EPA-905/4-75-005
Center tor Air Environment Studies
The Pennsylvania State University
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THE CENTER FOR AIR ENVIRONMENT STUDIES
The Center for Air Environment Studies at the Pennsylvania State University
was established in 1963 to coordinate research and instruction concerning the
interaction of man and his air environment. An interdisciplinary unit of Inter-
college Research Programs, the Center has a staff with backgrounds in many of the
physical, biological, social, and allied sciences.
A broad, flexible, research program is maintained within the Center. The
direction of this research depends largely upon faculty and student interest. Some
of the current programs are:
The operation of an air pollution information service utilizing computers
and other mechanized systems for the collection, retrieval, and
dissemination of air environment literature. (See inside back cover).
Research on effects of air pollutants on trees, food, and fiber crops;
predisposition to attack by other pathogens; and economic loss through
damage to plants.
Studies of small particle behavior, particle detectors, and particle
collection devices.
Development of high accuracy, low cost, mobile, analysis equipment for
routine sampling of ambient air.
Research on biological effects of pollutants on animals and vegetation.
Studies of combustion processes leading to lower contaminant emissions.
The application of Management Science - Operations Research techniques to
the study of the effects of pollution control measures on the decision
processes of potential polluters.
Development of rapid response, specialized instrumentation for the quanti-
tative measurement of contaminant concentration.
Controlled atmosphere air quality studies for a life-support system.
Fundamental research on the chemistry, photochemistry, and atmospheric
reactions of airborne contaminants.
Basic facilities and services are maintained and provided by the Center. In
addition, through the direct participation of all University departments, depart-
mental laboratories and facilities are utilized whenever possible. Collectively,
these provide an extensive resource for research at The Pennsylvania State University.
The Center has also developed air pollution training programs with grant support
from the Office of Air Programs of the Environmental Protection Agency. One, the
Graduate Training Program, is designed to train students from diverse academic back-
grounds for careers in air pollution control. The student conducts thesis research
on an air pollution problem in his major field and takes a minor course sequence of
air pollution related topics. The CAES conducts the program and organizes the course
sequence in cooperation with the Graduate School and the academic departments.
The Engineering and Administration of_ Air Pollution Control course, coordinated
by the CAES staff each summer, is designed to give the baccalaureate level student
and the control agency representative the specialized training necessary for an
appreciation of all phases of the air pollution problem. This training includes the
socio-economic, administrative, and enforcement aspects as well as related engineer-
ing and scientific principles and techniques. The eight-credit course is devoted to
lectures, discussions, laboratory experiments, field work, and public administration
simulation exercises. University faculty members, air pollution specialists, and
government and industrial representatives conduct the ten-week program.
-continued on inside back cover-
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EPA-905/4-75-005
Environmental Monitoring
February 27, 1976
ATMOSPHERIC INPUTS TO THE UPPER GREAT LAKES
BY DRY DEPOSITION PROCESSES
BY
W.J. Moroz, Ph.D., R.L. Kabel, Ph.D., M. Taheri, Ph.D.,
A.C. Miller, Ph.D., H.J. Hoffman, W.J. Brtko, and T. Cuscino
Center for Air Environment Studies
The Pennsylvania State University
226 Fenske Building
University Park, Pennsylvania 16802
Project C-5, ULRG-IJC
Program Element 2BH155
U.S. EPA Grant #R005168
Project Officer
Welburne D. Johnson
Great Lakes Monitoring Strategist
Great Lakes Surveillance Branch
Region V, 1819 West Pershing Road
Chicago, Illinois 60609
Cooperating Program
Great Lakes Initiative
Region V, 230 South Dearborn St.
Chicago, Illinois 60604
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY IN SUPPORT OF THE
INTERNATIONAL JOINT COMMISSION-UPPER LAKES REFERENCE
GROUP OF WORKING GROUP C
GREAT LAKES REGIONAL OFFICE
100 OUELLETTE AVENUE, 8TH FLOOR
WINDSOR, ONTARIO N9A6T3
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ii
This research was supported by Grant #R005168 from the Environmental
Protection Agency, Region V. This grant is administered by the Center
for Air Environment Studies of The Pennsylvania State University.
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iii
TABLE OF CONTENTS Page
ACKNOWLEDGEMENTS ii
TABLE OF CONTENTS iii
\ ABSTRACT vi
i
^ SUMMARY 1
INTRODUCTION 3
Project Objectives 3
*> General Definitions 4
rj
Definition Of The Upper Great Lakes 4
J* Air Quality Control Regions Near The Great Lakes Basin 4
^
} Report Format 4
N
s THE THEORETICAL MODEL 6
r
Introduction 6
Physical and Mathematical Model 7
The Diffusion Equation And Its Solution 7
Extension Of A Gaussian Plume To A Real Surface 10
Transport Over Water Surfaces 11
Transport Over Land 13
Extension To An Inversion Trap 14
Determination Of K and H 18
X/
APPLICATION OF THE THEORETICAL MODEL 27
Introduction
27
The Sources 27
Modeling An Area Source As A Point System 28
Defining A Coordinate System 29
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iv
Page
Modeling The Lakes 31
The Superposition Of Plumes 31
Application Of The Model At The Land-Water Boundary 35
Calculating The Flux Into The Lake 37
Confidence Level Of Model Estimates 38
DATA, POSTULATES AND INPUT PARAMETERS 40
Meteorology 40
The Pasquill-Gifford Curves 40
The Seasonal Variation of Mixing Depth and Stability 42
The Available Meteorological Data 44
Determination Of The Dry Deposition Time 44
Determining Transport Values For Gases 46
Determination Of K And H For N02 46
Determination Of The Deposition Velocity Over
Land For N02 53
Determination Of Particulate Transport Values 53
Determination Of The Particulate Deposition
Velocity In The Atmosphere 53
The Quasi-Polydispersoid Particulate Model 54
Background Concentrations 56
Background Concentrations For N02 56
Background Concentrations For Particulate 56
SPECIES CHARACTERIZATION 58
Pollutants Not Considered In The Model 58
Elimination Of Nitrous Oxide And Nitric Oxide
As Detrimental To The Upper Great Lakes 58
Elimination Of Ammonia From Model Considerations 59
Individual Pollutant Contributions To The Upper Great Lakes 59
Total Dissolved Solids 59
Chlorides 59
Total Nitrogen 60
Total Phosphorus 61
Dissolved Silica 61
Pesticides 62
The Source Strengths 62
Pesticides In Particulate Form 63
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Page
RESULTS - - - 65
A Parametric Study 65
Variation Of Results With Grid Size 67
Variation Of Results With Original Source Height 69
Variation Of Results With Deposition Velocity Over Land -- 69
Variation Of Results With The Addition Of A First
Inversion Over Land And A Second Inversion Over Water 69
Variation Of Results With The Addition Of A Background
Concentration 70
Variation Of Results With A Change In The Method Of
Background Concentration Addition 70
Variation Of The Predicted Input With The Correction
Of A Model Error 74
Variation Of Results With The Inclusion Of Several
Reflections In The Concentration Equation 76
Computer Output Samples 78
Quantification Of Pollutant Input By Dry Deposition Into The
Upper Great Lakes 83
The Yearly Input Of Pollutants Into The Upper Great
Lakes 83
Seasonal Variation Of Input Into The Upper Great Lakes -- 83
Seasonal Variation Of Total Particulate Input With
Size Range 89
The Fraction Of The Total Atmospheric Burden Of
Pollutants Deposited Into The Upper Great Lakes 89
CONCLUSIONS AND RECOMMENDATIONS 91
BIBLIOGRAPHY --- 94
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vi
ABSTRACT
A Gaussian plume model was modified to estimate the input of specific
atmospheric pollutants into the Upper Great Lakes by dry deposition processes.
The specific pollutants were: 1) total dissolved solids, 2) chlorides,
3) total nitrogen, 4) total phosphorus, 5) total silica, and 6) pesticides.
Pollutant removal at a land or water surface by dry deposition processes
was accounted for by including a deposition factor in front of the image terms
in the conventional Gaussian concentration equation. The inclusion of this
deposition factor necessitated a second equation which modeled the flux of
material to the surface. Common chemical engineering techniques for modeling
mass transfer at a gas-solid or gas-liquid interface were used.
The largest yearly input into the lakes was for chlorides (order of
magnitude was 105 metric tons/yr.). The second largest input was total
dissolved solids with the same order of magnitude input as chlorides. Pesticide
input into the Upper Great Lakes by dry deposition processes was negligible.
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SUWARY
A mathematical model was developed to. estimate the input of specific
airborne pollutants into the Upper Great Lakes by dry deposition processes.
The pollutants were: 1) total dissolved solids, 2) chlorides, 3) total
nitrogen, 4) total phosphorus, 5) dissolved silica, and 6) pesticides.
The Gaussian plume model coupled with the Pasquill-Gifford diffusion
curves formed the foundation for the model. Source strengths were acquired
from data compiled by U.S. and Canadian Air Quality Control Regions (AQCR)
contained in and around the Great Lakes Basin. Each AQCR was modeled as
a point source with an initial crosswind spread.
Dry deposition processes were allowed for by including a deposition
factor in front of the reflection term in the conventional Gaussian concen-
tration equation thus permitting less than 100% of the material that reached
the ground to be reflected. The inclusion of this deposition factor
necessitated a second equation which modeled the flux of material to the
surface. The flux of pollutants onto land was modeled as a function of
the overall mass transfer coefficient and pollutant concentrations in the
atmosphere and the land. Likewise, the flux of pollutants into water was
modeled as a function of the liquid phase mass transfer coefficient, the
solubility of the pollutant in water, the concentration of the pollutant in
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the atmosphere at the interface, and the bulk concentration of the pollutant
in the water. The flux equation also differed depending on whether one was
considering a gaseous or a particulate pollutant.
Meteorological data compiled at locations over the Great Lakes Basin
were used to determine an average yearly wind rose. Seasonal variation of
stability conditions over land and water surfaces was included in the model.
The total yearly hours of dry weather provided an estimate of the time
during which only the dry deposition processes were effective in pollutant
removal.
The predictions of pollutant input showed gaseous chlorides (order of
105 Mg/Yr) to be the most significant input with total dissolved solids
second in terms of quantity (0(105 Mg/Yr)). Total silica was third (0(10tf
Mg/Yr)). Total nitrogen was fourth (0(10^ Mg/Yr)). Total phosphorus was
fifth (0(103 Mg/Yr)) and pesticides were least with only 3 Mg/Yr predicted
to enter each Upper Great Lake from the atmosphere by dry deposition
processes. The input into Huron was 1.5 times the input into Superior for
every pollutant with two exceptions. The input of pesticides into Huron
was 1.1 times the input into Superior and the input of total nitrogen
into Huron was 1.9 times the input into Superior.
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CHAPTER 1
INTRODUCTION
It is possible that pollutants transported through the atmosphere and
deposited into the waters of the Upper Great Lakes could contribute
significantly to the pollutant loading of the lakes. Such deposition can
occur during precipitation events or by the vertical transport of gases and
particles. The introduction of pollutants into the lakes by surface
mechanisms and by precipitation scavenging is the topic of other International
Joint Commission (IJC) efforts. This report is concerned only with gaseous
and particulate deposition.
PROJECT OBJECTIVES
The specific objectives of this study are: 1) to develop a numerical
model which will permit estimation of the contamination of a water body by
airborne pollutants during dry meteorological conditions, and 2) to use this
model to provide estimates of the potential contribution from the atmosphere
to the whole lake burden in the Upper Great Lakes. The pollutants of
interest are total dissolved solids, chlorides, total nitrogen, total
phosphorous, dissolved silica and pesticides.
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GENERAL DEFINITIONS
Definition Of The Upper Great Lakes
Reference is made frequently to the Upper Great Lakes. This term
includes two lake regions: 1) Lake Superior, and 2) Lake Huron including
the North Channel and the Georgian Bay.
Air Quality Control Regions Near The Great Lakes Basin
The divide marking the Great Lakes Basin encompasses a portion of seven
states and the Canadian province of Ontario and all the state of Michigan.
The seven states are: New York, Pennsylvania, Ohio, Indiana, Illinois,
Minnesota, and Wisconsin. The divide is never farther than 125 miles from
the nearest point on one of the lake shores. The Great Lakes Basin is
shown in Figure 1.1 (Phillips & McCulloch, 1972).
Each of the states comprising the Great Lakes Basin is divided into
Air Quality Control Regions (AQCR). Each AQCR represents a pollutant source
and the two Upper Great Lakes represent pollutant receptors. The problem
consists in quantifying the pollutant input into the Upper Great Lakes.
REPORT FORMAT
The report begins with the presentation of the atmospheric transport
and deposition model. This is followed by the details of how the model is
applied to the problem at hand. Next, the methodology used to attain the
input parameters is discussed. The procedures to estimate the input of each
individual chemical species into the Upper Great Lakes are then considered
in turn. Finally, the results are presented.
4
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0
3
a
a
se-
ct
CD
Q
w
v^-.
MINNESOTA
GREAT LAKES BASIN
Scale in Statute Miles
25 0 25 5075 100
LEGEND
Basin Divide
State Boundaries
ILLINOIS
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CHAPTER 2
THE THEORETICAL MODEL
INTRODUCTION
The Gaussian plume model has for years been the primary device for
estimating air quality relative to the source location and emission rates.
It has been called upon in the making of critical air quality decisions.
These include forecasting of undesirable levels of pollution, abatement
strategies, long range air resource management programs and urban planning.
Gaussian plume models in the present form (Button, 1953; Turner, 1970)
are considered to be useful to predict the air pollution level, when the
ground is assumed to be a perfect reflector or a perfect sink. In reality
however, various pollutants may be absorbed or produced by the sundry
surfaces comprising the ground at a limited rate (Rasmussen, Taheri, and
Kabel, 1975; Hidy, 1973). The objective of this section is to present a.
mathematical treatment that considers the effect of absorption or desorption
at ground level on plume dispersion and flux distribution.
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PHYSICAL S MATHEMATICAL MODEL
The Diffusion Equation And Its Solution
The Gaussian distribution function is a fundamental solution of the
following simplified diffusion equation
where u is downwind mean velocity, C is the mean concentration, x is the
downwind direction, y is the crosswind direction, z is the vertical direction
K is the vertical eddy diffusion coefficient, and K is the crosswind
z J y
eddy diffusion coefficient. The simplifying assumptions necessary to write
the diffusion equation in the form of Equation 2.1 are:
1) steady conditions
2) K is not a function of z
3) K is not a function of y
4) there is no extraction of pollutant
5) the downwind transport greatly exceeds the downwind diffusion.
The system to be considered is shown in Figure 2.1 and has been described in
detail by Somers (1971). The solution for a pollutant continuously released
in an infinite medium from a point source of strength Q at x = y = 0 and
z = h is given by (Sutton, 1953) and (Pasquill, 1962) as:
Q y2 (z-h)2
C = - (exp (-1/2 ( - + - ) ) ) 2'2
2-rroau a 2 a2
y z y z
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Figure 2.1: The Point Source and the Gaussian Plume (Somers, 1971).
-------
where 0 and a are referred to as dispersion coefficients in the y and z
directions and are related to the eddy diffusion coefficients by the
following equation (expressed in tensor notation):
Gi = /2 x K./u ' 2.3
Equation 2.2 assumes that the windspeed is not a function of height.
Description of the concentration to include ground reflection is
obtained by use of the method of images (Somers, 1971). This consists of
establishing an image source of strength Q at x = y = 0 and z = -h and
adding the solutions for both the image and real source to yield:
C . (exp (-/2 (- + ) ) + exp (-/2 +
2TTcr cr u a 2 a 2 a 2 a 2
y z y z y z
2.4
Equation 2.4 satisfies the boundary condition of no flux at ground level or
Sz 'z = 0 "
For a perfect sink yielding a concentration of zero at the ground level, a
similar method is used. This consists of establishing a source of strength
Q at x = y = 0' and z = -h and subtracting the solution of the sink-image
from the solution of the real source:
c = - (exp (-/2 (.+ .^ _exp
2.5
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This solution satisfies the boundary condition of C = 0 at z = 0.
Evidence is mounting that surfaces on the ground level such as grass,
water, and soil do not act as a perfect reflector or a perfect sink. They
absorb various pollutants with a given rate based on mass transfer
coefficients, solubility data, and concentrations of the pollutants contained
in the receptors. In the following section a mathematical model is developed
for considering the effect of real surfaces on the dispersion of pollutants
in the atmosphere.
Extension Of A Gaussian Plume Model To A Real Surface
For a plume in which absorption or desorption occurs with a given rate
the following general equation is considered
c =
(exp (-
2iraou a 2 o 2 a 2 a 2
y z y z y z
2.6
where y is a correction factor and may change from (1) for perfect sink to
(-1) for perfect reflection and less than (-1) for desorption processes.
The specification of absorption at ground level as a boundary condition
establishes whether the surface acts as a sink or source or a perfect
reflector. In order to determine y, the continuity of fluxes in the gas
phase and the ground level surface is used as a boundary condition:
K .§£ j = k (C i . -C , ) 2.7
z 3z ' z = 0 v a z=0 abj
10
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where C is the gas phase concentration of the pollutant species, k is the
absorbing phase mass transfer coefficient, C i _n is the concentration
c*-1 Z» \J
of the pollutant on the absorbing phase side of the interface, and C^ is the
bulk concentration of the pollutant in the absorbing phase. Rewriting
Equation 2.3 in terms of K yields
if
a 2u
K = ^ 2.8
z 2x
Equations 2.7 and 2.8 thus provide the relationship for applying the
continuity of fluxes across the exposed surfaces where these surfaces
are not passive to the transport of pollutants. Transport over a water
surface is the easiest to describe since the absorption coefficient, k ,
J6
and the liquid bulk concentration are more easily defined and available
than for many other cases such as transport over soil or a vegetation region.
Therefore, the transport over water and land will be treated separately.
Transport Over Water Surfaces
For an absorbing-desorbing surface of water and for sufficiently dilute
systems, Henry's law can be used to relate the gas phase and liquid phase
concentrations at the interface:
2.9
H
where H is the Henry's law constant. For a number of gases H can be found
in Perry's Chemical Engineers' Handbook
11
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Upon substitution of Equations 2.8 and 2.9 into Equation 2.7 one can
obtain
k c 2-10
2x
Where C., is the bulk liquid phase concentration and k is the liquid phase
mass transfer coefficient. Representative values of k. can be found in the
A/
literature or predicted. For example, see Heines and Peters (1974), Liss
and Slater (1974), and Kabel (1975). Substituting the general equation of
concentration distribution (Equation 2.6 ) into both sides of Equation 2.10
yields:
Qh(ln) f \, ,Y2 h2 . k£ Q(l-y) 7 11
:i~i exp (~ i/2(- + - )) = u 2>il
47roax a2 o2 H 2iraau
y z y z y z
exp(-l/2(li . hf.)} _k£c£
a z a z
Y z
.Now the value of y ca^ be determined from Equation 2.11:
B-A - k.C.,
Y =
Y
A+B
where
A = , exp
4iraox r
y z y
k Q (y2 h2)
B = exp (-1/2 --
2irHa a u a z a z
y z 7 z
12
2.12
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Upon substitution of y in Equation 2.11, one can obtain
Qh(2B-k£C£b) y2 h2
Flux = F = exp ("VzC + )) 2'13
4 ir(A+B)a ax a 2 a 2
V Z V Z
For C., , the bulk concentration in the liquid phase,, larger than interfacial
concentration, the numerical value of y becomes less than (-1) and the flux
is from the liquid to the gas phase. For C?, equal to zero, Equation 2.12
is simplified to
k. hu k hu
Y =( - )/ ( + ) 2.14
Equation 2.14'indicates the value of y is a function of x. A similar trend is
reported by Johnstone et al. (1949) and Cuscino et al. (1975) for particle
deposition using an overall material balance approach.
Transport Over Land
The development of rate processes over land is in its primitive stage.
The bulk and interfacial concentrations are unknown. Very often the flux
is given in terms of deposition velocity (Chamberlain, 1960; Spedding, 1969;
Owers and Powell, 1974; Hill, 1971)
K dC I _ ry £)[ 2.15
z 9z 'z=0 d "z = reference height
where V, is the deposition velocity and is a function of the type of surface.
A more realistic approach is to write Equation 2.15 in terms of an overall
mass transfer coefficient:
KzHU = Kg CS-V 2'16
13
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where K is an overall mass transfer coefficient which is a function of
o
both the gas and the land mass transfer coefficients, C, is the bulk gas
phase concentration and C, *=H C , where C , is the bulk land phase concen-
tration. For a special case where C , =0 and C, is equal to the C|
ab b ' z = reference
height, Equation 2.16 would become identical to the familiar Equation 2. 1 5 and Kr
t>
would equal V,. Furthermore, if the reference height is taken as the ground
level, one obtains the following equation
K ! - rv n I
z 3z (z = 0 ~ (-VdLJ|z = 0 2.17
Again both sides of Equation 2.17 can be evaluated from the general Equation
2.6 to solve for y as follows:
,, , hu,. / ,. . hu,.
Y= CVd - 2£)/(Vd + 2l) 2.18
The vertical flux of a gas transported over land can then be expressed
= Kz z=0 = -T-x CThJT)^ C-/^ - 2)) 2.19
y z d = y z
' 2x 7
For general cases where more information is available on the rate process
over the land surfaces one can apply a similar treatment as over water and
obtain a more generalized equation for both concentration and flux
distribution.
Extension To An Inversion Trap
Another condition of interest is the effect of an inversion layer on
the concentration profile. Friedlander and Seinfeld (1969) and Sklarew
(1970) have included the effect of an inversion layer in a numerical
14
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approach to the problem. Heines and Peters (1973) presented an analytical
solution with no mass flux or absorption at ground level. Somers (1971)
presented the solution for an inversion trap using the method of images for
multiple reflections. .What follows is a modified image method for a case
of inversion with limited absorption or desorption on the ground level.
As shown in Figure 2.2, let the source be located at x = y = 0, z = h,
with an inversion layer reflecting at z = H'. For simplicity only the
first inversion reflection is considered. The plume is now trapped between
two reflecting surfaces. The upper edge of the plume is reflected first at
1 and then at 2 while the lower edge is reflected successively at 3, 4, and
5. The image sources are mathematical constructs to fulfill the physical
premise that no material is lost from between the two reflecting surfaces .
When the ground is not viewed as a perfect reflector, then the image sources
below the ground carry a correction factor of Y. The concentration is
given as the sum of the pollutant input from all the sources:
Q y2 (z-h)2 (z + h)2
c =
y z y z z
(z - 2H + h)2 (z - 2H' - h)2 (z + 2H + h)2
exp (-VzC z - )) + exp C-V2( 5-2 - )> - Y exp (-l/2C ^ - ))
Z'Z Z
(z + 2H' - h)2
- Y expfVzC 5-5 - ))> 2-20
In order to determine j, the equality of the pollutant flux leaving the
gas phase at z=0 and entering the absorbing phase at z=0 is used as a boundary
.condition over a water surface, the equality can be expressed as
C I
K I - k r z = ° r ^ 2 21
Kz 8z "z = 0 " \ C H V
15
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1st INVERSION IMAGE
ACTUAL
SOURCE
1st GROUND IMAGE
Figure 2.2: A Sketch of the Image Sources Used to Mathmatically Allow for Reflect
ions in an Inversion Trap (Somers, 1971).
16
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Upon substitution from Equation 2.20 to Equation 2.21 one obtains:
(-(-sO) (h exp (-1/2 Cjr)) + HY exp (-1/2 (^))
q x
y z y z z
- 2H-) exp (-l/2CC2ha"22H^2)) + (2H' + h) exp {~l/2((f[ +
z z
Y (2H' + h) exp (-l/2( * h)2)) + Y (2H' - h) exp (-1/2 ((^ " h)2)))
z
k Q y2 h2
(d - Y) exp (-l/2(-2))
a u
z y y
(1 - Y) exp (-1/2 (^ " h) )) + (1 - Y) exp (-1/2 (^ * h) )))-k.C. 2.22
az z * *
Solving for Y from Equation 2.22 yields
NT-M+N'-N+O'-O- k.C
Y = W + M + N' + N + 0' + 02'23
where
y z
y z
0 =
z y y z
z y y
17
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n*
0 =
z y y
for gas
*» «.
V, for particles (if considering particles, delete k C in Equation 2.23)
d x, x,
In order to obtain the flux, the value of Y obtained from Equation 2.23 is
substituted in either side of the following equation:
F = r^T6*? (-(-2))
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infinitely soluble or the liquid mass transfer coefficient is infinity. For
the perfect reflector, either the pollutant is insoluble or the liquid phase
mass transfer coefficient is zero. Although the limiting cases can simplify
the situation, in reality atmospheric pollutants can be absorbed by or
desorbed from bodies of water at finite rates (Rasmussen, et al, 1974).
Therefore, the pollutant solubility in water and the liquid phase mass
transfer coefficient must be considered in more detail.
The pollutant solubility in water, which is species dependent, can be
determined experimentally at various temperatures, pressures and pollutant
concentration levels. This is essentially an equilibrium determination in
which the liquid phase concentration of solute is determined as a function
of temperature, pressure and gas phase concentration. In many cases, a
correlation can be obtained relating the gas phase concentration to the
liquid phase concentration. This is accomplished by using the Henry's Law
constant, which is a measure of solubility. The definition of the Henry's
Law constant is
C .
H = p^i- 2.25
LU
where C . is the interfacial equilibrium concentration of the species in
the gas phase and C.. is the interfacial equilibrium concentration of the
species in the liquid phase.
The liquid phase mass transfer coefficient, which is also species
dependent, can be defined as
- p 2.26
i ' C£b
19
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where F is the mass flux of the species through the liquid, C.. is the
X* . Jol
interfacial concentration of the species in the liquid and C is the
XiD
concentration of the species in the bulk liquid phase. Many attempts have
been made to develop models to determine the liquid phase mass transfer
coefficient. For example, see Whitman (1923), Higbie (1935), and
Danckwerts (1951). These models retain one basic limitation. While they
may be capable of interpreting important experimental observations, great
difficulties remain in using them to predict liquid phase mass transfer
coefficients. This is due to the fact that all of them contain one or
more arbitrary parameters which cannot be specified a priori from the
experimental conditions of a situation of interest. To resolve this
problem, Fortescue and Pearson (1967) and Lament and Scott (1970) developed
models which contain parameters that can be obtained from physical
quantities characteristic of the turbulent flow field. These are the large
eddy model and the eddy cell model, respectively.
Before discussing the models, it is necessary to give a physical
picture of a water body. Figure 2.3 depicts a water body bounded vertically
by a free liquid surface and the water body bottom. It is also assumed that
there is a mixed region and a stagnant region separated by a thermocline.
This stratification does not occur in all bodies of water, but in large
lakes and oceans, it will exist in many situations. It has been observed
that airflow over water bodies induces a roll cell behavior in the liquid
near the surface, as shown in Figure 2.4. These concepts are assumed in
the models that follow.
20
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MIXED REGION
THERMOCLINE
STAGNANT REGION
-» AIR FLOW
Figure 2.3(Top): Schematic Diagram of a Stratified Water Body
Figure 2.4(Bottom): Wind Induced Roll Cells
21
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In the large eddy model and the eddy cell model, mass transfer is
assumed to take place due to large eddies and small eddies, respectively.
Then for the large eddy model of Fortescue and Pearson (1967), the mass
transfer coefficient is given by
k^ 1.46 (Y)V2 2'27
where D is the molecular diffusivity of the species of interest in the
liquid phase, u' is the root mean square of the turbulent fluctuating
velocity and A is the dimension of the roll cell. For the small eddy model
of Lament and Scott (1970), the mass transfer coefficient is given by
k. = 0.4(D/v)1/2 (ev)1/(+ - 2.28
A;
where v is the kinematic viscosity of the liquid phase and e is the rate
of turbulent energy dissipation. Both of these models should be applicable
to characterize the uptake of atmospheric pollutants-by water bodies if the
parameters u', A and e can be obtained from turbulent velocity field
measurements. In the more usual case when turbulence data are not available,
e can be obtained from a model of liquid phase behavior under wind shear as
discussed by Kabel (1975). For this reason, the small eddy model was used
in the overall air pollution model to determine the liquid phase mass
transfer coefficient.
The use of the small eddy model depends upon the assumption of a
logarithmic velocity profile in the liquid phase. While this might be
considered to be done by an analogy to the gas phase, the physical pictures
of momentum transport in the gas and liquid phases are really quite different
22
-------
because of the differing boundary conditions. Nevertheless it does turn
out (see Phillips, 1966; Shemdin, 1972), that a logarithmic velocity profile
in a neutral liquid phase can be well documented. Such a profile then is
described by the following equation.
w*
CO) - uw(z) =F-ln C~-) 2.29
ow
Parameters in this equation are the velocity in the water at the interface,
u (o) , the velocity in the water at some depth, u (z), the friction velocity
in the liquid phase, WA, von Karman's constant, k, the depth into the liquid
phase, z, and the parameter, z , which is the roughness height for the
aqueous phase. Following Kraus (1972) we take the rate of turbulent
dissipation of energy as
e = -w. w 2.30
If we differentiate the velocity profile equation to obtain the partial
derivative of u (z) with respect to z and substitute into Kraus's
relationship, Equation 2.30, we obtain
3
w*
e = FT 2-31
The liquid phase friction velocity w^. is not well known and in order to
apply this model we need to have some way of obtaining it. By the following
reasoning we attempt to obtain it as a function of the friction velocity in
the gas phase, which is much better characterized. We make the assumption
of continuity of momentum flux across the interface; thus the shear stress
in the air at the interface must be equal to the corresponding shear stress
23
-------
in the water, at the interface. The shear stress in the air is equal to
u*2p , where p is the density of the air and the shear stress in the water
** Kp' 'a.
2
correspondingly would be equal to w* p , where p is the density of the
water. This is written in equation form as
u*2pa = Ta = Tw = W*2pw 2'32
o o
Thus we have a relationship between u* and w^ through which we can eliminate
w* from Equation 2. 31 for e. The result is
u,3 Pa3/2
e=>
To obtain an effective value of the liquid phase mass transfer
coefficient over the entire mass transport region, we need to take this
e(z) and integrate it over the range to which the eddy mechanism applies.
This range is from a, the depth of the molecular sublayer at the surface,
to d, the depth of the mixed layer. Thus, the effective e is given by the
equation
3 3/2
w
When this effective rate of turbulent energy dissipation, , is
substituted into Lament and Scott's Equation 2. 28 for k^ we obtain the
following equation:
1/9 ^ n 3/2
1/2 3 p
24
-------
In this equation the molecular diffusivity of the pollutant, the kinematic
viscosity of the water, and the densities of the air and water phases are
all physical properties which should be known for any pollutant of interest.
Again k is the von Kafmalri constant, u* is obtained from meteorological
information, and d and a remain to be determined. The parameter, a, is the
depth of the molecular sublayer, that region where eddy transport does not
exist. This is commonly also called 6 and can be obtained from a relation-
ship given by Kraus (1972)
P 1/2
^
a = 6 = ~ 2.36
w u*k
The depth of the mixed layer, d, is given by Phillips (1966) as
d = w^/QsinX 2.37
where fi is the earth's angular velocity and X is the latitude.
Equations 2.35, 2.36, and 2.37 now can be used to determine the liquid phase
mass transfer coefficient. All of the physical quantities can be obtained.
All that is required is the determination of u^ for the desired situation.
This can be accomplished by using the following correlation presented by
Hicks (1973) for the drag coefficient under neutral conditions:
= (0.65 + 0.07 u(10)) x 10"3 2.38
n
where C^ is the drag coefficient under neutral conditions when the under-
n
25
-------
lying surface is water and u(10) is the mean wind velocity at a height of
10 metres above the underlying surface. Using the definition of shear
stress at the surface, which is
Ta =paCd U(10) . 2.39
o n
and the definition of the friction velocity at the surface, which is
/Pa 2.40
o
together with Equation 2.38, one obtains the following relation
2
U* = (0.65 + 0.07 u(10)) x 10"3 2.41
u(10)2
This relation relates the friction velocity at the surface to the wind-
speed at a height of 10 metres.
Using the above methods, one can determine the Henry's Law constant, H,
and the liquid phase mass transfer coefficient, k., for the pollutant under
36
consideration. With these quantities, the effect of the liquid phase on
the process of pollutant transfer into water bodies can be quantified.
26
-------
CHAPTER 3
APPLICATION OF THE THEORETICAL MODEL
INTRODUCTION
In this chapter the practical application of the theoretical model is
discussed. This includes: 1) the development of point sources, 2) the
determination of source heights, 3) developing a coordinate system,
4) mathematically defining the boundaries of the lakes for subsequent
computer usage, 5) application of the model at the land-water interface
where the vertical flux changes, 6) the method of calculating the flux
into the lake, and 7) the quantification of the meteorological variables
involved.
THE SOURCES
Each AQCR was modeled as a point source with an initial crosswind
plume width equal to the diameter of a circle having an area equivalent
to that of the AQCR. Every point source was modeled at a partially
arbitrary height of 10 m. This decision was guided by 2 criteria:
1) the Pasquill-Gifford curves apply only to near ground-level sources,
2) the model required that H not be zero to prevent mathematically
undefined statements.
27
-------
The choice of 10 m as a small, non-zero height was thus made.
Modeling An Area Source As A Point Source
In actuality, each AQCR is an area source. As stated above, each area
source was modeled as a point source with an initial crosswind spread.
Therefore, the new crosswind dispersion parameter was written as follows:
a ' = (a 2 + a 2)1/2 3.1
y y0 y
where
a ' = the new crosswind spread (m)
a = the initial crosswind spread at the source (m)
a = the crosswind spread as attained from the Pasquill-Gifford
curves (m)
For convenience, a ' will be written as a . It is this a that was used in
the previous equations of the theoretical development section.
There are two terms which are used in this report, the crosswind spread
and the crosswind plume width. The first, the crosswind spread or crosswind
dispersion parameter has been discussed. Since we have assumed the Gaussian
distribution, it is probable that 68% of the plume mass lies within ± a of
the plume centerline and thus, a is seen to be the standard deviation of
the particle displacement from the centerline. The crosswind spread is thus
a measure of dispersion. The second term, plume width, can be defined in
terms of the plume spread as follows
28
-------
w = 4.28 a 3.2
y
where w is the plume width. As a statistical parameter the distances of
± 2.14 a from the centerline define that point at which the concentration
drops to 10% of the centerline value.
DEFINING A COORDINATE SYSTEM
Figure 3.1 depicts a fixed Cartesian coordinate system with an
arbitrarily chosen origin overlaid on a map of the Great Lakes Basin and
the surrounding AQCR (Acres, 1975). Grid points in the coordinate system
are 53 km apart. The coordinates of each point source and of the lakes
were recorded originally in this fixed system. Since the Gaussian model
demands that the x direction be the downwind direction, measures were taken
to easily transform the coordinate system from the original fixed system to
whatever system was necessary to assure alignment of the x direction and
the wind direction. Using the meteorological convention of depicting wind
direction, i.e., 0 is from the north, 90° is from the east, etc., the
following equations were developed:
X'" = x sin© - y cos8 3.3
and
y" = x cos0 - y sinG 3.4
where
x' = the new x coordinate
y' = the new y coordinate
x = the old x coordinate in the fixed system
29
-------
Figure 3.1: The Coordinate System and Lake Shape Simplifications
30
-------
y = the old y coordinate in the fixed system
Q = the wind direction using the meteorological convention
Both the original coordinates of the point, sources and their original plume
widths and source strengths are listed in Table 3.1. The source strengths
in Table 3.1 were acquired from the 1973 National Emissions Inventory as
recorded in Acres (1975). This inventory was compiled using data from EPA
National Emission Inventories, state files and provincial files in Canada.
In the United States much of the basic data comes from State Implementation
Plans for air pollution control submitted to the EPA.
MODELING THE LAKES
In order to simplify the model, the shapes of the 5 major lakes in the
Great Lakes Basin were modeled as simple geometric figures as shown in
Figure 3.1. Superior and Huron were modeled as triangles while Michigan,
Erie, and Ontario were modeled as rectangles. This simplification was
necessary since the computer must be programed to locate every point on the
lake edge. Defining the lake edges by straight lines made this possible.
THE SUPERPOSITION OF PLUMES
The Gaussian model assumption is actually concerned only with individual
plumes and states that the distribution of pollutants in a plume from a single
point source is Gaussian in both the vertical and crosswind directions. Since
the more complex model of this research deal with the estimation of concentrations
at a receptor from several point sources, the method of superposition of plumes
was utilized. The contribution at the receptor'from every source individually
was calculated and then all the contributions were summed to yield the net
effect from the several sources.
31
-------
TABLE 3.1: SOURCE LOCATION AND STRENGTH
AQCR
65
66
*67A
67B
67C
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
103
122
123
124
125
x-COORD
8.6
11.8
12.0
11.8
13.2
7.3
8.5
8.4
10.4
11.0
10.7
11.0
8.8
16.3
13.7
17.2
17.3
14.9
16.5
15.1
15.1
13.8
20.3
17.6
19.7
19.0
17.5
y- COORD
7.0
5.8
9.8
8.4
8.0
11.0
8.8
2.4
8.3
0.4
10.1
2.6
5.2
5.6
0.9
0.9
3.4
4.8
7.5
8.8
3.1
5.9
2.0
12.5
10.4
8.5
9.9
ayoW
31360
40120
21200
21200
21200
41200
40000
40000
19000
23200
23200
41200
47200
21200
40000
47200
31400
23200
26800
32800
35400
44400
59000
62800
25000
16400
34000
NOX Source
Strength (Mg/YR)
115000
54000
443000
443000
443000
33000
85000
434000
21000
278000
46000
39000
142000
39000
101000
60000
180000
89000
36000
69000
95000
121000
139000
245000
2013000
118000
101000
Particulate Source
Strength (Mg/YR)
205000
101000
221000
221000
221000
22000
52000
355000
42000
175000
33000
47000
120000
41000
107000
271000
259000
78000
27000
72000
55000
133000
166000
196000
378000
122000
52000
* Indicates AQCR has been subdivided.
32
-------
TABLE 3.1: Continued
AQCR
*126A
126B
126C
126D
126E
126F
126G
126H
127
128
*129A
129B
129C
129D
129E
129F
129G
129H
1291
129J
131
133
158
160
162
164
173
x- COORD
10.8
11.4
14.1
16.1
16.0
16.2
17.3
18.0
4.9
6.2
9.0
7.2
5.3
6.0
7.5
6.0
7.8
9.3
6.8
9.4
4.9
1.8
30.7
27.9
26.3
27.1
17.8
y- COORD
18.6
18.4
17.9
17.8
16.8
14.8
15.3
15.0
18.1
14.5
21.8
22.1
22.6
20.8
20.5
19.7
18.6
18.4
18.0
17.0
16.3
16.2
13.1
11.4
11.2
10.0
5.2
a (m)
yo1- )
21600
21600
21600
21600
21600
21600
21600
21600
40200
78600
23400
23400
23400
23400
23400
23400
23400
23400
23400
23400
28400
52600
43400
31400
18600
31400
19000
NOX Source
Strength (Mg/YR)
5900
5900
5900
5900
5900
5900
5900
5900
17000
90000
6300
6300
6300
6300
. 6300
6300
6300
6300
6300
6300
166000
28000
103000
88000
90000
58000
82000
Particulate Source
Strength (Mg/YR)
11000
11000
11000
11000
11000
11000
11000
11000
15000
129000
11000
11000
11000
11000
11000
11000
11000
11000
11000
11000
43000
43000
25000
31000
77000
24000
177000
*Indicates AQCR has been subdivided.
33
-------
TABLE 3.1: Continued
AQCR
174
175
176
177
178
179
*1SOA
180B
181
182
183
195
197
*237A
237B
237C
238
239
240
**901
902
903
904A
904B
905
907
908
909
912
x- COORD
22.0
20.6
19.7
18.1
25.4
21.8
19.3
20.5
23.3
19.5
21.9
27.8
24.8
12.3
11.8
12.7
10.8
12.1
10.4
24.4
24.7
27.8
20.6
22.3
23.4
22.8
18-. 3
11.5
25.8
y- COORD
7.9
6.7
5.4
7.1
8.4
4.2
7.9
7.5
6.0
4.3
6.0
6.8
6.3
15.0
14.5
13.5
15.6
11.6
12.2
12.1
12.9
15.5
10.1
11.3
13.0
18.5
18.7
23.0
21.7
a (">)
yo1- J
23800
25000
16400
30000
49200
19000
12400
12400
25000
25000
23200
46400
31400
21800
21800
21800
41200
29200
37800
16400
16400
70800
22200
22200
49200
17400
9400
28400
16400
NOX Source
Strength (Mg/YR)
292000
34000
71000
63000
206000
102000
9500
9500
178000
19000
62000
85000
415000
38000
38000
38000
77000
129000
31000
110000
212000
12000
72500
72500
15000
5000
4000
5000
50000
Particulate Source
Strength (Mg/YR)
359000
46000
100000
47000
321000
91000
45000
45000
127000
58000
383000
203000
305000
39000
39000
39000
60000
140000
27000
53000
43000
5000
9000
9000
20000
24000
57000
23000
11000
*Indicates AQCR has been subdivided.
**900's indicate Canadian AQCR
34
-------
APPLICATION OF THE MODEL AT THE LAND-WATER BOUNDARY
The land-water boundary presents a point of discontinuity with respect
to atmospheric stability. The difference in stability over water as compared
to land is due in part to the difference in temperature between the water
and land surfaces. Because of this discontinuity, a two step model was
constructed.
The first step of the model consisted in applying the superposition of
several Gaussian plumes expanding over a height limited by the land surface
below and an inversion layer above. This part of the model was used to
calculate the concentration at the upwind edge of the lake due to all the
actual sources. Actually, a "wall" of concentrations was calculated at
selected grid points as shown in Figure 3.2 . The crosswind distance
between grid points, Ay, was chosen as 50 km for reasons explained in the
results section, and the vertical distance between grid points, Az, was
200 m except in the lowest 200 m of the atmosphere over the lake in the
summer when Az = 20 m.
The second step of the model consisted of forming new source strengths,
QN, at the upwind edge of the lake and, using these new source strengths
along with the superposition of the resulting Gaussian plumes expanding over
a height limited by the water surface and an inversion layer, calculating the
flux into the lake from these sources. The new source strengths were
acquired by averaging the concentrations at the four nodes of a grid and
then multiplying by the flowrate of air through ~the grid:
QN- . =fc+c +c +r i
35
-------
u
WALL OF
GRID POINTS
Figure 3.2: A Perspective Sketch of the Grid System at the Lake Edge.
36
-------
The new point source of strength QN was then located in the center of the
grid and given an initial crosswind plume width of Ay (where Ay = 4.28 a )
and an initial vertical plume width of Az (where Az = 4.28 a ).
r zo
When the case arose where pollutants were carried over one of the
Lower Lakes before arriving at an Upper Lake the procedure was more complex.
As in step one above, the concentration at the upwind edge of the first
lake from the original sources was calculated. Step two consisted in forming
new sources at the upwind edge and then using the model of the superposition
of Gaussian plumes expanding over a height limited by the water surface and
the inversion led to calculate the concentration at a second "wall" of grid
points formed at the downwind edge of the first lake. Step three again
began with the creation of still another set of new source strengths and
concluded with the calculation of the concentration at a third "wall" of
grid points at the upwind edge of the second lake. Finally, step four
consists in forming a third set of new source strengths and using these to
calculate the flux into the second lake which was an Upper Lake.
CALCULATING THE FLUX INTO THE LAKE
Using only the new sources formed on the upwind grid wall which were
beneath the first inversion over the lake, the flux into the lake at several
points was determined and then the average flux was calculated by summing
the point fluxes and dividing by the number of points. It was assumed
that the new sources above the inversion made no contribution to the input
into the lake since their plumes did not penetrate the inversion lid. The
coordinates of the 19 points on Lake Huron's surface and the 30 points on
37
-------
Lake Superior's surface are given in Table 3.2. The average flux into the
lake multiplied by the area of the lake (5.95 x lO^km2 for Huron and
8.23 x 144km2 for Superior) yielded the input rates into the lakes. This
input multiplied by the amount of dry deposition time (determined as
shown in the Meteorology section) yielded the yearly mass input into the
two major Upper Great Lakes.
Confidence Level Of Model Estimates
We are indebted to Mr. Gerald F. Regan (EPA, Region V) for emphasizing
that this report would be improved by some statement of confidence level of
estimates provided by this model. It should be noted that the diffusion
estimate for this model has required the estimation of parameters which are
not well known. Ground level concentrations based on Gaussian models are
considered to be valid within a factor of two to eight depending upon
atmospheric stability and distance downwind. We have attempted to use
realistic values considering the unique climatology of the Great Lakes
including atmospheric conditions over the Lakes themselves.
The techniques for estimating dry deposition into the lakes were developed
under this project. This is essentially a "new" model. Accuracy of these
estimates can be no better than that of the Gaussian model for predicting
atmospheric concentrations of pollutants. Despite this "order of magnitude"
potential deviation of predicted from actual values (we do not feel the
deviation is this large but many more samples must be collected to demonstrate
this) the model does serve as a planning tool which can be used to predict
the degree of pollution in the Upper Great Lakes resulting from airborne
contaminants.
38
-------
TABLE 3.2: LAKE COORDINATES AT WHICH FLUXES WERE DETERMINED
LAKE HURON
LAKE SUPERIOR
x-COORD
21.0
21.0
22.0
20.0
21.0
22.0
20.0
21.0
22.0
19.0
20.0
21.0
22.6
23.0
19.0
20.0
21.0
22.0
23.0
y-COORD
12.0
13.0
13.0
14.0
14.0
14.0
15.0
15.0
15.0
16.0
16.0
16.0
16.0
16.0
17.0
17.0
17.0
17.0
17.0
x-COORD
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
13.0
14.0
15.0
16.0
17.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
11.0
12.0
13.0
14.0
15.0
13.0
14.0
y-COORD
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
19.0
19.0
19.0
19.0
19.0
21.0
21.0
21.0
21.0
21.0
21.0
21.0
21.0
22.0
22.0
22.0
22.0
22.0
23.0
23.0
39
-------
CHAPTER 4
DATA, POSTULATES & INPUT PARAMETERS
METEOROLOGY
The Pasquill-Gifford Curves
The Pasquill-Gifford Curves (Turner, 1970) were fitted according to
the following equation (Lawrence, 1971):
Y = 10(A° + AI 10g X + A2(loS x)2 + A3 Clog x)3) 4il
where
Y = the horizontal or vertical dispersion parameter (m)
x = downwind distance (m)
AQ - A3 = coefficients best defining the Pasquill-Gifford curves.
Table 4.1 presents Lawrence's determination of the coefficients for the
stability classes defined by Pasquill where A is a highly unstable and
dispersive atmosphere and F is very stable and non-dispersive.
The Pasquill-Gifford curves were originally plotted for a range of
downwind distances from . 1 to 100 km. It has been stated (Turner, 1970)
that the accuracy of these curves decreases dramatically as one moves
farther downwind with no greater accuracy than a factor of 2 claimed at
40
-------
TABLE 4.1: VALUES OF THE COEFFICIENTS OF THE POLYNOMIALS
DESCRIBING PASQUILL'S AND GIFFORD'S ATMOSPHERIC DISPERSION
CURVES (Lawrence, 1971)
[Y = 10(A0 + .A1 10g X + A2
where x and Y are in metres
Stability
Category
A
B
C
D
E
F
Y=
a
y
o
z
a
y
a
z
a
y
a
z
a
y
a
z
o
y
a
z
a
y
a
z
Ao
- 0.25107
+15.074
- 0.91606
- 1.2415
- 0.97311
- 1.1571
- 1.2847
- 1.8630
+12.218
- 4.2034
+15.433
- 1.8971
Al
+ 0.86045
-16.138
+ 1.1497
+ .1.0935
+ 1.0685
+ 1,0252
+ 1.1405
+ 1.7337
-10.858
+ 3.5279
-13.805
+ 1.3812
A2
0.0
+5.9015
-0.037606
0.0
-0.023721
-0.015059
-0.033376
-0.26787
+3.4263
-0.74226
+4.2653
-0.12244
A3 .
0.0
-0.63405
0.0
0.0
0.0
0.0
0.0
+0.021036
-0.32572
+0.06037
-0.40344
0.0
41
-------
distances over 100 km. The large distances concerned with in this research
effort demanded that the curves be extrapolated beyond the 100 km limit
since dispersion parameters at distances up to 800 km were required. This
extrapolation was performed with recognition that the errors incurred in
the quantification of the dispersion coefficients were at the very least a
factor of 2. Other limitations of the Pasquill-Gifford curves which are
important are:
1) They apply for a roughness length, zQ^3cm
2) The 0 curves apply only for short sampling time T ^ 2-6 minutes
7 s
and
3) They apply only for ground level sources.
The Seasonal Variation Of Mixing Depth And Stability
An average mixing depth of 2000 m was assumed to extend over the land
during all seasons of the year. The 2000 m average mixing depth was chosen
after consideration of the changes in mixing depth with season, with synoptic
meteorological conditions and the depth of the atmosphere through which large
scale flow patterns are affected by the presence of the Great Lakes (Moroz,
1967, 1968, Koczkur et al. 1970). The model could be refined by using
Holzworth's mixing depths (Holzworth, 1972), over land, upstream from the
lakes at some penalty in computer time but use of these mixing depths downstream
from the lakes would be incorrect: (Petterssen $ Calabrese, 1949). Since
2000 m value incorporated mixing as a result of air passage over the Lower
Great Lakes for some wind directions, and since the model appeared to be
relatively insensitive to small changes in mixing depths, the 2000 "m average
mixing depth was consistently applied.
42
-------
The 2000 m mixing depth was regarded as the first inversion over
water during all seasons of the year except the summer during which
the cold water and the warm overlying air create a surface inversion
layer assumed to extend up to 200 m'over the water. Thus, during the
summer, the 2000 m mixing depth was regarded as the second inversion
over water. Table 4.2 shows the seasonal variation of mixing depths
and stability.
The stability over land and water is assumed to be the same in every
season but the summer when the water surface is cooler than the land
surface causing a more stable atmosphere over the water than over the
land. The variation of stability over land with seasonal change shows a
tendency toward a less stable atmosphere as one moves from spring through
winter.
TABLE 4.2: SEASONAL VARIATION OF MIXING DEPTH AND STABILITY
Season
Spring
Summer
Fall
Winter
Stability
Over Land
E
D
D
D
Stability
Over Water
E
F
D
D
Height of
First Inversion
(m)
2000
200
2000
2000
Height of
Second Inversion
(m)
2000
-
-
43
-------
This is due to the fact that in the spring the ground is still cold while the
air above is warm causing an increasing temperature with height and a conse-
quently more stable atmosphere in the spring. In the summer the ground is warm
and the overlying air is warm so that conditions are less stable than in
the spring. In the fall the ground is still warm while the air is cooler
than in the summer and again one finds less stable conditions than in the
spring. Finally, in the winter the ground is cold and air is cold again
providing a less stable situation than the spring.
The Available Meteorological Data
The meteorological data used was taken from 14 stations in the Great
Lakes vicinity as shown in Figure 4.1. All 14 stations yielded the daily
averaged wind speed and direction, and the amount and type of precipitation.
Ten of the 14 stations also yielded the number of hours of precipitation
on a daily basis. These daily data were available for the entire year
of 1973.
Determination of the Dry Deposition Time
The number of dry hours per year was determined in the following manner.
If any station indicated precipitation for more than 12 hours, the entire
24, hour day was labeled a wet day and subtracted from the total monthly
hours. This was simply a maneuver to reduce the great volume of data that
were manipulated. This reduced monthly total was further diminished by
subtracting all the hours of precipitation during the month considering only
days with less than 12 hours of precipitation. This final total was the
total monthly dry hours. Then the percent of time during a month that the
44
-------
(O
Ui
o
O
I
tn
I
S
o
o"
o'
Q_
0*
O*
O)
LEGEND
Meteorological
Stations
SCALE
O 50 100150200250
KILOMETERS
-------
wind was from a given direction at a given speed as averaged over the 14
stations was determined. This percent multiplied by the dry monthly hours
yielded the number of dry hours during the month that the wind was from a
given direction and at a given speed. Eight directional categories, N, NE,
E, etc., and 4 wind speed categories; 2.24, 4.48, 6.72, and 8.96 m/s were
used. The 12 monthly values for each of the 32 categories were added to
yield the yearly hours of dry weather. The addition of monthly values on a
seasonal instead of yearly basis yielded the seasonal hours of dry weather.
Since only data from January to December 1973 were available, winter was
defined as January, February, and December 1973. The other seasons were
divided normally. Tables 4.3 through 4.7 show the seasonal and yearly
yield of dry hours for each wind direction and speed.
DETERMINING TRANSPORT VALUES FOR GASES
Determination Of k. And H for N02
The theoretical model to determine k was developed for gaseous
pollutants in general. While the liquid phase mass transfer coefficient
for any gas could be obtained using Equations 2.32, 2.35, 2.36, 2.37, and
2.41, k. was actually calculated for N02 only since other gases were
X»
eliminated as important for various reasons considered in the section
entitled Species Characterization.
Examining Equation 2.35, the physical quantities necessary to determine
k for N02 are D, p , p and v. These quantities were found in the
literature at 25°C and 98.066 kPa to be 2.6 x 10"5 cm2/sec, 0.001185
g/cm3, 0.999044 g/cm3 and 0.008946 cm2/sec, respectively. The parameters
46
-------
TABLE 4.3; TOTAL DRY HOURS BY WIND SPEED AND DIRECTION
FOR THE ENTIRE YEAR 1973
NW
N
NE
E
SE
S
SW
W
2.24 m/s
136
244
125
589
141
472
297
575
4.48 m/s
249
418
185
523
109
479
417
800
6.72 m/s
114
129
39
55
28
89
164
270
8.96 m/s
42
26
8
13
7
30
83
102
47
-------
TABLE 4.4: TOTAL DRY HOURS BY SPEED AND DIRECTION
FOR WINTER, 1973
NW
N
NE
E
SE
S
sw
w
2.24 m/s
27
58
25
119
21
66
53
148
4.48 m/s
46
131
40
131
15
73
113
174
6.72 m/s
32
51
16
23
7
33
66
92
8.96 m/s
8
14
3
3
4
10
29
32
48
-------
TABLE 4.5: TOTAL DRY HOURS BY WIND SPEED AND DIRECTION
FOR SPRING, 1973
NW
N
NE
E
SE
S
sw
w
2.24 m/s
31
58
28
166
30
80
37
71
4.48 m/s
67
133
82
205
38
95
61
172
6.72 m/s
37
55
20
26
9
24
30
65
8.96 m/s
22
12
5
10
-
10
10
16
49
-------
TABLE 4.6: TOTAL DRY HOURS BY WIND SPEED AND DIRECTION
FOR SUMMER, 1973
NW
N
NE
E
SE
S
SW
W
2.24 m/s
40
59
36
170
37
192
146
198
4.48 m/s
55
86
40
72
30
184
153
214
6.72 m/s
17
12
-
4
'7
13
39
19
8.96 m/s
2
-
-
-
-
4
27
3
50
-------
TABLE 4.7 : TOTAL DRY HOURS BY WIND SPEED AND DIRECTION
FOR FALL, 1973
NW
N
NE
E
SE
S
SW
W
2.24 m/s
38
69
36
134
53
134
61
158
4.48 m/s
81
68
23
115
26
127
90
240
6.72 m/s
28
11
3
-
5
19
29
94
8.96 m/s
10
-
-
-
3
6
17
51
51
-------
required to determine k. are a, d and u*. The friction velocity, u*, was
obtained from Equation 2.41 for various wind speeds. Then the depth of the
molecular sublayer, a, was obtained from Equation 2.36 with k taken equal
to 0.4. Finally, the depth of the mixed layer, d, was calculated using
Equation 2.37with fi taken equal to 1.46 x 10"1* sin X and X taken to be 45 .
In Equation 2.37, the liquid phase friction velocity, w*, was determined
from Equation 2.32. In the model, wind speeds of 2.24, 4.48, 6.72, and 8.96
m/s were used. The results for the friction velocity, u±, and the
liquid phase mass transfer coefficient, k , for each wind speed are
presented in Table 4.8 for the system nitrogen dioxide - water at 25 C and
98 kPa total pressure.
TABLE 4.8: Determination of k for the system N02 - H20.
Jo
..... , cm, , . n Q cm,
u(10), m/s u*, /sec k x 103, /sec
2.24
4.48
6.72
8.96
6.36
13.90
22.50
31.90
0.69
1.07
1.39
1.68
The determination of the solubility of a species in a liquid phase is
fairly simple in most cases. However, in the case of nitrogen dioxide,
which reacts with the aqueous phase forming a variety of ionic species,
this determination becomes very complicated as indicated by Kabel (1975).
Also, very little data are available for the absorption of N02 in water.
However, a study performed by Wendel and Pigford (1958) yields some useful
52
-------
information. Using experimental results combined with thermodynamics,
Wendell and Pigford obtained the following result for Henry's Law constant
for the system nitrogen dioxide - water at 25°C and 98 kPa total pressure:
Cgi _2 g/cm3 gas
H = -ii=4.3xlO .
*-jj^ g/cm3 liquid
Determination Of The Deposition Velocity Over Land For N02
The deposition velocity over land was determined by observing its
counterpart over water, i.e. k /H. For N02, kn/H as determined from
Table 4.8 has values ranging from .00016 m/s to .0004 m/s. Since the
uptake over land should be less than the uptake over water, all variables
but the deposition rate considered equal, a value of .0001 m/s was
arbitrarily selected below the range of k /H values for the deposition
J6
velocity of N02 over land.
DETERMINATION OF PARTICULATE TRANSPORT VALUES
Determination Of The Particulate Deposition Velocity In The Atmosphere
Atmospheric particulate matter is characterized by an entire range
of sizes. Each particle size settles at its own individual velocity
dependent on gravitational forces and drag forces, turbulent eddy diffusion
and molecular diffusion. It is often assumed that the deposition velocity
is equivalent to the Stokes fall velocity, V , which only considers
gravitational and drag forces. This is satisfactory for a still atmosphere
and for particles large enough to allow the atmosphere to be viewed as a
continuum but for a turbulent situation or for particle sizes on the order of
53
-------
the mean free distance between air molecules, the actual deposition velocity
is larger than the Stokes settling velocity. This increase in deposition
velocity (V,) over the Stokes settling velocity (Vg) is shown in Figure 4.2.
The Quasi-Polydispersoid Particulate Model
The particles emitted from the various sources were assumed to be
amenable to representation as a log-normal size distribution. .The mass
mean diameter was chosen as 0.76ym with a geometric standard deviation of
5.0. The mass mean diameter was an average of one day samples taken
randomly over the year 1970 in the city of Chicago with measurements being
made by a modified Andersen Cascade Impactor (Lee, 1972).
With the size distribution defined, 3 size categories containing equal
mass were determined. The three ranges such that each contained 33% of
the mass were: .01-.33pm, .33-l,5ym, and 1.5-40um. Using Figure 4.2
(Sehmel, 1975), an average deposition velocity was selected for each size
range with consideration given to the effect of surface roughness,
atmospheric stability, friction velocity, particle density, and the height
at which the deposition velocity was being estimated. Particles from
.01-.33pm were estimated to have an average fall velocity of .011 m/s;
particles from .33-1.5pm were estimated to fall at .006 m/s, and particles
from 1.5-40ym were estimated to fall at .019 m/s. Note that the velocity
in the smallest category is larger than the velocity in the intermediate
size range. This is due to the increased molecular diffusion of the
smallest range. In using Figure 4.2, the average particle density was
assumed to be 4g/cm3; a stable atmosphere was assumed, a roughness length
54
-------
10
o
to
E
o
O
O
_J
tu
W IO-2
o
Q.
UJ
O
r If d 11H H kj i i i i i 11 ii A J
STABLE ATMOSPHERE p=M.5-*./ /
WITH ROUGHNESS HEIGHT,cm p=4*
'" " ~-'J»-~r-"-l'r-n"-""~ITr;T"~1-"1 r-r--r.mini_^_^^^v* /
i i i I Mill / I \/\ i i iIII I I I I I nil
io-' i
PARTICLE DIAMETER
io
Figure 4.2: Predicted Deposition Velocities at I Metre for u^-30 cm/sec and Part-
icle Densities of 1, 4 , and 11.5 g/cm* (Sehmel, 1975).
55
-------
of 3 cm was selected, a friction velocity of 30 cm/s was chosen and a depth
of 1 m above the ground was the depth over which the deposition velocities
were averaged.
BACKGROUND CONCENTRATIONS
Background Concentrations For N02
The source strength values for N02 given in Table 3.1 accounted for
industrial processes, fuel combustion, solid waste disposal and transporta-
tion processes but neglected background values from natural processes. An
analysis of the air composition for Duluth, Minnesota showed that the
minimum daily NO concentration measured over a 5 year period with samples
X
taken biweekly was 3 yg/m3 (HEW, 1962). This was assumed to have occurred
on a day when most sources were inoperative and when the wind was from the
NW bringing air from the unindustrialized Canadian grasslands and was
chosen as a quite conservative background N02 concentration. Other reports
have indicated that background concentrations for N02 of 2.0-2.5 yg/m3 are
reasonable estimates (Rasmussen, Taheri, Kabel, 1974).
Background Concentration For Particulate
As in the case of N02 gas, the AQCR source strengths did not include
particulate from fugitive dust sources such as vehicular travel on paved
and unpaved surfaces, agricultural activities, and wind erosion of soil to
mention a few. Again looking at Duluth as a representative city in the
Upper Great Lakes Region, the minimum particulate concentration measured
over the 5 year period from 1957-1961 was 19 yg/m3 for a 24 hour average.
56
-------
Again assuming that this occurred on a day when most sources were inoperative
and when the wind was from the unindustrialized Canadian grasslands NW of
Duluth, the value of 19 yg/m3 was chosen to represent the background
concentration.
57
-------
CHAPTER 5
SPECIES CHARACTERIZATION
POLLUTANTS NOT CONSIDERED IN THE MODEL
Elimination Of Nitrous Oxide And Nitric Oxide As Detrimental To The Upper
Great Lakes
Gaseous nitrous oxide, although being the most abundant nitrogen
compound in the atmosphere, was not considered a detrimental
pollutant to the Upper Great Lakes. Nitrous oxide is produced naturally
from bacterial decomposition of other nitrogen compounds within the soil;
however, there are very few data available to quantify these natural
emissions. More importantly, nitrous oxide is almost insoluble in water
and could not contribute significantly to the nitrogen budget of the
Great Lakes.
Gaseous nitric oxide is emitted from anthropogenic and natural sources.
Generally, estimates of emissions for NO and N0£ are included together as
NO such as in the National Emissions Inventory data listed in Table 3.1.
NO readily oxidizes to N02 and since this research deals with long range
transport, the oxidation was thought to be so complete that the emissions
data for NO could be considered to be completely N0£. Therefore, due to
.X
this oxidation process and, in addition, to the low solubility of NO in
water, NO was not considered to contribute significantly to the nitrogen
budget of the Great Lakes.
58
-------
Elimination of Ammonia From Model Considerations
Ammonia was not included in the model in either gaseous or particulate
form even though there is a significant gaseous input into the atmosphere
each year from predominantly natural sources (Rasmussen, Taheri, Kabel, 1974).
The reason for neglecting NHa is not because there is a 'dearth of emissions
nor because NHs is not soluble in water. This predominantly natural emission
was omitted due to a lack of emissions data. It is thought that ammonia
could have a significant impact on the nitrogen budget of the Great Lakes.
INDIVIDUAL POLLUTANT CONTRIBUTIONS TO THE UPPER GREAT LAKES
Total Dissolved Solids
The percent of the total particulate input into the Upper Great Lakes
that is water soluble was estimated by considering dustfall bucket measure-
ments taken in the Greater Windsor Area from 1951-1955 (Katz, 1961). The
water soluble fraction was calculated and found to vary from 20 to 30%. The
lowest value of 20% was selected for this application to allow for the re-
duction in readily dissolved sulfate emissions caused by the shift from coal
to oil and gas during the 1951-1973 period. With the tendency to shift back
to coal in this era due to energy considerations, the water soluble percentage
may again increase.
Chlorides
The percent of the total particulate input into the Great Lakes that
was chlorides was assumed to be equivalent to the percent of the total
particulate emitted from all the sources in the Great Lakes Region that was
chlorides. This latter percentage was calculated by Acres (1975) to be .52%.
It was also assumed that this percent represented the ratio of the average
chloride concentration to the total particulate concentration, so that the
59
-------
average chloride concentration was calculated as .52 yg/m3 using the National
Air Sampling Network (NASN) measurement of 104 yg/m3 as representative of
the total yearly particulate concentration (HEW, 1962). Katz (1961) indi-
cated that the maximum particulate chloride concentration measured by NASN
during an 18 month sampling period was 7.6 yg/m3 for a 24 hour period.
Katz also reported data from which it was determined that the average
urban concentration of gaseous chloride for a highly industrialized area was
.075 PPM by volume or 119 yg/m3. Thus the concentration of gas is, on the
average, 200 times as great as solids with differences as small as a factor
of 15 occurring over occasional short periods.
This large gaseous chloride input was an unexpected development discov-
ered late in the project. Because of the time element, the gaseous chloride
input was calculated simply as a factor of 200 times the particulate chloride
input. Were more time available, the gaseous chloride input could have
been better determined by multiplying each particulate source by .0052 x 200
and using these gaseous chloride source strengths and the k , H and V, for
gaseous chlorides to determine the input into the lake.
Total Nitrogen
The gaseous contribution to the total nitrogen budget of the Upper
Great Lakes was determined using the given AQCR source strengths, the given
meteorological data and the predictive model. The gaseous input consists
only of N02-
60
-------
The particulate contribution to the nitrogen budget was simply computed
as a given percentage of the total particulate input. NASN measurements
produced a five year geometric mean concentration for particulate nitrates
of 1.7 yg/m3. Since the total suspended particulate geometric mean for the
same period was 104 yg/m3, 1.6% of the particulate in the air, and con-
sequently, 1.6% of the total particulate input into the Upper Great Lakes
was estimated as particulate nitrates.
Total Phosphorus
The total phosphorus input was calculated solely as particulate since
there was no information available identifying any form of gaseous phosphorus
or gaseous phosphorus containing atmospheric pollutants either for natural
or anthropogenic sources.
The particulate phosphate input was calculated as a percent of the
total particulate input. Acres (1975) calculated that .0115 grams of
phosphate were in every gram of particulate emitted from sources in the
vicinity of the Great Lakes. Given that 1.15% of the particulate emitted
was phosphates, it follows that 1.15% of the total particulate input into
the Upper Great Lakes was particulate phosphate. The assumption depends on
a further assumption that the size distribution of the particulate phosphate
was similar to the size distribution of the total particulate.
Dissolved Silica
The total silica input into the Great Lakes was calculated as a percent
of the total particulate input. Cholak (1952) has measured the silica in
the air in Baltimore as 3.5% of the total particulate. Katz (1954) found
61
-------
that the mean (averaged over 23 samples) concentration of silica in the
Windsor area was 6.2 yg/m3 (expressed as elemental silicon) while the mean
total particulate concentration was 196 yg/m3. Therefore, 3.2% of the
total particulate was elemental silicon which would correspond to about 7%
silica. Unfortunately, what could not be estimated was the dissolvable
portion. Ultimately, Cholak's value of 3.5% was used. Thus 3.5% of the
total particulate input was silica and it is the total silica and not the
dissolved silica that is reported in the Results section.
Pesticides
The Source Strengths
The emission factors for pesticides originated from data showing the
amount of pesticides, that is, fungicides, herbicides, insecticides and
miscellaneous fumigants, defoliants, miticides, rodenticides, plant growth
regulators, and repellents used in the year 1971 (USDA, 1974). These data
were given on a regional basis with the three regions of importance being
the Lake States: Minnesota, Wisconsin, and Michigan, the Corn Belt States:
Iowa, Illinois, Indiana, and Ohio, and the Northeast States of which only
New York and Pennsylvania were in the Great Lakes Basin. Since only one
number was given for the pesticides emissions from a region, the decision
was made to determine the pesticides utilized in each state in the Great
Lakes Basin by modifying the regional value by multiplying it by the percent-
age of the region1 s farmland contained in each state. Thus, if a state
contained 50% of the farmland of its region, it was assumed to use 50% of
the region's pesticides. In this fashion, nine source strengths were
attained, each source representing an entire state. Each state was modeled
62
-------
as a point source located in the middle of the state with an initial cross-
wind plume width equal to the diameter of a circle with an area equivalent
to the total area of the state. The values of the weighted source strength
and the weighting factor used, along with the initial crosswind diffusion
coefficient are shown in Table 5.1.
Pesticides In Particulate Form
It was estimated that 50% of the applied pesticides did not settle on
the farmlands but rather, were dispersed into the atmosphere (Westlake and
Gunther, 1966). The pesticide particle remaining after the solvent in
which it was originally dispersed evaporated was assumed to be in the third
size category, 1.5 to 40 ym. Thus, the average pesticide particle's
deposition velocity was estimated as .019 m/s. Given the deposition
velocity, the initial source strengths and locations, the initial plume
widths and the meteorological data, the mathematical model was used to
determine the input of pesticides into the Upper Great Lakes. No background
concentration was utilized for pesticides.
63
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TABLE 5.1 : EMISSION FACTORS FOR PESTICIDES
Region
LAKE STATES
Minnesota
Wisconsin
Michigan
CORN BELT
Iowa
Illinois
Indiana
Ohio
NORTHEAST
Pennsylvania
New York
Airborne
Factor
.5
.5
.5
.5
.5
.5
.5
.5
.5
Weight
Factor
.466
.308
.226
.258
.221
.137
.135
.288
.341
Total Regional
Pesticides
(Mg/YR. )
16026.
45606.
9461.
Weighted
Emission Factor
(Mg/YR. )
3734.
2468.
1810.
5883.
5039.
3124.
3078.
1362.
1613.
o fm")
yo k '
131603.
107557.
109514.
107687.
107793.
86467.
92154.
96640.
101066.
64
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CHAPTER 6
RESULTS
The results presented in this report are only estimates. Some portions
of the quantitative modeling are familiar and well defined whereas other
aspects rely heavily on intuition. This section shows the effects on the
input into the lake of variation in some of the quantitative estimates of the
input values. Also shown is a sample of the computer output depicting concen-
tration and flux at a point on the lake edge. Finally, a compilation of re-
sults which shows the input of pollutants into the Upper Great Lakes is given.
A PARAMETRIC STUDY
The question to be considered in this section is how sensitive the
model is to variation in the input parameters, specifically, original source
height, grid dimension at the lake edge, inclusion of a background concen-
tration, inclusion of an inversion lid over land, and variation in deposition
velocity over land. Table 6.1 shows the results of varying these input
parameters for the specific case of N02 dispersion with D stability over
land and a first inversion of 200 m over water with the wind at 8.96 m/s
from the SW.
65
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TABLE 6.1 : VARIATION OF INPUT RATE OF N02 INTO THE UPPER GREAT LAKES AS A
FUNCTION OF MODEL INPUT PARAMETERS
MODEL INPUTS*
SOURCE
HEIGHT (m)
DEPOSITION
VELOCITY (mm/s)
BACKGROUND
CONCENTRATION
(yg/m3)
INVERSION LID
HEIGHT OVER
LAND (km)
STABILITY CLASS
OVER WATER
CROSSWIND GRID
DIMENSION (km)
MODEL OUTPUTS
INPUT RATE FOR
LAKE SUPERIOR (kg/s)
INPUT RATE FOR-
LAKE HURON (kg/s)
COMPUTER RUN NUMBER
1
1.0
0.0
3.0
2.0
F
50.
.34
1.3
2
1.0
0.0
3.0
2.0
F
25.
.42
1.8
3
1.0
0.0
3.0
2.0
F
12.
.29
1.3
4
1.0
0.0
3.0
2.0
F
6.2
1.2
5
1.0
0.0
3.0
**
F
50.
.34
1.2
6
10.
0.0
3.0
**
F
50.
.34
1.2
7
1.0
0.0
3.0
**
F
20.
_
.68
8
10.
0.0
0.0
**
F
50.
.13
1.1
9
10.
1.0
0.0
**
D
50.
.01
.23
10
1.0
1.0
3.0
2.0
F
50.
.21
.21
11
10.
0.1
3.0
2.0
F
50.
.30
.87
* Stability class over land was D and inversion lid over water was at 200m
for all runs. This parametric study yields input rates utilizing only
sources SW of the Upper Great Lakes.
** No lid existed.
66
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Variation Of Results With Grid Size
In the finite difference approximation of the diffusion equation for
computer solution, there is a direct relation between the increase in
accuracy achieved t>y using a finer grid network and the increased cost for
computer time incurred. Also, there exists a point where no finer grid can
be used due to the limitation of storage space in the computer. While the
model used in this research was not a partial differential equation, a grid
network was used at the lake edge and the above concepts were thought to
apply.
The variation of input rate with the crosswind grid dimension can be
seen by inspecting run numbers 1 through 4 in Table 6.1 . The variation is
more clearly depicted in Figure 6.1 where the variation in lake input is
plotted as a function of the crosswind distance between grid points. The
plot stops at 6 km because any computer run with Ay<6km was bound to exceed
the storage limit of 560K bits. (The actual storage limit when using the
Pennsylvania State University IBM Model 370 System is 280K. The 560K
storage requires special permission which is only given for debugging
purposes. Thus the 560K storage is not available for continuous use.)
The slopes in Figure 6.1 showed signs of decreasing to zero as Ay decreased
but it was not possible to confirm this fact due to storage limitations.
Fortuitously, the variation with grid size was not pronounced and the flux
values obtained at Ay=50km were near those obtained at Ay=6km. Therefore,
in order to minimize computer usuage in "terms" of time, storage and consequently,
cost, the grid size of Ay=50km was used in all the predictions.
67
-------
u
Q>
UJ
oc
1800-
1600-
1400-
1200-
IOOQ-
t 800-
UJ
600-
400-
200-
D
CI-
20 30
A Y(Km)
+ HURON
D SUPERIOR
40
50
Figure 6.1: The Effect of Varying Grid Size on Lake Input Rate
68
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Variation Of Results With Original Source Height
Since the source height was selected somewhat arbitrarily, it was
necessary to determine the sensitivity of the model to various source
height selections. Computer runs 5 and 6 on Table 6.1 show that there was
no variation of input into the lake with source height variations in the
range of 1 to 10 m.
Variation Of Results With Deposition Velocity Over Land
The variation of the input into the lakes with the deposition velocity
is shown by comparing computer runs 1, 10 and 11 in Table 6.1. The only
other variable that changes in these runs is source height and that is
known to produce no variation in input rate into the lakes over the given
range. The results indicate that the rate of input increased significantly
with a decrease from 1.0 to .lmm/s in deposition velocity over the land
followed by a less rapid increase in input rate with a decrease from .1 to
0 mm/s in deposition velocity over land. The conclusion is that the results
are sensitive to the selection of deposition velocity within certain ranges
and that the somewhat arbitrary choice of deposition velocity over land
used in this model for N02 could lead to a substantial error if the
arbitrary choice varied from the true deposition velocity.
Variation Of The Results With The Addition Of A First Inversion Over
Land And A Second Inversion Over Water
A comparison of computer runs 1 and 6 in Table 6.1 shows the effect of
adding an inversion lid at 2km above the entire Great Lakes Basin. This
lid was modeled as the first inversion over land and over water except in
69
-------
the summertime when the relatively cool water created another inversion at
200m. The effect of adding an inversion at this height was to cause an
insignificant change in input rate into the lakes. This can be attributed
to the fact that for the distances of travel under consideration, the
inversion was too high to allow reflection of pollutants to have any
significant effect in increasing the pollutant concentration obtained
without the inversion.
Variation Of The Results With The Addition Of A Background Concentration
A comparison of runs 6 and 8 on Table 6.1 indicates the effect of
adding a background concentration. Adding a background concentration
caused only a 9% increase in the input of NC>2 to Lake Huron while it
caused a 160% increase in the input to Lake Superior. This is understandable
since the concentrations of N0£ over Lake Huron were high enough so that an
additional 3 yg/m3 background did not really have a significant effect.
In contrast, the concentration of N02 over Lake Superior due to anthropogenic
sources were so low that the addition of a 3 yg/m3 background was extremely
significant.
Variation Of The Results With A Change In The Method Of Background Concentration
Addition
A theoretically more satisfying method of adding the background concen-
tration was developed but only after the work was completed. For completeness,
the new method is discussed and its effect on the final input values is
considered. The new method is presented first and the old method is then
discussed in light of the new.
70
-------
The new method of background addition can be best explained by considering
Figure 6.2. Source A represents the anthropogenic sources upwind of the
interferring lake; source NI represents the natural sources upwind of the
interferring lake; source N2 represents the natural sources in the interfer-
ring lake, and source N3 represents the natural sources between the inter-
ferring lake and the Upper Great Lake. The background concentration is
defined here as that concentration at the receptor caused by all upwind natural
sources. Therefore concentration wall A contained concentrations due to
sources A and Nj. Concentration wall B contained concentrations caused by
A, NI, and N2- Concentration wall C contained concentrations caused by A,
NI, N2, and N$. By definition the background concentration is a constant
value at any receptor and is due to all upwind natural sources. Thus, the
background concentration at concentration wall A due to source N, acting over
a distance Xj is equal to the background concentration at concentration
A
wall B due to source N2 acting over a distance \2 and to source Nj acting
B
over a distance Xj .
B
As has been explained previously, this model converts the concentration
grids into new source strength grids to allow a model to be used over several
incremental distances. Thus, neglecting for the moment the natural sources,
source A yields a source strength QA at concentration wall A, Source Q.
yields a source Qg at concentration wall B and source Q yields a source Q
at concentration wall C. The difference between the new and old methods occurs
when one considers how to include the natural sources in this incremental dis-
tance model. The new method takes the concentration at wall C resulting from
71
-------
(Q
C
(0
en
ro
o co
5; o
s I
0 S.
o'
o =
Q- c
o
3
O^
C
tn
Q
c
Q_
CO
O
C
o
01
3
O
3
<0
CONCENTRATION
WALL A
CONCENTRATION
- WALL B
CONCENTRATION
s~ WALL C
INTERFERRING
LAKE
X2B
IB
3C
2C
IC
UPPER GREAT
LAKE
-------
source QR (which just includes anthropogenic source A) and adds the back-
D J
ground concentration to it thus including at wall C the effect of NI, N£,
and NS. The sum of these two concentrations can then be converted to a new
source strength, QrM and used to calculate the flux into the Upper Great
Lake.
What has been done in this model is to add the background concentration
to the concentration at wall A calculated using anthropogenic source A (thus
including at effect of NI) and to convert this to a new source strength Q.,..
Then the new source QAM which included the effects of A and NI was used to
calculate a concentration at wall B, The background concentration was again
added to the concentration at wall B (thus including the effects of NI and
N2) and the resulting concentration was converted to a new source strength
0Dia. The problem becomes obvious. The effect of natural source Nj was in-
BN
eluded twice to get the concentration at wall B. First it was included in
the new source strength Q.^ which was used in the model to calculate the
concentration at wall B, and second, it was included in the background
concentration which was added to the calculated concentration at wall B.
This problem multiplies as one takes the next incremental step to wall C.
The new method adds the background concentration only at wall C. Thus
only the effect of source A will be felt in each incremental step until the
last step which is the determination of the concentration at wall C. Here,
the background should be added and the effect of natural sources NI, N2 and
NS will be felt only once as expected. This will actually change the input
into Lake Huron little as shown in the previous section where runs 6 and 8
were compared but the input into Lake Superior will increase by some value
less than 160% with this new method of considering background.
73
-------
Variation Of The Predicted Input With The Correction Of A Model Error
In the development of the original model, a conceptual error was made
which led to a sign error in the final flux equation. Unfortunately, all
the work was finished before this error was discovered. Thus, in this section,
the effect of this error is evaluated. The actual question of concern was
what the effect of this error was on the final predicted flux. Looking at
the expression for the flux, Equation 2.24, there are three exponential terms:
h2
Term 1 -> h exp (- = - )
z2
f\
Term 2 -> (2FT - h) exp (- ^ ~ h) - )
Term 3 -> (2H' + h) exp (
- C2
z2
In the erroneous model, Term 3 was negative instead of positive. The
magnitudes of these three terms were evaluated for various input parameters
and are recorded in Table 6.2 . The source height, h, was valued at 10m as
was done to acquire the final predicted inputs given in Table 6. 9 In the
first three columns, the third term is negligible in comparison to the others.
The effect of changing the sign on Term 3 from positive to negative is seen
to be potentially important only for the case of column 4. Actually, column 2
is most representative of the summer while column 3 is most representative of
the other 3 seasons. Thus in the summer this error should theoretically have
caused only a 2% lower predicted flux than reported while for the other seasons
a 15% lower flux than reported. The calculation for the first percentage can
be made as follows: 2% = (1 - (9.95 + .194 - .092)7(9.95 + .194 + .092))
These theoretical estimates of the error were actually checked (for the
summer only) by running the corrected computer model for NC^- The incorrect
versus the correct flux is shown in Table 6.3. The correct flux is 2% higher
74
-------
TABLE 6.2 : VARIATION OF THE TERMS IN THE FLUX
EQUATION FOR VARIOUS INPUT CONDITIONS
TERM 1
TERM 2
TERM 3
a = 100m
z
H' = 2000m
9.95
0.
0.
H' = 200m
9.95
.194
.092
a = 1000m
z
H' = 2000m
9.999
1.39
.917
H' = 200m
9.999
361.
376.
TABLE 6.3 : EFFECT OF THE SYSTEMATIC ERROR
INCORRECT FLUX
(kg/s)
CORRECT FLUX
(kg/s)
SUPERIOR
HURON
.3
.87
.298
.896
75
-------
for Huron as theory predicts while the correct flux is 2% lower for Superior.
While this second result is not readily explained the point is that the error
really has little effect on the-model.
Variation Of The Results With The Inclusion Of Several Reflections In The
Concentration Equation ~~~~~~ ~
The most complete expression of the concentration in an inversion trap is
exp (-1/2 (^-)2) . {exp (.1/2 (3. - h)2) _
y z y 0_
Y exp (-1/2 (~-^) + E {exp (-1/2 (z " ^2nH^ " h^21
z n=l . o~) J
Y exp (-1/2 (ijL + exp c.1/2 (_
* J
Y exp (-1/2
z
The concentration equation used in this model, Equation 6.1 , utilized only
one reflection (n=l). The importance of each term in Equation 6.1 is shown
in Table 6.4 for the special case of z=0. Under this condition, the expo-
nential terms can be expressed in the form
exp (- 1/2 (-h ±
a
z
or
exp (- 1/2 (-£!-)2 (-i-± 2n)2)
z
LI - i
The variation of this later expression for various values of and -fW- is
O H
z
shown in Table 6.4 . Recall that for this research, the smallest value of
H' was 200m in the summer and the source height, h, was 10m. Thus, h/H' was
76
-------
TABLE 6.4: THE VALUE OF THE EXPONENTIAL TERMS FOR VARIOUS
a ' H
z
r- and n
H'
a
z
2.5
2.5
1.25
1.25
.625
.625
.2
.2
h
H'
0.0
0.5
0.0
0.5
0.0
0.5
0.0
0.5
n=0
1.000
.458
1.000
0.822
1.000
0.952
1.000
0.995
n=l
0.000
0.000
0.044
0.008
0.458
0.295
0.923
0.882
n=-l
0.000
0.001
0.044
0.172
0.458
0.644
0.923
0.956
-n O
n-z
0.000
0.000
0.000
0.000
0.044
0.019
0.726
0.667
t-» O
n £
0.000
0.000
0.000
0.000
0.044
0.091
0.726
0.783
n=3
0.000
0.000
0.000
0.000
0.001
0.000
0.487
0.430
n=-3
0.000
0.000
0.000
0.000
0.001
0.003
0.487
0.546
n=4
0.000
0.000
0.000
0.000
0.000
0.000
0.278
0.236
n=-4
0.000
0.000
0.000
0.000
0.000
0.000
0.278
0.325
n=5
0.000
0.000
0.000
0.000
0.000
0.000
0.135
0.110
n=-5
0.000
0.000
0.000
0.000
0.000
0.000
0.135
0.164
-------
H**
always between 0.0 and 0.5. Values of - >_ 2 were most representative of
LJ
the conditions considered for all the seasons and consequently, one finds
from Table 6.4 that no error was incurred by considering only one reflection
COMPUTER OUTPUT SAMPLES
Tables 6.5 through 6.8 represent sample computer outputs for N02 con-
centration and flux at various lake edge coordinates for both Lakes Huron
and Superior. The sample results were calculated using the input parameters
specified under computer run 11 of Table 6.1. Recall that Table 6.1 was
developed for summertime dispersion under a wind speed of 8.96 m/s and for
a wind direction of 225°. The transformed x and y coordinates in Tables 6.5
through 6. 8 are the downwind and crosswind coordinates respectively. Recall
that with the wind from 225° instead of 270° for which the original coordinate
system was developed, a coordinate transformation is necessary. The height
in Tables 6.5 and 6.7 is the height above the ground at which the concentration
was calculated.
Several conclusions can be drawn from these tables. Looking at Tables
6.5 and 6.7 , one can see that the concentration is essentially constant
over height. This is reasonable considering the long distances of travel
(up to 700 km) that one is concerned with since the Gaussian distribution
degenerates into a constant valued distribution in the vertical as one moves
farther and farther downwind. As & second consideration, it is noteworthy
to discuss the high concentration of N02 at Sarnia shown on Table 6.5 .
This high value is due to the very close and very strong downwind source
of Detroit. A third point of discussion can be gleened by comparing Table 6.5
78
-------
TABLE 6.5 : PREDICTED N02 CONCENTRATIONS AT LAKE EDGE
COORDINATES ALONG THE SOUTHERN PORTION OF
LAKE HURON GIVEN 8.96 m/s WINDS AT 225°
Concentration
(yg/m3)
13.0
12.9
12.9
12.9
12.9
12.9
12.9
12.8
12.8
12.7
12.7
39.4
39.4
39.3
39.2
39.0
28.8
38.6
38.3
38.0
37.7
37.3
161.0
160.0
160.0
160.0
159.0
158.0
156.0
155.0
153.0
151.0
149.0
Height
M
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
Transformed
x coord
(km)
1240.
1240.
1240.
1240.
1240.
1240.
1240.
1240.
1240.
1240.
1240.
1230.
1230.
1230.
1230.
1230.
1230.
1230.
1230.
1230.
1230.
1230.
1210.
1210.
1210.
1210.
1210.
1210.
1210.
1210.
1210.
1210.
1210.
Transformed
y coord
(km)
-259.
-259.
-259.
-259.
-259.
-259.
-259.
-259.
-259.
-259.
-259.
-305.
-305.
-305.
-305.
-305.
-305.
-305.
-305.
-305.
-305.
-305.
-351.
-351.
-351.
-351.
-351.
-351.
-351.
-351.
-351.
-351.
-351.
Location
* Actual
Coordinates :
(20, 13)
@ 40 miles
NE of Saginaw
Actual
Coordinates :
(20.4, 12.3)
@ 60 miles
E of Saginaw
Actual
Coordinates :
(21, 11.5)
@ Sarnia,
Ontario
*Actual coordinates found in Figure 3.1
79
-------
TABLE 6.6: THE PREDICTED FLUX OF N02 AT VARIOUS POINTS
OF THE SURFACE OF LAKE HURON FOR 8.96 m/s
WINDS AT 225°
Flux
(ng/m2 - s)
44.2
6.4
38.4
11.4
4.1
5.6
26.0
10.1
3.7
9.9
20.6
23.4
9.2
3.4
4.9
8.7
18.7
21.5
8.5
Transformed
x coord
(km)
1240.
1270.
, 1310.
1270.
1310.
1350.
1310.
1350.
1390.
1310.
1350.
1390.
1420.
1460.
1350.
1390.
1420.
1460.
1500.
Transformed
y coord
(km)
-337.
-300.
-337.
-225.
-262.
-300.
-187.
-225.
-262.
-112.
-150.
-187.
-225.
-262.
-175.
-112.
-150.
-187.
-225.
The total input into Lake Huron is 873 g/s
where
n
total input = Z FLUX (i) AREA OF LAKE
NUMBER OF POINTS (N)
80
-------
TABLE 6.7: PREDICTED N02 CONCENTRATIONS AT LAKE EDGE
COORDINATES ALONG THE SOUTHERN PORTION OF
LAKE SUPERIOR GIVEN 8.96 m/s WINDS AT 225°
Concentration
(yg/m3)
4.66
4.66
4.66
4.65
4.65
4.65
4.64
4.64
4.63
4.62
4.61
5.10
5.10
5.10
5.10
5.09
5.08
5.07
5.06
5.05
5.03
5.02
5.71
5.71
5.71
5.71
5.70
5.69
5.69
5.68
5.66
5.65
5.64 ..
Height
(m)
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
Transformed
x coord
(km)
1220.
1220.
1220.
1220.
1220.
1220.
1220.
1220.
1220.
1220.
1220.
1250.
1250.
1250.
1250.
1250.
1250.
1250.
1250.
1250.
1250.
1250.
1320.
1320.
1320.
1320.
1320.
1320.
1320.
1320.
1320.
1320.
1320.
Transformed
y coord
(km)
198.
198.
198.
198.
198.
198.
198.
198.
198.
198.
198.
160.
160.
160.
160.
160.
160.
160.
160.
160.
160.
160.
83.7
83.7
83.7
83.7
83.7
83.7
83.7
83.7
83.7
83.7
83.7
Location
* Actual
Coordinates :
(13.7, 12.9)
110 km W. of
Sault Ste.
Maria
Actual
Coordinates :
(14.6, 18.9)
87 km W. of
Sault Ste.
Maria
Actual
Coordinates :
(15.5, 18.8)
65 km W. of
Sault Ste.
Maria
*Actual coordinates found on Figure 3.1
81
-------
TABLE 6.8: THE PREDICTED FLUX OF N02 AT VARIOUS POINTS
ON THE SURFACE OF LAKE SUPERIOR FOR 8.6 m/s
WINDS § 225°
Flux
(ng/m2 - s)
5.65
5.32
4.01
3.59
3.54
3.22
2.93
2.86
5.09
5.87
.015
.018
5.92
6.76
4.62
5.01
4.74
3.59
3.21
3.18
2.91
2.65
2.59
4.34
3.29
2.95
2.93
2.67
3.05
2.74
Transformed
x coord
(km)
1050.
1090.
1120.
1160.
1200.
1240.
1270.
1310.
1350.
1390.
1200.
1240.
1270.
1310.
1350.
1120.
1160.
1200.
1240.
1270.
1310.
1350.
1390.
1240.
1270.
1310.
1350.
1390.
1350.
1390.
Transformed
y coord
(km)
450.
412.
375.
337.
300.
262.
225.
187.
150.
112.
225.
187.
150.
112.
75.
450.
412.
375.
337.
300.
262.
225.
187.
412.
375.
337.
300.
262.
375.
337.
Total input into Lake Superior is 300 g/s
where
N
,P . . «.
Total input =
FLUX (i) AREA OF LAKE
N
82
-------
with Table 6.7 . The concentrations at all points along Lake Huron are seen
to be much higher than the concentrations along Lake Superior. This is
explainable when one considers that Lake Huron is much closer to the large
sources than is Lake Superior and when one considers that Lake Huron is
closer to the centerline of the plumes from the large sources than is Lake
Superior (for this particular wind direction of 225°). Finally, a comparison
of Table 6.6 with Table 6.8 shows that the average point flux into Huron is
larger than into Superior again due in' this particular case to the align-
ment of Huron with the large sources.
QUANTIFICATION OF POLLUTANT INPUT BY DRY DEPOSITION INTO THE UPPER GREAT LAKES
The Yearly Input Of Pollutants Into The Upper Great Lakes
Table 6.9 shows the prediction of specific pollutant yearly inputs into
the Upper Great Lakes by dry deposition processes. The total nitrogen input
to Lake Superior is actually 72% particulate nitrates and 28% gaseous N02
while the total nitrogen input to Lake Huron is 60% particulate nitrates and
40% gaseous N02- The phosphorus input into both lakes is all particulate in
form. The chlorides input for both lakes is 99.5% gaseous and .5% particulate
in nature. The remaining 3 pollutants listed in Table6.9 are all particulate
in nature. The two pollutants yielding a significant input into the Upper
Great Lakes in both gaseous and particulate forms are shown in Tables 6.10
and 6.11 where the quantity of each pollutant input by form is shown*
Seasonal Variation Of Input Into The Upper Great Lakes
Tables 6.12 and 6.13 show the variation of pollutant input into the Upper
Great Lakes as a function of season. The fall and winter seasons were
83
-------
TABLE 6.9 : FINAL PREDICTIONS OF YEARLY POLLUTANT
INPUT INTO THE UPPER GREAT LAKES IN Mg/YR
POLLUTANT
Total Nitrogen
Total Phosphorus
Chlorides
Total Silica
Total Dissolved Solids
Pesticides
SUPERIOR
11,300
5,860
534,000
17,800
102,000
3.3
HURON
20,000
8,730
792,000
26,500
151,000
3.6
84
-------
TABLE 6.10: GASEOUS AND FARTICULATE CONTRIBUTIONS TO
THE POLLUTANT BURDEN OF LAKE SUPERIOR
POLLUTANT
Total Nitrogen
Chlorides
INPUT (Mg/YR)
GASEOUS
3,160
531,000
P ARTICULATE
8,150
2,650
TABLE 6.11 : GASEOUS AND PARTICULATE CONTRIBUTIONS
TO THE POLLUTANT BURDEN OF LAKE HURON
POLLUTANT
Total Nitrogen
Chlorides
INPUT (Mg/YR)
GASEOUS
7,900
788,000
PARTICULATE
12,100
3,940
85
-------
TABLE 6.12: SEASONAL VARIATION OF POLLUTANT
INPUT INTO LAKE SUPERIOR
POLLUTANT
Total Nitrogen
Total Phosphorus
Chlorides
Total Silica
Total Dissolved Solids
Pesticides
SEASONAL INPUT (Mg/YR)
SPRING
2,470
1,230
112,000
3,750
21,400
1.077
SUMMER
1,590
549
49,800
1,670
9,600
1.08
FALL § WINTER
7,260
4,080
372,000
12,400
71,000
1.16
86
-------
TABLE 6.13: SEASONAL VARIATION OF POLLUTANT
INPUT INTO LAKE HURON
POLLUTANT
Total Nitrogen
Total Phosphorus
Chlorides
Total Silica
Total Dissolved Solids
Pesticides
SEASONAL INPUT (Mg/YR)
SPRING
4,460
1,730
157,000
5,250
30,000
1.18
SUMMER
2,980
490
44,600
1,490
8,520
.535
FALL & WINTER
12,600
6,510
591,000
19,800
113,000
1.9
87
-------
analyzed together since their stabilities and inversion lid heights were the
same (see Table 4.2 ) and thus, only one value representing the input for
both seasons was attained.
There are two major conclusions to be drawn from Tables 6. 12 and 6. 13
First, the input of pollutants in the summer into the Upper Great Lakes is
less than the input in the spring despite the fact that the summer had more
dry hours than the spring. Second, the input of pollutants in the summer
and spring taken together is less than the input of pollutants in the fall
and winter taken together, again despite the fact that the summer and spring
had more dry hours than the fall and winter. The reason for these conclusions
can be understood by considering the equation for caluclating the seasonal
input per unit area of lake surface, I :
84 S
1=1 E seasonal flux (i, j) seasonal dry time (i, j)
where the first summation from i=l to i=8 represents the 8 wind direction
categories and the second summation j=l to j=4 represents the 4 wind speed
categories considered in the model. It happens that the seasonal variation
of yearly input is directly related to the seasonal variation of flux and
that the seasonal variation of dry time does not alter this direct
relationship.
Furthermore, the seasonal variation of flux can be correlated to the
seasonal variation of stability. The summer atmosphere was most stable,
the spring yielded a slightly stable atmosphere, and the fall and winter
both displayed a neutral atmosphere. The suggestion is that, for a lake
with an inversion layer above, the more the atmosphere tends toward un-
stability, the greater the flux, and consequently, the input of pollutants
into the lake.
88
-------
Seasonal Variation Of Total Particulate Input With Size Range
Tables 6.14 and 6.15 show the seasonal variation of the total particulate
input, both soluble and insoluble, with size range. The total particulate
input into Lake Superior is equal to the sum of all the values in Table6.14.
Likewise, the total particulate input into Lake Huron is the sum of all the
values in Table 6.15 .
The Fraction Of The Total Atmospheric Burden of Pollutants Deposited Into
The Upper Great Lakes
The total N02 gas emitted from anthropogenic sources in the Great Lakes
area in 1973 was 9 x 106 Mg; the total particulate emitted from anthropogenic
sources was 7 x 106 Mg, and the total pesticides emitted were 7 x 101* Mg.
By dividing the value representing the input of the above pollutants into
the Upper Great Lakes by the above values, an estimate of what percentage
of the pollutants emitted into the atmosphere is deposited by dry deposition
processes into the Upper Great Lakes was obtained. These percentages are
not exact since the input into the lakes is actually composed of contributions
from both natural and anthropogenic sources while the above numbers represent
only anthropogenic sources. The percentages of the N02 gas emitted into the
atmosphere that are deposited into Lakes Huron and Superior are .08% and ,03%
respectively. The percentages of total particulates emitted into the atmo-
sphere that are deposited into Lakes Huron and Superior are 10.4% and 7.0%
respectively. Finally, the percentages of pesticides emitted into the atmo-
sphere that are deposited into Lakes Huron and Superior are .005% and .004%
respectively.
89
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TABLE 6.14: VARIATION OF SEASONAL PARTICULATE INPUT
(Mg/YR) INTO LAKE SUPERIOR WITH SIZE
PARTICULATE SIZE RANGE
.01 - . 33ym
.33 - 1.5pm
1.5 - 40vim
SPRING
39,600
30,000
37,400
SUMMER
3,590
18,800
25,300
FALL § WINTER
119,000
86,900
149,000
TABLE 6.15: VARIATION OF SEASONAL PARTICULATE INPUT
(Mg/YR) INTO LAKE HURON WITH SIZE
PARTICULATE SIZE RANGE
.01 - . 33vim
.33 - l.Sym
1.5 - 40vim
SPRING
55,300
43,200
51,900
SUMMER
3,260
17,500
21,800
FALL $ WINTER
191,000
140,000
235,000
90
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CONCLUSIONS AND IKOMDATIONS
The conclusions to be drawn from this research are:
1. The yearly input of all the pollutants considered was larger for
Lake Huron than for Lake Superior by factors varying from 1.1 to 1.9.
2. 20% of the particulate emitted into the atmosphere was deposited
into the Upper Great Lakes while < 1% of the N02 gas and pesticides emitted
were deposited into the Upper Great Lakes.
3. The input of pollutants into the lake in the summer was less than
the input in the spring and the combined spring and summer inputs were less
than the combined fall and winter inputs.
4. The more the atmosphere over a lake with an inversion layer above
tends toward unstability, the greater the flux of pollutants into the lake.
5. The final pollutant input value is sensitive to the deposition
velocity both over land and water.
6. Pesticide input from the atmosphere into the Upper Great Lakes by
dry deposition processes is negligible. This is due to the small source
strengths, the large area over which the sources were spread, and the large
distances of travel for pesticides.
91
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7. The total nitrogen input to Lake Superior was 72% particulate
nitrates and 28% gaseous N02- The total nitrogen input to Lake Huron was
60% particulate nitrates and 40% gaseous N02-
8. 99.5% of all chloride input into both Upper Great Lakes was
gaseous in form.
9. Only 79% of the total yearly hours was classified as dry yearly
hours. This reduced seasonally, in order of dryness, to summer, for which
85% of the season was dry, fall for which 79% of the season was dry, spring
for which 78% of the season was dry and winter for which 76% of the season
was dry.
10. The yearly dry time allotment according to wind speed category
resulted in the wind being less than 3.1 m/s during 37% of the time, between
3.1 and 5.8 m/s during 46% of the time between'5.8 and 8.1 m/s during 13%
of the time and greater than 8.1 m/s during only 4% of the total yearly
dry time.
11. The yearly dry time allotment according to wind speed category
resulted in the following percentages:
a) from N 12% of the time
b) from NE 5% of the time
c) from E 17% of the time
d) from SE 4% of the time
e) from S.15% of the time
f) from SW 14% of the time
92
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g) from W 25% of the time
h) from NW 8% of the time
The fact that the winds were from the S to W quadrant 54% of the time
caused a higher yearly atmospheric pollutant burden in the Upper Great Lakes
than if the predominant wind direction were from another quadrant. This is
because the closest large sources are located in the S to W quadrant.
There are several refinements which would afford estimates more
accurate than the current "order of magnitude":
1. Take the known estimate of 4 yg/m3 for background NHs concentrations
(Rasmussen, Taheri, Kabel, 1974), and calculate the input of NH3 into the
Upper Great Lakes from natural sources by building a wall of concentrations
of 4 yg/m3 at the edge of each Upper Great Lake and forming new sources at
this wall.
2. The background concentration should be added at the concentration
wall located on the upwind side of the Upper Great Lake of concern. This
will enable the natural sources to be accounted for only one time.
3. The data found in the literature suggests large amounts of gaseous
chlorides in the atmosphere. These gaseous chloride sources need to be
located and quantified. The prediction of gaseous chloride input into the
Upper Great Lakes can then be handled by calculating an appropriate value
for k. and proceeding in a manner identical to that of N02-
93
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Heines, T. S. and Peters, L. K., "The Effect of Ground Level Absorption
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from Chemistry of the Lower Atmosphere, S. J. Rasool (Ed.), Plenum
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Katz, Morris, "Air Pollution," Monograph Series No. 46, World Health
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TECHNICAL REPORT DATA
(I'lcasc read liiitriicnons on the /vi cm- hfjure
. REPORT NO.
EPA-905/4-75-005
4. TITLE AND SUBTITLE
ATMOSPHERIC INPUTS TO THE UPPER GREAT LAKES BY DRY
DEPOSITION PROCESSES
5. REPORT DATE February 27, 1976
Date of Submission
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
W. J. Moroz, R. L. Kabel, M. Taheri, A. C. Miller,
H. J. Hoffman, W. J. Brtko, T. Cuscino
8. PERFORMING ORGANIZATION REPORT NO.
I. RECIPIENT'S ACCESSION-NO.
9. PERFORM ING ORG-\NIZATION NAME AND ADDRESS
Center for Air Environment Studies
226 Fenske Laboratory
The Pennsylvania State University
University Park, Pennsylvania 16802
10. PROGRAM ELEMENT NO.
2BH155
11. CONTRACT/GRANT NO.
#R005168
12. SPONSORING AGENCY NAME AND ADDRESS
13.TYPE OF REPORT AND PERIOD COVERED
Draft of Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A Gaussian plume model was modified to estimate the input of specific atmospheric
pollutants into the Upper Great Lakes by dry deposition processes. The specific
pollutants were: 1) total dissolved solids, 2> chlorides, 3) total nitrogen,
4) total phosphorus, 5) total silica, and 6) pesticides.
Pollutant removal at a land or water surface by dry deposition processes was
accounted for by including a deposition factor in front of the image terms in the
conventional Gaussian concentration equation. The inclusion of this deposition factor
necessitated a second equation which modeled the flux of material to the surface.
Common chemical engineering techniques for modeling mass transfer at a gas-solid or
gas-liquid interface were used.
The largest yearly input into the lakes was for chlorides (order of magnitude was
105 metric tons/yr.). The second largest input was total dissolved solids with the
same order of magnitude input as chlorides. Pesticide input into the Upper Great Lakes
from the atmosphere by dry deposition processes was negligible.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENlTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (Tins Report)
21. NO. OF PAGES
99
20. SECURITY CLASS (This page)
22. PRICE
EPA Form 2220-1 J9-73)
99
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A two year program leading to an Associate Degree in Air Pollution Control
Engineering Technology is offered at the Berks Campus of the Pennsylvania State
University. The graduate of this program is trained to be responsible for the
calibration, installation, and operation of air sampling and monitoring equipment.
Address requests for more information concerning the training programs to
the Director, Center for Air Environment Studies, 226 Fenske Laboratory, The
Pennsylvania State University, University Park, Pennsylvania 16802.
Publications Available
AIR POLLUTION TITLES, a current awareness publication, is a quick guide to
current literature and has some capacity as a retrospective searching tool. Air
Pollution Titles uses a computer-produced, Keyword-in-Context (KWIC), format to
provide a survey of current air pollution and related literature. During the year
over 1,000 journals are scanned for pertinent citations.
Subscriptions to Air Pollution Titles are available on a January-December
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Air Pollution Titles subscriptions, cumulative issues for past years are available.
INDEX TO AIR POLLUTION RESEARCH was published in July of 1966, 1967, and 1968.
Each Index included government sponsored research in the air pollution field;
results of a survey of air pollution research projects conducted by the industrial,
sustaining, and corporate members of the Air Pollution Control Association and
the American Industrial Hygiene Association; and research supported by other
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The Index utilizes the Keyword-in-Context (KWIC) format for rapid scanning of
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Beginning with the 1967 edition, a section containing citations of papers resulting
from research in progress is included. Copies are available.
A GUIDE TO AIR POLLUTION RESEARCH (PHS Publ. No. 981) was prepared in 1969 by
the Center for Air Environment Studies under contract to the National Air Pollution
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of Documents, Government Printing Office, Washington, D. C. 20402. The 1972
edition of the Guide was prepared by the Center under contract to the Office of
Air Programs of the Environmental Protection Agency and is also available from the
Superintendent of Documents.
HANDBOOK OF EFFECTS ASSESSMENT; VEGETATION DAMAGE was published in 1969.
It describes in detail the many various sources of pollution and the effect of these
pollutants on vegetation. Included are color slides depicting the characteristic
symptoms of plant damage. This publication went into its second printing in 1974
and is available through the Center for Air Environment Studies.
Further information regarding orders for the above publications may be
obtained from: Information Services, Center for Air Environment Studies, The
Pennsylvania State University, 226 Fenske Laboratory, University Park, Pennsylvania
16802. Lists of other Center for Air Environment Studies Publications are avail-
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