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Driven Setdown and Setup JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. C3, PAGES 4629-4638, MARCH 15, 2001 Field observationsof wave-driven setdown and setup B. Raubenheimer WoodsHole OceanographicInstitution, Woods Hole, Massachusetts R.T. Guza ScrippsInstitution of Oceanography,La Jolla,California SteveElgar WoodsHole OceanographicInstitution, Woods Hole, Massachusetts Abstract. Wave-drivensetdown and setupobserved for 3 monthson a cross-shoretransect between the shorelineand 5 rn water depth on a barred beach are comparedwith a theoreticalbalance between cross-shore gradients of the mean water level and the wave radiation stress.The observedsetdown, the depressionof the mean water level seaward of the surf zone, is predictedwell when radiation stressgradients are estimatedfrom the observationsusing linear theory at each location along the transect. The observed setdownalso agreeswith analyticalpredictions based on offshorewave observationsand the assumptionof linear,dissipationless, normally incident waves shoaling on alongshore homogeneousbathymetry. The observedsetup, the superelevationof the mean water level owing to wave breaking,is predictedaccurately in the outer and middle surf zone, but is increasinglyunderpredicted as the shorelineis approached.Similar to previous field studies,setup at a fixed cross-shorelocation increases with increasingoffshore wave height and is sensitiveto tidal fluctuationsin the local water depth and to bathymetric changes.Numerical simulationsand the observationssuggest that setupnear the shoreline dependson the bathymetryof the entire surf zone and increaseswith decreasingsurf zone beach slope,defined as the ratio of the surf zone-averagedwater depth to the surf zone width. A new empiricalformula for shorelinesetup on nonplanarbeaches incorporates this dependence. 1. Introduction whereE isthe wave energy, 0 is the wave direction, and Cg andC arethe group and phase velocities, respectively. Wave setdownand setupare changesin mean water level Thetheoretical balance (1), withSxx given by (2), is con- thataccompany shoaling and breaking surface gravity waves. sistentwith observationsin narrowwave flumes(where 0 With no alongshorevariations in wavesor bathymetryand = 0) with smooth,impermeable, fixed bottoms and planar negligiblewind and bottomstresses, the cross-shorepres- [Bowenet al., 1968], barred[Battjes and Janssen,1978; sure gradient associatedwith the time-averagedwave set- downand setup r/theoretically balances the cross-shoregra- Battjesand Stive, 1985], and other [Gourlay, 1992] depth profiles.Predictions of setupdiffer in detailbecause of dif- dientof thetime- anddepth-averaged onshore wave momen- tum flux (the waveradiation stress $•) [Longuet-Higginsferent model dependencies of $x• on localwave properties (e.g., linear or nonlineartheory) and differentformulations and Stewart, 1962], of theeffect of waverollers [e.g., Svendsen, 1984; Diegaard os• o• et al., 1991;Sch•iffer et al., 1993]. Ox + pg(v+ h) - 0 (• ) Thereare few fieldtests of the balance(1) usingconcur- rent observationsof both r/ and $• acrossthe surf zone. where x is the cross-shorecoordinate, h is the still water Battjesand Stive[1985] integrated(1) usinga wavetrans- depth, p is the water density,g is gravitationalaccelera- formationmodel to predict$•x andobtained good agree- tion, andfor linear,shoreward propagating, monochromatic ment with setupobserved in 2 and 4 m depthduring a waves, storm. Assumingthat the depthand setupvary linearly acrossthe beach,Lentz and Raubenheimer[1999] showed - , (2) thatthe setup measured for 3.5years in 2 m waterdepth was modeledqualitatively well by (1) with Sz• estimatedwith (2) usingwave measurements in 8 and2 m depths.However, Copyright2001 by theAmerican Geophysical Union. the assumptionsof lineardepth and setupvariations were Paper number 2000JC000572. shownto leadto integrationerrors as largeas 50% of the 0148-0227/01/2000JC000572509.00 observedsetup. More accuratesetup predictions with $x• 4629 4630 RAUBENHEIMER ET AL.' WAVE-DRIVEN SETDOWN AND SETUP and h estimatedfrom wave and bathymetrydata collected buried pressuregages (setup sensors) located between the alonga cross-shoretransect agreed well with setupobserved shorelineand about 5 m water depth (Figure 1, solid cir- for 2 monthsin 2 m water depth,even thoughthe setupmea- cles). The setuppressure sensors were buriedto avoidflow- surementswere madewith unburiedpressure sensors subject induceddeviations from hydrostaticpressure (see Appendix to flow-inducedmeasurement errors (see Appendix A) and A). After correctingfor temporalchanges in water density offset drift. [Lentzand Raubenheimer,1999] with conductivityand tem- Field measurementsshow that surf zone setupdepends on peraturemeasured in 5 m water depth, mean water levels the local waterdepth and the offshorewave height [Nielsen, were calculatedfrom 512 s (8.5 min) recordsby assuming 1988; King et al., 1990]. Field observationsof setupat the hydrostaticpressure. shoreline77shore suggest Setup(setdown) was defined as the increase(decrease) of the mean water level relative to that observed at the most 77shore-- cHs,o, (3) offshoresetup sensor (cross-shore location x = 58 m). The observedshoreline setup was estimatedas the setupwhere whereHs,0 is the offshoresignificant wave height and c is the total water depth was < 0.1 m. Note that 77shorewas a constant between about 0.2 and 0.3 [Hansen, 1978; Guza measuredonly when the shoreline,defined as the intersec- and Thornton, 1981; Nielsen, 1988; Hanslow et al., 1996]. tion of the mean water level with the beach,approximately This result is consistentwith (1) and (2) assuminga mono- coincidedwith a setupsensor location, which occurredat tonic beachslope, normally incidentlong waves,and surf mostonce per rising(and falling) tide. zone wave heightsthat are a constantfraction of the wa- At all but the shallowest three locations, sensor offset ter depth. However, scatterabout (3) is considerable(of- drifts (typically equivalentto about 0.03 m of water over ten greater than 100% of 77shore),possibly because natu- the 3 monthexperiment) were removedby subtractingfrom ral beachesoften are barred or alongshoreinhomogeneous, eachtime seriesa quadraticcurve fit to setupestimated at wavereflection may be largenear the shoreline,and the ratio 17 times when negligiblesetup or setdownwas expected of waveheight to waterdepth may dependon thebeach slope (H•,0 < 0.35 m andh > 2 m). In shallowerwater (x > 350 and wave conditions. Additionally, observedmean water m), drifts were removedby adjustingthe calculatedmean levelsnear the shoreline(in bothfield andlaboratory studies) waterlevels (using a quadraticfit) sothat setupand setdown canbe sensitiveto the measurementtechnique [e.g., Holland were negligiblefor small nonbreakingwaves (estimated as et al., 1995] and to the definition of setup [e.g., Gourla3; locationsand times when the ratio 78 of significantwave 1992]. heightH8 to total waterdepth h + 77was < 0.2) and so that In contrastto (3), Holman and Sallenger [1985] found the water level equaledsand level when the saturatedsand no correlationbetween video-basedestimates of 77shoreand aboveswash zone sensorsfirst wasexposed during rundown H•,0, butinstead suggested that 77shore/Hs,o increased with [Raubenheimeret al., 1995]. increasingIribarren number •0 = •/v/H•,o/Lo, where• is the foreshorebeach slope and L0 is the offshorewave- ....... I ......... I ......... I ......... length of the spectralpeak frequency. Scatterin this rela- ß tionshipwas reduced by separatingthe resultsinto low, mid- dle, and high tidal stages,and it was hypothesizedthat the offshorebar morphologyinfluenced the low-tide shoreline setup. However,the observationsof Nielsen [1988] showed little effect of the offshorebarred bathymetry on the setup, and thus the importanceof barredbathymetry to 77shoreis _ uncertain. Here the balance (1) is tested with field observationsof waves and time-averagedwater levels measuredbetween the -4 shorelineand about5 m water depthon a barredbeach. Wa- ter levels are estimatedwith buried,stable pressure sensors. -6 Setdownand setupup are predictedby integrating(1) with 400 300 200 1 O0 0 Sxx basedon (2) usingthe wave observations.The observed Gross-shore Lo½ofionx(rn) setdownis consistentwith (1). Similar to Lentz and Rauben- heimer[1999], setupis predictedwell in 2 m waterdepth, Figure 1. Locationsof deeplyburied pressure sensors used butthe balance breaks down in depthsshallower than about to measuresetup (solid circles), colocated unburied pres- 1m. Setup near the shoreline isshown tobe sensitive tothe suresensors, current meters, and sonar altimeters (open cir- surfzone bathymetry andtidal fluctuations. cles),near-bed pressure sensors (open diamonds), andthe conductivitysensor (asterisk). The most seaward11 setup sensorswere accurateParoscientific gages. All pressure 2. Field Experiment and Data Processing measurementswere corrected for temperatureeffects. The solidcurves are selectedbeach profiles measured between 1 Observationswere acquired from Septemberthrough September and 31 November.The thick black curve is the November1997 on a sandyAtlantic Ocean beach near Duck, 13 Septemberprofile. The x axisis positiveonshore with the North Carolina. Bottompressure was measuredwith 12 originat thelocation of theoffshore sensor. RAUBENHEIMER ET AL.' WAVE-DRIVEN SETDOWN AND SETUP 4631 Beach profiles were surveyedevery few days with an Table 1. Least SquaresLinear Fits (With Intercept a and amphibiousvehicle, and seafloorelevations were measured Slopeb) of SetupPredictions
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