Comparison of computed and observed breaker wave heights

Coastal Engineering, 3 (1979) 39--50 39 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

COMPARISON OF COMPUTED AND OBSERVED BREAKER WAVE HEIGHTS

EDWARD BRYANT

Department Geography, University of Woliongong, Wollongong, N.S. W. 2500 (Australia)

(Received June 29, 1978; revised version accepted March 14, 1979)

ABSTRACT

Bryant, E., 1979. Comparison of computed and observed breaker wave heights. Coastal Eng., 3: 39--50.

Computer programs for wave refraction simulation, based upon work by Dobson, are being used more frequently to determine nearshore wave characteristics. While realistic refraction patterns can be simulated by such programs, correlations between calculated and observed wave heights have not been evaluated fully. In a study of four beaches in Broken Bay, N.S.W., Australia, computed and observed breaker wave heights were compared. Monochromatic swells with periods ranging from 5.6 to 12.0 sec and with deep-water wave heights from 0.17 to 2.96 m were used in the study. For these wave conditions, a significant one-to-one correlation between simulated and observed wave heights was obtained at the 0.01 level of significance using the Spearman's Rank Correlation and the Wilcoxon Matched-pairs Signed-ranks tests. As a first approximation, existing computer programs can be used to calculate breaker wave heights between 0.0 and 2.0 m for many different refraction and shoaling conditions over a narrow continental shelf.

INTRODUCTION

Wave energy and power parameters at the breaker point, or shore, are determined primarily by the incoming wave spectra after it has traversed offshore bathymetry and interacted, in a complex manner, with the nearshore circulation pattern. Secondary effects in determining these wave parameters involve wave reflection processes from the beach, and swash-incident wave phase differences at the shore (Kemp and Plinston, 1968). Attempts have been made at computing some of the theoretical interactions between the incoming waves and the nearshore circulation pattern (Noda, 1974; Noda et al., 1974; Birkemeier and Dalrymple, 1975; Wang et al., 1975); however, many practical computer studies have considered breaker wave parameters to be a function solely of deep-water wave characteristics after wave refraction, shoaling and frictional attenuation of energy across the continental shelf (Goldsmith and Colonen, 1970; Coleman and Wright, 1971; McCann and Bryant, 1973; May and Tanner, 1973; Wright and Coleman, 1973; Goldsmith, 1976; Armon and McCann, 1977). This latter approach can be extended now that rates of

40

.4

AUSTRALIA

~o

ti,""

" ' - . .

N E W : ~

~:~,, Ilroken ~ - nr°kue2y ,,~':~ %: nay

Fig. 1. Location map and ba thymet ry of Broken Bay, N.S.W., Australia.

41

longshore sediment transport at the breaker point, and across the surf zone, can be predicted theoretically, knowing breaker wave parameters (Komar and Inman, 1970; Komar, 1975, 1976). As a first approximation, wave characteristics and sediment transport rates near the breaker point can be predicted if nearshore bathymetry and deep-water monochromatic wave characteristics are known.

The spatial accuracy of computed wave orthogonals and hence, the accuracy of wave refraction coefficients and wave directions, has been validated for monochromatic waves in theoretical and real world situations (Dobson, 1967; Bryant, 1974; Poole, 1975). The approximation of computed breaker wave height values to observed ones, and hence the accuracy of the product of wave refraction, shoaling and frictional attenuation coefficients, has not been verified to the same degree. This aspect will be examined in this paper using computer-calculated and measured breaker wave height comparisons on four beaches in the Broken Bay area of New South Wales, Australia (Fig. 1).

COMPUTER PROGRAM

Many of the present computer wave-refraction studies are based upon a program developed by Dobson (1967). This program has been modified by Coleman and Wright (1971) for bottom friction attenuation of wave energy using the theory of Bretschneider and Reid (1954). In the Dobson (1967) program, a second-degree polynomial is fitted to regularly gridded bathymetry using a least-squares algorithm. Calculations of wave parameters are based upon progressive, linear, gravity-wave theory which assumes small wave steepness, constant water depth and a wave celerity and length that are constant unique functions of wave period and water depth. Additional- ly, it is assumed that: (1) wave diffraction and reflection are nonexistent; (2) waves are monochromatic; (3) refraction is independent of wave height; and (4) water percolation, bed disturbance and current effects are insignif- icant. While most of these assumptions have been challenged (diffraction: Worthington and Herbich, 1970; dependency on wave height: Chu, 1975, and Hebenstreit, 1977; bed permeability: Hunt, 1959, and Liu, 1977; bed disturbance: TunstaU and Inman, 1975, and Suhayda, 1977; currents: Johnson, 1947, Longuet-Higgins and Stewart, 1960, Peregrine, 1976), the greatest flaw in the program lies in the general usage of linear wave theory. Such theory is not applicable inside the breaker zone (Wood, 1970; Chandler and Sorensen, 1972) and is not totally appropriate in characterizing waves in nearshore and offshore areas (Iwagaki and Sakai, 1970; Wood, 1969; Whalin, 1972). These limitations must be realized when applying the Dobson program to real world situations.

AREA OF STUDY

Observed and computed breaker wave heights were compared on four beaches in Broken Bay, N.S.W., Australia between August 1974 and

42

January 1976 (Fig. 1). Two beaches, Palm and Putty, are situated in ex- posed positions adjacent to the mouth of the bay, while one, Pearl, lies sheltered within the bay and the other, Patonga, lies protected along the estuary proper (Fig. 2). These four beaches are suited ideally for computer wave-refraction studies. Except for one shoal area opposite Put ty beach, offshore bot tom contours are parallel to the shoreline along both ocean and bay beaches. Nearshore topographies and circulation patterns on these beaches are less complex than on those typical of the New South Wales coast (McKenzie, 1958; Eliot, 1974). At Pearl beach the nearshore is devoid of both a surf zone and nearshore barred topography and drops off rapidly to a 3 m depth at the north end. Waves break on this beach as either surging or plunging waves at the shoreline. At Patonga beach, the nearshore shelves to a depth of 2 m into Brisk Bay with waves again breaking as plunging breakers at the shore. This beach also is devoid of nearshore rhythmic topographic variation. Rhythmic topography and nearshore circulation patterns do develop on Palm and Putty beaches. On Palm, the bar system extended no more than 100 m from shore during the early part of the study and formed a system of arcuate nearshore bars with intervening rip channels. This bar system eventually welded to shore and in places formed a low shelf 0.5 m below the low-tide limit. Waves generally broke on this bar as spilling breakers. Similar, but less developed, bar topography also formed on the

? t km Depths in meters

o ; k m

1 2 3

0 ~ 0 1

k m k m

Fig. 2. Profile locations and nearshore bathyrnetry of Broken Bay beaches.

43

SOUth end of Putty. These bar systems, because of their dynamic nature, appeared to dominate the nearshore zone and control nearshore hydro- dynamics; however, they were not a permanent feature. They were poorly developed or nonexistent for 30 and 60% of the survey period on Palm and Put ty beaches, respectively.

For the computer wave calculations, a detailed and well-controlled bathy- metric grid of the Broken Bay area was constructed at less than 200 m intervals out to the continental shelf break (based upon Australian hydrographic chart no. 204). More detailed grids with intervals of 63.5 m were constructed adjacent to each beach using a separate hydrographic base map (Australian hydrographic chart no. 3351 A/3A V5/169). These latter grids were supplemented on Patonga, Pearl and Put ty beaches with survey measurements obtained in September 1975, inshore of the 3 m depth. The Palm beach bathymetry was supplemented with nearshore surveys undertaken in May 1975 by P. Cowell (pets. comm., Sydney University, Australia).

WAVE DATA

Deep-water wave input for the computer program was obtained from field observations and instrument recordings as part of a regular survey of the beaches carried out fifteen times at 4--6 weeks intervals. A summary of the wave input is presented in Table I. The wave climate for Broken Bay forms part of Davies' (1964) east coast swell environment. Measured wave trains during the study consisted of monochromatic swell from a single direction (variation in period ± 10%). Average, timed, modal wave periods ranged from 5.6 to 1 2 . 0 s w i t h a mean of 9.3 s. Deep-water significant wave height was measured by the New South Wales Department of Public Works using a wave rider buoy situated in 200 m of water offshore from Botany Bay, 30 km

TABLEI

Summary of deep-water wave statistics for Broken Bay, Australia, August 1974--January 1976

Direction Period Height

(%) (sec) (%) (m) (%)

S 6.7 5.0 2.2 0.0--0.5 4.4 SSE 24.4 6.0 2.2 0 .5 - -1 .0 24 .4 SE 15.6 7.0 6.7 1.0--1.5 44.5 ESE 20.0 8.0 28 .9 1 .5 - -2 .0 15.6 E 13.3 9.0 24.4 2.0--2.5 8.9 ENE 8.9 10 .0 20 .0 2 .5 - -3 .0 2.2 NE 11.1 11.0 15.6

= 9.3 ~ = 1 .29 s.d. = 1.4 s.d. ffi 0.56

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south of Broken Bay. Significant wave heights varied from 0.17 to 2.96 m with a mean value of 1.29 m. Deep-water wave direction was measured at the buoy each day as part of the wave rider collection program. These directions were verified and corrected using hindcast directions derived from weather charts for the preceding day, in the case of swell, and for the same day, in the case of lower-period waves (<8 s). Finally, the directions were checked against field notes to account for sea-breeze conditions that did no t appear on the weather charts. During the study period, SSE--ESE swell dominated for 60% of the time.

Wave refract ion diagrams of each of the four beaches were constructed using wave parameters defined for each of the fifteen field surveys. Wave paths were first computed across the larger scaled offshore bathymetr ic grid of the narrow continental shelf (<20 km width). This procedure allowed all deep-water wave input to be corrected for refraction, shoaling and frictional a t tenuat ion effects on the shelf. All frictional a t tenuat ion calculations were based upon the theory of Bretschneider and Reid (1954) and assumed an a t tenuat ion coefficient of 0.02. Corrected wave paths were then computed across the smaller scaled grids adjacent to each beach. Wave parameters were calculated for orthogonals spaced initially 60 m apart on these latter grids. For some wave periods and directions on the ocean beaches, areas of crossed orthogonals-caustics, were generated over offshore shoals. As linear wave theory cannot approximate wave heights through areas of caustics, the computed wave orthogonals were checked for these extreme refract ion effects using a limiting refraction coefficient of 2.0 (Mogel et al., 1970). Unaccept- able wave orthogonals were purged and breaker characteristics were calculated for the remaining orthogonals when the water depth to wave height ratio was less than 1.28 (Miche, 1944).

The breaker wave characteristics are summarized for each beach in Table II. A wide range of nearshore wave characteristics were generated on each beach by a common deep-water wave climate. Generally, wave conditions were similar on Pearl Beach and the two ocean beaches; however, longshore variation in wave characteristics along these beaches spanned the full range observed in the Broken Bay area. There was also strong contrast in wave characteristics between Patonga and the other beaches. Average wave power values both normal and parallel to shore on Patonga were two orders of magnitude less than on any other beach (64.0 vs 4923.7 watt m -~ for normal wave power and 4.6 vs 815.5 wat t m -1 for longshore wave power). This spatial variation between and along the Broken Bay beaches was also reflected in wave height values (0.0--2.98 m) and was due to refraction either over shallow topography at the protec ted ends of the beaches or into the embayment . Frictional a t tenuat ion of wave height into the bay was of minor importance. It amounted to only 3.3--4.3% of deep water wave height on the ocean beaches, and 10.2--11.2% on the bay beaches. This low degree of frictional a t tenuat ion resulted from the narrowness of the continental shelf off the New South Wales coast (Wright, 1976).

T A B L E II

Average c o m p u t e d b reake r wave cha rac te r i s t i c s o n B r o k e n Bay beaches ( range o f va lues is given in b r acke t s )

4 5

P a l m P a t o n g a Pearl P u t t y

D e p t h o f wa t e r (m) 1 .16 0 .29 1.03 1 .02 Breake r wave h e i g h t 1.01 0 .14 1.11 0 .91

(Hb) ( 0 . 0 1 - - 2 . 7 4 ) ( 0 . 0 1 - - 0 . 7 7 ) ( 0 . 0 1 - - 2 . 6 1 ) ( 0 . 0 1 - - 2 . 9 8 ) R e f r a c t i o n coe f f i c i en t 0. 79 0. 08 0 .74 0. 59

(Kr) ( 0 . 2 2 - - 1 . 9 7 ) ( 0 . 0 1 - 0 . 5 3 ) ( 0 . 0 9 - - 1 . 9 7 ) ( 0 . 1 1 - - 1 . 9 9 ) Shoa l ing coe f f i c i en t 1 .52 2 .40 1 .68 1 .65

(Ks) ( 1 . 1 6 - - 3 . 6 0 ) ( 1 . 3 7 - - 4 . 8 4 ) ( 1 . 2 0 - - 2 . 6 5 ) ( 1 . 0 8 - - 2 . 5 5 ) Fr ic t iona l a t t e n u a t i o n 0 .97 0 .90 0 .89 0 .96

coe f f i c i en t (Kf ) Wave p o w e r n o r m a l to 4 9 2 3 . 7 64 .0 6 2 4 2 . 5 4 8 0 9 . 9

shore (Pn) in w a t t m -~

Wave p o w e r l ongsho re 815 .5 4 .6 506 .3 504 .2 (Pl) in w a t t m -~

Hb = Kr Ks K f ( H o ) Kr = IBI ½ Ks = (Co/Cg) ~ K f = H f i / ( g r Ks Ho)

Hfi Hf]"-i

[(f~ Ax Hf f_ I ) /Ks jT" ] + 1.0 Hfi._ 1 = Hfy.__ 1 (Ks. /Ks. 1 ) (Kr'/Kr~--1) ¢ (p ~ S/3g2) (KsJs inh21rd /L)~ Pn =/9(1 -- sin~coscc ) Pl = P sin~cos~ P = Cg E / C t E = pgHb2L/8

T = wave pe r iod Co = deep wa te r wave ve loc i ty Ho = deep wa te r wave h e i g h t L ffi wave l eng t h C = wave ve loc i ty Cg = wave g r o u p ve loc i ty E = wave ene rgy P ffi wave p o w e r Pn = c o m p o n e n t o f P d i rec ted s h o r e w a r d s Pl = c o m p o n e n t o f P d i rec ted a l o n g s h o r e Hb = breaker wave h e i g h t

H~t__l = H a l ; e h e i g h t a f t e r f r i c t i °na l a t t e n u a t i ° n a t l ° c a t i ° n j ° n ° r t h ° g ° n a l ffi s o m e d i s t ance A x seaward on an o r t h o g o n a l

Ax = s o m e smal l d i s t ance seaward o f l oca t i on j on o r t h o g o n a l d = wa te r d e p t h f = b o t t o m f r ic t ion coe f f i c i en t g = acce le ra t ion due to g rav i ty p = wa te r d e n s i t y Kr = r e f r ac t i on coe f f i c i en t Ks = shoa l ing coe f f i c i en t K f = f r i c t ion a t t e n u a t i o n coe f f i c i en t IBI = wave o r t h o g o n a l s e p a r a t i o n f ac to r

= wave angle to b o t t o m c o n t o u r

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As part of regular beach surveying, five beach profiles were established at 200- -400 m intervals on each beach (Fig. 2). For each of the fifteen surveys carried out, average wave height at the breaker point was either measured using a range pole or judged visually to within 0.25 m on each profile. The former technique was used generally for waves less than 0.75 m in height breaking near shore, while the latter method was used for waves greater than 0.75 m in height breaking on the outer bars. The visual technique was compared on several occasions to measured wave heights between 0.75 and 1.25 m, and was judged accurate to the nearest 0 .25 m. This accuracy is similar to that obtained by Galvin and Savage (1966) for visual estimates of f North Carolina. Comparisons were made between computed and observed breaker wave heights only when a computed wave orthogonal met the beach within 30 m of a surveyed beach profile locale. Although 200 beach observations and 1272 wave orthogonals were used in the study, only 78 comparisons could be made because of this constraint.

CORRELATION OF COMPUTED AND OBSERVED BREAKER WAVE HEIGHTS

Paired observations of computed and observed breaker wave heights are plotted in Fig. 3. Actual wave measurements are delineated in this diagram

2.0

Computed

1.0

x

Spearman's r : 0 . 91 , / /

W i l c o x o n ' s z = 0 . 5 8 / ~ •

n: 78

S i g n i f i c a n c e < 0 . 0 1 .O~'~ ~#~; =

Level ,, / •

/

, /

/

¢ X / x

/ i

/ x

! " F, / • •

x x

/

/ I "; ' : '

x x

x

0

K /

I /

/

,, X

e s t i m a t e d x

m e a ~ r e d

I I 1

1.0 2 .0m

E s t i m a t e d o r M e a s u r e d

Fig. 3. Comparison of computed and observed breaker wave heights, Broken Bay, August 1974--January 1976.

47

by a dot while visually estimated values are depicted by a cross. Observed values ranged from 0.05 to 2.0 m while computed values ranged from 0.01 to 1.8 m. As the data were not strictly accurate, parametric linear regression analysis could not be used to evaluate statistically the correlation between computed and observed values (Poole and O'Farrell, 1971). Instead two nonparametric tests involving ranking of data were used (Siegel, 1956). The first test consisted of Spearman's Rank Correlation which evaluates the degree of association between two sets of paired data. Application of this test produced a correlation coefficient of 0.91 which is highly significant (significance level much less than 0.001). While this statistic indicates a high correlation, it does not indicate a one-to-one relationship between computed and observed wave heights. A second test, the Wilcoxon Matched-pairs Signed-ranks test was used to compare the magnitude of departure of paired observations from a one-to-one relationship. A z-score of 0.58 (probability 0.56) was obtained using the latter test. Both tests indicate that, while there may have been a large difference between computed and observed wave height~ at any one point, there was a consistent and statistically significant (<0.01 level) one-to-one correlation throughout the range of observations, irrespective of whether breaker wave heights were measured or estimated in the field.

CONCLUSIONS

Over the period August 1974--January 1976, breaker wave heights were measured or visually estimated along twenty profiles on four beaches in and around Broken Bay, N.S.W., Australia. At the same time deep-water wave statistics were collected from a wave rider buoy, and were used in conjunc- tion with field data, as input for a computer wave refraction program developed from the work of Dobson (1967). The breaker wave height data calculated using this program were compared, where possible, to observed wave heights, and a significant one-to-one correlation tested using nonparametric statistics. The correlation indicates that, as a first approximation, present computer programs (Dobson, 1967; Coleman and Wright, 1971) can be used to predict breaker wave heights near the shoreline for monochromatic swell having a range of periods between 5.6--12.0 s and a range of heights between 0.17--2.96 m.

The universal application of these conclusions is subject to at least two constraints. Firstly, the New South Wales continental shelf is one of the steepest in the world. Frictional attenuation of wave height across this shelf is much less than might be expected under similar circumstances in other parts of the world (Wright, 1976). Secondly wave conditions, used in the study, are atypical of storm waves which may predominate in higher latitudes. Waves along the New South Wales coast consist essentially of long-period, monochromatic, unidirectional swell, while those characteristic of higher latitudes, where storms are more frequent, consist of short-period sea waves

48

of variable period, height and direction superimposed upon swell. For waves in the former situation, linear wave theory, upon which the Dobson program (with modifications by Coleman and Wright, 1971} is based, can be used to approximate wave behaviour. In the latter situation, present computer wave refraction techniques cannot justifiably be used.

The results of the present study imply that breaker wave height can be approximated by present computer algorithms on beaches having uniform bottom topography and simplified linear wave characteristics, if the offshore bathymetry and deep water wave conditions are known accurately. Because breaker wave height is an important parameter in wave-energy equations and sediment-transport calculations, breaker wave power and sediment transport dynamics may also be approximated under simplified conditions. Computer calculation of these parameters may provide a more efficient means than extensive field measurements, of evaluating nearshore dynamics in these environments.

ACKNOWLEDGEMENTS

Wave data was supplied by N.V. Lawson of the New South Wales Maritime Services Board while bathymetry was provided by the Royal Hydrographic Office of Australia. Computer time was supplied by the Macquarie University Computing Center. Dr. Lionel Carter and Dr. Jerry Reinson critically read the manuscript.

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Documents

Comparison of computed and observed breaker wave heights