TRANSPORT PROCESSES
IN ESTUARIES:
RECOMMENDATIONS
FOR RESEARCH
i ,'<•'"
B. KINSMAN, J. R. SCHUBEL,
M. J. BOWMAN, H. H. CARTER,
A. OKUBO, D.W. PRITCHARD,
and R. E. WILSON
SPECIAL REPORT 6
REFERENCE 77-2
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MARINE SCIENCES RESEARCH CENTER
STATE UNIVERSITY OF NEW YORK
STONY BROOK, NEW YORK 11794
TRANSPORT PROCESSES IN ESTUARIES:
RECOMMENDATIONS FOR RESEARCH
B. Kinsman, J. R. Schubel, M. J. Bowman, H. H. Carter,
A. Okubo, D. W. Pritchard, and R. E. Wilson
April 25, 1977
Sponsored by United States Environmental Protection Agency,
United States Energy Research and Development Administration,
Office of Naval Research: Geography Branch, National Oceanic
and Atmospheric Administration: MESA, New York Bight Project,
United States Fish and Wildlife Service: Office of Biological
Services, and the Stony Brook Foundation
'. . :,,>A 13107
Special Report 6
Reference 77-2
Approved for Distribution
J. RT Schubel, Director
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PREFACE
Origin and Purposes of the Workshop on
Transport Processes in Estuaries
In the spring of 1976 a symposium
to review our knowledge of physical
transport processes in estuaries was
held at the Belle Baruch Institute.
At the conclusion of the symposium
the following statement, drafted by
J. R. Schubel,was endorsed by the
participants:
"On 20-22 May 1976 a group of estuarine oceanographers
from the United States, Canada, England, and South America
met at the Belle Baruch Institute for Marine Biology and
Coastal Research of the University of South Carolina to
review and critically assess our knowledge of estuarine
transport processes. It was the very strong consensus of
the group that recent data show many of our previous ideas
of estuarine transport processes to be overly simplistic
and that a greater level of sophistication of our under-
standing of these processes is required not only for a
significant scientific advancement, but also for effective
environmental protection and management.
"A knowledge of the physical oceanography is
fundamental to understanding the biological, chemical, and
geological processes that characterize an estuary. This
information is in turn necessary for the formulation of the
predictive tools needed by governmental agencies for
effective management and rehabilitation of the estuarine
environment. Reliable predictions can not be made of the
dispersion of pollutants, the resuspension and movement of
dredged spoil, or the assimilative capacity of an estuarine
system without a working knowledge of its characteristic
physical processes.
"While millions of dollars are being spent each year
on monitoring of the estuarine environment, the resulting
data are generally of little use to oceanographers
interested in processes, or in formulating, constructing,
and verifying analytical, numerical, or physical models.
The data are also, unfortunately, frequently of little value
to regulatory agencies in attaining their long-term
pervasive goal—effective management of the coastal
environment. Through proper coordination and planning,
experimental programs can be designed that not only satisfy
the short-term needs of regulatory agencies, but also
provide the oceanographers and managers with the data they
require for development of predictive models.
"A proposal will be submitted to appropriate Federal
agencies within a few weeks for support of a workshop to
identify the important problems of physical transport
processes in estuaries, and to explore the most effective
ways of attacking these problems. Efficient utilization
of existing manpower and facilities for an adequate field
study of the dynamics of any single estuary will probably
require collaborative efforts of scientists from several
academic institutions and from governmental and
management agencies."
Pursuant to the foregoing statement,
a Workshop on Transport Processes in
Estuaries was held at the Marine Sciences
Research Center, State University of
New York, Stony Brook, New York from
10 November to 14 November 1976. Thirty-
one participants from some 18 institutions
and agencies focused their discussions on
transports of water, salt, and fine-
grained suspended sediments.
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The primary goal of the Workshop was
to identify the important unresolved
problems of physical transport processes
in estuaries; problems that must be
solved, not only for their scientific
urgency, but also for effective manage-
ment and rehabilitation of estuaries.
The secondary goals of the Workshop
were:
(a) To assess the manpower and
materiel necessary for the field experi-
ments on which the solutions of important
unresolved problems must depend.
(b) To explore the means for inter-
institutional cooperation and collaboration
which will be required if the necessary
large-scale, extended field experiments
anticipated are to be made feasible.
(c) To explore ways in which current
monitoring programs, which are relatively
expensive, can be made more useful both
to management and to science.
The present report by the authors
was written with due consideration for
the discussions which occurred during the
Workshop and for the written suggestions
submitted by the participants but it
should not be interpreted as a report
which has been endorsed in full by all
participants. In this report we have
focused on the primary Workshop goal and
the first of the secondary goals listed
above.
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TABLE OF CONTENTS
Page
Preface: Origin and Purposes of the Workshop on Transport Processes in Estuaries i
Abstract 1
1. Why Should Transport Processes in Estuaries be Studied? 1
2. Modeling and Simulation of Transport Processes 3
2.1 What is a model? 3
2.2 How are models made? 4
2.3 Scales of averaging and observation and their effects on prediction . . 6
3. Analytic and Numerical Models 8
3.1 The equations 8
3.2 The boundary conditions 9
3.3 Verification and testing 11
3.4 The areas to be addressed 11
4. Field Experiments 11
4.1 Small-scale experiments 11
4.2 Large-scale experiments 12
4.3 Some comments and caveats 13
5. A Sketch of the Shape, Size, and Cost of the Field Experiment 13
5.1 The nonadveative flux experiments 13
5.2 The estuarine model experiments 14
5.3 The means 16
5.3.1 Instrument Requirements 16
5.3.2 Schedules, Salaries, and Ship Time 17
5.3.3 Other Costs 17
6. Conclusion 18
Bibliography . . . 19
Appendix A: Organisations Supporting the Workshop on Transport Processes
in Estuaries 20
Appendix B: Participants in the Workshop on Transport Processes in Estuaries 20
iii
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ABSTRACT
A review of the state of current knowledge of transport processes
in estuaries is presented. A better description and quantification of
those terms in the equations of motion not given a priori by the
physics of the flow and commonly referred to as "diffusive" or
"dispersive" remain elusive goals. Proper verification and testing of
three-dimensional time-varying models that are universally applicable
to different types of estuaries have yet to be undertaken.
A set of field experiments is outlined in broad terms. It is
hoped that these experiments will provide new insight into basic
nonadvective transport mechanisms in various types of estuaries
ranging from well-mixed to highly stratified.
1. WHY SHOULD TRANSPORT PROCESSES
IN ESTUARIES BE STUDIED?
Anything that moves water and its
dissolved and suspended material is a
transport process. Transport processes
range from movement by simple streaming
currents, through spreading by turbulence,
to diffusion by molecular motion. Among
the forces that produce transport are
river discharge, winds, and tides. Some
of the material is simply carried about
without change; substances such as the
water itself, dissolved salt, and fine-
grained sediments. Others change with
time, some slowly, some rapidly; things
like heat, dissolved oxygen, nutrients,
pesticides, and PCB's.
In order to know where these
substances will go in a particular estuary
we need to know how the processes which
move them work and which ones are impor-
tant there. As things are now, we know
something but not enough to say in much
detail what will happen in particular
situations. It will be wise to begin the
study of these transport processes by
concentrating on the movement of those
materials which do not change with time.
They are easier to understand and, if we
can understand the mechanisms which
transport them, we will be a long step
ahead in our understanding of the movement
of materials which do change with time;
which is a far more difficult problem.
Estuaries are a natural resource
having a wide variety of uses. Wisely
used they benefit many; misused, the
benefits are not realized and may even
become losses. Estuaries are a liveli-
hood to the waterman; to biologists,
large incredibly productive subaqueous
farms. The average man goes to estuaries
to boat, to hunt, to fish, to swim, or
simply to restore his soul. To physical
oceanographers they are huge natural
laboratories for the study of fluid
mechanics; to sanitary engineers, a dump
for their sewage; and to the ecologist,
an irreplaceable nursery for marine life.
The utilities use them to get rid of
their surplus heat and shipping uses them
as fluid highways. To developers their
water fronts are miles of the most
desirable real estate. The list could be
extended indefinitely. And all these
uses are not compatible. Use for one
purpose may make use for another
impossible. Therefore, to the coastal
zone manager estuaries are a gigantic
headache; places where a wrong decision
may cost millions of dollars, adversely
affect thousands of people, and, in
extreme cases, destroy the natural
resource whose protection is his aim.
To the extent that science under-
stands estuarine physical processes, of
which transport processes are among the
most basic, the manager can turn to the
scientist for information on the probable
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outcomes of the choices he is contem-
plating; he can act with confidence that
the good he proposes will be gained and
the evil he seeks to avert will be averted.
To the chagrin of the scientist and the
dismay of the manager, many estuarine
processes are not yet adequately
understood.
Estuaries are anything but simple
mechanisms. They are the regions where
rivers and ocean meet and dispute for
dominance. They change rapidly under the
influence of the tide, shifting winds,
variable river flows, intermittent ice
cover, and fluctuating evaporation. They
are highly complicated natural systems
worthy in themselves of scientific study—
arenas where physical, biological,
chemical, and geological systems meet,
mesh,and interact. An understanding of
the physics of estuaries, and in particu-
lar of the transport processes, is a
fundamental requisite for many problems
dealing with questions which are not
physical. Without it, understanding of
the biological, chemical, and geological
systems is, at best, uncertain if not
indeed impossible in many aspects.
But the need for more astute
management of our estuarine resources
also forces the need for a better under-
standing of transport processes. We can
not now say with much precision where such
things as spoil from dredging, nutrients,
sewage discharges, exotic chemicals,
spilled oil, or heat will go—whether they
will be flushed out of the estuary within
any given time span or whether they will
accumulate within the estuary; and where.
There is an increasing number of govern-
ment agencies which are "monitoring" the
movements of these materials. But unless
the transport processes are understood,
it is difficult to see how the measure-
ments are to be made at the right place
at the right time. It is even harder to
see how they are to be interpreted so that
they make useful sense. In the face of
this how can the manager manage?
Both man and nature are continually
changing estuaries or, in the case of some
man's efforts, attempting to change them.
Nature provides hurricanes, floods,
droughts, and a wide variety of other
caprices. Tropical Storm Agnes brought
more sediment into the Chesapeake Bay in
the 10 days between 21 and 30 June 1972
than had probably been brought in during
the previous 25 years. Man builds groins,
piers, dams, and wiers; dredges channels
and channelizes streams; creates islands
out of spoil and makes building lots out
of wetlands. This is just a small sample.
Many of his activities alter the transport
patterns. It would be as well to know
before the work was actually done and the;
money spent what changes, direct and
indirect, short-term and long-term, are
to be expected.
We can scarcely afford to go on
"experimenting" blindly with our estuaries
as we have in the past. An excellent
example of what we mean is the story of
what was done to Charleston Harbor,
South Carolina. Before 1941 the main
river entering the harbor was the Cooper,
a river whose discharge was quite low.
Transport of sediment was seaward at all
depths throughout the harbor and mainte-
nance dredging was nominal. But during
the 1930"s the Santee River was dammed
for hydroelectric power and conservation
and diverted to empty into the Cooper
River. The greatly increased flow into
Charleston Harbor altered the transport
patterns; sediment in the deeper water
now moving landward. Bars began to build
rapidly. Dredging costs to keep the
harbor usable shot up to $5 million a
year. It is now planned to put things
back—to the tune of $91 million. If
this is done, the dredging costs for
Charleston Harbor seem likely to return
to something more reasonable and the
rediversion of the Santee will probably
halt the severe delta erosion problem at
the mouth of the Santee. On the other
hand, it will destroy the lucrative hard
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clam industry that has grown up there
since 1941. You can't really put the
system "back." It would have been nice
to have an idea of what to expect when
the original diversion was decided on.
It would be nice to know what to expect
before we spend $91 million to redivert
the Santee.
We just can't afford this sort of
thing. The only remedy is to study
estuaries until we know enough of their
mechanisms to foresee the consequences
of our actions.
2. MODELING AND SIMULATION
OF TRANSPORT PROCESSES
2.1 What is a model?
Models are sometimes spoken of as
though they had an isolated independent
existence. This is never the case. A
model is, of necessity, one half of a
duality. There must always be both the
model and the thing modeled. A model
reproduces some, but never all, of the
features of the thing modeled. Thus, the
prime requisite of any model is that the
features of the thing to be modeled be
known. For example, a model of the
Cutty Sark may reproduce on a smaller
scale the masts and yards together with
the standing rigging but not the running
rigging. If the model is to be a "true"
model, the proportions of the spars and
the lead of the standing rigging of the
Cutty Sark must be known before the model
is built. The same can be said for a
model of transport in Long Island Sound
or of a model of the advection-diffusion
process. Without a knowledge of the
features of the original, no "model" is
possible.
Models can be constructed of many
kinds of materials and in many ways. For
the study of transport processes three
kinds are particularly useful: hydraulic
models, analytic models, and numerical
models. Hydraulic models, for example.
the Army Corps of Engineers model of the
Delaware at Vicksburg, Mississippi,
reproduce the shape of the basin being
modeled, usually with carefully controlled
distortions, fill the model basin with
fluid adjusted to match the known
properties of the original, impose a
force, such as tidal motions, and, after
adjusting the model to reproduce the
currents observed in the system being
modeled, go on to study the transports of
introduced contaminants. Such
"naturalistic" models are often very
large and very elaborate but even the
most complete of them never pretend to
reproduce every rock and sand bar of the
original. In fact, if the features to be
modeled are few, a simple rectangular
flume may "model" an estuary.
Analytic models and numerical models
are both mathematical. They deal with
the concepts, numbers and measurements,
which describe the features of the
original. The models are expressed in
the one case by analytical solutions to
sets of equations and in the other by
finite difference analogs of the equation
sets. They too, may be complex including
many features in great detail or simple
describing only a few crudely. Since the
number of known solutions to the dynamical
equations is quite limited, most mathe-
matical models are, in fact, numerical.
We build models in order to get
something more manageable than the
original. The word "model" comes from
the Latin modulus which means "a small
measure." Geometric models, e.g., ship
models, are literally smaller than their
originals. But if we take "smaller" to
mean "simpler" or "easier to handle," all
models are "smaller" in point of
complexity. We might, for example,
wonder how a particular estuary would
behave if a dam were built which diverted
nine-tenths of the freshwater inflow.
We dare not "experiment" with a real
estuary; we could hurt too many people
and it would be too big to play with.
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But if we have a satisfactory hydraulic
model, it's easy to turn off the tap. If
we have an analytic or numerical model,
it is only a matter of modifying a few
equations or changing some of the input
to the computer. We can "stimulate" the
behavior of the real estuary and, thus,
get some guidance on our decision to build
the dam.
But an extrapolation from model
behavior to the behavior of the thing
modeled is a chancy business. The way
the real estuary works, its mechanism,
is essentially unknowable. What we can
know of it is the measurements of a few of
its features under the range of conditions
which actually obtain. The model is a
quite different matter. We know how it
works; what pushes what and how. Further,
since it is a model we have been careful
to make it duplicate the known features of
the original. The leap we take is to
believe that, since we know the mechanism
by which the model duplicates the measured
features of the original, we know that
the same mechanisms are at work i-n the
same way in the original. But the set of
features modeled is always small. It is
quite possible to build other constructs
with quite different mechanisms which
reproduce the features. Which then is
the "true" model; the one that tells us
what is really going on in the original?
Perhaps the best approach is to hold all
models provisional. The mechanism of the
model that reproduces the known features
of the thing modeled and continues to
agree with observations taken after its
construction is more convincing than one
which does not. The mechanism of a model
which shows agreement with the original in
aspects for which it was not deliberately
designed becomes positively intriguing.
Clearly, an act of faith is required in
every inference from model mechanism to
original mechanism.
2.2 How are models made?
Model making of any kind is a craft,
an art. Two of the most important tools
the craftsman of mathematical models has
are approximation and averaging.
To illustrate the use of approxima-
tion consider Newton's Second Law of
Motion which says, in effect, that
momentum is conserved. When the law is
expressed in a form descriptive of fluid
flows we find that it says: The total
rate of change in the momentum of a flow
at each point is the sum of the forces
acting on the fluid. The total rate of
change is made up of two parts: the local
time rate of change in momentum at the
point and the advective transport of
momentum to the point by the sweep of the
fluid motion. The forces which can act
on a fluid are: the pressure-force, the
Coriolis force (which depends on the
earth's rate of rotation), the gravity
force (which is gravitation adjusted for
the centrifugal acceleration due to the
earth's rotation), and the frictional or
viscous force.
local rate of change
+ advection = total rate of change
= pressure + Coriolis + gravity
+ friction
Such an analytic "model" incorporates
everything that can influence the
momentum of any flow and is thus complete.
Unfortunately, it is so complex that it
is mathematically intractable; we can
deduce little or nothing from it.
However, in some flows not all the
forces at work are equally important.
Coriolis effects are very small in
comparison with the others when the flow
is of the size customarily found in
laboratories. In such flows the terms
representing the Coriolis effects can be
set equal to zero and an approximate
model constructed by omitting them.
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There are a number of steady large-
scale oceanic flows which show very little
momentum change with time so that the
total rate of change can be approximated
to zero, e.g., the Gulf Stream. Further,
water has a very small viscosity so that
the frictional terms can also be dropped.
A satisfactory model for these particular
oceanic flows says that the pressure,
Coriolis, and gravity effects are
substantially in balance, i.e., add nearly
to zero. The model says that in the
horizontal the pressure and Coriolis
effects are equal while in the vertical
the hydrostatic equation gives a good
description.
Knowing when you may safely
approximate a term to zero and when the
neglect will make what is retained useless
nonsense as a model for the particular
flow being studied requires an intimate
acquaintance with the characteristics of
the fluid flow you are trying to model.
The reduction in the complexity of a
mathematical model secured by approximat-
ing terms to zero is gained by throwing
away whole classes of effects. To the
extent that the real flow is only slightly
influenced by the neglected processes, the
model may be a good one.
The reduction in complexity secured
by averaging is of a quite different kind.
Averaging simplifies by blurring the
picture, not by throwing things away. In
a way, it is a technique that seeks to
bridge the gap between the instantaneous
point by point descriptions offered by
many analytic models and the world that
we, as humans, perceive. The water
temperature at each point within Long
Island Sound is a perfectly good idea
but one which humans are unlikely ever
to realize. If we average the temperature
over each square mile, we have a better
chance. If we average over the entire
Sound, we come up with just one tempera-
ture . The larger the interval over which
the average is taken, the simpler and
smoother our picture becomes; the details
have been blurred and can no longer be
seen.
But even though you can't see the
details, their effects are not lost. As
an example consider the way that the
advective transport processes enter the
equations describing the time rate of
change of a substance s. In the
instantaneous point by point description
it is represented by terms like u(8s/3x).
If we average u and s we get things like
u = V + u' and s = S + s' where U and S
are the averaged values of the instan-
taneous point values of velocity, u, and
substance, s, and u' and s1 are what you
have to add to the averaged values to
make them equal to the instantaneous point
values. The average of the advective
transport term exhibited is then
equivalent to U(3S/8x) + u1(3s'/3x).
The first of these terms is of the same
form as the original term and says that
the averaged value of the substance is
transported advectively by the averaged
velocity exactly as the instantaneous
value of the substance was transported
advectively by the instantaneous velocity.
However, the second term says
something quite different. It says that
the details smeared by the averaging are
not lost but appear on the average as
though they were a transport of the
substance by diffusion. In the instan-
taneous point form the only diffusion is
molecular. This apparent diffusion,
created by averaging, is usually much
much greater. It is one of the most
difficult problems introduced by averaging
since just how big it is depends on how
the averaging is done; and how it works
depends on how the smoothed out details
of the motion are related to the averaged
motion. After all, we average in order
to get rid of the details and here are
their effects right back again in another
disguise.
The art of the modeler is shown in
the way he relates this apparent diffusion
to the averaged motion. How he is to do
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it is something we don't yet understand
very well. It needs a lot nore work.
Models usually use both approxination
and averaging. They are often built by
first neglecting one or more processes and
then further simplified by averaging to
smooth out the picture. Whether the
result is a good model, a satisfactory
model, or even a model at all, can be
determined only by checking to see whether
it reproduces the features of the thing
modeled.
2.3 Scales of averaging and
observation and their effects
on prediction
All instruments have scales, the
intervals of time and space over which
they sense. In other words, instruments
do not give instantaneous point measures
but rather "averages" over more or less
restricted regions of space and time.
Oceanographers sometimes use these
•instrument scales which determine the
smallest features that can be seen but
more often they find them too detailed and
too responsive. Scientists smear the
detail and coarsen what can be seen
further by averaging, i.e., they put the
data through low-pass filters. The
averages chosen reduce our ability to
sense fluctuations in the quantities we
measure. They impose scales, which we may
call measurement scales, below which we
can no longer detect changes in the
quantities measured.
There are also upper limits which we
may call observation scales. They are
just as ubiquitous as instrument scales or
measurement scales although they are
seldom explicitly formulated or discussed.
Observation scales are the largest volume
of space and the longest period of time
over which we continue our observations.
The observation scales must be larger than
the measurement scales—which as a lower
limit are instrument scales—but, once
that restriction is met the choice of
observation scales depends on what use
the observer plans to make of his data.
Characteristically, a man using a hot-
wire anemometer picks the volume of the
working section of his wind tunnel,
perhaps 12 cubic feet, and a period of at
most a few hours. For comparison, the
meteorologist works with the "weather
net." The observational time scale is at
most about a century, the period during
which systematic weather observations
have been made. The corresponding
"instrument" scale is of the order of one
hour since observations are ordinarily
made each hour. Changes more rapid than
hourly can't be "seen." The spacing of
observation stations in the net provides
an "instrument" space scale by defining
the size of the "particle" of fluid with
which the meteorologist can work. The
observational volume scale covers the
surface of the globe in a patchy way and
extends to the height of routine use of
radiosonde balloons.
One must know both the maximum and
minimum scales applicable to any model
since the properties and even the laws
which govern them may change radically
with a change of scale. The models and
the kinds of predictions that can be made
from them also change just as radically
as do the laws.
As an example, consider studies of
the earth's atmosphere. There is a whole
heirarchy of scales on which it is
modeled.
The largest scale, the planetary
scale, is earth sized and, at that scale,
the atmosphere is a very thin shell as
compared with the earth's radius. The
horizontal gradients of atmospheric
properties are small but their vertical
gradients are large. The best size
"particle" for modeling is long and flat,
say 5000 x 5000 x 1 cubic kilometers.
The maximum volume is that of the earth
and its atmosphere. For time scales a
reasonable minimum is a year or two while
the maximum is, unfortunately, what we
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are stuck with; the length of time since
we began to make decent systematic' weather
records. On these scales the properties
of the earth's atmosphere are very simple.
The atmosphere is a thin layer rotating
with the earth at a constant rate. It has
large vertical gradients of temperature
and pressure. Relative to axes fixed to
the earth the law governing the motion is
inordinately simple: merely the velocity
is identically zero.
The next smaller scale is appropriate
to the study of the general atmospheric
circulation. A reasonable "particle" size
is now something like 1000 km x 1000 km
horizontally by 100 m vertically. For
time scales we should go to a minimum of a
month and for the maximum we are still
stuck with that 100 years or less of
available record. At these scales we
begin to see motions of the atmosphere
relative to axes fixed in the earth, i.e.,
we see the general circulation. Our
previous velocity law is now false, or
better, inapplicable, simply because of
the change in scale. Now we have that the
horizontal component of velocity is not
necessarily zero. However, the vertical
component of the velocity is still zero.
Still smaller is the meteorological
scale. Let it be the smallest made
possible by the net of the World
Meteorological Association. The "particle"
is still flat; something like 10 km x
10 km x 10 m at the very best. The
minimum time is 1 hour corresponding to
the hourly observations and the maximum
time is about 40 years, the period since
hourly observations were initiated. On
these scales we see the atmosphere as the
meteorologist sees it. There are air
motions additional to the general
circulation. In particular, the wind,
which was invisible on the previous
scales, emerges. Wind is, by definition,
horizontal so that we will still have a
zero vertical velocity component but
horizontal turbulence enters the problem
for the first time.
If the scale is again reduced to the
aerological scale, the "particle" at last
begins to be more cubical and is of the
order of a few meters on a side. The
maximum vQlume on aerological scales runs
around 100 to 200 cubic kilometers. The
minimum times are around a minute. This
is a sort of shortest time interval in
which cloud formations usually show
perceptible motions. Here, time lapse
photography helps us to see the motions
which turn out to be quite simple, e.g.,
cellular rotation. The maximum time is
the time it takes an observer to get tired
of observing—barring antlike dedication,
a few hours. When we look at the atmos-
phere at the aerological scale, which
being "man sized" is how you, as a person,
see it directly, we see nothing but
turbulent motions. They appear so complex
that the prospect of trying to formulate
laws and models is most discouraging. The
motion appears to be random and all three
velocity components may be non-zero.
Still smaller scales which we will
not go on to discuss are the aerodynamic
scale and the molecular scale.
In summary: the physical laws
appropriate to the organization of a
body of observations are critically
dependent on the scales at which the
observations were made. In every case,
before we begin to discuss, model, or
predict we must understand clearly:
Measurement Scales
The minimum volume which determines
the size and shape of the "particle" with
which we work. The minimum time which is
either the smallest response time of the
instruments used or the period of the
most rapid fluctuation passed by the
averaging process.
Observation Scales
The maximum volume defines the region
of space over which the observations
extend. The maximum time is the duration
of the observations.
The message for modeling in general
and modeling of transport processes in
-------
estuaries in particular is clear. You
can not model anything unless you have
first measured it. How you measure it,
the measurement and observation scales,
control the kind of model you can build.
The processes in estuaries are of many
scales, some of them very long. For
example, there is often an annual cycle
related to the seasonal variations in
river discharge and solar radiation. If
your observational scale is only one month,
you have absolutely no hope of modeling
the annual cycle. At least a year of data
is the minimum and 10 to 20 years is more
like it. Again, if the measurement space
scale is an average over 10 mile squares,
there is no reasonable prediction that can
be made of the course of an oil spill of
smaller dimensions and no point in asking
for a prediction of its detailed progress.
Again, if your observational scales cover
only New York Harbor, don't come around
asking for predictions for the New York
Bight.
It is nothing short of tragic that no
agency of the government has seen fit to
support the collection of estuarine data
on the extended and detailed scales
necessary for the construction of the
models upon which satisfactory prediction
can be based. We now find ourselves with
the problems which were foreseen and with
little or nothing with which to work.
About all that can be said is that we
ought to get at the job—right now. We'll
never start sooner.
3. ANALYTIC AND NUMERICAL MODELS
3.1 The equations
The best formulations of the kinematic
and dynamic equations which serve as a
basis for estuarine models are three-
dimensional in space and time dependent.
They contain terms representing all the
physical processes at work. Thus, they
are complete.
However, to use them for particular
estuaries and, in the face of our meager
data, they must be averaged. What emerges
is strongly affected by the averaging
methods chosen. Further, and more
important, averaging creates additional
terms, the nonadvective flux terms, e.g.,
the Reynolds flux of momentum, whose
forms are not determined a priori by the
physics of the flow. The principal
difficulty with estuarine modeling centers
on these nonadvective flux terms. As
artifacts of the averaging, not only are
they heavily dependent on the choice of
average, but they are critically dependent
on the choice of measurement scales in
both space and time. Since the non-
advective fluxes are not controlled by
the physics of the flow they must be
explored empirically. And that means
adequate and properly taken data.
It is axiomatic in fluid mechanics
that our understanding of real flows
depends on increasing our knowledge of
those terms not determined by the physics.
For example, the Reynolds momentum-flux
terms depend on variance and covariance
functions of the instantaneous
fluctuations of the velocity components
from their mean values. Except in highly
restricted flows unlikely to occur in an
estuary, they are complicated functions
of position and time (xlf x2, x3, t) as
well as of space and time separations
(rl7 r£, r3, T). For many years it has
been common practice to assume that they
could be expressed as a product of a
constant, the "eddy" coefficient, and the
gradient of the mean; a Fickian
assumption. That such a form for the
Reynolds momentum flux is inadequate to
represent the complexity of the covariance
function in general is so glaringly
obvious as to scarcely call for comment.
It is siirply wrong and it's use lends a
njtjhtrare quality to our perception of
the real world. But for all that, it
continues to be used faute de mieux. We
must measure the nonadvective fluxes
sufficiently well to intuit a better form
-------
than the Fickian assumption. Only then
will we be able to make a closer, more
useful contact with reality and,
incidentally, to retire the "eddy"
coefficient to the intellectual junk heap
where it so richly deserves to rest.
The time scales are somewhat easier
to explore than are the space scales.
An instrument can be mounted and kept
running for a considerable length of time.
When this was done in the Patuxent and the
Potomac by Elliott (1, 2, 3, 4, 5) the
variability characteristic of an estuary
became very evident. In contrast with
the open ocean, measurements of any
property within an estuary fluctuate much
more widely and rapidly with time.
Estuaries seldom reach steady state and
it is very difficult to guess what an
estuary's condition will be at any
instant. Elliott (1, 2, 3, 4, 5) shows
that during the year of his study, the
Potomac approximated one or another of
six different estuarine circulation types
but that more than half the time it didn't
look like any of the classical types.
Spatial variations in an estuary are
also highly irregular in comparison with
the open ocean. The space scales are
harder to study since they require
simultaneous measurement by many instru-
ments at many positions. We really know
far too little about the spatial variation.
If an estuary shows little sectional
variation laterally and with depth, then
it is attractive to average properties in
sections and attempt a one—dimensional
longitudinal model. If the section has
little longitudinal variation but does
show depth dependent variation, perhaps a
two-dimensional longitudinal-depth model
is in order. Similarly, if the estuary
is very wide and shallow with little
variation with depth, as in the case of
Corpus Christi, Texas, one might try a
two-dimensional longitudinal-lateral
model. Where the variation is marked in
all three dimensions only a full three-
dimensional model is really useful.
We do not know enough to say a
priori when a model of reduced dimen-
sionality will be satisfactory and useful.
In practice we have advanced only to the
use of two-dimensional models. There are
three pragmatic considerations which
account for this. The complexity of
three-dimensional models makes it very
hard to gather the data with which they
may be verified and tested. The computer
costs are high for three-dimensional
models. Finally, when nobody knows
anything much perhaps you can find some-
thing or other that will work from a
simple approach. But models with reduced
dimensionalities are not adequate.
Evidence is beginning to accumulate that
suggests that the three-dimensionality
plays an essential role in all estuaries.
Even strongly stratified estuaries and
wide shallow estuaries can not be properly
explained by models with less than the
three spatial dimensions.
3.2 The Boundary Conditions
In addition to the kinematic and
dynamic equations every model must
prescribe boundary conditions. These are
inherent parts of the model and, when
averaging is applied to the equations,
similar specifications must be applied
to the boundary conditions in order to
ensure compatible resolution in space and
time.
During periods when data are being
taken for the construction of a model,
the boundary conditions must also be
measured. During periods when data to
test a model are gathered, the boundary
conditions must also be measured. When
a model is used for prediction the
boundary conditions must also be
predicted. How well a model will predict
depends critically on how accurately the
boundary conditions can be predicted.
When a model is used to explore the range
of estuarine behavior, the boundary
conditions must be hypothesized.
-------
The boundary conditions relevent to
an estuary are:
(1) The freshwater flow to the estuary.
These flows include the flux of
water at the head of the estuary. If
rivers enter the reach, their fluxes must
also be known. In some estuaries there
may be an appreciable flux of ground water
through the bottom. Evaporation and
precipitation are, effectively, freshwater
fluxes out of and into the estuary through
the surface, respectively.
Freshwater fluxes from rivers are
perhaps the best known since many rivers
are gaged. The trouble is that the gages
are usually well above the head of the
estuary leaving substantial areas
uncovered. This won't do. We must
measure the freshwater fluxes where we
need to know them; not in the next county.
All of these freshwater fluxes are
time dependent and usually highly variable.
(2) The rise and fall of surface elevation
on a line across the mouth of the
estuary.
This is often supplied by one tide
gage or by two tide gages located on the
opposite shores; the elevations across the
mouth being inferred from theory or simply
assumed to follow some conveniently simple
function. Again, the condition is time
dependent and variable.
(3) The spatial distribution of salinity
as a function of time across a section
at the mouth of the estuary.
Present models often use some
artifice such as assuming that the
salinity present at the mouth is simply
advected seaward during ebb current and
then jumping it to full sea water on the
section when the current changes to
flood. This kind of thing won't do. The
spatial and temporal behavior of the
boundary salinity must be measured at a
level of resolution compatible with the
level used for the body of the estuary.
(4) The wind stress on the surface of
the estuary as a function of horizon-
tal position and time.
It is probable that we know less
about this boundary condition than about
any other. But we know that it can be
important. In shallow estuaries it can
produce water surface elevation changes
much larger than the astronomical tide.
Depending on the wind, as it does, it is
very highly variable in both space and
time. For the most part, while it is
included in the equations, it is ignored
in the models. We can't measure wind
stress on the water surface directly but,
at the very least, good wind velocity
measurements should be made. They alone
won't solve the problem since the
mechanism by which air motion transfers
stress to the water surface is not well
understood. There are forms for the
drag which can be used but they may be
inadequate. Like the nonadvective fluxes,
the wind stress on the surface is one of
those things not determined a priori by
the physics of the flow. Still, measure-
ment of the wind where it matters—over
the water; not some irrelevant five miles
away at an airport—should give us more
than simply turning our backs on an
important forcing function.
(5) The bottom configuration of the
estuary must be known.
In some estuaries it may be possible
to consider the bottom as a rigid
container but it is actually a slowly
varying function of time. Whether it is
a rigid boundary or an elastic one,
permeable or impermeable, may also need
consideration. Of one thing we must be
particularly careful: the spatial
resolution. If the resolution is too
coarse to define the essential topography
well enough, subscale bathymetric quirks
of individual estuaries will appear
falsely as dynamic effects thus rendering
the model useless in any estuary save the
one for which it was constructed. A
knowledge of the fractional drag on the
bottom is just as necessary as a knowledge
of the wind stress on the surface. It,
too, is not determined a priori by the
10
-------
physics and the same sorts of difficulties
arise.
To sum up; our knowledge of the
boundary conditions is inadequate. Many
of the models, as actually worked out, do
not include their critical time dependence.
Those that do include it do so only in the
most simple and unrealistic way. Here is
an area of ignorance and omission that
must be made good before progress in
estuarine modeling can be expected.
3.3 Verification and testing
All models should be verified. That
is to say that they should be able to
reproduce the data used to construct them
tolerably well and that they should be
shown to do so.
Any model in which we are to repose
much confidence should also be tested.
Once it has been made and is in existence,
at least one more set of data of the sort
on which it was verified and from the same
estuary should be taken. The model, if it
is to be taken seriously as a model,
should do just as well at reproducing the
second set of data; and that without
further modification.
No model which has not been both
verified and tested can be considered
anything but "work in progress." It is
something of a scandal that none of the
"models" we now have has been either
verified or tested in its complete form.
The data with which to do so have never
been taken.
3.4 The areas to be addressed
The problems which urgently need
attention fall under three general heads:
(1) A better comprehension of the
forms of the terms in the
averaged equations and boundary
conditions which are not
determined a priori by the
physics.
(2) A better definition of the
boundary conditions as they
actually exist.
(3) A clearer idea of the variability
in both space and time of the
properties and processes
occurring within and on the
boundaries of estuaries.
Progress in all of these areas turns on
the selection of averaging methods,
measurement scales (resolution limits),
and observation scales (extension limits).
Field experiments will be necessary.
4. FIELD EXPERIMENTS
The field experiments required to
resolve problems in the three areas and
to build a useful three-dimensional model
for estuaries are of two sizes: small- to
intermediate-scale experiments and large-
scale experiments.
4.1 Small-scale experiments
The primary purpose of small-scale
experiments is to obtain direct and
indirect measures of the nonadvective
fluxes of salt and momentum in all three
spatial directions, horizontal and
vertical. Proper measurements of all
boundary conditions must be made during
the course of each experiment. From these
data we can get:
(1) A more realistic form for the
nonadvective flux terms.
(2) A better partition between
advective and nonadvective
fluxes as functions of the
averaging methods and of the
time and space measurement-
scales.
The experiments, discussed in more
detail in section 5.1, will consist of
enclosing a carefully selected, relatively
modest volume of an estuary (the spatial
observation scale) with a ring of sensors.
Interior to this ring another ring of
sensors will be disposed. At the center
of the array a station instrumented with
11
-------
the most responsive sensors the state of
the art provides will be located. The
measurements from them will be recorded at
instrument scales.
Among the questions for which answers
can be expected are:
(1) What is the partition between
advective and nonadvective fluxes as a
function of the time average selected and
the time resolution chosen?
(2) What is the partition between
advective and nonadvective fluxes as a
function of the spatial average selected
and the spatial resolution chosen?
(3) What are the best empirically
determined mathematical forms for the
nonadvective flux terms temporally?
(4) What are the best empirically
determined mathematical forms for the
nonadvective flux terms spatially?
(5) What relations between the
nonadvective and advective fluxes exist?
How can they best be parameterized?
(6) What relations exist between the
nonadvective fluxes and the bulk para-
meters of the estuary, e.g., the
Richardson number?
(7) What relationships and values are
reasonable among the coefficients which
appear in models?
It is clear that these small- to
intermediate-scale experiments will shed
light on all three problem areas listed in
section 3.4.
The problem of the boundary condi-
tions is of a somewhat different kind.
They either force or modify the flow
within the experimental volume. We must
measure them every time our sensor array
is in operation if we are to have any
hopes of interpreting our data clearly.
Guessing at the boundary conditions will
vitiate the experiment.
4.2 Large-scale experiments
The large-scale experiments extend
the spatial observation scale from a
"modest volume" to an entire estuary from
head to mouth. Their primary purposes are
to construct, verify, and test an improved
model for an estuary based on the results
from the small- to intermediate-scale
experiments and to explore the conditions
and field-data effort required to transfer
a model from the estuary for which it was
constructed to another.
As a practical consideration, the
instruments necessary for the small- to
intermediate-scale experiments will serve
equally well for the large-scale
experiments. Few additional instruments
are required; only redeployment will be
necessary.
An estuary will be selected for
modeling and divided into five reaches
by six sections; one at the head, one at
the mouth, and the remaining four at
intermediate positions. The estuary
initially selected may be either partially
mixed or highly stratified (including
fjords). The first set of data taken from
it will be used to construct the model
and verify it. When this has been done,
a second set of data will be taken and
the model tested.
At the second stage another estuary
somewhat different from the first will be
chosen and data gathered. These data will
be used initially to test the model
exactly as it came from the first estuary.
If no adjustment of the coefficients is
required for satisfactory performance, the
transferability of the model to the second
estuary will have been established. If
adjustments of the coefficients are
required, they will be made and the
adjusted model verified. A second set of
data collected in the second estuary will
be used to test the adjusted model.
At the third stage, an estuary quite
different from the first and second
choices will be selected. The sequence
of estuaries can be taken in any order.
We could begin with a well mixed estuary
and finish with a highly stratified
estuary; or the other way around. Again
we will take data and test our model from
12
-------
the first estuary and our adjusted model
from the second estuary. Again, another
set of data will be taken for testing our
adjusted third model.
What will we have at the end of this
sequence of large-scale experiments?
First, we will have models for three
estuaries. These models will have much
closer contact with the real world than
any present models. Most important, they
will have been both verified and tested
and can thus be expected to perform
reliably. Second, we will have gained
valuable experience with the transfer-
ability problem. Should the model for our
first estuary not require adjustment for
use in our second estuary, we will have
immediately established a range of
applicability. Should adjustment be
required, we will have the means of
judging the minimum field effort required
to gather data on which the adjustment
could have been made. This will establish
the conditions for transferability to many
other estuaries. Third, we will have
comparative studies of the full range of
estuaries and so be able to move more
quickly and efficiently to the solution of
particular problems in individual
estuaries.
4.3 Some comments and caveats
The small- to large-scale experiments
suggested here collectively represent one
experiment which will go a long way toward
resolving the most troublesome deficiencies
in our knowledge of transport processes in
real estuaries. But it is important not
to conceive of this as a great monolithic
set piece which, once launched, is to go
thundering along a prescribed track with
results only at the end of it all. It is
rather a step by step process. At each
step computing and analysis must be swift
enough to guide the next step. Each step
will yield results of value but the full
value of each can be realized only in
relation to the whole.
We repeat: the boundary conditions
must be properly measured at each step.
There are many experiments which
might be run with mutual profit at the
same times and in the same places as the
proposed experiments. For example,
diffusion has been studied with both
Eulerian and Lagrangian measurement
techniques. Much data exists. Unfor-
tunately, statistical theory has, as yet,
only the most rudimentary information on
how to relate the statistics of one view
to the statistics of the other. Studies
using dye or drogues made concurrently
with the small- to intermediate-scale
experiments could give the empirical base
for improved relations between Eulerian
and Lagrangian information; thus making
data in hand more useful.
5. A SKETCH OF THE SHAPE, SIZE,
AND COST OF THE FIELD EXPERIMENT
The shape, size, and cost of the
field experiment can best be communicated
by sketching a possibility. But it must
be remembered that this is only a sketch
and a very incomplete one. Specific
arrangements and particular places will
be named but only as examples in order to
make a concrete picture. This is not a
proposal nor are the costs a budget.
Both are matters for consideration and
decision by the scientific community
during the planning period which must
precede the experiment.
Let us suppose that the Delaware has
been selected as the first estuary to
model, Long Island Sound as the second,
and the Duwamish as the third. This
gives a sequence from partially mixed
with classic geometry through partially
mixed with aberrant geometry to highly
stratified.
5.1 The nonadvective flux experiments
To have a brief name for the small-
to intermediate-scale experiments we will
13
-------
call them FLUX 1 and FLUX 2. FLUX 1 and
2 could be carried out in the Delaware
since their results will be applied there
during the first large-scale experiments.
However, they could as well be done in
any convenient partially mixed estuary.
The space scales are to be modest and the
idea in any case is to avoid local
idiosyncrasies which could induce non-
transferable results. An area with a
level bottom, or at most gentle relief,
with no nearby abrupt features would be
suitable. The water should be 15 to 20
meters deep and shoal water at the sides
at least a kilometer away from the
instrument array.
The instrument array should "enclose"
a volume of water 200 meters across and
extending from surface to bottom. It's
precise shape and the disposition of the
instruments is a matter for the planning
stage with modifications as the results
become available. It might look like this.
1
\
\
a recording velocity-salinity-temperature
meter of the ANDERA/ENDECO types. The
central station will be a fixed tower
mounting the fastest response 3-component
velocity, salinity, temperature sensors
that can be kept functioning under field
conditions, instruments such as those
developed and used by Smith (6). In
conjunction with the array, 10 paper-tape
recording tide gages, one meteorological
buoy station, and four shore-based
meteorological stations will be installed
and operated.
The array and its associated
instruments will be operated continuously
for a month at a time. During periods of
operation a barge with living and working
accommodations for a technician, tape
recorders, monitoring devices, repair
facilities, and power supply will be
anchored with the array.
FLUX 1 will consist of deploying
the array, operating it continuously
for one month (Which month is immaterial.),
performing the necessary calculations,
and analyzing the results for answers to
the questions posed. Analysis of the
dispositions and operation of the array
during FLUX 1 will also be made for
guidance in data gathering during FLUX 2.
Upon completion of FLUX 1, and not
before, the array will be modified as
indicated and FLUX 2 will repeat the
pattern of FLUX 1.
The analyses of FLUX 1 and 2 will
give us the forms, partitions, and
relations necessary for constructing,
verifying, and testing an improved three-
dimensional estuarine model.
200m-
•RING STATION
• CENTRAL STATION
There are eight stations in the outer
ring, eight stations in the inner ring,
and one central station. Each ring
station is to carry at each of five depths
5.2 The estuarine model experiments
The brief name for the large-scale
experiments which will give us verified
and tested three-dimensional models for
three estuaries will be EMEX 1, 2, 3, 4,
5, and 6.
If we use the Delaware for FLUX 1
and 2, then the Delaware will be used for
14
-------
EMEX 1 and 2. The estuary will be divided
into five reaches by six sections along
which the instruments used in FLUX 1 and 2
will be c eployed and operated continuously
for a mo ith at a time, the month chosen
not beirg critical. The landward and
seaward sections B0 and B , must be
J6 S
B,
occup: ad during each data collecting
perioc but all the internal sections need
not be occupied simultaneously. During
EMEX I , for example, we could occupy B^,
A, B, and B for one month followed by
B,, , C D, and B for another month.
i n section B^, which will be located
above the limit of sea-salt intrusion, the
prima y measurement will be of the fresh
water volume flux. At all other sections,
surfa> e elevation, salinity, temperature,
and v locity will be measured. Meteoro-
logic 1 measurements will be made during
all p riods of operation.
'ith the data in hand from EMEX 1 a
three dimensional model of the Delaware
will be constructed and verified against
the data. We can then proceed to EMEX 2.
EMEX 2 will repeat EMEX 1 and the
data used to test the model.
For EMEX 3 the data acquisition
pattern of EMEX 1 will be repeated in
Long Island Sound and the data used to
test the model from EMEX 1. One of two
outcomes may be anticipated:
(1) The model of EMEX 1 for the
Delaware performs satisfactorily for
Long Island Sound without modification.
(2) The model of EMEX 1 for the
Delaware requires adjustment of its
coefficients for satisfactory performance
in Long Island Sound.
Should outcome (1) materialize,
there will be no need for EMEX 4. The
data from EMEX 3 will test the model.
The effort planned for EMEX 4 could be
avoided or, perhaps invested in another
estuary even further removed from the
type of the Delaware, say Corpus Christi.
Should outcome (2) materialize, the
data from EMEX 3 would be used to adjust
the coefficients and to verify the
adjusted model.
EMEX 4 would then be similar to
EMEX 2 and the data used to test the
adjusted model for Long Island Sound.
EMEX 5 and 6 would repeat the pattern
of EMEX 3 and 4 in the Duwamish, a
strongly stratified estuary.
At each stage from EMEX 1 through
EMEX 5 computation and analysis will be
completed before the next stage is under-
taken and the results used to guide the
ensuing stage.
In the end we will have three-
dimensional models tested and verified
for the Delaware, Long Island Sound, and
the Duwamish v;hich represent a wide range
of estuarine conditions. We will have
also learned what adjustments are
necessary to adapt such models to
particular estuaries. It is likely that
the full weight of the field data
necessary for EMEX 1 through 6 will not
be required. We can hope to be able to
15
-------
say with some confidence what field
measurements are enough for model
transfers.
5.3 The means
The trained men, the supporting
services, the means of inter-institutional
cooperation, and the interest of the
scientific community are all available
for this experiment. What is lacking
are the instruments and the money.
5.3.1 Instruments and Hardware
Required by both FLUX and EMEX.
Number Description
100 salinity-temperature-velocity sensors
10 tide gages
1 meteorology buoy station
4 meteorology shore station
20 mooring systems
2 ENDECO-type readers
1 paper-tape reader, tide gage
1 positioning system, electronic
For the FLCX Central Tower
6 high resolution 3-con\ponent velocity
instruments
6 compatible high resolution instruments for
salinity and temperature
1 Attendant barge with living and working
space for a technician, tape recorders,
power supply, monitoring and data logging
devices for all instruments of the array,
and repair facilities
Estimated
Unit Cost
($)
8,000
2,500
10,000
5,000
750
5,000
3,000
26,000
Total
Cost
($)
800,000
25,000
10,000
20,000
15,000
10,000
3,000
26,000
909,000
Estimated cost:
Total:
100,000
$1,009,000
16
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17
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6. CONCLUSION
What needs to be done is clear. The
key to adequate prediction of estuarine
transport processes is in the nonadvective
flux terms; those not specified a priori
by the physics of the flow. We must
develop more adequate forms for them
empirically. We must relate them to the
advective fluxes. We must parameterize
them properly and relate them to the bulk
properties of estuaries. A successful
attack on these questions will require
careful attention to methods of averaging
and to the choice of instrument, measure-
ment, and observation scales in both space
and time. Completion of these tasks will
be a major step forward in our scientific
understanding of estuarine transport
processes.
However, increased scientific insight
is only the first requirement. The second
is to use our better grasp of estuarine
transport processes as a basis for the
construction of improved three-dimensional
estuarine models. These models must be
both verified and tested if we are to have
confidence in what they tell us about the
real world. Only such models give the
factual foundation that is a sure aid to
management decisions.
The third requirement is to explore
model transferability. Under what condi-
tions can a model fitted to one estuary
and successful as a predictor in that
estuary be used for another estuary?
What adjustments are necessary for
transfer? How much field data and of
what kinds must be gathered to make the
adjustments?
This, then, is the job to be done.
We know how to do it. With proper support,
the men, ships, and institutional capacity
are available to do it. It will take
something like five years and the support
required will be between 4 and 5 million
dollars.
Will it be worth doing from a
practical standpoint? On past experience
the answer is an unequivocal "Yes."
"Guidelines for Evaluating Estuary
Studies, Models and Comprehensive Planning
Alternatives" issued by the U.S.
Department of the Army, August 1969 lists
eight projects in which hydraulic model
studies whose costs were comparatively
small guided management decisions which
improved project design and saved millions
of dollars. They were
(1) The Columbia River Entrance,
(2) The Columbia River Entrance,
Jetty B,
(3) The Columbia River, Wauna-Lower
Westport Bars,
(4) The Delaware River Dikes,
(5) Narragansett Bay,
(6) St. Johns River, Florida,
(7) Galveston Harbor Entrance,
and (8) Lake Pontchartrain, Louisiana.
Hydraulic models are highly specific;
a separate hydraulic model must be built
for each estuary studied. They are
cumbersome and expensive and, most
important, not easily transferable.
Mathematical models are much more flexi-
ble. For a good one, only the computer
input needs to be changed to move it from
one estuary to another. Mathematical
models do not replace hydraulic models;
they complement them. As a tool for
management, improved mathematical models
have the potential of extending the
benefits already realized from hydraulic
modeling to a much wider range of
estuaries at much less effort and expense.
Another management area to which
improved, reliable mathematical models
could make an important contribution is
water quality monitoring. Much effort is
currently expended on gathering water
quality data. Unfortunately much of it
may be of little value; even for the
purposes of the agencies which collect it.
Good mathematical models could provide
guidance for water quality monitoring that
would make it both more effective and less
costly.
Our conclusion is that the problems
18
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discussed in this report should be taken
in hand as soon as possible. We feel that
the benefits, both in increased scientific
understanding and in more powerful
management tools, far outweigh the costs
of the undertaking.
BIBLIOGRAPHY
1. Elliott, A. J. and T. E. Hendrix.
1976. An analysis of the current
and salinity structure off Howell
Point in the upper Chesapeake Bay.
Chesapeake Bay Institute, The
Johns Hopkins University, Special
Report 53. 23 pp.
2. Elliott, A. J. 1976. A study of
the effect of meteorological forcing
on the circulation in the Potomac
estuary. Chesapeake Bay Institute,
The Johns Hopkins University, Special
Report 56. 66 pp.
3. Elliott, A. J. 1976. A mixed-
dimension kinematic estuarine model.
Chesapeake Science 17:135-140.
4. Elliott, A. J. 1976. The circulation
and salinity distribution of the
upper Potomac estuary. Chesapeake
Science 17:141-147.
5. Elliott, A. J. 1976. Response of the
Patuxent estuary to a winter storm.
Chesapeake Science 17:212-216.
6. Smith, J. Dungan. 1974. Turbulent
structure of the surface boundary
layer in an ice-covered ocean.
Papp. P.-v. Reun. Cons. Int. Explor.
Mer. 167:53-65.
19
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APPENDIX A
Organisations Supporting the Workshop on
Transport Processes in Estuaries
United States Environmental Protection Agency
United States Energy Research and Development Administration
Office of Naval Research: Geography Branch
National Oceanic and Atmospheric Administration: MESA,
New York Bight Project
United States Fish and Wildlife Service: Office of
Biological Services
Stony Brook Foundation
APPENDIX B
Participants •in fhe Workshop on
Transport Processes in Estuaries
K. Allen
R. Baltzer
Malcolm Bowman
Burt Brunn
Harry H. Carter
S. Chane smart
Dennis M. Conlon
T. John Conomos
Bruno d'Anglejan
Keith R. Dyer
Alan Elliott
John Festa
Robert Gordon
R. G. Ingram
Blair Kinsman
Bjorn Kjerfve
Ray B. Krone
G. Mayer
Tavit Najarian
Maynard M. Nichols
Charles B. Officer
Akira Okubo
David H. Peterson
Donald W. Pritchard
U.S. Fish & Wildlife
U.S. Geological Survey
Marine Sciences Research
Center
U.S. Fish & Wildlife
Chesapeake Bay Institute
NOAA
Office of Naval Research
U.S. Geological Survey
McGill University
Institute of Oceanographic
Sciences
NATO SACLANT ASW Research
NOAA
Yale University
McGill University
Marine Sciences Research
Center
University of South
Carolina
University of California,
Davis
NOAA
Chesapeake Bay Institute
Virginia Institute of Marine
Science
Marine Environmental Services
Marine Sciences Research
Center
U.S. Geological Survey
Centro de Investigacion
Cientifica y de
Educacion Superior
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APPENDIX B
(continued)
Maurice Rattray University of Washington
William S. Reeburgh University of Alaska
J. R. Schubel Marine Sciences Research
Center
D. P. Wang Chesapeake Bay Institute
Robert Weisberg North Carolina State
University
Robert E. Wilson Marine Sciences Research
Center
K. K. Wu Environmental Protection
Agency
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