US-CE -C Property ot the

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1 TA7 W34m no. CERC-96-5 '. 2 J US Army Corps of Engineers Waterways Experiment Station US-CE -C Property ot the UnUed States Governmont Misellaneous Paper CERC-96-5 June 1996 ndex and Bulk Parameters for Frequeny Diretion Spetra Measured at CERC Field Researh Faility, June 1994 to August 1995 by Charles E. Long Approved For Publi Release; Distribution s Unlimited Prepared for Headquarters, U.S. Army Corps of Engineers Metearh Llbrarv U Army lnginttr Waterways M*mlnt Stauon Vitkttug. tlaalsq,pi

2 Misellaneous Paper CERC-96-5 June 1996 TAl LuS-fm ndex and Bulk Parameters for Frequeny- :_a_;_ C f(t-7-~ Diretion Spetra Measured at CERC Field Researh Faility, June 1994 to August 1995 by Charles E. Long U.S. Army Corps of Engineers Waterways Experiment Station 399 Halls Ferry Road Viksburg, MS Final report Approved for publi release; distribution is unlimited Prepared for U.S. Army Corps of Engineers Washington, DC Under Civil Works Researh Work Unit 32484

3 US Army Corps of Engineers Waterways Experiment Station N...!5!Y. fiiofiiiindmitndrfoq!fricf: JUaUC AfFARS O'RC U. S. ARY ENOEER WATDWAYS -EKJJ'ATON _HAUB., YCCiaiiiO, -.,... PHON : (11JDWSZ... Waterways Experiment Station Cataloging-n-Publiation Data Long, Charles E. ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, June 1994 to August 1995/ by Charles E. Long; prepared for U.S. Army Corps of Engineers. 142 p. : ill. ; 28 em. - (Misellaneous paper ; CERC-96-5) nludes bibliographi referenes. 1. Wind waves - North Carolina - Duk - Statistis. 2. Water waves - North Carolina- Duk- Statistis. 3. Oean waves- North Carolina- Duk Statistis. 4. Frequeny spetra.. United States. Army. Corps of Engineers.. U.S. Army Engineer Waterways Experiment Station. ll. Coastal Engineering Researh Center (U.S. Army Engineer Waterways Experiment Station) V. Title. V. Series: Misellaneous paper (U.S. Army Engineer Waterways Experiment Station) ; CERC TA7 W34m no.cerc-96-5

4 Contents Prefae... tv 1-lntrodution Field Researh Faility... 3 Bathymetry... 3 Wave-Generating Winds nstrumentation Data Colletion Data Proessing Error Cheking... 1 Frequeny-Diretion Spetra Bulk Parameters Arhived Results Retrieving Proessed Data Summary ofresu1ts... 3 Referenes Appendix A: Table of Colletion Times and Bulk Parameters A 1 Appendix B: Time Series Graphs of Bulk Parameters... B1 Appendix C: Listing of FORTRAN Computer Program... C1 Appendix D: Listing of Sample Data File... D1 Appendix E: Notation... E 1 SF 298 iii

5 Prefae This report indexes parameters of and desribes means of aess to a series of wind wave frequeny-diretion spetral observations made with a 16-element, high-resolution diretional wave gauge at the Field Researh Faility (FRF) of the U.S. Army Engineer Waterways Experiment Station (WES). The work was motivated by a pauity of observations of diretionally distributed wave energy, whih has hindered understanding and modeling of the nearshore proesses that affet oastal engineering projets. This effort was authorized by Headquarters, U.S. Army Corps of Engineers (HQUSACE), under Civil Works Coastal Navigation Hydrodynamis Program Researh Work Unit 32484, "Diretionality of Waves in Shallow Water." Funds were provided through the Coastal Engineering Researh Center (CERC), WES, under the program management of Ms. Carolyn M. Holmes, CERC. Messrs. John H. Lokhart, Jr., Charles Chesnutt, and Barry W. Holliday were HQUSACE Tehnial Monitors. This summary report was prepared by Dr. Charles E. Long, under the diret supervision of Mr. William A. Birkemeier, Chief, FRF, and Mr. Thomas W. Rihardson, Chief, Engineering Development Division, CERC. The work was performed under the general supervision of Dr. James R. Houston and Mr. Charles C. Calhoun, Jr., Diretor and Assistant Diretor, CERC, respetively. The diretional wave gauge and its data proessing software were designed by Dr. Joan M. Oltman-Shay whileat-o!'egonstateuniversity :working through an ntergovernmental Personnel Agreement. The diretional wave gauge was physially maintained with diver oordination by Messrs. Mihael W. Leffler and C. Ray Townsend, FRF, and logistial support by Mr. Brian L. Sarborough, FRF. Gauge alibration was maintained by Messrs. Kent K. Hathaway and Paul R. Hodges, FRF. Aquisition, monitoring, and storage of raw data were done by Mr. Clifford F. Baron, FRF. At the time of publiation of this report, Diretor ofwes was Dr. Robert W. Whalin. Commander was COL Brue K. Howard, EN. The ontents of this report are not to be used for advertising, publiation, or promotional purposes. Citation of trade names does not onstitute an offiial endorsement or approval of the use of suh ommerial produts. iv

6 1 ntrodution Wind waves are among the dominant foring mehanisms in all oastal proesses. Estimation of wave fores for engineering design requires knowledge of sea state, whih is desribed, at a minimum, by an amplitude, a frequeny, and a diretion for eah omponent of a wave field. Historially, there have been many observations of wave amplitude and frequeny, but very few detailed observations of wave diretion, due primarily to additional tehnial requirements in making suh measurements. This represents a distint and very important void in the knowledge required for omprehensive engineering design. To begin to alleviate this dearth of knowledge, the Field Researh Faility (FRF) of the U.S. Army Engineer Waterways Experiment Station, installed a high-resolution, diretional wave gauge for long-term observations ofthe nearshore inident diretional wave limate at its site near Duk, NC (Figure ). The original gauge, onsisting of an alongshore linear array of nine pressure gauges, was installed in September 986. n September 99, an additional six gauges with a ross-shore alignment were inorporated, making a S-element, two-dimensional spatial array for estimating wave energy propagating in all diretions. Data thus obtained, whih take the form of wave frequeny-diretion spetra, are intended for use by the broadest possible group of researhers and appliation engineers, and have been arhived in a simple database. This report simplifies data dissemination by indexing and desribing means of aess to the set of observations olleted from July 1994 to August 1995, part of the eighth and all of the ninth year of deployment. This period inludes the dates of the DUCK94 experiment, a large-sale, interdisiplinary nearshore proesses investigation (for a orief summary, see Long and Sallenger ( 995)). ndexes for preeding years have been reported by Long (99a, 99b), Long and Smith (1993, 1994), Long and Atmadja (1994), Long and Pemberton (1994), and Long and Roughton (1994, 995). The main text of this doument desribes and larifies the substantial information ontained in the appendixes. Brief overviews are given of the measurement site, instrumentation, data olletion, and method of diretional spetral estimation. These subjets are desribed in greater detail in other publiations, to whih the reader is referred. Following the overviews is a desription of the arhived frequeny-diretion spetra and some haraterizing bulk parameters that an be derived from them. Appendix A is a listing of these haraterizing parameters and is intended to be used as a atalog of the set of spetra. Appendix B ontains Chapter 1 ntrodution 1

7 $OUndlnQS n fo,hons nou t 1 o n 1 e s k lloneters Figure 1. Loation and offshore bathymetry of the FRF graphs of time series of some of these parameters as a pitorial augmentation of the information in Appendix A. Appendix C illustrates a FORTRAN omputer program that an be used to read arhived data, of whih a sample listing is given in Appendix D. 2 Chapter 1 ntrodution

8 2 Field Researh Faility As shown in Figure 1, the FRF is loated on the barrier island hain of oastal North Carolina. A detailed desription of the layout, funtion, and apabilities of the FRF is given by Birkemeier et al. ( 1985). Of partiular relevane to diretional wave studies are the wave-steering bathymetry and wave-generating winds. Bathymetry The oastline in the viinity of the FRF is nearly straight for several tens of kilometers north and south (Figure 1 ). t is oriented suh that a shore-normal line (direted seaward) is very nearly 7 deg from true north. Waves and onshore winds an approah this site along an easterly 18-deg ar from 34 to 16 deg true. The adjaent ontinental shelf is wide, relatively shallow, and of somewhat omplex bathymetry. The diretion of nearest approah ofthe 1-m (328-ft) isobath, whih indiates the shelf break, is 1 to 15 deg south of east. On this azimuth, the shelfbreak is about 8 km (43 n.m.) distant. A typial bottom slope for the shelf is.1, but this is interrupted by numerous features of 1- to 1 -km (.5- to 5.4-n.m.) horizontal sales and 1-m (33-ft) vertial sales sattered irregularly aross the shelf. Within a few kilometers of the FRF, the offshore bathymetry is more regular, with isobaths nearly shore-parallel and a bottom slope of about.2 (Figure 2). Some irregularities exist. Within about 3m (984ft) of the shore, there exists a omplex and mobile bar system (Birkemeier 1984) that is strongly influened by nearshore- waves- and eurrents-. These proesses-have also reated.some...irre.gular... bathymetry in the viinity ofthe 6-m-long (1,97-ft-long) FRF researh pier (Miller, Birkemeier, and DeWall1983). Wave-Generating Winds The site is subjet to a variety of limates, whih gives rise to a diverse set of diretional wave onditions. Primary soures of high-energy waves are winds assoiated with hurrianes and frontal passages. Though no hurrianes passed diretly over the FRF during the period overed by this report, several passed near enough that signifiant wave energy ould be measured at the FRF. Notable among these were Hurriane Gordon, November 1994, and Hurriane Chapter 2 Field Researh Faility 3

9 .., "' -o Eo -"' CD :... o en.., _.,..... ~ \ \ ' \ 1\ ' ''N,~. ) ~ 1M ( ' D ~ \ \ --' \ \ v.){ U1 ' ' CD "r ':.1 \ Pi~r-E~d ; ) rmometers ' in Q) ',. r. e e "l, > o... <( E (X)... - ', v 1 N,, wave diretion oordinates X lzl x' pier oordinates.., lx _6_ -46 -&5G Distane (m) Figure 2. FRF nearshore bathymetry and oordinate system Felix, 15-2 August Low-pressure weather fronts, ofwhih several rossed the FRF site during this reporting period, were typially oriented northeastsouthwest with strong wave-generating winds oming from the northeast. For additional information, the National Oeani and Atmospheri Administration daily weather maps (U.S. Department of Commere 1994, 1995) ontain large-sale depitions of weather systems passing the FRF site during this 4 Chapter 2 Field Researh Faility

10 olletion period. Detailed, quantitative desriptions of the limate at the FRF, as determined from its arsenal of instrumentation, are given in a series of annual reports, of whih those by Leffler et al. (1995a, 1995b) are examples. Chapter 2 Field Researh Faility 5

11 3 nstrumentation The primary instrument in this study is a high-resolution diretional wave gauge. t onsists of two parts. The first is a spatial array of sensors that sample sea-surfae displaement at several points in (horizontal) spae. The seond, desribed in the following setion on data proessing, is the mathematial treatment of these data to obtain estimates of wave diretionality. The FRF array onsists of 5 pressure gauges mounted approximately.5 m (1.6 ft) off the bottom in the viinity of the 8-m (26-ft) isobath about 9 m (2,953 ft) offshore and to the north of the researh pier (Figure 2). ts loation satisfies three onstraints. First, it is generally outside the surf zone so that linear wave theory is appliable in data proessing. Seond, it is in water shallow enough that signals from 3-se waves, the shortest periods of interest here, are detetable above bakground noise at the bottom-mounted gauges. Third, it is loated away from the irregular isobaths around the pier and in the nearshore bar system, whih helps minimize bathymetrially indued inhomogeneities in the wave field. Spaing between gauges in the array appears irregular in Figure 2 but, for the most part, orresponds to the array-design riterion posed by Davis and Regier ( 977) that every gauge pair has a unique separation. Figure 3 is an enlarged view of the array layout and shows gauge spaing as well as the gauge naming sheme. A sixteenth pressure gauge (labeled T) in Figure 3 was part of a low-resolution diretional wave gauge that also inluded the urrent meter indiated in rigure ~. -pfior to o-november 994, data from gauge T were inluded in error heking proedures, and were available as bakup data in the event of failure of ertain other gauges, but were not used as part of the high-resolution array during this olletion period. Gauge T and the urrent meter were removed on 6 November 994. Thereafter, no further information was obtained from the site labeled Tin Figure 3. The array geometry enompasses onsiderable ranges in both sizes and numbers of gauge separations. Minimum gauge spaing is 5 m (16.4 ft) in both the alongshore and ross-shore diretions. Maximum spaing is 255m (837ft) in the alongshore diretion and 2 m (394ft) in the ross-shore diretion. ntermediate gauge spaings are in multiples of 5 m (16.4 ft). With 5 gauges, there are 5 possible unique spaings. n the FRF array, 2 redundant spaings are intentionally left for anillary examination of spaial homogeneity ofthe wave field, so that 93 unique spaings remain. 6 Chapter 3 nstrumentation

12 FRF 8-m Array o g.---~--~----~--~ ~--~----~--~----, 9 8 T 7 - E ) Q) u r::: o -Cl) Q)....J::. Cl) C> r:::...j CD A B E 5 6 ~ ~--~--~----~--~----~--~--~----~--~--~ 1 BOO 9 Cross-shore Distane (m) Figure 3. Spaing and numbering of linear array gauges With the exeption of gauge C prior to 11 May 1995, eah pressure gauge is a Senso-Metri Model SP973(C), in whih a piezo-eletri strain gauge detets displaement of a pressure-sensitive diaphragm referened to an evauated avity. Site alibrations indiate an auray of the pressure equivalent of ±.6 m (±.2 ft) of water for wave-indued flutuations about a stati water olumn height of 8 m (26 ft). Prior to 11 May 1995, gauge C was a Parosientifi Model 245AT resonating quartz absolute pressure transduer. The manufaturer's stated Chapter 3 nstrumentation 7

13 auray ofthis gauge is the pressure equivalent of±.3 m (±.1 ft) of water, whih is about twie as aurate as the Senso-Metri gauges. Voltage analogs of pressure signals are hard-wired through 1-Hz, fourth-order, Butterworth filters (primarily to eliminate 6-Hz noise) to an analog-to-digital signal onverter, and then to a Digital Equipment Corporation V AXstation 4 omputer for data aquisition. Disretization ofthe full-sale signal to 11-bit binary form results in a digitization step ofthe equivalent of.7 m (.23 ft) of water, whih is nearly the same as the auray of the Senso-Metri gauges. 8 Chapter 3 nstrumentation

14 4 Data Colletion Signals from eah of the pressure gauges were sampled at 2Hz and stored digitally as reords of 4,96 points (34 min 8 se). A olletion onsisted offour suh reords, or 16,384 points (2 hr 16 min 32 se) for eah gauge. This proedure resulted in a total of245,76 data points to produe one frequeny-diretion spetrum. Colletions ourred eight times daily with starting times 1, 4, 7, 1, 13, 16, 19, and 22 hr Eastern Standard Time (EST). With this sampling pattern, the maximum number of olletions is 2,92 in a 365-day year. Some olletions are missed, however, beause of neessary maintenane and repairs to the diretional array and the data olletion system. During the 15-month period overed by this report, a total of 3,581 frequenydiretion spetra (about 98 perent of the maximum possible) were obtained. A list of data olletion start times for these observations is given in Appendix A. Appendix B ontains time-series plots of spetral parameters with available wind and urrent observations as auxiliary environmental variables. Loations of referene anemometers and the urrent meter are shown in Figure 2. Chapter 4 Data Colletion 9

15 5 Data Proessing Conversion of measured time series to estimates of frequeny-diretion spetra requires produts of auto- and ross-spetral estimates from the array gauge data. For final results to be aurate, raw input data must be of exeptionally high quality so that spiky or drifty data from one gauge do not ontaminate all results. Hene, the proedure for data proessing is to hek raw data for errors before estimating frequeny-diretion spetra. Some bulk parameters an then be omputed to haraterize results. Error Cheking Beause multiple gauges were deployed in what was assumed to be a uniform sea, ertain statistial properties of raw data from eah of the set of gauges should be idential. One suh property is the frequeny spetrum S(j) (where f is frequeny)1 of raw (not surfae-orreted) pressure signals. Under the ideal irumstanes of onstant water depth, uniform gauge elevation from the bottom, and no statistial noise, frequeny spetra from all gauges are idential in every detail. Though these irumstanes are not met exatly in the FRF system, they are approximated suffiiently losely that an interomparison of the frequeny spetra from the array of gauges is an exellent method for identifying erroneous data reords. A onvenient way to effet suh an interomparison is to overplot frequeny spetra from all the gauges on a single graph. Wind wave signals attenuate with depth so that, in aordane with linearized wave theory, very little diret wind wave-energy is-expeted in the frequenynmge from about.4 Hz to the sampling Nyquist frequeny ( 1. Hz for normal FRF sampling). Spetra in this frequeny band should primarily indiate system noise, whih should be about the same for all gauges of like kind, and onsistent in time for all gauges. Exessively spiky data from one or more gauges appear as inreased noise levels relative to data from normally funtioning gauges. Strong low-frequeny drifts in data from one gauge appear either as deviations in the low-frequeny part of the spetrum, or as varying mean values from segment to segment through a data reord. n the pass band of wind wave frequenies for whih diretional estimates are omputed (.4 to.32 Hz for these data), one expets the frequeny spetra to be nearly 1 For onveniene, symbols and abbreviations ar listed in the notation (Appendix E). 1 Chapter 5 Data Proessing

16 idential. A malfuntioning gauge is learly identifiable in this type of interompanson. Figure 4 is an example of one set of overplotted frequeny spetra. Semi logarithmi oordinates have been used to emphasize the behavior of the low-energy, high-frequeny spetral tails. All pressure gauge signals have been onverted to equivalent heights of a stati water olumn for onveniene in interpretation. As an be seen in Figure 4, spetra in the wind wave frequeny pass band are very nearly alike, indiating that all gauges are funtioning reasonably well. The noise floor at high frequenies is very low relative to the wind wave signal and is nearly uniform for all but five gauges. Four of the Senso-Metri gauges have slightly elevated noise levels, but these levels do not have a signifiant effet in the wind wave pass band. The urve labeled C in Figure 4 represents data from the Parasientifi sensor, whih had an inherently quieter bakground noise level than the other gauges. The inset graph in Figure 4 reveals information about gauge mean values. Data reords were divided into 15 half-overlapping segments, eah having a duration of 17 min 4 se. Segment mean values were then omputed for eah gauge. deally, when gauge means are orreted for the depth of water in whih they were deployed and for the elevation of the gauge from the oean bottom, they would all give a measure of mean water level arising from tidal elevation, barometri overpressure, and any wind- or wave-indued setup. These means should all be the same for all loations in the array for that segment oftime. Experiene has shown that the Senso-Metri gauges used in the array tend to have a modest mean drift over time sales of months. For the analysis used to produe this report, an estimate of true water depth was omputed by finding the median of the set of orreted gauge means for eah segment. The inset in Figure 4 shows the deviation of individual gauge means from this median value as a funtion of segment number, and indiates, for this example, mean depth errors ranging from about.15 m (.49 ft) low to about.15 m (.49 ft) high. By referening all gauges to the median mean depth, potential errors in surfae orreting the wind wave part of the signal are redued. The triangular symbol in the inset in Figure 4 shows the deviation of the median mean depth from still-water level (based on the 1929 National Geodeti Vertial Datum) as a funtion- of segment number. The-resulting urve repfesentsthe ombined effets of tide, setup, and barometri overpressure. The square symbol in the inset of Figure 4 is the deviation of barometri pressure from one standard atmosphere in units of meters of sea water as a funtion of segment number. This urve indiates the magnitude of atmospheri pressure on pressure measurements of mean water level. This effet is removed from pressure gauge means by subtrating the exess of atmospheri pressure over one standard atmosphere from eah of the gauge means. t is noted that the present method of error heking is different from that used for results reported for the first four years of array analysis (Long 1991 a, 1991 b; Long and Smith 1993, 1994). The older method relied on moments and extremal harateristis derived from data time series in the time domain. The present method asts the data in the frequeny domain, but is sensitive to the same underlying harateristis that would flag data as suspet in the older method, and is Chapter 5 Data Proessing 11

17 8-Meter Array Frequeny Spetra (Bottom) Date: 22 Ot 94 Time: 4 Missing gages: NONE Pier End South: Speed ±.44 Wax 2.4) (mlae). Diretion ± 18.8 (deg) Pier End North: Speed.79 ±.77 Wax 2.3) (m/ae). Diretion ± 18.7 (deg) "' N -).ll..; r.i CN - en Cl ~ "' ~ '\ ~ 1\ ' w ~ ~ E... - j:: - rt ~ ~ E.lfi m ll. ll. ll.., ll ~ ' w_.,. 1.. Cl ": rt rt rt rf fl " rj v -Tide 2 e 1 12 Segment Number o - Barometer.,..n D - r._~;'.: ll-""~ ~~ ~"' ~ ~ ~!J'v>\.1\r.; ~,...; f (Hz) Figure 4. Example of overplotted frequeny spetra muh easier to use. n both methods, if a gauge demonstrated properties that deviated too muh from properties of the other gauges, it was flagged as being suspet, and the data were then further examined by hand to ensure that the flagging proedure had indeed identified a malfuntioning gauge. 12 Chapter 5 Data Proessing

18 f a gauge malfuntioned, it was not used in further analysis. The analysis programs were written so that data from a subset of gauges ould be analyzed. A few gauges ould then be lost without seriously ompromising the results. Using fewer gauges yields a somewhat redued diretional resolution. Some gauges are more ritial than others. f any of the gauge pairs with 5-m ( 16.4-ft) spaings are lost, results beome invalid at high frequenies due to spatial aliasing. n these ases, diretional analysis was trunated at a lower high-frequeny limit (generally.24 Hz instead of the normal.32 Hz). As disussed in the next setion, there are additional reasons for eliminating gauges from diretional wave estimation at some frequenies in a spetrum. However, fewer than four gauges are never used for any frequeny. To keep trak of the set of funtioning and not otherwise eliminated gauges, a parameter alled the gauge pattern was reated and stored with the results for eah frequeny in arhived diretional spetra. The gauge pattern is a 16-plae harater string that represents whih of the possible gauges (the 15 array gauges plus the optional gauge T) were used to ompute a diretional spetrum at a partiular frequeny. The string ontains the identifying haraters (based on the gauge identifiation sheme shown in Figure 3) of gauges that were used in analysis followed by blank haraters (if any) to fill out the string. This parameter an be of use in later analysis for assessing the diretional resolving ability of a partiular sub-array of gauges. This definition of gauge pattern differs from that used for the first four years of arhived data, but the automated analysis algorithm was modified in September 199 to be more dynami in gauge seletion (as desribed in the next setion), and so neessitated this hange. Frequeny-Diretion Spetra Two types of spetra Data from the array of gauges are proessed as two separate entities, both of whih are frequeny-diretion spetra, but having different properties. One of the entities is a frequeny-diretion spetrum using only the original nine gauges (gauges 1, 2, 3, 4, 5, 6, 7, 8, and 9 in Figure 3) ofthe alongshore linear array. Diretional spetra from this set of gauges are referred to as linear array results. The other entity is a frequeny-diretion spetrum using all gauges. Diretional spetral estimates using all gauges are alled 8-m array or full array results. There are several reasons for this distintion. One is that the database for the first four years ofthis study is based on results from the linear array. Comparisons of results over the full duration of the study and the aumulation of limatologial statistis require a ontinued analysis of the linear array as a unique entity. A shortoming of the linear array is that it annot distinguish seaward-propagating waves from inident waves. n proessing linear array data, it must be assumed that all wave energy is inident, whih does not allow for the possibility of refletions from the nearshore. This problem is overome by using the full array, whih inludes gauges at ross-shore loations (gauges, A, B, C, D, and E in Figure 3) off the line ofthe linear array. The full array an detet wave energy propagating in all diretions and so an be used to estimate the amount of wave energy refleted (and otherwise propagating) from the nearshore. Chapter 5 Data Proessing 13

19 deally, the full array would be adequate for all diretional spetral estimates. However, the analysis algorithm for the full array is based on the assumption that waves are propagating through water of onstant depth. n fat, the depth hanges by about.8 m (2.6 ft) over the ross-shore breadth of the array (from gauge E to gauge A), or roughly perent of the total depth. ntermediate- and shallow-water waves transform, largely by refration, as they propagate through water of hanging depth. This transformation introdues a slight shift in the phase differene between waves at two ross-shore loations relative to the phase differene of waves that are not transformed. Diretional spetral estimates depend ritially on aurate estimates of phase differene, and the effet of transforming waves, though slight, is to introdue an inreased spread in the diretional distribution of wave energy, espeially for waves at high angles of attak. An optial analogy is a amera with a poorly ground lens that will fous learly at the enter but is slightly blurred at the edges. The linear array does not have this blurring effet beause waves have the proper phase differene as they ross a line of onstant depth. Consequently, diretional spetral estimates from the linear array are better resolved in their detailed struture. Beause of this better resolution, linear array results are used in this report for all haraterizing parameters exept refletion oeffiients. Though full array results an be somewhat blurred, refletion oeffiients are based on total energy in 18-deg ars of diretion, and so are less sensitive to a lak of detailed resolution than are other parameters like peak diretion and diretional spread. Note, however, that both linear array and full array spetra and assoiated parameters are omputed, arhived, and available through the mehanisms desribed in this report for all olletions listed in Appendix A. Spetral estimation Estimation of the frequeny-diretion spetrum is done in five parts. First, a working gauge set-is identifred. -5lXund, time series of pressure data from eah of the working gauges are Fourier transformed to the frequeny domain. Third, these transforms are onverted to sea-surfae displaement transforms. Fourth, ross spetra of sea-surfae displaement are omputed between all unique gauge pairs for eah frequeny. Finally, an estimate is made of a diretional distribution of wave energy that orresponds to the omputed spatial variation in ross-spetral density for eah frequeny. The hoie of gauges to be used in a frequeny-diretion spetrum at a partiular frequeny depends on available gauges after error heking (desribed previously), the wavelengths of the waves to be resolved; and somewhat on the nature ofthe diretional distribution of wave energy being estimated. Oean wave signals at a given frequeny tend to beome unorrelated over distanes of a few wavelengths. Cross spetra of signals from two gauges of high-frequeny (short wavelength) waves are redued to noise if gauge separation is too great. Conversely, ross spetra of signals from two losely spaed gauges do not yield a great deal of information about very long waves beause the two signals are almost idential. Beause of these harateristis of oean waves, sub-arrays of both the linear and 8-m arrays are defined so that minimum gauge spaing and 14 Chapter 5 Data Proessing

20 maximum array extent are tuned to ranges of wind wave frequenies, and diretional spetra are estimated from the gauges in these sub-arrays. An additional onstraint on gauge usage is based on the observation by Davis and Regier (1977) that oasionally the diretional spetrum is of suffiiently simple shape that some of the ross-spetral information beomes redundant, meaning that too many gauges (or, perhaps, gauges in less than ideal loations) have been employed in the diretional estimate. An indiation of this ondition is that the matrix of ross-spetral estimates beomes singular in the mathematial sense, and diretional estimation beomes impossible. When this ours in the ourse of a omputation, the proedure is to eliminate a gauge from the sub-array being used, and restart the omputation. To avoid eliminating a ritial gauge, an order for gauge elimination was established that retained gauges known to be important. Beause this proedure ourred in automated proessing, a omplete gauge elimination pattern was defined. f fewer than four gauges remained at any point in proessing, the entire analysis was aborted for that olletion. Table 1 shows the wind wave frequeny band sub-ranges, the sub-array of gauges to be used with eah frequeny sub-range, and the elimination order of gauges in eah sub-array for the gauges of the linear array. A olumn under a gauge number that ontains an integer indiates a gauge to be used for the frequeny range shown in the left olumn. The integers in eah row indiate the order in whih gauges are to be eliminated. For example, in the next-to-highest frequeny range ofthe original array (.14 Hz < f ~.19 Hz in Table 1), gauges 1, 2, 3, 4, 5, and 6 define the sub-array. n the event that a gauge must be eliminated, gauge 3 is eliminated first. f a seond gauge must be eliminated, it is gauge 6, and so on, until the four-gauge limit is reahed (if neessary). Table 2 shows the same type of information for the full array. Table- 1- Linear Array Gauge Usage Range (Hzl '""'""' Gauge 8 9 T < f s;.8 5, < f ~ , < f s; < f s; , Beause gauge set definition varies with frequeny, and is somewhat dataadaptive in that some spetra require gauge elimination and others do not, it is important that a reord be kept of the set of gauges used for eah frequeny in a olletion analysis. This is the primary purpose of the gauge pattern parameter defined previously. The gauge pattern parameter is always kept with the arhived results, and the limit of the minimum of four gauges for eah diretional estimate is never violated. One the appropriate set of gauges has been identified, the subsequent analysis operations of Fourier transformation, surfae orretion, rossspetral omputation, and diretional spetral estimation an proeed. Chapter 5 Data Proessing 15

21 Table 2. 8-m Array Gauge Usage Frequeny Range (Hz) Gauge A B D E T.4 < f $ < f $ < f $ < f $ The Fourier transform is onventional. An 8, 92-se time series is divided into 5 half-overlapping segments of,24 se. Segments are tapered with a Kaiser-Bessel window (a modified Bessel funtion of the first kind, ompensated uniformly for loss of variane due to windowing) and fast Fourier transformed. An intermediate-resolution transform is found by averaging the 15 transformed segments, frequeny by frequeny. Final transforms are found by then averaging results over ten adjaent frequeny bands. Final resolution bandwidth is.976 Hz, and degrees of freedom are at least 5 (assuming eight ontiguous segments and ignoring any gain from lapped segments). Transform estimates are retained for 29 frequeny bands with band-enter frequenies ranging from.44 to.38 Hz. Conversion of pressure signals at depth to water-surfae displaement is done through the linearized wave theory pressure response fator as desribed in the Shore Protetion Manual (1984). After this onversion, omplex ross spetra in the form of oinident and quadrature spetra are omputed in the onventional way (Bendat and Piersol 971, Jenkins and Watts 968) between all unique gauge pairs for eah frequeny. Conversion of ross-spetral patterns in lag spae to diretional spetra is done with the terative Maximum Likelihood Estimation algorithm derived and desribed by Pawka ( 982, 1983 ). The algorithm is also desribed in appliation to data from heave-pith-roll buoys by Oltman-Shay and Guza (1984), and Long ( 995) gives a modestly expanded desription of the algorithm for two-dimensional spatial arrays. Auray of diretional estimates depends on frequeny, with high-frequeny waves (short wavelengths) being better resolved by an array of finite length. Tests with artifiial data indiate that the FRF linear array generally an resolve the diretion of a unidiretional wave train to within 5 deg and an distinguish two wave trains at the same frequeny if their diretions differ by at least 15 deg. The algorithm used here employs disrete diretion "bandwidths" or ars of about deg for all frequenies. Beause this inrement is finer than the resolution of any ofthe arrays, diretional results are smoothed by integrating over 2-deg ars and renormalizing by this ar width to reate evenly spaed diretional spetra at all frequenies. Beause linear array results are valid only in the 16 Chapter 5 Data Proessing

22 18-deg ar representing seaward approah diretions, dividing this range into 2-deg ars results in 91 ar enter diretions with whih to haraterize disretely the diretional distribution of wave energy from the linear array. The full array an detet wave energy from all diretions, so results are represented in 181 diretional bins of 2-deg width (the terminal bins are redundant). The primary result of data proessing is an estimate of the disrete frequenydiretion spetrum S (!,,em), whih represents the variane of sea-surfae displaement per frequeny resolution bandwidth df (=.976 Hz) per diretion resolution ar de (= 2 deg), where f" is the nth of N = 29 disrete frequenies and em is them th of M = 91 (for the linear array) or 181 (for the full array) disrete diretions. n this work, diretion is onsidered to be the angle from whih wave energy is oming, measured ounterlokwise from shore-normal (Figure 2). Numerial values of S (!,, e'") an range over many orders of magnitude, depending on the amount of energy in a given frequeny band and diretion ar, and this an require spae-onsuming formats for arhiving data. To simplify this problem, frequeny-diretion spetra are saved as diretional distribution funtions D ({", e'") defined by D(f.,e ) = S(f",e'") n m S(fn) (1) The diretional distribution funtion has units of deg 1, and its integral with respet to diretion over all diretions is unity. The frequeny spetrum S ({") in Equation 1 represents the sum over all diretions of sea-surfae variane per frequeny bandwidth and is defined in terms of the frequeny-diretion spetrum by M S(f") = L S(f", e'") de (2) '"= where the variables on the right-hand side are defined above. Note that this is idential to a onventional frequeny spetrum that would result from a time series of sea-surfae displaement at a single point in spae. Beause it is an integral of the frequeny-diretion spetrum, it is alled the integrated frequeny spetrum. A diretional analog of the frequeny spetrum is the integrated diretion spetrum, found by summing the frequeny-diretion spetrum over all frequenies for a fixed-diretion ar. t is omputed from N s(e'") = "Esu",e'">df (3) n=l Chapter 5 Data Proessing 17

23 Figures 5 and 6 show ways to display frequeny-diretion spetra and the orresponding integrated frequeny and integrated diretion spetra from the two types of array analysis for the same olletion time. Figure 5 displays results from the linear array, with some haraterizing parameters shown in the figure header. Note that energy is displayed only for inident waves ( -9 deg < em < 9 deg ). FRF Linear Array Frequeny-Diretion Spetrum Date: 22 Ot 94 at 4 EST for min with 16 dot Hmo.58 m f p.fo.13 Hz T p.fo 9.71 se Bp.Fo -4. deg mean depth- 8.2 m i ~ -o N ::J: - -"! OL ~ ~~------~--_... ~ ao eo 3 o -ao -eo - o B (deg) Figure 5. Example of a linear array frequeny-diretion spetrum 18 Chapter 5 Data Proessing

24 FRF 8-m Array Frequeny-Diretion Spetrum Date: 22 Ot 94 at 4 EST for min with 16 dof Hmo-.58 m f p.fo-.13 Hz T p.fo se Bp.Fo- 2. deg mean depth- 8.2 m -;; ~!..,.. ~ t i:;.. ~! Contours at 5% and then Tenths of Maximum S(f,B) ~r---~--~--~--~--~----~~~~~~~~~~~--~..... Q -o N ::t: ~ N.., ol.. ~--~--_.--~~~----~--.. ~------~ 11 &O eo 3 o -3 -eo &O (deg) Figure 6. Example of a full-array frequeny-diretion spetrum Figure 6 shows results from the full array. The haraterizing parameters derived from this spetral estimate are nearly the same as those for the linear array results in Figure 5, showing that the two estimates are onsistent in this regard, as expeted. n Figure 6, diretional energy estimates over a omplete irle. The small lumps entered near diretions ±14 deg and ±15 deg are indiations of refleted energy. Chapter 5 Data Proessing 19

25 Bulk Parameters Several parameters have been omputed to haraterize the observed spetra. There are five basi types of parameters: (a) harateristi wave height, (b) peak frequeny (or its inverse, peak period), peak diretion, (d) diretional spread, and (e) refletion oeffiient. n this report, the first four of these parameters are omputed from linear array results. The fifth is omputed using results from the full array. Beause there is more than one way to define some of these parameters, several alternate forms are presented here. Charateristi wave height Charateristi wave heights from spetral observations are most frequently given as H mo, whih is four times the standard deviation of sea-surfae displaement. t an be determined from the volume under the frequeny-diretion spetrum by the equation H~o N M = 16 L L S(f,., fjm) djdfj rr=l m=l (4) t an also be found from the integrated frequeny spetrum by N H~ = 16 L S(f,.) df rr=l (5) whih is its more onventional definition, or from the integrated diretion spetrum (Equation 3) by M 16 L S(fJm)dfJ m=l (6) Peak frequeny Peak frequeny, whih has the generi notation JP, an be defined in at least two ways. One way is to find the frequeny (and diretion) at whih the frequeny-diretion spetrum is maximum. This peak frequeny is denoted J;,.FD. Another way is to find the frequeny at whih the integrated frequeny spetrum is maximum. This is the more onventional definition, beause of the plethora of measured frequeny spetra, and is denoted J;,;Fs. The two peak frequenies may not be the same. f the diretional distribution is broad at the frequeny for whih the integrated frequeny spetrum is maximum, it is possible that another frequeny, at whih the frequeny-diretion spetrum has a narrow distribution, will denote the maximum of the frequeny-diretion spetrum. 2 Chapter 5 Data Proessing

26 Peak period Peak period is the harateristi wave period assoiated with spetral peak frequeny. Denoted generially by TP, it is related to peak frequeny by TP = 1/fP. Peak period from the frequeny-diretion spetrum is given by T FD = 1/f. FD. p, p, Conventional peak period, derived from the integrated frequeny spetrum, is given by T p, FS = 1 /f. p, FS. Peak diretion Peak diretion is the diretion representing the most energy density. Given the generi symbol 6P, it, too, an be defined in several ways. One peak diretion an be defined from the maximum of the frequeny-diretion spetrum. t is denoted by ap.fd. Another peak diretion an be assoiated with the maximum of the integrated diretion spetrum, defined previously. This peak diretion is denoted 6p,DS. t Can differ from 6p,FD if energy in the frequeny-diretion Spetrum is entered at different diretions for different frequenies. This ondition tends to smear energy along the diretion axis in the integrated diretion spetrum, thereby shifting the peak relative to the peak of the frequeny-diretion spetrum. A third measure of peak diretion is a weighted average peak diretion defined by e = 1 N "'s(f.)b p,sw ( )2 LJ rr p,rr -H n=l 4 mo (7) where e = p,ll s (J,) = peak diretion of the diretional distribution at the nth frequeny of the frequeny-diretion spetrum integrated frequeny spetrum from Equation T and Hmo is defined by Equation 4. This definition gives higher weights to the more energeti peak diretions, but does not rely on the single distribution with the most energy. Diretional spread A fourth type of harateristi parameter is diretional spread. This parameter, denoted generially as d6, gives a measure of the range of diretions from whih some signifiant fration of energy is propagating. The basi definition used here is the ar subtended by the middle two quartiles of a diretional distribution. As illustrated in Figure 7, the diretional distribution funtion D (J,, 6'") for a partiular frequeny f, an be integrated from one bounding diretion (here the shoreparallel diretion at +9 deg) to some arbitrary diretion 6 1 to make a umulative distribution funtion (J,, 6 1 ). The formal definition is Chapter 5 Data Proessing 21

27 U) N 4 EST 22 Ot 94 n = 7 fn =.13 Hz r-~--~--r-~--~-.--~--~-.--~--~-r--~~---r--t-~--, ' Cl Q) ~ - Cl :i (deg) a. Diretional distribution r-~~-,--t-"~-,~~~~.-~--~~~~~f==---~ ~A9 _. n ~ / :9 : 1 6",n 1 8 ; 9 2~" " 76," " (deg) b. Cumulative distribution 6 9 Figure 7. Diretional spread omputation 1(!,.,6 1 ) = t D(f,.,6,.) d6 111=1 (8) 22 Chapter 5 Data Proessing

28 where j is the index of a disrete angle bin. The three quartile diretions, alled 825%,n' 85%,n' and 875%.n' respetively, satisfy the equations (f. '825"' ) =.25 n...,n (9) (1) (f. n '875"',.,n ) =.75 (11) A diretional spread parameter for the nth frequeny is defined by ~e = e - e n 25%,n 75%,n (12) f Equation 12 is applied at the frequeny where the frequeny-diretion spetrum is maximum, a measure of diretional spread at the peak of the frequenydiretion spetrum is obtained. This parameter is denoted ~6FDP. f, instead of a diretional distribution funtion at a single frequeny, the normalized integrated diretional spetrum is used in the set of Equations 8 to 12, a measure of bulk diretional spread is obtained. This parameter is given the symbol ~ews A third measure of diretional spread is found from a spetrally weighted average of the spreads from all frequenies. Denoted as ~esw this parameter is found from (13) Equation 13 is like Equation 7 for the spetrally weighted peak diretion. Refletion oeffiient Following the definition in the Shore Protetion Manual (1984), a refletion oeffiient is a ratio of inident wave height to refleted wave height. This simple definition is based on the onept of unidiretional, monohromati waves, whih never our in the real oean. An adaptation of this definition for the purposes of this report is to use harateristi inident wave height H '"o,t and harateristi refleted wave height H mo,r to define an energy-based refletion oeffiient X as HNO, (14) nident and refleted wave heights are defined in terms of inident and refleted energy. Squaring both sides of Equation 14 then yields an estimate of the ratio of Chapter 5 Data Proessing 23

29 total refleted to total inident wind wave energy, a harateristi that may be useful in onsideration of nearshore dynamis. Some are must be exerised both in defining and interpreting the harateristi wave heights and their ratio. ntrinsi in all spetral estimates is some level of bakground system and analysis noise that is not related to wave signals, is often unevenly distributed in diretion, and is apable of severely degrading a ratio of entities like that in Equation 14. n a rough attempt to minimize the effets of bakground noise, a noise estimate is made by finding the minimum of the frequeny-diretion spetrum at eah frequeny S min (f"), and omputing inident energy E 1 and refleted energy E, relative to these minima. Using the full-array frequeny-diretion spetrum for these omputations, the inident energy is N 136 Ei = pg L L w,[s(fn,e,)- smin(fn) ]d8df n=l "'=46 (15) and the refleted energy is N 46 E, p g L L w, [ S(fn,e,) - s,;nlfn) ]de df n=l m=l N M (16) + pgl L w,[s(f",e,)- S, 1 "(f")]d8df n=l m=l36 where p is water density, g is gravitational aeleration, and all w, = 1, exept w 1 = w 46 = w 136 = w M = +. The w, are simply onvenient notations that show the proper ontributions of the spetrum to the end points of the sums in Equations 15 and 16, and do not otherwise affet the integrations. n terms of inident and refleted energies, the orresponding harateristi wave heights are _H.. = 4. El 111,1 -~ p g (17) and H mo,r =4~pEg, (18) so that, on substitution of Equations 17 and 18 into Equation 14, the refletion oeffiient beomes E:" X=~~ (19) 24 Chapter 5 Data Proessing

30 The simple noise estimate used here does not eliminate the effets of noise in omputing Equation 19 using Equations 15 and 16. This ondition is evident in the tabular listings in Appendix A and the plotted results in Appendix B. There is a persistent bakground level of X ::::.1, whih suggests that there is always about 1 perent of inident wave energy propagating bak out to sea, a ondition that is unlikely to be true. Syntheti tests by Long and Oltman-Shay (1993) using the algorithms desribed in this report indiate errors as large as 2 perent for x ::::.1, but with the error dropping rapidly for larger X. A reasonable way to interpret the results in this report is to onsider x ~.2 as indiative of some refletion, and then to examine suh spetra in detail for verifiation. n the spetrum shown in Figure 6, for example, the tabulated refletion oeffiient is.22, and the figure does indeed indiate some refleted energy. Parameter summary Together, the 12 parameters Hmo' J;,,FD' J;,,JFS' Tp.FD' Tp,JFS' ep,fd' ep,jds' ep,sw' A61DS' A6SW' A6FDP' and X give a bulk haraterization of some properties of the frequeny-diretion spetra disussed in this report. There are, of ourse, many other parameters that an be defined, but the present set is simple, and is easier to use than the 2,639 disrete spetral densities (29 frequenies x 91 diretions) required for a full desription of any linear array spetrum, or the 5,249 elements (29 frequenies x 181 diretions) of any full-array spetrum disussed here. Chapter 5 Data Proessing 25

31 6 Arhived Results Optial disks ontaining the sets of observed linear-array and full-array frequeny-diretion spetra from this olletion period have been reated to arhive the observations. Appendix A ontains a listing of the date, starting time (EST), and the haraterizing parameters defined previously for eah ase arhived. t serves as an index or atalog of the set of available ases. For reasons explained below, dates in Appendix A are given in the form yymmdd to represent year, month, and day, all in two-digit integer form. Graphi representations of data olletion times, some bulk parameters, and some auxiliary environmental variables are ontained in Appendix B. One graph is shown for eah month of the olletion period. The upper part of eah graph has time series plots ofthe bulk parameters Hmo' Tp,FS' ep,ds' and ABDS derived from the linear array, and X derived from the full array. The lower part of eah graph has stik figure plots of three environmental variables. First is a kind of rude wave vetor in whih the stik vetor has a length proportional to H mo and a diretion given by e p,ds + 18 deg. The 18 deg is added to provide a physial frame of referene onsistent with a vetor pointing in the diretion of energy propagation. Beause peak wave energy is always direted onshore, all stik vetors in this part of the graph will have a omponent direted upward on the page. The seond stik figure plot is a wind vetor as measured with one of the two FRFpier-end anemometers. Mounted at the Beaward end of the FRF pier (Figure 2) at an elevation 19.5 m above mean sea level, these instruments give a reasonable estimate of the wind limate in the viinity of the 8-m array. Both anemometers are of the impeller-vane type, and are separated horizontally by less than 2m (to ensure uninterrupted wind observations in the event offailure of one of them). Note that prior to 28 September 1994, there was only one anemometer at pier end. Anemometer data are vetor averaged and wind veloity varianes are omputed both in and perpendiular to the mean wind diretion. Arhived with wave spetral results are mean wind speed, maximum wind speed, wind speed standard deviation, mean wind diretion, and a measure of wind diretion variability (defined as the ar tangent of the ratio of ross-stream standard deviation of wind veloity to the mean wind speed). The third stik figure is the urrent vetor as measured with a urrent meter loated on the line of the linear array, about 7 m (23ft) southward of gauge 8 (Figure 2). This urrent meter is in a different loation from the one used in the 26 Chapter 6 Arhived Results

32 first three diretional spetral index reports (Long 1991 a, 1991 b; Long and Smith 1993), or the one used in the subsequent four reports (Long and Smith 1994, Long and Atmadja 1994, Long and Pemberton 1994, Long and Roughton 1994 ). Furthermore, this urrent meter was removed ompletely on 16 November 1994, so that no urrent meter data are available after that date. This instrument was approximately 2.4 m (7.9 ft) off the bottom in water about 8 m (26ft) deep and, therefore, sensed urrents near the bottom. All available urrent data are plotted. The urrent meter was subjet to storm damage, biologial fouling, and durationrelated eletroni problems, so that data overage is not omplete for the time when the urrent meter was in use. Of existing data, the reader may note a signifiant antiorrelation between ross-shore winds and ross-shore urrents. This is onsistent with the behavior of wall-bounded, shallow-water, wind-generated urrents. Additional details about the anemometers and urrent meter are given by Birkemeier et al. ( 1985). Chapter 6 Arhived Results 27

33 7 Retrieving Proessed Data The eletro-optial medium ontaining the diretional-spetral data arhive is ompat, but not very transportable. Consequently, a onversion program has been written to transform the data into a rather onventional, 8-olumn formatted form that is muh more easily distributed on ommon magneti media or over an eletroni network. A user requesting some or all of the data will, unless otherwise speified, reeive the data in formatted form. t may be possible to transfer the data in other ways, and speifi requests an be oordinated with the FRF. The data arhive for the period overed by this report ontains two sets of 3,581 files, one set for linear array results, and the other for full array results, with one file for eah olletion. n formatted form, a linear array file has a length of about 3, bytes, and a full array file is about twie this size. The omplete arhive for this olletion period ontains roughly 322 MB of information. A user may wish to onsider whether this quantity of information will take too muh system spae before trying to opy the whole arhive. Subsets of data overing speifi time periods an readily be reated by the FRF. An ASC-formatted file is usually named LAyymmddhhmm.ASC for a linear array frequeny-diretion spetrum, or FDyymmddhhmm.ASC for a full array frequeny-diretion spetrum. n these file names, the harater grouping yymmdd represents the data olletion date (as listed in Appendix A), and the harater grouping hhmm represents the data olletion start time as hour and minute, both in two-digit integer form (also from Appendix A). One a file is on equipment and in a position to be read, it an be input to a. Gomputer program through il {;et of ASGH r~ad statements. Appendix C ontains a listing of a FORTRAN program that an read the formatted data files. The variables ontained in a data file are listed in the header of the program in Appendix C. A listing of a sample data file of linear array results is given in Appendix D. Read statements in the program in Appendix C an be aligned with data fields of the listing in Appendix D if the user wishes to edit or visually read a data file. Program variable names, espeially those that have parallel symbols in this text, are also listed in the Notation (Appendix E). 28 Chapter 7 Retrieving Proessed Data

34 A user an obtain data by ommuniating with the FRF via: Surfae mail Telephone FAX Chief, Field Researh Faility 1261 Duk Road Kitty Hawk, NC (919) (919) or any of the following nternet addresses: More information about the FRF, a partial set of the statistis H, T Fs, and mo p. ep.fd from the full array, and all of the LAyymmddhhmm.ASC files are available at on the World Wide Web. Chapter 7 Retrieving Proessed Data 29

35 8 Summary of Results Data from the final three months of the eighth and all of the ninth olletion years of high-resolution diretional-spetral observations at the FRF have been put in a form that is easily aessible to researhers interested in nearshore proesses. The period overed by this report inludes the dates of the DUCK94 experiment. Diretional gauge array, diretional analysis algorithms, and definitions of haraterizing parameters are desribed in the body of this report, as are the loation and form of arhived data. Both a listing and a graphi presentation of data olletion times and harateristi parameters are given in the appendixes. The appendixes also ontain a sample data file and a listing of a FORTRAN program that an be used to read a data file. 3 Chapter 8 Summary of Results

36 Referenes Bendat, J. S., and Piersol, A. G. (1971). Random data: Analysis and measurement proedures. Wiley-ntersiene, New York. Birkemeier, W. A. (1984). "Time sales of nearshore profile hanges." Proeedings of the 19'h Coastal Engineering Conferene. Amerian Soiety of Civil Engineers, Houston, TX, Birkemeier, W. A., Miller, H. C., Wilhelm, S.D., DeWall, A. E., and Gorbis, C. S. (1985). "A user's guide to the Coastal Engineering Researh Center's (CERC's) Field Researh Faility," Tehnial Report CERC-85-1, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Davis, R. E., and Regier, L. A. ( 1977). "Methods for estimating diretional wave spetra from multi-element arrays," Journal of Marine Researh 35, Jenkins, G. M., and Watts, D. G. (1968). Spetral analysis and its appliations. Holden-Day, Oakland, CA. Leffler, M. W., Baron, C. F., Sarborough, B. L., Hathaway, K. K., Hodges, P.R., and Townsend, C. R. (1995a). "Annual data summary for 1992, CERC Field Researh Faility," Tehnial Report CERC-95-1, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS.. (1995b). "Annual data summary for 1993, CERC Field Researh Faility," Tehnial Report CERC-95-6, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E. (1991a). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1986 to August 1987," Misellaneous Paper CERC-91-6, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS.. (1991b). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1987 to August 1988," Misellaneous Paper CERC-91-7, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Referenes 31

37 Long, C. E. ( 1995). "Diretional wind wave harateristis at Harvest Platform,'' Tehnial Report CERC-95-4, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E., and Atmadja, J. (1994). "ndex and bulk parameters for frequenydiretion spetra measured at CERC Field Researh Faility, September 199 to August 1991," Misellaneous Paper CERC-94-5, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E., and Oltman-Shay, J. M. (1993). "Preliminary estimates of frequeny-diretion spetra derived from the SAMSON pressure gage array, November 199 to May 1991," Misellaneous Paper CERC-93-3, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E., and Pemberton, J. L. (1994). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1991 to August 1992," Misellaneous Paper CERC-94-7, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E., and Roughton, J. H. (1994). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1992 to August 1993," Misellaneous Paper CERC-94-6, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS.. (1995). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1993 to May 1994," Misellaneous Paper CERC-95-5, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Long, C. E., and Sallenger, A. H., Jr. (1995). "Experiment at Duk, N.C., beah explores nearshore proesses," Eos 76, 51. Long, C. E., and Smith, W. L. (1993). "ndex and bulk parameters for frequenydiretion spetra measured at CERC Field Researh Faility, September 1988 to August 1989," Misellaneous Paper CERC-93-1, U.S. Army Engineer Wa. te!'wa.ys Experiment Station, Vikshur~, MS.. (1994). "ndex and bulk parameters for frequeny-diretion spetra measured at CERC Field Researh Faility, September 1989 to August 199," Misellaneous Paper CERC-94-2, U.S. Army Engineer Waterways Experiment Station, Viksburg, MS. Miller, H. C., Birkemeier, W. A., and DeWall, A. E. (1983). "Effets ofcerc researh pier on nearshore proesses." Proeedings of Coastal Strutures '83. Amerian Soiety ofcivil Engineers, Arlington, VA, Oltman-Shay, J., and Guza, R. T. (1984). "A data-adaptive oean wave diretional-spetrum estimator for pith and roll type measurements," Journal of Physial Oeanography 14, Referenes

38 Pawka, S. S. (1982). "Wave diretional harateristis on a partially sheltered oast," Ph.D. diss., Sripps nstitution of Oeanography, University of California, San Diego, CA.. (1983). "sland shadows in wave diretional spetra," Journal of Geophysial Researh 88, Shore protetion manual. (1984). 4th ed., 2 Vol, U.S. Army Engineer Waterways Experiment Station, U.S. Government Printing Offie, Washington, DC. U.S. Department of Commere, Daily weather maps, published weekly, editions labeled May 3-June 5, 1994 through August 28-September 3, 1995 inlusive, National Oeani and Atmospheri Administration, Washington, DC. Referenes 33

39 Appendix A Table of Colletion Times and Bulk Parameters Table A1 Colletion Times and Bulk Parameters Time H r,,.,,,... r,,,., r,,., e,,l'd e,,d, e,....o.e..,,.o.e,,. Date EST m Hz Hz se se deg deg deg deg deg.o.e,., deg X a.z6v o-.zt>v. :s-. n: };. 42;. 23~6- ~3~ ; o'r (Sheet 1 of 68) Appendix A Table of Colletion Times and Bulk Parameters A1

40 Table A 1 (Continued) Time H ' "" ' "'' r,.fd r,_,. e,.fd e,_,.,, e,_,,. AS DS AS,,. AS""' Date EST m Hz Hz se se deg deg deg deg deg deg X o o '94-oCilO -a/too- ---o. 3 -o.-;-'+2 -o.iit2 --r.-o-4-7.-o-4- --a.-o- --a.-o --o s o o o (Sheet 2 of 68} A2 Appendix A Table of Colletion Times and Bulk Parameters

41 Table A 1 (Continued) ' Time H.,. r,,fd r,.fd r,. e,.fd e,,.,. e,,,,..o.e.,,.o.e,,...8fdp Date EST m Hz Hz se se deg deg deg deg deg deg X "6t7 ()4() -o o.n _.3.2.._ 28J (Sheet 3 of 68) Appendix A Table of Colletion Times and Bulk Parameters A3

42 Table A 1 (Continued) ' r,.fd r,., a,."" a,..,, a,.,.. t.aroa t.a,,.. t.afdp Time H.,. r,.fd Date EST m Hz Hz se se deg deg deg deg deg deg X o.n H.-98 -~ { o (Sheet 4 of 68) A4 Appendix A Table of Colletion Times and Bulk Parameters

43 Table A1 (Continued) Time H,.. r,,, ' "" r,..., e,... e, "'' e,... ll.81d ll.e,,. ll.s, Date EST m Hz ' ~ Hz se se deg deg deg deg deg deg X u: (Sheet 5 of 68) Appendix A Table of Colletion Times and Bulk Parameters A5

44 TableA1 (Continued) ' Time H.,. r,,fo r,.fo r,,,., a,,fo a,,.,, a,... t.a.,, t.a,,. t.a,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X t (Sheet 6 of 68) A6 Appendix A Table of Colletion Times and Bulk Parameters

45 Table A 1 (Continued) Time H ' 'D fp,f r,,'d Tp.F a,,fd a,..,. a,....o.a.,,.o.a,,...o.a_ Date EST m Hz Hz se se deg deg deg deg deg deg X '3.3Z '.93' '.93' to~72 i'~72 -io;o 4'; ~ l {) (Sheet 7 of 68} Appendix A Table of Colletion Times and Bulk Parameters A7

46 Table A 1 (Continued) Time H f,,fd,,,.,, r,,fd r,... a,""' a,..,, a,....o.a.,,.o.a,,..o.a_. Date EST m Hz Hz se se deg deg deg deg deg deg X ~ -43~ (Sheet 8 of 68} AS Appendix A Table of Colletion Times and Bulk Parameters

47 Table A 1 (Continued) Time H.,.,,,Ff) ' "'' r,.ff) r,..., e,.frj a,,.,, e,.sw t.e.,, t.e,w.1'.8,..,.. Date EST m Hz Hz se se deg deg deg deg deg deg X o l S 21. ~ 9- <!~2-16~6 -r:2r o o o o o (Sheet 9 of 68) Appendix A Table of Colletion Times and Bulk Parameters A9

48 Table A 1 (Continued) Time H,.. r,.'d fp.jp' r,.'d r,,,. a,.'d a,,.,. a,....o.a.,,.o.a,,...o.a,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X D D D8D4 19DO D.45 D.152 D D -36.D D8D4 22DD D.45 D.123 D D D85 D1DO D D D D D.3D 948D5 D4DD.42 D.132 D. tz3. 'l.56. 1Ll ~ -38~~ -36~4 2~ D8D5 7D.4D D -38.D D8D5 1DDD D.4D D.D64 D.D D -36.D -33.D DO.43 D.D64 D.D D D DD D.42 D.D64 D.D D -32.D D D5 22D D.42 D.132 D.D D -4.D D.31 94D86 D1DD D D.D 4.D D D D8D6 D4DD 1.92 D.162 D D D D D6 D7D D.142 D D D 2D.D D.2D 948D6 1DDD 1.58 D D D.19 94D86 13DD 1.46 D.123 D D 2.D 3D D.2D 94D86 16DD 1.38 D.152 D D D.2D 94D8D6 19DD 1.36 D.123 D D 28.D D8D6 22DO 1.32 D D D D.15 94D8D7 1DD D D D D D.14 94D8D7 4DD 1.27 D.152 D D D D.16 94D8D7 D7DD 1.2D.113 D D.O 18.D D D87 1DDO D D 18.3 D.16 (Sheet 1 of 68) A1 Appendix A Table of Colletion Times and Bulk Parameters

49 Table A 1 (Continued) Time H,.. f,,fd r,.fd r,,,, e,.fd e,,ds ' "'' e,... t.e"'' t.e,,. f.6fdp Date EST m Hz Hz se se deg deg deg deg deg deg X "48tt ~26 a.a t W.O- -37~7 37~2.. 33~ (Sheet 11 of 68) Appendix A Table of Colletion Times and Bulk Parameters A11

50 Table A1 (Continued) Time H,.. fp,fd r,,.., r,,,, e,,.., e,,.,. e,. w t.e.,, t.e,w t.e.., Date EST m Hz Hz se se deg deg deg deg deg deg X ' o o o o '142.' D 4D~D ; o (Sheet 12 of 68) A12 Appendix A Table of Colletion Times and Bulk Parameters

51 Table A1 (Continued) Time H.,. r,,fd r,,fd r,,,. e,,fd e,,.,. ' "'' e,.,.. t.e.,. t.e.,.. 6SFDP Date EST m Hz Hz se se deg deg deg deg deg deg X o o o o o (Sheet 13 of 68) Appendix A Table of Colletion Times and Bulk Parameters A13

52 Table A1 (Continued) r,,"" r,,,, e,,,., e,,..,, a,,,,... aid,..e,,..c.8fdp Date EST m Hz Hz se se deg deg deg deg deg deg X Time H ' "" ' o o US6. 13_.56. 4~1! -22~1! -~~ o o n o.n (Sheet 14 of 68) A14 Appendix A Table of Colletion Times and Bulk Parameters

53 Table A 1 (Continued) Time H.,. r,,,.., ' "" r,., e,,,.., e,,.,, e,. w t.e.,, t.e,w t.e,..,, Date EST m Hz Hz se se deg deg deg deg deg deg X ' ' %7 ~Q()() a Q _ -3B~O (Sheet 15 of 68) Appendix A Table of Colletion Times and Bulk Parameters A15

54 Table A 1 (Continued) Time H,.. ' 'D r,.fd r,., a,.'d a,jd. a,,,,..o.a,.,..o.a,,..o.ai'df" Date EST m Hz ' Hz se se deg deg deg deg deg deg X }.71-.l}.7~- -3!. -3!..() ().! (Sheet 16 of 68) A16 Appendix A Table of Colletion Times and Bulk Parameters

55 Table A 1 (Continued) ' Time H,.. r,.'d r,,'d r,.jf, e,,'d e, "'' a,... t.eid, toe,,. t.ei'd' Date EST m Hz Hz se se deg deg deg deg deg deg X t Slt Q,_162_ - ~.83_ ll n o.n n o.n (Sheet 17 of 68) Appendix A Table of Colletion Times and Bulk Parameters A17

56 Table A 1 (Continued) Time H r,.fo r,.f, r,,,., r,.f, e,,,., e,,..,, e,.,.,.o.e..,,.o.e,,.,.o.e,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X o o o ~ !~8. U.98. 6~~ ~~~ -~ o.n o.n 1o.n o.n o.n 1o.n o.n o.n 1o.n o.n o.n o.n o.n 1o.n o.n 1o.n (Sheet 18 of:;]! A18 Appendix A Table of Colletion Times and Bulk Parameters

57 Table A 1 (Continued) ' Time H r,.fd r,,fd r,., e. FD e,,d, e,,,,. t.eid, t.e,,. t.e""" Date EST m Hz Hz se se deg deg deg deg deg deg X o o.n /t noo- -t.il2' -o ()-,1{, _ _ (Sheet 19 of 68) Appendix A Table of Colletion Times and Bulk Parameters A19

58 Table A 1 (Continued) Time H f,,fo ' r,.fo r,. a,.fo a,,ld. a,... t.a.,. t.a,,. t.sfo, Date EST m Hz Hz sa se deg deg deg deg deg deg X _QtQO S z.z.o.Zit. '2.9.7 ' o D (Sheet 2 of 68) A2 Appendix A Table of Colletion Times and Bulk Parameters

59 Table A 1 (Continued) Time H r,,fd ' "' r,.fd r,. a,,fd a,..,. a... t.a..,. t.a,,. t.a_ Date EST m Hz Hz se se deg deg deg deg deg deg X ; o.orr 1u-. rr 1u-. rr r.o- 8';' ; <l (Sheet 21 of 68) Appendix A Table of Colletion Times and Bulk Parameters A21

60 Table A 1 (Continued) Time H ' 'D ' "'' r,.'d r,,,, a,.fd a,,.,. a,... A BO AS,,. AS,.,.. Date EST m Hz Hz se se deg deg deg deg deg deg X o.n (Sheet 22 of 68} A22 Appendix A Table of Colletion Times and Bulk Parameters

61 Table A 1 (Continued) Time H.,. r,,fd ' "'' r,.fd r,,,, e,.fd e, "'' e,... t.e"'' t.e,,. t.e_ Date EST m Hz Hz se se deg deg deg deg deg deg X , , o.n o o.n o T.s-6 -:m-.o- -~o- 33~6 27;5- za~ ;2- {),, o o o o.n (ShfHit 23 of 68) Appendix A Table of Colletion Times and Bulk Parameters A23

62 Table A 1 {Continued) Time H.,.. fp,fd fp,f r,.'d r,,,, e,,fd e,,,.,, e,,,,. AB 11 Ae,,. AB,..,. Date EST m Hz Hz se se deg deg deg deg deg deg X h~D. 41 ~D 36.!! tt'f'J o.n 1o.n o.n 1o.n o.n o.n 1o.n o.n 1o.n (Sheet 24 of 68) A24 Appendix A Table of Colletion Times and Bulk Parameters

63 TableA1 (Continued) Time H,.. f,,fo f,,f r,.fo r,.f, e,,fo e,,o. a,... t.am t.a,,. t.a,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X lH~ 22fl Q~4fl ~ B (Sheet 25 of 68) Appendix A Table of Colletion Times and Bulk Parameters A25

64 Table A1 (Continued) ' r,,r<o r,., e,,p'd e,,.,, e,... ll.e.,, ll.e,.. ll.9,.,. Time H r,,r<o Date EST m Hz Hz se se deg deg deg deg deg deg X o t2 t ! V1 4il n (Sheet 26 of 68} A26 Appendix A Table of Colletion Times and Bulk Parameters

65 Table A 1 (Continued) Time H r,,,., ' 'D r,,,, a,,"d a,,.,, a,... t:.aid. t:.a,,. t:.a"", Date EST m Hz Hz se se deg deg deg deg deg deg X ' o.n o o.nrr. s-.5. s-.sz-. 2~a ;8- -32;, ~ o o o (Sheet 27 of 68) Appendix A Table of Colletion Times and Bulk Parameters A27

66 Table A 1 (Continued) Time H,.. f,,fo ' "'' r,,fo r,,,, a,.fo a,..,, a,.,., lla,.,, lla,,., tla,_ Date EST m Hz Hz se se deg deg deg deg deg deg X o.n o o o.; ,,. -zs.a -~().1) o o (Sheet 28 of 68) A28 Appendix A Table of Colletion Times and Bulk Parameters

67 Table A1 (Continued) Time H,.. f,,fo '... r,.fd r,.f, e,..., e,,.,. e,.,...o.e.,,.o.e,,...81' Date EST m Hz Hz se se deg deg deg deg deg deg X o o o o o.n o.n o.n t!l 22{ n (Sheet 29 of 68} Appendix A Table of Colletion Times and Bulk Parameters A29

68 Table A1 (Continued) Time H r,.fo r,.fd r,,,, ' "'' a,.fd a,,.,. a,. w t.a.,, t.a,w t.a,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X o.o ;74. ; i5.i13-12.ii. 11i.li -a.s (Sheet 3 of 68) A3 Appendix A Table of Colletion Times and Bulk Parameters

69 Table A 1 (Continued) Time H ' "",,... r,,,., r,,,, e,,,., e,,,.,, a,... t.e,.,, t.e,,. t.e,.,.. Date EST m Hz Hz se se deg deg deg deg deg deg X lf n.m-- ~o-- ~o-. i3~it 33~;- 23~ j- 27;2. -o-.-1 ; o.n o.n o.n o.n o.n o.n (Sheet 31 of 68} Append.ix A Table of Colletion Times and Bulk Parameters A31

70 Table A 1 (Continued) Time H r,,"' ' "'' r,,fd r,,,, e,,"' e,.jd, e,,aw t.e.,, t.e,w t.e..,. Date EST m Hz Hz se se deg deg deg deg deg deg X )7. -; :rs- 1).1) (Sheet 32 of 68} A32 Appendix A Table of Colletion Times and Bulk Parameters

71 Table A1 (Continued) Time H.,. ' "" t,,.,. r,,,.., r,,,, a,,,.., a,,..,, a,....t.a..,,.t.a,,. AS,.., Date EST m Hz Hz se se deg deg deg deg deg deg X (Sheet 33 of 68) Appendix A Table of Colletion Times and Bulk Parameters A33

72 Table A 1 (Continued) Time H,.. r,.fo ' "'' r,,,., r,. a,.fo a,,.,, a,....o.a.,,.o.a,,..o.afop Date EST m Hz Hz se se deg deg deg deg deg deg X o.n o.n o.n o.n 1o.n o.n 1o.n ~5~t13 t O.Jl ~ JO o.n 1o.n o.n o.n o.n o.n 1o.n (Sheet 34 of 68) A34 Appendix A Table of Colletion Times and Bulk Parameters

73 Table A 1 (Continued) Time H.,. r,.fo r,.fo r,,,., e,.fo e,..,, ' "'' e,... t.eid, toe,,. t.efoo Date EST m Hz Hz se se deg deg deg deg deg deg X Jlt2n UQQ ~ 1 3T.4 5-:6 23-:2- o~ia (Sheet 35 of 68) J Appendix A Table of Colletion Times and Bulk Parameters A35

74 Table A 1 (Continued) Time H.,.. f,,fo r,.fo r,,,, a,,fo a,..,, a,,,,. t.a.,, t.a,,. t.a.,.. ' "'' Date EST m Hz Hz se se deg deg deg deg deg deg X ~ ~3- ~ , o.n (Sheet 36 of 68} A36 Appendix A Table of Colletion Times and Bulk Parameters

75 Table A 1 (Continued) Time H r,,,., ' "' r "'' e,,,., e,,,.,, e,... t.e.,, t.e,,. t.e,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X ' ). 1lt.if. it..o-. i4.it 3;3- zs~z- 1!Y;7- {); (Sheet 37 of 68) Appendix A Table of Colletion Times and Bulk Parameters A37

76 Table A 1 {Continued) ' r,,fo r,. e,.fd a,,.,, a,. w.t.b,.,,.t.b,w.t.b'>' Time H.,. r,.fd Date EST m Hz Hz se se deg deg deg deg deg deg X v5z (Sheet 38 of 68} A38 Appendix A Table of Colletion Times and Bulk Parameters

77 Table A 1 (Continued) ' r,.fd r,., e,."' e,..,, e,. w t:.e.,, t:.e,w t:.e"" Time H r,,fo Date EST m Hz Hz se se deg deg deg deg deg deg X o o ~ n_7oo LQQ lls32_ o ~9- ~o~:r ~o~;- -o: o o. 191 o (Sheet 39 of 68) Appendix A Table of Colletion Times and Bulk Parameters A39

78 Table A 1 (Continued) r,,,., ' ""' r, "'' e,,,., e,,.,, e,... tj.e.,, tj.e,,. ll.8~ Date EST m Hz Hz se se deg deg deg deg deg deg X Time H.,. t,,,., o o.n o.n (Sheet 4 of 68) A4 Appendix A Table of Colletion Times and Bulk Parameters

79 Table A 1 (Continued) Time H.,. t,,fl) ' r,,fl) r, e,,fl) e,,.,, e,... t.e.,, t.e,,. t.e_ Date EST m Hz Hz se se deg deg deg deg deg deg X f 2ZOU ~-tit o-. t32. t32. ;-.5& Ur.O. 11}; ~2-.7 ~2.,. ~ o (Sheet 41 of 68} Appendix A Table of Colletion Times and Bulk Parameters A41

80 Table A 1 (Continued) ' Time H,.. r,,fd ' "" r,... e,,,., e, "'' e,,sw t.e"'' t.e,w 681'1' Date EST m Hz Hz se se deg deg deg deg deg deg X o.o ~ 35~ (Sheet 42 of 68) A42 Appendix A Table of Colletion Times and Bulk Parameters

81 Table A 1 (Continued) Time H r,.,., ' "" r,,f e,."" e,..,. e,....t.e.,,.t.e,,..t.e_ Date EST m Hz ' Hz se se deg deg deg deg deg deg X o ~3t5 22M 1~ lr.o (ShiHit 43 of 68) Appendix A Table of Colletion Times and Bulk Parameters A43

82 Table A 1 (Continued) Time H r,,,., ' r,,,., r,., e,,,., e,,.,, e,... t.e.,, t.e,,. t.e,.. Date EST m Hz Hz se se deg deg deg deg deg deg X o o.n o.n o.n '!-9 -~5.74 O.i: s-o b.u l (ShHt 44 of 68) A44 Appendix A Table of Colletion Times and Bulk Parameters

83 Table A 1 (Continued) Time H r,.r> ' "' T,.R> T,.~s e,.'o e,..,. e,... t.e.,, t.e,,.!:.91' Date EST m Hz Hz se se deg deg deg deg deg deg X o o Ult b:z- ~llk ~5~9- u~; o El o o o.n (Sheet 45 of 68} Appendix A Table of Colletion Times and Bulk Parameters A45

84 Table A 1 (Continued) Time H.,. '.FD r,,, r,,,, a,,, a,,.,, a... t.a.,, t.a,,.. t.a,..,. Date EST m Hz ' Hz se se deg deg deg deg deg deg X o.o _.152..n ~.- fi.s ~.{} 4{} (Sheet 46 of 68) A46 Appendix A Table of Colletion Times and Bulk Parameters

85 Table A 1 (Continued) Time H '.FO r,.fo r,,,., e,.,.., e,,.,, e,...,.e.eio, t.e,.., t.e""' Date EST m Hz ' "'' Hz se se deg deg deg deg deg deg X D9 16DD D.62 D.318 D D -64.D D D D9 19DO D.59 D D9 22DD D D D D D D D D D4DD D -42.D D D D7.9.2D1.23D D D D D 13DO 1.84 D. 152 D D 3D.D D D.D D.171 D D 3D D D.17 95D41 22DD 1.61 D.123 D D 16.D D 12.8 D D1DD 1.41 D. 123 D D 14.D 29.D 3D D.6 D DD D D 16.D D D. 142 D D D 14.D D DDD 1.13 D.132 D D.D 1D.D D , 13DD D D 1D.D D D D 1.12 D D 1D.D D DD 1.D3 D.123 D D 8.D D.17 95D411 22DD 1.1D.113 D D D412 D1DO 1.12 D D.D 6.D D412 D4DO 1.D7 D D4 7.D D D 18.9 D D412 D7DD D.95 D.113 D D.D D.17 95D412 1DD.9D.113 D D 4.D D. 162 D D D412 16DD D.98 D.1D3 D D -4.D D DD D.97 D.162 D D.6 D.16 95D412 22DD D D Cl4U Q4QQ ~4 ~8-:2- ~8-:3- ti-:i D D D DO D DDD D DD.72.23D D D.O D414 19DD D.56 D.22D D D D414 22DD.46 D.24 D D D D D 54.D DOO D.67 D (Sheet 47 of 68) Appendix A Table of Colletion Times and Bulk Parameters A47

86 Table A 1 (Continued) ' r,,fo r,., e,.fo e,,.,, e,....o.e.,,.o.e,,..o.e_ Time H r,,fo Date EST m Hz Hz se se deg deg deg deg deg deg X D4'!-9 '!-9no ~14 o.n W ~i;.{l o o o o.o (Sheet 48 of 68) A48 Appendix A Table of Colletion Times and Bulk Parameters

87 Table A 1 (Continued) Time H '.1' r,,,., r,,,, e,,,.., e,..,, e,... t:.e,.,, t:.e,,. t:.e,., Date EST m Hz ' Hz se se deg deg deg deg deg deg X ~ ~ o.n o.n O.Sl r.m r. ;n- - s-. io - a~ io - lo;o 8-; 4-~ ~~ o (Sheet 49 of 68} Appendix A Table of Colletion Times and Bulk Parameters A49

88 Table A 1 (Continued) Time H,.. r,,,., ' r,.,., r,,,. e,,,., e,,,.,. e,. w t.e,.,, t.a,w t.e,.,.. Date EST m Hz Hz se se deg deg deg deg deg deg X t.h1..n.132..n.m. '! { () (Sheet 5 of 68) A 5 Appendix A Table of Colletion Times and Bulk Parameters

89 Table A 1 (Continued) Time H,.. ' "" r,,.,, r,."" T,,Fs e,."" e,..,, e,,,.,. ll.e,.,, ll.e,.,. ll.9fo' Date EST m Hz Hz se se deg deg deg deg deg deg X ~ o Tl.: tr. zs ~2;3-22;7 -ZO;CF {); (Sheet 51 of 68) Appendix A Table of Colletion Times and Bulk Parameters A51

90 Table A 1 (Continued) Time H.,. ' f'd r,."" r,., e "" e,,.,, e,. w t.e.,, t.e,w AB'OP Date EST m Hz ' Hz se se deg deg deg deg deg deg X o.n o.n (Sheet 52 of 68) A 52 Appendix A Table of Colletion Times and Bulk Parameters

91 Table A1 (Continued) r,."d r,., e,,"' e,,..,, e,....o.e.,,.o.e,,..o.e,..,.. Time H r,."d ' "' Date EST m Hz Hz se se deg deg deg deg deg deg X o o _. 4.D_. O..D_ ~3.3 ~ o.n o.n o.n o (Sheet 53 of 68} Appendix A Table of Colletion Times and Bulk Parameters A 53

92 ! Table la 1 (~onti~ued) Time H.,. r,.fo ' "'' r,,,.., r,., a,..., a,,.,, a,... t.a.,, t.a,,. t.ai'do Date EST m Hz Hz se se deg deg deg deg deg deg X o.o ta.2. 32~~ ~L~ 1~.7 ilh o.n o.o o.n (Sheet 54 of 68) i A 54 Appendix A Table of Colletion Times and Bulk Parameters

93 Table A1 (Continued) Time H ' "" ' "'' r,,,., r,,,, e,,., e,,.,, e,. w ~e.,, ~e,w ~a,., Date EST m Hz Hz se se deg deg deg deg deg deg X D D -4D.D D.16 95D6D5 22DD D.62 D.113 D.22D D.21 95D6D6 D1DD.72 D.171 D D.D -48.D D6 D4DD 1.9 D.162 D D.O -5D.D D.1 2D D.D9 95D6D6 D7DO 1.13 D.162 D D4-46.D -44.D D.D9 95D6D6 1DDD 1.16 D.142 D D D.O -4D.D D 16.5 D.12 95D6D D1 D.142 D D D -42.D D.14 95D6D6 16DD D D -42.D D D.1 95D6D6 19D 1.53 D D D -4D.O D D.13 95D6D6 22DD 1.2D D D D D D7 D1D.94 D.2D1 D D 46.D 2D D6D7 D4DD D.93 D.191 D D D.14 95D6D7 D7DD D.91 D D 24.D D.D D.11 95D6D7 1DDO D D 28.D D.11 95D6D7 13DD D.72 D.171 D D 3D.D D.D D6D7 16DD D.66 D.171 D D 3D.D D.17 95D6D7 19DO D 38.D D.16 95D67 22DD.64 D.123 D D -36.D 17.D D6D8 D1DO.7D D D4 7.D4 14.D 16.D D.3 D D8 4DD D D 16.D D D. 18 (Sheet 55 of 68) Appendix A Table of Colletion Times and Bulk Parameters A 55

94 Table A 1 (Continued). ' ' Time H.,. r,.m r,... e,.m e,.d. e,....o.e.,,.o.e,,..o.e..,. Date EST m Hz ' "" Hz se se deg deg deg deg deg deg X ' o.o S612 ~6 ~.37 ~ ~ ~1).5. 4~ () ' (Sheet 56 of 68) A 56 Appendix A Table of Colletion Times and Bulk Parameters

95 Table A 1 (Continued) ' r,,,., r,., e,.fo e,.d, e,,,,..o.e.,,.o.e,,...81'1' Time H,.. r,.fd Date EST m Hz Hz se se deg deg deg deg deg deg X o o. 132 o S6~9!}7 e.&~ Q ' !.- ll.'! 2' ~12_ (Sheet 57 of 68) Appendix A Table of Colletion Times and Bulk Parameters A 57

96 Table A 1 (Continued) Time H.,. ' "" r,.rl r,,,, ' "'' e,."" e,..,, a,... t.eid, t.e,.,. 68""' Date EST m Hz Hz se se deg deg deg deg deg deg X 95D621 19DD D.43 D. 1D3 D.D D D -4D.D D D.26 95D621 22DD D.57 D.21D D D.O -44.D D. 1 D.22 95D622 D1DD D.64 D.171 D D -44.D D D622 D4DD D.76 D. 162 D D -44.D D D7DD D.68 D. 142 D D D -46.D -42.D D.14 95D622 1DDD D.7D D.152 D D -46.D D.12 95D622 13DD D.73 D.152 D D -46.D D D.13 95D622 16DD D.71 D. 152 D D -46.D D.D D D622 19DD D.87 D. 152 D D4 12.D 14.D D. 1D 95D622 22DD D.7D D.142 D D4 7.D4 12.D 14.D D. 1D 95D623 D1DD D.78 D.162 D D -44.D -15.D 59.D D.1D 95D623 D4DD D.79 D. 162 D D.D -48.D -17.D D.11 95D623 D7DD D.74 D. 123 D D 1D.D D D.11 95D623 1DDD D.68 D.152 D D -42.D D.5 D.1D 95D623 13DD D.66 D. 123 D D -4D.D D.6 54.D 41.6 D D623 16DD D.65 D. 123 D D -36.D D D623 19DD D.69 D.132 D D4-4D.D -4D.D D.12 95D623 22DD D.65 D. 142 D D4 7.D4-4D.D -4D.D D D.11 95D624 D1DD D.68 D.142 D D4 7.D4-4D.D -38.D D D624 D4DD D.68 D.132 D D -42.D D D 35.7 D.13 95D624 D7DD D.65 D.132 D D.D -4D.D D.13 95D624 1DDD D.64 D.132 D D 12.D D.11 95D624 13DD D.66 D. 142 D D4 7.D4-42.D -42.D D D624 16DD D.64 D.132 D D -44.D D.13 95D624 19DD D.63 D. 123 D D -14.D -3.D D D624 22DD D.75 D.113 D D D D.12 95D625 D1DD D.9D D. 132 D D -2D.D D. 1D 95D625 D4DD D.8D D.123 D D -26.D D.15 95D625 D7DD D.77 D.123 D D -22.D D D625 1DDD D.67 D.123 D D -2D.D D.3 D.12 95D625 13DD D.74 D.123 D D -22.D D.13 95D625 16DD D.7D D.132 D D -14.D D D.14 95D625 19DD D.62 D.123 D D -16.D D D.16 95D625 22DD D.65 D.123 D D.D -16.D D D.14 95D626 D1DD D.67 D.123 D D.D -18.D D D.13 95D626 D4DD D.73 D.123 D D -12.D D D D626 D7DD D.71 D.132 D D -16.D -16.D o D626 1DDD D.69 D.123 D D -6.D D.13 95D626 13DD D.73 D. 132 D D -16.D D.13 95D626 16DD D.77 D.113 D D -16.D D.17 95D626 19DD D.82 D. 113 D D.D -1D.D D D626 22DD D.89 D.113 D D -1D.D D D.16 95D627 D1DD D.95 D.113 D D.D -1.D D D627 D4DD D.94 D.113 D D -18.D D D627 7D.88 D D D D D D627 16DD 1.D2 D D D627 19D D D D D627 22DD D.94 D D D628 D1DD 1.16 D.171 D D D D.9 95D628 D4D D D D D 95D628 D7DD 1.49 D D 18.D D.11 95D628 1DDO D D 12.D (Sheet 58 of 68) A 58 Appendix A Table of Colletion Times and Bulk Parameters

97 Table A1 (Continued) Time H.,. t,,,., ',... r,,,., r., e,,,., Bp,JDS e... flbds ae,,. llb'dp Date EST m Hz Hz se se deg deg deg deg deg deg X t6 11~. ~ ; (Sheet 59 of 68) Appendix A Table of Colletion Times and Bulk Parameters A 59

98 Table A 1 (Continued) Time H,.. ' 'D ' "'' r,.'d r,,,, s,,'d s,,ld, s,... lis.,, lis,,. lis'do Date EST m Hz Hz se se deg deg deg deg deg deg X " _o. 7'4 -~191 _ A.~ ~ ' (Sheet 6 of 68} J A6 Appendix A Table of Colletion Times and Bulk Parameters

99 Table A 1 (Continued) Time H.,. r,,, r,,,, a,., ' "" ' "'' a, "'' a,.,..6aj)..6a,,..6a,. Date EST m Hz Hz se se deg deg deg deg deg deg X a (Sheet 61 of 68} Appendix A Table of Colletion Times and Bulk Parameters A61

100 Table A 1 (Continued) Time H ' "' ' r,,., r,.., e,,,., e,,.,, e,. w.o.e.,,.o.e,w.o.e,.,. Date EST m Hz Hz se se deg deg deg deg deg deg X o.o o:o83 -o.-o83 -n.-w~ T1.-w zb (Sheet 62 of 68) A62 Appendix A Table of Colletion Times and Bulk Parameters

101 Table A 1 (Continued) Time H,.. r,,, '.JF r,,, r,.f, s,,, s,jd. s,. w AS.,, AS 1 w AS,.. Date EST m Hz Hz se se deg deg deg deg deg deg X o o.tu o.tu tt.a-7. a-.8" r ;.8- {}~29' (Sheet 63 of 68) Appendix A Table of Colletion Times and Bulk Parameters A63

102 Table A1 (Continued) Time H t,.fo t,,,. r,,,., r,,, e,.fo e,..,. e,... L.B.,, Ll.6,,. L.B...,. Date EST m Hz Hz se se deg deg deg deg deg deg X _~34 _~23 _~23 to.z2 'UU2 -ln..o !- ~ ) (Sheet 64 of 68) A64 Appendix A Table of Colletion Times and Bulk Parameters

103 Table A1 (Continued) ' Time H r,,., r,., e,,,.., e,,..,. e,.,. t.e..,, t.e,,. t.ei'>p Date EST m Hz ' "" Hz se se deg deg deg deg deg deg X o.o t2 Ot ~. - -a.o. -{);(,- -2fr., i6. it; i,_ (Sheet 65 of 68) Appendix A Table of Colletion Times and Bulk Parameters A65

104 Table A 1 (Continued) Time H.,. f,,fo ' r,.'o r,..., a,,'o a,,jd, a,,,.. ll.a.,, l!.s,,. l!.s'd' Date EST m Hz Hz se se deg deg deg deg deg deg X o l8 19 ~.19 -~ (Sheet 66 of 68) A66 Appendix A Table of Colletion Times and Bulk Parameters

105 Table A 1 (Continued) Time H.,. r,,, r,.,, e,,, e,,.,, e,. w.o.e.,,.o.e,w..9_. ' "" ' "'' Date EST m Hz Hz se se deg deg deg deg deg deg X o.n tooo.37 o. ts2. t32. ().59. ().59 -ltlt.o -41}; i); ;8- i);2c} o.n o.n 1o.n (Sheet 67 of 68) Appendix A Table of Colletion Times and Bulk Parameters A67

106 Table A 1 (Conluded) Time H.,. f,,fd ' JF r,.fd r,. e,.fd e,.jd. e,... t.e.,, t.e,,. t.efdp Date EST m Hz Hz se se deg deg deg deg deg deg X (Sheet 68 of 68) A68 Appendix A Table of Colletion Times and Bulk Parameters

107 Appendix B Time Series Graphs of Bulk Parameters Appendix B Time Series Graphs of Bulk Parameters 81

108 June Cl)'ot... Q)Pl -Q)('j E ~~~~~~~ T p,fs C/lO Q)CD ~ C)'ot Q)o "CN ~ TN Hmo and 8p,DS in Vetor Form ~: "C : u Q) (/) -(/)... Q) -Q) E "C : u Q) (/)... -(/) Q) -Q) E N.hlt.J!UU!.#~\~1/MW#.M''JJt JfJWi~Di:fP'<4"4td -'U. Current Vetor,,,...,,,..,...,...,...,...,,,...,...,,...,,,...,...,...,..., 111 '1' '1"'1 " ' pier Figure 81. Bulk data for June 1994 B2 Appendix B Time Series Graphs of Bulk Parameters

109 July ~ : - u CD.!!! ~ ;;..,. '- 1...,_-~J4~._~:.,.~At.~~,~~~ CD - E o Current Vetor l'"i'''l'"l'''l'''l'''l"'i"'l'''l'"''''l"'l'"i"'l'"l"'l"'l"'l'''l"'l'''l'.,...,...,...,...,...,...,...,...,..., Figure 82. Bulk data for July 1994 Appendix B Time Series Graphs of Bulk Parameters 83

110 August en"' a;.., -Q)N E "C - : Q) ~ (/) -->-; =--~..._ ~ ,.~,,,>-~,,_, r -... / j'>'...::== "'"" -::=- ' ""=""" 7-..,..., =- 4 Q) -Q) E o Current Vetor i'''l'''i'"l'''l'''l'"i'''l'"l'''l'''l'lijiiijiiijllljilljiiijilijiiijllljiiljilijliijilijllijilljliljilijiiljilijiiijlllj Figure 83. Bulk data for August Appendix B Time Series Graphs of Bulk Parameters

111 September (/)., a;.., -Q)N E Cll.n -:o o_ t.l ~t) T p,fs C/)U) G) G) "- Cl G)o "C. CllO G) CD ~ Cl" G)o "CN Cl)... Q) -Q) E E~ Hm-o- and Hfr.;os in Veto_r Fo_rm ~-~~AAiJ.UA!~\!~MA~ "C : t.l Q).!!! Cl)... G) -G) E "C : t.l G) Cl)... -Cl) G) -G) E ~~,~1.~.!\l\/~~~~- Current Vetor l'''i'''i'''i'''i'''l'''l'''l'''l'''i'''i'''l'''i'''l'''l'"l'''i'''l'''l'''l'''l'''i'''l'''l'''l'''l'''l'''l'''l'''l'''l pier Figure B4. Bulk data for September 1994 Appendix B Time Series Graphs of Bulk Parameters 85

112 (/)., Cii(") -Q)N E Otober """ ~~#~X~~~~~~~-=~L~-~,~~~~~~~~~~~~~~~~~~~~::J T p,fs no Q)U) Q)o C,<r Q)o "tjn ~~~~~~~~ww~~ww~~~ww~~~ww~~~~wwww~ww~ *f '"'~~~R/lii~~\\\~\\\\//Mii/ Jm~U4.1!mll 1~&11~\~\~ll~~"~H/Mind//l/i E o ~~~~~--~~~~~~~~~~.~ X>!< X 1 _and _8-p;tl':tS in Vetor Form :~4~\~~~-'t.:~~~~:_, "t:l : (,) Q) (/)... (/)... Q) -Q) E Current Vetor l'''i'''l'''l'''l'''l'''i'''l'''i'''i'''l'''i'''l'''l'''l'''l'"l'''l"'l'''fl''lilijliifiiijllljiiij,.,,,,,.)j, Figure 85. Bulle data for Otober Appendix B Time Series Graphs of Bulk Parameters

113 November en.n -:o o_ u G>.n en T p,fs 9p,DS eno Q)CD a>o, a>o "'CN ''"'' X X~ X o ~~~~~~~wwwwww~~~~~~~~~~~~~~~~~~~w X... en Q) -Q) E "'C : u Q)... en en... Q) -Q) E "'C : u Q) ~ en... Q) -Q) E F...n_JA!l/J/1~\~J/y, Current Vetor 1'"1"'1'"1'''1"'1'"1' 1 '1'''1"'1'"1'''1"'1'"1"'1'''1"'1 ''1'"1"'1"'1"'1'"1'''1"'1'''1' '1'"1"'1' '' pier Figure 86. Bulk data for November 1994 Appendix B Time Series Graphs of Bulk Parameters 87

114 . (/)... Q)M -Q)N E ~~ : o u- ~lll Deember ~ ~ -~)( ~ ~ v.. a.:~.. r -Ri ~ ~ '*' ~ ph :"""'6~ ~ ; X ~ T p.fs (/)) X Q) >s ~ ~X;~~ =~~--~~~~~~~~~~~~~~~~~~~~~ ~g ~~ (1) Q)<D ~ C). Q)o 'ON X 'tl : u Q) (/)... (/)... Q) -Q) E 'tl : u Q) (/)... (/)... Q) -Q) E N Gauge noperative Current Vetor 1'''1'''1'''1''' ,...,...,...,...,,...,...,...,,iiijl.,...,...,...,...,...,. ' ,...,...,...,...,, Figure 87. Bulk data for Deember Appendix B Time Series Graphs of Bulk Parameters

115 January (l)lt) ~)(-- "- : )( )(,_ ~ ~ ~rx ~ x ~#'!"-~~- ~ t) ~,!lie x A~~ ~ >ill1' r x ~ ~ )( T p,fs " i : N pier ~~~4 4 ~~~~' E o Ar P~Erid Wind Vetor " : - u Q) C/)... -C/) Q) -Q) E o Gauge noperative Current Vetor l'''l'''i'''l'''l'''l'''l'''i'''l'''i'''i'''l'''l'''i'''l'''l'''''''l'''l'''i'''i'''i'''i'''l'''i'''i'''l'''l'''i'''i'''l'''i Figure BB. Bulk data for January 1995 Appendix B Time Series Graphs of Bulk Parameters 89

116 February p.ds r ~ Hm.and.8"""'in Yetm Form ~ :.. ~-~~ b ~~~ ~\11~M\.;>., C: N u ~~~~~~~~! : \ 1/ T( / ~~ Pier-End Wind Vetor : u CD en -en ~ CD -CD E o Gauge noperative Current Vetor t'''i"'i'"l'''l"'i'''l"'l"'l'.,,,...,. '1'"1'''1'''1'"1'' i"'i..,...,...,...,...,...,...,...,..., pier Figure 89. Bulk data for February Appendix B Time Series Graphs of Bulk Parameters

117 Marh "C r::: N pier i \ -~ ~~~~~/ ~, e o P~ ~nd Vetor "C - r::: u Q) ~ () ~ Q) Gauge noperative -Q) E o Current Vetor l'''l'''l'''l'''l'''l'''l'''l'''l'''l'''l'''l'''i'''l'''i'''l'''l'''l'''l'''l'''l'''l'''l'''l'''l'''i'''l'''l'''l'''l'''l'''l Figure B1. Bulk data for Marh 1996 Appendix B Time Series Graphs of Bulk Parameters 811

118 "' en"'" a;..,... G>N E_ April en"' -:o o_ (J ~"' en Q) Q) "- C) a>o "CCD - Bp,DS T p,fs eno Q)CD G>o C,..r a>o "ON X en... Q)... Q) E Hmo and Bp.DS in Vetor Form " : (J Q) en -en... Q)... Q) E " : (J Q) en -en... Q) N Gauge noperative pier -Q) E Current Vetor l'''l"'l'"l"'l"'i'"l"'l'"i"'l'"l'''i'''l'"l'"i'''l"'l'"i'''l"'l'''l'"i"'l"'l' i",...,...,...,..., Figure B11. Bulk data for April 1995 B12 Appendix B Time Series Graphs of Bulk Parameters

119 en"' (D.., May C>N E:~~~~~~~~~~~~~~~ T p,fs en Cl> Cl>... Cl uo 'O ' > < X ' : Cl> Ul en Q) -Q) E ' : Q)... en Ul... Q) -Q) E o Gauge noperative Current Vetor 1'''1'''1'''1'''1'''1'''1'''1 1 1 ' '''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1'''1''' Figure 812. Bulk data for May 1995 Appendix B Time Series Graphs of Bulk Parameters 813

120 June T p.fs Hmo and Bp.tos in Vetor Form "C : u CD (/)... -(/) CD CD E "C : u CD (/) -(/)... CD... CD E Gauge noperative Current Vetor l'''l'''l'''l'''l'''i'''l'''l'''i'''i'''i'''l'''i'''i'''i'''i'''i'''l'''i'''l'''l'''i'''l'''l'''i'''l'''l'''i'''l'''l'''l pier Figure 813. Bulk data for June Appendix B Time Series Graphs of Bulk Parameters

121 July * X. X XX * JKJK ** ~-~~... ~ x~.,._ *xx X X X X "l's!\ ""'-!,.-, - -:.~... T p.fs en CD lid CD,... CD "ON ~~~~~~~wwww~~~~~~~~~~~~~~~~~~~~~~ Hmo and Bp,DS in Vetor Form ~ :L.L. L.~ L.~ " r:: (J CD ~ en... CD -CD E " r:: (J CD en -en... CD -CD E N Gauge noperative Current Vetor l'''l'''i'''l'''l'''i'''i'''i'''l'''l'''i'.,,,,...,,,,,,,,...,,,,,,,,, pier Figure 814. Bulk data for July 1995 Appendix B Time Series Graphs of Bulk Parameters 815

122 August () 't ml'l -CDN E (l)ll) -: oo u- ~ll) T p,fs 1... ~ Cl) - - E o "'C : (.) Cl) ()... -() Cl) -Cl) E "'C - : (.) Cl) ()... -() Cl) -Cl) E o Gauge noperative Current Vetor l'''l'''i'''i'''i'''l'''i"'l'"i'.,...,...,...,...,...,...,...,...,...,...,...,...,...,...,...,...,...,...,..,...,...,..., Figure 815. Bulk data for August Appendix B Time Series Graphs of Bulk Parameters

123 Appendix C Listing of FORTRAN Computer Program program readasii This program has the odes to read FRF 8-m array diretional spetral ASC output files. This program simply reads the ASC file and writes an ASC file as a test of the ode. You will have to tune the 1/ statements to your own system.. Variable names, units and meanings are: ======================================================================== datetime [harater*1] Date and Eastern Standard Time of beginning of data olletion in the order year, month, day, hour, minute and in the form yymmddhhmm (2-digit year, no blanks in any field) Hmo [m] Energy-based harateristi wave height= 4*sigma, where sigma"2 is the variane of sea surfae displaement = volume under frequeny diretion (f-d) spetrum fp [HZ] Frequeny at the peak of the frequeny spetrum thp [deg] Diretion at the peak of the diretional distribution at f=fp ifimle Algorithm flag: [1J=MLE estimate, [QJ=MLE estimate istot [se] Length of time series proessed sfrq [Hz] Data sampling frequeny in time series ifwindo. Windowing flag: [QJ=data segments not windowed, [1J=data segments windowed (Kaiser-Bessel window) ifdtrnd Detrending flag: [Q]=data segments not detrended, [1l=data segments detrended (linear trend removed) nfft Number of data points in a data segment nensb Number of half-lapped segments analyzed nband Number of frequeny bands averaged for frequeny smoothing idgfr Degrees of freedom of final frequeny spetral estimates nofrq Number of output frequeny bands delfs [Hzl Width of an output frequeny band Figure C 1. Listing of FORTRAN Computer Program (Sheet 1 of 4) Appendix C Listing of FORTRAN Computer Program C1

124 noang. Number of output diretion bins (ars) odelang... [deg] Yidth of an output diretion bin dmin.. [m] Minimum water depth during time series at 8 m array referene gage rname' dbar [m] Mean water depth during time series at referene gage dmax. [m] Maximum water depth during time series at referene gage rname Referene gage D (FRF gage name - get help if you need to know whih 8-m array gage it was) s9b. [m/sel Mean wind speed at pier end anemometer (19.5 m above mean sea level) during time series s9s. [m/se] Standard deviation of wind speed at pier end anemometer s9m [m/se] Maximum wind speed at pier end anemometer d9b [deg] Vetor averaged mean wind diretion at pier end anemometer - diretion from whih wind blows in wave diretion oordinates (degrees ounterlokwise from shore normal) d9s [degl Measure of variability of wind diretion at pier end anemometer= artangent[(standard deviation of ross-mean-streamline wind speed)/(mean wind speed)] s8b. - These are the same as s9b, s9s, s9m, d9b, s8s. and d9s, exept they are from the seondary s8m anemometer at the seaward end of the pier, less d8b than 2 m away from the primary anemometer and at d8s m above mean sea level oangle [deg] Array of wave diretion oordinates that aligns with the f-d spetral array nof (Within a loop) Frequeny index of(nof) [Hzl Frequeny osf(nof) [m"2/hz] Frequeny spetral density at frequeny of(nof) ogpat(nof) [harater*16] Enoded list of gages used to ompute --di-retional-di-stril:lution -of -ener~y _at this frequeny itero(nof) Number of MLE iterations used to ompute diretional distribution of energy at this frequeny osp(nof,noa) [1/deg] Normalized frequeny-diretion spetral den sity at frequeny of(nof) and diretion oangle(noa). Dimensional frequeny-diretion spetrum sp(nof,noa) [in m"2/(hz deg)] is found from: sp(nof,noa) = osf(nof)*osp(nof,noa) ======================================================================== links: none harater*4 rna me harater*1 datetime harater*16 ogpat(29) harater*16 infi le, out file dimension of(29), osf(29), itero(29) dimension oangle(181), osp(29,181) ask user for input and output file names write(*,'(2x,''enter input file name : ''>'> read(*,'(a)') infile write(*,'(2x,''enter output file name : '')') read(*,'(a)') outfile Figure C 1. (Sheet 2 of 4) C2 Appendix C Listing of FORTRAN Computer Program

125 open input file and read data open(1,file=infile,status= unknown,aess= sequential', & form='formatted 1 ) read(1,'(a1,f1.2,f1.5,f1.1,2i1,f1.2,i1)') & datetime, Hmo, fp, thp, & ifimle, istot, sfrq, ifwindo read(1,'(6i1,f1.5,i1) 1 ) & ifdtrnd, nfft, nensb, nband, & idgfr, nofrq, delfs, noang read(1,'(4f1.2,6x,a4,3f1.2) 1 ) & ode lang, dmin, dbar, dmax, & rname, s9b, s9s, s9m read(1, 1 (2f1.1,3f1.2,2f1.1) 1 ) & d9b, d9s, s8b, s8s, & s8m, dbb, d8s read(1, 1 (1f8.1)') (oangle(noa),noa=1,noang) do 7 nof=1,nofrq read(1, 1 (i1,f1.5,e2.7,4x,a16,i1)') & nof, of(nof), osf(nof), ogpat(nof), & i tero(nof) read(1, 1 (8f1.7)') (osp(nof,noa),noa=1,noang) 7 ontinue lose(1) open output file and write variables just read open(11,file=outfile,status= unknown,aess= sequential', &- fa-rm=- -f-o-rma-ttedj- )- write(11, 1 (a1,f1.2,f1.5,f1.1,2i1,f1.2,i1)') & datetime, Hmo, fp, thp, & ifimle, istot, sfrq, ifwindo write(11,'(6i1,f1.5,i1)') & ifdtrnd, nfft, nensb, nband, & idgfr, nofrq, delfs, noang write(11,'(4f1.2,6x,a4,3f1.2) 1 ) & odelang, dmin, & rname, s9b, dbar, s9s, inax, s9m write(11,'(2f1.1,3f1.2,2f1.1)') & d9b, d9s, s8b, sbs, & sbm, dbb, dbs write(11,'(1f8.1) 1 ) do 8 nof=1,nofrq (oangle(noa),noa=1,noang) write(11, 1 (i1,f1.5,e2.7,4x,a16,i1)') & nof, of(nof), osf(nof>, ogpat(nof), & i tero(nof) write(11, 1 (8f1.7) 1 ) (osp(nof,noa),noa=1,noang) Figure C 1. (Sheet 3 of 4) Appendix C Listing of FORTRAN Computer Program C3

126 8 ontinue lose(11) end Figure C 1. (Sheet 4 of 4) C4 Appendix C Listing of FORTRAN Computer Program

127 Appendix D Listing of Sample Data File E '.5~7'21.5~ (}.6489~ E E Figure D 1. Listing of sample data file (Sheet 1 of 7) Appendix D Listing of Sample Data File 1

128 E+OO E+OO E+OO o.oo4949 o.o3694 o.oo21665 o.-oom66 -o.-oo-t6939 o.oot8ooo o.oozo2n -o.oo2m E+OO E+OO Figure 1. (Sheet 2 of 7) 2 Appendix D Listing of Sample Data File

129 E+OO E E o.ool9t ~ Q._()()_19S-93- O-.Jl oooa !!9- o.ooo6387 o.ooo566o o.ooo5135 o.ooo475 o.ooo4462 o.ooo4239 o.ooo4o6o o.ooo E E Figure D 1. (Sheet 3 of 7) Appendix D Listing of Sample Data File 3

130 E E E o~{)4{)79 o~oog3592 o.ooo323 o.ooa296 o.ooo27s7 o.oooa6o5 o.ooo2-49l E E Figure D 1. (Sheet 4 of 7) 4 Appendix D Listing of Sample Data File

131 E E E E E E Figure D 1. (Sheet 5 of 7) Appendix Listing of Sample Data File 5