NOAA Technical Memorandum ERL PMEL-59 WAVE …2.1.3 Side-Looking Airborne Radar (SLAR) 2.1 Surface...
Transcript of NOAA Technical Memorandum ERL PMEL-59 WAVE …2.1.3 Side-Looking Airborne Radar (SLAR) 2.1 Surface...
NOAA Technical Memorandum ERL PMEL-59
WAVE AND CURRENT OBSERVATIONS AT THE COLUMBIA
RIVER ENTRANCE, 10-13 SEPTEMBER 1981
F. I. GonzalezM. R. MulhernE. D. Coke1etT. C. Kaiser
Pacific Marine Environmental Laboratory
J. F. R. GowerJ. Wallace
Institute of Ocean SciencesSidney, B.C.Canada V8L 4B2
Pacific Marine Environmental LaboratorySeattle, WashingtonDecember 1984
..(~~
•UNITED STATESDEPARTMENT OF COMMERCE
M.lcalm B.ldrl...S.crlllry
NAnONAl OCEANIC AND.ATMOSPHERIC ADMINISTRATION
Environmental Researchlaboratories
Vernon E. DerrDirector
NOTICE
Mention of a commercial company or product does not constitutean endorsement by NOAA Environmental Research Laboratories.Use for publicity or advertising purposes of information fromthis publication concerning proprietary products or the testsof such products is not authorized.
ii
CONTENTS
2. OBSERVATION METHODS
1. INTRODUCTION
3. DATA SUMMARY . . . .
7. REFERENCES .
, Page
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5658
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. . . . 74
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4.2.1 The Observations .4.2.2 Comparison with Linear, 1-D Theory
2.3.1 NOS Meteorological Station2.3.2 NDBC Buoy 460102.3.3 Clatsop County Airport
3.1 Regional Data3.2 Local Data . .
ABSTRACT ...
Surface Drifter DeploymentsCape Disappointment Radar TrackingJettg A Radar Tracking
2.2.1 NOS Subsurface Current Meters2.2.2 Surface Drifter Program
2.1.1 Wave rider2.1.2 NDBC Buoys2.1.3 Side-Looking Airborne Radar (SLAR)
2.1 Surface Wave Data
2.2 Current Data
2.3 Surface Wind
4.1 Wave Decay Upriver of Buoy 8
4.2 Wave-Current Interaction Seaward of Buoy 8
SUMMARY AND CONCLUSIONS
6.1 Real-time, Long-term Monitoring.6.2 Theory and Numerical Modeling6.3 Field Experiments
O. ACKNOWLEDGEMENTS
4. PRELIMINARY DATA ANALYSIS
6. RECOMMENDATIONS FOR FURTHER RESEARCH
5.
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APPENDIX. INTENSIVE OBSERVATION PERIODS DATA SUMMARY
Flood of 10 September 1981
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter Tracks
79
85
Ebb of 10 September 1981 · . . . . . . . . . . . 101
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
Slack of 11 September 1981 · . . . . . . . . . . . 119
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
Ebb of 11 September 1981 · . . . . . . . . . . . 137
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
Flood of 12 September 1981 · . . . . . . . . . . . 149
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
Ebb of 12 September 1981 · . . . . . . . . . . . 171
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
Flood of 13 September 1981 · . . . . . . . . . . . 187
Jiaverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
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--------
Ebb of 13 September 1981
Waverider Log, Tracks, and SpectraCape Disappointment Radar Log and Surface Drifter TracksJetty A Radar Log and Surface Drifter TracksSLAR Imagery
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Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8(a).
Figure 8 (b) .
Figure 8(c).
Figure 8(d).
Figure 8(e).
Figure 8(f).
Figure 9(a).
LIST OF FIGURES
Map of U.S. West Coast, showing location ofColumbia River entrance relative to varioussources of environmental observations. SOWKlocations refer to positions of grid pointsfor which the Fleet Numerical OceanographicCenter (FNOC) provides wave spectrum nowcastsand forecasts computed by the FNOC SpectralOcean Wave Model (SOWK) .
Reference map of Columbia River entrance.
PMEL Waverider 67135 predeployment calibrationcurve.....
NOAA data buoy 46010 at dockside in Astoria,Oregon. . • . . . .
Oregon Army National Guard Mohawk on areconnaissance flight of Mount St. Helens,Oregon. The SLAR antenna can be seen mountedunder the cockpit. . . . .
Nominal Mohawk SLAR flight lines 1 to 8.Circled numbers indicate the start of eachflight line and coverage extends 25 km to theright of each track. . . . . . . . . .
Sketch of surface drifter buoy equipped with radarcorner reflector. . .....
Surface pressure analysis for 1800Z, 8 September1981 . .
Surface pressure analysis for 1800Z, 9 September1981 . .
Surface pressure analysis for 1800Z, 10 September1981. . . . . · . · · . . · · .
Surface pressure analysis for 1800Z, 11 September1981. . . . . · . · · . . · · .Surface pressure analysis for 1800Z, 12 September1981. . . . . . . · · · . · · . .Surface pressure analysis for 1800Z, 13 September1981 . . . . . .
Wind and wave observations at NDBC 46002 for period7-13 Sept .
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5
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9
11
14
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Figure 9(b) .
Figure 9(c).
Figure 9(d).
Figure 9(e).
Figure 10.
Page
Wind and wave observations at NDBC 46004 for period7-13 Sept. · · · · · · . . · · . . 34
Wind and wave observations at NDBC 46005 for period7-13 Sept. · · · · · . · . · · · 35
Wind and wave observations at NDBC 46006 for period7-13 Sept. · · · · · . · . · · . 36
Wind and wave observations at NDBC 46010 for period7-13 Sept. · . · . . · · 37
Wind observations at Clatsop County Airport forperiod 9-14 Sept. 1981. . . 38
Figure 11.
Figure 12.
Figure 13a.
Figure 13b.
Figure Be.
Figure 13d.
Figure 14.
NOS current meter observations for stations C1 atdepths 5, 25, and 35 feet from the bottom for theperiod 10-13 September. . .
Waverider and NDBC 46010 intercomparison spectra.
Waverider significant wave height estimates as afunction of distance east of buoy 8 for 10 Sept.1981. .
Waverider significant wave height estimates as afunction of distance east of buoy 8 for 11 Sept.1981. .
Waverider significant wave height estimates as afunction of distance east of buoy 8 for 12 Sept.1981 . .
Waverider significant wave height estimates as afunction of distance east of buoy 8 for 13 Sept.1981. .
Drifter derived surface current vectors near thetime of peak ebb. (a) 10 Sept. 1981. (b) 11 Sept.1981. (c) 12 Sept. 1981. (d) 13 Sept. 1981.
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Table 1.
Table 2.
Table 3.
LIST OF TABLES
Predeployment calibration of Waverider 67135.
Characteristics of Motorola APS-94E SLAR.
NOS Data Station summary.
10
13
17
Table 4.
Table 5.
Table 6.
Table 7.
Table 8.
Table 9.
Table 10.
Table 11.
Table 12.
Table 13.
Table 14.
Specifications for Aanderaa Recording CurrentMeter Model 4. . . . . . . . . . 18
Characteristics of Corps of Engineers Wave ImagingRadar. . . . . . . . . . . . . . . . . . . . 21
Daily Jetty A Radar fixes for determination of vanorientation. . . . . . . . . . . . . . . . . . . . 24
Daytime slack, peak ebb, or peak flood predictionsfor intensive observation periods. 40
Summary of Waverider deployments. 41
Summary of Cape Disappointment Radar observationperiods. . . . . . . . . . . . . . 42
Summary of Jetty A Radar observation periods. 43
Summary of Mohawk SLAR observation periods. 44
Summary of selected surface drifter speed andWaverider significant wave height observations. 45
Drifter information for current vectors presentedin Figure 14. 54
Summary of observed wave and current characteristics andcomputed transfer function, T, during the intensiveobservation periods. . . . . . . . . . . . . . 57
Table 15a. Wave height amplification T CEq. 3) for d = 10 m,e = 0°. . · · · · · · · · · · · · ·0
Table 15b. Wave height amplification T CEq. 3) for d = 10 m,e = 30°. · . · · · · · . · · · · · · · ·0
Table 15c. Wave height amplification T CEq. 3) for d = 10 m,e = 60°. · · . · · · . · · · · · · · · ·0
Table 15d. Wave height amplification T CEq. 3) for d = 15 m,e = 0°. . · . · · . · · · · · · · · · ·0
60
61
62
63
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Table 15f.
Table 15g.
Table ISh.
Table lSi.
8 = 30°.o
Wave height amplification T (Eq. 3) for d = 15 m,8 = 60°. .o
Wave height amplification T (Eq. 3) for d = 20 m,8 = 0°. . . . . . . . . . . . . . . . . . . .o
Wave height amplification T (Eq. 3) for d = 20 m,8 = 30°. .
o
Wave height amplification T (Eq. 3) for d = 20 m,8 = 60°. .
o
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O. ACKNOWLEDGEMENTS
It is a pleasure to acknowledge here the numerous organizations andindividuals which contributed to the success of this field experiment.
The cooperation and assistance of the U.S. Coast Guard is gratefullyacknowledged, particularly that of the USCG Search and Rescue Station atCape Disappointment, commanded by LCDR J. Sprague. Coast Guard ET-l K.Stokes provided able and valuable assistance in tracking radar reflectorsas part of the surface current measurement program.
The National Marine Fisheries Service provided surface vessel supportduring the September experiment. Our sincere thanks to the crews of theEGRET, N. Zorich, R. Pettit, and W. Muir, and the NERKA, L. Davis, M.Laird, and E. Keller, for their cheerful assistance in frequently unpleasantconditions.
We are grateful to R. Patchen of the National Ocean Survey for permittingaccess to the important subsurface current meter data, to CDR o. Stephen,Commanding Officer of the NOAA Ship McARTHUR, for his enthusiastic cooperationand support, and to Lt. A. Snella for timely provision of the data in auseful format.
Much of the meteorological data was provided by R. Anderson, W.Burton, and K. Short of the National Weather Service, Seattle Ocean ServicesUnit, and by C. Krepke, R. Storey, and R. Tomes of the NWS Astoria fieldoffice. The valuable sea state and meteorological data collected by NOAAdata buoys were provided by G. Hamilton, F. Abbell, and A. Johnson of theNOAA Data Buoy Center Data Systems Division of the National Space TechnologyLaboratories (NSTL) Station in Mississippi. .
M. Stapp of PMEL ably solved numerous problems associated with theWaverider data transmission during the experiment. D. Zopf and C. Creechof Oregon State University provided seismic wavemeter records, and wereassisted by W. Watkins of NWS, Astoria.
We appreciate the contributions of S. Noble of the Portland DistrictCorps of Engineers, who provided valuable assistance and expertise, whoarranged for deployment of the Corps wave imaging radar, and who made theresulting radar data available to us. Similarly, we are grateful to G.Arnott of EPSCO, who arranged the loan of a demonstration radar van forour use in tracking surface current drifters.
The spectacular side-looking airborne radar (SLAR) imagery was providedby the l042nd MICAS unit of the Oregon Army National Guard. The consistentlyexcellent quality of this imagery testifies to the high professionalismand technical competence of the entire organization--aircraft and sensormaintenance and support crews, technical observers and pilots. Especiallyappreciated is the cooperation and support of the Commanding Officer,Major S. Hammons, the invaluable advice and assistance of Capt. C. Rosenfeld(who pioneered the use of SLAR at the Columbia River Bar), and SFC R.Hartmann, who bore the primary responsibility for scheduling and coordinatingall flights.
The assistance of the Office of Naval Research (ONR) is also verygratefully acknowledged. The field experiment was partially funded by anONR grant overseen by H. Do1eza1ek of the ONR Coastal Sciences Program.
Finally, we acknowledge the support of the Ocean Services Division ofthe National Ocean Service, which provided partial support for this preliminary analysis.
2
Wave and Current Observations at the Columbia
River Entrance, 10-13 September 1981.
F. I. GonzalezM. R. MulhernE. D. CokeletT. C. KaiserJ. F. R. GowerJ. Wallace
ABSTRACT. This technical memorandum presents the results of a joint exerciseundertaken by PMEL and lOS to measure waves and currents at the Columbia RiverBar during 10-13 September 1981. The waves were measured in situ with avertical accelerometer buoy (Waverider) and observed aloft with Side LookingAirborne Radar (SLAR). Drifters tracked by an independent radar systemprovided surface-current velocities within the river mouth.
Wave refraction occurs in this area owing to depth and current gradients.Upriver of Buoy 8 waves decay on ebb and flood currents due to depthrefraction away from the channel axis. During strong ebbs wave decay maybe enhanced by breaking within the channel itself. Seaward of Buoy 8waves amplify during peak ebbs and attenuate during peak floods. Most ofthe time the amplification and decay factors are predicted to within 20%by linear, one-dimensional theory. However, during one extreme ebb eventthe wave height was underpredicted by up to 50%. This was likely due tothe crossing of wave crests produced by the current jet. The accurateprediction of such an event awaits the application of a two-dimensionaltheory for both the currents and the waves.
Predictions of hazardous sea state on the Columbia River Bar could certainlybe improved by implementing recent analytical and numerical advances in waverefraction-diffraction theory. This should be complemented by Bar wave-heightobservations made available in real-time. These would provide accurate nowcasts and short-term forecasts and improve the intuition of forecasters andmariners. The observations would also provide a data base to tune thetheoretical models and verify forecasts.
Contribution Number 717 from the Pacific Marine Environmental Laboratory.
3
1. INTRODUCTION
The entrance to the Columbia River (Figs. 1 and 2) is one of the mosthazardous navigational regions in the world. Hundreds of search andrescue missions are run yearly by the Coast Guard facility at Cape Disappointmentand the Coast Guard Air Station at Astoria. Nonetheless, tragic loss oflife continues to occur; 22 were lost in Fiscal Year 1982 alone, duringwhich the Coast Guard performed 400 search and rescue missions (saving 21lives in the process).
Briefly stated, the physical processes which lead to dangerous seastate conditions are the interactions of incident swell and wind waveenergy at the entrance with local bathymetry and opposing surface tidalcurrents. Peak ebb velocities of 6 knots and more can double the significantwave height on the bar within a few hours. The process of wave steepeningand amplification is dependent not only on the tidal stage, but also onthe period and direction of the incident wave energy.
The National Oceanic and Atmospheric Administration (NOAA) is responsiblefor forecasting sea state conditions at the Columbia River entrance, aswell as a number of other potentially dangerous sites on the United Statescoasts. Thus, NOAA's National Weather Service (NWS) has supported researchwhich resulted in a semi-automated procedure for predicting sea stateconditions on the Columbia River Bar (Enfield, 1973). This investigation,though comprehensive, was nonetheless hampered by a lack of direct environmentalmeasurements at the river entrance, especially with regard to wave direction.
Some sea state observations at the river entrance were obtained byNOAA for the U.S. Corps of Engineers Coastal Engineering Research Center(CERC) for short periods during 1979 and 1980. In addition, the Corpsdeployed the CERC wave imaging radar, which provided wavelength and directionestimates out to a distance of about 3 nm from Cape Disappointment. InFebruary of 1980, an intensive three-week field experiment was organizedand conducted by NOAA, during which airborne remote sensing data wasgathered to supplement the in-situ observations. In particular, units ofthe Oregon Army National Guard provided side-looking airborne radar (SLAR)imagery of nearshore and deep water swell wavelength and direction. Theuse of such imagery at the Columbia River entrance had been pioneered byRosenfeld and Bell (1978).
A major field variable which was not directly measured in the February1980 experiment was the tidal current velocity. In September of 1981, anopportunity arose to gather in-situ and remotely sensed wave data coincidentwith the deployment of a number of subsurface current meters near theriver entrance by the National Ocean Service. To supplement these subsurfacemeasurements, a modest surface current measurement program was also implemented,which involved tracking surface drifters with two shore based radar units.This technique was developed by the Canadian Department of Fisheries andOceans and was successfully employed in an earlier effort to map surfacecurrents in the Strait of Georgia near the mouth of the Fraser River. Theresulting environmental information collected at the Columbia River entranceduring the 4-day period 10-13 September comprises the bulk of this report.
4
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• NOAA DATA BUOY
~ WAVERIDER BUOY
o SOWM GRID POINT
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Figure 1. Map of U.S. West Coast, showing location of Columbia Riverentrance relative to various sources of environmental observations.SOWM locations refer to positions of grid points for which the FleetNumerical Oceanographic Center (FNOC) provides wave spectrum nowcastsand forecasts computed by the FNOC Spectral Ocean Wave Model (SOWM).
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This report is organized in the following way. In §2 we discuss themethods for observing and recording surface waves, currents and windvelocities. Section 3 is a summary of the data collected on both theregional and local scales. In §4 we analyze and interpret the data interms of wave-current-bathymetry interaction at the Columbia River Entrance.Section 5 contains a summary, and §6 has recommendations for furtherresearch. One of the primary purposes of this report is to amalgamate theinformation gathered from various instruments and sources, to organize iton an event-by-event basis and to place it in one reference. The Appendixserves that purpose.
7
2. OBSERVATION METHODS
In this section, we describe the instrumentation and techniquesemployed to obtain estimates of surface waves, current speed and direction,and surface winds.
2.1 Surface Wave Data
Three sources of surface wave information are presented in thisreport: a Waverider buoy was deployed nearshore and inside of the entranceduring eight separate intensive observation periods; NOAA Data Buoy Center(NDBC) buoys acquired data 5 om southwest of the entrance every hour (NDBC46010) and about 300 om due west of the entrance every three hours (NDBC46005) (see Fig. 1); Side Looking Airborne Radar (SLAR) imagery was obtainedcoincident with each Waverider deployment on approximately eight separateflight lines.
Details of the instruments and their deployment are given below.
2.1.1 Waverider
This instrument is manufactured by the Datawell Corporation, and wascalibrated at the NOAA Ocean Wave Instrument facility just prior to itsuse in this experiment. A new modulator printed circuit board was alsoinstalled as recommended by Datawell; the board is designed to correctmeasurements for water temperature variations from the 22.4° C at whichthe buoy was calibrated. The calibration results are given in Table 1 andin Figure 3. The buoy sampling rate was 2 Hertz, and the data was telemeteredto shore and recorded both on a continuous strip chart and on a digitalmagnetic tape.
The buoy was deployed from a surface vessel on the end of a 300 foottether line attached to a 3-point buoy bridle. Stationary and driftingmodes of deployment were used. In the stationary mode, the launch waskept on station by steaming against the current, so that the Waveriderstreamed out behind the boat. Usually, this maneuver was performed near achannel marker buoy, which served as a reference point. In the driftingmode, the vessel was allowed to drift with the current in such a mannerthat the Wave rider tether remained slack.
During each intensive observation period, a typical observationprofile would consist of alternating 20-minute drifting and stationaryrecords. Sextant fixes were taken periodically on a number of landmarks.The surface vessel used for the deployment was a 43-foot National MarineFisheries Service (NMFS) vessel, the EGRET. During the observation periods,the EGRET was assigned the call sign "Waverider" for all field communicationsand log entries. In the Appendix, the logs, plotted tracks, and wavespectra for each of the observational periods are presented.
Each Waverider spectrum was obtained by subjecting a 17.07 minuterecord (2048 data points taken at 0.5 second sampling interval) to detrending, a 10% cosine bell filter, fast Fourier transform, and 11 point
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TABLE 1. Predeployment Calibration of Waverider 67135.Performed on August 25, 1981.
Y Actual X Actual ErrorProportion Seconds Proportion
-0.0023 4.33 0.004
0.0040 5.37 -0.006
-0.0066 6.38 0.002
-0.0078 7.54 0.001
-0.0113 8.71 0.001
-0.0110 10.03 -0.002
-0.0118 11.85 -0.004
-0.0201 13.80 0.002
-0.0211 16.02 0.001
-0.0229 18.48 0.002
-0.0191 22.17 -0.001
Residual Standard Error is =0.003 Proportion
Second Order Regression is for Waverider Calibration Minus Datawell Prediction Error.
Y is Waverider
Term
o
1
2
X is Period
Coefficient
1.6046E-02
-3.8403E-03
9.8909E-05
10
Degree Fit = 2
Figure 4. NOAA data buoy 46010 at dockside in Astoria, Oregon.
11
smoothing in the frequency domain. Because a running mean was employed,successive spectral estimates are not independent.· Those which are 11frequency bands apart are independent, however, and characterized by 22degrees of freedom. For a Chi-square distribution, there is 90% confidencethat the true spectral density is between 0.65 and 1.78 of the computedvalue.
2.1.2 NDBC Buoys
Hourly wave spectral estimates were provided by buoy 46010, locatedabout 5 nm southwest of the entrance in 200 feet of water (see Figs. 2 and4). The wave data analyzer (WDA) , consisting of an axial linear accelerometer, provided spectral estimates with a resolution of .01 Hz over arange of 1.01 to 0.05 Hz, with 48 degrees of freedom and 80% confidencethat the true value lies between 0.788 and 1.335 of the estimated value.This value must then be corrected for system noise and the power transferfunction of the buoy as described by Steele and Earle (1979). Similardata buoys have been compared with a 0.9 meter diameter Waverider buoy;the average percentage error in significant wave height estimates wasfound to be about 7%. It is believed that the performance of NDBC46010 is comparable or better. Examples of such spectral estimates arepresented in Section 3 and the Appendix. Figure 4 is a photo of NDBC46010 at dockside in Astoria, Oregon.
Similar spectral estimates were provided hourly at locations 46002,46004, 46005, and 46006 (Fig. 1). Summaries of the spectra from thesebuoys for the experimental period are also presented in Section 3.
2.1.3 Side-Looking Airborne Radar (SLAR)
SLAR imagery was acquired during seven of the eight intensive observationperiods and on two additional days when nO'Waverider or surface driftermeasurements were made. The radar units are Motorola APS-94E models withthe characteristics listed in Table 2. These radar units are mounted onGrumman OV-1 Mohawk aircraft (Fig. 5), flown by the Oregon Army NationalGuard from the Army Aviation Support Facility in Salem, Oregon.
Eight flight lines were flown on each mission, which was timed to becoincident with Waverider and surface current drifter data acquisition.The nominal flight lines and extent of the SLAR coverage are presented inFigure 6. The aircraft were flown at approximately 1000 m, and the swathsextended from nadir to the right of the aircraft for a distance of 25 km.
One of the best of the eight scenes acquired during each mission waschosen as an example, and these are presented in the Appendix. The primarySLAR information of interest in this experiment is the direction andlength of swell which are evident in most scenes, and in the refractiondue to bathymetry and currents which is obvious near shore. Wavelength anddirection estimates can be obtained from this imagery by means of two-dimensionaldigital Fourier transforms.
12
TABLE 2. Characteristics of Motorola APS-94E SLAR
Frequency: 9100 to 9400 MHz (Variable)
Wavelength: 3.3 to 3.2 cm
Range: 25, 50, or 100 km
Offset from nadir:
Modulation:
Pulse Width:
Pulse repetition frequency:
Resolution:
13
o to 60 km in 10 km steps
Pulse
0.2 ± 0.025 microsecond
750 pps
30 meters in range0.45 degrees beamwidth in azimuth
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Figure 6. Nominal Mohawk SLAR flight lines 1 to 8. Circled numbersindicate the start of each flight line and coverage extends 25 km tothe right of each track.
15
2.2 Current Data
There were two coordinated programs to obtain estimates of currentsnear the Columbia River entrance: the National Ocean Service (NOS)current meter moorings, and the PMEL/IOS surface drifter program.
2.2.1 NOS Subsurface Current Meters
As part of a larger scale Columbia River circulation survey, NOSdeployed 19 subsurface current meters at a total of 8 separate moorings.The location of the five stations nearest the river entrance are shown inFigure 2. Table 3 lists the current meter depths, additional instrumentation at each mooring and other NOS stations occupied during the experiment.Unfortunately, the wave pressure gage at location C2 and the near-surfacecurrent meter at C3 were lost.
The instruments used were Aanderaa recording current meters Model 4,with temperature, conductivity and pressure sensors. The current meterspecifications are given in Table 4, and examples of the output arepresented in the Appendix. It should be noted here that the data presentedin this report is raw field data quality, is unedited, and is uncorrectedfor errors due to effects of such things as sensor tilting.
Mulhern (1982) provides a detailed analysis of the data collected atstations C1, C3, C4 and C8, located at river mile 5 (RM 5).
2.2.2 Surface Drifter Program
As a supplement to the NOS subsurface current meter data, a modestsurface drifter program was implemented. Two shore-based radar were usedto track surface drifters equipped with 16-inch corner reflectors on8-foot masts (Fig. 7). This technique was developed and used successfullyby the Canadian Department of Fisheries and Oceans in a previous study ofsurface currents in the Strait of Georgia near the mouth of the FraserRiver. During that study the drifters were tracked over ranges out to 20nautical miles using the fixed observing stations of the Canadian CoastGuard's Vessel Traffic Management System. Tracking and position recordingmade use of the large display screens and positioning cursors of thissystem, and also benefitted from a computerized predictor system linked tothe cursor. Tracking used here was greatly simplified to make use ofavailable equipment. Several of the problems listed below could be avoidedwith a more sophisticated system. The drifter tracks are presented in theAppendix.
Surface Drifter Deployments.
The surface drifters were deployed from the 43 foot NMFS vesselNERKA. Four men were required: a helmsman, two persons to deploy andrecover drifters, and a fourth person to communicate by radio with theradar operators on shore. Good radio communication was a critical part ofthe operation. Sea clutter and small craft would frequently obscure the
16
TABLE 3. NOS Data Station Summary
St.ation Bottom Current Meter OtherNo. Depth Depth Instrumentation Location
(Ft. below MLLW) (Ft. above bottom)
Cl 50 5, 25, 35 CTD RM5
C2 50 20 Pressure RMl
C3 70 5, 43, 53 CTD RM5
C4 49 5, 21, 31 CTD RM5
C5 35 5 CTD, Tidal Height RM5
C8 36 5, 18 CTD, Tidal Height RM5
Cl7 34 5, 20 CTD, Tidal Height RM6.5
C18 38 5, 18, 25 CTD, Tidal Height RM6.5
M1 Wind Speed, RM12.5Direction, Air (PilingsTemperature, on DesdemonaPressure Sands)
0572 Tidal Height Jetty A
0573 Tidal Height Chinook, WA
9008 Tidal Height Ft. Steven, OR
0512 Tidal Height Oak Point, WA
9040 Tidal Height Astoria, OR
17
TABLE 4. Specifications for Aanderaa recording current meter Model 4.
CURRENT SPEED
Sensor:
Range:Accuracy:Starting velocity:
CURRENT DIRECTION
A rotor with magnetic coupling through the instrument case.Electronic counter registers the number of rotationsduring the period between two samplings.2.5 to 250 cm/sec± 1 cm/sec or ± 2% of actual speed, whichever is greater2.0 cm/sec
Sensor:Resolution:Accuracy:
Magnetic compass with needle clamped onto potentiometer ring0.35°± 7.5° for speeds of 2.5 to 5 cm/sec or 100 to 200 cm/sec± 5° for speeds of 5 to 100 cm/sec
Maximum Compass Tilt: 12° from horizontal
TEMPERATURE
Sensor:Range:Accuracy:Resolution:63% Response Time:
CONDUCTIVITY
Sensor:Range:Resolution:
PRESSURE
Sensor:Range:Accuracy:Resolution:
Thermistor (Fenwal GB32JM19)-2.46°C to 21.48°C± 0.15°C0.02°C12 seconds
Inductive cello to 70 mmho/cm0.07 mmho/cm
Bourdon tube driving a potentiometer0-100 PSI± 1 PSI± 0.1 PSI
18
8-CORr\IER RADAR REFLECTOR6 CORNERS HORIZONTAL2 CORNERS VERTICALLONG EDGE OF EACH CORNER IS14 INCHES LONG
81
SHACKLES
/ /
1611
FLOAT
/
WATER LEVEL
10 FOOT LONGCROSS BAR
CONCRETE REINFORCEMENTBAR FOR BALLAST
/
POLYETHYLENE DROGUE"V 10 FEET WIDE BY 6 FEET LONG
'"'"
/
SHACKLES
Figure 7. Sketch of surface drifter buoy equipped with radar cornerreflector.
19
target or confuse the radar operator. When a maximum of four drifters hadbeen deployed, the strategy called for the surface vessel to keep as manydrifters in sight as possible, and make frequent visits to each drifter inturn, pulling alongside, then proceeding to the next, all the while keepingthe radar operators advised of the vessel's position. In this way, theradar operators could make frequent checks on the validity of their targetidentification and tracking. If an operator was uncertain of a driftertarget or had lost its signal on the radar scope, he would request thatthe NERKA pull alongside that drifter momentarily for positive identification.
Cape Disappointment Radar Tracking.
The Portland Dis~rict of the Corps of Engineers deployed an X-bandimaging radar near the Cape Disappointment lighthouse at an elevation of220 feet above mean sea level. The system was designed to obtain wavelengthand direction information out to a range of 3 nautical miles. Table 5lists the specific design characteristics of this unit. An earlier,similar system is described by Mattie and Harris (1979).
The drifter buoys were tracked from Cape Disappointment using thisradar, which was equipped with a variable range marker with a resolutionin nautical miles to the second decimal place. All bearings taken wererelative to the radar orientation which was referenced to charted features.
Once a buoy was deployed by the surface vessel, that fact was communicatedby radio to the radar operator, and the target was identified on thescreen. Thereafter, until buoy recovery, range, relative bearing, andlocal time were taken at nominal five minute intervals. Fixes were takenmore frequently if the buoys moved at high speed. The observations andany appropriate comments were logged by an assistant.
Sea clutter and small craft drifting in the current created problemsin correctly identifying the drifting buoys. This problem was substantiallyeliminated by requesting the deployment vessel to run between the buoysand identify them as the vessel paused alongside. The deployment vesselmoved at high speed between buoys, and this made it an easy target for theradar operator to identify.
Another minor problem was the existence of dead sectors, or areaswhere the radar signal was blocked due to buildings, land masses, etc. Ingeneral, however, dead sectors were not a significant portion of the areaof interest; furthermore, the dead sectors of the Cape Disappointment andJetty A radars were different, so that a drifter fix could usually betaken by the unblocked radar.
Calibration fixes were taken to a few known fixed targets in thefield of view. These showed good accuracy when compared to charteddistances and bearings, and excellent repeatability from day to day.
The drifter tracks obtained in this manner were then plotted, and arepresented in the Appendix.
20
TABLE 5. Characteristics of Corps of Engineers Wave Imaging Radar
Model: Raytheon RM 1650j12XR
Frequency: 9375 ± 30 MHz (X-band)
Wavelength: 3.2 cm
Pulse width: 0.06 microsecond for .75 to 3 nm ranges0.5 microseconds for greater ranges
Range resolution:
Vertical beam width:
Horizontal beam width:
Antenna length:
Power:
Rotation rate:
Display scope:
Scope camera:
20 yards or 1% of range, whicheveris greater
22 degrees
0.65 degrees at 3 decibels
12 feet
50 kilowatts
27 rpm
16 inch diameter plan position indicator(PPI) cathode ray and tube, with fastdecay phosphor.
Bolex 16mm reflex
21
Jettv A Radar Tracking
In this section we describe how a mobile radar van was used to trackthe drifters. This radar system provided independent check on the positionsof the drifters as determined from the Cape Disappointment radar and itprovided the opportunity to evaluate the concept of using such a mobileradar unit for future drifter studies.
The radar van was on loan from Epsco Marine, 1030 Industry Drive,Seattle, WA. The vehicle was a Ford van of the type normally used forprivate transportation. It was equipped with an Epsco model S14 radarwhich operates at 10KW of peak power on an X-band frequency of 9275 MHzcorresponding to an electromagnetic wavelength of 3.23 em. The radar hadan optional 6 foot scanning antenna and a variable range marker (VRM).The latter is an illuminated ring which appears on the 7" radar scope andwhose diameter can be adjusted by the operator. The ring is expanded tointersect a specific target on the scope, and the range to that target isdisplayed on a digital meter. The bearing to a target can be ascertainedby aligning a radial line through the target and reading the bearing froma bearing ring graduated in degrees at the outer edge of the display.
The radar can operate on one of the following ranges: \,~, 1~, 3,6, 12, 34 and 50 nm. A short pulse length of 0.08~-sec. characterizes the\ to 1~ nm range settings, and a longer pulse length of 0.8 ~-sec. is usedfor the 6 to 50 nm settings. At the 3 nm setting, however, either pulselength is permitted. For the entire experiment the 3 nm-short pulsesetting was used. At this setting the drifting buoy images subtended anangle of 2° and were 0.02 nm in radial width when at a typical operatingrange of 1 to 1~ nm. Epsco sales literature advertises a bearing accuracyof 2° or better and a range resolution of less than 30 yards. Thesevalues are not at variance with what we observed. During operation a radarfix was taken by placing the radial bearing line through the center of thetarget and the range ring on the nearside of the target.
The radar range and bearing to a target gives the position of thetarget relative to the radar. In order to find the absolute location ofthe target the position and orientation of the radar must be determined.For each day of the experiment the radar van was positioned within 3 m ofthe same location. This location was determined from the following horizontalsextant fixes, in which the numbers in parenthesis refer to the objectslisted in Table Al of the Appendix.
left target:left angle: 44° 47'
center target:
right angle: 114° 20'right target:
right check angle: 37° 37'right check target:
(3) Large Sand Island Obs. Tower
(5) Jetty A light, "F1 4 sec. 31 ft.10 M"
(2) Cape Disappointment lighthouse,"Alt. F1 R&W 30. sec. 220 ft.18 M"
(18) Light on S tip large SandIsland, "F1 G 4 sec.15 ft. 'I'"
22
This position is on the landward end of Jetty A at 124° 02' 26" W, 46° 16'33" N according to NOAA chart 18521, 51st Ed., Jan. 3, 1981. The van wasoriented in such a way that 0° bearing on the radar corresponded to 0° ±1° True. This was achieved by aligning the van visually with a pair ofDayglo-orange signal cloth markers placed on the ground at distances fromthe van of approximately 10 and 20 m. On most occasions a final determination of the orientation of the van was obtained by taking radar fixes toknown landmarks. These fixes are given in Table 6. Those to the ClatsopSpit lookout tower are best since the localized steel structure gave astrong radar echo. The radar range recorded for this tower could be usedto calibrate the remaining radar fixes. This has not been done for thedrifter fixes reported here, but in general observed ranges should bemultiplied by a factor of actual distance/observed distance =3.18/3.13 =1.02.
The technique of tracking the drifters on the radar scope was refinedduring the course of the experiment. On the first two days, 10 and 11September, a hood and magnifier were attached to the scope. Although thishad the advantage of giving good picture contrast and an enlarged image,there was no convenient way for the operator to follow individual targetsexcept by simply keeping a watch on them. It proved impossible to followmore than 2 drifters by this approach since the radar scope was oftencluttered with too many other returns from as many as 30 to 40 smallfishing boats in the area. On 12 and 13 September, the hood and magnifierwere removed, and clear plastic overlays were placed directly on thescope. The track of each drifter was marked on the plastic with a greasepencil. For each drifter this gave the radar operator a reference line towhich he could return if his attention were diverted. Individual drifterfixes were taken every 2 minutes or as often as possible. The operatorwould set the variable range ring and bearing line on the target image andcallout the readings to an assistant who would log them. Time was recordedto the nearest minute, with the actual fix usually occurring within ± 15seconds of this time.
The radar operator used a portable FM radio transceiver to exchangeinformation on drifter deployment and location with the NERKA and with theCape Disappointment radar operator. When a drifter location was in doubt,verification was obtained by requesting that the deployment vessel rapidlyapproach, and then move away from, the drifter. The concommitant mergingand separating of the two radar blips then enabled the radar operator toidentify the drifter target.
Tracking the surface drifter corner reflectors with the Epsco radarand the Corps radar was a success. It appears that useful surface currentestimates can be obtained in this manner. However, eye strain and fatiguewere severe in the case of the Epsco radar operation. This would bealleviated with a larger radar screen, on the order of at least 12 inchesin diameter. Even better would be the projection of the image onto alarge television screen equipped with a light pen for the automatic loggingof range and bearing to target. Such systems are presently on the market.
Notwithstanding the inherent difficulty of gathering these data andthe necessary caveats regarding their quality, these field efforts arenecessary if we are to gain sufficient understanding of the physicalprocesses involved to improve the accuracy of Bar forecasting procedures.
23
TABLE 6. Daily Jetty A Radar Fixes to determine radar van orientation.
Range RadarDate & Tidal Stage Landmark (run) Bearing (0)
10 September Flood (19) Clatsop Spit lookout tower 3.14 157.5
(20) Bend in South Jetty 2.46 180
10 September Slack (19) Clatsop Spit lookout tower 3.14 157
(20) Bend in South Jetty 2.46 179
(21) Light on S tip of line of 2.73 114piles on S central side ofsmall Sand Island
(22) Seaward end of North Jetty 2.11 248
12 September Flood (19) Clatsop Spit lookout tower 3.13 156
(20) Bend in South Jetty 2.44 181
(18) Light on S tip of line 1.61 122of piles near SE corner oflarge Sand Island
12 September Ebb (Van orientation unchangedfrom Flood)
13 September Flood (Van orientation not logged)
13 September Ebb (19) Clatsop Spit lookout tower 3.12 157
(20) Bend in South Jetty 2.45 181
(18) Light on S tip of line 1.61 123of piles near SE end oflarge Sand Island
24
2.3 Surface Wind
Observations of surface wind speed and direction were made at threelocations: a meteorological station deployed by NOS, NOAA data buoy46010, and the NWS station at the Clatsop County airport.
2.3.1 NOS meteorological station.
The National Ocean Service meteorological station was located about 2miles northwest of the Port of Astoria, at river mile 12.5, on pilings atDesdemona Sands, at 46°12'38" North latitude and 123°52'30" West longtitude.The meteorological package is manufactured by Aanderaa. Wind direction isan instantaneous measurement, and wind speed is a 10 minute average recordedevery 10 minutes.
2.3.2 NDBC buoy 46010
NOAA data buoy 46010 consists of a Coast Guard large navigation buoy(LNB) outfitted with a General Service Buoy Payload (GSBP) manufactured byMagnavox. Wind speed and maximum wind gust estimates are obtained bymeans of a vortex shedder; one second samples are averaged for 8.5 minutesto get average wind speed, while the highest 8 second average in thatrecord is retained as the maximum gust. A vane and fluxgate compass alsosamples wind direction every second to provide an 8.5 minute average.
2.3.3 Clatsop County Airport.
The National Weather Service (NWS) maintains a standard F420C windsensor at the Clatsop County Airport, about 20 nm southeast of the ColumbiaRiver entrance. The sensor is manufactured by Electric Speed IndicatorCompany, and is mounted at an elevation of 10 meters. Both speed anddirection are instantaneous and continuous measurements. The outputs aredisplayed in the NWS office on needle guages, which are read and loggedevery hour by the NWS personnel on watch.
25
3. DATA SUMMARY
3.1 Regional Data
In this section, we present a general overview of the regionalmeteorology and wave conditions for the period 8-13 September. Figures 8a-fpresent the 1800Z (1100 PDT) surface pressure analyses for the period 8-13September, and Figures 9a-e summarize the wind and wave conditions at NOAAdata buoys 46002, 46004, 46005, 46006, and 46010 for the period 7-13September. Figure 10 presents the wind speed and direction measured atClatsop County airport from 9 to 13 September. Figure 11 presents theNOS current meter measurements for station Cl at depths 5, 25, and 35 feetfrom the bottom, for the period 10-13 September.
The timing of the experimental period, 10-13 September, was fortuitous.From 8-10 September, the low pressure systems shown in Figures 8a-c dominatedthe Northeast Pacific. As a result, significant wave height in deep wateroff the Washington-Oregon coast rose from a value of 1 m on 7 September to2.5 m on 10 September (Figs. 9a,c). Even higher waves were produced westof Vancouver Island; on 10 September, heights of 4 m were observed at0000 PDT (Fig. 9b), as the southeast storm sector, characterized by 50 knotwinds, made landfall on the Canadian coast (Figs. 8b,c).
Similarly, at the Columbia River entrance, significant wave heightrose steadily from a minimum of 1 m on 7 September to a peak value of 3 mat 0000 PDT on 12 September (Fig. ge). Substantial swell energy from thelow pressure systems was therefore present during the four-day experimentalperiod. Furthermore, in contrast to the previous three days, an offshorehigh pressure system dominated the Northwest's coast on 11-13 September,bringing northerly winds of up to 10 mls and adding significant local windwave energy to that of the swell already present (Fig. ge).
3.2 Local Data
During the four days (10-13 September) of the experiment, there were8 periods of a few hours each of intensive data collection. The intentionwas to collect data at predicted times of slack current, peak ebb current,or peak flood current. These times and the predicted tidal current speedsfor NOS Station 695 are presented in Table 7. Table 8 summarizes thetimes and modes of deployment for the Waverider. Tables 9 and 10 summarizethe periods during which surface drifters were tracked by the shore-basedradar units at Cape Disappointment and Jetty A, and Table 11 summarizesthe periods during which SLAR imagery was acquired by OANG Mohawks. Thedata for these intensive observation periods are collected together andpresented in the Appendix.
Table 12 summarizes the significant waveheight estimates derived fromWaverider observations obtained during the eight intensive observationperiods. The table also provides surface current estimates near the timeof Waverider deployments; these estimates are derived from two sources-surface drifter speeds, and the NOS algorithm for current speed at station 695.In addition, the SLAR image for each observation period is indicated inthe last column. The Waverider records are of varying length because the
26
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Day Date Predicted Tidal CurrentTime Speed Stage(PDT) (m/s)
Thursday 10 September 1015 1.3 FLOOD
Thursday 10 September 1545 -1.4 EBB
Friday 11 September 1330 0.0 SLACK
Friday 11 September 1630 -1.7 EBB
Saturday 12 September 1115 1.8 FLOOD
Saturday 12 September 1715 -2.1 EBB
Sunday 13 September 1145 2.0 FLOOD
Sunday 13 September 1745 -2.4 EBB
40
TABLE 8. Summary of Waverider deployments. Entries under stationary anddrifting columns refer to buoys.
Date Tidal Stage Time Period Deployment Mode(PDT) Stationary Drifting
10 September FLOOD 1030-1055 81055-1120 8~10
1131-1157 101157-1221 10~12
EBB 1444-1506 101506-1528 1O~8
1528-1555 81555-1629 8~1
11 September SLACK 1348-1409 101409-1447 1O~8
EBB 1548-1610 12~10
1612-1633 10
12 September FLOOD 0921-0955 460101041-1101 41127-1148 81200-1234 101248-1300 81300-1318 8~10
EBB 1644-1704 12~10
1758-1822 12
13 September FLOOD 1117-1137 81139-1202 8~10
1223-1245 81245-1310 8~10
EBB 1658-1724 19~11
1724-1746 111746-1808 11~9
1825-1856 10
41
TABLE 9. Summary of Cape Disappointment Radar observation periods.
Date Tidal Stage Time Period(PDT)
10 September FLOOD 1050-1225
10 September EBB 1450-1625
11 September SLACK 1301-1450
11 September EBB 1605-1628
12 September FLOOD 1041-1315
12 September EBB 1639-1833
13 September FLOOD 1130-1307
13 September EBB 1704-1830
42
TABLE 10. Summary of Jetty A Radar observation periods.
Date Tidal Stage Time Period(PDT)
10 September FLOOD 1050-1202
10 September EBB No Data
11 September SLACK 1307-1426
11 September EBB No Data
12 September FLOOD 1040-1314
12 September EBB 1640-1833
13 September FLOOD 1112-1304
13 September EBB 1703-1846
43
TABLE 11. Summary of Mohawk SLAR observation periods
Date
10 September
10 September
11 September
11 September
12 September
12 September
13 September
13 September
Tidal Stage
FLOOD
.EBB
SLACK
EBB
FLOOD
EBB
FLOOD
EBB
Time Period
1519-1731
1232-1345
1610-1736
1110-1227
1645-1748
1115-1300
1710-1835
44
Conunents
No flight.
A/C 925: Kaufman/Coursey.ADAS and log agree. Highaltitude test runs at 5100feet yielded no return.Flight line #1 (1519-1526)printed for report.
A/C 925: Rolfness/Coursey.ADAS and log time agree towithin 15 minutes. ADAS andlog time agree to within 15minutes. ADAS date is incorrect(10 Sept.). Flight line #1(1311-1319) printed for report.
AC/925: 7 / Anderson. ADASand log date incorrect (10 Sept.'81). Print line #1 (1628-1636).
A/C 957: Rux/Fough. ADAS andlog agree. Print line #1(1110-1123) .
A/C 957: Burns/Fogg. ADASincorrect.
A/C 957: Evans/Lakawsi. ADAStimes incorrect. Print line #3(1138-7) .
A/C 957: Dwyer/Galvin. ADAS andlog agree.
TABLE 12. SWlllllary of Selected Surface Drifter Speed and Waverider Significant Wave Height Observations.
Date Start End Hid Position Drifter Drift Drifter Drifter NOS Speed Waverider H SLARTime Time Time (Itm east ID Distance Time Speed (SU. 695) Rec. Length s
Image(PDT) (PDT) (PDT) of Buoy 8) (Fig/Buoy) (m) (min) (m/s) (m/s) (sec) (m) (Fig. )
10 Sep 1030 1047 1038 0.0 1.3 1024 1.510 Sep 1050 1058 1054 1.6 A8/1 640 8 1.3 1.210 Sep 1050 1059 1055 1.8 A7/l 640 9 1.2 1.210 Sep 1056 1104 1100 0.3 1.2 512 1.410 Sep 1104 1113 1108 0.8 1.2 512 1.510 Sep 1113 1120 1116 1.4 1.1 429 1.210 Sep 1131 1148 1139 1.9 1.0 1024 0.810 Sep 1157 1204 1200 2.1 0.6 443 0.910 Sep 1204 1213 1208 2.3 0.4 512 0.810 Sep 1213 1221 1217 2.8 0.2 478 0.8
10 Sep 1444 1501 1452 1.7 -1.2 1024 1.310 Sep 1506 1511 1509 1.4 -1. 3 324 1.610 Sep 1511 1520 1516 0.8 -1.3 512 1.910 Sep 1520 1528 1524 0.0 -1. 4 478 2.110 Sep 1523 1530 1527 3.0 A16/5 1110 7 -2.6 -1.4 A1810 Sep 1527 1535 1531 2.1 A16/4 825 8 -1.7 -1.4 A1810 Sep 1528 1545 1536 -0.3 -1.4 1024 2.210 Sep 1541 1550 1546 1.3 A16/2 1090 8 -2.3 -1.4 A1810 Sep 1537 1545 1546 1.7 AI6/3 1040 9 -1.9 -1.4 A1810 Sep 1555 1603 1559 -0.7 -1.4 473 2.410 Sep 1603 1611 1607 -1.4 -1.4 512 2.110 Sep 1611 1620 1616 -2.1 -1.4 512 2.410 Sep 1620 1629 1625 -2.7 -1.3 512 2.4
11 Sep 1315 1330 1323 2.2 A26/3 350 15 -0.4 0.1 A2811 Sep 1315 1330 1323 1.1 A26/4 250 15 -0.3 0.1 A2811 Sep 1348 1405 1356 1.7 -0.5 512 1.511 Sep 1400 1410 1405 0.1 A26/4 400 10 -0.7 -0.611 Sep 1409 1416 1413 1.6 -0.8 431 1.911 Sep 1410 1420 1415 -0.3 A26/4 490 10 -0.8 -0.811 Sep 1416 1425 1421 1.4 -0.9 512 2.011 Sep 1420 1430 1425 -0.7 A26/4 525 10 -0.9 -0.911 Sep 1425 1433 1429 1.1 -0.9 512 2.311 Sep 1430 1440 1435 -1. 2 A26/4 640 10 -1.1 -1.011 Sep 1433 1442 1437 0.7 -1.0 512 2.911 Sep 1442 1447 1443 0.3 -1.1 302 2.611 Sep 1440 1450 1445 -1.8 A26/4 750 10 -1.3 -1.1
11 Sep 1552 1601 1556 2.9 -1.7 512 1.511 Sep 1601 1609 1605 2.3 -1.7 512 2.411 Sep 1610 1618 1614 2.6 A34/3 900 8 -1.9 -1. 7 A3511 Sep 1615 1623 1619 1.3 A34/2 950 8 -2.0 -1.7 A3511 Sep 1620 1628 1624 1.2 A34/l 950 8 -2.0 -1.7 A3511 Sep 1612 1629 1620 1.8 -1.7 1024 3.4
12 Sep 1110 1120 1115 2.6 A45/3 890 10 1.5 1.8 A4712 Sep 1110 1124 1117 3.4 A45/l 1275 14 1.5 1.8 A4712 Sep 1120 1130 1125 3.4 A46/3 850 10 1.4 1.8 A4712 Sep 1127 1144 1135 0.1 1.8 1024 1.612 Sep 1155 1205 1200 0.9 A45/5 1040 10 1.7 1.712 Sep 1200 1210 1205 1.0 A45/6 1090 10 1.8 1.712 Sep 1200 1217 1208 2.0 1.6 1024 0.912 Sep 1206 1220 1213 0.2 A45/4 675 14 0.8 1.6
12 Sep 1640 1644 1642 2.3 A55/l 525 4 -2.2 -2.0 A5612 Sep 1642 1648 1645 1.9 A55/2 675 6 -1. 9 -2.0 A5612 Sep 1639 1651 1645 A54/1 1525 12 -2.1 -2.0 A5612 Sep 1645 1651 1647 1.7 A54/2 750 6 -2.1 -2.0 A5612 Sep 1644 1650 1648 3.2 -2.0 386 1.7 A5612 Sep 1646 1700 1653 0.8 A55/1 1900 14 -2.3 -2.0 A5612 Sep 1651 1657 1654 0.7 A54/1 750 6 -2.1 -2.0 A5612 Sep 1650 1659 1654 2.4 -2.0 512 2.2 A5612 Sep 1659 1704 1702 1.4 -2.0 297 3.9 A5612 Sep 1758 1815 1806 3.4 -1.9 1024 2.4
45
TABLE 12. (Continued)
Date Start End Hid Position Drifter Drift Drifter Drifter HOS Speed Waverider H SLARTime Tille Tille (lui east ID Distance Tille Speed (sta. 695) Rec. Length s ll1age(PDT) (PDT) (PDT) of Buoy 8) (Fig/Buoy) (II) (ain) (a/s) (a/s) (sec) (II) (Fig.)
13 Sep 1115 1130 1123 -0.5 A65/2 1225 15 1.4 2.0 A6913 Sep 1117 1134 1125 -0.4 2.0 1024 1.5 A6913 Sep 1117 1135 1126 -1.1 A65/3 1190 18 1.1 2.0 A6913 Sep 1121 1135 1128 0.0 A67/2 1300 14 1.6 2.0 A6913 Sep 1125 1136 1130 1.0 A67/1 1300 11 2.0 2.0 A6913 Sep 1125 1140 1133 -1.3 A65/4 820 15 0.9 2.0 A6913 Sep 1127 1140 1134 -1.2 A67/4 650 13 0.8 2.0 A6913 Sep 1133 1141 1137 -0.3 A67/3 725 8 1.5 2.0 A6913 Sep 1130 1145 1138 1.9 A65/1 1700 15 1.9 2.0 A6913 Sep 1139 1144 1142 0.2 2.0 273 1.4 A6913 Sep 1140 1151 1146 2.8 A67/1 1180 11 1.8 2.0 A6913 Sep 1143 1150 1147 0.6 A67/3 790 7 1.9 2.0 A6913 Sep 1143 1150 1147 -0.3 A67/4 560 7 1.3 2.0 A6913 Sep 1144 1152 1148 0.6 2.0 512 1.313 Sep 1146 1155 1151 2.4 A67/2 830 9 1.5 2.013 Sep 1152 1201 1156 1.3 2.0 512 0.913 Sep 1215 1227 1221 0.5 A66/5 1075 12 1.5 2.013 Sep 1220 1230 1225 0.5 A66/6 900 10 1.5 2.013 Sep 1222 1230 1226 -0.1 A66/7 700 8 1.5 2.0
13 Sep 1658 1702 1700 6.7 -2.2 226 0.713 Sep 1702 1710 1706 6.0 -2.2 512 0.713 Sep 1710 1719 1714 5.2 -2.3 512 0.713 Sep 1710 1720 1715 5.1 A76/1 1000 10 -1.7 -2.313 Sep 1710 1720 1715 5.4 A76/2 1275 10 -2.1 -2.313 Sep 1710 1720 1715 5.4 A76/3 1350 10 -2.3 -2.313 Sep 1709 1721 1715 5.4 A78/1 1425 12 -2.0 -2.313 Sep 1709 1722 1715 5.5 A78/2 1475 13 -1.9 -2.313 Sep 1710 1720 1715 5.5 A78/3 1250 10 -2.1 -2.3 ABO13 Sep 1719 1724 1722 4.2 -2.3 304 0.8 A8013 Sep 1720 1730 1725 4.1 A76/1 1250 10 -2.1 -2.3 A8013 Sep 1720 1730 1725 4.2 A76/2 1275 10 -2.1 -2.3 A8013 Sep 1720 1730 1725 4.2 A76/3 1410 10 -2.4 -2.3 A8013 Sep 1721 1731 1726 4.1 A78/l 1150 10 -1.9 -2.3 A8013 Sep 1722 1731 1726 4.3 A78/2 1300 9 -2.4 -2.3 A8013 Sep 1720 1732 1726 4.3 A78/3 1650 12 -2.3 -2.3 A8013 Sep 1724 1741 1732 4.0 -2.3 512 1.0 A8013 Sep 1735 1741 1738 2.6 A78/2 750 6 -2.1 -2.313 Sep 1735 1745 1740 1.9 A76/1 1475 10 -2.5 -2.313 Sep 1737 1744 1741 1.9 A78/1 1160 7 -2.8 -2.313 Sep 1746 1753 1750 3.5 -2.4 436 1.013 Sep 1753 1802 1757 2.7 -2.4 512 1.313 Sep 1802 1808 1805 1.4 -2.4 367 1.213 Sep 1803 1814 1809 3.9 A77/5 1525 11 -2.3 -2.313 Sep 1803 1814 1809 3.9 A79/5 1525 11 -2.3 -2.313 Sep 1805 1815 1810 4.2 A77/6 1475 10 -2.5 -2.313 Sep 1805 1817 1811 4.0 A79/6 1700 12 -2.4 -2.313 Sep 1814 1824 1819 2.4 A79/5 1525 10 -2.5 -2.313 Sep 1815 1825 1820 2.2 A77/5 1490 10 -2.5 -2.313 Sep 1820 1830 1825 2.0 A77/6 1550 10 -2.6 -2.213 Sep 1821 1830 1826 2.0 A79/6 1260 9 -2.3 -2.213 Sep 1825 1842 1833 1.7 -2.2 512 2.2
46
electronics was set to acquire individual records of length 512 seconds,with a I-second gap between them. In some cases, two records were combinedto form a 1024-second record; these were processed to a power spectrum, asdescribed above, and plots of these spectra are presented in the Appendix.In other cases, the Waverider was deployed after the start of a new record,so that the first portion of that record was discarded, leaving a recordshorter than 512 seconds. The significant wave height for these recordsof length 512 seconds or shorter was then computed as H =4a, where a isthe square root of the record variance. s
The river entrance is an extremely hostile environment. Large wavesand strong currents frequently stress in-situ instrumentation and mooringsto failure and, if the instrument survives these natural forces, there isstill a high likelihood that it will succumb to the heavy commercial andrecreational vessel traffic in that region. The technique of tethering aWaverider to a surface vessel was used primarily to avoid the risk ofinstrument loss, but while observations made this way are preferable to acomplete lack of data, the procedure does have potentially serious shortcomings. There is a question of how the currents, which frequently exceed5 knots, and the tether and bridle arrangement affect the response of theWaverider. Beyond this question of data interpretation, there is theconsiderable expense incurred in vessel support, and the inconvenience andpotential hazard involved in collection of the data in this manner.
On the morning of 12 September, a Waverider deployment was made at alocation within 100 yards of NDBC buoy 46010. The purpose was to checkthe method of Wave rider deployment using the tether arrangement describedabove. Figure 12 displays the resulting Waverider spectra and the twoNDBC 46010 spectra which bracket the time of the Waverider deployment.The Waverider spectra has been subjected to II-point frequency band averaging,so that the resulting frequency resolution of 0.0107 Hz is comparable tothe 0.01 Hz resolution of buoy 46010. As can be seen, there is goodagreement in significant wave height, and in the qualitative features ofthe individual spectra. Thus, although there were no currents presentduring this intercomparison (unlike deployments in the river entrance),this result does give some confidence in the accuracy of the rest of theWaverider observations.
47
00 12 SEP 10 PDT.• NOaC BUOY .6010
1981 JO 255 17 Z0 SIG HT .. 2.7 H(TERS0 U • 1. S HIS.,; WIND SPEE:D = 5.7 HIS,... WIND DIRN • 8. DEGS
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•
00..
,...N:r::'-0NOE •..,I&J
00
N
00
.0
" 0.0. 0.011
Figure 12.
12 SEP 09 PDTNDBC BUO{ .60101981 JD 255 16 ZSIG HT. 2.8 HE:TERSU. 1. 0 HISWIND SPEE:D • 5.3 HISWIND DIRN • 1•• DEGS
0.12 0.16 0.20 0.2. 0.2S 0.'1 0.S6F (HZ)
Waverider and NDBe 46010 intercomparison spectra.
0.•0
48
4. PRELIMINARY DATA ANALYSIS
We hypothesize that Buoy 8 roughly represents the boundary betweentwo wave regions. Landward of this site the waves decay due to bathymetricrefraction away from the main axis of the navigation channel, where thedepth is maintained at ~15m, toward the shallower regions to the north andsouth. Seaward of this site waves grow or decay along their propagationpath due both to wave-current interaction with ebb or flood currents andto shoaling.
4.1 Wave Decay Upriver of Buoy 8
Evidence for wave decay landward of Buoy 8 is presented in Figures 13a-d.The significant wave height, H , is plotted as a function of the distance,x, upriver of Buoy 8. These m~asurements were obtained from the tetheredwaverider deployments. Notice that during both ebb and flood conditionsthe waves decay upriver. The bending of the waves toward the shoals oneither side of the navigation channel can be seen in most of the SLARimagery, but it is clearest during the slack-to-ebb tide of 11 September(Figs. A28 and A29) when the current plays a lesser role. We conjecturethat depth refraction is the primary source of the wave decay. Diffractionfrom the tips of the jetties may also contribute.
Linear least squares fits have been made to the data of Figure 13 foro ~ x ~ 5 km. Each line, its equation, and the correlation coefficient ofeach fit are shown in the figure. The fact that the absolute values ofthe correlations are near unity indicates that the linear fit is a goodapproximation. The slopes range in value from -0.3 m/km on the firstflood (Figure 13a) to -1.7 m/km on the second ebb (Figure 13b).
The ebbs have larger upriver decay rates than the floods. This seemsstrange at first because an ebb current should refract the waves towardits axis hence mitigating the effects of bathymetric refraction toward theshoals. A flood current, on the other hand, should enhance the refractionaway from the channel axis.
One possible explanation for the behavior observed here is that themid-channel current magnitude decreases upriver from the vicinity of thejetty tips near Buoy 8 at x=O. If this happens on an ebb current thegradient would cause waves to refract away from the channel axis henceenhancing the decay rate, and vice versa on flood. This agrees qualitativelywith the observations. The converging jetty tips were designed to acceleratethe current to scour the channel. We might expect another current-speedmaximum upriver between Jetty A and Clatsop Spit.
Confirmation of the current gradients awaits a complete analysis ofthe drifter tracks and perhaps further observations. However, a preliminaryanalysis has been conducted near the time of peak ebb during four of theintensive observation periods. Tabulated results of the drift-distanceover periods of a few minutes are presented in Table 13. The inferredsurface-current vectors are shown in Figure 14. The ebb currents weremostly in excess of 2 m/s. Figure 14a shows some divergence just upriverof the jetty tips.
49
10SE
PT19
8114
44-
1629
PDT
(EB
B)
o o ·... ::J:o ....
.,0 ·
Nen :J
:
++
++
+HS
=2
.2-
0.5
XR
=-0
.96
U't o
o o cil
II
II
II
II
II
-3.0
0-2
.00
~1.00
0.0
01
.00
2.0
03
.00
•.00
5.0
06
.00
7.0
0X
.K
ILO
MET
ERS
EAST
OFBU
OY8
10SE
PT19
8110
30-1
221
PDT
(FLO
OD
)o o ·... ::J:o ..
...,
0 ·N
en :J: o o
HS
=1
.5-
0.3
XR
=-0
.94
-..
I+ ~---t +
I.:
t-
-2.0
0-1
.00
0.0
01
.00
2.0
03
.00
•.00
X.
KIL
OM
ETER
SEA
STOF
BUOY
85
.00
6.0
0
Fig
ure
13
a.W
aver
ider
sig
nif
ican
tw
ave
heig
ht
est
imate
sas
afu
ncti
on
of
dis
tan
ce
east
of
bu
oy
8fo
r10
Sep
t.1
98
1.
11SE
PT'
1981
1552
-162
9PO
T(E
BB
)o o · ..
.......
2:0
---.
.0 ·..
Nen ::
I:
o o
HS=
6.5
-1
.7X
R=
-1.0
U1 .....
0'
II
II
II
II
II
-3.0
0-2
.00
-1.0
00
.00
1.0
02
.00
3.0
04
.00
5.0
06
.00
1.0
0X
.K
ILO
MET
ERS
EAST
OFBU
OY8
11SE
PT19
8113
48-1
447
POT
(SLA
CK
-EB
B)
o o ·.......
..:E
o--
-..0 N
(f)
:::I:
HS=
3.1
-0
.8X
R=
-0.8
9
o o 0'
II
I,
II
II
II
-3.0
0-2
.00
-1.0
00
.00
1.0
02
.00
3.0
04
.00
5.0
06
.00
1.0
0X.
KIL
OM
ETER
SEA
STOF
BUOY
8
Fig
ure
13
b.
Wav
erid
ersi
gn
ific
an
tw
ave
heig
ht
est
imate
sas
afu
ncti
on
of
dis
tan
ce
east
of
bu
oy
8fo
r11
Sep
t.1
98
1.
12SE
PT19
8116
44-1
815
PDT
(EB
B)
o o .' :1:0 -.0
·N
(f) :::I:
+
=4
.8-
0.9
X=
-0.8
4
c.n N
o o 0"
II
II
II
II
II
-3.0
0-2
.00
-1.0
00
.00
1100
2.0
03
.00
•.00
5.0
06
.00
7.0
0X.
KIL
OM
ETER
SEA
STOF
BUOY
8
12SE
PT19
8111
27-1
217
PDT
(FLO
OD
)o o · • :1:0 -
.0·
N(f) :::I:
o o
HS=
1.6
-0
.4X
R=
-1.0
-2.0
0-1
.00
0.0
01
.00
2.0
03
.00
•.00
X.K
ILO
MET
ERS
EAST
OFBU
OY8
5.0
06
.00
Fig
ure
13
c.W
aver
ider
sig
nif
ican
tw
ave
heig
ht
est
imate
sas
afu
ncti
on
of
dis
tan
ce
east
of
bu
oy
8fo
r12
Sep
t.19
81.
VI
W
13SE
PT19
8116
58-1
842
PDT
(EB
B)
0 0
·.. -HS
=2
.9-
0.5
X~o
R=
-0.9
5-e
-+
·N
en :I:
I~
++
+0 0
·0
-3
. 00
-l.O
O-1
.00
0.0
01
.00
l.OO
3.0
0•.
005
.00
6.0
07
.00
X.K
ILO
MET
ERS
ERST
OFBU
OY8
13SE
PT19
8111
17-1
202
PDT
(FLO
OD
)o o ·.. - ~o -e ·N
en :J: o o
+~
HS=
1.4
-0
.4X
R=
-0.9
5
01
I1
II
II
II
1I
-3.0
0-l
.OO
-1.0
00
.00
1.0
0l.O
O3
.00
•.00
5.0
06
.00
7.0
0X.
KIL
OM
ETER
SER
STOF
BUOY
8
Fig
ure
13d.
Wav
erid
ersi
gn
ific
an
tw
ave
heig
ht
est
imate
sas
afu
nct
ion
of
dis
tan
ce
east
of
buoy
8fo
r13
Sep
t.19
81.
TABLE 13. Drifter Information for Current Vectors Presentedin Figure 14.
Date Start End Drifter Drift Drift DriftTime Time ID Distance Time Speed(PDT) (PDT) (Fig./Buoy) (m) (min) m/s
10 Sep 1540 1600 A16/2 2225 20 1.9
10 Sep 1550 1610 A16/3 2100 20 1.8
10 Sep 1540 1600 A16/5 2025 20 1.7
11 Sep 1610 1618 A34/1 975 8 2.0
11 Sep 1610 1618 A34/2 1150 8 2.4
11 Sep 1610 1618 A34/3 925 8 1.9
12 Sep 1642 1651 A54/1 1250 9 2.3
12 Sep 1642 1651 A54/2 1110 9 2.1
13 Sep 1735 1741 A76/1 925 6 2.6
13 Sep 1735 1741 A76/2 850 6 2.4
13 Sep 1735 1739 A76/3 475 4 2.0
13 Sep 1727 1734 A76/4 850 7 2.0
54
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(c)
I1_-......._
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U'1
Fig
ure
14.
Dri
fter
der
ived
surf
ace
cu
rren
tv
ecto
rsn
ear
the
tim
eo
fp
eak
ebb
.(b
)11
Sep
t.19
81.
(c)
12S
ept.
1981
.(d
)13
Sep
t.19
81.
(a)
10S
ep
t.19
81.
The enhanced wave decay rate on ebb may be due in part to wave breaking.The instance of greatest decay is on the ebb of 11 September, when breakingswell were observed visually. It is possible to estimate the wave steepnessnear Buoy 8 and compare this with maximum values limited by breaking. Fora wave spectrum we take the characteristic steepness to be \H k. Thewavenumber, k, can be estimated (rather inappropriately) fromslineartheory applied to slowly varying waves. Details are given in §4.2.2. His extrapolated from Figure 13. The characteristic steepness is given i~column 10 of Table 14 for each of the ebb and flood events observed. Forregular, periodic waves the theoretical maximum steepness is givenapproximately by (Miche, 1944)
(ak) =0.44 tanh kd.max(1)
where a is the wave amplitude and d is the depth. Due to the inherentunsteadiness of a real sea and the existence of wave groups, significantsporadic breaking can occur if the characteristic steepness is somewhatlower than this. For random waves in deltaic regions Battjes (1982)suggests the following empirical formula
(\H k) "" 0.2 tanh kd.s max ""(2)
For the full ebb on 11 September at 1615 the extrapolated characteristicsteepness exceeded this value. This points to wave breaking as being acause of the enhanced decay rate. SLAR images on this date (Figs. A35 andA36) show numerous highly radar-reflective regions in the channel entrancewhich are similar in size and shape to surf on nearby beaches. Thisprovides further evidence for mid-channel breaking, but it must be cautionedthat similar images occur in other locations and other scenes where breakingcould not be occurring. Thus there is not a unique correspondence betweenbreaking waves and such images.
4.2 Wave-Current Interaction Seaward of Buoy 8
Due to logistical and safety considerations we did not often measurewave heights in the vicinity of the channel entrance seaward of Buoy 8.Therefore to test the hypothesis that the waves grow or decay along theirpropagation path due to ebb or flood currents, respectively, we mustcontent ourselves with a comparison between two point measurements, oneoffshore and one at Buoy 8. The offshore wave measurements are those fromNDBC Buoy 46010.
4.2.1 The Observations
For each of the eight intensive observation periods the measurementsare summarized in Table 14 which is divided horizontally into two portionscorresponding to ebb and flood conditions. (Actually nine rows are shownsince at 1127 on 12 September the offshore spectrum had two peaks; hencethese are analyzed as two independent wave systems.) Columns 1 and 2 givethe date and time of the offshore and channel-entrance comparisons.
56
TABLE 14. Summary of Observed Wave and Current Characteristics and ComputedTransfer Function, T, During the Intensive Observation Periods
1 2 3 4 5 6 7 8 9 10Date Time Buoy 46010 1 Buoy 8 Current T = T T /T
0 c o cf Hs46 Hs8 Speed2
Hs8/Hs46 Eq. (1) Steepnessp
(PDT) (H ) (m) (m) (m/s) 8 =0 0 8 =00
0 0z
(8 =300 ) (8 =30 0 ) \H k0 0 s8
EBB
10 Sept 1528 0.09. 1.7 2.2 -2.1 1.3 1.4 0.9 0.07(1. 3) (1. 0)
11 Sept 1445 0.07 2.7 3.1 -1.3 1.1 1.3 0.8 0.07(1. 2) (0.9)
11 Sept 1615 0.07 2.9 5.2 4 -6.5 -2.0 1.84 -2.2 1.5 1.24 -1.5 0.124 -0.16(1.4) (1.3 4 -1.6)
12 Sept 1700 0.08 2.8 4.83 -2.2 1.7 1.5 1.1 0.14(1. 4) (1. 2)
13 Sept 1825 0.09 1.9 2.9 3 -2.3 1.5 1.5 1.0 0.10(1. 4) ( 1.1)
FLOOD
10 Sept 1030 0.08 1.8 1.5 1.3 0.8 0.9 0.9 0.03(0.9) (0.9)
12 Sept 1127 0.08 1.4 1.0 1.5 0.7 0.9 0.8 0.02(0.9) (0.8)
12 Sept 1127 0.11 2.4 1.2 1.5 0.5 0.8 0.6 0.03(0.8) (0.6)
13 Sept 1117 0.09 2.1 1.5 1.4 0.7 0.9 0.8 0.03(0.8) (0.9)
1 H and peak frequency f were interpolated from observationss p
bracketing the time of Waverider observations.
2 From drifter speed estimates in Table 12. Ebb currents arenegative, flood are positive.
3 From least square fit to data presented in Figs. 13b-d.
4 Lower value corresponds to limiting breaking height givenby Equation (2).
57
Columns 3 and 4 give the frequency of the offshore spectral peak, f , andp
the significant wave height at Buoy 46010, Hs46 . The significant wave
height at Buoy 8, H 8' is presented in column 5. Directly measuredvalues were used wh~n available, and when not, the linear least-squaresextrapolations from upriver of Buoy 8 were used. Figure 13a shows thatthese fits represent the data well when a comparison is possible. Thecurrent-speed estimates at Buoy 8 based on the drifter data of Table 12are shown in column 6. Finally, column 7 lists the observed wave heighttransfer function from offshore to onshore, i.e., the ratio of the significantwave heights, To = Hs8/Hs46·
Column 7 of Table 14 shows that for all ebb currents the waves wereamplified (T >1) from offshore to the channel entrance, and for all floodcurrents the~ decayed (T <1). Thus our hypothesis that wave-currentinteraction is reponsiblg for wave height changes seaward of Buoy 8 isconfirmed qualitatively, at least during maximum ebb and flood conditions.The amplification reached values as high as 2.2 on ebb (or perhaps 1.8 ifthe waves at Buoy 8 were indeed limited by the empirical breaking criterionof (2)) with an attenuation of up to 0.5 on flood.
4.2.2 Comparison with Linear, 1-D Theory
In a previous study, Gonzalez (1984) compared existing linear, onedimensional wave-current interaction theory with Waverider observationstaken hourly over ten tidal cycles at an offshore location and near Buoy 8.A theoretical amplification factor or transfer function, T, based on conservationof wave action density, A = E/a, is given by (see, for example, Phillips, §2.7,1977)
aao
= (uo + cgo coseo)\(~)\U + C cose ao
g(3)
where unscripted parameters refer to the river entrance and the subscript"0" indicates initial conditions, or offshore (deep water) values, andwhere
E = spectral energy density values,
a =wave height amplitude,
U = surface current velocity,
C =wave group velocity,g
e = relative wave-current direction
a = intrinsic wave frequency,
w = observed wave frequency,
d =water depth.
This expression accounts for shoaling, radiation stress (momentum transferfrom currents to waves), and offshore wave direction. It does not account
58
for 2-dimensional effects which produce convergence or divergence of waverays by features such as bathymetric headlands and current jets. Furthermore,the physical assumptions are that wave motion is purely periodic, thatwave amplitude is small compared to wavelength and depth, that wave andcurrent properties vary slowly over scales of many wavelengths, that waveperiods are small compared to tidal periods, that all quantities vary onlyalong the main axis of the current (no lateral variations), and that thereis no lateral current component across the main axis.
The theory also provides the following relations between the parametersin (3)
w = a + kUcose
a = (gk tanh kd)\ (4)
C 2kd a= \(1 + sinh 2kd) kg
where k is the wave number, and where an analogous set of equations can bewritten for the subscripted variables. A final relationship
k sine = ko sineo (5)
closes the system of transcendental equations which can be solved iterativelyto compute values of T as given by equation (3). For convenience, we havehere computed Tables 15a-i, which present T as a function of f(= w/2n) andU. Each of these nine tables correspond to specific values for the pair(d, eo), where the river entrance depth d takes on the values d = 10, 15,and 20 meters, and the offshore wave direction relative to the current'smain axis takes on the values eo = 0, 30, and 60 degrees. All tablesassume that the offshore current Uo = 0 and that the offshore depth do = 60 m(corresponding to the buoy 46010 location).
Strictly speaking, equations (3)-(5) apply to monochromatic waves. Torelate the predicted amplifications in Table 15 to the observed waves weapproximate the spectrum with a monochromatic wave whose frequency is thatat the spectral peak, f , and whose height is the significant wave height, H .
p s
The theoretically computed wave height transfer function, T , atBuoy 8 in 15 m of water is given in column 8 of Table 14 for each of theintensive observation periods. Values without parentheses refer to incidentangles of 0° and values with parentheses refer to 30° incidence. Qualitatively,the theory predicts wave amplification during ebbs and wave decay duringfloods just as has been observed. The change of the assumed angle ofincidence from 0° to 30° lowers the predicted amplification on ebb byabout 10% and does not affect the flood values in the first decimal place.
For convenience, the ratio of observed to computed wave amplificationsis presented in column 9. For all but one ebb the ratio is within 20% ofunity. There is no clear preference for one offshore incident angle overthe other. However for the ebb of 11 September at 1615 hours the waveheight was underpredicted by up to 50% at 0° incidence. It is for this
59
TAB
LE1
5a.
Wav
eh
eig
ht
am
pli
ficati
on
TC
Eq.
3)
for
d=
10m
,6
0=
0°.
DTH
ETA
ODO
UO1
0.0
O.
06
0.0
0.0
CURR
ENT
SPEE
DF
T-2
.50-2.25-~00-1.75-1.5
0-1
.25
-1.
00
-.7
5-.
SO-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.9
21
.84
1.7
71
.71
1.6
51
.60
1.5
51
.50
1.4
61
.41
1.3
81
.34
1.3
01
.27
1.2
41
.21
1.
18
1.
16
1.
13
1.
11
1.
08
.05
51
8.2
1.
89
1.
81
1.
74
1.
67
1.6
11
.~6
1.
51
1.4
61
.4
21.~8
1.3
41
.30
1.2
71
.24
1.2
11
.1
81
.1
51
.1
21
.1
01
.0
71.
05
.06
01
6.7
1.
85
1.
77
1.7
01
.6
31.
57
1.
52
1.
47
1.4
21
.3
81
.3
41
.3
01
.2
61
.2
31
.2
01
.1
71.
14
1.
11
1.0
91
.06
1.0
41
.02
·0
65
15
.41
.8
21
.7
41
.6
61
.5
91
.5
31.
48
1.4
31
.3
81
.34
1.
30
1.2
61
.22
1.
19
1.
16
1.
13
1.
10
1.
08
1.
05
1.
03
1.0
0.9
8.0
70
14
.31
.7
91.
70
1.
62
1.
55
1.
49
1.
44
1.
39
1.
34
1.
30
1.
25
1.
22
1.1
81
.1
51
.1
21
.0
91
.0
61
.0
41
.0
1.9
9.9
7.9
5.0
75
13
.31
.75
1.6
61
58
1.5
11
.45
1.4
01
.34
1.3
01
.25
1.2
11
.1
81
.1
41
.1
11
.08
1.0
51
.02
1.0
0.9
8.9
5.9
3.9
1.0
80
12
.51
.73
1.6
31
.55
1.4
81
.41
1.3
61
.30
1.2
61
.21
1.1
71
.14
1.1
01
.07
1.0
41
.01
.99
.96
.94
.92
.90
.88
.08
51
1.8
1.
70
1.
60
1.
52
1.
44
1.
38
1.3
21
.2
71.
22
1.
18
1.
14
1.
10
1.
07
1.
04
1.
01
.98
.95
.93
.91
.88
.86
.84
·0
90
11
.1
1.6
91
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1.4
91
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1.
35
1.
29
1.
23
1.1
91
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41
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71
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0.9
7.9
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7.8
5.8
3.8
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95
10
51
.69
1.5
71
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1.3
91
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1.2
61
.21
1.
16
1.
111
.0
71
.0
41
.0
0.9
7.9
4.9
2.8
9.8
7.8
5.8
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1.7
91
00
10
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91
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61
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61
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71
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01
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41
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81.
13
1.0
91
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51
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1.9
8.9
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6·
10
59
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1.
71
1.5
71
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61
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61
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91
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61
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71
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9.9
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4.8
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11
09
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1.7
51
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1.4
61
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1.2
81
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15
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71
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11
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71
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61
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9.9
6.9
2.8
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3.8
1.7
9.7
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4.7
3.7
10
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08
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1.
87
1.
65
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49
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37
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28
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20
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20
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13
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30
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72
.09
1.7
61
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1.4
11
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01
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11
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31
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71
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7.9
3.8
9.8
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7.7
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71
35
7.
42
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1.8
51
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1.4
41
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1.2
21
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71
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;9
7.9
2.8
8.8
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2.7
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7.7
4.7
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8.6
61
40
7.
12
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1.
95
1.
66
1.4
71
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31
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31
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41
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6.9
2.8
8.8
4.8
1.7
8.7
6.7
3.7
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7.6
51
45
6.9
2.9
12
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1.7
31
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1.
35
1.
24
1.
15
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08
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15
06
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65
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27
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81
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55
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38
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26
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16
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08
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15
56
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6.
71
2.
51
1.
91
1.
61
1.
41
1.
28
1.
17
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09
1.0
2.9
6.9
1.8
7.8
3.8
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7.7
4.7
2.6
9.6
7.6
5.6
31
60
6.3
****
2.8
52
.03
1.
67
1.
45
1.3
01
.1
91
.1
01
.0
2.9
6.9
1.8
7.8
3.7
9.7
6.7
4.7
1.6
9.6
7.6
5.6
31
65
6.
1**
**3
.41
2.1
81
.7
41
.4
91
.3
21
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01
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11
.0
3.9
7.9
1.8
7.8
3.7
9.7
6.7
3.7
1.6
8.6
6.6
4.6
2.1
70
5.
9**
**4
.67
2.3
61
.82
1.5
41
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1.2
21
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4.9
7.9
2.8
7.8
3.7
9.7
6.7
3.7
0.6
8.6
5.6
3.6
2·
17
55
.7
****
****
2.6
01
.91
1.
59
1.
38
1.
24
1.1
31
.0
4.9
8.9
2.8
7.8
3.7
9.7
5.7
2.7
0.6
7.6
5.6
3.6
1.1
80
5.6
****
****
2.9
22
.02
1.6
41
.41
1.
26
1.
14
1.
05
.98
.92
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.82
.79
.75
.72
.69
.67
.65
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.61
·1
85
5.
4**
****
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.3
92
.1
41
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01
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51
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81.
16
1.
06
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.92
.87
.82
.78
.75
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.60
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05
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****
****
4.3
02
.28
1.7
61
.48
1.3
01
.17
1.0
7.9
9.9
3.8
7.8
2.7
8.7
5.7
2.6
9.6
6.6
4.6
2.6
0·
19
55
.1
****
****
8.4
22
.45
1.8
31
.52
1.3
31
.19
1.0
81
.00
.93
.87
.83
.78
.75
.71
.69
.66
.64
.61
.59
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05
.0
****
****
****
2.6
51
.91
1.5
61
.35
1.2
01
.09
1.0
0.9
3.8
8.8
3.7
8.7
5.7
1.6
8.6
6.6
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1.5
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05
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9**
****
****
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21
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91.
60
1.
38
1.
22
1.1
01
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1.9
4.8
8.8
3.7
8.7
5.7
1.6
8.6
5.6
3.6
1.5
9.2
10
4.8
****
****
****
3.2
92
.08
1.6
51
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1.2
31
.11
1.
02
.94
.88
.83
.78
.74
.71
.68
.65
.63
.61
.58
.21
54
.7
****
****
****
3.8
92
.17
1.6
91
.43
1.2
51
.12
1.0
3.9
5.8
8.8
3.7
8.
'74
.71
.68
.65
.63
.60
.58
.22
04
.5
****
****
****
5.3
62
.28
1.7
41
.45
1.2
71
.13
1.0
3.9
5.8
9.8
3.7
8.7
4.7
1.6
8.6
5.6
2.6
0.5
8.2
25
4.4
****
****
****
****
2.
41
1.
79
1.
48
1.2
81
.1
41
.0
4.9
6.8
9.8
3.7
8.7
4.7
1.6
8.6
5.6
2.6
0.5
8.2
30
4.3
****
****
****
****
2.5
61
.84
1.5
01
.30
1.1
51
.05
.96
.89
.83
.79
.74
.71
.67
.64
.62
.60
.57
.23
54
.3
****
****
****
****
2.7
41
.89
1.5
31
.31
1.
16
1.0
5.9
7.8
9.8
4.7
9.7
4.7
1.6
7.6
4.6
2.5
9.5
7.2
40
4.2
****
****
****
****
2.9
71
.94
1.5
61
.33
1.1
71
.06
.97
.90
.B
4.7
9.7
4.7
0.6
7.6
4.6
2.5
9.5
7.2
45
4.
1**
****
****
****
**3
.29
2.0
01
.5B
1.3
41
.IB
1.0
6.9
7.9
0.8
4.7
9.7
4.7
0.6
7.6
4.6
1.5
9.5
7.2
50
4.0
****
****
****
****
3.7
B2
.07
1.6
11
.3
61
.1
91
.0
7.9
8.9
0.8
4.7
9.7
4.7
0.6
7.6
4.6
1.5
9.5
7
TAB
LEIS
b.
Wav
eh
eig
ht
am
pli
ficati
on
T(E
q.
3)
for
d=
10m
,e
=3
0°.
0
0T
HE
TA
OD
OU
O1
0.0
30
.0
60
.00
.0
CU
RR
EN
TS
PE
ED
FT
-2
.50
-2
.25
-2
.00
-1
.75
-1
.50
-1
.25
-1
.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.8
01
.73
1.6
61
.61
1.5
51
.50
1.4
51
.41
1.
37
1.
33
1.
30
1.
26
1.
23
1.
20
1.
17
1.
15
1.
12
1.
10
1.
07
1.
05
1.
03
.05
51
8.2
1.7
71
.7
01
.6
31
.5
71
.5
21
.4
71
.4
21
.3
81
.3
41
.3
01
.2
61.
23
1.
20
1.
17
1.
14
1.
11
1.0
91
.06
1.0
41
.02
1.0
0.0
60
16
.71
.7
41
.6
61.
60
1.
53
1.
48
1.
43
1.
38
1.
34
1.
30
1.
26
1.
23
1.
19
1.
16
1.
13
1.
11
1.0
81
.05
1.0
31
.01
.99
.97
.06
51
5.4
1.
70
1.6
31.
56
1.
50
1.
44
1.
39
1.
34
1.
30
1.
26
1.
22
1.
19
1.
16
1.
13
1.'
10
1.
07
1.
04
1.
02
1.
00
.98
.96
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01
4.3
1.
67
1.
59
1.
52
1.
46
1.
40
1.
35
1.
30
1.
26
1.2
21
.1
91
.1
51
.1
21
.0
91
.0
61
.0
31
.0
1.9
9.9
6.9
4.9
2.9
0.0
75
13
.31
.64
1.5
61
.49
1.4
21
.37
1.3
11
.2
71
.2
21
.1
81
.1
51.
11
1.0
81
.05
1.0
21
.00
.97
.95
.93
.91
.89
.87
.OB
O1
2.
51
.6
21.
53
1.
45
1.
39
1.
33
1.
28
1.
23
1.
19
1.
1~
1.
11
1.
08
1.
05
1.
02
.99
.96
.94
.92
.90
.88
.86
.84
.OB
51
1.8
1.6
01
.50
1.4
31
.36
1.3
01
.24
1.2
01
.15
1.1
11
.0
81
.0
41
.0
1.9
8.9
6.9
3.9
1.8
9.8
7.8
5.8
3.8
1.0
90
11
.1
1.~B
1.4
81
.40
1.3
31
.27
1.2
11
.1
71
.1
21
.0
81
.0
51
.0
1.9
8.9
5.9
3.9
0.8
B.8
6.8
4.8
2.8
0.7
8.0
95
10
.51
.5
81.
47
1.
38
1.
31
1.
25
1.
19
1.
14
1.
10
1.
06
1.
02
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.96
.93
.90
.88
.85
.83
.81
.79
.78
.76
·1
00
10
.01
.5
81
.4
71
.3
71
.2
91
.2
31
.1
71
.1
21
.0
71
.0
31
.0
0.9
6.9
3.9
0.8
8.8
5.8
3.8
1.7
9.7
7.7
6.7
4·
10
59
.5
1.6
01
.47
1.3
71
.29
1.2
11
.15
1.1
01
.06
1.0
1.9
8.9
4.9
1.8
9.8
6.8
4.8
1.7
9.7
7.7
5.7
4.7
2·
11
09
.1
1.6
31
.48
1.3
71
.28
1.2
11
.1
41
.0
91
.0
41
.0
0.9
6.9
3.9
0.8
7.8
4.8
2.8
0.7
8.7
6.7
4.7
2.7
10
'·
11
58
.7
1.
68
1.
51
1.
38
1.
29
1.
21
1.
14
1.
08
1.
03
.99
.95
.92
.89
.86
.83
.81
.78
.76
.74
.73
.71
.69
.....·
12
08
.3
1.
74
1.
54
1.
40
1.
29
1.
21
1.
14
1.
08
1.
03
.98
.94
.91
.88
.85
.82
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.77
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.73
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.70
.68
·1
25
8.
01
.82
1.5
91
.43
1.3
11
.2
21
.1
41
.0
81
.0
2.9
8.9
4.9
0.8
7.8
4.8
1.7
9.7
7.7
4.7
2.7
1.6
9.6
7.1
30
7.
71
.9
31
.6
41
.4
61
.3
31
.2
31
.1
51
.0
81
.0
2.9
8.9
3.9
0.8
6.8
3.8
1.7
8.7
6.7
4.7
2.7
0.6
8.6
7·
13
57
.4
2.0
91
.72
1.5
01
.35
1.2
41
.15
1.0
81
.02
.97
.93
•.8
9.8
6.8
3.8
0.7
7.7
5.7
3.7
1.6
9.6
8.6
6·
14
07
.1
2.3
01
.8
11
.5
51
.3
81
.2
61
.1
71.
09
1.
03
.9B
.93
.89
.86
.82
.80
.77
.75
.73
.71
.69
.67
.66
·1
45
6.9
2.6
21
.93
1.6
11
.4
21
.2
81
.1
81
.1
01
.0
3.9
8.9
3.8
9.8
5.8
2.7
9.7
7.7
4.7
2.7
0.6
8.6
7.6
5·
15
06
.7
3.1
92
.08
1.6
91
.46
1.3
11
.2
01
.1
11
.04
.98
.93
.89
.85
.82
.79
.76
.74
.72
.70
.68
.66
.65
·1
55
6.
54
.77
2.2
91
.77
1.5
11
.3
41
.2
11
.1
21
.0
5.9
9.9
3.8
9.8
5.8
2.7
9.7
6.7
4.7
2.7
0.6
8.6
6.6
4·
16
06
.3
****
2.
57
1.
88
1.
56
1.
37
1.
24
1.
13
1.
06
.99
.94
.89
.85
.82
.79
.76
.74
.71
.69
.67
.66
.64
·1
65
6.
1**
**3
.02
2.0
11
.63
1.
41
1.
26
1.
15
1.
07
1.
00
.94
.89
.35
.82
.79
.76
.73
.71
.69
.67
.65
.64
·1
70
5.
9**
**3
.89
2.1
71
.70
1.4
51
.28
1.1
71
.08
1.0
1.9
5.9
0.8
6.8
2.7
9.7
6.7
3.7
1.6
9.6
7.6
5.6
4·
17
5~.
7**
****
**2
.37
1.7
81
.49
1.3
11
.1
91
.0
91
.0
1.9
5.9
0.8
6.8
2.7
9.7
6.7
3.7
1.6
9.6
7.6
5.6
3·
18
05
.6**
****
**2
.64
1.8
81
.54
1.3
41
.20
1.1
01
.02
.96
.91
.86
.82
.79
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.73
.71
.69
.67
.65
.63
·1
85
5.
4**
****
**3
.02
1.9
81
.60
1.3
71
.23
1.1
21
.03
.97
.91
.86
.82
.79
.76
.73
.71
.69
.67
.65
.63
·1
90
5.
3**
****
**3
.68
2.1
11
.6
61
.4
11
.2
51
.1
31
.0
4.9
7.9
1.8
7.8
3.7
9.7
6.7
3.7
1.6
9.6
7.6
5.6
3·
19
55
.1
****
****
5.7
32
.25
1.7
21
.44
1.2
71
.15
1.0
5.9
8.9
2.8
7.8
3.7
9.7
6.7
3.7
1.6
9.6
7.6
5.6
3.2
00
5.
0**
****
****
**2
.43
1.7
91
.48
1.2
91
.16
1.0
6.9
9.9
3.8
7.8
3.7
9.7
6.7
3.7
1.6
9.6
6.6
5.6
3.2
05
4.9
****
****
****
2.6
51
.86
1.5
21
.32
1.l
B1
.07
.99
.93
.88
.83
.80
.76
.73
.71
.69
.66
.65
.63
.21
04
.8
****
****
****
2.
95
1.
94
1.
56
1.
34
1.
19
1.
09
1.
00
.94
.88
.84
.80
.76
.73
.71
.69
.66
.65
.63
.21
54
.7
****
****
****
3.4
12
.02
1.6
01
36
1.2
11
.10
1.0
1.9
4.8
9.8
4.8
0.7
7.7
4.7
1.6
9.6
6.6
5.6
3.2
20
4.
5**
****
****
**4
.31
2.
12
1.
64
1.
39
1.
22
1.
11
1.
02
.95
.89
.84
.80
.77
.74
.71
.69
.66
.65
.63
.22
54
.4**
****
****
****
**2
.23
1.6
81
.41
1.
24
1.
12
1.
02
.95
.89
.84
.80
.77
.74
.71
.69
.67
.65
.63
.23
04
.3
****
****
****
****
2.3
61
.73
1.4
41
.25
1.1
31
.03
.96
.90
.85
.81
.77
.74
.71
.69
.67
.65
.63
.23
54
.3**
****
****
****
**2
.5
11
.78
1.4
61
.27
1.
14
1.0
4.9
6.9
0.8
5.8
1.7
7.7
4.7
1.6
9.6
7.6
5.6
3.2
40
4.
2**
****
****
****
**2
.7
11
.8
31
.4
81
.2
81
.1~
1.
04
.97
.90
.85
.81
.77
.74
.71
.69
.67
.65
.63
.24
54
.1
****
****
****
****
2.9
61
.88
1.5
11
.3
01
.1
51
.0
5.9
7.9
1.8
5.8
1.7
7.7
4.7
1.6
9.6
7.6
5.6
3.2
50
4.0
****
****
****
****
3.3
31
.94
1.5
31
.31
1.
16
1.
06
.97
.91
.86
.81
.77
.74
.71
.69
.66
.64
.63
TABL
ElS
c.W
ave
heig
ht
am
pli
ficati
on
TC
Eq.
3)
for
d=
10m
,e
=6
0°.
0
DTH
ETA
OD
OU
O1
0.0
60
.06
0.0
0.0
CU
RR
ENT
SPE
ED
FT
-2
.50
-2
.25
-2
.00
-1
.75
-1
.50
-1
.25
-1
.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01.
75
2.0
02
.25
2.5
0
.05
02
0.0
1.
39
1.
33
1.
29
1.
24
1.
20
1.1
61.
13
1.
10
1.
07
1.
04
1.
01
.99
.96
.94
.92
.90
.88
.86
.85
.83
.82
.05
51
8.2
1.3
61
.3
11
.2
61
.2
21
.1
81
.1
41
.1
01
.0
71
.0
41.
01
.99
.96
.94
.92
.90
.88
.86
.84
.83
.81
.79
.06
01
6.7
1.
34
1.
28
1.
23
1.
19
1.
15
1.
11
1.
08
1.
04
1.0
1.9
9.9
6.9
4.9
1.8
9.8
7.8
5.8
3.8
2.8
0.7
9.7
7.0
65
15
.41
.3
11
.2
61.
21
1.1
61.
12
1.
08
1.
05
1.0
2.9
9.9
6.9
3.9
1.8
9.8
7.8
5.8
3.8
1.7
9.7
8.7
6.7
5.0
70
14
.31
.2
91
.2
31.
18
1.1
31
.0
91.
05
1.
02
.99
.96
.93
.91
.88
.86
.84
.82
.80
.78
.77
.75
.74
.72
.07
51
3.3
1.
27
1.2
11
.15
1.1
11
.0
61
.0
2.9
9.9
6.9
3.9
0.8
8.8
5.8
3.8
1.7
9.7
8.7
6.7
4.7
3.7
1.7
0.0
80
12
.5
1.
25
1.
18
1.
13
1.
08
1.0
41
.0
0.9
6.9
3.9
0.8
8.8
5.8
3.8
1.7
9.7
7.7
5.7
4.7
2.7
1.6
9.6
8.0
85
11
.8
1.2
31.
16
1.11
1.
06
1.0
1.9
7.9
4.9
1.8
8.8
5.8
3.8
1.7
8.7
7.7
5.7
3.7
1.7
0.6
9.6
7.6
6.0
90
11
.1
1.
22
1.
15
1.0
91
.0
4.9
9.9
5.9
2.8
9.8
6.8
3.8
1.7
8.7
6.7
4.7
3.7
1.6
9.6
8.6
7.6
5.6
4.0
95
10
.51
.2
21
.1
41.
08
1.0
2.9
8.9
4.9
0.8
7.8
4.8
1.7
9.7
7.7
5.7
3.7
1.6
9.6
8.6
6.6
5.6
4.6
3·
10
01
0.
01
.22
1.1
41
.07
1.0
1.9
6.9
2.8
9.8
5.8
2.8
0.7
7.7
5.7
3.7
1.7
0.6
8.6
6.6
5.6
4.6
2.6
1·
10
59
.5
1.2
31
.14
1.0
71
.01
.96
.91
.88
.84
.81
.79
.76
.74
.72
.70
.68
.67
.65
.64
.63
.62
.60
·1
10
9.
11
.2
61
.1
51.
07
1.
01
.95
.91
.87
.84
.81
.78
.75
.73
.71
.69
.68
.66
.65
.63
.62
.61
.60
0-
11
58
.7
1.
29
1.
17
1.0
81
.0
1.9
5.9
1.8
7.8
3.8
0.7
7.7
5.7
3.7
1.6
9.6
7.6
6.6
4.6
3.6
1.6
0.5
9N
12
08
.31
.3
31
.1
91.
09
1.0
2.9
6.9
1.8
7.8
3.8
0.7
7.7
5.7
2.7
0.6
8.6
7.6
5.6
4.6
2.6
1.6
0.5
91
25
8.0
1.3
91.
23
1.1
11
.0
3.9
7.9
1.8
7.8
3.8
0.7
7.7
5.7
2.7
0.6
8.6
7.6
5.6
4.6
2.6
1.6
0.5
91
30
7.
71
.4
61
.2
71
.1
41.
05
.98
.92
.87
.84
.80
.77
.75
.72
.70
.68
.67
.65
.64
.62
.61
.60
.59
13
57
.4
1.
56
1.3
21
.1
71
.0
7.9
9.9
3.8
8.8
4.8
1.7
8.7
5.7
3.7
0.6
9.6
7.6
5.6
4.6
2.6
1.6
0.5
9·
14
07
.1
1.
69
1.
38
1.
21
1.
09
1.
01
.94
.89
.85
.81
.78
.75
.73
.71
.69
.67
.66
.64
.63
_6
2.6
0.5
91
45
6.
91
.88
1.4
61
.25
1.1
21
.03
.96
.90
.86
.82
.79
.76
.73
.71
.69
.68
.66
.64
.63
.62
.61
.60
15
06
.7
2.
18
1.
56
1.3
01.
15
1.
05
.97
.91
.87
.83
.79
.76
.74
.72
.70
.68
.66
.65
.64
.62
.61
.60
15
56
.5
2.
78
1.
69
1.
36
1.
19
1.
07
.99
.93
.88
.84
.80
.77
.75
.72
.70
.69
.67
.65
.64
.63
.62
.60
16
06
.3**
**1
.86
1.4
31
.23
1.1
01
.01
.94
.89
.85
.81
.78
.75
.73
.71
.69
.68
.66
.65
.63
.62
.61
16
56
.1
****
2.
11
1.5
21
.2
71.
13
1.0
3.9
6.9
0.8
6.8
2.7
9.7
6.7
4:7
2.7
0.6
8.6
7.6
5.6
4.6
3.6
2·
17
05
.9
****
2.5
21
.62
1.3
31
.16
1.0
5.9
7.9
2.8
7.8
3.8
0.7
7.7
5.7
3.7
1.6
9.6
7.6
6.6
5.6
3.6
2·
17
55
.7
****
3.4
81
.75
1.3
81
.20
1.0
8.9
9.9
3.8
8.8
4.8
1.7
8.7
6.7
3.7
2.7
0.6
8.6
7.6
5.6
4.6
3·
18
05
.6
****
7.3
11
.92
1.4
51
.23
1.1
01
.01
.95
.89
.85
.82
.79
.77
.74
.72
.71
.69
.67
.66
.65
.63
18
55
.4
****
6.1
02
.14
1.5
31
.2
71.
13
1.0
3.9
6.9
1.8
7.8
3.8
0.7
8.7
5.7
3.7
1.7
0.6
8.6
7.6
5.6
4·
19
05
.3
****
****
2.4
71
.61
1.
32
1.
16
1.0
5.9
8.9
2.8
8.8
4.8
1.7
9.7
6.7
4.7
2.7
1.6
9.6
7.6
6.6
5·
19
55
.1
****
****
3.0
81
.71
1.
36
1.1
91
.0
7.9
9.9
4.8
9.8
5.8
2.8
0.7
7.7
5.7
3.7
1.7
0.6
8.6
7.6
5.2
00
5.
0**
****
**7
.15
1.8
21
.41
1.2
21
.0
91
.0
1.9
5.9
0.8
6.8
3.8
1.7
8.7
6.7
4.7
2.7
0.6
9.6
7.6
6.2
05
4.
9**
****
****
**1
.9
61
.4
71
.2
51
.1
21
.0
3.9
6.9
2.8
8.8
4.8
2.7
9.7
7.7
5.7
3.7
1.6
9.6
8.6
6.2
10
4.8
*«.*
***
****
**2
.1
41
.5
21
.2
81.
14
1.
04
.98
.93
.89
.85
.83
.80
.78
.76
.73
.72
.70
.68
.66
.21
54
.7
****
****
****
2.3
81
.59
1.3
11.
16
1.0
6.9
9.9
4.9
0.8
6.8
4.8
1.7
8.7
6.7
4.7
2.7
0.6
8.6
7.2
20
4.
5**
****
****
**2
.75
1.6
51
.34
1.1
81
.08
1.0
0.9
5.9
1.8
7.8
4.8
2.7
9.7
7.7
5.7
3.7
1.6
9.6
7.2
25
4.4
****
****
****
****
1.7
21
.37
1.2
01
.09
1.0
2.9
6.9
2.8
8.8
5.8
2.8
0.7
7.7
5.7
3.7
1.6
9.6
7.2
30
4.3
****
****
****
****
1.8
11
.4
11
.2
21
.1
11
.0
3.9
7.9
3.8
9.8
6.8
3_
81
.78
.76
.73
.71
.69
.67
.23
54
.3
****
****
****
****
1.9
01.
44
1.2
41
.1
21
.0
4.9
8.9
4.9
0.8
7.8
4.8
1.7
8.7
6.7
4.7
1.6
9.6
7.2
40
4.2
****
****
****
****
2.0
21
.48
1.2
61
.13
1.0
5.9
9.9
5.9
1.8
7.8
4.8
2.7
9.7
6.7
4.7
2.6
9.6
7.2
45
41
****
****
****
****
2.
16
1.5
11.
28
1.1
41.
06
1.
00
.95
.91
.88
.85
.82
.79
.77
.74
.72
.69
.67
.25
04
.0***~
****
****
****
2.3
51
.55
1.2
91
.16
1.0
71
.01
.96
.92
.89
.85
.82
.79
.77
.74
.72
.69
.67
TAB
LE15
d.W
ave
heig
ht
am
pli
ficati
on
T(E
q.3
)fo
rd
=15
m,
e=
0°.
0
DT
HE
TA
OD
OU
O1
5.0
O.
06
0.0
0.0
CU
RR
EN
TS
PE
ED
FT
-2.5
0-2
.25
-2.0
0-1
.7
5-1
.50-1.2~-1.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.
66
1.6
11.
56
1.
51
1.
47
1.
43
1.
39
1.
35
1.
32
1.
29
1.
26
1.2
31
.2
01
.1
81
.1
51
.1
31
.1
11
.08
1.0
61
.04
1.0
2.0
55
18
.21
.6
41
.5
81
.5
31.
48
1.
44
1.
40
1.
36
1.3
21
.2
91
.2
61
.2
31
.2
01
.1
71.
15
1.
12
1.
10
1.
08
1.0
51
.0
31
.0
11
.0
0·
06
01
6.7
1.6
21
.56
1.5
01
.46
1.4
11
.3
71
.3
31
.2
91
.2
61
.2
31
.2
01
.1
71
.1
41
.1
11
.09
1.0
71
.04
1.0
21
.00
.98
.97
.06
51
5.4
1.
59
1.
53
1.
48
1.
43
1.
38
1.
34
1.
30
1.
26
1.
22
1.
19
1.
16
1.
13
1.
11
1.0
81
.06
1.0
31
.01
.99
.97
.95
.93
.07
01
4.3
1.
57
1.
51
1.4
51
.40
1.
35
1.
30
1.
26
1.
23
1.
19
1.
16
1.
13
1.
10
1.
07
1.
05
1.
02
1.
00
.98
.96
.94
.92
.90
.07
51
3.3
1.
55
1.
48
1.4
21
.3
71
.3
21
.2
71
.2
31
.1
91
.1
61
.1
31
.09
1.
07
1.
04
1.0
1.9
9.9
7.9
5.9
3.9
1.8
9.8
7.0
80
12
.51.
54
1.4
71
.4
01.
34
1.
29
1.
24
1.
20
1.
16
1.
13
1.
09
1.
06
1.
03
1.
01
.98
.96
.94
.91
.89
.88
.86
.84
.08
51
1.
81.
53
1.4
51
.3
81
.3
21
.2
71
.2
21
.1
71
.1
31
.1
01
.0
61
.0
31
.0
0.9
8.9
5.9
3.9
1.8
8.8
6.8
5.8
3.8
1·
09
01
1.
11.
53
1.
44
1.
37
1.
30
1.
25
1.
20
1.
15
1.1
11
.0
71
.0
41
.0
1.9
8.9
5.9
2.9
0.8
8.8
6.8
4.8
2.8
0.7
8.0
95
10
.51
.5
41
.4
41
.3
61
.2
91
.2
31
.1
81
.1
31
.0
91
.0
51
.0
1.9
8.9
5.9
2.9
0.8
8.8
5.8
3.8
1.7
9.7
8.7
6.1
00
10
.01
.5
61
.4
51.
36
1.
29
1.
22
1.1
61
.1
21.
07
1.
03
1.
00
.96
.93
.90
.88
.85
.83
.81
.79
.77
.76
.74
·1
05
9.
51
.6
01.
47
1.
37
1.
29
1.
22
1.
16
1.
11
1.
06
1.
02
.98
.95
.92
.89
.86
.84
.81
.79
.77
.75
.74
.72
·1
10
9.
11
.6
51
.5
01
.3
91
.3
01
.2
21
.1
61
.1
01
.0
51
.0
1.9
7.9
3.9
0.8
7.8
5.8
2.8
0.7
8.7
6.7
4.7
2.7
1Cl
"I·
11
58
.7
1.7
21
.5
51
.42
1.3
11
.2
31
.1
61
.1
01
.0
51
.0
0.9
6.9
3.8
9.8
6.8
4.8
1.7
9.7
7.7
5.7
3.7
1.6
9w
·1
20
8.
31
.8
21
.6
01
.4
51.
34
1.
24
1.
17
1.
10
1.
05
1.
00
.96
.92
.89
.86
.83
.80
.78
.76
.74
.72
.70
.68
·1
25
8.
01
.9
41.
67
1.5
01
.3
61
.2
61
.1
81
.1
11
.0
51
.0
0.9
6.9
2.8
8.8
5.8
2.7
9.7
7.7
5.7
3.7
1.6
9.6
7.1
30
7.
72
.1
01
.7
61
.5
51
.4
01
.2
91
.1
91
.1
21
.0
61
.0
0.9
6.9
1.8
8.8
5.8
2.7
9.7
6.7
4.7
2.7
0.6
8.6
6·
13
57
.4
2.3
01
.87
1.6
21
.44
1.3
11
.2
11
.1
31
.0
61
.0
1.9
6.9
1.8
8.8
4.8
1.7
8.7
6.7
3.7
1.6
9.6
7.6
6·
14
07
.1
2.
59
2.0
01.
69
1.
49
1.
35
1.2
31
.1
51
.0
71
.0
1.9
6.9
2.8
8.8
4.8
1.7
8.7
5.7
3.7
1.6
9.6
7.6
5·
14
56
.9
3.
01
2.
16
1.
78
1.5
41
.3
81
.2
61
.1
61
.0
91
.0
2.9
7.9
2.8
8.8
4.8
1.7
8.7
5.7
3.7
0.6
8.6
6.6
5·
15
06
.7
3.7
42
.35
1.8
81
.6
01
.4
21
.2
91
.1
81
.1
01
.0
3.9
7.9
2.8
8.8
4.8
1.7
8.7
5.7
2.7
0.6
8.6
6.6
41
55
6.
56
.59
2.6
11
.99
1.6
71
.46
1.3
11
.2
D1.
11
1.
04
.98
.93
.88
.84
.81
.77
.75
.72
.70
.67
.65
.64
.16
06
.3**
**2
.95
2.
12
1.7
41
.5
11.
34
1.
22
1.
13
1.
05
.99
.93
.88
.84
.81
.77
.74
.72
.69
.67
.65
.63
·1
65
6.
1**
**3
.49
2.2
71
.82
1.5
51
.38
1.2
51
.14
1.0
69
9.9
4.8
9.8
4.8
1.7
7.7
4.7
2.6
9.6
7.6
5.6
3·
17
05
.9**
**4
.73
2.4
41
.90
1.6
01
.41
1.2
71
.1
61
.0
71
.0
0.9
4.8
9.8
5.8
1.7
7.7
4.7
1.6
9.6
7.6
4.6
2·
17
55
.7
****
****
2.6
71
.99
1.6
51
.44
1.2
91
.17
1.0
81
.01
.95
.89
.85
.81
.77
.74
.71
.69
.66
.64
.62
.18
05
.6
****
****
2.9
72
.09
1.7
11
.4
71.
31
1.1
91
.0
91
.0
2.9
5.9
0.8
5.8
1.7
7.7
4.7
1.6
8.6
6.6
4.6
21
85
5.
4**
****
**3
.43
2.2
01
.76
1.5
11
.3
31
.2
11
.11
1.
03
.96
.90
.85
.81
.77
.74
.7
1.6
8.6
6.6
4.6
2.1
90
5.
3**
****
**4
.3
22
.3
31
.8
21
.5
41
.3
61
.2
21
.1
21
.0
3.9
6.9
0.8
5.8
1.7
7.7
4.7
1.6
8.6
6.6
3.6
1·
19
55
.1
****
****
****
2.4
81
.88
1.5
71
.38
1.2
31
.13
1.0
4.9
7.9
1.8
6.8
1.7
7.7
4.7
1.6
8.6
6.6
3.6
1.2
00
5.
0**
****
****
**2
.68
1.9
51
.61
1.
40
1.
25
1.
14
1.
05
.97
.91
.86
.81
.77
.74
.71
.68
.65
.63
.61
.20
54
.9
****
****
****
2.9
32
.02
1.6
41
.42
1.2
61
.14
1.0
5.9
8.9
1.8
6.8
1.7
7.7
4.7
1.6
8.6
5.6
3.6
1.2
10
4.8
****
****
****
3.
29
2.
10
1.
68
1.4
41
.2
71
.1
51
.0
6.9
8.9
2.8
6.8
1.7
7.7
4.7
1.6
8.6
5.6
3.6
0.2
15
4.
7**
****
****
**3
.89
2.
19
1.7
21
.4
61
.29
1.
16
1.
06
.98
.92
.86
.82
.77
.74
.70
.67
.65
.62
.60
.22
04
.5
****
****
****
5.3
62
.29
1.7
61
.48
1.3
01
.17
1.0
7.9
9.9
2.8
6.8
2.7
7.7
4.7
0.6
7.6
5.6
2.6
0.2
25
4.
4**
****
****
****
**2
.42
1.8
01
.50
1.3
11
.1
81
.0
7.9
9.9
2.8
6.8
1.7
7.7
3.7
0.6
7.6
4.6
2.6
0.2
30
4.3
****
****
****
****
2.5
61
.85
1.5
21
.32
1.1
81
.08
.99
.92
.86
.81
.77
.73
.70
.67
.64
.62
.60
.23
54
.3**
****
****
****
**2
.7
41.
90
1.5
41
.3
31.
19
1.
08
.99
.92
.86
.81
.77
.73
.70
.67
.64
.62
.59
.24
04
.2**
****
****
****
**2
.98
1.9
51
.57
1.3
51
.19
1.0
8.9
9.9
2.8
6.8
1.7
7.7
3.7
0.6
7.6
4.6
1.5
9.2
45
4.
1**
****
****
****
**3
.29
2.0
11
.59
1.3
61
.20
1.0
91
.00
.92
.86
.81
.77
.73
.69
.66
.64
.61
.59
.25
04
.0**
****
****
****
**3
.78
2.0
71
.62
1.3
71
.21
1.
09
1.
00
.92
.86
.81
.77
.73
.69
.66
.63
.61
.59
TAB
LE1
5e.
Wav
eu
eig
ht
am
pli
ficati
on
TC
Eq.
3)
for
d=
15m
ta
=3
0°.
0
0TH
ETA
ODO
UO1
5.0
30
.06
0.0
0.0
CURR
ENT
SPEE
DF
T-2
.50
-2
.25
-2
.00
-1
.75
-1
.50
-1
.25
-1
.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.
56
1.5
11
.47
1.4
31
.39
1.3
51
.31
1.
28
1.
25
1.
22
1.
19
1.
17
1.
14
1.
12
1.
10
1.
08
1.
05
1.
04
1.
02
1.
00
.98
.05
51
8.2
1.
54
1.
49
1.4
41
.4
01
.3
61
.3
21
.2
91
.2
51
.2
21.
19
1.
17
1.
14
1.
11
1.0
91
.07
1.0
51
.03
1.0
1.9
9.9
7.9
5.0
60
16
.71
.5
21.
47
1.
42
1.
37
1.
33
1.
29
1.
26
1.
22
1.
19
1.1
61
.1
41
.1
11
.09
1.0
61
.04
1.0
21
.00
.98
.96
.94
.93
.06
51
5.4
1.
50
1.
44
1.
39
1.3
51
.3
01
.2
61.
23
1.
19
1.
16
1.
13
1.
11
1.0
81
.05
1.0
31
.01
.99
.97
.95
.93
.91
.90
.07
01
4.3
1.
48
1.4
21
.3
71
.3
21
.2
71
.2
31
.2
01
.1
61
.1
31.
10
1.
07
1.
05
1.
02
1.
00
.98
.96
.94
.92
.90
.89
.87
.07
51
3.3
1.4
61
.40
1.3
41
.29
12
51
.21
1.
17
1.
13
1.
10
1.
07
1.
04
1.
02
.99
.97
.95
.93
.91
.89
.87
.86
.84
.08
01
2.5
1.
45
1.
38
1.
32
1.
27
1.
22
1.
18
1.
14
1.
11
1.
07
1.
04
1.
01
.99
.96
.94
.92
.90
.88
.86
.85
.83
.81
.08
51
1.
81
.4
41.
37
1.
30
1.2
51.
20
1.
16
1.
12
1.0
81
.0
51.
02
.99
.96
.94
.91
.89
.87
.85
.84
.82
.80
.79
.09
01
1.
11
.4
41
.3
61.
29
1.
23
1.1
81
.1
41
.0
91
.0
61
.0
2.9
9.9
6.9
4.9
1.8
9.8
7.8
5.8
3.8
1.8
0.7
8.7
6.0
95
10
.51.
45
1.3
61
.2
91
.2
21
.1
71
.1
21.
08
1.
04
1.0
0.9
7.9
4.9
2.8
9.8
7.8
5.8
3.8
1.7
9.7
7.7
6.7
4·
10
01
0.0
1.
47
1.3
71
.2
91
.2
21
.1
61
.1
11
.0
61
.0
2.9
9.9
6.9
3.9
0.8
7.8
5.8
3.8
1.7
9.7
7.7
6.7
4.7
3.1
05
9.
51
.5
01
.3
91.
30
1.
22
1.
16
1.
10
1.
06
1.
01
.98
.94
.91
.89
.86
.84
.81
.79
.78
.76
.74
.73
.71
.11
09
.1
1.5
51
.4
11
.3
11
.23
1.1
61
.10
1.0
51
.01
.97
.94
.90
.88
.85
.83
.80
.78
.76
.75
.73
.71
.70
0'\
.11
58
.7
1.
61
1.4
51.
34
1.2
41.
17
1.1
11.
05
1.
01
.97
.93
.90
.87
.84
.82
.79
.77
.76
.74
.72
.70
.69
~
·1
20
8.3
1.
69
1.
50
1.3
71
.2
71.
18
1.
11
1.
06
1.0
1.9
7.9
3.8
9.8
6.8
4.8
1.7
9.7
7.7
5.7
3.7
1.7
0.6
8·
12
58
.0
1.8
01.
57
1.
41
1.
29
1.
20
1.
13
1.0
71
.0
1.9
7.9
3.8
9.8
6.8
3.8
1.7
8.7
6.7
4.7
2.7
1.6
9.6
8·
13
07
.7
1.
94
1.6
51.
46
1.3
21.
22
1.1
41
.0
81.
02
.97
.93
.89
.86
.83
.81
.78
.76
.74
.72
.70
.69
.67
·1
35
7.
42
.1
21.
74
1.5
21
.3
61
.2
51
.1
61
.0
91
.0
3.9
8.9
3.9
0.8
6.8
3.8
0.7
8.7
6.7
4.7
2.7
0.6
8.6
7·
14
07
.1
2.3
61
.86
1.5
81
.41
1.
28
1.
18
1.
10
1.
04
.99
.94
.90
.86
.83
.80
.78
.76
.74
.72
.70
.68
.67
·1
45
6.9
2.7
12
.00
1.6
61
.46
1.3
11
.2
01.
12
1.
05
.99
.95
.90
.87
.83
.81
.78
.76
.73
.72
.70
.68
.66
.15
06
.7
3.
29
2.
17
1.7
51.
51
1.3
51
.23
1.1
41
.06
1.0
0.9
5.9
1.8
7.8
4.8
1.7
8.7
6.7
3.7
1.7
0.6
8.6
6·
15
56
.5
4.
81
2.
38
1.8
51.
57
1.
39
1.2
61.
It>1
.0
81
.0
1.9
6.9
1.8
8.8
4.8
1.7
8.7
6.7
3.7
1.7
0.6
8.6
61
60
6.
3**
**2
.67
1.9
71
.64
1.4
31
.29
1.1
81
.09
1.0
3.9
7.9
2.8
8.8
4.8
1.7
8.7
6.7
4.7
1.7
0.6
8.6
61
65
6.
1**
**3
.11
2.1
01
.7
01.
47
1.
32
1.2
01
.11
1.0
4.9
8.9
3.8
8.8
5.8
1.7
9.7
6.7
4.7
2.7
0.6
8.6
61
70
5.
9**
**3
.96
2.2
61
.78
1.5
21
.35
1.2
21
.13
1.0
5.9
9.9
3.8
9.8
5.8
2.7
9.7
6.7
4.7
2.7
0.6
8.6
61
75
5.
7**
****
**2
.45
1.8
61
.56
1.3
81
.24
1.1
41
.06
1.0
0.9
4.8
9.8
6.8
2.7
9.7
6.7
4.7
2.7
0.6
8.6
6·
18
05
.6
****
****
2.7
01
.95
1.6
11
.4
11.
26
1.
16
1.0
71.
00
.95
.90
.86
.82
.79
.76
.74
.72
.70
.68
.66
·1
85
5.
4**
****
**3
.07
2.0
51
.66
1.4
41
.28
1.1
71
.08
1.0
1.9
5.9
0.8
6.8
3.7
9.7
7.7
4.7
2.7
0.6
8.6
6·
19
05
.3
****
****
3.7
12
.16
1.7
21
.47
1.3
01
.19
1.0
91
.02
.96
.91
.87
.83
.80
.77
.74
.72
.70
.68
.66
·1
95
5.
1**
****
**5
.75
2.3
01
.77
1.5
01
.32
1.2
01
.10
1.0
3.9
7.9
1.8
7.8
3.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
00
5.
0**
****
****
**2
.46
1.8
31
.53
1.3
41
.21
1.1
11.
03
.97
.92
.87
.83
.80
.77
.74
.72
.70
.68
.66
.20
54
.9
****
****
****
2.6
71
.89
1.5
61
.36
1.2
21
.12
1.0
4.9
7.9
2.8
7.8
4.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
10
4.8
****
****
****
2.
96
1.
96
1.6
01.
38
1.
24
1.1
31.
05
.98
.92
.88
.84
.80
.77
.74
.72
.70
.68
.66
.21
54
.7
****
****
****
3.4
12
.04
1.6
31
.40
1.2
51
.14
1.0
5.9
8.9
3.8
8.8
4.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
20
4.
5**
****
****
**4
.31
2.1
31
.67
1.4
21
.26
1.1
41
.06
.99
.93
.88
.84
.80
.77
.74
.72
.70
.68
.66
.22
54
.4
****
****
****
8.
15
2.
24
1.7
01.
44
1.
27
1.1
51
.0
6.9
9.9
3.8
8.8
4.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
30
4.
3**
****
****
****
**2
.36
1.7
41
.46
1.2
81
.16
1.0
6.9
9.9
3.8
8.8
4.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
35
4.
3**
****
****
****
**2
.52
1.7
91
.48
1.2
91
.16
1.0
7.9
9.9
3.8
8.8
4.8
0.7
7.7
4.7
2.7
0.6
8.6
6.2
40
4.2
****
****
****
****
2.
71
1.8
31
.5
01
.3
01.
17
1.
07
.99
.93
.88
.84
.80
.77
.74
.72
.69
.67
.66
.24
54
.1
****
****
****
****
2.9
61
.89
1.5
21
.31
1.1
71.
07
1.
00
.93
.88
.84
.80
.77
.74
.71
.69
.67
.65
.25
04
.0
****
****
****
****
3.3
31
.94
1.5
41
.32
1.1
81
.08
1.0
0.9
3.8
8.8
4.8
0.7
7.7
4.7
1.6
9.6
7.6
5
TABL
ElS
i.W
ave
heig
ht
am
pli
ficati
on
TC
Eq.
3)
for
d=
15m
,e
=6
0°.
0
0T
HE
TA
OD
OU
O1
5.0
60
.06
0.0
O.
0
CU
RR
EN
TS
PE
ED
FT
-2.5
0-2
.25
-2.0
0-1
.75
-1.5
0-1
.25
-1.0
0-
75
-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.2
21
.18
1.
15
1.1
21
.09
1.0
61
.03
1.0
1.9
9.9
7.9
5.9
3.9
1.8
9.8
8.8
6.8
5.8
3.8
2.8
1.7
9·
05
51
8.
21
.20
1.1
61
.13
1.1
01
.07
1.0
41
.01
.99
.97
.95
.93
.91
.89
.87
.86
.84
.83
.81
.80
.79
.77
.06
01
6.7
1.
19
1.
15
1.
11
1.
08
1.
05
1.
02
.99
.97
.95
.93
.91
.89
.87
.85
.84
.82
.81
.79
.78
.77
.75
.06
51
5.4
1.
17
1.
13
1.
09
1.
06
1.0
31
.0
0.9
7.9
5.9
2.9
0.8
8.8
6.8
5.8
3.8
1.8
0.7
8.7
7.7
6.7
5.7
3·
07
01
4.
31
.15
1.1
11
.0
71
.0
41
.0
1.9
8.9
5.9
3.9
0.8
8.8
6.8
4.8
2.8
1.7
9.7
8.7
6.7
5.7
4.7
3.7
1.0
75
13
.31
.14
1.1
01
.06
1.0
2.9
9.9
6.9
3.9
0.8
8.8
6.8
4.8
2.8
0.7
9.7
7.7
6.7
4.7
3.7
2.7
1.6
9.0
80
12
.51
.13
1.0
81
.04
1.0
0.9
7.9
4.9
1.8
8.8
6.8
4.8
2.8
0.7
8.7
7.7
5.7
4.7
2.7
1.7
0.6
9.6
8·
08
51
1.
81.
13
1.
07
1.
03
.99
.95
.92
.89
.87
.84
.82
.80
.78
.77
.75
.73
.72
.71
.69
.68
.67
.66
·0
90
11
.1
1.
13
1.
07
1.
02
.98
.94
.91
.88
.85
.83
.81
.79
.77
.75
.73
.72
.71
.69
.68
.67
.66
.65
.09
51
0.5
1.
13
1.
07
1.
02
.97
.93
.90
.87
.84
.82
.79
.77
.76
.74
.72
.71
.69
.68
.67
.66
.65
.63
10
01
0.0
1.
15
1.
08
1.
02
.97
.93
.89
.86
.83
.81
.79
.77
.75
.73
.71
.70
.68
.67
.66
.65
.64
.63
10
59
.5
1.
17
1.
09
1.
03
.98
.9:
3.8
9.8
6.8
3.
81
.78
.76
.74
.72
.71
.69
.68
.67
.65
.64
.63
.62
11
09
.1
1.
20
1.
11
1.
04
.98
.94
.90
.86
.83
.81
.78
.76
.74
.72
.71
.69
.68
.66
.65
.64
.63
.62
0\
11
58
.7
1.
25
1.
14
1.
06
1.
00
.95
.90
.87
.84
.81
.78
.76
.74
.72
.71
.69
.68
.66
.65
.64
.63
.62
U1
·1
20
8.
31
.3
01
.1
81
.0
91
.0
2.9
6.9
1.8
8.8
4.8
1.7
9.7
7.7
5.7
3.7
1.6
9.6
8.6
7.6
5.6
4.6
3.6
2·
12
58
.0
1.
38
1.
23
1.
12
1.0
4.9
8.9
3.8
9.8
5.8
2.8
0.7
7.7
5.7
3.7
2.7
0.6
9.6
7.6
6.6
5.6
4.6
3.1
30
7.
71
.4
71
.2
81
.1
61
.0
71
.0
0.9
5.9
0.8
6.8
3.8
0.7
8.7
6.7
4.7
2.7
1.6
9.6
8.6
7.6
5.6
4.6
3·
13
57
.4
1.
59
1.
35
1.2
01.
10
1.
02
.96
.92
.88
.84
.82
.79
.77
.75
.73
.71
.70
.69
.67
.66
.65
.64
14
07
.1
1.
74
1.
43
1.
25
1.
13
1.
05
.99
.93
.89
.86
.83
.80
.78
.76
.74
.72
.7
1.6
9.6
8.6
7.6
6.6
51
45
6.
91
.9
61.
52
13
11.
17
1.
08
1.
01
.95
.91
.87
.84
.81
.79
.77
.75
.73
.72
.70
.69
.68
.67
.65
15
06
.7
2.2
81
.6
41
.3
71.
22
1.1
11
.0
3.9
7.9
3.8
9.8
6.8
3.8
0.7
8.7
6.7
5.7
3.7
1.7
0.6
9.6
7.6
6·
15
56
.5
2.
87
1.
78
1.4
51
.2
61
.1
41
.0
61.
QO
.94
.90
.87
.84
.82
.79
.77
.76
.74
.72
.71
.70
.68
.67
·1
60
6.
37
.1
61
.97
1.
53
1.
31
1.
18
1.
09
1.
02
.96
.92
.89
.86
.83
.81
.79
.77
.75
.73
.72
.71
.69
.68
·1
65
6.
1**
**2
.2
11
.6
21.
36
1.2
11.
11
1.
04
.98
.94
.90
.87
.84
.82
.80
.78
.76
.75
.73
.71
.70
.69
·1
70
5.
9**
**2
.6
11.
73
1.
42
1.
25
1.
14
1.
06
1.0
0.9
5.9
2.8
8.8
6.8
3.8
1.7
9.7
7.7
5.7
4.7
2.7
1.6
9·
17
55
.7
****
****
1.8
51
.48
1.2
91
.17
1.0
81
.02
.97
.93
.90
.87
.84
.82
.80
.78
.76
.75
.73
.71
.70
·1
80
5.6
****
****
2.0
01
.54
1.3
21
.19
1.1
01
.04
.98
.94
.91
.88
.86
.83
.81
.79
.77
.75
.74
.72
.70
·1
85
5.
4**
****
**2
.2
11
.6
11
.36
1.2
21
.12
1.0
51
.00
.96
.92
.89
.87
.84
.82
.80
.78
.76
.74
.72
.7
1·
19
05
.3
****
****
2.5
21
.68
1.4
01
.24
1.1
41
.07
1.0
1.9
7.9
3.9
0.8
8.8
5.8
3.8
1.7
9.7
7.7
5.7
3.7
1·
19
55
.1
*·It*
***
**3
.1
11
.7
71
.4
41
.2
71.
16
1.
08
1.0
2.9
8.9
4.9
1.8
8.8
6.8
3.8
1.7
9.7
7.7
5.7
3.7
1.2
00
5.
0**
It*
****
7.
13
1.
87
1.
48
1.
29
1.
17
1.
09
1.
03
.99
.95
.92
.89
.87
.84
.82
.79
.77
.75
.73
.71
.20
54
.9
****
****
****
2.0
01
.52
1.3
11
19
1.1
11
.0
41
.0
0.9
6.9
3.9
0.8
7.8
5.8
2.8
0.7
7.7
5.7
3.
71
.21
04
.8**
****
****
**2
.16
1.
57
1.
34
1.
20
1.
12
1.0
51
.0
1.9
7.9
3.9
0.8
8.8
5.8
2.8
0.7
8.7
5.7
3.7
1.2
15
4.
7**
****
****
**2
.39
1.6
21
.36
1.2
21
.13
1.0
61
.01
.97
.94
.9
1.8
8.3
5.8
3.8
0.7
8.7
5.7
3.7
1.2
20
4.
5**
****
****
**2
.76
1.6
81
.38
1.2
31
.13
1.0
71
.02
.98
.94
.91
.88
.85
.83
.80
.78
.75
.73
.71
.22
54
.4
****
****
****
****
1.7
41
.41
12
41
.1
41.
07
1.0
2.9
8.9
5.9
2.8
9.8
6.8
3.8
0.7
7.7
5.7
3.7
0.2
30
4.
3**
****
****
****
**1
.82
1.4
31
.26
1.1
51
.08
1.0
3.9
9.9
5.9
2.8
9.8
6.8
3.8
0.7
7.7
5.7
2.7
0.2
35
4.
3**
****
****
****
**1
.91
1.4
61
.27
1.1
61
.08
1.0
3.9
9.9
5.9
2.8
9.8
6.8
3.8
0.7
7.7
5.7
2.7
0.2
40
4.
2**
****
****
****
**2
.02
1.4
91
.28
1.1
61
.09
1.0
3.9
9.9
5.9
2.8
9.8
6.8
3.8
0.7
7.7
4.7
2.6
9.2
45
4.
1**
****
****
****
**2
.1
61
.52
1.2
91
.17
1.0
91
.04
.99
.96
.92
.89
.86
.82
.79
.77
.74
.7
1.6
9.2
50
4.
0**
****
****
****
**2
.35
1.5
61
.31
1.1
81
.1
01.
04
1.
00
.96
.92
.89
.85
.82
.79
.76
.74
.71
.69
TAB
LE15
g.W
ave
heig
ht
am
pli
ficati
on
T(E
q.
3)
for
d=
20m
,e
=0
°.0
DT
HE
TAO
DO
UO
20
.0
0.0
60
.0o
0
CU
RR
EN
TS
PE
ED
FT
-2.5
0-2
.25
-2.0
0-1
.75
-1.5
0-1
.25
-1.0
0-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.5
21
.48
1.4
41
.40
1.3
61
.33
1.3
01
.27
1.2
41
.21
1.1
91
.16
1.1
41
.12
1.1
01
.08
1.0
61
.04
1.0
21
.00
.98
.05
51
8.2
1.
51
1.4
61
.42
1.3
81
.34
1.3
11
.2
71
.2
41
.2
11.
19
1.1
61
.1
41.
11
1.0
91
.07
1.0
51
.03
1.0
1.9
9.9
8.9
6.0
60
16
.71
.4
91.
44
1.4
01
.3
61
.3
21
.2
81
.2
51
.2
21.
19
1.
16
1.
13
1.
11
1.0
91
.06
1.0
41
.02
1.0
0.9
8.9
6.9
5.9
3.0
65
15
.41
.4
81.
43
1.
38
1.
33
1.
29
1.
26
1.2
21.
19
1.1
61
.1
31
.1
11
.08
1.0
61
.03
1.0
1.9
9.9
7.9
5.9
4.9
2.9
0.0
70
14
.31
.47
1.4
11
.3
61
.3
11
.2
71
.2
31.
20
1.
16
1.1
31
.1
01.
08
1.
05
1.
03
1.
00
.98
.96
.94
.92
.91
.89
.87
.07
51
3.3
1.4
61
.40
1.3
41
.29
1.2
51
.21
1.
17
1.1
41.
11
1.0
81
.05
1.0
21
.00
.98
.95
.93
.91
.90
.88
.86
.85
.08
01
2.5
1.4
51.
39
1.3
31
.2
81
.2
31
.1
91.
15
1.11
1.0
81
.05
1.0
21
.00
.97
.95
.93
.91
.89
.87
.85
.83
.82
.08
51
1.8
1.4
61
.38
1.3
21
.26
1.2
11
.1
71.
13
1.0
91
.0
61
.0
31
.0
0.9
7.9
5.9
2.9
0.8
8.8
6.8
4.8
2.8
1.7
9.0
90
11
.1
1.4
71.
39
1.
32
1.
26
1.2
01.
15
1.
111
.0
71
.0
41
.0
1.9
8.9
5.9
2.9
0.8
8.8
6.8
4.8
2.8
0.7
8.7
7.0
95
10
.51.
49
1.4
01
.3
21
.2
51.
20
1.1
41
.1
01
.0
61
.0
2.9
9.9
6.9
3.9
0.8
8.8
6.8
4.8
2.8
0.7
8.7
6.7
5·
10
01
0.0
1.5
31
.4
21
.3
31.
26
1.
20
1.
14
1.0
91.
05
1.
01
.98
.94
.91
.89
.86
.84
.82
.80
.78
.76
.74
.73
·1
05
9.
51
.5
81
.4
61.
35
1.2
71
.2
01
.1
41
.0
91
.0
41.
00
.97
.93
.90
.87
.85
.83
.80
.78
.76
.75
.73
.71
.11
09
.1
1.6
51
.50
1.3
81
.29
1.2
11
.15
1.0
91
.04
1.0
0.9
6.9
3.8
9.8
6.8
4.8
1.7
9.7
7.7
5.7
3.7
2.7
0e-
.11
58
.7
1.
74
1.
56
1.4
21.
32
1.
23
1.
16
1.
10
1.0
51
.0
0.9
6.9
2.8
9.8
6.8
3.8
1.7
8.7
6.7
4.7
2.7
0.6
9e-
.12
08
.3
1.8
51
.63
1.4
71
.35
1.2
51
.17
1.1
11
.0
51
.0
0.9
6.9
2.8
9.8
5.8
3.8
0.7
8.7
5.7
3.7
1.7
0.6
8·
12
58
.01
.9
91.
71
1.5
31
.3
91.
28
1.1
91
.1
21
.0
61
.0
1.9
6.9
2.8
8.8
5.8
2.8
0.7
7.7
5.7
3.7
1.6
9.6
7.1
30
7.
72
.1
61
.8
11
.5
91
.4
31.
31
1.
22
1.1
41
.0
71
.0
2.9
7.9
2.8
9.8
5.8
2.7
9.7
7.7
4.7
2.7
0.6
8.6
7·
13
57
.4
2.
37
1.9
31
.6
61
.4
81
.3
51
.2
41
.1
61.
09
1.
03
.97
.93
.89
.85
.82
.79
.77
.74
.72
.70
.68
.66
.14
07
.1
2.6
52
.06
1.7
41
.54
1.3
81
.27
1.1
81
.10
1.0
4.9
8.9
3.8
9.8
5.8
2.7
9.7
6.7
4.7
2.6
9.6
7.6
6·
14
56
.93
.06
2.2
21
.83
1.5
91
.42
1.3
01
.20
1.1
21
.05
.99
.94
.90
.86
.82
.79
.76
.74
.71
.69
.67
.65
15
06
.7
3.
78
2.
40
1.
93
1.
65
1.
46
1.
33
1.
22
1.1
31
.0
61
.0
0.9
5.9
0.8
6.8
2.7
9.7
6.7
4.7
1.6
9.6
7.6
5·
15
56
.5
6.6
02
.64
2.0
31
.71
1.5
01.
35
1.2.
41
.1
51
.07
1.0
1.9
5.9
0.8
6.8
2.7
9.7
6.7
3.7
1.6
9.6
7.6
5·
16
06
.3
****
2.9
72
.15
1.
78
1.
55
1.3
81.
26
1.1
61.
08
1.
02
.96
.91
.87
.83
.79
.76
.73
.71
.69
.66
.64
·1
65
6.
1**
**3
.51
2.2
91
.85
1.5
91
.41
1.
28
1.
18
1.
09
1.0
2.9
6.9
1.8
7.8
3.7
9.7
6.7
3.7
1.6
8.6
6.6
4·
17
05
.9
****
4.7
32
.46
1.9
21
.63
1.4
41
.30
1.1
91
.10
1.0
3.9
7.9
2.8
7.8
3.7
9.7
6.7
3.7
1.6
8.6
6.6
4·
17
55
.7
****
****
2.6
82
.01
1.
68
1.4
71
.3
21
.2
01.
11
1.0
4.9
7.9
2.8
7.8
3.7
9.7
6.7
3.7
1.6
8.6
6.6
4.1
80
5.6
****
****
2.9
82
.10
1.
72
1.5
01
.3
41.
22
1.
12
1.
04
.98
.92
.87
.83
.79
.76
.73
.70
.68
.66
.64
·1
85
5.4
****
****
3.4
32
.21
1.7
71
.5
21.
35
1.
23
1.
13
1.0
5.9
8.9
3.8
8.8
3.8
0.7
6.7
3.7
0.6
8.6
5.6
3.1
90
5.3
****
****
4.
32
2.
33
1.
83
1.
55
1.3
71
.2
41
.1
41
.0
6.9
9.9
3.8
8.8
3.7
9.7
6.7
3.7
0.6
8.6
5.6
3·
19
55
.1
****
****
****
2.
49
1.
89
1.
58
1.3
91.
25
1.
15
1.
06
.99
.93
.88
.83
.79
.76
.73
.70
.67
.65
.63
.20
05
.0**
****
****
**2
.68
1.9
51
.62
1.4
11
.2
61
.1
51
.0
6.9
9.9
3.8
8.8
3.7
9.7
6.7
3.7
0.6
7.6
5.6
3.2
05
4.9
****
****
****
2.9
32
.02
1.6
51
.43
1.2
71
.16
1.0
7.9
9.9
3.8
8.8
3.7
9.7
6.7
2.7
0.6
7.6
5.6
2.2
10
4.8
****
****
****
3.2
92
.10
1.6
81
.44
1.2
81
.16
1.0
71
.00
.93
.88
.83
.79
.75
.72
.69
.67
.64
.62
.21
54
.7
****
****
****
3.
89
2.
19
1.
72
1.
46
1.2
91
.1
71.
07
1.
00
.93
.88
.83
.79
.75
.72
.69
.66
.64
.62
.22
04
.5
****
****
****
5.3
62
.29
1.7
61
.48
1.3
01
.18
1.0
81
.00
.93
.88
.83
.79
.75
.72
.69
.66
.64
.62
.22
54
.4
•••*
****
****
****
2.4
21
.80
1.5
01
.31
1.
18
1.
08
1.
00
.93
.88
.83
.79
.75
.72
.69
.66
.64
.61
.23
04
.3
****
*i1;
;M.....*
*.**
2.
56
1.
85
1.
52
1.
32
1.1
91.
08
1.
00
.93
.87
.83
.78
.75
.71
.68
.66
.63
.61
.23
54
.3
****
****
****
****
2.7
41
.90
1.5
51
.34
1.1
91
.08
1.0
0.9
3.8
7.8
2.7
8.7
4.7
1.6
8.6
5.6
3.6
1.2
40
4.
2**
****
****
****
**2
.98
1.9
51
.57
1.3
51
.20
1.0
91
.00
.93
.87
.82
.78
.74
.71
.68
.65
.63
.60
.24
54
.1
****
****
****
****
3.2
92
.01
1.5
91
.36
1.2
01
.09
1.0
0.9
3.8
7.8
2.7
8.7
4.7
0.6
7.6
5.6
2.6
0.2
50
4.0
****
****
****
****
3.7
82
.07
1.6
21
.37
1.2
11
.0
91
.0
0.9
3.8
7.8
2.7
7.7
3.7
0.6
7.6
4.6
2.6
0
TAB
LEIS
h.
Wav
eh
eig
ht
am
pli
ficati
on
T(E
q.
3)fo
rd
=20
m,
e=
30
°.0
0TH
ETA
OD
OU
O2
0.0
30
.06
0.0
0.0
CU
RR
ENT
SPE
ED
FT
-2
.50
-2
.25
-2
.00
-1
.75
-1
.50
-1
.25
-1
.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.4
41
.40
1.3
61
.32
1.2
91
.26
1.2
31
.21
1.
18
1.
16
1.
13
1.1
11
.09
1.0
71
.05
1.0
31
.01
1.
00
.98
.97
.95
.05
51
8.2
1.4
21
.38
1.3
41
.31
1.
27
1.
24
1.
21
1.1
81
.16
1.1
31
.11
1.0
91
.07
1.0
51
.03
1.0
1.9
9.9
7.9
6.9
4.9
3.0
60
16
.7
1.
41
1.
36
1.3
21
.2
91
.2
51
.2
21
.1
91
.1
61
.1
31
.1
11
.08
1.0
61
.04
1.0
21
.00
.98
.96
.95
.93
.92
.90
.06
51
5.4
1.
40
1.
35
1.3
11
.2
71
.2
31
.2
01
.1
61
.1
41
.1
11
.08
1.0
61
.04
1.0
1.9
9.9
7.9
6.9
4.9
2.9
1.8
9.8
8.0
70
14
.31
.38
1.3
31
.29
1.2
51
.21
1.
17
1.
14
1.
11
1.0
81
.06
1.0
31
.01
.99
.97
.95
.93
.91
.90
.88
.86
.85
.07
51
3.
31
.3
81
.3
21
.2
71
.2
31
.1
91
.1
51.
12
1.
09
1.
06
1.
03
1.
01
.98
.96
.94
.92
.90
.89
.87
.85
.84
.82
.08
01
2.5
1.3
71
.3
11
.2
61.
21
1.1
71
.13
1.1
01
.07
1.0
41
.01
.98
.96
.94
.92
.90
.88
.86
.84
.83
.81
.80
.08
51
1.
81.
38
1.
31
1.
25
1.
20
1.
16
1.
12
1.
08
1.
05
1.
02
.99
.96
.94
.92
.89
.87
.86
.84
.82
.81
.79
.78
.09
01
1.
11
.39
1.
31
1.2
51
.19
1.1
51
.10
1.0
61
.03
1.0
0.9
7.9
4.9
2.9
0.8
7.8
5.8
4.8
2.8
0.7
9.7
7.7
6.0
95
10
.51.
41
1.
32
1.
25
1.
19
1.
14
1.
09
1.
05
1.
02
.98
.95
.93
.90
.88
.86
.84
.82
.80
.78
.77
.75
.74
10
01
0.
01
.4
41
.3
41
.2
61
.2
01
.1
41
.0
91
.0
51
.0
1.9
8.9
4.9
2.8
9.8
7.8
4.8
2.8
0.7
9.7
7.7
5.7
4.7
21
05
9.
51
.49
1.3
71
.28
1.2
11.
15
1.
09
1.
05
1.
01
.97
.94
.91
.88
.86
.83
.81
.79
.77
.76
.74
.73
.7
11
10
9.
11.
55
1.
41
1.
31
1.
23
1.
16
1.
10
1.
05
1.
01
.97
.93
.90
.87
.85
.83
.80
.78
.77
.75
.73
.72
.70
0\
11
58
.7
1.6
31
.4
71
.3
51
.2
51
.1
81
.1
11
.0
61
.0
1.9
7.9
3.9
0.8
7.8
5.8
2.8
0.7
8.7
6.7
4.7
3.7
1.7
0-.
.J1
20
8.
31
.7
31
.5
31.
39
1.2
81
.2
01
.1
31
.0
71
.0
2.9
8.9
4.9
0.8
7.8
4.8
2.8
0.7
8.7
6.7
4.7
2.7
1.6
91
25
8.
01.
85
1.
61
1.
44
1.3
21
.2
21
.1
51.
08
1.
03
.98
.94
.91
.87
.85
.82
.80
.77
.75
.74
.72
.70
.69
.13
07
.7
2.
00
1.
70
1.
50
1.
36
1.
25
1.
17
1.1
01
.0
4.9
9.9
5.9
1.8
8.8
5.8
2.8
0.7
7.7
5.7
3.7
2.7
0.6
9·
13
57
.4
2.1
91
.80
1.5
71
.41
1.
29
1.
19
1.
12
1.
06
1.
00
.96
.92
.88
.85
.82
.80
.77
.75
.73
.72
.70
.68
.14
07
.1
2.
43
1.
92
1.
64
1.
46
1.3
21
.2
21
.1
41
.0
71
.0
1.9
7.9
2.8
9.8
5.8
3.8
0.7
8.7
5.7
3.7
2.7
0.6
8·
14
56
.92
.77
2.0
61
.72
1.5
11.
36
1.
25
1.
16
1.
09
1.
03
.97
.93
.89
.86
.83
.80
.78
.76
.74
.72
.70
.68
.15
06
.7
3.
33
2.2
21
.8
11
.5
61
.4
01
.2
71
.1
81
.1
01
.0
4.9
8.9
4.9
0.8
6.8
3.8
0.7
8.7
6.7
4.7
2.7
0.6
8·
15
56
.5
4.
83
2.
43
1.
90
1.
62
1.
43
1.
30
1.
20
1.1
21
.0
5.9
9.9
5.9
0.8
7.8
4.8
1.7
8.7
6.7
4.7
2.7
0.6
8.1
60
6.
3**
**2
.70
2.0
11
.6
81
.4
71
.3
31
.2
21
.1
31
.0
61.
00
.95
.91
.87
.84
.81
.78
.76
.74
.72
.70
.68
·1
65
6.
1**
**3
.1
32
.1
31
.7
41
.5
11
.3
61
.2
41
.1
51
.0
71
.0
1.9
6.9
2.8
8.8
4.8
1.7
9.7
6.7
4.7
2.7
0.6
9.1
70
5.
9**
**3
.97
2.2
81
.81
1.
55
1.
38
1.
26
1.
16
1.
08
1.0
2.9
7.9
2.8
8.8
5.8
2.7
9.7
6.7
4.7
2.7
0.6
9·
17
55
.7
****
8.1
02
.46
1.8
81
.59
1.4
1I.
27
1.
17
1.
09
1.
03
.97
.93
.88
.85
.82
.79
.76
.74
.72
.70
.69
18
05
.6
****
****
2.
71
1.
96
1.
63
1.
43
1.
29
1.
19
1.
10
1.
03
.98
.93
.89
.85
.82
.79
.77
.74
.72
.70
.69
·1
85
5.
4**
****
**3
.07
2.0
61
.68
1.4
61
.31
1.2
01
.1
11
.0
4.9
8.9
3.8
9.8
5.8
2.7
9.7
7.7
4.7
2.7
0.6
9·
19
05
.3
****
****
3.7
12
.17
1.7
31
.49
1.3
21
.21
1.
12
1.
05
.99
.94
.89
.85
.82
.79
.77
.74
.72
.70
.68
.19
55
.1
****
****
5.7
52
.30
1.7
81
.51
1.
34
1.
22
1.
12
1.
05
.99
.94
.89
.86
.82
.79
.77
.74
.72
.70
.68
.20
05
.0
****
****
****
2.4
61
.83
1.5
41
.36
1.2
31
.13
1.0
5.9
9.9
4.8
9.8
6.8
2.7
9.7
7.7
4.7
2.7
0.6
8.2
05
4.
9**
****
****
**2
.67
1.
90
1.
57
1.
37
1.
24
1.
14
1.
06
.99
.94
.89
.86
.82
.79
.76
.74
.72
.70
.68
.21
04
.8**
****
****
**2
.9
61
.9
71
.6
01
.3
91
.2
51
.1
41
.0
6.9
9.9
4.8
9.8
5.8
2.7
9.7
6.7
4.7
2.7
0.6
8.2
15
4.
7**
****
****
**3
.41
2.0
51
.63
1.4
11.
26
1.
15
1.
06
1.
00
.94
.89
.85
.82
.79
.76
.74
.72
.70
.68
.22
04
.5
****
****
****
4.3
12
.14
1.
67
1.
42
1.
27
1.
15
1.
07
1.
00
.94
.89
.85
.82
.79
.76
.74
.71
.69
.68
.22
54
.4
****
****
****
8.
15
2.
24
1.
70
1.
44
1.
27
1.
16
1.
07
1.0
0.9
4.8
9.8
5.8
2.7
9.7
6.7
3.7
1.6
9.6
7.2
30
4.
3**
****
****
****
**2
.3
61
.7
41
.4
61
.2
81.
16
1.
07
1.0
0.9
4.8
9.8
5.8
1.7
8.7
6.7
3.7
1.6
9.6
7.2
35
4.
3**
****
****
****
**2
.52
1.7
91
.48
1.2
91
.17
1.0
71
.00
.94
.89
.85
.81
.78
.75
.73
.71
.69
.67
.24
04
.2
****
****
****
****
2.
71
1.
84
1.5
01
.3
01
.1
71
.0
71
.0
0.9
4.8
9.8
5.8
1.7
8.7
5.7
3.7
0.6
8.6
7.2
45
4.
1**
****
****
****
**2
.96
1.8
91
.52
1.3
11.
18
1.0
81.
00
.94
.89
.84
.81
.78
.75
.72
.70
.68
.66
.25
04
.0
****
****
****
****
3.3
31
.94
1.5
41
.32
1.1
81
.08
1.0
0.9
4.8
9.8
4.8
1.7
7.7
5.7
2.7
0.6
8.6
6
TABL
ElS
i.W
ave
heig
ht
am
pli
ficati
on
T(E
q.3
)fo
rd
=20
ffi,
e=
60
°.0
0TH
ETA
OD
OUO
20
.06
0.0
60
.00
.0
CU
RR
ENT
SP
EE
DF
T-2
.50
-2
.25
-2
.00
-1
.75
-1
.50
-1
.25
-1
.00
-.7
5-.5
0-.2
50
.00
.25
.50
.75
1.0
01
.25
1.5
01
.75
2.0
02
.25
2.5
0
.05
02
0.0
1.
13
1.
10
1.
08
1.
05
1.0
31
.0
1.9
9.9
7.9
5.9
3.9
1.9
0.8
8.8
7.8
5.8
4.8
3.8
2.8
1.7
9.7
8.0
55
18
.21.
12
1.
09
1.
06
1.
04
1.0
1.9
9.9
7.9
5.9
3.9
1.9
0.8
8.8
7.8
5.8
4.8
2.8
1.8
0.7
9.7
8.7
7.0
60
16
.71
.1
11
.08
1.0
51
.02
1.0
0.9
8.9
5.9
3.9
1.9
0.8
8.8
6.8
5.8
3.8
2.8
1.7
9.7
8.7
7.7
6.7
5:
06
51
5.4
1.
10
1.
07
1.
04
1.0
1.9
8.9
6.9
4.9
2.9
0.8
8.8
6.8
5.8
3.8
2.8
0.7
9.7
8.7
7.7
5.7
4.7
3.0
70
14
.31
.09
1.0
61
.03
1.0
0.9
7.9
4.9
2.9
0.8
8.8
6.8
4.8
3.8
1.8
0.7
8.7
7.7
6.7
5.7
4.7
3.7
2.0
75
13
.31
.0
91
.0
51.
01
.98
.96
.93
.91
.88
.86
.84
.83
.81
.80
.78
.77
.75
.74
.73
.72
.71
.70
.08
01
2.5
1.
09
1.
04
1.
01
.97
.94
.92
.89
.87
.85
.83
.81
.80
.78
.77
.75
.74
.73
.72
.70
.69
.68
·0
85
11
.8
1.
09
1.0
41.
00
.97
.94
.91
.88
.86
.84
.82
.80
.78
.77
.75
.74
.73
.71
.70
.69
.68
.67
.09
01
1.
11
.1
01.
05
1.0
0.9
6.9
3.9
0.8
7.8
5.8
3.8
1.7
9.7
7.7
6.7
4.7
3.7
2.7
0.6
9.6
8.6
7.6
6.0
95
10
.51.
11
1.
06
1.
01
.97
.93
.90
.87
.84
.82
.80
.78
.77
.75
.73
.72
.71
.70
.68
.67
.66
.65
10
01
0.0
1.
14
1.
07
1.0
2.9
7.9
3.9
0.8
7.8
4.8
2.8
0.7
8.7
6.7
5.7
3.7
2.7
0.6
9.6
8.6
7.6
6.6
51
05
95
1.
17
1.
10
1.0
3.9
8.9
4.9
1.8
8.8
5.8
2.8
0.7
8.7
6.7
5.7
3.7
2.7
0.6
9.6
8.6
7.6
6.6
51
10
9.
11.
22
1.1
31.
06
1.0
0.9
6.9
2.8
8.8
5.8
3.8
1.7
9.7
7.7
5.7
3.7
2.7
1.6
9.6
8.6
7.6
6.6
50
'\.1
15
8.
71
.2
71
.1
71
.0
91.
03
.97
.93
.90
.87
.84
.81
.79
.77
.76
.74
.73
.71
.70
.69
.68
.67
.66
(Xl
·1
20
8.3
1.
34
1.2
21.
12
1.0
51
.0
0.9
5.9
1.8
8.8
5.8
3.8
0.7
8.7
7.7
5.7
3.7
2.7
1.7
0.6
8.6
7.6
6·
12
58
.0
1.4
31
.2
71.
16
1.0
81
.0
2.9
7.9
3.8
9.8
7.8
4.8
2.8
0.7
8.7
6.7
4.7
3.7
2.7
0.6
9.6
8.6
7·
13
07
.7
1.
54
1.
34
1.2
11
.1
21
.0
5.9
9.9
5.9
1.8
8.8
5.8
3.8
1.7
9.7
7.7
6.7
4.7
3.7
2.7
0.6
9.6
8·
13
57
.41
.6
61
.4
11
.2
61
.1
61
.0
81.
02
.97
.93
.90
.87
.85
.82
.80
.79
.77
.75
.74
.73
.71
.70
.69
·1
40
7.
11
.8
21.
50
1.3
21
.2
01
.1
11
.0
5.9
9.9
5.9
2.8
9.8
6.8
4.8
2.8
0.7
8.7
7.7
5.7
4.7
2.7
1.7
0·
14
56
.92
03
1.6
01
.38
1.2
41
.14
1.0
71
.02
.97
.93
.90
.88
.85
.83
.81
.80
.78
.76
.75
.74
.72
.71
·1
50
6.
72
.33
1.7
11.
44
1.2
81.
18
1.1
01
.0
4.9
9.9
5.9
2.8
9.8
7.8
5.8
3.8
1.7
9.7
7.7
6.7
4.7
3.7
21
55
6.
52
.9
01
.8
41
.5
11.
33
1.2
11
.1
21
.O
b1.
01
.97
.94
.91
.88
.86
.84
.82
.80
.79
.77
.75
.74
.72
·1
60
6.
37
.1
32
.01
1.5
81
.37
1.2
41
.15
1.0
81
.03
.99
.95
.92
.90
.87
.85
.83
.81
.79
.78
.76
.75
.73
·1
65
6.
1**
**2
.2
41
66
1.
42
1.
27
1.
17
1.
10
1.
04
1.
00
.96
.93
.91
.88
.86
.84
.82
.80
.78
.77
.75
.73
17
05
.9**
**2
.63
1.
76
1.4
61.
30
1.
19
1.1
21.
06
1.
01
.98
.95
.92
.89
.87
.85
.83
.81
.79
.77
.75
.74
17
55
.7
****
****
1.8
71
.51
1.
33
1.2
11
.13
1.0
71
.03
.99
.96
.93
.90
.88
.86
.84
.81
.79
.78
.76
.74
18
05
.6
****
****
2.
02
1.
57
1.
36
1.
23
1.
15
1.
08
1.
04
1.0
0.9
6.9
4.9
1.8
9.8
6.8
4.8
2.8
0.7
8.7
6.7
41
85
5.
4**
****
**2
.22
1.6
31
.39
1.2
51
.16
1.1
01
.05
1.0
1.9
7.9
4.9
2.8
9.8
7.8
4.8
2.8
0.7
8.7
6.7
4·
19
05
.3**
****
**2
.52
1.
70
1.4
21.
27
1.
17
1.
10
1.
05
1.0
1.9
8.9
5.9
2.8
9.8
7.8
5.8
2.8
0.7
8.7
6.7
4·
19
55
.1
****
****
3.
111.
78
1.4
51
.2
91
.1
81.
11
1.
06
1.0
2.9
8.9
5.9
2.9
0.8
7.8
5.8
2.8
0.7
8.7
5.7
3.2
00
5.
0**
****
**7
.13
1.8
81
.49
1~1
1~(\
tt?
t0
71
.02
.99
.96
.93
.90
.87
.85
.82
.80
.77
.75
.73
.20
54
.9
****
****
****
2.0
01
.53
1.3
21
.21
1.
13
1.
07
1.
03
.99
.96
.93
.90
.87
.85
.82
.80
.77
.75
.73
.21
04
.8**
****
****
**2
.16
1.5
71
.34
1.2
21
.13
1.0
71
.03
.99
.96
.93
.90
.87
.85
.82
.79
.77
.75
.72
.21
54
.7
*-Il.
****
****
**2
.3
91
.6
21.
36
1.
23
1.1
41
.0
81.
03
.99
.96
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.87
.84
.82
.79
.77
.74
.72
.22
04
.5
****
****
****
2.7
61
.68
1.3
91
.24
1.1
51
.08
1.0
31
.00
.96
.93
.90
.87
.84
.81
.79
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.74
.7;:
'.2
25
4.
4**
****
****
****
**1
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1.4
11
.2
51.
15
1.0
91
.0
41.
00
.96
.93
.90
.87
.84
.81
.78
.76
.73
.71
.23
04
.:J
*11'*
11'
II•
If*
****
****
1.8
21.
43
1.2
61
.1
61
.0
91.
04
1.0
0.9
6.9
3.9
0.8
7.8
4.8
1.7
8.7
5.7
3.7
1.2
35
4.
3**
****
****
****
**1
.91
1.
46
1.
27
1.1
61
.0
91
.0
41
.0
0.9
6.9
3.9
0.8
7.8
4.8
1.7
8.7
5.7
3.7
0.2
40
4.2
****
****
****
****
2.
02
1.
49
1.
28
1.1
71
.0
91
.0
41
.0
0.9
6.9
3.9
0.8
6.8
3.8
0.7
7.7
5.7
2.7
0.2
45
4.
1**
****
****
****
**2
.16
1.5
21
.30
1.1
71
.10
1.0
41
.00
.96
.93
.89
.86
.83
.80
.77
.74
.72
.69
.25
04
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****
****
****
**2
.35
1.5
61
.31
1.
18
1.
10
1.
04
1.
00
.96
.93
.89
.86
.83
.80
.77
.74
.71
.69
case that a linear extrapolation from measured wave heights upriver leadsto a wave height at Buoy 8 which exceeds the empirical breaking criteriaof (2). If we presume the waves are limited by breaking then the waveheight could be the lower value in this table entry, and the "observed"height would exceed the predicted by 20%. It appears that the ebb of11 September falls into the category of an "extreme event" such as thatobserved previously at the Columbia River Entrance on 18 October 1979 byGonzalez (1984) and for which the simple one-dimensional theory fails topredict accurately. For the rest of the October 1979 observations Gonzalezfound generally good agreement between theory and observation.
If for the moment we assume that the one-dimensional, linear theoryis applicable and that the current at Buoy 46010 is zero, then there arethree variables in Eq. (3) which should be examined in search of some significantdifference which characterizes the 11 September ebb relative to the other cases.These are the current speed U, the wave frequency w = a , and the incidentwave direction a. From Table 14, we see that the estigated surfacecurrents were cogparable for each peak ebb, ranging from 2.0 to 2.3 m/s.Figure ge also show~ that the peak frequency of the wave spectrum graduallyincreased from a 10"" of 0.07 Hz on the ebb of 11 September to a value of0.09 Hz on the ebb of 13 September. This frequency shift is the characteristicsignature of dispersive waves detected at a distant point after propagatingfrom a localized source. An examination of the weather maps of Figure 8suggests that the source was the well-defined fetch region in the southto-southwest sector of the low pressure system dominating the central Gulfof Alaska on 10 September (Fig. 8c). An important implication of this isthat the direction of swell incident on the Columbia River entrance wasapproximately constant for the last three ebbs observed over the period 11to 13 September. It thus appears that both current speed and incidentwave direction were comparable on the last three ebbs, but that there wasa significant difference in wave frequency. However Table lSd, say, for0° incidence indicates that this frequency difference is not enough toaccount for an inferred amplification of 1.8 from offshore to Buoy 8.
Although less relevant for the sole prediction of hazardous waves, abetter test for the linear, one-dimensional theory is to compare observedand predicted wave heights at flood tides since nonlinear effects will beminimized due to reduced wave heights. Column 9 of Table 14 shows that theobserved values are consistently lower than the predicted ones for floodconditions. In one case their ratio is 0.6, but this was for one peak ofa two-peaked deep-water spectrum observed at 46010 (Fig. A44). At Buoy 8,three peaks were observed (Fig. A40); hence some uncertainty is associatedwith the interpretation of this case.
The most likely reason why the simple theory fails to the extent itdoes is due to two-dimensional effects. It is clear that within the entrancethe bathymetry varies markedly in a north-south direction, going from adredged channel to a shoal, to a jetty, to another shoal, to coastwiseJarallel bottom contours. The currents must also vary laterally especially(,utside the entrance. On ebb the current most likely takes the form of aconfined jet with marked lateral shear at its edges. On flood it isprobably more like a sink flow at the edge of a long, straight boundarywith streamlines converging from a wider fan-shaped region. SLAR imageryon the slack-to-ebb of 11 September (Fig. A2B) shows more or less straight
69
and parallel swell crests across the entrance. In contrast, 3 hours later atpeak ebb current (Fig. A35) the wave crests are strongly curved, and thedistinctive grid pattern of crossed waves is now apparent. Two-dimensionaleffects would explain why the wave heights are consistently overpredicted onfloods since wave ray divergence, not accounted for by the theory wouldlead to lower actual wave heights. The converse - that the theory shouldunderpredict wave heights on ebbs - need not be true. Bathymetric refractionover the deeper channel could mitigate the effects of wave focussing dueto currents. For the first two ebbs wave heights were overpredicted whileSLAR imagery showed little wave crossing. For the next two ebbs the waveheights were underpredicted when wave crossing was observed.
If wave crossing is known to occur then a rough correction to thepredicted transfer function can be made by assuming that, although theoffshore energy E remains constant, the energy E on the bar is double
othat predicted without wave crossing as if two independent wave systems
were present. Thus, from Eq. (3), T' = (iE)~ =~T, where T' implies two-o
dimensional refraction severe enough to induce crossing wave crests. Ifthis correction is applied to the entries for 11 September in Table 14, wethen obtain T'(6 =0°) =2.1 and T'(6 =30°) =2.0. The entries of column 9become c c
T /T'(6 =0°) =0.9 to 1.0 ando c
T /T'(6 = 30°) = 0.9 to 1.1, so that the agreement between observed andp~edtcted wave height amplification is thereby improved. The difficultywith this method is we still have to predict when wave crossing willoccur. This is probably best done with a proper two-dimensional theory;one for which the calculation just completed will be accounted for automatically.
On the basis of this result, let us assume that two-dimensional waverefraction and focusing by a current with jet-like lateral shear can be animportaqt mechanism for wave height amplification on the Columbia RiverBar. W~ have in mind here a physical setting similar to the wave/rip-currentinteraction problem examined by Arthur (1950), in which wave rays initiallyparallel to the main axis of a jet-like current were sufficiently refractedto induce crossing farther upstream. We should then ask what set ofparameters might control the magnitude of this effect on any particularebb. These include: (1) the incident wave frequency, f, (2) the relativeangle between the incident wave and the main axis of the current, 6 , and(3) the two-dimensional distribution of current shear at peak ebb. 0
The question is: Were any of these factors significantly differenton the ebb of 11 September, such that wave refraction and focusing wasintensified to the point that two-dimensional effects became important andthe simple one-dimensional theory of Eq. (1) therefore failed?
For a given incidence angle and current shear, two-dimensionalconvergence should be greater for higher frequency waves, since wave groupvelocity decreases with increasing frequency and the ratio U/C thereby
g
70
increases, indicating the current U is more effective in inducing refraction.Since peak wave frequency increased from 0.07 Hz on 11 September to 0.09 Hzon 13 September, this effect would have made two-dimensional refractionmore important on the ebbs of 12 and 13 September. However, this may havebeen offset by a relative wave/current incidence angle 8 which was closer
oto 0° on 11 September than on 12 and 13 September. This is because bathymetriceffects are frequency dependent, and the crests of lower frequency wavestend to become aligned with bathymetry faster than higher frequency waves.Since the set of the current at the river entrance is more or less perpendicularto the depth contours offshore, this suggests that the waves on 11 Septemberwere more nearly in direct opposition to the current, thereby increasingthe importance of two-dimensional wave refraction effects.
Later analyses of the SLAR data will yield wave direction estimatesdirectly. However, we can make a rough estimate now of the frequency-dependentbathymetric effects on the incident wave direction at buoy 46010 by usingEqs. (4) and (5). As noted above, all swell arriving at the ColumbiaRiver entrance during the period 11 to 13 September appear to have beengenerated in the same well-defined fetch area evident in Figure 8c. If weassume for simplicity that waves arrived from the northwest and wereincident on a region with parallel bathymetric contours oriented north-south,then 8 in Eq. (5) is 45° and we can combine (4) and (5) to geto
8(f) =sin- 1(sin8 tanhkd)o
where k satisfies the second relation in (4) and d =60 m at buoy 46010.Using the observed peak frequency values on 11 and 13 September, we obtain
~8 =8(0.09 Hz) - 8(0.07 Hz) - 43.1° - 38.2° =4.9°
as an estimate of the change in incident wave direction from ebb to ebb.
Although wave ray convergence may be quite sensitive to incident wavedirection, it seems unlikely that a 5 degree difference in wave directioninduced by bathymetry would produce the dramatic differences in observedwave height amplification. Judgement on this factor must thus await theanalysis of the SLAR imagery for incident wave direction.
We must also consider the possibility that the surface current propertieschanged significantly from ebb to ebb. The direction of the main axis ofthe current and the degree of lateral shear might be influenced by thestage of the spring/neap tidal cycle, the amount of fresh water discharge,the wind induced surface drift, and the magnitude and direction of alongshorecurrents (either large-scale, seasonal, geostrophic phenomena, or local,short-term wind-induced effects).
Unfortunately, there is very little current drifter data availablewith which to assess these possibilities. Figure 14 displays selectedcurrent vectors corresponding to drifter tracks which were obtained nearthe time of each peak ebb. (The drifter information and current computationsare summarized in Table 13.) The data sparseness is painfully evident,and few conclusions could be drawn. Mean direction is approximately thesame on 11, 12, and 13 September. Jet-like lateral shear is evident on
71
11 September, but the data are insufficient to draw conclusions onpresence or absence of similar shear structure on the other ebbs.the persistence of such structure downstream of these observationsthe region outside the entrance is unknown.
theFurthermore,and in
Nonlinear effects may play a role in the crossing wave patternsobserved at the Columbia River entrance as, for example, in the SLARimagery on 11 September (Fig. A35). In a series of wave tank experimentsSu (1982) has documented the evolution of similar patterns in steep, deepwater wavetrains through a process governed by nonlinear skew bifurcation.The initial steepness of these waves was in the range 0.16 ~ ak ~ 0.18.Using Eq. (4) with U =-2.0 mIs, W =2n(.07) s-l and d =15 m, we obtaink = 0.048. For a ~ 6.5/2 m = 3.3 m we then have an estimate of ak ~ 0.16for the wave steepness on 11 September. Su's experiments do not includethe effects of currents or finite depth, but it is conceivable that thesecould induce similar instabilities. Column 10 of Table 14 gives steepnessestimates for all the cases we observed, and there does seem to be acorrelation between estimated wave steepness and the presence of thegrid-like pattern in the SLAR imagery. Thus, on 10 September (ak ~ 0.07)the pattern is not clearly evident (Figs. A18 and A19), on 13 September(ak ~ 0.10) the pattern is not clearly evident (Figs. A80 and A81), on12 September (ak ~ 0.14) the pattern exists but somewhat indistinctly(Figs. A56 and A57), and on 11 September (ak ~ 0.16) the pattern is verydistinct (Figs. A35 and A36). However, we feel that wave-current-bathymetryinteraction, a zero-order effect, is the primary cause of wave amplification/attenuation at the Columbia River entrance. It is this effect that leadsprimarily to the steep waves and ultimately to wave crossing during extremeebb events.
72
5. SUMMARY AND CONCLUSIONS
Waves and currents have been observed with a unique mixture of instrumentsat the Columbia River entrance during the period 10-13 September 1981.Offshore wave spectra were calculated by NDBC Buoy 46010. Bar wave recordswere measured by a Waverider tethered in strong currents, and SLAR imagerygives a two-dimensional picture of the swell both offshore and in theentrance. The technique of tracking surface drifters at short range witha portable radar set rather than a large, fixed system was successful.
Navigational Buoy 8 in the river entrance is the approximate boundarybetween two wave regimes. Upriver of this site waves decay on both ebband flood tides. This is probably due to depth refraction away from themain channel axis toward the shoals on either side. Surprisingly, ebbsgive a larger decay rate perhaps because of a decrease in current speed asone moves upriver away from the converging jetty tips. Another possibilityis that the enhanced attenuation rate is due to wave breaking induced bythe strong adverse current. Sporadic breaking was observed visually andon SLAR images.
Seaward of Buoy 8 waves amplify during peak ebbs and attenuate duringpeak floods thus confirming the important effect of the current. With thecurrent specified, linear, one-dimensional theory can predict wave heightsto within 20% of observed values most of the time. Heights were consistentlyoverpredicted during flood tides while no consistent bias was observedduring ebbs. This is most likely due to two-dimensional effects.
During an extreme wave event on 11 September the waves were underpredictedby 50% on ebb. These were the highest and steepest waves observed duringthe experiment and were breaking sporadically. SLAR images indicate thatwave crests were crossing due to current refraction. An approximatecalculation suggests that the wave-height prediction should be increasedby a factor of ~ which would bring it closer to that observed. Forbetter wave predictions a two-dimensional theory which automaticallyaccounts for this factor should be applied.
It must be cautioned that strong ebb currents of up to 3.5 m/sec canoccur at the Columbia River entrance. Such currents, not encounteredduring this experimental period, can actually stop typical deep oceanswell, causing them to break for almost any initial, deep-water steepness.The linear, one-dimensional theory applied here becomes inappropriate nearthat limit, and we expect that prediction and observation will divergeradically.
73
6. RECOMMENDATIONS FOR FURTHER RESEARCH
There is a clear need for a systematic effort to improve operationalcapabilities to monitor, nowcast, and forecast hazardous navigationalconditions at coastal tidal inlets of which the Columbia River entrance isan example. This effort should concentrate on:
(1) real-time, long-term monitoring,(2) theory and numerical modeling, and(3) field experiments.
6.1 Real-time, Long-term Monitoring
The essential parameters to be measured are:
(1) nondirectional wave spectra at the inlet entrance, and(2) directional wave spectra offshore.
The technology to attempt these measurements is available now. Timpe(1983) has described the successful use of 6-meter long, boat-shaped NavyOceanographic Meteorological Automatic Device (NOMAD) buoys in very severeenvironments, and such a system may be well-suited for service at coastalinlets. It is recommended that a buoy of this type be deployed on theColumbia River Bar.
Also, NDBC has developed directional wave data analyzers (DWDA)(Steele, 1983). A successful deployment was recently accomplished aboarda 10-meter discus hull off the California Coast (Steele, 1984). Such asystem would provide valuable directional wave data which can be used inconjunction with equation (3) to predict wave height as a function of deepwater wave direction.
Benefits from such a monitoring system are as follows:
(1) Accurate nowcasts would be available. Such real-time informationon inlet conditions is valuable to mariners. A decision to attempt a barcrossing could then be based on measurements, rather than on visualobservations which may be unreliable and are not available during fog anddarkness.
(2) Short-term forecasts would be improved. Influence of short-termmeteorological or other local effects resulting in under or over forecastof wave height would be apparent to the forecaster and could be adjustedfor.
(3) Forecasts could be verified. At present, there is no way to testthe accuracy of bar forecasts.
(4) The intuition of forecasters and local mariners would be improvedas measurements provide "corrective feed-back" to judgements regardingftture wave height on the bar.
(5) A data base would be available for research.
74
6.2 Theory and Numerical Modeling
We have demonstrated at the Columbia River that two-dimensionaleffects should be accounted for if Bar forecasts are to be improved.Jet-like ebb currents contribute to unusually large waves on the Bar. Thedynamics of tidal jets should be investigated and modeled. A similaritysolution with a few parameters such as jet half-width and centerlinevelocity is one approach (Ozsoy and Unluata, 1982).
If the surface current field can be so specified, then along withefforts to better define the surface current field, recent analytical andnumerical techniques for computing the wave field should be investigated.Liu (1983) has re-examined the wave/rip current problem studied by Arthur(1950), and has derived a mild-slope equation which includes currents.This, combined with a parabolic approximation, leads to a computationallyefficient solution. The significant advantage of this approach is that,unlike wave-ray computations, the wave field is computed everywhere includingwhere caustics arise and ray theory fails.
This research will result in products to guide forecasters, such ast.ables, charts, nomograms, and computer algorithms.
6.3 Field Experiments
This experiment has provided a valuable data set for the study ofwave-current interaction. However it has several deficiencies. First,due to hazardous conditions, only limited observations were made at Buoy 8.Second, surface drifter measurements were not dense enough in space andtime to give good current estimates, nor were they available seaward ofBuoy 8. Third, while SLAR imagery can provide excellent information onlong swell, the resolution of the radar is too coarse to yield similardata on shorter, locally generated wind waves, which are an importantconsideration as a navigational hazard.
A comprehensive field experiment must therefore measure, as a minimum,
(1) nondirectional wave spectra on the Bar, near Buoy 8,(2) directional wave spectra offshore(3) surface current fields in the entrance and offshore.
In addition, these observations should be supplemented by SLAR overflightst) map out the two-dimensional wave field and by vertical salinity andtemperature profiles to determine the density structure which may play arole in the dynamics of the surface current especially during freshets.
Item (1) and (2), above, could be provided by the wave measurementtechnology mentioned earlier. Item (3) might be provided by a remotesensing technique such as the Coastal Ocean Dynamics Applications Radar(CODAR) developed by the NOAA/ERL Wave Propagation Laboratory (Barrick andLipa, 1979; Holbrook and Frisch, 1981). Ideally, an experiment would beat least a month long, and coincident wave/current observations could bemade at each peak ebb and at intervals of 1 to 3 hours between peak ebbs.A winter experiment and summer experiment would be desirable, since seasonalextremes in offshore wave energy and in fresh water runoff occur.
75
7 . REFERENCES
Arthur, R. S., (1950): Refraction of shallow water waves: the combinedeffect of currents and underwater topography. Transactions, AmericanGeophgsical Union, 31, 4, 549-552.
Battjes, J .A. (1982): A case study of wave height variations due to currentsin a tidal entrance. Coastal Engineering, 6, 47-57.
Barrick, D. E., and B. J. Lipa (1979): Ocean surface features observed byHF coastal ground-wave radars: a progress review. In: Ocean WaveClimate, M.D. Earle and A. Malahoff (eds.), Plenum Press, New York,129-152.
Enfield, D. (1973): Prediction of Hazardous Columbia River Bar Conditions.Final Report, Dept. of Commerce Contract 1-35356, 204 pp.
Gonzalez, F. I. (1984): A case study of wave-current-bathymetry interactionsat the Columbia River entrance. J. Phgs. Ocean. (in press).
Gonzalez, F. I., and C. L. Rosenfeld (1984): SLAR and in-situ observationsof ocean swell modification due to currents and bathymetry at theColumbia River entrance. IEEE Trans. Geosc. and Remote Sensing (inreview).
Holbrook, J. R., and A. S. Frisch (1981): A comparison of near-surfaceCODAR and VACM measurements in the Strait of Juan de Fuca, August 1978.J. Geophgs. Res., 86, 10908-10912.
Liu, P. L-F. (1983): Wave-current interactions on a slowly varying topography.J. Geophgs. Res., 88, 4421-4426.
Mattie, M. G., and D. L. Harris (1979): A System for Using Radar toRecord Wave Direction. U.S. Army Corps of Engineers Coastal EngineeringResearch Center Technical Report No. 79-1, 50 pp.
Miche, R,_(1944): Mouvements ondulatoires des mers en profondeur constanteou decroissante. Ann. des Ponts et Chaussees, pp. 25-78, 131-164,270-292, 369-406.
Mulhern, R. M. (1982): Current measurements in the Columbia River estuary.Dept. of Civil Engineering, University of Washington, Masters Report,60 pp.
Ozsoy, E. and U. Unluata (1982): Ebb-tidal flow characteristics nearinletf. Estuarine, Coastal and Shelf Science, 14, 251-263.
Phillips, D.M. (1977): Dynamics of the Upper Ocean, Second edition, CambridgeUniversity Press, Cambridge, 336 pp.
Rosenfeld, C. L., and J. W. Bell (1978): Monitoring Ocean Wave RefractionUtilizing Side-Looking Airborne Radar. Presented at APCG 1978,Portland, Oregon.
76
Steele, K. E. and M. D. Earle (1979):Wave Data Analyzer (WDA) Systems.Conference, 212-220.
The Status of Data Produced by NDBOIn: Proceeding of the Oceans '79
Steele, K. E. (1983): NDBC wave measurement activities and plans. In:Proceedings 1983 Symposium on Buoy Technology, Marine TechnologySociety, 182-188.
Steele, K. E. (1984): Personal communication.
Su, M.-Y., (1982): Three-dimensional deep-water waves. Part 1. Experimenalmeasurement of skew and sYmmetric wave patterns, J. Fluid Mech., 124,73-108.
Timpe, G. L. (1983): The use of NOMAD hulls as severe environment buoys.In: Proceedings 1983 symposium on Buoy Technology, Marine TechnologySociety, 72-78.
77
APPENDIX
Intensive Observation Periods
DATA SUMMARY
79
APPENDIX
Data for Individual Intensive Observations Periods
In this appendix, we present the data collected during each individualintensive observation period. The data is grouped by observation periodand consists of:
1. The Waverider (EGRET) positions, as plotted from the log.
2. Waverider Spectral estimates and time series.
3. NDBC 46010 Spectral estimates.
4. The Cape Disappointment surface drifter tracks, as plotted fromthe log.
5. The Jetty A surface drifter tracks, as plotted from the log.
6. Large scale print of the SLAR image judged to be the best ofthose collected during the observation period.
7. Small scale print of the SLAR image judged to be the best ofthose collected during the observation period.
8. The Waverider (Surface Vessel EGRET) log.
9. The Cape Disappointment radar log.
10. The Jetty A radar log.
In the logs of the EGRET, the following conventions have been used.Entries for vessel position through sextant fixes have the format
Sextant Fixes
Left angle
Right angleLeft or right check
angle (L~ or R~)
Objects
Left objectCenter objectRight objectLeft or right check
object (~ or R~)
All angles are measured left or right from the center object. Theidentification of all landmark objects was confirmed by check angles onindependent objects. Table Al lists the description given for each landmarkobject on the 1981 NOS chart 18521, shown in Figure AO.
In the Remarks column, the notations UW and WR imply "underway" and"Waverider." "Drift log" entries refer to current speed estimates obtainedby timing the drift of a small floater to the end of a 25 meter tether.Entries for ships heading are magnetic, referred to the compass on theEGRET, without correction for variation or deviation unless stated otherwise.From comparison of the compass with known directions, it appeared thatdeviation values were minimal and within the precision with which the
81
compa~s could be read (about 10 degrees). The magnetic variation islisted on the 1981 NOS chart 18521 as 20°30' East.
Range and bearing corrections determined from radar fixes on thelandmarks have not been applied to the drifter tracks. Neither have thetracks from two independent radar systems been corrected. to coincide withone another. These corrections will be made in later analyses.
82
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TABLE AI. Description of sextant fix objects as given by 1981 NOS Chart 18521.
Object Number
1
2
3
4
5
11
12
13
14
15
16
17
18
19
20
21
22
Description
North Head Gp FI(2) 30 sec 194 ft 26M
Alt FI R & W 30 sec 220 ft IBM
OBS. TOWER
OBS. TOWER
FI 4 sec 31 ft 10M
TOWER
E Int 6 sec 61 ft
Qk FI
TOWER
TR
R "2" FI R 4 sec WHISTLE (Buoy 2)
R "4" FI 4 sec WHISTLE (Buoy 4)
Light on S. tip of large Sand Island,"FI G 4 sec. 15 ft. '1'"
Clatsop Spit "Lookout Tower"
E side of bend in South Jetty
Light on S. tip of line of piles oncentral S. Side of small Sand Island,"FI 4 sec '5'"
Seaward end of N. Jetty
84
10 September 1981
FLOOD
85
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88
oo.; DRIfTING 1981
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89
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10 SEPT.JD 253
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Figure A4. Waverider raw amplitude, filtered amplitude, and power spectraldensi _y for 1131 PDT, 10 Sept. 1981.
90
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91
00 10 SEPT. 12 PDT.;
NDBC BUOY .60101981 JD 253 19 Z
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92
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FLOOD
Wave rider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
0930 UW from Hammond Basin
1018 WR in water holding station100 yards north of Buoy 8
(Drift log 25 m. 17, 18, 19sec. 1.4 m/sec.)
1030 Begin record holding station.
1032 36°10' 1 100 yards north of No. 82 1~ m. wave,
35°12' 3 12 second period.
1043 260 36°18' 1 5 foot wave from2 echo sounder
35°14' 3R,J 24°05' 5
llOO 34°15' 1 Begin drift at 1055.2 WR '" 100 yards
38°57' 3 down-current from boat
ll03 33°23' 12
40°46' 3
ll06 32°08' 12
42°55' 3
1109 30°38' 12
45°23' 3 WR ~ 50 yards NW of boatR,J 12°13' R,J 12
ll12 29°01' 12
48°02' 3
1115 27°34' 1 ~~ ~ 50 yards NW of boat2
50°10' 3
95
10 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1120 24° 39' 1 Stop drifting with2 WR. underway, towing WR.
54° 12' 330° 30' R.j 5
1131 24° 44' 1 On station.2 100 yds. N. Buoy 10.
64° 44' 339° 39' R.j 5
1153 25° 27' 1 On station.2
65° 07' 340° 22' R.j 5
1157 Begin drifting from100 yds. N. of Buoy 10.WR ~ 250 ft. downcurrent from EGRET.
1200 24° 14' 12
67° 00' 3
l203 19° 53' 12
69° 34' 3
1206 18° 12' 1 WR ~ 100 ft. NW2 of EGRET
71° 13' 3
1209 51° 48' 15
36° 52' 335° 20' L.j 2
1213 47° 37' 15
40° 37' 3
96
10 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1215 45° 05' 1 WR ~ 100 ft. NW5 of EGRET.
42° 20 3
1218 41° 55' 15
44° 39' 3
1221 27° 06' 2 End drift.5 Underway for Buoy 14.
47° 01 ' 3
1232 WR aboard. Underwayto Hammond Basin.
97
10 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg. ) Remarks
1 1050 1.13 3351055 1.05 3251059 1.03 317 Retrieved Buoy #1
2 1115 1.47 3351120 1.48 3281125 1.45 3201130 1.50 3131135 1.56 3071140 1.67 3021150 1.81 2931153 1.87 290 Pick up Buoy #2
3 1122 1.56 3221125 1.58 3171130 1.64 3111135 1.71 3051140 1. 79 3001145 1.87 2961149 1.90 293 Pick up Buoy #3
4 1130 1.20 3251135 1.19 3171140 1.21 3101145 1.24 3021150 1.30 2951155 1.37 2891200 1.47 2851205 1.58 2831210 1.69 2801215 1. 79 2791218 1.84 279 Pick up Buoy #4
5 1205 1.19 2811210 1.27 2801215 1. 31 2791220 1.33 2781225 1.36 278 Pick up Buoy #5
98
10 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (um. ) (deg. ) Remarks
6 1110 1.64 3351115 1.61 3291120 1.61 3221125 1.64 3151130 1.71 3081135 1. 78 3031140 1.85 2991145 1. 91 294
99
J10 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
1 104945 1.30 2191 105605 1.13 2091 105815 1.09 207 Buoy #1 picked up
2 111650 1.57 213 Drifters difficult to2 112030 1.53 208 see and follow.2 113950 1.52 182 If
2 114300 1.54 178 '12 115250 1.65 169 If
2 115550 1.65 167 If
3 112210 1.60 202 11
3 114525 1.69 174 11
4 113025 1.29 208 "4 113430 1.23 204 "4 113700 1.20 200 "4 115745 1. 21 169 "4 120150 1.25 165 "
5 122623 0.64 153 II
6 111210 1. 75 212 fI
6 111445 1. 71 208 II
6 114715 1.73 171 II
100
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Figure A10. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1444 PDT, 10 Sept. 1981.
104
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Figure All. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1506 PDT, 10 Sept. 1981.
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Figure A12. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1528 PDT, 10 Sept. 1981.
106
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107
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108
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113
10 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes
1444 060(into current)
1457 065 27° 38'
60° 38'38° 31'
Objects
123
5 R~
Remarks
Holding station.WR deployed100 yds. N ofBuoy 10. - 100 mline out.- 8 sec. 5-8 ft.(current 11, 12sec./25 m. driftlog).Holding station.
1501
1506
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1515
1519
152330
27° 53'
60° 17'
27° 27'
60° 04'
30° 37'
54° 00'
33° 30'
47° 48'
36° 33'
37° 44'
123
123
123
123
123
123
114
Begin drift fromon station. WR 100yds. down current.
Boat maneuveringto hold WR - 200ft. down currentfrom boat with slackin "towing" cableat all times.
Buoy streamingto leeward - 75 m.
---------
10 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
152730 36° 34' 12
34° 30' 3
1528 55- Holding position60° ~ 100 yds. NW ofMAG Buoy 8.
Drifted exactly intoposition. Wave ridersubmerges with topeven with water linebut follows the wavepattern very well.
1534 37° 33' 1 In position -2 referenced to
33° 00' 3 Buoy 8.
1542 36° 43' 1 8-10 ft. seas and2 8 sec. by visual
36° 32' 12 and stopwatch.36° 10 13R,J good
(drift log 10 sec. and10 sec. for 25 m.)
1555 36° 18' 1 Began drifting from2 in position N of
36° OS' 12 Buoy 8.
1559 35° 55' 1 EGRET maneuvering2 to stay ~ 150 to
32° 51' 12 200 ft. up currentfrom WR with slackin cable at alltimes.
1605 35° 11' 12
26° 03' 14
115
10 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
160930 340 10' 12
27 0 30' 12240 03' 14 Good
1614 330 06' 12
25 0 13' 12
1619 31 0 53' 12
20 0 IS' 14 .J Good
1629 End drift with WR.Underway for Buoy 4towing WR.
1653 720 OS' 117 (/14 buoy)
580 50' 16 (/12 buoy)51 0 06' 2
1655 72 0 OS' 1 Picked up drifter buoy17 (1/4 buoy) 5 min ago at about
57 0 50' 16 (112 buoy) 1650.52 0 12' 2 Cancel plans for
record at Buoy 4 dueto approach ofdarkness. Underwayfor Hammond.
116
10 September 1981
EBB
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg. ) Remarks
2 1450 2.4 2641537 1.01 3181540 1.05 3281545 1.16 3491550 1.30 0001555 1.49 0051600 1.72 010
3 1450 2.4 2621541 1.21 3061545 1.36 3171550 1.53 3261555 1. 70 3321600 1.93 3381605 2.14 3441610 2.39 3481615 2.57 3521620 2.80 3551625 2.96 357
4 1527 0.96 2951530 0.94 3051535 0.92 3221540 1.00 3411545 1.15 0011550 1.30 0061555 1.49 0141600 1.65 015
5 1523 1. 70 2811525 1.61 2921530 1.59 3021535 1.63 3121540 1. 74 3211545 1.84 3301550 2.04 3351555 2.28 3401600 2.45 344
117
BuoyNo.
2
Time(PDT)
153815
Range(nm. )
1.08
10 September 1981
EBB
JETTY A RADAR DATA
Bearing(deg.) Remarks
208 Drifters impossible to follow.
118
11 September 1981
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Figure A2l. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1348 PDT, 11 Sept. 1981.
122
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123
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11 SEPT. 14:26 PDTJD 254 21.26 6"T HS • 2.68 " U • -1.01 "/5
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TIME (SECS)
Figure A23. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1426 PDT, 11 Sept. 1981.
124
00 11 SEPT. 13 PDT.;
NDBC BUOY ~60101981 JD 2S~ 20 Z
0 SIG HT .. 2.~ METERS0 U .. .3 MIS.. WIND SPEED .. 8.6 MIS- WIND DIRN ..3~3. DEGS
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00 11 SEPT• 12 PDT.;
NDBC BUOY ~60101981 JD 2S~ 19 Z
0 SIG HT .. 2.2 METERS0 U .. 1. 2 MIS00 WIND SPEED .. 9.1 MIS- WIND DIRN ..3~9. DEGS
N:x:...... 0NOr..;.....U.I
00
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91.00 0.0. 0.08 0.12 0.16 0.20 0.24 0.28 0.S2 0.36 0••0F (HZ)
00 11 SEPT• 11 PDT•
NDBC BUOY ~60101981 JD 25~ 18 Z
0 SIG HT .. 2.2 METERS0 U .. 1. 5 MIS00 WIND SPEED .. 8.2 MIS- WIND DIRN ..357. DEGS
N:x:......0NOr..;.....U.I
00
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Figure A24. NDBC 46010 power spectral density for 1100, 1200, and 1300 PDT,11 Sept. 1981.
125
00.; 11 SEPT• 16 PDT
NDBC BUOY 460101981 JD 254 23 Z
0 SIG HT = 2.9 HETERS0 U = -1. 8 11/5... WIND SPEED = 9.5 HIS- WIND DIRN =345. DEGS
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00
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00 11 SEPT. 15 PDT•
NDBC BUOY 460101981 JD 254 22 Z
0 SIG HT = 2.8 HETERS0 U = -1. 4 11/5.. WIND SPEED = 9.9 HIS- WIND DIRN -342. DEGS
N%.......0NOX';-11.1
00
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00
11 SEPT. 14 PDT.;NDBC BUOY 460101981 JD 254 21 Z
0 SIG HT - 2.6 HETERS0 U = -.7 HIS.. WIND SPEED = 9.3 HIS- WIND DIRN =339. DEGS
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00
N
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Figure A25. NDBC 46010 power spectral density for 1400, 1500, and 1600 PDT,11 Sept. 1981.
126
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11 September 1981
SLACK
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1240 Recorder not on.
1315 WR deployed.
1320 Holding station Nof Buoy 10 ~ 100 yds.
Current nearly slack.
~ 15 kt. NW wind.Drift of buoy almostnegligible by visualobservation.
1329 22° 01 ' 12
05° 41 ' 3
1337 20° 30' 1 Recorder not on2 for above.
63° 55' 3 Data logger turnedon. (At 1342.)
1355 28° 01' 1 Holding position NW2 of Buoy 10 very
62° 30' 3 difficult due toopposed wind/current.Buoy 10 ~ 100 yds.
1358 Ebb increasing rapidly.One engine in gearreq'd 50% of time tohold position.
1400 27° 46' 1 WR bears ~ 245 Mag.2
62° 53' 3
1408 28° 15' 1 WR bears ~ 245 Mag.2
62°39' 3
131
11 September 1981
SLACK
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1409 Begin drift.
1411 28° 30' 1 Wave height2 1. 4 - 2 m.
61° 43' 3 ~13 sec.
1417 30° OS' 1 Free drift very2 difficult due to
58° 25' 3 wind.
1422 31° 18' 1 EGRET may be2 putting drag on WR
54° 26' 3 periodically.
1430 32° 53' 1 Buoy bears 350T.2
49° 42' 3
1432 32° 58' 1 Buoy bears 350T.2
47° 48' 3
1440 32° 50' 1 8 sec. 3 m.2
41° 28 3
1445 32° 28' 1 WR Buoy bears ~ 3402 250 ft.
38° 00' 3
1447 Underway to midchannel.End drift.
1507 WR aboard.
132
11 September 1981
SLACK
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
1 1301 2.11 2711305 2.16 2681310 2.15 2671315 2.19 2671320 2.23 2661325 2.21 2661330 2.23 2661335 2.26 2671340 2.26 2691345 2.25 2681350 2.25 2691355 2.22 2701400 2.19 2721405 2.18 2741410 2.19 2771415 2.23 2781420 2.31 2771425 2.39 276, Pick up Buoy #1 at 1428
2 1304 1.57 2631305 1.58 2621310 1.58 2591315 1.57 259 Lost Buoy #2 in blind spot
3 1315 1.17 3041320 1. 19 3071325 1.20 3101330 1.21 3131335 1.21 3161340 1.21 3221345 1.28 322 Waverider track starts1350 1.26 3221355 1.24 3231400 1.23 3231405 1.25 3231410 1.24 3241415 1.27 3261420 1.33 3291425 1.37 3321430 1.46 3361435 1. 61 340
133
11 September 1981
SLACK
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (om. ) (deg.) Remarks
1~40 1. 78 3431445 1.93 3451450 1.90 346 Pick up Buoy #3
4 1315 1.23 3341320 1.27 3361325 1.32 3371330 1.33 3381335 1.38 3401340 1.42 3411345 1.45 3431350 1.50 3441355 1.56 3461400 1.64 3481405 1. 70 3511410 1.81 3531415 1.92 3551420 2.05 3571425 2.18 3581430 2.30 0001435 2.44 0011440 2.63 0021445 2.85 0021450 3.04 002
134
11 September 1981
SLACK
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
1 1307 1. 79 1411319 1.85 1381330 1.85 1371335 1. 91 1401341 1.90 1411345 1.89 1401351 1.90 142135530 1.87 143140130 1.86 147140555 1.87 149140945 1.90 150141603 1.96 152142020 2.02 151142620 2.07 149
2 1306 1.22 1361319 1.18 1331326 1.20 1311330 1. 21 1321335 1.19 1321341 1.13 1351345 1.10 1371351 1.05 138135600 0.99 140140155 0.94 142140620 0.92 145141015 0.91 148141628 0.92 153142032 0.94 157
"Waverider" (Vessel EGRET) positions from 140635 to 142755:
140635 1. 31 206 Most likely "Waverider"141045 1. 30 207141647 1.36 209 Other targets nearby142112 1.44 211142755 1.54 214
4 1320 1.42 2171326 1.46 2181331 1.50 2181336 1.56 218
135
11 September 1981
SLACK
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
4 1341 1.60 2201346 1.64 2211352 1. 74 221135700 1. 78 223140230 1.87 224140710 1.90 225
136
11 September 1981
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Figure A31. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1552 PDT, 11 Sept. 1981.
140
oo.:: BUOY 10 1981
11 SEPT. 16:12 PDTJD 25_ 23.12 GMT WS • 3.39 " U • -1.79 "IS
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TIME (SECS)
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TIME (SECS)
Figure A32. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1612 PDT, 11 Sept. 1981.
141
00
• 11 SEPT• 19 PDTNDBC BUOY 460101981 JD Z55 Z Z
0 SIG HT = Z.8 METERS0 U = -.Z MIS.. WIND SPEED = 7.3 MIS- WIND DIRN =356. DEGS
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11 SEPT. 18 PDTOIl
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0 SIG HT = Z.5 METERS0 U = -1. 1 MIS.. WIND SPEED = 8.1 MIS- WIND DIRN -35Z. DEGS
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00
• 11 SEPT. 17 PDTNDBC BUOY 460101981 JD Z55 o Z
0 SIG HT = Z.8 METERS0 U .. -1.7 MIS.. WIND SPEED = 8.4 MIS- WIND DIRN ..34Z. DEGS
N:::r.......0NOEo.-W
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Figure A33. NDBC 46010 power spectral density for 1700, 1800, and 1900 PDT,11 Sept. 1981. 142
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EBB
Wave rider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1545 WR in water NE ofBuoy 12.
1548 79 0 39' 5 Begin drift.3 (1.5 m, 12 sec.)
19 0 50' 12 WR buoy W 200 ft.
1553 70 0 43' 53
130 51 ' 12
1559 35 0 18' 2 WR buoy NW 200 ft.5
500 08' 3
1604 400 27' 25
340 52' 3
1609 39 0 37' 25
26 0 01 ' 3
1610 Stop drift, maneuverto holding station.
1612 280 30' 1 On station.2 (8 sec. 2 m.)
39 0 40' 5
1625 29 0 OS' 1 (drift log2 13, 12, 12 sec.
61 0 53' 3 for 25 m.)
1633 29 0 24' 1 End holding sta.2
61 0 29' 3
1640 WR aboard.
146
11 September 1981
EBB
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg. ) Remarks
1 1605 1.12 2831610 1.10 2961615 1.08 3111618 1.14 3231620 1.17 3301623 1.26 3371626 1.39 3441628 1.48 348 Picked up Buoy #1
2 1606 1.29 2871610 1.29 2961615 1.23 3151618 1.31 3231620 1.37 3281623 1.47 335 Picked up Buoy #2
3 1610 1.45 299l615 1.47 311L618 1.51 318 Picked up 113
Targets impossible to follow.
\47
11 September 1981
EBB
JETTY A RADAR DATA
BuoyNo.
Time(PDT)
Range(nm. )
148
Bearing(deg. ) Remarks
Targets impossibleto follow.
12 September 1981
FLOOD
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• LIGHTSHIP 198112 SEPT.JD 255
09:25 PDT16125 G"T HS • 2.78 " u • t.Z8 M/S
oo
•-N:z:......~g-.;oenno
ooN
g.1-----.-L~I____+_-----+-~~~==F=__.....-~...........9».00 0.04 0.01 0.12 0.16 0.20 0.24 0.21 0.'2 0.36 0• .\0
FREQUENCY (HZ)
1000.00900.00100.00700.00400.00 500.00 600.00TIME (SEeS)
'00.00200.00100.00
.....g~
UJo::;)0.... 0-. ....J"0Xe:c
o0 0
UJ':a: I
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1000.00900.00700.00 100.00'00.00 500.00 600.00TIME (SEeS)
soo.oo200.00100.00
oo
(O)+------l~--_+---+_-----.~--_+---+_--__i~--_+---+_---~'0.00
Figure A38. Waverider raw amplitude, filtered amplitude, and power spectlaldensity for 0925 PDT, 12 Sept. 1981.
152
oo..- BUOY 4 1981
12 SEPT. 10:41 PDTJD 255 17.41 GMT HS • 2.65 M U. 1. 71 MIS
ooN--N
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g.p.--......L~--+---~-~~:::::~=+:~:::::::::::::::j;=-- ...--.....--.....----t0.01 0.12 0.16 0.20 O.U
FREQUENCY (HZ)0.21 0.S2 0.56
.....g~LIJo~o""0.......JQ.z:a::
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LIJ":a:: I
LIJ......J....01&.0
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TIME (SEeS)
If)-z:-
oo
"'+-.---i""----+I---+I----IIf----+1---....I----IIr----+1---+I----IIf--'0.00 100.00 ZOO.OO SOO.OO 400.00 500.00 600.00 700.00 100.00 900.00 1000.00
TIME (SECS)
l'igure A39. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1041 PDT, 12 Sept. 1981.
153
oN.. BUOY 8 1981
12 SEPT. 11:27 PDTJD 255 18127 SHT HS • 1.59 H U. 1.73 H/S
oenQ.
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FREQUENCY (HZ)
1000.00100.00700.00400.00 500.00 600.00TIME (5EC5)
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TIME (5EC5)
Figure A40. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1127 PDT, 12 Sept. 1981.
154
BUOY 10 .'8112 SEPT. 12:00 PDTJD Z55 I'. 0 6MT HS. .,. M U· 1.63 "IS
--N:x:.......NoX.-'ooen0-
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g~~:"";"--+-----i~--+----=:""'--'::'~~~+:::::=:::::~~~=-=tcb.OO 0.04 0.01 O.IZ 0.16 O.ZO O.Z' O.ZI 0.12 0.36 0.'0
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TIME (SECS
oo.;X-
&000.00100.00 900.00'00.00 500.00 00.00 700.00TIME (SECS
SOD. 00200.00100.00
oo--+-----i----+----+-----l...----+---'if-----lf-----+---+----...1-'0.00
Figure A41. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1200 PDT, 12 Sept. 1981.
155
oo.... DRIfTING 1981
12 SEPT. 13:00 PDTJD 255 20. 0 GMT HS • 2.04 " U· 1.05 "IS
ooN..-N
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TIME (SECS)
ooft-X
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TIME (SECS)
Figure A42. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1300 PDT, 12 Sept. 1981.
156
00 12 SEPT• 10 PDT.-
NDBC BUOY 460101981 JD 255 17 Z
0 SIG HT • 2.7 HETERS0
U • 1. 5 HIS.. WIND SPEED = 5.1 HIS- WIND DIRN = 8. DEGSN::I:-""'0NOS;•.....,IU
00
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00 12 SEPT. 09 PDTII»
NDBC BUOY 460101981 JD 255 16 Z
0 SIG HT = 2.8 HHERS0 U • 1. 0 HIS.. WIND SPEED = 5.3 HIS- WIND DIRN • U. DEGS
N::I:-""'0NOS;•.....,IU
00
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91.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.'2 0.36 0.40F (HZ)
g12 SEPT. 08 PDTII»
NDBC BUOY 460101981 JD 255 15 Z
0 SIG HT • 2.8 HETERS0 U • .1 HIS.. WIND SPEED = 6.5 HIS- WIND DIRN • 10. DEGS
Nx-""'0NOS;•.....,IU
00
N
00
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Figure A43. NDBC 46010 power spectral density for 0800, 0900, .Ind 1000 PDT,12 Sept. 1981.
157
00
• 12 SEPT. 13 PDTNDBC BUOY 460101981 JD 255 20 Z
0 SIG HT • 2.9 "ETERS0
U • 1.1 HIS.. WIND SPEED .. 6.1 "IS..... WIND DIRN .343. OEGS'"l:...... 0NO:r=.-w
00
N
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00 12 SEPT. 12 PDT•
NDBC BUOY 460101981 JD 255 19 Z
0 SIG HT • 2.8 "ETERS0 U .. 1. 6 "IS.. WINO SPEED = 5.3 MIS- WIND DIRN "358. DEGS
N:::E:....... 0NO:r=.-w
00
N
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00 12 SEPT. 11 PDT• NDBC BUOY 46010
1981 JD 255 18 Z0 SIG HT .. 2.8 METERS0 U .. 1. 7 MIS.. WIND SPEED .. 6.5 "IS- WIND DIRN • 7. DEGS
N:::E:.......0NO:r=.-w
00
N
00
'\.00 0.0' 0.01 0.12 0.16 0.20 0.24 0.21 0.S2 0.36 0.'0F (HZ)
Figure A44. NDBC 46010 power spectral density for HOOt 1200, and 1300 PDT,12 Sept. 1981.
158
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12 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time
""'0918
(0921)
0925
0950
0955
~1003
1037
1041
1041
Hdg. Sextant Fixes Objects Remarks
WR deployed.
(Data logger turned on.)
On station 100 yds.from Buoy CR holdingstation.(7 . 5 sec. 2 m.)
Little surfacecurrent apparent.WR cable alternatesbetween slack and alittle tension.Wind 8-10 kts.
Wave pattern"'" 1.5 m.superimposed on longswell, but wave patternnot very distinct.
Stop holding station.
Underway for B40Y 2.WR aboard.Fog.
On station Buoy 4.Fog.
Begin record. Buoy 4bears 270, 150 ft.
Bouy 4 bears NW 100ft. and Waveriderbears E magneticfrom EGRET, 100 m.Steady relationshipthroughout record.
163
12 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time
1041
1101
1104
1124
1127
1148
1151
1158
1200
Hdg.
250
250
Sextant Fixes Objects
164
Remarks
Light pull on towline.Drift log (20 m)takes greater than2 minutes (surfacecurrent indefinite)WR position indicatesslight flood to NE.
Complete station,begin WR recovery.
WR aboard.
Fog.
WR deployed adjacentBuoy 8.
Begin record.
Buoy 8 bears 250,100 ft (into current).Steady throughoutstation.(drift log17, 15.8, 16, 17.8,18.2 sec for 25 m)Approx. 1 m waveheight.
Complete station.
WR aboard. Underway.
WR deployed.
On station Buoy 10,EGRET 100 ft. downcurrent of buoy.
---------
12 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time
1210
1220
1234
1237
1248
1250
1300
1318
Hdg. Sextant Fixes Objects
253
165
Remarks
Begin record.
250 mag: intocurrent.
Clear visibility.
Steady conditions.Conat. range andbearing to buoy.(drift log16.20, 16.07, 16.08sec. per 25 m.)
End sta.
WR aboard.
Fog at Buoy 8.WR deployed.On station a beamBuoy 8. CG Cutter SEDGE anchoredon Buoy 8 and replacing buoy.(NOTE: Buoy 8later removed byCoast Guard.)
Buoy 8 posit. bearsS 100 yds.100 m. cable to WR.
Begin drift.
End sta.
12 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo (PDT) (nm. ) (deg. ) Remarks
1 1041 1.52 3571046 1.37 3481050 1.29 3411055 1.24 3301100 1.26 3181106 1.36 3051110 1.43 2981115 1.57 2901120 1.72 2821124 1.84 278 Picked up #1 at 1123 (fix
on boat)
2 1046 1.46 0091050 1.34 0071055 1.20 0041100 1.08 0001106 0.96 3561110 0.91 3531115 0.83 3461120 0.78 3401125 0.74 3321130 0.72 3251135 0.71 312 Picked up #2
3 1100 1.10 3371106 1.0 3221110 1.0 3131115 1.03 2981120 1.12 288 Picked up #3 1123
4 1206 1.58 0031210 1.53 3591215 1.45 3551220 1.41 3501225 1.39 3461230 1.36 3421235 1.36 3371240 1.36 3321245 1.36 3281250 1.36 3241255 1.37 3191300 1.41 315
166
----~-~ ------ ------ ---- ------- -
12 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (om. ) (deg.) Remarks
1305 1.44 3111310 1.48 3081315 1.51 305 Picked up /14
4 1155 1.57 3491200 1.48 3391205 1.40 3281210 1.39 3171215 1.46 3081220 1.54 2991225 1.64 2911230 1.77 285 Picked up /15
6 1200 1.83 3421205 1.80 3331210 1. 79 3231215 1.82 3141220 1.88 306 Picked up /16
7 1255 1.89 3521300 1.88 3461305 1.85 340 Picked up /17
167
12 September 1981
FLOOD
JETTY A RADAR DATA•
Buoy Time Range BearingNo. (PDT) (run. ) (deg. ) Remarks
1 1040 1. 78 2341042 1.71 2331045 1.60 2291047 1.53 2271050 1.45 2211052 1.41 2191054 1.38 2151056 1.33 2101058 1.31 208
2 1045 1.84 2441047 1.72 2431050 1.66 2441052 1.56 2431054 1.52 2431056 1.48 2421058 1.42 2411100 1.38 241110230 1.32 2401106 1.24 2391108 1.21 2381110 1.14 2381112 1.13 2371114 1.06 2361116 1.05 2331118 0.99 2321120 0.95 2311122 0.94 2291124 0.91 2281126 0.86 226Jl28 0.85 2241130 0.82 2211132 0.78 2211134 0.78 2171136 0.76 216
3 1102255 1.17 2201106 1.08 2121108 1.04 2081110 1.01 2051112 0.96 1981114 0.93 194
168
12 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (om. ) (deg.) Remarks
1116 0.92 1861118 0.92 1811120 0.93 1751122 0.94 1701128 1.11 154 Position confirmed as Nerka
approached1130 1.16 152 Drifter picked up
4 1250 1.40 2061254 1.40 2031256 1.40 2011258 1.40 1991300 1.40 1981302 1.40 1961304 1.39 1951306 1.41 1931308 1.41 1911310 1.41 1901312 1.41 1891314 1.41 188
5 1154 1.80 2271156 1.72 2241158 1.66 2221200 1.61 2191202 1.56 2161204 1.51 2121206 1.45 2101208 1.42 2061210 1.42 2011212 1.39 1991214 1.38 1921216 1.38 1891218 1.40 1851220 1.40 1811222 1.40 1781224 1.44 1741226 1.45 1701228 1.49 1661230 1.55 163 Drifter retrieved
169
12 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (om. ) (deg.) Remarks
6 1200 1.99 2191202 1.93 2161204 1.93 2131206 1.86 2091208 1.86 2071210 1.83 2031212 1.80 1991214 1.80 1961216 1.77 1921218 1.77 1891220 1. 78 186 Drifter retrieved
7 1256 2.08 2261258 2.08 2241300 2.04 223 Buoy 7?1302 2.04 2201304 2.01 2191306 2.00 217
170
12 September 1981
EBB
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FREQUENCY (HZ)
l00U.OO'00.00 500.00 600.00 700.00 100.00 900.00TIME (SECS)
'00.00200.00100.00
UJo::3
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1000.00700.00 100.00 fOO.OO.00.00 500.00 600.00TIME (SECS)
'00.00200.00100.00
oo
........----ll-----+---+------II----+----+------,I----+----+----I'0.00
Figure ASO. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1644 PDT, 12 Sept. 1981.
174
oo.... 8UOY 12 198112 SEPT.JD 256
17:58 PDT0.58 &"T HS • 2.39 "
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"'+----4----+---+1---...,11-----+1----41---...,11-----+1---...1----111--'0.00 100.00 200.00 SOO.OO '00.00 500.00 600.00 700.00 100.00 900.00 1000.00
TIME (SECS)
g...-:E-
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TIME (SECS)
Figure A5I. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1758 PDT, 12 Sept. 1981.
175
00.. 12 SEPT• 16 PDT
NDBe BUOY 460101981 JD 255 23 Z
0 SIG HT • 2.2 HETERS0 U • -1. 8 MIS.. WIND SPEED = 8.4 MIS- WIND DIRN ·339. DEGSN
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00 12 SEPT• 15 PDT•
NDBC BUOY 460101981 JD 255 22 Z
0 SIG HT • 2.4 METERS0 U .. -1.1 MIS"j HIND SPEED = 7.9 MIS- HIND DIRN =337. DEGS
N:r:'-0NOE.-&&.I
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00 14 PDT• 12 SEPT•
NDBC BUOY 460101981 JD 255 21 Z
0 SIG HT • 2.5 METERS0
U • -.0 HIS.. HIND SPEED. 6.8 MIS- WIND DIRN =337. DEGSN:r:'-0NOE.-&&.I
00
N
00
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Figure A52. NDBC 46010 power spectral density for 1400, 1500, and 1600 PDT,12 Sept. 1981.
176
00
• 12 SEPT. 19 PDTNDBC BUOY 460101981 JD 256 2 Z
0 SIG HT • 2.5 I1ETERS0 U • -1.1 11/5.. WIND SPEED. 8.0 11/5- WIND DIRN .352. DEGS
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00
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00 12 SEPT. 18 PDT• NDBC BUOY 46010
1981 JD 256 1 Z0 SIG HT • 2.3 I1ETERS0 U • -1. 9 11/5... WIND SPEED. 1.6 11/5
...... WIND DIRN 01353. DEGsN:J:......0NOE';....,&&.I
00
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00 12 SEPT. 17 PDT• NDBC BUOY 46010
1981 JD 256 o Z0 sIG HT a 2.8 I1ETERs0 U • -2.1 11/5.. WIND SPEED • 1.8 11/5- WIND DIRN 01345. DEGs
N:::J:......0NOE';-&&.I
00
N
001
~.OO O.Ot o.oe 0.12 0.16 O.ZO O.Zt o.ze 0.3Z 0.16 O.tOF (HZ)
Figure A53. NDBC 46010 power spectral density for 1700, 1800, and 1900 PDT,12 Sept. 198!.
177
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12 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects
1641
1644 16° 48' 25
82° 56' 3
1648 32° 40' 25
64° 42' 3
1652 46° 20' 25
42° 20' 3
1656 47° 23' 25
29° 12' 3
29° 34' 12
42° 48' 5
1704 34° 50' 12
37° 15' 5
.....1745
1758
1811
182
Remarks
WR deployed.
Begin recorddrifting.WR bears 270150 ft.
WR bears 270 150 ft.(8 sec., 2 m.vis. obs.)
End drift.Wave leading edgesvery steep. Waves 4to 5 more wavelengthsoffshore appear tobe beginning to break.Towing WR to Buoy 10.Continue towing upstream.
WR aboard .
WR deployed 100yds. on channelside of Buoy 12.
On station, record.(10.6, 11.6, 11.6/25 m.)
12 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1822 19° 54' 2 End station.5 Position steady
58° 35' 3 throughout station.
1828 72 End station.
1832 WR aboard.
183
12 September 1981
EBB
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg. ) Remarks
1 1639 1.10 2961642 1.09 307]645 1.21 3161648 1.26 3261651 1.36 3361654 1.44 3431657 1.60 349 Picked up #1
2 1642 1.20 3071645 1.21 3161648 1.33 325] 651 1.44 331 Picked up #2
3 1815 1. 91 2651818 1. 78 2671821 1.63 2681824 1.55 2701827 1.37 2741830 1.25 2781833 1.19 282 Picked up #3
4 1818 1.63 2621821 1.46 2641824 1.33 2651827 1.12 270 Picked up #4
184
--------
12 September 1981
EBB
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
1 1640 0.97 1861642 1.06 1931644 1.08 2011646 1.25 2041648 1.32 2091651 1.47 2171652 1.57 2201654 1.61 2221656 1. 74 2251657 1.84 2271700 2.00 230
2 1642 1.14 1941644 1.16 2001646 1.28 2041648 1.32 209 Buoy retrieved
3 1815 1.54 1401816 1.49 1411818 1.40 1421820 1.34 1441822 1.26 1471824 1.19 1491826 1.09 1531828 1.04 1561830 0.98 1611833 0.94 167
4 1820 1.16 1391822 1.04 1411824 0.94 1471826 0.86 1491828 0.77 156
Buoy in radar shadow.
185
13 September 1981
FLOOD
187
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TIME (SECS)
Figure A59. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1117 PDT, 13 Sept. 1981.
190
oN
'"DRIFTING 1981
13 SEPT. 11~39 PDTJD 256 18.S' GMT HS • 1.27 M U. 1.'4 MIS
of1)0..
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TIME (SECS)
Figure A60. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1139 PDT, 13 Sept. 1981.
191
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13 SEPT. 12:23 PDTJD 256 19.23 &"T WS • 1.39 " U. 1.13 "IS
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Figure A61. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1223 PDT, 13 Sept. 1981.
192
DRIfTING 198113 SEPT. 12:45 PDTJD 256 19.45 GNT HS • I.SS N U. 1. 71 "IS
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Figure A62. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1245 PDT, 13 Sept. 1981.
193
00
13 SEPT• 13 PDT.•NDBC BUOY .60101981 JD 256 20 Z
0 SIG HT .. 2.0 METERS0 U .. 1. 6 MIS..,; WIND SPEED .... 2 MIS- WIND DIRN "337. DEGS
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00 13 SEPT. 11 PDT•
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0 SIG HT .. 2.2 METERS0 U .. 1. 9 MIS• WIND SPEED .... 3 MIS- WIND DIRN "355. DEGS
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Figure A63. NDBC 46010 power spectral density for 1100, 1200, and 1300 PDT,13 Sept. 1981.
194
00 13 SEPT. 16 PDT.;
NDBC BUOY 460101981 JD 256 23 Z
0 SIG HT • 2.1 METERS0 U • -1.6 MIS.. WIND SPEED .. 4.1 MIS- WIND DIRN ..339. DEGS
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NDBC BUOY 460101981 JD 256 22 Z
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00 13 SEPT• 14 PDT• NDBC BUOY 46010
1981 JD 256 21 Z0 SIG HT • 2.0 METERS0 U = .1 MIS.. WIND SPEED .. 5.1 MIS- WIND DIRN =331. DEGS
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Figure A64. NDBC 46010 power spectral density for 1400. 1500. and 1600 PDT.13 Sept. 1981.
195
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13 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes ObjE!cts Remarks
NOTE: Buoy 8 has beenremoved by the CoastGuard.
1117 WR deployed.Begin record.Approx. position ofBuoy 8.
1121 35° 36' 1 WR bears 060,2 100 yds.
23° 17' 15
1125 35° 57' 12
24° 30' 15
1129 36° 41' 1 (7-8 sec, \ to 1 m)2
25° 42' 15
1134 38° 06' 12
26° 23' 15
1137 Underway for vessel traffic.End record.
1139 Begin drift, beginrecord.
1141 39° 52' 1 WR bears 060,2 100-150 ft
26° 30' 15
1145 38° 55' 1 Drifter buoy 200 ft2 south of WR.
29° 57' 15
1151 35° 06' 12
34° 55' 15
202
13 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1154 320 24' 1 Drift buoy ~ 2002 yds S of WR.
360 58' 15350 28' 5
1158 27 0 01 ' 12
390 40' 15
1200 Buoy 8 100 ft South.
1202 21 0 45' 1 End drift.2
400 07 1 15
1204 WR aboard.
~1218 WR deployed.
1223 380 18' 1 On station.2 Begin record.
23 0 28' 15
1230 360 39' 1 10.5 sec.2
230 02' 15
WR bears E 090100 m, steady.
(drift log 25 m16.4, 16.4, 19.2sec.)
1238 37 0 45' 1 (12.5 seC., 1.5 m)2
230 21 ' 15
1243 380 12' 12
230 25' 15
1245 End station, begindrift station.
203
13 September 1981
FLOOD
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1248 37 0 21' 1 WR 200 ft. bears E.2
240 20' 15
1253 360 01' 1 WR bears E 100 ft.2
260 16' 15
1258 330 40' 12
29 0 05' 15
12 sec -.J \ m.
1304 300 00' 12
300 25' 15
1310 260 16' 1 End drift.2
320 12' 15
1312 WR aboard.
204
13 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
1 1130 1. 70 3341135 1.60 3241140 1.50 3131145 1.52 3011151 1.65 288 Picked up //1
2 1115 2.38 2581120 2.21 3571125 2.05 3541130 1.80 3491135 1.63 3421140 1.48 3331145 1.36 3211151 1.39 3041155 1.47 ·298 Picked up //2
3 1117 2.48 0081125 2.31 0051130 2.15 0021135 1.97 3581140 1. 78 3551145 1.57 3491151 1.42 3361155 1.34 3311159 1.40 312 Picked up #3
4 1119 2.59 0131125 2.43 0121130 2.31 0101135 2.20 0081140 2.07 0051145 1. 91 0021151 1. 71 3551155 1.60 3491159 1.50 3411200 1.46 3381202 1.46 333 Picked up //4
5 1215 2.51 3411220 2.38 3371227 2.20 3291230 2.16 327
205
-_._--- ------
13 September 1981
FLOOD
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
1233 2.11 3231236 2.06 3191240 2.03 3151245 2.03 309125530 2.03 299 Picked up tiS
6 1218 2.27 3481220 2.26 3461227 2.03 3371230 1.99 3351233 1.90 3291236 1.85 3241240 1.81 3171245 1. 78 3091250 1.82 3001300 2.00 287 Pic~ed up tl6
7 1222 2.06 3571230 1.83 3481233 1.77 3431236 1. 74 3371240 1.71 3301245 1.69 3201250 1. 74 3111302 /17 picked up
8 1232 1.91 3571233 1.87 3541236 1.84 3501240 1.77 3431245 1. 70 3341250 1.69 3251307 tl8 picked up
206
13 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (mo. ) (deg.) Remarks
1 111240 2.61 224111410 2.55 224111600 2.47 224111840 2.36 223112020 2.30 222112340 2.15 220112440 2.10 219112620 2.00 217113020 1.84 212113235 1.72 209113420 1.64 206113610 1.59 203113810 1.52 199114020 1.46 194114200 1.45 190114400 1.43 184114550 1.41 180114800 1.41 175115040 1.46 168 1 retrieved
2 111430 2.65 231111620 2.58 231111830 2.51 230112030 2.45 230112320 2.33 229112640 2.21 227112840 2.10 226113030 2.01 225113250 1.91 223113440 1.81 221113630 1.72 220113830 1.63 215114040 1.54 213114410 1.43 206114610 1.37 202114910 1.31 195115123 1.30 190115440 1.34 182 2 retrieved
207
13 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
3 111640 2.79 238111820 2.75 238112110 2.68 238112250 2.64 238112520 2.58 237112710 2.53 236112920 2.45 235113100 2.39 235113320 2.31 235113500 2.24 234113710 2.16 233113850 2.07 231114100 1.99 229114230 1.91 229114430 1.80 227114640 1.72 224114930 1.60 220115140 1.56 216115530 1.46 208115710 1.43 204115810 1.41 202 3 retrieved
4 112220 2.83 244112540 2.71 243112720 2.69 242112940 2.65 242113120 2.61 242113350 2.55 240113530 2.49 240113720 2.44 239113930 2.37 239114120 2.31 237114250 2.27 236114510 2.20 236114650 2.11 234114950 1.99 232115210 1.91 229115650 1. 75 222115840 1.65 220120000 1.63 219120150 1.57 214 4 retrieved
208
13 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg. ) Remarks
5 121640 2.63 215121810 2.56 213122020 2.49 212122210 2.43 210122440 2.34 209122800 2.27 206123040 2.19 202123240 2.14 201123410 2.10 199123600 2.08 198123810 2.05 194124020 2.01 192124230 1.98 189124410 1.95 188124540 1.95 186124800 1.93 184124940 1.93 183125210 1.91 180125450 1.89 177125640 1.89 176 5 retrieved
6 121930 2.45 221122030 2.40 221122230 2.34 219122500 2.25 216122810 2.15 214123110 2.04 210123310 1.99 207123430 1.93 205123620 1.90 203123830 1.82 199124040 1. 79 196124250 1. 74 192124430 1. 73 191124600 1.71 188124810 1.68 184125000 1.69 180125230 1. 71 176125500 1. 73 172125720 1.77 169125910 1. 78 166 6 retrieved
209
13 September 1981
FLOOD
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
7 122250 2.28 230122620 2.16 228122830 2.07 226123130 2.00 222123320 1.95 220123450 1.90 218123630 1.85 215123900 1.81 211124100 1. 76 208124300 1. 74 205124450 1.71 201124620 1.71 199124830 1.68 195125020 1.65 192125250 1.67 187125530 1.67 183125740 1.69 180130010 1. 73 176130140 1.72 173 7 retrieved
8 123210 2.13 230123340 2.10 229123510 2.08 227123650 2.05 225123920 1.98 221124120 1.92 219124320 1.86 216124500 1.84 214124630 1. 79 212124840 1. 76 207125050 1. 74 204125320 1.71 200125550 1. 70 195125800 1.69 192130030 1.69 188130230 1.69 185130430 1.72 182 8 retrieved
210
13 September 1981
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1000.00100.00 ZOO.OO 500.00 400.00 500.00 600.00 700.00 100.00 NO.OOTIME (SECS)
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Figure A72. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1724 PDT, 13 Sept. 1981.
214
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DRIFTING 198113 SEPT.JD 257
17:46 PDT0••, GMT HS • 1.18 M
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TIME (SEeS)
Figure A73. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1746 PDT, 13 Sept. 1981.
215
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Figure A74. Waverider raw amplitude, filtered amplitude, and power spectraldensity for 1825 PDT, 13 Sept. 1981.
216
00
• 13 SEPT. 19 PDTNDBC BUOY 460101981 JD 257 2 Z
0 SIG HT - 1.8 METERS0 U - -2.0 MIS.. WIND SPEED - 4.1 MIS- WIND DIRN - I. DEGS
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Figure A7S. NDBC 46010 power spectral density for 1700, 1800, and 1900 PDT,13 Sept. 1981.
217
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EBB
Wave rider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1656 WR deployed.
1658 60° 01 ' 2 Begin drift.4
20° 30' 1244° 00' r..J 3
1659 McArthur eM Station.200 ft N.
WR bears W 200 ft.
1703 21° 47' 23
73° 32 12
1708 32° 23' 2 WR bears NW 150 ft.3
76° 11' 12
1713 53° 18' 2 WR bears NW 150 ft.3
65° 15' 12
1718 82° 03' 23
48° 14' 11
1720 92° 03' 23
31° 26' 12
1724 End drift. Holdingstation.
1726 107° 25' 2 Steady on station.3 WR bears W 100 m.
15° 08' 12
1730 108° 15' 23
14° 34' 12
224
13 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1734 Apparent currentincrease.
1736 1000 09' 23
180 15' 12
1744 Drift log 25 m.11.0, 4.7, 10.7 sec.
1746 1070 27' 2 Begin drift from3 station.
150 06' 12
1750 160 30' 25
950 50' 3
1752 330 53' 25
770 18' 3
1753 100 ft. S of Buoy 11.
1756 550 53' 25
460 01 ' 3
1757 WR bears SW 100 ft.
175830 620 32' 2 WR bears SW 100 ft.5
29 0 27' 3
1802 29 0 57' 12
580 55' 5
1807 430 18' 12
45 0 56' 5
1808 End drift. Underway.Move to position nearBuoy 10.
225
13 September 1981
EBB
Waverider LOG (Surface Vessel EGRET)
Time Hdg. Sextant Fixes Objects Remarks
1825 On sta. 100 ft. Wof Buoy 10.Begin record.2 m., approx. 8and 12 sec.WR bears W 100 m.
Drift log10.4, 9.7, 10.8
1843 26 0 50' 12
360 56' 5
1856 End station, endproject.
226
13 September 1981
EBB
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
1 1704 2.96 2581710 2.56 2611715 2.22 2621720 1.90 2621725 1.62 2671730 1.33 2721735 1.15 2931741 1.10 3201745 1.19 335 Picked up III
2 1705 3.18 2631710 2.8 2631715 2.46 2631720 2.09 2651725 1. 76 2681730 1.49 2781735 1.31 2931741 1.32 314 Picked up #2 after 1741 fix
3 1708 3.05 2671710 2.94 2661715 2.54 2651720 2.18 2661725 1.84 2701730 1.51 2791735 1.37 2941739 1.38 305 Picked up 1/3
4 1724 1.48 2801727 1.36 2921734 1.47 311 Picked up //4
5 1803 2.14 2731811 1.62 2831814 1.49 2891815 1.43 2931820 1.37 3091825 1.49 325 Pick up //5
6 1805 2.09 2681810 1.73 2711815 1.43 280
227
---.---_.- ---- --- ---.-_._ .._- -----
13 September 1981
EBB
CAPE DISAPPOINTMENT RADAR DATA
Buoy Time Range BearingNo. (PDT) (nm. ) (deg.) Remarks
1820 1.22 2951825 1.16 3151830 1.26 334 Pick up f/6
7 1807 2.12 2601817 1.44 2641820 1.21 2681825 1.01 269 Pick up f/3
228
13 September 1981
EBB
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (om. ) (deg. ) Remarks
1 1703 2.60 129170440 2.50 129170620 2.38 130170900 2.21 130171140 2.06 132171330 1.93 132171650 1. 71 134172100 1.45 137172320 1.32 140172530 1.22 145172830 1.10 152173100 1.05 159173220 1.00 167173510 0.98 178173700 0.99 186173830 1.03 193174020 1.07 203174250 1.20 211174410 1.28 216 1 picked up
2 170520 2.73 132170640 2.64 133170920 2.44 133171150 2.28 134171350 2.15 133171830 1.84 136172140 1.63 138172340 1.50 141172550 1.37 145172850 1.23 152173120 1.18 160173250 1.14 167173520 1.14 176173720 1.16 183173850 1.21 189174050 1.27 195 2 picked up
3 170740 2.69 135170940 2.57 136171210 2.39 136
229
13 September 1981
EBB
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
171420 2.23 136 ?171950 1.88 138 Found buoy 3. Previous fix
in error?172200 1. 70 140172410 1.55 143172610 1.43 147172910 1.28 154173140 1.21 161173320 1.21 168 3 lost radar reflector
after this173940 1.29 190 3 picked up
4 172250 1.25 155172800 1.20 173
5 180310 1.84 146180500 1. 70 148180650 1.58 151180900 1.46 155181340 1.29 169181510 1.27 175181820 1.27 186182030 1.32 193182340 1.45 204
6 180440 1.72 140180710 1.55 142180920 1.44 146181130 1.32 150181300 1.24 154181640 1.10 169181840 1.06 176182050 1.06 184182400 1.13 196182640 1.20 205182830 1.28 209183020 1.36 214 6 picked up
7 180750 1.66 131180940 1.54 133181200 1.38 135
230
--.- ------- --_._---
13 September 1981
EBB
JETTY A RADAR DATA
Buoy Time Range BearingNo. (PDT) (run. ) (deg.) Remarks
181400 1.26 137181700 1.07 142181900 0.94 146182110 0.82 152
8 181050 1.63 129181210 1.53 130181420 1.40 132181720 1. 18 136181920 1.04 140182130 0.89 144182440 0.73 154184600 0.42 193
231