DEVELOPING A NESTED HYDRODYNAMICAL MODEL FOR SAN
Contents
1. w u 2 5 Ot VGE f Gy On d C00 v VACIO uv O Gees Y Gee y Gin d V Gey Gin on fo Fe Me 1 Pu 1 E po Ga Ur 0 Or and Ou _ u Ov v Ov w v 2 6 at JGg 0 Gm On dtd UU On Gin l u Oy Gee V Gee V Gun d V Gee V Gin on fu Fy Mp 1 1 o Ov P 2 Vy A Po Gm d Oo Oo where u and v are the eastward and northward velocity in the physical domain respectively vy is the vertical eddy viscosity coefficient 34 Fe and Fy represent the unbalance of the horizontal Reynold s stresses M and M represent the contribution due to external sources or sinks and f is the Coriolis coefficient 2 2 3 Vertical Velocity Remember that w in Equations 2 5 and 2 6 is the vertical velocity relative to the sigma Plane and that it is not the vertical velocity in the physical domain w is calculated from the 11 continuity equation the vertical physical velocity is calculated only for post processing purposes as follows w Gon oF x tv Gee CS x 2 7 Ot On On EX E xx 2 2 4 Hydrostatic Pressure 1 w4 VJ Gee y Gm Remember that in Equation 2 5 and 2 6 pressure is defined as hydrostatic pressure Therefore in case of constant density the pressure terms in the momentum equation are 1 P g OC 1 OPatm Q 8 Po Ge VG DE poy Ge OE en g 0G 1 OPatm l 2 9 Pov Gin V Gin on Pov Gin on If the density is not constant one gets 1 g OC d f 52. 1 2008 at 12 00 LLL mam IIT LEZ yy 7 To LPS EL xw t 4 WSS oS V N NS Lar temporarily inactive water level points 01 Feb 2008 18 00 00 gt SS SEN tu venil NES NS BK NS SANTE BURNS HSS RS EAS NES ETS et e aN N GAZ ADS 1 3 5 x coordinate m gt 45 25 HUE EME lt w eyeuipjooo A Figure 4 10 Velocity vectors in Southern California coarse model on Feb 1 2008 at 18 00 28 4 2 50m RESOLUTION SAN DIEGO BAY MODEL In previous section the coarse single domain model was represented This section focuses on the fine resolution single domain model i e 50 x 50 m Again first it is explained how the model was setup followed by discussing the model output results 4 2 1 Model Setup The same coordinate system i e the UTM zone 11N and datum i e the WGS84 were used for the high resolution model The domain was spatially discretized using dx dy 50 m Total of 522 grid points were selected in the M direction i e the eastward direction and 402 grid points were selected in the N direction 1 e the northward direction Therefore the model covers an area of 26 1 km x 20 1 km Figure 4 11 Again those parts of land with an elevation of 20 m or higher were set to be always dry Any parts of land with an elevation lower than 20 m have the potential to become wet or dry Only one layer in the vertical direction was sel
3. Be RE AU 18 4 SINGLE DOMAIN SAN DIEGO MODEL sss 20 4 1 2 5 km Resolution Southern California Model 20 Z1 Model Setup cssc ee C EC daas Od edant ad odas Od od ass 20 2 1 7 Mod l Results 35 ov op ege C eC 22 4 2 50m Resolution San Diego Bay Model 28 22 1 Model Setups cori dta rh e d ten piv ep a SU QV US ce I M etus 28 422 Model Results NE nn Re nn oe eto 29 5 NESTED SAN DIEGO BAY MODEL ese 31 Sl p Mode SSSR a au dan ue a fac En 31 5 2 Model ROSES es na d PINE 32 6 CONCLUSION AND POSSIBLE FUTURE WORKS 34 BIBLIOGRAPHY ss AR ER edu A RU I M E IAE EE AER EP E RU 36 1X LIST OF FIGURES PAGE Figure 1 1 Southern California section nod LEE Qo eye tee c 3 Figure 1 2 San DiS SOB ay ideo m dte or ie ds 4 Figure 1 3 San Diego Bay bathymetry constructed by combining USGS South ern California bathymetry and a private data set 4 Figure 1 4 Approximate outline of the detailed San Diego Bay model red line nested inside the coarse Southern California model yellow boundary 5 Figure 2 1 An orthogonal curvilinear grid Each element is addressed with a pair of 7 coordinates source Delft3D Example 1 Deltares Delft DELO W User Manual den ere ias 7 Figure 2 2 Vertical Grid Sigma Coordinate left and Z Level right Source Deltares Delft3D FL
4. E S GROSS D SUTTON AND J W GARTNER Modeling tidal hydrodynamics of san diego bay california Journal of the American Water Resources Association 34 1998 pp 1123 1140
5. Mechanics 237 1992 pp 261 299 21 L LAURENT AND A THURNHERR ntense mixing of lower thermocline water on the crest of the mid atlantic ridge Nature 448 2007 pp 680 683 22 J J LEENDERTSE Aspects of a computational model for long period water wave propagation rm 5294 rr Rand Corporation Santa Monica 1967 23 J J LEENDERTSE Turbulence modelling of surface water flow and transport part 4a Journal of Hydraulic Engineering 114 1990 pp 603 606 24 J J LEENDERTSE R C ALEXANDER AND S K LIU A three dimensional model for estuaries and coastal seas technical report Rand Corporation Santa Monica CA 1973 25 J J LEENDERTSE AND E C GRITTON water quality simulation model for well mixed estuaries and coastal seas Technical Report Vol 2 Computation Procedures R 708 NYC Rand Corporation Santa Monica CA 1971 26 U LUMBORG AND A WINDELIN Hydrography and cohesive sediment modeling application to the romo dyb tidal area Journal of Marine Systems 38 2003 pp 287 303 27 J L MARTIN AND S MCCUTCHEON Hydrodynamics and Transport for Water Quality Modeling Lewis Publishers 1999 28 J MCCALPIN A comparison of second order and fourth order pressure gradient algorithms in a sigma coordinate ocean models International Journal Numerical Methods in Fluids 18 1994 pp 361 383 29 E MCDONALD AND R T CHENG Issues related to modeling the transport of suspen
6. and compiled on both Linux and Windows machines The following section explains how to compile the source code on each system 3 1 2 1 WINDOWS MACHINE To compile the Delft3D source code on a Windows platform the following software must be installed e Visual Studio 2008 VS2008 or Visual Studio 2010 VS2010 e Intel FORTRAN compiler Version 11 0 or Version 12 0 Note that Visual Studio is freely available for students and educational purposes However the student version of the Intel compiler is available for a moderate cost Recently the Intel FORTRAN compiler version 13 0 was also supported however in this project VS2008 and the Intel FORTRAN compiler version 11 0 were used to compile the code Once you have installed the above mentioned software you must open the project file in either VS2008 or VS2010 All that is needed then is to choose the build button or to press Control Shift B key combination Make sure that the release version is selected in the compile options Depending on your system the compile procedure may take some time 3 1 2 2 LINUX MACHINES According to Deltares the following packages are needed on a Linux machine prior to starting the compile procedure e GNU Auto Tools e GNU Lib Tools GNU C Compiler expat devel e GNU FORTRAN Compiler Mpich2 17 e Lex e Yacc OpenSSL Readline devel Ruby Interpreter Some of the above mentioned packages may have already been installed already
7. by default on your Linux platform All of these software packages are freely available It is advised to install them using the package manager of your Linux distribution such as apt get on Ubuntu Linux and Yum on Fedora Linux You can replace GNU FORTRAN compiler with Intel FORTRAN compiler Intel FORTRAN compiler provides faster binaries Unlike for Windows machines Intel FORTRAN compiler is available free of charge for personal use on the Linux environment Once the prerequisite packages are installed you can compile the source code The best option is to open autogen sh under the src folder and edit the variables to match them to those of the system One can control the compiler compiler flags and other options that are needed to successfully compile the code on a Linux machine Once the proper changes have been made one needs to execute autogen sh Instead of changing autogen sh it is easier to pass all the common variables at the command line For example to set compiler options try autogen sh CFLAGS 02 m64 fPIC autogen sh will create the required Makefile on your system Now to fully compile the source code and obtain the binaries one needs to issue make ds install 3 1 3 Testing Delft3D Once you have fully compiled the Delft3D source code it is advised to run some of the examples that are provided in the examples folder These examples should run without generating any errors If you are
8. diverse activities do not necessarily work in favor of the region s ecology One example being that the southern part of the San Diego Bay is covered with eelgrass which is considered to be a very valuable shallow water habitat that provides numerous ecological services such as shelter nutrient cycling a breeding habitat for various species stabilizing sediments and important organic material for near shore environments Eelgrass requires special conditions to flourish and is sensitive to tidal changes in the bay 13 However because of the extensive human activities in the region many parts of the bay have become impaired by the presence of toxic metals and organic pollutants 39 As a result many institutes organizations and corporations are performing water quality studies in the region in order to enhance the water quality and save the natural habitat of various local birds and sea life 13 39 A numerical model is perhaps the best method available for use in understanding the region and for modeling the quality of the water 39 However most biological and water quality models require a detailed hydrodynamic model of the region 31 39 Information about the hydrodynamics of a region including knowledge of the velocity water level and fluxes at every grid cell enables the researcher to perform a quantitative analysis of the water quality and provides an understanding of the behavior of the environment including determining th
9. open boundaries as follows e Astronomic The flow conditions are specified using tidal constituents amplitude and phases e Harmonic The flow conditions are specified using user defined frequencies amplitudes and phases e QH relation The water level is derived from the computed discharge leaving the domain through the boundary e Time Series The flow conditions are specified as time series Since we were interested in tidal simulation in this model the astronomic boundary condition was selected and the water level at the open boundary was defined It should be noted that over the open boundary each set of 10 cells were grouped together as a single boundary making it possible to change the boundary condition on a specified part of the domain However it was decided to set the same boundary condition over the entire open boundary The Earth s gravity was set to 9 81m s and the water density was set at 1024kg m The Manning formulation was chosen for the bottom friction Seven monitoring points were set as observation points and then introduced into the model Their names and locations in grid coordinates are listed below 22 e Santa Barbara Pacific Ocean 34 113 e Santa Monica Municipal Pier 77 95 Los Angeles Outer Harbor 85 82 Long Beach Terminal Island 87 83 Newport Beach Newport Bay Entrance Corona del Mar 100 76 La Jolla Scripps Institute 123 44 San Diego San Diego Bay 126 37 These moni
10. order to download the code one must first create a free user account The source code installation procedure and manual are available at http oss deltares nl web opendelft3d source code The above link can also be used to create the free user account required to download the full source code To download the code one needs to make use of a version control software for example SubVersioN SVN on Linux machines The Delft3D repository contains several branches however the fully tested and stable version of the code can be found in the tags folder The latest edition is the one with the highest version number At the time of this writing the latest version was 5 00 10 1983 To check for the latest version go to the following address https svn oss deltares nl repos delft3d tags If you are using a command line version control program such as SVN you can check for the latest version by issuing the following command svn checkout https svn oss deltares nl repos amp delft3d tags 5 00 10 1983 delft3d repository 16 Notice again that 5 00 10 1983 was the latest version as of this writing Under the Windows operating system you can make use of a graphical version control program such as TortoiseS VN which is freely available for download at http www http tortoisesvn net You can download TortoiseSVN for both 32 bits and 64 bits Windows operating systems 3 1 2 Compiling Delft3D Delft3D has been tested
11. region Unlike previous efforts the model developed in this project provides high resolution hydrodynamic data consistently for all areas of the San Diego Bay The grid resolution was set to 50 m throughout the entire domain and all of Coronado Island and the San Diego Bay s surrounding areas were covered by the high resolution mesh making this model capable of performing wetting and drying studies for cases of severe conditions More importantly this model is based upon available free source codes and data sets and can be executed on a regular desktop computer unlike the Navy model whose demonstration costs alone were over half a million dollars Two high resolution models were developed of the San Diego Bay for this project one that could act autonomously single domain model and one that needed to be nested inside a coarser model that covered a larger area multi domain or nested model Both models were successful at estimating water levels so why build the more complicated nested model The single domain model is limited to study events and features restricted to or originating in the San Diego Bay only assuming that all the boundary conditions are provided properly which is not always possible however the multi domain model nested model can be used to study the effects of events that occur beyond the San Diego region and how they can affect the bay and its ecology Since the detailed or the fine resolution model is nested insi
12. the entire domain The boundary conditions for the coarser grid were kept the same However the boundary conditions for the finer model nested inside the coarser model were changed to a time Series A set of observation points along the boundary of the finer grid were created in the coarser grid model After the coarser grid model was finished the water level from the coarser grid was fed at the boundary of the finer model This is only achievable by setting the boundary type to time series 32 The Earth s gravity was set to 9 81 m s and the water density was set at 1024 kg m The Manning formulation was chosen for the bottom friction Only one monitoring station was selected in the finer model and that was the San Diego domain The same monitoring points were kept in the coarse grid model The history file was written every 30 minutes and the map file was set to be written every 24 hours however no restart file was selected 5 2 MODEL RESULTS The coarse grid was run for 6 months again but only to be able to extract the data every 30 minutes at the boundary of the finer model Later the finer model ran for 2 days which took about 4 hours of computer time and it was forced with the time series data provided by the coarse grid The stable time step for the fine grid was 0 01 minutes hence the time series was linearly interpolated in time at each time step The model output for the water level at the San Diego Bay station is shown
13. 6 temporarily inactive water level points x 108 01 Feb 2008 00 00 00 3 85 0 08 28 0 07 0 06 3 75 0 05 E 37b 2 E 0 04 g S 3 65 o 0 03 36 0 02 8 55 0 01 35 1 5 2 25 3 35 4 45 5 55 x coordinate m gt Figure 4 7 Velocity vectors in Southern California coarse model on Feb 1 2008 at 00 00 temporarily inactive water level points x 108 01 Feb 2008 06 00 00 J 0 06 3 8 F N PES 0 05 375r Y AS SEN NS LL E j 0 04 3 77 zz 1 0 03 9 o a T zzz y coordinate m gt E ST hs n gt xX AS AS 0 02 m 36r MINE Ze esse DANS NUS 2D Aw gt I P AA ER uA NA A add ha ELLE SS ur NS gt i 77 SEE 0 01 Ss N j N 47 AAA SN i Su NES 1 1 1 1 1 i 15 2 25 3 3 5 4 45 5 5 5 x coordinate m gt Figure 4 8 Velocity vectors in Southern California coarse model on Feb 1 2008 at 06 00 27 0 14 0 12 1 0 08 0 06 0 04 0 02 y lo P le A A pe la E Yi ARA LL Y Y H A 1 3 Si 4 EM ULLA Ps HN E TAR y ar o uu m fs EON ETE e 8 A VAS PE 7 LL LEE A o 22 4 LEED 3 AAA aa BS DA do E PI TRG Nae i j Le f fey AY Y PA YES SINS NSS PAK WE EE AE EA Hie Y NX ES VS Tai SEGA HG Fe IRS SESS M NE PPDA y A EN EE E ER lt w jeuip1003 A x coordinate m gt Figure 4 9 Velocity vectors in Southern California coarse model on Feb
14. DB is MATLAB based one does not need to have MATLAB installed However MATLAB runtime libraries which are freely made available by Mathworks must be installed Instead of the DDB binaries one may decide to download the MATLAB source code for the DDB and use the software directly through MATLAB To do this first download The Open Earth Tool OET Although we utilized the MATLAB source code of the DDB and not the binaries for this project we omit the instruction on how to download the OET Still the instructions can be found in the Delft Dashboard manual at http publicwiki deltares nl display ddb Download 20 CHAPTER 4 SINGLE DOMAIN SAN DIEGO MODEL Both coarse and fine resolution models are initially setup using Delft Dashboard DDB Delft3D GUI was later used to fine tune the model including choosing a stable time step and setting the bed shear parameters 4 1 2 5km RESOLUTION SOUTHERN CALIFORNIA MODEL As mentioned earlier two single domain model were developed This section explains setting up the coarse resolution model i e 2 5 x 2 5 km First it is explained how the model was setup followed by discussing the model output results 4 1 1 Model Setup Before setting up the model using DDB one has to decide on the coordinate system Since the focus of this project is Southern California and San Diego it was decided to use the Universal Transverse Mercator UTM coordinate system UTM zone 11N covers Southern Californ
15. DEVELOPING A NESTED HYDRODYNAMICAL MODEL FOR SAN DIEGO BAY CA USING DELFT3D AND DELFTDASHBOARD A Thesis Presented to the Faculty of San Diego State University In Partial Fulfillment of the Requirements for the Degree Master of Science in Computational Science by Mohammad Abouali Spring 2013 SAN DIEGO STATE UNIVERSITY The Undersigned Faculty Committee Approves the Thesis of Mohammad Abouali Developing a Nested Hydrodynamical Model for San Diego Bay CA Using Delft3D and DelftDashboard DAD A 2 if A i TS Jose E Castillo Chair Computational Science Research Center d Peter bioman Department of Mathematics and Statistics 12 14 2012 Approval Date Copyright 2013 by Mohammad Abouali All Rights Reserved 111 DEDICATION To The San Diego Community iv The illiterate of the 21st century will not be those who cannot read and write but those who cannot learn unlearn and relearn Alvin Toffler vi ABSTRACT OF THE THESIS Developing a Nested Hydrodynamical Model for San Diego Bay CA Using Delft3D and DelftDashboard by Mohammad Abouali Master of Science in Computational Science San Diego State University 2013 In this project three hydrodynamic models of the San Diego Bay were developed The first one was a coarse model 2 5 km resolution covering all of Southern California This model affords valuable data for areas close to San Diego Bay but is not capable of prov
16. OW user manual Delft the Netherlands 2011 7 Figure 2 3 Staggered grid used in Delft3D Source Deltares Delft3D FLOW user manual Delft the Netherlands 2011 9 Figure 3 1 DelitDashboard screen shot 5 9 dede es epa dedico notre deed fee daas 19 Figure 4 1 Southern California coarse model and control stations The blue line shows the location of the open boundary 21 Figure 4 2 Changes in the water level at the La Jolla station Delft3D output blue line and station value red line 23 Figure 4 3 Changes in the water level at the Long Beach station Delft3D output blue line and station value red line 23 Figure 4 4 Changes in the water level at the Los Angeles station Delft3D output blue line and station value red line 24 Figure 4 5 Changes in the water level at the Newport station Delft3D output blue line and station value red line sess 24 Figure 4 6 Changes in the water level at the Santa Barbara station Delft3D output blue line and station value red line 25 Figure 4 7 Velocity vectors in Southern California coarse model on Feb 1 DOS AL 00 007 ta tendit e Cr a stare pee dfe vus ere dope uto euer 26 Figure 4 8 Velocity vectors in So
17. Op x e eg Fg do 2 10 Poy Gee 2 VGee 06 poy Gee Jo NOE Oo 0 1 g OG d 5 Op x e A ues EG dot 2 11 Po V Gm i V Gm ON Poy Gm Jo NOn 00 On 2 2 5 Horizontal Stresses The horizontal stresses in the momentum equation can be reduced to a Laplace s operator 3 6 38 as follow D 1 Pu 1 z 2 12 H i VC VE 082 VC Cm On 1 y 1 y F V E 2 13 Gi y Gin og V Ge y Gm 2 2 2 6 Equation of State The equation of state EOS determines the water density p as a function of the salinity and Temperature and features different formulations for seawater Delft3D supports both Eckart s equation 12 and the UNESCO equation 43 44 Eckart s equation has several limitations however the UNESCO equation also called EOS80 has proven to have better 12 performance 3 6 g m error Delft3D uses EOS80 by default EOS80 can be written as follows p po As Bs 2 Cs 2 14 where Po 999 842594 6 793952 10 t 9 095290 10732 2 15 1 001685 1041 1 120083 107644 6 536332 10 915 A 8 24493 107 4 0899 10 3 7 6438 107 t 2 16 8 2467 1077t 5 3875 10 B 5 72466 107 1 0227 107 t 1 6546 10 52 2 17 C 4 8314 1074 2 18 EOS80 is valid for t 0 C 40 C and s 0 5 ppt 43 ppt where ppt stands for part per thousands It should be noted that in the presence of other chemicals in the ocean water the abov
18. able to run these examples your compile procedure was successful 3 1 4 Delft3D GUI So far how to obtain the Delft3D Flow source code and compile it has been discussed By successfully compiling the code you will have access to the solver part of Delft3D There is a Graphical User Interface GUI available for Delft3D FLOW which facilitates setup of the model changing parameters and visualizing results Deltares is planning to make the 18 source code for Delft3D GUI known as Delft3d Menu publicly available However this promise has not yet materialized Meanwhile Deltares is providing the binaries for their GUI on Windows and Linux machines To obtain the GUI binaries and free license send an e mail to sales deltaressystems nl 3 2 DELFT DASHBOARD Delft Dashboard DDB is part of Open Earth Tools and is a stand alone MATLAB based software DDB provides a graphical user interface that supports the modeler in the setting up of a new model or in altering an existing model It is currently fully integrated with Delft3D FLOW DDB provides easy access to many online databases through Open source Project for a Network Data Access Protocol OPeNDAP One can access different measuring stations such as those of the International Hydrographic Organization IHO or the XTide Tidal Stations DDB also provides easy access to various bathymetry databases including e GEneral Bathymetry Chart of the Ocean GEBCO e National Geoph
19. d but also because it makes me to sit back relax for a while and review the wonderful and amazing memories and moments that I had with them Life particularly nowadays goes very fast However joy beauty love and the good memories are hidden away between the seconds of your life If you don t stop for a minute you might miss it Cashback the movie 2006 Despite spending a very short time to prepare this thesis there are many people whose assistance and help were absolutely necessary to make this thesis and project successful First of all I want to thank my supervisor Prof Jose E Castillo who let me to take some time off of my Ph D project to complete this project and obtain a second Master of Science MS degree I cannot thank him enough for his assistance in this project I want to thank my thesis committee Prof Peter Blomgren and Prof Barbara Bailey to share their time particularly so close to the end of the year and their inputs to make this thesis even better I want to thank Jessica Nombrano for proof reading my thesis and the wonderful job she did I want to thank Parisa Plant for taking care of the paper work administration and ordering all the computer hardware and software that I needed for this project I also want to thank all my friends for their support and the good time we had Particularly I want to thank Sara and Ali for all the time we spend together and all the nights that we were staying up late working on o
20. de a coarser model and located far from its boundaries errors in boundary conditions of the coarser model will have less effect on the finer model For example if a certain pollutant is released into the waters around the Los Angeles port would it end up in the San Diego Bay considering that the main water flow along Southern Californian coasts is from north to south The nested model is well suited to provide answers for these types of questions and modeling scenarios A majority of previous works provided only a single domain in fact as 33 far as the author is aware only one other nested model of the region exists which is also based on Delft3D However the fate of that attempt is unknown and no results have yet been made public aside from a few report pages Some past attempts also tried to force the model using the available measurements only at the boundaries however these measurements were performed sparsely and were used slightly off of the real locations For example in one case measurements of La Jolla were used to set the conditions at the San Diego Bay s entrance Moreover it appears that there is no study or model that uses data assimilation techniques in the San Diego Bay Therefore it is widely suggested to perform a simulation using data assimilation in the future Still the author believes that the quality of the results already attained without any data assimilation may demotivate the future researcher to go thro
21. ded sediments in northern san francisco bay california in 3rd International Conference on Estuarine and Coastal Modeling 1994 pp 1 41 30 T J PEELING A proximate biological survey of san diego bay california Technical Report 389 Naval Undersea Center San Diego California 1975 31 J PENG AND E Y ZENG An integrated geochemical and hydrodunamic model for tidal coastal environments Marine Chemistry 103 2007 pp 15 29 32 N A PHILLIPS A coordinate system having some special advantages for numerical 38 forecasting Journal of Meteorology 14 1957 pp 184 185 33 K POLZIN J TOOLE J LEDWELL AND R SCHMITT Spatial variability of turbulent mixing in the abyssal ocean Science 276 1997 pp 93 96 34 W RODI Turbulence models and their application in hydraulics in AHR Paper presented by the IAHR Section on Fundamentals of Division 2 Experimental and Mathematical Fluid Dynamics 1984 35 G S STELLING On the construction of computational methods for shallow water flow problems Technical Report 35 TUDelft Delft The Netherlands 1984 36 G S STELLING AND S P A DUINMEIJER A staggered conservative scheme for every froude number in rapidly varied shallow water flows International Journal Numerical Methods in Fluids 43 2003 pp 1329 1354 37 G S STELLING AND J J LEENDERTSE Approximation of convective processes by cyclic aoi methods in Estuarine and coastal modeling Procee
22. ding three components of the velocity the pressure salinity and temperature In general they can be divided into vector variables such as velocity and scalar variables such as pressure salinity and temperature Depending on how these different variables are arranged in a grid one can have different grid types known as type A B C D and E 15 Delft3D uses a C grid also known as a staggered grid Figure 2 3 In a staggered grid the scalar values are stored at the cell center and different components of the vector variables usually the velocity are stored at the middle of the cell faces Figure 2 3 Staggered grid used in Delft3D Source Deltares Delft3D FLOW user manual Delft the Netherlands 2011 2 2 GOVERNING EQUATIONS Delft3D uses nonlinear shallow water equations in 2D and 3D Shallow water equations SWE are derived by averaging the full Navier Stokes equation in the vertical direction Several assumptions have been made to derive these equations the main assumption is that the horizontal length scale is much larger than the vertical length scale This is normally true for any ocean flow model However this assumption practically reduces the vertical momentum equation to a hydrostatic pressure equation While this is a valid assumption in coarse resolution extra care must be taken in very fine resolution cases as well as those where fluid flow interaction with the bottom bathymetry is the dominant process 1 In
23. dings 2nd Conference on Estuarine and Coastal Modelling M L Spaulding K Bedford and A Blumberg eds Tampa 1992 ASCE pp 771 882 38 G S STELLING AND J A T M VAN KESTER On the approximation of horizontal gradients in sigma co ordinates for bathymetry with steep bottom slopes International Journal Numerical Methods in Fluids 18 1994 39 TETRATECH Receiving water model configuration and evaluation for san diego bay toxic pollutants tmdls technical report Tetra Tech Inc San Diego CA 2008 40 A THURNHERR AND K RICHARDS Hydrography and high temperature heat flux of the rainbow hydrothermal site mid atlantic ridge Journal of Geophysical Research 106 2001 pp 9411 9426 41 A THURNHERR K RICHARDS C GERMAN G LANE SERFF AND K SPEER Flow and mixing in the rift valley of the mid atlantic ridge Journal of Physical Oceanography 32 2002 pp 1763 1778 42 A THURNHERR AND K SPEER Boundary mixing and topography blocking on the mid atlantic ridge in the south atlantic Journal of Physical Oceanography 33 2003 pp 848 862 43 UNESCO Background papers and supporting data on the international equation of state 1980 Technical Report 38 UNESCO 1981 44 UNESCO The practical salinity scale 1978 and the international equation of state of seawater 1980 Tenth report of the Joint Panel on Oceanographic Tables and Standards 36 UNESCO 1981 45 P F WANG R T CHENG K RICHTER
24. e fate of different chemical compounds 8 17 18 26 27 29 As a result of its environmental and economic importance there are numerous hydrodynamic studies currently underway in the region Many measurements and experimental studies have taken place in San Diego Bay 45 including Wang s numerical hydrodynamic study dating back to 1998 45 Wang used a numerical grid with a 100 m spatial resolution and was able to simulate tidal water levels within an acceptable range of errors Since then many more numerical models have been developed most of which have been funded or performed by the US Navy One of the most detailed studies of the bay is that performed by the Environmental Security Technology Certification Program ESTCP 7 However the project s demonstration cost alone was approximately 580 000 which is a quarter of a million dollars more than the CH3D base model 329 106 7 The majority of San Diego Bay models have either been based on curvilinear grid hydrodynamics 3D CH3D or environmental fluid dynamic code EFDC however almost all of them share the same CH3D grid that was originally developed by the Navy for studies of the San Diego Bay The grid size in these models is on average 100 m with a maximum of 250 m and a minimum of slightly more than 18 m 39 Although the minimum grid length is reported to be 18 m it should be noted that this only applies to one direction of the grid cells and in those regions the cel
25. e mentioned equation may no longer hold true 2 2 7 Bed Shear Stress Delft3D uses the logarithmic law of the wall for 3D models to calculate the bed shear stress However in 2D models including for this project the quadratic friction law is used The quadratic friction law can be written as follows pogU a pe Et 2 y Cp 2 19 where a is the magnitude of the horizontal velocity C5p is the 2D Ch zy coefficient and Delft3D provides the following options e Ch zy Formulation user defined value in m s e Manning s Formulation Cop 2 20 n with n being the Manning s coefficients in mts e White Colebrook s formulation 12H G5 isto 2 21 S with k being the Nikuradse roughness length 13 2 3 TIME AND SPATIAL DISCRETIZATION Delft3D FLOW uses the alternating direction implicit ADI method as described by Leendertse 22 24 25 to integrate shallow water equations in time Delft3D FLOW uses three different spatial discretizations In all cases the discretization is at least second order accurate in space These schemes are e WAQUA Scheme 35 37 e Cyclic Method 37 e Flooding Scheme 36 Neither the WAQUA scheme nor the Cyclic scheme impose any time step restrictions and are both high order schemes The flooding scheme is suitable for problems including rapidly varying flows such as in hydraulic jumps This scheme however imposes a time step restriction by the Co
26. ected making it a true shallow water equation model SDBathy USGS SRTM USGS Southern California and GEBCO for a total of four data sets were combined to interpolate the bathymetry throughout the entire domain The start of the simulation time was set at January 1 2008 The stable time step using ADI scheme was found to be 0 01 minute One day of simulation took approximately two days and twenty hours to simulate As a result it was not possible to do any forecasting and so it was decided to simulate only one day The water level for the entire domain was set at Om over the entire domain Figure 4 11 High resolution San Diego Bay model 29 Over land no flow condition is enforced However as in southern California model astronomic boundary condition was used over open boundaries The Earth gravity was set to 9 81 m s and the water density was set at 1024 kg m The Manning formulation was chosen for the bottom friction Only one monitoring station was selected in this domain and that was the San Diego station All other tide stations were located outside the model domain However two extra points close to the bay entrance were also selected The history file was written every 30 minutes and the map file was set to be written every 6 hours however no restart file was selected 4 2 2 Model Results Before discussing any of the outputs it should be noted that the model ran for only 1 day which took 2 days and 20 hours of compu
27. ia and San Diego Bay World Geodetic System 84 WGS84 is used as the Datum The domain was spatially discretized using dy dy 2500 m 145 grid points where selected in the M direction 1 e the eastward direction and 122 grid points were selected in the N direction i e the northward direction Therefore the model covers an area of 362 5 km x 305 0 km Figure 4 1 Those parts of the land with an elevation of 20 m or higher were set to be always dry Any parts of the land with an elevation lower than 20 m have the potential to become either wet or dry Most of the southern and eastern parts of the domain are treated as open boundaries The reflection factor was set to a high number in order to prevent any reflection of waves back into the domain so that all waves can freely exit the domain Only one layer in the vertical direction was selected making the model a true shallow water equation model Only GEBCO bathymetry is interpolated onto the grid The simulation start time was set at January 1 2008 with a full six months to be simulated the stop time being set for midnight on July 1 2008 The stable time step using the ADI scheme was found to be 1 minute The water level for the entire domain was set at Om 21 Figure 4 1 Southern California coarse model and control stations The blue line shows the location of the open boundary Over land no flow condition is enforced However several options are available for the
28. iding any information from within the bay itself The second model is a standalone high resolution 50 m hydrodynamic model that is capable of simulating the hydrodynamics within the bay However this model is unaffected by the information from outside of the actual bay The third is a multi domain model of the San Diego Bay which is a high resolution model nested within the coarser model of Southern California This model is capable of simulating the hydrodynamics within the bay and enables the study of the impact of events originating well outside of the San Diego region hence it offers broader capabilities and applications All three of these models can be used to study the San Diego Bay s ecology including the effect of toxic pollutants and the overall water quality in the region Considering the fact that the San Diego Bay is extremely important to both the economy and ecology of the region and taking into account that the models developed here are based on free source code Delft3D and freely available data sets making the operation costs very low it becomes fairly certain that researchers scientists and institutions could benefit from the models developed in this project As a result this model could help the San Diego community better understand the local environment thereby enabling it to make better more informed decisions regarding projects affecting the ecology of the region vil TABLE OF CONTENTS PAGE ABSTRAC P ee eo
29. in Figure 5 1 It is clear that the model requires more spin up time and has not yet converged to the real solution Figure 5 2 compares the output of the nested model versus the output of the single domain model for the San Diego Bay It can be seen that both models follow the same trend however the single domain requires less spin up time WL 08 San Diego San Diego Bay California gt 0 6 0 8 L 1 Oh 12h Oh 12h Oh Figure 5 1 Changes in the water level at the San Diego bay station for the nested model during the first two days of the simulation Delft3D output blue line and station value red line 33 SanDiegoSanDiegoBayC 08 elevation m gt time gt Figure 5 2 Changes in the water level at the San Diego Bay station Nested San Diego Bay model blue line and single domain San Diego Bay model dashed red line 34 CHAPTER 6 CONCLUSION AND POSSIBLE FUTURE WORKS Another hydrodynamic model of the San Diego Bay was developed in this project Past modeling efforts of the region were mainly adapted using EFDC and CH3D models of San Diego Bay However they were all based on a curvilinear grid that was developed by the US Navy known as the CH3D Navy grid The CH3D grid on average provides a grid resolution of 100 m None of these models allowed for wetting and drying a process that is very important in defining the fate of certain important biological and ecological aspects of the
30. l Delft the Netherlands 2011 12 C ECKART Properties of water part 2 the equation of state of water and sea water at low temperatures and pressures American Journal of Science 256 1958 pp 225 240 13 R M GERSBERG San diego bay terrain model progress report technical report San Diego State University 2012 14 S GILLE M YALE AND D SANDWELL Global correlation of mesoscale ocean variability with sea floor roughness from satellite altimetry Geophysical Research Letters 27 2000 pp 1251 1254 15 S GRIFFIES C BOENING F BRYAN E CHASSIGNET R GERDES H HASUMI A HIRST A M TREGUIER AND D WEBB Development in ocean climate modelling Ocean Modelling 2 2000 pp 123 192 34 16 R HANEY On the pressure gradient force over steep topography in sigma coordinate ocean models Journal of Physical Oceanography 21 1991 pp 610 619 17 I JAMES Modeling pollution dispersion the ecosystem and water quality in coastal waters review Environmental Modeling and Software 17 2002 pp 363 385 18 S KARICKHOFF S DAVID AND A TRUDY Sorption of hydrophobic pollutants on natural sediments Water Research 13 1979 pp 241 248 19 K KRETTENAUER Numerische simulation turbulenter konvektion ueber gewelten flaechen PhD thesis DLR Oberpfaffenhofen Germany 1991 20 K KRETTENAUER AND U SCHUMANN Numerical simulation of turbilent convection over wavy terrain Journal of Fluid
31. lar and rectilinear grids are considered special cases of Cartesian coordinates In Cartesian coordinates the top lid of the domain is considered to be flat In spherical coordinates is the longitude and is the latitude In this coordinate the top lid of the model follows the Earth s curvature Spherical coordinates are also a special case of the orthogonal curvilinear grid where E A 2 1 n VGe Rcos Q 3 I ey where R 6378 137 km is the Earth s radius 4 Gc and G are coefficients used to transform curvilinear coordinates into a rectangular grid Figure 2 1 An orthogonal curvilinear grid Each element is addressed with a pair of n coordinates source Delft3D Example 1 Deltares Delft3D FLOW User Manual 2 1 2 Vertical Grid In the vertical direction Delft3D offers two coordinate options Figure 2 2 as follows e c coordinate system Sigma Coordinate e Z Model or Z Level Figure 2 2 Vertical Grid Sigma Coordinate left and Z Level right Source Deltares Delft3D FLOW user manual Delft the Netherlands 2011 Figure 2 2 illustrates how these two grids are different The sigma coordinate was originally developed by Phillips 32 and is designed in such a way that c 1 at the bottom and c 0 at the free surface The transformation from a physical z coordinate to o coordinates is done as follows 2 2 where e is the free surface elevatio
32. ls are elongated in the opposite direction 1 1 MOTIVATION Due to the importance of the San Diego Bay and the vital role it plays in the local economy it was decided to develop a high resolution hydrodynamic model for the region As described earlier the outputs of the previous hydrodynamic models have played a vital role in other studies including biogeochemical habitat and ecological modeling studies Numerous studies have already been performed in the region and a few were mentioned in the previous section However despite many successful modeling efforts made in the past the grid resolution of these models varies within the bay and does not provide the same high resolution for the entire area Since having a high resolution hydrodynamic model is vital for water quality and other environmental studies it was decided to develop a high resolution model for the San Diego Bay that would provide consistent resolution over the entire bay As some of the past efforts have proven to be very costly over half a million dollars 7 our goal is to use free and open source software that can be executed on a regular desktop computer and yet is still able to provide a consistently high resolution model of the entire bay It was also decided to provide a model that is capable of creating a wetting and drying scheme Although some of the past modeling efforts were capable of wetting and drying a curvilinear grid was used and only a narrow strip around
33. n above the reference plane e dis the the depth below the reference plane It should be noted that the sigma coordinate was originally developed for slopes up to 45 19 20 Slopes steeper than that will produce numerical errors and it has been shown that over very steep slopes sigma coordinates produce poor results 1 5 15 16 28 Partial derivatives can be calculated using the chain rule of derivation which will then introduce some additional terms 1 38 In coastal seas estuaries lakes and generally in places where there is steep topography or bathymetry the sigma coordinate can produce numerical errors The slope is also a function of the horizontal grid resolution In coarse resolutions the bottom bathymetry is represented smoothly and most of the high frequency variations in the bathymetry are filtered out 1 The sigma coordinate despite being a boundary fitted coordinate does not necessarily have enough resolution around the pycnocline 23 25 38 One approach to overcoming this issue is to use curvilinear coordinates in the vertical direction 1 Another common approach which is also supported by Delft3D is to use the Z level Z grid in the vertical direction In the Z grid the horizontal lines nearly match those of the isopycnal s lines i e they are parallel to the density interfaces 2 1 3 Staggered Grid In any hydrodynamic model including in Delft3D there are several variables that are simulated inclu
34. nd discussed 5 1 MODEL SETUP To create a nested model two models are needed a coarse resolution model and a fine resolution model For this project it was decided to use the previously developed model with a 2 5 km resolution as the coarse model The second model which is the high resolution model is then nested inside of the coarse resolution model It was decided to keep the same resolution used in our previous high resolution model i e dx dy 50m However in order to speed up the model simulation time we decided to decrease the total domain coverage For the finer grid a total of 399 grid points where selected in the M direction 1 e the eastward direction and 331 grid points were selected in the N direction i e the northward direction Therefore the model covers an area of 19 95 km x 16 55 km SDBathy USGS Southern California and GEBCO for a total of three data sets were combined to interpolate the bathymetry throughout the entire domain The simulation start time was set at January 1 2008 The stable time step using ADI scheme was found to be 0 01 minute Since the domain is much smaller 2 days of simulation took only a bit more than 4 hours of computer time It should be noted that most of this speed up is actually due to using a stronger machine equipped with an Intel 13 processor with 16GB of random access memory RAM Nothing was changed for the coarser model The water level for the entire domain was at 0 m for
35. s Monthly Weather Review 127 1999 pp 1928 1936 3 J M BECKERS H BURCHARD J M CAMPIN E DELEERSNIJDER AND P P MATHIEU Another reason why simple discretizations of rotated diffusion operators cause problems in ocean models Comments on isoneutral diffusion in a z co ordinate ocean model American Meteorological Society 28 1998 pp 1552 1559 4 T BELL Lee waves in stratified flows with simple harmonic time dependence Journal of Fluid Mechanics 67 1975 pp 705 722 5 J BERNSTEN Internal pressure errors in sigma coordinate ocean models Journal of Atmospheric and Oceanic Technology 19 2002 pp 1403 1414 6 A F BLUMBERG AND G L MELLOR Modelling vertical and horizontal diffusivities with the sigma co ordinate system Monthly Weather Review 113 1985 p 1379 7 D B CHADWICK I RIVERA DUARTE G ROSEN P WANG R C SANTORE A C RYAN P R PAQUIN S D HAFNER AND W CHOI Demonstration of an integrated compliance model for predicting copper fate and effects in dod harbors Project ER 0523 SPAWAR 2008 8 T CHRISTIANSEN P WIBERG AND T MILLIGAN Flow and sediment transport of a tidal salt marsh surface Estuarine Coastal and Shelf Science 50 2000 pp 315 331 9 B CUSHMAN ROISIN ntroduction to Geophysical Fluid Dynamics Prentice Hall Engelwood Cliffs 1994 10 DELTARES Delft3D FLOW User Manual Delft the Netherlands 2011 11 Delft3D Installation Manua
36. ta of the interior of the bay thanks to the high resolution bathymetry contour lines provided to us by the US Navy Without this data set this project would have been impossible The contour lines were interpolated using ILWIS and ArcGIS software to a 5 m spatial resolution grid Throughout this thesis we refer to this data set as SDBathy SDBathy was combined with the USGS s Southern California bathymetry using ArcGIS 9 3 software SDSU License Figure 1 3 As can be seen in Figure 1 3 the Navy s data does not match the USGS data set at the entrance to the bay However as this discrepancy did not appear to have much of an impact on the hydrodynamic model it was decided to take no action Later it is shown that even with this discrepancy our Tijuana Data SIO NOAA U S Navy NGA GEBCO Data E 2012 Google Google garth lat 32 646400 lon 5117 239357 elev 58 ft Eye alt 2821 mi Imagery Date 8 23 2010 Figure 1 2 San Diego Bay nested model was able to perfectly match changes in the water elevation within San Diego Bay 225 El Cajon a A AD o Data SIO NOAA U S Navy NGA GEBCO 2012 Google Data USGS Goosle earth Imagery Date 8 23 2010 32 39 18 97 N 117 10 44 35 W elev 15 ft Eye alt 35 64 mi Figure 1 3 San Diego Bay bathymetry constructed by combining USGS Southern California bathymetry and a private data set The SDBathy data set shows that the San Diego Ba
37. tations throughout the entire simulation time The San Diego station is located well inside the bay and neither the grid resolution nor the accuracy of the GEBCO bathymetry is capable of representing the location of the station properly Therefore it was not a surprise to get poor results for the San Diego station In fact this result was expected However the problem with the Santa Monica station is due to the inaccuracies in the GEBCO bathymetry data close to the coast The maximum water level reached only 1 m therefore throughout the simulation only a few cells changed their wet and dry WD status A stronger wave front is required to perform the water surge analysis Although only a few cells changed their WD status it was 23 sufficient to check whether Delft3D produces any wiggles in the solution As expected Delft3D did not introduce any wiggles into the solution WL P NW La Jolla Scripps Institution Wharf California gt o T D gt gt KT Econ 1 5 1 1 1 1 1 20 Jun 22 Jun 24 Jun 26 Jun 28 Jun 30 Jun time gt Figure 4 2 Changes in the water level at the La Jolla station Delft3D output blue line and station value red line WL Long Beach Terminal Island California gt 1 5 1 1 1 1 1 10 Jun 12 Jun 14 Jun 16 Jun 18 Jun 20 Jun time Figure 4 3 Changes in the water level at the Long Beach station Delft3D output blue line and station val
38. te ee dM MM Hue d ar dE vi LIST OE FIGURES tad ds dro emen em ad PETI UNS RUN TU I Puer gu S ix ACKNOWLEDGMENTS Aas desse Se tede pod adi en da IS OE xi CHAPTER I INTRODUCTIONS SR aq sa inva e bap a intr dta Pun dE M de su ai d 1 Mal MOOD sl MR en det Re oe E ete hee ke he ue 2 LE SU AT A MR D TD ees cane eee Mees ee S 3 2 DELFT3D MODEL DESCRIPTION 6 2 1 Delft3D Grid and Coordinate System 6 O 6 A Verucal Grid A INE TURF eee ee ALT arr 7 2 1 3 Staggered Grid Rep hisser 8 22 Goyernime Equis de 9 22 1 COM QUAL ORs iuc tox Coda t e E rede Cae tue reed eR ets 9 2 2 Momentum Equation in Horizontal Direction 10 2 2 3 Vertical Velocity ii o av fe Re A Re 10 2 241 Hydrostatic Pressure ie a etu AR pex E n EAR ARES 11 2 9 Honzont l SOS OS uet It tes cee Com AN eruta eut e tue ad 11 2 2 06 Equation Of Stale ssa eee Ree Bee Bee 11 24 Bed Shear Stress Ji cis cee er ne dr ode dn UAR RA NT esd 12 2 3 Time and Spatial Discretization need nee es 13 S INSTALLATION E ee 14 SA Deltt3D eie EIS OBAT A 14 3 1 1 Obtaining the Source Code uri IIo desees a das ue ax Panes Se dose gis 15 3 1 2 Compilng Delft D ed cod e eI e ETE HER UE ER E RARE eee pea EE 16 Sal Testne Wet 2 03 26sec E E POE Ue um WU E e UE eas 17 3 14 Delft3D GUL vais acs aiaee EE a et de eee 17 3 2 Delft Dashboatd ott ne RE ERE
39. ter time therefore the model has not yet gone through the complete spin up time However the water level profile during this period still matches relatively well with those of the San Diego Bay station Figure 4 12 The velocity field is shown in Figure 4 13 WL 06 0 47 0 2 if 02r E 0 4r San Diego San Diego Bay California gt 0 8 L L 1 Oh 6h 12h 18h time gt Figure 4 12 Changes in the water level during the first day of simulation Delft3D output blue line and station value red line 30 depth averaged velocity magnitude m s 01 Jan 2008 23 59 59 x10 58 Je Uu 18 je Y gt E z 10 AAA ee An Samen 77 bi cans 7 7 7 p A le I A x Eh VVS TUS pu uu 4 AP R EL He T Tr Mp SSII o ET D 2 os A to o m e e E e o e e a lt w ejeuip1ooo A x10 x coordinate m gt Figure 4 13 Velocity vectors in high resolution San Diego Bay Model 31 CHAPTER 5 NESTED SAN DIEGO BAY MODEL In previous chapter two different single domain model were presented Although both single domain models have their own applications it is recommended to generate a nested model i e a fine resolution model nested inside a coarse resolution model Nesting has many benefits including a better and more realistic boundary conditions provided for fine resolution model As before first the model setup is discussed Later the model outputs are presented a
40. the coarse Southern California model yellow boundary CHAPTER 2 DELFT3D MODEL DESCRIPTION This chapter is devoted to explaining the coordinate system governing equations and numerical schemes used in the Delft3D model This chapter only focuses on those aspects of Delft3D that have been used in this project however Delft3D is a very comprehensive model and includes many modules and features for use in different modeling scenarios and hydraulic structures For a full description of the model refer to the Delft3D Flow User Manual 10 2 1 DELFT3D GRID AND COORDINATE SYSTEM One must first select a coordinate system in order to represent a physical space or domain There are many choices available ocean modeling usually requires one approach to represent the horizontal direction and another to represent the vertical direction The horizontal grid can affect the stability of the numerical scheme and how well the lateral boundaries are represented However the vertical boundary is also very important as most of the parameterizations of the model are affected by the choice of vertical grid 2 In this section the different choices available in Delft3D for coordinate systems are discussed 2 1 4 Horizontal Grid In general for the horizontal direction Delft3D supports an orthogonal curvilinear coordinate system Two options are available e Cartesian coordinates n Figure 2 1 A e Spherical coordinates A Rectangu
41. the shoreline was included The model developed for this project covers the entirety of Coronado Island and is capable of performing both wetting and drying Only regions with a ground elevation exceeding 20 m were set as always dry 1 2 STUDY AREA The study area in this project is limited to Southern California Figure 1 1 and the San Diego Bay San Diego Bay is located at roughly 32 39 57 N and 117 8 22 W gt It is approximately 17 km long with a maximum curved path of roughly 22 km The width of the bay varies its widest part is approximately 3 7 km and it narrows down in the middle to 0 7 km The San Diego Bay s mouth is about 1 8 km wide shrinking immediately down to about 0 6 km Figure 1 2 Data SIO NOAA U S Navy NGA GEBCO Image 2012 TerraMetrics 2012 Google 3 b gt 2012 INEGI 8 Google earth 8 Ne lat 32 606899 lon 118 513346 elev 1193 ft Ey alt 637 32 mi Figure 1 1 Southern California The first item needed to create any ocean model is the bathymetry Depending on the resolution of the model the resolution of the bathymetry data set can also change There was no public data set available that included proper bathymetry information for the interior of the San Diego Bay as all public data sets were either too coarse to cover the bay or the maximum depth inside the bay was erroneously shown to be a mere 1 m However we were fortunate enough to have access to high resolution bathymetry da
42. these regions vertical velocity plays an important role in mixing and even in the carrying of the energy 1 4 9 14 21 33 40 41 42 Despite some of the limitations of nonlinear shallow water equations they can be still used for many applications In fact the majority of ocean models currently available use this set of equations The following reviews only the most important set of equations in Delft3D which were used in this project As mentioned before Delft3D has many other modules and capabilities For further information including the governing equations for those modules refer to the Delft3D Flow User Manual 10 2 2 1 Continuity Equation The depth averaged continuity equation with source and sink terms in Delft3D is written as follows a 1 d QU GS 1 d QV Ge Q 03 Ot 4 Gee Gag o V Gee V Gm on where e Gee and G are coefficients used to transform curvilinear coordinates to rectangular grid 10 e U and V are the depth integrated velocity in computational domain e Q is the source sink term which is defined as follows 0 Q uj din dou do P E 2 4 E In Equation 2 4 H d G P is the precipitation E is the evaporation qin is any source of water and qow is any sink for water such as an intake of power plant for its cooling system 2 2 Momentum Equation in Horizontal Direction The momentum equation can be written as Ou u u U u
43. toring stations are used to control the performance of the model It was decided to record all model outputs every 30 minutes at each of the monitoring stations This output was stored in a file known as the history file in Delft3D Furthermore every 6 hours the entire model output at each of the locations was stored on the hard disk This is known as the map file in Delft3D and is the largest output file The total storage for the map file was more than 650 MB It was also decided to store a restart file every 30 days 4 1 2 Model Results The low resolution Southern California model took slightly more than 4 hours to simulate a 6 month time period on an Intel 13 system it takes about 2 hours The model started at a zero water level everywhere but gradually began to adapt itself to the changes and the real profile of the water level The water level comparison is shown in Figure 4 2 Figure 4 3 Figure 4 4 Figure 4 5 and Figure 4 6 for the tide stations in La Jolla Long Beach Los Angeles Newport Beach and Santa Barbara respectively The blue line is the Delft3D output and the red line is the tide station output As can be seen Delft3D consistently under predicts the extremums of the water level by only few centimeters however this is within acceptable range However Delft3D was completely unsuccessful in estimating a proper water level for the San Diego Bay and Santa Monica stations The calculated water level is equal to zero for both s
44. ue red line 05r 0 5F Los Angeles outer harbor California gt o T AN WL 24 1 5 1 Jun 1 3 Jun L 7 Jun time gt 1 9 Jun 11 Jun Figure 4 4 Changes in the water level at the Los Angeles station Delft3D output blue line and station value red line 17 0 8r 06r 04r 0 27 o 0 2F 0 45 0 6r 0 8r Newport Beach Newport Bay Entrance Corona del Mar California gt WL E 1 10 May 1 12 May L 14 May L 16 May time gt E 1 18 May 20 May Figure 4 5 Changes in the water level at the Newport station Delft3D output blue line and station value red line 25 WL tr 08r 0 6H 0 4 0 2 0 2r 04 0 8r Santa Barbara Pacific Ocean California gt 1 1 fi 1 1 1 18 Apr 20 Apr 22 Apr 24 Apr 26 Apr 28 Apr time gt Figure 4 6 Changes in the water level at the Santa Barbara station Delft3D output blue line and station value red line Figure 4 7 Figure 4 8 Figure 4 9 and Figure 4 10 show a time series of how the velocity changes in Southern California Throughout the day except around noon the dominant direction of the velocity is from north to south as expected for Southern California It should be noted that the model is only forced with tidal forces at the boundary and no wind forcing has been set 2
45. ugh the hurdles of modeling with data assimilation San Diego Bay is not large thus except in severe storm situations wind stress plays little to no role in the hydrodynamics of the bay Moreover San Diego bay is well shielded by Coronado Island and its surrounding topography which causes further reduction of the wind speed and therefore wind stress making wind less effective inside of the bay Due to certain structures i e wave breakers at the bay s entrance Figure 6 1 the bay is also relatively protected against high waves from the Pacific Ocean However it is still recommended to add wind stress as a forcing factor in the model in order to determine whether this further reduces any error in the simulated water level It should be noted that though the results obtained in this project are within the range of acceptable error due to the lack of time available it was decided not to include the force of the wind moreover it was not possible for the author to obtain high resolution wind data for the model developed here Figure 6 1 The San Diego Bay s entrance and structures protecting the bay 36 BIBLIOGRAPHY 1 M ABOUALI AND J E CASTILLO Unified curvilinear ocean atmosphere model ucoam vertical velocity case study Mathematical and Computer Modelling doi 10 1016 mcm 2011 03 023 2011 2 A ADCROFT AND J MARSHAL new treatment of the coriolis terms in c grid models at both high and low resolution
46. ur projects I also want to thank my parents Parvin Arvaneh and Hossein Abouali for their unconditional love Despite being physically far away they kept encouraging me to invest in higher educations They have devoted their life to their children and there is no word to thank them properly I also want to thank my sister Azadeh Abouali for her support even from the far distance The last but not the least I want to thank my girlfriend Golnaz Badr for her endless love and enduring support She does a wonderful job in motivating me to proceed and advance in my life I want to thank her for standing by me and helping me through life CHAPTER 1 INTRODUCTION San Diego Bay like all bays provides dual usage for both commercial shipping and recreational activities San Diego Bay is also the home of one of the largest naval bases in the United States and a significant number of military activities occur there including training of the US Navy SEALs SEa Air Land teams Many changes have been made to the bay since 1962 when the Port of San Diego was established to make more land available for commercial and recreational activities For example most of the available marshland and more than half of all intertidal lands were reclaimed by 1975 30 Since the establishment of the Port of San Diego the region has grown extensively adding facilities such as a landmark convention center luxury hotels parks and cruise and cargo terminals Such
47. urant number for advection For further details please see the above mentioned references 14 CHAPTER 3 INSTALLATION In this chapter the general outline of installing both Delft3D and Delft DashBoard DDB is explained Delft3D is available on both Linux and Windows machines Both Delft3D and DDB are open source and are available freely for download The prerequisite packages and software will be also listed in this chapter 3 1 DELFT3D Delft3D is a modular open source code developed by Deltares and provides an integrated framework for a multi disciplinary approach to creating 3D computer simulations for rivers lakes and coastal and estuarine areas 11 Despite its name Delft3D is capable of simulation in both 3D and 2D in 2D cases shallow water equations are solved Shallow water equations are derived by integrating Navier Stokes equations in the vertical direction Delft3D can be used in various areas of application such as 10 Tide and wind driven flows i e storm surges Stratified and density driven flows River flow simulations Simulations in deep lakes and reservoirs Simulations of tsunamis hydraulic jumps bores and flood waves Freshwater river discharges into bays Salt intrusion Thermal stratification in lakes seas and reservoirs Cooling water intakes and wastewater outlets Transport of dissolved material and pollutants Online sediment transport and morphology Wave driven currents Non h
48. uthern California coarse model on Feb 1 2008 at 06 00 erts quur Op e oe RE pe ale desse nt Ses 26 Figure 4 9 Velocity vectors in Southern California coarse model on Feb 1 ZOOS ACI 200 siemens evar anand waged A rng etr biens 21 Figure 4 10 Velocity vectors in Southern California coarse model on Feb 1 2005 ACIS a a Me MU NE 27 Figure 4 11 High resolution San Diego Bay model seeeeeeeeeeeeeeeeeee 28 Figure 4 12 Changes in the water level during the first day of simulation Delft3D output blue line and station value red line 20 Figure 4 13 Velocity vectors in high resolution San Diego Bay Model 30 Figure 5 1 Changes in the water level at the San Diego bay station for the nested model during the first two days of the simulation Delft3D output blue line and station value red line esses 32 Figure 5 2 Changes in the water level at the San Diego Bay station Nested San Diego Bay model blue line and single domain San Diego Bay model dashed fed ne A dater in as 33 Figure 6 1 The San Diego Bay s entrance and structures protecting the bay 35 xi ACKNOWLEDGMENTS The best is usually kept for the last and perhaps that s the reason that the acknowledgements is the last part that gets written in any thesis I enjoy writing the acknowledgments not just because I get a chance to thank people who helped me to succee
49. y reaches a maximum depth of 72m A clear navigation channel is visible inside the bay which is designed to provide easy access for large ships and submarines going into and out of the bay At certain positions 5 further unnatural bathymetry is seen these positions are believed to be where submarines are located It should be noted that San Diego Bay is home to one of the largest naval bases in the United States and a significant amount of activity occurs there The goal here is to develop a high resolution model of the San Diego Bay nested inside a model of Southern California using Delft3D This model should be able to predict the tidal wave and water level as precisely as possible It should also be able to perform wet and dry computations i e depending on the depth of the water it should be able to calculate what part of the land is going to be underwater and what part will stay dry Such schemes usually introduce a significant number of oscillations wiggles in the water level calculations Therefore we will also check if Delft3D is able to produce an oscillation free solution Approximate boundaries for the larger Southern California model and the detailed model of the San Diego Bay are shown in Figure 1 4 In later chapters the full information for each grid will be provided lat 33 179112 lon 118 916477 5085 ft Eye alt 312 33 mi Figure 1 4 Approximate outline of the detailed San Diego Bay model red line nested inside
50. ydrostatic flows Delft3D can handle rectangular rectilinear and curvilinear grids However in the vertical direction it supports only sigma coordinates and Z levels Delft3D is a modular code and can be coupled with other models such as ecological and biological models There are 15 many utilities developed for Delft3D in order to facilitate both the preprocessing and post processing steps of a simulation task The followings are a subset of these utilities which are widely used e Delft3D RGFGRID This tool can be used to generate curvilinear grids e Delft3D QUICKIN This tool can be used to manipulate grid oriented data such as bathymetry or initial conditions e Delft3D NESTHD This tool can be used to generate boundary conditions while nesting two different models e Delft3D QUICKPLOT This tool which is mainly generated using MATLAB can be used to visualize the model output e Delft DashBoard This tool is also developed in MATLAB and can be used for the preprocessing step Delft DashBoard has access to many online databases and facilitates the setup of a model e OpenDA Originally developed in Java this tool can be used for data assimilation using Delft3D and other programs that support the OpenDA standard 3 1 1 Obtaining the Source Code Deltares decided to make the full source code of Delft3D FLOW including the morphology and Delft3D WAVE Engines available to the public under GPLv3 conditions In
51. ysical Data Center NGDC Coastal Relief Model e Shuttle Radar Topography Mission SRTM v4 1 Only Land data e United State Geological Survey USGS Hawaii e USGS San Francisco Bay e USGS Southern California e Rijks Water Staat e Southeastern Universities Research Association SURA Gulf of Mexico e European Marine Observation and Data Network EMODnet Adriatic Sea Ionian Sea Central Mediterranean e EMODnet Aegean Sea Levantine Sea e EMODnet Bay of Biscay Iberian Coast e EMODnet Celtic Seas e EMODnet Greater North Sea e EMODnet Western Mediterranean e Marine Scotland West of Lewis The user can also import his her own bathymetry into the DDB It should be noted that in this project we made use of a very high resolution bathymetry data that was made 19 available to us for the San Diego Bay Outside of the bay we made use of the GEBCO bathymetry data A screen shot of Delft Dashboard is shown in Figure 3 1 li alelx Fie Todbax Modd Doman Bathymetry Wew Coordnate System Optore Heb gt e km Teemax Dosentin indbons Boundaras Phys Parme Num Faramat recharges Manitoring Addtianai Output i Figure 3 1 DelftDashboard screen shot The Delft Dashboard DDB binaries can be downloaded from the following link https publicwiki deltares nl display OET DelftDashboard Once the binaries are obtained the installation is fairly straightforward Although the D
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