N PS ARCHIVE 1969 ROBINSON, D. SEICHING IN MONTEREY BAY by David Brooks Robinson DUDLEY KNOX LIBRARV 93943-5101 United States Naval Postgraduate School THESIS Seiching in Monterey Bay by David Brooks Robinson October 1969 Tkl& document ha& been approved ^on public ie- lexue. and laJLe.; i£t> cLu£>UbuuLLon aJ> unlimited. 133218 Seiching in Monterey Bay by David Brooks Robinson Lieutenant, United States Navy S., United States Naval Academy, 1963 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL October 1969 MPS A£ctUV£ -iu^^^y : c,\ ABSTRACT The effect of the Monterey Submarine Canyon on seiching in Monterey Bay is not well known. Spectral analyses of simultaneous tidal records from the north-south extremities of the bay were performed for 23 January and 20 April 1969 to investigate this effect. Both day's records had long-wave activity of which seiching was at least a con- tributing mechanism. Analyses of the computed spectra for the periods during the long-wave activity, and ten-hour periods both before and after, indicate that the seiching motion in Monterey Bay has similar amplitudes at the north-south extremities. TABLE OF CONTENTS I . INTRODUCTION 1 1 I I . INSTRUMENTATION 18 III. DATA ANALYSIS............ 21 A. Selection of Data 21 B. Digitizing Procedure for Monterey Data.......... 21 C. Digitizing Procedure for Santa Cruz Data.............. 22 D. Analysis 23 IV. DISCUSSION 35 A. Wilson's Three-Dimensional Model. 35 B. Interpretation of Spectra. 40 V. SUMMARY APPENDIX A Use of the Calma Co. Model 480 Digitizer 48 APPENDIX B Raw Spectra.. ........ .. . 52 LITERATURE CITED. 66 INITIAL DISTRIBUTION LIST. 68 FORM DD 1473. 71 LIST OF TABLES I. Long-Period Waves in Monterey Harbor 14 II. Marine Adviser's Data for Monterey Harbor 14 III. Marine Adviser's Data for Santa Cruz Harbor 14 IV. Periods of Oscillation from Residuation Analysis 15 V. Periods of Oscillation from Spectral Analysis 16 VI. Computed Response Characteristics of Santa Cruz Stilling Well.. 20 VII. Amplitude Coefficients for 23 January and 20 April 45 LIST OF FIGURES 1 . Monterey Bay 12 2. Smoothed Spectrum for Santa Cruz - 23 January 27 3. Smoothed Spectrum for Monterey - 23 January 28 4. Smoothed Spectrum for Santa Cruz - 20 April 29 5. Smoothed Spectrum for Monterey - 20 April 30 6. Smoothed Santa Cruz Before/After Spectra - 23 January 31 7. Smoothed Monterey Before/After Spectra - 23 January 32 8. Smoothed Santa Cruz Before/After Spectra - 20 April 33 9. Smoothed Monterey Before/After Spectra - 20 April 34 10. Numerical Calculations of Modes of Oscillation of Monterey Bay. 36 11. Numerical Calculations of Modes of Oscillation of Monterey Bay. 37 12. Numerical Calculations of Modes of Oscillation of Monterey Bay. 38 13. Numerical Calculations of Modes of Oscillation of Monterey Bay. 39 14. Schematic Representation of Spectra for 23 January 41 15. Schematic Representation of Spectra for 20 April 42 16. Computer Program CONVERT............. 50 17. Santa Cruz Spectrum, 1000-2243 23 January 52 18. Santa Cruz Spectrum, 1217 23 January - 0100 24 January 53 19 Monterey Spectrum, 1000 23 January - 1938 23 January.. 54 20. Monterey Spectrum, 1522 23 January - 0100 24 January 55 21. Santa Cruz Spectrum, 1100 20 April - 2058 20 April 56 22. Monterey Spectrum, 1100 20 April - 2048 20 April 57 23. Santa Cruz Spectrum - Before 23 January..... 58 24. Santa Cruz Spectrum - After 23 January 59 25. Monterey Spectrum - Before 23 January.............. 60 7 26. Monterey Spectrum - After 23 January 61 27. Santa Cruz Spectrum - Before 20 April ..... 62 28. Santa Cruz Spectrum - After 20 Apri 1 63 29 . Monterey Spectrum - Before 20 Apri 1 64 30. Monterey Spectrum - After 20 Apri 1 65 ACKNOWLEDGEMENT The author wishes to express his sincere appreciation to Professor Theodore Green, III under whose direction this paper was written. His encouragement, criticism, and experience were invaluable in the com- pletion of this research. In addition, the author is indebted to Mr. Sheldon Lazanoff, the Naval Oceanographic Office Liaison with Fleet Numerical Weather Cen- tral, for his technical advice and assistance in installing and cali- brating the tide gage in Santa Cruz, and to the Naval Oceanographic Office for the use of the portable tide gage used in this study. I. INTRODUCTION Monterey Bay, a large, semi-elliptical bay, is located approximate- ly sixty nautical miles south of San Francisco. It is bounded on the north by Point Santa Cruz and on the south by Point Pinos. The bay is bisected by the Monterey Submarine Canyon. The head of this deep canyon is located just off Moss Landing (Figure 1). Several studies have been conducted to investigate the long- period waves in the bay and its adjoining harbors. (For purposes of this research, a long-period wave is defined as any wave with a period greater than 1 min.) Hudson L1949] investigated the surge in Monterey harbor for the U.S. Army Corps of Engineers. The study provided data for a proposed model of the harbor. He used six months of continuous data (October 1946 to April 1947) obtained by three automatic Stevens water-level recorders which were electrically synchronized. The recorders were located within the present boundaries of the harbor. Hudson's results for long-period waves are shown in Table. I. The cause of these long-period waves in the harbor was not known and Hudson did not attempt to define the surge mechanism. Wilson, et al D965J , also working under the auspices of the Corps of Engineers, made a field study for a proposed surge-action model of Monterey harbor. Wilson analyzed the long-period waves in the entire bay, using data from several sources. Wave recorders installed by Marine Advisers (MA) at Monterey and Santa Cruz, the north-south extremities of the bay, provided excellent data. Three sensors were installed within the harbor at Monterey and were in continuous operation from October 1963 to April 1964. Two were 11 Moss Landing X-TIDE GAGE miles 5 j i arranged so that the tides and sea-swell were filtered out; a third re- corded the sea-swell approaching the harbor. Wilson found no correla- tion between the long waves in the harbor and the approaching sea-swell. This finding led him to conclude that the surge in the harbor is not a result of the incoming swell or surf beat. The MA sensor in Santa Cruz was inside the harbor, [Grauzinis, 1968J, Again, the short-period waves and swell were filtered out so that it functioned as a long-period wave recorder. This sensor was in con- tinuous operation from October 1963 to February 1964. A summary of the Monterey and Santa Cruz data is presented in Tables II and III. To obtain an independent evaluation of the oscillations in the bay, Wilson performed residuation analyses on several different records for various locations around the bay. Residuation analysis is accomplished by successively subtracting apparent periodicities from a wave record. The procedure is continued until a relatively smooth trace remains, and a sequence of apparent periods of oscillations is obtained. These results are presented in Table IV. Table V presents a synopsis of spectrum analyses for three days record of the Monterey MA sensors. In order to determine the cause of the surge, Wilson made an ex- tensive analysis of the two- and three-dimensional (i.e. two spatial and one time dimensions) oscillating characteristics of the bay using (1) approximate analytical solutions for a semi-enclosed basin, (2) numerical solutions for the modes of both two-dimensional and three dimensional oscillations, and (3) wave refraction diagram techniques. He concluded, based on the best fit of the observed sequences of periods in Tables IV and V with calculated modes of oscillation for the bay, that the Monterey Submarine Canyon causes the bay to 13 TABLE I Long-Period Waves in Monterey Harbor (after Hudson, 1949) PERIOD AVERAGE HEIGHT PERCENTAGE OF (min) (ft) Time PRESENT 1-2 0.4 20 2-4 0.5 30 4-15 not given 15 TABLE II Marine Adviser's Data for Monterey Harbor (after Wilson, 1965) SENSOR PERIOD AVERAGE HEIGHT PERCENT OF (min) (ft) TIME PRESENT 1 1.7-14 0.1-2.5 0-50 2 1-14 0.1-3.0 0-55 TABLE III Marine Adviser's Data for Santa Cruz Harbor (after Wilson, 1965) PERIOD (Min) AVERAGE HEIGHT (ft) PERCENT OF TIME PRESENT 1-2.3 0-18 2.3-4 0.2-2.0 20-70 10-14 0-25 14 " *- -£> o E ~ "* ** - S iTl r^ao'os in im m rq (NJ iN *M (M f\l fM o 2 u GO — J3 t M cr -« -D XI a r*> * ■«r ■*** -^r c<-| ^* -r m H 2 U OS o* in r- < i/i in in a. < _ fO u« o •a ^) u (i_fc u C"' 2 w 30 r*% sO ^ *r JO c> CO CO CO O w o — 1 u-i — i -o o o in -' z: m rv) r^ — . "n O- «*» — r\J r— rJ r- — * — < — • NO •n rg 1J cr rn ^ ""■ rM m r- f> m -O m rs) o 00 -o r^ r^ CO ?M A O o <£1 -0 O CO z « o 2 < 03 O J - CT> v u u n <4 o o o o a- a- o O — o o o O -• iM ^ *7 "7 T -"• o o o o^ -• — « fM ^ n u 22 -=2 pinoo ^j ^. H u £ £i co o — >N^ > o < Q b o V u o - - K "^ C O O o o -r rr U* 4 2 S 3 — o <=C in ID o CO o >> r— c C o •^ ■4-J fO ■a •^ 00 o s- O (T3 u CO O 4- O 10 T3 O "r— s- CD Q. 15 r~ 00 O o o — ~-i -H ^-4 r-i fM rg o *- o o rO ^H rg o rg rg (VJ rg rg rg rg rg' rg rg rg rg rg' rg' li~l vD •* m ■ <+4 0 <«J« m ro ■^ X* u c r- 00 00 r- r~ in in IT) m in m CO O^ c> o^ to CO rO ro ro ro m ro ro ro ro ro ~H .— 1 *-« ~* . — 4 *H r- r~ vO nO r- 1 -h rg rg rg rg rg rg fSJ rg rg rg rg rg rg rg rg rg rg rg m ro ro ro ro ro ro ro ro ^ » n ^ o . « « 0 _, rg m ^H rg ro i-4 rg ro cf,2 o S 2W * ■tf -O •*< ■£> 3^ sO O^ -H a- — < — « 0) id Q < •— 4 0 30 -~* u 2 to ,0 oo M 9 CO u (TJ OJ CT> C o to o u_ < (T3 s- +-> u <1J Q. CO I o o to o O 10 -o o CD Q- 16 essentially act as independent north and south open-mouth oscillating basins with the boundaries lying along the natural mouth of the bay and the center line of the canyon. That is, oscillations in one end of the bay do not effect oscillations in the opposi te*end; the north-south basins are "uncoupled." Raines El 967H analyzed twelve; selected long-period wave trains from three years of tide data (1964-1966) obtained with the Naval Post- graduate School (NPS) recorder located on Municipal Wharf #2, Monterey harbor. Using graphical methods, he found mean periods of 19-39 min and 1.5-2.0 min. Raines did not rule out the possibility that the longer period waves were bay seiching, but he strongly suggested, based on his spectra and barometric oscillations occurring simultane- ously with half of the wave trains analyzed, that the longer period waves were progressive waves produced by air-pressure fluctuations. Lack of adequate barometric pressure data precluded a correlation of the wave periods and air-pressure fluctuations. The shorter period waves were judged to be either harbor seiching or surf beat. This conclusion was based on the similarity of his results with those of Wilson El 9652 and Hopper D9671 . 17 II. INSTRUMENTATION The Monterey data for this study were obtained with a standard Coast and Geodetic Survey automatic tide gage [Manual of Tide Observations, 19651] . The gage, which is maintained daily by NPS personnel, is lo- cated on Municipal Wharf #2, Monterey harbor. This instrument senses changes in water level by means of a float/ pulley arrangement. The recording drum is advanced by a clock mecha- nism. The drum speed is designed to be 1 in/hr but the NPS gage has an hourly feed of approximately 1.06 in/hr. The marigram is recorded in rectilinear coordinates on plain white paper. The majority of higher frequency wind waves (periods of 4 min and below) are filtered by a stilling well which is a 12-in diameter steel pipe with a 1-in orfice in the bottom. The Santa Cruz data were obtained with a Bristol Model 28 gas- purging pressure (bubbler), portable tide gage located on the Santa Cruz wharf. This instrument senses changes in water level by means of a nitrogen-filled tube which is connected to a bellows system Qlanual of Tide Observations, 1965H . The marigram is recorded on a mechanical -clock strip-chart recorder in curvilinear coordinates. The design chart drive speed is 1 in/hr, but a substitution of drive gears increased this to 6 in/hr A bubbler orfice chamber was connected to the end of the sensing tube to reduce wave action. There was also a bellows inlet needle valve which could be throttled to further filter wave action from the record. The combination of these two filtering mechanisms proved inadequate. A stilling well was designed and installed to 18 attain the desired filtering of high frequency wind waves. The well was constructed of a 20-ft section of polyvinyl Chloride (pvc) 6-in inside- diameter pipe. The well was capped and 16, 1/4-in inside-diameter holes drilled in the side. Copper sleeves were inserted to eliminate fouling. The 16 holes provided the capability of increasing the orfice from a 1/4-in to a 1-in diameter opening. The response characteristics of the well were determined theo- retically for two orfice sizes and three different wave frequencies using the equation for the rate of water rise in a well QDoodson and Warburg, 194"Q : rate of rise of water in well = d^/dt = 0.6 a/A^2g(h0 - h^ ) where a = orfice area A = well area 0.6= empirical orfice flow coefficient g = acceleration due to gravity h0 = water height outside the well, i.e. the forcing function hj = water height inside the well. The forcing function, hQS was chosen to be a simple sine function of unit amplitude and frequency equal to the wave frequency of interest. The initial conditions were hi = o at t=0. The results are sum- marized in Table VI. The response characteristics for the Monterey stilling well were not calculated since the orfice area to well area ratio is larger, providing response characteristics better than those of the Santa Cruz well. A 1/4-in orfice was used in the Santa Cruz well. 19 PERIOD ORFICE DIAMETER (in) PHASE LAG (deg) AMPLITUDE REDUCTION (%) 20 sec 0.25 180 95 20 sec 1.00 72 45 60 sec 0.25 75 91 60 sec 1.00 30 5 25 min 0.25 6 1 25 min 1.00 0 0 TABLE VI Computed Response Characteristics of Santa Cruz Stilling Well 20 III. DATA ANALYSIS A. SELECTION OF DATA Because this study was concerned with the character of seiching motions affecting the entire bay (and not their frequency of occurrence), only those records with similar long-period wave characteristics at each station for equal intervals were considered for analysis. Also, the seiching had to persist long enough to provide an adequate number of data points for a meaningful analysis. The minimum persistence time considered was ten hours. Two days were selected which met these criteria; 23 January and 20 April, 1969. The Santa Cruz man" gram for 23 January was recorded at a rate of 1 in/hr with a 20- ft range instrument. Although the stilling well had not been installed, the trace was relatively narrow and free of wind-wave noise. The long-period waves lasted for approximately 15 hours (1000 23 January - 0100 24 January). The Santa Cruz marigram for 20 April was recorded at a rate of 6 in/hr with a 10- ft range instrument. The stilling well had been installed by this date. (In February, the 10-ft range instrument was substituted to improve the resolution of the record and the recording rate was increased to facilitate digitizing procedures.) The long- period waves for this day lasted approximately 10 hours (1100-2100 20 April). B. DIGITIZING PROCEDURE FOR MONTEREY DATA The Monterey record, a rectilinear trace, was digitized using a Calma Co. Model 480 mechanical digitizer (Appendix A). The sampling 21 rate, At, for the 23 January record was 33.87 sec whereas the sampling rate for the 20 April record was 33.77 sec. The difference in sampling rates was not due to the digitizer, which had a constant sampling in- terval of 0.01 in, but rather was a result of the different recording rates of the two records. The average recording rates were 1.063 in/hr and 1.066 in/hr for the 23 January and 20 April records respectively. C. DIGITIZING PROCEDURE FOR SANTA CRUZ DATA The Santa Cruz records were not digitized by the machine method because of the problems encountered in digitizing a curvilinear record with a rectilinear device. A simple geometrical relationship can be used to convert the rectilinear digitized data of a curvilinear record, but this conversion introduces errors and high frequency noise ^Steele, 1 967ZZI which were thought to be excessive for this study. These records were, therefore, digitized by hand. It was not possible to equal the Monterey data sampling interval of 0.01 in for the 23 January Santa Cruz record since the latter was recorded at 1 in/hr. A sampling interval of approximately 0.025 in was used, giving a sampling rate of 89.64 sec. This meant that the sampling rate for the Monterey record was about two and one-half times better than the Santa Cruz record for this date. The sampling interval for the 20 April record, a 6-in/hr record- ing rate, was selected to be as close as possible to that for the Monterey record. The resulting sampling rate was 33.14 sec, approxi- mately one-half second slower than that for the Monterey record. The problem, and avoidance, of aliasing in spectral analysis of a finite, discrete, record is thoroughly discussed in the literature. It is only important to note here that the sampling rates achieved in 22 this study are more than adequate since both tide gages are long-period recorders designed to filter out all waves with periods below 4 min. Aliasing, therefore, is not considered a problem and is not discussed below. D. ANALYSIS Before the data were analyzed, it was necessary to remove the trend due to tidal components. The detrending was accomplished to an adequate degree by forming a pure cosine curve, fyj , which closely approximated the tidal record for the specific interval digitized, and subtracting this "tidal curve" from the raw data, y-j . That is, fy = Acos(2/Tfi At-9) i = l,2,3,...,N where A =amplitude measured on marigram f =tidal frequency measured on marigram 8 =appropriate phase lag required to match data and 77. N =number of data points, and Yi = *i " (m +7f.) i = l,2,3,...,N where m is the mean measured on the marigram and Y is the detrended data. The Fourier coefficients of the detrended data were calculated using the IBM/360 library subroutine RHARM. This subroutine is a one-dimensional fast Fourier transform (FFT) analysis based on the Cooley and Tukey |_1965U algorithm., The program is designed to analyze N data points where N = 2m m = 3,4,5,. ..,20. 23 The FFT not only greatly reduces the number of calculations from earlier Fourier analysis schemes, but also reduces the round-off errors in the coefficients. Specifically, both the number of computations and round-off errors are reduced by essentially log£(N)/N [Cochran, et al , 19671] • Before the spectrum was formed, each Fourier coefficient was hanned. The raw Fourier transform is exact for the specific frequencies of the calculated coefficients. Adding, however, a term of the form Dcos(ft) where the frequency f is not one of the discrete frequencies, f .j , will alter all the Fourier coefficients in the time series. This is, in effect, an energy leakage into the discrete frequencies of the raw periodogram. Leakage can be defined as the altering of a spectral estimate for a specific bandwidth by the energy at more or less random frequencies outside the bandwidth of interest. The effects of leakage in the raw periodogram decay as 1/ |f-fjl as f- recedes from f. Hanning the coefficients before forming the spectrum increases the de- cay to l/lf-f^l [Jingham, et al , 19671]. If ai and b. are the raw Fourier coefficients, the hanned or modified coefficients are formed using: Ak = -(l/4)ak_! + 0/2)ak - (l/4)ak+1 Bk = -(l/4)bk_1 + (l/2)bk - (l/4)bk+1 The spectral estimates, (AJ* + B^), k=l ,2,3,. . . ,N/2, were normalized by multiplying each by the time interval analyzed. Figures 17-22 (Appendix B) are the computed spectra for the two days analyzed. The 15-hr period wave activity on 23 January is depicted by two, overlapping spectra for each station. This is a consequence of the RHARM restrictions on the number of data points. 24 The spectra are not the entire spectra, but rather only the low frequency portion. The dashed line on the low end of the spectrum in- dicates that all energy in the tidal components has not been removed. Similarly, the dashed line at the higher end of the spectrum designates the start of the high-frequency noise. There is approximately three hours difference in the Monterey and Santa Cruz time intervals for the spectra for 23 January, which is a consequence of the number of data points and the unequal sampling rates. The spectra for different stations on the same day show a certain amount of correspondence with each other, but it is difficult to match periods of oscillation between spectra since it is not easy to deter- mine with confidence which peaks in the spectra are spurious and which are real . Spectral estimates of a random process have a chi-squared distri- bution [Bartlett, 1955]] and are inconsistent estimates of the power spectrum. Each coefficient has 2 degrees of freedom, and the con- fidence in each spectral estimate can be increased by (1) averaging spectral estimates over a span of frequencies or (2) "blocking" the record, analyzing each block and averaging spectral estimates at equal frequencies [Jones , 1965; Hinich and Clay, 1968Z1 . The spectra in this study were averaged over three bandwidths. Smoothing the spectra in this manner gives more confidence in the true peaks, but the resolution in each spectrum is simultaneously degraded. The two spectra for each station on 23 January have been averaged together at equal frequencies to give a spectrum for the entire 15-hr period. When sequentially averaging over three bandwidths, there are three possible starting points, that is, three possible methods. 25 The spectra were averaged for all three possibilities which permitted de- termination of the resolution and stability of each peak. Schematic representations of the smoothed spectra are presented in Figures 2-5. These spectra represent a compilation of the three averaging methods for each spectrum. Only those peaks which were stable in shape and energy density are labeled with the bandwidth resolution. All peaks not labeled will not be considered further. Spectra for 10-hr periods both before and after the long-period wave activity on 23 January and 20 April were also calculated for each station (Figures 23-30, Appendix B). These spectra were smoothed in the same manner described above. Schematics of the "before" and "after" spectra for each station are presented in Figures 6-9. The original intention in this study was to compute the cross- spectra for the Monterey-Santa Cruz records. It was hoped that, with the cross-spectral values and average phase lags for each discrete frequency, a thorough understanding of the seiching motions in Monterey Bay could be obtained. The cross-spectra calculations were not feasible, however, for two reasons. The records were not accurately synchronized. It is estimated that an initial time difference of as much as 3 min between the two records could be present. This was due to the variability in the seperate gage clocks and the maintenance of the gages by different persons at varying intervals. This factor alone is not prohibitive since Grauzinis D968H has outlined a procedure for computing cross- spectra for records without initia-1 synchronization. A more serious error was created by the unequal digitizing rates between records from the two stations. A cumulative phase error was introduced by sampling at unequal rates. The data obtained in this study, there- fore, are considered unsuitable for cross-spectral analysis. 26 90 80 70- 60- ^\ 50 M e a 40 M ita •> E U 30 20 10- 27.0-27.6 min 13.1-14.1 min Frequency (mHz) Figure 2 Smoothed Spectrum for Santa Cruz - 1000 23 January to 0100 24 January 27 7- 6 * 3- 2- 1- 32.1-38.5 17.5-18.6 11.1-12.0 Frequency (mHz) Figure 3 Smoothed Spectrum for Monterey - 1000 23 January to 0100 24 January 28 30 25 \ 20 15 10 12. 8- 14.1 Frequency (mHz) 8.8-9.4 Figure 4 Smoothed Spectrum for Santa Cruz -1100 20 April to 2058 20 April 29 3- A = 2- 13.1 -14.0 9.9-10.6 8.2-8.8 Frequency (mHz) Figure 5 Smoothed Spectrum for Monterey - 1100 20 April to 2048 20 April 30 40.2-50.9 2- 1- BEFORE 41.8-58.8 AFTER Frequency (mHz) Figure 6 Smoothed Santa Cruz Before/After Spectra - 23 January 31 3- 2 -\ AFTER 25.1-28.9 1- Frequency (mHz) Figure 7 Smoothed Monterey Before/After Spectra - 23 January 32 51.6-63.0 1- A w 0- BEFORE 10.7-11.6 8.7-9.3 35.3-47.1 AFTER 2 8.8-9.3 6.9-7.2 Frequency (mHz) Figure 8 Smoothed Santa Cruz Before/After Spectra - 20 April 33 1- A CM 5 o BEFORE 48.0-64.0 20.5-24.0 - 5, 1- 33.9-38.4 AFTER Frequency (mHz) Figure 9 Smoothed Monterey Before/After Spectra - 20 April 34 IV. DISCUSSION A. WILSON'S THREE-DIMENSIONAL MODEL Wilson's numerical calculations for the three-dimensional oscil- lating characteristics of Monterey Bay are depicted in Figures 10-13. Figure 10(a) illustrates the grid points used for the solution. The numbers adjacent to each grid point are the water depths in feet. The dashed line connecting Point Santa Cruz with Point Pinos is the assumed boundary nodal line for the solution. The successive figures depict decreasing periods (increasingly complex modes) of oscillation. The contours are water level ampli- tudes normalized to the highest anti-node for the mode. The inset to the left of each figure is a simplified modal oscillation. The sequence of periods is Tn = 44.2, 29.6, 28.2, 23.3, 21.6, 20.4, 19.4, 18.7, 17.6,... ,13.3,..., 12.4,. ..min. Wilson notes that the assumed boundary nodal position could very well be incorrect and might be more to seaward, closer to the 100-fathom curve. Changing the assumed nodal line would alter the boundary conditions and would affect both the modal periods and the geometry of the oscillations. Modes 1 and 2 indicate strong oscillations in the northern portion of the bay and little effect in the southern portion of the bay. Mode 3 shows the first strong oscillation in the southern portion. Mode 4 indicates similar oscillations at both the northern and southern ends with weak oscillations over the canyon. Successive modes become more complex. 35 <4- O -M re i— r— *■""** •r- LT) U <£> (/) CX> O i— <4- « O C O to CO o CI) r— ■O t- O 3 QJ 2: S- E :3 4- O CD O S- ^ 4- J_ co » — c o >, •i- ra +-> co fO ■— >> 13 QJ <_> i. r— O C O >— s: fO u •1— s- cu E 36 c o •I-" ■M rtJ ^~ ^~ ^~ ■* •r- in U ID to CTt o <— M- " O C O > •i- CO (O 1— >> 3 (D 0 s- 1— O c 0 r— 2: fO 0 wrm s- O) E 3 37 c o • ^ •4-> •i- Lf> O to to O i— 4- O C o to to O) r- 00 ■a .,- o 3: s: 0) E S- **- o 3 O S- C7> 4- ^ to ' u_ c o >> •r- re +J CO fO •— >> =J OJ o s_ r— (C ^~ r— *^^ •1- lo O <£> 10 CT> O ■— M- •> O C O to c/i CD r— T3 -i- PO O 3 21 E CD M- O S- 0 s- =3 M- 0> p~ E Ll_ O >> •1- CQ (O •— >> =5 CD a s. 1— a> 0 e 0 .— 2: ta 0 ■r— S- 2 FORMATdHC ,2X,25H, SAMPLING INTERVAL E QU AL S, IX , E 1 5 . 7, 11X,7H SECONDS) PRINT 1C3,JJ 103 FORMATdHC ,9H JJ EQUAL S , 2X , I 2 ) DO 104 1=1,5000 U( I) =0.0 104 V(I)=O.C DO 1C6 1=1 ,3000 106 IBUFF( I)=0 CC'UNTX=0.r COUNTY=C.o NUM=3C0C M=l KB=0 CALL LIOF( 5LRBCD1, I BU FF, NUM, NPAR , NEUF ) IF(NEOF) 602,107 107 K=-7 KF=0 108 K=K+8 KA=K+8 KC=0 DO 109 KB=K,KA KC=KC+1 109 NK(KC)=IBUFF(KB) DFC0DE(80,110,NK) ( N ( I ) , I =1 ,80 ) 110 F0RMAT(8CR1) DO 12C 1 = 1 ,80 IF(N( I KEQ.47B) GO TO 111 IFIN( I ).EQ.50B) GO TO 113 IF(N( I ) .EQ.55B) GO TO 114 IF(N( I ).EQ.34B) GO TO 115 C SYMBOL "*%(47B), IS A FLAG. C SYMBOL "/", (50B), REPRESENTS AN INCREMENT TRAVEL IN C THE MINUS X OR Y DIRECTION. C SYMBOL "C", (55B), REPRESENTS ZERO TRAVEL IN THE X OR C Y DIRECTION. C SYMBOL "1", (34B), REPRESENTS AN INCREMENT TRAVEL IN C THE POSITIVE X OR Y DIRECTION. GO TO 12C 111 PRINT 112, M, I 112 FORMATdHC ,2I1C) IFIM.GT.1C ) GO TO 121 GO TO 120 113 RX=-C01 Kfi=K8+l GO TO 116 114 RX=0.0 K8=K8+1 GO TO 116 115 RX=0.01 K8=K8+1 116 K3=K8/2 K3=2*K3 IF(K3.EQ.K8) GO TO 118 COUNTX=COUNTX+RX IF(COUNTX.NE.O.O) GO TO 117 GO TO 120 50 117 U(M)=COUNTX GO TO 12C 118 COUNTY=COUNTY+RX IF(COUNTX.NE.O.O) GO TO 119 GO TO 120 119 V(M)=CCUNTY COUNTX=0.0 M=M+1 IFIM.GT.5f CO) GO TO 600 120 CONTINUE 121 TIME=(M*DELT)/3600. PRINT 122, TIME 122 FORMATdH ,1CX,28H TOTAL TIME OF RECORO EQUALS, 2X, E15.7,2X,7H HOURS. ) PRINT 123, (V(I ) ,1=1, M) 123 FORMATdH ,10X,14F7.2) PUNCH 124, (V( I ) , 1 = 1, M) 124 FORMAT d4F5. 2) 125 CONTINUE STOP 600 PRINT 601 601 FORMAT ( 1H1,20X,37H **** U AND V SPACE INADEQUATE ****) 602 STOP END 51 160- 140 120- 100 80 „\ 60- 27.3 APPENDIX B Raw Spectra FIGURE 17 Santa Cruz Spectrum 1000 - 2243 23 January N=512 1.0 Frequency (mHz) 2.5 52 120J 27.3 100 80^ * ~ 60- Santa Cruz Spectrum 1217 23 January-0100 24 January N=512 17.4 1.0 Frequency (mHz) FIGURE 18 25 53 J\ 0 + 0 Monterey Spectrum 1000-1938 23 January N=1024 1.0 1.5 Frequency (mHz) FIGURE 19 2.0 54 Monterey Spectrum 1522 23 January-0100 24 January N=1024 1.0 1.5 Frequency (mHz) FIGURE 20 2.5 55 35 30- 25^ 20 15- 10 5- Santa Cruz Spectrum 1100-2058 20 April N=1024 T— 1.5 1.0 Frequency (mHz) FIGURE 21 2.0 25 56 J\ Ul Monterey Spectrum 1100- 2048 20 April N=1024 1.5 Frequency (mHz) FIGURE 22 25 57 7 47.8 4- Santa Cruz Spectrum 2100 22 January - 0948 23 January Before N=512 1.0 1.5 Frequency (mHz) FIGURE 23 2.0 25 58 546 * 3 04- 0 Santa Cruz Spectrum 0100-1348 24 January After N=512 1.0 1.5 Frequency (mHz) FIGURE 24 2.0 2.5 59 1- 38.5 Monterey Spectrum 2400 22 January 0948 23 January Before N=1024 18.6 1.5 1.0 Frequency (mHz) FIGURE 25 2.0 2.5 60 27.5 ■X Monterey Spectrum 0100 - 1048 24 January N=1024 4- 2 .5 1.0 1.5 Frequency (mHz) FIGURE 26 2.0 25 61 51.5 Santa Cruz Spectrum 0200 - 1158 20 April Before N=1024 ~\ 3- 1 1.0 1.5 Frequency (mHz) FIGURE 21 2.0 25 62 -\ Santa Cruz Spectrum 0800-1758 21 April After N=1024 Frequency (mHz) FIGURE 28 63 4 ~\ Monterey Spectrum 0200 - 1148 20 April Before N=1024 57.6 1- 1.0 15 Frequency (mHz) FIGURE 29 2.0 2.5 64 * 7 4 3- 360 Monterey Spectrum 0800 - 1748 21 April After N=1024 2 1- O-W 1.0 1.5 Frequency (mHz) FIGURE 30 2.0 25 65 LITERATURE CITED 1. Bartlett, Mo, 1955, An Introduction to Stocahstic Processes, Cambridge University Press, Cambridge England, 2. Bingham, C , M.D. Godfrey, and J.W. Tukey, 1967, Modern Techniques of Power Spectrum Estimation, IEEE Transaction on Audio and Electroacoustics , Vol. AU-15, No, 2, June, 56-66, 3. Cochran, W.T,, and others, 1967, What is the Fast Fourier Transform?, IEEE Transaction on Audio and Electroacoustics, Vol. AU-15, No, 2, June, 45-55, 4. Cooley, J.W, and J.W, Tukey, 1965, An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation, Vol, 19, No. 90, April, 297-301. 5. Grauzinis, V.J. , 1968, An Analysis of Seiche Conditions in Santa Cruz Harbor, California, and Some Implications for the Proposed Harbor Extension, U.S. Army Corps of Engineers, San Francisco, California. 6. Hinich, M.J. and C.S. Clay, 1968, The Application of the Discrete Fourier Transform in the Estimation of Power Spectra, Coherence, and Bi spectra of Geophysical Data, Rev, of Geophysics, Vol. 6, No. 2, August, 347-363. 7. Hopper, J.H., 1967, Long Waves In and Near the Surf Zone, M.S. Thesis, Naval Postgraduate School, Monterey, California. 8. Hudson, R.Y., 1949, Wave and Surge Action, Monterey Harbor, Monterey California, Technical Memorandum No. 2-301 , Waterways Experiment Station, Vicksburg, Mississippi, U.S. Army Corps of Engineers. 9. Jones, R.H., 1965, A Reappraisal of the Periodogram in Spectral Analysis, Technometrics , Vol, 7, No, 4, November, 531-542. 10. Manual of Tide Observations, 1965, U.S. Coast and Geodetic Survey Publication 30-1, U.S. Government Printing Office, Washington, D.C, 11. Munk, W.H., 1962, Long Ocean Waves, The Sea, Volume One, M.N, Hill, ed. , Interscience Publishers, New York. 12. Raines, W.A. , 1967, Sub-Tidal Oscillations in Monterey Harbor, M.S. Thesis, Naval Postgraduate School, Monterey, California 13. Steele, B.T., 1968, Spectral Analyses of Waves and Associated Bottom Pressures Off Point Sur, California, M.S. Thesis, Naval Postgraduate School, Monterey, California, 66 14. Wilson, B.W., J. A. Hendn'ckson , and R.E. Kilmer, 1965, Feasibility Study for A Surge-Action Model of Monterey Harbor, California, Waterways Experiment Station, Vicksburg, Mississippi, U.S. Army Corps of Engineers. 67 INITIAL DISTRIBUTION LIST No copies 1„ Defense Documentation Center Cameron Station Alexandria, Virginia 22314 2. Library, Code 0212 Naval Postgraduate School Monterey, California 93940 3. Oceanographer of the Navy The Madison Bui ldmg 732 No Washington Street Alexandria, Virginia 22314 4. Professor Theodore Green, III Department of Meterology University of Wisconsin Madison, Wisconsin 57306 5. LT David B Robinson USS CANON (PG- 90) Fleet Post Office San Francisco 96601 6. Dr„ B.W. Wilson Science Engineering Associates San Marino, California 91108 7. UoSo Army Corps of Engineers Waterways Experiment Station Vicksburg, Mississippi 39180 8. Professor W„C. Thompson, Code 58Th Department of Oceanography Naval Postgraduate School Monterey, California 93940 9. Professor JCB. Wickham, Code 58Wk Department of Oceanography Naval Postgraduate School Monterey, California 93940 10o Asst Professor W.W. Denner, Code 58 Dw Department of Oceanography Naval Postgraduate School Monterey, California 93940 20 68 No. Copies 11. Asst Professor E.B. Thornton, Code 58Tm 2 Department of Oceanography Naval Postgraduate School Monterey, California 93940 12. Department of Oceanography, Code 58 3 Naval Postgraduate School Monterey, California 93940 69 Ilnclassifipd Security Classification DOCUMENT CONTROL DATA -R&D (Security classification of title, body of abstract and indexing annotation must be entered when tfie overall report is classified) . originating ACTIVITY (Corporate author) Naval Postgraduate School Monterey, California 93940 2a. REPORT SECURITY CLASSIFICATION Unclassified 2b. GROUP 3 REPORT TITLE Seiching in Monterey Bay 4 descriptive NOTES (Type of report and.inclusive dates) Master's Thesis; October 1969- 5. AUTHOR(S) (First name, middle initial, last name) David Brooks Robinson REPOR T D ATE October 1969 7a. TOTAL NO. OF PAGES 68 76. NO. OF REFS 14 8a. CONTRACT OR GRANT NO. b. PROJEC T NO. 9a. ORIGINATOR'S REPORT NUMBER(S) 96. OTHER REPORT NOIS) (Any other numbers that may be assigned this report) 10. DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is unlimited. II. SUPPLEMENTARY NOTES 12. SPONSORING MILI TARY ACTIVITY Naval Postgraduate School Monterey, California 93940 13. ABSTRAC T The effect of the Monterey Submarine Canyon on seiching in Monterey Bay is not well known. Spectral analyses of simultaneous tidal records from the north-south extremities of the bay were performed for 23 January and 20 April 1969 to investigate this effect. Both day's records had long-wave activity of which seiching was at least a contributing mechanism. Analyses of the computed spectra for the periods during the long-wave activity, and ten-hour periods both before and after, indicate that the seiching motion in Monterey Bay has similar amplitudes at the north- south extremities. DD """ 1473 1 NOV 83 ■ "T 1 *J S/N 01 01 -807-681 1 (PAGE 1) Unclassified 71 Security Classification A- 3140S Unclassified Security Classification key wo RDS Seiching Monterey Bay Spectral Analysis RO L E WT DD ,F,r.,1473 back S/N 0101-807-6821 Unclassified 72 Security Classification thesR6375 Seiching in Monterey Bay. 111 111 3 2768 001 94896 1 DUDLEY KNOX LIBRARY