AN ABSTRACT OF THE THESIS OF
Carl Raymond Goodwin
for the
in _lEnineering
Title:
presented on arci_974.
Estuarine Tidal H4aulics:
One-DiruensionalModel and.
ctive Alaorithm
Abstract approved:
Redacted for Privacy
Bard Glènne
Redacted for Privacy
Larry S./lotta
A otie-dimensional, implicit, finite-difference model is
developed, calibrated and verified for three estuaries along
the central Oregon coast.
The model is used to generate controlled
data for a large number of hypothetical estuaries.
Two non-dimensional coefficients, K.,
and. K,.
, are developed
incorporating physical characteristics of the estuary which
suarize the effects due to friction and inertia, respectively,
These coefficients are used to explain the variebility of tidal
response throughout the complete range of hypothetical estuaries
investigated.
A predictive algorithm based on the derived
relationships is presented and examples of its application to
real estuaries is given.
The results of this study can. be used to predict modifica-
tions in tidal response due to proposed physical changes in an
estuary, such as entrance dredging or filling of tidal flats.
Field data of velocity, temperature and salinIty for the
Yaquina, Alsea and Siletz estuaries is included with the paper.
©
1974
CARL RAYMOND GOODWIN
ALL RIGHTS RESERVED
Estuarine Tidal }ydraulics One Dimensional Model and
Predictive Algorithm
by
Carl Raymond Goodwin
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
June 1974
APPROVED:
Redacted for Privacy
Redacted for Privacy
Professors of Civil Engineering in charge of
jor
Redacted for Privacy
Head Lof Department of Civil En
Redacted for Privacy
Dean of Graduate School
Date thesis is presented
Typed by
Susan L, Lane
March 13, 1974
for
Carl Raymond Goodwin
Acknowledgements
Partial support for this study was provided by Oregon
State University National Science Foundation Sea Grant Institutional Grant GH-45 and Federal Water Pollution Control
Administration Grant No. WP-01385-Ol.
This support is appre-
ciated,
Many field measurements were made from a specially
equipped boat on loan from the U.S. Geological Survey.
This
assistance is also gratefully acknowledged.
The guidance, direction and encouragement of Dr. Bard
Glenne throughout the study has been particularly valuable and
is sincerely appreciated.
Thanks to Susan Lane is extended for competently preparing the final manuscript under difficult conditions.
Considerable credit for this product is due my wife,
Cathy.
Her devotion, understanding and willingness to type
two complete drafts have contributed greatly to the study.
TABLE OF CONTENTS
1,
Introduction.
,
1.1 Background.
1.2
1,3
2
2.6
1
1
, ,
TidalPredictionHistory..............................
2
. . . . . . . . . . . . . . . . . . . .. . .. .. . . .. .
10
Purpose. . . .
.
.
Model
3.1
3.2
3.3
Basic Equations...... . . . . . . . . . . . . ....... . . . . . . . . e . .
11
11
3.4
3.5
. .
. . . . . . . . . . . .
Assumptions...... . . . . . . . . . . . . . . . . . . . . . .. . .
Estuary Schematization. . . . . . . . . . . . .. . . . . . . . . . . . . . .....
FiniteDifferenceEquations...........................
Recursion Solution of the Implicit
Finite-Difference Equations...........................
StabilityandConvergence.............................
Applications. .
. . . . . .
. . . . . . . . . . . . . . .
. . . . .
.. . . . .
.
Description of Estuaries..............................
Data Collection..... . . . . .
Schematization. . . . . .
3.3.1
3.3.2
3.3.3
3.3.4
4.
,
.
e
The Model... . . . . . . . . . . . . . . . . . . . . ..s.... .. . . . . . . . . ........ . .
2.1
2.2
2.3
2.4
2.5
3
,
,
,
,
. . . . . . . . 1
. . .
. ....... . . . . a . . . . . . . . a... a.
. . .
. . .
. . . . . . . . . . . . . . . . . . . . .
Cross SectionalArea...........................
Surface Area...... . . . . .
. . . . . . . . . . . .......
. . .
Friction.......................................
. a..... .1
Estuary Dimensions...... . . . . . . . .
Prototype and Model Comparison........................
Conclusions...........................................
Correlating Parameters...... . . . . . . . a .....a.. . . . . . . . . . . . . . .
4.1
4.2
4 3
4.4
General Observations...... .
Frictional Coefficient. a a . . . . a . . . . . . a. .. . . . .. . . . ..
. . . .
Inertial Coefficient. . . . . . . . . . . . . a . . . . . . . .. . . .
. . . .
Idealized Embayment. . . .-. a a s a . . . a . a a. .. . . . .
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
4.6
. . .
a
a .
a a
Schematization..........................a......
a a.....
Displacement Curves....... .. . a......
Effect of Coefficients on Tidal Amplitude......
Effect of Coefficients on
Displacement Phase Lag.........................
Effect of Coefficients on Maximum Velocity.....
Effect of Coefficients on
Slack Water Phase Lag. . . . a a a
4.5
. a
. . . a...
. . . . . . . . . . a. a... a
. .
a a a a a .
. a a a
Semi-Idealized Embayment. . . . ..... .. . a...... a..a.......
4.5.1 SchexnatizationandApproach............a.......
4.5.2 Discussion and Recommendation..................
Estuaries with Multiple Segments.....................
4.6.1 Schematization...............a..aa...........a.
4.6.2 Reinterpretation of Coefficients...............
4.6.3 Effect of. Coefficients on
Amplitude, Displacement Lag and
Slack Water Lag. . . . . . . . . a
4.6.4
Selected Results. . . . . . . . a
a. s a a.... . a. . . . a a a a.
a a
.
. a
. .
. a
.
12
14
17
19
21
28
28
33
33
33
35
35
37
46
47
49
49
51
52
53
53
54
61
63
65
66
69
69
70
71
71
71
72
74
5
6.
Predictive Algorithm. . . . ,
. . . . . . . . . . . . . . . . . . . . . . . . . .
.
. . ,
5.1 Data Requirements and Assumptions.....................
5 1.1 Assumptions. . . . . . . . . . . . . . . . . . . . . . .. . . . . ... .
5.1.2 Physical Data..................................
5.1.3 Hydraulic Data.. . . . . . . ...... . . . .. . . . . ..
5.2 Computational Procedure and Graphical Analysis........
5.2.1 Single Segment Case...... . . . . . . . . . . ........ . . . .
5.2.2 Multiple Segment Case..........................
5.3 Discussion., . . . . . . . . . . . . . . . ........ . . . . . . . . . , , ,
5.3.1 Purpose. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .
5.3.2 Accuracy.......................................
76
76
76
76
77
Summary, Conclusions and Recommendations.........,..........
6.1
Summary.........................,.....,,,..,,,......,.
6.2 Conclusions.........,,.............,.......,.....,,..,
6.3 Recommendations for Further Study.....................
83
83
85
86
Bibliography.
. . . . .
87
Appendix A - Computer Model Documentation...................
91
.
. .
. .
.
. . . . . . . . . . . . . . . .
. . ,
78
78
79
80
80
81
Appendix B - Prototype and Model Comparison Details Yaquina Estuary. . . . .
.
.
. . . . .
. . ..
. .. . . . . . . .. . . .
114
Appendix C - Prototype and Model Comparison Details A.lsea Estuary.. . . . ..
.
. .
. .
. . .
. ..
. .
. . .
... . . . . .
134
Appendix D - Prototype and Model Comparison Details S iletz Estuary. . . . . . . .
.
. . . . . . .
. . . . .. .. .
.. . . . . . . .
149
Appendix E - Application of Predictive Algorithm - Examples. 163
Appendix F - Field Data: Velocity, Temperature,
Salinity, Density. . . . .
.
. . . . . . .. . .
.
.. . . . . . . ..
181
Estuarine Tidal Hydraulics One-Dimensional Model and Predictive Algorithm
1.
1.1
Introduction
Background
The
burgeoning population growth in the coastal regions
of the United States has produced increasing demands on the
resources of the country's estuaries and bays.
Estuaries
are presently being used by man for the following main purposes:
1
recreation activities
2Q
sport and commercial fishing
3.
shipping
4
waste water receival
5.
cooling water supply
6
land fill and borrow areas for commercial
and residential development
The basic natural function of estuaries is for the
production of shellfish and the spawning and rearing of a
multitude of marine
animal species prior to their migration
to the ocean.
In many instances the uses are conflicting and would be
mutually exclusive if carried to the extreme.
These conflicts
require that priorities be set and estuarine development
controlled to meet these priorities.
The guiding principle
of estuarine development, as stated by Congress in the pre-
2
amble to Public Law 90-454, 1968, The Estuary Protection Act
(U.S. Fish and Wildlife Service, 1970, attachment p. 1).
...the purpose of this Act (is) to provide a
means for considering the need to protect,
conserve, and restore...estuaries in a manner
that adequately and reasonably maintains a
balance between national need for such
protection...and the need to develop these
estuaries to further the growth and development of the Nation.
To provide the degree of management required to meet
this goal, the physical and biological systems in estuaries
and their interactions need to be well understood.
Predictive
tools need to he developed which can be used to access the
short and long-term impact of various natural and man-made
changes to the estuarine environment.
The prediction of
estuarine tidal hydraulics is the necessary first step in
developing such tools.
1.2
Tidal Prediction History
The measurement and prediction of tides in estuaries has
long been an important activity of man.
Early sailing vessels
as well as present day diesel, steam and nuclear powered ships,
are dependent in some manner on the tide.
Navigation of sailing
ships through narrow harbor entrances had to be accomplished
"with the tide", which means in the same direction as the tidal
current flow.
Large, mQdern passenger and cargo vessels are
also sometimes limited to departure and arrival times determined
3
by the depth of water beneath the keel.
of high tide are desirable in this case.
Information on times
The U.S. Naval aircraft
carrier Enterprise has a related problem when entering or
leaving San Francisco Bay.
She must wait until low tide in
order for the superstructure to pass safely beneath the Golden
Gate Bridge, which spans the entrance to the bay.
Depending
on the actual water elevation, she must at times also induce
a list of several degrees to provide the necessary clearance.
Tidal predictions are also important for the day-to-day
operations of commercial and sport fishermen as well as clam
diggers and oyster farmers.
Harmonic analysis can be used to advantage for prediction
of tidal characteristics.
Prior tidal elevation records at a
fixed location (usually inside a tidal inlet) can be closely
approximated as the sum of several sinusoidal components.
Each component is defined by its amplitude, frequency and
initial phase difference.
Prediction of water surface elevations
can then be done by extrapolating these component functions
and calculating their summation at any later time (Thompson, 1879),
(Darwin, 1883), (Doodson, 1922), (Munk and Cartwright, 1966).
The National Ocean Survey, NOS, formerly the U.S. Coast and Geodetic
Survey,
publishes annual tables of predictions for a
large number of locations on the coast of the United States
based on this technique.
Tidal current velocities are more difficult to measure,
and therefore also more difficult to predict.
Velocity measure-
4
ments can be made throughout a tidal period to determine maximum
ebb and flood currents and times of slack (no flow) conditions.
If done for several different tide ranges, reasonable velocity
predictions can be made based on water level information.
Although harmonic analysis provides a useful predictive
tool, it is inherently limited by conditions which existed at
the time the original data was taken.
Any physical change in the
hydrography of the bay could cause significant changes in its
tidal characteristics. Also, predictions are strictly valid
only at the point of data collection.
Changes caused by floods,
storms, shifting shoals, dredging or land filling all effect the
tide to some extent and there fore could negate the value of
Another drawback to
predictions based on prior conditions.
harmonic methods is that little insight is provided into the
basic mechanisms controlling
propagation of the tidal wave.
Prior to harmonic analysis, the basis for a more complete
understanding of tidal phenomena had been laid by investigators
who formulated the governing equations of motion and continuity
(Newton, 1687), (Euler, 1755), (Laplace, 1755), (Lagrange, 1781),
(Lamb, 1895).
These equations have been analytically solved
for a number of channel conditions.
Defant (1919, 1925) treated the rectangular basin case
neglecting Coriolis and friction forces.
Lamb (1932) provided
solutions for canals whose width and depth vary proportionally
to the distance from the closed end.
Taylor (1919) applied
frictional energy dissipation to tidal motion in the Irish Sea.
5
Fjeldstad (1929) developed the theory of two damped waves
of the same period traveling in opposite directions within a
channel.
One wave is incident at the mouth, the other reflected
at the closed end.
Redfield (1950) expanded on this theory to
provide a method to analyze tides in small embayments.
Evangelisti
(1955) has given the most general solution using this theory,
allowing variations in width and depth to be given by exponential functions.
Canals subject to tides at both ends were analyzed by
Einstein and Fuchs (1954, 1956) for the proposed Panama Sea
Level Canal.
Perroud (1959) analytically solved several simple
boundary conditions assuming the friction term invariant along
the length of the estuary.
Dorrestein (1961) has studied the
amplification characteristics of long waves under a variety
of boundary and friction conditions using numerical procedures.
Each mathematical solution of tidal flow for a particular
boundary configuration increased the ability to predict tidal
conditions within estuaries closely conforming to one of the
The Delaware and Thames river estuaries, for
idealized shapes.
example, have nearly constant depths and exponentially converging widths.
Most estuary boundaries, however, can not be so
simply defined.
For these cases no general analytical solutions
are yet available.
The lack of adequate theoretical tools to solve specific
tidal problems prompted the development of physical models
to
6
simulate tidal flows in selected estuaries.
In this country,
models built at the U.S. Army Corps of Engineers Waterways
Experiment Station at Vicksburg, Mississippi (Ippen and Harleman,
1958, 1961), (Simmons, 1969) have been successfully used to
determine the effects that proposed engineering works may
have on tidal flows.
Similar programs have been carried out
in other countries.
Large expenditures of time and money are
required to adequately develop models of this type, which
restricts their possible application to a few of the largest
seaports with the most urgent problems.
At this juncture in the history of tidal prediction, the
next logical step might well have been to undertake experimental research to determine parameters which would correlate
tidal observations taken in several different irregularly
shaped estuaries.
area, however.
Only limited work has been done in this
Standard flood routing techniques, as
described by Linsley, Kohier and Paulhus (1958), are used to
analyze the progress of a flood wave in rivers and streams.
These methods have very restricted applicability to prediction
of tidal hydraulics.
Because they are based solely on the
continuity equation, no energy or momentum effects can be
included in the analysis.
A time history of discharge at a
section is required to use these methods, and this information
is not generally available in an estuary.
O'Brien (1931, 1967 and 1971) has shown a relationship
between entrance cross sectional area and the tidal prism of
7
many estuaries of widely varying dimensions.
Keulegan (1967)
has analytically characterized the tidal response of an ernbay-
ment in terms of a "repletion" coefficient.
Johnson (1973)
has proposed that inlet behavior is a function of wave power.
None of these studies, however, attempt to define the changing
tidal characteristics as a function of changing estuary dimensions
as the wave progresses further into the estuary.
A numerical procedure presented by Glenne, Goodwin, and
Glanzman (1971) closely parallels the results of Keulegan (1967).
The development of large-capacity, high-speed electronic
computers provided another means to model estuarine hydraulics
and provide an alternative to the costly physical models.
It
also seemingly bypassed the necessity for experiments and research
in the classical parametric vein.
The computer provided researcher
with a powerful means for
simulating tidal flow systems numerically.
One of the first
applications of a two-dimensional numerical model was of the
North Sea by Hansen (1956).
A variety of one- and two-
dimensional models have been developed and applied to a large
number of separate estuaries and seas.
Many of these inves-
tigations were directed toward solving problems related to
diffusion and mixing in estuaries, but also added significantly
to the understanding of numerical procedures applied to tidal
phenomena.
Pritchard (1952) used one-dimensional, finite-difference
modeling concepts on the St. James estuary in Chesapeake Bay.
Kent (1960) applied similar methods in the Delaware River
estuary.
Dronkers (1964) presented details for numerically
modeling one- and two-dimensional tidal flow using both
characteristics and finite-difference techniques.
The model
developed in this paper is based on the information given
by Dronkers.
U.S. Geological Survey work in explicit, implicit
and characteristic tidal models is summarized by Baltzer and
Lai (1968).
O'Connor (1965) studied longitudinal distribution of sub-
stances in estuaries by using models valid during slack periods
only.
Leendertse (1967) greatly advanced the art of two-dimensional, finite difference modeling with his work in the North
Sea.
In addition, he studied important aspects of stability
and convergence in the solution technique.
Additional theoret-
ical work and application of the model to Jamaica Bay, New York
have also been reported (Leendertse, 1970, 1971, Leendertse
and Gritton, 1971).
Jeglic (1967) applied advanced one-
dimensional modeling techniques to the hydrodynamic and water
quality simulation of the Delaware River estuary.
Two-dimensional modeling of Galveston Bay was reported
by Reid and Bodine (1968).
This work was extended to other
shallow irregular estuaries by Masch (1969).
Orlob, Shubinski, and Feigner (1967) studied pollution
problems in the San Francisco Bay and Delta region using
networks of links and nodes of uniform channel segments.
Callaway, Byram and Ditsworth (1969) used a similar procedure
in the lower Columbia River.
A one-dimensional numerical
technique was applied by Glenne and Selleck (1969) to determine
the longitudinal diffusion characteristics of San Francisco Bay.
Bella and Dobbins (1968) used a finite-difference scheme
to calculate DO and BOD profiles in a hypothetical, constant
area estuary.
Tidal motion in the St. Lawrence River and Estuary was
studied by Kamphuis (1968) using one-dimensional techniques.
Verma and Dean (1969) applied the Galveston Bay model (Reid and
Bodine, 1968) to Biscayne Bay in Florida.
Even with the availability of numerical and physical
modeling techniques as well as an extensive theory for regularly
shaped estuaries, the likelihood is small that all of the
inlets and estuaries of the United States will ever be modeled
or described with these tools.
At the present, models exist
for only some of the bays which have the worst problems.
a few others lend themselves to theoretical analysis.
Only
The
majority of estuaries, many of them small, have very real or
potential problems which should not be neglected.
For these
reasons, it would be advantageous to pursue the classical parameter-correlation approach mentioned earlier to provide some
quantitative tools for evaluation of possible tidal changes
10
in unmodeled estuaries.
The work reported in this paper is
based largely on the previous studies by Keulegan (1967) and
Glenne, et.al. (1971).
1.3
Purpose
It is the purpose of this paper to define the physical
parameters which control the propagation of tidal waves into
real estuaries and to group these parameters into useful
coefficients to provide a predictive algorithm for tides in many
estuaries which have no detailed simulation model available.
To achieve this objective, a quasi one-dimensional model
has been built to generate the data on which a predictive method
could be based.
The model has been verified for three signifi-
cantly different estuaries on the central Oregon coast.
11
The Model
2.
Basic EquatIons
2.1
After the development by Dronkers (1964), the
o1iowing
equations governing tidal flow in estuaries were cscn as
the basis for this model.
The simplified equacion of motion is:
+
i
gAC
BC
.
t
gAC2
t
2.1.1
jQ =
C2AC
and the continuity equation is:
Q+AS=O
fT
or
2.L2
where:
H
=
the instantaneous difference in height hotween the
actual water level and mean sea level - f*t (FT)
Q
=
the instantaneous discharge through a cr-f. ; section -
cubic feet per second (CFS)
x
=
a coordinate measuring distance along the length of
the estuary - feet (FT)
AS = the total surface area of a channel segmt
square
feet (FT2)
AC
=
the cross sectional area of the conveying portion of
the channel - square feet (FT2)
BT
the total surface width of both the convewL ug and
storage portions of the channel - feet (
:)
12
BC
=
the surface width of the conveying portion of the
channel - feet (FT)
per second (FT/SEC2)
C
=
Chezy friction coefficient - feet½
g
=
acceleration due to gravity - feet per second per
second (FT/SEC2)
t
2.2
time - seconds (SEC)
Assumptions
The major assumptions inherent in these equations are;
1.
one-dimensional motion
2.
a homogeneous fluid
3.
negligible wind force
4.
negligible Coriolis force
5.
no tributary inflow along the length of the estuary
6.
flow to and from the storage areas has no inertial
effect on the motion in the main channel
7.
the momentum and kinetic energy correction factors
have the value of unity
8.
the water particle velocity is less than the
critical velocity, j, where D is the instantaneous
hydraulic depth in feet
9.
the slope of the channel bottom within each
river section is zero
10.
the Chezy relationship is adequate to describe
frictional effects in tidal flows
13
It is important to understand the significance of each
term in equations 2.1.1 and 2.1.2.
The
ax
term represents the
hydrostatic forces which are present in all open channel flows
due to the effect of gravity.
term represents the local
The
flow unsteadiness or local acceleration.
The Qll
term in
equation 2.1.1 represents the nonuniformity of the flow or
convective acceleration experienced by a fluid particle in moving
from one point to another in the flow field.
recognized form of this term,
tution of equation 2.1.2.
Q
Both the
The more readily
, can be seen by substiand Q
terms can
also be interpreted as representing the inertial forces in the
system.
The last term in equation 2.1.1 represents the frictional
forces produced by the flow.
The quadratic and directional
nature of this term is preserved by use of the absolute value
sign.
The continuity expression, equation 2.1.2, requires that
the net volume of flow into or out of a channel section over a
given time period be accompanied by an equal increase or decrease,
respectively, of the volume of water within that section.
The methodology exists for numerically integrating these
partial differential equations in at least two principal ways.
The method used in this paper is a direct approximation of the
original equations using finite differences.
The other technique
first resolves the original set of equations into four total
differential equations using the "method of characteristics".
14
This new set of equations is then also approximated by finitedifferences.
The method of characteristics is especially useful for
studying discontinuities in the flow, such as tidal bores or
moving hydraulic jumps which occur in the Amazon River and
other river estuaries of the world.
Since discontinuities are
beyond the scope of this study, the direct approximation method
was chosen due to its ease of application.
2.3
Estuary Scheinatization
Before presenting the finite-difference forms of the basic
equations, the concept of how the
estuary is visualized
schematically must be understood.
Figure 2.3l shows a plan
view of a hypothetical estuary typical of those found along the
Oregon coast.
The schematic portrayal of the same estuary is
also shown.
The object of segmentation is to describe the original
shape with as little distortion as possible within the limitations of a one-dimensional model.
To facilitate this, there is
no restriction on segment length, channel width or storage
width built into the model.
Typical segment end points are the
ocean and landward limits of a bay, a shallow or constricting
point in the river, and other similar features.
Features of the estuary and the tide which are defined at
the odd station numbers (section centroids) are:
FIGURE 2.3.1
Estuary Schemattzation
Ocean.
I
I
I
I
I
I
t-----sucnnnw
Time-Station Grid System
FIGURE 2.3.2
-
.3+1
-i
U.-
3
4
I
41
Time
Units
3
2l
4
I
I- 1
1
01
I
I nit i a 1
Conditions
2
1
3
4
5
I-i
I
1+1
Station Number
0
Displacement
Discharge
C)
C)
o
o
k
--
__________
16
17
H
-
tidal water surface displacement (PT)
AS
-
segment surface area (FT2)
BT
-
total surface width of segment (PT)
Features and parameters which are defined at the even
numbered stations (segment ends) are:
Q
-
tidal discharge (FT3/SEC)
V
-
tidal velocity (FT/SEC)
AC
-
channel cross sectional area (PT2)
BC
-
channel surface width (FT)
L
-
channel length between segment centroids (FT)
C
-
Chezy friction coefficient (FT½/SEC)
The tidal parameters (H, Q, and V), which are functions of
time as well as distance, must also be determined at appropriate
time intervals.
t
Displacement values are defined at times:
= nt
where:
t
n
0, 2,
= time interval (SEC).
Discharge and velocity values are similarly defined at times:
t
=
n At
n
=
1, 3, 5,...........
The x-t grid, boundary conditions, and initial conditions
are summarized in Figure 2.3.2.
2.4
Finite-Difference Equations
Expressing the segment numbers as I and time increments
as J, finite-difference approximations to equations 2.1.1. and
2.1.2 can be written as:
18
JJ-2
gAC
2L
BT''Q(H
g(AC )
t
Hr) BC'IQ1Q
= 0
(C )(AC)
At
2.4.1
Q2-Q+
AS 1+1(1+1
+\
\11J±1'J_l)
2.4.2
0
which apply when:
I
=
.3
=
0, 2, 4, 6........
,
,
,
Rewriting 2.4.1 to simplify and consolodate coefficients gives:
_K3QH
2L1
where:
Ki =
H)+K2jQJQ
;
gAC'At
2.4.3
2L'BT1
2L1BC'
K2 =
0
.;
K3 =
g(AC1)2t
(C52(AC')
At every time step, the equations of motion and continuity
can be written for
each estuary segment.
are 2n equations available.
For n segments there
The total number of unknos in the
system at each time step is 2n + 2, representing
and displacement for each estuary segment plus
discharge
river inf low
19
and ocean displacement.
By providing the latter two variables
as input functions, the number of unknowns reduces to 2n.
With
matching numbers of equations and unknowns the system becomes
determinate and solutions can be found by iterative techniques
for the remaining unknowns.
In addition to the boundary conditions just mentioned,
initial conditions to start the interative process must be
provided for the discharge and displacement at each segment.
(see Figure 2.3.2)
In the development of the numerical equations 2.4.2 and
2.4.3, major consideration has been given to the choice of a
differencing scheme which most closely approximates the real
situation.
The continuity equation, for instance, when applied
over a finite time period, provides a time averaged discharge
value.
The equation of motion, however, requires an instantan-
eous discharge.
To negate this inherent conflict as much as
possible, time averaged displacements were incorporated into the
equation of motion, thus making time averaged discharges acceptable.
The resulting formulas are of the implicit type since a
single H or Q value cannot be determined independently of all other
H and Q values at a given time step.
2.5
Recursion Solution of the Implicit Finite-Difference Equations
With boundary conditions given and initial conditions
assumed, the iterative solution for discharge and displacement
20
values at each time increment proceeds as follows:
1.
I is set equal to 2 and a trial value is assumed
for the displacement at the. centroid of the first
1+1
section, Hj+i.
2.
Equation 2.4,3 is used in the followingform to
find the discharge at I.
by
The Q
term is approximated
to linearize the equation which is then
solved for Q.
Ki
1+1
H14"
I-i
2.5.1
1+K;(Q2)=:3(H+nkf)
3.
Equation 2.4,2 is then used to find the discharge
at the next upstream adjacent segment boundary
ASI+l
1+2
QJ
4.
I
/ 1+1
1+1
2.5.2
Equation 2.4.3 is again used in a diffrent form,
to determine the displacemant at the cenroid of
the next segment.
I±2QI
+K3Q
1+2
- l+K3Q
I-Fl
I+3HI+l
J±l
1+2
2.5.3
21
5.
I is incremented by 2 and steps 3 through 5 are
repeated for all segments sequentially in upstream
order except the last.
6.
The required river inflow to the last segment is
computed using equation 2.5.2 and compared with the
given boundary value.
If not within a specified
error limit, ER, a correction is made to the initial
assumption, step 1, and the entire procedure repeated
until the error condition is satisfied.
The process is repeated for each sequential time step until
a tidal cycle has been completed0
At this point a comparison is
made with the assumed initial conditions0
If agreement is not
within a predetermined convergence limit, ERR, another cycle of
computations is started with the new set of computed initial
conditions.
This procedure is repeated until the convergence
criteria is met, normally in two or three cycles.
26 Stability and Convergence
The stability of equations 2.4.2 and 2.4.3 is difficult
to determine rigorously.
Similar equations can be analyzed,
however, to provide insight into the present case.
Simplified equations of motion and continuity can be
combined into what are conmionly called the "wave" equations.
The one-dimensional frictionless equation of motion neglecting
convective acceleration terms is:
22
gt
x
2.6.1
Continuity is:
2.6.2
=0
+
The derivative of 2,61 with respect to x and the
derivative of 2.6.2 with respect to
+
t
gives:
0
2.6.3
= 0
2.6.4
g
CU
+
xt Dt2
Upon substitution:
1
x
Recognizing that gD
speed, gives
the
gDàt
S2
, the square of the local wave
wave equation:
= s2
This equation represents a simplified versic
2.6.6
of the
same phenomena described by equations 2.1.1 and 2,1.2.
Leendertse (1967) has analyzed the stability of iulicit
finite-difference approximations to equation
determined that
He
the formulations were unconditionrüly
23
stable.
It is not unreasonable to expect that related
equations, such as 2.4.2 and 2.4.3, describing similar
motion, would also be unconditionally stable.
Finitedifference equations are considered to be
convergent if decreasing grid sizes produce solutions
correspondingly closer to the analytical solution of the
Figure 2.6.1 shows that
original differential equations.
this scheme is convergent for a test case analytically
described by Ippen (1966).
It also converges to the condition
predicted by Dorrestein (1961).
A frictionless channel was
used for this test with a constant prismatic rectangular cross
section 50 feet deep and 500 feet wide with a total channel
length of 240,000 feet.
The ocean tidal amplitude used is
2 feet with no fresh water inflow.
Figure 2.6.2 shows the percentage error in tidal
displacement to be expected in this case for a variety of
x and At grid combinations.
Reduction of grid size generally
produces results which closer approximate the analytical solution.
Optimum combinations of Ax and
figure.
t values are indicated in this
For a given segment length, the error of the numerical
procedure can be reduced by decreasing the time increment.
If
reduced beyond the 0.0 error line, however, truncation errors
accumulate to override any benefits gained by further At
reduction.
A parallel argument holds if the time increment is
held constant.
Computational benefits can be obtained by
FIGURE 2.6.1
- -
Convergence of Numerical Procedure
with Decreasing Segment Length
-
3.0
/
V
/
Dorrestcin(l
Ippen(l966)
2.6
0
U
tL-ft
Symbol
C3
o
120,000
60,000
40,000
2.4
S
30,000
Frictioriless case
Time step = 3
/
2.2
2.0
0
60
180
120
Distance from Nouth
xl000 ft
240
FIGURE 2.6.2
Percentage Displacement Error of Numerical Procedure
(frictionless case)
0.25/
//
:0.10
0.0
/
0.10
2.00
1.00
0.50
0.25
0
0
40
20
60
80
100
120
140
Segment Length- xl000 ft
SLC.
i
-jUau
.
.: . -F--
.
Ui
41
reducing the segment length to the 0.0 error line.
Beyond this
point, computational errors again dominate.
Each grid reduction also increases the computation time
necessary to reach the numerical solution.
Figure 2.6Q2 was
used as a guide to determine the grid size for model operation
in this study.
The number of cycles needed for dissipation of erroneous
initial conditions is also regarded as a different type of
convergence.
In nearly all cases,
convergence in this sense
was accomplished in two to three tidal cycles.
Figure 2.6.3
demonstrates this for a typical case0
Model documentation; including flow diagram, list of
variables, program code and sample input and output; is given in
Appendix A of this paper.
FIGURE 2.6.3
Convergence of
Numerical
Procedure at Successive
Cycles
3.4
3.2
3.0
-
Frictionless case
Time step
10°
/
2.8
,17
L
0
2.6
E
Q)
U
Initial value
After 1 cycle
After 2 cycles
2.4
After 3 cycles
24
z
2.O}------Q-- -------- -0 ---------- -0----l.8L
0
60
120
180
240
Distance from Mouth- xl000 ft
N.)
30
3.1
Model Applications
Description of Estuaries
The Yaquina, Alsea, and Siletz estuaries are prominent
physiographic features of the central Oregon coast (Figure 3.1.1).
Fishing, logging, and tourism provide the major economic base
of the region0
The Yaquina is the largest and most important of these
estuaries.
It is presently being used as a port for a large
commercial and sport fishing fleet, a terminal for log shipping
operations, a storage area for logs destined for pulp and saw
mills, the home port for the oceanographic activities of Oregon
State University, as well as a number of recreational pursuits.
The city of Newport at the bay mouth is the hub of fishing,
shipping and tourism activities.
Toledo is situated five to
six miles inland on a tide effected reach of the Yaquina River
and
is the focal point of logging operations over a wide area.
The small town of Elk City is located near the head of high
tide influence in the river approximately 26 river miles from
the mouth of the bay.
The Yaquina estuary has a total surface area of about four
and onehalf square miles as measured at mean tide level (MTL).
(Kuim and Byrne, l967)
The surface area of water changes
markedly as extensive tidal flat, shoal, and shallow slough
areas are either emersed or submerged in response to the tide.
Location Map
FIGURE 3.1.1
123030'
124°00'
124°30'
45°00'
Sietz
123000'
I
Oceanloko
Estuary
Yaquina
Se
Newpor
Estuary
Corvalli
Ibany
Toledo
-
44030' rndewater
34
Waldport
Yachats
28
Junction
City
Eugene
L
44°Od
10
0
0
20
30 MILES
0
30
The maximum water area occurring at mean higher high water
(MHHW) tide level is approximately five and one-half square
miles.
The area of tidal flats reported by Blanton (1969) is
about two and one-half square miles, which gives a minimum
water area at mean lower low water (MLLW) of approximately
two square miles representing the surface area of the conveyance channel.
The area of tidal flats predominate over the
channel area in the Yaquina estuary.
The primary hydraulic function of the channel is to
convey water into and out of the estuary in response to tidal
action and river inflow.
The primary hydraulic function of
the tidal flat areas is to store the water which overflows the
channel and distribute it to the variety of marine plants and
organisms growing in these regions.
The channel also has a
secondary storage function.
Channel improvements have been made in the past to aid
navigation, provide a safe harbor, and allow for deeper draft
shipping vessels.
Rock jetties have been built and maintained
to protect the dredged channel from excessive shoaling,
depths greater
Channel
than 30 feet below MLLW exist from the bay
mouth upstream to McLean Point.
Depths decrease generally to
20 feet at Oneatta Point, 15 feet at Toledo and 10 feet at Elk
City.
Depths decrease very rapidly a short distance above Elk
City so that even small boat travel is possible only during
times of high tide.
31
A drainage area of about 160 square miles at the head of
high tide supports an average July flow in the Yaquina River
of approximately 80 cubic feet per second (CFS).
This is based
on U.S. Geological Survey, USGS, records at Mill Creek (1961-67).
Waldport, at the mouth of the Alsea estuary, is located
13 miles south of Newport and is a fishing and tourist center.
The town of Tidewater is situated some 12 river miles from
the coast and, as its name implies, is near the head of high
tide.
The surface area of this estuary at MU is approximately
two and one-half square miles.
This total is equally divided
between tidal flats and the conveyance channel.
The entrance
is unimproved with an offshore bar causing a hazard to navigation.
Depths greater than 35 feet exist naturally in some sec-
tions of the entrance channel.
The channel shallows vary rapidly
and depths greater than ten feet are seldom found in Alsea Bay.
Upstream river depths vary from eight to twelve feet depending
on local conditions.
At Tidewater,
the depths are reduced to
four feet.
A drainage area of 350 square miles at the head of high
tide produces average low flows in August of 104 CFS (USGS,
1961-67).
The Siletz estuary is located about 20 miles to the north
of Newport.
Three small communities of Taft, Cutler City and
Kernville serve the sport fishing and tourist industries of the
area.
No other towns exist along the 24 miles of river before
32
reaching the head of high tide.
The Yaquina and Alsea estuaries are characterized by
rather gradual widening of the rivers in a downstream direction
into large bays with gradual narrowing again to the ocean
entrance.
This is not so with the Siletz.
The river-to-bay
and bay-to-ocean transitions are very abrupt.
The total surface area of the estuary is a little
than two and one-half square miles at MU.
less
Less than one
square mile of surface is contained in the conveyance channel
which leaves about one and one-half square miles of tidal flat
area in Siletz Bay.
The Siletz has a drainage area of 270 square miles at the
head of high tide with an average river flow in September of
110 CFS (USGS, 1961-67).
Mixed semi-diurnal tides occur along the Oregon coast and
have an average tidal range of 5.5 feet.
Each estuary modifies
the tide according to its own unique set of physical characteristics.
In the Yaquina, the tidal wave undergoes gradual
amplification as it progresses through the bay and up the river.
The Alsea first attenuates the wave which is then amplified as
it continues toward the estuary head.
A similar, though more
pronounced attenuation, occurs at the entrance to Siletz Bay.
The characteristic amplification is again observed in the river.
This phenomenon and additional information are more completely
presented by Goodwin, Emmett and Glenne (197O)
33
3.2
Data Collection
Hydraulic data necessary to design
and verify computer
simulation models of the Yaquina, Alsea and Siletz estuaries
were collected during the summer of 1969.
Tidal elevation and
velocity data was published as part of the report by Goodwin,
et al. (1970), referred to in the previous section.
Previously
unpublished salinity and temperature data are given in
Appendix F
of this paper.
This information can be used to
a) determine how well
the prototype estuaries meet the assumptions and restrictions
of the numerical model, and to
b) determine how well the
model simulates prototype conditions.
It should be reiterated here that the purpose of this
study is not to develop a sophisticated estuarine model, but
rather a simple one which is viable for a variety of field
situations.
If this is established, the model can then be used
in a research effort with a high degree of confidence that
results will have applicability to real as well as hypothetical
situations.
3.3
Schematization
3.3.1
Cross Sectional Area
The conveyance channel cross-sectional areas were determined as indicated in Figure 3.3.1.
At sections where no tidal
FIGURE 3.3.1
Channel Schernatization
channel
Without tidal flats
-is
35
flats occurred, the entire area above mean lower low water (MLLW)
was approximated as a trapezoid with equal side slopes.
For
sections with tidal flats or shoals, a trapezoidal channel was
assumed to extend above the points of maximum width of the
main channel.
All of the flow is assumed to pass through the
conveyance portion of the total channel area.
3.3.2
Surface Area
Surface areas of each segment were determined as a function
of water surface elevation.
Planimetric methods were used when
suitable charts were available.
Data from U.S. Army Corps of
Engineers dredging projects were especially useful.
and Geodetic Survey sheet number 6055 was also used.
U.S. Coast
To compute
the surface area of upstream river segments, for which no adequate charts are available, the average end width of each seg-
ment, for several elevations, was multiplied by the segment
length.
The width information was available at several locations
from Oregon State University field surveys of cross-sectional areas.
Segment lengths were scaled from U.S. Geological Survey
topographic sheets.
3.3.3
Friction
The remaining parameter necessary to define the
physical characteristics of the estuary is the Chezy friction
coefficient, C.
It was decided that a range of allowable C
36
values, determined from the literature, would be tested in the
model.
Values providing the best simulation of a portion of
for incorporation into the
the prototype data would be chosen
models.
Mother segment of measured data would then be used
to verify the adequacy of each model calibration.
The reasoning used here is not uncommon in model studies
of this type, since friction coefficients are not directly
measurable quantities.
Indirect methods for determining C in
tidal waters are fraught with difficulties.
The Chezy coeffi-
cient is defined for steady flow conditions in open channels;
therefore, the inherent unsteadiness of tidal flows poses
serious problems to its field determinations.
Some credence can be placed on the practice of adjusting
friction factors in a model if
values are found which satisfy
In addition, if similar C
a large range of tidal conditions.
values are found to apply in a number of estuaries, even more
faith can be placed in the method.
Brunn (1966) gives Chezy C values for ten tidal inlets in
the United States and one in Denmark.
96 ft2/sec
with an average of
They range from 76 to
86 ft Isec.
Dronkers (1964)
indicates that experience in the Netherlands shows C variations
in rivers from 82
being 90 ft2/sec.
to
127 ft½/sec
with the most common value
He also indicates that C values of 109
ft2fsec have been computed for tidal inlets on the Dutch coast.
In contrast to these C values for sandy inlets, Gleime and
37
Simensen (1963) report a value of
45 ft/sec
for a rocky
inlet to a Norwegian fjord.
The Chezy values actually used in the model vary with
the 1/6 power of the depth.
C = K D116
K
is a constant for each section and is equal to 1.49/n
where n is the Manning friction factor.
Manning's equation
is used since it provides better simulation results.
The Chezy
form is used for computational simplicity.
3.3.4
Estuary Dimensions
A plan view of the schematized Yaquina Estuary as segmented for the model is shown in Figure 3.3.2.
Table 3.3.1 gives a description of station locations and
the value of each parameter used in the schetnatization.
The
It
table also shows at what section each parameter is defined.
should be pointed out that the cross-sectional area listed in
Table 3.3.1 is the conveyance portion of the total section.
The cross-section values given in Table 1 of Goodwin, et al,
(1970) is the total area including conveyance and storage
portions.
Note that the conveyance cross-section is largest at
the mouth and decreases continuously toward the head of the
estuary.
The scheinatization of the Alsea Estuary is shown in
Figure 3Q3.3, with Table 3.3.2 defining station locations and
Yaauina Estuary Schematization
TABLE 3..l
1-Section
1
2
----i-:--------
rChange in Surface
Conveyance
Channal
Width
ICross-Section
in
feet
Length
Area in ft2
Conveyance
LCctiO1
atSl
-
in ft2 at
t/Lt
atSL
L4S L
Area with
Displacement
jnft2/ft_-
Chezy
C
Ocean
Seaward
o
end
letties
226O0
650
10000
Oneat;cu Point
l9lOO
:Ver eno Marina)
------------ ----
900
-.----.
90
2
11III T'IIL
4
Surface Area
Side
Slope
1530
10
90
io
----
19,000
90
20
__________-
2.60 x
io
2.0 x io6
--I
-I
6
Georgia Pacific
ioadng dock
15,100
-- -------
1,300
27,500
24
go
3.50x10
j
7
8
Mouth of Miii
Creek
---H
42O0
400
23,500
30
j
9
3.OxlO°
6.00 x 10°
85
1.0 x 10 5
47
Details of the model-prototype comparisons and hypothetical predictions are given in Appendices B, C, and D;
representing the Yaquina, Alsea and Siletz estuaries, respectively.
The degree of verification achieved in the three modeled
estuaries is generally within 0.15 feet for displacement,
two and six degrees for phase, and generally less than 0.5 feet
per second for velocity.
This is considered adequate for the
purposes of this study.
3.5
Conclusions
From the information presented, it is concluded that many
aspects of tidal hydraulics in the Yaquina, Alsea, and Siletz
estuaries can be adequately simulated with the one-dimensional
finite difference model described in Chapter 2 and Appendix A.
If the limitations inherent in the basic equations are not violated
too strongly, these models can be used to predict the hydraulic
reaction to many natural or man-made changes.
Of more significance to this paper, it is also concluded that
this type of model can be used as an investigative tool for research
in the area of tidal hydraulics.
Specifically, many types of
hypothetical estuaries can be simulated to provide consistent data
from which interrelationships might be more easily observed than
from field data.
TABLE 3.31
Yaquina Estuary Schematization - continued
Conveyance
CroSs-SectiorL
Section
Number
Location
Area in ft2
at MSL
Elk City
2,100
*'
10
ii
12
Conveyance
Width
Channel
in feet Length
at MSL in feet
Side
Slope
ft/ft
Surface Area
in ft2 at
MSL
Disp1acment
C
in ft /ft
)
250
38,500
6
85
5.20 x i0
Head of high tide
Change in Surface
Area with
Chezy
5.0
FiGURE, 3.3.3
Alsea Schematization
Ocean
Head
Wa ic1pOt
1
2
I
I
I
Station Number
6
7
8
Alsea Estuary Schematization
TABLE 3.3.2
yatice
Location
Cross-Section
Area in ft2
at MSL
2
Bay mouth
8,500
3
Waldport pier
4
near mouth of
Drift Creek
Section
umber[
5
6
7
8
Conveyance
Width
Channel
in feet Length
at MSL in feet
1,050
10,000
Side
Slope
ft/ft
Kozy Kove
fish camp
90
5.40 x 1O7
6,000
1,400
20,000
250
33,000
8.45 x
75
90
2.00 x io
3,500
Change in Surface
Area with
Chezy
Displacement
C
in ft2/ft
60
Oakland's
Marina
Route 34
bridge
Surface Area
in ft2 at
MSL
1.42 x 106
4
90
0.68 x 10
7
0.83 x 106
Headof
high tide
4:-
-i
FIGURE 33.4
Cutler
Taft
Ocean
City
Siletz Schetrtatiation.
Kernville
Head
-
jI
Station Number
7
8
9
10
TAiU, 3,1.3
SacLLon
Number
1
2
Siletz Estuary Schematization
Conveyance
Conveyance
Cross-Section
Width
JChannel
Area in ft2
in feet Length
at NSL
2t MSL !.n feet
Lccatoa
I
I
Side
Slope
ft/ft
Taft
fishing pier
3,300
295
7,000
8
j(ernvile
(Chinook Marina)
6,100
4O
28,000
iO
8.00 x 10
10
90
1.90 x io
I
0.10 x 106
Private Dock
(Howards)
3,600
400
41,300
1
85
1.20 x
7
8
90
3.20
5
6
Change in Surface
Area with
Chezy
Displacement
C
n fc2/ft
Ocean
3
4
Surface Area
in ft2 at
MSL
Private Dock
(Strome's)
1,300
35,500
300
1
io6
1
9
1
0.08
_____ _____
85
0.40 x
0.30 x io6
TABLE 3.3.3
Section
Nuaiber
10
Location
Siletz Estuary Schernatizacion - continued
Conveyance
Conveyance
Cross-Section
Width
Channel
Area in ft2
in feet Length
at MSL
at MSL in feet
Side
Slope
ft/ft
Surface Area
in ft2 at
MSL
Change in Surface
Area with
Chezy
Displacement
C
in ft2/ft
Head of
high tide
-
L ____________ _____________ ________ _____
_____ __________ ______________ _____
Ui
46
parameter values.
In this case, the cross-section at the mouth
is slightly smaller than the next section.
The schematization of the Siletz Estuary is shown in
Figure 3.3.4, with Table 3.3.3 defining station locations and
parameter values.
The conveyance cross-section at the mouth
has considerably less area than the first upriver section.
This
difference between the three estuaries is one of the principal
factors causing the observed differences in their response to
the ocean tidal function.
3,4
Prototype and Model Comparison
To adequately show that the model actually simulates a given
estuary, the following procedure is used.
One segment of
field data is chosen as a "calibration period" for adjustment
of physical parameters and friction factors within the
model.
When a match has been attained, the true
test of model
adequacy is made when a different segment of time is simulated
and then compared with measured field data for the same period.
If the comparison is within acceptable limits, the model can
be considered verified and useful predictions can then be made
concerning effects of possible future changes to the estuary.
This procedure was followed for all three estuaries under consideration.
A hypothetical future event is simulated for each estuary
as a sample of the predictive capability of the models.
48
FIGURE 4.1.1
Tidal Prism vs. Cross Sectional Area
/
/
F
I
-
D)A
/
0
/
/A/\
/
io8
/
0/
L
Mouth
I,-'
&
Alsea
/
I
-o
from Goodwin, Etett, and Glenne
(1970)
0
710
10 I
I
A
0
Siletz
//
-1
Interior
0
aquina
10'
Cross Section Area-ft
2
49
4.
4.1
Correlating Parameters
General Observations
The calibration, verification and testing of the estuarine
simulations given in Appendices B, C, and D has indicated that
the parameters of cross-sectional area, surface area and
friction all play important roles in controlling the tidal
phenomena.
O'Brien's (1931) observations, see Figure 4.1.1,
indicate a general relationship between entrance area and tidal
prism.
Since the tidal prism, in its simplest form, can be
expressed as surface area times tidal range, O'Brien's curve
can be interpreted as describing the influence of surface area
and cross-sectional area on the tidal range.
The description is not complete, however, as pointed out
by O'Brien (1969), Johnson (1973) and further illustrated in
Figure 4.1.1 by data from Goodwin, Emmett and Glenne (1970).
For "choked't conditions, i.e. with an amplification factor less
than 1.0, and for points other than at the mouth of estuaries,
additional relationships must be found to describe the tide.
Keulegan's (1967) analysis of tidal flow in entrances
introduced a parameter which he termed the "repletion coefficient",
The numerical value of this coefficient is determined
by the physical dimensions of the entrance and embaynient as
well as the amplitude and period of the ocean tide.
expression is:
The
AC (L3?
T
KR
where:
2irH
0
AS
4.1.2
i'L±mR)
KR
is the repletion coefficient-dimensionless
T
is the tidal period-seconds (SEC)
H
is the ocean tidal amplitude-feet (IT)
R
is the hydraulic radius of the entr.
feet (FT)
L
is the length of the entrance channel
/3
is a frictional coefficient - dimer3ionless
m
ce channel -
feet (IT)
is a velocity distribution coeffici:t at the
entrance (assumed to be unity)-dimeiinionless
Assuming conditions with negligible inertial
ffects and
with no variation of surface area (As) and cross-c :ctional area
(AC) with tidal elevation, Keulegan analytically xpressed tidal
characteristics as a function of
KR
Glenne, Goodwin, and Glanzman (1971) used nuinecical
techniques to solve a similar problem.
Their results were also
expressed in terms of a coefficient directly analogous to
Ke3gfl5 repletion parameter.
Both of these studies also assumed that the basin connected
to the ocean acted as a simple integrator of entrcce flows.
All points within the bay were assumed to rise and fall in
unison.
In most natural estuary systems this ass. :ption is
violated to some degree0
The fact that amplification of the tidal wave is observed
in many estuaries indicates that inertial effects èan not always
51
It appears that two coefficients may be required
be neglected.
to describe tidal conditions when friction and inertia forces
both play important roles.
4.2
Frictional Coefficient
The equations of motion and continuity, 2.1.1 and 2.1.2,
are rewritten here neglecting the inertial term in 2.1.1.
4.2.1
3IQIQ = 0
CAC
x
Q+AS=O
4.2.2
For positive Q values (flooding flow), subsUtution gives:
+
L
BC
AS2(
C2AC3
4.2.3
0
t/
where the space derivative is expressed in finite form with
h0 representing the ocean displacement, h. the displacement
inside the bay, and L the intervening length of channel.
Assuming a cosine function for the ocean tide,
h
0
= H CosCt,
4.2.4
0
and a phase shifted periodic function for the bay tide,
H f(t-Ø),
4.2.5
equation 4.2.3 can be rewritten as:
2
H cosçt-H.f(Qt-)+
0
1
L As H1G
2
(.tø2
CAC
Solving for the amplification factor gives:
= 0
4.2.6
52
4.2.7
H
f(t_Ø)_KFEf'(Qt.ØJ
where the frictionai coefficient, HF
,
is defined as,
4BCLAS2H
KF
4.2.8
C AC T
This coefficient, aside from the different chce of
resistance factors, is the inverted square of Keulcan's
repletion coefficient, equation 4.1.2, except for one detail.
The ocean tidal amplitude te2:m,
tidal amplitude, H.
,
the by
is replaced F
s a practical matter, it
akes little
difference whether H0 or H. appears in the equatio
defining
the friction parameter, HF The two amplitudes are related
through the non-dimensiona1 ratio
normally a known quantity and H
suggested that H0
Ht
Sine
is to be determicd? it is
be used instead of H
in equaton 4.28
to avoid possible trial and error situations which culd
inject uinecessary complications in further analyse.
4.3
Inertial Coefficient
Using a similar procedure to that in the previous section,
the equation of iotion written without the fricti; al term is,
431
gACt
èx
The time derivative of equation 4.2.2 is
=
'AS
.
?t2
4.3.2
53
Combining 4.3l and 4.3.2 and using the saie notation as in
section 4.2 gives,
AS
L
gAC
jj
4.3.3
t2
Rewriting in terms of the periodic functions, equations 4.2.4
and 4.2.5,
_H0cost+Hf(t_Ø)_
LH2
f''(ot4)
and solving for the amplification factor gives,
cost
H
f(t-Ø)-K1f(Ot-Ø)
5
where the inertial coefficient, K1 is defined as,
4.3.6
K
gACT
This parameter is not directly dependent on either the
pcean or bay tidal amplitudes.
As will be shown later, the inertial coefficient in conjunction with the frictional coefficient provides a means for
analyzing tidal phenomena which has not been avaiLble before.
4.4
Idealized Embayment
4.4.1
Schematization
The hypothetical embayment to be presented here is one
54
which integrates the tidal flow through the entrance. All
physical parameters such as depth, surface area, cross-sectional
area and the friction factor are assumed constant or, more
properly, are not a function of tidal stage.
and Glenne, Goodwin, and Glanzinan
(1970)
Keulegan
(1967)
have studied this
situation with the additional assumption of negligible inertial
effects. In spite of these severe limitations, considerable
insight
can be gained into the mechanisms of tidal flow which
is helpful in interpreting more complex situations. An illustration of this embayment is shown in Figure 4.4.1.
4.4.2
Figures
Displacement Curves
4.4.2
through
4.4.6
represent normalized tidal
displacement curves for various combinations of friction and
inertia forces acting on the simple system described above.
In each instance the heavy dark line is the cosine forcing
function at the mouth of the einbayment.
For the case of no inertia (I( =0), Figure
4.4.2,
increasing
friction values (Is,) clearly cause a reduction of the tidal
amplitude in the embayment,
This is the same effect reported
by Keulegan and called "tidal choking" by Glenne, et al.
It
should be noted that no embayment amplitudes greater than the
forcing function are possible under these conditions. Also,
at the time of extreme conditions (high and low water) in the
enibayment, the water elevation in the ocean and enibayment are
4
U,
U,
1.5
FIGURE 4.4.2
-
Idealized Displacement Curves for Various KF
with K1=O
0
1.0
Ocean tide
N
-
K = 0.1
.
K=10
F
7'
f
K=2.5
o...
0.5
-
-
ct
. _\.._\
-.
U
\'
......
.....
/
i<.io.o
imc angle
.,
.
I,
.
I,
..
n degrPe\j0
.
//
.
I,
...'
.
0
I
-.
.
F
.
...
/
.
\__
J0,_
/
40fl
FIGURE 4.4.3
1.5
Idealized Displacement Curves for Various
with
0.1
, --0
1.0
-
Ocean tide
T11T. FE
a)
-
4-J
5=100
-''I--a)
0
\\
C
a)
£
E
a)
U
me angle
..
'\.-.
400
a)
0.
a;
.4.0
Ui
I
1,5-
FIGURE 4.4.4
Idealized Displacement Curves for Various KF, with K1
0.2
,
/
'-,
/
-.-
\
\
\
/-
,-1
o
0.5
.
Ocean tLde
K = .0.1
'
\
.r-
/
lIz
1/
,F
-
V
/
-.-.--. . Y= 2.5
V'.
'.
\
\
.. _..
"S..
'
"c,
1/
1
iO.0
K,
'
/
"S
-4-..
...
...
./
/
.
/
/
"s'>..
"
'I
Time angle in degrees
I
bo
'.
'S
200
..
300
/
'S
I
'S.,
'.
N
/
I
...
I
L
...
I
\
/
\
/
'S
/
,
,:
/
/
...
/
/
I
'
5"
....
.,'
'.-
'5._S.
I
,.
'S....
'\
4
w
/
'-S
N
'.
-1.()
/'
.
/
/
,.
0
'
/
S.
'
'H
-
,
/
/
/
o
/
/
,-.
1/
:/
-.-..
-/
/..
400
I.
FIGURE 4.4.5
Idealized Displacement Curves for Various K , with KT= 0.3
F
0
iI
____
1.
Ocean tide
/
0.
0
4J
in'e angle in degre\
I,
Q
..'.
I
c.
\\
U)
0
-0.
....
/
/
....
,..-1
/
I
/
/
\
\%
/
/
I,.
.,.
/
/;
I..
./.
-1.
/
/
/
/
/
1
/
UI
. -.
-
61
equal.
This is true for all values of the frictional coefficient.
The succeeding four figures show how the embayment
displacement curves are modified by increasing inertial effects.
It is apparent that amplitudes in the bay can be greater than
that in the ocean for some KF, K1 combinations.
the inertial coefficient,
The larger
the greater can be the amplification.
At times of high and low water the ocean and bay water levels
are no longer equal.
from these graphs.
One additional observation can be made
The amplification effect is most pronounced
for low values of the frictional coefficient.
4.4.3
Effect of Coefficients on Tidal Amplitude
The effects which friction and inertia have on the
normalized bay amplitude are summarized in Figure 4.4.7.
The
noninertial case (K1 =0) as reported by Keulegan and Glenne, et al,
and this study is shown approaching unity at KF values below 0.2.
Increasing friction results in decreasing bay amplitudes.
Increasing inertial effect, not included in previous work,
is represented by a family of curves offset upwards from the
non-inertial case.
As pointed out before, the largest amplifi-
cations occur at low KF
values.
With increasing friction, the
curves become asymptotic to the original non-inertial case.
At K.. values less than about 0.1, inertia plays the
dominant role in determination of embayinent amplification or
attenuation.
Conversely, at K
values above 2.0, inertial
2.2.
Inertia
Coefficient
FIGURE 4.4.7
.1
Effect of
and
on Tidal Amplitude Ratio
0.8
-
0.6
0.4
o
0.2
0
r4
0
.01
L
I
I
TLL.
0.1
I
I
I
I
I
.1 LLL
.1..
.1
1.0
'riction Coefficient (K )
1
L. t
I
I
I L...
10
i
i
100
63
effects become small and friction becomes the dominant factor.
For the transition region between these limits however, both
friction and inertia are important and both effects must be
considered.
4.4.4
Effect of Coefficients on Displacement Phase Lag
The time delay, in degrees of a full tidal cycle, between
the occurrence of high (or low) water in the ocean and the
occurrence of high (or low) water in the embayment is called
the displacement phase lag.
This tidal characteristic was
alluded to in section 4.4.2 when describing the non-inertial
displacement curves.
Figure 4.4.8 defines how the phase lag varies for
different K1
and KF
conditions.
Again, the non-inertial case
is given by the lowermost curve with a family of curves offset
above, each representing increased values of the inertial coefficient.
K1
.
Phase lag is an increasing function of both KF and
Throughout the range of values studied, both friction
and inertia are important for definition of phase lag.
For
very high KF values, inertia becomes somewhat less important.
For the simple, single segment case, the ordinate in Figure
4.4.8 may be interpreted as stated above.
This is true since
slack tide at the bay entrance occurs at the same instant as
high, or low, water in the bay.
FIGURE 4.4.8
100
and K on High Tide and Slack
Effect of
Water Phase Lag Beween Adjacent Segments
E
)
80
1)
0
:
60
U
.3)
Note:
max
40
2 / /
1/
o
U
U
U
U
ilti-mentcae
1Hmax
i+2
H
'i
fcrsnggnent_case
20
/ inertia
Coefftcierit
(I)
U
1
.2
.01
0.1
1,0
Friction Coefficient (1(F)
100
65
L45 Effect of Coefficients on Maximum Veloc:Lty
Another important characteristic of tidal f1ow
is the
maximum velocity attained in the entrance channel.
The rela
tion between maximum velocity, basin dimensions a
ocean tide
can he determined through an empirical expression
or the tidal
prism. Tidal prism (ay') is defined as the volume e
water
which could be. contained between the high water and low water
planes within an embayment.
The tidal prism volua
equivalent to the average rate of inflow,
for half a tidal cycle.
to
The tidal prism volume c
approximated as tiie maximum inflow rate
of a tidal cycle (Keulegan, 1967).
V
Q,
:he embayment
also be
for I/FT fraction
Symbolically,
441
2
The above approximation can be expressed in terms
coefficient, C
is also
a
V
4'
Since
L
2AS II.
4.4.3
AC V
4;4.4
and
Qm
m
substitution of 4.4.3 and 4.4.4 into 4.4.2 gives,
ACVmT
2TrASH.
445
v
1
or, solving for V
V =
m
f
vAC
H.
i
4.4.6
This expression can be used to compute the maximum velocity
when C
V
is known as a function of the inertial and frictional
coefficients K1
known and H
and KF .
It is assumed that T, AC and AS are
has been determined, as outlined in section 4.4.3.
1
As shown in Figure 4.4.9, all C
values fall between 0.82 and 1.0.
Increased friction causes a reduction in C
v
occurs at K1 equal to 0.1 for KF
of Cv
The minimum value
values of 1.0 or less
Above K,. = 1.0, the minimum C value occurs at K... = 0.
V
I
A comparison of the non-inertial case, K1 = 0, indicates
some disagreement between Keulegan's analytical results and
that presented by this study using numerical methods.
4.4.10 shows the difference between the two cases.
Figure
If terms
originally neglected by Keulegan are retained, a shift in the high
KF
range of his initial curve is produced, shown as a dashed line
in Figure 4.4.10.
This modification brings the analytical and
numerical curves into agreement for both high and low asytntotes.
The starting and ending values agree but the shape of the curves
do not.
It seems probable that inclusion of higher order terms
in Keulegan's expansions are necessary for a better approximation to the distribution of C
V
4.4.6
Effects of Coefficients on Slack Water Phase Lag
Probably the most confusing aspect of tide prediction to
the week-end fishermen and tourist concerns the time lag
between high tide and high slack water or low tide and low slack
FIGURE 4.4.9
Effect of K, and KT oi' the Velocity Coefficient (Cu)
1.0
05
.10
.95
C)
.25
.50
.90
.0
L)
c)
.6
10
2.
Friction Coefficient
.80'
0
I
0.1
02
0.3
0.4
inertia Coefficient (K1)
0.5
0.6
0.7
0.8
C'
-s
FIGURE 4.4.10
Comparison of Analytical and Numerical Computation of Velocity Coefficient
1.00
.98
.
.96
-
.94.
0
92.
'
Keulegan (1967)
\
:
--- Keulegan (1967), recalculated
\
.90
0
0
.88.
82
0 Numerical analysis
.
80
.01
1
J
I
I
I
I
Li
.10
I
L
I
I
1.0
Friction Coefficient (KF)
10
-
--- --
water.
A typical conversation on this topic normally includes
a few choice expletives and an observation that the tide did not
turn until over an hour past the prediction.
The chances are
that the prediction forecast the time of the peak water level
and that it was nearly correct.
Since the fisherman has no
available tide gage, times of slack water have much more significance for him.
For any single element embayment, such as that under study
in this section, no time lag exists between tidal amplitude
extremes and the corresponding slack water in the entrance
channel.
If no water is being added to storage in the embay-
ment, by definition there is no flow in the entrance (assuming
no other inflow sources).
This is not true in general, and will
be taken up again later.
Figure 4.4.8 can be used directly to predict the time of
slack water for the idealized embayment.
4.5
Semi-Idealized Embayment
4.5.1
Schematization and Approach
For most natural estuaries, the assumption of constant
surface area and cross-sectional area is unduly restrictive.
section is included to investigate conditions when AS
and AC
are allowed to vary individually and then simultaneously with
displacement0
The plan view of the embayinent is the same as
shown in Figure 44.1
This
70
The approach originally taken was to define two additional
coefficients representing the surface and cross-sectional area
variability with stage.
Numerous graphs giving corrections to
apply to the ideal case were developed using these coefficients
as third variables.
4.5.2
Discussion and Recommendation
The results of the approach outlined above proved to be too
cumbersome and unwieldy for the purposes of this paper.
Inclusion
of the entire results would serve no useful function and be
unnecessarily confusing.
Some relevant findings from this work,
however, include the fact that the effects due to surface area
variability and the effects due to cross-sectional area variability can be superimposed to give net results.
The effects are
also off-setting throughout the range investigated and indeed
cancel each other in many instances.
As a substitute procedure, it is recommended that the upper
and lower sections of the tide wave be considered separately.
The various parameter values should be chosen at reference levels
representative of the average conditions prevailing during each
portion of the tide.
This procedure is followed in the multiple
segment sample computation in Appendix E with very satisfactory
results.
71
4.6
Estuaries With Multiple Segments
46.l
Schematization
The representation of a multiple segment, enibayment-river
system is the same as shown in section 33.
4.6.2
Reinterpretation of Coefficients
In the multiple segment case, additional water volume
upstream of a particular segment in question requires that the
K
and K.
definitions be modified.
All but one term in
these coefficients are either constants or are defined at fixed
points.
The terms B, L, AC, and C define a channel segment and
can all be considered lumped at the even numbered nodes.
The
AS term, however, is a measure of all the upstream surface area
in the system but it must be defined at the next adjacent upstream
node.
In the single segment case, AS can be interpreted as the
volume of water capable of being stored upstream of the entrance
cross section for a unit rise of water level in the embayinent.
For multiple segments a simple sum of the individual
surface area terms is not adequate because in doing so a tacit
assumption is made that the maximum displacement in each segment
is
the same0
To provide a more representative AS term, the
tidal prism concept is invoked.
Simply stated:
How much total
surface area, AST, when multiplied by the maximum displacement
72
of the first adjacent upstream segment, is needed to equal the
entire upstream tidal prism?
Mathematically this is:
AST.H. = AS.H. +AS.
j
j
j
where:
+AS.j+4H.j+4 + .....
1u1)
AST. =
or:
H.
3+2 j+2
j
('O,,4 .....)4.6.l
j is the odd numbered segment node in question and
N is the total number of segments.
For the single segment case,
required ASTJ = AS
equation 4.6.1 reduces to the
Since all the H values are twt known
prior to the computation, initial assumptions must be made and
later modified in an iterative procedure.
for the single segment case.
This is not necessary
The procedure will b
described
in detail in Chapter 5
The frictional and inertial coefficients for multiple
segment estuaries must now be written as:
47J2BL (AsT.)2H.
f
11
CACT2
\
Ii
%,
-
1
and
(K1).
4 114L.AST.
1
1
4.6.3
gAC.T
4.6.3
Effect of Coefficients on Amplitude, Displacement
Lag and Slack Water Lag
Figure 4,4.7 can be used directly to determine the ratio of
maximum displacements of any segment to the adjace:t downstream
H.
segment,
.
Figure 4.4.8 can aio he used to determine
FIGURE 4.6.1
Effect of KF and K1 on Maximum Amplitude Phase Lag Between Adjacent Segments
100
4J
0
0
2
Note: Use only for multi-segment
case
2Hmax
U
20
i
ØH
max i-2
0)
rtia
icient
44
:T )
0)
CO
0i
.1
1.0
Friction Coefficient (K)
10
-4
74
the lag of slack water in degrees, after the occurrence of high
water in the adjacent downstream segment.
The displacement lag
for the multiple segment case must now be determined from
Figure 4.6.1.
This figure shows that for any given KF , K
conibination the
displacement maximum occurs earlier in a multiple segment estuary
than in the single segment case.
Since slack water occurs at the same time in both cases,
this explains the observations referred to in section 4.4.6.
Many
locally published tide predictions list times of high and low
water only.
In the case of fishermen who can only judge the
tide by its direction of flow, the high-low prediction may be
several minutes to nearly an hour ahead of when slack water
really occurs.
4.6.4
Selected Results
Table 4.6.1 summarizes
the results of eight hypothetical,
two-segment estuaries covering a wide range of KF , K
conditions.
For each segment the computed and graphically determined values
of the amplitude ratio, displacement phase lag, and slack water
phase lag are given for comparative purposes.
Most graphically
determined values agree very well with their numerically computed
counterparts.
The graphical procedure may tend to overestimate
the amplitude ratio at low KF and high K1
combinations.
Table 4.6.1
Verification of Graphical Procedure for Determination
of Amplitude Ratio Amplitude Phase Lag and Slack
Water Phase Lag for To Segment Estuaries
Scgment 1
KF
.43
Segment 2
Kr
ornp.
graph.
.21
1.10
1.14
T21
T'
,19
.17
.38
.24
.70
.38
.23
.66
1.03
Th14
1.26
2.93
.97
,83
.60
.36
.24
.63
9,2
8.0
9.Q
J69
.3
.23
comp.
ax
graph.
comp.
graph.
29
51
59
28
50
34
60
59
73
65
62
78
32
58
73
79
84
75
68
68
83
77
92
91
88
87
91
91
90
88
7i
68
øax0
H2/111
_____ØQ=0
comp.
graph.
.10
.10
.10
.10
1.12
1.09
1.12
1.09
.92
.67
.92
.68
38
68
89
105
.40
.40
.40
.40
L58
1,42
1.06
1.58
1.40
1.04
99
105
115
.70
.68
KF
K1
.11
.34
.95
2.4
.11
.30
.89
2.4
comp.
i
graph
33
65
91
Tö
9
107
120
126
-4
U,
76
5.
5.1
Predictive Algorithm
Data Requirements and Assumptions
5.1.1
Assumptions
All assumptions inherent in the digital model used to
develop these procedures are fully applicable.
are listed in section 2.2.
The assumptions
In addition, the fresh water inflow
must be neglibible when compared with the tidal flow at any
cross-section.
5.1.2
Physical Data
In order to apply the methods presented in this chapter,
certain basic information must be available.
Much of this can
be readily determined from published charts, maps or aerial
photographs.
Extensive field surveys should not be necessary
in most instances.
The following is a list of physical parameters needed for
performing the necessary computation.
1.
AS, the surface area of the enibayment or of each
unit in the multi-segment case - FT2
2.
AC, the entrance cross-sectional area of the
embayment or of each unit in the multi-segment
case - FT
2
77
3.
L, the length of the exnbayment entrance channel
or length between segment centroids if in the
multi-segment case - FT
4.
B, the conveyance width of the entrance channel or of
each channel reach in the multi-segment case - FT
Each of these parameters should be defined at the mid-tide
elevation of the ocean tide applied at
the entrance. Normally
this is taken as Mean Sea Level.
5.1.3
Hydraulic Data
The following hydraulic parameters must also be known or
estimated:
1.
T, the period of the forcing tidal function at the
entrance - SEC
2.
C, the Chezy coefficient of friction in the entrance
channel or in each channel segment if in the multi3-
segment case - FT2 /SEC
3.
H0
, the amplitude of the tidal forcing function at
the entrance - FT
4.
B2
, H
, H6 ......, the initial estimate of tidal
amplitude within each segment of a multi-segment
estuary - FT
r1
5.2
Computational Procedure and Graphical Analysis
5.2.1
Single Segment Case
Given the data listed above, the procedure far a single
segment estuary is quite straightforward.
1.
Compute the frictional and inertial coefficients:
K
22
411 2BL(As)21j.
F
1
C ACT
gAC T
7
2.
Enter graph 4.4.7 to determine the ampiitu1e
H
ratio between the eobayment and the ocea,
3.
Enter graph 4.4.8 to determine, the phas
the Ocau and
in degrees, between high tide i
high tide in the ebayment
(
4Ø
of 'high tide in the eayment (0
water in the channel
lag,
)
Hmax
The time
) c"d slack
) are the smc- for this
case.
4.
Enter graph 4.4.9 to determine the veloc'ty
coefficient
.
Compute the maximum vioctiy
attained in the connecting channel as:
v
max
_2iL
T
vAC H V
With this procedure it is possible to predict ;hat effect
a change in any of the physical or hydraulic paramt ers will have
on the response of the system as defined by ampiitie, phase lag,
and maximum velocity.
'I'
79
Multiple Segment Case
5.2.2
The algorithm for a multiple segment estuary is, unfortunately,
more complex
segment case.
than the procedure just outlined for the. single
The reason is that downstream and upstream responses
are not independent, making it impossible to compuc one without
knowledge of the other.
This drawback can be overcome, however,
if a set of initial conditions is assumed and an iterative
procedure applied.
The basic steps in this algorithm are as
follows:
1.
Assume a maximum tidal amplitude value in each of the
estuary segments upstream of the mouths
Unless other
information is available, segment amplitudes are
normally set equal to the ocean tide fo cing function
ampi:tude,.
2.
Compute the frictional and inertial coefficients of
the next upstream segment starting at the estuary mouth.
K
F
NOTE:
K
=
C2AC3T2
gAC 16
The surface area term is defined as an
amplitude weighted sum of upstream segment surface
areas as given in section 4.6.2.
3.
Determine the first approximation to thc maximum
amplitude in the next upstream scgtnant from Figure 4.47.
4.
Repeat steps 2 and 3 for each estuary segment.
5.
Repeat this procedure until satisfactory
convergence
of the amplitude in each segment has been achieved.
6.
Once convergence is attained, use the final KEand K
values for each segment to determine the phase lag of
slack water from Figure 4.4.8.
The phase lag of high
water can be found from Figure 4.6.1.
Fully developed examples of both single and multiple segment
cases can be found in Appendix E.
5.3
Discussion
5.3.1
Purpose
The fact that a relatively simple, lumped parameter approach
can produce valid and representative descriptions of complex tidal
phenomena in a real estuary is significant and verifies the
hypothesis of this paper.
The procedure illustrated with the two examples in Appendix
E was developed to aid the study of real estuaries and the effects
of proposed changes (dredging, filling, etc.) when more sophisticated
techniques are not available or cannot be implemented because of
time, fiscal or other constraints.
Even when simulation models
are available, it is often desireable to have a screening technique
to reduce the number of conditions which must be tested.
algorithm would be very effective in this capacity.
The
81
5.3.2
Accuracy
The accuracy of any method is, of course, no better than the
accuracy of the input data.
Of the two coefficients, KF and K1
the former varies over a much wider range of values and is more
sensitive to inaccurate or nonrepresentative data.
Representa-
tiveness is perhaps the largest potential source of error.
Engineering judgment plays a large roll in this aspect of the
procedure.
1.
The guidelines are few and very general.
Use what appear to be controlling cross-sectional
areas to define the break between segments.
2
Keep physically similar regions, which may respond
as a unit, together in one or more segments; in
other words, do not combine a portion of a bay and
a portion of a river in the same segment.
Because of the diversity of natural conditions, and because
of the range of information available on different estuaries, it
is impossible to define accuracy limits.
Each user will have to
judge the quality of his particular input to determine the
probable quality of output.
In the example using the Siletz estuary, Appendix E, the
physical data was largely taken from existing charts with some
local supplements where needed.
but certainly not ideal.
It can be considered as adequate
In this case the probable
errors are:
,
displacement
--
0.2 feet
displacement phase --
5 degrees
slack water phase
5 degrees (more at low slack)
--
maximum velocities --
20 percent
6.
6.1
Summary, Conclusions and Recommendations
Sununary
A one-dimensional computer model was developed to simulate
tidal flow in estuaries.
Solution of the partial differential
equations of conservation of mass and momentum is done implicitly
using a carefully chosen finite-difference approximation to the
governing equations.
After appropriate convergence and accuracy tests using an
analytically solvable case, the model was calibrated and
verified for three Oregon estuaries; the Yaquina, Alsea, and
Siletz0
With knowledge that the model performed well on three
real cases, it was then applied in a research function.
hypothesis investigated with the aid of the model is:
The
The
response of some natural estuaries to ocean tides can be defined
in terms of lumped coefficients which incorporate physical and
hydraulic parameters defining the unique characteristics of a
particular estuary and the imposed tide.
To this end, two coefficients were theoretically derived
which characterize the forces dominating the tidal phenomenon,
friction and inertia.
The friction coefficient, KF , incorporates
the parameters of channel width, channel depth, channel roughness,
channel cross-sectional area, surface area, tidal amplitude and
tidal period.
The inertial coefficient, K1 , incorporates
channel
length, channel cross-sectional area, surface area, tidal period
84
and the acceleration due to gravity.
Both coefficients are
dimensionless.
To determine whether these coefficients would indeed be
useful in defining estuarine tidal response, several hundred
hypothetical estuaries were tested in the model.
By selectively
varying different parameters both individually and in unison,
behavior of the coefficients could be observed and patterns
recognized.
By using this technique, a large volume of inforxna-
tion on a wide range of estuaries was obtained in a relatively
short time.
The model-generated data defined several, graphical relation-
ships which describe the maximum and minimum displacement, displacement phase, slack tide phase, and maximum ebb and flood velocities
as functions of the friction and inertial coefficients.
With
this foundation, an algorithm was implemented which incorporates
the graphical results into a step-by-step procedure which can be
applied to any estuary meeting the stated assumptions and acknowleged
limitations of the investigation.
A method is shown to handle
assymetric distortion of the tidal wave due to variations in
physical parameters with water depth.
The algorithm was tested with two completely described
examples.
The first is Marquarie Harbour Inlet, Tasmania, which
The
is a single segment embayinent described in the literature.
second case is the Siletz Estuary for which data was available
from the early stages of this work.
Both cases proved to be
very satisfactory with algorithm and observed results generally
well within acceptable accuracy limits.
6.2
Conclusions
From the results of this study, several conclusions can be
drawn:
1.
Relatively simple models can be successfully applied
to simulate many types of natural estuaries.
2.
The upper and lower segments of the tide wave can be
considered to react nearly independently of each
other and therefore can be handled as separate cases.
This enables meaningful investigations of estuaries
whose characteristics vary considerably with water
depth.
3.
In general, the inertial coefficient, K1
, does not
vary as widely as the frictional coefficient, KF
In many instances KF can be considered the dominant
term with K1
acting in a "finetuning" capacity.
In no instance can either coefficient be neglected,
however.
4.
In general, increasing KF values cause decreased
amplitudes and increased phase lags.
Increasing K1
values cause increased amplitudes and increased
phase lags.
5.
The friction and inertial coefficients developed in
this paper can be applied in natural estuaries to
determine response to ocean tides.
6.
The procedures presented can also be used to predict
the hydraulic changes expected from proposed engineering works at the mouth or within the estuary.
6.3
Recommendations for Further Study
Several aspects of this investigation could be amplified
and extended.
1.
The model itself could be made more efficient by
redefinition of the arrays and by use of a faster
convergence scheme.
2.
Determination of bottom friction in estuaries is
presently very subjective.
More precise definitions
should be developed.
3.
Theoretical development of the friction and inertial
coefficients should be extended or modified to include
effects of upstream river inflow,
This would make the
present analysis even more powerful by increasing the
potential number of applications.
4.
It is possible that the concepts put forth in this
paper may have useful corrolaries in two-dimensional
models which would aid in their calibration.
Presently,
two-dimensional model calibration is a very subjective
art.
Bibliography
Baltzer, R.A. and C. Lai. 1968. Computer simulation of unsteady
flows in waterways. Proceedings American Society of Civil
Engineers, HY4, 94: 1083-1117.
Bella, D.A. and W.E. Dobbins. 1968. Difference modeling of stream
Proceedings American Society of Civil Engineers,
SA5, 94: 995-1016.
Blanton, J. 1969. Energy dissipation in a tidal estuary. Journal
of Geophysical Research 74(23): 5460-5466
Bruun, Per0 1966. Tidal inlets and littoral drift. Amsterdam,
North Holland Publishing Company, l93o
Callaway, R,,J., Ky. Byram and G,R0 Ditsworth0 1969. Mathematical
model of the Columbia River from the Pacific Ocean to Bonneville Dam, Part I. Corvallis, Oregon, Federal Water Quality
Administration N0W0 Water Lab.
Darwin, G.H. 1883. Report on the harmonic analysis of tidal observations. Cambridge, British Association for Advancement of
pollution0
Sciences.
Defant, A0 l9l9 Die hydrodynamisehe Theorie der Gezeiten und
Gezeitenstromungen in Englischen Kanal und dem sudwestlichen
Teil der Nordsee0 Denkschr. Wiener Akad0 Wiss, 96
Defant, A0 l925 Gezeitenprobleme des Meeres in Landnahe. Probleme
der Kosmischen Physik, 6:8Op.
Defant, A. 1960. Physical Oceanography. Oxford, Pergamon, 598p.
Doodson, A.T0 1922. The harmonic development of the tidegenerating potential. Proceedings Royal Society of London,
100:305-329.
Dorrestein, R. 1961. Amplification of long waves in bays. Gainesville, University of Florida, XV(12):2lp.
Dronkers, J0J. 1964. Tidal computations in rivers and coastal
waters. Amsterdam, North Holland Publishing Company, 5l8p.
Einstein, H0A. and R.A. Fuchs. 1954. The prediction of tidal flows
in canals and estuaries. 3Op, (First report on Contract
DA-22-079-eng-124-eng U.S. Army Corps of Engineers)
Einstein, H.A. and R.A. Fuchs. 1956. The calculation of tidal
flows in the Panama-Sea-Level Canal by the linearized method.
4p. (Second report on Contract DA-22--079-eng-l24-eng-U.S.
Army Corps of Engineers)
Euler, L. 1755. Principes generaux du mouvement des fluides.
Hist.Acad.R.Sci. Belles Lettres, 274p.
Evangelisti,
1955. On tidal waves in a canal with variable
cross section. In: Proceedings Sixth General Meeting International Association for Hydrualic Research, The Hague,
Netherlands. paper A-b.
Fjeldstad, J. 1929. Contributions to the dynamics of free progressive tidal waves. Scientific Research Norwegian North
Polar Expedition
1918-1925, 4(3).
G0
"Maud't
Glenne, B., C.R. Goodwin and C.F. Glanzinan. 1971. Tidal choking.
Journal of Hydraulic Research, 9(3):321-333.
Glenne, B. and R.E. Selleck. 1969. Longitudinal estuarine diffusion
in San Francisco Bay, California. Water Research, 3:1-20.
Glenne, B. and T. Simensen. 1963. Tidal current choking in the
landlocked fjord of Nordasvatnet. Sarsia 11, University of
Bergen, Norway, March 19:43-73.
Goodwin, C.R., E.W, Emmett and B. Glenne. 1970. Tidal study of
three Oregon estuaries. Corvallis, Oregon State University,
Bulletin 45, 33p.
Hansen, W. 1956. Theorie zur Errechnung des Wasserstandes und der
Stromungen in Randmeeren nebst Anwendungen. Tellus, 8(3):
287-300.
Ippen, A.T. (ed.). 1966. Estuary and coastline hydrodynamics.
New York, McGraw-Hill. 744p.
Ippen, A.T. and D.R.F. Harleman. 1958. Investigation of influence
of proposed international Passamaquoddy tidal power project
on tides in the Bay of Fundy. Report to U.S. Army Corps of
Engineers, Boston.
Ippen, A.T. and D.R.F. Harleman. 1961. Analytical studies of
salinity,intrusion in estuaries and canals, phase 1:
One-dimensional analysis. Technical Bulletin No.5, Committee
on Tidal Hydraulics, U.S. Army Corps of Engineers.
Jeglic, J.M. 1967. Mathematical simulation of the estuarine
behavior. 84p. (Report on Contracts PH 86-66-119-and
P0 50577-67 U.S. Federal Water Pollution Control Administration)
Johnson, J.W. 1973. Characteristics and behavior of pacific coast
tidal inlets. Proceedings American Society of Civil Engineers, WW3, 99:325-339.
Kamphuis, J.W. 1968. Mathematical model study of the propagation
of tides in the St. Lawrence river and estuary. Ottawa,
National Research Council of Canada, 152p.
Kent, R.E. 1960. Turbulent diffusion in a sectionally homogeneous
estuary. Proceedings American Society of Civil Engineers,
SA2, 86:15-47.
Keulegan, G.H. 1967. Tidal flow in entrances, water-level
fluctuations of basins in communication with seas. Technical
Bulletin 14, U.S. Army Corps of Engineers. 88p.
Knudsen, H. (ed.). 1901. Hydrographical Tables, reprinted,
Copenhagen, Tutein and Koch.
Kulm, L.D. and J.V. Byrne. 1967. Sediments of Yaquina Bay, Oregon.
Estuaries, American Association for the Advancement of
Science, 226-238.
Lagrange, J.L. 1781. Memoire sur la theorie du mouvement des
fluides, Nouv, men. Acadamie Sd. Belles Lettres Berlin,
4:p695.
Lamb, H. 1895. Hydrodynamics. Chapter VIII, Cambridge University
Press.
Lamb, H. 1932. Hydrodynamics. 6th ed. Canibridge University Press,
Laplace, P.S. 1775. Recherches sur plusieurs points dii systeme
du monde. Mem. Acad. R. Sci. p75.
Leendertse, J.J. 1967. Aspects of a computational model for longperiod water wave propagation. Santa Monica,The Rand
Corporation, 165p.
Leendertse, J.J. 1970. A water-quality simulation model for wellmixed estuaries and coastal seas: Volume I, Principles of
computation. Santa Monica, The Rand Corporation, 7lp.
Leendertse, J.J. 1971. A water-quality simulation model for
well-mixed estuaries and coastal seas: Volume II, Computation
procedures. New York, The New York City Rand Institute, S3p.'
Leendertse, J.J. and E.C. Gritton. 1971. A water-quality simulation
model for well-mixed estuaries and coastal seas: Volume III,
Jamaica Bay simulation. New York, The New York City Rand
Institute, 73p.
Linsley, R.K. Jr., M.A. Kohier and J.L.H. Paulhus. 1958. Hydrology for Engineers. New York,McGraw-Hill, 34Op.
Masch, F.D. 1969. A numerical model for the simulation of tidal
hydrodynamcis in shallow irregular estuaries. Technical
Report HYD 12-6901, The University of Texas at Austin.
Munk, W.H. and D. Cartwright. 1966. Tidal spectroscopy and
prediction. Philosophical Transactions Royal Society of
London.
Neumann, G. and W.J. Pierson, Jr. 1966. Principles of Physical
Oceanography. London, Prentice-Hall, 545p.
Newton, I. 1687. Philosophiae naturalis principia mathematica.
(Cited in: Proudman, J. 1952. Dynamical Oceanography.
New York, Dover, p14)
M.P. 1931. Estuary tidal prisms related to entrance area.
Civil Engineering, American Society of Civil Engineers,
1(8) :738-739.
O'Brien, M.P. 1967. Equilibrium flow areas of tidal inlets on
sandy coasts. In: Proceedings Tenth Conference on Coastal
Engineering, American Society of Civil Engineers, 676-686.
O'Brien, M.P. 1971. Notes on tidal inlets on sandy shores.
Hydraulic Enigneering Laboratory Report No. HEL-24-5,
University of California.
O'Connor, D.J. 1965. Estuarine distribution of non-conservative
substances. Proceedings American Society of Civil Engineers,
SAl, 91:23-42.
Orlob, G.T., R.P. Shubinski and K.D. Feigner. 1967. Mathematical
modeling of water quality in estuarial systems. In:
Proceedings National Symposium on Estuarine Pollution,
Stanford University, 646-6 75.
Perroud, P. 1959. The propagation of tidal waves into channels
of gradually varying cross section. Technical Memorandum
No. 112, Washington, D.C., Beach Erosion Board.
Pritchard, D.W. 1952. Salinity distribution and circulation in
the Chesapeake Bay estuarine system. Journal of Marine
Research, 11(2) :106-123.
Proudman, J. 1952. Dynamical Oceanography. New York, Dover, 4O9p.
Refield, A.C. 1950. The analysis of the tidal phenomena in narrow
embayiuents. Papers in Physical Oceanography and Meteorology
No. 529 Woods Hole Oceanographic Institution, 11(4).
Reid, R.O. and B.R. Bodine. 1968. Numerical model for storm surges
in Galveston Bay. Proceedings American Society of Civil
Engineers, WW1, 94:33-57.
Simmons, H.B. 1969. Use of models in resolving tidal problems.
Proceedings American Society of Civil Engineers, HYl,
95:125-146.
Taylor, G.I. 1919. Tidal friction in the Irish Sea. Philosophical
Transactions Royal Society of London, 22O:pl.
Thompson, W. 1879. On gravitational oscillations of rotating
water. Proceedings Royal Society of Edinburgh, lO:p92.
Tracor, Inc. 1971. Estuarine modeling; an assessment. 497p.
(Report on contract 14-12-551 Water Quality Office, U.S.
Environmental Protection Agency).
U.S. Fish and Wildlife Service. 1970. National Estuary Study.
Volume 1, 9Op.
U.S. Geological Survey. 1961-1967. Surface Water Records of
Oregon.
U.S. Coast and Geodetic Survey. 1969. Tide tables, high and low
water predictions, west coast North and South America, 224p.
Van de Kreeke, J. 1967. Water-level fluctuations and flow in
tidal inlets, Proceedings American Society of Civil Engineers,
WW4, 93:97-106.
Verma, A.P. and R.G. Dean. 1969. Numerical modeling of hydromechanics of bay systems. Proceedings Civil Engineering
in the Oceans-Il.
Appendicies
91
Appendix A
Computer Model Documentation
Initial developmental work on the model was accomplished
using the time sharing system implemented on the CDC 3300
computer at Oregon State University.
Finalization of the pro-
gram and production runs were made using a revised version of
The
the model on a batch process IBM 360-65 in Tampa, Florida.
following model documentation is based on the IBM version.
A.l
Input
Data input to the model is accomplished in two steps.
First, a set of cards describing the physical characteristics
of the estuary are read.
There is one of these "characteristic"
cards for each estuary segment.
Following this is a card
defining the forcing function, time step, and convergence
parameters to be applied to the estuary in question.
Any num-
ber of "parameter" cards can follow the "characteristic" cards.
Each "parameter" card contains the information for one model
rim under the previously defined estuary characteristics.
Flags
can be placed in the data stream so that any nuxiberof
"characteristic" - "parameter" combinations can be included in
a single program submittal.
Table A.l shows a typical set of
"characteristic" data along with the associated "parameter"
data.
Variables in the table headings are defined in this
appendix under the List of Variables section.
92
TABLE A.l Model Input
Characteristic Data
INPUT DATA FOP EACH CHANNEL SEGMENT IN FOLLOWING ORDER
IS
LLC
CAVG
IC
SC
ULC
90.0
90.0
85.0
85.0
0.330E
0.Ô1OE
0.360L
0.130E
0.800E
0.100E
0.100E
0.100k
04
04
04
04
SS
0.92SF
0.100E
0.800E
0.300E
01
02
01
01
ULS
07
06
05
06
0.+50E
0.300E
0.300E
O.550E
0.600E
0.h00L
0.600E
0.400E
0
0+
04
0#
0.100E
0.150E
0.JOUE
0.JOOE
LLS
08
08
08
07
B
04
04
04
03
0.308E
0,190E
0.120E
0,400L
L
0.800E 07 0.295E 03 0.700E
0.11OE 08 O.480E 030.280E
0.600E 07 0.400E 03 0.413E
0.380E 07 0.300E 03 0.355E
Parameter Data
SECTICNS=
4
TIME INCREMENT
10.0
RIVEP FLOW=
0.0
OCEAN AMPLIT[JDE= 3.81
OCEAN QFS[T= 0.53
ERROR LiMIT(CFS)
1.00
[PROP LJMIT(FT)
0.0400
ITERtTION LIMIT
100
08
08
08
07
04
05
05
05
93
A.2
Sample Output
Sample output is shown in Table A.2.
Values of H are
given at 30 degree increments for each odd numbered station.
Q and V values are given for each even numbered station at
one-half a time step prior to the corresponding displacement
value.
A summary table is provided which gives the following
information.
1.
Maximum and minimum displacements and their times
of occurrence in degrees.
2.
Maximum and minimum discharges and their times of
occurrence in degrees.
3.
Maximum and minimum velocities and
their times of
occurrence in degrees.
4,
Times of slack water (no flow) in degrees.
Interpolation for maximum and minimum points is done using
fitted parabolic sections.
Linear interpolation
is used for
determining the time of slack conditions.
A flow chart, listing of the program and list of variables
are given in the next three sections.
TABLE A.2 Model Output
ANGLE
STATION NUMBER--(1)
(2)
(3)
(4)
(5)
(6>
(7)
(8)
(9)
(10)
-5, 0
-5. v:
2.0536
0.3232
2.5795
1.2161
-0.4290 00
0.1340
04
0.5131)
04
0.2260 05
0.1080 05
0.123E
01
0.912E
00
0.550E 01
0.150E 01
30. H.
25. 0:
25. v:
1.7409
3.0170
2.3937
3.2604
3.8296
-0.408D 00
0.5561)
04
0.1770
04
0.9920 04
0.157D 05
0.955E 00
0.121E 01
0.360E 01
0.130E 01
60. H:
55. 0:
55. v:
2.4350
90, H:
3.6775
2.4780
3.2206
2.0230
0.5300
-0.1820 05 -0.7311) 04 -0.2251) 04 -0.9660 02 -0.6710 00
-0.470E 00 -0.411E-01
-0,463E 01 -0.999E 00
0. H
85. 0:
85. v:
4.3400
-0.4300 0'+
-0.101
01
3.0370
d.'.08[)
3.1436
3.3343
0.4201) 04
0.1700 04 -0.1440 00
0.858E 00
0.765E 00
3.3476
0/+
0.527E 00
2.6108
2.2358
1.6040
120. H -1.3750
1.0754
-0.2090 05 -0.9600 04 -0.5020 04 -0.1651) 04 -0.4740 00
115. 0:
-0.578L 01 -0.1408 01 -0.1138 01 -0.7858 00
115. V:
1.5031
0.6122
1.2237
-0.0109
150, H: -2.7695
0.7200 00
1z5. 0
-0.1940 05 -0.9720 04 -0.4440 04 rO.121L) 04
-0.6888 00
-0.I1OE 01
-0.5888 01 -0.1548 01
145. V:
180. H
175. 0
175. V
0.342
-0.4166
0.2777
-1.0691
-3.2800
0.3520-01
04
-0.9320
03
-0.391D
-0.1510 05 .-0.904D 0
-0.5068 01 -).15b6 01 -0.1078 01 -0.6318 00
(11)
(12)
(13)
210.
H
205. 0:
205. V:
-2.7698
-1.7689
-1.3063
-0.5810
-0.1190
-0.9540 04 -0.7511) 04 -0.342D 04 -0.7740 03 -0.9700 00
-0.34b6 01
-0.104E 01
-0.139E 01
-0.628L 00
240. H: -1.3750
-1.6385
-1.76o6
-1.3030
-0.7651
2:35. 0:
-0.2010 04 -0.4000 04 -0.272D 04 -0.6181) 03
O.626D 00
235. V:
-0.720E 00
-0.760E 00 -0.900E 00 -0.606E. 00
270. H:
265, 0:
265. V:
0.5300
300. H:
295. 0:
295. V:
0.4688
2.4350
-0.1000
-0.9293
-1.4114
0.3031) 04
0.1780 05
0.8020 04
0.1290 00
0.1300 03
0.516 01
0.9u9E 00
0.138E 00
0.131E 01
330. H:
0.9547
3.H2'5
1.5510
-0.7870
0.0810
0.2220 05
0.4231) 04
0.8301) 03
0.82D 04
0.2360 00
0.589E 01
0.720E 00
0.113E 01
0.148E 01
325. 0:
325. V:
3f0. H:
355. 0:
355. V:
,,
-1.1094
-1.6346
-0.5665
-1.2656
0.4940 04 -0.6420 03 -0.453D 03 -0.515D01
0.344E 01
0.682E 00 -0.IOL 00 -0.512E 00
0.1081) 05
2.5793
4.3400
0.2261) 05
0.550E 01
2.0583
1.2156
0.3223
0.513D 04
0.1340 04 -0.5120 00
0.912E 00
0.123E. 01
0.1SOL 01
0.1081) 05
HMAXT
HMTNM
0MXIT
QMINT
-1.d4J'1.6
3.368, 54.4
-1.1hb2'+1.2
-2096?.117.8
-9796.,133.2
VMAXIT
VMINIT
5.9c,331.6
-5.9b,133.1
-1.56,164.7
00T,T
3.325, 40.3
2319r.,3'+d.6
50.3,?38.8
10832.
1.+
1.51,.-i45.2
64.1,24.1
3.482, 73.0
-1.64/,266.2
5566.,
22.1
-50d2.,115.7
1.24,
7.2
-1.14,122.6
76.6,268.9
3.719, 84.0
-1.455,291.2
1836., 38.5
-1646.,114.7
0.96, 17.5
-0.79,119.1
84.0,291.2
A.3
Simplified Plow Chart
START
DATA INPUT
TTT..Tr
TABLE HEADING
DISPLACEMENT, DISCHARGE, AND
VELOCITY VALUES AT EACH SEG-
NENT OF THE ESTUARY FOR EACH
TIME INTERVAL
HAS
ADJUST
CONVERGENCE
no
INITIAL
BEEN REACHEr) AT
VALUE S
N:::
yes
no
REACHED BETWEEN
SUCCESSIVE ,,/
\ CYCLES?/
yes
97
4,
WRITE DATA OUTPUT TABLE
OF SEQUENTIAL DISPLACE-
MENT, DISCHARGE, AND
VELOCITY VALUES
.:r-1.1
COMPUTE MAXThUN AND MINIMUM
DISPLACEMENT, DISCHARGE AND
VELOCITY VALUES WITH TINES OF
OCCURRENCE AND ALSO THE TIMES
OF SLACK WATER AT ALL SEGMENTS
WRITE MAX, AND MIN
PARAMETERS FOR EACH SEGMENT
IS
ANOTHER
GO
CASE OR DIFFEREN\
yes
TO
ESTUARY TO BE
[TART
YZED
no
I END
A.4
Program Listing
DDENSION B(20)
1V (20,2) ,SC (20) ,SS (20) ,HMAX (20) ,HMIN (20) ,QMAX (20)
00030
2QMIN(20),TMAXH(20),TP1INH(20),TMAXO(20),
3HR(20) ,TMIN((20) TO1 (20) ,TQ2(20) ,ULC(20) ,ULS(20)
0005Ô
4SST(23),CA(20),CVU(20),CVL(20),
5HRU(20) ,HRL(20) cVP(20) VMAX(20) ,VMIN(20) ,TMAXV(20),
6flhJNV(20),00(20),CCON(20)
00070
00080
00090
INTEGER XXX,XXX
REAL.
1ST (23)
L(20),IC(20),IS(20),LLS(20),LLC(20)
(20) ,KI (20) ,KSS (20) KCS (20) ISTH (20)
2KG (20) , ISHL (20) KIL (20) , ISTL (20)
00120
DOUBLE PRECISION H(20,2),HP(2O,HT,DH,HTT,Q(20,2),AS(2O),
1AC(20) *CC(20) ,8B(20) ,A].,A2,HAVG,DQ
24
210
READ(5,210) X
FORMAT(12)
XX=2*X
Ix=xx+1
00160
00170
00180
I
XXXXX+2
JPITE (6,212)
212 FORMAT('l',/////.' INPUT DATA FOR EACH CHANNEL SEGMENT IN
I
,FOLLOWING ORDER'/'
CAVG
IC
SC
ULC',
2
LLC
IS
SS
ULS
LLS',
3
'
'
8
DO 1 Ir2,XX,2
READ(5,211) CA(I) ,IC(J) ,SC(I) ,ULC(j) ,LLC(J) IS(I1) ,SS(I+1)
1ULS(I.1),LLS(I1),B(I),L(I)
211 FORMAT(F4.0,1OE70)
DOt!)=IC(I)/8(I)
CCON(I)=CA(I)/(DOCI)**.167
WRITE(6,201)CA(I),IC(I),SC(I),ULC(I),LLC(I),IS(I.1),
1SS(I1),ULS(I1),LLS(I1),B(1),L(I)
201 FORMAT(' ',
F6,I,1OE1O.3)
1 CONTINUE
21 REO(S,213) DT,DST,OR9H0,DH0,ERRER,LIM
213 FORMAT C7F10.0I5)
00190
00330
00350
IF(OT) 25e24,22
22 DTTOT44700./360.
QROR
00410
00450
J JM = 0
WRITE (6,108) X,DT,QR,H0,DHO,ER.ERR,LIM
108 FORMAT('1',/////,' SECTIONS ',13/' TIME INCREMENTS ',FS.1/
RIVER FLOW= ',F8.1/' OCEAN AMPLITUDE ',
1
?FSr2/ OCEAN OFSETS 'F5.2/ ' EPR0 LD4IT(CFS)
',S.2/
ERROR LIMIT(FT)= F6.4/ ' ITERATION LIMIT ',IS///)
3
'
'
IC (XXX) =JC(XXX-2)
00 3 P2XXX,2
IIJ-1
Q(I,1)0R
QP(I)0R
VP(I)=OR/IC(I)
00650
00660
0O680
H(II,1)H0+DHO
HP (II) H0DH0
Q1AX(I)=QR
OMIN(I)OR
VMAX(I)=QP/IC(I)
VMIN (I) =OR/IC (I)
3 HTTH0+DH0
C=1
TO.
00700
00710
00720
jIT=0
9 TT+DT
TPT_.5*DT
00730
00740
IF(T.EQ.DT) JIT=JIT+1
IF(JIT.LE.20) GO TO 79
WRITE (6,78)
78 FORMAT(' EXCEEDED CYCLE LIMIT')
GO TO 21
79 MMO
JJ=0
00750
00760
1
I
D0O
00770
H(1,2)DHO+H0*COS(T*3.14159/180.)
DH=(H(1,1)-+3(1,2) )*(,1)
00800
00810
H(3,2)H(3,1)
7 HT=H(3,2)
Q(X.XX,1)zQ(XXX,2)
HAVGH(3,2)
00820
JJ=JJ+1
IF(JJGT.JJM) JJM=JJ
IF(JJ.LT.LIM) GO TO 50
WRITE(6,107) JIT,T
TIME',Fé.0)
107 FORMAT(' EXCEEDED ITERATION LIMIT - CYCLE'.13,'
GO TO 21
50 Ac(2)=Ic(2).B(2)*H(3,2) +SC2)*H(3,2)*DABS(H(3,2))
00830
BBC2)BC)+SC(2)*H(3,2)
IFC-H(3,2)GED0( )) FIAVG=_0.9*D0(2)
CC ( 2) =CCON (2)* ( ( DO () 'HA VG)
167)
IF(CC(2).GT.(CA(2)+0.)) CC(2)CA(2)+20.
IF(AC(2).LT.LLC(2)) AC(2)=LLC(2)
IF(AC(2).GT,ULC(2)) AC(2)ULC(2).
IF(88(2).GT02.0*B(2)) 8B(2)2.O*B(2)
00880
00890
IF(88(2)LT.3*B(2)) B8(2)=,3*B(2)
A1
A2
(L(2))/(32.174*AC(2))
L(2)*88(2)/(CC(2)*CC(2)*AC(2)*AC(2)*AC(2))
Q(2,2)((2.*A1*Q(2,1)/DTT)_H(392)H(3,1)+H(192)
1.H(1,1))/((2.*A1/DTT)+2.*A2*DABS(Q(2,1)))
V(2,2)Q(292)/AC(2)
IF(T.NE.370.) GO TO 602
00940
WRITE(6606) T9JJ,JIT
606 FORMAT(' 'F4.0,1X,2(I3.1X,I2))
WRITE(6,601) CC(2),AC(2),BB(2),H(3,2),OH
601 FORMAT(' 'F17.131XF17.11 ,1Xpl8X,F17.13,1X,18X,F17.12,1X,F17.12)
602 IF(X.EQ.1) GO TO 4
DO 4 I4,XX2
HAVG=(H(I+1,1)+H(I_1,2))*.5
00950
00960
VG+SC (J) *HAVG*DABS (HA VG)
88(I) =8(I) .SC (I) *HAVG
AC ( I) =IC (I)
)
IF(-HAVG.GE,DO(I)) HAVG=_O.9*DO(I)
CC (I) =CCON( I) * ((DO (I) +AVG)**167)
IF(CC(I) 0GT. (CA(I).2O)) CC(I)CA(I)+20.
AS(I-1)=IS(1-1) +.5*SS(I...1)*(H(j...1,2).H(I.1,1)
IF(AC(I)LTLLc(I)) AC(I)LLC(!)
IF(AC(I),GT,ULC(I)) AC(I)=ULC(I)
IF(AS(I-1).LT,LLS(j-1)) AS(I-1)LLS(I-j)
IF(AS(I-1).GT.ULS(I-1)) AS(I-1)=ULS(I-1)
IF(BB.(I)..GT2O*B(i)) BB(I)=2.O*B(I)
!FU3B(I) LT.3*B(I)) BB(I)=.3*8(I)
(L(I))/(32.174*AC(I))
Ai
#2 L(I)*BB(fl/(CC(I)*CC(I)*AC(I)*AC(I)*AC(1)
00990
01000
01010
01020
O(I,2)=(AS(I_1)/DTT)*(H(J_1,1)_H(I_i,2))+Q(I_2,2)
V(I,2)QU2)/AC(I)
H(I+i,2)H(I+1,1)H(I_I,2).H(I_1,1)_2.*A2*Q(I,2)
01080
1*DA8S(O(I,2))_2.*A1((0(I,2)_Q(I,1))/DTT)
IF(T,NE.370.) GO TO 4
WRITE(6,604) CC(I) ,AC(I) ,AS(I-1) ,B8(I) ,Q(I,2) ,I1(I.1,2)
604 FORMAT(
',F17.l3,1X,F17,l1,1X,Fl78,1x,F17.12,1x,E17.9,1x,F17.12)
6 CONTINUE
AS(Xxx_1)=IS(XxX_1).5*SS(xXX_1)*(H(xxX_1,2)+H(xxx_1,1))
JF(AS(XXX-1).GT.ULS(XXX-1)) AS(XXXi)=ULS(XXX1)
Q(XXX,2)=(AS(XXX-1)/OTT)*(H(XxX1,1)_H(xXX1,2))
iQ(XXX-22)
IF(T.NE.370.)GO TO 603
WRITE(6,605) AS(XXX-1),Q(XXX,2)
605 FORtAT(° ',36X,F17,8,19X,E179)
603 JF(DA8S(O(XXX2)-QR).LT.ER) GO TO 6
IF(MM.EO.].) GO TO 32
IF(H(392).EQ.H(31)) GO TO 30
IF(DABS(Q(XXX,2).OR).LT.DABS(DQ).ANO.DQ*(Q(XXX,2).QR).GE.0.)
1 GO TO 30
01110
01120
01140
01150
01160
01180
01190
01210
IF(OABS(Q(XXX,2)_QR).GT.DABS(DQ).AND.DQ*(Q(XXX,2)_QR).GE.0.)
I GO TO 31
MMJ
G01032
31
IF(JJ.EQ.9) GO TO 75
IF(JJ.GT.2) O(XXX,2)=.99*Q(XXX,1)
IF(JJ.GT.2) GO TO 30
75
DH-OH
H(3,2)H(3,2)-DH
GO TO 36
30
36
DQQ(XXX,2)-QR
h(32)=H(3,2)-DH
GO To 1
32 IF(DQ*(.Q(XXX,2)_QR)) 33,33,34
33
0H-DH/2.
GO TO 35
34 DHDH/2.
35 DQ0(XXX2)-QR
H(3,2)H(3.2)-DH
GO TO 7
6 CONTINUE
IF(M.NE.1) GO TO 12
DO 39 12,XX,2
T1T_2*DT
T2T-DT
T3T
D( ( (H(I1,1)-H(I+1,2) )/(T2-T3 )-( (H(I.1,1)-HP(J.1) )/
1(T2-T1)))/(T3-T1)
E=UH(I.1,1)_HP(I+1))/(12_T1))_D*(12.T1)
FHP(I+1)_D*T1*T1.E*T1
IF(H(i41,1),GT.HP(I41).ANO.H(I1,1),GE.H(I41,2)) GO TO 52
GO TO 53
52 TMAXH(I+1)_E/(2,*O)
HMAX(I+1)D*THAXH(I+1)**24E*THAXH(i+1)+f'
53 IF(4U.1,1).LT.HP(I.1).ANOHC1+j,1),LEH(I.1,2)) GO TO 54
01230
01240
01250
01230
01290
01300
01310
01320
01330
01340
01350
01360
01370
01380
01390
01440
01450
01460
01470
01480
01490
01500
01510
01520
01530.
01540
01550
01560
GO TO 55
54 TMiNUI+1)=E/(2,*D)
HMIN(i+1)=D*TMINH(I.i)**2.E*TMINH(I+1)+F
55 D( ((O(1,1)Q(I,2) )/CT2-T3) )-( (0(I,1)-QP(I) )/(T2-Tl) ))/
1(13-11)
E((Q(1,1)_QP(1))/(T2_T1))_D*(12+T1)
FOP(I)_O*T1*T1_E*T1
IF(O(I,1).GT.QP(I).AND,Q(I,1).GE.Q(I,2))
1GO TO 81
GO 10 57
81 1F(O(-11).GE.QMAX(I)) GO TO 56
W1TE(6,82) 12,1
INSTABILITY QMAX: AT 1= ',Fó.l,' STA= ',13)
82 FORPlAT(
GO TO 57
TMAXO(1)=_E/(2,*D)
QAX(I)D*TMAXQ(I)**2.E*THAXQ(I)+F
fl4AXQ(I)=TMAXQ(I).5*DT
57 IF(Q(I,1)LT.QP(I).AND.Q(I,1).LE.Q(1,2)) GO TO 83
GO TO 43
83 IF(Q(1,1).LE.QMIN(I)) 60 10 58
%
01570
01580
01590
01600
01610
01620
01630
01640
01660
01670
01680
01690
01710
Wi)E6,84) T2,I
84 FORMAT(' INSTABILITY QMIN'
T 1= 'F6.1,' STA
',I3)
GO TO 43
58
TMINQ(I)E/(2*O)
QMIN(I)=DDTMINQ(1)**2,E*TMINQ(I)+F
TF4INO(1)=TMINQ(1)_,5*DT
43D(((V(I1)-V(i,2))/(T2-T3))-((V(I,1)-VP(I))/(T2-T1
1)))/(13-Tl)
E=UV(1,1)VP(1))/(T2_T1))_D*(T2,T1)
FVP(1)_D*T1*Tj_E*T1
IF(VC11)GT.VP(I).AN0.V(1,1).GE.V(1,2)) GO 1085
601060
01800
85 IF(V(I,1).GE.VMAX(I)) GO TO 59
WRITE(6;86)T2,I
86 FORt'AT(' INSTABILITY VMAX: Al T
01720
01730
01740
01750
01760
01770
01780
',Fô.l,' STA
',13)
GO TO 60
59 TMAXV(I)_E/(2.*D)
VMAX(1)D*TMAXV(I)**2,E*TMAXV(I).F
TMAXV(I)=TP4AXV(I)_.5*DT
60 IF(V(I.1),LT.VP(I).AND.V(I,1).LE.V(I,2)) GO TO 87
GO TO 62
87 IF(V(I1).LE.VMIN(I)) GO TO 61
WRITE(6,88) T2,I
8
'eF6.1.' STA ',13)
FOtMAT(
INSTABILITY VMIN AT T
001062
01850
01860
01870
01880
01890
01900
01910
01920
01930
01940
01950
01960
TMINV(I)=_E/(2.*D)
VMIN(I)=0*TMINV(I)**2,E*TMINV(I),F
TPINV(I)=TM1NV(I)_.5*DT
62 IF(Q(I,1)*Q(I,2)) 45,39,39
45 IF(Q(I,2)) 66,39,48
46 101 (j)T_(DT*Q(I,2)/(0(I,2)_Q(I,1)) )_.5*DT
GO TO 39
61
48TQ2(I)T_(DT*Q(I,2)#(Q(I,2)Q(I,1)))_.5*DT
39 CONTINUE
IF(T.NE.DST*C)
01810
01820
01830
GO TO 12
C=C1.
GO TO 17
18 WPJTE(6,214) JJM,JIT
214 FORMAT(' MAX. ITERATIONS USED ',13/ ' CYCLES FOR ',
',13)
1'CONVERGENCE
WRITE(6,400)
400 FORMAT(//'l ANGLE',SX,'STATION NUMBER---'/)
WRITE(6,700)
(7)',
(5)
(6)
(3)
(4
(2)
700 FORMAT(' ',ilx,' (1)
1'
(8)
2'(lô)
(12)
(10)
(11)
(20)')
(19)
(18)
(13)
WRITE(6,300) T,(H(I,2),I=1,IX,2)
300 FORMAT(/' ',F4.O,' H:',1Q(F3.4,4X))
WRITE(6,500)TP,(Q(j,2),1=2,XXX,2)
',10(2X,E10.3))
500 FORMAT(' 'eF4.0,' 0:
17
-
(9)
(17)
(14)
(15)
',
00630
00640
01970
0
WRITE(6,600)TP,(V(I,2),I=2,XX ,2)
600 FORMAT(' ',F4.O,' v:
',10(2X,E10.3))
IF(T.EQ.0.) GO TO 10
12 IF(T.NE.360.) GO TO 10
IF(M.NE.1) GO TO 38
02030
02040
02050
02060
HR(1)1.0
ISTH( IX+2) 0.
ISHL(IX2)0.
SST(IX2)0
HMAX(1)H0DHC
HMIN(1)=-HODH0
DO 72 I=3,1X92
HR(I)0.
HRL(I)0.
02110
tr i-u.
KG ( I)
0.
<I(I)0.
KIL(I)0.
C5(1)0.
KSS(I)0.
cvu(fl=0.
CVL(I)0.
72 CONTINUE
IF(H0EQ.0,) GO TO 51
DO 51 13,IX,2
02100
HR(I)=(HMAX(I)_HMIN(I))/(2.*H0)
HRL(I)CHMIN(I)-DHO)/(HMIN(I-2)-DHO)
HRU(I)=(HMAX(I)-DHO)/(HMAX(I-2)-DH0)
II-I3IX
02160
IS(II)15(lI) +SS(II)*DHO
CONTINUE
IC (Il-i )=IC(II-1) .B(II-1) *DH0,SC(II1) *DHO*ABS(DHO)
B (IT-i )=B (Il-I) +SC (TI-i )*DHO
ISTH(II)ISTH(II+2)+IS(II)*U*IAX(II
)-DHO)
ISHL(II)ISHL(II+2),IS(II)*(_HMIN(II
IST(II)ISTH(II)/(HMAX(II )DHO)
ISTL(Ii)ISHL(II)/(-HMIN(II )+DHO)
)+DHO)
SST(II)=SS1(II2)SS(II)
02180
KF(II)(1,98E.8*B(iI_1)*L(II_1)*IST(1I)*IST(II)*
1(HP4AX(II_2)_OHO))/(CA(II_1)*CA(II_1)*(IC(II_1)**3))
KOCh)
1.98E8B( TII)
C II'-1) *ISTL C ii) *ISTL C
1(_HMIN(hI_2),oHo))/(CA(hI_IicA(hI_1)*(Ic(II_1)**3))
02220
KIL(tI)=KI(II)*ISTL(II)/IST(iI)
cCS(II)(HX(II_2)_H1IN(II_2))*(B(II_1)+SC(II_1)*(HMAX(hI2)
1HMIN(II-2)))/IC(I1l)
KSS(II)SST(II)*(HMAX(II_2)_HMINCII_2))*2./(IST(II)+ISTL(II))
CvU(II)=(Ic(II_I)*vMAx(II_I))/((14E:4)*IST(hI)*(HMAx(hI)_DHo))
CVL (II) =( IC C Ili) *VMIN( LIi) )/( (1.4E-4) *ISTL (II)* (HMIN( II) DHO) )
SI CONTINUE
, I3IX ,2)
(MAXT',8X,8(F839',',F5.1))
100 FORHAT('i',/////,'
WRITE (6, 101) (H1IN(I) ,TMINH (I) , 1=3, IX ,2)
WRITE (6, 100) (HMAX ( I) ,TMAXH (I)
101 FORMATI.' ,*1INVt,8X,8(F8.3,b',1,F541))
WRITE (6, 102) (OMAX (I) ,TMAXQ( I)
, I2eXX,2)
102 FORMAT(' QhAXIT',8X,8(F8,O,',',F5I))
WRITE(6,103)(QMIN(I),TMINO(I),12,XX92)
103 FORPiAT(! QMINIT',8X,8(F8,0,',',F5.1))
, I2'XX2)
112 FORMAT(' VMAXT',8X,8(F8,2'',F5.1))
WRITE (6,113) C VMIN( I) ,TMINV(I) , 12,XX,2)
WRITE (6,112) ( VMAX( I) TMAXV(I)
113 FORMM(' VINIT',8X,8(F8.2,',',F5l))
WRITE(6,104) (101 (I) ,T02(I) ,12,XX,2)
104 FORMT(' Q0T,T',8X,8(F81,','F5.1))
WRITE (6, 1O9HHR( I)
WRITE(6,111)
WRITE(b,50i)
WPITEC6,502)
WPITE(6,503)
, 1=3,
IX,2)
(HRU(I),13,IX,2)
(1RL(I),I,IX,2)
(KF(I),13,IX,2)
(KG(I),13,IX,2)
02250
WRITE(6,504) CKIU),I3,jX,2)
WP!TE(6,509) (KIL(j),J=3,IX,2)
WRXTE (6,507) (CVU (I) , 13, IX,2)
WRITE (6,508) (CVI. (1) ,I3IX,2)
WPhTE(6,505 (KCS(I) ,13,IX,2)
WRITE(6,506)(KSS(I),13,IX,2)
,//,' HR:
,Bx,8(sx,Fo.3,3x):
109 FORMAT(°
UI FORMAT(' ',/,' HRU:
,8X,8(5X,F63,3X))
501 F0RT(' HRL: '8X,8(5X,F6.3,3X))
502 FORMAT(' '.1,' KFU:
',8X,8(5X.F63,3X))
503 FORHAIC' KFL:
'8X,8(4X,F703,3X))
504 FORMT( ',/,' KIU:
',8X8(5XF6.3,3X))
509 F0T(' KIL: ',8X,8(5X,F6.3,3X))
507 F0RMiT(' ',/,' CVU
',8X,8(5X,F6.3,3X))
508 FORtAT(' CVL:
',8X,8(5X9F63,3X))
535 FORMAT(' ',/,. KC:
8X,8(5XE8.3,IX))
506 F0RP-T' ',/,' KS:
',BX,8(5X,E8.3,1X))
GO TO 21
38 IF(DABS(H(XXX-1,2)-HTT).LE.ERR) P41
HTT=H (XXX-1 ,2)
T=00
TP-DT/2.
IF(M.EQ1) GO TO 18
10 CO 8 i=2,XXX,2
OP (I) =0 (1
1)
HP(i-j)H(I-1,I)
VP ( I) zV( 1, 1)
V( I 91)V (1,2)
O(I,i)Q(1s2)
8 H(i-1,1)=H(I-1,2)
GO TO 9
25 CONTINUE
cPdfl
.1
02650
02670
02680
02690
02710
02720
02730
02740
02750
02760
02770
02780
02820
02830
-4
A.5
List of Variables
Description
Symbol
AC
Cross sectional area of conveyance
-
Dimensions
FT2
channel at each segment as function
of displacement
2
AS
-
Surface area of estuary landward of
FT
a given segment as function of displacement
B
-
Width of conveyance channel for
FT
each segment
CA
-
Value of Chezy Friction Coefficient
FT2 /SEC
at Mean Sea Level for each segment
CC
-
Value of Chezy friction coefficient
FT2/SEC
as function of water depth
CCON
-
Constant in equation defining CC
FT2 /SEC
-
Constant in parabolic curve fitting
variable
equation
DUO
-
Eccentricity of forcing tidal function
FT
from Mean Sea Level
DO
-
Depth of water at Mean Sea Level for
FT
each segment
DQ
-
Difference between computed and
F1/SEC
actual river inflow
DST
-
Time increment requested for data
output
DEGREES
109
Description
Symbol
DT
-
Time increment used in finite-
Dimensions
DEGREES
difference computations
DTT
-
Time increment used in finite-
SEC
difference computations
E
-
Constant in parabolic curve fitting
variable
equation
ER
-
Allowable error between computed
FT3/SEC
and actual river inflow
ERR
-
Allowable error between displacement
FT
values for successive tidal cycles
F
-
Constant in parabolic curve fitting
variable
equation
H
-
Displacement at each segment as a
FT
function of time
1111
-
Initial value of displacement at each
FT
segment
HMAX
-
Maximum displacement at each segment
FT
}ININ
-
Minimum displacement at each segment
FT
HO
-
Amplitude of pcean tidal forcing
FT
function at estuary mouth
HP
-
Value of displacement at each
FT
segment during previous time
increment
HR
-
Ratio of tidal range at each segment
to tidal range in ocean
FT/FT
110
Description
Symbol
URL
-
Ratio of minimum displacement at each
Dimensions
FT/FT
segment to minimum displacement in
ocean
HRU
-
Ratio of maximum displacement at each
FT/FT
segment to maximum displacement in
ocean
IC
-
Value at NSL of relation between
FT2
function of AC and H at each segment
IS
-
Intercept at MSL of linear relation
FT2
between function of AS and H at each
segment
1ST
-
Summation of IS values of upstream
FT2
segments
JJ
-
Counter for number of iterations at
-
each time increment
/
1(1
-
Convenient grouping of terms for
SEC2 /FT2
computations L/(g * AC)
K2
-
Convenient grouping of terms for coin-
SEC2 /F15
putations (L * B) / (CC2 * Ad3)
at each segment
KCS
-
Ratio of SC to IC
KY
-
Non-dimensional friction coefficient
based on high tide conditions at each
segment
F'11
-
111
Description
Symbol
KG
-
Non-dimensional friction coefficient
Dimensions
-
based on low tide conditions at each
segment
KI
-
Non-dimensional inertial coefficient
-
at each segment
KSS
-
Ratio of SST to 1ST at each segment
FT'
L
-
Length between segment centroids
FT
LIM
-
Iteration limit at each time step
LLC
-
Lower limit of cross sectional area
-
FT
2
at each segment
LLS
-
Lower limit of surface area at
FT
each segment
M
Q
-
Indicator for cyclic convergence
-
-
Indicator for inflow convergence
-
-
Discharge at each segment as a func-
FT 3/SEC
tion of time
3
QMAX
-
Maximum discharge at each segment
FT /SEC
QMIN
-
Minimum discharge at each segment
FT3/SEC
QP
-
Value of discharge at each segment
FT3/SEC
during previous time increment
QR
-
River inflow
FT3/SEC
SC
-
Side slope of conveyance channel
FT/FT
SS
-
Slope of linear relation between AS
and H at each segment
FT2/FT
112
Description
Symbol
SST
Summation of SS values of upstream
-
Dimensions
FT2/FT
segments
T
Time used in Finite-difference equations SEC
-
Ti, T2, T3-
Time values used in parabolic curve
SEC
fitting equation
TMAXH
-
Time at which HMAX occurs at each
SEC
segment
TMAXQ
-
Time at which QKAX occurs at each
SEC
segment
TMAXV
-
Time at which VNA.X occurs at each
SEC
segment
TMIN}I
-
Time at which IH'{IN occurs at each
SEC
segment
TMINQ
-
Time at which QMIN occurs at each
SEC
segment
TMINV
-
Time at which VMIN occurs at each
SEC
segment
TP
-
One-half time interval before T for
SEC
which Q and V are valid
TQ1
-
Time of high tide slack for each
SEC
segment
TQ2
-
Time of low tide slack for each
segment
SEC
113
ULC
Dimensions
Description
Symbol
-
Upper limit of cross-sectional area
FT2
at each segment
ULS
-
Upper limit of surface area at each
FT2
segment
V
-
Velocity at each segment as a
FT/SEC
function of time
VMAX
-
Maximum velocity at each segment
FT/SEC
VMIN
-
Minimum velocity at each segment
FT/SEC
VP
-
Value of velocity at each segment
FT/SEC
during previous time increment
X
-
Number of segments
schematization
in estuary
114
Appendix B
Prototype and Model Comparison Details - Yaquina Estuary
Using the dimensions given in Table 3.3.1, the model of
the Yaquina Estuary was calibrated to prototype tidal data
collected on July 4, 1969.
The primary assumption, that a
vertically "well-mixed" system did exist during the month
of July, is documented in Appendix F.
The density differ-
ence between top and bottom waters in the estuary averaged
about 0.15%.
Figures B.l and B.2 show the comparison of tidal
displacement and phase at successive locations along the
estuary.
The peak values generally agree within 0.1 feet
and times of occurrence to 6 degrees or 12 minutes.
This is
generally within the accuracy of the field data and is
considered to be adequate.
Figures B.3 through B.6 show the displacement and phase
comparisons achieved when the model was applied to two check
periods, July 10 and July 21, 1969.
The agreements are gener-
ally within 0.2 feet and 5 degrees or 10 minutes, which is a
true measure of the model capability.
In addition to displace-
ment, velocity determinations were made during the July 21
period.
Figures B.7 through B.9 show reasonable agreement
between model and prototype.
Peak velocities are within 0.2
feet per second in the lower reaches of the estuary using
boats as observation platforms.
Locations on docks for the
115
upriver stations seem to provide peak velocity values from
0.4 to 0.6 fps less than the computed value.
water agree within 2 degrees or 4 minutes.
Times of slack
Comparisons of
this type should be made in a very broad sense.
The model
value represents an average velocity in the cross-section,
whereas the prototype value is a vertically integrated velocity at one station in the cross-section.
One exception to
this is at Oneatta Point where sufficient field data was
collected to compute average velocities which compare very
favorably to the model values.
Amplification data is condensed in Figure B.lO showing
the change in tidal range with distance upstream for both
model and prototype.
The amplification factor is defined
as the local tidal range/ocean tidal range.
The Yaquina
is characterized by "nonchoked" or amplifying conditions,
except at Toledo for large tidal ranges.
Hypothetical flood conditions were simulated using the
model to illustrate its predictive ability and usefulness.
Flood flows of 5000 CFS and 10,000 CFS were assumed at the head
of the estuary with the same ocean tide which existed on July
4, 1969.
Flood and non-flood displacement, phase, velocity
and slack conditions are compared in Figures B.11 through B.17.
It should be remembered that if the estuary becomes stratified
as a result of continuous large fresh water inflows, a primary assumption used in the model development will be violated.
116
The model predictions should then be interpreted in a more
qualitative manner.
For the 10,000 CFS flood, water elevations 3 feet above
normal high tide can be expected at Elk City, decreasing to
less than 1 foot above normal between Toledo and Newport.
An
onshore wind causing additional coastal "setup" would exaggerate the condition just described.
----
4
FIGLTRE B.l
Displacement Calibration - Yaquina Estuary July 4, 1969
C'
-4
4-4
0
0
U
----
Observed
Computed
--4
C
-41--
0.l---
_
0
T. -
"-4
-6 L_____.____L
0
20
40
60
80
Distance from Mouth- xi000 ft
100
120
-4
-FIGURE B.2
Phase Calibration - Yaquina Estuary July 4, 1969
80r
/
- 240.
0 Observed
----
Computed
"0"
4O
-220
20
200
O
0
20
I
40
60
80
I
100
0)
- 180
120
Distance from Mouth- xl000 ft
03
FIGURE B.3
Displacement Verification - Yaquiria Estuary July 10, 1969
0'
Cl)
4-'
4J
2
I----- -
-
:g
-2
O-
-
-O Observed
------Q Computed
-4 -__L ___.__L_.
0
20
40
60
Distance from Mouth-
80
iO0O ft
100
120
FIGURE 13.4
Phase Verification
Yaquina Estuary July 10, 1969
60-
.240
w
0
e -----
40 -
0 Observed
Computed
220
H
0
Hide
20 -
0
200
.
H
H
Low tide
I
0
0
20
40
60
80
Distance from Mouth- xl000 ft
100
180
120
PIG1JRE B.5
Displacement Verification - Yaquina Estuary July 21, 1969
C'
C'
'I
4
Ir
-
CL)
4J
- - -
-=----- 0
'-H
lJ
c
E
2-
ci)
C-)
0
-o Observed
O-----G Computed
r
.
.-
H
-o
C',
E
--------- 0
-----0
-------.-.---Q-- --- ______Q
-
-4
0
20
40
60
80
Distance from Mouth- xl000 ft
100
120
F-Phase VerificatiOn - Yaquina Estuary July 21, 1969
FIGURE B.6
80
260
-
60
240
0
0 Observed
Low tide
40
-
--- -, Computed
220
tide
2O
2O0
-
I
0
0
20
40
I
60
80
Distance from Mouth- xl000 ft
180
100
120
FIGURE
B.7
Velocity Verification - Yaquina Estuary
Flood Flow July 21, 1969
2.0
Q-------Q
Observed
Computed
1.5
H.0.
0.5
o______
20
0
I
40
60
80
Distance from Mouth- xl000 ft
100
120
FIGURE B.8
80
High Slack TIde Verification - Yaquina Estuary July 21, 1969
-
w
60
o
___ -
20
O
Observed
Computed
-
0
I
20
40
60
100
80
Dis Lance from Mouth- xl000 ft
120
_ -- - p
__-___________
FIGURE B.9
260
Low Slack Tide Verification - Yaquina Estuary July 21, 1969
-
0
(0
w
240
-
-
0
220
-
200
-
----
0
Observed
Computed
0-
180
1
I
0
20
40
60
I
80
100
120
Distance from 11outh- xl000 ft
Ui
FIGURE B.l0
Tidal Amplification - Yaquina Estuary
r&!
1.4
in
10
I bU
4
4
F
6
0
V
0
-4
E1
1.1
0
'--4
- 0
8
H
1,0
20
40
60
80
100
120
140
Distance from Mouth- xi000 ft
I',)
FIGURE B.11
Effect of Hypothetical Floods on Tidal Displacement
July 4, 1969
Yaquina Estuary
JJ
.1-,
0)
03
.---
J:x
River flow- cfs
0
2
.,-4
H
-1
0
5,000
s'-,
0
10,000
-2
03
E
0
0
-6
[I]
20
40
60
80
100
120
Distance from 4outh- xl000 ft
-4
FIGURE B.12
Effect of Hypothetical Floods on Tidal Phase of High Tide
Yaquina Estuary July 4, 1969
80 -
U)
1)
w
River f1ow- cfs
:
20
a
I
0
20
40
I
60
80
Distance from Mouth- xl000 ft
100
120
FIGURE B.13
Effect of Hypothetical Floods on Tidal Phase of Low Tide
Yaquina Estuary - July 4, 1969
320
280.
River flow-
.-4
200
- p
180
-'
I
0
20
40
60
80
Distance from Mouth- xl000 ft
100
120
FIGURE B.14
Effect of Hypothetical Floods on tidal Flood Velocity
July 4, 1969
Yaquina Estuary
4
River flow- cfs
0
0
0
3
5,000
()
0
4J
10,000
2
C)
0
1.L
0
0
0
0
0
No upstream flow occurs
1
0
0
20
40
60
80
100
120
Distance from Mouth- xl000 ft
C
FIGURE B.15
Effect of Hypothetical Floods on Tidal Ebb Velocity
Yaquina Estuary - July 4, 1969
4
River flow- cfs
3
Q
w
l)
(3
0
0
0
1
0
20
60
80
40
Distance from Mouth- xl000 ft
100
120
(Jj
FIGURE 3.16
Effect of Hypothetical Floods on High Slack Tide
Yaquina Estuary - July 4, 1969
River flow- cfs
o
0
C)
C)
5,000
4
C)
60
-
10,000
0
H
0
U
U]
40
-
U]
0
0
20
C)
H
No tide reversal
I
0
0
20
40
60
80
Distance from Mouth- xl000 ft
100
120
FIGURE B.17
Effect of Hypothetical Floods on Low Slack Tide
Yaquina Estuary - July 4, 1969
260
070
0
U,
4)
4)
240
4)
-o
) tide reversal
0
River flow- cfs
H
0
9
220
0
5,000
0
0
10,000
4-3
0
200
a)
"-3
H
180
1
0
20
40
60
80
Distance from Mouth- xl000 ft
100
120
134
Appendix C
Prototype and Model Comparison Details - Alsea Estuary
Using the dimensions given in Table 3.3.2, the model of
the Alsea Estuary was calibrated to prototype tidal data collected on August 16, 1969.
As in the Yaquina,
a vertically
"well-mixed" system did exist during the month of August and
documentation is given in Appendix F.
The average density
difference between top and bottom waters was 0.19%.
Figure C.l compares maximum and minimum model and
prototype tidal displacements along the Alsea Estuary.
peak values agree within 0.1 feet.
These
Times of occurrence of
these peaks as shown in Figure C.2 agree generally to within
3 degrees or approximately 6 minutes, except at low tide upriver, where a difference of 6 degrees is observed.
Figures C.3 and C.4 show the displacement and phase corn-
parisons during the verification phase of model development.
Data collected on August 28, 1969, was used for this purpose.
Agreement attained is again within 0.1 feet except at one
point, which is 0.2 feet off,
The phase comparisons are within
5 degrees or 10 minutes.
Velocity data for the same period are given in Figures
C.5 and C.6.
Model and prototype values are within one-half
of a foot per second, with observed values being higher.
Since
field readings were taken in the center of the channel, computed averages should be lower.
Times of slack water are not
135
easily determined quantities.
The agreement shown in Figure C.7
is considered adequate and within measurement and simulation
accuracy.
The amplification and/or attenuation characteristics of
the Alsea Estuary are summarized in Figure C.8.
For small
tidal ranges, an initial attenuation or choking is followed by
amplification of the tidal wave as it progresses upriver.
Large tidal ranges produce more pronounced choking which continues further inland with only slight amplification in the
upper half of the estuary.
Figures C.9 through C.13 show the effects which a channel
deepening of 50% and widening of 50% in the indicated reach
A hypothetical increase of
would have in the Alsea Estuary.
125% in the controlling conveyance cross-sections from the
estuary mouth to a point approximately 4 miles upriver was
used to generate this information.
The tidal wave becomes
less choked under this situation which allows more ocean water
to penetrate further upstream.
This produces larger tidal
ranges and higher velocities as indicated in the figure.
The
most pronounced changes, however, are in the reduction of time
lags of high, low and slack tide conditions.
Before dredging,
low tide occurs nearly three hours later at Tidewater than at
the mouth.
After dredging this lag is only about one hour.
a
Displacement Calibration - Alsea Estuary August 16, 1969
FIGURE C.1
4
...-.
-
-. ...
---- -,_f
i-1
cI
4J
2-
0
0
-. - -
Z
-2
Observed
Computed
-
0
0
10
20
30
40
Distance from Mouth- xl000 ft
50
60
70
Z3
UOjqrpj
-
1v
Sfl2ny
'91 6961
/
I
09
- -
tD
ac
0z
iu9
I
rD
I
I
I
I
0
I
_J
o
1
N
I
0
____
(D
J4
'J(,
N0
Ptj
P&Sq
/;c/
Pnc1wo3
091r
0
09
or
2fl0N
OOO
0L
I
FIGURE C.3
0
L
Displacement Verification * Alsea Estuary - August 28, 1969
0
Observed
2----Ø Computed
0
0H
-2
-
-
- -o
6
2'O
Distance from Mouth- xl000 ft
7
FIGURE C.4
Phase Verification - Alsea Estuary - August 28, 1969
280
100
Cl)
C)
C)
C)
C)
C)
C)
'C)
240
60
0
fr:1
0
b
40
,).)n
,__ff_.
e'O
high Lide
/0
C)
C)
'.4
H
H
'/8
20
0-
Q
Observed
/7,
200
--
Computed
80
10
20
30
40
Distance from Nouth- xl000 ft
50
60
FIGURE C.7
Slack Tide Verification - Alsea Estuary - August 28, 1969
-
100
-
280
-
260
-
240
-
220
1ack tide
80
-
60
-
High slack tide
,'
40
0
0
--I
20
0
10
20
I
30
40
Distance from Mouth- xl000 ft
Observed
Computed
1___
50
200
I
60
70
4
70
60
50
ft xl000 Mouth- form Distance
40
30
20
10
0
1
0.7
H
0
-4
F'
0.8
9
-4
-4
o
4-1
0
0
1
0
3
0
5
0
7
0
.41
-4
0
0.9
o
C)
4J
0
H
H-4
qj
4J
1.1
0
ft
ranze
tid
1.2
)ce
Estuary Alsea
-
Amplification Tidal
C.8 FIGURE
FIGURE C.9
Effect of Hypothetical Dredging on Tidal Displacement
Alsea Estuary - August 16, 1969
5-
----
4
'-4
4J
4-4
channel width
and depth
increased by
2
E
0
- 50% in this
0-
0
Observed tide before dredging
O----S
Predicted tide after dredging
reach, channel
area increased
by 125%
.-4
E
.-4
0
-2
---------°
----I
4
0
10
4
20
40
Distance from Nouth- xl000 ft
30
I
50
60
70
FIGURE C.lO
Effect of Hypothetical Dredging on Tidal Phase
Alsea Estuary - August 16, 1969
270
:::.
channel area
increased by l257
J)
C)
C)
so
C)
']
60
/
0
/
_--
0
Observed lag before dredging
240
Predicted lag after dredging
High tide
0
so
220
40
0
0
so
/
Low tide
/0
C)
20
C)
//
200
High tide
0
10
20
40
30
Distance from Mouth- xl000 ft
50
60
7
o180
-Is
U,
FIGURE C.11
Effect of Hypothetical Dredging on Flood Velocity
Alsea Estuary - kugust 16, 1969
4
0
3
0
0
- -
0
0
Computed before dredging
Predicted after dredging
2
0
0
'-4
1
channel area
- increased by
1 257
o
0
10
20
30
Distance from Nout1i
40
50
60
xi000 ft
1-
FIGURE C.12
Effect of Hypothetical Dredging on Ebb Velocity
Alsea Estuary - August 16, 1969
4
3
C)
Cl)
0
Computed before dredging
- - - 0
Predicted after dredging
0
4-3
2
0
0
- ----------------
1
channel area
increased by
1 257,
01
0
I
I
I
I
10
20
30
40
Distance from Mouth- x1000 ft
50
60
149
Appendix D
Prototype and Model Comparison Details - Siletz Estuary
Using the dimensions given in Table 3.3.3, the computer
simulation of the Siletz Estuary was verified using field data
collected on September 15, 1969.
As with the previous two cases,
a vertically "wellmixed" system existed during the period of
model calibration and testing.
Appendix F contains salinity and
temperature data which verify this.
The average density
difference between top and bottom waters was 0.04Z.
Figures D.l and D.2 show model to prototype comparisons
of tidal displacement and phase along the estuary.
Peak values
agree within 0.1 to 0.2 feet and times of occurrence to 2
degrees or 4 minutes.
Figures D.3 and D.4 give displacement and phase compar
isons for September 12, 1969, which was chosen as the checking
period.
Agreement is again within 0.2 feet and 2 degrees, which
indicates a good level of verification.
Velocity data for September 12 are given in Figures D.5
and D.6.
Ebb flow measurements were not made on this estuary.
Model and prototype values are within 0.3 feet per second with
times of slack water agreeing generally within 2 degrees or
4 minutes, except for low slack near the head of the estuary.
The large discrepancy
here may indicate a timing error in the
data.
The amplification characteristics of the Siletz are
150
suimnarized in Figure D.7.
A large initial attenuation of the
tidal wave occurs through the relatively restricted entrance.
An. additional small attenuation occurs as the bay portion of the
estuary is traversed.
Varying degrees of amplification are
then produced as the wave continues upriver.
The largest gains
are made by waves with the smallest ranges and vice versa.
probable
The
displacement, phase, velocity and slack changes due to a
larger entrance cross-section at the mouth of the Siletz
Estuary are shown in Figures D.8 through D.12.
Doubling of the
entrance area would nearly eliminate the "choked" condition and
produce significant changes in the tidal characteristics throughout the estuary.
Larger tidal ranges would be produced.
lags of high, low and slack tide would be reduced.
Velocities
at the mouth would decrease but would increase elsewhere
throughout the estuary.
Time
FIGURE D.l
Displacement Calibration - Siletz Estuary
September 15, 1969
C'
.------------p- 0-0
4J
4J
E
U
0
2
Cl)
0
Observed
0-- --0
Computed
,-1
9
-0
,-1
z
'C
.-,--
-2
/
I
E
/
I
cI
4
I
L...
0
20
80
60
40
Distance from Mouth- xl000 ft
100
120
LIl
Lii
N)
lDL
c
CD
H
U
S4d
degrees
CD'
-
uotq z'tg
qmds 'ci 6961
o
\'
CD
0
Li'
'
Tide Low of Lag Time
Li'
0'
\\0
0
degrees Tide- High of Lag Time
icinsa
N)
0
0
0
0
0
0
N)
0
I zc
rt
x
0
Q
rt
0
CD
0
rt
September 12, 1969
FIGURE D.3 Disp1acep Verification - Siletz Estuary
5'-4
4%
-------
O-_---
Observed
11110
Q
Computed
/
"-4
;
-2
0
20
40
60
from Mouth
tOO
x1000
120
Ui
//
FIGURE D.5
Velocity Verification - Siletz Estuary - Flood Flow
September 12, 1969
8-
6
0
0
Observed
---4
Computed
Cl,
4-
1
I'
0
\
\
2
0
0
20
I
I
I
40
60
80
Distance from Mouth- xl000 ft
100
120
U,
U,
0
I
cc
0
Estuary
cc
0
;-
0
.0
0
aunj
cf
;o 53rj
Si1et
Slack Tide Verification
September 12, 1969
C)
C)
-
-
saiEp -pj LO
FIGURE D.6
F
4)
'0
.,-
ci
-4)
"
'%
"
'\
"
"
'\
%\
M
"
'1
'\
'\
'\
'\
''
O\ 0'
'\
saip -PLL 4TH 3°
156
I)
4J
157
FIGURE D.7
Tidal Amplification - Siletz Estuary
Ocean
Tide
age-ft
1.21
11
1.1
0
"-4
c
4
H
0
2
0.9
4J
C-)
0
0
"-4
4J
CJ
0.8
C
--4
4
/
ci
H
4
0.7
0.6 L
0
20
40
60
Distance from Mouth- xl000 ft
80
100
FIGURE D.8
Effect of Hypothetical i)redging on Tidal Displacement
Siletz Estuary - September 12, 1969
5
C'
----,
C'
4
0
4J
0
0
cI-
44
0
2
0
Observed tide before dredging
U
-4
channel 'entrance-
- - Ø Predicted tide after dredging
area doubled
-4
0
0
--4
H
0
--4
-'-1
..
0
-e
-2
--5
b
S
*
S
--4
4I
I
0
20
I
40
60
80
Distance from Nouth- xl000 ft
100
120
U,
Co
Low
0 tide
100
,
280
,
,
,
,
80
D
Chennel entrancearea doubled
260
Nh
High
tide
C)
C)
(D
C)
Cl)
C)
/
/
C)
,,
C)
(t
bJD
C)
- -
240 °
-.
C)
H
.r-I
/
'
ci)
)rt
p-h
C)
C)
0
rj
220
C)
/
bO
r
l)
C)
,
/
rp
rPn'
'<
,
H-
/ _._
-
C)
/
'1
0
H
0--- 0 Observed lag before dredging
,-
Ni
H
200
----0 Predicted lag after dredging
-7
'-0 P)
0
I,
p)
I,
I,
CD
- 180
0
0
(I)
Pj
/
0'
40
N
tci 0
-.
to
.h 0
i-i
C)
0
t-i
20
40
60
80
100
120
Distance from Mouth- xl000 ft
-Il
-0
FIGURE D.1O
Effect of Hypothetical Dredging on Flood Velocity
Siletz Estuary - September 12, 1969
E3
channel entrancearea doubled
'1
C)
U)
4-i
0
0
Computed before dredging
3-i
.,-4
C)
Predicted after dredging
4
0
0
0
r
2
0
20
40
60
80
Distance from Mouth- xl000 ft
100
120
FIGURE D.l1
Effect of Hypothetical Dredging on Ebb Velocity
Siietz Estuary - September 12, 1969
channel entrancearea doubled
U
Computed before dredging
Predicted after dredging
U
0
c)
2
\
20
40
60
80
i)istance from Mouth- xl000 ft
100
120
125
305
0
0
channel entrancearea doubled
High
slack
280
cl
C)
C,
C)
C)
'-I
/
C,
C)
c,o
-0
H
-
rr
-0
0
/
_,
C)
Low
slack
H
0
-
o
trirt
rI-Cr,
rf
,
o
50
/0'
0
230
-----
1'
O
cj
/
1'
/
C)
/
0
/
rIQ
0
/
0
Computed before dredging
C)
S
JI'
CD
"-4
Predicted after dredging
25//
205H
N
CJ
.
ii
Ijh''
CD
I
0
0
20
40
I
60
Distance from Mouth
80
xi000 ft
100
- 180
120
I-
163
Appendix E
Application of Predictive Algorithm - Examples
E.l
Simple Embayment
Van de Kreeke (1967) supplies the following values
defining the physical and hydraulic characteristics at
Macquarie Harbour Inlet, Tasmania:
im2
AS
=
2.8 x
AC
=
4200 m2
7000m
L
B
=
700 m
T
=
24 hrs = 86400 sec
C
=
50 m½tsec
= 45m
g
=
9.6 rn/sec
Following the procedure in section 5.2.1, KF and K1
are computed resulting in KF = 4.95 and K1 = .257.
From
Figure 4.4.7, the amplitude ratio between embayment and ocean
is 0.50.
H.
= H
The maximum displacement in the bay then is
x .50 = .225 m which agrees very closely with Van de
Kreeke's result.
From Figure 4.4.8 the phase lag is determined to be 70
degrees or 4.67 hours.
This is higher than the 4 hour lag
given by Van de Kreeke and is explainable by the inclusion of
164
inertial or acceleration terms in the present work.
By arbi-
trarily setting the K1 factor equal to zero (no inertial effect)
Figure 4.4.8 gives 61 degrees or 4.06 hours.
The maximum velocity in the entrance can be found from
Figure 4.4.9 and application of equation 4.4.6.
ample C
In this ex-
= 0.85 with the velocity computing out to be .865 m/sec.
To compare this result with Van de Kreeke's we must compute the
discharge and add a fresh water increment of 350 m3/sec.
Q = .865 (4200) + 350 = 3990 m3/sec
This is quite comparable to the 4000 m'/sec given by Van de
Kreeke.
E.2
Multiple Segment Case
The Siletz estuary was chosen as an example to demonstrate the multiple segment procedure outlined
in section 5.2.2.
The characteristics of the estuary at Mean Sea Level are given
in Table 3.3.3.
The ocean tidal displacement used is that
which occurred on September 15, 1969, and is graphically shown
as part of Figure D.l.
This is a reasonably
complex case for two reasons.
the tide is not centered on Mean Sea Level.
First
Second, and more
important, the surface area and particularly the cross-sectional
area of each segment, cannot be considered constant over the
entire range of the tide.
To account
for these conditions,
which are the rule rather than the exception in the real world,
165
the computations will be divided into two parts,
Oaa will be
characterized by conditions existing during the upper half of
the tidal cycle.
The other will be valid for condJitions exist-
ing during the lower half of the tidal cycle.
doubles the
ThI
amount of computation but provides more accurate information
where eccentricities in the tide are expected becaui;e of
widely variable physical characteristics.
For the particular period in question, the ocean tide is
centered at the halftide level of (4.9.-.3.6)/2
O65 feet with
an amplitude of (4.9 ± 3.6)/2 = 4.25 feet.
Calculations of upper and lower tide characteristics are
based on the time averaged elevation of a sinusoid of ainpli--
tude, H
,
for each channel segment, i, adjusted by the ocean
halftide datum.
In this case the upper reference level is
defined as:
1
H
I
sind
+ 0.65
=
0 637H +0 65
lr/2
I',
The lower reference level is therefore:
0.637 H
+ .65
1
where H may have different values in the upper an
'
lower tidal
domains.
To initiate the computations, upper and lower reference
elevations must be determined or assumed for each :stuary
segment.
Since field observations indicate that L'rge changes
in tidal amplitude sometimes occur at the mouth,
is advis-
able to approximate this change with a preliminary calculation,
166
Initial values of the friction and inertial coefficients
can be determined using the half-tide values of the parameters
involved at an elevation of 0.65 feet.
AC
=
3495 ft
AS
=
7.21 x l0
B
=
305 ft
C
=
90 ft/sec
ft2
and from equations 4.6.2 and 4.6.3:
KF =
2.70
K1
and
.089
=
which, from Pigre 4.4.7, shows a substantial decrease in tidal
amplitude from that in the ocean.
4.25 = 2.80 ft.
The new amplitude is .66 x
The corresponding upper and lower reference
levels are .637(2.80) + .65 = 2.43 ft and -.637(2.80) + .65 =
-1.13 ft, respectively.
These elevations are used in Table E.l
to base calculations for the initial characteristics at each
segment.
The channel width, B, of each segment is assumed constant
at the ocean half-tide level.
Table E.2 gives these values.
Other parameters are not a function of tidal elevation.
Table E.2
Half-Tide Channel Width
Segment
Width-B ft
1
305
511
401
301
2
3
4
167
The first approximation of the amplitude-weighted surface
areas for each segment can then be computed for both upper and
Since H. is the same for all
lower tides, as shown in Table E.3.
segments, the AS.H.
1
term need not be computed.
Information from tables E.l, E.2, and E.3 can then be
used in the appropriate place in Table E.4 to produce the first
approximation to KF
and K,
and the resulting estimate of upper
and lower amplitudes at each segment,
The half-tide datum
correction is also applied to produce elevations relative to
Mean Sea Level (MSL).
Revised reference levels can then be computed from the
new amplitude values on which to base refined calculations of
AC and AS, shown in Table E.5.
The same procedure as before
carries through Tables E.6 and E.7 to give second-approximations of KF , K1
and amplitude.
The third round of tables, E.8, E.9 and E.lO produce
values very close to the second round, indicating that conver-
gence has occurred and calculations may stop.
In fact, it may
be noted that for most practical purposes the first approximation would have been sufficient.
It may have been fortui-
tous in this case, however, so additional calculations are
recommended.
A plot of observed maximum and minimum displacements
and those produced from Table E.1O (predictive algorithm) is
shown in Figure E.1.
The consistent 0.1 to 0.2 foot differ-
ence is interesting, but most likely reflects the accuracy
of the procedure and the sensitivity in this case to the KF
value of the first segment upstream of the mouth.
A small
change in KF in that region produces a substantial change
in computed amplitude.
Figure E.2 shows the corresponding comparison between
observed and predicted phase lags of high and low tide as
computed from Figure 4.6.1.
Deviations are again an indica-
tion of the procedural accuracy.
The procedure is outlined
in Table E.l1.
Since no observations of slack tide were made on September 15,
1969, a comparison between the computer model and the predictive
algorithm is presented in Figure E.3.
The computations, shown in
Table E.l2 are based on Figure 4.4.8.
A possible explanation for the lack of agreement on the low
slack tide phase may be found in Figure 3.4.32.
On September 12,
1969, when slack conditions were observed, the model seems to underestimate the low water slack phase lag for the most upstream
segment.
The algorithm results in Figure E.3 may well be more
accurate than the model results.
The maximum flood and ebb velocities can be determined from
application of eqation 4.4.6 and Figure 4.4.9.
In multi-segment
cases the surface area is defined in the amplitude-weighted sense
as given in Table E.9.
FIGURE E.1
- Siletz Estuary
0lsplacernent Comparjso
Septemhp 15, 1969
6r
I-'
'-4
'
U)
4
------
___Q
C)
C)
Observed
2
-_ -e
Predictive Algori
0
E
z
-2
---Djtanc
--_-- -------
from Mouth- xl000 ft
FIGURE E.2 Displacement Phase Comparison
Siletz Estuary - September 15, 1969
125
305
Low tide
100
U)
U,
'.4
-e
)
75
-
-e
o'2
....--
..
High
-,
tide
255
'Ti
"-4
H
H
9
bO
0
4-4
0
4-4
C)
50
:----
p
bO
.0
.
230
0 -0 Observed
O-----O
H
Predictive Algorithm
..-'
H
"II
"
25
205
u.
I
j
I
1
I
OL_
0
I
20
60
80
40
Distance from Mouth- xl000 ft
100
-J
FIGURE E.3 Slack Tide Phase Comparison
Silet.z Estuary - September 15, 1969
305
125
/
t40W tide
rJ)
280
100
/
U)
/
0
'0
High tide
'0
F-'
255
75
0
'0
H
U
U)
U)
/
0
-4
0
0
0
50
230
Observed
0
oO
- - -
Predictive Algorithm
H
H
205
25
___I__
0
C)
20
__J
80
60
40
Oistance from Nouth- xl000 ft
100
-'80
12
172
Table E.13 shows the velocity computations and a comparison
with the values produced by the computer model.
The average 20 percent overestimate by the algorithm is also
partially explainable by referring to the velocity measurements
taken on September 12, 1969, during a similar tide and shown in
Figure 3.4.31.
The model results in this case are about 10 to 20 percent
low.
Again the algorithm may produce results closer to the
case than does the model.
real
This line of reasoning should not be
pursued further, however, since the inaccuracies in velocity
measurement are on the same order of magnitude as the differences
being discussed.
Siletz Segment Characteristics
Table E.1
Sept. 15, 1969
1st Approx.
UPPER
LOWER
Segment
J
_Raf Elev.
1
2
3
4
-1,13
-1.13
-1.13
-1.13
ASft
AC-f
2956
5545
3147
960
2.29
1.89
1.19
0.37
x 10"
x IO
x
x iO
Amr1ii_t7c.if-c1
Ref Elev.
AC-ft2
AS-ft2
2.43
2,43
2.43
2.43
4064
4.50 x
1.92 x 1O
1.22 x
7325
4578
2034
0.47
1O
3rd Annrnx
ii-fzr'c Area
Lower
AS1H.
Segment(i)
AS
H
ASH
AS.H.
AS.H.
AS,H.
H2
H3
-
-
-
-
-
xl 0
1
2
3
4
2.29
1.89
1.19
0.37
-2.80
-2.80
-2.80
.2.80
2.29
1,89
1.19
0.37
5.74 x I0
AST
1.89
1.19
0.37
3.45 x 10'
1.19
0.37
0.37
1.56 x 10/ 0.37 x
Upper
1
4.50
2
1.92
1.22
0.47
3
4
AST
2.80
2.80
2.80
2.80
4,50
1.92
1.22
0.47
8.11 x 10
-
1.92
1.22
0.47
3,61 x
-
-
-
-
1.22
0.47
1.69 x 10'
-
0.47
0.47 x 10
-1
1st Approx.
KF, K1 and Segment Amplitudes
Table E.4
Locer
4uL
4BL
1
Segment (j)
1
2
3
4
C2AC3T2
2.01 x
2.05 x
io16
io16
1.45 x i0'5
3,30 x
o14
AST 2
3.29 x 10
1.19 x io
2.43
H_1
-4.25
-2.68
-2.65
K
2.81
0.65
0.93
1.11
1.37 x io13
246
6.58
1.30
2.86
2.21
4.25 [2.17
3.06
.35
.44
3.27
.26
3.43
gACT2
I
AST
2.27 x io8
5.74 x
x
1.56 x
0.37 x
.083
io? .107
101 .126
io .084
1.06
2.35
5.54
1.07
8.11
3.61
1.69
0.47
io
io
,o
io
1.45 x 10
3.10 x
10's
8.05 x
10's
H
K1
io
ll,
II
(Mb1L)
.63
.99
.93
.87
-2.68
-2.65
-2.14
-2.03
-2.00
-1.81
-1.49
.72
1.07
1.05
1.05
3.06
3.27
3.43
3.60
3.71
3.92
4.08
4.25
-246
[
Upper
1
7.76
2
8,88 x 10-17
3
4.69 x iO6
4
io
x io
x 1015
x io15
x b'4
x o'
x i0
x io
x
x io-8
x
x
x
x
.086
.085
.094
.050
Siletz Segment Characteristics
Table. E.5
Sept. 15, 1969
2nd Approx.
UPPER
LOWER
Segment
Ref Elev.
1
2
3
-1.06
-1.04
- .92
4
.76
AC-ft
2978
5590
3231
1071
AS-ft2
Ref Elev.
AC-ft2
2.35 x io
1.89
10
1.19 x iO
0.38 x 1O7
2.59
2.73
2.83
2,94
4118
AS-ft2
4.50
1.93
1.22
0.49
7485
4740
2191
2nd Approx.
Amp1itude-Weihted Surface Area
Thble E.6
x 1O7
x
x
x
Lower
Segtaent(i)..
1
2
3
4
AS
2.35
1.89
1.19
0.38
H1
-2.68
-2,65
-2.46
-2.14
ASH1
6.30
5,01
2.93
0.81
AST
IAS1H
AS1H
H2
H3
-
-
-
-
-
2.35
1.87
1,09
0.30
1.89
1.09
1.19
.30
.33
5.61 x 1O7
3.28 x
-
1.52 x 10
0.38
0.38 x 10
Upper
1
2
3
4
AST
4.50
1.93
1.22
.49
3.06
3.27
3.43
3.60
13.77
6.31
4.18
1.76
4.50
2.06
-
1.37
0.58
x 10
1.93
1.28
0.54
3.75
-
-
-
-
1.22
0,51
10
L3
-
10d
0.49
0.49 x
I-,
Ui
2nd Approx.
KF, K1 and Segment Amplitudes
Table E.7
Lower
4Tr&BL
Segment(i)
1
2
3
4
-
C2ACST2
1.97
2.00
1.34
2.38
io6
x
x 10
x 10
x io-14
4
AST2
1015
3.15
1.08 x l0
2.31 x 10
1.44 x io13
Hi_i
-4.25
-2.76
-2.76
-2.62
L
AST
KF
gACT2
2.63
0.59
0.85
0.90
1.44 x l0
3.07 x 101
7.84 x 10
5.61
3.28
1.52
0.38
H
K1
x 1O7
x l0
x 10
x
.081
.101
.119
.077
2.03 x io8
_____________ _____________ ______ _____ ___________ __________ ____
.65
1.00
.95
.91
-2.76
-2.76
-2.62
-2.38
H (MSL)
-2.11
-2.11
-1.97
-L73
_1______ ________
Upper
1
7.46 x io7
2
8.32 x io
3
4.2 x
4
2.78 x
io6
7.24 z 10
1.41 x 10
2.99
1o14
2.40 x io3
4.25
2.98
3.19
3.38
2.3011.05
.35 2.30
.40 5.35 x
.22j0.99_
10
io-
io
io-8
8.51 x 10
3.75
10
1.73 x io
0.49
.089
.086
.093
.049
.70
1.07
1.06
1.06
2.98
3.19
3.38
3.58
3,63
3.84
4.03
4.23
C.'
Siletz Segment Characteristics
Table E.8
Sept. 15, 1969 3rd Approx.
UPPER
LOWER
I
___Segment
Ref
Eiev.IACft:2
-1.11
-1.11
-1,02
-0.87
1
2
3
4
Ref E1ev
2.55
2.68
2.80
2.93
2.31 x iO
1.89 x 107
1.19 x 10
0.37 x107
2963
5555
3191
1038
AC-ft2
4.50 x
1.93 x
1.22 x
4109
7458
4729
2188
1O7
io
0.49 x i07
Amniitude-Weihted Surface Area
9
Tphi(.
I
AS-ft2
3rd Arrnrox.
Loer
AS.H1
Segment(i)
1
2
3
4
AS
2.31
1.89
1.19
0,37
H
-2.76
-2.76
-2.62
-2.38
AS1H
ASH
6.38
5.22
3.12
0.88
AST
2.31
1.89
1.13
0.32
H
H
-
-
-
-
-
-
x
1.13
0.32
3.34 x 10
8.54 x
1.93
1.29
0,55
3.77 x 1O
565
ASH
1.19
-.
0,34
0.37
1.53 x 10'
Tx
10
Upper
1
2
3
4
AST
4.50
1.93
1.22
0.49
2.98
3.19
3,38
3.58
13.41
6.16
4.12
1.75
4.50
2.07
1.38
0.59
-
-
-
-
-
1.22
0.52
1.74 x
-
0.49
0.49 x
io
-J
Table E.10
KF, K1 and Segment Amplitudes
3rd Approx.
Lo
Segment(i)
4'irBL
ASTL
H._1
Kr
3
4irL
ç,T 2
.
H.1
AST
Kr
II.
i- j
t
H(SL)
C2AC T
1
2
3
4
2.00
2.0e
1.39
2.61
x o-16
x l0
x 10
x i0'
319 x io15
1.16 x 1015
2.34 x iol4
1.37 x io3
-4.25
-2.72
-2.72
-2.58
2.71
0.64
0.88
0.92
1,45
3.09
7.94
2.09
x 10
x 10
x io
x io8
5.65
3.34
1.53
0.37
x 1O7 .082
x
.103
x io
.121
x io .077
4.25
2.93
3.14
2.34
0.35
0.40
0.22
1.05 x io2.31 x o5.36 x 10
io_8
0.99
8.54
3.77
1.74
0.49
x
x
x l0
x
.64
1.00
.95
.91
-2.72
-2.72
-2.58
-2.35
-2.07
-2.07
-1.93
-1.70
2.93
3.14
3.33
3.53
3.58
3.79
3.98
4.18
Upper
1
7.54 x i017
2
8.41 x 10-17
3
4.25 x 1016
4
2.79 x io
7.29
1.43
3.03
2.40
x
x
x
x
ioiS
i0
io14
io13
333
.090
.087
.093
.049
.69
1.07
1.06
1.06
-I
Co
Table E1l
Determination of Hih and Low Tide Phase La
UPPER
Segment
K
K1
{
1
2
3
4
2.34
0.35
0.40
0.22
LOWER
(Hi1
.090
.087
.093
.049
402
0
40
40
54
14
16
70
9
(Hx)i
40
54
70
79
KF
2.71
0.64
0.88
0.92
K1
.082
.103
.121
.077
UPPER
1
2
3
4
Hmjnj
i_I
180
222
244
271
42
22
27
26
122
244
271
297
4Oi
(øQ=o)
55
29
36
235
251
280
305
Determination of Hich and Tow Slack Tide Phase T
Table EA2
Segment
0Hmjn
I<F
1<1
2.34
0.35
0.40
0.22
.090
.087
.093
.049
LOWER
(0Q0)j
OHmaxj..i
40
54
53
19
21
70
11
0
53
59
75
81
KF
2.71
0.64
0.88
0.92
K1
.082
.103
.121
.077
(OHmin)i1
180
222
244
271
34
Determination of Maximum Ebb and Flood Velocity
Table E.13
Lower-Ebb
Segment:
KF
KT
1
2
2.71
0.64
0.88
0.92
.082
.103
.121
.077
3
4
.845
.860
.857
.855
As/Ac
27/T
1.91 x
.60 x 1o4
.48 x
.36 x
1.40 x 1O
1.40 x 10
1.40 x 10
1.40 x 10
V
V
model
/. error
-2.72
-2.72
.2.58
-2.35
-6.18
-1.97
-1.49
-1.01
-6.16
-1.53
-1.20
-0.88
+29
+24
+15
2.93
3.14
3.33
3.53
7.37
1.94
1.50
1.02
6.14
1.54
1.26
0.93
+20
+26
+19
+10
+0.3
Upper-Flood
1
2
4
1
2.34
0.35
0.40
0,22
.090
.087
.093
.049
.847
.873
.870
.915
2.12 x iO
.51 x
.37 x io
.22 x
1.40 x 10
1.40 x io
1.40 x IO
1.40 x 10
181
Appendix F
Field Data:
Velocity, Temperature, Salinity,
,
a;:,
Average Density
Figure F.l shows the location of sites where measurements
were made on the Yaquina, Alsea and Siletz estuaries during the
summer of 1969,
numbers.
The site designations are the sane as the table
Tables F.l through F.8 are on the Yaquina, F.9 through
F.11 on the Alsea and P.12 through F.15 on the Siletz estuary.
Table P.16 gives a summary of the density differences
observed between the top and bottom waters of the estuaries at
the time of measurement.
183
Table F.l
Estuary: Yaquina
Location: Newport - near highway gridge
Date: 7-21-69
Time
?DT
0815
Sample Position
Approximate fraction of depth Velocity Temp Salinity
fleoth - ft
from water surface ft/sec* °C
0/00
37.5
0.88
.9
.7
.5
.3
.1
0845
38.0
.9
.7
.5
.3
.1
0925
1005
36.8
35.5
.9
.7
.5
.125
.3
1.50
.1
L65E
.9
0.30
0.60
0.55
0.75
i.00E
0.25
0.45
0.50
0.70
1.00E
0.50
0.40
0.30
0.25
0.40
0.40
0.2-0.6
0,5-0.7
0.2-0.5
0,35
0.75
0.50
0.60
0.75
0.65F
.7
.5
.3
.1
1030
35.5
.9
.7
.5
.3
.1
1105
34.0
.9
.7
.5
.3
_.1
1205
17,5
.9
.7
.5
.3
1235
17.3
.9
.7
.5
.3
.1
*
E- Ebb flow
F- Flood flow
1.30
1.70
1.75
2.1OE
0.75
1.40
1.50
1.75
1.80E
0.65
0.80
-
-
Density.
I
G
-
10.1
31.0
24.91 23.85
11.0
33.1
26.59 25.22
10.5
10.1
32.8
26.35 25.18
25.63
11.5
32.7
26.27 24.92
12.2
10.5
31.5
33.3
25.31 23.87
26.75 25.57
11.0
33.3
26.75 25.47
12.8
10.7
31.6
33.0
25.39 23.82
26.51 25.30
13,0
10.6
29.3
33.1
23.53 22.01
11.5
32.8
26.35 25.00
13.1
31.2
25.07 23.47
33.3126.75
11.0
for tables F.1 through F.15
26.5925.4O
184
Table F.1 - continued
Time
PDT
1305
Sample Position
Density
Approximate fraction of depth Velocity Temn Salinity
C
0/00
Depth - ft from water surface ft/sec
26.27 25.01
32.7
10.6
0.90
.9
17.3
1.00
.7.
32.1
25.79 24.52
11.2
1.10
.5
.3
.1
1340
29.0
.9
.7
.5
.3
.1
1405
33.7
.9
.7
.5
.3
1440
26.3
.9
.7
.5
.3
.1
1530
35.0
.9
.7
.5
.3
1600
36.0
.1
.9
.7
.5
.3
.1
1630
36 .8
.
9
.7
.5
.3
1700
36.0
.1
.9
.7
.5
.3
.1
1735
30.5
.9
.7
.5
1.20
1.00F
1.00
1.10
1.20
1,45
1.4SF
0.80
0.80
1.20
1.50
1.8SF
1.50
1.85
12.1
9.3
32.2
35.5
25.87 24.43
28.53 27.49
8.9
34.0
27.32 26.37
33.4
26.84 25.80
8.3
34.1
27.40 26.55
8.3
34.1
27.40 26.55
8.3
8.2
34.2
34.2
27.48 26.63
8.3
34.2
27.48 26.63
8.4
8.3
33.9
34.3
27.24 26.38
27.56 26.71
8.3
34.0
27.32 26.47
8.4
34.3 J27.56 26.70
9.7
t
1.75
1.75
1.75F
1.70
1.75
1.75
2.20
2.20F
1.50
1.50
1.75
1.90
1.7SF
1. 25
1.50
1.60
1.75
1.70F
1.10
1.20
1.40
1.30
1.2SF
1.20
0.40
0.20
T.48
.3
.1
Table F.2
Estuary: Yaquina.
Location: Oneatta Point (River Bend Marina)
Station 1 (see sketch)
Date: 7-21-69
Time
PDT
1000
1120
Approximate Depth
in feet
31.2
29.5
Sample Position fraction
of depth from
Water surface
.9
.7
.5
.3
.1
.9
.7
.5
.3
1255
30.1
Density
Q
t
31.5
25.31 23.09
17.5
28.8
23.14 20.68
18.5
16.0
16.2
16.7
17.0
24.1
31.0
29.8
28.9
27.2
19.36
24.91
23.94
23.21
21.85
19.0
16.2
23.5
29.5
18.87 16.30
23.69 21.45
16.2
17.0
17.0
19.0
16.5
16.5
17.0
17.5
18.6
28.5
28.8
26.9
23,5
29.3
28.8
28.3
26.1
24.6
22.90 20.75
23.t74 20.80
21.60 19.34
18.87 16.30
23.53 21.29
23.14 20.91
22.73 20.42
20.97 18.63
19.76 17.25
Temp
degrees
°C
16.0
ft/sec
.38
.36
.30
.93
l.45E
.24
.68
.46
.32
0
0
0-270
180
190
200
200-90
30-45
15
30-0
350
160-220
150-110
120
.9
.60
.19
.7
.5
.3
.57
.76
.85
35
25
25
.1
1205
Salinity
0/00
Velocity Azimuth
.1
.41F
40
30.6
.9
.19
10
1.03
20
-_______________
.7
.5
.3
.1
.79
.76
.85F
5
35
15
I
16.88
22.71
21.75
20.94
19.58
Ui
Table F.2 - continued
Time
PDT
1350
1450
1625
1715
Approximate Depth
in feet
32.6
33.7
35.5
36.4
_________ ___________________
1800
36.6
1845
36.2
-________ ____________________
Sample Pos±tion fraction
of depth frem
water surface
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
Velocity Azimuth
ft/sec deerees
.80
.85
.63
.85
.52F
.67
.93
1.23
1.17
.621?
.68
1.04
.96
.96
.511?
.3
.68
.73
.85
.93
.93F
.38
.52
.43
.24
.1
.161?
.9
.7
.5
.3
.1
.19
.32
.43
.87
.1
.9
.7
1.l5E
5
20
0
15
25
'
10
15
15
25
0
15
25
20
20
30
Temp
1
16.5
16.0
16.0
16.5
17.5
16.0
16.0
16.0
16.1
16.5
15.0
15.0
15.2
15.5
15.2
Salinity
0/00
30,1
30.0
29.9
28.3
Density
21.90
21.94
21.86
20.56
30.7
30.7
30.3
30.1
29.9
32.0
31.8
31.7
31.5
31.5
24.18
24.10
24.02
22.76
21.21
24.66
24.66
24.34
24.18
24.02
25.71
25.55
25.46
25.31
25.31
32.8
32.7
32.8
32.8
26.35
26.27
26.35
26.35
24.53
24.62
24.73
24.71
33.0
32.6
32.3
31.9
31.2
26.51
26.19
25.95
25,63
25.07
24.85
24.60
24.33
23.91
23.29
_26.4
l886
22.47
22.47
22.16
22.00
21.75
23.69
23.54
23.41
23.20
23.27
5
30
20
20
15
20
14.0
13.1
12.9
13.0
340
13.8
180-210 13.1
245
12.8
205
13.0
210
13.6
200
14.0
0
5
5
32.4_ 26.0324.25
Table F.3
Estuary: Yaquina
Location: 0neatt Point (River Bend Marina)
Station 2 (see sketch)
Date: 7-21-69
Sample Position fraction
Approximate Depth
Time
in f..4-
PT)T
21.4
1020
1
1130
___________________
22,0
of depth from
Velocity Azimuth
i1-
Temp
.9
.7
.5
.43
.13
.49
.3
.1
.9
1.26
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.71
.54
.41
30
0
300-240
235
210
210
1.42E
0 -320-
.52
Salinity
finn
..,.
Density
(t
f
rn..
17.0
17.0
17.8
30.3
29.1
27.1
24.34 21.94
23.37 21.02
21.76 19.32
18.8
19.0
16.5
24.6
24.1
29.1
19.76 17.20
19.36 16.75
23.37 21.13
17.0
17.2
17.2
19.0
17.0
17.0
17.5
18.1
19.1
17,0
16.9
17.5
18.2
19.0
16.2
16.0
16.9
17.5
17.5
29.0
27.6
26.9
23.6
29.3
27.6
26.6
25.0
23.5
29.3
29.0
26.5
25.3
24.5
30.1
30.1
28.7
28.1
27.4
23.30
22.17
21.60
18.96
23.53
22.17
21.37
20.08
18,87
23.53
23.30
21.29
20.32
19.68
24.18
24.18
23.06
22.57
22.01
340
1215
23.3
1300
23.3
1405
25.8
10
10
315
.63E j
.49
.79
.82
.68
,38F
.77
1.39
1.04
1.17
1.02F
1.23
1.10
1.20
1.58
1.IOF
J
225_
0
20
20
25
30
10
20
20
10
0
0
10
0
15
20
20.96
19.83
19.29
16.38
21.17
20.88
19.01
17,66
16.27
21.17
20.98
18.93
17.85
17.07
21.97
22.01
20.70
20.14
19.61
I-
Table F.3 - continued
Time
PT)T
1505
Approximate Depth
tn
c26,5
Sample Position fraction
of depth from
wfr nrfi
.9
.7
.5
.3
.1
1640
1725
1810
28.1
28.4
30.4
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
Velocity Azimuth
ft/e dr
1.06
1.45
1.72
1.58
l.17F
1.06
1.30
1.31
1.31
l.3lF
.76
1.01
.98
.71
.74F
.16
0
20
20
20
15
15
Temp
Salinity
°C
0/00
30,7
30.4
30,3
30.2
29.3
32,0
32.2
31.9
31.5
31.0
31.7
31.8
31.6
31.9
15.9
15.8
16.1
16.2
17.0
15.0
14.5
14.7
14.6
15.5
15.2
14.0
13.5
13.9
14,2
13.1
Density
32.9
24.66
24.42
24.34
24.26
23.53
25.71
25.87
25.63
25.31
24.91
25.46
25.55
25.39
25.63
25.23
26.43
13.0
13.1
14.0
32.8
32.6
32.6
26.35 24.72
26.19 24.54
26.19 24.36
330
260-240
-270
14.1
32.3
25.95 24.11
185
210
210
190
190
13.0
13.0
13.0
13.8
14.0
32,7
32.6
31.9
32,1
31.3
26.27 24.64
26.19 24,56
25.63 24.03
25.79 24.02
25,15123.36
15
25
20
15
30
15
15
15
15
30-0-
_31.4
22.49
22.26
22.14
22.05
21.18
23.69
23,95
23.68
23.39
22.81
23.41
23.73
22,69
22.85
22.40
24.77
325 - 0
.7
.5
.3
.27
.27
.22
.1
.25E
__________ ______________________ ___________________________
1855
27.6
.9
.7
.5
.3
.1
.32
.41
.93
1.20
1.45E
30-165
100-0
10-0
03
Co
Table F.4
Estuary: Yaquina
Location: Oneatta Point (River Bend Marina)
Station 3 (see sketch)
Date: 7-21-69
Time
PDT
lo5[
1140
Approximate Depth
in feet
9.1
9.0
Sample Position fraction
of depth from
water surface
Velocity Azimuth
.7
.5
.3
.1
.60
.68
degrees
190
200
1.34
1.29
l.31E
205
210
210
.8
.65
.9
ft/sec
50-90
Density
°C
Salinity
0/00
18.7
18.5
19.0
19.0
25.6
25.7
24.4
24.4
20.56
20.64
19.60
19.60
18.5
25.4
20.40 17.86
18.7
19.2
18.1
18.8
19.2
17.8
18.5
19.0
17.0
17.0
17.6
24.1
23.5
25.5
24.2
23.5
26.5
24.7
24.4
29.0
28.6
28.4
28.0
19.36
18.87
20.48
19.44
18.87
21.29
19.85
19,60
23.30
22.98
22.82
22.49
22.82
24.58
Temp
17.97
18.09
16.99
16.99
-110
1225
1310
1415
1515
9.7
.5
.35
.2
.8
.49E
.68
.5
.55
.2
.58F
10,6
.8
.80
12.5
.5
.2
.9
1.26
.96F
1.06
1.36
13.4
.7
.5
.3
.1
.9
.7
.5
.3
.1
.63
219
2.19F
0
240
15
30
15
15
10
20
35
20
15
20
25
_28.4
15
18.1
17.0
16.5
15
16.2
30.6
20
16.0
16.3
30.4
30,2
.87
0
1.53
1.39
1.75
_i.31F
18.1
25
30.6
30,6
1689
16.25
18.03
16.83
16.25
18.06
17.33
16.99
20.95
20,65
20.36
19.94
20.25
22.17
24.58122.28
24,58 22.35
24.42 22.24
24.26 22.02
Table F.4 - continued
Approximate Depth
Time
in15.2ft
PDT
1650
1735
1
15.5
I
15.8
1820
15.5
1905
1
Sample Position fraction
of depth from
tr siirfe
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
Velocity Azimuth
fi/c
.82
1.04
1.15
1.26
l.36F
.35
.60
.63
.52
.60F
.22
.7
.23
.5
.3
.1
.9
.7
.5
.3
.1
.35
.32
.71E
.60
1.01
1.26
1.39
1.42E
Temp
Oç.
$allnity
()/flfl
Density
6
I
(J
15.2
14.5
14.2
14.5
15.0
31.7
31.7
31.8
31.7
31.8
25.46
25.55
25.46
25.55
290-210
-160
150-180
150-180
14.0
32.6
26.19 24.36
14.0
32.4
26.03 24,21
210
230
185
210
200
200
205
200
14.0
14.0
15.1
13.2
14.0
13.5
14.0
14.0
32.6
32.3
31.3
32.5
32.3
32.1
31.9
31.7
26,19
25.95
25.15
26.11
25.95
25.79
25.63
25.46
15
25
20
15
30
23.41
23.55
23.71
23.55
23,54
5
10
30
50
0
24.36
24.13
23.13
24.44
24.13
24.08
23.83
23.66
Table F.5
Estuary: Yaquina
Location: Oneatta Point (River Bend Marina)
Station 4 (see sketch)
Date: 7-21-69
Time
PDT
1040
1150
1230
1320
1425
1525
Approximate Depth
in feet
9.3
9.4
9.8
10.8
11.8
13.3
-______________
Sample Position fraction
of depth from
water surface
.8
.5
.2
Velocity Azimuth
ft/sec
.43
.68
Temp
degrees
°C
190
200
210
18.5
18.8
19.0
18.8
.8
1.09E
.54
.5
.2
.30
.41E
.8
.71
10
.5
.68
.2
.8
.5
.2
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.65F
1.01
1.12
1.53F
1.67
1.83
2,16
1.97
1.78F
1.14
1.17
1.69
1.74
1.72F
10
15
5 -8030
55
30-0270-0
5
25
25
15
5
25
15
30
10
15
15
15
25
Salinity
0/00
27.2
Density
c7
19.23
17.72
16.99
17.42
25.3
24.4
24.9
21.85
20.32
19.60
20.00
18.9
19.2
24,7
23.9
19.85 17.24
19.30 16.56
18.0
19.0
19.5
18.5
19.0
19.5
17,3
17.5
17.8
18.0
18,2
16.1
15.9
15.9
16.1
17.0
26.2
24.2
24.0
25.5
24.4
24.6
28.2
28.4
27.9
26.8
26.8
30.5
30.6
30.6
30.0
28.6
21.05
19.44
19.28
20.48
19.60
19.76
18.60
16.84
16.57
17.94
16.99
17.03
22.6520.27
22.82
22.41
21.53
21.53
24,50
24.58
24.58
24.10
20.38
19.93
19.05
19.00
22.30
22.41
22.41
21.91
22.9820.65
I-.
Table F.5 - continued
Time
PnT
Approximate Depth
1655
15.1
-________
1745
fri ft
15.6
1830
15.3
1910
15.1
Sample Position fraction
of depth from
water surface
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
.9
.7
.5
.3
.1
Velocity Azimuth
ft/sec
.93
.96
1.04
1.01
l.09F
.32
.38
.27
.32
.32F
.63
.43
.30
.49
degrees
20
15
20
20
15
0
5
Tamp
°C
Salinity
Density
14.5
14.1
14.2
14.5
15.0
0/00
31.8
31.8
31.8
31.2
30.4
25.55
25.55
25.55
25.07
24.42
23.65
23.73
23.71
23.18
22.46
14.0
14.0
14.0
14.7
31.6
32.5
31.9
31.7
25.39
26.11
25.63
25.46
23.59
24.29
23.83
23.51
G
350
55
55
150-230
.71E
230
215
215
210
.79
270-210
13.6
32.1
25.79 24.06
215
215
210
220
215
13.7
13.5
13.9
13.5
32.1
31.8
31.8
30.5
25.79
25.55
25.55
24,50
.98
1.15
.93
.82E
24.04
23.85
23.77
22,84
'.0
193
Table F.6
Estuary: Yaquina
Location: Georgia Pacific Loading Dock near
Date: 7-21-69
Time
PDT
0800
Sample Position
Approximate fraction of depth
Depth - ft
from
water surface
15.7
.9
.7
.5
.3
.1
0830
15.3
.9
.7
.5
.3
.1
0900
14.7
.9
.7
.5
.3
.1
0930
14.0
.9
.7
.5
.3
.1
1000
13.6
.9
.7
.5
-
1030
.3
________
13.1
_____
.1
.9
.7
.5
.3
.1
1100
12.5
.9
.7
.5
1130
12.4
.3
.1
.9
.7
.5
.3
.1
1200
12.3
.9
.7
.5
.3
.1
Velocity Temp
ft/sec
0.33
1.22
1.44
1.22
1.56E
0.40
1.16
1.24
1.24
l.3lE
0.40
1.25
1.14
1.34
1.58E
0,35
1.07
1.07
1.13
l.52E
0.26
1.02
0.91
1.20
t,45E
0.13
0.62
0.86
1.07
l.14E
0.13
0.46
0.60
0.87
0.98E
0.08
0.13
0.28
0.55
0.69E
0.35
0.24
0.26
0,17
0.13
°C
19.5
Toledo
Salinity
0/00
Density
0
t
Oe
18.66
14.99 12.52'
19.5
16.88
13.55 11.17
19.3
19.0
15.55
18.28
12.49 10.22
14.68 12.35
19.5
16.12
12.94 10.59
19.3
20.0
14.67
17.17
11.78 9,56
13.79 11.28
19.7
14.54
11.68
20.0
20.5
20.5
20.7
20.0
20.0
21.5
13.82
15.93
14.23
13.73
13.46
13.43
14.79
11.09 8.75
12.79 10.23
11.42 8.94
11.02 8.52
10.80 8.47
10.78 8.45
11.88 9.13
21.5
13.16
10.56
7.90
21.3
22.5
13.11
14.65
10.52
11.76
7.91
8.78
22.5
12.52
10.05
7.18
22.0
23.0
12.30
12.83
9.87
10.29
7.13
7.27
22.5
12.23
9.81
6.95
22.0
22.7
11.81
12.41
9.47
9.96
6.75
7.04
21.8
12.03
9.65
6.96
220
,5
11.65
12,88
9.35
10.34
6.64
7.45
22.0
21.8
12.23
9.81
7.111
21.5
21.8
11.66
9.59
6.91j
9.37
194
Table F.6 - continued
Time
PDT
1230
Sample Position
Approximate fraction of depth Velocity Temp Salinity
Depth - ft from water surface ft/sec
°C
0/00
13.2
.9
.7
.5
.3
.1
1300
13.6
.9
.7
.5
.3
.1
1330
14.4
.9
.7
.5
.3
1400
14.7
.1
.9
.7
.5
.3
.1
1430
15.7
.9
.7
.5
.3
.1
1500
16.1
.9
.7
.5
.3
.1
1530
16.5
.9
.7
.5
.3
.1
1600
17.2
.9
.7
.5
.3
.1
1630
18.0
.9
.7
.5
.3
.1
0.19
0.42
0.40
0.51
0.37F
0.20
0.33
0.30
0,53
0.37F
0.24
0,62
0.48
0.55
0.30F
21.5
13.38
Density
0
Tt
10.74 8.06
21.5
13.11
10.52
7.85
21.8
21.8
12.32
13.90
9.89
11.16
7.19
8.38
21.5
13.40
10,75
8.08
22.0
12.86
14.75
10.32
11.84
7.55
14.77
11.85
13.60
17.4
10.92
14.00
l7.36
13.94
15.10
17.43
12.13
14.00
17.57
14.12
15.95
18.53
12.81
14.88
18.45
14.82
46.72
13.42
15.68
15.47
15.31
14.97
0.3T
0.55
0.69
0.57
0.17F
0.22
0.62
0.60
0.49
0.38F
0.26
0.44
0.64
0.60
0.33F
0.46
0.57
0.51
0.53
0.26F
0.30
0.76
0.64
0.44
0.38F
0,40
0.76
0.64
0.51
0.38F
12.81
12.56
12.48
12.12
1420 11,31
16.32 13,37
21.0
21.3
20.9
21.2
21.5
21.2
19.52
19.26
19.06
18.64
17.68
20.32
20.9
19.01
15.27 12.45
21.5
21.7
18.65
21.12
14.98 12.03
16.96 13.84
20.8
21.05
16.91 14.02
21.1
19,91
15,99 13.08
195
Table F.6 - continued
Time
PDT
1700
1730
1800
1830
Sample Position
Density
Approximate fraction of. depth Velocity Tenip Salinity
GC
Q
Qi
0/00
Depth - ft from water surface ft/sec
13.91
20.6
22.18
17.81
18.3
.9
0.44
0.68
.7
22.05
17.71 13.87
20.4
.5
0.71
.3
0.33
20.96 16.83 13.96
0.24F 20.7
.1
18.53 15.54
23.07
20.8
19.1
.9
0.38
23.03 18.50 15.61
20.4
0.62
.7
22.98 18.46 15.60
20.3
.5
0.68
22.57
18.13 15.24
20.5
.3
0.38
21.36 17.15 14.29
0.11F 20.6
.1
23.37
18.77 15.89
19.1
.9
0.44
.7
23,41
18.81 16.00
20.0
.5
0.51
.3
0.13
20.96 16.83 14.07
0.1OF 20.3
.1
TT9 23.52 18.89 16.10
0.08
19.0
.9
0.06
.7
22.98 18.46 15.62
20.2.
0.06
.5
I
ö- '3
.3
.1
1900
19.0
.9
.7
.5
.3
.1
1930
18.4
.9
.7
.5
.3
.1
2000
17.9
.9
.7
.5
.3
.1
2030
17.0
.9
.7
.5
.3
2100
16.4
.1
.9
.7
.5
.3
.1
0.37
0.22
0.04
0.42
0.68
0.80
0.58E
0.30
0.84
1.22
1.25
1.29E
0.42
1.04
1.38
1.56
l.47E
0.48
1.29
1.13
1.54
1.85E
0.37
1.34
1.38
1.78
1.87E
20.6
20.0
20.73
23.45
16.65 13.82
18,83 16.02
20.6
21.56
17,32 14.45
20.6
20.0
20.80
23.09
16.70 13.87
20..8
20.24
16.25 13.38
20,6
20.0
20.4
20.6
20.7
21.0
19.8
20.26
22.30
20.68
20.07
19.60
19.34
21.69
16.28'13.47
17.92 15.15
20.3
19.11
15.35 12.67
20,7
19.5
18.18
21.15
14.60 11.87
16.99 14.41
20.2.
17,77
13.79 11.23
20.5
16.83
13,52 10.91
75
l6.61l3.83
16.12
15.74
15.54
17.42
13.32
12.96
12.68
14.74
196
Table F.7
Estuary: Yaquina
Location: Mill Creek
Date: 7-21-69
Time
PDT
0749
Sample Position
Approximate fraction of depth Velocity Temp Salinity
Depth - ft from water surface ft/sec
°C
0/00
16.5
.9
0,09
19.0
4.98
.7
.5
.3
0800
15.7
.1
.9
.7
.5
.3
0830
15.2
.1
.9
.7
.5
.3
.1
0900
14.7
.9
.7
.5
.3
.1
0930
14.1
.9
.7
.5
.3
.1
1000
13.7
.9
.7
.5
.3
.1
1030
13.1
.9
.7
.5
.3
.1
hOC)
12.8
0.67
0.85
1.02
0.80E
1.02
1.09
1.07
0.87
0.74E
0.54
0.78
0.80
0.84
0.80E
.9
.7
.5
.3
.1
0.60
0.52
0.73
0.52E
0.51
0.54
0.62
0.56
0.56E
0.40
0.45
0,54
0.67
0.49E
0.38
0.54
0.67
0.45
0.32E
0.29
0.29
0.43
0.38
0.21E
Density
3.95
2.26
19.0
19.0
3,86
3.04
1.41
19.0
20.0
3.16
2.64
2,48
2,05
0.88
0.27
20.5
2.90
2.27
0.37
20.8
21.1
2.57
2.00
1.99
0.04
TTT3
öTs
21.1
1.97
1.51 -0.47
21.1
21.3
1.90
1.26
1.45 -0.53
0.93 -1.06
21.5
1.32
0.98 -1.05
21.5
21.5
21.8
21.8
21.8
22.0
22.0
1.32
0.59
0.55
0.44
0.45
0.35
0.26
0.98
0,42
0.38
0.31
0.32
0.25
0.18
22.0
0.23
0.16 .-1.93
22.0
22.5
0.19
0.14
0.14 -1.95
0,10 -2.11
22.0
0.12
0.09 -2,00
22.0
0.16
0.11 -1.98
-1,05
-1.58
-1.67
-1.74
.l.73
-1.84
-1.91
197
Table F,7 - continued
Time
PDT
1130
Sample Position
Approximate fraction of depth Velocity Temp Salinity
Depth
ft
from water surface ft/sec
°C
0/00
12.6
.9
0.12
23.0
0.08
.7
.5
.1
1200
12.5
.9
.5
.1
1230
12.7
.9
.5
.1
1300
13.3
.9
.5
.3
1330
13.7
.1
.9
.7
.5
.3
.1
1400
14.4
.9
.7
.5
.3
.1
1430
15.0
.9
.7
.5
.3
.1
1500
15.8
.7
1530
16.5
L63
.3
0.63
0.74F
0.63
0.65
0.71
0.76
0.82F
0.73
0.63
0.69
0.74
0.80F
.1
.9
.5
.3
.1
17.2
0,23E
Th.07
0.25
0.23
0.20
0.23
0.23F
0.38
0.73
0.80
0.80F
0.27
0.42
0.51
0,60
0.43F
0,45
0.40
0.43
0.43
0.6SF
0.43
0.42
0.58
0.69
0.51F
0.45
0.54
.5
.7
1600
0.25
0.23
.9
.7
.5
.3
.1
Density
0.06 -2.25
22.0
0.12
0.09 -2.00
22.3
22.3
22.5
0.04
0.03
0.03
0.04
0.13
0.13
0.14
0.11
0.09
0.19
0.13
0.35
-2.16
-2.12
-2.17
-2.04
-2.03
-2.03
23.0
0.06
0.05
0.05
0.06
0.19
0.19
0.20
0.16
0.12
0.27
0.19
0.50
23.0
0.55
0.38
-L95
22.5
23.0
0.61
1.28
0.43 -1.79
0.96 -1.42
23.0
1.47
1.11 -1.28
23.0
23.0
2.46
2.29
1.90 0.54
1.77 -0.67
23.0
2.47
1.91 -0.53
23.0
23.5
23.0
23.0
23.0
23.0
23.0
2.52
3.65
3.85
4,07
4.28
3,76
5.77
1.96 -.0.49
0.24
2.87
3.03 :0.51
3.22 0.69
3.38 0.85
2.96 0.44
4.59 1.96
22.5
5.99
4.77
2.25
22.0
23.0
6,12
7.18
4,88
5.73
2.47
3.03
22.5
7.22
5.77
3.19
23.0
7.33
5.85
3.14
22.0
22.3
22.3
22.5
22.0
-.2.07
-1.98
-1.98
198
Table F.7 - continued
Time
PDT
1630
Sample Position
Approximate fraction of depth Velocity Temp Salinity
Depth - ft from water surface
ft/sec
0/00
°C
17.8
.9
.7
.5
.1
1700
18.5
.9
.7
.5
.3
.1
1730
18.9
.9
.7
.5
.3
.1
1800
19.3
.9
.7
.5
.3
.1
1830
19.3
.5
.3
.1
18.9
.9
.7
.5
.3
.1
1930
18.6
.9
.7
.5
.3
.1
2000
17.9
.9
.7
.5
.3
.1
2030
17.2
22.5
8.11
6.48
3.85
22.5
8.22
6.58
3.95
22.5
22.5
22.5
22.5
8.22
8.82
9.03
9.11
9.09
9.09
9.72
6.58
7.06
7.22
7.29
7.28
7.28
7.79
3.95
4.38
4.53
4.60
9.72
7.79
9.74
10.07
7.80
8.07
10.44
8.37
10.11
8.10
8.19
6.55
9.26
7.42
22;O
9.38
8.56
7.51
6.85
4.30
21.5
8.66
6,93
4.49
20,5
8.72
6.98
4.83
.9
.7
1900
0.60
0.60
0.76
0.63
0.52F
0.47
0.65
0.47
0.65
0.65F
0.47
0.56
0.60
0.54
0.73F
0.32
0.32
0.36
0.40
0.58F
Density
.9
.7
.5
.3
.1
0.12
0.12
0.18
0.23F
0.31
0.42
0.36
0.54
0.32E
0.27
0.40
0.71
0.62
0.60E
0.58
0.58
0.65
0.65
O.36E
0.45
0.47
0.62
0.69
0.43E
199
Table F.8
Estuary: Yaquina
Location: Elk City
Date: 7-21-69
Time
PDT
0930
1040
Sample Position
Approximate fraction of depth Veloctiy Temp Salinity
Depth
ft
from water surface ft/sec
°C
0/00
43.0
no
0.77
.8,
< 01
.2
0.78E data
43.0
.8
0.60
.6
.4
.2
1110
43.0
.8
.6
.4
.2
1200
1230
1255
1320
340
1415
1435
1455
1520
1345
1630
Surface
Surface
Surface
Surface
Surface
Surface
Surface
Surface
Surface
Surface
43.0
.8
.6
.4
.2
43.0
.8
.6
.4
.2
1740
43.0
.8
.6
.4
.2
1800
43.0
.8
.6
.4
1840
43.0
.2
.8
.6
.4
.2
1855
1910]
Surface
Surface
0.64
0.66
0.71E
0.53
0.58
0.59
0.58E
0.32E
0.43E
0.46E
0
<.1 F
0,29F
0.47F
0.50F
0.5SF
0.66F
0.86
0.82
0.85
0.86F
0.75
0.75
0.83
0.86F
0.61
0.67
0.79
0.77F
0.55
0.61
0.70
0.68F
0.13
0.26
0.27
0.26F
0
0.38E
Density
0
0
0t
200
Table F.8 - continued
Time
POT
1920
Sample Position
Approximate fractjpi of depth
DeDth - ft from water surface
43.0
.8
.6
.2
2010
43.0
.8
.6
.4
43.0
43.0
0.99
0.93
.2
.8
0.90
.8
.6
.4
2105
ftIse
0.56
0.57
0.67
0.59E
0.93
0.99E
0.85
0.95
0.97
0.71E
.2
2035
Velocity Temp
.6
.2
0.93
0.90
0.93E
°r
no
data
Salinity
oioc
<.01
Density
a:
I
201
Table F.9
Estuary: Alsea
Location: 100 yds East of Rt. 1 bridge
Date: 8-28-69
Time
PDT
0835
Sample Position
Approximate fraction of depth Velocity. Temp Salinity.
C
0/00
DeDth - ft from water surface ft/sec
1.5
.8
0900
2.5
.2
.8
0920
2.8
0945
3,2
14.9
14,9
15.2
15.2
15.0
15,0
14.6
14.6
14.5
14.7
14.7
14.6
14.6
14.4
14.4
.2
.8
.2
.8
.5
1005
4.1
.2
.8
.6
.4
1020
5.0
.2
.8
.6
.4
14.3.
.2
1050
5.1
1120
6.0
.8
.6
.4
.2
.8
.5
1150
8.0
.2
.8
.6
.4
.2
1220
1300
1330
1415
8.2
8.4
8.6
9.0
.2
.2
2.38F
.2
1.8Th'
.8
.5
.2
1430
9.0
1455
9.0
1515
9.0
1545
9.0
0.78F
.8
.5
.2
0.46E
.8
.2
l,04E
.8
.2
l.58E
.8
.2
1.87E
14.3
i3.2
13.2
12.9
12.9
12.6
12.6
12.5
12.5
12.5
12.6
12.6
12.5
12.7
12.5
12.8
12.7
12.8
13.0
13.0
12.9
13.3
12.9
13.4
13.3
13.2
13.2
23.5
23.6
23.1
23.0
24.4
24.5
25.2
25.2
25,3
25.9
25.8
25.8
25.8
27.0
27.2
27.3
27.5
30.0
30.4
30.5
30.9
31.8
31.9
31.8
32.4
32.3
32.3
32.3
32.3
32.0
32.3
32.2
32.2
32.3
32.2
32.2
32.2
32,3
32.2
32.2
32.2
32.2
32.3
Density
0
18.9
19.0
18.6
18.5
19.6
19.7
20.2
20.2
20.3
20.8
20.7
20.7
20.7
21.7
21.8
21.9
22.1
24.1
24.4
24.5
24.8
25,5
25.6
25.5
26.0
25.9
25,9
25.9
25.9
25.7
25.9
25.9
25.9
25.9
25.9
25,9
25.9
25.9
25,9
25.9
25.9
25.9
25,9
17.2
17.1
16.9
16.8
17.9
17.9
18.5
18.5
18.6
19.1
19.0
19.0
19.0
20.1
20.2
20,2
20.4
22.5
22.8
23.0
23.3
24.0
24.1
24.0
24.4
24,4
24.4
24.4
24.3
24.4
24.3
24.3
24.3
24.3
24.3
24.3
24.2
24.3
24.2
24.2
24.2
24.2
202
Table F.9 - continued
Sample Position
Time
PDT
Approxinate fraction of depth Velocity Temp Salinity Density
0/00
Depth - ft from water surface ft/sec °C
1615
8.0
1645
7.0
1715
-7ö
1745
6.T
1815
5.6
1845
1915
1
2000
3.8
2015
3.7
2030
2045
2105
2115
2130
2145
2,8
2.7
3,7
3.9
4.1
4.5
.8
.2
.8
.2
.8
.2
.2
.8
.2
.8
.2
.8
.2
.8
.2
.8
.2
.8
.2
.2
.2
.2
.2
.2
.2
2.30E
3.3lE
2.74E
2.85E
2.63E
2.27E
2.30E
2.27E
2,05E
l.76E
1.40E
1,07E
.42E
.02
.57F
,93F
13.1
13.1
13.8
13.8
13.5
13.5
13.6
13.7
14.0
14.0
14.6
14.7
14.8
14.8
TT
15.2
15.4
15.5
15.7
15,6
15.8
15.4
15.8
15.9
15.7
15.2
32.2
32.2
32.0
32.0
32.1
32.1
32.0
32.0
31.9
31.9
30.8
30.8
30.6
30.5
28. 7
29.0
27.9
27.9
27.1
27.0
26.7
25.8
25.3
25.3
26.5
28.6
25.9 24.3
25.9 24.3
25.7 23.9
25.7 23.9
25.8 24.1
25.8 24.1
25.7 24.0
25.7 24.0
25.6 23.8
25.6 23.8
24.7 22.8
24.7 22.8
24.6 22.7
24.5 22.6
TT 21.2
23.3 21.4
22.4 20.4
22.4 20.4
21.8 19,8
21.7 l97
21,4 19.4
20.7 18.8
20.3 18.4
20.3 18.4
21.3 19.3
23.0 21.0
Table F.l0
Estuary: Alsea
Location: Oakland Marina
Date: 8-28-69
Time
PDT
0840
Sample Position fraction
of depth from
Approximate Depth
in feet
8.0
0905
7.5
0915
7,0
0930
7.0
945
1000
1015
1020
7.0
7,0
7,0
7.0
1035
1040
7.0
7.0
1050
1055
7.5
7.5
1130
8,0
wtr urf
.8
.1
.6
.4
.2
.1
.8
.5
.2
.8
.5
.2
.8
.5
Velocity Azimuth
F-I
.67
80
1..1IE
.70
85
80
.62
75
.56
60
.4 2E
10
75
.2
.6
.6
.6
.8
.5
.2
.6
.8
.5
.2
.6
.8
.5
.2
.6
.65E
.42E
.32F
.93F
1.91F
Temp
i-.o
var.
Salinity
Density
(Iflfl
(T
16.6
17.7
17.3
17.3
17,3
16.5
17.3
17.6
16.9
17.3
17.6
16.5
17.4
17.6
19.9
16.6
15.9
15.7
15.3
19.8
16.0
15.3
19.8
16.0
15,1
19.6
15.6
14.7
16.0
13.3
12.8
12.6
12.3
15.9
12.8
112.3
15.9
12.8
12.1
15.7
12.5
11.8
15.8
17.4
18.1
24.0
15.2
14.0
19.3 17,4
12.2 10.3
11.2 9.3
15.9
17.3
17.9
23.2
15,2
14.1
18.6 16.7
12.2 10.3
11.3 9.4
16.3
17.5
18.1
21.1
15.0
14.5
16.9 15.0
12.0 10.1
11.6 9.6
14,1
11.5
10.9
10.7
l0;5
14.0
10.9
10.4
14.0
10.9
10,2
13.9
10.6
9.9
270
270
270
Table F. 10 - continued
Sample Position fraction
Time
PDT
1255
Approximate Depth
in feet
11.8
.9
.8
.6
.4
.2
.lF
1310
12.5
1350
13.4
Velocity Azimuth
of depth from
water surface
1
ft/sec
1.77
1.99
2.02
2.02
2.08
2.26
degrees
280
.1
.IF
1435
14.7
.9
.8
.5
.2
.IF
1500
15.0
.9
1.11
1.42
1.56
1.35
255
275
275
270
270
260
var
var
var
.51
var
.2
.52
.27
.07
.1
.21
var
var
var
var
,1F
.14.7
.84
270
275
280
270
.20
.29
.38
.73
.36
.8
.5
.2
1520
1.36
1.64
1.99
2.35
2.31
.9
.8
.5
Salinity
0/00
16.5
16.5
16.5
16.5
16.9
23.9
23.8
24.1
23.8
23.9
19.2
19.1
19.4
19.1
19.2
17.1
17.1
17.3
17.1
17,1
15.0
15.0
15.1
15.7
29.1
28.8
28.7
28.0
23,4
23.1
23.1
22.5
21.5
21.2
21.2
20.5
14.4
14.4
14.8
14.8
31.6
31.4
31.1
30.8
25.4
25.2
25.0
24.7
23.5
23.3
23.0
2.8
14.1
14.1
14.7
14.7
32.0
31.7
31.5
31.0
25.7
25.5
25.3
24.9
23.9
23.7
23.3
23.0
14.3
14.5
15.2
15.3
32.0
31.6
30.8
30.6
25.7
25.4
24.7
24.6
23.9
23.6
22.7
22,6
Density
275
275
270
270
270
.8
.6
.4
.2
.9
.8
.5
.2
°C
Temp
00
270
I'.)
4:-
Table F. 10 - continued
Time
PDT
Appro-imate Depth
in feet
1135
8.0
1145
9.0
1200
9.5
1225
1245
10.0
10.5
Sample Position fraction
of depth from
water surface
.8
.6
.5
.4
.2
.1
.8
.7
.6
.5
.4
.2
.1
.8
.6
.2
.9
.8
.7
.6
.5
.4
.3
.2
.1
.8
.6
.4
.2
.1
Velocity Azimuth
ft/sec
degrees
1.33
1.77
1.97
1.93
2.06
2.10
2.20F
265
265
270
275
270
275
265
2.00
1.99
2.04
2.22
2.35
2.10
2,17
2.31
270
275
270
270
270
265
275
265
265
2.31F
Temp
°C
Salinity
Density
16.5
16.8
17.0
17.5
17.5
17.5
0/00
19.7
18.9
17.9
16.5
16.3
15.9
15,8
15.2
14,4
13.2
13.1
12.8
[T'T
17.4
17.3
17.4
17.4
17.8
17.8
17.6
17.0
14.3
14.3
14.1
13.6
12.3
12.3
12.1
11.7
17.0
16.8
17,1
17.2
17.0
20.2
20.3
20.3
20.2
20.1
16.2
16.3
16.3
16.2
16.1
14.2
14.3
14.3
14.2
14.1
13.3
12.5
11.3
11.2
10.9
N.)
C
Table F.lO Time
PDT
1535
ft
Approximate Depth
in
14.7
Sample Position fraction
of depth from
water surface
.9
.8
.5
.2
_______
1550
________________________
14.5
13.4
1735
1825
12.7
11.8
10.8
.60
.89
.94
1,13
.2
1.22
,1
.9
.8
.2
.1
.9
.8
.5
°C
Salinity
0/00
90
80
100
14.4
14.4
14.9
31.6
31.2
30.8
.2
30 '3
21
14.6
31.2
25.1
85
80
14.0
15.7
30.2
29.4
24.3 22.3
23.6 121,5
80
90
90
15.8
29.1
2.2
21,3
15.2
16.1
29.7
27.3
23.9
21.9
90
90
16.4
19.8
19.5
80
16.9
26,9
_4 .4
21,9
21.6
19,6
17.5
15.2
16.5
17.2
17.5
29.7
26.1
23.2
21.8
15.8
16.7
17.4
17.7
25,1
20.2 18.3
24,7
21.0
20.5
19.8
16.9
16,5
17.7
14.8
851
Temp
91E. _.._.8fl_. I
.5
.5
1645
ft/sec
l,l4E
.73
1.20
1.29
1,40
10E
90
85
.52
1.13
90
85
1.29
90
85
80
65
.2
.1
.9
.8
1.42
.5
.2
1.20
.1
1.46_
.60
1,50E
.51
1.33
1.44
Density
degrees
Velocity Azimuth
.65
1,14
1.38
.9
.8
1620
continued
90
90
25,4
25.1
24.7
23,6
23.2
22.8
22
- '3
23,2
23.9 21.9
21.0
18.6
18.9
16.5
,j2.5
15.3
.8
1.58
85
80
85
85
16.8
24.0
19.3
17.2
.5
85
85
17.5
19.8
.2
1.69
1.53
17.7
19.3
.1
1.58E
85
17,7
19.3
15.9
15.5
15.5
13,8
13.4
13.4
.9
-_
14.4
Table F.iO - continued
Tirnc
PDT
1905
Approximate Depth
in feet
10.2
Sample Position fraction
of depth from
water surface
.8
.7
.5
_________ ___________________
1955
9.2
2045
2110
2140
2210
8.6
8.4
8.2
8.2
.3
.1
.8
.7
.5
.3
.1
.8
.7
.5
.3
.1
.8
.7
.5
.3
.1
.8
.7
.5
.3
.1
.8
.7
.5
.3
.1
Velocity Azimuth
ft/sec
.98
1.44
1.47
1.44
l.40E
.87
1.02
1.18
1.22
1,35E
.73
1.16
1.16
1.22
1.31E
.51
1.00
1.02
1.06
1.24E
.42
.78
.89
.96
1.09E
.38
.10
.40
.62
.78E
Temp
Salinity
0/00
Density
16.7
17.5
17.7
17.8_
23.9
19.7
19.0
19.0
19.2 17.1
15.8 13.7
15.3 13.2
lS
J.3_2_
16.9
17.6
17.6
17.6
22.8
18.9
18.1
17.9
18.3
15.2
14.5
14,4
16.2
13.1
12.5
12.4
17.2
17.8
17.8
17.5
20.4
17.5
17.2
16.8
16.4
14.1
13.8
13,5
14.4
12.2
11.8
11.5
17.2
17.7
17.7
17.5
20.5
17.2
16.7
16.4
16.5 14.5
13.8 11.8
13.4 11,2
13.2 11.3
80
85
85
85
275
16.9
17.7
17.8
17.6
23.7
16.9
16.5
16.0
19.0
13.6
13.2
12.8
16.9
11.6
11.3
10.9
var
16.4
17.5
17.9
19.0
24.7
16.5
16.2
15.7
19.8
13.2
13.0
12.6
17.7
11.3
11.1
10.4
degrees
75
85
85
90
_B5__
80
80
85
90
85
75
80
80
85
85
80
85
85
85
85
var
80
85
80
°C
-4
Table F,10 - continued
Time
Approximate Depth
Sample Position fraction
of depth from
Velocity Azimuth
Temp
salinity
16.9
17.5
17.7
17.7
22.0
17.5
16.5
16.3
Density
4r
8.2
L_________ ____________________
.8
.7
.5
.3
.1F
.
.74
.49
.27
.10
Th?T
270
275
265
270
l77
14.1
13.2
13.1
15.7
12.1
11.3
11.2
Q
Co
209
Table F 11
Estuary: Alsea
Location: Kozy Rove Fish Camp
Date: 8-28-69
Sample Position
Approxiu'ate fraction of depth Velocity Temp Salinity
°C
PflT T-h
fFrrrn wif:r snrfce ft/sec
(u/flfl
8.2
.8
8.3
1010
Time
1T
Idata
.6
.4
.2
1015
1030
8.5
0.75E
.8
.6
.4
.2
1035
1045
8.7
0.63E
.8
.6
.4
.2
1050
1100
8,3
slack
.8
.6
.4
.2
1105
1115
8.3
0.86F
.8
.6
.4
1120
1130
.2
1
8.5
0.86F
.8
.6
.4
1135
1200
.2
9.2
.8
.6
.4
.2
1205
1230
10.2
1320
11.9
1345
13.0
.8
.6
.4
.2
1.50F
.8
.6
.4
.2
2.07F
.8
.6
.4
-- _ --
. 2
2. 07F
4.5
2.6
2.0
10.0
5.7
2.6
2.0
9.8
7.1
2.7
1.9
9.6
9.0
8.2
2.2
9.6
8.9
4.9
2.3
9.3
7.5
3.2
3.0
8.7
7.3
5.2
3.7
9.2
8.6
6.9
5.2
9.4
8.7
8.3
7.2
9.8
9.4
9.5
7.2
Density
t
I
6.6
3.6
2,0
1.5
8.0
4.5
2.0
1.5
7.8
5.7
2.1
1.4
7.7
7.2
6.6
1.7
7.7
7.1
3.9
1.8
7.4
6.0
2.5
2,4
7.0
5.8
4.1
2.9
7.3
7.0
5.5
4,1
7.5
7.0
6.6
5,8
7.8
7.5
7.6
5.8
210
Table F.11 - continued
Time
PDT
1415
Sample Position
Approximate fraction, of depth VelocityTemp Salinity
Depth - ft from water surface ft/sec
°C
0/00
14,1
.8
.6
.4
.2
1445
14.9
1.34F
.8
.6
.4
.2
1515
14.8
0.55F
.8
.6
.4
.2
1535
15.0
O.41E
.8
.6
1555
15.2
.4
.2
.8
l.12E
.6
1630
14,0
1705
14.1
.4
.2
.8
.6
.4
.2
.8
1.34E
1.16E
.4
.2
.86E
1730
13.0
TO
.8
.6
.4
.2
.86E
12.4
.8
.6
.4
.2
1830
10.5
l.08E
.8
.6
.4
.2
1900
11.2
1.08E
10.2
9.6
9.4
9.4
10.5
10.4
9.2
8.5
10.2
10.7
8.8
8.4
10.1
9.5
9.1
7.4
7.7
7.2
6.9
6.8
7.7
7.1
7.0
7.0
7.6
7.7
7.0
7.0
7.1
7.6
6.5
6.1
6.5
6.0
5.4
4.9
6.2
5.1
5.0
4.9
.8
5.8
.6
5.5
4.3
4.3
.4
.2
l.O1E
Density
Q
8.2
7.7
7.5
7.5
8.4
8.3
7.4
6.8
8.2
8.6
7.1
6.7
8.1
7.6
7.3
5.9
6.2
5.8
5.5
5.4
6.2
5.7
5.6
5.6
6.1
6.2
5.6
5.6
5.7
6.1
5.2
4.9
5.2
4.8
4.3
3.9
4.9
4.1
4.0
3.9
4.6
4.4
3.4
211
Table F.11 - continued
Time
Sample Position
Approximate fraction of ç1,pth
-
P1)1
DepErl
it:
l 930
.6
.4
.2
_______
1945
10.8
.8
.6
.4
.2
2025
10.3
.8
.6
.83E
2040
10.0
___________
2100
2130
.97E
3.0_
.8
.6
3.6
.4
.2
2.7
2.6
.72E
_.. ._
.75E
.-.
2.1
2.0
3.6
2.8
2.1
2.0
-..-
.8
_____ _____
.6
.4
.2
9.3
.8
4.4
3.6
.4
.2
...,.
9.1
.....
2.5
2.2
.64E
4.2
3.2
2.2
1.9
.4
.2
8
.6
.4
.2
22.40
..
.... .
2.4
3.8
3.2
.61E
.8
8.8
3.5
2.8
2.1
1.9
3.0
2.5
1.9
1.7
3.3
2.5
1.7
1.4
3.7
3.1
2.6
1.4
2.7
.83E
.6
225
4.4
4.2
3.1
3.0
3.8
3.6
2.8
2.4
3.4
3.2
5.5
5.3
3.9
3.8
2.7
2.6
4.5
9.7
___________
2245
fl/O0
4.3
4.1
.6
2200
r
4.8
4.5
3.5
.4
.2
Density
Velocity Temp Salinity
iron' WLL UL-I
.
.-
.35E
.IOF
.24F
.68F
90F
3.9
3.3
1.9
I
212
Table F.12
Estuary: Siletz
Location: Mouth (at Taft)
Date: 9-12.69
Time
PDT
0845
Sample Position
Approximate fraction of depth Velocity Temp Salinity
Depth
ft
from water surface ft/sec
°C
0/00
26.0
.8
1.53
24.2
.6
0910
26.0
.4
.2
.8
.6
.4
.2
0920
26,0
.8
.6
.4
.2
0930
26.0
.8
.6
.4
.2
1000
27.0
.6
.4
.2
1030
28.0
.8
.6
.4
.2
1100
29.0
1.42
1.06
0.85E
.84
.43
.63
.91E
.31
.29
.29
,32E
.73
.60
.65
.85F
2.56
2.42
3.29
3.05F
2.93
3.18
3.29
4.19F
.8
.6
.4
.2
1220
30.0
.8
.6
.4
.2
1240
31.0
.8
.6
.4
1300
31.0
.2
.8
.6
.4
.2
1330
31.0
.8
.6
.4
.2
4.74F
4.74
6.36
6.54
7.20P
5.46
7.09
7.09
7.38F
5.60
6.54
6.72
7.38F
4,83
5.64
6.00
6.29F
24.2
24.2
24.2
24.3
24.1
24.1
24.1
24.4
24.2
24.1
23.9
24.0
24.1
24.2
24.2
26.6
26.6
26,6
26.7
26.6
26.6
26.6
26.6
26.6
26.6
26.6
26.5
Densiy
19.4
19.4
19.4
19.4
19.5
19.4
19.4
19.4
19.6
19.4
19.4
19.2
19.3
19.4
19.4
19.4
21.4
21.4
21.4
21.4
21.4
21.4
21.4
2L4
21.4
21.4
21,4
21.3
213
Table F.l2 - continued
Time
PDT
1400
Sample Position
Approximate, fraction of depth Velocity Temp Salinity
ft
Depth
from water surface ft/sec
0/00
°C
30.0
.8
3.83
.6
3.36
.4
4.19
.2
3,74F
1430
.8
.84
.6
1.06
1.00
.91F
2.57
2.75
2.75
2.57E
.4
.2
1500
29.0
.8
.6
.4
.2
Density
0
I O
214
Table F.13
Estuary: Siletz
Location: Kernville
Date: 9-12-69
Time
PDT
0850
Sample Position
Approximate fraction of depth Velocity Temp Salinity Density
Depth - ft from water surface ft/sec
C
0/00
0
10.9
.8
.6
.4
.2
0910
10.7
.8
.6
.4
.2
0930
10.8
.8
.6
.4
.2
0945
1000
1020
11.0
11.2
12.2
.13
.22E
.8
.6
.60
.43F
.8
1.09
1.20
1,08
1.17F
1.17
1,36
1.72
l.56F
1.47
1.91
1.97
l.75F
1.83
1.86
1.97
l.83F
1.67
2.00
2.30
2.08F
1.42
1.58
1.83
l.78F
.8
.8
.6
.4
.2
13.5
.8
.6
1220
14.1
.4
.2
.8
.6
.4
1250
J4.6
.98
1.06
.4
.2
.2
1150
.71E
.2
.4
12.8
.13
.46
.74
.4
.6
1120
1.12
l.l7E
.57
.32
.2
12.4
.76
.87
.6
.8
.6
.4
1050
.76
1,20
1.28
l,39E
.2
.8
.6
.4
.2
14.3
13.7
14.1
14.4
14.5
14.1
14.3
14.5
14.8
13.8
14.1
14.5
14.7
T4.0
14.2
14.4
14.7
13.6
14.2
14.4
14.5
13.6
13.7
13.6
13.9
12.9
12.9
13.0
13.2
12.1
12,2
12.2
12.2
9.2
9.0
9.7
9,8
8,4
8.4
8.5
9.2
18.2
20.0
18.8
18.2
17,6
19.5
18.4
17.7
17.2
19.9
18.8
17.7
17.2
19.6
18,4
17.9
17.4
21.1
19.3
18.2
184.
20.9
21.1
20,8
20.2
23,3
23.3
23.0
22.6
26,0
25.9
25.9
25.6
31.5
31.6
30.8
30,3
32.9
32,9
33.0
31.6
14.6
16.1
15.1
14.6
14.1
15.7
14.8
14.2
13.8
16.0
15.1
14.2
13.8
15.7
14.8
14.4
14.0
16.9
15.5
14.6
14.8
16.8
16.9
16.7
16.2
18.7
18.7
18.5
18.2
20.9
20.8
20.8
20,6
25.3
25.4
24.7
24,3
26.4
26.4
26,5
25.4
13.2
14.8
13.7
13.2
12.7
14.3
13.4
12.8
12.4
14.7
13.7
12.8
12.4
14.3
13.4
13.0
12.6
15.6
14.1
13.2
13.4
15.5
15.5
15.4
14,8
17.4
17.4
17,2
16.9
19.6
19.5
19.5
19.3
24.4
24.5
23,7
23.3
25.6
25.6
25,6
24.5
215
Table F.13 - continued
Time
PDT
1320
Sample Position
epth Velocity Temp Salinity
°C
from water surface ft/sec
0/00
Approximate, fraction of,
Depth - ft
15.0
.8
.6
1350
15.5
1420
15.8
.4
.2
.8
.6
.4
.2
.8
.6
.4
.2
1450
1500
1510
15.8
15.7
15.7
1.31
1.61
1.75
l.56F
1.12
1.26
1.53
1.36F
.85
1.06
1.15
1.06F
.6
.4
.38
.49
.52
.2
.22F
.8
.2
.8
.4
.13
.22
.13
.2
.05F
.8
.11
.11
.08
.6
.4
15.5
.8
.6
1530
15.5
0
.4
.11
.30
.24E
.19
.27
.35
.2
.41E
.4
.2
.8
.6
8.3
8.3
8.5
9.2
8.4
8.3
8.4
8.6
8.5
8.5
8.5
8.7
8.6
8.5
8.6
8.7
8.5
33.3
33.2
33.1
31.7
33.2
33.2
33.1
32.7
33.3
33.2
33.2
33.1
33.4
33.3
33.3
33.3
33.3
26.8 26.0
26.7 25.9
26.6 25.7
25.5 24.6
26.7 25.9
26.7 25.9
26.6 25.7
26.3 25.4
26.8 25.9
26.7 25.8
26.7 25.8
26.6 25.7
26.8 25.9
26.8 25.9
26.8 25.9
26.8 25.9
26.8 25.9
8.5
8.5
8.5
8.9
33.6
33.3
33.3
33.2
25,9
26.8 25.9
26.8 25.9
26.7 25.8
.05F
.2
1520
Density
216
Table F.14
Estuary: Siletz
Location: Howard s
Date: 9-12-69
Time
PDT
0950
Sample Position
Approximate fraction of depth Velocity Temp Salinity
0/00
°C
Depth - ft
from water surface ft/sec
14.0
.8
.6
.4
.2
1020
15 .0
.8
.6
.4
.2
1040
16.0
.8
.6
.4
.2
1115
16.0
.8
.6
.4
.2
1145
17.0
.8
.6
1215
1245
18.0
17.0
.4
.2
.8
.6
.4
.2
.8
.6
.4
.2
1410
17.5
.8
.6
.4
.2
1440
18.0
.8
.6
.4
:1510
18.5
.8
.2
.80
.84
.82
.73E
26
.08
.11
.19F
.86
1.13
.
1.18
1.31F
1.31
1.33
1.67
1.69F
1.06
1.67
1.62
1.80F
L34
1.65
1.78
1.69F
1.65
1.78
1.80
l.80F
1.22
1.44
1.52
1.62F
1.09
1.13
1.31
1.27F
.4
.75
.89
.84
.2
.69F
.6
17.5
17.8
17.7
17.7
17.7
17.7
17.7
17.6
17.8
17.8
17.8
17,6
17.9
17,8
17.9
17.9
18.0
18.0
17,8
17.8
18.0
18.0
18.2
18.1
18.2
18.2
18.2
18.2
18.3
18.4
18.4
18.4
18,4
18.4
18.4
18.4
18.5
18.4
13.5
.20
.24
.32
.20
.24
.24
.16
.16
.28
.16
.12
.21
.16
.12
.28
.20
32
.32
.32
.32
.36
.40
.40
.40
.48
.48
.48
.48
1.48
1.48
1.44
1.44
2.12
2.12
2.20
2.04
. 2.76
2.76
2.76
2.64
Density
O
.07 -1.10
I
.10 -1.12
.17 -1.04
.07 -1.13
-1.10
-1.10
-1-16
-1.14
-1.09
-1.18
-1.11
-1.11
-1.20
-1.22
-1.11
.07 -1-17
.17 -1.09
.17 -1.09
. 10
.10
.04
.04
.14
.04
.00
.08
.04
.00
.14
.17
.17
.20
.23
.23
.23
.30
.30
.30
.30
-.1.06
-1.06
-1.03
-1.04
-1.04
-1.08
-.
.99
- .99
..
.99
- .99
.25
1.11
1.11 - .27
1.08 - .31
1.08 - .31
.20
1.63
.20
1.63
.27
1.70
.15
1.57
.69
2.15
2.15
.67
2.15
.69
.58
2.05
217
Table F.l4 - continued
Time
PDT
1525
1540
1555
1620
Saiple Position
Approximate, fraction of depth Velocity Temp Salinity
0/00
°C
Depth - ft from water surface ft/sec
2.76
18.5
.49
.8
18.0
2.68
18.3
.39
.6
2.68
18.6
.31
.4
2.64
18.4
.30F
.2
2.9r
18.3
.17
.8
T75
2.76
18.3
.19
.6
2.60
.17F 18.6
.4
2.44
18.6
.48
.2
2.80
18.2
.38
.8
17.0
2.66
18.2
.71
.6
2.68
18.4
.75
.4
2.52
.78E 18.5
.2
2.48
18.4
.93
.8
17.0
2.24
18.6
1.07
.6
2.12
18.6
1.16
.4
2.00
18.4
1.18E
.2
Density
2.15
2.09
2.09
2.05
2.28
2.15
2.02
1.89
2.18
2.05
2.09
1.96
1.92
1.73
1.63
1.53
.67
.65
.59
.60
.83
.70
.53
.41
Ti
.63
.63
.49
.47
.26
.16
.11
218
Table F.15
Estuary: Siletz
Location: Strome
Date: 9-12-69
Time
PDT
1020
Sample Position
Approximate fraction of depth Velocity Temp Salinity
0/00
°C
from water surface ft/sec
Depth .. ft
2.0
.8
.5
.57
.70
.77E
1045
2.0
.8
.5
.2
1100
3.0
.8
.6
.4
.2
1125
3.5
3.6
.4
.2
.44E
.8
.4
.22
.29
.18
.2
.26E
.8
.26
.22
.26
.6
1200
3,8
1220
4.0
1250
4.8
1330
6.0
1400
7.0
.6
.4
.2
.8
.6
.4
.2
.8
.6
.4
.2
.8
.6
.4
.2
7.5
1510
.62
.73
.51F
.62
.73
.91
1.13F
.99
.6
1.17
1.13
.99F
.8
.6
.4
8.0
.15F
.36
.99
.62
.62F
.62
.8
.4
.2
1445
.70E
.44
.44
.62
.62E
.36
.33
.44
.8
.6
1130
.55
.59
.2
.8
.77
.77
.95
.99F
.4
.77
.51
.70
.2
.77F
.6
Density
219
Table F15 - continued
Time
PDT
Sample Position
Approximate fraction of depth Velocity Temp Salinity
°C
ft/sec
ft
from wat er surface
Depth
0/00
.8
.6
.4
.2
1605
8.5
.8
.6
1630
8.0
.4
.2
.8
.6
.4
.2
.36
.47
.55F
.26
.29
.36
.26E
.47
.51
.81
.77E
Density
I
220
Table P.16
Top and Bottom Density Difference
Average Bottom Average Top
Yaguina
orQ
Newport
Oneatta #1
Oneatta #2
Oneatta #3
Oneatta #4
GP Dock
Mill Creek
25.86
22.80
22.80
20.91
20.79
12.42
0.17
Percent
Diffe e
24.82
19.82
20.40
19.91
19.52
10.81
0.02
1.04
3.08
2.40
1.00
1.27
1.61
0.15
ffemce
verage
Percent
Diff.
0.10%
0.30%
0.23%
0.10%
0.12%
0.16%
0.01%
0.15%
Alsea
Hwy. I Bridge
Oakland's
Kozy Kove
22.08
17.51
6.04
22.04
14.18
3.60
0.04
3.33
2.44
0.004%
.33%
.247.
0. 19%
Siietz
Mouth
Kernville
Howard
20.28
20.39
-0.33
20.21
19.31
- 0.42
0.07
1.08
0.09
0.007%
0.11%
0.009%
S trome
0, 047.