STATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS. w : :. 4 Ill. Marc Perlin

TA7 w : :. 4 Ill l o. CERf ~~4 6 cop MISCELLANEOUS PAPER CERC-84-6 STATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS by Mrc Perlin Costl Engineering Reserch Center DEPARTMENT OF THE ARMY Wterwys Experiment Sttion, Corps of Engineers PO Box 63 Vicksburg, Mississippi 398 July 984 Finl Report... -- - - -... -... - Approved For Public Relese; Distribution Unlimited Prepred for DEPARTMENT OF THE ARMY US Army Corps of Engineers Wshington, DC 234

I Unclssified SECURITY C LASSIFICATIO N OF T HIS PAG E (When Dt Entered) READ INSTRUCTIONS REPORT DOCUMENT AT ION PAGE BEFORE COMPLETING FORM. REPORT NUMBER 2. GOVT ACCESSION NO. 3 RECIPIENT'S C ATALOG N UMBER Miscellneous Pper CERC-84-6 4. TITLE ( ~~~nd Subtitle) s TYPE OF REPO RT 6 PERIOD COVERED STATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS Finl report 6 PERFORM ING ORG. REPORT NUMBER 7. AUTHOR( e) 8 CONTRACT OR GRANT N U MBER( ) Mrc Perlin 9. PERFORMING ORGANIZATION NAME AND ADDRESS. PROGRAM ELEMENT. PROJEC T, TASK AREA 6 WORK U NIT NUMBERS us Army Engineer Wterwys Experiment Sttion Costl Engineering Reserch Center PO Box 63. Vicksburg, Mississiooi 398 II. CONTROLLING OFFICE NAME AND ADDRESS 2. REPORT DATE DEPARTMENT OF THE ARMY July 984 us Army Corps of Engineers 3. NUMBER OF PAGES Wshington, DC 234 49 4 MONITORING AGENCY NAME ADDRESS( ff different from Controlllnll Office) IS SECURITY CLASS. (of thle report) Unclssified S. DECL ASSI FICATION7DOWN GRADING SCHEDULE 6. DISTRIBUTION STATEMENT (of thle Report) Approved for public relese; distribution unlimited. 7. Dl ST RIBUTION STATEMENT (of the be trct entered In Block 2, If different from Report) 8. SUP PLEM ENTARY NOTES Avilble from Ntionl Technicl Informtion Service, 5285 Port Royl Rod, Springfield, Virgini 226. 9. KEY WORDS (Continuo on revettj& tjid II nece B.,ty llln d Identify by block number) Wter wves--mesurement (LC) Wter wves--observtions (LC) Ocenogrphy--Sttisticl methods Anlysis of vrince (LC) (LC) 2, ABST'RACT ('C4Uti:u.,..,.r_ efo If nee-..,.:nl ldon.llly by block number) This report presents results of s tudy conducted to determine the vribility of observtions mde simultneously by severl different observers, to compre those observtions with instrument mesurements when vilble, nd to look t the temporl vrition of observed littorl conditions over 25-hour period. Littorl Environment Observtions (LEO) tken by individul observers were compred with the mens of the observtions obtined by ll DO FORM '.J"'f n 473 EDITION OF t NOV 65 IS OBSOLETE Unclssified (Continued) SECU RITY CLASSIFICATrON OF THIS PA';E ( lt'?ren D t Entered)

Unclssified SECU RI TY CLASSI FICATIO N O F THIS PAGE(Wh- Dt Entered) 2. ABSTRACT (Concluded) observers nd with inst rument-recorded dt when vilble for prt iculr vrible. Sttisticl nlyses were per formed for the different LEO vr ibles t o determine the following :. Confidence i ntervls. b. Correltion coefficients. c. St ndrd devitions. d. Consistency between observer nd gge. e. f. Effect of tides on estimtion of prmeters (i. e., did the estimtes depend on the distnce between observer nd wves?) The sttisticl wve height to which LEO wve heights should be compred. The field experiment ws conducted t Duck, North Crolin, t the Field Reserch Fcility (FRF) of the Costl Engineering Reserch Center on 5-6 August 978. Six observers simultneously recorded hourly LEO observtions. Concurrent wve mesurements were mde from the FRF pier with gges nd rdr. Unclssified SE CUR IT Y CL ASSIFIC ATION OF THIS PAGE(When D t Entered)

PREFACE This report presents the results of study conducted by the Costl Engineering Reserch Center (CERC) under the Littorl Dt Collection Methods nd Engineering Applictions work unit of the Shore Protection nd Restortion Reserch Progrm. Mrc Perlin, formerly of CERC, currently t the Costl nd Ocenogrphic Engineering Deprtment, University of Florid, prepred the report under the generl guidnce of Dr. J. Richrd Weggel, former Chief, Costl Structures nd Evlution Brnch (CSEB), Mr. N. E. Prker, former Chief, Engineering Development Division, nd Dr. R. W. Whlin, Chief, CERC. Dr. J. R. Weggel, Dr. T. L. Wlton, nd Dr. E. Thompson, CERC, reviewed the report. CERC ws relocted to the U. S. Army Engineer Wterwys Experiment Sttion (WES) in July 983. Commnder nd Director of WES upon publiction of this report ws COL Tilford C. Creel, CE; Technicl Director ws Mr. F. R. Brown.

CONTENTS PREFACE LIST OF TABLES LIST OF FIGURES CONVERSION FACTORS, INCH-POUND TO METRIC (SI) UNITS OF MEAS UREMENTS.......... PART I: INTRODUCTION..... PART II: THE FIELD EXPERIMENT PART III: DATA COLLECTION AND TRANSFORMATION. Wve Heights nd Periods. Wve Angle t Breking... Foreshore Slope.... Width of the Surf Zone. Longshore Current Prmeters Wve Type....... Wind Speed nd Direction.. PART IV: METHODS OF ANALYSIS. Men nd Stndrd Devition. Correltion Coefficients Confidence Intervls PART V: RESULTS REFERENCES APPENDIX A: APPENDIX B: APPENDIX C: Wve Period........................... 2 Wve Height......................... 28 Wve Angle.......................... 28 Foreshore Slope................. 3 Surf Zone Width............ 3 Longshore Curr ent............. 33 Wve Type nd Wind Speed/Direction........... 33 Possible Improvements......... 34 TABLES PLOTS OF OBSERVATIONS VERSUS OBSERVATION MEANS. ACTUAL TIDE VERSUS SURF ZONE WIDTH AND PREDICTED TIDAL CURVE Pge 3 3 4 5 7 2 2 3 4 4 4 5 6 7 7 8 8 2 35 Al Bl Cl 2

No. 2 List of Tbles Men, Stndrd Devition, nd Confidence Intervls of the Observers Correltion Coefficients Pge 22 26 No. 2 3 4 5 6 7 8 List of Figures Loction mp for the Field Reserch Fcility t Duck, North Crolin Observers nd gge loctions during the experiment Front of stndrd LEO form, used to record dt Bck of stndrd LEO form, used to obtin wve ngle Observed wve period versus mesured wve period Observed wve height versus mesured wve height Observed wve ngle versus rdr-mesured wve ngle Tidl elevtion versus foreshore slope Pge 8 9 27 29 3 32 3

CONVERSION FACTORS, INCH-POUND TO METRIC (SI) UNITS OF MEASUREMENT Inch-pound units of mesurement used in this report cn be converted t o me t ric (SI) units s follows: Multiply miles (U. S. sttute) feet By.69347.348 kilometers meters To Obtin 4

STATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS PART I: INTRODUCTION. The Littorl Environment Observtion (LEO) progrm ws estblished in 968 by the Costl Engineering Reserch Center (CERC) to obtin nershore wve, wind, nd current climtologicl dt t specific costl sites. progrm is discussed in some detil by Berg (969), Szuwlski (97), Bruno nd Hiipkk (973), Blsillie (975), nd Schneider (977). The As prt of the progrm, reltively inexpensive equipment is used by n observer to visully estimte or mesure severl vribles pplicble to costl engineering problems. Vribles mesured include wve period, wve height, wve ngle t breking, wve type, wind speed (using hndheld nemometer), wind direction, foreshore slope (using clinometer), width of surf zone, longshore current velocity (by pcing off the distnce trvelled by dye pcket), nd the presence nd spcing of rip currents nd bech cusps. These dt hve been used to predict longshore trnsport rtes, to verify models for other costl phenomen s uch s bech cusp spcing, nd to estblish generl wve nd wind climtologies. 2. The present study ws conducted to determine the vribility of observtions mde simultneously by severl different observers, to compre those observtions with instrument mesurements when vilble, nd to look t the temporl vrition of observed littorl conditions over 25-hour period. LEO observtions tken by individul observers were compred with the mens of the observtions obtined by ll observers nd with instrument-recorded dt when vilble for prticulr vrible. for the different LEO prmeters to determine the following:. Confidence intervls. b. Correltion coefficients. c. Stndrd devitions. d. Consistency between observer nd gge. Sttisticl nlyses were performed e. Effects of tides on estimtion of prmeters (i.e., did the estimtes depend on the distnce between observer nd wves?) f. The sttisticl wve height to which LEO wve heights pper to correspond. 5

3. The field experiment described herein ws conducted t CERC ' s Field Reserch Fcility (FRF) t Duck, North Crolin, on 5-6 August 978. Six observer s s imultneously recorded hourly LEO observtions. Concurrent wve mesurements were mde from the FRF pier with gges nd rdr. 6

PART II: THE FIELD EXPERIMENT 4. The FRF t Duck, North Crolin, shown in Figure ws the site of the field experiment. Six observers recruited from the CERC stff were sttioned 725 ft* north of the pier (Figure 2). To simulte the vribility of experience embodied in personnel who typiclly tke LEO mesurements in the field, individuls prticipting in the experiment included one experienced observer nd two completely inexperienced observers. All individuls were exposed to the trining session given to typicl field observers. 5. Hourly observtions of ll LEO vribles were mde by ech observer during 25-hour period (26 observtions) (the stndrd LEO form is shown in Figures 3 nd 4). Observers were instructed not to discuss their observtions during the experiment; ech observer is therefore believed to hve provided n essentilly independent observtion, unbised by the observtions of the others. The experiment's durtion included two tidl periods to introduce vrible distnce between the breking wves nd the observer nd to evlute this effect on the observers' estimtes. Becuse of profile conditions, the surf zone t high tide for given wve height ws reltively nrrow due to the steepness of the bech slope. For n equivlent wve condition t low tide, the surf zone ws wider. 6. At the sme time the visul observtions were tken, Bylor gges on the FRF pier mesured wve heights nd lnd-bsed X-Bnd rdr (Figure 2) provided screen imges of the se surfce which were then photogrphed. For descriptions of the rdr nd wve gges, see Mttie nd Hrris (979) nd Thompson (977), respectively. * A tble for converting the inch-pound units of mesure used in this report to metric (SI) units is found on pge 4. 7

Vir9inio Bech Sntt ;....., &- ~ Elizbeth City Duck Kity ~ Howt... Novs Heod -- -- -:- i,. ' ' ' '.. \ s' Cpt HofltrflS Figure. Loction mp for the Field Reserch Fcility t Duck, North Crolin 8

Dune Line\ I Shoreline -,- Loction of Observers ( 725 ft from pier) Temporry Dt Collect ion Center Rdr Un i t ~c:: A 8 C D E F G ~~~~~=c~==~====~ Reserch Pier Bylor Wove Gges Distnce Sewrd Along Pier, ft A 62 8 7 c 78 D 9 E I,6 F I, 42 G I, 9 APPROXIMATE SCALE 2 4 6 ft Figur e 2. Observers nd gge loctions during t he experiment 9

LITTORAL ENVIRONMENT OBSERVATIONS RECORD ALL DATA CAREFULLY AND LEGIBLY SITE NUMBERS YEAR MONTH DAY T IME I 2 3 4 5 6 7 8 9 II Record time 2 3 4 5 I I I I I I rn rn OJ I I I I I us ing the 24 hour system WAVE PERIOD 6 7 8 BREAKER HEIGHT 9 2 2 Record the t ime in seconds for I I I I Record the best est imte of the OJ.O overge wove he ight to the nerest eleven (I I ) wove crests to pss o sttionry point. If clm record. tenth of o foot. WAVE ANGLE AT BREAKER 22 23 24 WAVE TYPE 25 Record to the nerest degree the I I I I - Clm 3 - Surg ing direction the wves ore com ing from I -Sp illing 4- Sp ill I Plunge using the protrctor on the reverse side. if clm. 2- Plungng WIND SPEED 26 27 WIND DIRECTION_ ~~rect i.on the wnd 28 OJ I S comng from. Record wi nd speed to the nerest -N 3-E 5-S 7-W - Clm 2-NE 4-SE 6-SW 8-NW mph. If clm record. FORESHORE SLOPE 29 3 WIDTH OF SURF ZONE 3 32 33 34 Record foreshore slope to the OJ Estimte in feet the distnce from I I I I I nerest degree. shore to brekers, if c lm record. LONGSHORE CURRENT DYE 36 37 38 Estimte dstonce in teet from shoreline to point of dye injection. I I I I CURRENT SPEED 43 44 45 CURRENT DIRECTION 46 47 Mesure in feet the distnce the dye I I I I No longshore movement OJ ptch is observed to move during o one (I) minute period; If no longshore movement record. +I Dye moves towrd right -I Dye moves towrd left RIP CURRENTS 49 ~ ~I 52 If rip currents ore present indicte spcing (feet). If spcing is irregulr estimte overge spcing. If no rips record. I I I I I BEACH CUSPS 54 ~5 56 If cusps ore present i nd icte spc ing (feet). If spc i ng is irregulr estimte overge spcing. If no cusps record. PLEASE PRINT : I I I I SITE NAME OBSERVER Plese Check The Form For Completeness REMARKS : CERC 3-72 8 Mr 72 Moke ny dd itionl remrks, computtions or sketches on the reverse side of th is form. Figure 3. Front of stndrd LEO form, used to record dt

OCEAN 7 8 t 9 6 2 5 3 4 SHORELINE OBSERVER SHORELINE 8 NOTE : If per s used for n observton pltform : plce - 8 l ne on the roll p rll e l to the center lme of the per, ste long the crest of the brekng wves nd rec ord the ngle observed. Figure 4. Bck of stndrd LEO form, used t o obtin wve ngle

PART III: DATA COLLECTION AND TRANSFORMATION 7. A description of the visul nd mesured dt is presented below. No rip currents or bech cusps were observed during the experiment; hence, no further discussion of them is included herein. Wve Heights nd Periods 8. Twenty-minute wve gge records of the se surfce were nlyzed to determine significnt wve heights nd periods. Dt from ech gge were recorded t the rte of four points per second for 2-minute durtion, nd the record, composed of 496 dt points, ws nlysed using the stndrd CERC computer nlysis. In this nlysis, the first step is to edit the dt for non-numeric chrcters or nomlous spikes. Usully, highly questionble points re rejected nd the record supplemented by interpoltion. If more thn 2.5 percent of the points re deemed bd, the routine rejects the record s unsuitble for nlysis. For cceptble records the distribution function nd its first five moments re computed nd dt window pplied to the dt points--this technique produces greter resolution of the frequency spectrum of the record. The progrm then computes the vrince spectrum. Significnt wve height is obtined s four times the stndrd devition of the record. Significnt wve period is defined s the reciprocl of the frequency t the middle of the spectrl bnd with mximum energy; when two wve trins occur, the significnt wve period is tken s the one ssocited with the lrger energy pek. For complete discussion of CERC gge dt nlysis, see Thompson (977). 9. Wve Gge No. 675, locted 42 ft sewrd of the lndwrd end of the FRF pier in pproximtely 2.7 ft of wter referenced to men se level (msl), ws chosen s reference becuse it provided the most consistent record during the experiment (i.e., Gge No. 675 filed to obtin mesurements t only six hourly intervls, wheres the other gges filed more frequently). Therefore, lthough the visul observtions were recorded 26 times, the dt set contins only 2 complete (gge nd visul) observtions nd mesurements.. The wve height t breking ws computed by the liner wve theory sholing eqution, with the breking depth given by 2

() where Hb - db - breking wve height wter depth t breking Refrction ws not considered in the wve height trnsformtion.. As mentioned bove, the significnt wve period for the gge records ws defined s the period ssocited with the frequency t the middle of the spectrl bnd with mximum energy. Visul observtions of period were determined by timing wve crests pssing sttionry point nd then dividing by ten. Timing strted when the first crest pssed the point nd ended when the eleventh crest pssed. Wve Angle t Breking 2. The wve ngle t breking ws determined from the forementioned rdr system. The system included Rytheon 2/9XR Mriners Pthfinder X-bnd rdr with pulse width of.5 microsecond, rnge resolution of -2 m (32.8-65.6 ft), nd 2.74-m (9-ft) slotted rry ntenn with horizontl bem width of.9 degree t 3 db nd rottion t 33 rpm. Pulses of electromgnetic energy with nominl wvelength of 3 em nd nominl fre- quency of hertz re bemed over the wter, nd prt of the energy is bckscttered to the ntenn (for complete discussion, see Mttie nd Hrris (979)). Nine pictures were tken of the rdr scn ech hour. Lter, the dt were reduced by mesuring the nine wve ngles from ech hourly set of photogrphs nd verging to the nerest degree. Visul observtions of wve ngle were estimted to the nerest degree by the six observers using the protrctor provided on the bck of the stndrd LEO form (Figure 4). A wve ry pproching perpendiculr to the shoreline ws recorded s hving 9-degree wve ngle; wve pproching from the right of norml to the bech for n observer looking sewrd ws considered to hve wve ngle greter thn 9 degrees; while wves pproching left of the norml were considered smller thn 9 degrees. 3

Foreshore Slope 3. The slope of the wetted bech fce ws mesured by the LEO observers with clinometers. Becuse the clinometer is itself n instrument, no dditionl ''truth'' dt were tken. Observtions of slope mesurements were compred mong observers to obtin "confidence intervls"; the use of confidence intervls ssures tht slope vries with loction rther thn mong different observers. Width of the Surf Zone 4. LEO observers estimted the distnce from the wetted limit of the shoreline to the breking wves; hence, these vlues were simply compred to ech other to estblish the consistency of observtions by different observers. No instrument mesurements (truth dt) were mde of surf zone width. Longshore Current Prmeters 5. Fluorescein dye pckets were thrown into the surf zone by LEO observers to estimte the longshore current. The following three seprte mesurements were tken:. The estimted distnce in feet from the shoreline to the point of dye injection. b. The distnce the dye ptch trvelled in 6-second period s pced off long the shoreline by the observer. c. The direction the dye trvelled (positive is defined s movement to the right when looking sewrd). 6. Since the mgnitude of the longshore current velocity vries with distnce from shore cross the surf zone, ech observtion should be reduced to common bsis in order to compre one longshore current observtion with nother. In n ttempt to do this, the theoreticl longshore current velocity distribution of Longuet-Higgins (97) (for plne bech) ws used. According to Longuet-Higgins, for vlue of his mixing prmeter P of.4 (/49)X - (5/7)X ln X < X < v - (2) (/49)X-S/ 2 < X < oo 4

where v X v v - dimensionless current velocity - v/v - dimensionless distnce - x/xb - velocity t distnce X into the surf zone - longshore current velocity t the breker line if horizontl mixing is neglected - distnce to the breker line Eqution 2 is vlid only when P, the dimensionless mixing prmeter which expresses the reltive importnce of horizontl mixing in trnsferring momentum, is tken to be.4. Other vlues of P led to more complex reltionships, but P =.4 ppers to be n upper limit to observtions of the longshore current distributions. All the vlues needed to solve Eqution 2 re vilble in the LEO dt set except for the vlue of v which cn be considered reference current velocity. Eqution 2 ws solved for v for ech LEO observtion, nd these clculted reference compred. longshore currents were 7. It ws discovered tht the distribution of velocity could not be used to normlize the observtions becuse of inccurcies in estimting either surf zone width or the distnce from shoreline to point of dye injection; in severl instnces, the surf zone width hd been estimted to be only frction of the distnce from the shoreline to where the dye pcket ws thrown, resulting in unrelistic vlues for son between the LEO current observtions ws v. Therefore, direct comprio mde without correcting for loction in the surf zone. meters operting t the FRF pier. At the time of the experiment there were no current Wve Type 8. The type of breking wve ws ssigned number nd recorded s follows:. (clm). b. (spilling). c. 2 (plunging). d. 3 (surging). e. 4 (spill/plunge (trnsition between spilling nd plunging)). 5

Tble Al, Appendix A, shows the vrition of breker types observed during the experiment. Wind Speed nd Direction 9. As with wve type, wind speed nd direction s recorded in the LEO progrm re not suited to n nlysis which clcultes men, stndrd devition, nd confidence intervls. These prmeters re vectors, nd their direction is given by compss sector. Wind speeds could hve been hndled seprtely; however, it is the combined effect of direction nd speed tht is importnt. Therefore, no sttisticl nlysis of these dt ws performed; wind speed nd direction dt re presented in Tble A2, Appendix A. 6

PART IV: METHODS OF ANALYSIS 2. The s ttisticl nlyses were performed using stndrd equtions s discussed below. Out of possible totl number of 248 LEO dt entries, excluding wve type nd wind speed/direction dt, ten dt entries were not reported. These missing dt vlues were estimted s being equl to the verge of the remining observtions for the sme vrible tken tht hour; thus n error, lthough smll, ws introduced. As mentioned in prgrph 9, six wve gge redings were not obt ined during the experiment due to equipment filure ; therefore, only 2 complete dt sets (observtions versus wve mesurements) were nlyzed. Men nd Stnd r d Devition 2. The men nd stndrd devitions were clculted using the two following equtions, respectively (see Benjmin nd Cornell 97): n X - l l: x. n i= (3) s = n -:----:- ~ (n- ) L...J i= - 2 (x. - x) (4) where X. x = smple men s = smple s t ndrd devition, unbised estimtor n - number of observtions in the -vlue of the ith observtion smple Correltion Coefficients 22. Correltion coefficients were computed by using the following formul (see Benjmin nd Cornell 97): 7

n!~ X. - X y ~ r - x,y s s X y i=l (5) where r - the correltion coefficient between vribles X nd y x,y. th X. nd y. - the ~ observtion of the vribles X nd y ~ ~ s nd s - the bised stndrd devitions of the X nd y X y vribles, respectively X nd y - the mens of the smples n - the number of observtions The correltion coefficient r is mesure of how well two vribles re x,y linerly correlted. The reltionship between the LEO observt ions nd corresponding gge/rdr mesurements should be liner, nd t he correlt ion coefficient should pproch.. If the vribles re uncorrelted, r should x, y pproch., while for negtively correlted vribles r should pproch x, y -.. Confidence Intervls 23. Confidence intervls were computed using the t - sttistic becuse the smple size ws smll nd the uncertinty ssocited with not knowing the popultion vrince could not be ignored. The t-sttistic distribution is broder thn the norml distribution nd reflects the greter uncertinty introduced becuse good estimte of the stndrd devition is not vilble. The following eqution ws used (see Benjmin nd Cornell 97): p X - t (/2,n- l) rn s < m < X + t (/2,n-l) rn s - - (6) where p - probbility ( - ) - desired confidence bnd s - stndrd devition of the smple t (/2, n- l) - t - sttist ic with n- degrees of freedom m - popultion men 8

x = smple men (Eqution 2) n - number of observtions in the smple Eqution 6 sttes tht the probbility tht the popultion men is between the limits given by the terms in brckets is (l- ). Or stted nother wy, for the desired level of probbility tht the popultion men is included between two limits, the confidence bnd must be mde s wide s indicted by the term in brckets. In ll of the nlyses of confidence intervls herein, vlue of.95 ws used for (l- ). The confidence intervls listed in this report re the vlues of intervl width on ech side of the smple men. 24. Nrrower confidence estimtes cn be estblished with lrger dt sets (i.e., s n increses, the bnd required for the sme level of confidence decreses). An idel version of this experiment would hve involved 2 observers, ech tking simultneous observtions; in lieu of this idel, six observers took mesurements spred over period of time. A lest squres regression line ws then fitted to both upper nd lower confidence limits. The slope, y-intercept, nd R 2 vlues found in Tble A3 were computed from Equtions 7, 8, nd 9 (Drper nd Smith 966), respectively: n L i=l x.y. - n i=l 2 (x.) - n n i=l X. n y. /n /n ' (7) b - n L i=l (y.) - n (bl) L i=l n X. (8) R 2 - SS /SS reg men (9) 9

where x nd y - b - ordinte nd bsciss vlues, respectively slope of the regression line b - y-intercept of the regression line R 2 - proportion of totl vrition bout the men explined by the regression SS - reg sum of squres due to regression SS - men sum of squres bout the men The SS is simply ~ (y. - y) 2, where y is the men. SS is men ~ reg ~" - 2 ~(yi - y) where y. " l is the vlue predicted by the regression line. If the regression line is good representtion of the upper or lower limits of the confidence bounds (i.e., if the regression line is good predictor), SS pproches SS nd R 2 pproches.; the smller R 2 gets, the reg men more sctter nd the worse predictor the regression line is. R 2 therefore gve some insight into how vrible the confidence bnds were for ech of the 2 observtions. 25. Another method used to obtin confidence intervls involved plotting the observtions of the six observers for ech hour of the test ginst the men of the six observtions nd lso ginst the vlue mesured by the gge. This method of grphing the "spred" of the dt is discussed further in Prt V. 26. Becuse the ssumption tht observtions re distributed ccording to norml distribution is required to determine confidence intervls, the rtio of confidence intervl width to stndrd devition is constnt. 2

PART V: RESULTS 27. This prt summrizes nd discusses the results of the sttisticl nlyses. Individul observed vribles will be discussed seprtely. Becuse of the limited scope of the experiment, the vrious sttistics generted by the nlyses should not to be interpreted s representtive of ll LEO dt. Severl similr or broder experiments re needed to better quntify the vribility of visul wve observtions. The observers themselves were vribles. The six persons who prticipted in this experiment could hve been better or worse thn the "verge" field observer retined for LEO dt gthering. It is not known whether LEO observers improve with experience or whether they continue to hold ny bises they my hve hd t the strt of their observtion experience. The observers in this experiment were not typicl observers since they were pressed into service for this experiment lone, nd they my thus hve exhibited bises tht would not hve persisted hd they been continuing observers. Wve Period 28. Tble lists the mens, stndrd devitions, nd confidence intervls for wve period, wve height t breking, wve ngle t breking, foreshore slope, surf zone width, nd longshore current velocity. During the experiment, the gge recorded significnt wve periods between 8 nd seconds. The mens of the LEO observtions fell in the sme rnge; however, the verge width of the confidence intervls ws +3.42 seconds (the verge width of the confidence intervls from the 2 dt sets ws considered to be n estimte of the overll confidence intervl). The 95 percent confidence limits on wve period were, therefore, 9.5 ~ 3.42 seconds (i.e., 6.-2.9 seconds). Note tht the upper limit is more thn twice the lower limit, vrition due lrgely to vritions in the observers' decisions on wht constitutes wve. Did observers include wve which hd previously broken? Did they count only the lrger wves? If n observer sw lrger wves breking frther offshore nd chose n imginry point pst which to count wve crests, wve periods would certinly turn out to be longer becuse the smller wves were not counted, giving bis to the longer period wves. Whether or not the observer counted smll perturbtion on lrger irregulr wve would lter the 2

Tble Men, Stndrd Devition, nd Confidence Intervls of the Observers Observtion Stndrd Prmeter No. Men Devition Wve period (sec) 8.65 3.36 2 8.9 3.562 3.67 3.445 4.533 3.49 5 9.35 4.26 6 9.767 2.395 7 9. 433 2.46 8 9.25 2.898 9 8.6 3.2 9.433 3.73.47.35 2 9.2 3.27 3 8.867 3.64 4 8. 767 2.785 5 9.667 3.777 6.27 4.345 7.7 3.636 8.233 3.33 9 9.33 3.327 2.467 4.594 Averge 9.5 3.26 Wve height (ft) 2.67.327 2 2.25.536 3 2. 483.688 4 2.83.59 5 2.65.622 6.85.586 7 2..74 8.967.794 9 2.2.66 2.383.794 2.683.875 2 2.7.75 3 3.5.35 4 2.967.294 5 3..974 6 2.483.43 7 2.233.36 8 2.33.266 9 2.57.553 2 2.367.589 Averge 2.4.7 (Continued) Confidence Intervl 3.48 3.739 3.66 3.588 4.473 2.54 2.525 3.42 3.7 3.33.38 3.282 3.26 2.923 3.964 4.56 3.86 3.495 3.492 4.822 3.42.343.562.722.62.653.65.739.834.693.833.98.233.37.358.22.452.379.279.58.68.74 22

Tble (Continued) Observtion Stndrd Confidence Prmeter No. Men Devition Intervl Wve ngle (deg) 3. 333 9.39 9.77 2 4.833 8.62 9.39 3 4.333 9.933. 426 4.333 8. 238 8.647 5 5.667. 72.676 6 5.5.3. 664 7 5. 9. 252 9.7 8 5. 667 9.66.82 9 5.833.43.696 3.833 8. 353 8. 767 4. 667. 58 2.89 2 3.5 9.72 9. 522 3 5.5 9. 67.49 4 2.667 8. 64 9. 7 5.833 3. 497 4.66 6. 667 9.626.4 7 3.333. 622 2. 98 8 6.667.255. 83 9.333 9.92 9.543 2 4.. 973.57 Averge 4... 5 Foreshore slope (deg) 4.67. 722.88 2.333 2.733 2.868 3 2.333.366. 434 4 2.333.33.84 5.833 3.545 3.72 6 4.833.753. 79 7 2.833.753. 79 8 3.67. 983. 32 9 3.67.69. 227 3.5.837.878 6.67 2. 563 2.69 2 8. 333 2. 25 2.363 3.5.225.286 4.5. 225. 286 5. 2.9 2.3 6 7.333.56.542 7 4.5.548.575 8 2.833.48.429 9 2..632. 664 2 2.5.548.575 Averge.4.4 (Continued) 23

Tble (Concluded) Observtion Stndrd Confidence Prmeter No. Men Devition Intervl Width of surf zone (ft) 5.833 36.32 38.3 2 9.67 65.758 69.2 3 56. 27.276 28.629 4 77.5 54.475 57.77 5.667 6.698 64.759 6 85. 38.47 4.379 7 87.333 9.54 2. 8 99.67 33.826 35.53 9 88.333 6.633 7.458 4.667 39.429 4.385. 48.99 5.42 2 88.333 28.42 29.8 3 74.67 2.837 2.87 4 55.833 29.226 3.676 5 74.5 36.25 38. 6 94.67 66.74 7.5 7 9.667 33.267 34.97 8 98. 9.3 2.8 9 22.5 73.263 76.898 2 35. 65.879 69.47 Averge 94. 4.7 42.8 Longshore current velocity -.88.34.39 (ft/sec) 2 -.25.64.645 3 -.897.343.36 4 -.967.366.384 5 -.978.388.47 6 -.356.44.52 7 -.439.366.384 8 -.57.558.586 9 -.475.57.543 -.45.445.467 -.67.59.67 2 -.878.36.379 3 -.78.399.48 4 -.494.349.367 5 -.8.352.37 6.4.658.69 7 -.56.49.429 8 -.869.584.63 9 -.497.654.686 2 -.88.327.343 Averge.42.44 24

period; lso, whether the observer counted the short-crested wve, or merely the long- crested wves, is nother fctor contributing to the vrition in observer- determined wve periods. Another fctor is the occurrence of bimodl spectr; for instnce, observers my only hve included wves coming from one of two predominnt directions. (This is lso fctor in determining gge-mesured periods becuse the wve period ssigned to wve record is the period of mximum density energy, irrespective of direction. Bimodl spectr do not provide n verge period, such s n observer tends to see, but rther the period of mximum energy density.) 29. Although confidence intervls provide rnge of vlues within which given observer cn be expected to estimte prmeter, more importnt fctor is how the individul observtions correlte with the ctul wve period. As mentioned bove, the gge- mesured period ws lso subject to mbiguity in the cse of bimodl spectr. Chrcterizing the wves by monochromtic wve period when in relity n irregulr se exists cn led to questionble results. Neglecting this, LEO observtions were correlted with wve gge significnt periods chosen t the middle of the frequency bnd with mximum energy, regrdless of whether the spectr were bimodl. The correltions between observed conditions nd () the gge/rdr-determined vlues nd (b) the men of the observers re listed in Tble 2. Correltion coefficients pproch ~ if the pirs of vlues lie long stright line with the sign of the coefficient depending on the slope of the line. If n observer ' s vlues correlte well with gge vlues, positive vlues ner. will be computed; if lrger thn verge observtions occur with smller thn verge gge mesurements (nd vice vers), negt ive vlues of t he correltion coefficient result. 3. For this experiment, poor cor reltion between observtions nd mesured vlues resulted. The discrepncies between observtions nd observtion mens with gge vlues cnnot be ttributed to observtionl errors lone. Vritions occur becuse of the difficulty of deci ding wht constitutes wve nd when to count disturbnce s wve; problems re lso cused by the somewht rbitrry method of obtining significnt wve period from gge mesurements. All of these contribute to the sizeble differences between observed nd mesured wve periods. 3. Appendix B presents plots of ech observtion versus the observermen; Figure 5 plots observtion versus gge/rdr vlues. An observer 25

Tble 2 Correltion Coefficients Observer No. Observer vs Observer Men Observer Gge vs Wve period 2 3 4 5 6.335.57 -.68.639. 22. 28.44 -.45.89 -.2 -.32.88 Wve height t breking 2 3 4 5 6.88.55.55. 78.467. 6 -.27. 49.8 -. 332.398.424 Wve ngle t breking 2 3 4 5 6.642. 55.55.4. 4.68 -. 53 -.24.37.235 -. 29. Foreshore slope 2 3 4 5 6. 953.854. 97.92.976.96 Width of surf zone 2 3 4 5 6.76.342. 248.43. 689.564 Longshore current velocity 2 3 4 5 6. 6.675. 63. 595. 8.488 26

~,---------------------------------------------------------------------------------~ - IP ~...... -46 6 I im 2 33 s 6 s 6 s f 2 6 6 4 3! 4 i s '4-~-------r--~----~----------r---------y---------~---------r---------,--------~ "'"4.oo s.oo 8.. 2. ~. 6. 8. 2. T (OBS), sec Figure 5. Observed wve period versus mesured wve period 27

bis cn be detected from observtion of these plots (the plotted number represents the observer who mde the estimte). Figure 5 shows tht Observer 5's estimtes were generlly lrger thn gge vlues, while observers 4 nd 6 usully gve estimtes tht were smller thn gge vlues; this suggests the possibility of "clibrting" n observer so tht his observtions could on the verge be corrected to provide fir estimte of gge vlues. On the other hnd, how could observers, such s, 2, nd 3, who sometimes overestimte nd sometimes underestimte the gge vlues, be clibrted? Wve Height 32. The confidence intervl for wve height estimtion mong observers ws computed to be +.74 ft (Tble ). Averge wve conditions during the experiment were pproximtely -3 ft. Correltion coefficients between observer nd gge were gin low. Observer 6 ws closest to the gge mesurements with correltion coefficient of.42; Observer 4 ws the worst with r =.33 Correltion between observtions nd the observtion men ws fir (Figure B2), suggesting tht visul observtions of wve height my be difficult to estimte ccurtely, but observers my hve consistently estimted incorrectly s group. Also, the rnge of wve heights encountered during the experiment ws smll, which my ccount for some of the sctter. Figure 6 shows tht greement between observtions nd gge mesurements of trnsformed significnt wve height ws poor. Recll tht only sholing trnsformtion ws performed, with refrction nd energy dissiption ignored 33. To determine whether the verge of the observed wve heights would provide better estimte of the gge wve heights, the correltion coefficient ws clculted. A vlue of r = -.34 ws obtined, indicting tht the verge wve height of severl observers provided n extremely poor estimte of gge heig~ts. Wve Angle 34. The verge 95 percent confidence intervl for wve ngle t breking ws +.5 degrees in this study (Tble ). Correltion between observed ngle nd the rdr-determined men ngle ws poor. Figure 7 shows tht observers were more consistently bised in estimting ngle thn in estimting 28

~,---------------------------------------------------------------------------~ lf) c-.. - lj) IJ') -.q. 3 6 5 lf) t""- - (T") 3 2 5 ~ 6 - LU (.!) < (.!) {'I") co ::r:: lf) c-. - c-. 3 2 6 6 ~ 3 5 ~ 6 2 5 8 2 ~ 3 6 53 i ~ 5 I 3 5 i 2 J 2 I 6 lf) -... I 6 6 53-462 3 98 2 6 5 2 2 5 3 3 6 I 5 5 I 2 2 6 ~ 5 3 6 2 I 6 2 s ~.4 ~ lf) t""-. - ~-------.---------.--------~------~--------~------~--------~------~ tt.oo.75 '.so 2'.25 3'.oo 3.75 4'.so s'.25 6. HB OBS, ft Figure 6. Observed wve height versus mesured wve height 29

wve height or period, usully estimting lrger wve ngles thn those which ctully occurred. Rdr imges for given hourly mesurement hd mximum vrition in wve.ngle t breking of pproximtely ~5 degrees. This rithmetic verge of number of rdr imges ws compred with the LEO observtions. Foreshore Slope 35. Foreshore slope ws mesured using hnd level s clinometer; therefore, there ws little possibility of n error in mesurement. The difference between two concurrent observtions ws rther due to the vribility of bech foreshore slope nd the fct tht observers plced the clinometer t different plces on the bech. The sttisticl nlyses, therefore, give the rnge of foreshore slope vribility on given bech. The verge of the stndrd devitions ws ~.4 degrees (Tble ) (note tht slope i s recorded on the LEO form to the nerest degree). Correltion between observers nd the men of the observtions ws very good. The vlues of the correltion coefficient rnged from.854 to.976, indicting tht foreshore slope is the most consistent nd probbly the most ccurte of the dt collected in the LEO progrm. If bech cusps hd been present, greter sptil vribility would hve existed in the bech slopes, nd therefore lower correltion coefficients might hve been expected. Further demonstrtion of the qulity of the foreshore slope dt is shown in Figure 8 which plots foreshore slope versus tidl elevtion. The dt clerly show tht s the tidl elevtion incresed, foreshore slope lso incresed. This ws s expected since for n equilibrium bech profile (see, for exmple, Den (977)) the profile should be steeper t the men high wter line. Surf Zone Width 36. The observed surf zone width during the experiment verged bout 94 ft (Tble ). The verge of the confidence intervls ws +42.8 ft. The verge confidence intervl ws thus nerly hlf of the verge vlue of the surf zone width estimte-- poor correltion. Correltion coefficients vried from.248 to.76. 3

3 2 CID "' Q) Q) ~ c:n Q) -c w ~ > : w (/) lxi w ~...J (/) w : :I: (/) w : u. 2 <( w ~ 9 8 7 6 5 4 3 2 oo ($) -3. -2. -.. 2. 3. TIDAL ELEV, ft Figure 8. Tidl elevtion versus foreshore slope (observer men) 32

37. Surf zone width increses s tide level decreses provided the wve height remins firly constnt; this is becuse the surf zone is on the fltter prt of the bech profile. It is possible tht the width of the confidence intervl will increse s the surf zone width increses. Conversely, nrrower surf zone suggest smller estimte error; however, the rtio still produces lrge stndrd devition nd hence brod confidence bnd. To test which is correct, tidl elevtions were plotted ginst confidence intervls (Figure Cl). The sctter on the grph suggests tht neither interprettion is correct. Longshore Current 38. As mentioned, difficulties were encountered in ttempting to rtionlly compre the observers ' longshore current dt. The currents were compred directly without correction nd neglecting the effects of the offshore distnce to the point of current mesurement. The verge confidence. intervl ws +. 44 ft per second (Tble ). Correltion coefficients rnged from.488 to.8 between observed velocities nd the observer men. Since current mesurements long the pier were not mde during the experiment, correltion with mesured dt ws not possible. Wve Type nd Wind Speed/Direction 39. The types of wves observed during the experiment re tbulted in Appendix A, Tble Al. At no time during the experiment did ll six observers gree on the wve type, nd only once did five of the six observers gree. Four of the six observers greed five times. On one- hlf of the observtions, ll four wve types were reported. Clm conditions were never reported. 4. Wind speed nd direction observtions re tbulted in Tble A2. As with wve types, t no time did ll observers record either the sme speed or direction. Rnges of speed nd direction re lso listed in Tble A2. There is lrge discrepncy mong observers. Twelve times one or more observers recorded clm conditions while other observers recorded some wind. In one cse, two observers recorded clm, while other observed recorded speeds between 2 nd 6 miles per hour. Only once did five of the six observers recorded identicl wind speeds; however, direction vried by s much s 33

9 degrees. A vrition of 8 degrees ws the mximum observer vrition in wind direction reported. Possible Improvements 4. The LEO surf observtion progrm is ttrctive becuse of its reltively low costs. Improving the qulity of the dt must be weighed ginst ny increse in the cost of obtining better qulity dt. Also, since most observers re unpid volunteers, chnges tht increse the mount of time required to obtin set of dt must be crefully considered. Simple instrumenttion might possibly be developed tht would neither significntly increse cost nor increse the mount of time required to obtin dt set. For exmple, in res where costl structures re present, grduted wve stffs could be instlled nd used to estimte wve heights. Rnge finder/stdi type instruments might be developed to mesure surf zone width nd wve height; however, the cost of such equipment might be prohibitive. 42. The results of the experiment point out some of the limittions of the LEO dt nd suggest some wys to improve dt qulity. The importnce of crefully trining observers nd periodiclly meeting with them in the field to observe their methods is indicted. The dt should be reviewed periodiclly to detect ny obvious errors, nd feedbck to the observers should be provided to correct procedures nd to offer encourgement. Idelly, fter few dys of dt hve been obtined by new observer, these dt should be reviewed nd the observer informed of the results of the review. He should then be observed tking set of observtions nd his dt compred with n independent set of dt tken by the individul providing the trining. Lrge dscrepncies should be brought to his ttention nd their cuse determined. In recruiti ng observers, individuls with some technicl bckgr ound should be sought since they re more likely to be ble to estimte distnces, etc. 43. Further evlution of LEO observ t ions is required to better define the rnge nd cuse of errors. Quntifying the vribility of LEO dt is necessry to estblish how much confidence user cn hve in the dt. 34

REFERENCES Blsillie, J. H. 975. "Anlysis nd Interprettion of Littorl Environment Observtion (LEO) nd Profile Dt Along the Western Pnhndle Cost of Florid," TM 49, Costl Engineering Reserch Center, U. S. Army Engineer Wterwys Experiment Sttion, Vicksburg, Miss. Benjmin, J. R., nd Cornell, C. A. 97. Decisions for Civil Engineers, McGrw-Hill, Probbility, Sttistics nd New York. Berg, D. W. 969. "Systemtic Collection of Bech Dt," Proceedings of the th Conference on Costl Engineering, Americn Society of Civil Engineers, Vol, pp. 273-277. Bruno, R.., nd Hiipkk, L. W. 973. ''Littorl Environment Observtion Progrm in the Stte of Michign," Proceedings of 6th Conference on Gret Lkes Reserch, Interntionl Assocition of Gret Lkes Reserch, pp. 492-57. Den, R. G. 977. "Equilibrium Bech Profiles: U. S. Atlntic nd Gulf Costs," University of Delwre Ocen Engineering Report No. 2, Newrk, Del. Drper, N. R., nd Smith, H. 966. Applied Regression Anlysis, John Wiley nd Sons, Inc., New York. Longuet-Higgins, M. S. 97. cident Se Wves, 2," Journl pp. 679-68. "Longshore Currents Generted by Obliquely of Geophysicl Reserch, Vol 75, No. 33, In- Mttie, M. G., nd Hrris, D. L. 979. "A System for Using Rdr to Record Wve Direction," TR 79-, Costl Engineering Reserch Center, U. S. Army Engineering Wterwys Experiment Sttion, Vicksburg, Miss. Schneider, C. 977. "Visul Surf Observtions/Mrinelnd Experiment," Costl Sediments '77, Americn Society of Civil Engineers, New York. Szuwlski, A. 97. "Littorl Environment Observtion Progrm in Cliforni, Preliminry Report, Februry-December 968," MP 2-7, Costl Engineering Reserch Center, U. S. Army Engineer Wterwys Experiment Sttion, Vicksburg, Miss. Thompson, E. F. 977. "Wve Climte t Selected Loctions Along U. S. Costs," TR 77- Costl Engineering Reserch Center, U. S. Army Engineer Wterwys Experiment Sttion, Vicksburg, Miss. U. s. Deprtment of Commerce, Ntionl Ocenic nd Atmospheric Administrtion, Ntionl Ocen Service. 978. "Est Cost of North nd South Americ Including Greenlnd--978 Tide Tbles, High nd Low Wter Predictions," Rockville, Md. 35

APPENDIX A: TABLES Al

Tble Al Wve Type Observtion Observer Number / Observer 2 Observer /3 Observer 4 Observer 5 Observer 6 Plunging 2 Surging Surging Plunging * 3 4 5 6 Plunging 7 Plunging 8 Plunging Plunging Plunging Surging Surging Surging k* 9 Plunging Plunging Plunging Plunging Plunging Plunging 2 3 Plunging 4 Plunging Surging Surging Plunging Plunging Plunging Plunging Plunging Plunging 5 Plunging Plunging Plunging J~J. ",.. Plunging 6 Plunging 7 8 Plunging 9 2 Plunging Surging Surging Surging Surging Surging Plunging Plunging Plunging Plunging Plunging * Observtion not recorded. nd plunging. A2

Tble A2 Wind Speed (mph)/direction* Observtion Observer Observer Observer Observer Observer Observer Rnges Number Ill 2 3 4 lis 6 Mx-Min/Mx-Min 7/4 7/4 6/4 6/ 6/ 7/2 7-6/4-2 2 7/4 6/3 7/4 6/ 7/3 7/2 7-6/4-2 3 7/5 6/3 4/4 5/ 6/3 5/2 7-4/5-2 4 6/5 6/3 6/4 7/ 4/3 5/3 7-4/5-3 5 4/4 4/3 6/4 4/ 5/3 4/2 6-4/4-2 6 3/5 3/3 3/4 / / / 3-/5-7 5/4 5/4 5/4 5/ 4/3 5/2 5-4/4-2 8 5/6 3/4 3/3 4/ 3/4 3/3 5-3/6-3 9 4/5 4/3 5/5 4/ 4/4 4/3 5-4/S-3 4/6 5/3 3/5 3/ / / 5-/6-4/7 5/3 / / 3/4 / 5-/7- > w 2 3/5 5/3 / 2/ 3/4 2/2 5- /5-3 4/7 6/3 2/4 2/ / / 6- /7-4 5/6 /3 / 2/ 2/4 / 5- /6-5 3/7 /3 / 4/ 2/7 / 4-/7-6 3/7 2/7 / 2/ 2/7 4/8 4-/8-7 2/7 2/7 / 2/ / / 2-/7-8 3/7 3/7 / 2/ / 2/8 3-/8-9 2/7 3/7 4/6 / 3/3 3/4 4- /7-2 3/5 4/7 / 4/ 4/7 4/4 4- /7- * Symbols for direction r e defined s follows: ( = clm) = N 5 = S 2 = NE 6 = SW 3 = E 4 = SE 7 = W 8 = NW Observtions not recorded.

Tble A3 Lest Squres Regression Anlysis on the Upper nd Lower Confidence Intervls of the Observed Dt Confidence Intervl* Slope Reg Line Y-Intercept Wve period p M.424.4 4.55 7.93.49.339 Wve height p M.576.954.68.89.92.45 Wve ngle p M.577.6 37.85 46.844.665.59 Foreshore slope p M.86.82 -.28.985.967.947 Width of surf zone p M.526.6 22.9 63.244.83.27 Longshore current p M.749.82 -.49.24.8.754 * P = upper limit of confidence intervl; M - lower limit of confidence intervl. See Eqution 8. A4

APPENDIX B: PLOTS OF OBSERVATIONS VERSUS OBSERVATION MEANS Bl

,----------------------------------------------------------------------. N co... u - Q.) en. Cl)v z... - <t > :: ~ co on U- z <t UJ :EO -.... I- 3 4 3 2 I ~ ~ 33 3 s 2 3 ' 6 l 2 s 5 2 3s 5 s s 2 3 s s 2 s I 6 2 s 2 ~ 6 co ~-------.--------.--------.--------.--------.--------.--------.------~ v4.oo 6.o.oo o.oo 2. 4. tg.oo t.oo 2. T (OBS), sec Figure Bl. Observed wve periods versus men of wve period observtions B2

~~--------------------------------------------------~----~ l/) N l/) l/) - _...:: l/) (f) c- z (T) - <t: > cr UJ (f) co (T) u... z <t: UJ -::Elf) N co I N 3 2 3 2 s 3 s 2 s 6 2 s e 5 3 ~ 6 i 2 i 3! 6 25 46 2 3 3 6, 5 ~ 2 5 I 8 6 5 3 66 ffi2 3 s r I 6 5 l/) l/) c- '4-------~--------~------~------~~------~------~--------~------~ 9J.oo.75 so 3. 3.75 cso 5.25 HB (OBS), ft Figure B2. Observed wve heights versus men of wve height observtions B3

~~---------------------------------------------------------------------,... IJ) N... (J) <l.) <l.).._ N... Ol <> -co - - IJ) (/) z... o... I- <( > :O UJ (/) co... L.L.... z <(o wo ~.. IJ) coo (.!:)... z <(... 3 3 2 3 l 8 2 '3 I 2 I 3 6 I 2 s s s 6 s 6 5 6 ~------~--------.--------.--------.--------.--------.--------.------~ eng. 9S.OO. los.oo. ls.oo 2. 2S.O ~"' :3. ANGB (OBS), degrees Figure B3. Observtions of wve ngle versus men of wve ngle observtions B4

~ ~--------------------------------------------------------~ ~-... N_... 8 I 6 en Q.) Q.)... e> ~ -.::: _ en... z - <t > :: UJ en. ~ ~- u... z <t UJ ~ - UJ Q... _J en (() - ~ - N 2 s 8 6 I 6 I 2 2 6 s ' I 8 3 I s 8 6 I I I I I I ' 3 6 6 s 5 6 6 I I I I CU.oo s'.oo '.oo tb.oo t2.oo SLOPE (OBS), degrees I 4-6. Figure B4. Observtions of foreshore slope versus men of for eshor e slope obs ervtions B5

~~---------------------------------------------------------------------. N -N... -...::. U) ZIJ') or-- - 4:: > : UJ U) CO, Oo LL v... z 4:: UJ O :2 - Nlf) U)o :;::- r-- 6 2 3 2 " 3 " ~ 4 3 6 ~ ~ 5 2 ~s 6 I 5 5 o4 6 3 5 6 5 3 I 2 6 3.(2 3 2 5 s ' 5 6 3 s l ls') (") 2 2 l 3 3 '4--------.--------.--------.--------.--------.--------~-------.------~ <=t:j.oo 35. 7. 5. 4n.oo s.oo 2. 245. WSZ (OBS}, ft Figure BS. Observtions of surf zone width versus men of surf zone width observtions B6

/) ~~--------------------------------~... If) - u Q) en _. -. - U) z.,_ <t: > ::) LU (f) co, u... Z <t: LU, ~- -,...J LU > 3 3 3 3 8 s 3 tli " 2 4 ~s~~ 6 6 6 2~ 43 2i6 2St e 6 2 4f it s 34 2 2 l~ It lt ~ 4 2 '2 s 6 /)... I ~ I /) ~+-------~--------.--------.--------,-------~--------,-------~------~ '-2.6 -z... oo -.so -. -o.6o.o o.so.oo.6o VEL (OBS), ft/sec Figure B6. Observtions of longshore current velocity versus men of longshore current observtions B7

APPENDIX C: ACTUAL TIDE VERSUS SURF ZONE WIDTH AND PREDICTED TIDAL CURVE Cl

9 w z N u. cc => en u. :X: - s: I _, <t > cc w - z w (._') z w u. - z (._') 8 7 6 5 4 3 2 ($) rc -3. -2. -.. 2. 3. TIDE ELEV, ft Figure Cl. Actul tide versus confidence intervls for surf zone width C2

3. 2. 2 w -~ --. w - (..) - w : Q.. MSL 6 -. 2 8 9-2. 2 6 2 5 AUGUST 978 24 4 8 2 6 AU GUST 978 6 TIME (EST) Figure C2. Predicted ocen tide for Kitty Hwk, North Crolin C3