NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS 53HliZ A MODEL ADAPTED TO FOR TIDAL MONTEREY CIRCULATION BAY, CALIFORNIA by Christine W • S c ho maker September 1983 Thesis Advisors: W. E. E. B. Hart Thornton Approved for public release; distribution unlimited , SECURITY CLASSIFICATION OF THIS PAGE (Wnmn Dm Entered) REPORT DOCUMENTATION PAGE 1. flCPO»T NUMBER READ INSTRUCTIONS BEFORE COMPLETING FORM 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER 4. TITLE ana Subtitle) A Model for Tidal Circulation Adapted to Monterey Bay, California 5. TYPE OF REPORT & PERIOD COVERED Master's Thesis September 1983 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORS Christine W. Schomaker B. CONTRACT OR GRANT NUMBERf*) »• PERFORMING ORGANIZATION NAME ANO ADDRESS Naval Postgraduate School Monterey, California 93943 10. PROGRAM ELEMENT, PROJECT, TASK AREA 4 WORK UNIT NUMBERS II. CONTROLLING OFFICE NAME ANO ADDRESS Naval Postgraduate School Monterey, California 93943 12. REPORT DATE September 1983 14. MONITORING AGENCY NAME 4 AOORESSfff different treat Controlling Office) 13. NUMBER OF PAGES 99 15. SECURITY CLASS, (of this report) 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE 14. DISTRIBUTION STATEMENT (of thla Report) Approved for public release, distribution unlimited. 17. DISTRIBUTION STATEMENT fat the ebtttect entered In Block 20, If different iroai Report) It. SUPPLEMENTARY NOTES IS. KEY WORDS (Continue an reveree tide II neceeeary and Identity by block number) Hydrodynamic Model Tide Correctors Tidal Model Hydrographic Survey Monterey Bay Tidal Circulation 20. ABSTRACT 'Continue on reveree tide II neceeeary and Identity by block number) An implicit numerical model for two-dimensional hydrodynamic flow in coastal seas by Leendertse (1967), as modified by Hart (1976), was applied to Monterey Bay. The model was tested against available water-level and current observations. The responses of Monterey Bay to tidal forcing and steady-state winds were simulated. Under tidal forcing it was found to provide reasonable estimates of sea-surface elevations. Currents were not well predicted, indicating that other mechanisms such as wind, density stratification, and oceanic currents generally dominate the forcing of the circulation in DO FORM 1 JAN 73 1473 EDITION OF I NOV «S IS OBSOLETE S/N 01P2- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Snterec SECURITY CLASSIFICATION OF THIS PAGE (When Datm Enfrmd) Block 20 cont'd. Monterey Bay. The model in its present form was found to be potentially suitable for providing real-time tide correctors during a hydrographic survey, achieving an RMS error of 4.5 cm in predicting sea-surface elevations. S'N 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS RAGEfWh»n Dmlm Enfrmd) Approved for public release; distribution unlimited A Model for Tidal Circulation Adapted to Monterey Bay, California by Christine W. SchDnaker Lisa tenant, NDAA Sc.B., Brown University, 1972 Submitted in partial fulfillment of th< requirements for the degree of MASTER DF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY) from the NAVAL POSTGRADUATE SCHOOL September 1933 DU ABSTRACT An implicit numerical aodel for two-dimensional hydrody- naraic flow in coastal seas by Leendsrtse (1967), as modified by Hart (1976) , was applied to Montsrey Bay. The model was tested against available water-levsi and current observa- tions. The responses of Monterey Bay to tidal forcing and steady-state winds were simulated. Under tidal forcing it was found to provide reasonable estimates of sea-surface elevations. Currents were not well predicted, indicating that other mechanisms such as wind, density stratification, and oceanic currents generally dominate the forcing of the circulation in Monterey Bay. The msdei in its present form was found to be potentially suitable for providing real-time tide correctors during a hydrographic survey, achieving an RMS error of 4.5 cm in predicting ssa-surface alevations. TABLE OP CONTENTS I. INTRODUCTION 10 A. PURPOSE 10 B. HISTORY OF THE MODEL 11 C. CIRCULATION STUDIES OF MONTEREY BAY 12 II. DESCRIPTION OF THE NUMERICAL MODEL 17 A. HYDRODYNAMIC THEORY 17 B. STRUCTURE AND COMPONENTS 21 1. Computational Scheme 21 2. Computer Program 23 C. USE AND ADAPTATION 25 1. Input Data Requirements 25 2. Subroutine Modifications 26 3. Computer Implementation 27 III. APPLICATION OF THE MODEL TO MONTEREY BAY 29 A. VALIDITY OF ASSUMPTIONS 29 B. CONSTANT INPUT 29 1. Time and Space Dimensions 30 2. Bathymetry and Datum 34 3. Bottom Friction 35 C. TIME-VARYING INPUT 36 1. Initial Conditions 36 2. Boundary Tidal Amplitudes 36 3. Boundary Currents 39 4. Wind 39 D. DATA FOR COMPARISON 4 0 1. Mater-level Observations . 41 2. Current-meter Observations 42 IV. RESULTS 43 A. COMPARISON CF MODEL RESULTS WITH OBSERVATIONS 43 1. Sea-surface Elevation Comparisons .... 43 2. Current Comparisons 52 B. MODELED CIRCULATION OF MONTEREY BAY 53 1. Tidally Forced Circulation 53 2. Tidally Forced Circulation with Wind ... 58 V. CONCLUSIONS 60 A. VALIDITY OF THE MODEL 60 B. HYDROGRAPHIC SURVEY APPLICATIONS 60 APPENDIX A: TIDAL CONSTITUENTS 54 APPENDIX E: TIDALLY FORCED SEA-SURFACE ELEVATIONS ... 66 APPENDIX C: TIDALLY FORCED CURRENTS 80 BIBLIOGRAPHY 94 INITIAL DISTRIBUTION LIST 97 LIST OF TABLES I. Components of the Numerical Sodel 24 II. Comparison of Pelagic and Coastal Tidal Constituents 38 III. Effect of Various Manning Factors 44 IV. Effect of Boundary Amplituda Phasing on Grid B . . 52 LIST OF FIGURES 1.1 Map 3f ths Study Area, Showing Model Grids ... 13 1.2 Bathymetry of Monterey Bay Viewed from Southwest 14 2.1 Staggered Grid of the Numerical Model 22 3.1 Depth Contours for Grid A 31 3.2 Depth Contours for Grid B 32 3.3 Depth Contours for Grid C 33 3.4 Locations of Bathyraetric Data in Grid A .... 34 3.5 Observing Periois for Comparison Data 41 4.1 Sea-surface Elevations at .ionterey, Grid A ... 44 4.2 Elevations at Monterey, At=3600 s 45 4.3 Elevations at Moss Landing, At=3600 s 46 4.4 Elevations at Monterey, M = .10 m/s 47 4.5 Elevations at Moss Landing, M=.10 m/s 47 4.5 Elevations at Monterey, At = 900 s 48 4.7 Elevations at Moss Landing, A-=900 s 48 4.3 Spectra, Elevations (SE) at Monterey 49 4.9 Spectra, Elevations (SE) at Moss Landing .... 50 4.10 Elevations Using Predicted Boundary Amplitudes 51 4.11 Currants near Santa Cruz 54 4.12 Currants South of the Salinas River 55 4. 13 Currants North of the Salinas River 56 4.14 Spectra of Currents naar Santa Cruz 57 4.15 Currant Field for Grid A at 760702 1500 .... 59 5.1 Time Step Lag During Real-time Model 62 ACKNOWLEDGMENTS The author expresses har appreciation to Drs. Hart and Thornton for their encouragement: and guidance. She also thanks Mr. Joe Muilin, Mr. Don Simpson, LT Steve Conrad, and Dr. Terry Hendrix for their help in obtaining digitized field observations. Shs ^specially thanks Mr. Eric Schomaker for his unflagging confidence and invaluable editorial assistance. I- INTRO DUCTI3W A. PURPOSE This study grew out of a desire to extend tidal data observed at a few locations to the entire area of a hydro- graphic survey. With sea-surface elevations modeled over the whole field, survey depths may be corrected automati- cally by subtracting realistic values of the surface's variation from datum at any point, at any time. Tidal zoning to obtain sea-surface elevations is, at present^ a subjective affair requiring numerous water-level stations to indicate the progress of a tidal wave into an inlet. The pattern of propagation at points distant from the observing stations is inferred only qualitatively from bathymetry. Correctors are determined by defining zones graphically and computing appropriate phase and amplitude adjustments for each zone to apply to tidal values observed at the reference stations. This process dees not provide a continuum of correctors. It requires subjective judgment and considerable experience to achiave adequate results. The analysis is typically performed well after the survey, when it is too late to use depth data corrected for observed tides to provide cross-checks on the positional accuracy of the data. Errors that might have been detected and corrected during the survey may pass unnoticed until an expensive return to the survey area or downward classifica- tion of the survey is necessary. Use in the field of a two-dimensional, numerical model for circulation and sea-surface elevation would alleviate these difficulties. Such a model must be simple and flex- ible if it is to be applied in real or near-real time on 10 fisld-type microprocessors. In coastal seas and inlets, it should be able to provide sufficiently accurate surface elevations. To test this concept, the two-dimensional, hydrodynamic model of Leendertse (1967), as modified by Hart (1976) and during this study, was applied to Monterey Bay. The model had previously been used with some success in shallow coastal seas and estuaries, but not in an area with such a dominant bathymetric feature as the Monterey canyon. Although no attempt was made to compare this model to any of the broad spectrum of models in use throughout the oceano- graphic and co a stal- engineering communities [Tracor, Inc., 1971], its relative simplicity, ease of implementation, flexibility, and accurate output are all important to its potential usefulness as a tidal zoning system during field operations. An additional purpose of this study is to incorporate large-scale non-tidal forces into the model to explore their effects on the circulation and sea-surface elevation of a coastal body of water. Various investigators have suggested, in fact, that tidal forces are overridden in their effect on the circulation of Monterey Bay by the influence of offshore currents and atmospheric conditions. The potential significance of such factors, and the ability to incorporate real-time observations of them into the model, are also important to the model's usefulness as a tidal zoning system. B. HISTORY OF THE MODEL The original version of the numerical model used during this study was described by Leendertse (1967). His "multioperationai" finite-difference scheme, using both implicit and explicit techniques to solve the equations of 11 fluid motion, provided advantages is computational stability and efficiency over the explicit models then current [Hart, 1976]. In particular, the model remains stable regardless of the time step used; in a relatively deep embayment such as Monterey Bay the investigator is not restricted to time steps of the order of seconds as is common with explicit models such as that used by Lazanoff (1971) in his study of the bay. The model has been widely applied, both in small harbors [Leendertse, 1967; Leendertse and Lu, 1975; Chiang and Lee, 1982] and in coastal seas [Leendertse, 1967; Hart, 1976; Spaulding and Beauchamp, 1983]. In past applications, length scales ranged to 290 km and depths ranged to 100 m. This study extends the model to a much deeper area with pronounced vertical relief. C. CIRCULATION STUDIES OP HONTEBEY BAY Monterey Bay is a relatively large (16 by 42 km), nearly symmetric embayment on the central coast of California. Its most notable bathymetric feature is the Monterey canyon, which curves into the bay from the southwest, severing the continental shelf. Within the bay proper, depths rise from 750 m at the seaward end of the canyon to an average 55 m en the shelf. The bay presents to the Pacific Ocean one uninterrupted open boundary, some 36 km long. Consequently, oceanic tides and currents and offshore atmospheric effects are primary driving forces of circulation within the bay itself. Local winds and seasonal river runoff may have some effects, espe- cially in the shallower portions of the bay to the north and south. The relative importance of these various influences is not well-understood. 12 71 Sfzurdr; : ihrril!!! M^SB^^^^B I ■TTTT-r4 - 77^ 3 si 4 — Ml i §~#t th s iff/ f s dya- ( ^_ Z( ,; J \ „jT7 <5^< ' -V J •'» *-'--sVT'%\ v - «- ——'■?■ •• « - __2 ' s' •K £ >» * I 1 f ■_». 4 iff •vt? - -> £',«S - * ' jl -1020 ■ -■>-- jfv 3 ..J." $ 5 |s" *0 ••*•' , !»-!= 3 a,,3f.o a ^ -f ;s> i— i *J -~,--^----, v/ — i — bah* _o Qttfa -li-Sip *\ 006t-tMi | \ \ ggg i ) iggmn — cmi i ng g a i : ,;f,ii| i :t-^t msanaamm 0) •H C5 0) o c •H * o en (d 0) M <: >i T3 4J a, (d a> u 13 Figure 1.2 Bathymetry of Monterey Bay Viewed from Southwest Three oceano graphic "seasons" for this portion of the coast were first described by Skogsberg (1936). From November through February the Davidson Current flows north- ward along the coast in conjunction with southerly or weak northward winds and the onshore transport of surface water. From March through August a period of upwelling is accompa- nied by the southward flowing California Current, strong northwest winds, and offshore transport of surface water. In September and October the oceanic period is marked by relative calm and an increase in surface temperatures. All available data concerning circulation within the bay proper were summarized and analyzed in 1973 as part of a ma}or oceanographic study [Scott, 1973]. Normal circulation 14 was found to be northward through the bay, with a small gyre forming in the southern bight. A more recent analysis by Broenkow and Smethie (1978) also concluded that flow is generally northward, with water entering primarily along the axis cf the canyon and having a residence time of 2 to 14 days during upwelling periods. They also suggest that a volume of 109 a3 pumped into and out of the bay by internal tidal mixing may be responsible for the frequent presence of cool, nutrient-rich waters at the head of the Monterey Canyon near Moss Landing. Most circulation studies of the bay proper have relied primarily on temperature and salinity data collected at oceanographic stations. Although drift cards and similar devices have been used to map surface currents, long-term current-meter observations have not been available until the last ten years. During predesign studies for sewer outfalls, current meters were deployed for periods of a year or more near Santa Cruz [Brown and Caldwell, Inc., 1978], the Pajaro River [Environmental Research Consultants, Inc., 19^6], and the Salinas River [Engineering-Science, Inc., 1977]. In general, these studies suggest that the net flow of water is northward along the coast, with some dependence on the local diurnal wind. Tidal forcing has not been examined closely in any of the aforementioned studies. However, an explicit numerical model was employed by Lazanoff (1971) to study the tidal circulation within the bay. Although field observations indicated that the primary driving force for circulation derived from oceanic currents, the tide- and wind-driven model did predict correct sea-surface elevations and current phases and directions for the short time periods over which it could be run. Current magnitudes appeared too large near coastal boundaries. 15 More recently Bretschneider (1930) analyzed the effects of various ocaanographic conditions on the sea-level changes observed at Monterey. Variations ia geostrophic current flow, atmospharic pressure, sea-surface temperature, and meridional wind stress were shown to correspond to observed variations in sea-surface elevation at Monterey. 16 II. DESCRIPTION OF THE NUMERICAL MODEL A. HYDRODYNAMIC THEORY The numerical model of Leendertse (1967) relies on the basic equations that describe conservation of momentum and mass for incompressible fluid motion. In the Cartesian coordinate system of the model, with x- and y-axes embedded in a horizontal f-plane tangent at the origin to the undis- turbed sea surface (the datum) and with the z-axis oriented upward, these well-known equations are: 5u 6u 5u 6u 1 6s p , _ c? "\\ ■*— + U-k— + V-s— + W^— = - jf*- + F I * • ' I Ot ox Oy oz p ox x 6v 5v <5v 5v 1 5p _ f> ~>\ Ot Ox oy oz p Oz y 5w 5w 5w 5w 1 5p _ /9 -3» ■j— + u-~— + v-t— + wp- = — -^- + F l-^-Jj Ot Ox oy oz p oz z £l+£L+^ = o (2.4) Ox Oy Oz Ths variables u, v, and w are components of velocity parallel to the x- , y-, and z-axes respectively, p is pres- sure, and p is density. The appliad forces per unit mass (F. ) represent effects of the Earth*s rotation, the Earth's gravitation, viscous and turbulent stresses in the fluid, and astronomical tides. 17 These equations are simplified by making assumptions appropriate to the examination of long-period forcing in a two-dimensional, shallow field. Detailed derivations may be found in Leendertse (1967) and Hart(1976). A more general development of shallow water equations may be found in Csanady (1982). The necessary assumptions are summarized in the following paragraphs. First, because a coastal sea or estuary is generally shallow relative to the horizontal scale of motion, the vertical velocity is assumed small relative to the hori- zontal velocities. Therefore, both convective-inertia terms and rotational effects that involve the vertical velocity in equations 2.1-2.3 may be neglected. Second, the equations 2.1-2.4 ace averaged to model fluid motions with periods greater than those of short- period turbulent motions. Third, the hydrostatic approximation is made by analysis of equation 2.3. The vertical component of tha rotational effect may be considered negligible (of the order 10-2 cm/s2) and so may vertical stress-gradient effects (10-3 cm/s2 according to Csanady, 1982). Furthermore, since mean vertical velocties are unlikely to be greater than 10 cm/s, over sufficiently longtime periods (>103 s or 15 minutes) the total vertical acceleration will be of similarly small order. Neglecting for the moment tidal effects, an expres- sion for pressure may be obtained by integrating the remaining terms over depth: P = p + g p<5z l^-D) 3. z In this expression, n is the sea-surface elevation and p_ is at the atmospheric pressure at the sea surface, both functions of x and y. The gravitational acceleration, g, is assumed constant and equal to its mean value at the undisturbed s<^a surface. 18 Equation 2.5 permits computation of pressure gradients, 5p/6x and 5p/6y, from horizontal gradients in sea-surface elevation and density. Gradients in atmospheric pressure may be neglected since their effect is small relative to the turbulent stress induced at the surface by the wind. In the numerical model, tidal forcing is accomplished by generating gradients of sea-surface elevation rather than by attempting tc simulate directly the astronomical forces that cause the tides. Fourth, the Boussinesg approximation is made, in which the influence of vertical density variations is assumed to be negligible. For this to be true the area to be modeled must be vertically well-mixed, an assumption that is not generally applicable. Although the version of Leendertse's mcdel used in this study requires this assumption, some compensation for density stratification might be made by modifying the model +o integrate estimated values for the vertical density variation over the depth at each point to obtain the additional density-induced sea-surface elevation [Csanady, 1982]. Fifth, the mean viscous -shear stresses of the fluid are assumed negligible, leaving only the turbulent stresses (Reynolds stresses) at boundaries within and external to the fluid to be formulated. Of these, sharp density gradients within the fluid are neglected as a source of stress. Closed lateral boundaries are considered by applying the coastal boundary condition that velocity into the boundary is zero. Two other boundaries are considered, the sea surface and the bottcm, and algorithms for modeling stresses on these boundaries must prepared. Sixth, since interior stresses resulting from sharp density boundaries are assumed negligible, equations 2.1 and 2.2 may be integrated vertically to provide implicit expres- sions for horizontal velocities averaged over depth. 19 Applying the kinematic boundary coalition at the free surface and at the bottom (assumed impermeable) , equation 2.4 may also be integrated vertically using the Leibnitz rule of integration. Three equations implicit in three unknowns are then available for the vertically integrated, horizontal velocities U and V and tie free, sea-surface elevation n : «H. t o«£ + J» = -g |a + fv + (fm - - )/P(h«,) <2-6> ot Ox Oy Ox Wx Bx Sv + JSv v6v m 5n _ + _ )/p(h+n) Ot 5x Oy oy Wy By \*«'J 6n 6(h+n)u o(h+n)v n (2.8) In these equations f is the Coriolis parameter, h is the depth, ? is tfte surface friction stress due to wind, and P . is the bottom friction stress. U aad 7 are mean horizontal velocities over the water column. This simplification results in a two-dimensional model with which patterns of circulation and sea-surface elevation may be quantitatively determined. Finally, since bottom stress depends on the fluid velocity, a well-known quadratic model is assumed so that the stress term may be incorporated directly into Leendertse's computational scheme. The formulation for bottom stress is : F = pgU(u2+v2) /C2 (2.9) Bx 20 2 ,tt2 h/c2 (2.10) fb = pgvdr+v*) /c The empirical Chezy coefficient, C, may be computed in any of various ways and must be specified for the area to be modeled. B. STRUCTURE AND COMPONENTS A derivation of the numerical model, a discussion of its computational stability, and a program listing are given by Leendertse (1967). Key features of the computational scheme and the computer program used during this study are presented here. 1 . Computational Scheme In ths numerical model, equations 2.6-2.8 are approximated with a finite- differencing scheme extending over two time levels, each a half time step. At the first half time step, t+1/2, the velocity U(t + 1/2) and the sea- surface elevation n( t+1/2) are computed implicitly and the velocity V (t+1/2) is computed explicitly. At the second half time step, t+ 1 , the velocity V(t+1) and sea-surface elevation n (t+ 1 ) ire computed implicitly and U(t+1) is computed explicitly. Computations are spatially controlled by a uniform grid of squares laid over the f-plane (Figure 2.1). Depths relative to the undisturbed sea surface, here taken to be mean lower low water (MLLW) , must be supplied for the corners of each square, values of horizontal velocity are computed at the centers of the sides of each square, and values of sea-surface elevation are computed at the center of each square. W'ind-str = ss and bottom-friction factors must be specified or computed at the centers of each square. This staggerei-grid is basic to the spatial realization of 21 Figure 2.1 Staggered Grid of the numerical Model. Leendertse* s f inite-diff era ncing scheme in that the mean velocity into or out of each square is used to compute the change in sea level within. The grid also permits the coastal constraint cf zero transport perpendicular to sea/land boundaries. During the first half time step, implicit computa- tions proceed row by row from left to right and explicit computations proceed columa by column from the bottom to the top of the grid. During the second half time step this process is reversed, "centering" the results in space as well as time. 22 2 . Computer Program The computer program used to model Monterey Bay is a modified version of a Fortran program developed by Hart (1976), It includes provisions for modeling wind stress, steady flow at boundary points, and overflow at boundary points, none of which were available in Leendertse's orig- inal listing. To increase the flexibility of the program, additional modifications have been made during this study. These include: • Introduction of date and time computations to permit the program to search time-coded files for data items reguired at each half time step. • Direct computation of bottom-friction factors from an average bottom-type parameter or from a grid of bottom types. • Creation of an interactive subroutine to start the program by prompting the user for parameters critical to each run. • Output of time series of currents and sea-surface elevation for up to nine points in the model grid. • Further modularization of the model's functional components. The core of the program is subroutine MODEL, which contains the finite-differencing scheme of Leendertse. Other subroutines serve auxiliary functions: Interactively starting the run, acquiring both constant and time-dependent data, specifying conditions at boundary points, specifying numerical models for wind and bottom stress, and supplying 23 results in various output formats. An outline of the program is presented in Table I. TABLE I Components of the Numerical Model MAKEGEID Generate depth and computation-control grids. BAYMODEL Main program to control each run of the model. START Interactively input run-time parameters. DIMENS Input constant data for grid of area. FIND Locate water sections to be modeled. INVAL Initialize variables everywhere in grid. INCURR Initialize currents as desired. MODEL Multioperational finite- difference scheme. CHEZY Supply Chezy coefficient at each grid point. WIND Supply wind stress term at each grid point RESULT Compute output values in desired units. OPEN Specify sea-surface elevations at open bounds. STEADY Specify currents at open bounds and rivers. OVFLO Specify overflow currents at boundaries. OVFLD Specify overflow threshholds. INTIDE Set tide from a time-coded file. INWIND Set wind from a time-coied file. HEADS PRINT Output headers for each output file. Output results for. desired times. PLOT Output results needed fcr graphic display. SERIES Output results for specific points. PTGRID Utility print of input gridded data. CALEND Utility for number of days in month. ADTIME Utility to increment time. BAYPLOT Provide graphic presentation of results ELEVCOMP Compare elevation series with observed data. CURRCCMP Compare current series with observed data. i— _ Some subroutines, such as OPEN, must be prepared specifically for the area to which the model is applied, while others, such as MODEL, should not be altered. Modularization of the program permits the user to readily 24 change the appropriate functions when adap-ing the model to different coastal areas (and computars) . C. OSE AND ADAPTATION When applying the numerical modal to a specific area, certain requirements concerning input data and program modi- fication must be met. These are discussed below. 1 • Input Data Requirem ents Each run of the numerical model requires specifica- tion of start and end times, time-step length, and an interval at which results must be output. For experimental (as opposed to operational) use, other things may be speci- fied: Points at which series output is desired, the type of output, and oiission of certain terms in the hydrodynamic equations. Input values that are uniqua to the area to be modeled and that do not change from one run to the next must also be supplied. These values ara most conveniently stored in a separate file. They include: • A location title and central latitude. • Dimensions of the grid. • Depths for each grid corner. • Ccntrol numbers for each grid square (land=0, water=1, overflow=2). • A general bottom-friction parameter or a bottom-type indicator for the center of each grid square. • Number of tide stations supplying data for boundary conditions. • Number of wind stations supplying data. 25 Selection of the size of grid to be used is limited by the size of the area to be modeled and the available virtual memory and CPU time of the computer. Since depths, friction and wind factors, output data, and two half-time- step values for each velocity component and the sea surface elevation must be available for each grid square at all times, at least 12 arrays must be dimensioned according tc the grid size and survey area. The maximum dimensions of 80 by 80 used in this study reguired close to 1 megabyte of virtual computer memory and approximately 0.5 s of CPU time per time step on the IBM 3033 mainframe computer. 2 . Subroutine Modifications Stresses at the bottom and surface must be modeled in the subroutines CHEZY and WIND. Since Leendertse's model already assumes a quadratic formulation for bottom friction, only the Chezy factor, C, need be provided by the subroutine CHEZY; however, many empirical techniques exist for computing the factor, most of which rely on a description of the bottom type. The user may select the Technique which best applies. Similarly, the user must program a wind-stress fcrmulaticn in the subroutine WIND. Values for wind speed and direction are obtained from time-coded data sets using the subroutine INWIND. Subroutines OPEN, STEADY, OVFLO, and OVFLD supply time-varying values for sea-surface elevation, currents, and overflow conditions at both open and closed boundary points in the grid. In OPEN, an algorithm must be provided to compute the variation of sea-surface elevation along the open boundaries of the grid. The necessary tidal amplitudes are obtained from time-coded sets of data for established tide stations, using subroutine INTIDE. STEADY permits currents to be assigned to individual grid points, 26 overriding "the computed currents. An initial current field may be entered using subroutine INCJRR. Finally, OVFLO and OVFLD permit conditions of flooding to be ascertained and modeled at grid points assigned the control value 2. When implementing the model on various computers and for various purposes, modifications may be necessary in the input/output subroutines START, DIHENS, HEADS, PRINT, PLOT, and SERIES. RESULT may also be modified to compute additional quantities of interest, sucn as horizontal transports. 3 . Computer Implementation For this study, the numerical model was implemented on an IBM 3033 mainframe computer at the Naval Postgraduate School. Only a few minor language changes were required before the system's Fortran H compiler could be used on the program originally supplied by Hart. Subsequent modifica- tions were made and all jobs were run from remote terminals under the School's interactive time-sharing system. The system made possible the development of several programs that facilitated preparation of data for input to the model and production of graphic output. Especially useful among these were: MAKEGRID, a program that generates input depth and computation-control grids from digital bathymetric data already available for the area, simplifying the otherwise laborious task of creating a grid on chart overlays; programs that generate predicted tidal amplitudes from constituents, or from data supplied in the NOS Tide Tables; and, ELEVCOMP and CORRCOMP, programs that plot time-series output from the model against observed data from the same time period for verification of model accuracy. Although the programs themselves may not be transferable to other computers, supplying similar auxiliary software together with the model (or even incorporating the 27 algorithms into the model program) greatly enhances the ready application of the model to other coastal areas. Data necessary to running the numerical model were stored in computer files distinguished by type. All constant, gridded data were stored in one file while time- varying data were stored in separate files by type and year (for example, MONTEREY TIDE76) . In this way, a new file of input data did not have to be created for each run of the model. The sources and selection of input data are discussed in sections 3. B and 3. C. 28 III. APPLICATION OF THE MODEL TO MONTEREY JAY A. VALIDITY OF ASSUMPTIONS The applicability of the numerical model to Monterey Bay was checked by examining the assumptions outlined in section 2. A. The assumption of negligible vertical velocity was confirmed for tidal forcing by noting that the maximum depth of the area modeled is much less than the wavelength of the semidiurnal tide (3 km << 7600 km). Other, horizontal, forcing conditions of currents and wind were applied as steady-state phenomena in the model. In addition, since this study concerns large-scale fluid motions over time periods of 15 minutes or more, short-period turbulent effects and vertical accelerations were neglected: the hydrostatic approximation holds. Although Monterey Bay is not vertically well-mixed [Scott, 1973], in depths of a few hundred meters or less the difference in dynamic height between that of the assumed, homogeneous density profile and that of a more typical profile is less than 1 cm, which is negligible for the purpose of this study. In depths of 1000 m or more, the effect is more significant (several centimeters) ; however, since such depths occur outside the bay proper, the effect of density stratification was ignored and horizontal veloci- ties were averaged over depth to obtain a general picture of circulation in the bay. B. CONSTANT INPUT The numerical model was applied to three different grids covering Monterey Bay (Figure 1.1 and Figures 3.1 - 3.3). Grid A, a small-scale, 1- or 2-km grid, 80 by 80 km, was 29 designed to permit the introduction of offshore, non-tidal currents as a steady forcing condition and to place the bay far enough away from the three open boundaries to remove their associated spurious effects. Since this grid was particularly vulnerable to numerical instabilities in the model, two other grids were devised. Grid B, a large-scale, 1-km grid, 23 by 50 km, covered the bay and reduced the number of open boundaries to one. 3rid C, a 1-km grid, 40 by 72 km, covered both the bay and sufficient area to permit offshore, non-tidal currents to be introduced. All grids were skewed 20° east, cf north to align the boundaries perpendicular to the tidal forcing conditions. The dimen- sional and constant data incorporated into these grids are discussed below. 1 • Time and Space Dime nsions A time step of one hour was chosen to permit assess- ment of the model over periods of several days without necessitating extensive use of CPU time. Normally the model should run for 12-24 hours (one tidal cycle or store depending on the tidal phase differences between various parts of the area) to establish realistic conditions of current and sea-surface elevation throughout the area [Hart, 1976]. The one-hour interval provided a sufficient number cf data values for ccmparison with hourly or half-hourly observations of sea-surface elevation and currents. Since computed values are offset in the staggered- grid scheme of the model, use of a relatively small grid size in regions of steep bathymetric relief is important to model accuracy. With the constraint on array dimensions in mind, the smallest grid size possible (1 km2) was generally selected to permit the greatest spatial resolution for the area of concern. 30 100-M CONTOURS ■ =OBSERVED TIDES • = OBSERVED CURRENTS : moss_ AMDING X (KM) 80 Figure 3.1 Depth Contours for Grid A, 31 I I I I I. I I 9 y MOSS LANDING MONTEREY 50-M CONTOURS ■ = OBSERVED TIDES • = OBSERVED CURRENTS O I 1 I r~ i — i — i — i — i — r ~i — 1 — r l I ! X (KM) 23 Figure 3-2 Depth Contours for Grid B. 32 o J I I ! i i I I i I I I I I I I I ANO NUEVO 7 I ' I | | iTTT 100-M CONTOURS ■ = OBSERVED TIDES • - OBSERVED CURRENTS MOSS LANDING MONTEREY i ! i i | r\ rrrr ] tt t~tt tt~T X (KM) 40 Figure 3.3 Depth Contours for Grid C, 33 2. Bathymetry and Datum Digital bathymetry was provided by the NOAA National Geophysical Data Center, where depth data from past hydro- graphic surveys are archived for most coastal areas of the United States. The depths were positioned by latitude and longitude in a 36-sec grid and were referenced to a mean- lower-low-water (MLLW) datum. * .« 5 *7' ■Vr-T '■. '?•<.■'■'.''•'» ?-r""'-'.*'f,"! AMO »"<*»»« ill i | | ■• ".■<■. Ktsfcv ■ L.-r-f ■ "*■•<; *■ . .- «!s5l! ■ ■» * i i II ■ 1 . I ! ; "V" m.'I-jVI'-V'^'1"''! t f* -V ■'-■'' -s'^-Vt -"J 1 1 H : J.,' *« ■Mi't-V'-f,''..!' ■K.T*! "J'-VM-" ' • £ 1" !r '-"'J I f > ;■ -?,v} -V; -.";*. | ! j h i fc .]-,'■ 1 /Mil 1 i 1 ^ZL i "« ", }.:Mt'^:;:*"<:^:*-!:!':^'^A I 1 1 Jf *>4 ■ "*t -Nu 'W-^t-^Fvi"'"TA-H- 1 1 «l I"*- _i_ b l"J rT 1 t" 1 i Si'ii > "Tift- 1 1- L."n"1 1 C «,. : *«i..l •■<"«.. ■'..'•l'--. ."■..'•/" ! , ! S El fa, •*1." TO . ri«L i "-v--.r-« L7-JS.1- V-wt-.Vs; 1 1 ^ANTA PRl'7 - , _!"■ !«, ' * %"t,l i ^> i*4?V-?AVJ|««*",i*£1**3?pw f* ' J ill ill 1, «4,J i f^ J'^/.^-/'-;^r/».^-i;'-l"'^7-v.';-J'l;-'...-<1^.i ! ' ■* »- Ij-i -i "w--l ! i*1- V ■■■ . '/ >■','--' ^ -,,'-»■ !W **■;■■ ■ ''*-,' fi 2*! i | -Ss* t+ni ■»-.." ..'• ■ 1- V -■>-'.""■■■''■- i-..V--"--t-' ";■*"*- ; 1 .■fcETH.n" *• < • • « * ■ • • ■ •-' *■-■* ■» ■ • - -7-' ; ' "• ■' • ■ ■' *«' • • : n "1 T*»«J '•4.'V"'V'-. '•'.';•< ■'*■ *'.Vv.;--. 'Tf""*iSfd> ' M ! ■>*pj :•-■, ["!*+ *- '■•C;-r.'';^1:;-/j-v.V-.v--.':^;;-^'',..;- i a t" *■ >.J i '-.t •*■ p«T ■■.?■! i •■»w4, '•.>v,*.r,i.; ".«■ KP'Cl1" «-T'H- 1 *.[■( * . '. I ST T'H'i l- i T-i 'V'rrJ i - ' !»-{,, *'?.■'-..■'> *■;,'• ,"4. !•». *:V*>. -T"'^ ■«.»■. ."v. '■« Z I r r i *. ' hr; "-L , 1 '., '">.r .'.■!■ ■;.•;■'.' ■-■.■..;•.:■■ ■.■;.;v;.':--.,*--'.-y.V-..Vf- vir;c,^ ™t ' LANDING '* p 31 r f"^ ' 1 «»TJ,7«}*«Vi<£m^'7-V/]|''-«« WWiAV '•">'■" V»V?'< : ! ^7 £E ■J. ! V ."■". "■ . ■•''■• [''•.'." "."••V." ■"■?*<."'•"." '•''■'''' i ' r-r*i- rH * ■ •' ■ ■>- 7-i V- i""--»" '■•-■■ "if-i 1 1 3 ?! 1 !*t*lJ,*/fc£«4.^.;. ,,L-.. k. , v- -.■/-. :-.-t :v ■ v.- .•■ ,'.•••■,!• I *=" ZE^ 1 «> ,« § *E ■ ry-4. i .". '.•f-.'.--.^f-.v-..-.-[.- - p.-i-«« i "1 "* JJ 1 ! I-WJ ••!.-. .-.■■.■J.--.-.J-.v->> 1 1 1 -.:-: 1 ! 1 : , -. r T "*'K i i ! t" !•}•-', 7 f-T'i- i-iTi-ii ,L ' MONTPi?P> .i-J-irtT + LI r.l*l '■ii'V-.M::.^ i i 1 1 . 1 <■ Li "i HPH "+• rt«T"fri ;->l"v-W'£J Cakmi MM ,» *■ EM THh ""• j- ";"i-' '-t-f-rI M 1 ! ! i ■ MJ5r.l WJ ■< HA- ftjW.'f^rfcfrJ II I I ! 1 ' 1 i ■ ! ! Figure 3.4 Locations of Bathy»etric Data in Grid A. To computer-generate a grid of depnhs for the model, the program MAKEGRID was prepared. The program first projects the bathymetric data onto the grid coordinate system (for example, grid A), which is a modified-transverse Mercator projection skewed about a specified origin 34 (Figure 3.4). Depths are then interpolated at the corners of each grid square. Since depths are referenced :o MLLW and a straight- forward correction to mean sea level is not possible, the datum for sea-surface elevations computed by the model was taken to be MLLW. All input tidal amplitudes ware likewise referenced to MLLW. From the gridded depths a computation-control grid was automatically generated by assigning 1's to all water squares and 0» s to all land squares (assigned dummy eleva- tions in the depth grid) . Both grids could be altered if necessary before their use in the model. 3 . Bottom Friction To model bottom stress, the empirical Manning equa- tion for the Chezy coefficient, C, was used: c = (h+n)1/6/M <3-1) The coefficient is a function of depth, h, instantaneous sea-surface elevation, n , and the banning factor, M, which describes bottom roughness. M increases with bottom rough- ness. Clean and straight natural river channels typically require M=0.025 to 0.030 m/s, while winding channels may require M=0.033 to as high a value as 0.15 m/s in very weedy, overgrown areas [p. 99, Henderson, 1966]. Although bottom stresses may be modeled as a func- tion of the bottom type or texture in each grid square (thus requiring input of a bottom-type grid), this option was not exercised for Monterey Bay. Over the large area covered, the variation in depth from square to square is likely to have more influence than the relatively small variations in bottom roughness that occur in Monterey Bay. Following Spaulding and Beauchamp's study of a coastal sea (1983) and 35 after some experimentation (section IV. A), a constant value of M=0.04 m/s was used throughout the bay. C. TIME-VARYING INPUT The forcing conditions of tide and wind were accessed from time-coded files. Tidal amplitudes were applied only along the open boundaries of the model, whereas wind stress was applied over the entire grid. The sources and applica- tion cf these data are discussed in this section. 1 • Initial Conditions At ths start of a run of tha model, sea-surface elevations were approximated by assigning a coastal tidal amplitude at the starting time to every point in the grid. The tidal amplitude at Monterey was used for this purpose. This approximation is suitable for Monterey Bay since the narrow continental shelf and the absence of any barrier islands permit the tidal wave to propagate relatively rapidly through the area. A zero velocity was initially assigned to each grid point, except for runs including an offshore, non-tidal current; in these cases, the steady-state current velocity was initially assigned to offshore grid points. 2. Boundary. Tidal Amplitudes A major factor in the successful application of the numerical model vas the provision of suitable tidal forcing conditions along the open boundaries. Tidal amplitudes are predicted in the NOS Tide Tables 1.976 for four stations near and within Monterey Bay: Ano Nuevo, Santa Cruz, Monterey, and Carmel. Tidal-constituent amplitudes and phases are available for Monterey and Moss Landing (Appendix A) . Since 1963, continuous observations of water level have been made 36 at Monterey. A two-year series of asarly continuous obser- vations was made at Moss Landing from 1976 through 1977. To obtain amplitudes along the boundaries of the model grid, coastal values such as these must ba extrapolated. Several attempts have been made to formulate the effects of continental shelves on the open-ocean tide [Clarke and Battisti, 1980; Gill and Porter, 1980; Munk, et al. , 1970]. Because of the narrow continental shelf and bisecting canyon, Monterey Bay does not satisfy the assump- tions necessary to apply these formulations. However, to gain some insight into the effect of the extreme depth difference between the tide station at Monterey and the offshore boundary points of the modal, a comparison was made between tidal constituents obtained at Monterey and at a pressure gage located in 3903 m of water offshore [Cartwright, at al. , 1979]. The results are presented in Table II. The coastal and pelagic phasas clearly do not corre- spond since the pelagic gage was located at seme distance from Monterey (see Figure 1.1), but the agreement of the amplitudes suggests that the aforementioned depth difference has little effect. In the absence of any more certain method for extrapolating tidal amplitudes, the values at the coastal station were applied directly along a line of constant phase extending out from shore. Examination of cotidal/cophase charts by Munk, et al. (1970), Luther and Wunsch (1975), and Parke and Henderschott (1980) , suggests that, in the vicinity of Monterey Bay, the tidal wave propagates nearly parallel to the coast. The model grids were, therefore, skewed in such a way that the open boundaries wera perpendicular or parallel to the coast. At each time step the forcing ampli- tude was made to vary directly with the tide at Monterey all along the southern boundary, with the tide at Ano Nuevo all 37 1 TABI ■ w II Comparison o f Pelagic and Coastal Tidal Constituents Montere I Pelagic 38°09«N 36 °36« 121°53» H 124°54' W 8 m 3903 m g (cm ) M2 50 55 S2 13 13 N2 1 1 13 K2 4 — , K* 37 43 01 23 23 P* 12 - — Ql 4 — — k (°) ^2 297 66 S2 296 84 N2 272 30 K2 288 — K* 98 334 01 8 1 32 1 Pi 93 — Q1 73 along the northern boundary, and with linearly interpolated values between the two along the western boundary. The tidal values used to set the boundary conditions may be interpolated from the NOS Tide Tables 1976, computed from constituents [Schureman, 1940], or taken directly from observed data. The last was preferred since the first two predictive techniques cannot take into account atmospheri- cally forced or anomalous changes in sea level, such as storm surge. However, as mentioned previously, observations were available only at Monterey and Moss Landing. Some experimentation was necessary to model the phase lags between Monterey, Santa Cruz, and Ano Nuevc (section IV. A). 33 3. Boundary Currents Two types of flow may be imposed at ths boundaries of the numerical model. First, the discharge of rivers along otherwise closed boundaries may be represented as a vertically averaged current velocity assigned to the appro- priate coastal grid point during each rime step. The mean annual discharge of all major streams and rivers entering Monterey Bay is 1.85 x 106 mVday [Broenkow and Sraethie, 1978], which amounts to a vertically averaged current velocity of only 0.2 cm/s were all rivers to enter at one point. As a result, rhe river inflow was judged negligible for this application. A second type of flow, currents due to non-tidal effects, may be imposed in offshore regions of the model. The narrowness of the continental shelf near Monterey Bay leaves the bay particularly open to forcing by large-scale oceanic currents. Previous studies of the area suggest that such currents are an important force driving the circulation of the bay [Lazanoff, 1971; Garcia, 1971; Bretschneider , 1982]. The presence of an offshore current was simulated by assigning initial velocities to the offshore portion of grids A and C for some runs of rhe model. The convective- inertia terms in -he numerical model propagate the current influence into the inshore portions of the grid. A north- ward current of 25 cm/s (0. 5 knots) was assigned. This value was proposed by Scott (1973) as a simple, steady-state model for the offshore circulation. U. Wind Wind stress, F , was parameterized within the numer- i ical model by the familiar quadratic law [Dronkers, 1964]: 39 F. = (2.6xl0_3)p w|w|/p(h+T|) (3.2) i a W represents the wind velocity vector, Pa is atmospheric pressure, p is the mean density of the water, h is the depth, and r\ is the time-varying saa-surface elevation. The model permits input of wind direction and amplitude as a forcing condition over the whole field of the grid for a specified range of time steps. Monthly distributions of wind at Santa Cruz and Moss Landing for the period May, 1976, through May, 1977, were obtained from the Santa Cruz Wastewater Facilities Planning Study [Brown and Caldwell, Inc., 1978]. Average and maximum values for the wind were applied to sone runs of the model (see section IV. B) . D. DATA FOR COMPARISON The numerical model was calibrated by comparing modeled sea-surface elevations and current velocities at specific grid points with observed values at the same locations. The comparison process was limited by a paucity of suitable, long-term water-level and current-mater observations for Monterey Bay. Water-level data are available only for National Ocean Service tide stations at Monterey and Moss Landing. The primary sources for current-meter data are predesign studies conducted for tha emplacement of sewage outfalls near Santa Cruz, the Pajaro River, and the Salinas River, but only data for Santa Cruz and the Salinas River could be obtained. In some fortuitous instances, both water-level and current-meter data were collected concur- rently (Figure 3.5). The period July-August 1976 yielded sufficient data for comparisons at the two water-level and at three currant-meter stations; thair locations are plotted on each model grid (Figures 3.1 - 3.3). 40 1975 1976 1977 1978 1979 liiniiiiiiiliiiiii|i|i>liniiiiiiii|iiiniiiin|inii'iiiiil Water-level Observations; Monterey ZZZZZZZZZZ^^^^^ZZZZZZZZZZZl Moss Landing Xm' 2 ' f f S <'\ Cnrrent-meter Observations: Santa Cruz Pa jar o River Salinas River izzzza EZZ22Z3 Figure 3.5 Observing Periods for Comparison Data. 1 • Water-level Observations Water-level observations have been made nearly continuously since 1963 at NOS Tide Station 941-3450 on the seaward end of Municipal Wharf 2 in Monterey. The float- type tide gage is located in 6.2 m of water. Recorded times are accurate to within 6 minutes and heights are resolved to 3.0 cm [ Bretschneider, 1980]. Digitized hourly heights for the period 11/8/73 to 3/2/83 were obtained from the National Ocean Service, Tidal Datums Section N/0MS123. The heights were corrected to MLLW and converted from feet to meters. In addition to providing comparison data, these observations were used to determine boundary amplitudes for some runs of the model. At Moss Landing water-level observations were made for 20 months as part of the California Marine Boundary Program [National Ocean Survey, 1981]. NOS Tide Station 94 1-3616 was a float-type tide gage located at the seaward end of the Moss Landing Ocean Pier in 9.1 m of water. 41 Digitized hourly heights were obtained for the entire period 5/9/76 to 1/10/78 and processed as for the station at Monterey. 2- Current- meter Observations As part of the Santa Cruz Wastewaters Facilities Planning Study, a current-meter station was located 1 mile offshcre of Terrace Pcint in 30 m of water [Brown and Caldwell, Inc., 1978]. Two AMF Vector Averaging meters were installed at 9- and 15-m depths for the periods June to November, 1976, and January to May, 1977. The only data that could be obtained for comparison purposes covered July and August, 1976, at the 15-m deptn. The data included 7.5-minute averages cf current speed and direction, expressed as a pair cf orthogonal velocity vectors. Two current-meter stations were occupied approxi- mately 1 nautical mile north and south of the Salinas River during oceanogra phic investigations for the Monterey Peninsula Water Pollution Control Agency [Engineering-Science, Inc., 1977]. At each station, two ducted-impeller-type meters were installed at 9 and 15 m for the overall period January, 1976, to January, 1977. Current speeds and direction were averaged at 30-minute intervals and expressed as a pair of orthogonal velocity vectors. 42 IV. RESULTS A. COMPARISON OF MODEL RESULTS WITH OBSERVATIONS Comparison of the model with observations was used both to "fine tune," or calibrate, the numerical model, and to assess its general validity. The affects of varying input constants such as the siza and resolution of the grid, the time step, and the bottom-friction coefficients were consid- ered. In addition, schemes for determining boundary tidal amplitudes and for including non-tidal current fields were tested in an effort tc match observed elevations and currents as closely as possible. Application of the model to grid A revealed apparent numerical instabilities that caused overflew in the computa- tions after as few as 1.25 days (33 time steps). The sudden oscillations in sea-surface elevation at Monterey were due to propagation into the bay of extreme amplitudes and currents generated in the offshore portion of the grid (Figure 4.1). The overflow condition was unaffected by changing the resolution of the grid from 2 to 1 km, but was very sensitive to changes in the phasing of the tidal ampli- tudes along the open boundaries. Under the premise that tne presence of three open boundaries enhanced instabilities, grid B (with one open boundary) and grid C (with two open boundaries) were subsequently used during the comparison process. 1 • Sea-surface Elevati on Comparisons A run of the model for twelve days at the one-hour time step produced seme agreement between modeled and observed sea-surface elevations at Monterey and very good 43 o MOO OBSIIFV :i.e) :d = ®n;>.6 cm Figure 4.1 Sea-surface Elevations at Monterey, Grid A. agreement at floss Landing (Figures 4.2 and 4.3). Varying the Manning bottom-friction factor improved this result (Table 3.1 and Figures 4.4 and 4.5). TABLE III Effect of Various Banning Factors M (m/s) = .03 .04 .05 .06 Monterey 7.4 6.8 6.3 5.8 Moss Landing 4.6 4.5 4.4 4.3 . 10 4. 8 4.0 Table values are the RMS errors in centimeters for comparisons between modeled and observed sea-surface elevations. 44 The seemingly unrealistic Manning factor of 0.10 m/s may serve as a description of the bottom roughness over the large area of each grid square, if roughness is thought of in terms of the steep slope that is otherwise not accounted for in the model. The higher Manning factors did not, however, improve the results of currant comparisons; -hey served primarily to damp out noise. o "to o I 10 MODELED OBSERVED RMS ERROR = 6.8 CM j. 12 13 14 13 16 17 JULY 1976 18 19 20 21 22 Figure 4,2 Elevations at Monterey, At=3600 s. An oscillation that appeared forced by the time step was evident in the modeled curves. It was especially evident at Monterey and when a shorter, 15-minute time step was used (Figures 4.6 and 4.7). The noise may be the result of applying observed tidal amplitudes as the boundary forcing condition. The observed water levels, digitized hourly, may include jumps and/or contaminating frequencies due to the recording 45 o '10 o 10 MODELED OBSERVED RMS ERROR = 4.5 CM 11 12 13 14 15 18 17 JULY 1976 18 19 20 21 22 Figure 4.3 Elevations at Boss Landing, A t=3600 s. instruments. Linear interpolations required between the hourly amplitudes for each half time step may have exagger- ated the instrumental effects. To better judge the use of a shorter time step, raw water-level observations, usually made at a 6-minu-e interval, should be applied to the model. Spectral analysis of the modelad and observed curves, in addition to reflecting -heir general agreement, reveals spurious frequencies generated by the model at Monterey (Figures 4.8 and 4.9). The incoherent freguencies, which are also found in the spectra for currents at Santa Cruz (Figure 4.14), correspond to apparent periods of 3.0 and 2.2 hours. These periods are longer than the 1-hour, fundamental seiche period for Monterey Bay [Lynch, 1970]. 46 - o •* o MODELED OBSERVED MLLW 2.0 " I \ A A a ABOVE 0 1.0 if Mrtrt / V v y v * UJ o RMS ERROR = 4.8 CM Q « tiii i i i i i i i i 1 1 9 11 12 13 14 13 16 17 18 19 20 21 22 I _. JULY | 1976 j I 1 Figure 4.4 Elevations at Monterey, M=-10 b/s. o O I 10 11 MODELED OBSERVED RMS ERROR = 4.0 CM j_ 12 13 14 15 18 17 JULY 1976 18 19 20 21 22 Figure 4.5 Elevations at Moss Landing, M=.10 m/s. 47 ""' 1 o. •* o MODELED OBSERVED MLLW 2.0 Miflifliiliiii A k A A A ABOVE 0 1.0 M^mMMvM^A V i If » » UJ o x? RMS ERROR = 13.2 CM o 1 1 1 1 1 1 1 1 1 1 1 1 ! 1 0 11 12 13 14 15 18 17 18 19 20 21 22 JULY 1976 L . - - — ■ - ___._..__ _. i Figure 4.6 Elevations at Monterey, At=900 s. o •+ o MODELED OBSERVED 2* *•— «* 2So —J ~ 1 k k _j CM A A A * 2 fl i n « A t A l i i a a A * A £s -a/ W IV A/1 AA M Aa AaAaA aA /sA O v i v v mm v\ vv uv \/v \ /▼ \ m W U u u vvvV w » - NORTHWARD CURRENT COMPONENT ( V) ^0i$Mm& o o > m m CM I m to I 10 _L_. 11 12 13 14 i MODELED i 1... OBSERVED 1 i i i l 15 16 JULY 1976 17 18 19 20 21 22 in m CM c*£ EASTWARD CURRENT COMPONENT (U) / warn 20 21 JULY 1976 22 Figure 4.11 Currents near Santa Cruz. 54 NORTHWARD CURRENT COMPONENT ( V) in in CN £ o m I L ft ' 1 J 4 *, it n 1 1 ' I, ' V ft t _L i>i_A i i i ' i • ft i r i > i \ l i ■ i i i i <1 U-Ht 57 o _J UJ m >T in l in lO I i y I I / I I If '*. " ' M I I • I < I' III.' ' I \f *' I! if ii MODELED OBSERVED M \ it i 10 12 13 14 15 16 17 JULY 1976 18 19 20 21 22 m m CM w2 O Lu T EASTWARD CURRENT COMPONENT ( U) <*i. 1 1 10 n i 9 'V i' ' ii k t fc. 'i ii ii i i / i I 'i J i i i i i ' i ^h if i « i i* i i V if > 'i MODELED OBSERVED l L_ i i 12 13 14 15 16 17 JULY 1976 18 19 20 21 22 Figure 4.12 Currents South of the Salinas River. 55 m O m NORTHWARD CURRENT COMPONENT (V) <; 4J \ fa 1 1 JU n n I* |l I*. I I ii' ' fl H ii >JU*w ..> t- i i n ii n 1 1 i i i' i 1 ^fc^i Unr%< 57 o >T I U") I MODELED OBSERVED _1 L_ 10 12 13 14 15 16 17 JULY 1976 IS 19 20 21 22 in m CM C/)S o >T m CN l o l EASTWARD CURRENT COMPONENT (U) i! ft ^^pjiii^^^^iAi^^w^'ll^ g.fcti» !fr fd.^Swifr,^ »»' 1 jD> ,i^iX'iW 8 • ii ii ii ii 1 1 i i ■ 1 n > i < i ' .<• M I ( 111 TV ■i ii 'j ii LlL *^jW MODELED OBSERVED J 1 L_ 10 12 13 14 15 16 17 JULY 1976 18 19 20 21 22 Figure 4.13 Currents North of the Salinas River. 56 o. i— — ' •— • CO Q o- X. CM ENSEMBLE SPECTRRL DENSITY FUNCTIONS ■ 4.3x10" MODELED U o.o SflNTfl CRUZ FREQUENCY RESOLUTION (HZ! OBSERVED U 2.8 5.6 8.3 11. 1 13.9 *10" 95X CONFIDENCE LEVEL 13.9 *10" 5.6 8.3 FREQUENCY (HZ) 13.9 *10" Figure U. 14 Spectra of Currents near Santa Cruz. 57 The current plots show generally weak (<5 cm/s) tidal flow into and cut of the bay, corresponding to periods of flood and ebb. In the southern part of the bay, a strong east-west current (up to 30 cm/s) appears just north cf the Monterey peninsula. This jet is consistent with the strong currents experienced by divers in taa area.1 In the northern part of the bay, a broader current (10 cm/s) flows along the depth contours. Of especial interest is a current pattern that develops between Ano Nuevo and Santa Cruz on current plots made using grid A (Figure 4.15). The gyre, which the model predicts to have speeds ranging froa 2 to 10 cm/s, is consistent with the observations of Carter and Kazmierczak (1968) who noted a closed circulation in the area with similar speeds. 2- Tidallv Forced Circulation with Wind When an average wind of 3 m/s (7 mph) from the weet-northwsst was applied over the entire field of grid B, the tidally forced circulation was unchanged. A maximum wind of 10 m/e (30 mph) from the west-northwest also produced essentially unchanged circulatory patterns. A 12-day series cf modeled elevations at Monterey and Moss Landing under the same maximum wind yielded results nearly identical to those without wind. lPer conversation with Dr. E. C. Haderlie, Dept. of Oceanography, Naval Postgraduate Sohooi, 9/27/83.' 58 ONE GRID SlOt c 9 cu/IC C Pigure 4.15 Current Field for 3rid A at 760702 1500. 59 V. COHC LOS IONS A. VALIDITY OF THE MODEL The numerical model has been shown by comparison with observations to provide reasonably accurate sea-surface elavations. Although the modeled current doss not account for the total observed current at comparison stations, it probably accurately reflects the contribution due to the barotropic tide. Much of the remaining observed current may represent response to diurnal wind stress, offshore non- tidal currents, and/or forcing due to internal waves, the last requiring a more complex, three-dimensional model for further investigation. Application of observed winds on a timsstep-by-timestep basis might ba a fruitful avenue for further investigation. That numerical instabilities exist in the model has been noted by various authors [!loe, at ai., 1978; 3engue, at al. , 1982], who have proposed some improvements in the model's formulation. The flexibility and accuracy of the model might be improved by further investigation of their suggestions. B. HYDROGSAPHIC SURVEY APPLICATION A numerical model such as that implemented by this study can improve the process of correcting depths for changes in sea-surface elevation during a hydro-graphic survey. Advantages of the two-dimensional model ever simple extra po- lative techniques or more complex, three-dimensional models result from the model's relative simplicity, flexibility, ability to operate in a real-time data collection system, and ability to compute sea-surface elevations with suffi- cient accuracy. 60 The tasted model is a relatively simple FORTRAN program to implement and use, particularly with the interactive modifications made during this study. It could be further improved in this respect by adding an interrupt/restart routine to permit changes of constants, such as time step or output frequency, during the course of a single computer run. The model is flexible, since it can be readily applied to various coastal areas by means of the gridding software developed during this study. To implement the model on a microprocessor during data collection in the field, requires the availability of suffi- cient virtual storage capacity and CPU time to permit unim- peded computations. The virtual storage required depends upon the dimensions of the grid; a iiore economical use of arrays in the model program can reduce the requirement. In the real-time mode of operation, computations should immedi- ately follow boundary-amplitude updates at each half time step to make efficient use of CPU time. At the conclusion of each full time step the resulting, updated sea-surface elevations are then promptly available. The time step used depends upon the interval at which water-level observations are available from one or more locations suitable for establishing boundary amplitudes. In the real-time mode, presumably such data could be teleme- tered to the survey vessel at the standard tide gage frequency of 6 minutes, permitting a model time step of 12 minutes. Since updated elevations can only be available at the conclusion of a time step (Figure 5. 1) , a 6-minute lag exists that may be removed only by post-survey processing. Another factor in real-time operation cf the model is the start-up time required. The model should be calibrated to establish the validity of friction models and boundary- amplitude algorithms, preferably by comparing the output for several tidal cycles with observed tides at a location in 61 Corrector available t+h t+1 t+l*s t+2 Corrector valid Figure 5. 1 Ti«e Step Lag During Real-time Model. the interior of the survey area. If historical data are not available, this could require several days of observation and analysis prior to the survey. The accuracy of the model in conputing sea-surface elevations from tidal forcing alone has been estimated during this study as 4-3 cm (1 RMS error) . Survey require- ments are 3a < 9. 1 4 ♦ 0.005h cm, where a is the standard error and h is the depth in centimeters [Mcbiey, 1982]. The depths at the tide gages in this study were about 3 m, permitting a 3o equal to 13.1 cm. This value was attained a- Moss Landing (3 RMS arror = 12 cm) and, if the trouble- some noise could be removed by post-survey processing of water-level observations to obtain a smooth tidal forcing function, it nay be generally attainable. The model itself requires further development, both in the application to Mcnterey Bay and in general. Further testing of the application to Monterey Bay should include the introduction of time-varying wind and oceanic currants, as well as forcing at a time step using tidal amplitudes observed at a shorter interval than the 1-hour interval used in this study. The model should also be applied to and 62 quantitatively tested against other coastal configurations and bathymetries to ensure that sufficient accuracy can be consistently achieved. 63 APPENDIX A TIDAL CONSTITUENTS TIDAL CONSTITUENTS FOR MONTEREY Monterey Harbor, Municipal Wharf #2, CA Station 941-345Q 36°36»30 N 1 21°53!30 W H k M2 1.6280 297.43 sa .4250 295.54 N2 .3660 272.02 K* 1.2160 97.76 M* .0050 164.11 Oi .7630 81.44 M* .0020 306.67 MK3 .0000 .00 S* .0030 165.89 HH* .0030 83.55 NU2 .0690 279.36 S* .0030 41.80 MU2 .0460 234.42 2N2 .0460 248.48 OOi .0390 119.59 LAMBDA2 .0090 281.74 S* .0380 202.27 Mi .1170 114.33 Ji .0710 106.99 MM .0150 354.41 SSA .0300 278.51 5A .1460 173.10 MSP .0160 156.68 MF .0530 180.53 RHOi .0290 72.73 Qi .1370 72.90 T2 .0170 271.39 R2 .0050 136.85 2Qi .0190 63.33 P* .3810 92.74 2SM2 .0050 97.96 M3 .0100 356.26 L2 .0280 285.41 2MK3 .0020 220.13 K2 .1210 287.69 M9 .0020 143.35 MS* .0040 134.56 64 TIDAL CONSTITUENTS FOR MOSS LANDING Moss Landing, Ocean Pier, CA Station 941-36 16 36°4S! 10 N 121°47!40 W H M2 1.6636 29 5.3 3 S2 .4182 295.84 N2 .3419 269.50 K* 1. 1349 99.28 M* .0178 160.69 01 .7278 81.83 M6 .0172 63.79 MK3 .0000 .00 S* .0064 141.43 MN* .0000 .00 N0« .0663 272.96 S* .0047 194.21 MU2 .0000 .00 2N2 .0455 243.67 OOi .0313 116.72 LAMBDA2 .0116 295.57 Si .0000 .00 Mi .0517 90.55 Ji .0575 108.00 MM .0000 .0000 .00 SSA .00 SA .0000 .00 MSF .0000 .00 MF .0000 .00 RHOi .0277 74.33 ?i .1412 73. 1 1 .0247 295.84 R2 .0033 295.84 ir .0189 64.39 .3757 99.28 2SM2 .0000 .00 M3 .0000 .00 L2 .0466 321. 16 2MK3 .0000 .00 K2 . 1 137 295.84 M« .0110 336.39 MS* .0000 .00 65 APPENDII § TIDALLT FORCED SEA-SORFACE ELEVATIONS SEA-SURFACE ELEVATIONS AT MONTEREY JULY 1976 Tidal cycle for the following 2-hour time series. 66 760711 0 *s SANTA CRUZ s> at m \ / o ^v a \* /s / '6 /\ Si MONTEREY ^ r MOSS LANDING 1-CM CONTOURS 67 760711 200 ^ f r ^ SANTA CRUZ *» a 00 !> / ^4 MONTEREY \ V f MOSS LANDING 1-CM CONTOURS 68 760711 400 SANTA CRUZ // A / i be / ^T o 1 MONTEREY \ / \ \ I MOSS LANDING 1-CM CONTOURS 69 760711 600 ^ i SANTA CRUZ I I u V MONTEREY \ \ MOSS LANDING 1-CM CONTOURS 70 760711 800 SANTA CRUZ \ * \ MONTEREY \ \ ( MOSS LANDING 1-CM CONTOURS 71 760711 1000 SANTA CRUZ MONTEREY to at \ \ r MOSS LANDING 1-CM CONTOURS 72 760711 1200 SANTA CRUZ zx II CM rV^ \ T CM // CM m CM MONTEREY \ \ MOSS LANDING 122 1-CM CONTOURS 73 760711 H00 SANTA CRUZ 2 i (7> 01 qj at / \=x /\ MONTEREY \ \ r MOSS LANDING 1-CM CONTOURS 74 760711 1600 SANTA CRUZ ^> ^ ^T >4 / \ MONTEREY \ \ ( MOSS LANDING 1-CM CONTOURS 75 760711 1800 / SANTA CRUZ O ^ o •^4 MONTEREY \ \ ( MOSS LANDING 1-CM CONTOURS 76 760711 2000 s SANTA CRUZ 7^ -4 O 7 / V ro \ ^^ \ MONTEREY \ O a 3 o r MOSS LANDING 1-CM CONTOURS 77 760711 2200 to II 0» SANTA CRUZ 195- "^ MONTEREY \ Xs r MOSS LANDING 1-CM CONTOURS 78 760712 0 II \ SANTA CRUZ P N^ /\ MONTEREY \ As MOSS LANDING 1-CM CONTOURS 79 AP PENDIX C TIDALLY PORCED CURRENTS SEA-SURFACE ELEVATIONS AT MONTEREY JULY 1976 Tidal cycle for the following 2-hour time series. 80 760711 0 4 ^^ SANTA CRUZ / "^v s k / 4 X 1ft 7 3 4 3 2 s IS 14 11 10 t 7 4 ■ 4 3 2 1 1 N 1 X* !• 14 1Z 11 * 7 * 4 9 * 4 2 1 L 1ft 17 14 12 12 f S 7 4 3 9 3 2 1 \ < 2* 14 19 14 13 11 » • 4 » • 4 3 < 2 < 1 2t IS 14 14 11 11 • 4 4 7 f 4 < 3 < 2 1 X 21 1* 14 19 14 12 10 • 4 4 4 < 7 < 9 4 < 3 < 2 < 22 2* 17 19 14 12 4 10 < t 4 9 4 6 < 7 4 9 < 4 < 3 < 2 A 22 24 17 19 14 12 10 • • 4 7 9 4 < 3 < 2 « < 4 4 4 < 22 29 17 19 14 12 < 10 < t < < a < 7 < 9 < 4 < 3 < 3 4 < « < < < 23 1* 17 19 14 12 < 10 < • < 4 < a < 7 < 4 < 4 < 3 4 2 1 \ 4 4 4 < < < 21 21 12 14 If 13 < 11 < 11 < 11 < 10 < a < 7 < 4 < ■ 4 < 1 < 2 A 1 2* 2ft 1ft 19 IS 13 11 < •a < 11 < 10 < t < 7 < a < S < 4 3 1 1ft 1ft 1ft IS 11 14 12 < 13 < 12 < 10 < a < 7 < a < 9 < 4 A 3 2 at ia ia is la is 13 13 12 11 a 4 a S 4 3 2 1ft 2ft 17 17 17 IS 13 < 12 < 11 < 10 < a < 7 a 9 4 3 2 2 1 • \ 22 21 1ft 17 14 14 11 12 11 10 a a a a S 4 3 2 1 21 21 1ft 17 17 14 13 12 11 10 a a 7 a 4 4 3 2 1 22 21 14 1ft 17 14 14 13 12 11 10 4 7 a 4 4 3 2 1 22 21 21 14 14 17 16 14 13 12 11 11 a 7 4 « 3 2 1 23 23 23 21 22 19 14 14 19 13 12 10 a 7 ft S 3 2 1 2ft 2S 2 4 23 21 20 17 17 14 IS 13 11 10 a 7 3 4 1 ' / 2ft 24 22 21 20 1ft 14 IB IB 13 U 10 a a 9 4 2 ' f 27 2ft 22 20 14 17 14 15 14 13 12 4 a 4 S 4 3 ' s 27 23 2ft 17 17 14 11 12 12 10 a 7 a 4 3 2 1 J MOSS 2ft 21 1ft 1ft 13 13 11 10 10 9 a a 4 3 2 1 LANDING 23 2ft 17 14 14 12 10 9 9 a 9 9 3 2 1 22 14 1ft 13 14 12 10 1 9 7 a 9 3 2 1 20 17 IS 13 12 10 • S < 4 a s 3 2 1 21 17 13 13 12 10 I • 4 a s 3 2 1 21 1ft 13 13 12 11 » 4 4 4 i 4 2 1 44 4444 21 17 14 12 11 t 6 7 7 3 4 2 1 22 17 19 12 11 9 » 7 7 i 4 2 1 •- • 4 < < < 21 14 13 10 10 4 A 7 S A 3 4 3 1 17 1ft 11 4 4 4 7 A 4 S A 3 3 4 > 4 4 3 J < 2 1 12 14 12 4 4 7 ■■^V *> » A * ^^ 2 5 3 4 A 4 I 2 1 ^^ 3 1 4 A S 1 1 A 1 < 1 ^^ 1 RE Y TRANSPORT X100 ( ONE GRID SIDE = K :u-m/s MONTE! ) CM/S 81 760711 200 MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 82 760711 400 SANTA CRUZ \ \ / MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 83 760711 600 14 1* 11 10 * * t 7 7 1 7 • 5 5 14 14 12 10 • 10 10 • • • a a • 9 13 u n it io 10 io io • g i a r a u 12 11 10 a io 11 io io io a a 7 a ii to io a • a io a • a a 7 • • / MOSS LANDING TRANSPORT X100 CU-M/S MONTEREY ONE GRID SIDE = 10 CM/S 84 760711 800 MOSS .ANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIOE = 10 CM/S 85 760711 1000 SANTA CRUZ 1 » » 4 m l » > I 1 s * 4 V • 7 • 4 4 4 » » » » » 3 3 a i i » » 7 0 7 4 4 > > > > » 4 3 3 12 > > 7 • > 7 > 7 > > • 4 » » 7 • > • > 7 > > 4 4 > > 7 • > • > 7 > > 4 4 > * 7 10 > 4 > 7 > > S 4 7 10 > 4 > 7 > > 4 4 7 11 > 4 > 7 4 4 7 "?, > 4 7 4 4 » la 4 4 S 4 7 la 4 4 C 4 « la 4 4 S 4 7 12 4 4 3 4 a ia 4 « 7 S a ia f 7 • 9 11 M 4 4 4 S 14 ia 10 4 4 3 18 M 10 t 7 4 Y* i i 14 14 11 10 4 7 ta 14 12 10 t a 3 2 1 ia ia 11 11 4 7 3 2 1 ia u 11 11 4 7 ii ii 10 10 4 7 10 11 10 « a a • 10 1 4 7 3 t 10 • 4 7 a f 10 • 4 7 4 0 10 • S 7 a 0 0 9 4 7 4 a io 1 4 7 a > » • 10 • > 1 8 4 t 10 > 1 7 8 10 11 10 » 4 4 12 It 11 1 4 4 to It 11 10 > » 4 4 0 i7""is * 4 <• < 4 3 a, 4 V 3 1 » V 1 t t 1 A 4* 7 3 » * » ^r \ \ / MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 86 760711 1200 MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 87 760711 14-00 MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 88 760711 1600 SANTA CRUZ X 10 It fa u IS t 1 1 1 2 I 2 2 2 2 2 2 2 2 3 2 2 2 4 2 4 2 2 4 2 2 2 2 2 t 2 t 2 1 2 1 V •\ 7 MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 89 760711 1800 SANTA CRUZ X 11 11 • • 7 • • S 3 4 J 2 1 14 IX 11 • • 8 7 8 • 5 * 3 2 1 IS 13 11 10 1 8 • 7 « f 3 ♦ X 1 1* 14 12 11 * * • 7 7 7 • ♦ J 2 14 16 IX 11 t ■ • 8 7 7 • « 3 1 MOSS LANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 90 760711 2000 4 ^_^ SANTA CRUZ / \ \__ / X 3 1 1 • • 7 • 4 3 1 V 14 13 12 11 • • 7 3 • 4 3 2 1 > \ 13 1* 13 12 10 * a 7 4 i 4 1 2 1 l it ia 14 13 11 • s 7 a 1 3 4 2 1 \ \ IT IT II 1) 12 10 t 4 7 a 0 4 3 2 I 17 17 11 14 12 10 I « 7 7 a 4 3 2 1 X » 4f » » » » ia so io 14 12 io > 10 3 *• 7 *> T * a > 3 > 4 > 2 2 1 IB 10 10 14 12 10 10 4 7 7 t 3 3 2 2 1 ► *►►»> 1* 19 10 14 12 10 > 10 > S > 7 > 7 > a > 3 > 3 > 2 2 1 » * » » > > 1* SO 10 14 12 10 > t > s > 7 > 7 > a > S > 3 3 3 1 10 2* 10 13 11 10 > > « > 7 > 7 > a > 3 > 3 2 2 1 X 1fl 22 17 14 12 11 > 10 > I > • > a > 7 > 4 > 4 > 3 3 3 A ^ * f > > t» 21 ia i3 11 io 11 10 > » > • > 7 ■> a > 4 3 3 1 > > a 2i ia 13 a 12 11 11 • t > 7 > a 4 3 2 1 ia 20 ia i« 1a 13 13 11 • > a 7 a 4 3 3 i ia 23 17 18 13 12 12 10 t > a 7 4 4 3 2 1 23 24 ia ia 13 11 10 t 4 a a s 4 3 2 I : A Zm 24 21 17 14 13 11 10 • a 7 a • 4 3 2 2 2 1 32 2a 21 ia ia 13 12 11 • • a 7 I 4 3 2 3 2 1 32 27 22 20 17 IB 14 11 10 10 a 7 a 3 4 J 3 2 1 32 27 24 22 10 3 It 13 12 11 10 a 7 S 4 4 I 3 2 1 3a 28 23 23 20 17 17 14 13 12 ia a 7 a S 4 t 3 2 1 31 2S 23 22 ia ia T7 13 13 12 11 a 7 a 3 4 > 4 3 ' / 2a 23 21 20 17 15 13 13 11 11 0 a a 4 3 : 1 2 1 f » » > ii 23 2a ia ia 14 > ia 12 11 11 a a a 4 3 1 2 « ) 23 2a 17 ia 14 12 11 10 « a 7 3 4 3 2 1 1 y moss 21 ia ia is 12 11 20 ia 13 14 12 id 11 10 A 3 ■ A 4 a a 7 a a 3 4 3 2 2 1 1 LANDING ia 17 is 14 12 10 10 1 a 7 a 4 3 1 17 ia 14 13 12 10 10 A 9 A 7 A a 3 4 2 1 ia ia 14 14 12 10 > 10 > * A 7 A 7 3 4 2 1 ia 17 IS 14 12 10 10 3 a 7 A 3 A 4 2 1 ia ia 14 13 11 • 1 S A 7 A a 3 3 1 to ia ia 14 11 t ( » 7 a 3 J 1 -^ ♦ ♦ m » > 21 ia ia 13 11 * 4 > 7 A a 3 A 4 A 2 2a 24 ia 14 11 • • 4 4 i 4 t 13 a 1 ♦ 3 2 I ♦ V 4 ¥ 3 V 2 ¥ X> '♦ 1 1 3 ¥ 2 V 3 * 2 ¥ 2 ¥ 1> V yi z * 2 y >. ii TRANSPORT XI 00 ( :u-m/s MONTEREY ONE GRID SiDE = 10 CM/S 91 760711 2200 MOSS .ANDING MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 92 760712 0 SANTA CRUZ < * « < < 1* IB 10 17 17 < V < < < 17 »« 1ft 17 17 * * < k 1« IS i» 1* 13 i« is n 17 as 13 24 it IS 1ft 11 U II II 17 M II It 17 17 ii is ia i» 17 is ia ia 17 <• 13 18 20 18 10 10 2ft 22 21 23 2ft 2 4 2* 13 23 2ft 2 4 23 23 23 10 17 < 1ft 17 17 14 17 14 1ft IS 1« 10 18 17 21 1ft 23 21 22 20 12 11 » a < < < < < i4 u ii • a < < < < < is u ii • a < < < < < It 14 12 10 • IS 14 12 10 S 22 2a 2 4 22 12 21 ia •* * < < < -< 24 29 22 IS 20 IS ia 12 23 20 18 ia i« 20 ia 17 is 17 13 18 13 13 12 10 14 13 11 14 12 10 18 13 12 15 IS 12 IS 17 14 20 IS 13 IS 18 19 18 17 13 IS 19 12 14 12 10 12 11 S 1ft 2ft IS It 18 18 13 12 11 i 17 1ft 18 14 14 14 12 10 9 « 17 1ft 10 14 14 14 U 10 » 4 17 1ft ia 14 14 14 11 10 » 7 1ft 1ft 18 13 13 13 11 s 7 3 17 17 18 13 13 13 11 8 7 i 1ft 1ft 14 11 11 12 * 7 S 4 "ft 18 13 11 11 12 10 7 a J a a a a a a io a 11 11 12 11 13 11 12 11 11 11 10 s s y a s s 3 4 3 4 3 4 3 3 2 3 2 < < S • a a < < a a a s 7 7 a 7 a t a s 10 a 11 a 10 a \ \ 10 s s < « •< t 8 3 4 3 4 3 3 3 4 2 4 2 3 1 1/ 8 3 4 3 4 3 MOSS LANDING 11 18 IS 18 18 MONTEREY TRANSPORT X100 CU-M/S ONE GRID SIDE = 10 CM/S 93 BIBLIOGRAPHY Bretschneider, D. 2. , Sea Level Variations at Monterey, California. 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T. , Circulation in the Coastal Ocean, D. Re id el, Dronkers, J. J. , Tidal Computations in Rivers and Coastal inters, North-HoIIand7~T9'5^. Engineering-Science, Inc., Oceanographic Investigations in Central Monterey Bay. Sur vey~A"c"tivi€res"~JuTy T97o - "flarch T22I7"T977: — L L x Environmental Research Consultants, Inc., Watsonville 94 Garcia, R. A., Numerical Simulation of Currents in Mcnterey Bay., M.Sc. rhesisT NavaI""Posfgra3uafe ScHooTT 7"97T. Gill, S- K. and Porter, D. L., "Theoretical Offshore Tide Range Derived from a Simple Defant Tidal Model," International Hydro graphic Review, v. 57, pp. 155-167, January, 7980." Hart, W. E.. A Numerical Study of Currents, Circulation and Surface Elevations in cSancTeleur^Br etqn SounUs7 Louisiana, PE7T37 Thesi3 7~TJouIsiana S?aTe~"TJniversity , iy/5*. Henderson, F. M. , 0£en Channel Flow, Macmillan, 1966. Lazanoff, S. M. , An Evaluation of a Numerical Water Elevation and TiHalTurff "n£~Pf e die € Ion ~*flocT6l~A*p plied to Hon^erey Bay 7 H75c7 TEesIs, Nav alTos^gr a"3Hat e School, TO777 Leendertsef J, J., Aspects of a Computational Model for Long-period Water rwaveTr opaga£ioQ7"Th"e Ian d~Ccrpo ration Leendertse, J. J., and Liu. S. K., A Water-Quality Simulation Model for Well Mixed Estuaries anctToastal 5"easT~*VoT. 7IT, A Bind cast, Th"e RanHTorporaTion ~ R-T774-TT7C, "T9757 Luther, D. and Wunsch, C, "Tidal Char-s of the Central Pacific Ocean," Journal of Physical Oceanography, v. 5, pp. 222-230, 1 9757" Lynch, T. J., Long Wave Study of Monterey Bay., M.Sc. Thesis, Naval Postgraduate School, 19707" Mobley, W. L.. Item 10. in U.S. Dept. of Commerce, NOAA, Charting and Geodetic Service letter: C. W. Hayes N/CG2 to J. S. Midgely N/CGx2, Subject: Hyirographic Thesis Topics for the Naval Postgraduate School, January F, '798T7 Moe, J., Mathisen, J. P., and Hodgias, S. , "An Improved Method for the Computation of Shallow Water Waves," Numerical Methods in Laminar and furbulerrt Flow, pp. 5TJ-9-FTB7~PehTecE-pfess7~TTre. * Munk, w. , Snodgrass, F., and Wimbush, M., "Tides Offshore: Transition from California to Deep Ssa Waters," Geophysical Fluid Dynamics, v. 1, pp. 16 1-2 35, 1970. National Geophysical Data Center, U.S. Depx. of Commerce, NOAA, Digital Bathymetric Data for the U.S. Coastal Regions. 95 National Ocean Survey* U.S. Dept. of Commerce, NOAA. California Marine Boundary Program Final Report, 1981. National Ocean Survey, U.S. Dept. of Commerce, NOAA, Tide Tables .19 76, West Coast of North and South America, T975. Parke, M. E. and Henderschott , M. C. , "M2, S2 , K1 Models of the Global Ocean Tide on an Elastic Earth," Marine Geodesy* v. 3, pp. 379-408, 1980. Schureman, P., Manual of Harmonic Analysis and Prediction of Tides. U.S. Dept7~ofTommerce, Coal- an? Seeds tic Survev7~ 5TTT98, 1940. Scott, D. A., AMBAG Oceanographic Survey, Oceanographic Services, Inc7""¥ 16'&=77~1?TT: Skogsberq, T., "Hydrography of Montarey Bay, California - Thermal Conditions, 1929-1933," Transactions of the American Philosophical Society, v7~29, pp7~T-T52, T93 6. Spaulding, M. L. and Beauchamp, C. H. , "Modeling Tidal Circulation in Coastal Seas." ASCE Journal of Hydraulic Engineering, v. 109, pp. 1 16 -13T7" January , TJ81 ." Tracor, Inc., Estuarine Modeling: An Assessment, U.S. Environmental PTotecTion "Agency , "fat =r PoTIuTion Control Research Series 16070 DZV, 1971. 96 INITIAL DISTRIBUTION LIST 2. No. Copies 1. Defense Technical Information Center 2 Cameron Station Alexandria, VA 22314 Library, Code 0 142 Naval Postgraduate School Monterey, CA 93943 3. Chairman (Code 63Mr) Department of Oceanography Naval Postgraduate School Monterey, CA 93943 4. Chairman (Code 63Rd) Department of Meteorology Naval Postgraduate School Monterey, CA 93943 5. Dr. William Hart {Code 8100) Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 6. Dr. Edward B. Thornton (Code 68Tm) Department of Oceanography Naval Postgraduate School Monterey, CA 93943 7. Christina W. Schomaicer, LT, N3AA NOAA, NGDC E/GC3 325 Broadway Boulder, CO 80303 8. Director Naval Oceanography Division Naval Observatory 34th and Massachusetts Avenue NW Washington, D.C. 20390 9. Commander Naval Oceanography Command NSTL Station Bay St. Louis, MS 39522 10. Commanding Officer Naval Oceanographic Office NSTL Station Bay St. Louis, MS 39522 11. Commanding Officer Fleet Numerical Oceanography Canter Monterey, CA 93943 12. Commanding Officer Naval Ocean Research and Development Activity NSTL Station Bay St. Louis, MS 39522 97 13. Commanding Officer Naval Environmental Prediction Research Facility Monterey, CA 93943 14. Chairman, Oceanography Department 0. S. Naval Academy Annapolis, MD 2 1402 15. Chief of Naval Research 800 N. Quincy Street Arlington, VA 2 2217 16. Office of Naval Research (Code 420) Naval Ocean Research and Development Activity 800 N. Quincy Street Arlington, VA 22217 17. Scientific Liaison Office Office of Naval Research Scripps Institution of Oceanography La Jolla, CA 92037 18. Library Scripps Institution of Oceanography P. of Box 2 367 La Jolla, CA 92 037 19„ Library Department of Oceanography University of Washington Seattle, WA 98105 20. Library CICESE P. 0. Box 4 80 3 San Ysidro, CA 92073 21. Library School of Oceanography Oregon State University Corvallis, OR 97331 22. Commander Oceanographic Systems Pacific Box 1390 Pearl Harbor, HI 96860 23. Director, Charting and Geodetic Services (N/CG) National Oceanic and Atmospheric: Administration Rockville, MD 20852 24. Chief, Program Planning, Liaison, and Training (NC2) National Oceanic and Atmospheric Administration Rockvilla, MD 20852 25. Chief, Nautical Charting Division (N/CG2) National Oceanic and Atmospheric Administration Rockvilla, MD 20852 26. Chief, Hydrographic Surveys Branch (N/CG24) National Oceanic and Atmospheric Administration Rockville, MD 20852 27. Director, Pacific Marine Centar (N/MOP) National Ocean Service, NOAA 180 1 Fairview Avenue East Seattle, WA 98102 98 28. Director, Atlantic Marine Centar (N/MOA) National Ocean Service, NOAA 439 W. York Street Norfolk, VA 23510 29. IHO/FIG International Advisory Board International Hydrographic Bureau Avenue President J. F. Kennedy Monte Carlo, Monaco 30. Library Moss Landing Marine Lab California State Collages Sandholdt Road Moss Landing, CA 95039 31. Dr. Luciano Meiorin 600 Bancroft May Berkeley, CA 94710 32. Dr. Terry Hendrix SCCWEP Mailcode A-022 Scripps Institution of Oceanography La Jolla, CA 92093 33. LCDR Gerald B. Mills (Code 68Mi) Department of Oceanography Naval Postgraduate School Monterey, CA 93943 99 0 0- 29 AUG 88 ti 0 0 2 6 •'■"•33 Thesis S34ll|2 c.l Schomaker A model for tidal cir- culation adapted to Monterey Bay, Calif or- •^faifefl. a 0 0 2 6 16 Kftfl .9' 0 0 3 7 2 The sis S3Ulii2 n 1 20 ":93 Schomaker A model for tidal cir- culation adapted to Monterey Bay, Califor- nia.