NOAA Technicol Report NOS CS 4

TIDAL CONSTITUENT AND RESIDUAL

INTERPOLATION (TCARI): A New Method for

the Tidol Correction of Bothymetric Doto

Kurt Hess

Richord Schmqlz

Chris Zervqs

Woyne Collier

Jufy 1999

[Revised June 2OO4l

n OO q Nofionol Oceonic ond Atmospheric Administrotion

U.S. DEPARTMENT

oF co^/t ^ERCE

Wlliom Doly, Secrefory

Office of Coost Survey

Coptoin Dovid MocForJond

Notionol Oceonic ond

Almospheric Ad mi nistrotion

D. Jomes Boker, Under Secrefory

Notionol Oceon Service

Noncy Foster

fusisfo nf Ad m i n istrotor

Coost Survey Development

Loborofory

Bruce Porker
NOTICE

Mention of q commerciol compony or product does nof constitute on

endorsement by NOAA. Use for publicity or odvertising purposes of

informofion from this publicotion concerning propriefory products or the

fests of such products is not oulhorized.
TABLE OF CONTENTS

LISTOFFIGURES ....v

LISTOFTABI-ES .:.. ....iX

EXECUTIVESUMMARY ..... xi

l.INTRODUCTION

2. TrDAL CONSTTTUENT AND RESTDUAL TNTERPOLATTON (TCARI) . . . . . . 3

2.1. Tide Corrections . .. . . .. ..3

Z.Z.TideZoning .....3

2.3. AstronomicTides andTidalConstituents ......5

2.4.Spatiallnterpolation ......5

2.5.TCARI .. .... ...7

z.6.Tc\RlDataRequirements .....8

2.T . Other Methods of Providing Corrections

3. INTERPOLATION BY SOLUTION OF LAPLACE'S EQUATION . . . 11

3. 1. Laplace's Equation . . 

'1 I

3.2. BoundaryConditions ....12

3.3. Natural Distributions of Corange and Cophase Lines . . . . 13

3.4. Solution by Finite Differences

3.5. Grid Generation

3.6. Rectangular Basin Test Case . . . 15

4. APPUCATION TO GALVESTON BAY . . . . T9

4.l.ShipTrackData ....19

4.2.Water Irvel and Model Data . .2O

4.3. Grid and Weighting Functions

4.4.Constituentlnterpolation .....24

4.5. Residual Water Irvels . . .25

4.6. The Offset and Datum . . .27

4.7. SensitivityTests ....27

4.8. AccuracyTests .... .30

' .-

5. APPLICATION TO SAN FRANCISCO BAY . . . . 35

5.1. ShipTrackData ....35

5.2.Water Irvel and Model Data . .36

5.3. Grid and Weighting Functions . . . . .37

5.4. Constituentlnterpolation .....37

5.5. Residual Water I-evels . . . 4t

5.6. The Offset and Datum . . . . 4L

5.7 . Accuracy Tests

1il
6. COMPUTER PROGRAMS . . .47

6.1.PA:GridGeneration. ....47

6.2.P8: Weighting Function Calculation . . . .52

6.3. PC: Calculation of the Tide Correction . . 55

7. SUMMARY AND CONCLUSIONS . . . 59

7.l.Summary. .....59

7.2. Major Results . . 6I

7 .3. Production of Ellipsoidally-Referenced MLLW Fields . . 62

T.4.FutureEnhancements ....64

ACKNOWLEDGMENTS . .65

REFERENCES . .65

APPENDX A. TIDE WAVE SOLUTION . . . . .67

APPENDX B. TIDE DATA FOR GALVESTON BAY . .69

APPENDX C. GALVESTON BAY NUMERICAL CIRCULATION MODEL . . . .73

APPENDD( D. SIMULATED CONSTITUENT FIELDS FOR GALVESTON BAY . . . . 85

APPENDX E. TIDE DATA FOR SAN FRANCISCO BAY

APPENDD( F. SIMULATED CONSTITUENT FIELDS FOR SAN FRANCISCO BAY . . . .97

iv
LIST OF FIGURES

Figure 1.1. Schematic showing the depth sounding,Dsi the correction, h*;thetide zoned

correction, hr*,andothersurveyvariables... .....1

' Figure Z.l.The tide zones in Galveston Bay. . ... .4

Figure 2.2.The influence of land on M2 phases forthree nearbygauge locations. . . . .6

Figure 3.1. (a) Gridforrectangulartest case. Cells are0.5 nmi on aside. (b) Gridforthe

rectangular test region, but rotated 45 degrees . . . . . 15

Figure 3.2. Solution for G in an idealized basin, solving I;iplace's Equation with boundary

values of O = 100 atpoint A andO =0 atpointB fortwo values ofa. . . . . . 16

Figure 3.3.Contours created by spatial interpolation of values 100 at point A and 10

at point B. . .

Figure 3.4. Contours created by spatial interpolation of the sine and cosine of values 100

point A and 10 at point B. . . 18

Figure 4.1. Galveston Bay locations of ellipsoidally-referenced water level measurements .. . .19

Figure 4.2.I-ocations, numbers, and names of 14 Galveston Bay water level gauges

that supplied data used in this study.

Figure 4.3. Grid generated by coastline for solving the LE in Galveston Bay . .22

Figure 4.4. Weighting function g@, y) for the water level station at Smith Point (877-0931) . .23

Figure 4.5. Distribution of M2 epoch (local) from (a) the numerical model and (b) the LE

interpolation method. . . .24

Figure 4.6. Distribution of M, amplitude from (a) the numerical model and (b) TCARI . .25

Figure 4.7. Residual water levels in Galveston Bay during 1995 . . . . .26

Figure a.8. (a) Offset (m) of MSL minus MLLW, Ho, and (b) tide datum MSL relative to

the ellipsoid, HE. .

Figure 4.9. Scatter plot showing the corrections determined by tide zoning and those

determined by TCARI. The correlation coefficient is 0.861 . . .32

Figure 4.L0. Scatter plot showing the kinematic GPS-measured water levels and the TCARIpredicted water levels, both referenced to the ellipsoid . .34
Figure 5.1. Location of water level measurements (denoted by a '+') in San Francisco Bay

madebyNOS duringMarch andJune of 1997. .... ....35

Figure 5.2. Present and past locations of NOS water level gauges in San Francisco Bay where

tidal constituent and/or time series data were used. . . . . .36

Figure 5.3. TCARI gnd for San Francisco Bay. Cell size is 0.25 nautical miles. . . . . 38

Figure 5.4. The weighting function, g@,y), for San Irandro Marina(941-4688) shown as a

percentage. .... ....39

Figure 5.5. Mr amplitudes (cm) as generated by (a) TRIM and (b) TCARI. . . . . 40

Figure 5.6. M, local epoch (degrees) as generated by (a) TRIM and (b) TCARI. . . . .40

Figure 5.7. Residual water levels at four locations in San Francisco Bay . . . . . 4I

Figure 5.8. Distribution of the MSL-Io-MLLW offset (m) in San Francisco Bay as

generatedbyTcARl. ....42

Figure 5.9. Distribution of ellipsoidally-referenced MSL datum (m) computed with the

TCARI method in central San Francisco Bay. . . . .43

Figure 5.10. Scatter plot showing 939 ellipsoidally-referenced, measured water levels and the

TcARl-predicted water levels for the s:rme time and location . . . . M

Figure5.ll.TidezonesforSanFranciscoBay. ..:. .....45

Figure 6.1. Galveston Bay region showing coastline data (solid lines), the grid window

(dashed lines), the ocean boundary (dotted lines), and the location of the water cell. . . . 48

Figure 6.2. Control file used to provide input to Program A and Program B as applied to

Galveston Bay. only data above the dashed line is read. . . . . . 50

Figure 6.3. Typical records from acoastline file . . . .51

Figure 6.4. All records from the ocean boundary file for Galveston Bay. . . . . . 51

Figure 6.5. The Station file, showing tide station locations and other data for Galveston Bay . .52

Figure6.6.Sampleportionof agridfile.. ......53

Figure 6.7. Sample portion of the g field file. . . . 55

Figure 6.8. Tidal constituent data for a single station in a NOS standard format, . . . . 56

Figure 6.9. A portion of the equilibrium arguments and lunar node factors file . . . , 56
Figure 6.10. File with the residual file names. . . . 56

Figure 6.11. Control file forProgram C. 

: 

. . . . . .57

Figure 6.12. Sample of the Program C output file . . . . 58

Figure 7.1. TCARI's ellipsoidally-referenced MLLW field (m) in Galveston Bay. . .63

Figure 7.Z.TCAR['s ellipsoidally-referenced MLLW field (m) for San Francisco Bay . . .64

Figure C.1. Curvilinear grid used in the three-dimensional hydrodynamic model study

of Galveston Bay

Figure D.1. For K,,.distribution in San Francisco Bay of epoch from the model (a) and

TCARI (b), and amplitude from the model (c) and TCARI (d). . . . 85

Figure D.2. For O,, distribution in San Francisco Bay of epoch from the model (a) and

TCARI (b), and amplitude from the model (c) and TCARI (d).

Figure D.3. For P,, distribution in San Francisco Bay of epoch from the model (a) and

TCARI (b), and amplitude from the model (c) and TCARI (d). . . .87

Figure F.1. TRIM and TCARI fields for K, phase and amplitude . . . . 97

Figure F.2. TCARI fields for S, phase and amplitude. . . . . 98

Figure F.3. TCARI fields for O, phase and amplitude. . . . . 98

Figure F.4. TCARI fields for P1 phase and amplitude. . . . . gg

Figure F.5. TCARI fields for N, phase and amplitude. . . .99

vlr
viii
LIST OF TABLES

RMS differences between predicted water levels (using three methods) and GPS-measured

water level.. xii

Table 3.1. For an angle varying from 0degrees at one end to a range of values at the other end, the

maximum difference (degrees) between two solutions. . . 18

Table 4.1. Tide and related data used in the Galveston Bay ship track data comparison. . . 2l

Table 4.2. Results of the benchmark run and the sensitivity tests. Errors are in cm. . . . . .28

Table 4.3. Results from the use of hourly or 6-minute observed data for the calculation of the

residualwaterlevels. ....29

Table 4.4. Results for full TCARI, total water level interpolation, and ignoring the residual water

level. Errors are in cm. . . .29

Table 4.5. Results from the accuracy tests. GPS measured water levels were compared to water

levels observed at four gauges. In TCARI, the predicted water levels were compared to

those measured in Huff and Gallagher. . . 30

Table 4.6. Enors (cm) based on water levels estimates using tide zoned corrections. Results are

for preliminary tide zoning (one station), final zoning with five stations, and final zoning

with eight stations. . . 31

Table 4.7. Results from comparing errors in water level estimates using spatially-interpolated

discrete tide zoning corrections and TCARI

Table 4.8. Mean and RMS error and standard deviation of the predicted water level as compared

to the measured water level in Galveston Bay using various methods of prediction . . . .34

Table 5.1. Mean elror, standard deviation, RMS elror, and maximum value of the error (the

predicted minus the measured) in water levels in San Francisco Bay (cm) for several

methods of estimation as compared to the kinematic GPS measurements . . . 46

Table 7.1. Comparison of errors in tide zoning and TCARI in estimating the post-processed water

leveldata ,....62

Table B.1. Observed tidal constituent amplitudes (mm) in Galveston Bay . . . . .69

Table B.z.Observed tidal constituent Greenwich epochs (degrees) in Galveston Bay. . . .70

Table 8.3. Observed tidal constituent local epochs (degrees) in Galveston Bay . . . .70

Table B.4.Methods of harmonic analysis and length of time series . .7I

ix
Table C.1. Tidal constituent amplitudes, A (cm), and local epochs, K (degrees). Values are shown

for the Tide-Only (May 1995) run, NOS accepted values, the elror, and values for the Tide

PlusWindrun .....77

Table E.1. Observed tidal constituent amplitudes (mm) in San Francisco Bay. . . . . . 89

Table E.2. Observed tidal Greenwich epochs (degrees) in San Francisco Bay. . . . . . 91

Table 8.3. Observed tidal local epochs (degrees) in San Francisco Bay. . .92

Table E.4. Methods of Harmonic Analysis and Irngth of Time Series Used. . .94
EXECUTIVE SUMMARY

The Problem The National Ocean Service's (NOS's) hydrographic survey data are processed to

give water depth at the point of the measurement. To produce a depth relative to Mean Lower Low

Water (MLLW), which is the chart datum, the measured depth must be corrected to account for the

departure of the instantaneous water level from MLLW. This departure is due to the astronomic tide,

river flow, water density effects, and meteorological influences. At present, discrete tide zoning is

used to provide this correction. Discrete tide zoning rests on the simplifying assumption that the water

level in an entire zone has a fixed magnitude and phase relationship to the measured water level at a

single nearby gauge. However, this method has several drawbacks. It is inaccurate because it cannot

account for changes in the type of tide (e.g., diurnal, semidiurnal, or mixed) between stations and it

assumes that non-tidal components vary in space and time the same way that tidal components do. It

produces a discontinuity when crossing from one zone to the next. Finally, it cannot be used to

reference survey data to the GPS ellipsoid

A New Method of Solution A new method of making this correction takes values at the tide gauges

and spatially interpolates them throughout the survey region. The values at the gauges which are

spatially interpolated are:

o each tidal constituent's amplitude and phase value,

o the residual, or non-tidal, water level,

o the offset, which is the difference between local Mean Sea Irvel (MSL)

and MIIW, and

o a tidal datum (either MSL or MLLIV) relative to the ellipsoid.

The correction for the time and location of the ship is computed by summing the astronomic tide

(computed from the interpolated constituents), the interpolated residual, and the interpolated offset.

In addition, for a GPS-supported survey, the ellipsoidally-referenced MLLTV values can be spatially

interpolated and used to determine MLLW depth. The spatial interpolation at the core of this method

is carried out by the use of a set of weighting functions that quantify the local contribution from each

of the shore gduges. The weighting funCtionsare generated numerically by solving I-aplace's Equation

on a grid. The new method is called Tidal Constituent And Residual Interpolation (TCARI).

Accuracy of the New Method The TCARI method was tested for accuracy using post-processed

kinematic GPS measurements of water level collected by NOS in Galveston Bay, Texas, and San

Francisco Bay, California. The measurements themselves had an accuracy estimated to be from 7 (San

Francisco Bay) to 9 cm (Galveston Bay). The results (Table) indicate that TCARI was more accurate

than either the numerical model or tide zoning. Although TCARI had lower elrors than tide zoning,

both methods had errors approximately equal to those in the measurements. It is therefore difficult to

detennine whether the difference between TCARI and tide zoning is significant.

x1
Table. RMS differences betweenpredicted water levels (using three methods) and GPS-measured

water level in Galveston Bav andSan Francisco B

Conclusions The following conclusions about TCARI's application can be made:

o TCARI is more objective and somewhat more accurate than tide zoning when compared to

post-processed kinematic GPS water level data.

TCARI is a data-intensive method. Because of this, results should be better in coastal areas

that have many historical locations where tidal constituents, tidal datum offsets, and

ellipsoidally-referenced tidal datums are known. TCARI generally gives better results with

6-minute observational water levels, rather than hourly, because the non-tidal variation is

more accurately represented.

TCARI can improve tide zoning and tide prediction. TCARI can be adapted to predict the corange and co-phase lines that are used to establish the tide zones. TCARI also offers a new

method of hindcasting tidal variations in coastal areas

TCARI can be used to develop ellipsoidally-referenced MLLW fields. Thus TCARI is

positioned for use for future NOS surveys, although it needs many stations where

ellipsoidally-referenced tidal datums are known.

o TCARI and numerical model fields can be combined to give improved products. Model

effors in estimating the ellipsoidally-referenced water levels may be reduced by using the

TCARI spatial interpolation scheme to produce the model datum field. Also, constituent fields

could be improved by correcting the model-generated constituent distributions with TCARI's

spatially-interpolated error fi elds.

o

o

fanclsco

Prediction Method Galveston Bay San Francisco Bay

Numerical Modeling 15 cm not available

Tide Zoning 9.4 cm 9.8 cm

TCARI 7.5 cm 8.8 cm

xll
1.INTRODUCTION

Bathymetric survey data collected by ships are estimates of total water depth at the points where the

measurements are obtained. Survey depths must be corrected for several effects, one of which is the

departure of the instantaneous water level from mean lower low water (MLLW). MLLW is the datum

for NOS charts (Figure 1.1). This departure, which is subtracted from the measured depth, is called

the 'tide correction' and is due to both the astronomical tide and the non-tidal effects such as wind

setup and river runoff. Today, discrete tide zoning is the method NOS uses to provide this correction.

Discrete tide zoning rests on the assumption that the water level in a zone has a fixed magnitude a1d

phase relationship to the measured water level at a nearby gauge. However, this method has kno*n

inaccuracies and it produces a discontinuity when crossing from one zone to the next. The objective

of the present study is to develop a new method of estimating the tide correction which is not linked

to discrete tide zones and which relies on separating the astronomical tide from the non-tidal

component.

In discrete tide zoning(Gill, 1 998),

a number of geographic zones are

constructed, each covering a

portion of the coastal area being

surveyed. The tide correction

within any zone is computed by

multiplying the amplitude of the

water level above MLLW

measured at a nearby gauge by a

ftilnge factor and by applyng a time

difference. Within each zone, the

range factor and time difference

are considered to be constant.

However, since range ratios and

time differences are applied to the

total observed water level

variation (relative to MLLW), this

results in a correction which can

be inaccurate because it cannot

account for changes in the type of

tide (e.g., diurnal, semidiurnal, or

mixed) between stations and it

assumes that non-tidal components

vary in space and time the same

way that tidal components do.

The new approach described here

is to (1) create an estimate of the

local astronomical tide by spatially

interpolating the ti dal constituents,

which have been determined from

the harmonic analysis of a time

series of prior observations at each

Figure 1.L. Schematic showing the depth sounding , Dsi

the correction, h*;thetide zonedcorrection, ht*; the sea

surface elevation relative to the ellipsoid , Dcrsithe offset

between MSL and MLLW, Ho; the MSL elevation

relative to the ellipsoid, Hei the depth at MLLW, Drow'

the MLL\M surface relative to the ellipsoid, Hri and the

bottom elevation relative to the ellipsoid, Hu.

GPS Ellipsoid
station, to the required location and then reconstructing the astronomical tide by summing the

constituents, and (2) create an estimate of the non-tidal component by spatially interpolating the

residual waterlevel (observed total water level minus the reconstructed tide). These two components

wouldbe summed to give the final, more accurate correction to thebathymetric data. The new method

is called Tidal Constituent and Residual Interpolation (TCARI), and is discussed in Section 2.

The approach to spatial interpolation of data required additional research. The method selected for

spatial interpolation of the tidal harmonic constituents is obtained by assuming that spatial variation

of the amplitude and phase of all tidal constituents obeys l-aplace's Equation (LE), the solution of

which is found numerically. The method was tested for a rectangular basin (Section 3).

Data from Galveston Bay (Section 4) and San Francisco Bay (Section 5) were used to evaluate the

approach. Another spatial distribution of tidal constituents has been generated from the Galveston Bay

numerical circulation model, and these were compared to the interpolated constituents. The new

estimate of the tide correction will be compared to that generated by the NOS Galveston Bay

hydrodynamic model (Section 4 and Appendix C),

TCARI could be used in post-survey data processing and potentially for ship-board data processing.

Several programs have been written in Fortran to generate the necessary files and data (Section 6).

The use of bathymetric data combined with GPS-measured water level (relative to the ellipsoid) is

a technology that is quickly becoming practical. TCARI can easily be used to, for example, estimate

the distribution of MLLW (relative to the ellipsoid) throughout the survey area, provided some data

are available (Section 7). Discrete tide zoning does not have this capability.

This project supports the Promote Safe Navigation element of the NOAA strategic plan byimproving

the accuracy of NOAA's nautical charts and reducing processing time. More accurate information on

local tides and nontidal water levels will result in more accurate bathymetric data (relative to MLLW)

for NOS's nautical charts, and hence more accurate under-keel depth information for shipping and

accident avoidance.
2. TTDAL CONSTTTUENT AND RESTDUAL TNTERPOLATTON (TCARI)

2.1. Tide Corrections

As discussed previously, the depth at MLLW, which is the NOS chart datum, is computed from the

survey depth sounding, D, (which has been corrected for variations in ship motion, water density, etc.)

by subtracting the tide correction, ft* (in practice, the correction is defined as the negative of ft* so

it can be simply added to the sounding value):

Dru*-Ds-h*. (2.r)

The correction qonsists of three quantities: the astronomical tide, ry^;the residual (non-tidal) effect

(such as wind setup), r7o; andthe difference between the mean sea level (MSL) and mean lower low

water, I{o. Thus

h*= Qe,*Qn+Ho (2.2)

At present, h* is computed by the method of tide zoning. In this paper, the new method called Tidal

Constituent And Residual Interpolation (TCARI) is discussed. TCARI is a way of using both the

observed water level values at gauges located in the survey area and historical data (the constituents)

at the same gauges. Application of the method requires knowledge of astronomical tide prediction,

harmonic analysis, and spatial interpolation. Before these topics are covered, discrete tide zoning is

briefly summarized.

2.z.Tide Zoning

Discrete tide zoning was developed as a way of estimating water levels at any location in a survey

area (Gill, 1998). A desktop computer-based method of drawing the zones was developed by Collier

et al. (I999).In discrete tide zoning, a number of geographic zones are constructed, each covering

a portion of the coastal areabeing surveyed. The tide correction within any zone,hr*, at time f is

calculated by multiplying the amplitude of the water level above MLLW at a nearby gauge, e* by the

range factor for that zone, r, and by applying the time difference for that zone, r, as follows:

h)@ =' rrys? - r)

Within each zone,the range factor and time difference are considered to be constant.

The tide zoning scheme for Galveston Bay is shown in Figure 2.I.The configuration of each zone is

determinedbyoceanographers in NOS's CenterforOperational Oceanographic Products and Services

(CO-OPS) by estimating the variations of the tide between two or more NOS water level stations and

drawing the zone so that the change in the amplitude of the tide correction between adjacent zones is

limited to 0.2 feet and the time change is limited to 0.3 hour. Range and time changes between stations

are therefore assumed to be approximately linear. For each zone, CO-OPS estimates a range factor

(2.3)
Figure Z.l.The tide zones in Galveston Bay. Within each zone (shown as a polygon), the tide

correction has a fixed ratio and time difference relative to the tide measured at one or more water

level gauges.

and a time difference for high water and low water in the zone relative to the same variables in one

or more reference water level gauges. For preliminary tide zoning, an initial zone configuration is

developed and range factors and time differences are generated for (typically) a single, long-term

water level station. For final tide zoning, alterations in the polygons may be made and ratios and time

differences are generated for (typically) several more stations.

For the automated processing of bathymetric data by NOS's Hydrographic Surveys Division (HSD),

the high water and low water ratios are combined into a single value, as are the high water and low
water time differences. The tide correction is obtained by applying the amplitude ratio and time

difference to the observed (and smoothed) tide from one or more nearby tide stations to get a local

(i.e., ship location) tide.

2.3. Astronomic Tides and Tidal Constituents

The conceptuali zationof the tide in terms of a set of constituents is fundamental to TCARI. NOS uses

the following equation (Schureman, 1958) to predict the astronomic tide, q, relative to mean lower

low water (MLLW) at any location and time r:

N

rl!)=Ho+) fnaocos[cr)nt+(Vo+u),-Gni Q.4)

n=l

The tide , Q, isthe sum of a constant offset value (the difference between MSL and MLLW ), Ho, and

a cosine series of Ntidal constituents. For each constituent,J, is the lunar node factor , anisthe angular

speed, and Vo+u is the equilibrium argument; these are determined from knowledge of the

astronomical motions of the earth-moon-sun system and they apply to all locations. The constituent

amplitude, ao, and Greenwich epoch, G,,, (for predictions in Greenwich, or universal, time) are

determined from the analysis of a time series of observations, and apply at asingle location. Time is

reckoned from the start of the year.

Predictions made using local time require the local epoch. The local epoch, rc'n,canbe found from the

Greenwich epoch at any time zone longitude, S, by

r', = Gn * S a/( 15 degreeslhour) (2.s)

where west longitude is negative [note: the above conventions differ from that of Schureman (1958)].

For Galveston Bay, the time zone longitude, S, is -9Odegrees, so Sl 15 = -6 hr; for San Francisco Bay,

S is -120 degrees, so S//5 = -8 hr.

2.4. Spatial Interpolation

The new approach described here depends on a method of spatial interpolation. The common

approach (widely used in meteorology) is to create'a two-dimensional field from a limited number

of observations by the use of a distance-dependent weighting function, w. For example,

M

F(x,)) = \w(d)Ff (2.6)

m=l

where d*(x, y) is the straight line distance between the location of the observation, F *, andthe point

(at x, 1l) in the field. w decreases as d increases.
The weighting fUnction approach will produce highly inaccurate results when applied to tidal data

because it does not account for the influence of land. An example of the problem is shown in Figure

2.Z.TheGreenwich phase forthe M, constituent at High Island in the Gulf of Mexico isT7L.4degrees,

while at the nearby Rollover Pass the value is 17.8 degrees and at Smith Point it is 8.6 degrees. The

latter two stations are in Galveston Bay. Clearly, any approach that does not account for the existence

of the intervening land (in this case the Bolivar Peninsula) or uses the straight line distance between

stations will produce inaccuracies.

Therefore, to overcome these difficulties, the approach taken here is to create a set of weighting

functions that are the solution of a differential equation that includes spatial derivatives. The equation

is solved numerically on a grid. The use of a spatial derivative means that the value at any grid point

is directly related to the value at the adjacent grid points. The ultimate effect is to create pathways

around land features. The result is a set of new weighting functions, g(x, y, m)thatcan be used in place

of the function w inEqn. 2.6.The computation of the new weighting functions is covered in Section

3.

Figure 2.2.The influence of land on M, phases for three nearby gauge locations. Although the

High Island gauge is located near the Rollover Pass and Smith Point gauges, its phase is quite

different. The difference is due to the intervening land (the Bolivar Peninsula) and the land's affect

on tide wave propagation.
2.5. TCARI

As explained earlier, the correctio nh*at any location can be expressed as the sum of the astronomical

tide (r7), a residual water level component (r7), and the MSL to MIIW difference (F/o) as

h* = Ue+ Tn + Ho Q.2)

For each constituent of the astronomical tide, TCARI creates an interpolated amplitude, A, and epoch,

K, which are calculated with the numerically-generated weighting functiotrs, g., as follows:

M,

A,(x,)) = I, g" (x,y,ffi)e*,n

nrl

(2.7a,b)

M,

K n(x, l) = 2 S,Q, l, r/t)K,,,,

m=l

where g"(x, y, m)is the weighting function for tidal constituents at location (a y) for the tide gauge

location m, and r is either the Greenwich or the local epoch. There are M, locations where tidal

constituent data are available. Hence, using the prediction equation2.4,

N

Ue

n=l

The offset (the difference between MSL and MLLW) is also interpolated by

Mo

s(x,]) = 2 s "(*, !,fti)H o,^ Q9)

where go is the weighting function for offsets for the Mo gauges where the offset, Ho,*, is known.

Now suppose that there are M,contemporary water level gauges in the survey area. These stations are

not necessarily the same as the first set of M., but their constituents must be known. Then the residual

component (relative to MSL) at any location is

M,N

rln

m=l n=l

where e^isthe observed water level (relative to MSL) at gauge m andg, is the weighting function

for the set of M, gauges.
In order to make comparisons with the post-processed RTK water level measurements in Galveston

and San Francisco Bay, an independent estimate of the water surface elevation at any time and location

relative to the ellipsoid, D'Grs, is needed. This can be computed by the TCARI method as follows

DLrr=Tle*4n*Hu

where F/" is the ellipsoidally-referenced tidal datum (MSL)

H u(*, !) =2 S"(x, y,fti)H r,^

m=l

(2.rr)

(2.r2)

Also, TCARI can readily be adapted for survey bathymetric data referenced to the GPS ellipsoid. Irt

the elevation of the bottom of the water column relative to the GPS ellipsoid be Hr(being comprised

of the ellipsoidal distance to the GPS antenna, the antenna-to-sounder distance, and the sounding

measurement itself. See Figure 1.1). Then

Drrr*=Dr-HL

where f/. is the spatially-interpolated value of MLLW relative to the ellipsoid,

(2.r3)

H r(*, Y) = =Hr-Ho (2.r4)

In sum, TCARI generates either a tide correction or an ellipsoidally-referenced water level by the

addition of three components: a astronomical tide which is generated from spatially-interpolated tidal

phases and amplitudes, a spatially-interpolated residual (non-tidal) water level, and either the offset

(difference between MSL and MLLW) or the ellipsoidally-referenced MSL datum. The generation of

the weighting functions is covered in the next Section. Four sets of variables (see Section 2.6) are

required at locations in or near the survey area; because tide stations often lack one or more of the

four, a separate set of weighting functions is needed for each vmiable set.

2.6. TCARI Data Requirements

For tide corrections, three sets of variables (tidal constituents, residual water levels, and offsets) are

required at locations in or near the survey area.For an ellipsoidally-referenced survey, one additional

variable (an ellipsoidally-referenced datum) is needed. Historical tidal constituent data (amplitude

and phase) and the offset (the difference between MSL and MLLW) are often available a numerous

locations. The residual water level at a location requires both tidal constituents and contemporary

observations at the tide gau ge at the time of the survey.

Generally speaking, results should improve with the addition of more locations. Since the

contemporary measurements are needed for only the residual water level, forehand knowledge of the

M"

2, s"(x, y,ffi)H r,,,

m=l
spatial patterns of residual water level variability may allow for design of a minimal configuration

of gauges. In this study, data collected originally for the purpose of tide zoning was used to assess

TCARI; no special data (with the possible exception of the an ellipsoidally-referenced datums) was

used. There was also no attempt to determine optimal configurations of water level station locations

or lengths of time series that would improve TCARI's accuracy.

2.7. Other Methods of Providing Corrections

Beside discrete tide zoning, there are other methods designed to provide tide correction information.

However, these methods have significant drawbacks. One such method is function fitting, which is

widely used in meteorology.This method uses an analytical function in two-dimensional space which

fits the observations (e.g., Barnes, 1964). This method is not suitable for interpolating tidal data

because it cannot account for the large differences in tidal characteristics across land features such

as peninsulas.

A second method is numerical circulation modeling (Stawarz and Metzner, 1994; Schm alz,I996),in

which a model is used to determine both the instantaneous water level with respect to MSL and, with

a sufficiently long time series, the difference between MSL and MLLW. Although the application of

hydrodynamic models is potentially the most accurate approach to determining tidal constituents

because these models simulate the dynamics of time-dependent, shallow-water tidal wave motion, in

practice numerical circulation models typically require a long time (months to years) to develop to

a state where they meet the required accuracies (for examples of accuracy requirements, see National

Ocean Service, L999). In contrast, TCARI was developed so that existing gauge and historical data

can be utilized rapidly (on the order of months). In addition, although numerical models are usually

calibrated using gauge data, they may not perfectly match the data at the gauges. TCARI, however, uses

the gauge data so as to exactly match values where they are available (although this inevitably raises

questions about data quality and the spatial density of gauges).

A third method is to generate a tidal datum surface by first selecting a field that has already been

referenced to the ellipsoid (the geoid, for example) and then generating a new surface by minimi zing

the error at the stations with known values (Muller and Groten,1992). However, the MSL is known

to depart significantly from the geoid because of the effects of currents.
10
3. INTERPOLATION BY SOLUTION OF LAPLACE'S EQUATION

3.1. Laplace's Equation

The method chosen for spatial interpolation is to describe the variable (offset, amplitude or phase)

as a two-dimension field, select a field equation that describes the spatial distribution, then compute

the numerical solution of that equation. First we let the arbitrary variable G(x, y) represent the offset,

amplitude, or phase (or any other property). We then assume that the variable obeys the twodimensional Laplace' s Equation (LE)

azc a2G

E+ *=u

and that G matches the observed value at the locations where data are available,

(3.1)

G(x^,!^) - G3 (3.2)

The LE was chosen because, in one dimension, it gives a solution that has a constant slope between

data points. In two dimensions, the solution between three data points can be a flat plane. A planar

solution is desirable because it is the simplest way to interpolate between data points, even though

it does not incorporate any tidal physics. Another attractive feature of a numerical I,E solution is that

information on tidal constituents in one grid point will be related to the values in adjacent grid points,

and will thus be able to propagate information around corners. Finally, note that this is the equation

in mathematical physics that describes the temperature distribution in an insulated plate of constant

thickness and constant heat conduction coefficients.

The LE approach will produce an objectively interpolated field for amplitude and phase, although

without including any tidal physics such as wave speed, friction, or depth variation. Since amplitude

and phase are computed independently, natural distributions such as amphidromes will not be

accurately reproduced. A potentially more accurate approach, which is based on the solution of

lineartzed, single-constituent tide wave equation in a constant-depth basin, solves for amplitude and

phase together. A short discussion appears in Appendix A.

Straightforward application of Eqn. 3.1 to a typical geographic area would result in a very large

number of fields. In addition to the field for the offset, there would be7 4 fields, because for the NOS

standard suite of 37 tidal constituents, two fields (i.e., an amplitude field and a phase field) are needed

for each constituent. And for the residual water level, a new field would have to be generated for each

time a new observation were available; i.e., every 6 minutes. Therefore, to save computer time and

memory, the approach was extended by defining a set of weighting functioils, B, such that

M

I

tn=l

G(x, 1l) = g(x,y,d GI

1 1

(3.3)
where M is the number of locations where observations, Go , are available. The field g then obeys

Laplace's equation

d'g , o'g n

wt af-v Q-4)

and has a value of either zeroor unity at the locations where observed values are available,

g(x,,yi,m)= 6,^ (3.s)

(3.6)

(3.7)

That is, for the selected station ffi, g is unity there but is zero at all the other stations, f. This approach

is faster and simpler than solving Eqn.3.1 because it requires that only one solution field be

calculated for each water level station for which there are data. After that, the G field is constructed

from Eqn. 3.3 using whatever data is desired. In addition, whenever updated values of the

observations become available, there is no need to recompute the g functions.

3.2. Boundary Conditions

Boundary conditions fer G and g ffieneeded at water level stations, ocean boundaries, and land

boundaries. As discussed above,"at station locations where observed values are available, the

boundary condition are Eqns. 3.2 and3.5. The ocean boundary condition is that g has azero slope in

the normal direction,

*=o dE

where ( is the direction normal to the boundary. The boundary condition for G is obtained by

substitutrngG forg in Eqn. 3.6. At landboundaries, the zero slope condition @qn. 3.6) is an obvious

possibility. However, this condition (which is analogous to a thermally-insulated boundary in the heat

flux case) proved to cause the local izedpacking of contours around the data points, especially near

corners, which is not realistic in manycases. Therefore,asecondboundarycondition was developed.

This condition is based on the concept that the variation of g near the shore is determined by the

variation in the water level a small distance away from the shore. This is implemented by setting the

boundary slope to be proportional to the mean interior slope, i.e.,

ag 

_ odr

og dE

where the overbar represents the spatial average (over the few surrounding cells) of the derivative

and the proportionality constant is restricted by

0<a<l

L2

(3.8)
This approach allows the zero normal condition to be implemented by simply setting a=O and the

full proportionality condition by setting d= t.

3.3. Natural Distributions of Corange and Cophase Lines

The actual spatial distribution of constant amplitude (corange) andconstantphase (cophase) lines will

be needed to evaluate the parameter a.In Chesapeake Bay (Browne and Fischer, 1988), cophase lines

tended to be normal to the boundary, but if the shore tends to be shallow, then cophase lines curve to

give a near-shore phase lag. Corange lines (i.e., lines of constant amplitude) did not show a simple

pattern, but were oriented both normal and parallel to the shore. Data on both observed and

numerically-simulated tides in Tampa Bay (kwas,1993) show again that cophase lines tended to be

normal to the shore, but corange lines were oriented both normal and parallel to the shore.

Defant (1961) presents a summary of information on the distributions of corange and cophase lines

for the North Sea, the Baltic, the English Channel, the kish Sea, the Adriatic, the Black Sea, the

Persian Gulf, the Indonesian Archipelago, the Eastern China Sea, the Sea of Japan, the Okhotsk Sea,

the Gulf of Mexico, the Gulf of St. Lawrence, the North Siberian Shelf. Cophase lines tend to intersect

the land at near-normal angles when (1) they are radiating around amphidromic systems and (2) in

long, n:urow embayments. Corange lines, which intersect and are roughly normal to cophase lines,

show evidence of being oriented both normally and parallel to the shore.

Thus it appears that no single value of a will correctly describe all natural distributions.

Experimentation will therefore be necessary to settle on a useful value.

3.4. Solution by Finite Differences

The solution to the LE is approximated by the numerical equivalent. For cells equally spaced in each

direction, the finite difference form of Eqn. 3.4 at location i, j and iteration k is

Solving for g!,, gives an estimate that solves the equation

8!+t,i * S!-r,i * 8!,i*,* 8!,i-,-48!,,:o

li,i = i (S!rr,i *8!-ti + 8!,y, + g!,i-r)

(3.e)

(3.10)

where g* is an intermediate solution. Using the method of successive over-relaxation (SOR) (Press

et al., 1992), the next estimate (i.e., at iteration k+/) is obtained by

g!,:' - ot7i,i + (1 - aDd.i (3.11)

where L < ax 2. The array g is iterated until the following convergence criterion was met:

13
*u*lsfi' - s!,,1s e(max (G:) - min( Gb) (3.12)

Good results were obtained for t = 5 x 10-s. The final values of the numerical solution, and in fact

convergence itsell was highly sensitive to the exact form of the boundary conditions. Therefore,

considerable time was spent in testing different forms.

3.5. Grid Generation

The numerical solution to the I-aplace's Equation can only be determined by solving the equations on

a grid composed of square cells representing either land or water. The gfid is generated from (a) the

window in latitudeJongitude space, (b) the cell width, (c) the coastline (defined as a set of latitudelongitude pairs), and (d) the location of one water point. No bathymetric data are required.

The process is as follows. First, a geographic window is selected. It is specified by the longitude

limits (lonmac, lonmin) and the latitude limits (latmax, andlatmin). Then, given a cell width, wcell

(in nautical miles), a grid of undifferentiated cells is generated by dividing the width into Imac

intervals and height into Jmax intervals, where

Imatc = 

Co 

=(lonmatc - lonmin) ' wcell

Jmax - co

*rri(latmar 

- latmin)

(3. 13)

where Coand Co convert degrees to nmi. wcell should be considered a nominal value. Since Imatc and

Jmasc are integer values, the division of either the width by Imasc or the height by Jmax will result in

actual cell widths that are slightly larger or smaller than wcell.This distortion is small (less than I7o)

when Imax and Jmax are large and is ignored in the numerical solution.

Next, the land-water boundary in this grid is determined by checking all cells that (a) contain at least

one point in the coastline data file, or (b) are intersected by a line drawn between points defining the

coastline. Finally, starting from the known water point, all cells adjacent to it which are not tagged

as the land-waterboundary are also set to represent water. The remaining cells are therefore land. The ' land-water boundary cells are set to either land or water.

In general, the generation of grids for complex coastlines requires serious consideration. First, the

window must be selected so it covers the entire area of the bay to be zoned. If there is coastal ocean

within the window(which is the usual case), the method requires that the coastline file contain data

polnts outside the window; if not, the process of filling land points will run around the end of the

coastline and all cells will be turned into water. Cells, which are square, should be small enough so

that important features such as entrances and straits will have at least two or three cells across them,

although the computation is faster with larger cells.

t4
3.6. Rectangular Basin Test Case

For the test cases, the water area is a simple six-sided region with parallel sides. The six corners are

specified by latitude-longitude pairs. For a window bounded by latitudes 28o 54'and 29o 50'and by

longitudes -95o 20' and -94o 5'and wcell = 0.5 nmi, the resulting grids (one oriented so that its sides

are parallel to the borders of the window, and another rotated 45 degrees clockwise) are shown in

Figures 3.La and 3.lb.

Figure 3.La. Grid for rectangular test

region. Cells are 0.5 nmi on a side.

Figure 3.Lb. Grid for the rectangular

test region, but rotated 45 degrees.

A set of test cases was developed to implement and refine the numerical scheme. The basin has

straight sides and occupies a region approximately the size of Galveston Bay. A gnd (Figure 3.la)

was then generated which had square cells measuring 0.5 nautical mile on a side. The resulting grid

array had dimensions 87 by 100, and approximately 367o represented water. The maximum width and

height of the basin was 59 cells. The test cases consist of finding the solution with four different

boundary conditions. For each test cast, the boundary values consisted of setti ngG" = 100 in the lower

left corner and G" - 0 on the right side about two-thirds the way up.

For the first test cast, the boundary condition is zero gradient in the normal and tangential directions.

The solution for this case (a = 0) is shown in Figure 3.2a. The solution was achieved after 698

iterations using t= L.25 x 10-5. Although contour lines intersect the side as required, contours are

packed around the two locations where the input values are given (Points A and B in the figure). This

undesirable packing results naturally from the solution of the LE andthis specific boundarycondition,

which are analogous to a temperature distribution with thermally-insulated boundaries, and is

characteristic of a saddle point.

15
.a-.'.'-'.4:

. .so.

..:::: . 

e' .j:11 : . ii . 

n.1

:::

::::::::

.?i.. . .

: lr \ \ \ t / l. :

'29 '

.f0.'.'.'.'

.B'.'."'.& . . J

"" ' a

.'.'.'.'.'.29

,,,,: ;:;V

w G

Initial basin, a= 0.0 Initial basin, a= l.O

Rotated basin, a= O.O Rotated basin, a= 1.0

Figure 3.2. Solution for G in an idealized basin, solving Laplace's Equation with boundary values

Go = 100 at point A and Qo = 0 at point B for two values of a.

L6
At the opposite extreme, using the full extrapolation (a = 1) produces a different set of contours

(Figure 3.2b). This solution required l4L9 iterations to complete and results from the condition that

the gradient of G in each spatial direction is a constant. This solution is mush less affected by

boundary influence than the previous solution. The lines are approximately straight in the lower left

corner (Foints A), and have nearly uniform spacing; this solution approximates the idealizedsolution

of a flat plane.

A severe test of the numerical solution is to see whether the same solution results when the basin is

rotated by 4ldegrees. The solution for d=0 (Figure 3.2c) and q= 1 (Figure 3.2d) show that the

unrotated solution is reproduced to within about 5, which is 5Vo of the full scale. Maximum

displacement of the contours was about 10 cells (5 km) and occurred near the center of the basin.

Since this level of error is relatively small,, the numerical scheme is judged to be acceptable. The

number of iterations required were 717 and 651 for a= 0 and 1, respectively.

In each basin, the contours for a= 1 are slightly curved. The curvature can be reduced by taking a

smaller value for gor a smaller grid size, although convergence requires a larger number of iterations.

Also, the above distributions were createdby solving Eqn. 3.1 for G(x, y) with the boundary input

values 0=100 at point A and O=0 at point B. An equivalent distribution can be generated by solving

the Eqn. 3.4 for g@, y), then solving Eqn. 3.3 for G(x,y). Comparison of the two solutions shows

differences of less than IVo of full scale

Neither of the distributions shown in Figure 3 .2 is entirely realistic as compared to cotide or cophase

lines. An intermediate solution, one which has contours approaching normal intersection with the coast

but without the packing of contours around the input boundary locations, can be generated by setting

ato an intermediate value. The solution for a=0.9 is shown in Figure 3.3.

A final point to consider about the test boundary values (G" = 100, Go - 0) is that, if G" represents

phase angle in degrees, then Go = 0 is equivalent to G'= 360. The solution for this case would be

significantly different. One approach is to spatially interpolate the sine and cosine values separately,

then add them together. In this case the field G is generated by

G(x, y) =

K

I t(", y,k)cos(Gf )

k=l

(3.14)

For Go = 100 degrees at point A and Qo = 0 degrees at point B, the result is shown in Figure 3.4. The

field generated this wayhas slightly more uniform spacing of contours, andthe maximum difference

is approximately 5 degrees.

K

I g(", y,k)sin(Gf )

k=l -" '[

L7
.B'.'.'.'.,s

. .. -:o

" :2t .'.'.'.'.'.&

Figure 3.3. Contours created by spatial

interpolation of values Go = 100 at point A

and Go = 10 at point B (a= 0.9).

.B'.-.'.'.4

' ' 'c)

"2'

.'. 

'.' 

. 

'. ' 

.tc'

Figure 3.4. Contours created by spatial

interpolation of the sine and cosine of values

Qo = 100 at point A and Go = 10 at point B

(a= 0.9).

The difference between the two solutions was studied by setting up an analytical case. The angle

varied between 0 degrees at one end and a different value (from 20 degrees to 110 degrees) at the

other. Two solutions were determined, one by linear interpolation of the angle, the ottr"r by linear

interpolation of the sine and cosine of the angle and'a reconstruction by the arctangent. The table

below shows the maximum difference (in degrees) between the solutions as a function of the

difference between the end values. The difference in solutions is less than 1 degree when the

difference between end values is less than about 58 degrees. ,

Table 3.1. For an angle varying from Odegrees at one end to a range of values at the

other end, the maximum difference (degrees) between the solutions obtained by (1) ' linear interpolation between the end angles and (2) linear interpolation between the

slne ine ando cosinel oft then end angles, then reconstruction of the an le ,he arctan

End Angle 110 100 90 80 70 60 50 40 30 20

Difference in

Solution Angles

7.8 5.5 4.0 2.7 1.8 1.1 0.6 0.3 0.1 0.04

18
4. APPLICATION TO GALVESTON BAY

Galveston Bay was selected as the next test case because it was the site of an intensive water level

data collection project during L995 (Huff and Gallagher, 1996). The Bay has recent tide data,

ellipsoidally-referenced water level data (WGS-84), and a numerical circulation model developed

by Schmalz (1996).

4.1. Ship Track Data

During the summer of lggs,extensive measurements of water levels referenced to the WGS-84

ellipsoid were made from a small craft traveling around Galveston Bay as part of a NOAA research

program (Huff and Gallagher, 1996). The locations where the 618 measurements were made are

shown on Figure 4.1. The accuracy of these measurements is discussed in Section 4.8.

Figure 4.1. Galveston Bay locations (denoted by a '+')

of ellipsoidally-referenced water level measurements.

L9
Most of the measurements were made in the mid-bay region along a triangular course with vertices

close to operating NOS water level gauges. At each of the observations the time, location (latitude and

longitude), water level relative to the ellipsoid, and ship speed are known. The measurements were

made on 17 days beginningJune 13 (day 164) andendingJuly 7 (day 188).

4.2. Water Level and Model Data

There are 14 water level stations which had tide data used in this study. Their locations are shown

in Figure 4.2. During the NOAA research program, contemporary water level time seiies

Figure 4.2.I-ocations ("*"), numbers, and names of

in this study. The station numbers shown are the last

three digits are 877 .

14 water level gauges that supplied data used

four digits of the seven-digit number; the first

20
measurements were made by NOS and the Conrad Blucher Institute (CBI) of Texas A. and M.

University at Corpus Christi. These included 12 shore-based stations, a station located on a platform

near the Houston Ship Channel (877 -lO2I), and a temporary, offshore location on a GPS-fitted buoy

(877 -1624). Time series (at both 6-minute and hourly intervals) are available at 10 locations within

the Galveston Bay and coastal region, and tidal constituents were available for those stations. In

addition, tidal constituent data derived from past measurements were available at the other four

stations. Eight stations had a datum (usually Mean Tide Irvel, which is equivalent to MSL) referenced

to the ellipsoid. The data available at each location are shown in Table 4.1. A listing of the tidal

constituents and details of the harmonic analysis methods is given in Appendix B.

Table 4.L. Tide and related data used in the ship track data comparison. Columns show the location

niune, the institute (Ins) which collected the data (NOS or CBI), the station number, the number of

constituents available (NC), whether an observed time series (Obs) is available, and the offsetHoand

WGS-84 ellipsoidal

Another part of the NOAA project was the development of a numerical circulation model of the Bay

(Schmalz, 1996). The model was calibrated for the survey period and produced tidal constituent

amplitudes and phases. These will be discussed in Section 4.4. A description of the model appears

in Appendix C.

I datum H",rn meters (I/, values from Schmalz,1996 na means not available.

No. Name Ins Sta. Num NC Obs Ho HE

1 Round Pt. CBI 877-0559 37 r' 0.213 -29.0t4

2 Morgans Pt. CBI 877-0613 37 r' 0.198 -29.053

3 Umbrella Pt. NOS 877-0625 37 na na na

4 High Island NOS 877 -0923 37 na 0.366 na

) Smith Pt. NOS 877-093r 37 r' 0.195 -28.845

6 Rollover Pass NOS 877-0971 37 na 0.2r3 -28.725

7 Eagle Pt. CBI 877-r0r3 37 r' 0.r74 -28.775

8 Trinity River Chn. NOS 877-r02r 20 r/ 0.177 na

9 Port Bolivar CBI 877 -1328 37 ./ 0.214 -28.624

t0 Galveston,Pier 2t NOS 877-1450 37 ( 0.253 na

1 1 Tiki Is. NOS 877-1481 23 na na na

l2 Pleasure Pier NOS 877-1510 37 r' 0.366 -28.537

13 GPS Buoy NOS 877-1624 25 r' na na

T4 Alligator Pt. NOS 877-1801 37 ( 0.092 na

2l
4.3. Grid and Weighting Functions

Application of the LE method described in Section 3 for interpolation requires the generation of a

numerical grid and the subsequent computation of influence functions. The numerical grid was

generated using a digital coastline file (Figure 4.3). A cell size (wcell) of 0.35 nmi was chosen

because it approximates the mean size of the numerical model's cells and it is small enough to include

most of the important narrow channels such as the entrance to the Bay. For the longitude limits

(Ionmar-94" 18', Ionmin=-95o 20'), Imurl34, and for the latitude limits (Iatmar 29o 50',

latmin=Z8o 52'), Jmar,I65. The actual cell width is 0.351 nmi and the height is 0.352 nmi.

Figure 4.3. Grid generated by coastline for solving the LE in Galveston Bay. Cell widths

are 0.35 nmi.

22
Editing of the gdd was necessary. To insure that all the major water bodies were included in the grid,

five cells were forced to be water by editing. These included one cell near Tiki Island, two cells near

the southeastern end of the Texas City Channel spoil island, and two cells near the southwest entrance

to the Bay at San Luis Pass. Also, the positions of a few tide gauges were adjusted by 0.1 or 0.2 nmi

to insure that the gauges were not enclosed by land. Finally, although the cell size is not small enough

to resolve the Galveston Channel (which separates Pelican Island from the city of Galveston), the Pier

21 gauge (877 -L450) was automatically included as a water cell (as are all tide gauge cells).

The weighting functions were

computed for each set of variables.

For the tidal constituents, all L4

locations were used. For the residual

water levels, only 9 of the 10

locations were used: the GPS-fitted

buoy observations were not used

since there were significant gaps in

the data. G fields were computed for

the offset (the MSL-Io-MLLW

difference) and the ellipsoidallyreferenced MSL datum.

An example of one of the weighting

functions is shown in Figure 4.4.The

function, g, is shown for the tidal

constituents at station 877 -093I at

Smith Point. The function has the

value 100 there and has the value 0 at

all other water level locations. There

are 12 other distributions, one each

for the other water level gauge

locations. The function shows at any

location throughout the bay what

percentage of a field, such as a

constituent's phase, is due to the

value at the Smith Point gauge.

Figure 4.4. Weighting fUnction g@, y) for the water level

station at Smith Point (877 -0931). Contours are lines showing

the percentage of the final interpolated field value that is due

to the value at Smith Point.

23
4.4. Constituent I nterpolation

The distribution of the M, tide was chosen for the first test. The distribution of the epoch angle as

generated by the hydrodynamic model (Appendix C) and by the LE method are shownln Figu ie a.5.

The LE model parameter u (0.9) was calibrated to provide the best fit in the lower portion of the Bay

where the phase increases from 1 10 degrees at the entrance to 2lOdegreesin mid-bay. Rememberthat

the T F distribution method matches the data at the water level gauge stations, while the modeled

distribution does not necessarily match. For the stations'in the portion of the Bay shown in the figure,

the model's error ranges from -11.5 degrees at Morgans Point to 28.7 degrees at Eagle Point

(Appendix C).

Figure 4.5a. Distribution of M, epoch (local)

from the numerical model.

Figure 4.5b. Distribution of the M, epoch

(local) from the LE interpolation method.

A comparison of the M, arnplitudes generated by each method @gure 4.6) show that the overall

pattern of the distribution differs more than in the previous comparison, although the amplitudes are

similar. For the stations in the portion of the Bay shown in the figure, the model's error ranges from

-2 cm at Pleasure Pier to 0.7 cm at Eagle Point (Appendix C).

24
Figure 4.6a.Distribution of M, amplitude (cm) Figure 4.6b.Distribution of M2 amplitude (cm)

from the numerical model. from the TCARI method.

Plots of the distributions of the epochs and amplitudes of the K,, O,, andP, constituents (which, along

with the l\dr, comprise the four largest in amplitude) generated by the numerical model and the TCARI

method are shown in Appendix D.

4.5. Residual Water Levels

The residual water level is generated from Eqn. z.l}using data taken at the set of tide gauges for

which both constituents and an observed, hourly water level time series are available. The residual

is the observed water level minus the reconstructed astronomical tide. A plot of the residual water

levels for the period of the NOAA research project is shown in Figure 4.7 . The water levels show

events at Days 163 and 170 that seem to originate from outside the Bay, and an event at Day 187 that

seems to be confined to inside the Bay.

25
3 4

o

o

J

o

o

=

160 165 170 175 180

Doy in Yeor

185 190

Figure 4.7. Residual water levels in Galveston Bay during L995. Stations plotted nearer the

bottom are nearer the Galveston entrance. The top row shows the demeaned kinematic GPS

measurements.

26
4.6. The Offset and Datum

The offs et, Hodefined as the difference between MSL and MLLW (or the elevation of MSL relative

to MLLW), and the datum , Hu,(the elevation of MSL relative to the WGS-84 ellipsoid) are shown in

Figure 4.8. The distributions were generated by the LE method and used the values shown in Table

4.1.

Figure 4.8a. Ho , the offset (m) (MSL

minus MLLW). Contour interval is

0.01m.

Figure 4.8b. Hu,the datum (m) (MSL

relative to the ellipsoid). Contour

interval is 0.10 m.

4,7. Sensitivity Tests

TcARl-generated, ellipsoidally-referenced water levels were computed according to the methods

described in Section 2.5 and compared to the measured values in Galveston Bay.The operative

equation for the ellipsoidally-referenced water levels is

DLrr=Tle*4n*H, (2.13)

where D'orris the ellipsoidally-referenced water level, r1othe astronomical tide relative to MSL, 17^

the residual water level, andHtis the ellipsoidally-referencedlVlSl. Because of the lack of reliability

27
in the values of the amplitude and phase of the long-period constituents (Mm, Mf, Msl Ssa, and Sa),

these constituents were masked out in the calculation of the astronomical tides; the net effect was to

shift them to the residual water levels. At each time of a ship-based measurement, a TCARI prediction

of the water level was made at the four gnd cells surrounding the location of the ship; the water level

value at the precise location of the ship was then computed using bi-linear interpolation.

Benchmark Tests

Tests of the sensitivity of the solution were carried out after a benchmark run was completed. Out of

618 observed values, 557 were used in the comparisons; values not used fell on grid land cells. For

the benchmark run, which used hourly water levels observations, the mean effor was 0.01 cm, the

RMS error was 9.7 cm, and the maximum error was 27.1 cm. An analysis of the data showed that

relatively large elrors of consistent sign occurred for the water levels measured near the GPS-fitted

buoy (the TCARI predictions were about 13 cm too low). This error is probably due to the absence

of a measured offset for that location. When these measurernents were excluded from the comparison,

the RMS error dropped to 8.8 cm.

The first set of sensitivity tests involved changing the key parameters in the TCARI method. These are

the following (the benchmark values appear in parentheses): the grid size, wcell (0.35 nmi); the

boundary slope condition coefficient, a(O.9);the coastline Index (0); and the error ratio, e (5 x 10-s).

The coastline index sets the coastline cells to either 0 for land or I for water. The new values tested

were: wcell=0.175 nmi, d=t 0,Index=l, and e=5x 104. Withtheexceptionof excludingtheGPSfitted buoy values, the accuracy was only modestly affected by changes in the parameter values (Table

4.2).

Table 4.2. Results of the benchmark run and the senslitiVI tests. Errorsare ln cm.

Run Mean Error RMS Error Max. Error

Benchmark 0.01 9.7 27.1

Exclude GPS Buoy 1.5 8.8 27 .l

Change wcell from 0.35 to 0.175 -0.6 9.9 27.7

Change afromO.9 to 1.0 o.o2 9.7 27.2

Change Coastline Index from 0 to 1 -1.7 9.6 28.8

Change cfrom 5 x 10-5 to 5 x 10a -0.2 10.1 27.3

Hourly vs. 6-Minute Water Levels

The second set of tests involved the use of 6-minute water level observations instead of the hourly

values. During initial TCARI development, the 6-minute data were not used because there were

significant gaps (greater than 2 hours) in the data files for stations 877-0 931 ,877 -0559, and 877 -t328 

.

it

28
The maximum gap was M.7 hours. The TCARI program was revised so it uses the 6-minute data if

they are available, and uses the hourly data if the 6-minute data are unavailable. The use of six-minute

data gave a lower error (Table 4.3).

Table 4.3. Results from the use of hourly or 6-minute observed data for the calculation of the residual

water levels. Errors are in cm: Skip Gaps means that when the water level data were missing, the ship

track data were not used. Interpolate means that the water level for the required time was interpolated

from the observed data, regardless of the time gap. Substitute means that when the water level

interpolated from the 6-minute values was missing (the gap was greater than t hour), the water level

interpolated from the hourly values was substituted. Num. Gaps is the number of data points that were

skipped ki because of missine 6-minute data.

Run Mean Error RMS Error Max. Error Num. Gaps

Hourly (Benchmark) 0.01 9.7 27.r 0

6-Min, Skip Gaps -0.01 8.4 24.6 t12

6-Min, Interpolate 0.6 8.3 24.6 0

6-Min, Substitute 0.4 8.4 24.6 0

I nterpolation Variables

A third test of sensitivity was to alter the parameters that were subject to interpolation. In full TCARI,

the,tidal component of the water level is generated from the interpolated constituent amplitudes and

phases, and the residual water level is interpolated directly. For the first test, the tidal component was

zeroed out and total water level at the gauges was interpolated directly. For the second test, the

residual water level was zeroed out, so that the water level at the ship location was only the tidal

component. The results (Table 4.4) show that full TCARI gave the smallest errors.

Table 4.4. Results for full TCARI, total water level interpolation, and ignoring the residual water

level. Errors are in cm.

Run Mean Error Std. Dev. RMS Error Max. Error

Full TCARI 0.5 8.4 8.4 24.6

Interpolate Total W.L. 0.3 8.6 8.6 24.8

No Residual W.L. -5.6 It.7 12.3 42.4

29
4.8. Accuracy Tests

Accuracy of the GPS Water Level Data

Huff and Gallagher ( 1 996) estimated the error in the measurements using two sets of data, each subj ect

to specific restrictions. For Set 1, the restrictions was: (1) the ship was within2.5 km of one of four

gauges (Port Bolivar, Smith Point, Trinity River Channel Platform, ffid Eagle Point), (2) ship speed

was less than 0.5 mls, (3) the GPS data for the relevant 6-minute interval had a relatively small

number of erroneous values (less than 167o), and (4) the RMS deviation from the 6-minute mean of

the l-second samples measured at the water level gauge was less than 6 cm. Their result was that the

GPS measurements of water level had a mean error of 0.07 cm and a standard deviation (SD) of 4.7

cm. For Set 2, the restrictions were: (1) the ship was within 5.0 km of one of the four gauges, (2) ship

speed was less than 15 m/s, and (3) the RMS deviation was less than 30 cm. Their result was that

the mean error was 2.13 cm, the RMS error was 9.1.cm, and the SD was 9.0 cm. The errors for the

second set are probably more representative of errors in all the data.

Accuracy of TCARI Near the Tide Gauges

The TCARI method was applied to measurements that, for simplicity, met only the first two criteria

of the second set. (Since TCARI will exactly match the measured water levels at the gauges, use of

Set 1 data will not provide useful data.) The predicted water levels had a mean effor of 3.0 cm, RMS

of 8-3 cm, and an SD of 7.8 cm. Since these errors are approximately equal to those of the

measurements, we conclude that the TCARI water levels are consistent with what was measured by

post-processed kinematic GPS near the gauges (Table 4.5).

Table 4.5. Results from the accuracy tests. Errors are in cm. In Huff and Gallagher (lgg6),GPS

measured water levels were compared to water levels observed at four gauges. In TCARI, the

predicted water levels (which match exactly at the gauges) were compared to those measured in Huff

and Gallagher, Set 2.

Method Mean Error Std. Dev. RMS Error Max. Error

Huff & Gallagher, Set 1 0.0 4.7 4.7

Huff & Gallagher, Set 2 2.r 9.0 9.1

TCART 3.0 7.8 8.3 24.6

Accuracy of Discrete Tide Zoning

Tide zoning corrections, h7*,for the data were generated using the polygons shown in Figu re2.1, the

6-minute water level observations, and the range ratio and time lag data for each polygon. Not all the

measured water level locations lie within the tide-zoned area; of the 618 measurements,536 had

corresponding corrections. A direct comparison of the tide corrections with the measured water levels

30
is not possible because tide zoning does not provide a distribution of the MLLW field relative to the

ellipsoid. However, TCARI does. Therefore, an esiimate of the ellipsoidally-referenced water level

which incorporates the tide-zoned correction and the TcARl-generated offsets was computed as

follows

D'Jrr-h;-Ho*H" (4.1)

where D" oo, is the ellipsoidally-referenced water level and Ho is the spatially-interpolated (using

LE functions) datum offset (MSL minus MLLW). As before ,48lpoints were used in the comparisons.

Three sets of estimated ellipsoidally-referenced water levels were generated. Each set consists of an

estimate generated using the standard tide zoning method forcorrections, and an estimate based on the

standard method, but with spatially-interpolated corrections. In the second method, the interpolated

value is the weighted mean of the original correction and the corrections in adjacent zones. The

weights are equal to the fraction of the area of a circle that lies in the respective zones; the circle has

an origin at the center of area of the origrnal zoneand has a radius equal to the area of the zonedivided

by its perimeter. The first set of estimates was based on the preliminary tide zoning corrections.

Preliminary conections were generated using the 6-minute water level observations from a single

water level gauge, that at Pleasure Pier (877 -L450). The corrections are termed preliminary because

data from only a single water level gauge were used. The second set of estimates was based on the

final zoning corrections. The final corrections had access to the 6-minute data from five stations (877-

0613, 877 -L0I3,877 -L021,877 -t450, and 577 -L510); data from three of the eight locations (stations

877 -0559 ,877 -093I, and 877 -1328) were not used because they had gaps. The third set of estimates

was like the second, but with access to all eight stations. The results are shown in Table 4.6.

Table 4.6. Errors (cm) based on water levels estimates using tide zoned corrections. Results are for

preliminary tide zoning (one station), final zoning with five stations, and final zoning with eight

stations.

Tide ZoningMethod Mean Error Std. Dev. RMS Error Max. Error

Preliminary -5.4 7.4 9.2 33.9

Preliminary, Interpolated -5.4 7.4 9.2 34.2

Final, 5 Stations -6.4 7.8 10.1 38.2

Final, 5 Stations, Interpolated -6.4 7.6 9.9 38.8

Final, 8 Stations -6.0 7.3 9.4 38.2

Final, 8 Stations, Interpolated -6'0 | 7.0 9.2 38.8

3 I
The corrections from final tide zoning were less accurate than those from preliminary zoning. This may

be partially due to the fact that, for GPS observations in the zone containing Galveston Pier 21 (877 -

1450), the water levels from the Pon Bolivar (877 -L328) gauge, not the Pier 2l gauge, were used to

compute the corrections.

Comparison of TCARI with Tide Zoning

A major objective of this study is to compare the results of TCARI with those of discrete tide zoning.

A plot of the corrections produced by each method is shown in Figure 4.9. Not all the measured water

level locations lie within the tide-zoned area; of the 618 measurements, 536 had corresponding

corrections, and of these, 481 also had a TcARl-generated offset value. The TCARI corrections are

generally greater than the zoning corrections; the reason for this will be discussed below. This direct

comparison has limited value because there is yet no way to determine which one is more correct.

-o.2 0.0 0.2 0.4 0.6 0.8

T|DE ZONTNG CORRECTTON (M)

Figure 4.9. Scatter plot showing the corrections determined by

tide zoning and those determined by TCARI. The correlation

coefficient is 0.861

However, since both the tide-zoned estimates and the TCARI estimates depend on Hu,a reliable

assessment of the relative accuracies of discrete tide zoning and TCARI can be made only if theeffor

contribution of fy', is small. A comparison of the errors for zoning and TCARI was made using only

7A/

o u.+

tr()

LrJ

E

U.

o

O

o.2

v.

O

F

32
the points where both were available. The results (Table 4.7) shown that tide zoning is generally less

accurate than the TCARI method.

Table 4.7. Results from comparing errors in water level estimates using spatially-interpolated

discrete tide zoning (both preliminary and final) corrections and TCARI when the same set of

observations was used. Errors are in cm.

Method Mean Error Std. Dev. RMS Error Max. Error

Preliminary Zonrng -5.4 7.4 9.2 34.2

TCARI 1.9 7.3 7.6 24.6

Final Zonrng (8 Stations) -6.0 7.0 9.2 38.3

TCARI 1.6 7.3 7.5 24.6

Accuracy of the Numerical Model

The numerical model for Galveston Bay (Appendix C) was used to generate water levels for

comparison with the kinematic GPS measurements. The model was run forthe month of June 1995 and

included tidal, density, and meteorological forcing. At each water level gauge the ellipsoidallyreferenced model datum (corresponding to 7=0 in the model's coordinate system) was computed by

assuming that the monthly mean of the modeled water level was equal to the monthly mean of the

ellipsoidally-referenced observed water level. An ellipsoidally-referenced model datum field was

generated by weighting the values of the ellipsoidally-referenced model datum at the water level

gauges. The weight at each cell for each gauge was the square of the inverse distance to the gauge,

normalized by the sum of the squares of the inverse distances to all gauges. The ellipsoidallyreferenced instantaneous water level was then computed as the sum the instantaneous modeled water

level and ellipsoidally-referenced model datum. Comparisons were made at470locations, and were

stratified based on distance from the nearest water level gauge and the speed of the ship, The RMS

difference for the numerical model was 15 cm, and there was no appreciable dependency on distance

or speed. The TCARI RMS error for the 453 June measurements which were located within a

numerical model water grid cell was 8.3 cm.

Summary

To summ artze,TCARI has produced realistic estimates of the water levels measured with kinematic

GPS (Huff and Gallagher, 1996). Better TCARI estimates are obtained when 6-minute observations

at the gauges are used, rather than the hourly data. The TCARI estimates appear to be better than those

produced by both prelimin3ry and final tide zoning (without spatial interpolation), but those results

are dependent on an estimate of Ho from TCARI and the assumption that F/o has negligible error.

Results are summaizedin Table 4.8 and a scatter plot of the measured water levels and the TCARIpredicted values appears in Figure 4.I0.

33
Table 4.8. Mean and RMS error and standard deviation of the predicted water level as compared to

the measured water level in Galveston Bav usi

-28.2

-28.4

-28.6

-28.8

-29.O

-29.2

-29.2 -29.O -28.8 -28.6 -28.4 -28.2

MEASURED WATER LEVTL (M)

Figure 4.10. Scatter plot showing the kinematic GPS-measured water

levels and the TcARl-predicted water levels, both referenced to the

ellipsoid. The correlation coefficient is 0.863.

J

t!

|rl

J

u

Ld

F

=

O

L.l

F

s2

O

KJ

v.

ou

O

F

measured water level rn veston Bay uslng various methods of predictron Errors are in cm

Method Mean Error Std. Dev. RMS Error Max. Error

Numerical Model 15

Final Zoning -6.0 7.3 9.4 38.3

TCART 1.6 7.3 7.5 24.6

34
5. APPLICATION TO SAN FRANCISCO BAY

5.1. Ship Track Data

Water level data were gathered in San Francisco Bay during L997 as part of a NOS-sponsored study

(Huff et al., 1998). Figure 5.1 shows the location of the 968 locations where measurements of the

water level [referenced to the NAD 83 (86) ellipsoid] were made during March 6 to 10 and June 10

to 23. The data were processed to account for settlement in the water, which is a function of ship

speed.

Figure 5.1. L.ocation of water level measurements (denoted by a '+') in San Francisco

Bay made by NOS during March and June of t997.

35
5.2. Water Level and Model Data

Historical NOS water level data was available at the 42 stations shown in Figure 5.2. Real-time data

were also available at three stations which are part of the NOS PORTS installation; these are San

Francisco (94I-4290), Alameda (94L-4750), and Richmond Chevron Pier (94I-4563). Additional

water level data are available from Dumbarton Bridge (94I-4509). Tidal constituent amplitudes and

gpochs, and information on the harmonic analyses is given in Appendix F.

Figure 5.2. Present and past locations of NOS water level gauges in

San Francisco Bay where tidal constituent and/or time series data were

used. NOS station numbers a.re as above but precededby a94L Station

names are given in Appendix E.

36
Ellipsoidally-referenced [NAD 83 (86)] MSL is available for the PORTS gauges. The values are

-3I.631 m for San Francisco, -31.462 m for Alameda, and -31.355 m for Richmond Chevron Pier.

A numerical circulation model for the Bay, called the Tidal, Residual, Intertidal Mudflat (TRIM)

model (Cheng, et al., Lgg3),provides additional tidal data. The model was developed and calibrated

for the astronomical tide, and plots were generated of the amplitudes and epochs of the M2 and K, tidal

constituents. The modeled distributions will be used for comparison to the TcARl-generated

distributions. The TRIM model employs two-dimensional, depth-averagedEulerian equations of water

level, velocity, and density (which is related to salinity by a simplified equation of state that is

independent of temperature). Horizontal advection of momentum is treated by an imbedded I-agrangan

numerical scheme. Numerical calculations were made on two gnds composed of square cells: a

coarse-mesh grid with cell sides of 500 m and a fine-mesh gdd with cell sides of 250 m. The model

was driven by astronomical tide and variable density at the ocean boundary and without winds.

Calibration consisted in adjusting the depth-dependent values of n in the Chezy-Manning bottom drag

formulation, and altering the ocean boundarytidal constituents to provide the best match to constituent

amplitudes and phases at 24 tide gauge locations and 11 current meter stations. Tidal data were

collected in 1979 and 1980 during a joint USGS-NOS circulation survey (Welch et al., 1985). The

modeled tides on the fine-mesh gnd had the following accuracy: For the Mz constituent, the amplitude

had a mean error of 0.70 cm and a standard error of 1.61 cm, and the epoch had a mean error of -2. 10

degrees and a standard error of 2.18 degrees. For the K, constituent, the amplitude had a mean error

of -0.06 cm and a standard error of 0.80 cm, and the epoch had a mean error of 2.19 degrees and a

standard error of 0.68 degrees.

5.3. Grid and Weighting Functions

A gnd for the Buy, with a grid size of O.zsnautical miles (chosen to represent small features such as

the channels between islands in the central Buy) was generated (see Figure 5.3). The grid covers the

areas where measurements were made, specifically the entrance to the bay, South San Francisco Bay,

and San Pablo Bay. A typical weighting function is shown in Figure 5.4.

5.4. Constituent Interpolation

The distribution of tidal constituents was generated as in Section 4. The M, tide was studied for

comparison. The TRIM (Cheng et al., 1993) model-computed amplitudes are shown in Figure 5.5a,

and the TcARl-computed amplitudes are shown in Figure 5.5b. The patterns are similar, although

TCARI amplitudes are generally greater in a narrow band along the.eastern side of South Bay; this

difference is most likely due to the shallowness of the water in that area. The TRIM (Cheng et al.,

1993) model-computed M2 phases are shown in Figure 5.6a,and the TcARl-computed phases are

shown in Figure 5.6b. The patterns are similar. Comparisons for the K, tide and additional TCARI

distributions are shown in Appendix F.

37
Figure 5.3. TCARI grid for San Francisco Bay. Cell size is 0.25 nautical miles.

38
Figure 5.4. The weighting function, g@,y), for San Irandro Marina (94t-4688) shown as a

percentage.
0 5 l0mi

-#

0 5 lOkm

Figure 5.5a. M, amplitudes (cm) as

generated by TRM.

Figure 5.6a. M, local epoch (degrees)

as generated by TRIM

Figure 5.5b. M2 amplitudes (cm) as generated

by TCARI.

Figure 5.6b. M2 local epoch (degrees) as

generated by TCARI.

0 5 lOmi

#

0 5 l0km
5.5. Residual Water Levels

The residual water levels at four stations and the GPS-measured water levels during the survey are

shown in Figure 5.7. One panel of the figure represents a 5-day period in March and the other panel

represents a 15-day period in June. The residual variations, which are the total water level from

which the reconstructed tide has been subtracted, are relatively small (only a few centimeters), given

that the tidal range is approximately 1 meter.

1 0 1 0

GPS

l\l/l

\\r,

941 -4863

941 -4750

W

941 -4509

941 -4290

.. ..._.t | |

Doy in Yeor

(a)

Chevron

^ &

ni'er' (b+ i:4d6J)

Aromedo (941-4750)

an\O^.An/: nr\/ uumDor[on t'nqge tY+ | -+cuv/

Son Froncisco (941 -4290)

lttlDoy in Yeor

(b)

- 6

2

C.,

_94

t-(u

o

= z

- 6

2

q')

0(I)a

J

L

q)

o

= z

o

- 2

o

- 2

65 66 67 68 69 70 160 162 164 166 168 170 172 174

Figure 5.7. Residual water levels at four locations in San Francisco Bay (four lower lines) and the

demeaned kinematic GPS measured water level (top line) for (a) 5 days in March 1997, and (b) 15

days in June L997.

5.6. The Offset and Datum

The offset, which is the difference between MSL and MLLW, and the MSL datum (the elevation of

MSL relative to the ellipsoid) are shown in Figures 5.8 and 5.9, respectively. Values are discussed

in Section 5.2.

4l
Figure 5.8. Distribution of the MSL-Io-MLLW offset (m) in San Francisco Bay as generated

by TCARI. Values rango from 0.92 near the northwest part of the Bay tol.44 in the southern

part of the Bay.

42
Figure 5.9. Distribution of ellipsoidally-referenced [NAD 83 (86)] MSL

datum (m) computed with the TCARI method in central San Francisco Bay.

The three locations where offset values are known are shown as filled

squares. In the Bay, the values range from -31.63 m near the entrance to -

3t.36 m near the northern border of the plot. The contour interval is 2 cm.

5.7. Accuracy Tests

For the third test, TCARl-generated, ellipsoidally-referenced water levels were computed according

to the methods described in Secti on2.5 and compared to the measured values in San Francisco Bay.

As in Galveston Bay, the long-term constituents were masked out. A total of 968 data values were

available

Benchmark Runs

Using the TCARI method and hourly water level data, the RMS effor was 9.2 cm for the939 points

used (unused points lie outside the model grid). When the 6-minute observed water level time series

43
were used, the RMS elror was 9.1 cm. The fact that there is very little difference when the hourly

water levels were used is probably because the residual water levels are relatively small (see Figure

5.7). With the 6-minute data, the RMS error of 9.1 cm is slightly larger than for Galveston Bay (8.4

cm; see Table 4.3) because the tide range is larger (standard deviation of 16 cm for Galveston Bay

and 55 cm for San Francisco Bay). A scatter plot of the results using the 6-minute data appears in

Figure 5.10.

-31.0

-31.5

-32.0

-32.5

- 33.0

-33.0 -32.5 -32.O -31 .5 -31 .0 -30.5 -50.C

MEASURED WATER LEVEL (M)

Figure 5.10. Scatter plot showing 939 ellipsoidally-referenced, measured

water levels and the TcARl-predicted water levels for the same time and

location. The correlation coefficient is 0.986.

Discrete Tide Zoning

An assessment of the discrete tide zoning method was also made. The tide zones for San Francisco

Bay are shown in Figure 5. I 1 . Zones in the bay south of the entrance are referenced to the water level

gauge at San Francisco Presidio (941-4290), and zones north of the entrance are referenced to the

Alameda gauge (94I-47 50). The RMS error for final zoning with 907 points was 10.1 cm, or about

the same as for Galveston Bay. With the interpolated corrections (see Section 4.7),the RMS error was

9.8 cm.

J

|rJ

td

J

E.

trJ

F

=

o

LrJ

F

S2

o

l!

t

o_

G

()

F

44
Figure 5.LL. Tide zones (polygons bounded by dashed lines) for San

Francisco Bay.

Comparison of TCARI and Tide Zoning

TCARI and discrete tide zoning were compared at locations where both estimates of water level were

available. The results for all cases are shown in Table 5.1. TCARI has a lower RMS error and a

lower maximum elror than either tide zoning or interpolated tide zoning. RMS errors in the

measurements (Hufl personal communication) were 6.8 cm, which probably establishes the lower

bound on determining the accuracy of either method. :

45
Table 5.L. Mean error, standard deviation, RMS error, and maximum value of the emor (the predicted

minus the measured) in water levels in San Francisco Bay (cm) for several methods of estimation as

compared to the kinematic GPS measurements. WL is water levels. Results for tide zoning and TCARI

are for 907 locations where both methods produced a value. GPS measurements vs. Gauge (Huff,

personal communication) is an estimate of the error of the kinematic GPS water level when taken

within a few km of an NOS water level

Summary

TCARI was used to estimate water levels for comparison to the kinematic GPS measurements of water

levels in San Francisco Bay. The use of 6-minute observed water levels in generating the residual

water levels gave only a modest improvement over the use of hourly data. This is because the tide

range is large relative to the amplitude of the residual water levels. For the ship track locations where

both estimates were available, the estimated water levels from TCARI had less RMS error (8.8 cm)

than those from tide zoning (9.8 cm). The measured water levels had an estimated RMS error of 6.8

cm.

an w

Method Mean Error Std. Dev. RMS Error Maximum

Error

Tide Zoning -o.4 10.1 10.1 46.7

Tide Zoning, Interpolated -0.4 9.7 9.8 46.8

TCARI with Hourly WL r.2 8.8 8.9 42.2

TCARI with 6-minute WL r.4 8.6 8.8 4r.5

GPS Measurements vs. Gauge 4.4 5.2 6.8

46
6. COMPUTER PROGRAMS

TCARI is implemented by the successive application of three Fortran programs, designated here as

simply Program A (PA), Prograrn B (PB), and Program C (PC),

The PA creates the numerical grid which will be used by PB to generate the weighting

functions. PA reads in a control file that defines the grid limits in geographic coordinates and

sizes, and a geography file that contains the digitized coastline data. The program then creates

the grid, which is defined by an array of elements with a value 0 for land, a I for water, or 2

for ocean boundary. The control file contains both the input parameters and the names of the

input and output files.

PB creates the weighting functions g(a y) and the offset functions G(x, y) on the grid. The

program reads the same control file that was read by PA, the grid, and the tide data and then

creates the distributions. In general, the output files created by PA and PB are generated once

for the area being surveyed, and need not be updated unless additional tidal stations are added.

PC creates the tide corrections along the ship track, and so is run after the survey data are

collected. PC uses the data files generated by PA and PB, the tide data files, and the ship track

file. PC has its own control file.

The program functions are explained in detail below.

6.1. PA: Grid Generation

The numerical solution requires a gnd mesh with square cells representing land and water. This grid

is generated by PA by reading the input values from the control file, following the steps in a process,

and generating output files.

Input Data

The grid is generated from the following data:

the grid window in latitude-longitude space,

the digitizedcoastline (defined by a set of latitude-longitude pairs),

the digitized ocean boundary (defined by a set of latitude-longitude pairs),

the cell width (nmi),

the latitude-longitude location of one water point, and

the tide station locations

o

o

o

o

o

o

No bathymetric data are required.

47
The grid window is a rectangle in latitude-longitude space and it defines the limits of the grid. It is

specified by the limits lonmax, lonmin, latmanc, and,Iatmin. The window is selected to (1) enclose

the coastal area being surveyed, (2) be as small as possible to minimize computer time and storage

requirements, and (3) minimizethecrossing of waterareas. Forexample, the gridwindow (shown as

a dashed line) for the Galveston Bay region is plotted in Figure 6.1 along with the digitized coastline.

-95 45 -95 30 -95 15 -95 0

-94 {5 -94 30 -94 15 -94 0

29

45

29

45

29

3n

29

30

29 29

l 5 l 5

29 29

0 0

28 28

{5 45

-9s 45 -95 30 -95 ls -9s 0

-94 45 -94 30 -9{ 15 -94 0

fer CeLL

Figure 6.L. Galveston Bay region showing coastline data (solid lines), the

grid window (dashed lines), the ocean boundary (dotted lines), and the

location of the water cell. Note that, as required, the digitized coastline

extends outside the grid window.

A digitized coastline file, such as used in plotting, is required. In this study the files are in ASCtr

format; each record contains a longitude, a latitude, and a pen up/down command. It is an important

requirement that the coastline extend beyond the grid window.

The ocean boundary data determines the seaward extent of the grid. Because the grid window will

often enclose a large portion of the coastal sea (which may have little useful data and may be outside

the area to be surveyed), a way to exclude this area is needed. The removal is possible with the

insertion of ocean boundaries, which are read from another digitized file.

48
The cell width specifies the resolution of the mesh in the region, and the location of a water cell is

needed to start the solution. The area within the grid window and the ocean boundary lines are shown

in Figure 6.1.

Finally, the locations of tide stations is required so they may be included in the grid.

The Process

The process for generating the grid proceeds as follows. The first step is the generation of the

undifferentiated grid mesh using wcell. For a cell width, wcell (in nautical miles), a grid of

undifferentiated (neither land nor water) cells is generated by dividing the width into Imar intervals

and height into Jmax intervals, where

Imasc = 

Co 

,, 

(lonmac - Ionmin)

wceII

Jmax = 

Cn,= (Iatmax - latmin)

wcell

(3.r2)

where Coand Co convert degrees to nmi. Since Imax and Jmax are integer values, the division either

of the width by Imax or the height by Jmax will result in actual cell widths that are slightly larger or

smaller than wcell. Therefore,wcell should be considered a nominal value. This distortion is small

(in the Galveston Bay and San Francisco Bay examples, it was less than LVo) when Im*r and Jmax

are large and is ignored in the numerical solution.

The next steps differentiate between land, water, and ocean boundary. Initially, all cells are given an

Index equal to 0 (i.e., they are set to land). Then the land-water boundary in this grid is determined

by checking all cells that (a) contain at least one point in the coastline data file, or (b) are intersected

by a line drawn between points defining the coastline. These points are given an Index equal to 2.

Then, the cells along the ocean boundaries are identified using the locations in the ocean boundary

data file and interpolating; these cells are given an Index equal to 3.

Finally, the known water point is given an Index value of 1 (for water). Then, sweeping through the

grid several times, all cells adjacent to a water cell (Index equals 1) which are not tagged as either

land-water (Index equals 2) or ocean boundary (Index equals 3) are also set to a value of 1. At the end

of all the sweeps, the unchanged cells remain as land. Then the land-water boundary cells (Index of

2) areset to land (Index equals 0), and the cells containing a tide station are set to water (Index equals

1).

Following the grid generation, two sets of checks are made. The first set of checks consists of

determining the number of water cells that surround each tide station cell; an error flag appears if the

number is zero (indicating a land-locked cell). The second set of checks consists of computing (a) the

total number of land-locked tide gauge cells (which should be equal to zero), (b) the total number of

coastline cells (which should be greater than zero), (c) the percentage of cells that are land (which

49
should be greater than 5Vo and less than 957o), and (d) the percentage of cells that are water (which

should be greater than 5Vo and less than 95Vo). Another flag appears if any one of the above four

values falls outside the acceptable range.

Running the Program

The program is run using a control file. The Unix command is

pa.x 1 gen.ctl

where gen.ctl is the input control file (see Figure 6.2). The output consists of a print file (which for

Galveston Bay was a lengthy 53,000 lines) and the grid file. The control file contains the values of

the necessary parameters (latmanc, latmin, lonmaJc, lonmin, wcell, latwat, lonwat, npmin, npsave) and

the names of the input files for the coastline data, the ocean boundary data, and the tide station location

data. A sample of a coastline file is shown in Figure 6.3. The ocean boundary data file is shown in

Figure 6.4.

9 Galveston Bay Version, Title

28 52.0 29 50.0 -95 20.0 -94 26.0 Lat/ lon window

29 37.0 -94 48.0 latllon of water ce1l

0 .35 . 5e-4 0 . 90 1 1-0 wcell, rerr, a1f a, npsave, npmin

0 0 1 1-00 icon1, iresl, iof f , komegra

/dtr2lkhess /Zone/GalvlData/galv_sta. 3 .dat Station data locations

/dir2lkhess /Zone/Ga1vlData/txshore.dat Coastline data file

/dir2lkhess /Zone/Ga1vlDat,a/oceanbnd.dat Ocban Boundary data file

/dtr2lkhess /Zone/GaLv/C/galv_grid.02 crid f ile

/dir2lkhess /Zone/GaIv/C/galv-gc.O2 Con g file

/dtr2lkhess /Zone/Galv/C/9a1v_9r.02 Residual

/dir2lkhess /Zone/Ga]-v/C/galv_go.01 of fset (MSL MLLW)

/dir2lkhess /Zone/Ga}v/C/galv-ge.01 Datum (MSL in ellipsoid ref )

0 95 153 100 Rpr, print cell i, j, kstart

0 1 '2 3 5 10 20 30 50 1-00 250 500 kpr, new kprnt

5 62 7t L 76 84 l- 77 84 1- 32 38 1- 33 38 1- nedit, cell i, j, ifield

wcel I

rerr

alfa

npsave

npmj-n

iconliresl

ioff

komega

mpr

kpr

nedit

cell width (naut,ical miles )

relative error

land boundary condition parameter

in coastline fi1e, save every npsave

o, rnin number of for islands

1=generate 9c, 0=do not

1=generate gr, O=do not

1=generat.e gh, 0=do not

keep omega constant (=1 . 5 ) until 'komega' iterat j-ons

number of icj s,

number of cells to be edited

Figure 6.2. Control file used to provide input to Program A and Program B as applied to Galveston

Bay. Only data above the dashed line is read.

50
29 .666566

29.640000

29.6001_55

29.s92909

29.5725L9

29 .567987

29 .555073

29.538074

29 .507 248

29.506336

29.552580

29.s52s80

29.550766

29.55L447

29.550537

29.549862

29 .548s00

29 .551"220

29 .552580

29 .00000

29 .00000

29.4s000

29.58333

-94.0s0000

-94.166666

-94.250023

-94.26956L

-94.320297

-9 4 .33 477 0

-94.366287

-94.415382

-9 4 . 495209

-9 4 .500244

-94.467934

-94.47026L

-94 .47L809

-94 .472588

-94.472839

-94.47]-802

-9 4 . 471,283

-9 4 . 468445

-94.467934

1

0

0

0

0

0

0

0

0

1

1_

0

0

0

0

0

0

0

1-

Figure 6.3. Typical records from a coastline file. Data in each record are latitude, longitude (both in

decimal degrees), and a pen index. An index of I denotes the start or end of a line segment.

-9s.2s000 '-9s .00000

-94.33333

-94.33333

L

0

0

1-

Figure 6.4. All records from the ocean boundary file for Galveston Bay. Data in each record are

latitude, longitude (both in decimal degrees), and a pen index. An index of 1 denotes the start of end

of a line segment.

The tide station data for Galveston Bay (Figure 6.5) contains, among other things, the 7-digit NOS

station number, the latitude (degrees, minutes), and the longitu{e (degrees, minutes) of each station.

5 1
4 1,4 Galveston Bay Tide Stations.

877 0559 29 44 .3 -94 42 .4 1_ 1 0 .213

877L450 29 18.8 -94 47 .2 1- 1- 0 .253

8771-5L0 29 17.2 -94 47 -4 1_ l_ 0.366

877t624 29 18.93 -94 36.56 l_ 0 99 .

877L328 29 2L.8 -94 46.7 l- 1- 0.2]-4

877 097L 29 31- . 1 -94 30 . 8 1_ 0 0 .2t3

8?7101-3 29 29 . g -94 54 .7 1 t- O .1,7 4

877tO2L 29 3r-.13 -94 5L.25 1 l_ 0.L77

87709232932-9 -9422.2 l-0 0.366

817 093l. 29 32 -L -94 47 .20 l- 1_ 0 . 19s

87706L329 40.5 -94 58.9'L1- 0.198

877 0625 29 40 . 8 -94 52 .0 1_ 0 99 .

877L481 29 L7 .7 -94 54.3 t_ 0 99.

877L801 29 1-0.0 -9s 07.7 l_ 1_ 0.O92

0000000 00 00.0 00 00.0 0 0 00.0

-29 .0L4 Round pt.

-28.525 Pier 2L (in narrow channel)

-28.537 Pleasure Pier

99.00 cPS buoy (est position)

-28.624 Port Bolivar

-28.725 Rollover (1at was 29 30.9)

-28 .7 7 5 Eagle pt .

99.00 Trinity Ri Chan (est posit)

99.00 High Island

-28.845 Smith Pt. (lon was -94 46.9)

-29.053 Morgans pt. (new position)

99 . 00 Umlcrella point

99.00 Tiki Is (lat was 29 18.0)

99.00 Alligator p t

00.00

Figure 6.5. The Station file, showing tide station locations and other data for Galveston Bay.

Following the header line, the data includes the 7-digit NOS station number, the latitude (degrees,

minutes), the longitude (degrees, minutes), the indices icon and ires which denote whether data for

tidal constituents or a residual water level are available, the offset (m) of MSL relative to MLLW (m),

the offset (m) of MSL relative to the WGS-84 ellipsoid, and the station name. For the offsets, a value

of 99 denotes a missing value.

The Output Files

Beside the screen print file, only one output file is created: the grid file. The file contains a header line

with several grid parameters and is followed by records containing the cell row number and cell

indices (3=ocean boundary, l=water, 0=land). A sample appears in Figure 6.6. The header line

contains the grid array limits (Imax, Jmax), the number of columns of data in each of the following

records (ncol), and the latitude and longitude limits (latmax, latmin, Ionm.asc, lonmin). The grid file

is used by Program B to generate the weighting and offset functions.

6.2. PB: Weighting Function Calculation

Following the generation of the grid as described in the previous section, Program B generates the set

of functions g that are required for the interpolation. The data and the g functions for the following

are generated:

o Tidal Constituent Stations gc(i, j, m)

o Residual Water Irvel Stations gr(i, j, m)

. The Offset of MSL from MLLW go(i, j)

o The Datum of MSL referenced to the ellipsoid ge(i j)

52
1,34 L62 60 28.86667 29.83333 -95.33334 -94.43333 i, jmax, nper1, 0=land

L62 000000000000000000000000000000000000000000000000000000000000

r_ 6 1_ 0 00 0 000 00 0 000 000 0 00 0 0 0 0 0 000 0 0 0 0 00 0 0 0 0 0 0000 0000'00 00 000 0 0 0 0 0 0

1_60 000000000000000000000000000000000000000000000000000000000000

1-s9 000000000000000000000000000000000000000000000000000000000000

L58 000000000000000000000000000000000000000000000000000000000000

]-s7 000000000000000000000000000000000000000000000000000000000000

1-56 0 00 0 0 0 0 0 0 00 000 0 0 0 0 0 0 0 00 00 0 l-l_ 1_ 00 0 0 0 0 0 0 0 0 0 0 0 00 00 0 00 000 00 0 0 0 0 0 0

t-55 0000000000000000000000001_11_1_1_L000000000000000000000000000000

1-54 00000000000000000000001_1LL1_1-i-0000000000000000000000000000000

153 0000000000000000000011-11111_r_1L000000000000000000000000000000

L52 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 L 1-1 1 1- 1 11 1 1- L 1- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 00 0 0 0 0 0 0

l_sl_ 000000000000000001r-1r_11_111_1_r_1-11_r-1_000000000000000000000000000

l-50 00000000000000001-r-t-11-1-111r-l-11-11-1-1-000000000000000000000000000

L49 000000000000000111-1"1_i,1-11_1LL11_11_11_l_00000000000000000000000000

L48 000000000000001-1-1-1111-1-11_11_1-l_l_1r_l_1r-00000000000000000000000000

L 47 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1_ r- 1- 1_ r_ 1 1 1 1 1 1 1 1_ 11- 1 1_ 1- 1- 1_ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

L46 00000000000011_11_1-11-111_11r_11_1_r-11L1_L10000000000000000000000000

L45 0000000000001_1_1_11l_l-11_11_11-L11-i_1_l-1-1110000000000000000000000000

3,44 0000000000011_1-1_1111_1_l_111-1_t_1_1_1-1-l_1_1_11-0000000000000000000000000

L43 000000000001_11_1_1_11-111-11_1111-1_1-1_1111l-0000000000000000000000000

1_42 00000000001_r_r_r_r.111_r_111_111_1_1_l_1_111_11_1_00000000000000000000.00000

L4t 00000000001-1-11-1r-l-L1-11-1-1-1-1-11-1111111-00000000000000000000000000

1_40 00000000001-l_1-11-1-11_1_11 1-1_11r-1-111_11_1100000000000000000000000000

Figure 6.6. Sample portion of a gnd file. The file contains aheaderline with several gridparameters,

and is followed by records containing the cell row number and cell indices (0=land, l=water,

3=ocean boundary). The header line contains the grid array limits (Imax, Jmax\, the number of

columns of data in each of the following records (ncol), and the latitude and longitude limits (latmatc,

latmin, lonmax, lonmin).

For each group, there is either a two-dimensional function or a three-dimensional function. The first

two sets typically have three-dimensional g functions, representing at cell 1,7 a value of the weighting

function for each individual tide station location, m.The second two sets have only a two-dimensional

g function, which represents the offset value at each cell i, j.

Input Data

The program requires the following data, which are read in from the control file, gen.ctl (see Figure

6.2); relative error (e), boundary condition factor (a), indices for the groups to be addressed (iconl,

iresl, iofr), and an iteration parameter (komega). There are also print output control parameters.

The Process

For the three-dimensional g files, the process is as follows. First, the specific type of data (tidal

constituents or residual water levels) is selected. Then one particular station location is selected.

Next, all the water cells are given a flag; locations up to one cell away from all the tide stations in the

group are given a special flag. Flags include -3 for land, -Z for ocean boundary, -1 for the tide

stations, 0 for an interior water cell, 1 through 6 for various types of land-water boundary cells.

53
Then the numerical solution for g is computed by iteration. At the start of the iteration, the value of g

at the selected station (and its adjacent cells tagged as a -1) are set to l00%o (Go,,*,), and the values

at all other stations (and their adjacent cells) are set to OVo (Go*,,).Iteration begins at step ft=1 and

continues until (1) the convergence condition in Eqn.6.1 is met,

maxlsl; - s!,j'l = u (G;. -cf* I(6.1)

(2) k equals 15,000, or (3) the maximum difference gets too large

max;sf I

,- s!,,'l t*to;. -G*,) (6.2)

Theiterationsequencedependson a4.For tlessthanorequal tokomega,a4= l.Otherwise,

1

@*=

1- + P'0 o-,

(6.3)

P - +tcos(j-) + cos( *>l lmQ)c Jnurx

However, if k > komegaand the maximum difference at step k exceed the maximum difference at step

k - km (where km = 20), then cqis reset to 1.

Once the g field for that station has been computed and saved, the next tide station is selected and its

g field is computed. This process is repeated until all stations in the group have been selected. Then

the values for all functions in the group are written to the output file.

Then the numerical solution for the two-dimensional g functions is computed in a similar way.

However, at the start of the iteration, the value of g at each tide station (and its adjacent cells which

are tagged as a -1) are set to the value of the offset.

Output Files

Beside the print file, there are four output files, one each for: the weighting functions for tidal

constituents (gc.out), the weighting functions for residual water levels (gr.out), the offset for MSL

relative to MLLW (go.out), and the datum of MSL relative to the ellipsoid (ge.out).

Each file has the following format. The firs-t line contains a brief text desciiption. The second line

contains grid anay limits and latitude-longitude limits. The third line contains information on the water

level stations used. The fourth and all succeeding lines contain, for a particular water cell, the indices,

latitude, longitude, and numerical values for each weighting function. A sample output file is shown

in Figure 6.7.

54
PB:

L34

Galvest,on Bay w/ocean bnds.

1_65 1- 0.500E-02 28.86667 29.83333

1 1 5 t-5 8770559

8771,328 877 097L 8771-01_3 877L02L

8771,481, 8771801 877200L 9712002

15 l_9 1_ 28.97504997 -95.23594666

0.00000 0.00000 0.00000 0.00000

0.00000 100.00000 0.00000

19 23 3 28.99848557 -9s.20908356

0. 00r_1_9 0. 00002 0 . 00002 0 .00004

90.84222 0.6044s 0-1,6s47

i-9 24 L 29.00434303 -95.209083s6

0. 001_1"8 0 . 00002 0.00002 0 .00004

90.84204 0.60685 0.L6s47

20 23 3 28.99848ss7 -9s.20236206

0. 001-L8 0. 00002 0 . 00002 0 .00004

90.84083 0.60857 0.1,47t4

20 24 L 29 .00434303 -95.20236206

0 . 001_17 0. 00002. 0. 00002 0 .00004

90.84016 0.61-099 0.1_471,4

Version,. Title

-9s.33334 -94.43333 0.90

877L450 8771_51-0 877L624

877093L 87706L3 8770625

0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000

0 . 00000 0 . 00000 0. 00000 0. 00'000

0.00002 0.00000 0.00000 6. s5683

0.00000 0.00000 0.00000 0.00000

0 - 00002 0.00000 0 - 00000 6.5544L

0.00000 0.00000 0.00000 0.00000

0.00002 0.00000 0.00000 6.55269

0.00000 0.00000 0.00000 0.00000

0.00002 0.00000 0.00000 6.5502s

Figure 6.7. Sample portion of the g field file. The first line contains a brief text description. The next

line contains grid array dimensions (Imasq Jmax), and latitude-longitude limits (latmax, latmin,

lonmax, Ionmin), and the value of alpha used. The third line contains information on the water level

stations used. Each data record contains, for a particular water cell, the indices, latitude, longitude,

and numerical values for each weighting function.

6.3. PC: Galculation of the Tide Correction

Given a data file containing a ship's time and position, Program C uses the previously-derived

weighting functions plus any contemporary observations of water levels to compute the tide correction

for the time and place of the ship's observation. Program C also has the capability of generating a

water level referenced to the ellipsoid that can be used for comparison with measurements.

lnput Data

The input data required is as follows:

Time and height units

Local time reference (hours)

Weighting function and offset files (see Section 6.2)

Tidal constituent (amplitudes and phases) data

Equilibrium argument and lunar node file

Time series file of total water levels

Ship time and position

The time and height units determine whether the tide correction output should be in Greenwich Mean

Time (GIvIT) or Local Standard Time (LST) (itime =1 or 2, respectively), and whether the tide

correction should be in meters or feet (imetr = 1 or 2, respectively). The local time reference is the

o

o

o

o

o

o

o

55
c

number of hours that is added to GMI to get IST; for Galveston Bay it is -6 hours and for San

Francisco Bay it is -8 hours.

The tidal constituent data (Figure 6.8) is provided for all stations, and the file containing the

equilibrium arguments and lunar node factor for 37 constituents (Figure 6.9) . A sample of the residual

tide series name file is shown in Figure 6.10. The tide series files themselves have records containing

the year, the day of the year (for example, a value of 1.500 corresponds to noon on January 1), and the

water level value (relative to MSL)

677 -1-51-0 Galveston, Pleasure

0. 94.8 0, 0 ( -

0. 94.8 0 .

44027 48 1_00273 0

003 74 002 L04

024 705 0043385

259t71"8 088301_7

005 43s L62 25L

002 693 0122383

Pier, Texas T.M. 90 W.

a, b, tlon, iunit ( 0=f t., l=met€r, 2=cm) x1-000 )

(t1on= time meridian: 0=Greenwich, -90=1oca1)

t062s7L 551 287 0192008 507 207 0042337

008L563 02L25L3 0022573 01_518L2 0252240

a433295 043 4]-7 034 91- L032652 365 57L

01-02 0t-1- 026 t-80 1,L2 48 0L42984 007 201,2

003 282 005 434 01-s3185 0033423 0L52734

151-0 1_

1_510 2

1_51-0 3

L 51-0 4

1_510 5

t_5L0 6

Figure 6.8. Tidal constituent data for a single station in a NOS standard format.

L995 0 Lt032 r.821-000 010323464 90s Ls5r-065 364 84s3597L099 546 934 338 1 L

1995 0 21000 0L065 46L032 6701_000 01032 35310323L47 5662L7210321494 1_ L

L99s 0 310001800 792 4B 864 50211-11 318100020041-00028021032341-8 69tL987 L l -

1-99s 0 4 84s 486 84s32801_000 27L000L773 845296210003498103234L8L0482073 r_ L

1995 0 5!2L02293 964 208 7842L031134 728LO32 L82 7L3 97L032 284 872 673 L 1_

1995 0 6 8453399 845 31-065 3181065 46 8453496 8092285L0653329t2892340 1_ 1

1-995 0 712892657 809L921- 5543358 979 979 634 788 83511_79 654 924 8453597 l_ 1

1995 0 8 905 l-56 8723462 809228sL0323464128926s7L099 s46L249247sL06s3329 1 1_

1995 o 9L2102293 899 44 899 361 964 s2o 934 338 732244LL065 262LOgg 648 l- L

1995 0L0 964 202L032 L821-099 228t065 461065 364133A2204L099351L1,2492475 L L

1-995 03-LL28926s7 809228sr.330252213302839 8352467 928 226 995 66 899 361- L 1

L995 0t2 68322821099 228L099 546L055 364L734 93LL34 410L2892657L373302L 1- 1

1-995 0131-3302839 86L2649 83s2467L027 248L027 566]-027 884 99s 702tL7L s92 L 1

L995 014LL7L 9L0l_134 4L0Lt34 728L33028391-099 546]-027 8841-L71_ 592LL7L 910 L 1

L995 01-51373302]-L134 728L000352sL000 75L0002105 8723296 782 6s8 71"33277 L 1

t99s 0r-69642087842L0369231,46453439 0 0 0 0 0 0 0 0 1 L

L996 1 110371-1831-000 01_0373578 885 L22L0752366 8121-0481_1Ls3548 9L8L30s L 1-

Figure 6.9. A portion of the equilibrium arguments and lunar node factors file.

Residual w1 station file names (10) for Galveston Bay. jtime:l=GMt,2=1oca1

8770559 L /dtr2lkhess /Zone/GalvlData/Tides /8770559.ut

877 0931' 1 / di-r2lkhess /Zone/GalvlData/Tides / 8770931- .ut

877t02I 1 /dtr2lkhess /Zone/Ga1v/Data/Tides /8771021-.ut

8771,450 1- / d:-r2 /khess /Zone/Galv/Data/Tides / 8171450 .ut,

877L624 1 / dtrTlkhess /Zone/GalvlDat,a/Tides / 8771624.ut

877 0613 1- / dLr2lkhess / Zone/GalvlData/Tides / 8770613 .ut.

877tOL3 1 /dtr2lkhess /Zone/GalvlDat,a/Tides / 8771-013 . ut

877L328 l- /dir2lkhess /Zone/GalvlData/Tides / 8771328 . ut

8771-510 l- / dtr2lkhess /Zone/GalvlData/Tides / 877151-0 . ut

8771-801 1- /dtr2lkhess /Zone/GalvlData/Tides /8771801.ut

Figure 6.10. File with the residual file names.

56
The Process

The program is run using a control file (trak.ctl) to provide input as follows.

pc.x < trak.ctl

A sample of the control file trak.ctl is shown in Figure 6.11.

4 Input file for pc. NEW offset file

1_ -5 1_ itime, ihrref, imetr

1 0 1_ BB 10000

/ dir2lkhes s / Zone / GaLv / C/galv_g c . 02

/ dir2lkhess / Zone / GalvlC /ga1v_gr . 02

/ dir2 /khess /Zone/Galv/C/galv_go . O2

/ dtr2lkhes s / Zone / GaIv / C/galv_ge . 02

itcari, iskip, icallp, ica1Lp2 , icallmx

/ dir2lkhess / Zone / GalvlData/constitl-9 . dat

/ dir2lkhes s / Zone / GalvlDat a /yW. dat

/ dir2lkhess / Zone / Galv/Data/residL0a. dat

/ dir2lkhess / Zone / GalvlData/residl- 0 . dat

/ dir2lkhess / Zone / GalvlData/ ship_gps . dat

0 0

Weighting for Constituents

Weighting for Residual

Offset of MSL from MLLW

Datum of MSL from Ellipsoid

Tidal Constituent File

Tidal Constants File

6-min Residual File Names

Hrly Residual File Names

Ship Track File

Time and Space Windows

itime :

ihrref :

imetr :

itcari :

iskip :

icallp :

ica11p2 :

icallmx :

convert all times to 1=Greenwich, 2=1oca1

local time (hrs) in relation to Greenwich

1=a11 data converted to meters , 2=feet

1=ful1 TCARI, 2=interpolate the total signal, 3=TCARI w/resid=O

skip over the first 'iskip' records in track file

print for ica11 LE icallp

print for ica11 = ica11p2

it.erations will stop if icall' reaches icallmx

Figure 6.L1. Control file for Program C.

After the files are opened and read in, a check for consistency of stations is made. Using the stations

in the weighting functions for constituents file, a check of the stations numbers in the constituent data

file @gure 6.8) is made to insure sufficient data are available. Similarly, using the stations in the

weighting functions for residuals, a check of the stations numbers in the residual names (Figure 6.7)

and the residual data file is made. Also, since a tide prediction is needed to compute the residual, a

check of the stations numbers in the constituent data file is made.

Next, the ship trackline file is read. Each record of the file contains the year (four digits), day in the

year, latitude, and longitude. The day in the year is computed so that noon on January t has a value of

1.500. Using the year value, the astronomical constants (equilibrium phases and lunar node factors)

are set.

Then the tide is computed. Using the weighting functions and data from the tide stations, the tidal

constituent amplitudes and phases are computed for the four closest cells; then these are intefpolated

bi-linearly to produce amplitude and phase values at the precise location of the ship. Then the tide at

the ship is computed by creating and summing the constituents.

57
The residual water level is computed. First the residual at each tide station is computed by subtracting

the predicted tide from the observed tide. Then, using the weighting functions and the residual from

the tide stations, the residuals at the four closest cells is computed; then these are interpolated bilinearly to produce the residual water level at the precise location of the ship.

Then the offset and datum are computed. Values at the four closest cells are interpolated bi-linearly

to produce the offset and datum at the precise location of the ship.

Finally, the tide correction and the estimated water level relative to the ellipsoid are computed and

saved to an output file.

The Output Files

Besides the screen print file, two output files are created. The first is used for processing soundings

and contains the ship's time and location, followed by the tide correction, and the estimated water

level relative to the ellipsoid (Figure 6.12). The second is used for analysis and contains, in addition

to the data in the first file, the tide, the residual, and the two offsets.

L995 t64. s9166 -94.9084

1995 1,64.59584 -94.9089

l_995 1,64.72084 -94 -7012

1995 164.72501, -94.7026

1995 L64.72917 -94.7098

l_99s 1-64.73334 -94.7191,

1995 l-64.73750 -94.7282

1_995 L64.741,61 -94.7376

L995 1,64.7 4583 -94.7 47L

1-995 1,64.75000 -94.751,6

1995 t6 4 .7 5 41,7 -g 4 .7 592

1_995 1-64.75833 -94.7680

29 .4977

29 .4984

29 .7 29L

29.7275

29.7190

29.7 083

29 .697 I

29 .6869

29 .6758

29 .67 0 6

29.6630

29.6sr_6

0 . 1498 -28 .7992

0 . 1537 -28 .7 953

0.ss00 -28.673L

0.5483 -28.671,2

0. s362 -28.6660

0.52s3 -28.6610

0 . st67 -28 .6564

0. s091- -28.6s19

0 . 5 024 -28 .6473

0 . s003 -28 .6443

0 .49s8 -28 .6416

0 .4893 -28 .6377

Figure 6.12. Sample of the Program C output file. Each record contains the year (four digits), day in

year, longitude (degrees), latitude (degrees), tide correction (meters), and the estimated water level

relative to the ellipsoid (meters)

58
7. SUMMARY AND CONCLUSIONS

7.1. Summary

The National Ocean Service's hydrographic surveydata are processedto give waterdepth atthe point

of the measurement. To produce a depth relative to Mean Lower Low Water (MLLW), which is the

chat datum, the measured depth must be corrected to account for the departure of the instantaneous

water level from MLL\M. This departure is due primarily to the astronomic tides, river flows, water

density effects, and meteorological influences. At present, discrete tide zoning is used to provide this

correction. Discrete tide zoning rests on the simplifying assumption that the water level in an entire

zone has a fixed rnagnitude and phase relationship to the measured water level at a single nearby

gauge. However, this method is difficult to apply because selection of zones is somewhat subjective,

the method has known inaccuracies in its assumptions about how tides var/, it produces a discontinuity

when crossing from one zone to the next, and the data it produces is not referenced to the GPS

ellipsoid.

A new method, Tidal Constituent And Residual Interpolation (TCARD, has been developed to

estimate the tide corrections for bathymetric data. TCARI separately interpolates:

each tidal constituent's amplitude and epoch (phase) value,

the residual, or non-tidal, water level,

the Mean Sea Irvel (MSL) offset, which is the difference between local MSL and

MLLW, and

the MSL datum, which is the difference between MSL and the ellipsoid

This method has the advantages that it treats the astronomical tide and the residual water level

separately, it eliminates the mismatch when moving between discrete zones, and it can be used in an

ellipsoidal reference system. However, TCARI requires significant computer resources to generate

the weighting functions, its accuracy is dependent on the existence of tide data at many locations in the

survey area, and it does not alleviate the need for contemporary tide measurements.

The spatial interpolation at the core of this method is carried out by the use of a set of weighting

functions that quantify the local contribution from each of the shore gauges. The weighting functions

themselves are generated numerically by solving Laplace's Equation 0 F) on a gnd.

The LE approach provides a spatially-smooth solution that exactly matches the observations. There

are four sets of weighting functions, one seteach foreach of the quantities in the above list of bullets.

The LE is:

o

o

o

dzc O'G

w+ N=o (7.1)

The variable G canbe tidal constituent amplitude, constituent epoch, or an offset. The grid on which

the LE is solved is generated rather easily from a digitized coastline file, and does not contain any

depth information. The solution is by the method of successive over-relaxation (SOR), with

convergence being defined as the acceptably small difference between solutions between iterations.

Using the tide and water level data and the weighting functions, TCARI generates a tide correction for

59
the time of the depth measurement at the four cells in the grid that are closest to the location of the ship.

The final correction is interpolated to the precise location of the ship.

TCARI's specific data needs to produce tide corrections for traditional surveys include ( 1) a digitized

coastline file for th e area, (2) tidal constituent amplitudes and epochs, the MSL-Io-MLLW offset, and

the ellipsoidally-referenced MSL datum at all water level gauge locations near the survey area, and

(3) observations of total water level at gauges for the time of the survey. These are sufficient for

producing the set of weighting functions relevant to the suite of water level gauges and, with (4) aship

trackline file, the corrections for the time of the survey. For shipboard processing of data in near-."uitime (NRT), NRT water level observations are needed. The weighting functions can be generated

before the survey and need not be updated. For a ellipsoidally-referenced survey that includes GPS

measurements of the distance from the ellipsoid to the sea bottom, (5) the ellipsoid-to-MllW offsets

at locations near the survey area are needed.

Three Fortran computer programs were written to implement TCARI. The first, Program A,reads a

digitized coastline file and generates the gnd. Cells in the grid can be selectively added or removed

to better represent the coastal region. The second. Program B,reads the grid and generates the

weighting functions. This program requires the longest time to run and it produces the files containing

the weighting functions. The third, Program C, reads the ship track file and generates the corrections

as well as additional output that can be used for statistical analysis

Initial tests of TCARI were carried out on a simple, semi- rectangular region (maximum height of the

area of 30 nmi, maximum width of the area of 30 nmi, and a cell size of 0.50 nmi). Convergence of

the solution is not guaranteed, but is somewhat dependent on geometry. The program was optimized

for convergence, with the additional capability to force convergence (if necessary) by adjusting the

SOR weighting factor and the convergence criteria. The solution was extremely sensitive to the value

of the boundary parameter, a(see Eqn. 3.7). A small value (ad) gave rise to a distribution similar

to the temperature distribution with an insulated boundary, and a large value (eI) gave a solution

in which the contours were nearly parallel lines. The second solution was judged to be representative

of co-tide and co-phase lines in nature. Errors in the numerical solution under the test case (rotation

of the region by 45 degrees) with two input locations were about 57o of the maximum, or about 5

degrees in phase. Maximum errors occured near the center of the computational region. It was

determined that more accurate distributions of phase angles could be produced if the sine and cosine

of the phase angle were interpolated separately, then combined by the arctangent to create the final

distribution.

Further sensitivity testing and calibration of TCARI's solutions were made using the kinematic GPS

water level data obtained in Galveston Bay. For the benchmark run, which used hourly water levels

observations, the mean error was 0.01 cm, the RMS error was 9.7 cm, and the maximum error was

27 .I cm (there were four instances of errors 20 cm or greater). Out of 6 18 observed values, 557 were

used in the comparisons; values not used fell on grid land cells. Many of the unused observations were

in the Galveston Channel leading to Pier 2I and around the Port Bolivar gauge, and geographic

features near these gauges were not included in the grid, which had a cell-size of 0.35 nmi. The value

of q which determines the land boundary condition, was selected to produce the best fit (visually)

to contours of the M, epoch produced by the numerical model, especially in the lower bay near the

entrance. Sensitivity tests were made on the following (nominal values appear in parentheses): the

grid size ,wcell (0.35 nmi); the boundary slope condition coefficient, a(O.9);the coastline index (0);

60
and the error ratio, e(5 x 10"). The coastline index sets the coastline cells to either 0 for land or 1 for

water. Results were not overly sensitive to changes in any of the above parameters. Errors for

predictions of water levels near the GPS buoy (877-1624) averaged about -13 cm and were due

mainly to the fact that the ellipsoidally-referenced MSL was not available (we can infer an value of

-28.44 from the data). Finally, because of the lack of reliability in the values of the amplitude and

epoch of the long-period constituents (Mm, Mf, Msf, Ssa, and Sa), these constituents were masked out

in the calculation of the astronomical tides; the net effect was to shift them to the residual water levels.

In the application to Galveston Bay (cell size of 0.35 nmi), TCARI reproduced the measured water

levels with a mean emor of 0.4 cm, an RMS error of 8.4 cm, and a maximum error of 24.6 cm. The

estimated RMS effor on the kinematic GPS measurements ranges from 4.7 cm (light wave conditions

and no forward ship motion) to 9.1 cm (all wave conditions and ship speeds up to 15 m/s). The use

of 6-minute water levels produced a large improvement over the use of hourly water levels, probably

because wind effects are large due to the shallowness of the bay.

In the application to San Francisco Bay (cell size of 0.25 nmi), TCARI reproduced the measured

water levels with a mean error of 1.4 cm, an RMS effor of 8.7 cm, and a maximum effor of 41.5 cm.

The grid cell size was 0.25 nmi, and of the 968 measurements, 939 were used. The use of 6-minute

water levels produced only a small improvement over the use of hourly water levels, probably

because wind effects are small due to the deepness of the bay.

7.2. Major Results

Major sources of error in TCARI appear to be (1) nume{cal interpolation errors in regions far from

the input data of as much as 5 degrees in phase and 57o in amplitude, (2) the lack of tide data for

locations not adjacent to land, (3) poorly-known constituent values at the gauges, and (4) the lack of

water depth in determining the distributions.

TCARI and discrete tide zoning were compared, and TCARI had a lower effor. A direct comparison

of the tide corrections with the measured water levels is not possible because tide zoning does not

provide a distribution of the MLLV/ fieldrelative to the ellipsoid. However, TCARI does. Therefore,

an estimate of the ellipsoidally-referenced water level which incorporates the tide-zoned correction

and the TcARl-generated offsets was computed. Three sets of zoning methods were used: preliminary

zoning, final zoning, and spatially-interpolated final zoning.. Preliminary zoning for Galveston Bay

is referenced to one gauge: Pleasure Pier (877 -1510). Final zoning added references to four additional

gauges: Port Bolivar (877 -1326), Morgans Point(877 -0613), Trinity River Channel (877 -L021), and

Pleasure Pier (877 -1510). However, because of tide zoning station priorities, data from Pleasure Pier

was not used in the final zoning. In spatially-interpolated tide zoning, the interpolated value is the

weighted mean of the original correction and the corrertions in adjacent zones. The weights are equal

to the fraction of the area of a circle that lies in the respective zones; the circle has an origin at the

center of area of the original zone and has a radius equal to the area of the zone divided by its

perimeter. The results are summartzed in the following table.

6r
Table 7.1. Comparison of RMS errors (cm) in tide zoning and TCARI in estimating the postwater level data. NA means not applicable.

Method Galveston Bay San Francisco Bay

Tide Zoning, Preliminary 9.2 NA

Tide Zoning, Final 9.4 10.1

Ti de 7-oning, Interpol ated 9.2 9.8

TCARI 7.5 8.7

TCARI was compared to numerical modeling, and TCARI had a lower eror. The numerical model

for Galveston Bay (Appendix C) was used to generate water levels for comparison with the kinematic

GPS measurements. The model was run for the month of Jun e 1995 and included tidal, density, and

meteorological forcing. At each wateq level gauge the ellipsoidally-referenced MSL was computed

as the monthly mean of the ellipsoidally-referenced observed water level minus the monthly mean of

the modeled water level. An ellipsoidally-referenced MSL field (assumed here to be equivalent to

the Mean Tide lrvel) was generated by weighting the values of the ellipsoidally-referenced MSL at

the water level gauges. The weight at each cell for each gauge was the inverse distance to the gauge,

normalized by the sum of the inverse distances to all gauges. The ellipsoidally-referenced

instantaneous water level was then computed as the sum the instantaneous modeled water level and

ellipsoidally-referenced MSL. Comparisons were made at 470locations, and were stratified based

on distance from the nearest water level gauge and the speed of the ship. The RMS difference was 15

cm, and there was no appreciable dependency on distance or speed. The TCARI RMS error for the

June measurements which fell within both the TCARI and numerical model grid was 8.3 cm.

7.3. Production of Ellipsoidally-Referenced MLLW Fields

TCARI can be used to generate ellipsoidally-referenced MIIW fields, F/, (see Figure 1.1). The

existing software generates the ellipsoidally-referenced MSL field (Hr) and the MSL-Io-MLLW offset

field (H). The new field can be generated by the difference in the two fields:

Hr=Hu-Ho (7.2)

A second approach to generating F/. would be to subtract the I/, value from the Hu value at each

station where both values exist, then create a MLLW field directly from the values at the stations. In

either case, it'is desirable to have both values at all stations. The fields for Galveston Bay and San

Francisco Bay computed by the first method are shown below. Recall that in Galvesto nBay,7 stations

have F/" values and 1 1 stations have Iy'o values. In San Francisco Bay, there are only three stations (all

in the central buy) that have F/u values, and 37 stations have I/, values. Therefore, outside the central

bay all the variation shown in the figure is due to variations in Ho.

62
Figure 7.L. TCARI's ellipsoidally-referenced MLLW field (m) in Galveston Bay.

63
Figure 7.Z.TCAR['s ellipsoidally-referenced MLLV/ field (m) for San

Francisco Bay.

7.4. Future Enhancements

Potential future enhancements of the TCARI method, in approximate order of greatest to least

improvement in accuracy, are as follows: The use of the complex version of the shallow-water,

uniform-depth, single-constituent tide wave equation rather than the LE, which would include depth

and tidal frequency differences into the solution. The use of variable grid spacing in the I .E solution

to obtain better resolution in narrow entrance areas. The use.of depth weighting in the present I .F.

solution to account (in an indirect way) for tidal dependence of phase on gravity wave speeds. The

use of an equation other than the LE (such as a fourth-order differential equation) for spatial

interpolation.

TCARI and numerical model-generated fields can be combined to produce more accurate information.

First, the numerical model's simulation of ellipsoidally-referenced water levels now relies on a

64
Barnes (I964)interpolation scheme. Since this scheme does not account forthe presence of land, there

will be errors in the water levels. However, it is likely that the errors can be reduced by using

TCARI's TrE-based method of interpolation for this field. Second, TCARI's tidal constituent and other

fields were generated without information on the local bathymetry. Since the numerical model's tidal

constituent fields were generated using the bathymetry, the model fields contain the influence of depth.

The modeled fields could be used in TCARI after subtracting an effor field which would be generated

by spatially-interpolating the errors (with the LE method) at the gauges.

ACKNOWLEDGMENTS

Dr. Bruce Parker, Chief of the Coast Survey Development Laboratory (CSDL), provided many of the

key concepts of spatial interpolation of tidal constituents. CSDL's Douglas Martin provided

invaluable assistance in accessing NOS historical data and in defining terms like GPS and ellipsoid.

CSDL's Dr. Lloyd Huff organized the field surveys that collected the water level measurements.

Steven Gill of NOS's Center for Operational Oceanographic Products and Services (CO-OPS)

provided information on tides and tide zoning policy, and CO-OPS's Mike Gibson and Cary Wong

provided zoning data for Galveston Bay and San Francisco Bay.

REFERENCES

Barnes, S. L., 1964: A Technique for Maximizing Details in Numerical Weather Map Analysis.

Journal of Apptied Meteorology, 3,396 - 409.

Browne, D. R., and C. W. Fischer, 1988: Tide and Tidal Currents in the Chesapeake Bay. NOAA

Technical Report NOS OMA 3,84 pp + appendices.

Cheng, R. T., V. Casuli, and J. W. Gartner, 1993. Tidal, Residual,Intertidal Mudflat (TRIM) Model

and its Applications to San Francisco Bay, California Bstuarine, Coastal and Shelf Science, 36,235

- 280.

Collier, W. C., G. Glang, andL.C. Huff, I999:ManagingTidelnformation forHydrographic Surveys.

Proceedings of the Eleventh Biennial International Symposium of the Hydrographic Society

(HYDRO99), January 5-7 ,1999, University of Plymouth, UK. (Special Publication No. 39). p. 1-1

to L-7 .

Defant, A. , 1 96 1 : Physical Oceanography, Volume II. Pergamon, pp 598. (Esp. 202 - 2L6 and364 -

4s6).

Gill, S., 1998: Description of Discrete Tide hning. NOS, Center for Operational Oceanographic

Products and Services (personal communication).

Hufl L. C., B. J. Gallagher, and E. C. Snead, Jr., 1998. On-the-Fly GPS forDetermination of Vertical

Ship Motions. Proceedings, Ocean Community Conference '98, The Marine Technology Society

Annual Conference. 785 - 791.

65
Huff, L. C., and B. J. Gallagher, 1996. On-the-Fly GPS for Vertical Control of Hydrographic Surveys.

Proceedings of Hydro '96 The Tenth Biennial International Symposium of the Hydrographic Society.

Rotterdam, The Netherlands. 191 - L99.

Muller, T., andE. Groten, lggz.AccuracyEstimation of Mean Sealrvel Determination in the Baltic

Sea Using a Combined Method. Sea level Changes: Determination and Effects. Geophysical

Monograph 69, ruGG Vol 11. 189-196.

National Ocean Service, 1999: NOS Procedures for Developing and Implementing Operational

Nowcast and Forecast Systems for PORTS. NOAA Technical Report NOS CO-OPS 20. 33 pp.

Press, W. H., S. A. Teukolsky, W.T. Vetterling, and B. P. Flannery, L992. Numerical Recipes.

Cambridge University Press. 963 pp.

Schmalz, R. A., 1996: National Ocean Service Partnership: DGPS-Supported Hydrosurvey, Water

Irvel Measurement, and Modeling of Galveston Bay. NOAA Technical Report NOS OES L2. 136

pp + appendices.

Schureman, P., 1958. Manual of Hamonic Analysis and Prediction of Tides. U.S. Department of

Commerce, Coast and Geodetic Survey, Special Publication No. 98 [revised lg4}edition, reprinted

19881. 3r7 pp.

Stawarz, M., and M. Metzner , lgg4.Altimetric Geoid of the Indonesian Waters Derived from ERS- I

Radar AltimeterData. Proceedings, International Symposium on Marine Mapping (INSMAP)

1994.299 - 310.

Welch, J. M., J. W. Gartner, and S. K. Gill, 1985: San Francisco Bay Area Circulation Surv ey: I9t79-

1980. U.S. Department of Commerce, NOAA. NOS Oceanographic Circulation Survey ReportNo.

7. 180 pp.

kwas,C.Z.,(editor), 1993:TampaBay Oceanography Project: Physical Oceanographic Synthesis.

NOAA Technical Report NOS OES 2. 184 pp.

66
APPENDIX A. TIDE WAVE SOLUTION

Another approach is to apply the equation for a simplified, shallow-water tide wave with gravity g,

constant depth F/, linearized friction y, Coriolis accelerati onf, and a single constituent frequency o.

Then for water level, r7,

rl -- zei'' (A,1)

Z is the solution to the shallow water equation ,

A2Z O'Z

-+-+KZ_O (A.z')

dx- dywhere complex K is

* =(<t-it>'.:r*>'\4 (A.3)

t I-i+ )su

(see Fan g,Z.,A. Ye, and G. Fang, I99l: Solutions of tidal motions in a semi-enclosed rectangular gulf

with open boundary condition specified. In Tidal Hydrodynamics, B. Parker ed, 153 - 168). The finite

difference expression of A.2 is

(Z*u - Zi,i) - (2,,i - Zrr,,) + (Z,.ir, - Z,.i)

+(2,,i -L,i-r)+ 82,,,= $ 

(A'4)

where B = NlK.Rearranging gives an estimate for Z

z:,, =fi(z^'i * 2,-,,j) (A'5)

This equation ib analogous to that for the I F., Eqn. 3.10.

67
68
APPENDIX B. TIDE DATA FOR GALVESTON BAY

The following (Tables B.1,8.2, and B.3) list the tidal constituent amplitudes and epochs for 14

stations in Galveston Bay. Methods of harmonic analysis, time series data, and other notes appear in

Table 8.4. The locations and names of the stations appear in Figure 4.2.

Table B.1. Observed tidal constituent amplitudes (mm) in Galveston Bay.

Station 559 6L3 .625 923 931 971- 1013 L02L L328 14s0 1481 1s10 L624 ]-80L

L M2 60 54 52 191 42 s't 32

2321313t2531515L0

3N2 13L2t246 1_0t48

4 K1 116 L23 1r.3 205 r.14 118 109

5M4 4 L 3 I 2 5 2

6 01 119 114 11_3 189 11_9 109 LA2

7M6 10L2111

8MK33222252

9S401-0311-0

l_0MN43113241

LLNU22335321

t2s51001000

13Mu22345332

L4 2N 6 4 5 9 I r_ 3

150018LL15815t210

16LAM22Lt2L21

L7S1_24L2 158158

18 M1 11 13 I L7 10 L3 10

19,11_5328724

20 MM 2L 35 25 24 51 t't 34

2L SSA 11_9 LL6 35 183 1.70 l-31 1L4

22 SA 138 81 235 96 150 84 74

23 MSF 19 37 63 4t 43 33 31

24MF1L92L344911

25 RHO1 8 8 4 8 3 4 6

25 Q1 23 23 23 39 23 L9 2 0

27T22235321

28 R2 0 1 2 4 L 1 1

292Q154t274

30 P1 32 35 27 6t 3L 37 3 1

312SM2L210L2

32M32L11030

33L25639243

342MK32102252

35K2t2 1t_l_0 10995

36M8 1 0 0 0 0 1 0

37MS43024131

38 77 84 47 134 1_35 3 3

92323L730377

10 2t 2L r_0 32 4t 9

107 L26 ].'29 LL1 158 L77 78

1142650

116 L27 119 1_r.0 1s5 L'73 '19

011r_L20

0L020t02

L1L2130

012020r_

233268L

0 1 1 1 t .2 0

L44L531

1951852

51_3 105778

03101_1L

0 1_1_ 11 0 1_3 0 11

858813L24

969910L41

093L031022

0 117 113 0 111 0 153

0138780790115

0452602702

035103051

5674874

22 27 24 2t 34 34 ! 7

153]-42L

01202Ql

3523252

3s 3s 39 39 49 s9 2 2

0210101_

0320202

t22L542

0810102

2L44551-06

0L0r.L20

0120400

69
Table 8.2. Observed

Galveston Bay.

tidal constituent Greenwich epochs (degrees) in

station 559 613 525 923 93i- 971 L0L3 1021 L328 1450 1481 1510 1624 1801

L M2 53 67 s9 272 9 18 19 31 292 295 33L 275 275 25

2 52 45 53 46 269 343 L7 2L 13 289 298 335 273 270 3s

3 N2 29 48 33 249 349 348 354 359 266 278 307 257 259 7

4 K1 L04 115 L11 27 90 93 100 94 60 55 83 29 23 10s

5 M4 3s5 352 339 2L9 220 331_ 209 238 2L 257 266 2oL 223 335

5 01 97 10L 104 L9 83 84 87 91 52 45 74 2t 25 9 3

7 M6 326 46 24! 232 51 208 45 0 307 263 L23 234 310 2.tO

8 MK3 53 97 26 339 270 332 259 0 135 156 0 ? 0 10s

9 s4 l-80 357 L79 357 15 t62 332 t24 35 20 40 10 239 196

10 uN4 328 308 320 L72 208 299 207 o 286 2L5 0 L56 0 349

t L NU2 333 59 48 247 337 J25 345 4 278 27L 31"1 25:- 26! 15

t2 s5 136 258 169 L29 52 248 29 0 66 285 226 257 204 LAs

13 rtrvz 296 283 250 L8G 280 293 265 ztt 242 2L9 135 i_81 92 198

L4 2N 26s L42 290 235 265 178 L75 331 272 209 282 224 243 136

15 00 Lt2 tzL 118 48 93 113 tL2 98 113 98 91 7L 2L 105

15 L?*t2 59 109 90 1L3 49 2L3 57 0 51 290 0 339 273 348

L7 St 205 260 274 288 315 336 348 0 353 360 0 330 o 56

18 ML L96 163 228 56 200 151- 1.55 93 109 74 ?8 42 24 205

L9 ,r1 58 47 t27 43 359 1L 51 96 32 29 87 9 22 53

20 MM 327 255 37 29L 350 315 250 0 L29 266 0 265 0 11

2l ssA 42 65 s2 60 29 65 62 0 58 61 0 57 o 42

22 sA l2r 150 1-41 140 119 1-41 166 0 185 t7 5 o L72 0 146

23 MSF L88 327 195 293 L44 328 319 o L92 308 0 302 o zLg

24 MF 359 154 111 319 33L l-08 155 0 251 115 o 2oL 0 300

2s RHOI- 43 8L L42 49 87 118 82 89 25 56 7o 18 26 :-24

26 Q1 66 88 72 5 55 66 75 89 29 27 59 5 26 7 9

27 T2 94 97 LL0 333 240 190 68 350 346 292 335 298 270 133

28 R2 183 58 93 191 1s5 331 170 0 18 2t6 0 201 270 37

29 2Q 266 L52 287 205 L73 202 L47 8? 305 LzO 65 44 27 222

30 pl- 109 114 114 19 86 80 99 94 45 48 82 25 23 115

3t 2sM t74 2L6 69 340 94 60 285 o 345 288 o 28 0 115

32 M3 274 331_ 239 260 35 194 61 o 248 73 0 43 o 223

33 L2 73 106 93 304 63 44 97 64 348 52 352 3L9 292 6s

34 2MK3 40 156 57 277 240 347 253 0 11? 196 o 342 0 ?8

35 K2 59 91 72 288 47 62 80 13 15 13 336 273 270 13

36 M8 83 105 295 262 262 91 351 0 180 170 1?8 69 L37 l_48

37 MS4 326 285 344 230 227 344 226 o 24 280 0 238 o 2gg

Table 8.3. Observed tidal constituent local epochs (degrees) in Galveston

Bay.

Station 559 5l-3 525 923 931 971 1013 LO2L ]-328 r.450 1481 1510 1_624 1801

L M2 239

2 s2 225

3N2218

4K114

5M47

5 01 l_3

7 M6 L64

8 MK3 L48

9 S4 180

t 0 MN4 343

L1 NU2 L62

L2 56 316

13 I,IL[2 L28

L4 2N 98

L5 00 15

16 LAM2 243

L7 SL 1l_5

18 ut_ L09

l_9 .T1 334

20 MM 323

2L SSA 4L

22 sA t2t

23 MSF 182

24 MF 353

25 RHOI_ 322

26 Q1 346

27 t2 274

28R22

29 2Q 189

30 P1 1 9

31 zSM 348

32 M3 13

33 L2 255

34 2MK3 L43

35 K2 239

3 6 M8 1_07

37 1'{S4 332

253 245

233 226

237 223

25 2 0

4 351

L7 2 0

244 79

L93 L21,

357 L79

324 335

247 237

78 349

115 9 2

335 L23

24 2 L

292 273

t7 0 l_84

76 t4t

313 3 3

25L 33

64 5 1

150 I4L

32]- 190

147 1_05

350 6 1

7 352

277 29L

238 273

75 210

24 2 5

30 243

70 339

289 276

258 159

271, 252

L30 3r.9

29L 350

99 19s

89 163

78 t79

297 360

232 232

296 359

1A 259

756

357 15

187 223

76 165

309 242

18 tt2

67 98

3r.1 356

296 233

198 226

329 r.13

309 265

288 347

60 2 8

140 118

287 138

3L2 325

328 6

286 33s

l_54 50

11 335

L28 96

290 357

154 267

359 135

427 246

1-9 343

107 227

287 287

236 233

204 20s

197 20]-

L77 183

3L0

343 22L

0 4

46 243

68 354

L52 332

3L4 223

154 L75

68 209

L25 98

107

16 t 5

36 240

246 258

64 6 8

278 3L8

3L2 255

54 6 2

l_40 166

322 3L3

l_01_ 148

37 1

346 354

10 248

L5t" 350

t25 70

350 9

234 99

293 160

227 280

90 355

24L 259

l_1_5 1s

3s0 232

2t7 118

193 l_09

189 9 5

4 330

250 33

7 328

0 1_45

0 23L

L24 35

0 301

L92 L07

0 246

43 7 4

t64 105

1 t 6

0 235

0 263

622

2 298

0 125

068

0 184

0 L85

0 244

I 304

9 308

1_80 166

0 198

10 229

4 3L6

0 1_59

0 347

247 t1L

0 2L9

L93 L95

0 205

030

L22 1,57

118 1_55

107 136

32s 352

269 278

323 350

101 32L

252 0

20 4 0

23L 0

L00 140

Los 4 6

5t 327

42 115

1. 354

L13 0

270 0

347 351.

296 353

252 0

51 0

L75 0

302 0

L08 0

335 349

307 349

LLz l_57

36 0

43 348

318 352

L02 0

L72 0

235 L75

298 0

L92 1_56

L94 202

286 0

r_01 101_ 2tt

93 90 21,s

86 88 196

298 293 t_5

2L3 235 348

297 301 1 0

72 L49 108

103 0 201

10 239 1_96

L7205

80 90 204

77 24 329

l_3 284 30

57 75 329

334 284 9

L62 96 t1t

240 0 336

315 297 Ll_8

2't 6 288 319

25207

5704L

L72 0 146

296 0 2L3

19s 0 294

297 305 43

284 306 358

1r_9 90 314

2L 89 2L6

326 3L0 L44

295 293 25

202 0 290

L43 0 322

L4L 11 5 248

85 0 1_80

93 89 193

94 L6L L73

244 0 305

70
Table 8.4. Methods of harmonic analysis and length of time series used.

ing occurs at low water levels. *xAnalyzed at Lamar Universi

Station Name Harmonic

Analysis

Begin End Days Datum

(feet)

Notes

0559 Round Point * LSQHA uLt95 t2t3U95 365 0.8 231 hours

missing

0613 Morgans Point LSQHA Ult94 ta3lt94 365 0.7

0625 Umbrella Point LSQHA 9nt95 5t3u96 274 o.7

0923 High Island ** LSQHA 6tu94 5t3u95 365 1.3

0931 Smith Point LSQHA 6tu95 ru30t95 183 o.7

0933 Clear Lake LSQHA |tu94 uU94 365 0.6

097r Rollover Pass ** LSQHA 6tu94 5t3Lt95 365 0.7

1013 Eagle Point LSQHA ULt94 ta3u94 365 0.6

L02l Trinity River Channel

Platform

HA29 5t2u95

6t19t95

7tr8t95

29

29

29

0.6 Average of

3 H.A.

1328 Port Bolivar LSQHA uu96 Lzt3u96 366 0.8

t4t6 Galveston Bay Ent.,

South Jetty

LSQHA 2tu96 7t3U96 182 t.2

1450 Galveston,

Pier 2l

LSQHA LtLt94 t2t3u94 365 0.8

1481 Tiki Island HA29 8tr5t95

9tr2t95

rOtt0t95

29

29

29

o.7 Average of

3 H.A.

1510 Galveston, Pleasure

Pier

LSQHA uLt94 rzt3U94 365 1,.2

1516 Offatts Bayou HA29 9t22tg5

t0t20t95

29

29

0.7 Average of

2H.4.

t624 Galveston GPS Buov HA29 7tr3t95 29 1.3

1801 Alligator Point * LSQHA Uu95 tzt3U95 365 0.5 71 hours

missing

r904 Galveston Offshore LSQHA l,ll196 8t3u96 2M 1.2

2132 Christmas Bay LSQHA uu94 tu3u94 365 0.5

7 I
72
APPENDIX C. GALVESTON BAY NUMERICAL CIRCULATION MODEL

Model Formulation

The NOS numerical model for Galveston Bay is an adaptation of the Princeton three-dimensional

numerical circulation model (Blumberg and Mellor, 1987) [Note: references cited here appear at the

end of this Appendixl. The model is capable of simulating water surface elevation fluctuations in

Galveston.Bay at small time scales (minutes) for long time periods (up to 3 months). To represent

accurately the significant horizontal and vertical salinity and temperature gradients that were observed

by NOS in Galveston Bay during the water density measurement component of the hydrosurve5l, and

to simulate density effects on water levels within and outside the navigation channels, the model

includes:

three-dimensional and time-dependent velocities, salinities, and temperatures;

a free-surface;

non-linear horizontal advection ;

horizontal and vertical density gradients; and

variable grid spacing to resolve major navigation channels.

The model solves the equations of fluid motion (momentumbalance, mass conservation, equation of

state, salinity and temperature conservation, and hydrostatic balance) at all cells in the threedimensional grid. The equations in three-dimensional Cartesian space are recast in generalized

horizontal orthogonal curvilinear coordinates and further transformed using the dimensionless sigma

coordinate. The model uses a level 2-ll2 turbulence closure scheme to compute vertical diffusion

coefficients from turbulent kinetic energy and a mixing length. Details of the derivation are given in

Blumberg and Mellor (1987), Blumberg and Herring (1987), and Mellor (1993).

The major focus of the model application in Galveston Bay in this study is on the accurate

representation of the water surface elevation fluctuations due to astronomical and meteorological

forcing. Since meteorological forcing are also considered, it is hoped that the modeling effort might

also be used to provide nowcast and forecast of curren{s within the Houston Ship and Galveston

Entrance Channels based on the Galveston Bay Physical Oceanographic real-Time System (PORTS)

(NOS, 1995). A further potential use of the model would be to provide nowcast and forecast of

salinity and temperature fields throughout the Bay to monitor the effects of freshwater inflows in

conjunction with oysterpopulation management. Thus the model developedhere represents both water

level fluctuations and circulation of shelf, Buy, and navigation channel waters.

The Model Grid

The Galveston Bay model runs on an orthogonal curvilinear grid closely fitted to the Bay's lateral

boundaries (Figure G.1).A 181 x 101 = 18,281-cell, orthogonal curvilinear mesh was formed using

an elliptic equation gnd generation technique developed by Wilken (1988) based on the conformal

mapping algorithm of Ives andZacharias (1987). The actual grid generation code was obtained from

Professor George L. Mellor, Princeton University.

o

o

o

o

o

73
-9r 30 -9{ 20 -9t l0

a

lo

%

29

30

a

n

q,'(

7

29

l0

*r,

t

29

0

o

o

(

(

c) c,

o o

- - ( -

€ t\)

t

28

50

28

50 -95 20 -95 l0 -95 0 -9{ 50 -9{ {O -9r 30 -9{ 20 -9r to

Figure C'1. Curvilinear grid used in the three-dimensional hydrodynamic model study. Cells 1

through 5 are the approximate locations in the grid where the boundary water level signals are

supplied. Water levels at intervening cells along the ocean boundary are computed by interpolation.

Grid cells are closely spaced in regions where higher resolution is needed, such as near the major

navigation channels, and through the Galveston Bay entrance. The gfid configuration includes the two

Entrance jetties to Galveston and the Texas City dike. Cell spacing varies from 254 meters tci'2428

meters and from 580 meters to 3502 meters in the x and y directions, respectively. Each cell has a

depth value obtained from bathymetric data for Galveston Bay available from NOAA's National

Geophysical Data Center in gridded (l5-second interval) format.

A substantial number of cells cover the Texas shelf region east of the Bay entrance. This placement

of the boundaries allows forinternal dynamics to dominate the simulation of currents and the density

field in the bathymetrically complex Galveston Entrance region, rather than increase uncertainty by

specifying the boundary condition in an oversimplified manner and risk imposing a dynamic

74
inconsistency. The grid has additional connections to the shelf through San Luis Pass at the entrance

to West Bay and through Rollover Pass in East Bay.

The grid covers most of the water area of Galveston Bay, but cannot resolve all the small features along

the shore such as the Gulf Intracoastal Waterway. The grid is detailed enough to represent the following

features explicitly: Trinity River, San Jacinto River, Buffalo Bayou, and the Houston Ship Channel.

In the vertical, there are six sigma levels of varying thickness: o - (0.0, -.!667 

, 

-.4L67,-.5833, -.7643,

-.9L67 ,-1.00).This is considered sufficient to resolve the density stratification observed. Considering

cell lengths and depths, the model is run with an external-mode time step of 10 s and an internal mode

time step of 60 s. A 30-day simulation requires approximately 15 hours on an SGI Challenge L

computer using four CPUs at full utilization with level two (O2) optimization.

Ocean Boundary Conditions

The numerical model simulation requires driving forces (water levels, river discharges, winds) that

are applied at the open boundaries on the grid. Each open boundary cell along the Texas shelf requires

a water level value and salinity and temperature values at all vertical levels at each model time step.

The river boundaries require discharge, salinity, and temperature values. The wind is applied at the

surface of all cells. At the closed boundaries there is zero momentum, salt transfer, and heat transfer.

Water level signals at selected gnd cells along the ocean boundary are computed at each step, and the

water levels at the remaining cells are computed by linear interpolation based on distance. The signals

at each of the cells consisted of (1) a tidal component, (2) a time-varying, non-tidal component, and

(3) a constant offset. Tidal constituent amplitudes and phases were generated using values at the nearby

coastal stations and applylng an amplitude factor and a phase lag. The values for each constituent are

given in Table 3.2 (pages 26 and 27) in Schmalz (1996). The time-varying non-tidal component was

taken to be equal to the non-tidal component measured at Galveston Pleasure Pier. The offsets were

generated by testing and analysis of the resulting signals at shore stations. Initially there were five

selected cells (see Figure G.1), but a special adjustment was made at the southern boundary. An

additional cell (Celt 1A) was added there; the signal at Cell lA is identical to that at Cell 1. Further

discussion of the open ocean and river boundary conditions appears in Sections 3 and 4 in Schmalz

(Lee6).

Model Runs for Tidal Constituents

The NOS Galveston Bay model was run in two scenarios to simulate water levels for tidal constituent

analysis. The first (Tide Only) scenario (May 1995) was focused on calibrating the model for the

astronomical tide and so involved no winds. Climatological river inflows, salinities, and temperatures

were included. The second (Tide-plus-Wind) scenario (June 1995) was focused on the total water

level response and so involved the astronomical tide and included the winds. The results of the second

scenario were used to determine the tidal constituent amplitudes and epochs.

75
For the Tide-plus-Wind scenario, the model was used to replicate the conditions encountered during

the performance of the DGPS hydrosurvey during June 1995. Meteorological conditions were simulated

as completely as possible. Seven meteorological gauge stations were used to develop surface wind and

pressure fields for every 3 hours over the 30-day period. Salinity and temperature initial and boundary

conditions were derived from measurements reported by Temple et al. (1977) and Orlando et al.

(1993), which were used to define a climatology. In addition, sea surface temperature was specified

in lieu of heat flux and was also based on this climatology. Daily average USGS observed flow rates

were specified for inflows of the Trinity River, San Jacinto River, and Buffalo Bayou. Despite the

climatological forcings for salinity and temperatuie and the use of a one day spin-up, the model

reproduced the salinity fields to order 2-3 psu and the temperature fields to within 1-2 'C.

For each 30-day run, the model was initialized and run with a l-day spin-up period. While it is

possible to employ a longer simulation period to account for model spin-up of the density fields, the

l-day spin-up period used in this study appeared adequate due to the nearly dynamically consistent

initial density fields. Hourly time series of water surface elevations at all 8672 water cells were saved

for subsequent analysis. The standard NOS 29-day harmonic analysis program @ennis and Long , lg7 I)

was the used to determine amplitudes and phases for 24 tidal constituents.

The results of the Tide-plus-Wind run (Table C.1) show that the model demonstrated considerable skill

in reproducing the tidal constituents throughout the Galveston Bay. Note that in comparing the model

harmonic constants to the accepted constants, at most stations the accepted constants are based on a full

year of observations enabling a least squares analysis (Schureman, 1958). However, as noted in

Schmalz (1996), 29-day analyses were performed at Smith Point, Round Point, Galveston GPS Buoy,

and at the Trinity River Platform due to length of observed series.

The agreement between the Tide Only results, which included river inflow influences, and the

observations was order 2-3 cm rms. These rms values were determined from the differences between

observed and modeled amplitude and phases for each of the 24 constituents after Hess (1994). A

weighted gain (model vs. observation) and phase (model minus observation) are also reported in Table

C.l based on the magnitude of the observed constituent amplitudes; o.g., see Hess and Bosley (1992).

The results for the Tide-plus-Wind run are also given in Table C.1. In comparing, these results with

those obtained from the May 1995 astronomical calibration, one notes that at most station differences

in constituent amplitudes are order 1 cm and phases are within 10 degrees. This range of differences

is consistent with those obtained by comparing different 29-day harmonic analyses of observations

themselves.

Model Runs for Ellipsoid Reference

Simulated water surface elevations with respect to the GPS ellipsoid and tidal epoch MIIW at 470

Iaunch hydrosurvey track locations were generated for June 1995 for direct comparison with RTK GPS

measurements. To obtain the ellipsoidally-referenced water levbl, the modeled water level (with

respect to the model mean level of zero) was added to a spatially-interpolated value of the

ellipsoidally-referenced MSL. Spatial interpolation was based on values at 10 shore stations and an

inverse-distance weighting for each.

76
Table C.1. Tidal constituent amplitudes, A (cm); and local epochs, K (degrees). Values are shown for

the Tide-Only (May 1995) run, NOS accepted values, the error, and values for the Tide Plus Wind run.

The Gain, Phase, and Estimated RMS Difference are fot th" Tid"-Only R*

GALVESTON PLEASURE PIER 677L5L0

NOS Accepted tide Only tide a Wind tide Only Tide A Wind

Values Values Values Error Error

No. Name A K A K A K A K A K

1 M(2) r-3.0 1-00.9 L2.7 91.6 1-1-.9 93.3 -0.7 :9.3 -L.l- -7.6

2 s (2 ) 3 .0 93 .0 3 .3 89.0 3 .8 83 .7 0.3 -4.0 0.8 -9.3

3 N(2) 3.0 86.s 3.3 78.7 3.0 ?0.s 0.L -7.8 0.0 -15-9

4 K(1) 1-7.0 298.s 14.3 292.4 L3.2 280.4 -2.s -6.1 -3.8 -L8.1

s M(4) 1-0 21-3.0 0.4 203.9 0.s :l.42-8 -0.2 -9.1 -0.s -70.2

6 0(1) 15.0 297.0 L4.3 29s.3 L3.4 292.3 -L.l" -L.7 -1-.6 -4.8

7 M(6) 0.0 72-0 A-2 6L.4 0.? 28L.3 0.1 -10.6 0.7 -150.7

8 S (4) 0.0 10.4 0.1 325 .2 0 .3 2t0 . s 0.0 -45.2 0.3 -L59.9

9 NU(2) 1.0 80-2 0.6 80.4 0.6 73.6 0.0 0.2 -0.4 -6.7

10 s(6) 0.0 77.3 0-1 34.L 0.3 1s8.s 0.0 -43.2 0.3 8L.2

11 MU(2) 0.0 13.4 0.0 0.0 0.4 47.7 -0.5 -r3.4 0.4 34.3

t2 2N(2) 1.0 s6.6 0.4 6s.B 0.6 268.s -0.4 9.2 -0.4 -L48.2

r-3 oo(1) 1.0 333.7 0.6 289.6 0.1 88.8 -0.L -44.1, -0.9 L15.1

14 LtdD(2) 0.0 16L.8 0.1 90.4 0.9 286.3 0.0 -7L.4 0.9 L24.5

1s M(1) 1.0 31,4.7 1-.0 293.8 1.r- 274.s -0.3 -20.9 0.1- -40.3

76 ,r(1) 1.0 275.6 1.1 29L.0 0.5 297.4 0.L 15.4 -0.5 2L.8

L7 RHO(1) 1.0 297.2 0.5 296.5 2.6 298.2 -0.3 -0.7 1.6 l-.0

r.8 Q(1) 3.0 284.4 2.8 296.6 0.2 84.0 -0.6 t2.2 -2.8 L59.6

L9 T2 0.0 118.7 0 .2 89. L 0.0 83 .3 -0 .2 -29 .5 0.0 -35.4

20 2g$) 0.0 326.4 0.4 298.0 0.4 304.L 0.3 -28.4 0.4 -22.3

2L p(1) s.0 29s.4 4.7 292.6 4.4 28L.3 -0.2 -2.8 -0.6 -14.L

22 L(21 0 . 0 !4r.4 0.5 72 .2 0 .4 54.0 0. 0 -69 .2 0.4 -77 - 4

23 K (2 ) 0.0 92 .9 0.9 88. 8 1.0 82 .9 0.4 -4.L l-.0 -10. L

24 M(8) 0.0 93.7 0.1- 344.9 1-.0 3O2.6 0.0 -108.8 1-.0 -151.0

cArN (-): 0.91- PIIASE (HR): -0.25 EST. RMs (M): 0.03

GPS BUOY 877L02t

NOS Accepted ride Only tide & Wind tide Only

Values Values Values Error

No.Name A K A K A K A K

M(2 )

s(2)

N(2)

K(1)

M (4)

o(1)

M(6)

s (4)

9 NU(2)

10 s(6)

1_L MU(2 )

t2 2N(2)

L3 oo(i)

3.4 r,uo (2 )

1s M(1)

16 .l(1)

t7 RHO(1)

L8 Q(1)

19 T2

20 2Q (11

2L P(1)

22 L (21

23 K{2')

24 M(8)

GAIN (-)

L4.0 10L.5

4.0 89 . 9

4.0 88. s

1_8.0 292.5

0.0 234 - 9

t-? .0 301-.2

0.0 148.6

0.0 239 . L

1.0 90 . 2

0.0 24.2

0.0 283 . 9

1.0 75 . 3

L.0 283 . 9

0.0 96 - 2

1.0 296 . 8

1.0 288.3

1.0 30s.0

3.0 305.5

0.0 90 . 3

0.0 309.8

6.0 293 .1-

0.0 t14.6

1_.0 89.0

0.0 t6L-4

: 0.86

L2.9 9L.9

3.3 85.0

3.4 74.5

L4.4 296.0

0 .4 2]-3 .7

14.8 297.8

0 .2 58.4

0.1_ 345.2

0.7 76.8

0.l_ 29 . 2

0.0 0.0

0.s 57.0

0.6 294.3

0.1 88.7

1.0 296 . 9

L.2 295 . 2

0.6 298.6

2.9 298.7

0.2 85.2

o.4 299.6

4.8 296 . 2

0.5 67 . 9

0.9 84.4

0.1 352.5

PIIASE (nx-*)

tL.7 94.5

3.2 73 - 7

2.9 72.8

L3.4 28s.9

0.4 L78.5

L3.8 297 . 9

0.6 283.8

0.4 L99 . 2

0.6 75 - 7

o .2 224.8

0.4 51. r _

0.6 27 4.0

0. L 84.8

L.0 29L.9

r.. L 280.0

0. s 303 . 0

2.7 303.8

4.2 74-5

0.0 72.8

0.4' 309.7

4.5 286.8

0.4 66.3

0.9 72-0

0.8 283.0

: -0 .11-

-0.6 -9 - 6

-0.4 -4-9

-o .7 -1_4.0

-3.3 3.s

-0.1 -2L - 2

-2-5 -3.4

0.0 -90 . 2

-o .2 106.1

-0.t -13.4

-0.1- 5.0

-0.3 76.L

-0. L -r-8.3

-0. L L0.4

0.0 -7 . 5

-0.2 0.1

-o .2 6.9

-0. L -6.4

-0.5 -6.8

0.0 -5.2

-0.1 -LA . 2

-1.1 3 . 0

0.1 -46 . 7

-0 

. L -4.6

-0.1 -158.9

EST. RMS (M) :

Tide & Wind

Error

A K

-2 .3 -7 . 0

-0.8 -L6.2

-1-. L -L5.7

-4.6 -6.6

0 .4 -56 . 4

-3.2 -3.4

0.6 L35.3

0.4 -39.9

-0.4 -L4.5

o .2 -]-59 .4

0.4 L27 . 2

-0.4 -16L.4

-0.9 161.0

1_.0 -t64 - 3

0.1_ -1_6. 8

-0.5 14.7

t.7 -1.2

-2.8 ]-29 - O

0.0 -L7 . 5

0"4 0.0

-l_.5 -6.3

0.4 -48.4

-0.1 -17 . 0

0.8 L2L.6

0.04

1

2

3

4

5

6

7

I

77
Table C.L. Continued.

HIGH TSLAIVD 877 0923

NOS Accepted Tide Only tide s Wind tide Only Tide & Wind

Values Values Values Error Error

No. Name A K A K A K A K A K

1 Nr(21 L6.0 98.6 L4.9 97 -4 L3.1 100.0 -1.1 -L.2 -2.9 L.4

2 S(21 4.0 B9.l_ 4.2 82-0 3.2 77.0 -0.2 -7.L -0.8 -12.1

3 N(2) 4.0 78.s 3.8 74.6 3.s 77.9 0.0 -3.9 -0.s -0.6

4 K(1) L7.O 295.9 15.5 300.3 L4.7 291,.6 -1_.6 3.5 -2.3 -5.3

5 M(4) 1.0 23L.7 0.6 224.9 0.3 28L.7 0 .0 -6.8 -O .7 50.0

6 O(1) 16.0 295.5 1_6.0 300.5 L5.2 300.1 0.2 4.9 -0.8 4.5

7 M(6) 0.0 70,3 0.3 s7.4 0.L 158.? 0.1 -t2.9 0.1 98.4

8 S(4) 0.0 357.1- 0.2 L3.0 0.4 166.0 0.0 Ls.9 0.4 1_68.9

9 NU(2) 0.0 7s.6 0.7 77.7 0.7 80.9 0-2 2.! 0.7 5.3

10 s(6) 0.0 309.3 0.L s.1 0.3 1_s1.4 0.0 5s.8 0.3 -ts7.9

11 Mn(2) 0.0 18.0 0.0 0.0 0.s ss.8 -0.s -1_8.0 0.s 37.8

t2 2N(2) 1-.0 67.4 0.s s1.8 0.7 283.L -0.3 -L5.6 -0.3 -L44.4

1-3 00(L) 1.0 3L1".4 0.7 300.2 0.L 89.4 0.0 -1,L.2 -0.9 138.0

L4 LMD(2) 0.0 296.0 0.1 90.3 1.1" 295.8 -0.1 1s4.3 1.L -0-1

15 M(1) L.0 328.6 1.1 300.4 L-2 287.4 -0.3 -28.2 A.2 -4L.3

t6 .l(1) L.0 309.2 L.3 300.3 0.6 303.8 0.6 -8.9 -0.4 -5.4

1"7 RHO(1) 1.0 327.9 0-6 300.5 2.9 304.3 -0.1 -27.4 1.9 -23.s

18 Q(1) 3.0 28s.6 3.r. 300.s 0.2 77.9 -0.1 ]-4.9 -2.8 Ls2.3

L9 T2 0.0 L53.6 0.3 82.7 0.0 76.1 -0.2 -70.9 0.0 -77.5

20 2Q$) 0.0 t28.1 0.4 300.6 0.4 308.s 0.3 L72.5 0.4 -179-5

2L p(1) s.0 289.s 5.L 300.3 4.9 292.2 0.0 10.8 -0.L 2.7

22 L(21 1.0 1,27.0 0.s 68.1_ 0.s 7]-.4 -0.3 -58.9 -0.s -55.7

23 K(2) L.0 107.1 t.2 80.8 0.9 75.2 0.3 -26.3 -0.1 -32.O

24 M(8) 0.0 286-6 0.L 33L.2 0.3 L-7 0.1 44.6 0.3 75.1

GAIN (-): 0.96 PIIASE (HR): 0.09 EST. RMS (M): 0.02

ROLLOVER PASS 877 0971

NOS Accepted Tide Only Tide & Wind Tide Only

Values Values Values Error

A K

4.7 1"29 - 5

L.6 88.6

1-. r- 1_05 . L

8.9 32L.6

0.3 260 . 4

9 -L 341, - L

0. L l_50.5

0.l_ 80 . 2

0 .2 108.4

o -2 185.0

0.1 80.8

0 .4 302 . L

0.0 L10.5

o.7 331_.3

o -7 3l_1_.9

0.4 349 . 5

1_.8 350.8

0.1, 90 . 3

0.0 87 . 0

o .2 0.5

2.9 323 . L

o .2 98.6

0 .4 85.3

0.4 295 . 9

-1. 9 8

A K

-0.8 -79.3

-0.3 -78. s

-0.3 -79 . L

-2.7 -20.6

-0,3 -7 4.5

-1.3 -23 . 2

0. r- 40.8

0.1- -94.9

0.0 -sL.7

0.1 -61_.9

-0.3 -t25 . L

0 .1 6L.9

-0.8 -28 - 2

-0.2 8s.9

-0.5 -84.7

0.7 67 . 2

0 .0 -62.3

0 .0 -1-1-, r_

-0.1_ 1-09. 1 _

-0.4 -Ls3 . 3

-0 .7 -8.3

-0 .2 -t34.9

-0.5 -1,22.9

0.0 -5L.5

EST. RMS {M) :

Tide & Wind

Error

A K

-L.3 -7 4.5

-0.4 -L08.7

0.1 -72.2

-3 .1 -4t.4

-o .7 -83 . 1

-L.9 -L9 . 2

0.1 r_04.1

0.1 -81_.6

0.2 -45.2

0 .2 LL7 . 0

0 . L -44.3

0.4 -68.0

-l_.0 94.7

o .7 -64.7

-0.3 -Lt2 . 5

0.4 71_.8

1.8 -46.4

-1-.9 1_04.6

0.0 77.0

-0. 8 -L24.8

-1. L -27 . 2

0 -2 -L28.1

-0.6 -1ss.9

0.4 -L79.6

0 .07

M

s

N

K

N

1_

2

3

4

5

6

7

I

9

1_0

1_1

t2

1 3

L 4

L 5

1 6

T 7

l-B

1 9

2 0

21-

2 2

2 3

2 4

o. Name

2 l

2 )

2 l

1 )

M(4)

o(1)

M(6)

s(4)

NU(2)

s(6)

Mu(2)

2N(2)

oo(1)

LMD(2)

M( 1 )

r(1)

RHO(1)

Q(1)

t2

2Q(1)

P(1)

L(21

K(2)

M(8)

GATN (-)

AKAK

6. 0 204.0 4.9 L24.7

2.0 t97 .3 L.3 1_18. I

1. 0 t77 .4 1_. 1_ 98 . 3

L2.0 3 .0 9 .L 342 . 4

1.0 343. s 0.3 269 . O

11-.0 0.3 9 .6 33?.1

0.0 46-4 0.2 87.2

0.0 L51.8 0 .2 66 . 9

0.0 1_s3 . 6 0 .2 L0t . 9

0.0 68.0 0.1_ 6 . t

0. 0 L25 .t 0.0 0. 0

0.0 L0.1 0.2 72-0

1.0 L5.1 0.4 347.6

0.0 36.1 0.0 122.0

1.0 64.4 0 .7 339 . 7

0.0 277 .7 0.8 344.9

0.0 37.2 0.4 334.9

2 .O 345 .7 1 .9 334.6

0.0 9.9 0-1 L19.0

L.0 t25-3 0.3 332.0

4,0.350.3 3.0 342.0

0.0 226.7 0 .2 91. 8

1. 0 24L.2 0 .4 118 . 3

0.0 r_15.5 0.1_ 64.0

: 0.81- PHASE (FIR) :

78
Table C.L. Continued.

CHRISTMAS BAY

No. Name A .K A K

1 M(2) 3.0 L92.6 4-2 2sr-s

2 S (2 ) l-.0 207.9 0. 5 89.9

3 N(2 ) 1-.0 t82.0 1. s 23s . 5

4 K(1) 7.0 1.3 8.0 31_.6

s M(4) 0.0 247.9 0.4 330.8

6 O(1) 7-O 3s8.0 7.2 29-0

7 M(6) 0.0 25t.2 0.0 275.s

I s (4) 0.0 L0s.0 0.0 93 . 0

9 NU(2) 0.0 L73.0 0.3 237.6

10 s(6) 0.0 L9.2 0.0 32.7

1_L mr(2) 0.0 28.9 0.0 0.0

L2 2N(2) 0.0 237.8 0.2 2L9.s

L3 00 (1) 0.0 1-2.6 0.3 34.3

L4 LV'D(2 ) 0.0 2r5 - 9 0.0 t76.5

15 M(1) 1.0 70.0 0. s 30 - 3

L6 .r(1) 0.0 9.7 0.6 33.0

L7 RHO(1) 0.0 334.9 0.3 27.9

1_8 Q(1) 1.0 342.3 1.4 27-7

L9 T2 0.0 160.1 0.0 96 - 4

20 zQ(t) 0.0 60.s o-2 26-4

2L P(1) 2.O 3.3 2.6 31.4

22 L(21 0.0 208 -7 0 .2 228 - 9

23 K(2) L.0 1-61-.9 0.L 75.9

24 l,r(8) 0.0 263.3 0.0 2L6.6

GAIN (-): L.O1 PHASE (HR):

6772L32

NOS Accepted Tide Only Tide & Wind Tide Only

Values Values Values Error

A K

3 .2 248 . 4

1_.1 3s0 . I

1.2 229 . 8

7 -6 11..9

0. L 270.9

7.5 35-0

0. r_ 53 . 2

0.3 37 . 0

0.2 232.3

0.L 42.7

0 .2 2LL.3

0.3 348.8

0.0 295 . 9

0.s 23-4

0.6 0 . 4

0.3 44 - 9

L.5 46-4

0. r- 346 . 7

0.0 3s4.9

0.2 57 . 9

2.5 r.3.6

o -2 223.3

0.3 359.L

0.1 27 . 7

L.63

A K

L.0 58.9

-0.2 -1-L2 - O

0.9 53.5

0.5 30 . 4

0.2 82.9

-0.1 31.0

0.0 24 - 3

0.0 -t2-o

0.r_ 54-6

0.0 13.5

-0.2 -28.9

-0. L -18.3

-o .2 2r.7

-0.1 -39.4

-0.1 -39 . 7

0.4 23 - 3

0.0 53 . 0

0.1 45.4

-0,1 -63 . 7

0.0 -34.1"

0.4 28.r

-0.l_ 20 - 2

-0. s -85.0

0.0 -46 . 7

EST. RMS (M) :

A K

-o .7 -9 . 3

0.0 -9 . 7

0. L -r2.9

-2.9 0.6

-0. L -20 . 5

-L.3 2.3

0.1- -1_6.1

0.0 6.8

0.1 -3 . 2

0. L -33.6

-0 .4 -sL.3

-0.3 33.9

-0. s -35. l -

0.0 -2.L

0.0 -2L.9

-0.l_ 29 . 8

-0.3 -10.1

-0.3 L8.0

-0 -2 -3.7

0.1 -78.3

-0.5 6 . 9

o .2 -1_46.8

0.2 -84.B

0.1 -97.6

EST. RMS (M) :

Tide & Wind

Error

A K

o -2 55.8

0.1_ 1-48.9

0.2 47 . 8

0.5 10.6

0. r. 23 . 0

0. s 36.9

0 - 1_ L62.O

0.3 -68.0

o -2 59.3

0.1 - 23 . 5

0.2 -L77 . 6

0.3 1_10.9

0.0 -76.7

0. s 167.5

-0.4 -69 . 6

0.3 35.2

L.5 7l..5

-0 .9 4.4

0.0 -L65. L

0.2 -2.6

0.5 L0.3

0.2 L4.s

-o -7 -L62 . 8

0. L L24-4

0 .05

Tide & Wind

Error

A K

-2 .0 -6.5

-o .2 -t5.2

-0.1 5 . 7

-3 .7 -15.9

0 .4 -94.9

-1.8 4. 5

0.3 -L24.5

0 .1 s9.3

0.4 L3.2

0.3 L25 - B

0 .3 58.8

-0.6 -1_L1.0

-1.0 108.6

o .7 -154.9

-0.2 -47 . L

-0.6 39.0

L.0 1-.3

-1.9 156.4

0.0 -9 - 9

0.3 -s7.6

-0.9 -8.1_

0.3 -t28.3

0. s -91.0

0 .2 LAL.9

0.03

GALVESTON PIER 21

No.NAme A K A K A K

1 M(2) 8.0 L22.4 7.7 r-13.L 6.0 11s.9

2 S (2 ) 2 -O LL1 .7 2 .3 1_08.0 L. I L02.5

3 N(2) 2.0 L07.3 2.2 94.4 L.9 r.13.0

4 K(1) L3.0 324-9 r-0.0 32s-4 9.3 309.0

s M(4) 0.0 269.0 0.3 248.s O.4 ]-74.L

6 O ( 1) L2 .O 322 - 6 1-0 .7 324 .9 1,0 .2 327 - t

7 M(6) 0.0 101.5 0.2 85.4 0.3 337.0

8 S (4) 0.0 20 .0 0.1_ 26.8 0.1- 79 . 3

9 NU(2) 0.0 1-00.1 0.4 96-9 0.4 1_13.4

1-0 s(6) 0.0 L05.2 0.2 7L.6 0.3 23L.0

1-1_ MU(2) 0.0 s1_.3 0.0 0-0 0.3 1_L0.1

L2 2N(2) L.0 41,.8 0.3 75.7 0.4 290.8

L3 0o0(1) 1.0 L.1 0.s 326.0 0.0 109.7

L4 Lr4D (2 ) 0.0 rL2 .9 0. I 1_10 - 8 0 -7 318.0

r_5 u(1) 1_.0 347.1 0.8 325.2 0.I 300-0

l-6 .r(1) L.0 295.9 0.8 325.7 O .4 334.9

L7 RHO(1) L.0 334.8 0.4 324.7 2.0 336.1

1,8 Q(1) 2.0 306,7 2.1 324.7 0.1- 1_03.L

19 T2 0.0 t-1_1. I 0.1 108.2 0.0 L02.0

20 2Q(t) 0.0 42 .7 0.3 324.4 0.3 345.1

2L p(1) 4.0 318.s 3.3 325.4 3.1_ 310.3

22 L(21 0 ,0 234.7 0.3 87 .9 0 .3 l_06 . 4

23 K(21 0.0 L92.4 0.5 L07 -6 0.5 L01.4

24 M(8) 0.0 L93.9 0.r- 96.3 0.2 335.8

GAIN (-): 0.87 PHASE (lIR): -0.04

677l.450

NOS Accepted Tide Only Tide & Wind Tide Only

Values Values Values Error

79
Table C.L. Continued.

PORT BOLIVAR 677L328

NOS Accepted Tide Only tide & Wind Tide Only Tide & Wind

Values Values Values Error Error

NO.Name A K A K A K A K A K

l_ M(2) 7.0 1r-9.5 6.6 1_1-0.6 s.6 LL3-9 -0.1 -8.9 -t.4 -s.6

2 S(2) 1.0 L52.0 2.s 100.3 1_.9 75.s L.s -5L.7 0.9 -76.5

3 N(2) 2-0 93.5 L.8 9s.9 L.6 LL0.2 -0.1_ 2.4 -0.4 16.8

4 K(1) 1L.0 333.8 1_0.0 329.O 8.9 313.2 -1_.0 -4.8 -2.L -20.6

5 u(4) 0.0 89.s 0.L ]-60.7 0.4 148.8 -0.1 7l..2 0.4 s9.3

6 0(1) L2.O 335.2 L0.7 328.5 9.7 331.s -L.0 -6.7 -2.3 -3.8

7 M(6) 0.0 13s.9 0.1 93.8 0.3 279-8 -0.1 -42.r 0.3 L43.9

8 S(4) 0.0 L02.7 0.1 309.1- 0.1- 42.9 0.0 -1s3-5 0.1_ -59.8

9 NU(2) L.0 66.9 0.3 97.8 0.3 1L0.? -0.2 30-9 -0.7 43.8

10 s(6) 0.0 ]-20.3 0.1 s6.9 0.3 222.0 0.1 -63.4 0-3 L0L.?

1_1 MU(2) 0.0 51-.9 0.0 0.0 0-2 106.5 -0.2 -sL.9 0.2 54.6

L2 2N(2) 0.0 22.8 0.2 81_.1_ 0.4 294.9 -0.3 58.3 0.4 -88.0

13.Oo(1) '2.0 9.6 0.5 329.6 0.0 96.1_ -1.0 -40.0 -2.0 86.s

L4 LMD(2) L.0 270.6 0.0 L05.8 0.7 322.3 -0.6 -i-64.8 -0.3 sL.7

L5 M(L) 1.0 34L.8 0.8 328.7 0.8 304.1 -0.3 -l_3 

. L -O.2 -37 - 7

1-6 ,J(1) 0.0 349.1 0.8 329.3 0.4 339.3 0.3 -1_9.8 0.4 -9.8

t7 RHO(I) L.0 31,2.4 0.4 328.2 t.9 340.6 -0-7 L5.8 0.9 28.2

18 Q(1) 3.0 317.6 2.'t 328.2 0.1_ 77.0 -0.s 10.5 -2.9 LL9-4

t9 T2 L.0 93.6 0.1_ L00.7 0.0 74.0 -0.5 7.2 -L.0 -L9.6

20 2Q{.t) 0.0 1L5.8 0.3 327.9 0.3 349.6 -0.L -L4'7.9 0.3 -L26.I

2t p(1) 4.0 356.0 3,3 329.0 3.0 3L4.5 -0.4 -27.0 -1".0 -41_.5

22 L(21 0.0 220.7 0.3 89.3 0.2 L03.? -0.1--131.4 0.2 -L1_?.0

23 K(2) 2.0 1-76.2 A.7 99.5 0.s 72.4 -L-6 -76.7 -L.5 -l-03.8

24 M(8) 0.0 2]-3.6 0.0 9t-.0 0.3 32L.8 0.0 -L22.6 0.3 tO9-2

GAIN (-): 0.86 PIIASE (HR): -0.72 EsT. RMs (M) : 0.03

EAGLE POIMf 677L0L3

NOS Accepted Tide Only Tide & Wind Tide Only

Values Values Values Error

No.Name A K A K A K A K

L M(2) 3.0 204.6 3.8 235.2 3.7 233.3

0.4 107.r_

1.1 L87.3

8.3 4. 8

0 .2 264.1

9.5 r.8. r -

0. l_ 68.7

0,1 6L. 0

0.2 r_93 . 5

0.2 49 . 9

o .2 1_4L.3

0.4 35L.5

0.0 L7 4.8

o .7 LL.5

0.8 358.2

0.4 23 . 9

L.9 24.8

0.0 L]-2.2

0-0 L02.L

0.3 3L.4

2.7 5.8

o-2 1-80-8

0.1 96 . 9

0.0 330.9

0.32

0.6 30.5

0.0 -38.4

0.4 34.6

-0.6 8.8

-0.1 153 . 6

-0.2 8.3

0.0 37 . 3

0.0 81- 3

0. L 45.3

0.0 -t64 - 9

-0.2 -97 . 6

-0. L -166.9

-0. 6 l_0.3

-0.1 -39.0

-0.3 -s2 . 3

0.4 64.3

-0.2 7.4

-0.1 l-4.0

0.0 -82 . 8

-0.1 -65.0

0.3 9 . 6

-0. 1_ -68 . 8

-0.2 -103 .1_

0.0 -l_38.7

EST. RMS (M) :

Tide & Wind

Error

A K

0.7 28.7

-0.5 -93.5

0.1 4.0

-2.7 -5 - 2

0.2 43.2

-0.5 14.5

0.1 -t74.4

0. L 88.6

0 .2 L8.5

o .2 -r_59.0

0.2 43.7

0.4 -15.9

-1.0 t_59 . 4

o -7 L3]-.2

-0.3 -69.4

0.4 66.0

0.9 23 . 3

-2.0 1-L7.8

0.0 -LAs . 9

0.3 -38.6

-0 .3 -2 . 9

0 .2 -99 . 4

-0.9 -L62 . 5

0.0 -44.4

0.03

2 S (2 ) 1_.0 200.5 1.0 ]-62 . 2

3 N(2) 1.0 r_83.3 ]--2 2L7.9

4 K(1) 11.0 1_0.r. 10.3 l_8.8

5 M(4) 0.0 220 .9 0.1 14.5

6 0(1) 1_0.0 3.6 L0.0 1l_.9

7 M(6) 0.0 243.L 0.1 280.4

8 S(4) 0.0 332.4 0.0 53.7

9 NU(2) 0.0 ]-74.9 0.2 220.2

10 s(6) 0.0 208.9 0.0 44.0

11 MU(2) 0.0 97.6 0.0 0.0

L2 2N(2) 0.0 7.4 0.2 200.5

13 00(1) 1".0 1s.4 0.4 25.7

L4 LMD(2) 0.0 24O.3 0.0 20L.3

15 M(1) 1.0 67.6 0.7 1_5.3

t6 J(1) 0.0 3L7 .9 0.8 22 - 2

L7 RHO(1) 1_.0 l_.5 0.4 8.9

L8 Q(1) 2.0 354.4 1.9 8.4

t9 T2 0.0 247 .9 0.1_ t65 . 2

20 2Q$) 0.0 70.0 0.3 s.0

2t P(1) 3.0 8.8 3.4 18.3

22 L(21 0.0 280.1 0 .2 2L1,.3

23 K(2) 1.0 259.4 0.3 156.3

24 M(8) 0.0 1s.3 0.0 236 . 6

GAIN (-): 0.97 PHASE (HR):

80
Table C.L. Continued.

TRINITY RIVER CHANNET PLATFORM 877LO2L

NOS Accepted Tide Only tide & Wind Tide Only

Values Values Values Error

No. Name A

1 M(2) 4.0

2 s(2) 1.0

3 N(2 ) L.0

4 K(1) 1-0.0

5 M(4) 0.0

5 0 (1) r2.0

7 M(6) 0.0

I S (4) 0.0

9 NU(2) 0.0

10 s(6) 0.0

L1_ Mu(2) 0-0

L2 2N(2 ) 0.0

13 00(1) 0.0

L4 Lt4D (2 ) 0.0

L5 M(1) 1.0

16 .t(1) l_.0

L7 RHO(I) 0.0

L8 Q(1) 2.0

L9 T2 0.0

20 2Qlt) 0-0

2t P(1) 3.0

22 L(21 0.0

23 K(2) 0.0

24 M(8) 0.0

GAIN (-):

SMTTH POINT

2L6.6 3.4 2L6.8

2L4.2 1. L 1_49,0

192.4 1.0 200.7

4.3 10 .0 L2 . 4

257 .5 0.1 234.8

4-8 9-9 s.9

282 .8 0.1_ 275 . 3

1,87 .5 0.l- 106.4

195.6 0 .2 202.9

237 -4 0.0 s3.3

29 -3 0.0 0.0

1_68. r_ 0. r_ r.84.6

3.8 0.4 18.9

2L5.5 0.0 t_85.3

4-6 0.7 9.2

4.0 0. 8 t5 . 7

5.L 0.4 3.2

5.1 1_.9 2.7

2t4.3 0. L LsL.7

5.4 0.3 359.s

4.3 3 .3 12 . 0

240 -7 0. L t94.2

2L4.0 0.3 143 . 5

0.5 0.0 256 . 9

0.92 PTTASE (lrR) :

No,Name A K A K

L M(2) 4.0 L88.7 3.7 L97 . 7

2 S (2 ) L.0 1-63 .5 1_.3 135.5

3 N(2) 1.0 l.62.9 r-.1 1-82.s

4 K(1) 10.0 353.9 10.1 5.7

s M(4) 0.0 213-2 0.3 250.L

5 0(1) t2-O 3s9.4 10.0 359.s

7 M(6) 0.0 29A.3 0.1_ 282.5

8 S (4) 0.0 286 .t 0.1 r_5s.1-

9 NU(2) 0.0 166.3 0.2 r_84.6

L0 s (6) 0.0 73 .4 0.0 32.6

L1 MU(2) 0.0 24.4 0.0 0.0

L2 2N(2) 0.0 137.0 0. L L67 . 4

13 OO(1) L. o 348.3 0.4 11.9

14 LMD (2 ) 0 .0 L77 .L 0 .0 r-68. 8

15 M(1) 1.0 356.6 A.7 2.6

15 ,J(1) L.0 35L.1- 0.8 8.8

t7 RHO(1) 0.0 1_.9 0.4 356.9

1-8 Q(1) 2.0 2-3 L.9 3s5.s

t9 T2 0.0 L64.6 0-1- t37.9

20 2Q(t) o. o s.1- 0.3 3s3 . 4

2L P(1) 3.0 3s4.3 3.3 5.2

22 L(2) 0.0 2L4.6 0.2 L76.0

23 K (2 ) 0.0 1_61_.5 0.4 130.4

24 M(8) 0.0 3LL.L 0.r. 26s.8

GArN (-): 0.89 PHASE (HR):

877093 1

NOS Accepted Tide Only Tide & Wind Tide Only

Values Values Values Error

A K

3 -4 2L8.2

0.6 L06.4

1.L 174-L

8.1_ 357.4

0 .2 228 - t

9.3 L2 . 2

0.l_ 45 . L

0.1 28-4

o -2 180.l_

0. 1 24.3

0. r- 1_30.0

0.4 342.6

0.0 166.3

0 .7 4.8

0.7 350.0

0.4 18.5

L. B 1-9.5

0.0 110.9

0.0 10L.9

0.2 26 - 9

2.7 358.5

0.2 t67 - 6

0.2 97 . 3

0.L 47 - 4

0.16

A K

-0.l_ o . 2

0.1 -65 . 2

0.1 8 . 3

-0.1_ 8.1

-0-1 -22.7

-L.7 1_. t0.0 -7 . 5

0.0 -81.1

0.0 7 . 3

-0. L L75 . 9

-0. L -29 . 3

0.0 l_6 - 5

-0. L L5.1

0.0 -30 . 2

-0.1 4-6

-0.1 3.L.7

0.0 -1.9

-0.4 -2 - 4

0.0 -62.5

0-0 -5.9

0.0 7 . 7

0.0 -46 . s

0.0 -70. s

-0.L -1_03.6

EST. RMS (M) :

A K

-0.4 9 . 0

o -2 -28 - 0

-0.2 L9.6

-0.4 L1 - 9

0.0 36.9

-2.2 0.l-

-0.3 -7.8

0 . 1- -r2'J, .0

0.0 18.3

-0. L -40.8

-0. l- -24.4

-0,1_ 30.4

-0.1_ 23.6

0.0 -8.3

-0.2 5.0

-0.2 17 . 7

-0.1- -5 . 0

-0.5 -5.8

0.0 -26.6

0 . 0 -1,L.7

-o.2 10.9

0.1 -38.6

0.1 -31.1

-0.1_ -45.3

EST. RMS (M) :

Tide & Wind

Error

A K

-0.6 1.6

-0.4 -L07 . 8

0.l_ -L8.2

-L.9 -6.9

a .2 -29 . 4

-2.7 7 - 3

0.1 L22.3

0.1 -l_59.1_

0 .2 -15.6

0.l, t46 - 9

0. r- 100 . 7

o.4 L74.4

0.0 t62 - 6

o .7 L49.3

-0.3 -L4.6

-0.6 L4-6

1. B 14.5

-2.0 l-05.8

0.0 -L!2 - 3

o.2 2L - s

-0.3 -5.9

0.2 -73 . L

0 .2 -LL6.7

0.1 46.9

0.02

Tide & Wind

Error

A K

-0.s ]-3.4

-0.3 -6r_.0

0,1_ 4.6

-1-. B -3 . 6

o.4 8.8

-2.7 7.4

0.1_ 63 . 9

0.2 77.4

0 -2 5.8

0.2 -69.5

0.1 108.5

0.4 -163.4

-l_.0 L67 . 6

o-7 -178.6

-0.3 -L4 - 6

-0.6 22.8

L.8 1,3.2

-2.0 l.04.2

0.0 -66.0

o .2 l.8.2

-0.3 -2.8

0 .2 -53 . 7

0.2 -67 . L

0.1 1-26.4

0.02

A K

3 .5 202.L

0.7 L02 . 5

1.1 L67 . 5

8.2 350.2

0-4 222.O

9.3 6.8

0 .1- 354 - 2

0.2 3.5

0.2 L72.L

0.2 3.9

0. L L32 - 9

0.4 333.6

0.0 1-55 . 9

0.7 358.5

0.7 342 - 0

0.4 13.9

L.8 1_5.0

0.0 106. s

0.0 98.5

4.2 ' 23.2

2 .7 351_.5

0 .2 L60.9

0.2 94-4

0.1_ 77 . L

0.31

8 1
Table C.1. Continued.

CLEAR LAKE

NOS Accepted

Values

No. Name A K

l- ttr(21 4,0 283 . 5

2 s(2) L.0 276.8

3 N(2) 1.0 263.2

4 K(1-) 11_.0 42.3

5 M(4) 0.0 Ls.8

6 0(1) 10.0 33.8

7 M(6) 0.0 73.L

8 S(4) 0.0 21l..2

9 NU(2) 0.0 282.3

,10 s(6) 0.0 33s.8

11 MU(2) 0.0 t23.4

L2 2N(2 ) 1.0 349 . 7

L3 00 ( 1) L.0 3L.8

L4 LMD(2) 0.0 266.5

15 M(1) 1.0 98.4

l-6 J(1) 0.0 342.4

L7 RHo(1) L.0 1_6.3

L8 Q(1) 2.0 3L.0

1_9 T2 0.0 321.0

20 2Q(t) 1.0 80.3

2L P(1) 3.0 42.s

22 L(21 0.0 305.0

23 K (2 ) 1.0 281.7

24 M(8) 0.0 t77.7

GAIN (-): l-.00

MORGANS POINT

677 0933

Tide Only Tide & Wind Tide Only

Values Values Error

AKAKAK

4.9 236 . 9

t.2 1_68.6

L.5 2L9 . O

10.8 19.5

0.3 332 . 5

10.4 L2.5

0.3 294.8

0.0 286.5

0.3 22L.4

0 .0 s4.3

0.0 0.0

o .2 201.0

0.4 26 . 6

0.0 205.2

o .7 1_6.0

0.8 23.0

0.4 9 . 4

2 .0 9.0

0.1_ L71.3

0.3 5.5

3 .6 1_9.0

0 .2 2L2 . 4

0.3 1_63 . 0

0.0 265.9

PHASE (HR) :

4.6 238 . L

0.5 L27 . 7

L.2 L89.5

9.0 1_L.6

0.3 302.3

9 .7 L9.1

o -2 70.L

0.l_ 69 . 7

o -2 L96.0

0.3 s2.2

0.2 140.9

0.4 4.L

0.0 L85.9

0.7 L5.4

0.8 7 . 9

0.4 22.4

1.9 22.9

0.0 1,32.2

0.0 ]-23 . 3

0.3 26.6

3.0 L2.2

0.2 ]-82.9

0. r_ l_L8.8

0.2 229.3

-1.89

1. L -46.6

0 .2 -108.2

0.7 -44.2

-0.4 -22.9

0. L -43 . 3

0.1- -2L.3

0.3 -L38.3

0.0 75-3

0.1 -60.9

0.0 78 . 5

-0.3 -1,23 . 4

-0.3 -L48.7

-0 .7 -5.2

0.0 -61 . 3

-o .7 -82 . 4

0 .5 40.6

-o -2 -6.9

0.0 -22 . 0

0.0 -1,49 . 6

-0.3 -7 4.8

0. s -23 . 5

-0.3 -92.6

-0.7 -tLg . 7

0.0 88.2

EST. RMS (M) :

Tide & Wind

Error

A K

0.6 -45.4

-0.5 -L49 . L

0.2 -73 . 7

-2.0 -30.7

0.3 -73 . s

-0.3 -L4.7

4.2 -3.0

0. 1 -14r.. s

o .2 -86.3

0.3 76 - 4

0.2 L7 - 5

-0 

. 6 1_4.3

-1.0 1_55.1-

o .7 108.9

-o .2 -90.5

0.4 40.0

0.9 6.6

-2.0 L9L.2

0.0 1,62.4

-0. I -53 . 7

0.0 -30.4

0.2 -1,22.L

-0.9 -L62 . 9

0 .2 51.6

0.0s

677 06t3

NOS Accepted Tide Only Tide & Wind Tide Only Tide & Wind

Values Values Values Error Error

No.Name A K A K A K A K A K

1 M(2) 5.0 252.8 5.4 239.6 s.0 24L.3 0.0 -L3.2 0.0 -1_L.s

2 s (2 ) L.0 233 .3 1".3 L72 .L 0.5 t43 .2 0. O .6L.2 -0.5 -90.1

3 N(2) 1-.0 237.L 1.6 222.2 L.2 L9L.4 0.4 -!4.9 0.2 -45.6

4 K(1) L2.0 24.5 11.0 L9.7 9.0 11.6 -1.3 -4.8 -3.0 -L3.0

5 M(4) 0.0 3.7 0.3 34L.9 0.2 297.8 0.2 -2L.8 0.2 -65.9

6 0(1) 1_1-.0 17.3 Lo.s L2.5 9.6 L9.8 -0.9 -4.8 -L.4 2.4

7 M(6) 0.0 244.L A.2 292.0 0.2 77 .0 0.2 47 .9 0.2 -!67 . L

8 S (4) 0.0 356.8 0.l- 306.3 0.2 60.4 o. o -50 - 5 o .2 63 . 6

9 NU (2 ) 0.0 247 .4 0 .3 224.5 0 -2 198 . 1_ 0.0 -22 .9 o .2 -49 . 3

1-0 s(5) 0.0 78.2 0.0 44.6 0.2 69.0 0.0 -33.6 0.2 -9.2

LL MU(2) 0.0 i-15.1- 0.0 0.0 0.2 LAL-5 -0.3 -L15.1 0.2 26.4

L2 2N(2 ) 0.0 334.6 0 .2 204.8 0.4 3.3 -0.2 -1,29 .8 o .4 28.7

13 00(L) 1.0 24.3 0. s 26 .9 0.0 L95.8 -0.6 2.6 -L.0 L?1.5

t4 LMD(2) 0.0 292.5 0.0 208.3 0.? Ls.6 -0.1 -84.2 0.7 83.2

Ls M(1) 1-.0 76.2 0.7 L6.1 0.8 7.5 -0.6 -60.L -O.2 -68.8

16 J(1) 0.0 31-3.s 0.8 23.3 0.4 23.3 0.s 69.8 0.4 59-8

t7 RHO(I) 1.0 3s9.9 0.4 9.5 L.9 23.8 -0.4 9.6 0.9 24.0

L8 Q(1) 2.0 7.4 2-0 9.0 0.0 t47.L -0.3 L.6 -2.0 L39.7

19 t2 0.0 276.9 0.1- !74.8 0.0 L39.2 -O.t -!02.L 0.0 -]-37 - 6

20 2Q(1) 1.0 74.9 0.3 5.4 0.3 27.9 -0.3 -69.s -0.8 -47.0

2L p(1) 4.0 24.5 3.6 L9.2 3.0 L2.2 0.1 -5-3 -L.O -L2.3

22 L(z') L.0 288.9 0.2 2]-5.7 0.2 1,84-9 -0.4 -73.2 -O.8 -l_04.0

23 K(2) L.0 270.8 0.4 L66.7 0.L t3s.2 -0.7 -L04.1_ -0.9 -135.6

24 M(8) 0.0 130.0 0.0 333.7 0.2 229.9 0.0 -Ls6.3 0.2 99.9

cArN (-): 0.89 PHASE (HR): -0.58 Esr. RMs (M): o.o3

82
Table C.L. Continued.

ROUND POINT 877 0559

NOS Accepted tide Only tide & Wind Tide Only Tide & Wind

Values Values Values Error Error

No. Nanne A K A K A K A K A K

1- ttr(21 6.0 238.0 5.7 229.6 5.3 23]-.6 -0.2 -8.4 -0.7 -6.4

2 S(2) L.0 222-6 L.4 L66.4 0.3 r_38.4 0.0 -56.2 -0.7 -84-2

3 N(2) 1_.0 232.3 !.7 2t4.5 L.3 Lgt.4 0.s -r-7.8 0-3 -40.9

4 K(1) 14.0 25.3 tL.2 Ls.7 8.7 2.3 -2.7 -9.6 -5.3 -23.0

5 M(4) 0-0 3s6.8 0.7 324.8 0.4 301.2 0.3 -32-O 0.4 -5s.6

6 0(1) t2-0 4.8 L0.7 8.5 9.8 L7.t -0-9 3.8 -2.3 t2.2

7 M(6) 0.0 L97-2 0-2 70.9 0.1 131.4 0.L -126.3 0.1- -55.8

8 S(4) 0.0 23L.9 0-2 2s5.3 0.4 34.5 -0.2 23.4 0.4 l.62.6

9 NU(2) 0.0 233.0 0.3 2L6.s 0.3 L96.8 0.L -16.5 0.3 -36.3

10 s(6) 0.0 38.0 0.0 39.7 0.0 24.2 -0.L t-7 0.0 -L3.8

11- MU(2) 0.0 64.0 0.0 0.0 0.2 r-51.r- -0.2 -64.0 0.2 87.1-

L2 2N(2) 0.0 226-5 0.2 199-4 0.4 347.s 0.1- -27.L 0.4 L20.9

1-3 00(1) 0.0 4s.8 0.s 22.7 0.0 188.4 0.0 -23.L 0.0 ]-42.6

L4 LMD(2) 0.0 230.9 0.0 200.3 0.7 9.6 0.0 -30.6 O.7 1-38.8

L5 M(r.) 1.0 15.1 0.8 L2.L 0.8 354.9 0.0 -3.0 -0.2 -2O.2

L6 .t(1) L.0 35.4 0.8 L9.2 0.4 23.4 -0.L -L6.2 -0.6 -t2.0

L7 RHo(1) 0.0 3s5.0 0.4 s.5 r_.9 24.4 0.0 9.s r-.9 28.4

1-8 Q(1) 2.0 3s4.6 2.L s.l- 0.0 L42.2 -0.2 10.s -2.O 147.6

L9 T2 0.0 223 .t 0. L 1_68.9 0.0 L34.7 0.0 -54.3 0.0 -88 - 4

20 2Q(r) 0.0 344.5 0.3 r_.6 0.3 3L.8 0.0 L7.L 0.3 47.3

21, p(r-) 5.0 23.8 3.7 r.5.1- 2.9 3.4 -0.9 -8.6 -2.1 -20.4

22 L(21 0-0 243.7 0.2 207.9 0.2 r.84.8 0.L -3s.8 0-2 -s8.9

23 K(2) 0.0 22L.3 0.4 161.3 0.r- r-30.9 0.0 -60.0 0.1 -90.4

24 M(8) 0.0 r-83.4 0.0 25L.6 0.2 324.1 -0.2 68.2 0.2 r40.7

GAIN (-): 0.90 PHASE (HR) : -0.32 EST. RMS (M): 0.03

Model References

Blumberg, A. F., und H. J. Herring, 1987: Circulation modeling using orthogonal curvilinear

coordinates. in Three-Dimensional Models of Marine and Estuarine Dynamics (J. C. J. Nihoul and

B. M. Jamart, eds), Elsevier Oceanography Series, 45,55 - 88.

Blumberg, A. F., and G. L. Mellor, L987: A description of a three-dimensional coastal ocean

circulation model. Three-Dimensional Coastal Ocean Models, (ed. Heaps), American Geophysical

Union, Washington, DC., 1 - 16.

Dennis, R. E., and E. E. Long, 197l: A user's guide to a computer program for harmonic analysis of

data at tidal frequencies. NOAA Technical Report NOS 41. NOAA, National Ocean Service, Office

of Oceanography and Marine Assessment, Rockville, MD, 31 pp.

Hess, K. W. , 1994: Tampa Bay Oceanography Project: Development and Application of the Numerical

Circulation Model. NOAA, National Ocean Service, Office of Ocean and Earth Sciences, NOAA

Technical Report NOS OES 005, Silver Spring, ItD.

_ and K. T. Bosley, 1992: Techniques for validation of a model for Tampa Bay, Proceedings

Second International Conference on Estuarine and Coastal Modeling, Tampa, FL, November 1 1-

L3, r99r,83-94

83
Ives, D. C. and R. M.7-acharias, 1987: Conformal mapping and orthogonal grid generation, Paper No.

87-2057, AIAA/SAE/ASME/ASEE 23rd Joint Propulsion Conference, San Diego, CA.

Mellor, G. L., 1993: User's guide for a three-dimensional, primitive equation, numerical ocean model.

Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ, (unpublished

manuscript).

NOS, 1995. Houston/Galveston Physical Oceanographic Real-Time System (PORTS): FY 95

Implementation Plan, NOAA, National Ocean Service, Rockville, MD.

Orlando, S. P., L. P. Rozas, G. H. Ward, and C. J. Klein, Lgg3.Salinity characterization of Gulf of

Mexico Estuaries, NOAA, Office of Ocean Resources Conservation and Assessment, Silver Spring,

MD.

Schmalz, R.A., 1996: National Ocean Service Partnership: DGPS-Supported Hydrosutroy, Water

Irvel Measurement, and Modeling of Galveston Bay-Development andApplication of the Numerical

Circulation Model. NOAA, National Ocean Service, Office of Ocean and Earth Sciences, Silver

Spring, MD. NOAA Technical Report NOS OES 12. 136 pp plus appendices.

Schureman, P., 1958: Manual of Harmonic Analysis and Prediction of Tides. U.S. Department of

Commerce, Coast and Geodetic Survey, Special Publication No. 98 [revised 1940 edition, reprinted

19881, Rockville, Nfl).

Temple, R. F., D. L. Harrington, J. A. Martin,1977 .Monthly temperature and salinity measurements

of continental shelf waters of the northwestern Gulf of Mexico, 1963 -1965.,

NOAA Technical Report NMFS SSRF-707, Rockville, MD.

Wilken, J.L.,1988: A computer program for generating two-dimensional orthogonal curvilinear

coordinate gnds, Woods Hole Oceanographic Institution, (unpublished), Woods Hole, MA.

84
APPENDIX D. SIMULATED CONSTITUENT FIELDS FOR GALVESTON BAY

Distribution of constituent amplitudes and Greenwich epochs computed with the numerical model

(Appendix C) and the TCARI method. Locations where constituent data was used (tide gauges) are

shown as open squares.

(c) (d)

Figure D.1. For K,, distribution of epoch from the numerical model (a) andTCARI O), and amplitude

from the numerical model (c) and TCARI (d).

85
Figure D.2.For O,, distribution of epoch from the numerical model (a) and TCARI (b), and amplitude

from the numerical model (c) and TCARI (d).

86
Figure D.3. ForP,, distribution of epoch from the numerical model (a) andTCARI (b), and amplitude

from the numerical model (c) and TCARI (d).

87
88
APPENDIX E. TIDE DATA FOR SAN FRANCISCO BAY

The following (Tables E.1, E.z,and E.3) list the tidal constituent amplitudes and epochs for 44

stations in San Francisco Bay. Station numbers are the last fourdigits of the 7-digitNos number;

the first three digits are 941_ Methods of harmonic analysis, time series data, and other notes

appear in Table E.4.

Table E.L. Observed tidal constituent amplitudes (mm) in San Francisco Bay.

sEation 4290 4305 4317 4358 4392 4449 4458 4501 4509 4510 45L9 4523 452s 457s 4637 4688 4724

L M2 570

2 52 134

3 N2 t22

4 K1 358

5M426

5 0r_ 229

?M62

8 MK3 20

9S40

10 MN4 l_0

11 NU2 28

12 s6 1-

13 MU2 10

L4 2N 15

t5 00 t 4

16 LAM2 5

L't sl- 5

L8 Mt L4

l_9 J]_ 2L

20 MM L8

2l ssA 83

22 SA 47

23 MSF 2

24 MF 20

25 RHO1 10

25 Q1 40

27T28

28R22

292e6

30 P1 118

31 zSM 3

32M33

33 L2 2 4

34 2MK3 L6

35 K2 42

36M80

37 MS4 L2

607 647 699

14L L42 L75

L29 L33 L43

375 3?8 385

29 23 2 0

23t 23L 234

256

26 27 2 4

001

LL85

27 27 3 4

001_

795

L4 L3 15

13 13 12

88]-2

7215

13 13 Lr.

l_9 1_6 L7

20918

46 24 7 8

27 47 9 5

18169

79L6

107L3

40 39 4 0

894

zzzz

534

t20 L23 130

254

989

19 25 2 9

1_9 2t 24

4L 44 4 8

tl_l_

L276

738 786 812 862 894 918

163 L76 L78 L87 20L 203

153 159 L64 L73 L82 r.88

392 384 403 40s 391 4r_0

9 1 3 13 t7 1.8

235 240 241 24L 227 243

768L21-215

2L 27 25 31 44 2 8

1_12]-11 2

323768

33 27 38 4t 48 5 7

10109L

919L725342L

15 t4 L5 t4 28 L7

12 L7 t4 L4 38 16

4 L7 15 l't L4 L7

r_8 2L t2 15 20 19

15 L3 L4 15 t4 L6

18 t6 L7 L6 30 1 9

2L615s20L2

46 482 42 11 58 6s

27 1430 34 61- 28 67

5' 9 6 4 L5 L 4

t3 1-5 7 t2 2L l7

1_0 10 11 7 25 t_0

43 45 44 42 26 4 7

Ll-9910L22

122432t7 1l6353L29

L2r 122 t25 L32 11-8 130

75875L2

8867L610

39 47 48 54 76 7 2

26 33 33 4t 55 4 6

.51 72 58 60 79 7 L

l_12254

25593L2

929 879 862 950 831 '774 778

L79 20L t77 200 L82 180 L59

170 r_8s 161 1.91 l_65 162 1.55

395 411 367 430 398 387 398

45L25267 1_335

225 24L 199 240 243 .238 238

2L1010301038

0208556252428

6231025

062325744

33 40 43 50 40 36 3 5

401L004

22 L't 39 4t 26 L2 L4

23 t7 23 L2 15 27 l_8

101513L229L59

72L2525189L4

023L4440L211

15 74 15 2L 1_6 24 L4

18 L9 13 L8 2L 19 15

0L2L2525274

04s4090692368

0 1.40 82 L40 2L82 L26 61

0845L4194L

0 L0 20 l-5 37 L7 L7

9r.r_11 6579

44 47 37 38 43 44 4 2

11 r_3 13 t4 L0 26 L3

L654028 1

6l_L61293

r.31 133 1r-0 L43 r29 L29 L23

01_1 811 10 107

073015355

26 46 84 67 38 38 4 5

035936s383334

49 54 8L "t2 57 76 55

4349010

0 7 23 31 8 3 6

89
Table E.L. Continued.

4746 47s0 4764 4779 4782 4805 48r-6 4818 48L9 4837 4849 4863 4873 4874 4881 4906 5009

t M2 559 669 662 626 535 550 6]-4 590 564 57L 601 6t_0 587 s74 610 s80 593

2 S2 145 L50 L49 L42 L47 L29 135 L34 l-31 t54 L34 139 130 13? 140 130 L23

3 N2 136 137 141 131 131- L22 L27 L25 ]'2o 122 Lzg L2g L24 L30 L28 t24 L2o

4 KL 367 376 374 3?3 365 363 353 367 365 35? 360 370 359 355 359 374 344

5 M4 25 20 19 L6 l-5 l_9 L2 18 !7 1-4 9 12 L4 8 L5 24 15

6 01 224 228 23t 228 225 226 225 227 224 2L6 223 223 2L4 ztg 224 238 2L2

7M5 3 6 5 4 4 2 4 4 4 2 5 5 6 4 5 1 1 0

8MK3282320 18 16 1-5 1-0 15 11 L40L20L1 0024

9S4 1_ 0 2 0 1 0 2 0 L t_ 1 0 1 1 o 2 L

10MN4 9 8 8 5 s 7 6 8 6 5 0 5 0 4 0 0 s

t1 NU2 33 32 28 27 27 24 27 28 2! 23 25 26 24 30 25 24 2 4

t2 s6 r_ 0 0 l_ 0 1 2 I 0 0 1 0 1 0 t L 0

13 MU2 5 4 L2 7 8 7 6 1L 7 6 L4 6 L4 4 LL L4 1t_

L4 2N 18 16 l-8 ts L5 L2 1t_ L4 1L 1_6 L7 13 .15 t9 L7 L7 L 4

15 00 L4 12 t4 14 13 10 14 t3 L2 L2 10 11 g 7 10 l_O 11

15LAt{258891089109104L04184410

LT St 11 1L 4 t-3 15 s L4 5 8 4 0 13 0 3 0 0 23

18 Mt L2 l-5 l-0 l-1 13 11 L2 L4 1_3 t_3 l_6 9 15 t_l- 1_6 t7 15

L9 J1 19 2L !7 1-8 1,9 20 L9 19 20 L7 18 L9 L7 L4 18 19 L4

20 MM I t4 2t 15 L5 9 10 13 6 1s O 8 o 22 0 0 1 3

2L SSA 10L 88 82 76 49 59 59 64 47 104 0 s9 o 74 0 o 77

22SA494942L279873191546]'260250910043

23 MSF 9 5 10 8 1 't 6 4 6 9 0 L5 o 7 o 0 9

24 MF 14 20 32 l-9 L2 1s 7 L2 22 18 0 15 0 15 o 0 2L

25 RHOL 10 10 6 13 9 7 10 lL 7 9 8 9 8 I 8 9 7

26 Qt 38 ,40 39 39 39 39 38 40 37 38 43 38 4L 37 43 46 3.7

27 a2 10 11 L7 8 11 8 6 L0 7 25 8 13 8 5 8 7 5

28 R2 L 2 6 4 3 l_ 8 2 2 28 1 3 L 6 1 1 16

292Q 5 6 6 5 2 5 5 4 1 3 6 2 6 6 6 6 5

30 P1 L2s L20 L20 L27 L07 115 LtA 1L5 LL7 105 119 !L7 1L9 Ltz t_1_9 L24 gg

31_2SM 4 5 6 4 5 2 3 4 4 3 0 4 0 5 0 0 5

32M3 7 6 5 7 5 0 2 3 L 4 o 21 0 3 o 0 6

33 L2 35 37 30 20 23 17 26 30 19 20 L7 23 L6 24 L7 15 3 5

342MK325242L181-61113L4L2L20130130027

35 K2 49 47 s2 39 44 37 40 40 42 29 35 4t 35 34 38 35 4 4

36M8 1 0 0 2 0 1 I 2 1_ L 2 2 2 L 0 1 L

37 MS4 9 I 8 6 9 3 9 8 s 0 5 0 4 0 0 6

5052 5056 5o?4 5111 51_43 5144 5L65 5218 5252 5338

t M2 6L2 634 650 525 507 508 635 59-1 5s4 s3?

2 52 t20 t62 L2L 108 130 107 1_40 L29 130 107 n

3 N2 LzL 153 126 99 118 95 1_30 L20 109 1_00

4 Kr_ 355 37 4 344 307 333 285 34.1 337 335 3:-7

5M4 96L68l_6 11 6L23542

6 01 21,4 232 206 L79 202 165 zt\ 2oA 204 L78

7M6 8411 711_10L0 1045

8MK32L02217L2282L195968

2L1_L112t22

L0MN4405355341515

l_L NU2 30 30 31 23 3t 22 23 25 24 2L

12 56 0010100000

13 UU2 t_3 15 2L l_8 18 18 13 l_6 29 25

142NL22010L11513108159

r.s oo L7 10 11 11 8 9 l_s !2 1_6 1_3

16 LAM2 11 4 L4 t4 15 15 19 L4 l_5 22

1751 340L6823 1_3 12L6 15L4

L8 M1 L4 15 L4 L"7 16 L2 4 Ls 2L 23

1_9 ,JL 18 t8 L4 7 9 7 1,L t4 L2 L4

20 MM 20 0 34 6 10 21 31 t_9 24 22

2L SSA 338 0 20 40 32 70 78 84 45 2!2

22 SA 1036 0 49 37 85 26 56 33 82 263

23 MSF 7 0 30 20 20 40 19 25 18 30

24 MF 32 0 28 29 28 24 46 23 23 2 7

25 RHO1 t-L 9 7 6 L2 12 8 7 4 4

25 Ql 37 4s 37 30 33 25 33 32 35 3 4

27t25101310L2619514

28 R2 15 1 19 3 5 4 2 6 5 15

292Q667234g553

30 P1 97 L24 104 90 95 ?8 110 99 101_ 91

31 2SM s 0 5 6 5 6 5 4 8 9

32 M3 9 0 6 4 6 7 7 5 l_5 L8

33 L2 35 18 26 33 42 30 27 23 33 2 6

34 2MK3 27 0 36 29 27 36 27 32 62 7 L

35 K2 42 44 55 45 49 43 5.1 51 61 69

36 1,t8L2201_01222

37MS4608368781721

954

90
Table 8.2. Observed tidal Greenwich epochs (degrees) in San Francisco Bay.

L M2 209

2 32 2t5

3 N2 L84

4 KL 226

5 M4 t43

6 0L 2L0

7M691

8 MK3 130

9 54 32L

10 MN4 1l_8

t_l NUz 195

L2 55 1"65

13 MU2 135

L4 2N Ls3

l_5 00 242

15 LAM2 214

t7 s1 22L

18 M1 238

L9 ,J1 245

20 MM 22]-,

2L SSA 285

22 SA 2'19

23 MSF 269

24 MF LO2

25 RHOI_ 209

26 Q1 203

27 T2 198

28 R2 328

29 2Q 202

30 P1 225

3L 2SM 43

32 M3 2L0

33 L2 23s

34 2t4K3 94

35 K2 207

36 M8 3s0

37 MS4 151_

4'7 46

t tr2 224

2 32 234

3 N2 200

4 K1 233

5 M4 t_38

6 0r. zL'l 't Nr6 74

8 MK3 1-18

9S449

L0 l.rN4 L13

11 NU2 204

L2 56 L47

13 MU2 1,24

14 2N 181

L5 00 246

16 LAM2 27L

L7 St 262

t8 M1 246

1.9 J1 254

20 r{M 239

2L SSA 277

22 SA 300

23 MSF 1-L0

24 MF L45

25 RHOL 201

26 QL 2LL

27 T2 ]-94

28 R2 108

29 2Q 2L2

30 Pl 232

3t_ zsM 62

32 M3 18s

33 L2 249

34 2MK3 86

35 K2 224

35 M8 228

37 MS4 143

2L3 2L9 223

22L 228 235

r.87 194 199

227 230 233

L36 ]-34 r_38

21-0 2L3 2L5

s9 s8 5 5

L24 tt'? 113

159 41 L94

109 11_1 105

L92 198 198

62 132 181

88 58 5 2

154 154 t?5

253 254 27L

2L5 228 220

277 259 282

249 255 243

249 249 256

L48 18r. L56

307 3l_4 8

L29 L23 26t

L75 t46 21L

L74 LAL 2L9

L99 2L7 1-84

203 2LO 2LO

202 224 151

7 26t 249

185 225 L94

224 226 233

56 51 5 4

30 34 3 6

225 230 238

92 84 8 2

2L2 2L7 208

274 2s2 252

t47 r.50 158

4750 4764 4'779

225 225 222

235 230 229

20L 195 r_96

233 23s 232

t-51 L70 t-56

2L7 2t6 275

35 36 9 9

118 13L 130

L24 69 160

L25 1ss L42

2t0 205 199

t-45 0 154

63 58 LL4

172 155 L67

25L 278 253

2L3 206 2t4

224 325 279

25L 281. 244

26L 25s 260

224 t62 L37

284 183 29

29L 236 288

332 s 184

L06 LL1 2L6

2L5 185 l_93

2LL 207 208

20r 262 2L5

6 26L 2TL

2t8 191 159

233 234 23L

57 5l_ 62

178 77 3 4

235 248 236

81 82 9 8

224 227 2L5

22t 0 243

L62 205 L'16

235 236 235

247 256 252

2L3 2Ls 2L5

238 240 239

L79 L33 L4

222 223 223

79 23 3 3

1,15 100 90

130 40 7 2

L49 32 345

193 229 2]-5

220 11_8 263

4546

L94 185 193

29L 266 282

187 189 2L8

28L l_9L 235

267 255 268

272 262 274

131 254 130

299 s9 309

75 L20 L02

138 L37 166

160 184 150

195 244 202

220 2t9 22L

L97 254 225

24 1_55 5s

229 26L 22L

238 240 237

31 52 5 5

43 359 4

234 22t 228

87 64 6 9

229 225 234

125 63 68

203 33r. 357

4782 4806 48t5

22L 2]-5 220

230 222 232

r.96 189 195

230 229 23t

L52 L57 1 93

215 2L3 2r5

59 29 t22

LL7 L44 L47

292 287 330

l_30 l_s0 178

203 198 208

111 72 164

82 110 99

151 161_ 168

275 248 239

2L0 224 249

252 2L9 234

244 236 237

255 246 245

184 s0 3 1

1_96 305 278

25t 294 t

84 L97 229

155 254 324

204 220 201

207 20't 209

203 204 1,92

146 255 119

223 206 2L9

227 227 228

59 44 8 3

39 357 180

227 243 247

86 L05 8r.

2L8 2L4 2LT

2t0 L59 276

184 177 23'1

45'ts 4637 4688 4724

255 239 239 240

278 256 260 257

23't 2L7 22L 22L

248 243 240 24L

46 L4 98 8 0

235 224 226 225

75 s1 46 '74

82 87 92 7 8

L74 0 45 111

23 340 337 4 4

226 208 208 22L

346 0 299 357

7t5353

225 155 zLt 195

332 304 29L 28L

22L 23L 191 209

205 0 210 262

282 292 294 292

294 282 266 289

190 t32 50 L97

347 113 227 332

25t 323 286 131-

38 355 35 222

89 726 150 198

198 233 2r2 198

23s 222 223 224

277 280 265 242

139 0 18L 3L6

334 L73 .22L 230

245 246 240 240

75 73 31 4 8

344 119 2L 10

228 236 237 242

76 55 70 7 0

25t 25L 239 239

153050

6398054

4874 4881 4906 5009

229 229 202 236

242 242 205 242

200 205 t77 2t2

237 236 224 238

225 L93 150 L74

222 2L9 207 22L

109 90 44 109

L24 0 0 L25

L4 0 277 L52

20s 0 0 138

195 208 180 2L5

19s 29 358 323

188 20L L78 57

198 18L 151 180

225 253 24L 278

215 235 204 24L

305 0 0 250

259 228 2t6 262

262 245 232 260

7500191

296 0 0 30L

306 0 0 315

293 0 0 5r164 0 0 170

255 2L2 200 228

2n 2tL 199 224

292 24L 20s 181

114 242 206 294

2t3 202 191 244

233 235 223 238

108007s

100 0 0 !62

234 252 228 250

840086

22L 243 206 252

253 0 80 186

245 0 0 t74

4290 4305 43r_7 4358 4392 4449 4458 4501 4s09 4s10 4sL9 4s23 4525

24t 245

250 258

22t 22L

24L 243

L4 57

226 230

50 8 9

92 103

79 335

359 198

222 233

266 133

5 350

200 198

294 28t

zLt 113

L86 180

273 237

275 309

240 25L

257 277

L32 323

95 7 4

L00 179

2t6 206

227 2L0

243 83

3s5 L26

288 153

237 24L

62 325

359 2L3

225 231

68 7 4

240 257

L20 ztt

10 285

481_8 4819

2L7 2L5

225 222

L92 190

230 23t

195 18L

2L3 2t3

44 3 7

157 140

25 251

L67 161

20L 200

7Q l_37

92 113

1_56 L61

272 243

230 2t5

257 270

239 239

248 246

204 224

3L2 303

326 23s

43 11_1

t67 28L

2L3 222

207 207

zLL 239

265 2L6

206 235

228 228

47 4I

209 110

234 245

94 9 5

2L6 2]-3

209 zLL

198 191

246 249

254 273

22't 224

243 248

358 3 1

227 234

48 6 0

t02 0

79 223

342 0

2l-s 227

10 15

350 204

225 1_98

289 262

234 260

236 0

272 24L

289 255

223 0

252 0

178 0

2L0

159 0

209 228

227 227

203 272

s5 274

265 22L

244 247

700

11 0

243 274

81 0

249 27s

106 141

250

4837 4849

224 22r

23L 230

].97 195

232 23L

I73 202

2L7 2L7

66 10r.

138 0

330 331

L52 0

203 199

L23 L76

131 328

l_63 169

273 246

.209 225

309 0

240 224

2s8 239

203 0

246 0

340

1L3 0

L32 0

204 2Lt

208 zLO

249 229

354 230

222 203

230 230

420

480

223 248

100 0

246 230

19r_ 187

zAL 0

239 2s0

257 270

2L9 233

240 249

297 8 s

224 238

31 153

t02 95

97 190

299 75

2t0 23]-

L57 349

345 2 3

223 2L6

295 288

199 235

239 187

259 28t

273 331

s6 328

285 235

20L L76

318 2 2

L76 184

208 2L7

224 247

22L 230

54 6 0

242 283

240 244

50 7 3

23 355

240 243

7L 7 7

242 258

96 315

344 1L6

4863 4873

223 229

234 237

198 206

233 239

208 2L3

217 2L9

90 9 3

t45 0

23 186

188 0

202 209

83 2 9

83 200

L65 L82

26L 26Q

223 233

253 0

236 229

255 249

L27 0

282 0

2s9 0

343 0

138 0

2L7 2LL

2L2 209

205 237

115 237

206 199

231 238

620

135 0

249 252

940

224 238

L76 L49

2L2 0

9l
Table 8.2. Continued.

5052 50s6

L M2 247 240

2 32 256 250

3 N2 222 2L2

4 K1 250 240

5 M4 12 118

5 01 232 223

7 yr6 t_38 l.t 8

8MK3950

9 s4 85 243

10 MN4 358 0

1L NU2 237 2L6

L2 55 345 1 6 9

13 MU2 49 2L0

L4 2N L92 184

15 00 306 257

16 rAM2 250 245

t7s1240

18 M1 236 232

19 .t1 275 248

20 uM 150 0

2L SSA I57 0

22 sA 169 0

23 r{SF 2L 0

24 MF L56 0

25 RHO1 234 2L5

26 Q1 232 2ts

27 12 293 249

28 R2 16 250

29 2Q 273 206

30 P1 237 239

31 zSM 83 0

32 M3 1_75 0

33 L2 264 269

34 2MK3 65 0

35 K2 241, 250

35 M8 339 344

3? MS4 23 o

5074 51LL 5143

247 274 258

262 285 27A

22L 248 233

245 263 25L

10 L5 334

230 246 233

L22 t87 L32

90 L25 105

L1-5 L52 77

341 L7 319

227 253 244

25t 3t7 2L1

58 87 7 3

20L 242 206

282 325 328

245 265 258

L73 300 249

328 320 280

272 315 288

69 1_34 L97

138 22L 332

Lt1 238 L28

52 L4 31_

t7L 158 L64

232 239 237

234 257 240

268 254 233

L7 149 178

230 L52 263

242 266 256

68 LL4 87

158 L78 163

257 2't5 272

75 111 9 3

242 279 260

289 26]. 243

37 77 t 4

52L8 5252 5338

255 257 264

268 270 275

228 238 242

25L 255 26L

19 80 L09

234 24L 249

L30 1_96 294

108 89 104

63 L7 5 Lt-6

335 70 9 2

23L 240 255

2t2 353 155

51 48 5 2

2LL 245 296

293 300 3l_0

259 234 267

226 L52 249

325 295 307

285 335 324

L53 279 203

305 2 343

307 22 285

69 66 72

155 15t L29

224 2t7 24L

232 249 263

238 L76 277

L87 L70 L2'7

2t9 252 325

255 250 267

87 86 84

1s3 312 327

265 244 254

84 68 8 2

260 255 269

3L7 44 L22

54 gi 11L

5r.44 5165

28s 250

298 270

259 235

270 253

L23 50

255 237

240 t44

L34 LL4

L74 86

104 350 '268 

24L

r.8 320

99 7 L

250 187

332 311

273 2s5

256 29L

322 5 3

325 268

44 4 0

272 30s

24 333

11 2 5

189 227

230 278

264 24L

24s 226

198 28L

328 246

257 2s6

L28 r.08

29 L77

289 283

L20 84

287 269

90 4 5

138 6 1

Table 8.3. Observed tidal local epochs (degrees) in San Francisco Bay.

4290

I M2 338

2 52 335

3 N2 315

4 KL 106

5M440

60198

'7 M6 l_l_5

8 !,rK3 13 8

9 S4 20L

10 l.rN4 L9

l_1 NU2 328

12 56 166

l_3 }iu2 27 L

t4 2N 290

15 00 L13

t5 LAU2 339

t7 s1 L01

18 M1 L22

19 .tl 1,21

20 r{M 2L7

2L SSA 284

22 SA 279

23 r'fsF 26L

24 MF 93

25 RHOL 101

26 Q1 9 s

27 12 3t_8

28 R2 88

29 2Q r.00

30 P1 105

31- 2Sl'I 1-55

32 M3 222

33 L2 358

34 2MK3 L10

35 K2 327

36 M8 L43

3? MS4 40

4305 4317 4358 4392

34t 347 352 4

34L 348 355 7

320 326 33L 346

107 109 Ltz 1_18

32 30 35 7 5

98 t02 L04 110

84 82 90 104

L32 L24 t2t 1-23

49 28L 74 L0

91,26s0

324 330 330 325

62 L32 18L 220

224 205 188 181

29L 29L 313 331

13 4 1_3 5L42 161

340 352 344 3L2

t57 1"39 1,62 161

133 139 L27 L51

L24 L24 141 L47

L44 L75 t52 L27

307 314 7 299

L28 123 261. 7s

L67 138 202 130

L65 r-33 2L0 L52

91 110 77 87

96 l_03 1_03 113

322 345 271 3L7

L27 2L 9 L44

83 L22 9t L26

104 107 113 118

l_68 t62 l_56 L43

42 47 48 5 5

349 354 1 358

108 101_ 99 103

331 336 327 348

67 45 45 279

35 38 46 9 1

4449 4458

4 5

16 L2

348 347

L20 118

30 270

LL2 TL2

47 5 8

1_08 97

280 3L2

293 247

L 347

1L8 263

L4L T42

322 330

L37 L53

31_3 342

7t 115

139 L52

138 L50

250 t26

58 308

120 101

L29 L57

L75 L51

135 9 4

L12 l_13

L4 346

275 175

158 11 8

L2L LL'l

163 L67

\2 15

344 351

81_ 85

344 354

2L6 220

2L9 245

450L 4509

9 l_3

20 1.8

354 353

L2L L23

27L 3L3

L15 tt9

75 113

100 1r.r_

3r_9 2L5

260 99

354 5

256 1_33

143 L26

337 334

165 152

335 237

66 6 0

l_57 L2L

L50 184

235 247

266 277

L32 322

86 6 6

91_ t70

109 9 9

1L9 103

4 204

r.t_5 246

186 5 t

1L7 LzL

L't 4 77

L2 225

349 35s

85 9 1

360 t_6

272 4

259 7't1

45r_0 4519

t4 L7

24 3 3

360 3s6

L22 L28

254 288

1_16 L23

73 8 4

1L0 0

3L9 103

242 0

347 359

L0 r.5

136 34L

2 335

L60 133

358 2 4

1_L6 0

156 L25

L55 130

2t8 0

252 0

1?8 0

130

150 0

L02 L2t

L20 L20

323 32

L74 34

163 118

r25 L27

L82 0

240

7 3 8

970

934

259 294

4523 4525

718

L7 3 0

351 5

L20 L29

L94 34r.

LL2 L26

55 L77

L10 L03

337 7 0

200 336

342 3

L57 349

L22 1.59

360 352

L57 159

324 359

119 6 7

143 165

L49 206

s2 324

28s 234

20L ]-76

3L0 L4

1,57 L7 6

100 109

LL1 140

34L 350

]-74 180

r.39 180

tzL t24

L62 185

357

4 7

88 9 4

1_ l_8

249 108

)1) A

4575 4637

237

38 L 6

9 350

L28 L22

302 270

L25 LL2

99 7 6

89 9 5

540

283 24L

358 340

346 0

r.43 151

3 292

203 L75

346 355

850

166 t76

L69 157

L86 L28

347 1L3

25L 323

29 347

80 LL7

91 t25

L28 115

38 4 0

259 0

23L 70

125 L26

188 185

356 13r.

35r. 360

92 72

20 10

305 0

11) ?Cq

4688 4724

8 8

20 L 7

3s4 353

L2O L2L

355 337

114 LL4

70 9 8

100 86

286 351_

238 305

340 353

299 357

L1L 139

348 331

162 1s1

315 334

90 L42

178 ]-76

LAL L64

s6 1_93

225 331-

286 131

28 2L4

L4L 190

105 90

115 LL1

252

300 7 5

r.1-8 ]-28

LzL I2O

143 160

33 2 2

L 5

87 8 7

3s9 358

L58 0

92

273 328 302
Table 8.3. Continued.

47 46

L yt2 353

2 52 354

3 N2 332

4 KL 113

5M434

5 01 105

7 146 99

8 MK3 L26

9 54 289

10 UN4 14

11 NU2 335

L2 56 L47

13 WJz 250

14 2N 318

15 00 lt?

16 LAM2 35

L7 51 r42

18 M1 130

19 .Tl. 140

20 MM 234

2L SSA 276

22 SA 300

23 r.rsF L02

24 t[F 136

25 RHO1 94

26 Q1 104

27 t2 314

28 R2 228

29 2Q L09

30 P1 1L3

31 2SM t74

32 M3 t97

33 L2 13

34 2MK3 103

35 K2 343

36 u8 20

37 MS4 32

4750 4764

353 353

355 350

334 329

113 1L5

47 6 6

105 104

59 6 0

L26 L38

4 309

25 5 5

342 337

t45 0

200 L94

308 302

131 L49

338 330

104 205

135 15s

1.35 l-30

220 1 58

283 183

29t 236

323 357

97 108

107 78

104 99

321 23

L26 20

LL5 88

1L3 L]-4

1_69 163

190 9 0

359 t2

98 9 8

343 346

130

50 9 3

5052 5056 5074

159L5

16 10 2 2

355 34s 354

130 L20 L25

269 t4 266

L20 Ltz 1r_9

t52 142 L47

103 0 97

325 t23 355

2s9 0 242

9 348 359

345 159 25L

L8s 347 L94

328 32L 338

L77 L28 L52

L59L0

264 0 53

L20 1i.5 2L3

151 L24 t47

145 0 65

L57 0 138

L69 0 116

13044

L48 0 163

L26 108 L25

L25 r.08 L27

53 10 2 9

l-36 10 L37

L70 104 L27

rL? 119 L23

195 0 179

187 0 170

28 33 3 1

8t- 0 92

010 1

L32 136 81

27L 0 285

4779 4782 4806

350 350 343

349 350 342

328 328 322

111 l_r.0 r"09

53 48 6 3

103 104 101

L23 93 54

138 L25 L52

40 L72 L67

42 31 5 1

331_ 335 330

164 1r_1 '12

250 2L9 245

304 288 297

133 L46 r_19

338 33s 348

159 L32 99

L29 L28 L20

136 1 30 r22

133 180 4 6

29 195 30s

288 254 293

t76 75 189

207 t47 245

85 96 LLz

100 100 100

335 323 324

331 255 L4

56 L20 103

L11_ t_07 108

L74 L1L 155

46529

350 351 7

LLA 103 L22

335 338 333

35 3 31_1

6s 72 6 6

5111 51_43 5144

42 26 5 3

45 30 5 8

2L631

143 131 149

273 23L 19

L34 L22 L43

ztL 156 265

133' 1r_3 14L

32 317 5 4

278 220 5

25 L6 4 0

3L7 zLL 18

223 249 236

r_9 343 27

L96 r.99 203

30 23 3 8

L80 ]-29 L46

204 r.64 206

191 r54 20L

l-30 L93 40

220 331 27L

238 L28 24

6232

]-49 155 180

L32 L29 L23

L49 L33 t5'1

L4 353 6

268 298 318

49 160 226

L47 L37 147

226 r.99 240

1_91 175 42

40 35 5 3

L27 l_10 136

39 i-9 47

54 36 243

325 263 26

4815 4818

348 346

352 345

327 32s

110 110

89 9i_

103 t_01

L46 68

155 L64

2L0 25s 't8 57

340 333

)-64 70

235 228

305 293

11_0 L43

13 355

114 L47

t2L L24

t20 L24

26 200

278 3LL

L 326

22L 35

315 158

94 105

1,02 100

313 3 3 1

239 2s

1L6 1_03

109 108

r.95 L59

L92 22L

11_ 358

98 t r.L

330 33s

692

r25 8?

48r.9 4837

344 3s2

342 351

322 330

110 LL2 't7 59

L02 10s

61 9 L

148 L45

131 2L0

61 5 3

332 33s

I37 L23

249 267

298 300

LTA L44

340 333

150 189

L23 L24

LzL 133

2L9 199

302 245

235 33

103 105

272 L23

114 9 5

r_00 L01

350 9

336 tt4

L32 1L9

109 110

153 154

L22 60

9 347

LIz LL1

333 6

4 343

79 8 9

4849 4853

3s0 35r_

350 354

328 330

111 113

98 104

105 105

L26 115

0 154

2tt 263

089

331, 334

l'16 83

105 2L9

305 303

LL'I L32

3s0 348

0 133

r.08 1-20

114 130

0 L23

o 282

0 2s9

0 335

0 l_30

103 110

103 105

3s0 325

350 235

L00 L03

11L Lr2

o L74

0 l-48

11 13

0 LLl350 344

340 329

0 100

4873 4874

35'1 3 57

357 2

338 332

LT9 LL1

l_09 L22

108 110

Lt1 L34

0 L32

66 254

0 1_05

341 327

29 195

335 324

319 334

130 9 6

357 340

0 185

1L3 153

L25 L37

0?0

0 295

0 305

0 285

0 156

103 r47

L02 tt4

357 52

357 234

96 1l_0

1t_8 113

0 220

O LL2

L6 358

0 100

35? 340

302 45

0 L3s

4881 4905 5009

357 330 4

23252

338 309 344

116 1_04 LL8

89 45 7 0

108 96 110

114 69 134

00L32

0 157 3 2

0039

340 3L2 347

29 358 323

338 314 194

3l_8 288 3L7

L24 L1.z 149

359 328 5

0 0 r_30

tL2 100 L46

L20 108 135

0 0 l_86

00300

00316

0043

0 0 l_61

104 92 L20

104 92 Lt1

2 326 302

2 325 54

99 88 141

L1_s 103 118

0 0 r_87

0 0 L74

16 352 L4

00L02

2 325 11

0 232 339

0062

LM2

252

3N2

4K1

5M4

501

7 yr6

8 !4I(3 1

954

10 uN4

11 NU2

L2 S6

L3 wJ2

L4 2N

15 00

15 LAM2

t7 s1

18 I'1L

19 ,Jl

20 l4M

2L SSA

22 SA

23 MSF

24 MF

25 RHOL

26 Q1

27 T2

28 R2

?e 2 Q

30 P1

31 2SM

32 M3

33 L2

34 2MK3

35 K2

36 M8

37 MS4

516s 5218 5252 5338

29 23 25 3 2

30 28 30 3 5

I 1- 10 t 5

132 13L 134 L4].

307 276 337 5

t25 L23 130 r.38

158 154 22t 3r_9

t22 116 97 LL2

326 303 56 3s5

25L 236 331 3s3

l_3 3 L2 2'7

320 2L2 353 L65

207 L97 184 t_88

324 348 22 73

L82 164 L71, l_8r_

20 23 3s8 3r_

L1L 106 32 L29

297 209 180 191

143 150 2L0 200

3 5 158 275 r_99

304 304 1 343

333 306 22 285

L7 6L 58 6 4

2L9 L47 t42 L20

L'lL LL? L09 133

134 L24 L42 156

347 358 296 37

4L 306 289 247

L43 116 t49 222

l_36 135'L30 t47

220 r_99 L98 1_96

L89 r-66 324 33 9

4729818

100 101 85 9 8

29 L9 L4 2 9

1_98 1L0 196 275

309 302 341_ 2

93
Table 8.4. Methods of Harmonic Analysis and knglh of Time Series Used.

Sta.

No.

Name Harmonic

Analysis

Begin End Days Datum Notes

4290 San Francisco LSQHA uu80 ru3u80 366 3.18

4305 North Point LSQHA Ltu7 5 r2l3u7 5 365 3.29

43t7 Pier 22Vz LSQHA 5tu7 5 u28t76 304 3.39

4358 Hunters Point LSQHA rctza74 4n3t75 t74 3.61

4392 Oyster Point LSQHA uu75 tayn5 365 3.78

4449 Coyote Point LSQHA 5t9t75 9t29t7 5 t44 3.94

4458 San Mateo Bridge

West End

LSQHA uu75 LU3u75 36s 4.08

4501 Redwood Creek

Channel Marker

LSQHA 6nt75 3t3u76 305 4.2t

4509 Dumbarton Bridge LSQHA l/1/80 t2l3u80 366 4.50

4510 Dumbarton RR Bridge LSQHA Uu84 l2t3u84 366 4.49

4519 Mowry Slough IJA29 r2llt84 29 4.55

4523 Redwood City Wharf 5 LSQHA 8tt6t83 5t17t84 276 4.30

4525 Palo Alto Yacht

Harbor

LSQHA 5iz84 Ltt3t85 257 3.82

4575 Coyote Creek LSQHA t0tv7 5 3t3u76 183 4.83

4637 San Mateo Bridge East

End

LSQHA t2tL7t76 4tt3t77 tt7 4.12 2 blocks of

data

4688 San lrandro Marina T,SQHA 4nt82 tU30t82 244 3.92

4724 San Irandro Channel LSQHA t0n4t74 3t3u76 383 3.60 7 blocks of

data

4746 Oaklnd/Alameda Park

St. Br.

LSQHA tugt79 8/19/80 285 3.46

47 50 Alameda LSQHA 1/l/80 rzt3u80 366 3.49

4764 Oakland Inner Harbor LSQHA r2lu76 715177 170 3.44 4 blocks of

data

4779 Oakland Matson Wharf LSQHA IuU74 4t30t75 181 3.33

4782 Yerba Buena Island LSQHA 3t493 9t20t93 203 3.34

4806 Sausalito LSQHA uu78 t2t3u78 365 3.10

4816 Berkeley LSQHA u7t79 8t3u79 201 3.35 3 blocks of

data

4818 Angel Island LSQHA 51u80 Lu30t80 2t4 3.25

94
Sta.

No.

Name Harmonic

Analysis

Begin End Days Datum Notes

4819 Sausalito COE Dock LSQHA 8t29t78 5t24t79 269 3.13

4837 Point Chauncey LSQHA u25t93 8t9t93 t66 3.10

4849 Richmond Inner

Harbor

HA29 tot20t94

w2494

r2124t94

u26t95

29

29

29

29

3.25 Average of

4 H.A.

4863 Richmond Chevron

Pier

T.SQHA uU96 t2t3l196 366 3.25

4873 Point San Quentin HA29 9t7t79

9t30t79

29

29

3.r2 Average of

2H.A.

4874 Corte Madera Creek LSQHA 7tu77 6t30t78 365 3.14

4881 Point Orient H.A29 9t8t79

rcnn9

4tu83

5l19l93

6tr6t93

7tr3t93

29

29

29

29

29

29

3.22 Average of

6 H.A.

4906 Point Bonita HA29 4tr0t80

5trst80

29

29

3.34 Average of

2H.4.

5009 Point San Pedro LSQHA 5tU80 I 1/30/80 214 3.16

5052 Galinas LSQHA 717t79 l,v20l7g 137 3.t4

5056 Point Pinole HA29 4tu83 29 3.23

5074 Hercules LSQHA 9t5t86 2t3t87 152 3.47

5111 Benicia LSQHA lntSl tzt3u8r 365 2.75

5143 Crockett LSQIIA 4tu80 I 1/30/80 24 3.04

5r44 Port Chicago LSQHA ult93 ra3rD3 365 2.55

5165 Mare Island Strait LSQHA u26n8 9t9t78 227 3.15

52r8 Mare Island Naval

Shipyard

LSQHA uu86 tzt3u86 365 3.05

5252 Petaluma River Ent. LSQHA 71u85 u3u86 215 3.24

5338 Sonoma Creek Ent. LSQHA 9t5t85 3t24t86 20r 2.88

95
96
t

-

I

al

!.

APPENDIX F. SIMULATED CONSTITUENT FIELDS FOR SAN FRANCISCO BAY

Distribution of constituent amplitudes andepochs computed with theTRIM numerical model (Cheng

et al., 1993) and the TCARI method. Tide stations are shown as open squares.

K, local epoch (degrees) from TRIM. Kl local epoch (degrees) from TCARI.

K, amplitude (cm) from TRIM. K, amplitude (cm) from TCARI.

Figure F.L. TRIM (left column) and TCARI (right column) fields for Kr phase and amplitude.

0 5 lOni

r+-#

0 5 l0km

Xr Anditudc

io cntiocrcn

97
52 local epoch (degrees) from TCARI.

Figure F.2. TCARI fields for 52 phase and amplitude.

52 amplitude (cm) from TCARI.

01 local epoch (degrees) from TCARI. 01 amplitude (cm) from TCARI.

Figure F.3. TCARI fields for O, phase and amplitude.

98
P1 local epoch (degrees) from TCARI.

Figure F.4. TCARI fields for P, phase and amplitude.

P, amplitude (cm) from TCARI.

N, local epoch (degrees) from TCARI. N, amplitude (cm) from TCARI.

Figure F.5. TCARI fields for N2 phase and amplitude.
100