation. Taking a value of +- 2 standard deviations (which should include approximately 95% of the variation) it can be shown that the ~pread is of the order of ± 10 ° . However, assuming that samples are drawn from the same population, the sampling variability o f each mean direction estimate is given by its standard error (Table I); this gives 95% confidence limits for this m e t h o d of -+ 2 °, and assumes that the errors are randomly distributed, no account having been taken of systematic errors. The largest systematic error influencing the mean direction estimates will be that due to the finite
262 TABLE I A compilation of 23 sets of mean direction estimates obtained by the repeated analysis of the same radar image by 3 different operators Anallysis no.
Mean direction with respect to x axis in Fig. 10
Standard deviation (°)
Skewness
Kurtosis
3.0 1.3 2.8 3.0 3.0 3.0 2.7 2.2 5.1 1.5 3.0 1.9 3.0 2.5 2.2 4.2 4.4 6.3 3.1 1.9 2.1 2.6 2.1
5.56 5.79 5.79 4.93 5.36 5.45 6.70 6.51 5.53 6.03 6.26 5.95 5.87 5.05 5.74 6.48 5.67 5.72 6.05 6.27 5.02 4.70 4.73
0.36 0.08 0.56 0.21 0.32 0.10 0.56 1.12 -0.20 -0.27 -0.05 -0.28 0.12 0.57 -0.25 0.00 -0.18 0.63 -0.14 0.09 -0.03 -0.04 0.26
2.49 2.58 2.74 2.06 2.33 3.38 3.80 6.16 2.93 3.59 3.11 4.12 2.90 1.99 3.49 2.86 2.51 3.75 3.78 3.39 3.82 4.10 3.08
2.91
0.15
3.26
-+1.13
+-0.35
+0.87
(°)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Mean values Standard errors
With respect to T R U E NORTH mean direction of wave approach with 95% confidence limits is 239 ° +- 2.21 °. s w e e p t i m e o f t h e r a d a r (i.e. a p p r o x i m a t e l y 2 s p e r r e v o l u t i o n ) . T h i s w i l l i m troduce a skew into the observed wave pattern and for typical wave lengths a n d w a t e r d e p t h s t h i s e r r o r is o f t h e o r d e r o f 0 . 2 ° , t h a t is a b o u t 1 0 % o f t h e s a m p l i n g e r r o r (+-2 °). E r r o r s d u e t o g e o m e t r i c d i s t o r t i o n o f t h e r a d a r i m a g e as a result of screen curvature and the photographic process are not known but are c o n s i d e r e d t o be less t h a n t h a t d u e t o t h e f i n i t e s w e e p t i m e .
263
The mean direction estimate in Table I of 239 ° may be compared with the figure of 231 ° obtained from the first method. Bearing in mind that the first method covers a smaller area of the radar image, and thus may be less representative of the wave climate than the second method, the two figures are in comparatively good agreement. Although the latter method is more precise than the simple technique described previously, it is more time-consuming and has not therefore been used extensively in this study. However future work with this method is planned. Some measure of the reliability of the radar's representation of the sea-surface may be obtained by comparing estimates of the wave period derived from the radar (TR) with those derived from a nearby seabed pressure wave recorder (TwR) measured at approximately the same time (Fig. 1). Here TWR has been taken as the zero up-crossing period (Tz). The wave period T is given by: T
=
(4)
L/c
Here, L is now the wavelength of long surface gravity waves and c the wave propagation velocity, given by:
(5)
c = [(gL/27r) tanh (2~ h / L ) ] ',4
where g is the acceleration due to gravity and h is the water depth. Therefore
15r + 10 o ~9 v I
Correlation Coeffic ient
~E S
r .79
I 5 TWR
I 10
Significance Levels
17.
.17.
•43
53
I 15
(Seconds)
mR = ' 9 8
TWR.I- " 2 3
Fig. 11. Scatter plot of radar-derived estimates of the wave period (T R ) and those obtained from a nearby wave recorder (TwR) at Port Talbot. This diagram shows a highly significant correlation between the two estimates.
264 by m e a s u r i n g t h e crest t o crest separation (L) o f the waves o n t h e radar images {usually m e a s u r e d over several waves) and b y taking t h e local w a t e r d e p t h (h) it is p o s s i b l e t o e s t i m a t e t h e w a v e p e r i o d ( T R ) . Figure 11 s h o w s that d e s p i t e t h e u n c e r t a i n t i e s in interpreting t h e radar image, surprisingly g o o d a g r e e m e n t is o b t a i n e d b e t w e e n T R and TWR over a range in w a v e p e r i o d s o f 7 - - 1 3 s, alt h o u g h strictly s p e a k i n g this w o u l d o n l y be e x p e c t e d in t h e case o f a n a r r o w swell s p e c t r u m . H o w e v e r , this e v i d e n c e suggests t h a t there are n o t likely to be a n y serious p r o b l e m s w i t h s h a d o w i n g o f w a v e s b e h i n d larger crests and t h a t t h e image is a fairly accurate t w o - d i m e n s i o n a l r e p r e s e n t a t i o n o f t h e major swell features o n the sea's surface. SOME RESULTS FROM
D I F F E R E N T SITES
Port Talbot T h e w a v e c l i m a t e in S w a n s e a B a y and at Port T a l b o t is d o m i n a t e d by its o p e n f e t c h w i t h t h e N o r t h Atlantic, a p o t e n t i a l d i s t a n c e o f s o m e 3 0 0 0 miles in a SW direction. This also c o r r e s p o n d s t o t h e prevailing o n s h o r e w i n d direc(a) f-"l W i n d 20"
Waves
15c t0o ©
5" I ~ I-I 90
I 180 Direction
i
1
270
360
(°T)
~
80%
20-
(b)
r-'l Wind
1731 W a v e s 15-
10o 0
5I--1
t--~
I 90
! 270
! 180
Direction
I
360
(°T)
Fig. 12. Plots of the percentage occurrence of wind directions and radar-derived wave directions at Port Talbot, showing: (a) the occurrence of a SW swell with winds from the NW and with offshore winds from the E in the period 6/1/77--19/1/77; (b) the prevailing conditions 0f SW swell and SW winds in the period 31/10/77--11/11/77. N denotes the number of observations in each case.
265
tion (see Fig. 7). Even with winds blowing f r o m t he E or NW an underlying SW swell can o f t e n be detected. This is illustrated in Figs. 12a, b which show, as expected, th at during a prolonged period of SW winds the measured wave directions were in t he range 220--240 °. However, during a period o f E and NW winds, although t h e overall occurrence of swell is lower, t he d o m i n a n t direction is still roughly the same, t ha t is 2 2 0 - - 2 4 0 ° , with only a very low occurrence o f locally generated seas f r o m 150--160 ° . T he observed range o f directions of wave approach is shown in Fig. 1. In fact, the wave directions at Port T a l bot measured over a period o f a b o u t 1 year show these same characteristics (see Fig, 13) with t he recorded swell arriving from directions between 220 ° and 250 ° for about 40% of the time and with waves f r o m directions between 150 ° and 160 ° being observed for less than 1% of t he time. However, it should be n o t e d that these figures probably only apply to waves higher than a b o u t I m, and t hat measurements were n o t continuous in t h e I year period. E i
100
t~l
S
w =
N
Wind N • 1389
FT")l W a v e s
10
I r-
I--
3
-1
=
i
i
i
i
,
i
|
"~
180 Direction
I
360 (°T)
Fig. 13. A summary of radar-derived wave direction estimates measured at Port Talbot in a 1 year period between October 1976 and November 1977. This figure shows that for about 40% of the time swell was incident from a narrow range of angles between 220--250° (T). The annual wind direction characteristics for the area are also shown. N is the total number of radar observations.
8tart Bay Observations o f wave direction using similar e q u i p m e n t have also been carried o u t by the Institute in Start Bay in the English Channel (see Fig. 1). Some examples o f radar imagery from this site are shown in Fig. 5 and these illustrate to a s o mew ha t b e t t e r e x t e n t the ability o f the radar t o resolve different directions o f wave approach. At this location waves m a y be incident
266
on the coast from two principal directions. A SW swell may be refracted into the Bay (Hails, 1975), to give directions in the SE sector, this condition corresponding to that of the prevailing SW winds. NE winds give wave directions in the NE sector. In Fig. 5 it is apparent that the radar is able to detect both these directions w i t h o u t much difficulty. It is also clear in Fig. 5b that the radar is able to detect wave refraction. CONCLUSIONS
This work has shown that radar may be used simply and effectively to obtain estimates of wave direction in coastal waters. Two methods of analyzing the data are discussed, the first and simplest of these giving a mean direction to within an estimated + 5 ° or better. The second m e t h o d is more precise and can be shown to give a mean direction to within + 2 ° (95% confidence limits). Radar has an advantage over the more sophisticated techniques of measuring velocity and pressure fluctuations under waves or measuring surface elevations using arrays of wave staves, in t h a t it is relatively simple to operate and service and does not require a detailed and perhaps costly analysis of the data. In m a n y coastal engineering problems direction estimates are only required to within + 5 ° and radar is quite capable of providing this resolution or better under suitable environmental conditions. In addition, radar will provide information on refraction and diffraction processes. The observations at Port Talbot have shown that of those waves which could n o t be detected by the radar some 80% fall below a wind speed of 5 m s-' and a significant wave height of 1 m. Clearly, therefore, the use of radar is restricted to periods of comparatively strong winds and appreciable surface wave activity. However, these are also likely to be the periods of greatest interest to coastal engineers. ACKNOWLEDGEMENTS
The co-operation of the British Transport Docks Board and the British Steel Corporation in the work at Port Talbot is gratefully acknowledged. We would also like to t h a n k Mr. T. Chung for his help with this work, and our colleagues at IOS Taunton. This work was supported financially by the Department of the Environment.
REFERENCES Battjes, J.A., 1972. Long-term wave height distributions at seven stations around the British Isles. Dtsch Hydrogr. Z., 25: 179--189. Cart, A.P., Heathershaw, A.D. and Blackley, M.W.L., 1977. S w a n s e a Bay (Sker) Project. Progress Report for the period August 1976 to July 1977, IOS Rep. No. 48/77, 32 pp. Crornbie, D.C., 1955. Doppler spectrum of sea echo at 13.56 Mc/s. Nature, 175: 681---682. Daley, J.C., 1973. Wind dependence of radar sea return. J. Geophys. Res., 78: 7823-7833.
267 Elachi, C. and Brown, W.E., 1977. Models of radar imaging of the ocean surface waves. IEEE J. Oceanic Eng., OE 2 (1): 84--95. Elachi, C., 1978. Radar imaging o f the Ocean surface. Boundary-Layer Meteorol., 13: 165-179. Fortnum, B.C.H. and Hardcastle, P.J., 1979. Waves recorded at Port Talbot on the South Wales Coast, IOS Rep. No. 78/79, 8 pp. Graf, K.A., Tremain, D.E. and Guthart, H., 1977. Induced-current effects on microwave backscatter. IEEE J. Oceanic Eng., OE 2(1): 36--42. Guinard, N.W., Ransone, J.T. and Daley, J.C., 1971. Variations of the NRCS of the Sea with increasing Roughness. J. Geophys. Res., 76(3): 1525--1538. Hails, J.R., 1975. Sediment distribution and Quaternary History (of Start Bay), J. Geol. Soc., 131: 19--35. Jones, W.L., Schroeder, L.C. and Mitchell, J.L., 1977. Aircraft measurements o f the microwave scattering signature of the ocean. IEEE J. Oceanic Eng., OE 2(1 ): 52--61. Keller, W.C. and Wright, J.W., 1975. Microwave scattering and the straining of wind generated waves. Radio Sci., 10: 139--147. Lee, P.H.Y., 1977. Doppler measurements o f the effects of gravity waves on wind-generated ripples. J, Fluid Mech., 8(2): 225--240. Oudshoorn, H.M., 1961. The use of radar in hydrodynamic surveying, Proc. 7th Conf. Coastal Eng., The Hague, Netherlands, 1960, pp. 5 9 - 7 6 . Plant, W.J., 1977. Studies o f backscattered sea return with a CW, duel-frequency, X-band radar. IEEE J. Oceanic Eng., OE 2(1): 28--36. Wright, J.W., 1966. Backscattering from capillary waves with application to sea clutter. IEEE Trans. Antennas Propag., AP 14: 7 4 9 - 7 5 4 . Wright, J.W., 1978. Detection of ocean waves by microwave radar; the modulation of short gravity-capillary waves. Boundary-Layer Meteorol., 13: 87--105.
249
WAVE DIRECTION ESTIMATES IN COASTAL WATERS USING RADAR
A.D. HEATHERSHAW, M.W.L. BLACKLEY and P.J. HARDCASTLE
Institute o f Oceanographic Sciences, Taunton, TA 1 2DW (Great Britain) (Received March 6, 1979; revised version accepted November 12, 1979)
ABSTRACT Heathershaw, A.D., Blackley, M.W.L. and Hardcastle, P.J., 1980. Wave direction estimates in coastal waters using radar. Coastal Eng., 3: 249--267. This paper describes the use of a conventional X-band radar in determining wave direction characteristics in coastal waters. It is shown that under suitable environmental conditions it is possible to determine a mean wave direction to within an estimated ± 2° and to observe wave refraction and diffraction processes in the vicinity o f harbours and on open coastlines. It is also shown that the radar may be used to estimate wave periods and the use o f the radar in determining the "annual" wave direction characteristics for a specific location is discussed. Examples of radar imagery are given together with technical details of the radar installations and equipment. Experience in the use of the radar at different sites and on different range settings suggests that the o p t i m u m height for the scanner, in this particular application, is in the range 15--20 m above mean sea level. Observations with the radar have been made simultaneously with measurements of the wave height, wave period and wind speed. It has thus been possible to establish some lower limits for the detection of swell waves by radar. In particular it has been found that about 80% of the waves not seen by the radar occur at wind speeds of less than 5 m s-1 and have significant wave heights of less than 1 m. These results are discussed in relation to the mechanism of wind wave generation and Bragg scattering from the sea surface. INTRODUCTION
Estimates o f wave direction are frequently required in m a n y coastal engineering problems. Semi-empirical methods of calculating littoral drift require this information as do studies in harbour design and location. In addition, this t y p e of information may assist in the planning o f ship and boat operations. In this article the use of radar to study wave direction in the vicinity of a large tidal harbour is described. Comparisons are also made with similar observations on an open coast. It is shown that despite a number o f obvious limitations, radar can provide a simple and effective means of studying wave direction in coastal waters, and under certain conditions can also provide information on wave period.
250 EQUIPMENT AND METHODS B e t w e e n O c t o b e r 1 9 7 6 and N o v e m b e r 1977 t h e I n s t i t u t e o f O c e a n o g r a p h i c Sciences o p e r a t e d a r a d a r i n s t a l l a t i o n at t h e end o f t h e s o u t h e r n b r e a k w a t e r at Port T a l b o t , S o u t h Wales (Fig. 1). T h e p u r p o s e o f t h e s e o b s e r v a t i o n s was to o b t a i n i n f o r m a t i o n on wave d i r e c t i o n t o b e used in c o n n e c t i o n w i t h b e a c h e r o s i o n studies o n t h e f o r e s h o r e near P o r t T a l b o t (Carr et al., 1977). A similar i n s t a l l a t i o n h a d b e e n o p e r a t e d p r e v i o u s l y b y t h e I n s t i t u t e in S t a r t Bay, D e v o n (Fig. 1) b e t w e e n A u g u s t 1 9 7 2 a n d J u n e 1974.
OOA; ON Or StO0
I~, ~
f~]~
4°'00'
X#e c :e4
BAY
wave approach
I
I
Key
5'0://
,'--~'-~ ~ { ~" Dredged navigati(:~...<--,-~ L~b#IBLES - _ , I ' " channel ~ _~
~,
T*~ORTBOT--
S# ISEA
p. . . . . . .
t .....
(~)
Beach wave d irectbon Measurements
ecorders
0 contour '
'
1 k
/
k
/ j S, a......... 4Light
,1~
~"'\u J
(~) Radar installations "-~-5m
\
.~M
"-.,'
35 %
~.-< ~
~x--~"J/=- "~
|
~k
PORT TALBOT
.... ~,~.~.~ Kms , i
J
5 ,
I
I
I
[ ]
" - L-..----! 25'4
Fig. 1. Location map showing the positions of the radar installation at Port Talbot and in Start Bay. The positions of wave recorders in relation to the radar at Port Talbot are also shown. Previous w o r k (e.g. O u d s h o o r n , 1 9 6 1 ) has established t h a t f o r a r a d a r t o be used in this p a r t i c u l a r a p p l i c a t i o n it is n e c e s s a r y f o r it t o o p e r a t e in t h e 3 c m or 8 m m b a n d (see f u r t h e r discussion), w i t h a pulse length o f less t h a n 0.1 Us a n d a h o r i z o n t a l aerial b e a m w i d t h o f 1 ° or less. T h e s e f a c t o r s a f f e c t t h e resolution a n d d e t e r m i n e t h e s h o r t e s t sea w a v e l e n g t h t h a t can be resolved. Because o f c o s t a n d w a v e l e n g t h c o n s i d e r a t i o n s , a 3.2 c m ( X - b a n d ) D e c c a T y p e 9 1 9 River R a d a r was selected. T h e s c a n n e r has a h o r i z o n t a l b e a m w i d t h o f 0.8 ° and r o t a t e s at 28 r p m . T h e r a d a r n o r m a l l y has a t r a n s m i t t e d pulse length o f 0.05 .us on d i s p l a y ranges u p t o 2 k m . M o d i f i c a t i o n s a l l o w e d this pulse length t o b e used u p t o t h e 8 k m range. T h e pulse r e p e t i t i o n r a t e is 3 4 0 0 per
251 second with a peak pow er of 3 kW and mean power o f 0.5 W. This gives a range resolving p o w e r of a b o u t 8 m and angular resolving power of 14 m at 1 km range. Although the o p t i m u m height for the scanner has n o t been determined, it has been f o u n d th at t he minimum for successful operation is about 10 m above mean sea level (MSL). As the height is raised so t h e reflection o f signals f r o m distant waves increases. However, experience with a similar radar installation at Mumbles in 1975 (Fig. 1) has shown that 50 m above MSL is t oo high f o r a radar o f this t y p e and results in a complete loss of the radar image. Experience with the radar at Port Talbot suggests that the o p t i m u m height for the scanner is probably in t he range 15--20 m above MSL. Details o f the installation at Port Talbot are shown schematically in Fig. 2. The radar aerial was m o u n t e d on a 6 m tubular-steel t ow er bolted to a concrete base, giving it a height above MSL of a pp roxi m at el y 14 m. In Start Bay a smaller tower was used t o m o u n t the aerial on the edge of a cliff at a height o f a p p r o x imately 16 m above MSL. In bot h cases the recording e q u i p m e n t was located nearby in a small hut. Radar Scanner steel tower
Breakwater
~'
on
6.!Oml
Fig. 2. Schematic diagram of the radar :installation at Port Talbot showing the relative height of the scanner with respect to High and Low Water Springs (HWS and LWS) and Mean Sea Level (MSL). An Autocamera Mk 3 instrumentation camera was fitted and so arranged as to automatically phot ogr a ph one complete sweep of the display tube every three hours. B o th radar and camera were operated from 24 volt lead-acid batteries which needed recharging m ont hl y. For collecting information on nearshore wave direction characteristics at Port Talbot, the radar was operated on a 2 km range. However, at Start Bay the o p p o r t u n i t y was taken to experiment with different ranges: 1.6 km was used f o r nearshore wave direction and a 4.0 km range was used for investigating wave refraction effects. At b o t h sites wave recorders were located near the radar installations. At
252 Port Talbot a single cabled-in frequency-modulated (FM), seabed-pressure wave recorder was used and located approximately 1.5 km from the radar (see Fig. 1). In Start Bay, a similar type of recorder was used, one on either side of the radar, at distances of 2.8 and 1.2 km N and S respectively. It has thus been possible to compare the radar pictures with wave data collected at or about the same time. Information on the local wind speed (W) and direction at both sites was also available for these analyses. BRAGG RESONANT SCATTERING AND THE RELATION BETWEEN RADAR IMAGES AND SEA WAVES During the past t w e n t y years or so there have been considerable theoretical and technical developments in the use of radar to study the sea's surface. It is beyond the scope o f this paper to review this work in full. However, excellent summaries of recent developments in this field may be found, for example, in papers by Plant {1977), Graf et al. {1977), Elachi and Brown (1977), Elachi (1978) and Wright (1978). To explain how radar images sea waves it is necessary to consider two related aspects of the interaction between electromagnetic waves and the waves which form on the sea-surface. These are: (a) the mechanism whereby radar signals are reflected from the sea's surface; and (b) the relation between radar images of the waves and the waves themselves. Crombie (1955) observed discrete lines in the frequency spectrum of high frequency (10 MHz) radar signals scattered from the sea-surface and correctly hypothesized that these occurred as a result of a resonant interaction with surface gravity waves whose wavelength was precisely one half of the electromagnetic wavelength, that is about 15 m. This p h e n o m e n o n was demonstrated conclusively in laboratory experiments by Wright (1966) using microwave radar, although in this case the resonant interaction was with much shorter wavelengths. It is now generally believed (see e.g., Plant, 1977) that this mechanism, Bragg resonant scattering, is the means whereby coherent radar returns are obtained from the sea-surface. Bragg resonant scattering from an equally spaced array of point scatterers (Fig. 3) occurs when the path length differences are an integral number of half wavelengths of the radar. If the wavelength of the radar is LR then the distance L between scatterers will therefore be given by:
nLR
L-2sin0,n=l,
2 .....
(1)
where 0 is the angle of incidence (Fig. 3). For an X-band radar used at low grazing angles (i.e. 0 -* 90 °, and for the first-order Bragg scattering, i.e. n = 1, LR ~ 3.2 cm and therefore L = 1.6 cm. This suggests that the scatterers are
253
,~
(a)
Crests of swel I waves A""'--
~Radar beam
E
~~,
(b) Radar scanner
Fig. 3. Schematic diagram showing (a) the Bragg scattering mechanism for capillary waves superimposed on a long period swell and (b) the azimuthal dependence of the radar return. e is the angle of incidence and ~ the azimuth of the radar beam.
small wavelets or capillary waves of wavelengths L ~" 1.6 cm. The first point (a) therefore is that at low grazing angles coherent radar returns from the sea surface are almost certainly provided b y a Bragg scattering mechanism. The a m o u n t o f energy in a radar signal reflected from the sea-surface is usually measured (see Guinard et al., 1971; Daley, 1973) in terms of a scattering coefficient a0 (sometimes referred to as the normalized radar scattering cross section) defined by: Oo
-
1 Lt A R-*~
where R incident Early ied with
4 n R 2 (Ps/Pi)
(2)
is the range to the scattering surface, Ps and ~ are the scattered and powers, respectively, and A is the area illuminated b y the radar. work with radar concentrated on determining the w a y in which a0 varsea-surface roughness and wind speed (W). In particular the earlier,
254 a n d m o r e r e c e n t w o r k ( J o n e s e t al., 1 9 7 7 ) , h a s s h o w n t h a t f o r a g i v e n p o l a r i z a t i o n o f t h e r a d a r s i g n a l a n d a n g l e o f i n c i d e n c e 0, o0 e x h i b i t s a c o m p l e x p o w e r - l a w d e p e n d e n c e . F o r e x a m p l e i t h a s b e e n s h o w n ( s e e G u i n a r d e t al., 1 9 7 1 ) t h a t f o r a n a n g l e o f i n c i d e n c e o f 3 0 °, o0 v a r i e s as W 3 f o r W < 5 m s -1 and W 1/2 f o r W > 5 m s -1 . I n n e i t h e r t h e e a r l y n o r m o r e r e c e n t w o r k d o l o c a l v a r i a t i o n s in t h e s c a t t e r i n g c r o s s s e c t i o n a0 a p p e a r t o h a v e b e e n e x t e n s i v e l y studied. N
Range 2 km Waves: Height
H s =3.11m
Period
T z =10-5s
D i r e c t i o n 235 ° (T) Wind:
Speed lOms -~ D i r e c t i o n 270 ° (T)
H
Range
2kin
Waves : Height
Hs = 4'63m
Wind:
20ms-' Direction 26(~ (T)
Fig. 4. Typical radar images of the sea-surface in the vicinity of Port Talbot. Note that waves have been detected arriving well inshore at the beach and that there is considerable wave diffraction inside the harbour. Values of the significant wave height (Hs) and zero crossing period (Tz), at the time the radar images were recorded, are also shown.
255
However, it is precisely these variations which lead us to point (b); that is the relation between the radar image (see Figs. 4 and 5) and the sea-surface itself. The radar image is a two-dimensional presentation o f local variations in the scattering cross section (o0) of the sea-surface and, as pointed out by Elachi and Brown (1977) and Plant (1977), there are at least three modulating mechanisms which might lead to a localization of Bragg scatterers on swell waves and perhaps explain how radar images these features. These are: (1) tilt modulation in which the angle of incidence o f the radar wave with the capillary wave varies according to its position on the longer period swell wave;
Range 1-6 km
(~)
(~ Fig. 5. Typical radar images obtained from the Start Bay radar installation showing the two dominant directions of wave approach (a) from the NE and (b) from the SE.. Note that on the larger range setting (b) it is possible to see the effects of wave refraction.
256
(2) a roughness modulation in which the wavelength of the capillary wave varies according to position on the swell wave; (3) modulation effects due to the orbital velocity of the swell waves which lead to doppler shift effects and defocussing of the image. In addition there will be some modulation of the capillary waves by tidal currents and in practice we may expect the reflected signal to exhibit all these modulation effects although Bragg scattering provides the fundamental resonant interaction between the radar signal and the capillary waves on the sea's surface. The importance of tilt modulation in the case of a horizontally polarised radar at low grazing angle (which is the type used here) has been demonstrated by Guinard et al. (1971) who showed that the reflected signal levels could only be explained theoretically by introducing a tilting of the sea-surface, in other words by introducing swell in an ad hoc manner. It is worth noting that this is a requirement which arises without the need to explain the radar images of the sea waves. Recent laboratory work by Lee (1977) has shown t h a t capillary waves tend to become localised on the crests of swell waves, their amplitude reaching a m a x i m u m in this position, with virtually no radar signal being reflected from the troughs where the capillary wave amplitude is greatly diminished. Earlier evidence for this was provided by Keller and Wright (1975). This mechanism would certainly explain our observations (Figs. 4 and 5b) where it is clear t h a t the radar successfully images the waves from behind as well as from in front thereby discounting localisation of capillary waves 6n the forward facing slopes. However, it is likely that the mechanism is considerably more complex than this and as pointed out by Elachi and Brown (1977), radar imagery of the ocean is a comparatively new field of research and much more work is required before the content of the radar image is fully understood. In the light of this evidence, therefore, it does n o t seem unreasonable to assume that the radar images the wave crests. However, it should be borne in mind t h a t Bragg resonant scattering will be strongest from those parts of the wave field where the radar beam is parallel to the direction of ripple propagation (Fig. 3) and that the radar system imposes a filter which is not only frequency dependent, that is it selects capillary wavelengths given by eq. 1, but t h a t it also has a directional dependence. Since the direction of ripple propagation and that of the underlying swell may be different, it is clear that the latter may be very complex and, in the absence of more precise information on the directional characteristics of the swell waves and capillary waves, may n o t be determinable. Despite these uncertainties however, it appears in practice (Figs. 4 and 5) that the directional response is approximately cosine so that, referring to Fig. 3, the wave-like pattern is most clearly revealed when the radar beam is parallel to the direction of wave propagation (i.e. ~ = 0 ° or + 180 ° ) with the least coherent image being obtained when the radar beam is parallel to the wave crests (i.e. ~ = + 90°).
257 INTERPRETATION OF RADAR IMAGES
Typical radar images of the sea-surface from the Port Talbot and Start Bay sites are shown in Figs. 4 and 5. For the Port Talbot site values of the significant wave height (Hs), zero crossing period (Tz), mean wave direction, wind direction and wind speed, are also shown. Wave direction was measured from the radar images with a protractor. It is interesting to note in these pictures the presence of considerable wave diffraction inside the harbour and that waves have been detected arriving well inshore at the beach to the north of the tidal harbour; the radar is thus able to "see" the backs as well as the fronts of the waves. However, it should be noted that the radar does not see the waves when the radar beam is parallel with the wave crests. For a good radar image of the sea-surface to be obtained using a low-grazing angle microwave radar, it is necessary that small wavelets or capillary waves having wavelengths comparable with that of the radar, be superimposed on wave and swell trains (see previous discussion). Wavelets are usually generated by local winds and there is thus the possibility that swell may be present and yet remain undetected by the radar. In fact, in this work we have found that during periods of calm or settled weather, swell in excess of 1 m with periods o f about 10s could on occasions be measured on a wave recorder and yet n o t be observed on the radar (see later discussion). However, these are comparatively rare events. Whether the radar will detect swell waves or not is therefore governed by the presence of capillary waves on the underlying swell. A detailed analysis of the radar images from the Port Talbot site has shown that on 952 occasions when waves were measured on the wave recorder (see Fig. 1) a wave pattern could n o t be detected on the radar for some 24.26% of the time (231 occasions). Observations during periods of rain were excluded from this analysis. The annual wind and wave climate for the area (see Figs. 6 and 7) shows that for 25% of the time significant wave heights (/-its) and wind speeds (W) are less than 0.25 m and 4 m s -1 respectively. However, it is wrong to think of these as lower limits to the detection of sea waves by radar in this particular application. Firstly there is no clear " c u t - o f f " in terms of wind speed and wave height and clearly there is some danger in using a single fractile estimate in this manner because it does not indicate how those waves which were not detected by the radar were distributed in terms of wave height and wind speed. Therefore we have attempted to look directly at the correlation between the observed waves and the meteorological data. Figure 8 shows the results of this analysis and indicates that there is a progressive increase in the number o f waves n o t detected by the radar as both windspeed and wave height decrease to zero so that of the waves not detected by the radar some 80% had significant wave heights less than 1 m and occurred at wind speeds of less than 5 m s-1.
258 20Offshol e
Onshore
i f - - 1
•
i
c
10-
100, WHOLE
YEAR 0 100 "
c
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(T)
360
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i
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Significant wave height
I ~ l ' l l l l I . H ,
2 Hs
(metres)
3
4
5
5
10 15 Wind speed
20 (ms -t )
Fig. 6. Percentage exceedance curve for significant wave height (Hs) measured at Port Talbot over a period o f 1 year (after F o r t n u m and Hardcastle, 1979). Fig. 7. Annual s u m m a r y of w i n d speed and direction characteristics at Port Talbot.
The fairly rapid increase in the number of waves not detected by the radar at wind speeds less than about 5--7 m s -1 may occur as a result of the scattering cross section a0 changing to a higher power-law dependence at lower wind speeds in the manner described b y Guinard et al. ( 1 9 7 1 ) (see previous discussion). Details o f the wave conditions at Port Talbot during those periods when radar observations were made are shown in Fig. 9. This shows the expected bias o f the radar towards higher waves, by virtue of their being associated with higher winds, and also suggests that wave steepness may be important in determining whether they will reflect radar signals or not. In Fig. 9 lines of constant wave steepness have been plotted to include shallow-water effects, where the steepness s has been taken as the ratio of significant wave height Hs to the wavelength L which in terms o f the zero crossing period Tz may be expressed as: s = T z [ ( g L / 2 ~ ) Hstanh (2n h / L ) ] ,/2
(3)
Here g is the acceleration due to gravity and h the mean depth which for these calculations has been taken as 12 m. For deep water waves this reduces to the usual expression (see Battjes, 1972) s = 2n H s / g Tz 2 .
25
259
N = 721
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Fig. 8. The n u m b e r o f o c c a s i o n s w h e n waves were d e t e c t e d (a) and n o t d e t e c t e d (b) by the radar at Port T a l b o t as a f u n c t i o n o f significant wave height (Hs) and w i n d speed (W); (b) s h o w s that a b o u t 80% o f the waves n o t d e t e c t e d by the radar occurred at w i n d speeds o f less than 5 m s - ' and significant wave heights (Hs) o f less than 1 m. N is the n u m b e r o f o c c a s i o n s that waves were recorded in each category over a 1 y r period.
260
/11/ 2-
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Fig. 9. Scatter plot of measured significant wave heights (Hs) and zero crossing periods (Tz) for the data shown in Fig. 8. Solid contours represent the recorded waves and broken contours represent those waves "seen" by the radar. Curves indicating wave steepness and calculated using eq. 3 are also shown. D u e t o shoaling e f f e c t s t h e m e a s u r e d w a v e heights s h o w n in Figs. 6, 8 a n d 9 s h o u l d b e increased b y a b o u t 10% t o o b t a i n the heights o f the waves seaward o f t h e radar; h o w e v e r this c o r r e c t i o n is c o n s i d e r e d s u f f i c i e n t l y small t o be n e g l e c t e d in this case. T w o m e t h o d s o f a n a l y z i n g t h e r a d a r images f o r w a v e d i r e c t i o n h a v e b e e n e m p l o y e d in this s t u d y . T h e first o f t h e s e enables r a p i d i n t e r p r e t a t i o n t o be carried o u t . E a c h f r a m e o f the d e v e l o p e d film was v i e w e d o n an enlarger a n d t h e angle b e t w e e n the d o m i n a n t w a v e c r e s t d i r e c t i o n (at a p o i n t a p p r o x i m a t e l y 1 k m s e a w a r d o f t h e radar) and a h e a d e r m a r k m e a s u r e d w i t h a p r o t r a c t o r t o w i t h i n an e s t i m a t e d + 5 ° , or b e t t e r , d e t e r m i n e d b y r e p e a t e d m e a s u r e m e n t w i t h d i f f e r e n t o p e r a t o r s . T h e m e a s u r e m e n t on a n y o n e i m a g e can be rep e a t e d several t i m e s t o o b t a i n a n average direction. T h e s e c o n d m e t h o d , w h i c h is less subjective t h a n t h e first, and w h i c h pror i d e s useful a d d i t i o n a l data, consists o f dividing a s e c t i o n o f an enlarged image i n t o 50 e l e m e n t s (Fig. 10); a line is t h e n d r a w n in e a c h square c o r r e s p o n d i n g t o t h e o r i e n t a t i o n o f an a c t u a l wave c r e s t w h e r e o n l y o n e is p r e s e n t and well d e f i n e d , or t h e e s t i m a t e d m e a n o r i e n t a t i o n o f a w a v e c r e s t w h e r e o n e or m o r e c o m p l e t e or i n c o m p l e t e images are p r e s e n t . T h e p o s i t i o n c o o r d i n a t e s o f t h e s e
261
P o s i t iq Radar
id
Fig. 10. 2 × 1 k m grid used in determining wave direction c h a r a c t e r i s t i c s at P o r t T a l b o t . The lines in each s q u a r e are e x a m p l e s o f f i t t e d o r actual wave crests.
lines are then recorded using a D-MAC digitising table and the mean of the 50 uniformly distributed direction estimates calculated together with the standard deviation, skewness and kurtosis. This procedure was carried out 23 times on the same image by different operators and the results of such an analysis are shown in Table I. This method has been tested with three different operators who have been found to agree to within _+ 3 ° on mean direction. This method can of course only be applied where it is known t h a t a single mean direction for the waves is applicable (i.e. there is no refraction or diffraction within the area of the grid). The results in Table I suggest t h a t this is the case for the particular record shown, with the 50 estimates of wave direction being distributed r a n d o m l y about each mean giving in most cases skewness and kurtosis values close to 0 and 3 respectively, i.e. the values for a Gaussian distribution. The variation of wave direction in each grid element (which to some extent is a combination o f actual variation and h u m a n error) is indicated by the standard deviation. Taking a value of +- 2 standard deviations (which should include approximately 95% of the variation) it can be shown that the ~pread is of the order of ± 10 ° . However, assuming that samples are drawn from the same population, the sampling variability o f each mean direction estimate is given by its standard error (Table I); this gives 95% confidence limits for this m e t h o d of -+ 2 °, and assumes that the errors are randomly distributed, no account having been taken of systematic errors. The largest systematic error influencing the mean direction estimates will be that due to the finite
262 TABLE I A compilation of 23 sets of mean direction estimates obtained by the repeated analysis of the same radar image by 3 different operators Anallysis no.
Mean direction with respect to x axis in Fig. 10
Standard deviation (°)
Skewness
Kurtosis
3.0 1.3 2.8 3.0 3.0 3.0 2.7 2.2 5.1 1.5 3.0 1.9 3.0 2.5 2.2 4.2 4.4 6.3 3.1 1.9 2.1 2.6 2.1
5.56 5.79 5.79 4.93 5.36 5.45 6.70 6.51 5.53 6.03 6.26 5.95 5.87 5.05 5.74 6.48 5.67 5.72 6.05 6.27 5.02 4.70 4.73
0.36 0.08 0.56 0.21 0.32 0.10 0.56 1.12 -0.20 -0.27 -0.05 -0.28 0.12 0.57 -0.25 0.00 -0.18 0.63 -0.14 0.09 -0.03 -0.04 0.26
2.49 2.58 2.74 2.06 2.33 3.38 3.80 6.16 2.93 3.59 3.11 4.12 2.90 1.99 3.49 2.86 2.51 3.75 3.78 3.39 3.82 4.10 3.08
2.91
0.15
3.26
-+1.13
+-0.35
+0.87
(°)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Mean values Standard errors
With respect to T R U E NORTH mean direction of wave approach with 95% confidence limits is 239 ° +- 2.21 °. s w e e p t i m e o f t h e r a d a r (i.e. a p p r o x i m a t e l y 2 s p e r r e v o l u t i o n ) . T h i s w i l l i m troduce a skew into the observed wave pattern and for typical wave lengths a n d w a t e r d e p t h s t h i s e r r o r is o f t h e o r d e r o f 0 . 2 ° , t h a t is a b o u t 1 0 % o f t h e s a m p l i n g e r r o r (+-2 °). E r r o r s d u e t o g e o m e t r i c d i s t o r t i o n o f t h e r a d a r i m a g e as a result of screen curvature and the photographic process are not known but are c o n s i d e r e d t o be less t h a n t h a t d u e t o t h e f i n i t e s w e e p t i m e .
263
The mean direction estimate in Table I of 239 ° may be compared with the figure of 231 ° obtained from the first method. Bearing in mind that the first method covers a smaller area of the radar image, and thus may be less representative of the wave climate than the second method, the two figures are in comparatively good agreement. Although the latter method is more precise than the simple technique described previously, it is more time-consuming and has not therefore been used extensively in this study. However future work with this method is planned. Some measure of the reliability of the radar's representation of the sea-surface may be obtained by comparing estimates of the wave period derived from the radar (TR) with those derived from a nearby seabed pressure wave recorder (TwR) measured at approximately the same time (Fig. 1). Here TWR has been taken as the zero up-crossing period (Tz). The wave period T is given by: T
=
(4)
L/c
Here, L is now the wavelength of long surface gravity waves and c the wave propagation velocity, given by:
(5)
c = [(gL/27r) tanh (2~ h / L ) ] ',4
where g is the acceleration due to gravity and h is the water depth. Therefore
15r + 10 o ~9 v I
Correlation Coeffic ient
~E S
r .79
I 5 TWR
I 10
Significance Levels
17.
.17.
•43
53
I 15
(Seconds)
mR = ' 9 8
TWR.I- " 2 3
Fig. 11. Scatter plot of radar-derived estimates of the wave period (T R ) and those obtained from a nearby wave recorder (TwR) at Port Talbot. This diagram shows a highly significant correlation between the two estimates.
264 by m e a s u r i n g t h e crest t o crest separation (L) o f the waves o n t h e radar images {usually m e a s u r e d over several waves) and b y taking t h e local w a t e r d e p t h (h) it is p o s s i b l e t o e s t i m a t e t h e w a v e p e r i o d ( T R ) . Figure 11 s h o w s that d e s p i t e t h e u n c e r t a i n t i e s in interpreting t h e radar image, surprisingly g o o d a g r e e m e n t is o b t a i n e d b e t w e e n T R and TWR over a range in w a v e p e r i o d s o f 7 - - 1 3 s, alt h o u g h strictly s p e a k i n g this w o u l d o n l y be e x p e c t e d in t h e case o f a n a r r o w swell s p e c t r u m . H o w e v e r , this e v i d e n c e suggests t h a t there are n o t likely to be a n y serious p r o b l e m s w i t h s h a d o w i n g o f w a v e s b e h i n d larger crests and t h a t t h e image is a fairly accurate t w o - d i m e n s i o n a l r e p r e s e n t a t i o n o f t h e major swell features o n the sea's surface. SOME RESULTS FROM
D I F F E R E N T SITES
Port Talbot T h e w a v e c l i m a t e in S w a n s e a B a y and at Port T a l b o t is d o m i n a t e d by its o p e n f e t c h w i t h t h e N o r t h Atlantic, a p o t e n t i a l d i s t a n c e o f s o m e 3 0 0 0 miles in a SW direction. This also c o r r e s p o n d s t o t h e prevailing o n s h o r e w i n d direc(a) f-"l W i n d 20"
Waves
15c t0o ©
5" I ~ I-I 90
I 180 Direction
i
1
270
360
(°T)
~
80%
20-
(b)
r-'l Wind
1731 W a v e s 15-
10o 0
5I--1
t--~
I 90
! 270
! 180
Direction
I
360
(°T)
Fig. 12. Plots of the percentage occurrence of wind directions and radar-derived wave directions at Port Talbot, showing: (a) the occurrence of a SW swell with winds from the NW and with offshore winds from the E in the period 6/1/77--19/1/77; (b) the prevailing conditions 0f SW swell and SW winds in the period 31/10/77--11/11/77. N denotes the number of observations in each case.
265
tion (see Fig. 7). Even with winds blowing f r o m t he E or NW an underlying SW swell can o f t e n be detected. This is illustrated in Figs. 12a, b which show, as expected, th at during a prolonged period of SW winds the measured wave directions were in t he range 220--240 °. However, during a period o f E and NW winds, although t h e overall occurrence of swell is lower, t he d o m i n a n t direction is still roughly the same, t ha t is 2 2 0 - - 2 4 0 ° , with only a very low occurrence o f locally generated seas f r o m 150--160 ° . T he observed range o f directions of wave approach is shown in Fig. 1. In fact, the wave directions at Port T a l bot measured over a period o f a b o u t 1 year show these same characteristics (see Fig, 13) with t he recorded swell arriving from directions between 220 ° and 250 ° for about 40% of the time and with waves f r o m directions between 150 ° and 160 ° being observed for less than 1% of t he time. However, it should be n o t e d that these figures probably only apply to waves higher than a b o u t I m, and t hat measurements were n o t continuous in t h e I year period. E i
100
t~l
S
w =
N
Wind N • 1389
FT")l W a v e s
10
I r-
I--
3
-1
=
i
i
i
i
,
i
|
"~
180 Direction
I
360 (°T)
Fig. 13. A summary of radar-derived wave direction estimates measured at Port Talbot in a 1 year period between October 1976 and November 1977. This figure shows that for about 40% of the time swell was incident from a narrow range of angles between 220--250° (T). The annual wind direction characteristics for the area are also shown. N is the total number of radar observations.
8tart Bay Observations o f wave direction using similar e q u i p m e n t have also been carried o u t by the Institute in Start Bay in the English Channel (see Fig. 1). Some examples o f radar imagery from this site are shown in Fig. 5 and these illustrate to a s o mew ha t b e t t e r e x t e n t the ability o f the radar t o resolve different directions o f wave approach. At this location waves m a y be incident
266
on the coast from two principal directions. A SW swell may be refracted into the Bay (Hails, 1975), to give directions in the SE sector, this condition corresponding to that of the prevailing SW winds. NE winds give wave directions in the NE sector. In Fig. 5 it is apparent that the radar is able to detect both these directions w i t h o u t much difficulty. It is also clear in Fig. 5b that the radar is able to detect wave refraction. CONCLUSIONS
This work has shown that radar may be used simply and effectively to obtain estimates of wave direction in coastal waters. Two methods of analyzing the data are discussed, the first and simplest of these giving a mean direction to within an estimated + 5 ° or better. The second m e t h o d is more precise and can be shown to give a mean direction to within + 2 ° (95% confidence limits). Radar has an advantage over the more sophisticated techniques of measuring velocity and pressure fluctuations under waves or measuring surface elevations using arrays of wave staves, in t h a t it is relatively simple to operate and service and does not require a detailed and perhaps costly analysis of the data. In m a n y coastal engineering problems direction estimates are only required to within + 5 ° and radar is quite capable of providing this resolution or better under suitable environmental conditions. In addition, radar will provide information on refraction and diffraction processes. The observations at Port Talbot have shown that of those waves which could n o t be detected by the radar some 80% fall below a wind speed of 5 m s-' and a significant wave height of 1 m. Clearly, therefore, the use of radar is restricted to periods of comparatively strong winds and appreciable surface wave activity. However, these are also likely to be the periods of greatest interest to coastal engineers. ACKNOWLEDGEMENTS
The co-operation of the British Transport Docks Board and the British Steel Corporation in the work at Port Talbot is gratefully acknowledged. We would also like to t h a n k Mr. T. Chung for his help with this work, and our colleagues at IOS Taunton. This work was supported financially by the Department of the Environment.
REFERENCES Battjes, J.A., 1972. Long-term wave height distributions at seven stations around the British Isles. Dtsch Hydrogr. Z., 25: 179--189. Cart, A.P., Heathershaw, A.D. and Blackley, M.W.L., 1977. S w a n s e a Bay (Sker) Project. Progress Report for the period August 1976 to July 1977, IOS Rep. No. 48/77, 32 pp. Crornbie, D.C., 1955. Doppler spectrum of sea echo at 13.56 Mc/s. Nature, 175: 681---682. Daley, J.C., 1973. Wind dependence of radar sea return. J. Geophys. Res., 78: 7823-7833.
267 Elachi, C. and Brown, W.E., 1977. Models of radar imaging of the ocean surface waves. IEEE J. Oceanic Eng., OE 2 (1): 84--95. Elachi, C., 1978. Radar imaging o f the Ocean surface. Boundary-Layer Meteorol., 13: 165-179. Fortnum, B.C.H. and Hardcastle, P.J., 1979. Waves recorded at Port Talbot on the South Wales Coast, IOS Rep. No. 78/79, 8 pp. Graf, K.A., Tremain, D.E. and Guthart, H., 1977. Induced-current effects on microwave backscatter. IEEE J. Oceanic Eng., OE 2(1): 36--42. Guinard, N.W., Ransone, J.T. and Daley, J.C., 1971. Variations of the NRCS of the Sea with increasing Roughness. J. Geophys. Res., 76(3): 1525--1538. Hails, J.R., 1975. Sediment distribution and Quaternary History (of Start Bay), J. Geol. Soc., 131: 19--35. Jones, W.L., Schroeder, L.C. and Mitchell, J.L., 1977. Aircraft measurements o f the microwave scattering signature of the ocean. IEEE J. Oceanic Eng., OE 2(1 ): 52--61. Keller, W.C. and Wright, J.W., 1975. Microwave scattering and the straining of wind generated waves. Radio Sci., 10: 139--147. Lee, P.H.Y., 1977. Doppler measurements o f the effects of gravity waves on wind-generated ripples. J, Fluid Mech., 8(2): 225--240. Oudshoorn, H.M., 1961. The use of radar in hydrodynamic surveying, Proc. 7th Conf. Coastal Eng., The Hague, Netherlands, 1960, pp. 5 9 - 7 6 . Plant, W.J., 1977. Studies o f backscattered sea return with a CW, duel-frequency, X-band radar. IEEE J. Oceanic Eng., OE 2(1): 28--36. Wright, J.W., 1966. Backscattering from capillary waves with application to sea clutter. IEEE Trans. Antennas Propag., AP 14: 7 4 9 - 7 5 4 . Wright, J.W., 1978. Detection of ocean waves by microwave radar; the modulation of short gravity-capillary waves. Boundary-Layer Meteorol., 13: 87--105.