PHYSICAL PROCESSES
AFFECTING THE MOVEMENT AND SPREADING
OF OILS IN INLAND WATERS
HAZMAT Report 95-7
September 1995
prepared for
The U.S. Environmental Protection Agency, Region V
Chicago, Illinois
-------
Purpose and Use of This Guidance
This manual and any internal procedures adopted for its implementation
are intended solely as guidance. They do not constitute rulemaking by any agency
Rmay not be relied upon to create a right or benefit, substantive or procedural,
"orceable by law or in equity, by any person. Any agency or person may take
action at variance with this manual or its internal implementing procedures.
-------
PHYSICAL PROCESSES
AFFECTING THE MOVEMENT AND SPREADING
OF OILS IN INLAND WATERS
^ or
R. Overstreet and J.A. Gait
NOAA / Hazardous Materials Response and Assessment Divivison
Seattle, Washington
HAZMAT Report 95-7
September 1995
prepared for
The U.S. Environmental Protection Agency, Region V
Chicago, Illinois
-------
Contents
1.0 Introduction I
2.0 Oil Properties
2.1 General 4
2.2 Classes of Petroleum 4
2.3 Density, Specific Gravity, and °API Gravity 6
2.4 Viscosity 7
2.5 Pour Point 9
2.6 Distillation Temperature 9
2.7 Flash Point II
2.8 Emulsification 12
3.0 Transport Processes
3.1 General 13
3.2 Flow in Rivers 14
3.3 Modification to River Flow by Structures 17
3.4 Lake Circulation 19
3.5 Wave and Wind Effects 19
3.6 Special Considerations 23
3.7 Spills in Ice 23
4.0 Modeling Techniques
4.1 General 25
4.2 Scaling 26
4.3 Averaging 27
4.4 One-dimensional River Flow Models 27
4.5 Two-dimensional River and Lake Models 29
4.6 Vertically Mixed Lakes.... 30
4.7 Three-dimensional Models 31
4.8 Special Considerations 32
-------
Contents, «>nt
5.0 Trajectory Analysis Procedures 35
Summary 37
6.0 References 38
Index 43
Appendix A-1
-------
figures
1-1 Steps in spill response 2
2-1 Simplified classification of petroleum hydrocarbons 5
2-2 Frequency distribution of specific gravity of oils 7
2-3 Viscosity, boiling range, and specific gravity for typical fuel oils 10
2-4 Kinematic viscosity as a function of temperature for typical
fuel oils 11
3-1 Cross-section of a meandering stream showing secondary flow 16
3-2 Flow in a meandering river 16
3-3 Vertical mixing in the tail waters of an overflow dam 18
3-4 Langmuir cells showing flotsam at surface convergences 22
4-1 River cross-section approximated by trapezoids 29
Tables
2-1 General range of oil viscosities at room temperature in terms of
familiar substances 9
-------
1.0 Introduction
When considering the movement and spreading of oil in lakes and rivers it is important
to understand the general characteristics of the physical environment, such as flow rates,
basin shapes, wind patterns, and mixing. It is also important to have a historical
perspective on the nature, extent, and course of spills that are likely to occur in these
waters. We know, for example, that rivers and lakes are popular recreational sites for
sport fishing and boating. Their associated activities often lead to small spills of a few
cubic centimeters of fuel which may leave rainbow or transparent sheen over tens of
square meters of water. Additionally, urban runoff from parking lots and roads may
wash down small amounts of hydrocarbons to create local sheens and detectable levels
of oil pollution. These sources of pollution, although technically spills, are reportable as
"visual sheens," will typically be below our level of concern, and whatever environmental
effects they cause are likely to be attributed to chronic conditions. At the other
extreme, Very Large Crude Oil Carriers (VLCC), such as super tankers, typically do not
enter lakes and rivers, and our experience has yet to supply us with an Amoco Cadiz or
Exxon Valdez-sized spill of crude oil in inland waters. Therefore, we will focus on
intermediate-sized spills, which are usually of refined products.
By focusing on intermediate-sized spills, we can think of a typical small spill as one
resulting from overfilling a product barge or a railway car derailing into a waterway.
These spills will generally range from a few hundred to a few thousand gallons. Large
spills are more likely to be associated with shoreside facilities that either cross the
water or are adjacent to it, or with groundings or collisions with towed tank barges
Examples are pipeline breaks such as the Buckeye pipeline rupture on the Allegheny
River in 1990; storage tank failures such as the Ashland Oil Company spill on the Ohio
River in 1993; or multiple-barge collisions such as those that occurred at St. Louis in
I 983 (see NOAA 1992). These types of incidents, where the amount of oil spilled may
be in the hundreds of thousands of gallons, demand an immediate, active response to a
pollution threat that could range from several miles to several hundreds of miles of
river- or lakefront. For this level of spill, it will be critical for the responders to
understand the physical processes that cause the oil to move and spread and the
distribution of the pollutant as it moves through the freshwater environment.
Our focus here is to examine the physical factors that determine how the spilled
pollutant will move. However, we should never lose sight of the fact that the trajectory
analysis is only a single link in the chain of information that is needed to help the
decision-making process during spills. This information must be relevant to decision-
makers' actual choices.
In its simplest form, scientific or technical support for spill response can be thought of
as answering a series of five questions (Figure I-1):
-------
What can
be done?
What damage
will be done?
What was
spilled"?
What will it
impact?
Where wi
it go?
Figure l-l. Steps in spill response.
First, we need information about the nature and extent of the spill. Second, we need to
estimate how the pollutant will spread and what form it will take as it moves in the
waterway. (Perhaps one of the key factors that distinguishes spills in water from those
on land is the complex and relatively rapid mobility of the spilled material.) Third, we
need to identify valuable resources (both natural and commercial) in the spill's
trajectory. Fourth, we need to understand the sensitivity of the various resources
encountered to the pollutant, and the kinds of damage that might be expected. Finally,
what do we do with these data? Are there any options open to responders that will
make a positive difference in the outcome of the spill or that will reduce the probability
that resources will be damaged?
When describing the movement and spreading of a pollutant, the physical scientist
should provide analyses that are as accurate as possible. However, it is at least as
important to know what the analysis does not include as it is to know what it does
include. This can be exemplified by procedures used in game theory, where decisions
must be made under critical, time- and data-sparse, and hence, uncertain, conditions.
In any game where chance plays a part, the players draw on all of the information
available to try to achieve a "maximum win." This would provide the best chance of
maximizing the players' return. An alternate, and generally different, game strategy
might be appropriate if a player is protecting very high- value resources. In this case, the
player would attempt to "minimize regret" rather than "maximize win." Thus a decision
must be made on a strategy that will make sense of the many variables associated with
spills. In spill response, a "maximum win" strategy would develop a forecast using as
accurate information as possible on winds, currents, and the pollutant's initial
distribution. This "best shot," or most probable scenario, contrasts with a "minimum
regret" strategy that uses a range of analysis techniques to investigate the sensitivity of
various estimates to error in the data used (See, for example, Operations Analysis Study
2
-------
Group 1977). A "minimum regret" strategy also incorporates the implications of
alternate hydrological and wind conditions. For example, what is the significance of an
atmospheric frontal passage six hours before the predicted time of arrival of an oil slick?
What is the likelihood of a heavy rain causing a rapidly changing discharge or flash flood?
The resulting analysis can provide the response organization with the "best guess" and,
at the same time, cover alternate scenarios that might present a significant threat. The
major difference between these two approaches is that the second one can identify less
likely, but extremely dangerous or expensive, scenarios that may require the
development of alternate protection strategies. These might include setting up
monitoring or reconnaissance activities and identifying reserve equipment or personnel.
With these considerations in mind, we can now describe some of the physical aspects of
the movement and spreading of oil spills in inland waters. We will discuss what is
thought to be happening physically as well as the modeling and algorithmic approaches
that are used to represent what is happening. To the extent that the computational
procedures fall short of representing reality, or that the required input data may be
uncertain, we must incorporate appropriate measures of uncertainty in the response
advice that is generated. It is only after this process is completed that we can technically
support a "minimum regret" spill response strategy.
In Section 2, we will discuss properties of oil both as it is originally shipped and as it
starts to weather once it is spilled. Section 3 briefly outlines and describes the physical
processes that affect the movement and spreading of oil from a hypothetical spill site to
potential resources. Section 4 describes some of the more commonly used
computational, or algorithmic, procedures that describe these processes. Finally,
Section 5 discusses trajectory analysis procedures and modeling strategies that
contribute important information to support spill response efforts.
3
-------
This page intentionally left blank.
4
-------
2.0 Oil Properties
2.1 General
Crude oil is the liquid component of petroleum, which also exists as petroleum gases
such as propane and butane, and in a number of solid forms such as asphalt and bitumen.
Any of these states can coexist, depending on the history of local geochemical
processes. As discussed by (Clark and Brown 1977), crude oil is a mixture of complex
organic and inorganic compounds, whose composition can vary greatly from one oil field
to the next, within the same field, and even at different times and depths within the same
drill hole. This variability is documented by NOAA (1994a), Environment Canada
(I 994), and others.
According to Clark and Brown (1977), crude oil contains somewhere between 50 to 98
percent hydrocarbons (those compounds consisting of only hydrogen and carbon
atoms). The non-hydrocarbon fraction is made up mostly of organic compounds that
contain nitrogen, sulfur, oxygen, and heavy metals such as nickel and vanadium. We
mention these non-hydrocarbon impurities for three reasons.
First, because they are often used as descriptors of oil composition, such as "sour" as
applied to crude oil having a high sulfur content. For example, Kuwait crude is
considered "sour" because it has a sulfur content almost ten times that of South
Louisiana crude, which is "sweet."
Second, it is now believed that the non-hydrocarbon fraction of oil is an important
ingredient in emulsification, in which large quantities of water droplets can be
incorporated into spilled oil to form emulsions composed mostly of very small water
droplets. Under certain chemical and turbulent energy conditions, this phenomenon
can result in the formation of so-called "chocolate mousse", a very viscous fluid having
significantly different physical properties than those of the parent oil.
Third, the non-hydrocarbon fraction is generally more soluble and often more toxic
than the hydrocarbon fraction. This fact is particularly important for freshwater spills,
where dilution capacity might be restricted and dispersion into the water column could
affect drinking and industrial water supplies. Also, in some cases, toxicity to aquatic
organisms is believed to be relatively greater in fresh water than in salt water due to
decreased capacity to maintain osmotic balance (Green and Trett 1987).
2.2 Classes of Petroleum
The hydrocarbon component of petroleum is a complex mixture of organic compounds
which, for simplicity, can be placed into three general classes, according to their
molecular structures. These three classes, which have a number of sub-classes, provide
a working description of oils. The classes are:
Paraffins. These are also known as alkanes (not to be confused with alkenes).
Paraffins have all carbon atoms arranged in open chains, either straight or branched.
5
-------
They exist in gaseous, liquid, and solid or semi-solid form, such as petroleum jelly,
depending on how many carbon atoms they possess (Figure 2-1). Paraffinic
hydrocarbons are slightly less dense than other hydrocarbons with equal carbon
atoms.
Naphthenes . These are also known as alicydic compounds, and often have the
carbon atoms arranged in one or more rings (hence the suffix -cyclic). Naphthenes
resist weathering and are slightly denser than paraffins at the same boiling
temperature.
Aromatics. The classical six-carbon benzene ring is the basic building block of
aromatic hydrocarbons. Aromatic compounds are then composed of various
combinations of linked and fused benzene rings, which are often linked to paraffinic
chains. Generally, the amounts of aromatics in petroleum are relatively small
compared to paraffins and naphthenes. This is fortunate since aromatics are
generally considered to include compounds which can be toxic, carcinogenic, or
both.
(open-chain)
(one or more rings)
(benzene rings)
< 5 carbon atoms
at room temperature
5-16 carbon atoms
at room temperature
>16 carbon atoms
at room temperature
gas
HYDROCARBON
COMPONENTS
solid
semi-solid
AROMATIC
PARAFFINS
(ALKANES)
NAPHTHENES
(ALICYCLIC)
Figure 2-1. Simplified classification of petroleum hydrocarbons.
Note that oil classification does not follow a rigid scheme, as comparison of the above
simplified form used by Clark and Brown (1977) with an equally simplified, but slightly
6
-------
different, scheme used by Bobra (1990). One of Bobra's main interests has been the
chemistry of water-in-oil emulsions. He and others have identified the importance of
the following compounds in this process (Bobra 1990):
Waxes . The high molecular-weight paraffinic components of oil which are in crystal
form when the oil is below its pour point.
Asphaltenes. Asphaltenes are non-hydrocarbons and are defined in terms of their
solubilities, rather than their compositions. By definition, asphaltenes are soluble in
aromatic solvents and insoluble in alkane solvents. Hence, the physical behavior of oils
depends on, among other things, the ratio of the concentrations of aromatics and
alkanes.
Resins. Resins are non-hydrocarbons, consisting of high-molecular weight, polar
compounds containing oxygen, nitrogen, and sulfur.
These compounds are considered to be key ingredients in the emulsification process,
since they provide the necessary surfactants and colloidal solid particles at the oil-water
interface (Bobra 1990; Fingas etal. 1995)
2.3 Density, Specific Gravity, and °API Gravity
The density (or equivalently, specific gravity or degrees API gravity), viscosity, pour
point, and distillation temperatures are the most important physical properties of
petroleum. The density of a material is defined as its mass per unit volume. For,
example the density of sea water is approximately 1,025 kg/m^, depending on its
temperature and salinity; the density of fresh water is about 1,000 kg/m^, depending on
its temperature. Specific gravity is a commonly used, non-dimensional description of
density. Specific gravity is defined as the ratio of the mass of a given material to the mass
of fresh water, for the same volume and at the same temperature. For example, the
maximum density of fresh water is exactly 1,000 kg/m^ at 4°C. So, the specific gravity of
a substance, such as oil, is exactly the same as its density relative to the density of fresh
water at 4°C. Also, oil becomes slightly more dense as its temperature decreases, and
vice versa.
The U.S. petroleum industry has customarily used the so-called °API (Degrees API
Gravity), an arbitrarily chosen function named after the American Petroleum Institute
(API) that is inversely proportional to the true specific gravity and given by
141.5
° API 131.5 , where s is the specific gravity.
£
The specific gravity of most crude and refined oils lies between 0.78 and 1.00 (Clark and
Brown 1979). This can also be seen in Figure 2-2, which shows a frequency distribution
of specific gravity of the roughly 1,000 oils contained in the ADIOS™ oil library (NOAA
1994). Therefore, the °API gravity, as defined above, places most oils within a
convenient range of 10 - 50 °API.
7
-------
0.4-
0.3-
0.2-
0.1-
SPiCl • C GRAVITY
- 400
300
- 200
- 100
0 . 60
1.15
1 . 70
2.25
Figure 2-2. Frequency distribution of specific gravity of oils
It is important to note that in Figure 2-2 there are oils, albeit not very many, whose
specific gravity fall outside the normal 0.78 to 1.00 range. Of particular importance, of
course, are those oils whose specific gravity is greater than 1.00, since they are not
buoyant relative to fresh water and will thus sink during spills. Presently, there is
considerably interest in these oils, which carry the acronym LAPIO (Low API Oils).
2.4 Viscosity
An oil's viscosity is the second most important physical property to know because,
along with density, it helps determine the oil's behavior during a spill. The viscosity
determines the spreading rate of oil slicks; it controls the dispersion of oil into the
water column; it controls the stability of emulsions, since water droplets cannot escape
from viscous oils; and it affects the success of cleanup operations, since very viscous oils
are difficult to skim and pump. It also may affect evaporation rates of volatile fractions.
The viscosity of a fluid is a measure of the fluid's internal resistance to flow. The
dynamic (or absolute) viscosity (i is defined as "...the force required to move a plane
surface area of one square centimeter above another plane surface at the rate of one
centimeter per second when the two surfaces are separated by a layer of fluid one
8
-------
centimeter in thickness..." (Clark and Brown 1977). The unit of measurement of
dynamic viscosity is the poise (P). For numerical convenience, the centipoise (cP) is
often used and is defined as cP = I/100 P.
It is also convenient to define an alternative, kinematic viscosity v, which is simply the
fluid's dynamic viscosity divided by its density. The unit of measurement of kinematic
viscosity is the stoke (St). Again for convenience, the centistoke (cSt) is often used and
is defined as cSt = l/l00 St. Both dynamic and kinematic viscosities are used in oil spill
work. Since the density of oil is not too different from that of water, rough calculations
involving oil viscosity are not very sensitive, numerically, to which version is used.
Speight (1991), NOAA (1994a) and others show that the viscosity of a given oil increases
with increasing density, although the relationship can be highly variable. Fresh oils and
refined products have viscosities that range from less than I to almost 100,000 cSt
(NOAA 1994a).
As in the case of oil density, discussed earlier in the section on specific gravity, oil
viscosity also increases with decreasing temperature. The relative change with
temperature depends on the oil. However, it appears to increase with an oil's paraffin
and hence, wax content. Viscosity increases as the oil is aged by evaporation of the
lighter (low-molecular weight) components, and by photochemical and microbial
processes. These and other related processes are generally known as "weathering."
The viscosity of most fresh oils under normal temperatures exhibits what is known as
"Newtonian" behavior. Recalling the previous definition of absolute (dynamic) viscosity,
a fluid is considered Newtonian if its deformation, or strain, is directly proportional to
the stress that is applied to it (starting from zero stress). The slope of the resulting
straight line is then, by definition, the coefficient of viscosity. Oils with large
concentrations of waxes or those that have been exposed to the elements (or other
conditions that could increase their viscosity) may behave more like a visco-elastic or
plastic material. These types of product exhibit complex flow behavior known as non-
Newtonian, which influences the spreading and vertical dispersion of spilled oil and, by
extension, the efficacy of cleanup methods (for example, the use of shovels vs. pumps).
Table 2-1 gives a general feel for the range of oil viscosities encountered in terms of
more familiar substances. As a rough rule of thumb, oil can be considered non-
Newtonian at viscosities above about 100,000 cP. Recently, Berger and Mackay (1994)
have discussed the important behavior of high-viscosity oils on evaporation.
9
-------
Table 2-1. General range of oil viscosities at room temperature in terms of familiar
substances (Bourne 1982; Weast 1988; NOAA 1994a).
Liquid
Viscosity (cP)
Water
1
Diesel fuel
10
Light machine oil or olive oil
100
Glycerin or castor oil
1,000
Honey
10,000
Molasses
100,000
Sucrose (cane sugar)
1,000,000
2.5 Pour Point
Pour point is the temperature below which an oil cannot be poured. The pour point is a
property whose value is determined by methods defined by the American Society for
Testing and Materials (ASTM). Clark and Brown (I 977) note that the pour point
corresponds to the temperature at which an oil's kinematic viscosity is about 300,000
cSt. This is particularly useful information in colder climates, where knowing whether
oil is fluid enough to be pumped without special heating equipment, for example, would
certainly affect cleanup and salvage decisions. Perry et al. (1984) report pour point
ranges in refined fuels of -60°C for jet fuels to +46°C for waxy No. 6 fuel oils. The spill
from the motor vessel Presidente Rivera into the Delaware River in I 989 is a good
example of the latter (NOAA 1992). In this case, the pour point of the product was
greater that the temperature of the water, so that the spilled oil congealed into tar-like
globules in which 90% of the oil was not visible from the surface. In general, however,
the concept of pour point should be used with care when applied to real oil spilled on
water, because of the inherent difference between conditions in the laboratory and in
actual spill conditions. Also, laboratory measurements of pour point can be highly
variable, since it involves the crystallization of waxy oil components. This can result in a
liquid/solid mixture whose kinematic viscosity is some undetermined combination of
the viscosity of the two phases (Clark and Brown 1977).
2.6 Distillation Temperature
Information on oil properties, including viscosity and specific gravity, is equally important
for understanding the behavior of both crude and refined oil. However, many accidents
involve refined oils of one type or another, especially in freshwater environments. Since
liquid petroleum itself is not a very useful product in its raw state and since many
accidents involve refined products of one type or another, the remainder of the
discussion will deal mostly with refined products. Refineries use fractional distillation to
extract and separate the various hydrocarbon components of petroleum. The crude
10
-------
petroleum can be a mixture of components ranging from gases such as methane to heavy
substances such as bitumen. As mentioned earlier, crude petroleum contains many
impurities, such as sulfur. Impurities are often chemically removed to the extent
practicable, depending on the intended use of the final product.
The boiling temperature of the material in distillation columns continuously increases as
the distillates are removed. The distillates are then collected according to a range of
boiling temperatures. These products are often refined again separately to produce
finer "cuts." The final distillates are then blended according to desired properties and
used commercially. Fuels from American refineries are then named No. I - No. 6, as
defined by ASTM (see Perry et al. 1984).
Fractional distillation is a process in which the more volatile components of petroleum
boil away, leaving a residuum. Therefore, both the density and the viscosity of the
refined oils should increase with boiling range. Figure 2-3 shows this expected
relationship, including ranges of density and viscosity.
200
E0Cl°Cae
-------
20000
Maximum viscosity
for typical storage
blamtium viscosity
fccf pumping and handling
0 50 100 150 200°C
1 I 1 1 1
0 100 200 300 400° F
Figure 2-4. Kinematic viscosity as a function of temperature for typical fuel oils (adapted
from Perry et al. 1984).
Clark and Brown (1977) note that a typical No. 2 fuel oil contains roughly 30% paraffins,
45% napththenes, and 25% aromatics; while a Bunker C fuel oil contains about 15%
paraffins, 45% napththenes, and 25% aromatics. The remaining 15% is made up of non-
hydrocarbons.
2.7 Hash Point
Drysdale (1985), who discusses the flash point of combustible liquids in some detail,
defines it succinctly as "...the lowest temperature of the liquid at which the vapor/air
mixture will ignite..." The flash point of combustible liquids is inversely proportional to
their equilibrium vapor pressure, so that such liquids are often classified according to
flash point, which can be used as an index of hazard: the lower the flash point, the
greater the hazard. The flash point of an oil, a mixture of many components, can be
estimated by using Raoult's law and the vapor pressures of its main components. The
flash point could be an important consideration in operations such as in-situ burning of
large spills, or in accidental fires involving large amounts of oil collected in restricted
areas of rivers and embayments.
12
-------
2.8 Emulsification
As mentioned earlier, many oils form long-lived emulsions when water droplets are
incorporated into oil. This "chocolate mousse" can contain as much as 80 % water and
can be extremely stable with respect to water removal. Studies by Bobra (1990) and
others have shown that emulsification occurs in oils with relatively high
asphaltenecontents. Moreover, many laboratory experiments and casual observations
attest to the fact that high-energy environments enhance emulsification. However, the
understanding of the chemical and physical processes leading to this phenomenon is still
so poor that, in most cases, mathematical models cannot reliably predict emulsion
formation. Nonetheless, most oil-weathering models include an algorithm for mousse
formation that may be invoked, depending on the user's confidence in the algorithm or
his/her ability to use it, to calculate an answer judged to be reasonable.
Assuming that an oil can form an emulsion chemically, it has been shown that the
emulsification rate is proportional to the intensity of the water turbulence (Wang and
Huang 1979; Mackay et al. 1980; Fingas et al. 1995). Also, it appears that emulsification,
once started, proceeds quite rapidly. Mackay et al. (1980) have proposed a simple first-
order rate law for mousse formation. This and similar formulations have been
discussed by Payne 1985.
Not only do emulsification and evaporation change the physical properties of the
material in a slick, and thus, perhaps, the type of response necessary, but they also
increase the volume of the material to be dealt with in the response, as in the case of
the Exxon Valdez spill (NOAA 1992)
13
-------
This page intentionally left blank.
14
-------
3.0 Transport Processes
3.1 General
When considering transport processes in inland waters, it might appear that the
problems are less complex than what we would expect to encounter in oceans and
estuaries. For example, in rivers the flow is generally in one direction and lakes typically
have quite weak currents. In some ways, these simplifications are true, but the actual
details are more complicated. To understand oil spill trajectory analysis in inland waters
it is important to review the resources to be protected. Then we can consider the
transport mechanisms that might move the oil in such a way as to threaten these high-
value resources.
In marine oil spills, it is very unusual to consider the water itself as a resource to be
protected. Spilled oil may move over or through the water, but the water itself is not
generally thought to be damaged. For inland spills this is not true. In most cases, the
water is used as a primary resource (potable water) and threats to the water supply are
a public health problem, immediately escalating the level of concern in inland spills. The
movement of oil toward drinking-water intakes is a critical trajectory analysis problem.
Time of first arrival and duration of the threat need to be known so that emergency
measures, such as filling storage facilities, drawing from backup wells, processing
shutdown, and rationing, can all be planned in the least disruptive manner. Beyond
drinking water supplies, power-plant intakes that use water as a coolant and industrial
processing intakes are often threatened by potential degradation of water quality.
Questions related to these intake points will typically follow the public-health issues.
For most inland water spills the shoreline is threatened with pollution almost at once
and the prospect of large-scale dissipation of oil, as at sea, is not even a remote
possibility. As in marine spills, the nature of the shoreline will determine the amount of
potential damage that a spill could cause. For example, steep or manmade shores will
probably not sustain long-term impacts while marsh and wetland areas will be
significantly threatened by oil impacts. Inland waters have insignificant tides (except for
possible upstream approaches to estuaries); the segment of shoreline actually
threatened by oiling tends to be smaller than would a marine intertidal area shoreline.
However, irregular, longer-term changes in water level can have some influence. For
example, flooding can strand pollution at high levels and threaten larger areas than might
otherwise be expected. Flooding also occurs in large, relatively shallow lakes, most
notably Lake Erie, which is well-known for its rapid response to extra-tropical storms.
Strong winds and changes in atmospheric pressure can produce seiches and lake setup to
the extent that the lake's surface elevation may vary by more than a meter between the
two ends of the lake.
Inland waters have an enormous recreational potential. Moreover, large numbers of
people place value on the aesthetic appeal and use these waters as a destination for
fishing, camping or swimming. Oil pollution events seriously degrade the recreational
value of the areas and thus become a serious cleanup issue.
15
-------
When a spill occurs in inland waters there are a number of technical issues that need to
be considered. To understand these issues it will be necessary to first answer some
questions about the physical processes that affect the movement and spreading of the
oil. At a minimum, there are three problems that will present themselves in nearly all
inland spills. These problems involve:
1. Predicting the travel time of the leading edge of the pollutant plume and the
duration of the plume's passage for points (typically water intakes) along rivers
and lake shores;
2. Identifying shoreline areas where oil is likely to strand or accumulate; and
3. Estimating the residence time for objectionable concentrations of floating or
suspended oil in high-use areas.
3.2 Row in Rivers
The spill response community has a great deal of experience in ocean and estuarine
environments compared with experience with rivers. At first, it might seem that at least
the physical processes portions of this experience could simply be applied to rivers as
though they were oceans or bays. This is a bit misleading even when we account for the
changes in shoreline shape and current direction, because of the fundamental difference
in the turbulence levels and current shears typical in rivers. In oceans or large lakes,
surface-wave activity is the major source of turbulence. Because of this, turbulence
levels typically drop off with depth. Although floating pollutants may be mixed into the
water column by breaking waves, they usually refloat and concentrations remain
essentially a two-dimensional distribution.
In contrast, shear in currents along the river bottom and banks are typically the major
source of turbulence. Thus, mixing and dispersion caused by the interaction of the shear
and the turbulence can move significant amounts of oil below the surface (particularly if
it is relatively dense, such as a heavy No. 6; or if it is finely distributed as droplets). The
shear-dominated river regimes tend to produce spill distributions having higher
subsurface oil concentrations than would be expected in marine spills.
Shear-dominated flows cause another effect that characterizes river spills. The lower
speeds along the banks and bottom of a river indicate that the surface and center of a
river move downstream faster than the flow along its boundaries. Therefore, mixing
will continuously exchange water and pollutants between the slower, near-bank regions
and the faster, center regions of the river, with the resulting smearing of the distribution
along the axis of the flow. More specifically, some patches of the pollutant will move
out of the mainstream, slow down, then return to the main flow somewhat behind their
initial location. This difference in current speed is typically the major mixing mechanism
that spreads a pollutant patch out as it moves down a river. As a result, it controls the
shape and size of a plume and the distance over which a pollutant concentration will
remain above a particular level of concern. The response to a given size spill is then
largely controlled by the details of the shear in the channel's flow.
16
-------
A second consequence of shear-dominated flow is that, although the leading edge of the
pollutant distribution may move as a relatively sharp front (at the current speed in the
middle of the channel), the tail end of the distribution is continually mixed and smeared.
Therefore, the actual pollutant distribution will begin to resemble a comet, i.e. with a
relatively distinct front followed by a fuzzy tail. This "holdup" in rivers due to "dead
spots" in the flow are discussed by Fischer et al. (1979) and others. From a practical
point of view this means that, although it might be possible to predict the initial arrival of
a pollutant at an intake point along the river, it will be considerably more difficult to
estimate when the threat is past, since the slower areas in the river are continually
supplying pollutant to the main stream, even after the "comet's" head is past. For
example, the first arrival time (shut-down schedule) could be estimated by a simple
calculation that divides the discharge data from the river by the cross-sectional area and
integrates the resulting velocity displacements along the channel. However, this method
would tell the responder nothing about the distribution at any particular point, nor
would it tell municipal authorities when it is safe to reopen water intakes.
On a long, straight channel the flow is unidirectional. Small-scale mixing across shear
boundaries is the major mechanism for moving pollutants across the river. However,
few natural channels are actually straight, and it is necessary to consider the effects of
shoals and, particularly, bends in rivers. As water moves around the bend in a river,
centrifugal force tends to pile water up along the outside edge of the turn. This causes a
pressure gradient directed toward the inside of the turn that is just sufficient to actually
accelerate the water around the bend. Since water does not leave the channel, it must
be that the pressure gradient at the surface must just balance the velocity- dependent
centrifugal force. Near the bottom of the river, the velocity decreases due to friction.
Therefore the centrifugal force is smaller and no longer balances the pressure gradient
force. This unbalanced pressure force causes a secondary flow that moves water along
the bottom toward the inside of the river bend. To conserve water there must be a
weak return flow toward the other side of the river bend throughout the water column
(above the bottom friction layer). This secondary flow, when superimposed on the
normal, and usually much stronger, down-channel flow produces a slow, helical motion
as shown in Figure 3-1. Its effect can be seen in older river channels where the flow
tends to deposit bottom silt and sediments along the inside of river bends with stronger
currents along the outer bank of the turns.
¦MM
Figure 3-1. Cross-section of a meandering stream showing secondary flow.
17
-------
This leads to the meander patterns seen across the flood plains of mature rivers as
shown in Figure 3-2.
Figure 3-2. Flow in a meandering river.
From a pollution distribution point of view, the secondary flow slightly deflects the
streamlines in the flow as the river moves around bends. More significantly, secondary
flow helps move oil particles across the shear boundaries and greatly increases the
smearing, or dispersion, of the pollutant patch in the downstream direction. Thus
pollutants tend to spread more rapidly, decreasing their peak concentrations relative to
what would be expected for a straight channel.
Many river cross-channel profiles are very irregular, with rapids at one extreme and bays
at the other. These features either accelerate or decelerate the average flow down the
river. It is also clear that these irregularities will cause pollutant distributions to speed
up or slow down and contribute to the shear in the current pattern. In trajectory
analysis, such features require us to modify time-of-travel estimates to predict first
arrivals. We should expect that these differences will significantly increase the along-
channel spreading of the pollutant distribution.
3.3 Modification to River Row by Structures
Rivers that are likely to be used to transport large volumes of hydrocarbons are, by
definition, navigable. As such, they will usually have engineering modifications. Typical
examples would be the jetty and flow restrictors that are common along some sections
of the Mississippi River or the lock and dam systems that are seen in the Ohio and
Columbia rivers.
18
-------
Flow restrictors are intended to control sediment migration in navigation channels and
to maintain current velocities to avoid excessive silt buildup. While accomplishing these
objectives, they also introduce artificial side bays that may have recirculation eddies and
backwaters, where the flow may even move upstream temporarily. These flow features
can change the shear patterns in the current and often provide convergent traps where
floating pollutants accumulate. These areas may be natural collection points where
impacts are likely and cleanup and recovery options may be necessary.
Lock and dam systems control the river's slope, reduce velocities, and provide sufficient
water depth to maintain navigation channels. Each lock position has a spillway to drop
excess volume flow. These structures are usually dams with either overflow weirs or
underflow channels (sluice gates). In either case, the drop in potential energy causes
turbulence that is distributed throughout the water column, so that any pollutant that
passes through them is rapidly mixed from top to bottom (Figure 3-3). The speed with
which a floating pollutant refloats and appears at the surface will depend on its particle
or droplet size and its relative buoyancy. For example, during the Ashland oil spill the
No. 2 (diesel) fuel oil that overflowed dam spillways typically took a number of
kilometers before its distributed droplets returned to the surface and coalesced into a
continuous, recognizable slick. NOAA (1994b) and NOAA and the American Petroleum
Institute (1994) discuss response options in cases where the natural flow is interrupted
by flow-control structures.
IPS
uMm
*. V* "
yrr* ¦ ¦ s *
Miiibi «1(i ij n ' 7.;
-
Figure 3-3. Vertical mixing in the tail waters of an overflow dam.
There is a striking difference in the ways overflow and underflow dams affect a floating
pollutant. Overflow dams will take the shallow sheet of water and pollutant at the
surface and plunge it into a full-depth mixing zone on the downstream side of the dam.
This is extremely effective in achieving a well-mixed distribution. Just downstream from
such dams we would expect to find the highest concentrations of oil distributed in the
water itself and, subsequently, the greatest threat to subsurface water intakes. On the
other hand, sluice gates usually discharge near the base of dams, so that they tend to
19
-------
restrict the discharge of floating pollutants and, in this respect, make fairly effective
booms. As such, these are areas where virtually all floating material accumulates,
making them good oil collection and recovery points. However, there are often large
amounts of other flotsam that present an extensive oiled waste and disposal problem. If
the flow through dams using sluice gates exceed about a knot, oil that accumulates
behind them will then be entrained through the system. The dam's booming
characteristics will thus fail to stop the oil, just as any boom would fail under these
conditions.
3.4 Lake Circulation
Currents within lakes are usually relatively weak except during periods of strong winds
or relaxation from storm events, which must be considered as special events. The flow
associated with the inflow from rivers and the drainage into other rivers is usually weak
except quite close to river mouths. From a floating-pollutant point of view, there is a
significant difference between these relatively small inflow and outflow regimes. Where
water enters a lake, the currents spread both horizontally and vertically and thus show a
marked deceleration. This is accompanied by strong, localized surface convergences
that tend to collect floating material. The velocity fan formed as the river enters a lake
is a natural collection point for oil coming down the river, which may be useful during a
response. In contrast, the outflow from a lake into a river creates an acceleration zone
where floating oil is likely to accumulate. Response schemes for both input and outflow
areas are discussed by Breuel (1981).
Wind-driven flow in lakes forces the water downwind until the resulting pressure
gradient (retarded by bottom friction) forces a return flow. This behavior is controlled
by the geometry of the lake and the time dependence of the wind, and may result in
complex current patterns. If the wind blows long enough, water will move downwind in
the shallow regions and set up a return flow in the deeper regions of the lake. Since a
net mass balance is required, the downwind currents in the shallow regions are stronger
than the return flows where it is deep. This is a major simplification of wind-driven
flow in lakes, but the details are case-specific. Typically, computer simulations are used
to generate current patterns, as described in Section 4.
Strong weather events can cause large lakes to behave like inland seas. Circulation
patterns will have to be closed, but within a local area, such as along a particular
shoreline, relatively strong coastal currents can develop. In addition, fast-moving storms
may cause significant surges that cause oscillations in the currents and may change the
position of the shoreline. This will be a significant factor in wetlands along the edges of
large lakes. From a pollutant response point of view, the trajectory problem becomes
significantly more difficult under these circumstances. Oil can be stranded on shorelines
or submerged by the return to normal lake levels. The potential difficulties and
uncertainty associated with these events must be factored into trajectory analysis
procedures.
3.5 Wind and Wave Effects
The effect of wind and waves on inland oil spills differs, depending on whether the spill is
in a river or in a lake. In rivers, the currents tend to be strong with a relatively small
20
-------
fetch over the water. Wind and wave effects are thus usually of secondary importance.
Thus, for river spills, the currents and shear dominate the distribution processes with
the wind acting in a minor way to determine which bank of the river the spill will trend
toward. It may be of interest to point out that many large rivers act as state boundaries
so that the wind, although secondary in the actual movement of the oil, may determine
which state the pollutant landfalls are located and thus change the jurisdiction of the
major concerns. Unlike rivers, lake currents tend to be small. In lakes, wind and wave
factors typically dominate the distribution processes, both directly and indirectly by the
wind-induced currents.
Waves affect the movement and spreading of oil spills in several different ways, and the
relative importance of these processes change as the pollutant weathers. Initially, as the
oil spreads to form a thin film, short-gravity waves are absorbed by the film, forming an
oil "slick." The slick appears smooth compared to the oil around it. The thinnest
transparent films are really only distinguishable by this change in surface roughness, and
can be likened to looking at the difference between silk and corduroy materials. In any
case, as these waves are absorbed by the oil film, momentum is transferred from the
waves to the film. This has several effects.
First, small waves approaching from a dominant direction tend to push oil slicks in the
direction of wave propagation, so that floating oil films move slightly faster than the
surface of the water that they are floating on. This differential oil-water velocity has
been measured a number of times at spills and ranges between 0.7% and 1.4% of the
observed wind speed (Gait 1994). Note that, although this depends on the waves, it also
correlates reasonably well with the wind, since it is the wind that generates these small
waves in the first place. This wave/oil-film interaction will tend to be significant as long
as the oil continues to form a slick. It will be reduced somewhat as the oil breaks into
streaks and streamers. As the oil weathers and forms tarballs, this wave stress and
momentum transfer becomes negligible.
A second transport mechanism associated with waves is the current generated by short,
relatively steep waves. This so-called "Stokes drift" results in a surface current that will
move the oil in the dominant wave direction, which again is downwind.
A third process associated with waves is vertical dispersion, which has already been
mentioned. This process is related to the turbulence created by the waves and thus
depends less on the general wave field than on that fraction of the waves that are
breaking. As waves break, the resulting plunging water creates turbulent wake, carrying
particles of oil down into the water column. Some of the particles are so small that
their rate of refloating is essentially zero, and they are permanently "dispersed" in the
water column. For larger particles these excursions below the surface are usually
temporary and, due to the oil's buoyancy, can be considered as only spending some
fraction of their time away from the surface. As mentioned in Section 2, oil is less
buoyant in fresh water than in sea water, so the submergence time of these oil droplets
is relatively greater in fresh-water than in marine spills.
Another phenomenon often observed in turbulent conditions is so-called
"overwashing," where oil particles or tarballs can be driven some distance below the
surface. As larger fractions of the oil particles are below the surface, the actual spill
21
-------
becomes progressively more difficult to observe from the air. Under these conditions,
it is not uncommon for reconnaissance flights to report that the spill has dissipated, only
to find that it seems to have returned when the weather improves and the sea state
decreases. This "disappearing act" and the fact that, from a boat, it is often possible to
observe a tarball below the surface, have led to reports that the oil is sinking at nearly
every major spill. During the 1979 IXTOC I spill in the Gulf of Mexico, divers collected
information on the subsurface distribution of tarballs. Strong wind conditions drive the
tarballs deeper into the water; quiet conditions allow them to move back toward the
water surface. In fresh-water spills this "disappearing act" could be even more
pronounced.
It appears that oil sinks in the same way that dead leaves fly from the ground. Actual
sinking, in the sense that oil is permanently removed from the surface, only occurs if (I)
the oil is denser than the surrounding water, (2) the buoyant rise of very small oil
droplets will be impeded by friction of the water; or (3) if the oil has been mixed with
enough sediment.
It is commonly understood that wind significantly affects the movement and spreading of
oil spills. However, the effects are not direct, but rather occur through other processes
that the winds cause, which in turn affect the movement of the pollutant. The wave
processes mentioned above are examples of this indirect wind forcing. As was seen, it
is not the wind that is interacting with the oil, but rather the waves which, in turn, are
well correlated with the observed winds. Therefore, from an algorithmic point of view,
the winds become one of the primary prediction parameters.
In addition to forming waves, wind stress drives a number of complex surface currents
that will also contribute to the movement of floating oil. The actual dynamic processes
of how the wind moves the water are very involved and require extensive, non-linear
analysis to develop a reasonably complete theory. Fortunately, for the purposes of
trajectory analysis it is sufficient to use simple theories to describe the processes that
we cannot technically predict.
The movement of water in a thin surface layer is the primary current directly caused by
the wind. In the original theories describing this current, the flow direction was at
45 degrees to the right of the wind, in the northern hemisphere. A more detailed
analysis suggests that the deflection angle is considerably less than that and is more likely
to be in the ten-degree or less range. As a practical response algorithm, it is usually
adequate to simply assume a wind-driven surface current having a velocity that is about
two percent of the wind speed and in approximately the same direction as the wind.
However, it is important to recognize that these quantities are rough averages obtained
from different experiments, at different places and times and variability can be large, as
shown by Brown (1991) and others. Also, it should be remembered that, when
predicted winds are being used for trajectory analysis, they are typically only specified by
quadrant direction, so that errors associated with a few degrees are thus usually not
significant for practical purposes.
The two-percent wind drift rule is a reasonably good approximation to the primary
wind-driven flow, but a closer look shows that the actual flow is unstable and tends to
break up into more complex patterns called "Langmuir cells." These phenomena begin
22
-------
to appear if the wind becomes stronger than a few knots. Their structure is
characterized by a series of counter-rotating vortices, whose axes are approximately
parallel the wind direction. Convergence lines form within adjacent pairs of cells and
divergence zones form between pairs of cells, as shown in Figure 3-4. In a sense, the
surface current moves in the direction of a series of alternating right- and left-handed
corkscrews lying in the surface and pointing in the direction of the wind. The distance
between adjacent corkscrews, or convergence lines, varies from a few meters to tens of
meters. Obviously, the surface flow is still generally downwind, but much more
complex in detail. Langmuir cells, which are ubiquitous in the ocean and in lakes, are
believed to form as a result of a complex interaction between surface currents and
surface waves. They are considered to be a major mechanism for the exchange of
atmospheric gases and other material at the water surface. In particular, the
convergence lines are easily visible as band-like water slicks, or more importantly as
sites of floating debris. It is important to note the asymmetry in cell spacing, which
indicates that the downward velocities in the convergence zones are greater than the
upward velocities in the divergence zones. It is known that Langmuir circulation in the
presence of waves is an important mechanism for aeration of surface waters by injection
small air bubbles. Dispersed oil droplets and air bubbles are comparable in size and
behavior, and it is possible that Langmuir circulation provides an efficient pathway for
vertical transport of oil from the surface (Thorpe 1984; Zedel and Farmer 1991; Farmer
and Li 1994).
Figure 3-4. Simplified Langmuir cells showing flotsam at surface convergences.
A floating oil film will be affected by Langmuir cells and will tend to thicken and collect in
the convergence bands. Between the convergence bands where the surface flow is
diverging, the oil film may rupture and form a banded gap. Together, it is likely that
Langmuir cells will cause a distribution of floating oil that is banded, or in streaks and
streamers oriented in the direction of the wind. Under strong wind conditions, oil
slicks rupture and become banded quite quickly, often within minutes, depending on the
type of oil and the size of the spill.
From a cleanup point of view, there are some significant implications of floating oil
distributions that break up into streaks and streamers under the influence of Langmuir
23
-------
circulation. It is often thought that oil spills form a more or less continuous layer of oil
but this is not true once oil breaks into streaks and streamers.
Over any particular region, the major portions of the oil may only cover a relatively
small fraction of the actual water surface. Guidelines for many cleanup procedures, such
as chemical dispersants, suggest that they be applied at rates correlated with the
thickness of the oil and the area covered. Once the oil slick has broken into bands or
streaks it is not at all clear what area the oil covers; any spray application will certainly
be treating primarily open water. This fractional surface coverage is also significant for
any remote sensing attempts to observe oil. The oil may extend as streaks and bands
over a very large area, so that the sensor is actually looking mostly at open water, and
returning a weak or ambiguous signal.
3.6 Oil Spills in Ice
In northern areas, ice can complicate and modify the movement and spreading of floating
pollutants. Oil spilled under a solid ice sheet tends to form a lens that may remain
relatively thick. With currents the lens can move along the underside of the ice and
present a particularly complex problem. Oil under broken ice behaves quite differently:
the oil floats up in the small water channels between the pieces of ice and may spread
over larger areas (Yapa et al. I 993). In this case, however, the oil tends to move with
the ice. In several winter spills in the Hudson River shore-fast ice in the coves and small
bays acted as booms that confined the oil to the center of the channel. This natural
booming protected shorelines in these areas from oiling and reduced the along-channel
mixing that would be expected from the normal river shear produced by these low-
current regions.
There is a second significant physical process associated with ice and oil spills. Oil
pooled under a thin layer of ice while active freezing is increasing the thickness of the ice
can be frozen into the plate of ice and held there until the ice melts. During the Ashland
oil spill on the Ohio River, a sudden drop in temperature just after the spill produced
this type of situation. Samples of ice collected along the river showed numerous
examples of globules of oil frozen within the plates. A rough estimate of the area
involved and the percent coverage of ice suggested that as much as 20% of the oil that
reached the river might have been incorporated into the ice at one time or another.
From a spill response point of view, this means that some fraction of the spill may seem
to disappear only to return as the weather moderates.
Is should be pointed out that many of the important processes discussed in this section
are not amenable to mathematical modeling. For example, in lakes, where surface wind
is very important, Langmuir circulation, as previously mentioned, is thought to be the
major factor in the production of streamers and streaks of spilled oil in the absence of
density fronts. However, there are no well-established models that can predict the
generation and dissipation of Langmuir cells. The latest theory on this phenomenon is
that they are always present in a statistical sense, but are ephemeral as individual cells.
This then presents a daunting prospect for modeling them, since they appear to be
closer to small-scale, near-surface turbulence than to organized motion, even though
their structure is clearly organized. The importance of scale to this, and similar types of
motion, are discussed further in Section 4.
24
-------
3.7 Special Considerations
Some processes that take place in inland waters are dominated by seasonal or episodic
changes in runoff and rainfall. Some of the easiest of these changes to observe are the
changes in water level and increases in river speed in response to rains. Many rivers
have correlation tables that relate the river gauge height to volume discharge (rating
curves). These tables can be used to estimate the average channel velocity. Whenever
estimates of spill trajectories are needed on such rivers it is always necessary to
compare the estimated river flow with their nominal values. Regional river forecast
offices of the National Weather Service or Army Corps of Engineers operations are
often a good place to obtain such information (see Appendix A for listing of NOAA
River Forecast offices)
These runoff variations also change the water level, stranding pollutants on the shoreline
at different levels. For example, falling water levels may strand oil so that it will not
refloat, which removes it as a secondary source for a new spill, but may leave a
persistent shoreline cleanup problem. On the other hand, rising water levels may wash
off beached oil and reintroduce floating pollution, or they may cover up oil that is
adhered to sediment or vegetation.
Changes in water level can be very important in the manmade inland water bodies and
can even change the nature of the drainage system. In arid regions of the West,
catchment dams will form large lakes during periods of abundant rainfall, which usually
return to rivers during droughts. Parts of Lake Shasta in California and some of the dam
systems on the upper Missouri River are good examples of this. At the other extreme,
when discharge rates are high, some lock and dam systems behave like a river with a
series of waterfalls. However, they may end up more like a series of slightly connected
lakes when the flow drops off. Sections of the upper Ohio and Mississippi rivers are
good examples. Under these situations, historical data collected under alternate flow
conditions may be very misleading. Special care must be taken when developing
estimates of movement and arrival times.
Floods are perhaps the most extreme form of water level change and introduce a whole
new set of problems to trajectory analysis efforts. Some waterways do not even appear
to be in the same area as they were before the flood. Numerous side lakes develop
and, obviously, any models or algorithmic solutions based on normal river location or
dynamics may be irrelevant. Flood conditions place much stress on the normal
infrastructure of communities by cutting roads, communications, and dislocating
populations. Planners must be aware that, under these conditions, spill response will be
difficult and more than likely not authorities' highest priority. In addition, it is possible
that flood conditions will threaten riverside facilities and may destabilize structures
enough to cause spills, exacerbating an already difficult situation.
25
-------
26
-------
4.0 Modeling Techniques
4.1 General
Oil spill trajectory models vary greatly in complexity and, at times, in their practical
utility. Suitable models depend on many important factors, such as shape, bathymetry,
and sedimentology of the water body; relative importance of forcing functions, such as
winds, runoff, and local hydrography; the chemical characteristics of the spilled product;
and the ease of use and accuracy of the chosen model. It is very important to remember
that any model simplifies reality and that a mathematical model is only one of a number
of types of models , including one's own intuition.
The formulation of the complete set of hydrodynamic equations is well known. The
solution of the equations is quite another matter. The key to successfully using
mathematical models depends on the modeler's ability to make prudent simplifications
of these equations that still retain the essential features of the problem. Ideally, model
users should understand the assumptions of the model and should immediately become
suspicious when these assumptions are violated. Computer models should be
considered as an important, but not the only, analytical tool available, and their output
should never replace experience and common sense.
In most cases, the ideal model user is the model developer. This is especially true for
complex models requiring large amounts of input data. This is also true for models
whose computational idiosyncrasies are unfamiliar to the inexperienced, and for models
that sometimes must operate on the edges of their domains of validity. However, it is
clearly impractical for models to be restricted to the use of their developers only. This
problem is partially solved by the modern, widespread use of menu-driven models,
which not only make data entry much easier but also reduce errors by flagging
improbable values, based on the modeler's experience.
For their practical use in emergencies, complex geophysical-scale models are faced with
two fundamental problems. First, the combination of their mobilization time and
computing time could be excessive, depending on the circumstances. Second, the quality
of the input data is often not high enough to warrant the time and expense involved in
the use of complex models, whose output might be no more reliable than that of
simpler models requiring fewer uncertain input data. However, in some cases,
contingency planning for fixed facilities or critically sensitive areas might also include a
considerable collection of environmental data that would be useful input to more
complex models.
In general, the prediction of pollutant trajectories in water bodies can be thought of as a
three-part process:
First, the best estimate possible should be made of the location, time of spill, and
magnitude of the source.
Second, the temporal and spatial distribution of water motion must be
determined, since this will determine the trajectory of the main body of the
pollutant.
27
-------
Third, the spread of the pollutant about its center of mass must be found.
Analyses based on these three processes are carried out simultaneously, and often by
iteration, since model input data are often incomplete, inaccurate, or subject to change
during the course of the response. The location and (potential) magnitude of the source
can often be used to gauge the urgency and the type of response required. However,
once the decision has been made that trajectories are required, then the determination
of the flow field is the most important ingredient in the analysis. Turbulent mixing and
dilution is certainly important; however, since the turbulence itself depends on the
structure of the main currents, the determination of the latter is essential.
The pollutant is considered to be a scalar quantity satisfying an equation that expresses a
balance between the observed time rate of change in concentration at a point with its
change due to its movement by currents; turbulence; addition of material by sources;
and the rate of removal of material by such processes as evaporation, sediment
adsorption, and photo-oxidation.
As mentioned earlier, there is a large gap between formulating an advection-diffusion
problem completely and solving it. A good feel for the scale of the problem and the use
averaging over space and time are the two most effective methods available to reduce
the complexity of the original problem into a more manageable form.
4.2 Scaling
In formal scale analysis, estimates are made of the relative magnitudes of each term in
the equations that express the conservation of mass, momentum, and energy. This
comparison is made on the basis of so-called "characteristic values" of variables, such as
water velocity, breadth and depth of basin in question, effects of the earth's rotation
(Coriolis effect), and other parameters. In this procedure, the model equations are
manipulated in such a way that the variables of interest are made dimensionless and of a
magnitude of about one, or O(l). Comparison of the magnitude of terms in a particular
equation is then governed by the relative magnitudes of dimensionless groups of
multiplicative constants made up of "characteristic values" of the variables. For instance,
the characteristic time in estuary problems is often chosen to be the period of the
largest tidal constituent, since many estuaries' behavior is governed by tides (similarly, a
problem in one of the Great Lakes might use the seiche period as a natural time scale).
The characteristic length in some river problems could be the average depth, since
depth is part of most formulations for turbulent dispersion. Such heuristic arguments
often allow a rough estimate of the relative sizes of all the terms in a particular equation;
only the largest terms in the equation are retained to form a simpler system. In some
cases, a surprising number of terms in the original equations are not very important in
the "big picture" and can simply be dropped in favor of those that describe the main
features of the problem at hand.
Fischer et al. (1977) discuss the importance of this "order-of-magnitude" analysis as a
means of getting a feel for the scope of a problem. It is important to realize that some
form of scale analysis is almost always done, either on paper or by use of intuition or
28
-------
experience. As a typical example; sometimes Coriolis force is important in oil spill
problems, and sometimes it is not. Formal scale analysis, while possibly tedious at
times, usually gives criteria for guidance. On the other hand, one's intuition, rather than
mathematics, would say that Coriolis force should not play much of a role in spills on
small lakes and reservoirs, simply because the body of water involved is too small for
Coriolis force to cause any appreciable deflection of moving water (and hence
pollutants). In marine waters or in the Great Lakes, on the other hand, where spatial
scales can be larger, the Coriolis force can produce very important effects and thus
generally cannot be ignored. In the case of ordinary rivers, for instance, most models
ignore Coriolis effects, again because of lateral constraints. However, such effects can
clearly be seen after many rivers have widened into larger-scale estuaries. Then,
freshwater discharge favors the right hand side of most estuaries (looking downstream
in the northern hemisphere, and vice versa), with the core of the saltwater intrusion on
the opposite side.
4.3 Averaging
The fewer the places where model equations are averaged in time or space, the greater
the computational requirements. This can easily make the difference between the use
of a personal computer (or even a hand calculator) and a sophisticated mainframe
computer. Time averages are used to remove the effects of phenomena whose
characteristic time scales are shorter than the time scale of interest. A similar analogy
can be used for spatial averaging. Two-dimensional circulation models are much
cheaper and easier to use than three-dimensional models.
An extremely important point to notice is that, when taking averages, everything with
scales smaller than the chosen averaging scale is considered turbulence, and hence not
predictable with the model in question. A practical example of the effects of averaging
on the accuracy of spill response, could be the use of a "steady-state" (i.e., a large
averaging time) river model during a spill in which the discharge is fluctuating. Implicit in
this simplification is the assumption that the model is to be used for time scales greater
than the typical scale for fluctuations in discharge.
4.4 One-Dimensional River Row Models
One-dimensional models result from spatial averaging over a river's cross-section. For
example, averaging the time-dependent equations of conservation of mass and motion
produces the well-known river discharge equations, in which the flow is driven primarily
by the gradient of the hydraulic head, modified by friction and non-linear effects. The
conservation of mass requires that the rates of additions or losses of water from the
river due to runoff, water use and so forth, maintain a downstream gradient in discharge
rate be balanced by the rate of change in time of river's local cross-sectional area (In
other words, water is incompressible). These balances, known, mathematically, as the
St. Venant equations, are discussed by Linsley et al. (1986), Shen et al. (1993), and
others. One-dimensional river models use cross-sectional averages of all properties.
Changes in concentration, for example, can only occur in the downstream (or upstream
in some cases) direction.
29
-------
The bulk downstream transport of a pollutant is then determined from a one-
dimensional, advection-diffusion equation well known in water quality problems
(Thomann and Mueller 1987) and is appropriate for a pollutant distribution that is well-
mixed laterally. Unfortunately, this problem requires knowledge of the longitudinal
dispersion coefficient, which is often difficult to determine in non-tidal rivers, especially
in the presence of flow control systems. Therefore, pollutant concentrations are
difficult to calculate accurately . The output of such models are generally Gaussian in
shape. However, in reality, the downstream distribution of pollutants is almost always
skewed toward a comet shape, with the head pointing downstream and the peak
traveling at about the same speed as the river. The main reason for this discrepancy in
plume shapes is the difficulty in choosing the proper dispersion coefficients that take
into account the longitudinal stretching of plumes due to irregularities in river shape,
such as shoals and side pockets. Fischer et al. (1979) discuss the important effects of
these "dead zones" on longitudinal dispersion in rivers and streams.
As discussed earlier, the morphology of natural streams can produce flows that are
much more complex than those that might be found in artificial channels. In addition to
the influence of meanders and irregular cross-section, the flow in many rivers is also
controlled by structures such as dams and locks. In this case, computation of average
stream velocity might be very difficult at times.
The main application of one-dimensional models is for prediction of long-term water
quality in rivers, where spatial averaging is generally adequate. Such models are also
used to estimate the time of arrival of short-term injection of pollutants. For instance,
the U.S. Army Corps of Engineers has adapted a one-dimensional Gaussian dispersion
model for use in oil spills on the Upper Mississippi River. This model, known as
REMM, an acronym for Riverine Emergency Management Model, predicts the time of
arrival (TOA) of spilled oil at designated downstream freshwater intakes (Pomerleau
1995 ). The model formulation includes a first-order reaction rate term allowing for
estimation of non-conservative behavior. The model also incorporates an evaporation
algorithm used by the riverine modeling group at Clarkson University (Shen etal. 1993)
The morphology of rivers might be so complex and the river be under the influence of
so many flow control structures that it might be considered to consist of a series of
irregular open channels, punctuated by high-energy mixing zones caused by locks and
dams, as mentioned in the previous section. In some cases, purely empirical formulas
for average velocity in given river stretches have enjoyed some success. These models,
which are discussed by Thomann and Mueller (1987), use a form of dimensional analysis
rather than kinematic and dynamic equations, and are based on regional hydrology and
local hydraulic properties of the river. Essentially, the river velocity is determined as a
simple regression equation in terms of discharge, drainage area, bottom slope, and
distance from a given origin.
Fennell (1988) used this method to estimate velocities and plume arrival times in the
Ohio River during the Ashland Oil spill. Fennell's regression equation was applied to
each of the 21 navigational stretches in a total distance of more than 900 miles. A
different regression formula was determined experimentally for each navigational pool
using a combination of NWS's real-time (and forecast) river gauge data and fluorometric
observations of the oil plume within each pool. This procedure provided a useful
30
-------
method of estimating time of arrival of the oil at downstream freshwater intakes, which
did not necessarily coincide with the location of the gauging station. Also, this method
appeared to work well during the high rain period during the spill.
4.5 Two-dimensional River and Lake Models
It is important to keep in mind that one-dimensional models express the conservation
of water and momentum in an integral and not a local sense, so that the velocity at any
point is yet to be determined. The lateral distribution of flow can be determined by
using the so-called "stream tube," or "cumulative discharge," method. A stream tube is
an imaginary tube oriented in the direction of flow, which contains a specified, constant
volume of the river's total discharge and whose boundary is always parallel to the flow.
Hence, transverse accumulation of stream tubes is equivalent to the river's cumulative
discharge. The past application of this method is discussed by Yotsukura and Cobb
(1972), Fischer etal. (1979), and more recently by Yapa etal. (1993). The required input
data for this method are digitized river bathymetry, the total discharge rate, and an
estimate of the bottom friction (using Manning or Chezy coefficient) for each stream
tube, which can be estimated by standard formulas and tables used in hydraulic
engineering for open-channel flow (Blevins 1984).
The river bathymetry is approximated by a downstream series of river cross sections,
one of which is shown schematically in Figure 4-1. Each cross-Section Is composed of a
simple succession of trapezoids. The number of sections and the number of trapezoids
within each Section Is determined by the desired resolution (or the available data).
SURFACE
BOTTOM
BANK
Figure 4-1. River cross-section approximated by trapezoids.
The use of stream-tube analysis of rivers is a powerful tool, since it allows a river to be
analyzed as either a one- or a two-dimensional problem, depending on whether cross-
channel averaging of the bathymetry is performed. Also, this is a well-known procedure
for simplifying the advection-diffusion equation for irregular, meandering rivers, so that
analytic solutions can often be found (Yotsukura and Cobb 1972, Codell etal. 1982). It
is important to recognize that the walls of stream tubes are only imaginary. While all
individual stream tubes carry constant amounts of water (allowing for sources or sinks),
31
-------
they do not necessarily carry the some water, and exchange exists between tubes as long
as its net amount is zero. So cross-channel, secondary flows, as discussed in detail in
Section 3, and stream tubes coexist.
Since the stream-tube method is based on cumulative discharge rather than velocities, it
accommodates multiple river channels and islands with relative ease. It must be
remembered, however, that since the flow uses "natural" coordinates oriented with the
flow, care must be taken at sharp bends in the river and near islands, where secondary
flows and the approach and lee regions of islands could present difficulties. Yapa et al.
(1993) and Shen et al. (1993) discuss the implications of these problems in some detail.
Under sponsorship of the U.S. Army Corps of Engineers' Cold Regions Research &
Engineering Laboratory and the St. Lawrence Seaway Development Corporation, Shen
and Yapa (I 994), Shen et al. (1993), Yapa and Shen (I 994), and Yapa et al. (1993) have
developed a series of two-dimensional river models (ROSSI, ROSS2 and ROSS3) that
combine the time-dependent river discharge and stream-tube models to calculate the
distribution of spilled oil and chemicals in rivers. The ROSS3 model includes the effects
of ice and fluctuations in shoreline position due to flooding and drying. The models have
been implemented in the St. Lawrence Seaway and in the St. Clair River/ Lake St. Clair
region of the Upper Great Lakes. Also, ROSS2 has been implemented on the
Allegheny-Monongahela-Ohio River system. These models, which are menu-driven, and
personal-computer-mounted, are in place at Clarkson University, Potsdam, New York.
4.6 Vertically Mixed Lakes
Currents in lakes are generated by winds and the internal distribution of mass (or in the
case of fresh water—temperature). For large bodies of water, such as the Great Lakes,
the effects of the earth's rotation can also be important, as mentioned earlier. From the
viewpoint of modeling for emergency response, baroclinic effects of the temperature
distribution can complicate the picture considerably. They produce depth-dependent
currents, which in turn change the temperature distribution, which in turn changes the
currents in a continuous feedback process. However, it has been found that, in most
cases, vertically averaged, or "well-mixed" (barotropic as opposed to baroclinic )
currents seem to be adequate for oil spill modeling. An important concern about
currents in the Great Lakes is their response to transient winds. For this reason,
trajectory analyses might require time-dependent models that account for seiches,
surges, and other meteorological driven forces. An important characteristic of these
and similar models is their sensitivity to bottom topography, since they express
conservation of "vorticity" generated by wind stress, bottom shape, and the earth's
rotation. From a responder's point of view, it suffices to mention that the surface
expression of vorticity is convergence and divergence of flow, which can collect or
disperse, respectively, floating material.
There are numerous models of this type that only differ in small details. They have been
used for many years in estuarine and coastal oceanography. For input data, these models
require information on winds, bathymetry, and coastal lake level. They form the basis
32
-------
for the circulation model used in "Pathfinder," developed and used by the Great Lakes
Environmental Research Laboratory (GLERL) to predict lake circulation and particle
trajectories (Schwab 1984; Schwab et al. 1984); and similar models developed and used
extensively by NOAA's Hazardous Materials Response and Assessment Division
(NOAA 1991).
4.7 Three-dimensional Models
Three-dimensional models are sometimes used in lakes and other areas where time-
dependent variations in surface elevation, or the effects of non-linear processes are
important. For example, Lake Erie is well-known for its rapid response to extra-
tropical storms, as mentioned in Section 3, resulting in complex counter-flows and shelf
wave phenomena. Such transient behavior would require a model that includes the
time-dependence of the surface elevation and the associated currents. Another, quite
different, example of three-dimensional behavior is the subsurface injection of
contaminated river water into a deep reservoir and its subsequent movement by
thermally (density)-driven currents.
The general mathematical formulation of three-dimensional circulation models has been
described by Blumbergand Mellor (1987) and others. The circulation is driven at the
surface by known distributions of wind stress, heat flux, and fresh water exchange due to
runoff and evaporation. These models use a variety of numerical discretization
schemes, both finite difference and finite element methods. Regardless of the specific
details of formulation or methods of solution, these models possess a common
characteristic: They all require large amounts of input data and they are expensive to
run, both in terms of time and hardware requirements.. Their usefulness in real oil-spill
emergencies will depend on whether they can be mobilized in the relatively short "real"
time span required for response, and whether their added accuracy is warranted over
simpler, quicker methods. It is important to note that spatial averaging can simplify
most three-dimensional models into two- or even one-dimensional models.
In some cases, three-dimensional models are designed as parts of long-term, water-
quality programs for specific locations. For example, NOAA and Ohio State University
(OSU) are developing a real-time forecasting system for the Great Lakes (Bedford and
Schwab 1990; Kelley et al. 1993). This effort is part of a long-term program by Federal,
state/provincial, and local agencies to provide real-time information for use in water
quality decisions and response to emergencies in the Great Lakes. The model, which is a
freshwater, enclosed-basin adaptation of the well-known Blumberg-Mellor coastal ocean
model (Blumberg and Mellor 1987) runs on OSU's super computer and is presently
used in Lake Erie as part of the Great Lakes Forecasting System (GLFS). Recently, this
system has been placed on the Internet as a PC-based, menu-driven application known as
GLFSView, which provides short-term forecasts of lake levels, vertically-averaged
currents, winds, wave fields, and other properties (Bedford and Chu 1995).
33
-------
4.8 Special Considerations
Mixing. As mentioned at the beginning of this section, the calculation of currents is the
major component of trajectory analysis. However, turbulent mixing is also important
since a spill does not remain a "spot" on the surface. In a sense, the "trajectory" of a
spill is a statement of the location of its center of mass (centroid). Important questions
remain, though, as to the distribution of pollutants about the center of mass as it moves
with the current. The determination of turbulent diffusion or dispersion coefficients in
natural water bodies can be a major undertaking. Modelers and users must always be
vigilant to the uncertain nature of these parameters. In the absence of experimental
data, which is often the case, the results of some trajectory (used in the loose sense)
calculations are closer to hindcasts than forecasts. Often, the most practical way around
this dilemma is by calibrating the model "on the fly," using the latest observations as
updated initial conditions.
In flow through straight channels, the horizontal and vertical mixing coefficients can be
estimated reasonably well, based on the hydraulic properties of the channel. The
accuracy is somewhat less for straight, but irregular-sided streams. However, lateral
turbulent mixing in alluvial rivers, which are characterized by meanders and sharp bends,
as discussed earlier in Section 3, is much greater than it is for channels (with a rough
rule of thumb that the a common lateral mixing formula is six times that for a straight
channel). This value can vary greatly, and can only be determined by direct observation.
This type of information can be very useful for responses in rivers, for example, since
the value of the lateral diffusion coefficient can provide a "first-cut" calculation of where
spilled oil will touch one or both sides of the river (see Fischer et al. 1977).
In lakes, as mentioned earlier, turbulence that mixes spilled oil is generated at the
surface by winds, rather than at the bottom and side boundaries. The practical
consequence of this fact is that there are no easily available rules-of-thumb based on
hydraulic engineering practice. Presently, the most popular method for calculating
horizontal dispersion of floating material is the use of so-called Lagrangian elements, a
large-scale application of the random-walk method. In this technique, the spill source is
broken up into an ensemble of many parcels which are then released instantaneously or
sequentially in order to represent either catastrophic or continuous releases. The
motion of these parcels is then determined at each time step by the addition of a
random-velocity vector to the main flow, producing a spreading random-walk
superimposed on the main flow.
Evaporation. Evaporation under natural conditions is simply the beginning of the
process of fractional distillation discussed in Section 2. Evaporation and vertical
dispersion caused by turbulence are the two major processes that remove spilled oil
from a floating slick. Of the two, evaporation generally plays the more important role
during the early stages of a spill. Fingas (1994a, 1995) notes that light crude oils can lose
as much as 75% of their original volume within the first few days after a spill; medium-
weight crudes might lose as much as 40% of their original volume. Heavy crude or
residual oils, on the other hand, will probably only lose about 10% of their volume in the
first few days. This relatively small loss rate is to be expected, since these oils are at the
end of a previous distillation process, either intentionally or naturally.
34
-------
Evaporation of spilled oil is generally considered to be a convection process driven by
(I) a mass transfer coefficient, determined primarily by the wind speed and the diffusivity
of the oil (in the form of a molecular Schmidt number for the oil), and (2) the oil's vapor
pressure. From a traditional modeling perspective, the evaporation flux (mass/unit
time/area of slick) is the direct product of the mass transfer coefficient and the vapor
pressure. This is a common approach for calculating evaporation from spilled pools of
single-component chemicals. However, an immediate complication arises for
evaporation from oil slicks, namely, the question of what vapor pressure should be
used, since the oil's composition is continually changing during the evaporation process.
(Note that changes in the oil's Schmidt number, and hence its mass transfer coefficient,
have generally been considered less important than its change in vapor pressure).
There are two common approaches to calculating the vapor pressure of multi-
component mixtures whose composition changes with time. The first is the so-called
"evaporative exposure" method of Stiver and Mackay (1984), which is based on
approximations using the Clausius-Clapeyron equation and Trouton's rule. This
approach requires the modeler to know the initial bubble point of the oil and its
subsequent linear change with respect to the fraction of oil evaporated. The second
approach, the so-called "pseudo-component" method, considers the oil's vapor
pressure as the sum of the individual pressures (Dalton's law) corresponding to those of
discrete, distillation temperature "cuts." Each component is then assumed to obey
Raoult's law, expressing the equivalence of the partial vapor pressure of the tth
component to its mole fraction in the oil slick (Drivas 1982).
For practical and modeling purposes, however, it is important to point out that there is
now considerable doubt about many oils' ability to supply vapor molecules to the
surface fast enough to support saturation concentrations at the air-oil interface. This
phenomenon could be particularly important for heavy oils or those subject to
"skinning." In those "diffusion-limited" cases, the internal composition of the oil could
be the most important consideration, and the assumption that wind speed sets the scale
for evaporation could be invalid (Berger and Mackay 1994; Fingas 1994).
Vertical dispersion. Vertical dispersion due to turbulence is the other important
process that removes oil from the water surface. As mentioned in Section 3, the
turbulence in large bodies of water is primarily generated by wind waves, and in rivers by
small-scale, bottom and shoreline features.
Vertical dispersion in lakes is essentially the same process as in the ocean. We know
that the turbulent wake of breaking waves dissipates the potential energy of the wave
spectrum by producing a "universal" size spectrum of droplets. For each breaking wave,
most of the oil refloats due to its buoyancy. However, those droplets whose diameters
are less than about 70 |jm remain in the water column as permanently "dispersed" oil.
Moreover, it is only the number of droplets dispersed by waves that is a function of oil
properties and wave energy. The shape of the droplet spectrum, however, is
independent of both oil type and wave energy. Delvigne and Sweeney (1988), Lunel
(1993, 1995), and others propose that the "universal" shape of the droplet spectrum
must be determined by the microscale of turbulence that splits droplets into ever-
decreasing sizes. Delvigne and Sweeney (1988) have shown this to be the case in wave
tanks and turbulence-producing grids. Lunel's direct observations at sea have confirmed
this. Delvigne and Sweeney (1988) developed a popular dispersion model in which the
35
-------
permanent flux of oil into the water column is proportional to the droplet size
distribution of submerged oil and the wave spectrum, which can either be measured or
estimated from known wind speeds.
These results have important implications for modeling vertical dispersion in
freshwater. As previously mentioned, the dispersion in lakes should be controlled by
these same processes. Furthermore, Delvigne (1993) proposes that his present model
should hold whenever the turbulent dissipation of potential energy is known, as in the
case of breaking waves. In particular, this method should also be applicable to the flow
of oil slicks over dams and hydraulic jumps in rivers.
36
-------
5.0 Trajectory Analysis Procedures
A series of computational algorithms or numerical look-ups into databases is at the core
of many trajectory analysis procedures. These are usually referred to as "trajectory
models" and, for many people in spill response, it is assumed that these models are
totally responsible for the process of trajectory analysis. However, there really are no
available systems that can be used as stand-alone, or turnkey, trajectory analysis
components in an operational spill response. If experienced personnel are not available
to set up and interpret model results, then there is a significant chance of getting results
which are of marginal use, or perhaps even misleading. Nevertheless, in spite of the fact
that computational systems cannot answer the entire trajectory analysis problem, they
are still a substantial help (Gait 1995). It is worthwhile to consider how various
computational procedures could be used for planning or during a spill response.
Generally, it is assumed that trajectory modeling or analysis is intended to forecast the
future distribution of a pollutant, based on the initial or present distribution of the
material. In this sense, models are used in much the same way as a standard weather
forecast model. In fact, this is the most common first request during operational spill
responses. However, this is only one of the potential ways to use trajectory models or
analysis techniques. Forecasts of where the oil will go are very useful for immediate
response activities, but they are limited by the length of time for which weather
forecasts are available (most significant spills will last a great deal longer). For major
spills, it is necessary to plan for contingencies well beyond the time scales that are
reliably covered by direct forecasts. Several other modeling and analysis techniques can
produce information for this longer-range planning.
One alternate trajectory analysis approach is to focus on the locations of high-value
resources rather than the oil distribution. This technique is referred to as "receptor
mode" analysis. In this approach, a high-value target, such as a sensitive environmental
region, is identified and the problem is formulated in terms of where the oil or pollutant
could originate. To solve this problem, the transport processes are reversed and the
spill is hypothesized to come from the target. If the procedure is done in a statistically
correct way, the output is a map that gives the joint probability distribution that oil
coming from any particular point could move to the target. In essence, this procedure
produces a zone in which spilled oil represents a threat to a high-value target, so that
some protective response may be called for. It is also possible to use this same inverse
modeling procedure to overlay minimum time-of-travel contours on the threat zone
map so that response personnel can estimate not only whether a threat is developing,
but also how long they may have to respond to it. During large spills it is generally a
good idea to look in a "downstream" direction for the spill movement and carry out
receptor analysis for all major high-vaiue targets. This, then, is very useful for staging
equipment and committing scarce resources only to threats that have a significant
probability of developing.
A second type of trajectory analysis is based on a statistical use of climatological
distributions for transport processes. In this statistical analysis, a particular weather
forecast and discharge regime is replaced with a sequence of wind and current patterns
that represents a statistically accurate synthetic climatology. Since each realization is
37
-------
independent, the resulting distribution is a probabilistic representation of an ensemble
of spills. This representation is a composite of all the places that might need protective
consideration during a spill.
Obviously, either of the two previous types of analysis could be done before the spill
and thus contribute equally well to contingency planning for spills. If they have not been
done as part of a planning activity they should be carried out as part of the package of
analyses used to compile the overall spill response recommendations generated by the
trajectory team.
During any complex spill response, the focus and degree of concern within the activities
will shift from place to place and encompass more or less detail. Modeling and analysis
procedures will need to be flexible and easy to use. It is absolutely essential that models
be able to assimilate quickly new data that may become available so that they can re-
establish their initial conditions. In operational response, this requirement is typically
far more important than trying to include progressively more complex representations
of dynamic processes that may give a better explanation of the physics but cannot be
supported with real-time data corrections. It is important to remember that the very
best full-scale representation of the spill process is the actual spill itself. If the trajectory
analysis techniques cannot recognize and take advantage of this fact, then the results will
be substandard, no matter how complex the algorithmic representations and colorful
the data presentation.
As important as it is to take full advantage of the information that is gathered during
actual spill events, a good deal of care must also be exercised to make sure that the
information used in the analysis is consistent. For example, current patterns that do not
conserve mass must be re-analyzed to avoid extraneous convergences or divergences
which, would destroy the usefulness of any analysis results. In addition, during any spill
different observers report oil position data. Many of these observers are untrained and
may not have much experience in looking at floating oil. Under these conditions, a
surprising number of false-positive sightings are reported. If all reports are used to
correct model output, the results will be chaotic at best. There are methods of
statistical analysis that make it possible to identify and classify variations between
predicted and observed results. In many cases it is possible to separate the
discrepancies into physically inconsistent cases (which are likely to be false positives and
errors) in the transport processes and use these to update and calibrate model results.
Experienced observers can investigate the small number of remaining ambiguous
discrepancies.
In conclusion, the major physical processes that affect the movement and spreading of
oil have been outlined along with a number of trajectory analysis procedures and
possible model use strategies. At some stage it becomes necessary to integrate these
components so that they can be used to support operational spill response activities.
Clearly, the results should be packaged in such a way that they relate to required
operational decisions and realistic response options.
In general, the product of trajectory analysis is a focused, detailed briefing to response
personnel. Wonderful explanations of subtle process may thrill the trajectory analyst
but they have no place in the operational briefing unless they relate to the questions at
38
-------
hand. Various data, components, and model output may be used, but individual pieces
can never replace the important synthesis that views the data in terms of the overall
response activities. Any briefing must include the processes that are not represented
and the potential errors that might occur. It cannot be overstated that, whenever
trajectory models are used, it is at least as important to know what they cannot say as it
is to know what they do say. Responders absolutely must know how much they can
count on the analysis results and what the potential unresolved questions may be. A
detailed briefing should also be ready to suggest additional investigations that might help
resolve outstanding questions if they become critical.
It is important to remember that trajectory analysis is more than just a map of where
the oil may go. Physical process data has many uses throughout the response. Weather
forecasts are important for planning field operations. Flow data are critical for designing
boom placement and mooring strategies. The sensitivity of recommendations to
possible errors in the scenario description and input data should be a standard part of
the analysis procedures, with the results part of the briefing package. Models should be
run both forwards and backwards in time, and statistically. The implications of uncertain
input data should be explored and the error bounds mapped through to the final
recommendation. In some respects trajectory analysis could be thought of as a task that
attempts to explore all potential scenarios that result from the release, movement, and
spreading of pollutants. This task is, of necessity, interactive because each new view of
the spill as it develops changes its initial reality and requires a new round of
investigations and synthesis.
The ultimate usefulness of a trajectory analysis depends on the relevance of the advice
generated to the actual response. It is clear that more than just trajectory models, and
input on river flow, runoff, and meteorology are required for successful trajectory
analysis support. An understanding of the spill response options and available tools is
also critical. In addition, it is very important to understand operations in an
environment that is initially data sparse and driven by truly phenomenal pressures to
respond immediately. Many formal, very powerful computational and analysis
procedures are simply not feasible because the required input information is not known
and cannot be obtained in time to be applied to the problem.
The fragments of available information will often be unreliable, so that any projections
into the future about predicted environmental conditions or the arrival of needed
response equipment will also be unreliable. In the face of all this, the response
community must sort out what is known, select equipment, and get it to where it is
needed. During this time, hundreds of non-responders — in government, industry,
private groups, and the press —are forming their own opinions based on sparse and,
possibly, wrong data. These opinions are translated into advice, or demands to
response personnel, thereby setting the stage for the general cacophony that
characterizes most large oil spills. The crux of the problem, then, is determining how
trajectory analysis can help guide the response, so that what gains in environmental
protection are possible can actually happen. Successful trajectory analysis focuses where
they are needed most.
39
-------
40
-------
6.0 References
Bedford, K. W. and D.J. Schwab. 1990. Preparation of real-time Great Lakes forecasts.
Cray Channels: Summer 1990.
Bedford, K. W. and Y.-F. Chu. 1995. Great Lakes Forecasting System. Summary
Features of GLFSView. Viewing Application. Columbus, Ohio: Ohio State University,
Department of Civil, Environmental Engineering and Engineering Graphics. 12 pp.
Berger, D. and D. Mackay. 1994. The evaporation of viscous or waxy oils - when is a
liquid-phase resistance significant?, Seventeenth Arctic Marine Oil Spill Program
(AMOP)Technical Seminar, Vancouver, Canada, June 8-10, 1994, Vancouver, British
Columbia: Environment Canada, pp. 77 -92.
Blevins, R. D. 1984. Applied Fluid Dynamics Handbook. New York: Van Nostrand
Reinghold Company. 558 pp.
Blumberg, A. F. and G. L. Mellor. 1987. A description of a three-dimensional coastal
ocean circulation model. N. S. Heaps, ed. In: Three-dimensional Coastal Ocean Models,
Coastal and Estuarine Sciences 4. 1-16.
Bobra, M. 1990. A study of the formation of water-in-oil emulsions. Proceedings of
13th AMOP Seminar. Edmonton, Alberta, Canada, June 6-8, 1990, Ottawa, Ontario,
Canada, Environment Canada, pp 87-1 17.
Brown, J. 1991. The final voyage of Rapaiti: A measure of sea-surface drift velocity in
relation to the surface wind. Marine Pollution Bulletin 22(1): 37-40.
Breuel, A., ed. 1981. Oil Spill Cleanup and Protection Techniques for Shorelines and
Marshlands. Pollution Technology Review No. 78. Park Ridge, New Jersey: Noyes Data
Corporation.
Burke, R. 1983. Velocity equation for water quality modeling in Georgia. American
Water Resources Association. Water Resources Bulletin I 9(2):27l -276.
Clark, R. C., Jr. and D. W. Brown. 1977. Petroleum: Properties and analyses in biotic
and abiotic systems. In: Effects of petroleum on Arctic and subarctic marine environments
and organisms. Volume I. Nature and fate of petroleum, pp 1-89. Malins, D. C. ed. New
York, NY: Academic Press, Inc. 321 pp.
Codell, R. B., K. T. Key, and G. Whelan. 1982. A collection of mathematical models for
dispersion in surface water and groundwater. Washington, DC.: Office of Nuclear Reactor
Regulation U.S. Nuclear Regulatory Commission. 256 pp.
Curl. H , Jr. and K. O'Donnell. 1977. Chemical and Physical Properties of Refined
Petroleum Products. Boulder, Colorado: Marine Ecosystems Analysis Program, NOAA
ERL. NOAA Technical Memorandum ERL MESA-17.
41
-------
Delvigne, G. 1993. Natural dispersion of oil by different sources of turbulence,
Proceedings of the Sixteenth Arctic and Marine Oil Spill Program (AMOP) Technical
Seminar, Calgary, Alberta, June 7-9, 1993, Ottawa, Ontario: Environment Canada, pp
415-419.
Delvigne, G. and C. Sweeney. 1988. Natural dispersion of oil. Oil & Chemical Pollution
(4): 281-310.
Drivas, P. J. 1982. Calculation of evaporative emissions from multicomponent liquid
spills. Environmental Science and Technology 16: 726-728.
Drysdale, D. 1985. An Introduction To Fire Dynamics. New York, NY: John Wiley and
Sons. 442 pp.
Farmer, D. and M. Li. 1994. Oil dispersion by turbulence and coherent circulations.
Ocean Engineering 2 I (6):575-587.
Fennell, Scott. 1988. The Ashland oil spill of January 1988 and ORSANCO's technical
response. Assessment and recommendations. 68 pp.
Fingas, M. 1994a. Studies on the evaporation of oil spills, Seventeenth Arctic Marine Oil
Spill Program (AMOP)Technical Seminar, Vancouver, Canada, June 8-10, 1994, Vancouver,
British Columbia: Environment Canada, pp I 89 - 210.
Fingas, M. 1994b. Physical properties, chemical composition, dispersibility, and toxicity
of Orimulsion™. Emergencies Science Division, Environment Canada. Ottawa, pp.
Fingas, M. 1995. A literature review of the physics and predictive modelling of oil spill
evaporation. Journal of Hazardous Materials 42:157-1 75.
Fingas, M. 1995. Understanding the mechanism of dispersion through oil droplet size
measurements at sea. In.The Use of Chemicals in Oil Spill Response, ASTM STP 1252. pp.
240-285. P. Lane, ed., American Society for Testing and Materials, Philadelphia:
pp. 340.
Fingas, M., D. Kyle, and E. Tennyson. 1995. Dispersant effectiveness: Studies into the
causes of effectiveness variations. In The Use of Chemicals in Oil Spill Response, ASTM STP
I 252. pp. 92-1 32. P. Lane, ed., American Society for Testing and Materials, Philadelphia:
pp. 340.
Fischer, H. B., E. J. List, R. C. Y. Koh, J. Imberger. and N. H. Brooks. 1979. Mixing in
Inland and Coastal Waters. New York: Academic Press. 483 pp.
Gait, J. A. 1994. Trajectory analysis for oil spills. Journal of Advanced Marine Technology
Conference II: 91-126.
Gait, J. A. 1995. The Integration of trajectory analysis into spill response information
systems. Presented at IMO Second International Oil Spill R&D Forum, London,
England, May, 1995.
42
-------
Gait, J. A. and D. L. Pa/ton. 1981. Finite element routines for the analysis and
simulation of nearshore circulation. Mechanics of Oil Slicks, International Association for
Hydraulic Research, Paris, France, September 7-9, 1981. Paris: pp 121-132.
Green, J. and M. W. Trett eds. 1989. The fate and effects of oil in freshwater. New
York: Elsevier Applied Science. 338 pp
Kelley, J. G. W., C.-C. J. Yen, K.W. Bedford, J. S. Hobgood, and D. J. Schwab. 1993.
Coupled Lake Erie air-sea, storm resolving forecasts and predictions, M. Spaulding, K.
Bedford, A. Blumberg, R. Cheng, and C. Swanson, eds., Proceedings of the 3rd
International Conference, Estuarine and Coastal Modeling III. Oak Brook, Illinois,
September 8-10, 1993, New York, American Society of Civil Engineers, pp 202-215.
Lehr, W. J., R. Overstreet, R.Jones, and G. Watabayashi, 1992. ADIOS-automatic data
inquiry for oil spill, Fifteenth Arctic Marine Oil Spill Program (AMOP)Technical Seminar,
Edmonton Alberta, Canada, June 10-12, 1992, Ottawa, Ontario: Environment Canada,
PP
31-45.
Lehr, W.J., J. Gait, R. Overstreet. 1995. Handling uncertainty in oil spill modeling.
Proceedings of the Eighteenth Arctic and Marine Oil spill Program (AMOP) Technical Seminar,
June 14 - 16, 1995, Edmonton, Alberta, Canada, Environment Canada,
759-768/
Linsley, R.K., M. A. Kohler, and J.L.H. Paulhus. 1986. Hydrology for Engineers. McGraw-
Hill, Inc. New York. 508 pp.
Lunel, T. 1993. Dispersion: Oil droplet size measurements at sea.. Volume 2.
Proceedings of the Sixteenth Arctic and Marine Oil Spill Program (AMOP) Technical
Seminar, Calgary, Alberta, June 7-9, 1993, Ottawa, Ontario: Environment Canada, pp
1023-1056.
Lunel, T. 1995. Understanding the mechanism of dispersion through oil droplet size
measurements at sea. In The Use of Chemicals in Oil Spill Response, ASTM STP 1252. pp.
240-285. P. Lane, ed., American Society for Testing and Materials, Philadelphia:
pp. 340.
Mackay, D., I. Buist, R. Mascarenhas. and S. Paterson. 1980. Oil Spill Processes and
Models. Environment Canada Report EE-8. Ottawa, Ontario:
NOAA. 1991. OSSM. An oil spill modeling workshop. Seattle: November 18-22,
1991, Seattle, Hazardous Materials Response and Assessment Division, NOAA.
NOAA. 1992. Oil Spill Case Histories 1967 - 1991. Seattle. Hazardous Materials
Response and Assessment Division, NOAA. Report No. HMRAD 92-1 I Prepared for
the U.S. Coast Guard Research and Development Center, Groton Connecticut
NOAA. 1994a. ADIOS™ (Automated Data Inquiry for Oil Spills) User's Manual.
Seattle: Hazardous Materials Response and Assessment Division, NOAA. Prepared for
the U.S. Coast Guard Research and Development Center, Groton Connecticut. 50 pp.
43
-------
NOAA. . 1994b Oil spills in riverine environments, a training course, Moline Illinois.
NOAA and American Petroleum Institute. 1994. Options for minimizing
environmental impacts of freshwater spill response. Seattle: Hazardous Materials
Response and Assessment Division, NOAA. 157 pp.
O'Connor, W. P. and D. J. Schwab. 1993. Sensitivity of Great Lakes forecasting system
nowcasts to meteorological fields and model parameters, M. Spaulding, K. Bedford, A.
Blumberg, R. Cheng, and C. Swanson, eds., Proceedings of the 3rd International
Conference, Estuarine and Coastal Modeling III. Oak Brook, Illinois, September 8-10, 1993,
New York, American Society of Civil Engineers, pp 148-157
Operations Analysis Study Group. 1977. Naval Operations Analysis. Second Edition.
Annapolis, Maryland: Naval Institute Press. 372 pp.
Payne, J. R. and C.P. Phillips. 1985 Petroleum Spills in the Marine Environment. Chelsea,
Ml: 148 pp.
Perry, R. H., D. W. Green, and J. O. Maloney eds. 1984. Perry's Chemical Engineers'
Handbook., Section 9 New York, NY: McGraw-Hill Book Company, pp 1-92
Pomerleau, R. 1995. Riverine Emergency Management Model (REMM).
US Army Corps of Engineers, St. Paul District. Personal Communication.
Schwab, D.J. 1992. Hydrodynamical modeling in the Great Lakes from 1950 to 1990
and prospects for the 1990s. F. E. P. C., Gobas and J. A. McCorquodale, eds., In:
Chemical Dynamics in Fresh Water Ecosystems. Ann Arbor, Ml: Lewis Publishers, pp 41-
62.
Schwab, D. J., J. R. Bennett, and E. W. Lynn. 1984. "Pathfinder"—A trajectory prediction
system for the Great Lakes. NOAA Technical Memorandum, ERL GLERL-53. Ann Arbor,
Ml: NOAA. 37 pp.
Shen, T. S., P. D. Yapa, D. S. Wang, and X. Q. Yang. 1993. A mathematical model for oil
slick transport and mixing in rivers. Special Report 93 -21. U.S. Army Corps of Engineers,
Cold Regions Research & Engineering Laboratory and St. Lawrence Seaway
Development Corporation.
Spaulding, M. L. 1988. A state-of-the-art review of oil spill trajectory and fate modeling.
Oil & Chemical Pollution. 4: 39-55.
Speight, James G. 1991. The Chemistry and Technology of Petroleum.Second Edition,
Revised and Expanded. New York: Marcel Dekker. Inc.
Stiver. W. and D. Mackay. 1984. Evaporation rate of spills of hydrocarbons and
petroleum mixtures. Environmental Science and Technology 18:834-840.
Thomann, R. V. and J. A. Mueller. 1987. Principles of Surface Water Quality Modeling and
Control. New York, NY: Harper & Row, Publishers. 644 pp.
44
-------
Thorpe, S. A. 1984. The effect of Langmuir circulation on the distribution of
submerged bubbles caused by breaking wind waves. Journal of Fluid Mechanics. 142:151-
170.
Wang, H. and C. P. Huang. The effect of turbulence on oil emulsification (oral
presentation). Proceedings, The Physical Behavior of Oil in the Marine Environment, Princeton
University, Princeton New Jersey, May 8-9, 1979.
Weast, R. C. 1988. Handbook of Chemistry and Physics, 1st Student Edition...Boca Raton,
FL: CRC Press, Inc. ppFI9-F26.
Yapa, P. D. and H. T. Shen. 1994. Modelling river oil spills: a review.
Journal of Hydraulic Research 32:765-781.
Yapa, P. D„ H. T. Shen, and K. S. Angammana. I 993. Modeling oil spills in a river-lake
system. Report No. 93-1. Department of Civil and Environmental Engineering.
Potsdam, NY: Clarkson University. 95 pp.
Yapa, P. D., S. A. Weerasuriya, D. P. Belaskas, and T. Chowdhury. 1993. Oil spreading in
surface waters with an ice cover. Report No. 93-3. Department of Civil and
Environmental Engineering. Potsdam, NY: Clarkson University. 84 pp.
Yotsukura, N. and E. D. Cobb. 1972. Transverse diffusion of solutes in natural streams.
Professional Paper 532-C. U.S. Geological Survey.
Zedel, L. and D. Farmer. 1991. Organized structures in subsurface bubble clouds:
Langmuir circulation in the open ocean. Journal of Geophysical Research 95/C5:8889-
8900.
45
-------
Appendix
USGS River Forecast Offices
Denver, CO (303) 236-5920
--Coverage includes CO, IA, KS, MN, MT, NE, NM, ND, OK, SD, TX, WY
Reston, VA (703) 648-5293
-Coverage includes CT, DE, DC, IL, IN, KY, ME, MD, MA, Ml, NH, NJ, NY, OH, PA,
Rl, VT, VA, WV, Wl
Norcross, GA (404) 408-7701
-Coverage includes AL, AR, FL, GA, LA, MS, MO, NC, PR, SC, TN, VI
Menlo Park, CA (415) 329-4414
—Coverage includes AK, AZ, CA, GU, HI, ID, NV, OR, UT, WA
U.S Amy Corps of Bigineers District Offices
AK Anchorage, AK (907) 753-2504
AL Mobile, AL (334) 690-2516
AR Little Rock, AR (501) 324-5551
CA Los Angeles, CA (21 3) 894-5300
CA Sacramento, CA (916) 557-7490
CA San Francisco, CA (415) 744-3021
FL Jacksonville, FL (904) 232-2241
GA Savannah, GA (912) 652-5226
IL Chicago, IL (312) 353-6400
IL Rock Island, IL (309) 794-4200
KY Louisville, KY (502) 582-5601
LA New Orleans, LA (504) 862-2204
MD Baltimore, MD (410) 962-7608
Ml Detroit, Ml (313) 226-6413
A-1
-------
MN St. Paul. MN (612) 290-5200
MO Kansas City, MO (816) 426-3201
MO St. Louis, MO (314) 331-8000
MS Vicksburg, MS (601) 631 -5000
NC Wilmington, NC (910) 251-4501
NEOmaha, NE (402) 221-3900
NM Albuquerque, NM (505) 766-2732
NY Buffalo, NY (716) 879-4200
NY New York, NY (212) 264-0100
OK Tulsa, OK (918) 669-7366
OR Portland, OR (503) 326-6021
PA Philadelphia, PA (215) 656-6500
PA Pittsburgh, PA (412) 644-6924
SC Charleston, SC (803) 727-4229
TN Memphis, TN (901) 544-3221
TN Nashville, TN (615) 736-5626
TX Fort Worth, TX (817) 334-2300
TX Galveston, TX (409) 766-3002
VA Norfolk, VA (804) 441-7601
WA Seattle, WA (206) 764-3742
WA Walla Walla, WA (509) 522-6658
WV Huntington, WV (304) 529-5395
A-2
-------
National Weather Service River Forecast Centers
Slidell, LA (504) 641-4343
Peachtree City, GA (404) 763-7258
Tulsa, OK (918) 581-7632
Fort Worth, TX (817) 334-3833
(outside) Minneapolis, MN (612) 361-6664
Wilmington, OH (513) 383-0527
Kansas City, MO (816) 540-5 15 I
Anchorage, AK (907) 271-3477
Bohemia, NY (516) 244-01 I I
Portland, OR (503) 249-0666
Woods Hole, MA (508) 824-4608
Norfolk, VA (814) 234-9701
A-3
-------
INDEX
ADIOS™, 7
aiicyclic, 6
aikanes, 5, 7
Allegheny River, 32
American Petroleum Institute, 7
Amoco Cadiz, I
API, 7, 11, 19
aromatics, 6-7, 12
arrival time, 15, 17, 18, 25, 30, 39
Ashland Oil Company spill. I
asphaltene, 7, 13
averaging, 28, 31, 33
baroclinic, 32
bathymetry, 27, 31, 32
bends in rivers, 17-18, 32, 34
benzene,6
best guess, 3
bitumen, 5, 11
boiling temperatures, I i
booms, 20, 24, 39
bottom slope, 30
breaking waves, 16, 35-36
Buckeye pipeline, I
Bunker C, II, 12
buoyancy, 19, 21, 35
carbon, 5, 6
catchment dams, 25
center of mass, 28, 34
centipoise, 9
centistoke, 9
centrifugal force, 17
cantroid, 34
channel flow. 16-18, 19, 24, 30-32, 34
characteristic values, 28
Chezy coefficient, 31
chocolate mousse, 5, 13
circulation, 20, 23-24, 33
one-dimensional, 29
two-dimensional, 29
three-dimensional, 33
cleanup. 8-10, 15, 19, 23, 25
climatology, synthetic, 37
Columbia River, 18, 19
concentrations, 7-9, 16, 19, 28-30, 35
contingency planning, 27, 38
convergence, 20, 23, 32, 38
Coriolis force, 28, 29
crude oil, 1,5, 11, 34
cumulative discharge, 31, 32
currents, 2, 15-24, 28, 32, 34, 37, 3&
dams, 19, 30, 36
catchment dams, 26
flow-through, 20
overflow, 20
underflow, 20
data, 3, 27,31-32, 39
dead zones, 17, 30
Degrees API Gravity, 7
density, 7-9, II, 24, 33
diesel, 10
dilution, 5, 28
dimensional analysis, 30
discharge, 3, 17. 19, 25, 29, 31-32, 37
dispersion, 5, 8, 9, 16, 30, 35, 36
distillation, 7, 10-11, 35
divergence, 23, 32, 38
drainage, 20, 25, 30
emulsification, 5, 7-8, 13
ensemble, 34, 38
estuaries, 15, 28, 29
evaporation, 8-9, 13, 28, 30, 33-35
Exxon Vatdez, 1,13
false-positive sightings, 38
flash Point, 12
floating pollutants, 16, 19-21,23-25, 32,
34, 38
flooding, 15, 18, 25, 32
flow, 9. 15-17, 36
average, 18
data, 39
excess volume, 19
rates, I
restrictors, 18
return, 17, 20
shear-dominated, 16
wind-driven, 20, 22
flow-through dams, 20
fluctuations, 32
fluorometry, 30
forecast, 1-3, 25, 30, 37,
formulation, 27, 30, 33
freezing, 24
-------
freshwater, 1, 5, 7, 8, 10,.21, 32, 33, 36
discharge, 29
intakes, IS. 30-31
exchange, 33
friction, 17,20, 22, 29,3!
game theory, 2
gauging station, 25, 30-31
Gaussian, 30
Great .Lakes, 28-29, 32-33
Great Lakes Environmental
Research Laboratory, 33
Great Lakes Forecasting System, 33
GLFSView, 33
Hazardous Materials Response, 33
Hazardous Materials Response and
Assessment Division, NOAA, 31
heat flux, 33
high-value resources, 15, 37
Hudson River, 24
hydraulic head, 29
hydrocarbons, I, 5, 6-7, 10-12, 18
hydrography, 27
Ice, 24, 32
in-situ burning, 12
inland waters. 1,3, 15-16,25
intakes, 15-17, 19
islands, 32
Ixtoc, 22
Lagrangian elements, 34
Lake Erie, 15, 33
Lake St. Clair, 32
lakes, I, 15, 16, 20, 23-25, 32-36
Langmuir circulation, 22-24
leading edge, 16
maximum win, 2
meteorology, 39
methane, 11
minimum regret, 2
Mississippi River, 18, 25, 30
Missouri River, 25
mixing coefficients, 34
models, 13, 24-25, 27-32, 37, 39
one-dimensional, 29-31, 33
three-dimensional, 29, 33
two-dimensional river, 31, 32
modification to river flow, 18
monitoring, 3
Monongahela River, 32
movement and spreading, I -3, 15-16,
21-22, 24-25, 28, 33, 37-39
naphthenes, 6
No. 2 fuel oil, It-12, 19
No. 6 fuel oils, 10, 11
Ohio, I, 18,24,25, 30, 32
Ohio State University, 33
oil, 1-13, 15-16, 18-25, 27, 29, 30, 32,
34-39
Bunker C, 11-12
crude, 1,5, 11, 34
diesel, 10
droplets, 5,8, 13, 16, 19,21-23,
35
No. 2 fuel, 11-12, 19
No. 6 fuel, 10, 11
refined, 7, 10-11
South Louisiana crude, 5, 11
oil-film, 21
overflow dams and weirs, 19
overwashing, 21
paraffins, 5-6, 12
Pathfinder, 33
petroleum, 5-7, 10-11
photo-oxidation, 28
plume, 16, 30
poise, 9
pollutants, 1-2, 15-18, 20, 22, 25, 27-30;
34-37. 39
potential energy, 19,
pour point, 7, 10
Prudhoe Bay, 11
rain, 3, 25, 31
random-walk method, 34
rating curves, 25
receptor mode, 37
refloatation of oils, 16, 21, 25
remote sensing, 24
reservoir, 33
residence time, 16
residuum, I I
response, 1-3, 13, 15, 19, 20, 22, 28, 32.
34, 37-39
rivers, I, 12, 15-18, 20, 25, 29-32, 34-36
Allegheny, 1, 33
alluvial, 36
Columbia, 18
gauge, 25, 30-31
Hudson, 24
-------
meanders, 18, 30-32, 34
Mississippi, 18, 25, 30
Missouri, 25
Monongahela, 33
morphology, 30
Ohio. 1,19, 25-26, 32-33
St. Clair, 32 ,
ROSSI, 32
ROSS2, 32
ROSS3, 32
runoff, I, 25, 27, 29, 33, 39
salinity, 7
saltwater intrusion, 29
scale analysis, 28-29
scenarios, 3, 39
secondary flow, 17-18, 32
sediments, 17, 19, 28
seiches, 15, 32
setup, 15
shear, 16, 18, 21, 24
sheen, I
shoreline, 15-16,20,24-25, 35
slick, 3, 13, 19,21,23-24, 34-36
solution, 25, 27, 31, 33
source, 16, 25, 28, 34
sources, I, 32
specific gravity, 7, 11
spills,. I-3, 9-10, 15-16, 19-21,24, 27,
29, 32-34, 38-39
response, 3, 16, 24-25, 29, 37-38
spillways, 19
spreading, 8-9, 18, 34
St, Clair River, 32
St. Lawrence Seaway, 32
St. Venant equations, 29
staging equipment, 37
statistical analysis, 37-38
stoke, 9
Stokes drift, 21
storms, 15, 20, 33
streaks, streamers, 21, 23-24
stream-tube analysis, 31
streamlines, 18
streams, 30, 34
stress, 9, 21, 25
structures, 5, 19, 25, 30
sulfur, 5, 7, 11
surface elevation, 15, 33
surface flow, 23
surges, 20, 32
tarballs, 21
temperature, 6-7, 9-12, 24, 32, 35
tides, 15, 28
time dependence, 20
time of arrival, 3
time-of-travel (TOA),l8, 30-31, 37
trajectory, 2, 27
trajectory analysis, 1,3, 15, 18, 20, 22,
25, 32, 34, 37-39
turbulent mixing, 1, 16-17, 24, 28, 30,
34
uncertainty, 3, 20, 27, 39
vapor pressure, 12, 35
viscosity, 7-12
coefficient of, 9
dynamic, 9
kinematic, 9-10, 12
Newtonian, 9
non-Newtonian, 9
vorticity, 32
water level, 15, 25
water quality, 15, 30, 33
waterways, 25
waves, 2-23
waxes, 9
weather, 3, 20, 22, 24
weathering, 6, 9, 13
wetlands, 15, 20
wind. 1,3, 20-24, 35, 37
drift, 22
speed, 21-22, 35, 36
stress, 22, 32-33
------- |