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Flow and Hydrography in a Semiarid Bay of the Gulf of California

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Title:
Flow and Hydrography in a Semiarid Bay of the Gulf of California
Creator:
Miskel, Patrick G
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (116 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Coastal and Oceanographic Engineering
Civil and Coastal Engineering
Committee Chair:
VALLE-LEVINSON,ARNOLDO
Committee Co-Chair:
SLINN,DONALD NICHOLAS
Graduation Date:
12/19/2014

Subjects

Subjects / Keywords:
Atmospheric temperature ( jstor )
Current density ( jstor )
Ellipses ( jstor )
Goodness of fit ( jstor )
Gyres ( jstor )
Latitude ( jstor )
Least squares ( jstor )
Salinity ( jstor )
Temperature distribution ( jstor )
Velocity ( jstor )
Civil and Coastal Engineering -- Dissertations, Academic -- UF
hydrography -- nyquist -- salinity -- semiarid -- semienclosed
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Coastal and Oceanographic Engineering thesis, M.S.

Notes

Abstract:
To better understand coastal conditions in a semienclosed basin within the Gulf of California, Acoustic Doppler Current Profiler (ADCP) and Conductivity-Temperature-Density (CTD) data were collected in March of 2005 within Bahia Concepcion, then analyzed using MATLAB processing methods. First, current systems are analyzed through processing of the ADCP data by removing bad data, applying a Joyce correction to adjust for survey boat velocity, then calculating a least squares fit of the sample velocities to an assumed K1 and M2 tidal harmonic to adjust for tidal variations. Second, salinity, density, and temperature conditions are analyzed from the CTD data and correlated to current and bathymetric features in the bay. Third, a tidal analysis is performed by calculating a statistical goodness of fit between the observed and predicted velocities to quantify reliability of the results. Contours of tidal component amplitude are compared to those of current magnitude and direction, salinity, temperature, and density. Illustrations of tidal ellipses are constructed to better visualize the magnitude and orientation of tidal flow. The large spatial extent of the data collected for this study allows for confirmation and further analysis of findings from previous studies of Bahia Concepcion. It is shown how the cyclonic gyre located at the southern end of the bay varies throughout full depth. Along-bay density gradients are quantified and compared to density variations with depth to understand their influence on current systems. Density variations are shown to correlate more closely with temperature than salinity. Lastly, a previously identified decrease in tidal influence toward the head of the bay is calculated and mapped. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: VALLE-LEVINSON,ARNOLDO.
Local:
Co-adviser: SLINN,DONALD NICHOLAS.
Statement of Responsibility:
by Patrick G Miskel.

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UFRGP
Rights Management:
Copyright Miskel, Patrick G. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
974373190 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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FLOW AND HYDROGRAPHY IN A SEMIARID BAY OF THE GULF OF CALIFORNIA By PATRICK GLENDON MISKEL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2014

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© 2014 Patrick Glendon Miskel

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To my mother and sister, for all their support

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4 ACKNOWLEDGMENTS I would like to thank my advisory professor Arnoldo Valle Levinson for offering to include me on this project and for guiding me through the analytical process over the past year and a half. Jorge Armando Laur el was very helpful and patient when offering ongoing assistance with processing in MATLAB ® . Jackie Branyon also assisted in the final review of the report. I would also like to thank my mentor, Ronald Noble, for providing me with ongoing inspiration and i nsight to the field of coastal engineering.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURE S ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 2 DATA TYPES AND ANALYSIS METHODS ................................ ............................ 18 Data Sampling ................................ ................................ ................................ ........ 18 Data Processin g ................................ ................................ ................................ ..... 20 3 ADCP DATA ANALYSIS ................................ ................................ ......................... 26 Flow Fields ................................ ................................ ................................ .............. 26 Transect Contours ................................ ................................ ................................ .. 28 4 CTD DATA ANALYSIS ................................ ................................ ........................... 45 Overview ................................ ................................ ................................ ................. 45 Geometric Variation ................................ ................................ ................................ 45 Depth Va riation ................................ ................................ ................................ ....... 47 Temporal Variation ................................ ................................ ................................ . 50 5 TIDES AND GOODNESS OF FIT ................................ ................................ ........... 68 Goodness of Fit ................................ ................................ ................................ ...... 68 Tidal Analysis ................................ ................................ ................................ .......... 70 6 CONCLUSION ................................ ................................ ................................ ........ 82 APPENDIX: MATLAB PROGRAMS DEVELOPED FOR THIS THESIS ........................ 84 PlotCircuitQuiver.m ................................ ................................ ................................ . 84 TidalEllipses.m ................................ ................................ ................................ ........ 87 PlotTransectContour.m ................................ ................................ ........................... 89 GoodnessOfFitContour.m ................................ ................................ ....................... 95

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6 Platin umVideo.m ................................ ................................ ................................ ..... 98 PlotAllCircuits.m ................................ ................................ ................................ .... 100 CTDPlotAll.m ................................ ................................ ................................ ........ 104 CTDTransectContour.m ................................ ................................ ........................ 107 CTDStationContour.m ................................ ................................ ........................... 112 LIST OF REFERENCES ................................ ................................ ............................. 115 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 116

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7 LIST OF TABLES Table page 2 1 Survey boat circuit times and number of repetitions. ................................ .......... 23

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8 LIST OF FIGURES Figure page 1 1 Map of Mexico ................................ ................................ ................................ .... 17 1 2 Map of Baja California Sur ................................ ................................ .................. 17 2 1 ADCP Trajectories and Transect Numerical Designations ................................ . 23 2 2 CTD Sample Locations and Numerical Designations ................................ ......... 24 2 3 Circuit A, Transect 1, Depth 10 [m] Leas t Squares Fit ................................ ........ 25 2 4 Sample Location For Figure 2 3 ................................ ................................ ......... 25 3 1 Velocity Vectors: 5 [m] Depth ................................ ................................ ............. 33 3 2 Circuit A Velocity Field at 5 [m] Depth ................................ ................................ 33 3 3 Circuit B Velocity Field at 5 [m] Depth ................................ ................................ 34 3 4 Circuit C Velocity Field at 5 [m] Depth ................................ ................................ 34 3 5 Circuit D Velocity Field at 5 [m] Depth ................................ ................................ 35 3 6 Circuit E Velocity Field at 5 [m] Depth ................................ ................................ 35 3 7 Circuit E Velocity Field at 10 [m] Depth ................................ .............................. 36 3 8 Google Earth Gyre Image ................................ ................................ ................... 36 3 9 Circuit A Transect 1: Speed of Mean Flow ................................ ......................... 37 3 10 Circuit A Transect 1: Direction of Mean Flow ................................ ...................... 37 3 11 Circuit B Transect 1: Speed of Mean Flow ................................ ......................... 38 3 12 Circuit B Transect 1: Direction of Mean Flow ................................ ...................... 38 3 13 Circuit C Transect 1: Speed of Mean Flow ................................ ......................... 39 3 14 Circuit C Transect 1: Direction of Mean Flow ................................ ..................... 39 3 15 Circuit D Transect 4: Speed of Mean Flow ................................ ......................... 40 3 16 Circuit D Transect 4: Direction of Mean Flow ................................ ..................... 40 3 17 Circuit E Transect 4: Speed of Mean Flow ................................ ......................... 41

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9 3 18 Circuit E Transect 4: Direction of Mean Flow ................................ ...................... 41 3 19 Location of the town of Mulegé ................................ ................................ ........... 42 3 20 Historical Wind Speed (Source: www.myweather2.com) ................................ .... 43 3 21 Annual Wind Direction Distribution (Source: www.windfinder.com) .................... 43 3 22 Depth Contour ................................ ................................ ................................ .... 44 4 1 Salinity at 10 [m] Depth ................................ ................................ ...................... 54 4 2 Temperature at 10 [m] Depth ................................ ................................ .............. 54 4 3 Density at 10 [m] Depth ................................ ................................ ...................... 55 4 4 Historical Atmospheric Temperatures (Source: www.myweather2.com) ............ 55 4 5 Circuit A, Transect 1: Salinity ................................ ................................ .............. 56 4 6 Circuit B, Transect 1: Salinity ................................ ................................ .............. 56 4 7 Circuit C, Transect 1: Salinity ................................ ................................ ............. 57 4 8 Circuit D, Transect 4: Salinity ................................ ................................ ............. 57 4 9 Circuit E, Transect 4: Salinity ................................ ................................ .............. 58 4 10 Circuit A, Transect 1: Temperature ................................ ................................ ..... 58 4 11 Circuit B, Transect 1: Temperature ................................ ................................ ..... 59 4 12 Circuit C, Transect 1: Temperature ................................ ................................ .... 59 4 13 Circuit D, Transect 4: Temperature ................................ ................................ .... 60 4 14 Circuit E, Transect 4: Temperature ................................ ................................ ..... 60 4 15 Circuit A, Transect 1: Density ................................ ................................ ............. 61 4 16 Circuit B, Transect 1: Density ................................ ................................ ............. 61 4 17 Circuit C, Transect 1: Density ................................ ................................ ............. 62 4 18 Circuit D, Transect 4: Density ................................ ................................ ............. 62 4 19 Circuit E, Transect 4: Density ................................ ................................ ............. 63 4 20 CTD Station 3: Salinity ................................ ................................ ....................... 63

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10 4 21 CTD Station 16: Salinity ................................ ................................ ..................... 64 4 22 CTD Station 27: Salinity ................................ ................................ ..................... 64 4 23 CTD Station 3: Temperature ................................ ................................ ............... 65 4 24 CTD Station 16: Temperature ................................ ................................ ............. 65 4 25 CTD Station 27: Temperature ................................ ................................ ............. 66 4 26 CTD Station 3: Density ................................ ................................ ....................... 66 4 27 CTD Station 16: Density ................................ ................................ ..................... 67 4 28 CTD Station 27: Density ................................ ................................ ..................... 67 5 1 Circuit A Transect 1, 10 [m] depth: K1 & M2 Frequency ................................ ..... 73 5 2 Circuit E Transect 4, 10 [m] depth: K1 & M2 Frequency ................................ ..... 73 5 3 K1 & M2 Frequency Goodness of Fit: 10 [m] depth ................................ ............ 74 5 4 K1 Tidal Frequency Goodness of Fit: 10 [m] depth ................................ ............ 74 5 5 M2 Tidal Frequency Goodness of Fit: 10 [m] depth ................................ ............ 75 5 6 Circuit A Transect 1: Amplitude of K1 Tidal Cu rrent ................................ ........... 75 5 7 Circuit A Transect 1: Amplitude of M2 Tidal Current ................................ ........... 76 5 8 Circuit B Transect 1: Amplitude of K1 Tidal Current ................................ ........... 76 5 9 Circuit B Transect 1: Amplitude of M2 Tidal Current ................................ ........... 77 5 10 Circuit C Transect 1: Amplitude of K1 Tidal Current ................................ ........... 77 5 11 Circuit C Transect 1: Amplitude of M2 Tidal Current ................................ .......... 78 5 12 Circuit D Transect 4: Amplitude of K1 Tidal Current ................................ ........... 78 5 13 Circuit D Transect 4: Amplitude of M2 Tidal Current ................................ .......... 79 5 14 Circuit E Transect 4: Amplitude of K1 Tidal Current ................................ ........... 79 5 15 Circuit E Transect 4: Amplitude of M2 Tidal Current ................................ ........... 80 5 16 Circuit B Tidal Ellipses at 5 [m] Depth ................................ ............................. 80 5 17 Circuit C Tidal Ellipses at 13 [m] Depth ................................ ........................... 81

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11 LIST OF ABBREVIATIONS ADCP Acoustic Doppler Current Profiler CTD Conductivity Temperature Density s Second hr Hour GMT Greenwich Mean Time cm Centimeter m Meter km Kilometer N North S South E East W West PSU Practical Salinity Units C Celcius kg Kilogram

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12 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FLOW AND HYDROGRAPHY IN A SEMIARID BAY OF THE GULF OF CALIFORNIA By Patrick G lendon Miskel December 2014 Chair: Arnoldo Valle Levinson Major: Coastal and Oceanographic Engineering To better understa nd coastal conditions in a semi enclosed basin within the Gulf of California, Acoustic Doppler Current Profiler (ADCP) and Conductivity Temperature Density (CTD) data were collec ted in March of 2005 with in Bahía Concepción, then analyzed using MATLAB ® processing methods. First, current systems are analyzed through processing of the ADCP data by removing bad data, applying a Joyce c orrection to adjust for survey boat velocity , then calculating a least squares fit of the sample velocities to an assumed K1 and M2 tidal harmonic to adjust for tidal variations. Second, salinity, density, and temperature conditions are analyzed from the CTD data and correlated to current and bathymet ric features in the bay . Third, a tidal analysis is performed by calculating a statistical goodnes s of fit between the observed and predicted velocities to quan tify reliability of the results. C ontours of tidal component amplitude are compared to those of current magnitude and direction, salinity , te mperature, and density. I llustrations of tidal ellipses are constructed to better visualize th e magnitude and orientation of tidal flow.

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13 The large spatial extent of the data collected for this study allow s for confirmation and further analysis of findings from previous studies of Bahía Concepción. It is shown how the cy c lonic gyre located at the southern end of the bay va ries throughout full depth. A long bay density gradients a re quantified and compared to density variations with depth to understand their influence on current systems . Density variations are shown to correlate mo re closely with temperature than salinity. Lastly, a previously identif ied decrease in tidal influence toward the head of the bay is calculated and mapped.

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14 CHAPTER 1 INTRODUCTION Bahía Concepció n is an elongated, semi enclosed bay located in the Mexican state of Baja California Sur , opening to the Gulf of California ( Figure 1 1 ). Despite the fact that Bahía Concepción is one of the largest bays in the region, the area surrounding the bay is largely uninhabited by humans. With minimal nearby development, Bahía Concepción is a popular travel destination for those attracted to its natural beauty. Bahía Concepció n also contains diverse marine wildlife including clams, oysters, scallops , and over 900 fish species . from the Gulf of California . As a result, the extensive commercial fishing has adversely affected the wildl ife ecosystem s . U nsustainable human impacts pose risks to species such as the vaquita, which exist s only in the Gulf of California and is considered to be one of the most highly endangered marine mammals in the world . ecological condition is largely dependent on coastal conditions, such as the rate/degree of water exchange between the basin and the adjacent gulf/ocean (Ponte et al . 2012 , p. 940 ). A goal of this study is that findings may assist in atte mpts to preserve the state of Bahía Concepción and other similar bays around the world . As shown in Figure 1 2 , Bahía Concepción opens on the eastern coast of the Baja California peninsula to the Gulf of California, which extends to the Pacific Ocean at 22 ºN latitude. The centroid of the bay is located at 111.82 ºW longitude and 26.69 ºN latitude, and spans roughly 40 km in length by 5 10 km in width. Depths along lateral (east west) transects typically range from 15 to 30 meters. The region within the vi cinity of Bahía Concepción is arid, historically experiencing less than 250 mm yr 1 of rain, and averaging 1 day of precipitation per

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15 month between March and June. Daily average relative humidity ranges from 40 60% throughout the year. Temperatures range from an average high around 35 ºC during the summer months to an average low of 11 ºC in December and January. For this study , ADCP and CTD data collected within Bahía Concepción are analyzed using MATLAB ® processing methods. This study builds upon previou s research of Bahía Concepción by further analyzing observations of flow patterns , tides, and variations in temperature , salinity , and density stratification. Specifically, Caliskan et al. (2008), Cheng et al. (2010), Ponte et al. (2012), and Winant et al. (2013) provide observations a n d predictions of the aforementioned conditions and what factors influence their variations. This study builds upon those previously performed by analyzing a more spatially expansive data set. The trajectory of the survey boat encompasses a plan view area of the bay from the mouth to the head at full bay width , spatial extent allows for interpolation of conditions throughout the entire bay in both area and in depth, pro viding a previously non existent 3 dimensional mapping of Bahía Concepción . R elationships between current speed and direction , salinity, temperature, density, and tidal influence identified in this study will be compare d to the findings in the aforementioned papers. Specific goals are to better understand the cyclonic gyre identified at the southern end of the bay at full depth, describe the distribution of density throughout the bay, identify influences for densi ty gradients, correlate density gradients to current speed and direction, prove that tidal influences are minimal in the bay and decrease toward the head, and provide an effective 3 dime nsional mapping of conditions throughout the bay.

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16 C onditions throughou t the bay vary significantly d ue to influences from wind patterns , bathymetric non uniformities , tides, etc . The following chapter s will fully map these variations in conditions to better und erstand how they relate to each other and where they arise from . Findings will provide general insight to influences on coastal conditions within a semienclosed basin, and may function as a basis of comparison for future studies looking to validate results of models , or to document variations in conditions within Bahía Concepción over a different period of time.

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17 Figure 1 1. Map of Mexico Figure 1 2. Map of Baja California Sur

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18 CHAPTER 2 DATA TYPES AND ANALY SIS METHODS Data Sampling Between March 10 and March 16, 2005 ADCP and CTD data w ere collected throughout Bahía Concepción by t Sproul ship . Figure 2 1 shows the 5 circuits correspond ing to the trajectories of the survey boat over the 5 day sample period . Along these circuits , ADCP data was collected continuously in 20 second intervals , and samples of CTD data were collected intermittently by stopping the survey boat represented by the black dots in Figure 2 2. E ach edge of a circuit is refe Circuits A, D, and E each have 4 transects, and Circuits B and C each have 6 transects. The followed the trajectory of each circuit continuously in repetition s for roughly 24 hours to obtain multiple sample s at any given location . These paths follow a clockwise trajectory in the case s of Circuits A, D, and E, and cross from c lockwise to counterclockwise along Circuits B and C. The measurement method applied was a towed ADCP in 1 me ter bins up to 40 m eters deep . The entire data collection for this study corresponds to March 11 th and March 24 th , 2005. The data collection schedule for each circuit is l isted in Table 2 1 . It is important to note the time scale of the data collected. All circuits were surveyed over a roughly 24 hour period to include a full diurnal tidal cycle , and ranged from 22 hours and 45 minutes (Circuit A) to 24 hours and 50 minute s (Circuit D). Surveying any less than this period would not provide an adequate sample range to

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19 sufficiently determine the diurnal tidal influence on currents, temperature, etc. The time period over which the data w as collected can be considered short enough that influences from seasonal changes, such as dominant wind direction , d o not need to be considered . Although, there wa s a certain degree of influence from variations in hourly/daily wind speeds , atmospheric tempe rature , etc. that could not be adjusted for . The maximum number of repetitions that a single transect was surveyed is 10. In the case of Circuit A, a 22 hour and 45 minute survey time with 8 repetitions results in a mean sample repetition time step of hours. This corresponds to a Nyquist Frequency of cycles per hour, or a period of hours. The Nyquist Frequency is the theoretical highest frequency that can be resolved given a sample interval. In practi ce, for a sinusoidal type oscillation, it is desired to have a minimum of 2 sample intervals (3 data points) over the oscillation period. Over the 24 hour period that each circuit was sampled, 2 full semidiurnal cycles are expected, each requiring 3 data points for a total of 6 samples over time for each sample location for each circuit. The minimum number of samples taken along any transect was 7, meaning that a sufficient number of samples was taken to de tide the ADCP data for both the K1 (diurnal) and M2 (semidiurnal) harmonic frequencies to properly analyze currents in the bay , assuming no bad data . The 7 10 repetition sample size is close to the minimum of 6 needed for the M2 cycle. As a result , only a couple bad samples could induce significant inac c uracies when calculating tidal components from observed values . Because there is high sensitivity to bad data due to the limited sample size , i t s hould be expect ed that the results contain a certain degree of error . Throughout this study , the degree of er ror is

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20 both qualitatively and quantitatively considered when stating observations and findings. I f a more accurate understanding of conditions in a specific area of the bay is required, then future studies sh ould increase the number of samples in this case, transect repetitions over a single tidal cycle to obtain a more complete fit to the oscillatory data values . Unlike the ADCP sample time interval, the CTD sample time interval did not always sufficiently meet the minimum sample frequency required fo r de tiding semidiurnal frequencies, even in the ideal case where there is assumed to be no bad data in the samples. Each CTD station was sampled between 3 and 5 times. The case of 4 samples over 24 hours results in a Nyquist Frequency of cycles per hour , or a period of h ou r s . While this sample frequency is theoretically sufficient for applying a least squares fit to a semidiurnal harmonic, a higher frequency is generally recommended in practice ; even one errant sample value could completely skew the data. Because the Nyquist frequency for 4 samples corresponds to roughly a 12 hour period, it can be deduc ed that the stations with 3 samples over 24 hours do not have a theoretically sufficient sampli ng rate for satisfying the sampling criteria for a semidiurnal tidal frequency . As a result , the CTD data will only be de tided using t he diurnal K1 harmonic . Data Processing Processing of the ADCP and CTD data require d numerous steps. Most steps include d simple filtering of data, processes related to internal MATLAB ® organization of data structures, or basic princip les of mathematics and geomatics. These processes a re not complex enough to require a full explanation in this report, there fore only specific

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21 calculations will be described . Two advanced methods were applied, first to correct for the velo city of the survey boat included in the recorde d current velocity values, and second to obtain tidal component values. To adjust for survey boat velocity, a Joy ce correction (Joyce 1989 ) was applied using the following calculations: (2 1) (2 2) (2 3) (2 4) Where and represent the east and north velocity components , respectively , denotes bottom track velocity denotes ship velocity values denotes corrected values, and brackets denote average values , in this case for each transect repetition. caused by the intraday tidal oscillations . To de tide, a least squares fit method is applied to obtain the amplitude and phas e of the tidal component associated with each sample value. The least squares fit is calculated at each unique sample latitude longitude coordinate and depth by grouping all survey poin ts taken at that location over time , then fitting the m with a curve minimizing the su m of the squares of the error for each value . Once the current mean value , tidal amplitude , and tidal phase are obtained, values can be reconstructed for any point in time within the tidal cycle using the following equation:

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22 (2 5) Where represents mean flow, represents time , and is the total number of harmonics, each with a corresponding amplitude , frequency , and phase . Equation 2 5 specifically uses east component current velocity as an example, but the same formula is used to de tide north component current velocity , salinity, tempera ture, and density values . When applying this formula , K1 diurnal and M2 semidiurnal tidal frequencies a re assumed for Bahía Concepción. The process of fitting the data points with a curve is illustrated in Figure 2 3 , which shows ADCP data values surveyed at the location illustrated in Figure 2 4 .

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23 Table 2 1. Survey boat circuit times and number of repetitions. Circuit Date (2005) Time Start (GMT) Date (2005) Time End (GMT) # Repetitions A March 11 11:54 March 12 10:39 8 B March 12 14:54 March 13 14:00 10 C March 13 14:26 March 14 15:05 7 D March 14 16:00 March 15 16:50 8 E March 15 17:01 March 16 17:10 8 Figure 2 1 . ADCP Trajectories and Transect Numerical Designations

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24 Figure 2 2. CTD Sample Locations and Numerical Designations

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25 Figure 2 3. Circuit A, Transect 1, Depth 10 [m] Least Squares Fit Figure 2 4. Sample Location For Figure 2 3

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26 CHAPTER 3 ADCP DATA ANALYSIS In this chapter , current conditions observed throughout Bahía Concepción over the 5 day sample period ar e analyzed. Factors such as wind speed and bay bathymetry will be cor related to current speed and direction at different locations in the bay to better un derstand the various influences on current system s . Flow Fields To visualize the current flow field in Bahía Concepción , velocity vector plots are constructed by applying the least squares fit method to the ADCP data . By s umming the mean current velocities with the tidal component amplitudes and phases associated with the K1 and M2 harmonics (Equation 2 5) , expected current vectors at a specific time within the tidal cycle can be illustrated throughout the bay, as shown in Figure 3 1 . This particular illustration depicts current conditions at a depth of 5 m during the flood tide into the bay. Flow speeds at this time appear to range between 5 and 15 cm s 1 . C urrent entering the bay has a rela tively uniform flow direction near the mouth, but south of the narrow region around 26.8 ºN latitu de discernible non uniform flow patterns develop . The flow characteristics for eac h circuit at a depth of 5 m are further illustrated in Figures 3 2 through 3 6 , where the uniformity of surface flow magnitude and direction a t Circuit A diminishes toward Circuit E at the head of the bay . The degree of non uniformity at each circuit will be further analyzed with depth below. Bahía Concepción view geometry is largely responsible for the generation of non uniform current flow patterns. Figure 3 1 illustrates how the geometry influences the magnitude and directio n of current velocity. Because of the boundary condition of zero flow through the land interface , flow is generally directed

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27 along the bay. Flow s peed increases at narrower region s of the bay , then slows at wider regions to conserve the volumetric flow rate. This conservation principle derives from the continuity equation, which takes the form when the boussinesq approximation of relatively small density changes in time and space is applied. H ere , , and represent velocities in the , , and direction, respectively. From the mass conservation principle, one can derive that volumetric flow rate is also conserved for a fluid of constant density, since . Volumetric flow of a fluid can be represented by the equation and has units of m 3 s 1 , where represents volumetric flow rate, represents velocity, and represents area . If the flow rate, , remains constant, then a decrease in bay cross sectional area, , must induce an increase in flow velocity, , as can be seen when comparing lateral cross sections of varying wid th in Figure 3 1 . Figure 3 1 shows the current generally flowing in a net along shore path in the upper half of the bay, corresponding to the orientation of the oscillatory tidal flow. C urrent entering the bay at the north end flows s outh s outh east, then at 26.8 ºN latitude is re directed s outh s outhwest, then returns to s outh s outheast at 26.7 ºN latitude. At each step of current re direction into the bay there is a discernible decrease in uniformity of flow , until reaching the southern end of the bay where a strong rotatio nal pattern develops to exchange between inflow and outflow. Figures 3 5 and 3 6 illustrate the rotational surface flow at Circuits D and E, located in the southern region of the bay closer to the head. Figure 3 8 is a satellite image from Google Earth looking north from the head of the bay at the southern end , and shows streak lines following this gyre . Because Bahía Concepción is located in the

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28 northern hemisphere, counter clockwise flow corresponds to the presume d flow direction induced by the Coriolis force. The flow cycle displayed at Circuit E can Th is cyclonic gyre has been identified and analyzed in previous studies of Bahía Concepción (Ponte et al. 2012; Winant et a l. 2013). Winant et al. 2013 states that cyclonic recirculation observed during With the more spatially expansive data set in this study, the gyre structure can be fully illustrated with depth. Figure 3 7 shows the same Circuit E location as Figure 3 6, but at a depth of 10 m rather than 5 m . Here it is shown that the cycl onic gyre persists , but does not remain uniform , at greater depths shallower region along the eastern edge of Circuit E, an interpolation of the velocity vector field can only be performed at up to 10 m, but contours of flow with depth along each transect will be shown below to better illustrate the cyclonic gyre. Various factors influencing t he counter clo ckwise direction of rotation , such as s geometric dimensions, have been identified in previous studies . Despite a cyclonic flow pattern, the direction of rotation is largely independent of influences from the Coriolis force because the bay is too shallow and small in area for the differences in rotational speed at one end v ersu s the other due to significant ly affect flow conditions. Findings from previous studies regarding influences on the cyclonic gyre will be analyzed results below . Transect Contours Figures 3 1 through 3 6 provide illustration s of surface currents, but do not consider variations with depth. To include a mapping of the depth dimension, c ontours

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29 of speed and direction of mean flow are illustrated along depth distance axes. These contours are shown in Figures 3 9 through 3 1 8 , where each transect cross section c orresponds to the northernmost lateral transect at each circuit. The mean values in these figures are the outputs of the least squares fit without the addition of the residual tidal flow components (i.e. without the summation term in Equation 2 5) . It shou ld be considered that these transects do not spatially align perfectly along equilateral east west cross sections , therefore the x axis of these contours is oriented with the left side of the plot (smaller values) more west than the right side , but representing the distance along the actual transect, rather than distance along an east west plane. Similar to the surface circulation patterns identified in Figure s 3 1 through 3 6 , the contour plots in Figures 3 9 through 3 18 reveal various sub s urface circulation patterns corresponding to exchange flow systems . These patterns are expected because, aside from the opening at the mouth of the bay, Bahía Concepción is an enclosed basin, therefore without considering temporary volumetric changes due t o wind setup, tidal oscillations, etc. there cannot be a net inflow to , or outflow from the bay. In other words, volumetric flow into the bay must be matched by returning volumetric flow out. Direction of Mean figures (Figures 3 10 , 3 1 2 , 3 1 4 , 3 1 6 , and 3 1 8 ) . At Circuits A, B, and C , net southward flow (into the bay) is concentrated in the shallower portion of the water column. Conversely, net northward flow (out of the bay) is concentr ated in the dee per portion of the water column. T ogether this flow structure represents vertically sheared exchange flow. At Circuits D and E there is a more defined area of net northward flow in

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30 the eastern portion of the bay, and net southward flow in the western portion of the bay, representing laterally sheared exchange flow. At Circuit B (Figure 3 12) the dominant mean flow direction in terms of area is north, whereas at Circuit A (Figure 3 10 ) the dominant direction is south. Figure 3 18 shows that the cyclonic gyre at Circuit E shown to exist at depth s of 5 and 10 m in Figures 3 6 and 3 7 exists throughout the ful l depth of this portion of the b ay , where a northward flow on the eastern porti on and a southward flow on the western portion of the cross section represent a counter clockwise rotation. A notable feature of the cyclonic gyre in Figure 3 18 is the large area of directly southward flow on the western end of the bay, but a shift from d ominant northwest to northeast direct ed flow with depth on the easte rn end . A unique exchange flow feature can be identified at Circuit C, where there appears to be a vertically sheared 3 layer structure of flow in the east west direction . The top of Figu re 3 14 shows a general net westward flow at depths less than 7.5 m, then a net eastward flow from 7.5 to 13 15 m, then regions of westward flow from 13 15 m to the bottom. A similar 3 layer vertical flow structure has been documented in other bays, and is theorized to lead to better flushing than the classical 2 layer estuarine circulation (Choi et al. 2003) . Further research would be useful for better understanding this flow structure. There is no clear and consistent relationship b etween current magnitude and direction in the bay. Each circuit appears to have only a small region where mean flow speed exceeds 10 m s 1 . R egions of high flow speed tend to appear at mid depth in the center of the bay or at the surface, as shown in Figur es 3 9 and 3 13 , respectively . T he

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31 surveyors specifically noted that high winds were experienced during the days that data for Circuits D and E were collected , which likely explains high surface speeds shown at Circuit E in Figure 3 17 . Wind speeds were es timated to persist at 12 m s 1 during sampling for Circuit D, and over 10 m s 1 during sampling for Circuit E. Wind forces generally ha ve a large influence on current conditions in Bahía Concepción (Cheng et al. 2010, p. 1243; Ponte et al. 2012, p.941) . Page 946 of P onte et al. (2012) identifie s Reliable wind data for Bahía Concepción can be obtained from the nearby Mulegé Airstrip, located in the town of Mulegé. As shown in Figure 3 19 , Mulegé Airstrip is located roughly 4.6 km west of the northwest corner of Circuit A. Wind data from this station in Figure 3 20 shows the historical average and maximum daily wind speed for each month of the yea r. Expected average wind speeds in March, when the data for this study was collected, are slightly higher than the months of October through January, and slightly less than the months of April through August. The dominant wind direction generally alternates from southeastward in the winter to nor th northwestward in the summer (Caliskan et al. 2008, p.1702). Wind data from Mulegé from 2012 to 2014 did not confirm these observed direction s , but do es show significant variation throughout the year. The wind rose in Figure 3 21 displays wind direction and speed from 2012 and 2014, and illustrates how wind direction can alternate throughout the year. These wind trends allow us to understand how current c onditions observed in this study may change in time . Due to s within the bay are influenced by bathymetry . Figure 3 22 shows depth variations throughout the

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32 bay. At latitudes higher than 26.7 ºN the bay is deeper along its eastern edge than its western edge, but at latitudes lower than 26.7 ºN the bay is deeper along its western edge. Lateral variations in bathymetry are most significant at Circuits B, C, and E. Generally, frictional effects from the bottom can influence both the magnitude and direction of flow throughout the bay. This effect cannot be clearly identified in the contours of mean flow speed. Specifically, Figure 3 11 shows relatively large flow speeds near the bottom along the easter n edge of Circuit B, and Figure 3 1 7 shows relatively large flows speeds (~10 cm s 1 ) in the shallower region along the eastern edge of Circuit E. From these observations it can be determined that bathymetric effects in certain regions of the bay have a le ss significant impact on currents than other factors, such as wind, density gradient s , etc. T his relativity is impossible to quantify from the illu strations in this chapter alone, therefore , i n the following chapter, influences from along bay density gradients, intraday variations in temperature , etc. will be analyzed and compared to the flow systems displayed in this chapter .

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33 Figure 3 1. Velocity Vectors: 5 [m] Depth Figure 3 2. Circuit A Velocity Field at 5 [m] Depth

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34 Figure 3 3. Circuit B Velocity Field at 5 [m] Depth Figure 3 4. Circuit C Velocity Field at 5 [m] Depth

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35 Figure 3 5. Circuit D Velocity Field at 5 [m] Depth Figure 3 6. Circuit E Velocity Field at 5 [m] Depth

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36 Figure 3 7. Circuit E Velocity Field at 10 [m] Depth Figure 3 8 . Google Earth Gyre Image

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37 Figure 3 9 . Circuit A Transect 1: Speed of Mean Flow Figure 3 10 . Circuit A Transect 1: Direction of Mean Flow

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38 Figure 3 1 1 . Circuit B Transect 1: Speed of Mean Flow Figure 3 1 2 . Circuit B Transect 1: Direction of Mean Flow

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39 Figure 3 1 3 . Circuit C Transect 1: Speed of Mean Flow Figure 3 1 4 . Circuit C Transect 1: Direction of Mean Flow

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40 Figure 3 1 5 . Circuit D Transect 4: Speed of Mean Flow Figure 3 1 6 . Circuit D Transect 4: Direction of Mean Flow

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41 Figure 3 1 7 . Circuit E Transect 4: Speed of Mean Flow Figure 3 1 8 . Circuit E Transect 4: Direction of Mean Flow

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42 Figure 3 19. Location of the town of Mulegé

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43 Figure 3 20 . Historical Wind Speed (Source: www.myweather2.com) Figure 3 2 1 . Annual Wind Direction Distribution (Source: www.windfinder.com )

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44 Figure 3 2 2 . Depth Contour

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45 CHAPTER 4 CTD DATA ANALYSIS Overview In the previous chapter , ADCP data was analyzed to understand current patterns and their relative influence s from wind forces, bathymetric variation , and bay plan view geometric variation . In this chapter , CTD data is analyzed to discover what temporal and spatial salinity, temper ature, and density gra di e n ts exist throughout the bay, and how each may influence currents. Previous studies estimate that within Bahía Concepción the magnitu de of density driven flow ranges from 75% to 150% of wind drive n flow , depending on the season (Cheng et al. 2010, p.1247 ) . T he ratio of density driven to wind driven flow influence is maximum during seasons of low wind speeds , and minimum during seasons of high wind speeds. Figure 3 20 show s that, historically, winds speeds are near mean speeds experienced throughout the year . Therefore, it is assumed that the influence from density driven flow relative to wind driven flow will change from that identified in this chapter by increasing during mild winter winds , and decreasing during strong summer winds . Plan view Geometric Variation Figures 4 1 through 4 3 show contours of de tided salinity, temperature, and density values collected at the CTD data stations shown in Figure 2 2 . The sample depth for these CTD contours is arbitrarily specified at 10 m, but a similar distrib ution can be expected all depths . For all three cases, the values a re de tided by a pplying a least squares fit to only the K1 diurnal tidal frequency due to an insufficient sampling

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46 size , as explained in Chapter 2. The units specified in this chapter are grams of salt per kilogram of water (the ionic salt concentration) for salinity , degrees Celsius for temperature, and kilograms per cubic meter for density. The salinity contour in Figure 4 1 shows salinity at a depth of 10 m in the bay ranging from 35.3 to 35.75 g kg 1 . As expected, salinity in the bay increases from the mouth of the bay to the head, where there is a lower flushing rate with the Gulf of California . The warm and arid climate at Bahía Concepción makes it a region of net evaporation, resulting in the relatively high salinity values throughout the bay. For reference, the gobal oceans and seas range in salinity from 30 32 g kg 1 in the Ar c tic Ocean to 38 g kg 1 in the Medit er ranean S ea. The temperature contour in Figure 4 2 shows temperature at a depth of 10 m in the b ay ranging from 20.2 to 21.6 ºC. In the northern hemisphere in 2005, the spring equinox began on March 20 th , meaning these values were collected at the very end of winter. I n the region of Bahía Concepción , historical monthly averaged daily low atmospheric temperatures are twice as high in August than in March, and are 21% lower in January than in March (Figure 4 4) . Historical monthly averaged daily high atmospheric temperatures are 33% higher in August than in March, and are 11% lower in Jan uary than in M arch. W ater temperature s in the bay can be expected to change relative to atmospheric temperature s , but are also largely influenced by conditions in the Gulf of California and the Pacific Ocean. The along bay temperature range of 1.4 ºC at 10 m depth is relatively large, and will be considered when analyzing density driven currents below .

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47 Figure 4 3 shows a density range from 24.75 to 25.1 kg m 3 at a depth of 10 m in the bay. The along bay density distribution follows a more similar trend to temperature than salinity , whereas there is not a clear uniform increase or decrease from the mouth of the bay to the head. There do not appear to be clear trends in along bay density variation, but certain distributional characteristics can be identified. For exampl e, there is a pocket of high density at the head of the bay in the region of Circuit E, and at latitudes above 26.65 ºN the shallower western edge of the bay is generally less dense than the eastern edge . Page 945 of Ponte et al. (2012) states bay gradients of density not directly related to the wind stress could potentially explain the cyclonic a depth of 10 m it is evident that along and cross bay density gradients are large enough to d rive currents, thereby influencing the cyclonic circulation. Despite this, the horizontal spatial distribut i on of density does not clearly illustrate a pattern that would specifically induce cyclonic flow. Therefore, along bay density gradients likely are not the most signifi cant influence on the cyclonic circulation near the head of the bay . Depth Variation To better undersand salinity, temperature, and density distributions with depth , contour s along specific transects can be compared to previously iden tified current patterns . Figures 4 5 through 4 1 9 show contours of salinity , temperature, and density variation with depth along the northernmost lateral transects at each circuit, corresponding to the same contours shown in Figures 3 9 through 3 1 8 . These contours support Ponte et al. (2012) by confirm ing that horizontal gradients of salinity, temperature, and density are significantly greater than vertical gradients (not necessarily on a per distance basis, but when considering the overall change) .

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48 Figure s 4 5 through 4 9 show depth distance contours of salinity . Overall, vertical salinity gradients throug hout the bay are insignificant ly small. At the mouth of the bay ( Figure 4 5 ; Circuit A) , the difference in salinity between the s urface and the bottom is greater than at the head of the bay ( Figure 4 9 ; Circuit E); s alinity ranges from 35.25 g kg 1 to 35.31 g kg 1 at the mouth of the bay, and from 35.695 g kg 1 to 35.710 g kg 1 at the head a 75% decrease in nominal variability. The in crease in salinity with depth at Circuit s A and B (Figures 4 5 and 4 6) is characteristic of expected salinity depth profiles, since a higher saline content in water increases density , causing the water to fall to the bottom. Increasing salinity with depth also corresponds to a stable water column, meaning that vertical gradients of this structure would n o t greatly induce flow . Figures 4 10 through 4 14 show depth distance contours of temperature at the same transect locations previously analyzed for salinity. Temperature va ries slightly more with depth than salinity varies with depth. Vertical temperature variation is more extensive at the mouth of the bay ( Figure 4 10; Circuit A) where temperatures range from 19.2 ºC to 20.6 ºC, than at the head of the bay ( Figure 4 14; Cir cuit E) , where temperatures range from 20.69 ºC to 20.79 ºC. Salinity and temperature show similar vertical distribution patter n s. For example, at Circuit B (Figures 4 6 and 4 11) there is a relatively large and uniform decrease in temperature with depth , corresponding to the increase in salinity with depth. At any given cross bay location there is a nearly linear decr ease in temperature with depth , representing an expected distribution for a vertically stable water column since colder water is denser and falls to the bottom . Figures 4 1 5 through 4 1 9 show depth distance contours of density at the same transect locations previously analyzed for salinity and temperature . The vertical density

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49 distribution in each portion of the bay is highly similar to the ve rtical temperature distribution, except density increases with depth while temperature decreases with depth , as expected . Generally, within a salinity range from 0 to 40 and a temperature range from 0 to 30, changes in salinity will have a greater influenc e on density than an equal change in temperature. These relations can be quantified by values of the thermal expansion coefficient ( ) and saline contraction coefficient ( ), where , , and generally . Specifically for a salin ity value of 35.5 g kg 1 and temperature value of 21 ºC, which are roughly the averages in the bay, , and . This yields , meaning that a unit change in salinity will cause a 2.7 times greater change in density than a unit change in temperature. Despite the relative values of alpha and beta, the transect contours i llustrate that density variations in the bay correlate mostl y with variations in temperature, rather than salinity. Th e beta to alpha ratio can be compared to actual along bay and vertical temperature and salinity variations existing in the bay . The ratio of temperature to salinity v ariation with depth at Circuit A is , and the along bay (from the head to the mouth) variation ratio at 10 m depth is . Comparing the se actual ratio s of temperature to salinity variation to the beta to alpha ratio, it is determined that vertical variation in density due to temperature is roughly 48% greater than that due to salinity, and horizontal variation in density due to temperature is roughly 270% greater than that due to salinity. Thus , it is shown that density correlates more closely with temperature than salinity within Bahía Concepción.

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50 Figure 4 19 shows a vertical and cross bay density range of only ~0.035 kg m 3 in the region of Circuit E . This area of strong rotational flow has effectively no vert ical density gradient ; therefore , it can be assumed that vertical density gradients have a negligible influence on current systems, specifically in the case of the cyclonic gyre. It should be considered that d ue to the hilly terrain inland of Bahía Concep ción, there are numerous potential freshwater inputs that could influence vertical density stratification. This influence is not a factor for the data collected in this study because conditions were dry during sampling. L ikewise , throughout most of the yea r there is such little precipitation that any potential source of freshwater is dried out. Bahía Concepción occasionally experiences heavy rain storms and hurricanes that w ould induce large freshwater inputs , b ut even in less heavy rains freshwater inputs could develop and directly influence density stratification and current conditions in the bay. Temporal Variation Salinity, temperature, and density vary significantly throughout the bay in both time and space. Because the analysis in th is chapter includes interpolating between data taken at different times over the 5 day sample period, it is useful to understand the extent to which conditions may have varied over that time . This is done by plotting contours of salinity, temperature, and de nsity values on time depth axes at individual CTD stations. As detailed in Chapter 2, each data station corresponds to a single latitude/longitude geographic location ( Figure 2 2 ). M easurements for each station we re taken in intervals within t h e transect r epetition cycles for each circuit. 3 specific stations of interest will be analyzed: Station 3 at the northern end of the bay on Circuit A, Station 16 near the central portion of the bay on Circuit C, and Station 27 near the southern end of the bay on Circ uit E. All 3 of the stations are located at the center of their respective

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51 transects. Each station had samples taken over a single day; Station 3 had 4 samples taken on March 11 12, and Stations 16 & 27 each had 3 samples taken on March 13 14 and 15 16, re spectively. For each of the 3 CTD stations, Figures 4 20 through 4 2 2 show salinity variations, Figures 4 2 3 through 4 2 5 show temperature variations, and Figures 4 2 6 through 4 2 8 show density variations. The most notable feature of these figures is that density variations in time correlate more closely with temperature than salinity, as was the case with vertical and horizontal distributions . Assuming spikes in surface and bottom bin values are noisy and should not be considered reliable, there does not a ppear to be any significant intraday temporal changes in salinity at any location with in the bay; the maximum salinity change at any given depth for the three stations is roughly ±0.05 g kg 1 . Unlike salinity , there are clearly discernible variations of temperature and density throughout the day . At the mouth of the bay ( Figure 4 23 ; Station 3 ), temperatures at a depth of ~5 m change up to 0.5 ºC throughout the day, and at the head ( Figure 4 25 ; Station 27 ) temperatures change up to 0.1 ºC. At Station 27 temperature is nearly uniform with depth throughout the day , indicating a well mixed water column. At all three stations, larger temperature variations over time occur near the surface than near the bottom, and near the mouth than near the head. Historical ly, in March the atmospheric temperature ranges from an average monthly high of 27 ºC to an average monthly low of 14 ºC. This large temperature range implies that daily atmospheric temperature variations are likely large enough to influence water conditio ns more significantly than intraday variations in salinity.

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52 Patterns of density variation s throughout the day closely resemble those of temperature variation s . Intraday density variations at a given depth range d from 0.1 kg m 3 at the mouth of the bay (Fig ure 4 2 6; Station 3 ) to 0.03 kg m 3 at the head (Figure 4 2 8; Station 27 ) . It is mentioned above that density driven flow during the season that these data samples were taken general l y influences currents by a magnitude equal to 75% of wind driven flow. T he most dramatic intraday changes in density occur at the surface, likely as a result of differing wind and atmospheric temperature conditions. A t Station 3 there is a ~0.1 kg m 3 change in density throughout the day at a depth of 30 m. Considering the fet ch distance at the mouth of the bay, wind influences on currents are greatly diminished at a depth of 30 m where this deeper density varia ti on occurs. Therefore, the density driven flow to wind driven flow ratio is expected to vary with depth, presumably i ncreasing as depth increases. This deeper intraday density variation shows that factors other than wind or atmospheric temperature are also significantly influencing condit i ons in the bay . Overall i ntraday variation s in bay conditions are shown to be relatively large. In the case of te mperature, the intraday range at Station 3 ( Figure 4 23 ) i s 0.5 ºC, whereas the total along bay range in Figure 4 2 is 1.4 ºC. Much of this variation is due to tidal oscillation s , which are adjusted for in the de tiding process, but wind and atmospheric temperature induced variations will result as error in the results when interpolating between samples taken at different points in time . This data set is insufficient in scale for fully understanding how conditions vary over time. Ideally, samples would be taken from these stations over longer pe r iods of time than a single day w

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53 be accounted for. A larger da ta set in general would provide a better understand ing of how temperature, salinity, and density vary throughout the bay, and how these changes influence current patterns.

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54 Figure 4 1. Salinity at 10 [m] Depth Figure 4 2. Temperature at 10 [m] Depth

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55 Figure 4 3. Density at 10 [m] Depth Figure 4 4. Historical Atmospheric Temperatures (Source: www.myweather2.com )

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56 Figure 4 5 . Circuit A, Transect 1: Salinity Figure 4 6 . Circuit B, Transect 1: Salinity

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57 Figure 4 7 . Circuit C, Transect 1: Salinity Figure 4 8 . Circuit D, Transect 4: Salinity

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58 Figure 4 9 . Circuit E, Transect 4: Salinity Figure 4 10 . Circuit A, Transect 1: Temperature

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59 Figure 4 1 1 . Circuit B, Transect 1: Temperature Figure 4 1 2 . Circuit C, Transect 1: Temperature

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60 Figure 4 1 3 . Circuit D, Transect 4: Temperature Figure 4 1 4 . Circuit E, Transect 4: Temperature

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61 Figure 4 1 5 . Circuit A, Transect 1: Density Figure 4 1 6 . Circuit B, Transect 1: Density

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62 Figure 4 1 7 . Circuit C, Transect 1: Density Figure 4 1 8 . Circuit D, Transect 4: Density

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63 Figure 4 1 9 . Circuit E, Transect 4: Density Figure 4 20 . CTD Station 3: Salinity

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64 Figure 4 2 1 . CTD Station 16: Salinity Figure 4 2 2 . CTD Station 27: Salinity

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65 Figure 4 2 3 . CTD Station 3: Temperature Figure 4 2 4 . CTD Station 16: Temperature

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66 Figure 4 25 . CTD Station 27: Temperature Figure 4 2 6 . CTD Station 3: Density

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67 Figure 4 2 7 . CTD Station 16: Density Figure 4 2 8 . CTD Station 27: Density

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68 CHAPTER 5 TIDES AND GOODNESS OF FIT Goodness of Fit Chapter 2 detail ed how the ADCP and CTD data are de tided at every geometric location of multiple samples by applying the least squares fit method . Each time that the least squares fit is performed, a goodness of fit analysis can be applied to quantify how well the estimated variations caused by the K1 and M2 tidal harmonics statistically correlate to the observed values . For this analysis , a normalized root mean square calculation is performed, resulting in a goodness of fit value from 0 to 1 for each fit , where 0 implies a bad fit and 1 implies a perfect fit. The calculation used for the goodness of fit is as follows: (5 1) W east observed values after being calibrated via the Joyce correction method explained in Chapter to the K1 and /or M2 harmonic ( s ) , and the bracket s denot e mean values . This formula corresponds to the built in goodnessOfFit function in MATLAB ® version R2012b. The summation iterates a number of times equal to the number of observed values at that specific location. Each least squares fit calculation has a nu mber of observed input values equal to the number of transect repetitions for the ADCP data, or casts for the CTD data , since these data values correspond to the same latitude/longitude coordinate. It should be considered that u and v are oriented east -

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69 west and north south, respectively, which does not necessarily correspond to directly into, out of, or across the bay. Figure 5 1 shows a histogram of goodness of fit values at the mouth of the bay along T ransect 1 of Circuit A at a depth of 10 m . Again, t he total number of data points for this example transect would equal the number of histogram bars multiplied by the number of transect repetitions. The goodness of fit values show how well variations caused by specific tidal harmonics explain the total var iation in the data. At Circuit A intraday current variation is largely dependent on the influence from the K1 and M2 tidal harmonics , as indicated by a mean goodness of fit value of 0.7 3 for the east component of velocity . Comparing t he mean north componen t velocity goodness of fit of 0.39 to the larger east component goodness of fit value of 0.73 reveals there are greater non tidal influences on currents in the along bay direction in this region . Figure 5 2 shows a histogram of goodness of fit values at the head of the bay along Transect 4 of Circuit E at a depth of 10 m. The goodness of fit values at the head of th e bay are shown to be much less than at the head, indicating a decrease in tidal influence. Figures 5 3 through 5 5 show contours of goodness of fit values throughout the entire bay at a depth of 10 m . Figure 5 3 shows the goodness of fit for the combined K1 and M2 harmonics, whereas Figures 5 4 and 5 5 individually show the goodness of fit for the K1 and M2 harmonics, respectively. Comparing th e combined K1 and M2 goodness of fit value s to those for the individual K1 or M2 harmonics reveals how the tidal oscillatory cycle in Bahía C oncepción consists of both K1 and M2 harmonics that together more fully explain the variation in the data than each harmonic does individually. Bahía Concepción is located near a

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70 describes the total variation in the data. Tidal Analysis Figures 5 6 through 5 15 show contours of the east and west component tidal amplitudes for both the K1 and M2 frequencies at the same lateral transects analyzed in Chapter s 3 and 4. These representations of tidal com ponent data supplement the previous cha analyses by providing an understand ing of the influence of tides on current systems in the bay. T oward the head of the bay from Circuit B there is a sharp decline in tidal component amplitude, with the maximum M2 amplitude occurring at Circuit B, a nd the maximum K1 amplitude occurring at Circuit A. Winant et al. (2013) calculated that the ratio of diurnal to semidiurnal tidal constituent s at the mouth of the bay is 2.4, therefore there should be a clear diurnal domina nce . This feature is not display ed in either the goodness of fit contours or in the tidal amplitude contours , where there is no clear overall tidal frequency dominance. Contrarily , at Circuit C it appears that the M2 amplitudes are larger than the K1 amplitudes. One important observatio n made in Ponte et al. (2012) is amplitudes are expected to be maximum at the mouth and decrease toward the head This trend is clearly displayed in Figures 5 6 through 5 15, where tidal amplitudes are negligibly close to 0 at Circuit E . By combining the frequencies of the K1 and M2 harmonics with the amplitudes and phases output from the least squares fit calculation, a tidal ellipse representation can be constructed at each sample location. This calculation is performed u sing the following formula:

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71 (5 2) (5 3) For major axis amplitude , minor axis amplitude , phase , frequency , and time . To better visualize the orientation and magnitude of the tidal ellipses throughout the bay, the tidal ellipses in Figures 5 16 and 5 17 are scaled down to relative longitude and latitude values and overlaid on the Circuits B and C sample trajectories; thus, the amplitude of these tidal ellipses are qualitative, and only the relative scale and orientation should be considered. The tidal features displayed at Circuits B and C in Figures 5 8 through 5 11 are alternately displayed by the tidal ellipses in Figures 5 16 and 5 17, where the highest amplitudes occur at Circuit B and diminish further into the bay. Again, there is no clear dominant tidal component, and in certain areas there are greater semidiurnal amplitude s . Among all the c ircuits, Circuit s B and C are in the only region s where coherent tidal ellipse illustration s can be displayed at all depths for both tidal components. Further toward the head of the bay from Circuit C the tidal amplitudes are negligibly small. This result supports page 945 of Ponte et al. (2012), which identif ies from samples in the southern portion of the bay. The small tidal influence on currents in the bay is due to the large water depths in the bay, whi ch minimize the relative influence on volume and thus , minimize volumet ric flow rate of a given change in water elevation. This explains why tidal component amplitudes are greatest in the relatively shallow and narrow region of Circuit B. Despite the small tidal component amplitudes, the tidal ellipses correlate with the cir cuit vector field plots in Chapter 3 . Most notably, they are oriented in the same

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72 direction as the dominant currents. This analysis confirm s that the tidal influence on currents is weak in the southern portion of the bay in the region of the cyclonic gyre , and therefore influences from wind, density gradients, etc. are of greater interest .

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73 Figure 5 1. Circuit A Transect 1, 10 [m] depth: K1 & M2 Frequency Figure 5 2 . Circuit E Transect 4 , 10 [m] depth: K1 & M2 Frequency

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74 Figure 5 3 . K1 & M2 Freq uency Goodness of Fit: 10 [m] depth Figure 5 4 . K1 Tidal Frequency Goodness of Fit: 10 [m] depth

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75 Figure 5 5 . M2 Tidal Frequency Goodness of Fit: 10 [m] depth Figure 5 6 . Circuit A Transect 1: Amplitude of K1 Tidal Current

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76 Figure 5 7 . Circuit A Transect 1: Amplitude of M2 Tidal Current Figure 5 8 . Circuit B Transect 1: Amplitude of K1 Tidal Current

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77 Figure 5 9 . Circuit B Transect 1: Amplitude of M2 Tidal Current Figure 5 1 0 . Circuit C Transect 1: Amplitude of K1 Tidal Current

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78 Figure 5 1 1 . Circuit C Transect 1: Amplitude of M2 Tidal Current Figure 5 1 2 . Circuit D Transect 4: Amplitude of K1 Tidal Current

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79 Figure 5 1 3 . Circuit D Transect 4: Amplitude of M2 Tidal Current Figure 5 1 4 . Circuit E Transect 4: Amplitude of K1 Tidal Current

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80 Figure 5 1 5 . Circuit E Transect 4: Amplitude of M2 Tidal Current Figure 5 1 6 . Circuit B Tidal Ellipses at 5 [m] Depth

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81 Figure 5 1 7 . Circuit C Tidal Ellipses at 13 [m] Depth

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82 CHAPTER 6 CONCLUSION This study an analysis of interrelations between current amplitudes and magnitudes, salinity, temperature, density, and tides in Bahía Concepción . The results are unique to Bahía Concepción, considering that Bahía C oncepción has its own unique bathymetric features, seasonal variation patterns, etc., but in various ways this analysis can assist in similar studie s conducted for the purpose of understand ing current systems and general c oastal conditions in other semi enc losed basins. Instead of analyzing seasonal variations or macro trends, a high degree of sampling throughout the bay over 5 days provided a more thorough understand ing of conditions during a short period. These results differ from, and build upon, previou s studies of Bahía Concepción because of the large spatial extent of the data set, which provides a full 3 dimensional mapping of conditions . This spatial extent specifically provide s a better understanding of the structure cyclonic gyre identified at the southern end of the bay at full depth. The density distribution throughout the bay i s illustrated and correlated to that of salinity and temperature, revealing a greater influence on density from temperature than salinity. Density distributions a re illustrated to better understand how along bay density gradients influence current systems. Finally, it i s proven that tidal amplitudes decrease toward the head, and likely have a minimal ov erall influence on the structures of current systems. Further work could build upon this analysis by surveying in a similar manner under different seasonal conditions to deduce the degree to which conditions in the bay are dependent on specific factors su ch as wind or temperature, which vary significantly

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83 throughout the year. Previous studies applied various models and formulas to predict conditions in the bay. No predictive models are used in this study, whereas the results are ex c lusively representations of the processing of field observations. Therefore future studies could use these results as a comparison for pre dictive modelling of Bahía Concepción or other bays . Overall, the consistency and statistical significance of the results show that the analys is of the ADCP and CTD data is reliable and conclusive. The main concerns regarding reliability and use of this data arise from the strong wind conditions during the s ampling of Circuits D and E, and the sensitivity of the results to ba d data due to the li mited sampling frequency .

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84 APPENDIX MATLAB ® PROGRAMS DEVELOPED F OR THIS THESIS PlotCircuitQuiver.m clear all; close all; clc % Selectors: circuit='E'; depth=10; %[m] w1=2*pi/(12.42/24); %M2 [days] w2=2*pi/(23.93/24); %K1 [days] %% Plot Transect Path Flow set(0,'DefaultFigurePosition', [20 20 1000 600]); figure set(gcf,'color','w'); subplot(1,2,1) hold on if circuit=='A' load('platinum_A'); t=0.1875; elseif circuit=='B' load('platinum_ B'); t=1.7813; elseif circuit=='C' load('platinum_C'); t=1.8125;%t=0.0833; elseif circuit=='D' load('platinum_D'); t=0.6771; elseif circuit=='E' load('platinum_E'); t=0.1875; end numtrans=P{1,18}; allu=[]; allv=[]; allLat=[]; allLon=[]; myLat=[]; myLon=[]; for i=1:numtrans clear lat; clear lon; depthidx=find(P{i,14}==depth); %Tidal Component Only; Without Residual % u=P{i,2}(depth/.5 3,:).*sin(w1*t+P{i,3}(depth/.5 3,:))+P{i,4}(depth/.5 3,:).*sin(w2*t+P{i,5}(depth/.5 3,:)); % v=P{i,7}(depth/.5 3,:).*sin(w1*t+P{i,8}(depth/.5 3,:))+P{i,9}(depth/.5 3,:).*sin(w2*t+P{i,10}(depth/.5 3,:)); %With Residual u=P{i,1}(depthidx,:)+P{i,2}(depthidx,:).*sin(w1*t+P{i,3}(depthidx,:))+P{i,4}( depthidx,:).*sin(w2*t+P{i,5 }(depthidx,:)); v=P{i,6}(depthidx,:)+P{i,7}(depthidx,:).*sin(w1*t+P{i,8}(depthidx,:))+P{i,9}( depthidx,:).*sin(w2*t+P{i,10}(depthidx,:)); %find row that doesn't have NaNs:

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85 % first=1; % lat=P{i,11}; % while 1>0 % if sum(isnan( lat(first,:)))==0 % break % end % first=first+1 % end % P{k,11}=latg;P{k,12}=long % Get non NaN valued lat/lon % for k=1:size(P{i,11},2) % lat(k)=nanmean(P{i,11}(depthidx,k,:)); % lon(k)=nanmean(P{i,12}(depthidx,k,:)); % end for j=1:size(P{i,11},2) clear col; for k=1:size(P{i,11},1) col(k)=nanmean(P{i,11}(k,j,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lat( j)=NaN; else lat(j)=col(min(find(isnan(col)==0))); end end for j=1:size(P{i,12},2) clear col; for k=1:size(P{i,12},1) col(k)=nanmean(P{i,12}(k,j,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lon(j)=NaN; else lon(j)=col(min(find(isnan(col)==0))); end end ave=3; %number of cells to average for j=1:floor(size(u,2)/ave) %columns (distance/time along transect) unew(j)=nanmean(u((1+(j 1)*ave):(ave+(j 1)*ave))); vnew(j)=nanmean(v((1+(j 1)*ave):(ave+(j 1)*ave))); latnew(j)=nanmean(lat((1+(j 1)*ave):(ave+(j 1)*ave))); lonnew(j)=nanmean(lon((1+(j 1)*ave):(ave+(j 1)*ave))); end u=unew; v=vnew; lat=latnew; lon=lonnew; %%%%%%%%%%%%%%%%% % u(end)=u(end 1); v(end)=v(end 1); % u(1)=u(2); v(1)=v(2); %%%%%%%%%%%%%% allu=[allu,u]; allv=[allv, v]; allLat=[allLat,lat]; allLon=[allLon,lon];

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86 end lonRange=max(allLon) min(allLon); latRange=max(allLat) min(allLat); xmin=min(allLon) lonRange*.1; xmax=max(allLon)+lonRange*.1; ymin=min(allLat) latRange*.2; ymax=max(allLat)+latRange*.2; scale x=(xmax xmin)/8; % can change this however without altering scale scaley=(ymax ymin)/8; scale=min(scalex,scaley); quiver(allLon, allLat,0.1*scale*allu,0.1*scale*allv,0,'b'); xlabel('LON') ylabel('LAT') axis('equal') plot_google_map('Alpha',0.6) xLimits = get(gca,'XLim'); yLimits = get(gca,'YLim'); P1u=[allu,[10 0]]; %for the first subplot P1v=[allv,[0 10]]; P1Lat=[allLat,[yLimits(2) 0.11*(yLimits(2) yLimits(1)) yLimits(2) 0.11*(yLimits(2) yLimits(1))]]; P1Lon=[allLon,[xLimits(2) 0.17*(xLimits(2) xLimits (1)) xLimits(2) 0.17*(xLimits(2) xLimits(1))]]; quiver(P1Lon,P1Lat,0.1*scale*P1u,0.1*scale*P1v,0,'b'); text(xLimits(2) 0.18*(xLimits(2) xLimits(1)),yLimits(2) 0.14*(yLimits(2) yLimits(1)),'10 [cm/s]') %% Mesh Field Plot lonrange=[min(allLon) : 0.005 : max(allLon)]; lonrange=transpose(lonrange); latrange=[min(allLat) : 0.005 : max(allLat)]; [longitude,latitude]=meshgrid(lonrange,latrange); % Remove NaN: idx=find(~isnan(allu)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allv)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allLon)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allLat)); allu=allu(idx);allv=allv(idx); allLon= allLon(idx); allLat=allLat(idx); ugrid=griddata(allLon,allLat,allu,lonrange,latrange); vgrid=griddata(allLon,allLat,allv,lonrange,latrange); subplot(1,2,2) X=[longitude;[NaN*zeros(1,size(longitude,2))]];

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87 Y=[latitude;[NaN*zeros(1,size(latitude,2))]]; U= 0.1*scale*[ugrid;[NaN*zeros(1,size(ugrid,2))]]; V=0.1*scale*[vgrid;[NaN*zeros(1,size(vgrid,2))]]; ind=find(isnan(U)~=1 & isnan(V)~=1); quiver(X(ind),Y(ind),U(ind),V(ind),0,'b') xlabel('LON') ylabel('LAT') axis('equal') plot_google_map('Alpha',0.6) xLimits = get(gca,'XLim'); yLimits = get(gca,'YLim'); X=[longitude;[NaN*zeros(1,size(longitude,2) 2) xLimits(2) 0.17*(xLimits(2) xLimits(1)) xLimits(2) 0.17*(xLimits(2) xLimits(1))]]; Y=[latitude;[NaN*zeros(1,size(latitude,2) 2) yLimits(2) 0.11*(yLimits(2) yLimits(1)) yLimits(2) 0.11*(yLimits(2) yLimits(1))]]; U=0.1*scale*[ugrid;[NaN*zeros(1,size(ugrid,2) 2) 10 0]]; V=0.1*scale*[vgrid;[NaN*zeros(1,size(vgrid,2) 2) 0 10]]; ind=find(isnan(U)~=1 & isnan(V)~=1); quiver(X(ind),Y(ind),U (ind),V(ind),0,'b') text(xLimits(2) 0.18*(xLimits(2) xLimits(1)),yLimits(2) 0.14*(yLimits(2) yLimits(1)),'10 [cm/s]') suptitle(['Circuit ' circuit ' Velocity Field at ' num2str(depth) ' [m] Depth']) set(0, 'DefaultFigurePosition', [20 230 500 400]); Tid al Ellipses .m close all; clear all; clc; circuit='A'; % selector: A,B,C,D,E depth=5; %[m] scale=.001; if circuit=='A' load('gold_A'); load('platinum_A'); numtrans=4; % scale=.001; elseif circuit=='B' load('gold_B'); load('platinum_B'); numtr ans=6; % scale=.0008; elseif circuit=='C' load('gold_C'); load('platinum_C'); numtrans=6; % scale=.002; elseif circuit=='D' load('gold_D'); load('platinum_D'); numtrans=4; % scale=.002; elseif circuit=='E' load('gold_E'); load('platinum_E'); numtrans=4; % scale=.002; end w1=2*pi/(23.93/24); %K1 [days] w2=2*pi/(12.42/24); %M2 [days]

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88 set(0, 'DefaultFigurePosition', [20 230 600 500]); figure(1) set(gcf,'color','w'); hold on xlabel('LON') ylabel( 'LAT') title(['Circuit ' circuit ' ' 'Tidal Ellipses at ' num2str(depth) ' [m] Depth']) Kxloc=[]; Kyloc=[]; Mxloc=[]; Myloc=[]; for transect=1:numtrans depthidx=find(P{transect,14}==depth); M2ampU=P{transect,2};M2phU=P{transect,3}; K1a mpU=P{transect,4};K1phU=P{transect,5}; M2ampV=P{transect,7};M2phV=P{transect,8}; K1ampV=P{transect,9};K1phV=P{transect,10}; clear lon; clear lat; for j=1:size(P{transect,11},2) clear col; for k=1:size(P{transect,11},1) col(k)=nanmean(P{transect,11}(k,j,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lat(j)=NaN; else lat(j)=col(min(find(isnan(col)==0))); end end for j=1:size(P{transect, 12},2) clear col; for k=1:size(P{transect,12},1) col(k)=nanmean(P{transect,12}(k,j,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lon(j)=NaN; else lon(j)=col(min(find(isnan(col)==0))); end end plot(lon,lat,'.k','MarkerSize',3) num=size(P{transect,2},2); %columns(locations) for gp=[floor(num/3) floor(num/3)*2] if (circuit=='B') & transect==3 break end for frequency=1:2 %1:2 if frequency==1 ua=K1ampU; va=K1ampV; up=K1phU; vp=K1phV; elseif frequency==2

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89 ua=M2ampU; va=M2ampV; up=M2phU; vp=M2phV; end ua=ua(depthidx,gp); up=up(depthidx,gp); va=va(depthidx,gp); vp=vp(depthidx,gp); Qc=.5.*(ua.^2+va.^2 2.*ua.*va.*sin(vp up)).^.5; Qcc=.5.*(ua.^2+va.^2+2.*ua.*va.*sin(vp up)).^. 5; thetac=atan2((ua.*sin(up)+va.*cos(vp)),(ua.*cos(up) va.*sin(vp))); thetacc=atan2(( ua.*sin(up)+va.*cos(vp)),(ua.*cos(up)+va.*sin(vp))); M=Qcc+Qc; m=Qcc Qc; % ellipticity=m./M; % p hase= .5.*(thetacc thetac); phi=0.5.*(thetacc+thetac); %"orientation" for t=0:0.005:1%0:.01:24 if frequency==1 x=M.*cos(phi).*cos(w1*t) m.*sin(phi).*sin(w1*t); y=M.*sin(phi).*cos(w1*t)+m.*cos(phi).*sin(w1*t); Kxloc=[Kxloc lon(gp)+scale*x]; Kyloc=[Kyloc lat(gp)+scale*y]; else %frequency==2 x=M.*cos(phi).*cos(w2*t) m.*si n(phi).*sin(w2*t); y=M.*sin(phi).*cos(w2*t)+m.*cos(phi).*sin(w2*t); Mxloc=[Mxloc lon(gp)+scale*x]; Myloc=[Myloc lat(gp)+scale*y]; end end % phi is orientation % sigma is our w end %frequency end %distance point end %transect plot(Kxloc,Kyloc,'.b',Mxloc,Myloc,'.r','MarkerSize',5) ylim([min([Kyloc Myloc]) .01 max([Kyloc Myloc])+.01]) axis('equal') % plot_goo gle_map('Alpha',0.6) legend('K1 Frequency','M2 Frequency','Location','NorthEast') l=findobj(gcf,'tag','legend') ; a=get(l,'children'); set(a(1),'markersize',15,'MarkerEdgeColor','r'); set(a(4),'markersize',15,'MarkerEdgeColor','b'); set(0, 'DefaultF igurePosition', [20 230 500 400]); PlotTransectContour.m close all; clear all; clc;

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90 circuit='E'; % selector: A,B,C,D,E transect=4; % selector:1,2,3,4,5,6 cnum=41; %Number for shading of contour if circuit=='A' if transect==1 | transect==2 o='H'; else o='V'; end load('gold_A'); load('platinum_A'); elseif circuit=='B' if transect==1 | transect==3 | transect==5 o='H'; else o='V'; end load('gold_B'); load('platinum_B'); elseif circuit=='C' if transect==1 | transect==3 | transect==5 o='H'; else o='V'; end load('gold_C'); load('platinum_C'); elseif circuit=='D' if transect==2 | transect==4 o='H'; else o='V'; end load('gold_D'); load('platinum_D'); elseif circuit=='E' if transect==2 | transect==4 o='H'; else o='V'; end load('gold_E'); load('platinum_E'); end lat=P{transect,11}; lon=P{transect,12}; distance=P{transect,13}; depth =P{transect,14}; meanU=P{transect,1}; meanV=P{transect,6}; %% Plot of Flow Speed set(0, 'DefaultFigurePosition', [20 230 800 350]); figure(1) set(gcf,'color','w'); hold on %Include bottom depth line: Glat=G{transect,4}; Glon=G{transect,5}; Gdist=G{transect,6}; Gdepth=G{transect,7}; Gmdepth=G{transect,8};

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91 maxdepth=Gmdepth; % Orient so left side is always North or West: flipped=0; if o=='H' & nanmean(lon(5,1:5,1))>nanmean(lon(5,end 5:end,1)) distance=fliplr(distance); Gdist=fliplr( Gdist); flipped=1; end if o=='V' & nanmean(lat(5,1:5,1))>nanmean(lat(5,end 5:end,1)) distance=fliplr(distance); Gdist=fliplr(Gdist); flipped=1; end speed=(meanU.^2+meanV.^2).^.5; [c,h]=contourf(distance,depth,speed,cnum); set(gca,'YDi r','reverse','CLim',[0 15]); % set(h,'ShowText','on','TextStep',5,'LabelSpacing',1000,'LevelStep',1,'LineSty le','none') set(h,'LevelStep',1,'LineStyle','none') if o=='V' xlabel('N S Distance Along Transect [km]') else %o=='H' xlabel('W E Distance Along Transect [km]') end ylabel('Depth [m]') % To set the axis so you don't see blanks: Lidx=0; %for beginning of xlim while 1<2 Lidx=Lidx+1; if nanmean(speed(5:end,Lidx))>0 break end end Ridx=size(speed,2) +1; %for beginning of xlim while 1<2 Ridx=Ridx 1; if nanmean(speed(5:end,Ridx))>0 break end end if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) end

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92 title(['Circuit ' circuit ' Transect ' num2str(transect) ': ' ' Speed of Mean Flow']) colorbar h=colorbar; ylim(h,[0 15]) ylabel(h,'[cm/s]') plot(Gdist',maxdepth,'k','LineWidth',2); %% Plo t of Flow Direction % set(0, 'DefaultFigurePosition', [20 70 700 500]); figure(2) set(gcf,'color','w'); %West East Direction [theta,rho] =cart2pol(meanU,meanV); theta=theta*180/pi; % theta=abs(theta); % theta=abs(theta 180); for i=1:size(theta,1) for j=1:size(theta,2) if theta(i,j)>=0 & theta(i,j)<180 theta(i,j)=theta(i,j)+90; elseif theta(i,j)> 180 & theta(i,j)< 90 theta(i,j)=270+180 abs(theta(i,j)); elseif theta(i,j)>= 90 & theta(i,j)<0 the ta(i,j)=90 abs(theta(i,j)); end end end % subplot(2,1,1) hold on [c,h]=contourf(distance,depth,theta,cnum,'LineStyle','none'); set(gca,'YDir','reverse'); ylabel('Depth [m]') title(['Circuit ' circuit ' Transect ' num2str(transect) ': ' ' Direction of Mean Flow']) colorbar; h=colorbar; ylabel(h,'South East North West') set(h,'YTick',[]) plot(Gdist',maxdepth,'k','LineWidth',2); if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) end % %North South Direction % [theta,rho] =cart2pol(meanU,meanV); % theta=theta*180/pi; % for i=1:size(theta,1) % for j=1:size(theta,2) % if (theta(i,j)>=0 & theta(i,j)<=90) | (theta(i ,j)>= 180 & theta(i,j)<= 90) | (theta(i,j)> 90 & theta(i,j)<0); % theta(i,j)=theta(i,j)+90; % elseif theta(i,j)>90 & theta(i,j)<=180

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93 % theta(i,j)= 180+(90 (180 theta(i,j))); % end % end % end % theta=abs(theta); % subplot(2,1,2) % hold on % [c,h]=contourf(distance,depth,theta,cnum,'LineStyle','none'); % set(gca,'YDir','reverse'); if o=='V' xlabel('N S Distance Along Transect [km]') else %o=='H' xlabel('W E Distance Along Transect [km]') end % ylabel('De pth [m]') % colorbar; % h=colorbar; % ylabel(h,'South North') % set(h,'YTick',[]) % % plot(Gdist',maxdepth,'k','LineWidth',2); % if flipped==0 % axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) % else %flipped==1 % axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) % end % %% Plot of Transect Location % set(0, 'DefaultFigurePosition', [550 30 500 600]); % %position = [left bottom width height]; % figure(3) % set(gcf,'color','w'); % title('Transect Location') % xlabel('LON') % ylabel('LAT') % axis('equal') % ylim([26.54 26.93]) % hold on % load('coradcp_A');plot(silverA(:,3),silverA(:,2),'.','MarkerSize',.2); % load('coradcp_B');plot(silverB(:,3),silverB(:,2),'.','MarkerSize',.2); % load('coradcp_C');plot(silverC(:,3),silverC(:, 2),'.','MarkerSize',.2); % load('coradcp_D');plot(silverD(:,3),silverD(:,2),'.','MarkerSize',.2); % load('coradcp_E');plot(silverE(:,3),silverE(:,2),'.','MarkerSize',.2); % for i=1:size(lon,3) % plot(lon(5,:,i),lat(5,:,i),'r','LineWidth',2.5); % end % plot_google_map('Alpha',0.6) % set(0, 'DefaultFigurePosition', [20 230 500 400]); %% Plot the Tidal Amplitudes M2ampU=P{transect,2}; K1ampU=P{transect,4}; M2ampV=P{transect,7}; K1ampV=P{transect,9}; set(0, 'DefaultFigurePosition', [20 70 700 500]);

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94 %position = [left bottom width height]; % K1: figure(4) set(gcf,'color','w'); subplot(2,1,1) [c,h]=contourf(distance,depth,K1ampU,cnum,'LineStyle','none'); set(gca,'YDir','reverse','CLim',[0 15]); ylabel('Depth [m]') title(['Circuit ' circuit ' Transec t ' num2str(transect) ': ' ' U Component Amplitude of K1 Tidal Current']) colorbar; h=colorbar; ylabel(h,'[cm/s]') % set(h,'YTick',[]) hold on plot(Gdist',maxdepth,'k','LineWidth',2); if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) end subplot(2,1,2) [c,h]=contourf(distance,depth,K1ampV,cnum,'LineStyle','none'); set(gca,'YDir','reverse','CLim',[0 15]); ylabel('Depth [m]') title(['Circuit ' circuit ' Transect ' num2str(transect) ': ' ' V Component Amplitude of K1 Tidal Current']) colorbar; h=colorbar; ylabel(h,'[cm/s]') if o=='V' xlabel('N S Distance Along Transect [km]') else %o=='H' xlabel('W E Distance Along Transect [km]') end % set(h,'YTick',[]) hold on plot(Gdist',maxdepth,'k','LineWidth',2); if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max (maxdepth)+2]) end % M2: figure(5) set(gcf,'color','w'); subplot(2,1,1) [c,h]=contourf(distance,depth,M2ampU,cnum,'LineStyle','none'); set(gca,'YDir','reverse','CLim',[0 15]); ylabel('Depth [m]')

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95 title(['Circuit ' circuit ' Transect ' num2str(transect) ': ' ' U Component Amplitude of M2 Tidal Current']) colorbar; h=colorbar; ylabel(h,'[cm/s]') % set(h,'YTick',[]) hold on plot(Gdist',maxdepth,'k','LineWidth',2); if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) end subplot(2,1,2) [c,h]=contourf(distance,depth,M2ampV,cnum,'LineStyle','none'); set(gca,'YDir','reverse','CLim',[0 15]); ylabel('Depth [m]') title(['Circuit ' circuit ' Transect ' num2str(tran sect) ': ' ' V Component Amplitude of M2 Tidal Current']) colorbar; h=colorbar; ylabel(h,'[cm/s]') if o=='V' xlabel('N S Distance Along Transect [km]') else %o=='H' xlabel('W E Distance Along Transect [km]') end % set(h,'YTick',[]) hold on plot(Gdi st',maxdepth,'k','LineWidth',2); if flipped==0 axis([distance(Lidx) distance(Ridx) 3 max(maxdepth)+2]) else %flipped==1 axis([distance(Ridx) distance(Lidx) 3 max(maxdepth)+2]) end GoodnessOfFitContour.m % Includes trajectories clear all; close all; clc; plotinterval=200; % Selectors: depth=10; %[m] f=3; % tidal frequency: 1 for K1, 2 for M2, 3 for K1M2 lonall=[]; latall=[]; uGOFall=[]; vGOFall=[]; for i=1:5 % number of circuits if i==1 load('platinum_A'); elseif i==2

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96 load('platinum_B'); elseif i==3 load('platinum_C'); elseif i==4 load('platinum_D'); elseif i==5 load('platinum_E'); end numtrans=P{1,18}; for transect=1:numtrans KuFIT=P{transect,19}; KvFIT=P{transect,20}; MuFIT=P{transect,21}; MvFIT=P{transect,22}; KMuFIT=P{transect,23}; KMvFIT=P{transect,24}; if f==1 uFIT=KuFIT; vFIT=KvFIT; elseif f==2 uFIT=MuFIT; vFIT=MvFIT; else %f==3 uFIT=KMuFIT; vFIT=KMvFIT; end latg=P{transect,11}; latg=(nanmean(latg,3)); latall=[latall nanmean(latg,1)]; long=P{transect,12}; long=(nanmean(long,3)); lona ll=[lonall nanmean(long,1)]; deptharray=P{transect,14}; didx=find(deptharray==depth); uGOFall=[uGOFall uFIT(didx,:)]; vGOFall=[vGOFall vFIT(didx,:)]; end %transect clear P; end %circuit %Remove negative: idx=find(uGOFall<0 | isnan(uGOFall)); uGOFall(idx)=[]; vGOFall(idx)=[]; lonall(idx)=[]; latall(idx)=[]; idx=find(vGOFall<0 | isnan(vGOFall)); uGOFall(idx)=[]; vGOFall(idx)=[]; lonall(idx)=[]; latall(idx)=[]; %% Plot lonrange=[min(lonall) : (max(lonall) min(lonall))/30 : max(lonall)]; lonrange=transpose(lonrange); latrange=[min(latall) : (max(latall) min(latall))/30 : max(latall)]; [longitude,latitude]=meshgrid(lonrange,latrange); uGOFgrid=griddata(lonall,latall,uGOFall,lonrange,latrange); vG OFgrid=griddata(lonall,latall,vGOFall,lonrange,latrange); %Set land values to NaN: Llon=[ 111.863352; 111.873738; 111.874682; 111.803621; 111.865771; 111.886927; 111.895418; 111.873546; 111.874600; 111.888641; 111.896861; 111.881525; 111.802398; 111.8 85245; 111.894140; 111.869483; 111.886026; -

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97 111.907440; 111.892053; 111.901534; 111.813554; 111.876504; 111.862524; 111.867639; 111.870914; 111.860961; 111.867480; 111.796704; 111.870674; 111.885869; 111.884169; 111.871808; 111.868888; 111.859570]; %values to left of bay LHlat=[26.807364;26.832105;26.796549;26.626474;26.813149;26.840338;26.846517; 26.833778;26.780186;26.842992;26.850839;26.838834;26.622134;26.840871;26.8426 62;26.778827;26.841512;26.882895;26.852821;26.862051;26.633516;26.838511;26.8 16399;26. 826658;26.765776;26.783931;26.780689;26.612161;26.834348;26.845365;2 6.842671;26.836712;26.831534;26.803644]; %upper boundary LLlat=[26.781927;26.781927;26.771149;26.618840;26.790550;26.818684;26.834012; 26.831341;26.755205;26.841554;26.845783;26.836780;26 .614925;26.833939;26.8331 07;26.775133;26.838692;26.875469;26.844082;26.853622;26.624727;26.834023; 26.807069;26.819383;26.751217;26.774732;26.761531;26.605829;26.830837;26.8386 95;26.838707;26.829038; 26.828027;26.782422]; %lower boundary for i=1:numel(Llon ) idx=find(longitudeLLlat(i)); uGOFgrid(idx)=NaN; vGOFgrid(idx)=NaN; end Rlon=[ 111.814944; 111.823509; 111.796477; 111.764205; 111.756150; 111.801297; 111.844838; 111.852611; 111.836390; 111.824393; 111.81 5787; 111.797248; 111.781801; 111.764278; 111.746299; 111.736681; 111.728210; 111.807246; 111.826486; 111.765898; 111.740483; 111.731116; 111.829889; 111.840701; 111.775112; 111.795215; 111.763402; 111.847963; 111.847291; 111.832357]; %values to right of b ay RHlat=[26.845967;26.839918;26.782452;26.743799;26.743799;26.749537;26.880737; 26.880537;26.857202;26.829894;26.777901;26.735698;26.718897;26.698844;26.6961 32;26.684253;26.682037;26.725009;26.841958;26.714154;26.674644;26.661601;26.8 49398;26.864092;26.683 075;26.690901;26.669542;26.871236; 26.862386;26.831647]; %upper boundary RLlat=[26.719692;26.778174;26.691415;26.666845;26.658913;26.702314;26.853576; 26.872188;26.832799;26.782865;26.717005;26.690501;26.681090;26.664944;26.6543 27;26.646453;26.637549;26 .700957;26.806024;26.667560;26.650132;26.641435;26.8 27370;26.847859;26.679048;26.688280;26.663302;26.864505;26.851948;26.823879]; %lower boundary for i=1:numel(Rlon) idx=find(longitude>Rlon(i) & latitudeRLlat(i)); uGOFgrid(idx)=NaN; vGOFgrid(idx)=NaN; end set(0,'DefaultFigurePosition', [20 50 850 500]); figure set(gcf,'color','w'); subplot(1,2,1) contourf(longitude,latitude,uGOFgrid,41,'LineStyle','none'); xlabel('LON') ylabel('LAT') colorbar; caxis([0 1]) h=colorbar; % ylabel(h,'Goodness of Fit') % ylim(h,[0 1]) ylim([26.54 26.92]) axis('equal') plot_google_map('Alpha',0.6)

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98 title('u component') subplot(1,2,2) contourf(longitude,latitude,vGOFgrid,41,'LineStyle','none'); xlabel('LON') ylabel('LAT') colorbar; caxis([0 1]) h=colorbar; % ylabel(h,'Goodness of Fit') % ylim(h,[0 1]) ylim([26.54 26.92]) axis('equal') plot_google_map('Alpha',0.6) title('v component') if f==1 suptitle(['K1 Tidal Frequency Goodness of Fit: ' num2str(depth) ' [m] depth']) elseif f==2 suptitle(['M2 Tidal Frequency Goodness of Fit: ' num2str(depth) ' [m] depth']) elseif f==3 suptitle(['K1 & M2 Frequency Goodness of Fit: ' num2str(depth) ' [m] depth']) end set(0, 'DefaultFigurePosition', [20 230 500 400]); PlatinumVideo.m clear all; close all; clc; % Selector: circuit='A'; % selector: A,B,C,D,E depth=5; %[m] w1=2*pi/(12.42/24); %M2 [days] w2=2*pi/(23.93/24); %K1 [days] if circuit=='A' load('platinum_A'); elseif circuit=='B' load('platinum_B'); elseif circuit=='C' load('platinum_C'); elseif circuit=='D' load('platinum_D'); elseif circuit=='E' load('platinum_E'); end numtrans=P{1,18}; %% Animation f or Transect 1

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99 dt=(1/24)/4; %15 minutes maxTime=2; %days tstep=0; while tstep
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100 end figure(1) xlabel('longitude [degrees]') ylabel('latitude [degrees]') title('Tidal Flow Without Residual Flow') lonRange=max(allLon) min(allLon); latRange=max(allLat) min(allLat); xmin=min(a llLon) lonRange*.1; xmax=max(allLon)+lonRange*.1; ymin=min(allLat) latRange*.2; ymax=max(allLat)+latRange*.2; scalex=(xmax xmin)/8; % can change this however without altering scale scaley=(ymax ymin)/8; scale=min(scalex,scaley); allu=[allu,[10 0]]; allv=[allv,[0 10]]; allLat=[allLat,[ymax 0.5*scaley ymax 0.5*scaley]]; allLon=[allLon,[xmax 0.8*scalex xmax 0.8*scalex]]; quiver(allLon, allLat,0.1*scale*allu,0.1*scale*allv,0,'b'); text(xmax 1*scalex,ymax 0.9*scaley,'10 [cm/s]') axis equal; axis([xmin 0.005 xmax+0.005 ymin 0.002 ymax+0.006]); % pause(.1) tstep=tstep+dt end PlotAllCircuits.m clear all; close all; clc % Selectors: depth=10; %[m] w1=2*pi/(12.4 2/24); %M2 [days] w2=2*pi/(23.93/24); %K1 [days] %% Plot Transect Path Flow % 'defaultfigureposition',[x y w h]' set(0,'DefaultFigurePosition', [20 20 900 600]); figure set(gcf,'color','w'); subplot(1,2,1) hold on allu=[]; allv=[]; allLat=[]; allLon=[]; for i=1:5 % number of circuits if i==1 load('platinum_A'); t=0.1875;

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101 elseif i==2 load('platinum_B'); t=1.7813; elseif i==3 load('platinum_C'); t=1.8125;%t=0.0833; elseif i==4 load('platinum_D'); t=0.6771; elseif i==5 load('platinum_E'); t=0.1875; end numtrans=P{1,18}; for j=1:numtrans clear lon; clear lat; depthidx=find(P{j,14}==depth); meanU=P{j,1};M2ampU=P{j,2};M2phU=P{j,3};K1ampU=P{j,4};K1phU=P{j,5}; meanV=P{j,6};M2ampV=P{j,7};M2phV=P{j,8};K1ampV=P{j,9};K1phV=P{j,10}; % latg=P{j,11};long=P{j,12}; %With Residual u=meanU(depthidx,:)+M2ampU(depthi dx,:).*sin(w1*t+M2phU(depthidx,:))+K1ampU(de pthidx,:).*sin(w2*t+K1phU(depthidx,:)); % depth/.5 3 finds the index for that depth v=meanV(depthidx,:)+M2ampV(depthidx,:).*sin(w1*t+M2phV(depthidx,:))+K1ampV(de pthidx,:).*sin(w2*t+K1phV(depthidx,:)); for n=1:size(P{j,11},2) clear col; for k=1:size(P{j,11},1) col(k)=nanmean(P{j,11}(k,n,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lat(n)=NaN; else lat(n)=col(min(find(isnan(col)==0))); end end for n=1:size(P{j,12},2) clear col; for k=1:size(P{j,12},1) col(k)=nanmean(P{j,12}(k,n,:)); end if isempty(col(min(find(isnan(col)==0))))==1; lon(n)=NaN; else lon(n)=col(min(find(isnan(col)==0))); end end ave=5; %number of cells to average for k=1:floor(size(u,2)/ave) %columns (distance/time along transect)

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102 unew(k)=nanmean(u((1+(k 1)*ave):(ave+(k 1)*ave))); vnew(k)=nanmean(v((1+(k 1)*ave):(ave+(k 1)*ave))); latnew(k)=nanmean(lat((1+(k 1)*ave):(ave+ (k 1)*ave))); lonnew(k)=nanmean(lon((1+(k 1)*ave):(ave+(k 1)*ave))); end u=unew; v=vnew; lat=latnew; lon=lonnew; allu=[allu,u]; allv=[allv,v]; allLat=[allLat,lat]; allLon=[allLon,lon]; end %transect if i==1 lonRange=max(allLon) min(allLon); latRange=max(allLat) min(allLat); xmin=min(allLon) lonRange*.1; xmax=max(allLon)+lonRange*.1; ymin=min(allLat) latRange*.2; ymax=max(allLat)+latRange*.2; scalex=(xmax xmin)/4; % can change this however without altering scale scaley=(ymax ymin)/4; scale=min(scalex,scaley); end clear P; end %circuits quiver(allLon, allLat,0.1*scale*allu,0.1*scale*allv,0,'b'); xlabel('LON') ylabel('LAT') axis('equal') plot_google_map('Alpha',0.6) xLimits = get(gca,'XLim'); yLimits = get(gca,'YLim'); P1u=[allu,[10 0]]; %for the first subplot P1v=[allv,[0 10]]; P1Lat=[allLat,[yLimits(2) 0.11*(yLimits(2) yLimits(1)) yLimits(2) 0.11*(yLimits(2) yLimits(1))]]; P1Lon=[allLon,[xLimits(2) 0.17*(xLimits(2) xLimits(1)) xLimits(2) 0.17*(xLimits(2) xLimits(1))]]; quiver(P1Lon,P1Lat,0.1*scale*P1u,0.1*scale*P1v,0,'b'); text(xLimits(2) 0.18*(xLimits(2) xLimits(1)),yLimits(2) 0.14*(yLimits(2) yLimits(1)), '10 [cm/s]') %% Plot Grid Flow: lonrange=[min(allLon) : 0.008 : max(allLon)]; lonrange=transpose(lonrange); latrange=[min(allLat) : 0.008 : max(allLat)]; [longitude,latitude]=meshgrid(lonrange,latrange); % Remove NaN: idx=find(~isnan(allu)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allv));

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103 allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allLon)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); idx=find(~isnan(allLat)); allu=allu(idx);allv=allv(idx); allLon=allLon(idx); allLat=allLat(idx); ugrid=griddata(allLon,allLat,allu,lonrange,latrange); vgrid=griddata(allLon,allLat,allv,lonrange,latrange); %Set land values to NaN: Ll on=[ 111.863352; 111.873738; 111.874682; 111.803621; 111.865771; 111.886927; 111.895418; 111.873546; 111.874600; 111.888641; 111.896861; 111.881525; 111.802398; 111.885245; 111.894140; 111.869483; 111.886026; 111.907440; 111.892053; 111.901534; 111.81355 4]; %values to left of bay LHlat=[26.807364;26.832105;26.796549;26.626474;26.813149;26.840338;26.846517; 26.833778;26.780186;26.842992;26.850839;26.838834;26.622134;26.840871;26.8426 62;26.778827;26.841512;26.882895;26.852821;26.862051;26.633516]; %upper bou ndary LLlat=[26.781927;26.781927;26.771149;26.618840;26.790550;26.818684;26.834012; 26.831341;26.755205;26.841554;26.845783;26.836780;26.614925;26.833939;26.8331 07;26.775133;26.838692;26.875469;26.844082;26.853622;26.624727]; %lower boundary for i=1:numel(L lon) idx=find(longitudeLLlat(i)); ugrid(idx)=NaN; vgrid(idx)=NaN; end Rlon=[ 111.814944; 111.823509; 111.796477; 111.764205; 111.756150; 111.801297; 111.844838; 111.852611; 111.836390; 111.824393; 111.81578 7; 111.797248; 111.781801; 111.764278; 111.746299; 111.736681; 111.728210; 111.807246; 111.826486; 111.765898; 111.740483; 111.731116; 111.829889; 111.840701; 111.775112; 111.795215; 111.763402]; %values to right of bay RHlat=[26.845967;26.839918;26.782452 ;26.743799;26.743799;26.749537;26.880737; 26.880537;26.857202;26.829894;26.777901;26.735698;26.718897;26.698844;26.6961 32;26.684253;26.682037;26.725009;26.841958;26.714154;26.674644;26.661601;26.8 49398;26.864092;26.683075;26.690901;26.669542]; %upper bounda ry RLlat=[26.719692;26.778174;26.691415;26.666845;26.658913;26.702314;26.853576; 26.872188;26.832799;26.782865;26.717005;26.690501;26.681090;26.664944;26.6543 27;26.646453;26.637549;26.700957;26.806024;26.667560;26.650132;26.641435;26.8 27370;26.847859;26.679 048;26.688280;26.663302]; %lower boundary for i=1:numel(Rlon) idx=find(longitude>Rlon(i) & latitudeRLlat(i)); ugrid(idx)=NaN; vgrid(idx)=NaN; end subplot(1,2,2) X=[longitude;[NaN*zeros(1,size(longitude,2))]]; Y=[latitude;[NaN*zeros(1,size(latitude,2))]]; U=0.1*scale*[ugrid;[NaN*zeros(1,size(ugrid,2))]]; V=0.1*scale*[vgrid;[NaN*zeros(1,size(vgrid,2))]]; ind=find(isnan(U)~=1 & isnan(V)~=1); quiver(X(ind),Y(ind),U(ind),V(ind),0,'b') xlabel('LON')

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104 ylabel('LAT') axi s('equal') plot_google_map('Alpha',0.6) xLimits = get(gca,'XLim'); yLimits = get(gca,'YLim'); X=[longitude;[NaN*zeros(1,size(longitude,2) 2) xLimits(2) 0.17*(xLimits(2) xLimits(1)) xLimits(2) 0.17*(xLimits(2) xLimits(1))]]; Y=[latitude;[NaN*zeros(1,size(latitude,2) 2) yLimits(2) 0.11*(yLimits(2) yLimits(1)) yLimits(2) 0.11*(yLimits(2) yLimits(1))]]; U=0.1*scale*[ugrid;[NaN*zeros(1,size(ugrid,2) 2) 10 0]]; V=0.1*scale*[vgrid;[NaN*zeros(1,size(vgrid,2) 2) 0 10]]; ind=find(isnan (U)~=1 & isnan(V)~=1); quiver(X(ind),Y(ind),U(ind),V(ind),0,'b') text(xLimits(2) 0.18*(xLimits(2) xLimits(1)),yLimits(2) 0.14*(yLimits(2) yLimits(1)),'10 [cm/s]') suptitle(['Velocity Vectors: ' num2str(depth) ' [m] Depth']) set(0, 'DefaultFigurePosition' , [20 230 500 400]); CTDPlotAll.m % ONLY DIURNAL COMPONENT clear all; close all; clc % Selectors select='S'; %'S' for Salinity,'T' for Temperature,'D' for Density depth=10; % Select any depth (max=30, 15 or less for full data set) % w1=2*pi/(12.42/24); %M2 [days] w2=2*pi/(23.93/24); %K1 [days] % omega=[w1 w2]; omega=w2; showFit=0; tidetime=0; long=[]; lati=[]; dep=[]; yarray=[]; for i=1:32 load(['ctd' num2str(i)]) if select=='S' y=s; idx=find(y>35 & y<36); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Salinity'; unit='[g/kg]'; elseif select=='T' y=te; idx=find(y>18 & y<23); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Temperature'; unit='[deg C]'; elseif select=='D' y=de;

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105 idx=find(y>23 & y<26); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Density'; unit='Density Anomoly [Kg/m^3]'; end %Break into separate columns for time: lon2=lon(1); lat2=lat(1); d2=d(1); t2=t(1); y2=y(1); n=2; k=1; for j=2:numel(d) if t(j)>t(j 1)+0.01 k =k+1; n=1; else n=n+1; end lon2(n,k)=lon(j); lat2(n,k)=lat(j); d2(n,k)=d(j); t2(n,k)=t(j); y2(n,k)=y(j); end idx=find(d2==0 | d2<2.5 | d2>40); lon2(idx)=NaN; lat2(idx)=NaN; d2(idx)=NaN; t2(idx)=NaN; y2(idx)=NaN; %Raise values in each column so there are no NaN's at top: for j=1:size(d2,2) first=min(find(isnan(d2(:,j))==0)); lon2(1:numel(lon2(first:end,j)),j)=lon2 (first:end,j); lat2(1:numel(lat2(first:end,j)),j)=lat2(first:end,j); d2(1:numel(d2(first:end,j)),j)=d2(first:end,j); t2(1:numel(t2(first:end,j)),j)=t2(first:end,j); y2(1:numel(y2(first:end,j)),j)=y2(first:end,j); end %Remove NaN Rows at end last=1; while sum(isnan(d2(last,:)))size(d2,1) break end end lon2(last:end,:)=[]; lat2(last:end,:)=[]; d2(last:end,:)=[]; t2(last:end ,:)=[]; y2(last:end,:)=[]; %Average Data to An Even Interval of Depth: d3=5:1:30; d3=d3'; d3=d3*ones(1,size(d2,2)); for j=1:size(d3,2) %through each time column for b=1:size(d3,1) %through each time column idx=find(d2(:,j)
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106 end %De tide data: idx=find(d3(1:end,1)==depth); long=[long; nanmean(lon3(idx,:))]; lati=[lati; nanmean(lat3(idx,:))]; %Perform least squares fit sample=y3(idx,:); time=t3(idx,:); [meanS,amp,phase]=hale ssqfit(omega,time,sample,showFit); % yarray=[yarray; meanS+amp(1).*sin(w1*tidetime+phase(1))+amp(2).*sin(w2*tidetime+phase(2))]; yarray=[yarray; meanS+amp.*sin(w2*tidetime+phase)]; % cc=lsqfit(w1,w2,time,sample); % yarray=[yarray; cc(1)+ cc(2).*sin(w1*tidetime+ cc(3))+ cc(4).*sin(w2*tidetime+ cc(5))]; clear lon; clear lat; clear d; clear t; clear y; clear lon2; clear lat2; clear d2; clear t2; clear y2; clear lon3; clear lat3; clear d3; clear t3; clear y3; end lonrange=[min(long) : (max(long) min(long))/100 : max(long)]; lonrange=transpose(lonrange); latrange=[min(lati) : (max(lati) min(lati))/100 : max(lati)]; [lon,lat]=meshgrid(lonrange,latrange); ygrid=griddata(long,lati,yarray,lonrange,latrange); %Set la nd values to NaN: Llon=[ 111.863352; 111.873738; 111.874682; 111.803621; 111.865771; 111.886927; 111.895418; 111.873546; 111.874600; 111.888641; 111.896861; 111.881525; 111.802398; 111.885245; 111.894140; 111.869483; 111.886026; 111.907440; 111.892053; 111.901534; 111.813554; 111.876504; 111.862524; 111.867639; 111.870914; 111.860961; 111.867480; 111.796704; 111.870674; 111.885869; 111.884169; 111.871808; 111.868888; 111.859570]; %values to left of bay LHlat=[26.807364;26.832105;26.796549;26.626474;26.8 13149;26.840338;26.846517; 26.833778;26.780186;26.842992;26.850839;26.838834;26.622134;26.840871;26.8426 62;26.778827;26.841512;26.882895;26.852821;26.862051;26.633516;26.838511;26.8 16399;26.826658;26.765776;26.783931;26.780689;26.612161;26.834348;26.845365; 2 6.842671;26.836712;26.831534;26.803644]; %upper boundary LLlat=[26.781927;26.781927;26.771149;26.618840;26.790550;26.818684;26.834012; 26.831341;26.755205;26.841554;26.845783;26.836780;26.614925;26.833939;26.8331 07;26.775133;26.838692;26.875469;26.844082 ;26.853622;26.624727;26.834023; 26.807069;26.819383;26.751217;26.774732;26.761531;26.605829;26.830837;26.8386 95;26.838707;26.829038; 26.828027;26.782422]; %lower boundary for i=1:numel(Llon) idx=find(lonLLlat(i)); ygri d(idx)=NaN; ygrid(idx)=NaN; end Rlon=[ 111.814944; 111.823509; 111.796477; 111.764205; 111.756150; 111.801297; 111.844838; 111.852611; 111.836390; 111.824393; 111.815787; -

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107 111.797248; 111.781801; 111.764278; 111.746299; 111.736681; 111.728210; 111.807246; 111.826486; 111.765898; 111.740483; 111.731116; 111.829889; 111.840701; 111.775112; 111.795215; 111.763402; 111.847963; 111.847291; 111.832357]; %values to right of bay RHlat=[26.845967;26.839918;26.782452;26.743799;26.743799;26.749537;26.880737; 26.880537 ;26.857202;26.829894;26.777901;26.735698;26.718897;26.698844;26.6961 32;26.684253;26.682037;26.725009;26.841958;26.714154;26.674644;26.661601;26.8 49398;26.864092;26.683075;26.690901;26.669542;26.871236; 26.862386;26.831647]; %upper boundary RLlat=[26.71 9692;26.778174;26.691415;26.666845;26.658913;26.702314;26.853576; 26.872188;26.832799;26.782865;26.717005;26.690501;26.681090;26.664944;26.6543 27;26.646453;26.637549;26.700957;26.806024;26.667560;26.650132;26.641435;26.8 27370;26.847859;26.679048;26.688280;2 6.663302;26.864505;26.851948;26.823879]; %lower boundary for i=1:numel(Rlon) idx=find(lon>Rlon(i) & latRLlat(i)); ygrid(idx)=NaN; ygrid(idx)=NaN; end set(0, 'DefaultFigurePosition', [700 10 650 650]); figure(2) set(gcf,'color','w '); hold on contourf(lon,lat,ygrid,26,'LineStyle','none'); colorbar; h=colorbar; ylabel(h,unit) % pcolor(lon,lat,ygrid); % shading interp; freezeColors xlabel('LON') ylabel('LAT') title([plotstr ' at ' num2str(depth) ' [m] Depth']) % load('coradcp_A');plot(silverA(:,3),silverA(:,2),'k.','MarkerSize',.15); % load('coradcp_B');plot(silverB(:,3),silverB(:,2),'k.','MarkerSize',.15); % load('coradcp_C');plot(silverC(:,3),silverC(:,2),'k.','MarkerSize',.15); % load('coradcp_D');plot(silverD( :,3),silverD(:,2),'k.','MarkerSize',.15); % load('coradcp_E');plot(silverE(:,3),silverE(:,2),'k.','MarkerSize',.15); ylim([26.52 26.93]) axis('equal') plot_google_map('Alpha',0.6) set(0, 'DefaultFigurePosition', [20 230 500 400]); CTDTransectContour.m % De tided with K1 frequency close all; clear all; clc; circuit='E'; % selector: A,B,C,D,E select='D'; %'S' for Salinity,'T' for Temperature,'D' for Density transect=4; % selector:1,2,3,4,5,6 note: not all transects have CTD casts

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108 w2=2*pi/(23.93/24); %K1 [days] omega=w2; showFit=0; tidetime=0; % Load CTD Data: if circuit=='A' & transect==1 ctdarray=[1,2,3,4,5]; load('gold_A'); elseif circuit=='A' & transect==2 ctdarray=[6,7,8]; load('gold_A'); elseif circuit=='B' & transect==1 c tdarray=[9,11]; load('gold_B'); elseif circuit=='B' & transect==5 ctdarray=[12,13,14]; load('gold_B'); elseif circuit=='C' & transect==1 ctdarray=[15,16,17]; load('gold_C'); elseif circuit=='C' & transect==5 ctdarray=[18,19,20]; load('gold_C'); elseif circuit=='D' & transect==4 ctdarray=[21,22,23]; load('gold_D'); elseif circuit=='D' & transect==2 ctdarray=[24,25,32]; load('gold_D'); elseif circuit=='E' & transect==4 ctdarray=[26,27,28]; load('gold_E'); elseif circuit=='E' & transect==2 ctdarray=[29,30,31]; load('gold_E'); end long=[]; lati=[]; dep=[]; yarray=[]; for i=ctdarray load(['ctd' num2str(i)]) %Remove Bad Data: if select=='S' y=s; idx=find(y>35 & y<36); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Salinity'; unit='[g/kg]'; CMIN=35.15; CMAX=35.80; elseif select=='T' y=te; idx=find(y>18 & y<23); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx);

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109 plotstr='Temperature'; unit='[deg C]'; CMIN=19.15; CMAX=22.05; elseif select=='D' y=de; idx=find(y>23 & y<26); lon=lon(idx); lat=l at(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Density'; unit='Density Anomoly [Kg/m^3]'; CMIN=24.65; CMAX=25.25; end %Break into separate columns for time: lon2=lon(1); lat2=lat(1); d2=d(1); t2=t(1); y2=y( 1); n=2; k=1; for j=2:numel(d) if t(j)>t(j 1)+0.01 k=k+1; n=1; else n=n+1; end lon2(n,k)=lon(j); lat2(n,k)=lat(j); d2(n,k)=d(j); t2(n,k)=t(j); y2(n,k)=y(j); end idx=find(d2==0 | d2<2.5 | d2>40); lon2(idx)=NaN; lat2(idx)=NaN; d2(idx)=NaN; t2(idx)=NaN; y2(idx)=NaN; %Raise values in each column so there are no NaN's at top: for j=1:size(d2,2) first=min(find( isnan(d2(:,j))==0)); lon2(1:numel(lon2(first:end,j)),j)=lon2(first:end,j); lat2(1:numel(lat2(first:end,j)),j)=lat2(first:end,j); d2(1:numel(d2(first:end,j)),j)=d2(first:end,j); t2(1:numel(t2(first:end,j)),j)=t2(first:end,j); y2(1:numel(y2(first:end,j)),j)=y2(first:end,j); end %Remove NaN Rows at end last=1; while sum(isnan(d2(last,:)))size(d2,1) break end end lon2(last:en d,:)=[]; lat2(last:end,:)=[]; d2(last:end,:)=[]; t2(last:end,:)=[]; y2(last:end,:)=[]; %Average Data to An Even Interval of Depth:

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110 d3=ceil(min(min(d2))):0.5:floor(max(max(d2))); d3=d3'; d3=d3*ones(1,size(d2,2)); for j=1:size(d3,2) %through each time column for b=1:size(d3,1) %through each time row idx=find(d2(:,j)
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111 set(0, 'DefaultFigurePosition', [20 70 800 350]); figure set(gcf,'color','w'); % plot(dii,maxdepth,'k','LineWidth',2); hold on for i=1:size(yi,2) for j=1:size(yi,1) if isnan(yi(j,i))==1 & j>2 yi(j 2:end,i)=NaN; break end end end % To set the axis so you don't see blanks: Lidx=0; %for beginning of xlim while 1<2 Lidx=Lidx+1; if nanmean(yi(5:end,Lidx))>0 break end end Ridx=size(yi,2)+1; %for end of xlim while 1<2 Ridx=Ridx 1; if nanmean(yi(5:end,Ridx))>0 break end end diststep=Gdist(2) Gdist(1); for i=1:size(distance,1) for j=1:size(distance,2) Gidx=find(Gdist>(distance(i,j) diststep) & Gdist<(distance(i,j)+diststep)); distance(i,j); if sum(depth(i,j)>maxdepth(Gidx))>0 yi(i,j)=NaN ; end end end % Range=max(max(yi)) min(min(yi)); % PercentChange=(Range/max(max(yi)))*100 [c,h]=contourf(distance,depth,yi,81,'LineStyle','none'); set(gca,'YDir','reverse'); % axis([distance(1,Lidx) distance(1,Ridx) 3 max(maxdepth)+2]) if max(max(distance(:,Lidx:Ridx)))>Gdist(max(find(~isnan(maxdepth)==1))) xmax=Gdist(max(find(~isnan(maxdepth)==1))); else xmax=max(max(distance(:,Lidx:Ridx))); end

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112 if min(min(distance(:,Lidx:Ridx)))35 & y<36); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Salinity'; unit='[g/kg]'; elseif select=='T' y=te; idx=find(y>18 & y<23); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Temperature'; un it='[deg C]'; elseif select=='D' y=de; idx=find(y>23 & y<26); lon=lon(idx); lat=lat(idx); d=d(idx); t=t(idx); y=y(idx); plotstr='Density'; unit='[Kg/m^3]';

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113 end %Break into separate columns for time: lon2=lon(1); lat2=lat(1); d2=d(1); t2=t(1); y2=y(1); n=2; k=1; for j=2:numel(d) if t(j)>t(j 1)+0.01 k=k+1; n=1; else n=n+1; end lon2(n,k)=lon(j); lat2(n,k)=lat(j); d2(n,k)=d(j); t2(n,k)=t(j); y2(n,k)=y(j); end idx=find(d2==0 | d2<2.5 | d2>40); lon2(idx)=NaN; lat2(idx)=NaN; d2(idx)=NaN; t2(idx)=NaN; y2(idx)=NaN; %Raise values in each column so there are no NaN's at top: for j=1:size(d2,2) first=min(find(isnan(d2(:,j))==0)); lon2(1:numel(lon2(first:end,j)),j)=lon2(first:end,j); lat2(1:numel(lat2(first:end,j)),j)=lat2(first:end,j); d2(1:numel(d2(first:end,j)),j)=d2(first:end,j); t2(1:numel(t2(first:end,j)),j)=t2(first:end,j); y2(1:numel(y2(first:end,j)),j)=y2(first:end,j); end %Remove NaN Rows at end last=1; while sum(isnan(d2(last,:)))size(d2,1) break end end lon2(last:end,:)=[]; lat2(last:end,:)=[]; d2(last:end,:)=[]; t2(last:end,:)=[]; y2(last:end,:)=[]; %Average Data to An Even Interval of Depth: d3=c eil(min(min(d2))):0.5:floor(max(max(d2))); d3=d3'; d3=d3*ones(1,size(d2,2)); for j=1:size(d3,2) %through each time column for b=1:size(d3,1) %through each time row idx=find(d2(:,j)
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114 %De tide data: for j=1:size(d3,1) long=[long; nanmean(lon3(j,:))]; lati=[lati; nanmean(lat3(j,:))]; dep=[dep; d3(j,1)]; %Perform least squares fit sample=y3(j,:); time=t3(j,:); [meanS,amp,phase]=halessqfit(omega,time,sample,showFit); yarray=[yarray; meanS+amp.*sin(w2*tidetime+phase)]; end % clear lon; clear lat; clear d; clear t; clear y; % clear lon2; clear lat2; clear d2; clear t2; clear y2; % clear lon3; clear lat3; clear d3; clear t3; clear y3; set(0, 'DefaultFigurePosition', [20 70 800 500]); figure(1) set(gcf,'color','w' ); trange=[min(min(t3)):(max(max(t3)) min(min(t3)))/30:max(max(t3))]; deprange=[min(dep):(max(dep) min(dep))/30:max(dep)]; deprange=transpose(deprange); [tgrid,depgrid]=meshgrid(trange,deprange); ygrid=griddata(t3,d3,y3,trange,deprange); % To set th e axis so you don't see blanks: Lidx=0; %for beginning of xlim while 1<2 Lidx=Lidx+1; if sum(isnan(ygrid(:,Lidx)))
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115 LIST OF REFERENCES Caliskan, H. , & Valle Levinson, A. (200 8 ). Wind wave transformations in an elongated bay. Continental Shelf Research 28 , 1702 1710. Cheng, P. , Valle Levinson, A., Winant, C. , Ponte, A., Gutiérrez de Velasco, G., & Winters, K.B. (2010). Upwelling enhanced seasonal stratification in a semiarid bay. Continental Shelf Research 30 , 1241 1249. Choi, K.W., Lee, J.H.W., & Wong, K.T.M. (2003). Field Verification of Diffusion Induced Circulation in Sok Kwu Han, Hong Kong. International Conference on Estuaries and Coasts, November 9 11, 2003, Hangzhou, China. Journal of Atmospheric and Oceanic Technology 6 , 169 172. MATLAB R2012b (2012). The MathWorks, Inc. Natick, Massachusetts. Ponte, A.L. , Gutié rrez de Velasco, G., Valle Levinson, A. , Winters, K.B., & Winant, C.D. (2012 ). Wind Driven Subinertial Circulation inside a Semienclosed Bay in the Gulf of California. Journal of Physical Oceanography Volume 42 , 940 955. Winant, C. , Valle Levinson, A., Ponte, A. , Winant, C., Gutiérrez de Velasco, G., & Winters, K.B. (2013). Obser vations on the Lateral Structure of Wind Driven Flows in a Stratified, Semiarid Bay of the Gulf of California. Estuaries and Coasts , Journal of the Coastal and Estuarine Research Federation Volume 36 Number 3.

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116 BIOGRAPHIC AL SKETCH Patrick Glendo n Miskel was born in 1990 in San Francisco , California. As a student in the accelerated 3/2 Dual Degree engineering program within the University of California system, he spent his first 3 years of college at University of California, Santa Cruz, then the fo llowing 2 years at University of California, Berkeley. At Santa Cruz he received a Bachelor of Arts in American Studies. At Berkeley he received a Bachelor of Science in Ci vil Engineering as a precedent to pursuing a coastal engineering career. Following h is undergraduate education he obtained a Master of Science degree in Coastal & Oceanographic Engineering at University of Florida , where he was the recipient of the 2014 2015 Bob & Phyllis Dean Fellowship award and the Achievement Award for New Engineering Graduate Students. During his college career he spent 2 summers interning at Riedinger Consulting in Sausalito, California consulting for project management and construction. His summer between semesters at University of Florida was spent as a coastal en gineering intern at Moffatt & Nichol in Tampa, Florida.