AN EVALUATION OF A NUMERICAL WATER ELEVATION AND TIDAL CURRENT PREDICTION MODEL APPLIED TO MONTEREY BAY by Sheldon Mark Lazanoff United States Nava! Postgraduate Schco THESI AN EVALUATION OF A NUMERICAL WATER ELEVATION AND TIDAL CURRENT PREDICTION MODEL APPLIED TO MONTEREY BAY by Sheldon Mark Lazanoff Thesis Advisor: E . B . Thornton March 1971 AppAovzd faon. pubtic klZzcaz; d-iitilbLitlon ubitunutud. Hl j8l An Evaluation of a Numerical Water Elevation and Tidal Current Prediction Model Applied to Monterey Bay by Sheldon Mark^Lazanof f Civilian, United States Naval Oceanographic Office B. S., Pennsylvania State: University, 1963 Submitted in partial fulfillment of the requirements for the degress of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL March 1971 LIBRARY NAVAL POSTGRADUATE SCHOOL' MONTEREY, CALIF. 93940 ABSTRACT The Hansen Hydrodynamical - Numerical model was evaluated for Monterey Bay with actual field data. Tides and winds are the principal driving forces of the Hansen model. Analysis of the field data indicated that the principal driving force of the circulation in the bay was the oceanic currents and not the tides and winds. The tidal heights and phases and current directions were calculated correctly by the model, but the calculated current speeds were an order of magnitude too large. The inaccuracy of the current speeds was attri- buted to the inaccurate calculations of the currents along the open boundary and the large ba thyme trie gradients of the Monterey Submarine Canyon. TABLE OF CONTENTS i I. INTRODUCTION 12 A. REVIEW 12 B. OEJECTIVES 14 II. THE HANSEN HYDRODYNAMICAL MODEL 17 A. MATHEMATICAL MODEL 17 B. COMPUTER MODEL 22 C. MONTEREY BAY 27 1. Grid 31 2. Time Step 33 3. Tides 33 4. Horizontal Eddy Diffusivity 37 5. Bottom Stress 38 6. Wind Stress 39 III. COMPUTER MODEL RESULTS AND DATA ANLYSIS 40 A. DATA ANALYSIS 40 B. COMPUTER MODEL RESULTS 48 IV. CONCLUSION 56 APPENDIX A 59 BIBLIOGRAPHY 142 INITIAL DISTRIBUTION LIST 144 FORM DD 1473 147 LIST OF FIGURES _ ig 1 Hansen Coordinate System 23 2 Model Grid System ~" 3 Tide, Wind and Current Meter Stations 28 4 Depth of Canyon Thalweg 29 5 Transverse Profiles of Monterey Canyon 30 6 Hansen Grid System for Monterey Bay 32 7 Computed vs. Actual Tide at Santa Cruz 36 8 Semi-diurnal Rotary Tidal Current 42 A-l Actual Tides at Monterey and Santa ^Cruz^for ^ 12-13 August 1970 A-2 Actual Tides at Monterey and Santa^Cruz^for 18-19 August 1970 A-3 Actual Tides at Monterey anc^Santa^CruzJor ^ 6-7 November 1970 A-4 Actual Tides at Monterey and Santa Cruz Jjor ^ 8-9 November 1970 A-5 Actual Tides at Monterey and Santa Cruz^for ^ 10-11 November 1970 A-6 Actual Tides at Monterey and Santa^Cruz^for ^ 12-13 November 1970 A-7 Actual Tides at Moss Landing for 6-7 November ^ 1970 A-8 Actual Tides at Moss Landing for 8-9 November ^ 1970 A-9 Actual Tides at Moss Landing for 10-11 November___ ^ 1970 A-10 Actual Tides at Moss Landing for 12-13_November___ ^ 1970 70 A-ll Tracks of Drogues 1-5 71 A-12 Tracks of Drogues 6-13 4 A-13 Tracks of Drogues 28-32 72 A-14 Tracks of Drogues 34- Z 73 A-15 Tracks of Drogues 35-38 74 A-16 Tracks of Drogues 35-36 continued and closed- current system between Pt. Ano Nuevo and Santa Cruz 75 A-17 Currents vs. Tides and Winds for Drogue 1 76 A-18 Currents vs. Tides and Winds for Drogue 2 77 A-19 Currents vs. Tides and Winds for Drogue 4 78 A-20 Currents vs. Tides and Winds for Drogue 5 79 A-21 Currents vs. Tides and Winds for Drogue 6 80 A-22 Currents vs. Tides and Winds for Drogue 7 81 A-23 Currents vs. Tides and Winds for Drogue 8 82 A-24 Currents vs. Tides and Winds for Drogue 10 8 3 A-25 Currents vs. Tides and Winds for Drogue 12 84 A-26 Currents vs. Tides and Winds for Drogue 13 85 A-27 Currents vs. Tides and Winds for Drogue 28 86 A-2 8 Currents vs. Tides and Winds for Drogue 29 87 A-29 Currents vs. Tides and Winds for Drogue 30 88 A-30 Currents vs. Tides and Winds for Drogue 31 89 A-31 Currents vs. Tides and Winds for Drogue 33 90 A-32 Currents vs. Tides and Winds for Drogue 34 91 A-33 Currents vs. Tides and Winds for Drogue x 92 A-34 Currents vs. Tides and Winds for Drogue y 93 A-35 Currents vs. Tides and Winds for Drogue z 9 4 A-36 Currents vs. Tides and Winds for Drogue 35 95 A-37 Currents vs. Tides and Winds for Drogue 36 96 A-38 Currents vs. Tides and Winds for Drogue 37 97 A-39 Currents vs. Tides and Winds for Drogue 3 8 9 8 5 A-40 Currents vs. Tides and Winds for Current Meter Station 1 99 A-41 Currents vs. Tides and Winds for Current Meter Station 1 100 A-42 Currents vs. Tides and Winds for Current Meter Station 2 101 A-43 Currents vs. Tides and Winds for Current Meter Station 3 102 A-44 Current in Lagrangian Format for Current Meter Station 1 103 A-45 Currents in Ocean adjacent tc Monterey Bay 104 A-46 Currents in Ocean adjacent to Monterey Bay 105 A-47 Calculated Tides and Currents in Monterey Harbor for 7 November 1970 106 A-4 8 Calculated Tides and Currents, in Monterey Harbor for 8 November 1970 107 A-49 Calculated Tides and Currents; at Santa Cruz for 7 November 1970 108 A-50 Calculated Tides and Currents at Santa Cruz for 8 November 1970 109 A-51 Calculated Tides and Currents at Moss Landing for 7 November 1970 110 A-52 Calculated Tides and Currents at Moss Landing for 8 November 1970 111 A-53 Calculated Tides and Currents in Deep Part of Monterey Canyon 8 November 1970 112 A-54 Calculated Tides and Currents in Shallow Part of Monterey Canyon for 8 November 1970 113 A-55 Calculated currents in Monterey Bay at Higher Low Water plus 0.5 hours 114 A-56 Calculated currents in Monterey Bay at Lower High Water minus 2 hours 115 A-57 Calculated currents in Monterey Bay at Lower High Water plus 1 hour 116 A-5 8 Calculated currents in Monterey Bay at Lower Low Water minus 2.5 hours 117 A-59 Calculated currents in Monterey Bay at Lower Low Water 118 A-60 Calculated currents in Monterey Bay at Lower Low Water plus 3.5 hours 119 A-61 Calculated currents in Monterey Bay at Higher High Water minus 2.5 hours 120 A-62 Calculated currents in Monterey Bay at Higher High Water plus 0.5 hours 121 A-63 Calculated currents in Monterey Bay at Lower Low Water minus 2.5 hours 122 LIST OF TABLES A-I Comparison of Tides at Monterey Bay Reference Stations 123 A-II Wind Measurements in Monterey Bay 126 A-III Drogues Course/Speed Data 135 LIST OF SYMBOLS A. area of Monterey Bay A. Fourier constituent D A tidal amplitude of n constituent B. Fourier constuent C De Chezy coefficient D thickness of fluid DL 1/2 mesh length DT 1/2 time step H total water depth K, horizontal eddy diffusivity M Hansen grid coordinate M„ semi diurnal tidal constituent N Hansen grid coordinate P fluid pressure P atmospheric pressure U. horizontal velocity over depth th (V +U ) value of equilibrium of the n x tidal constituent on ^ W wind velocity Z Hansen symbolic grid point a' wind, bottom and lateral shear stresses combined f Coriolis parameter (planetary vorticity) f factor for reducing tidal amplitude A to year of prediction g gravitational attraction of the earth h distance from ocean bottom to mean sea level h average depth across the entrance of the bay h maximum depth of the bay max r -* 1 grid mesh length 1 length of the entrance of the bay n bathymetry line perpendicular to flow r bottom stress coefficient t time u current velocity u average velocity at the bay entrance X grid coordinate a horizontal viscosity parameter k tidal epoch of the n constituent X wind drag coefficient ri deviation of water surface from mean sea level rv/T average increase in water elevation in the bay during a given time period C relative vorticity p fluid density o Fourier frequency t time step between two grid points b t bottom shear stress x wind stress v horizontal eddy viscosity 10 ACKNOWLEDGEMENT The author wishes to express his sincere appreciation tD Professor Edward B. Thornton, under whose direction this paper was written. His encouragement and criticism were invaluable in the completion of this research. In addition, the author is indebted to Captain Willard S. Houston, Commanding Officer, Fleet Numerical Weather Central (FNWC) for permission to run the Monterey Bay numerical model on FNWC computers. The author also wishes to thank Dr. Taivo Laevastu and Mr. Chuck Hines , FNWC, for technical and pro- gramming assistance respectively; ^eo J. Fisher and Donald B. Burns, U. S. Naval Oceanographic Office for providing ocean- ographic .instrumentation; the staff of Monterey office of the National Marine Fisheries Service for technical advice and typing services; and Professor Jerry Gait, whose discussions of numerical modeling were stimulating and educational. Finally, the author is deeply grateful to his wife, Linda, without whose ability the graphics for this report could not have been completed. 11 I. INTRODUCTION A. REVIEW During the normal course of events, tidal circulation in coastal areas, estuaries and rivers affects a diverse number of paramenters including: marine life in the inter-tidal and near shore zones; the flow of man-made sewage and other pollu- tants dumped into the water; off-shore structures, channel dredging and other engineering projects; and, of course, ship traffic. Furthermore, in areas where intense storms occur, the wind can create storm surges which combined with the tides can kill and injure people and destroy property on the sur- rounding low lands. Before the advent of high speed digital computers, the prediction of tidal heights and currents was difficult and cumbersome. The tidal circulation in deep water is primarily due to the attraction by the moon and sun; however, the tides in shallow water are also strongly affected by the geography and bathymetry of the area. The techniques for tide prediction developed by the US Coast and Geodetic Survey (USCGS) and the British Admiralty, among other international agencies, in the late nineteenth century have become standard throughout the world. The pro- cedure requires tidal height and current data measured for at least 29 days which covers the principal lunar constituents, preferably for a year which covers the principal solar con- stituents and ideally for 18.6 years which covers all possible 12 tidal constituents. The tidal constituents, or harmonic coefficients, are then used to predict the tidal elevation. The accuracy of the predictions increase with the length of the record. The data are analyzed by harmonic techniques and tidal constituents are produced. In the past the tidal con- stituents were used as input to lairge tide prediction machines which produced hourly heights and tidal currents (Schureman, 195 8) . The machine needed at least twelve hours to produce yearly predictions for one station. One serious problem with this technique is that if tide data are not available for a location of interest, then the predictions have to be inter- polated between known stations as shown in the USCGS Tide Tables. The interpolated tide values can be inaccurate and more detrimental than helpful for real time operational planning. The U.S. Navy became acutely aware of this problem when using French tide tables for riverine and coastal oper- ations in Vietnam. The necessary equations of motion needed to describe the tides were developed by Bernoulli and Laplace in the 18th century. However, because the equations are non-linear, simplfying assumptions had to be made and tedious analytical methods were used to obtain solutions. Analytical methods are not practical for real time predictions. By using computers these equations can be solved in less time by more sophisticated methods. For example, yearly tide predictions for one station can now be calculated on a computer in 1.7 minutes (Pore and Cummings , 1967) compared to twelve hours for the mechanical tide prediction machine. Several 13 computerized mathematical models using different numerical schemes and boundary conditions have been developed to predict assorted circulation parameters in a two dimensional field rather than for one point. An operational hydrodynamical model to compute water elevations and currents has been developed by Professor Walter Hansen, Universitat Hamburg. The two driving forces in the model are the tides at the open boundary and the wind stress acting at the surface over the entire grid. The Hansen Model was initially begun in 1938 (Laevastu and Stevens, 1969), culminating in a two dimensional model of the North Sea in 1952 (Mungall and Matthews, 1970). In 1966 the North Sea model was programmed for the computer by Jensen, Weywadt, and Jensen (1966). Th<2 predictions compared favorably with field observations. Some of the general characteristics of Hansen's two dimensional model are that density is uniform over depth; the water transport is averaged over depth; bottom and wind stresses are represented by quadratic formulas; Coriolis force is assumed to be constant over small geographical areas; the effect of atmospheric pressure is neglected; and there are no more than two open boundaries on the rectangular grid. B. OBJECTIVES Since June 196 8 Fleet Numerical Weather Central (FNWC) and U.S. Naval Oceanographic Office (NAVOCEANO) personnel have modified and adapted the Jensen, et. al. program to other geographic areas such as the South China Sea, DaNang Bay, Gulf of Tonkin, Straits of Gibraltor, Gulf of Mexico and the 14 Chesapeake Bay. Even though Hansen himself has indicated (Hansen, 1966) that synoptic field data are extremely impor- tant in verifying the results of the computer calculations, the results for the above mentioned projects have only been compared to atlas data and sparse field data, leaving some doubt as to the accuracy of the predictions. The U.S. Naval Oceanographic Office does oceanographic surveys in shallow water, semi-enclosed embayments throughout the world to fulfill specific requirements in supporting naval operations such as mine sweeping and diffusion studies. Because of ever changing world politics, oceanographic surveys cannot always be made in vital areas before they are needed and then, circumstances can prevent a proper survey from being made in these areas. Such situations have occurred in Vung Tau and DaNang Bay in the Republic of Vietnam. Thus, the: object of this report is to evaluate the accuracy of Hansen's mathematical model for a shallow water, semi-enclosed embayment; varying parameters such as boundary conditions and the horizontal eddy viscosity parameter to determine their effects on the predicted eleva- tions and currents and to determine the minimum field data requirements needed to satisfactorily verify the computer results. For several reasons Monterey Bay appeared to be an excel- lent site to evaluate the model. Monterey Bay has similar geometrical features to many of the NAVOCEANO areas of interest. Unlike Southeast Asia areas there is no significant river run-off to influence the results (Lazanoff and Clarke, 1970) . Winds are fairly steady and predictable over a long 15 period of time allowing the model to be evaluated for two steady-sta~e conditions -summer calm conditions and fall and winter storm conditions. Finally, Monterey Bay, which is bisected by a one of the deepest submarine canyons in the world allows the model to be tested over a large change of depth in a short horizontal distance. 16 II. THE HANSEN HYDRO DYNAMICAL MODEL A. MATHEMATICAL MODEL Although the Hansen two-dimensional model is detailed by Jensen, et . al. , the following is a review of the more impor- tant characteristics of the model. The coordinate system and surface and boundary conditions are shown in Figure 1. Some of the basic assumptions made in the analysis scheme are: 1) the fluid is homogeneous and incompressible, 2) the fluid is in hydrostatic equilibrium in the vertical direction, 3) the geographical and the vertical variations of the Coriolis force is neglected. The equations used in the Hansen model are derived from the conservation of momentum and the conservation of mass which are respectively: the conservation of momentum ' £ + ^ £ ♦ ,-„ «♦« fuj + i£-+ai + gi=0U, where, i,j = 1,2,3 u. is the velocity component in the i direction, t is time, f is the Coriolis parameter, p is the fluid density and, based on assumption (1) , is constant over depth, P is the pressure of the fluid, 17 H Hrh^ri X- x2 ■>■ X-, Figure 1 . Hansen Coordinate System 18 ar represents the wind, bottom and lateral shear stresses combined, g. represents external body force which is here limited to the gravitational attraction of the earth, and the conservation of mass, ~ 8pu. !£ + inr=0 i=1>2>3 (2) D The density of sea water is assumed constant by assumption (1) . This assumption is a limitation of the model and was made because of computer memory and time limitations at the time of the development of the original model. A multi-layer model is being developed at Fleet Numerical Weather Central under the guidance of Professor Hansen and Dr. Taivo Laevastu. The model was not available for use in Monterey Bay. From assumption (2) , equation (2) in the vertical direc- tion reduces to P = p(x3) g dX3 + Pq -h (3) = pg (n+h) + PQ where P is the atmospheric pressure. o r The boundary condition at the bottom, X-j = 0, is u.-n = 0 (4) l where n is the unit normal to the bottom. 19 The boundary condition at the surface, X^ = n + h is f+V &7-V i = 1'2 ' <5> where n is the water surface elevation and u., is the velocity in the vertical direction. The baratropic atmospheric pressure term has been elimin- ated from the Monterey Bay model. Admittedly, the water height will increase by one centimeter as the atmospheric pressure decreases or increases one millibar (Lazanoff, 1969); however, this fluctuation is relatively insignificant compared to the fluctuations caused by the wind stress (Jensen, et . al. ) and over the distance of Monterey Bay the atmospheric pressure varies only slightly except during very stormy periods. The convective terms, u. i , has also been neglected 3 from the Hansen model. If a rather large value of 100 cm/s3C (about 2 knots) is assigned to both u. and the change of u. with respect to X. and the distance between grid points is 900 meters (actual mesh length for Monterey Bay) , then the -5 / 2 convective term has a value in the order of 10 cm/sec . Under the same conditions, the local acceleration term will be of order one; the Coriolus term will be on the order of 10 cm/sec and the gravitational term will be at least on -2 2 the order of 10 cm/sec . Thus, the convective term will at least two order of magnitude less than any of the other terms in the equation. By integrating the remainder of terms in equations (1) and (2) over depth, combining terms and defining the mean 20 velocity as "i-J n u± dX3 i = 1,2 (6) -h where H = n+h and is the total water depth, the following equations arise: 2 x w-t h 3Ui Cj+1) 3 Ui ni ni 9n ,_. i/j = 1,2 and 3(HU.) M + -^x^=0 <8> l where v is horizontal eddy diffusivity coefficient (lateral shear stress coefficient) , w . 2 x. is the wind stress in the X. direction in dynes/cm T- is the bottom shear stress in the X. direction in i l dynes/cm . Equations (7) and (8) are the equations used in the Hansen mode 1 . The wind stress term (t ), as used in Hansen's model, i is assumed to be a quadratic expression in windspeed. This expression is tW = pA W. (W2 + W2)1/2 (9) 21 where X is the wind drag coefficient (dimensionless) and W. and W . are the wind components . The bottom stress term (t ) is represented similiarly A • 1 to the wind stress term and is x£ = p r U. (U? + uh1/2 (10) A^ X 1 J where r is the bottom friction coefficient (dimensionless) and is assumed constant. Both the bottom stress and wind stress terms are nonlinear and have been derived by empirical means. This formulation is an approximation and its applicability to deep water is questionable as it was originally formulated for shallow water application. B. COMPUTER MODEL A central differencing scheme i.s used to program equations (7) and (8) . The grid system is shown in Figure 2 (Laevastu and Stevens, 1970). A "leap frog" method is used whereby the grid is staggered in time and space (Mungall and Matthews, 1970) . N and M correspond respectively to the X and X^ coordinates. The Z points are the symbolic depths indicating land, sea and boundary points. The finite approximations (Ortiz, 1964) are: (t,T) = ~(t) _ /% L(t-T) (t) . H(t-T) (11) n(N,M) n(N,M) V* V WlM) °1, , , \ 1(N+1,M) lw+1'M' ■L(N-1,M) Un + H^"^ uiT) - H^-T) U<« ^N-^M) U2(N/M.1} 2(N,M-1) °2(N/M+1) (N,M+1) 22 1 >zv 24 N «> 3-^ 4-» -Sir M r^ 3 zu N = 2 M=2 ^ ZV> N=3 M = 2 N=2 M=3 4 X Z-point, • ZU-point, o ZV-point Figure 2. Model Grid Syste m 23 where t is the time step between two Z points and I is the mesh length between two Z points U (t+2x) (N,M) (1-Q(N/M)) ^t} + 2TfU*(t) K ' ' X(N,M) (N,M) " I* (12) (t+T) n(t+T) (N+1,M) l(N-l,M) - 2t t W(t) X (N,M) Similarly, U (t+T) 2(N,M) ll-Q^ | U^ - 2xfU* 2(N,M) ~ t5 (t+T) _ n(t+T) \ n(N,M+l) n(N,M-l) + 2t T W(t) X. (N,M) (13) The terms used in the previous equation can be defined as: H (t) U-, hU (N,M) W) + ^2 (t-T) (t-T) n(N+l/M) n(N-l,M) (14) H (t) = hU. (N,M) (N,M) + 1/2 (t-T) (N,M-1) (t-T) (N,M+1) (15) (t) •x. = 2rT U (N,M) i(t) I2 + k(t) X(N,M) \ ^(N,M) 1/2/ (t+T) /HU, (N,M) (16) Q (t) x„ = 2rT (N,M) u*(t) (N,M) U* (t) (N,M) 1/2 (t+T) /Hu2 (N,M) (17) 24 UJ and U* are the averaged velocities for the four Zu and Zv points about a Z point. fl<« = <> H- i- U> + U^' ,18, ■ (N,M) -"(N.M)- q \ ±(N+1,M) 2(N-1,M) + U.(t) + U,(t) ±(N,M-1) i(N,M+l) (t) U,(t) = aU^ + i=« U^ + U2, n , <19> 2(N,M) 2(N,M) 4 I 2(N+1,M) (N~1,M) + u2(t) + ul^ (N,M-1) 2(N,M+1) n(NlM) -^S1m)+ T* r&llM + "(£-l,M) (20) + n(t) +n(t) '(N,M-1) n(N,M+l) Alpha (a) is a function of the horizontal eddy diffusivity term, mesh length and time (0 <_ a £ 1) . This term will be discussed in more detail in a later section. If any of the above calculations occur at a boundary, then the values of r\ , U. and U- are taken at the actual point rather than from the surrounding points. The primary forcing function for this model is the tide at the open boundary points. When the model was applied to other areas, predicted tides were generated for each time step using the following equation (Schureman) : ri = A + l f A cos [at + (V +U ) - k ] (21) o ,nn n on n n=l 25 where, r\ = height of the tide at any time A = mean height of water level above datum line, A = amplitude of the n amplitude f = factor for reducing amplitude A to year of predictions , A = speed of the n constituent, t = time calculated from some initial epoch such as beginning of year of predictions, (V +U ) = value of equilibrium of the n constituent o n' when t = 0 , 4- Vi k = epoch of the n constituent. n Equation (21) is applied only at the open boundary. Since the objective of this particular project is to evaluate Hansen's hydrodynamical model and not the prediction of astronomical tides, a different method was used to calculate the input at the open boundary points. A Fourier analysis was made of the actual tide records which are used in this study. The Fourier constituents were used in the following equation : N n = 1/2 A + Z (A. cos. at + B. sin. at) (22) ° A=l 3 ^ 3D where. A . A. and B. are the Fourier constituents, determined from the actual records N is the total number of constituents used, j is any given constituent, a = — and T is the length of time that spans the entire record. 26 The principal parts of the Hansen hydrodynamical model have now been detailed and the following section describes the application of the model to Monterey Bay. C. MONTEREY BAY Monterey Bay (Figure 3) is a semi-enclosed (one open bound- ary) , approximately symmetrical embayment. Because Monterey Canyon very nearly bisects the^bay, there is an unusually large variation of depth (400 fathoms) in a relatively small area (approximately 175.5 square miles). The depth of the canyon thalweg from the mouth of the bay to the shoreline is shown in Figure 4. The thalweg from the shoreline to six miles off "he coast has an extremely steep slope of 1:18. Two transverse profiles of the bay are shown in Figure 5. The gradients of the canyon wall is steeper on the south side than on the north side but both canyon walls are extremely steep. Lynch (1970) found that the canyon tends to divide the bay into two dis- tinct basins in which long period oscillations such as seiche occur independent of each other. The results of the Hansen model appear to indicate that this also occurs for tides which have longer periods than seiches. The total circulation of Monterey Bay is affected by density gradients as well as tides , wind stress and air pressure gradients. All these mechanisms can be important and it is not really correct to separate the density gradients from the other parameters. Unfortunately, the complex com- puter models needed to combine these parameters would consume too much computer storage and running time to be practical and economically feasible on the present day computers. 27 50* Copy of C.8G. S. ,yi%&***^ H Map 5402 - 20 FATHOMS SO 100 100 1000 Figure 3. Tide, Wind and Current Meter Stations. 28 CD en CO o 2 -j LU > LU to LU CD .— i rd X! H C O >, c O O Xi a 0) Q (D <£> LU CL O >- < 00 WOHJLVJ 001- =H0NU -< >■ 29 UJ c* c o >. c (0 U CD 0) -4-1 o en CD o CD W > C r0 s- H (1) I. Cn -■-I Q < S3' ||AI L 30 However, to complete the picture of the circulation of Monterey Bay, some mention should be made of the semi-perma- nent density currents that occur in the ocean adjacent to the bay. Depending on the climatological season, the circulation in Monterey Bay appears to be strongly influenced by the California or Oceanic current, Davidson current and upwelling. The California current can be as much as 420 miles in breadth and have an average speed of 0.5 knots (Carter and Kazmierczak, 196 8). The current flows south during September, October and a portion of November. During the months of November through February, the Davidson current, which is approximately 40 miles wide and has a maximum velocity of 0.44 knots, flows north. The upwelling period extends from March through July. Carter, et . al . claim that the upwelling current flows south in the open ocean and north along the coast. The upwelling current velocities average about 0.5 knots over depth with a maximum speed of 0.6 knots at the surface. The influence of the Monterey Canyon on the oceanic currents is not really known and the currents created inside the bay do not neces- sarily flow in the same direction as the oceanic current. 1. Grid The choosen grid size is 19 (ordinate) by 46 (abscissae) with a mesh length of 0.5 nautical miles (Figure 6). The bottom depths were obtained from C & GS Chart No. 540 3 (Scale 1:50000) which was updated in June 1970. The grid was selected so that the open boundary coincides with the nautral opening of the bay and Monterey Canyon is adequately defined. 31 <* iO^ FATHOMS SO — 100 --•00 1000 Figure 6. Hansen Grid for Monterey Bay. 32 2. Time Step The time step between grid points was determined by using the Courant-Friedrich-Lewy criterion which is ££ < l/(2gh )1/2 (23) DL — ' ^ max v ' where, DT = 1/2 time step, DL = 1/2 mesh length (1500) ft. h = Maximum bottom depth of the arid area (400 max * 3 fathoms) In this case the maximum DT is 3 seconds. If a time step greater than the maximum allowed by the Courant-Friedrich-Lewy criteria is selected, then the results of the model rapidly diverge. The author has experimentally verified this when applying Hansen's model to the South China Sea and the Gulf of Mexico. It is interesting to note that when equation (23) is rearranged, then the formula is different only by a factor of /2~ from the deep water wave celerity formula: §± < /2 /gh (24) DT — ^ max 3. Tides Since the tides are the primary forcing function across the open boundary, they need to be accurately defined. Ideally the tides should be known at every point on the open boundary; however, this is impractical. The optimum situation for Monterey Bay would have been to measure the tides at three points along the open boundary - at both ends of the 33 boundary and in the canyon which bisects the open boundary. Unfortunately, the tides were only measured near the open boundary at Monterey Wharf No. 2 (Point A on Figure 3) which is 3.3 miles from the closest open boundary point at the southern end of the grid and the Santa Cruz Municipal Pier (Point B on Figure 3) which 0.3 miles from the closest northern open boundary point. It had been planned to place a submerged tide guage in the Canyon but the necessary equipment could not ba assembled before the field survey commenced. Hourly tidal height records from Monterey and Santa Cruz are shown in figures (A-l) through (A-6) and for Moss Landing in figures (A-7) through (A-10) . The Monterey records have been corrected to a datum level. The tide records fcr the other stations contain the correct phases and relative amplitudes. The relative amplitudes for the three stations are compared to each other in Table A-l. The maximum difference between amplitudes of any two stations is less than 0.75 feet and for most cases there was no difference at all. The Santa Cruz and Moss Landing records compared more favor- ably with each other than they did with the Monterey Wharf records. The fact that the tides at Santa Cruz and Moss Landing were measured by the same type of instrument while the tides at Monterey were measured by a different type of recorder may explain part of the difference. Since the tidal phases and amplitudes at Santa Cruz and Monterey were very nearly equal and there was no knowledge of the tidal behavior in deep water, only the Santa Cruz data were Fourier analyzed. 34 The Santa Cruz constituents were used at every open boundary point. An example of the computed tide compared to the actual tide is shown in Figure (7) . Before actual tide data were used as input to the model, a test run was made to determine the length of running time needed for the model to propagate the tidal wave through- out the entire bay. The M~ (lunar-semi diurnal tide) sine wave recycles every 12 hours, 25 minutes. The Monterey M~ consituent was used for the test runs. The tide travelled from the mouth of the bay to Moss Landing in less than a half hour. This does not mean that all the perturbations caused by the initial wave placed on the grid have been dampened. In the original Hansen model the wave heights at all the grid points were set equal to zero and then the initial wave was inserted at the open boundary points. It seemed that if the initial tide was at either high or low water, then large transients would be induced as the tide travelled across the grid. Several test runs were made to test if the entire grid should be initialized at the same tidal elevation rather than just at the mouth of the bay. It had been hoped that this would keep the initial shock of the induced wave to a minimum. Unfortunately, this technique caused a separate wave to be generated along the closed boundary. It was decided that for Monterey Bay all computer runs would be made so that the initial tide would be at mean sea level. Then, since the tide moves quite rapidly across the bay, the transients would be kept to a minimum. 35 8 7- 6- 5 v- LU LU 4-- LL. 3 2 1 0 MEASURED TIDE SANTA CRUZ COMPUTED TIDE SANTA CRUZ 0 2 4 G 8 10 12 14 16 18 20 22 0 HOURS 12 AUGUST 1970 Figure 7. Computed vs. Actual Tide at Santa Cruz 36 4. Horizontal Eddy Diffusivity The parameter alpha (Equations 20-22) which is a function of the horizontal eddy diffusivity coefficient, mesh length and time step has been described as a horizontal viscosity parameter (Laevastu and Stevens) and as a stability factor (Mungalls and Matthews and Hansen, 1966). Ortiz (after Lax and Richtmeyer, 1956) defines alpha as K.DT a = 1 - 4 -~- (25) DIT where, K, is the horizontal eddy diffusivity term. Oritz and Hansen claim that the numerical calculations converge analytically as alpha approaches 1, but are unstable when alpha is equal to one. Alpha equal to one implies the eddy diffusivity coefficient K, is equal to zero, i.e. no diffusion of momentum. Since the time step and mesh length are arbitrarily selected for each problem, alpha depends primarily on the variability of the horizontal eddy diffusivity term. A general solution does not exist for eddy diffusivity. Empirical solutions must be developed for specific areas of interest. Garcia (1971) claims that the value of horizontal 7 8 eddy diffusivity for Monterey Bay ranges from 10 to 10 2 dynes/cm . The latter produces an alpha of less than 0.5 which is unrealistic. The former value produces an alpha of approximately 0.9 4 which is far more satisfactory. Test runs were made with alpha equal to 0.95, 0.990 and 0.99 8 for the M2 constituent and 0.900, 0.940 and 0.950 for the actual tide. The best results for the tidal heights appeared to be 37 obtained with alpha equal to 0.9 50. This corresponds to a 7 2 value of K, equal to slightly less than 10 dynes/cm Current speeds were not satisfactory but if alpha was decreased, then the tidal heights were over-dampened. 5. Bottom Stress As previously mentioned the quadratic expression (Equation 12) used to represent bottom stress has been in existence for sometime; however, there seems to be some discussion as to what value should be assigned to the bottom stress coefficient (r) . The bottom stress coefficient is defined as r = g • C~2 (26) 1/2 where C (cm / /sec) is the DeChezy coefficient and is a function of bottom roughness and bottom material. Experience in the coastal waters around the Netherlands (Dronkers, 1964) has shown that a reasonable range for r -3 -3 -3 varied from 2 . 4 x 10 to 2.8 x 10 with 2.7 x 10 the most common value used. Although Hansen (1966) used the values -3 -3 -3 of 2.8 x 10 , 3 x 10 and 8.6 x 10 for r without comment, -3 it appeared that 2.8 x 10 was used when the model depth was equal to or less than 50 meters (25 fathoms). Mungalls, _3 et. al . , used 4 x 10 for Cook Inlet, Alaska which has numerous mud flats and shoals. Pekeris and Accad (1969) -3 suggested that 2 x 10 should be used in shallow water. -3 -3 Test runs were made with r equal to 3.0 x 10 , 8.6 x 10 _3 and 3.2 x 10 for Monterey Bay. It will be shown in the 38 following section that the errors in the current speeds calculated by the mathematical model appeared to be quite large and the adjusting of the bottom friction coefficient does not seem to change the results significantly. The -3 value of 8.6 x 10 seems to be the most satisfactory value to use. 6 . Wind Stress If little is known about bottom stress, less is known about the interaction of the atmosphere and sea water. It is exceedingly difficult to make the micro-measurements needed to accurately determine the wind stress coefficient. The wind stress or drag coefficient (X) is defined similarly to the bottom stress coefficient. Munk and others used the -3 value of 2.6 x 10 (dimensionless) for wind velocities from 12 to 40 knots (Dronkers) . The drag coefficient is a function of the elevations at which the velocities were measured. Based on Cardone ' s investigation (1970), a drag coefficient -3 of 1 x 10 was selected for Monterey Bay. The bottom stress term originally included the density of sea water and the wind stress term included the density of air. Thus, when equation (1) was divided by the density of sea water, density was eliminated from the bottom stress term but not from the wind stress term. 39 III. COMPUTER MODEL RESULTS AND DATA ANALYSIS A. DATA ANALYSIS Tides, currents and winds were measured on 12 , 13, 18 and 19 August and 6-13 November 1970 for the purpose of evaluating the mathematical model. The tides were measured at the three stations mentioned in the previous section by mechanical gauges. Non-linear time errors can occur on the tide records if the mechanical gauges are not maintained properly. The Monterey and Santa Cruz tide records were timed by chronometers. The August tide records for Moss Landing were not accurately timed and contain errors. Thus, only the tidal amplitudes from the August records of Moss Landing were used for compar- ison. The tides were mixed (almost diurnal) during the 12- 13 August time period, semi-diurnal during the 18-19 August time period and shifted from semi-diurnal to mixed during the 6-13 November 1970 time period. Wind data obtained from land stations and the USNS De Steiguer are listed in Table A-2 . The land stations were located at the shore line. The exact location of the USN De Steiguer at any given time can be determined by noting when the current meters were emplanted and the current drogues were launched. Since Monterey Bay is a small geographical area for large-scale climatological parameters and the wind records from the various stations around the bay appear to be in fairly good agreement, the complete wind records from Moss Landing 40 (Figure 3) were considered to be representative of the entire grid for each analysis period. Currents were measured in a Lagrangian sense by current drogues and, during portions of the survey, in an Eulerian sense by current meters. The structure and application of the current drogues are described by Stoddard (1971) . Drogues were not placed north of the Monterey Canyon as there were no facilities to track them. The tracks of the current drogues are shown in Figures (A-ll) - (A-16) and the hourly speeds and directions are shown in Table 3. The location and depth of the current meters are shown in Figure 3. The relationship between the currents derived from the drogues and some of the current meters, winds and tides are show in Figures (A17) - (A-43) . Data from other current meters did not appear to be realistic and were not used. The currents are plotted on the tidal curvas. The heads of the current and wind vectors are set in the direction in which the parameters are moving. Tidal currents can either be the reversing type where the currents are zero at the anti-nodes and a maximum at the nodal points or the elliptical type where the current direction passes through all points of the compass and the speed is seldom zero. Reversing currents can be found along the coast or in rivers. Elliptical or rotary currents, as shown in Figure (8), occur in the open ocean or large embayments . The elliptical currents move in a clock -wise direction in the Northern Hemisphere. Maximum speeds usually occur mid-way between turning points and minimum speeds at high and low waters. If surface currents are primarily induced by wind 41 L+2HRS^ L+3HR3 L-1HRv -2HR5 H-1HR /H + 1HR H+2HRS H+3HRS L = LOW TIDE H = HIGH TIDE HR/HR5 ■ HOURS Figure 8. Semidiurnal Rotary Tidal Current 42 Current meter data (Station 1 in Figure 3) , plotted in a Lagrangian format (Format A-44) indicated that the currents at this location, with only slight deviations, flowed in a steady northwesterly direction. Thus, the NPGS data seems to indicate that the oceanic currents had more influence during these surveys on the circulation in Monterey than the tides and winds . Professor William Broenkow, Moss Landing Laboratories, has measured surface currents in the vicinity of Moss Landing with drift poles (personal communication) . The measurements were made during April, May, November and December, 1970. The poles were never tracked for longer than 3 hours and 15 minutes. The maximum current speed occurred during flood tide and was perpendicular to the coast. Currents with speed up to 1.5 knots and moving parallel to the coast were measured north of the canyon. South of the canyon, the speeds never exeeded 0.7 knots. The maximum current speeds occurred either during flood or ebb tide in some cases. In other cases, the maximum speed occurred at high water. There were not enough observations at this point to accurrately correlate the currents near Moss Landing with the tides; however, it did appear that the current flowed southwest during ebb tide and northwest during flood tide. In most cases, the poles travelled along equal depth lines McKay (19 70) , towed a Geomagnetic Electrokinetograph (GEK) from a moving ship in Monterey Canyon during July and August 1970 to measure the currents . The GEK only performed satis- factorily in areas where the water depth was greater than 75 44 fathoms. McKay believed that the measured currents which ranged in speeds from 0.05 to 1.35 knots, were dependent on tides. Closer observation of the data indicated that the GEK was probably measuring extremities or eddies of the California or up-welling current. In one case, which McKay stated that the currents were a result of flood tides, the currents flowed in a direction that would not be usually associated with flood tides. The average speed of the current was 0.5 knots. As with the other current measurements, most of the GEK measurements tended to follow the contour lines of the canyon. Defant (1961) indicates that if a strong current or up- welling exists in the adjacent ocean, standing vortices can occur in coastal bays such as Monterey Bay. The flow of the standing vortex is such that the currents on the seaward side of the bay follows the main current while on the landward side the current is opposite the main current. Theoretically, standing vortices would have the same water mass circulating within it and there would be no water transfer from the main current. In actuality, this is not the case. Variations in the oceanic current or upwelling will perturb the stationary vortex and renew the water circulating in the bay. Carter and Kazmierczak claims that a permanent closed circulation system which moves in a counter-clockwise^ direc- tion extends from Ano Nuevo, north of Monterey Bay, to Moss Landing (Figure A-16) . The average speed of the system is 0.1 knots. Coastal engineers at Pacific Gas and Electric Company (P.G. & E.) believe that they have accumulated enough field data to confirm this phenomena (personal communication) . 45 Over a three year period P.G. & E. has launched a number of drogues at the 6 fathom line north of Monterey Canyon. The drogues were launched during all three climatic seasons and at different phases of the tidal cycle. The drogues consis- tently follow the contour line towards the northwest. The maxi- mum speed of the drogues never exceeded 0.5 knots and usually was quite less. The field data collected by NPGS in the bay during August and November 19 70 only implied, but did not absolutely prove, that the oceanic currents and upwelling were the primary forces of the circulation of Monterey Bay. It should be noted that the oceanic currents and upwelling were the primary driving forces of the circulation of Monterey Bay. The NPGS data were collected during the transitory times between the upwelling and California currents and the California and Davidson currents respectively. To properly correlate the currents in the bay with the oceanic circulation, measurements were needed in the adjacent ocean. Twelve hydrocasts were made in the open ocean during 8-9 November and again during 13-14 November 19 70. Five current drogues were also launched on 8 November 19 70. The results from this data are shown in Figures (A-45) and (A-46). The dynamic height calculations for the first time period indicate that the oceanic current diverged, with speeds ranging from 0.1 to 0.6 knots, as it approached the coast. The drogues which were launched north of the canyon continued to move north fairly rapidly. The second set of dynamic height calculations showed a more complicated current pattern in the ocean. A large eddy was 46 present southwest of Monterey Bay. The current speeds for this set of data were similar to that of the first set. The oceanic flow may be affected by Monterey Canyon. The current north of the canyon moves north and vice-versa. The observa- tions in the bay seems to substantiate the oceanic data. How- ever, there was very little current data available for the north basin of Monterey Bay and more surveys need to be made in this area. Ideally, simultaneous current measurements should be made in the ocean and the bay on a seasonal basis to really understand the circulation patterns in the bay and the adjacent ocean. It is obvious -chat measurements in the bay without corresponding measurements in the ocean are really not significant. It should also be noted that the Hansen hydrodynamical model is not designed to handle density currents and their presence will not appear in the computer calculations for the bay. One point should be made about the tendency of the current measurements to follow lines of constant bathymety. This implies that potential vorticity is being conserved. Potential vorticity is comprised of several components. The planetary vorticity, or Coriolis parameter (f ) , is related to the rotation of the earth and varies as the flow of water moves from the poles to the equator and vice-versa. In a small area such as Monterey Bay, planetary vorticity can be con- sidered constant. Relative vorticity (£) is a function of the motion of a fluid relative to the earth and can be defined as 9u~ 3u, r = £ - ± (27) 47 The sum of the relative and planetary vortices is the absolute vorticity. The conservation of vorticy equation (Stommel, 1966) is at (h*) -» where D is the thickness of the fluid. When equation (2 8) is integrated, it can be shown that potential vorticity is f * ^ = constant (29) If flow is along lines of constant bathymetry (D = con- stant) , and f is assumed constant, then absolute vorticity, C, is constant. B. COMPUTER MODEL RESULTS The computer results were compared with the field data. The parameters compared were water elevation heights and phases and current speeds and directions. The results were plotted in two different formats by an automated plotter. One format shows the current circulation in the entire bay at any given time. Only every third row is plotted in this format and some of the calculated details, especially along the coast, are now shown. The other format shows the currents plotted on the tidal curve for individual grid points. The calculated water heights and phases compared quite favorably with the real tides at Monterey Harbor, Santa Cruz and Moss Landing as can be seen when Figures (A-47) through (A-52) are compared to Figures (A-3) , (A-4) , (A-7) and (A-8) and Table 48 A-l. The model indicated that the tidal range was less in the canyon than it was in shallow water as seen in Figures (A-53) and (A-54) . Although this could be expected, it would have been more satisfying if there had been actual tide data available in the canyon to indicate if this was correct. The calculated directions also seemed to be accurate. Some of the calculated circulation patterns in Monterey Bay are shown in Figures (A-55) through (A-5 3) . As anticipated, the model produced two gyres - one in the northern basin and the other in the southern basin - separated by the canyon. The gyres were more predominant during the ebb and flood periods; The northern gyre rotated in a counter-clockwise direction (Figure A-61) and the southern gyre rotated in a clockwise direction (Figure A-60) on the flood tide and vice versa on the ebb tide. The maximum currents occurred at high water (Figure A-62) and low water (Figure A-59) . At high water the currents diverged from the canyon into the basins and at low water the currents converged towards the canyon. The currents in the canyon are shown to be reversing currents. Although not shown in the figures, the model also depicted the currents along the coast-line as reversing currents. With few exceptions, the calculated circulation pattern is disimiliar to the circulation pattern depicted by the field measurements. This is another indication that the tidal current is dominated by the oceanic currents. The calculated current speeds appear to be an order of magnitude too large. Except for near Moss Landing, the maxi- mum current speeds measured in the bay was 0.7 knots and the 49 average speed was 0.3 knots. Since it has been concluded that the oceanic currents have more influence in Monterey Bay than the tides and winds, then it would be expected that the tidal currents would be in the order of 0.1 knots or less. There are two other reasons to expect that tidal currents would be low. First, the fact that the tidal phases are nearly equal throughout the bay implies that the horizontal current speeds would be low. Second, the magnitude of the current is a function of the water nass displaced horizontally during the rise and fall of the tides and the cross-sectional area through which it moves, (Simmons, 1966). Mathematically, this can be represented by (ue) (he) Ue) = VV'T) (30) where, u is the average velocity at the entrance of the bay, h is the average depth across the entrance of Monterey Bay (approximately 612 feet) , £ is the length of the entrance of Monterey Bay (19.5 miles) , A, is the area of Monterey Bay (approximately 175.5 square miles) (nh/T) is the average increase in water elevation in the bay during the time period T As an example, on 7 November 1970 there was an increase of two feet in water elevation from low to high water in 5 hours and 30 minutes. Thenu is approximately 0.05 knots. For the same time period, the model calculated an average 50 speed 0.1 knots for the south end of the opening; 0.2 knots for the canyon; and close to 1.0 knots at the north end of the opening. Thus, it appears that the model does not correctly calculate the current speeds in Monterey Bay. The model computer program was checked thoroughly for errors. The continuity equation (Equation 11) and the con- servation of momentum equations (Equations 12 and 13) were checked by hand calculations. Decreasing the viscosity parameter (a) and increases the stress coefficient (r) dampens the current velocities; however, if either term is varied too greatly, then the water elevations are over-dampened. This occurred in the test cases when a and r were set equal -2 to 0.9 0 and 3.2 x 10 respectively. These two parameters are useful only when the computer results need a fine adjustment. During most of the test runs, the computer program was only run out to 24 hours. It was thought possibly that even though all the tidal heights on the grid reached their correct height in a short time, the transients created by the initial waves moving across the grid would need more time to be completely damped. One case, commencing 1900 PST, 6 November 1970, was run out to 64 hours. The length of the computer run did not improve the calculations, which implies equilibrium conditions are obtained after about one hour. Several test runs were made so that the computer calcula- tions at every time step between 0 and 120 seconds and 7200 to 7320 seconds could be observed. It became apparent that the velocities increased greatly as the waves moved from the 51 deep canyon areas to the much more shallow basins. Some irregularities in the currents occurred along the very shallow (less than 5 fathoms) coastal boundaries. It was decided to smooth the bottom by the following technique : h (»i »»\ = 0*5 h .... ... + 0.125 (h /vt , , ... + h ,.T , ... N,M) (N,M) (N+1,M) (N-1,M) + h(N/M+l) + h(N/M-l) (31) There was approximately a ten percent improvement in the current speeds, particularily about the canyon, when the bathymetry was smoothed once and approximately 15 percent improvement when the bathymetry was smoothed twice using equation (31). It would appear that the model, employing the grid spacing used here, has difficulty coping with the great variance in depth over as small an area as Monterey Bay. The large lateral and transverse slopes of the canyon (Figure 4 and Figure 5) are significant bathymetric problems. It is believed that if a finer grid was used, the accuracy of the calculated current velocities would be improved. This point was proved in reverse when the grid was changed to 12 x 25 with a mesh length of one nautical mile, the currents became larger. Assuming that the present grid is inadequate for Monterey Bay, some mention about the computer requirements for this model need to be made. Remembering that the grid size is 19 x 46 and the time step is 6 seconds, the Control Data Computer (CDC) 6500 computer at FNWC utilizes 53000g computer words, requiring 3.2 5 hours to compute a real time interval 52 of 24 hours. If a finer grid and, thus, a smaller time step was used, the computer core storage and running time would be greatly increased and the model would be impractical to use. At the suggestion of Dr. Tiavo Laevastu, FNWC research oceanographar , the bathymetry of all grid points which were less than 10 fathoms, were increased to 10 fathoms. This suggestion seemed to be appropriate since the current speeds would then become less along the coast and possibly the lower speeds would be diffused into the rest of the bay. A test run was made for 2 4 hours. The calculated current speeds did improve at the head of the canyon and other areas where there was a large slope in the bathymetry, but in the flat basins the currents speeds became larger. A more serious problem than the large variation in the Monterey Bay bathymetry is the inability of the model to correctly calculate the currents along the open boundary of the grid. Equation (30) and analysed field data indicate that for Monterey Bay the average tidal currents across the open boundary should be less than C.l knots. The current speeds calculated by the model were an order of magnitude larger. The difference between the calculated and actual current speeds seem to remain fairly constant throughout the bay. The inability to calculate the proper currents along the open boundary may be an inherent trait of the Hansen model. This author has found that the model produced unusually large currents at the entrances of the Gulf of Mexico and the South China Sea. Maury Pelto, National Marine 53 of 24 hours. If a finer grid and, thus, a smaller time step was used, the computer core storage and running time would be greatly increased and the model would be impractical to use. At the suggestion of Dr. Tiavo Laevastu, FNWC research oceanographar , the bathymetry of all grid points which were less than 10 fathoms, were increased to 10 fathoms. This suggestion seemed to be appropriate since the current speeds would then become less along the coast and possibly the lower speeds would be diffused into the rest of the bay. A test run was made for 2 4 hours. The calculated current speeds did improve at the head of the canyon and other areas where there was a large slope in the bathymetry, but in the flat basins the currents speeds became larger. A more serious problem than the large variation in the Monterey Bay bathymetry is the inability of the model to correctly calculate the currents along the open boundary of the grid. Equation (30) and analysed field data indicate that for Monterey Bay the average tidal currents across the open boundary should be less than C.l knots. The current speeds calculated by the model were an order of magnitude larger. The difference between the calculated and actual current speeds seem to remain fairly constant throughout the bay. The inability to calculate the proper currents along the open boundary may be an inherent trait of the Hansen model. This author has found that the model produced unusually large currents at the entrances of the Gulf of Mexico and the South China Sea. Maury Pelto, National Marine 53 Fisheries Service, has observed the same phenomena when using the model for Bristol Bay, Alaska. The large currents at the open boundaries of these three models did not seem to be transmitted across the grid. However these areas were much larger than Monterey Bay and the mesh lengths were of the same order of magnitude as the entire Monterey grid. It may be that for larger geographical areas, the frictional terms in Equation (7) may dampen out the higher speeds as the tides move across the grid. There may be an additional prob Lem with the Monterey Bay open boundary. The assumption that the tidal ranges and phases were equal for all the grid points along the open boundary may be part of the reason that the current speeds were too lfirge. As mentioned previously, since the Monterey and Santa Cruz tide records were in good agreement, the Santa Cruz tides were used along the open boundary. In most embayments ,. this would have posed no problems; however, since the canyon crosses the entrance of Monterey Bay, the tidal range in the canyon could be different than the range at the more shallow end points. If the tidal range was less in the canyon area, then the current speeds would have been smaller as the wave moved into the basins. It then becomes quite apparent that the tides and currents along the open boundary have to be more accurately defined. Since the calculated current velocities did not appear to be correct, it did not seem apropos to run the model with wind fields. Only one twenty-four hour run was made with a 54 wind field included. The run began 1200 PST, 12 August 1970. The wind field had a velocity of 10 knots and a direction of 225°. Although it is difficult to make a general statement about the influence of a wind field on Monterey Bay based on one computer run, in this case the tidal range seemed to be increased by approximately one foot and the current speeds by 0.1 to 0.2 knots. It should be remembered that the actual tides and not the predicted tides are inserted at the open boundary and the wind effects are already included. By adding a wind field, the additional increeises in water elevation and current speed result in slight over predictions. 55 IV. CONCLUSION As the field data analysis and the computer test runs progressed, it became quite obvious that the assumption that Monterey Bay would be an excellent site to evaluate the Hansen numerical model was invalid. First, field data collected by NPGS and other groups indicated that the principal driving force of the circulation in Monterey Bay was the adjacent oceanic current rather than the tidas. At least one standing vortex appears to exist in Monterey Bay. Except for the Moss Landing area, maximum current speeds in the southern basin was 0.70 knots. Currents at the head of Monterey Canyon are undoubtedly influenced by the tides where the currents reached measured speeds of 1.5 to 2.2 knots. The canyon may also influence the oceanic flow but there was not enough data to really confirm this hypothesis. Comprehensive field surveys need to be made on a seasonal basis in the bay and adjacent ocean to fully understand the circulation patterns of the area. If the density currents are the predominent currents in Monterey Bay, then the tidal-induced currents would be less than the density currents and, except for the shallow coast- line, should be on the order of 0.1 knots. The computed velocities were as much as an order of magnitude too high. It is speculated that the steep slopes of the canyon and conditions imposed at the open boundary are the principle 56 cause of the large errors in the current speeds. A finer grid system may solve the problem but would not be practical on present-day computers . Smoothing the bathymetry and adjusting the horizontal eddy viscosity parameter and the bottom stress coefficient did not improve the current predic- tion results appreciably. Increasing the shallow water depths to a minimum of ten fathoms did improve the results. The calculations of water elevation and phase and current direc- tion which indicates that separate gyres exist in the northern and southern basens appears to be correct. This thesis points out the important fact that when the Hansen model or any other numerical model is applied to specific areas of interest, the calculations should be correlated with actual field data. Parameters such as the horizontal eddy diffusivity term and bottom stress coeffi- cient can be considered empirical in nature and vary from location to location. It is very important to properly define the tide and current input along the open boundary. If, as in Monterey Bay, there is a large variance in the depths across the open boundary, then the tides should be accurately measured at all locations. Depending on the size and com- plexity of the area of interest, at least one and preferably several tide gauges should be used along the closed boundary. In the case of Monterey Bay, there was a noticeable lack of field data for the north basin. Thus, it was difficult to make definite conclusions about the circulation in this area. Finally, this report demonstrated the need to understand all the forces that govern the circulation in embayments. In 57 cases similar to Monterey Bay, where either permanent or seasonal oceanic currents exists, one must look at the embay- ment as part of a larger system. Ideally, computer models should include all the factors governing the circulation in an embayment but the amount of computer time required for these more sophisticated models makes this suggestion impractical on present-day computers . Thus, in applying any model to an area, there should be some prior knowledge as to which model would be more significant for the area. 58 APPENDIX A Monterey Bay Tide, Current and Wind Data for 12-13, 18-19 August and 6-13 November 1970 59 ^ 1*4 C3 V © CO 3E c/> J3 I I / V v. x N \ t/> =3 CM ex \ 91 N \ / UJ o < h- (J < i < i_ D L m •*■ <*> cm — cs m ^ •* c«) «N — 60 t T— ■ 1 1 1 V V \ V ^v N w \ r»j J s*> 2 ^^ o» Cd / 1** o- yS 1_ ^^ o* *~ S o> <^* p»» * — / X. ^**««. 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Ill 4 i A o C Of i T r CO ^ o J »— o O o o o o OO o o o o o o GO o rc o ^ o o If) tO N - O r- JL33J OJ CO in i o o CO o o o O O O o o >■ c rd O >, Q) i-i U 0 ■ 1 >-? (TJ t—i O CO • OO LD < CD !-i 3 Di 112 o o o CO o o oo c o c (0 U >1 o S-. Q) +j C O o o vO (0 a or o or < C_J CVJ _ en o z in — i 1 i » co cm •- o 133J o o o o go o X> o o O 2 3 5° LT5 CO 113 MONTEREY BAY 67.5 cm/sec 1.25 KNOTS Figure A-55. Calculated Currents in Monterey Bay at Higher Low Water plus 0.5 hours. 114 MONTEREY BAY i 67.5 cm/sec 1.25 KNOTS Figure A-56. Calculated Currents in Monterey Bay at Lower High Water minus 2 hours. 115 MONTEREY BAY i I 67.5 cm/sec 1.25 KNOTS Figure A-5 7. Calculated Currents in Monterey Bay at Lower High Water plus 1 hour. 116 MONTEREY BAY I 67.5 cm/sec 1.25 KNOTS Figure A- 5 8 Calculated Currents in Monterey Bay at Lower Low Water minus 2 . 5 hours . 117 MONTEREY BAY i 1 67.5 cm/sec 1.25 KNOTS Figure A-59. Calculated Currents in Monterey Bay at Lower Low Water. 118 MONTEREY BAY i 67.5 cm/sec 1.25 KNOTS Figure A-60. Calculated Currents in Monterey Bay at Lower Low Water plus 3 .5 hours . 119 MONTEREY BAY 67.5 cm/sec 1.25 KNOTS Figure A-61. Calculated Currents in Monterey Bay at Higher High Water minus 2.5 hours 120 MONTEREY BAY 67.5 cm/sec 1.25 KNOTS Figure A-62. Calculated Currents in Monterey Bay at Higher High Water plus 0.5 hours. 121 MONTEREY BAY 67.5 cm/sec 1.25 KNOTS Figure A-63. Calculated Currents in Monterey Bay at Lower-tew Water minus 2.5 hours. 122 Table a-I. Comparison of Tides at Monterey Bay Reference Stations Monterey Santa Cruz Moss Landing Day/Time (PST) High- Low Diff- erence Day /Time (PST) High- Low Diff- erence Day/Time (PST) High- Low Diff- erence August 12/0200 12/0900 12/1200 12/1900 13/0300 13/1000 13/1300 13/2000 3.35 6.45 6.3 8.9 2.9 6.8 6.3 9.4 17/2200 9.4 18/0500 2.5 18/1130 8.1 19/1200 8.5 19/1800 4.3 20/0000 8.0 3.10 0.15 2.6 6.0 3.9 0.5 3.1 6.9 5.6 4.2 3.7 August 12/0300 12/1000 12/1230 12/1930 13/0300 13/1000 13/1300 13/2000 2.2 5.3 5.1 7.7 1.7 5.6 5.15 8.20 17/2230 8.4 18/0300 1.25 18/1100 7/00 18/1700 3.35 18/2300 7.7 19/0600 2.0 19/1200 7.45 19/1800 3.15 20/0000 7.00 3.10 0.2 2.6 6.0 3.9 0.45 3.05 7.15 5.75 3.65 4.35 5.7 5.45 4.3 3.85 August 12 12 13 13 13 13 18 18 18 18 19 19 19 5.65 8.55 2.50 6.35 6.00 9.15 8.9 1.7 7.55 3.70 8.65 2.65 8.3 2.9 6.05 3.85 0.35 3.15 7.2 5.85 3.85 4.95 6.0 5.65 123 Comparison of Tides at Monterey Bay Reference Stations (Cont'd) Monterey Santa Cruz Mc ss Landin g Day/Time High- Diff- Day/Time High- Di f f - Day/Time High- Diff- (PST) Low erence (PST) Low erence (PST) Low erence November November November 6.6 06/0503 - 0.8 06/1000 5.25 1.6 06/1000 5.8 1.35 06/1600 6.85 4.75 06/1530 7.15 4.55 06/2300 2.10 4.3 06/2300 2.6 4.4 07/0600 6.40 2.0 07/0600 7.0 2.0 07/1100 4.40 1.9 07/1100 5.0 1.9 07/1630 6.30 4.15 07/1700 6.9 4.3 08/0000 2.15 4.6 08/0000 2.6 4.6 08/0630 6.75 3.10 08/0600 7.2 3.0 08/1230 3.65 2.65 08/1300 4.2 2.5 08/1800 7.6 3.9 08/1800 6.3 3.75 08/1800 6.7 3.55 09/0000 3.7 5.0 09/0000 2.55 4.75 09/0000 3.15 4.75 09/0700 8.7 4.85 09/0700 7.3 4.45 09/0700 7.9 4.45 09/1300 3.85 3.85 09/1300 2.85 3.4 09/1330 3.45 3.3 09/1900 7.7 3.65 09/1900 6.25 3.10 09/1900 6.75 3.15 10/0700 4.5 5.15 10/0100 3.15 4.6 10/0100 3.6 4.7 10/1400 3.2 4.5 10/1400 2.15 4.05 10/1430 2.7 3.95 10/2030 7.5 2.9 10/2000 6.2 2.75 10/2000 6.65 2.7 11/0130 4.6 4.9 11/0200 3.45 4.65 11/0200 3.95 4.8 124 Comparison o f Tides a t Monterey Bay Reference Stations (Cont'd) Monterey S anta Cruz Mc ss Landin g Day/Time High- Diff- Day/Time High- Diff- Day/Time High- Di f f- (PST) Low erence (PST) Low erence (PST) Low erence November 9.5 November 8.10 November 8.75 11/0800 11/0800 11/0800 7.1 - 6.75 6.8 11/1500 2.4 4.9 11/1500 1.35 4.65 11/1500 1.95 4.55 11/2200 7.3 2.4 11/2130 6.00 2.25 11/2100 6.5 2.2 12/0230 4.9 4.8 12/0200 3.75 . 4.45 12/0200 4.3 4.45 12/1000 9.7 7.9 12/0830 8.2 7.4 12/0800 8.75 7.25 12/1200 1.8 5.5 12/1600 0.8 4.55 12/1530 1.5 5.45 12/2300 7.3 2.3 12/2200 5.35 1.55 12/2230 6.25 1.65 13/0300 5.0 4.5 13/0300 3.0 4.4 13/0300 4.6 4.3 13/1000 9.5 8.0 13/0900 8.2 7.5 13/0900 8.9 7.65 13/1700 1.5 5.7 13/1630 0.7 5.05 13/1630 1.25 5.0 14/0100 7.2 1.1 13/2300 5.75 1.15 13/2300 6.25 1.15 14/0430 6.1 3.5 14/0300 4.60 3.6 14/0330 5.1 3.7 14/1100 9.6 7.8 14/1000 8.2 2.45 14/1000 8.8 7.45 14/1830 1.8 14/1700 0.75 • 14/1700 1.35 125 to Q> oo CO I O) o s- t- •I- +J to QJ QJ S- cn O) Q o o o o r~» r— ^— en CM CO CO "D to <1J 4-> QJ O OO i^ (T3 CJ A3 U rO U in I qj o S- -r- «3 LO CM CM rO XJ to QJ -t-> QJ O oo :*: r-^ fd m >i qj 0) -p c o c •H w -p e QJ e QJ U en fd QJ 2 C •H H I QJ H fd cn {= •r— •o c ro 1 to u c OJ OJ c a; i- •1- S- i — 3 +J cn O) O t/> to o "O to QJ O CL £= to ^. 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Course Approx. Speed (3cts) Drogue #1: 121800 Aug. 088 0.70 1900 046 0.70 2000 099 0.50 2100 112 0.40 2200 124 0.30 2300 114 0.25 130000 152 0.15 0100 144 0.25 0200 134 0.40 0300 166 0.34 0400 179 0.20 0500 187 0.10 0600 198 0.15 0700 218 0.10 0800 162 0.05 Drogue #2: 122000 Aug. 328 0.20 2100 285 0.30 2200 275 0.20 2300 267 0.10 130000 255 0.30 0100 255 0.20 0200 255 0.10 0300 298 0.25 0400 274 0.25 0500 272 0.20 0600 258 0.34 0700 237 0.05 0800 201 0.10 0900 167 0.20 Drogue #3: No track (never gained contact) Drogue #4: 130200 Aug. 143 0.15 0300 130 0.15 0400 156 0.10 0500 160 0.10 0600 182 0.15 130700 191 0.10 135 Drogue #5: Drogue #6: Drogue #7: 0800 026 0.10 0900 028 0.10 1000 030 0.15 130200 Aug. 132 0.40 0300 169 0.40 0400 150 0.34 0500 16-8 0.20 0600 175 0.15 0700 135 0.15 0800 094 0.20 0900 097 0.20 182100 Aug. 112 0.25 2200 090 0.25 2300 124 0.20 190000 238 0.175 0100 221 0.20 0200 215 0.25 0300 120 0.075 0400 132 0.125 0500 043 0.10 0600 097 0.075 0700 065 0.025 0800 056 0.30 0900 069 0.225 1000 130 0.30 1100 134 0.25 1200 144 0.375 1300 143 0.20 1400 132 0.225 1500 133 0.275 182100 Aug. 017 0.225 2200 074 0.125 2300 334 0.20 190000 327 0.20 0100 342 0.30 0200 019 0.275 0300 031 0.40 0400 034 0.275 0500 034 0.20 190600 034 0.425 0700 069 0.50 0800 101 0.425 0900 107 0.50 1000 163 0.25 136 Drogues #8: 1100 1200 1300 1400 1500 182200 2300 190000 0100 0200 0300 0400 0500 0600 0700 0800 Aug 200 096 081 084 143 034 353 328 328 003 030 071 089 080 087 090 Drogue #9: No track (lost contact after 15 min.) Drogues #10 : 182300 190000 0100 0200 0300 0400 0500 0600 0700 0800 0900 1000 1100 1200 1300 1400 Aug. 214 252 285 356 003 037 065 093 087 146 165 180 207 235 237 263 0.225 0.225 0.15 0.275 0.20 0.20 0.325 0.225 0.275 0.45 0.20 0.20 0.275 0.15 0.125 0.25 0.175 0.40 0.175 0.30 0.45 0.15 0.275 0.175 0.175 0.20 0.25 0.375 0.40 0.325 0.225 0.05 Drogues #11: Very short track. Moved due south 250 yds., 2300-2400. Shifted to approximate head 250 for 30 min. covering 200 yds. Reversed track to about 070 for 2 hrs . covering 400 yds. Lost contact at 190230 (shadow zone?) Drogue #12 190000 0100 0200 0300 0400 Aug 230 229 261 293 026 275 325 425 275 40 137 Drogue #13 Drogue #2 8: 0500 056 0.425 0600 012 0.375 0700 064 0.30 0800 117 0.175 190000 Aug. 355 0.125 0100 292 - 0.30 0200 305 0.075 0300 272 0.05 0400 028 0.075 0500 055 0.125 0600 016 0.175 0700 068 0.325 061300 Nov. 310 0.275 1400 310 0.125 1500 290 0.20 1600 311 0.20 1700 327 0.20 1800 327 0.10 1900 281 0.10 2000 257 0.05 2100 257 0.05 2200 244 0.25 2300 246 0.175 070000 248 0.325 0100 253 0.425 0200 283 0.333 0300 280 0.325 0400 273 0.375 0500 298 0.40 0600 315 0.375 0700 327 0.40 0800 330 0.475 0900 352 0.55 1000 348 0.45 1100 338 0.325 1200 342 0.30 1300 336 0.325 1400 327 0.325 1500 342 0.34 1600 342 0.275 1700 336 0.125 1800 277 0.10 1900 250 0.05 2000 248 0.10 2100 247 0.15 2200 247 0.15 2300 247 0.275 180000 276 0.225 138 0100 290 0200 275 0300 292 0400 314 0500 316 0600 304 Drogue #29: 061200 Nov. 048 061300 048 1400 051 1500 040 1600 056 1700 082 Drogue #30: 071800 Nov. 268 1900 263 2000 244 2100 183 2200 207 2300 241 080000 249 0100 248 0200 258 0300 253 0400 263 0500 311 0600 302 0700 345 0800 352 0900 358 1000 002 1100 002 1200 348 1300 310 1400 276 1500 264 1600 244 Drogue #31: 071900 Nov. 293 2000 278 2100 278 2200 259 2300 251 080000 260 0100 290 0200 272 0300 303 0400 294 0.30 0.325 0.30 0.425 0.34 0.40 0.175 0.175 0.20 0.15 0.25 0.25 0.25 0.175 0.15 0.20 0.125 0.225 0.30 0.275 0.325 0.30 0.275 0.25 0.225 0.325 0.30 0.325 0.325 0.325 0.175 0.10 0.10 0.15 0.275 0.10 0.05 0.05 0.225 0.175 0.40 0.30 0.45 0.375 0.325 139 { 0500 319 0600 339 0700 002 0800 010 0900 021 1000 046 1100 031 081200 009 1300 333 1400 333 1500 338 1600 338 Drogue #32: Very short track . Mov approximate head ing 1 contact : (shadow zone? Drogue #33: 072000 Nov. 095 2100 117 2200 152 2300 229 080000 234 0100 237 • 0200 253 0300 284 0400 325 0500 344 0600 359 0700 012 0800 030 0900 048 1000 051 1100 043 1200 021 . 1300 041 1400 054 1500 267 Drogue #34: 101000 NOV. 246 1100 233 1200 238 1300 226 Drogue "X": 100800 Nov. 240 0900 234 1000 231 1100 232 1200 236 1300 244 0.225 0.65 0.325 0.34 0.475 0.40 0.25 0.175 0.05 0.10 0.10 0.125 0.175 0.20 0.15 0.325 0.275 0.34 0.30 0.175 0.275 0.225 0.10 0.375 0.225 0.40 0.325 0.275 0.10 0.125 0.275 0.15 0.34 0.45 0.375 0.40 0.25 0.34 0.20 0.375 0.45 0.34 Lost 140 Drogue "Y" : 100900 Nov. 190 1000 164 1100 118 1200 166 1600 236 1700 232 1800 229 1900 232 2000 236 Drogue "Z": 101100 Nov. 137 1200 151 1600 192 1700 195 1800 210 1900 219 2000 203 Drogue #35 Drogue #36 Drogue #37 Drogue #38 132000 0300 0400 0500 0600 0700 0800 130300 0400 0500 0600 0700 0800 130300 0400 0500 0600 0700 0800 130500 0600 0700 0.15 0.20 0.125 0.25 : * 0.40 0.425 0.475* 0.425 0.475 0.40 0.25 * 0.34 0.325 0.45 0.375 0.45 Nov. 180 0.325 164 0.425 182 0.34 191 0.375 201 0.575 223 0.575 231 0.575 Nov. 210 0.45 213 0.45 205 0.475 229 0.70 241 0.65 230 0.675 Nov. 162 0.225 180 0.325 205 0.375 214 0.45 212 0.50 214 0.475 Nov. 219 0.275 225 0.45 228 0.525 interrupted Track 141 BIBLIOGRAPHY 1. Broenkow, W. X., 1971, personal communication, Moss Landing Biological Station, Moss Landing, California. 2. Cardone , V. J., 1969, Specification of the Wind Distribu- tion in Marine Boundary Layer for Wave Forecasting , N ew York University, Department of Meteorology and Ocean- ography, Geophysical Sciences Laboratory TR-69-1. 3. Carter, R. C. and E. J. Kazmierczak, 1968, Special Oceanographic Studies, Engineering-Science, Inc. Final Report, Task Vll-la, State of California State Water Quality Control Board, San Francisco Bay-Delta Quality Control Program. 4. Defant, A., 1961, Physical Oceanography, Volume 1, Pergammon Press, New York. 5. Dronkers , J. J., 196 4, Tidal Computations in Rivers and Waters , North-Holland Publishing Company, Amsterdam. 6. Garcia, R. A., 1971, Numerical Simulation of Currents in Monterey Bay, M.S. Thesis, Naval Postgraduate School, Monter€;y, California. 7. Hansen, W. , 19 66, The Reproduction of the Motion in the Sea by means of Hydrodynamical-Numerical Methods, Mitteilungen des Instituts fur Meereskunde der Universitat Hamburg, Subcommittee on Oceanographic Research Technical Report 25, Hamburg, Germany. 8. Jensen, H. E., S. Weywadt and A. Jensen, 1966, Forecasting of Storm Surges in the North Sea, Part L, NATO Subcommittee Oceanographic Research Technical Report 28. 9. Laevastu, T. and P. Stevens, 1969, Application of Numerical Hydrodynamical Models in Ocean Analysis Forecasting, Part I - The Single-Layer Model of Walter Hansen, Fleet Numer- ical Weather Central, Technical Note 51. 10. Lazanoff, S. M. , 1969, An Investigation of Seiches in DaNang Bay, Vietnam, U.S. Naval Oceanographic Office IR No. 69-81. 11. Lazanoff, S. M. and D. K. Clark, 1970, Preliminary Report on the Numerical Prediction of Tides and Tidal Currents for Various Wind Conditions in che South China Sea, U.S. Oceanographic Office IR No. 70-41. 142 12. Lynch, J. L. , 19 70, Long Wave Study of Monterey Bay, M. S. Thesis, Naval Postgraduate School, Monterey, California. 13. McKay, D. A., 1970, A Determination of Surface Currents in the Vicinity of the Monterey Submarine Canyon by the Electromagnetic Method, M.S. Thesis, Naval Postgraduate School, Monterey, California. 14. Mungall, J. C. J. and J. B. Matthews, 19 70, A Variable- Boundary Numerical Tidal ModeJL , University of Alaska, Institute of Marine Sciences, Report Number R70-4. 15. Ortiz, N. G. , 1964, Numerisch-Hydrodynamische Untersuchen in Golf von Mexico, Ph.D. Dissertation, Universitat Hamburg, Hamburg, Germany. 16. Pacific Gas and Electric Company Engineering Research Department, 1970, personal communication, Emoryville, California. 17. Pekeris, C. L. and Y. Accad, 1969, Solution of Laplace Equation for the M2 Tide in the World Oceans , Philosophical Transactions of The Royal Society of London, Mathematical and Physical Sciences Volume 265, No. 1165, pages 413-- 436. Pore, N. A. and R. A. Cummings , 1967, A Fortran Program for the Calculation of Hourly Values of Astronomical Tide and Time and Height of Hich and Low Water, Weather Bureau, Techniques Development Laboratory, WRTM TDL-6 . 19. Schureman, P., 1958, Manual of Harmonic Analysis and Prediction of Tides , United States Coast and Geodetic Survey Special Publication No. 98. 20. Simmons, H. B., 1966, Tidal and Salinity Model Practice, Estuary and Coastline Hydrodynamics, A. T. Ippen, ed. McGraw-Hill Book Company, New York. 21. Stoddard, H. S., 1971, Feasibility Study on the Utiliza- tion of Parachute Drogues and Shore Base Radar to inves- tigate Surface Circulation in Monterey Bay, M.S. Thesis, Naval Postgraduate School, Monterey, California. 143 INITIAL DISTRIBUTION LIST No. -Copies 1. Defense Documentation Center - ' 2 Cameron Station Alexandria, Virginia 22314 2. Library, Code 0212 2 Naval Postgraduate School Monterey, California 93940 3. Oceanographer of the Navy 1 The Madison Building 732 N. Washington Street Alexandria, Virginia 22314 4. Department of Oceanography, Code 5 8 3 Naval Postgraduate School Monterey, California 9 39 40 5. Dr. E. B. Thornton, Code 5 8Tm 3 Department of Oceanography Naval Postgraduate School Monterey, California 93940 6. Dr. W. C. Thompson, Code 5 8Th 1 Department of Oceanography Naval Postgraduate School Monterey, California 93940 7. U.S. Army Corps of Engineers 1 Waterways Experiment Station Vicksburg, Mississippi 39180 8. Mr. Sheldon M. Lazanoff 5 U.S. Naval Oceanographic Office Representative Fleet Numerical Weather Central Monterey, California 9 39 40 9 . Commander 1 U.S. Naval Oceanographic Office Washington, D. C. '20390 10. Mr. Leo J. Fisher 5 U.S. Naval Oceanographic Office Code 7300 Washington, D. C. 20390 144 No. Copies 11. Commanding Officer 1 Fleet Numerical Weather Central Monterey, California 9 394 0 12. Mr. Walter Howard 1 U.S. Ship Research and Development Laboratory- Code 746 Panama City, Florida 32401 13. Mr. Orville T. Magoon 1 U.S. Army Engineer District Corp of Engineers 100 McAllister Street San Francisco, California 94102 14. Mr. M. J. Doyle, Jr. 1 Pacific Gas and Electric Company Department of Engineering Research 4245 Hollis St. Emeryville, California 94608 15. Mr. W. T. Burns 1 Kaiser Refractories Moss Landing, California 95039 16. Mr. R. H. Bethel 1 Park/Recreation Department Civic Auditorium Santa Cruz, California 95060 17. Dr. D. J. Baumgartner 1 Federal Water Quality Administration Northwest Region Pacific Northwest Water Laboratory 200 Southwest 35th Street Corvallis, Oregon 97330 18. Mr. Robert Ford 1 State of California Department of Water Resources P.O. Box 9137 Sacramento, California 95816 19. Dr. Phillips 1 Hopkins Marine Station Cabrillo Point Pacific Grove, California 93940 20. Dr. John Harville 1 Moss Landing Marine Laboratory Moss Landing, California 95039 145 No. Copies 21. Dr. R. G. Dean Coastal and Oceanographic Engineering Department University of Florida Gainesville, Florida 32601 22. Environmental & Fishery Forecasting Center National Marine Fisheries Service National Oceanic & Atmospheric Administration U.S. Department of Commerce c/o Fleet Numerical Weather Central, NPS Monterey, California 9 3940 146 Security Classification DOCUMENT CONTROL DATA -R&D' i Security c las si I ic at ion ol title, body ol abstract and indexing annotation must be entered when tlie overall report is classili 'd) I originating activity (Corporate author) Naval Postgraduate School Monterey, California 93940 24. REPORT SECURITY CLASSIFICATION Unclassified 2b. GROUP 3 REPOR T TITLE An Evaluation of a Numerical Water Elevation and Tidal Current Prediction Model Applied to Monterey Bay 4 DESCRIPTIVE NOTES (Type ol report and.inclusive dates) Master's Thesis; March 1971 5 AU TMORlSI (First name, midole initial, last name) Sheldon Mark Lazanoff 6 REPOR T O A TE March 1971 7a. TOTAL NO. OF PAGES 148 76. NO. OF RE FS 21 S« CONTRACT OR GRANT NO. b. PROJEC T NO 9a. ORIGINATOR'S REPORT NUMBER(S) 96. OTHER REPORT NO(S) (Any other numbers that may be assigned this report) 10 DISTRIBUTION STATEMENT Approved for public release; distribution unlimited II. SUPPLEMENTARY NOTES 12. SPON SO RING Ml LI T AR Y ACTIVITY Naval Postgraduate School Monterey, California 93940 13 ABSTRACT The Hansen Hydrodynamical - Numerical model was evaluated for Monterey Bay with actual field data. Tides and winds are the principal driving forces of the Hansen model. Analysis of the field data indicated that the principal driving force of the circulation in the bay was the oceanic currents and not the tides and winds. The tidal heights and phases and current directions were calculated correctly by the model, but the calculated current speeds were an order of magnitude too large. The inaccuracy of the current speeds was attributed to the inaccurate calculations of the currents along the open boundary and the large bathymetric gradients of the Monterey Submarine Canyon. ~* DD,Fr:..1473 S/N 0101 -807-681 1 (PAGE 1) 147 Security Classification A-31408 Security Classification key wo R OS Tides Currents Numerical Model Shallow Water Embayments no L E W T DD ,F°1M473 (back) S/N 0101 -807-6821 148 Security Classification A- 3M09 Thesis 126453 L345 Lazanoff c." An evaluation of a numerical water eleva- tion and tidal current prediction model ap- plied to Monterey Bay. / DUDLEY KNOX LIBRARY 3 2768 00036716 3