Air pollution control : an economic analysis of a Montana smelter's SO2 emissions
by Edward Barry Asmus
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY in Agricultural Economics
Montana State University
© Copyright by Edward Barry Asmus (1971)
Abstract:
This paper presents a model which is capable of estimating efficient emission control levels for a
particular smelter and which can be adapted to other emitters and other pollutants, The focus of the
analysis is the development and use of a methodology to empirically estimate the damage costs of
sulfur dioxide pollution.
The household damage costs are estimated using local weather data in a computer program along with
local population and housing data, and the value data from a St. Louis property value study by Ronald
Ridker. Agricultural damages from SO2 are found using a methodology to estimate pollution
concentration, the absorption rate of the plant, and the duration of fumigation. By combining the
estimates of pollution costs with control costs estimated by the Environmental Protection Agency and
E. Van Dornick, the total cost equation is written and the minimum point is found which indicates the
most efficient level of emission control under the basic assumptions and alternative assumptions using
sensitivity analysis.
The analysis indicates that zero emission control is optimal for the smelter studied. Although
significant damages are estimated, the high costs of control relative to estimated damages would
indicate that zero control is socially efficient.
72 906 300
AIR POLLUTION CONTROL: AN ECONOMIC ANALYSIS OF AMONTANA'SMELTER'S Sp EMISSIONS
by
EDWARD BARRY ASMUS
A thesis submitted to the Graduate Faculty in partial
fulfillment of the requirements for the degree
of
DOCTOR OF PHILOSOPHY
in
Agricultural Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
August, 1971
ill
ACKNOWLEDGMENTS
I
want to express my sincere thanks to Professor Richard Stroup
for his valuable guidance, detailed suggestions, and encouragement
throughout rhe writing of this thesis.
By sharing with me his philosophy
and approach to economics, he has made this past year a stimulating
and rewarding one.
Particular thanks are also due to Professor
Norman Dudley for his careful reading and useful comments and. to
Professor Eugene Sharp, who helped me through the biological aspects ■
•of this paper.
I owe a particular debt of gratitude to Professor -Richard J.
McConnen, Department Chairman, for his help on this thesis and
for the guidance and friendship exhibited during my years in graduate ..
school.Also deserving special thanks are Harlen Hames for his help in
computer programming, to Ben Wake who is head of Montana's Air
Pollution Control Office, to Stan Lane who is manager of the American
Smelting and Refining Company, and to fellow graduate students Diane
Reklis and Charles Hash.
Last but certainly not least, I express a deep.appreciation for
my wife Mandy, who had to relinquish countless hours of my time that
rightfully belonged to her.
Her encouragement during my years of
graduate school have been most important..
iv
T M L E OF CONTENTS
Chapter
I.
IT.
III.
' Page
INTRODUCTION............ ................ ..............' I
THE LITERATURE ON POLLUTION . . . . .
................
4
General Literature on Air Pollution .......... . . . . .
Economic Literature on Air Pollution..................
The Literature on Plant Injury by .Air Pollutants. . . .
4
7
14
AN ECONOMIC PRESENTATION: DIAGRAMMATICAL AND MATHE­
MATICAL ............................................ .. . ' 20
Diagrammatic. ...........
Mathematical.............. .. . . . . . .
IV.
STUDY AREA— ElUTTERS............ '.............. ..
Problem Area................
Plant Description ..........
V.
20
...........22.
. . . . . . .
. .
....
.......
24
24
26
ESTIMATING THE DAMAGE COSTS OF POLLUTION.................29
Household Damage Costs....................
' Damage Costs to Agriculture . ............
29
33
VI. ■' ESTIMATING THE CONTROL COSTS OF POLLUTION . ' '.......... 45
VII.
SENSITIVITY OF RESULTS TO PARAMETER CHANGES ............. 50
Comments bn Results .
. . . ... .. ... . ............. 56
Implications of Results ........
.......
58
VIII.
SUMMARY M D
CONCLUSIONS
. . .
.. . . . . .
Limitations of.Study. . . . . . . . . .
Future R e s earch.................
... . . . ... •
61
62
63
APPENDIX A. ' A NARRATriE DESCRIPTION OF THE COMPUTER PROGRAM' ., 66
Listing of Computer Program . ....... . ..
. ...... .
78
APPENDIX B . ■ A DESCRIPTION AND LISTING OF PROGRAM TO CALCULATE
■CROSS-WIND DISTANCE . '. . . '. . .' . ... . . . . .
83
V
TABIiE OF CONTENTS (continued)
Page
APPENDIX C.
ADJUSTING POLLUTION CONCENTRATION LEVELS........ 88
APPENDIX D.
GLOSSARY OF SYMBOLS USED IN THE P R O G R A M ........ 94
LITERATURE CITED ......................... ............... . . .
97
Vi
LIST OF TABLES
Table
Page
I
RELATIVE SENSITIVITY OF CULTIVATED AND NATIVE PLANTS
TO INJURY BY SULFUR DIOXIDE................................. 17
II
EMISSION FROM COMBUSTION AND PROCESS OPERATIONS, HELENA, '
EAST HELENA, HELENA VALLEY, MONTANA......................... 25
III
IV
V
VI
VII
VIII
ANNUAL HOUSEHOLD DAMAGE COSTS............ '......... ..
32
AVERAGE ANNUAL HOUSEHOLD DAMAGE COSTS AT. 6 DISCRETE
LEVELS OF CONTROL........................................... 32
AVERAGE ANNUAL DAMAGE COSTS TO ALFALFA AND BARLEY FOR
YEARS 1965-1969.......................
44
MARKET PRICES- OF ELEMENTAL SULFUR NEEDED TO FORCE CONTROL
COSTS TO ZERO GIVEN THREE RATES OF INTEREST USED TO CONVERT
CAPITAL COSTS TO ANNUAL COSTS.......... . . ............... ' 46
COST DATA FOR SULFUR EMISSION CONTROL. . . ............... 48
THE DISCRETE CASE CONTROL COSTS ESTIMATED BY EPC AND
E . VAN DORNICK ...".....
53
Appendix- Table
A-I
A-2
STABILITY CLASS AS A FUNCTION OF NET RADIATION AND WIND
SPEED. ■.................... • . .......................... 68
STABILITY CLASS AS A FUNCTION OF SOLAR RADIATION . . . . . .
70
vii
LIST OF FIGURES
Figure
■
■ Page
1
System D i a g r a m ..............
19
2
Control Costs, Damage Costs, and Emission Rates.............20
3
Total Costs. . .............
4
Total Costs................
21
5
Pollution Concentration Diagram..................
40
6
Estimating Pollution Concentration and Fumigation Duration
. ........................... 21
Appendix Figure
A-I
Generalized Flow Chart for the Computer Program..........
77
C-I
Spatial Distribution of Sulfation Measurements ..........
90
C-2
Spatial Distribution of Sulfation Measurements (July 1969X
91
C-3
Spatial Distribution of Sulfation Measurements (September
1969) .....................
52
C-4
An Iso-Error Spatial Distribution of Percentage Differences
Between Actual and Predicted Sulfation Measurements ■
(July-November 1969) . ... . . . . ....................... 93.
viii
ABSTRACT
This paper presents a model which is capable of estimating
efficient emission control levels for a particular smelter and which
can be adapted to other emitters and other pollutants, The focus of
the analysis is the.development and use of a methodology to empirically
estimate the damage costs of sulfur dioxide pollution..
The household damage costs are estimated using local weather data
in a computer program along with local population and housing data, and
the value data from a St. Louis property value study by Ronald Ridker.
Agricultural damages from SOg are found using a methodology to estimate
pollution concentration, the absorption rate of the plant, and the
duration of fumigation. By combining the estimates of pollution costs
with control costs estimated by the Environmental Protection Agency arid
E. Van Dornick, the total cost equation is written and the minimum
point is found which indicates the most efficient level of emission
control under the basic assumptions and alternative assumptions using'
sensitivity analysis.
The analysis indicates that zero emission control is optimal for
the smelter studied. Although significant damages are estimated, the
high costs of control relative to. estimated damages would indicate
that zero control is socially efficient.
CHAPTER I
INTRODUCTION
Air, the thin envelope of gases and particles- surrounding the
earth, is a resource whose quantity and quality play a significant
role in determining man's economic, social, and esthetic well-being.
Used as a sewer, the atmosphere has varying capabilities for waste
disposal.
If pollution emitters discharge their wastes with Iitt.].e 'cost
to thems e l v e s t h e quality of the atmosphere will deteriorate.
This
creates a problem,.that, demands increased attention.
In order to minimize.society's problem, both the costs of pollu­
tion control and the cost of pollution damage must be specified.
As
the following passages note, specifying these costs become a necessary
first step in making good pollution control decisions.
We must have a description of the damage per unit
of each object affected as a function of the intensity of
air pollution, all other factors that could cause such "
damage being held constant [48,p.15].
In sum, the positive and negative values (costs)
associated with external effects on environmental quality
are ordinarily difficult to gauge and some can never'be
measured with precision. Nevertheless, there are oppor­
tunities for research which should yield information useful
for more rational and effective management of environmental
quality [26,p.88].
Without benefit-cost calculations, we cannot deter­
mine the desirable amount of abatement [20,p.102].
The process of proceeding from criteria to clean air,
which might be termed air management, might be divided into
the various steps: I. Determine the [economic] effects
of various pollutant concentrations and exposure durations
on people, animals, plants,- and property [33 ,p. 214] .-
-
2
Everything worthwhile has a. cost.’ Whenever'you
think you are getting something for nothing, look again someone, somewhere, somehow is paying for it. .. . . The "
task of ecological economics is to figure Out how to
restructure the economic- system so that these hidden costs ■
will be brought out into the open, with the ■ultimate aim
that no one who benefits from the use of the environment
will be able to escape without paying in full [15,p.14].
It is the lack of information (on the costs of. pollu­
tion). that.is the crux of the matter. . . . I think you
will agree that there is no hope of estimating the
welfare damages of pollution by simply asking people
what they would pay to avoid them. I don't think- they
.•
know [13,pp.40,43].
This, study represents an attempt to. measure some of the individual,.
'property, and agricultural damages from sulfur dioxide pollution in
the Helena Valley cf Montana, connect these damage costs with the
appropriate costs of control, and by.answering the what and.bow
questions discussed in elementary economic textbooks,. indicate how
pollution costs could be minimized.
1.
"What" emission levels will minimize costs?
2.
"How", can resources be combined most efficiently to attain .
that level?
Sensitivity analysis will then be used to examine the economic,
importance of various assumptions, about the -parametric data.- Changing
'the parameter estimates with'in the "reasonable range" of each will
indicate ,.potential payoffs-to narrowing that range of-estimates for
.
■each parameter by appropriate research, subject to interaction effects
between parameter levels.. It will be demonstrated that without -better
3
information on.some of these physical and economic parameters, mistakes
will occur, the effects of which will vary from.minor to extremely
costly.
The level of these costs will depend oh the parameter in
question.
In this manner', researchers in each area can receive
guidance and, in the appropriate instances, support in concrete terms
for the contention that a proposed piece of research would be valuable
to society.
CHAPTER II
" THE LITERATURE ON AIR POLLUTION
General Literature on Air Pollution
Although receiving considerable recent attention, air pollution
is an enigma that has plagued man for more than 600 years.
Members
of the nobility petitioned Edward I concerning coal smoke in London
in 1300 A.D.
One hundred years later, Henry V passed a regulation
restricting the movement of coal into.the London area, particularly
to reduce air pollution [55].
A paper written in 1661 entitled, "Fumifugium", [17] caused such
public concern that the English Parliament appointed numerous
committees to appraise and recommend solutions to the problem.
In America, Spanish explorers in the sixteenth century, discovered
layers of smoke in the Los .Angeles area emanating from Indian camp­
fires.
Although not reaching dangerous proportions until: 1943 [6],
inversion layers' have continually plauged the Los. Angeles air basin.
Although public awareness was slow in coming, the study of
pollution problems and concern for the environment is growing.
The American Public Health Association [4] has recently prepared
a Guide to the Appraisal and Control of Air Pollution which includes a .
general discussion of the effects of air pollution,an estimation of
the quantities■of pollutants emitted into the atmosphere, meteoro­
logical aspects, detection■and measurement, and a general appraisal of
air pollution problems.
5
The National Air Pollution Control Association's' Abstract
Bulletin [39] provides one .survey; of the research being conducted
in this field.
The. research is categorized into 14 broad subject
fields, some of which include:
Emission Sources
The characteristics of specific classes of emission sources
including types, rates, and the industries involved.
Control Methods
The operating principles, design, operation, and efficiency o.f
equipment and methods of removing pollutants.
Measurement Methods.
■ The development, testing, and evaluation of pollutant determina­
tion methods and equipment.
Effects on Human Health
Medical and' epidemiological, studies.
Effects on Plants and Livestock.
Pollution.effects- on plants and livestock.
Effects on Materials .-'
Research'on the corrosion and deterioration .of physical materials
buildings, and structures.•
6
Economic Aspects •
.
.
Studies that relate and examine pollution damage costs and
pollution control costs.
Standards and CriteriaRecommended or adopted guides, criteria, and standards for
allowable emission limits or pollutant concentrations, air quality,
equipment characteristics, and fuels.
Other periodical guides to the air pollution literature include
Air Pollution Titles [3] , APCA Abstracts [2], and Air Pollution
Abstracts [1].
Important periodicals such as Environmental Pollution, The
Journal of the Aii Pollution Control Association and Environmental
Science and Technology publish an array of papers dealing with air
'
pollution.
.
The Natural Resources Journal and Land Economics
specialize in the.economics and sociology of environmental control,
while papers on the health aspects of air pollution occasionally
appear in the American Journal of Public Health, and the Archives of
Environmental Health..
Hagevick [23] has recently written an excellent book on air
pollution control. •.After a brief introduction examining the pollu^
tants responsible for the current.situation, he examines the economic,
political, and institutional issue's by applying them to a specific
airshed.
Through case studies of Los. .Angeles and New York City, a
I
basis is provided for integrating decision-making with the economist's
minimum-cost solution (Chapter III of this thesis develops this
concept), pointing out the strong as well as the weak decision­
making strategies.
Before good decisions can be made, estimates of
the total damages attributable to air pollution in the airshed at
various possible emission levels must be made.
The Report of the Air Conservation Commission resulted in a book
entitled. Air Conservation [14].
Authored by 12 leading authorities
from many fields of specialization, this book provides a wide ranging
view of air pollution, including meteorology,- pollutants and their
effects, the need for air conservation, pollution control, and the
socio-economic factors that accompany air pollution arid urban develop­
ment.
Because of its complexity, the authors outline the broad tasks
facing the scientific community, including basic and applied research
on pollutant interactions, effects, and control.
The task of govern­
ment would be one of supporting the appropriate research/ helping
gather the necessary information, enforcing pollution decisions, and
educating its citizens to create a broad public understanding of the problem. ■'
Economic Literature on Air. Pollution
Whenever the welfare of an economic unit (or units) is directly
affected by. the activities of another, externalities exist.
Air poilu
8
tion represents a classic example of an externality.
Because air
appears to the emitter as a free resource, it is overused.
Overuse
reduces efficiency in that receptors suffer more from damages than '
emitters will save, in not having to control their pollution.
Overuse
affects equity by forcing owners of air rights (unless all rights are
owned by emitters) to suffer damages without proper compensation.
Various possible solutions to the externality problem are examined
by Coase [10] and Mill [20] .
The possibilities include emission taxes.,
payments based on marginal pollution damages, flexible emission stan­
dards, zoned emission standards, prohibition ,of emissions, factor .
subsidies, and others.
Care must be taken to account for the' addi­
tional and informational costs associated with each proposed solution.
When external effects cause a misallocation of production, the
goal becomes one of accounting for all the benefits and costs flowing
from the economic activity being studiedv.
Treatments of benefit-cost analysis and its application to the
micro-economic theory.aspects of pollution control can be found in
Eckstein [16], Grosse [22] , Harberger [25] ,. Herfindahl and Kneese [27] ,
Brest and Turvey [46] , Steiner [58] , Wilson and Minnotte [74], Zerbe
[77], and Stroup [60].
These papers present the elements of a research
strategy for conceptualizing the problem, specifying the relationships
and variables necessary for making "changes in control decisions, and
applying empirical information to actual case study situations.
9
Prest and Turvey1s paper is perhaps the most comprehensive survey
of benefit-cost literature and it does provide an extensive' bibliog­
raphy.' Benefit-cost analysis, these authors note, is a way of setting
out the factors which need to be taken into account to make certain
economic choices.
Questions such as Which' costs and which benefits
are to be included in the analysis?
How are they to be valued?
At
what interest rate are they to be discounted? and What a.re the partic­
ular constraints applicable to the analysis? are a few of the'generalprinciples of benefit-cost analysis that are enumerated.
'Wide divergence of opinion-exists over the usefulness of.benefitcost analysis.
At one extreme is Hall's statement [24,p.173]:
We have begun to grope our way towards a practical concept
of economic planning which may prove in a few. years' time
to be as revolutionary in its policy implications as was
the Keynesian revolution in economics thirty years ago.
It also originated, many years ago, with a Cambridge
economist: Keynes' contemporary Pigou. • It is the
concept of social costs and social benefits. . . . This
leads to the revolutionary concept that we can actually
. add up the social costs■and benefits, in money terms, by
asking what value people would themselves put.on them.
. We can then express them as a rate of return on capital,
as an ordinary capitalist would, and so determine our
investment rationally, from the point of the community
as a whole, just as the capitalist can now do from his.,
private point of view.
Another statement indicating an opposing view is by Smithies
[56,pp.344-345], which states:
The foregoing discussion [on benefit-cost analysis] leads
to two major'conclusions: First, judgment plays such an
important role in the estimation of benefit-cost ratios ■
10
that little significance can be attached to the precise
numerical results obtained. . . . Second, competition is
likely to drive the agencies towards increasingly optimis­
tic estimates; and far from resolving the organizational
difficulties, computation of benefit-cost ratios may in
fact make them worse.
Brest and Turvey [46] take a position between the two extremes,
recognizing that even if benefit-cost analysis cannot give right
answers, it can play the negative role of screening projects and .
rejecting those answers which are less promising.
They.argue the
case for benefit-cost analysis is strengthened if its limitations
are openly recognized and emphasized.
Many of the estimates of the damage costs of smoke and air pollu­
tion from the turn of the twentieth century until 1950 can be found
in papers by Bennet [7], Flagg [18] , Gibson [19] , Johnson [31,34] ,
Obermeyer [41], Parsons [43,44,45], Bolleston [50], Shaw and Owens'
[53], Simon [54,57] , Mellon Institute ■[63,72]-, Uhlig [75], and the
Beaver Committee [21].
Basically, these articles represent rough estimates of. the smoke
damages suffered by various cities and countries.
Annual smoke
damages (1939) to Indianapolis, for example, were estimated to be
$15 million [31], while Milwaukee suffered $10 million [34].
Simon
[57] estimated the annual smoke damages (1946) to Great Britain to '
be $50 million.
S . B. Flagg [18]. added an interesting twist to the
11
damage cost estimates cited by other authors.
He viewed smoke in terms
of damage to emitters, rather than receptors.. Because smoke indicates
inefficiency in fuel consumption, half-burnt coal, and dividends that
should be distributed to stockholders, he called for an improved
design of furnaces and mechanical equipment.
The incentives for
improving "control equipment" would come from a strict enforcement of
statutes controlling emissions.
Research in the last■decade on the damage costs of air pollution
would include Mchelson and Tourin [35,36,37], Ridker [48], Ridker
and Henning [49], Aiiderson and Crocker [5], Wilson and Minnotue [74],
and Stroup [50].
Michelson and Tourin [37] used questionnaires to estimate the
added household expenditures of cleaning resulting from•suspended '
particulates.
Although interesting, their .study suffers from the
problems associated with questionnaire techniques and the difficult
question of how to evaluate the damages of pollution which were not
paid for in the form of extra cleaning, laundry, painting, etc.
Ridker, in his book, Economic Costs of Air Pollution [48], used
a number of approaches in an attempt to measure air pollution
damages.. In an effort to link the incidence of disease with air
pollution, he examined correlations between polluted areas and
premature deaths, treatment, and absenteeism.
The costs would be .
the value of medical treatment and foregone income. ' His study
12
revealed, no conclusive evidence using this method.
Another approach
was one similar to Michelson and Tourin's questionnaire determining .
soiling costs.
By comparing the laundry, dry cleaning, and other
costs associated with pollution of different cities, Ridker hoped to
capture an amount people actually did pay for living in a polluted
area.
Here again, the results were indeterminate.
Ridker's third
approach, and. the one whose results are used in this thesis, investi­
gated the differences in property values resulting from polluted "
versus nonpolluted;s i t u a t i o n s U s i n g a cross-section study of
St. Louis property values, Ridker was able to explain 92 percent of
the variation in property values with a regression equation.
Using
sound econometric analysis, he showed that St. Louis residents were
2
willing to pay about $245 more for a. house for each .25 mgSO^/lQO cm /
day avoided.
IIere, ..a single market price reflects what people were
willing to pay to get away from pollution where they lived.
Anderson and Crocker's study of air pollution.and residential
real estate values also proceeds on the basis that a‘ substantial portion
of air pollution damages to artifacts and organisms is capitalized
negatively into the value of lcind.
They first develop 'a qualitative-
model to determine residential property values which include charac­
teristics of both households and properties as explanatory, variables.Basically, they used the postulates of Lancaster's development of
consumer behavior theory.
Using log linear forms estimated by
13
Ordinary Least Squares, instead of a linear fit which appeared to be
best for Ridker, they showed that marginal property values were
reduced from $300 to $700 per property because of pollution..
I
Anderson and Crocker used particulates as an explanatory variable,
whereas Ridker reported unsatisfactory results using particulates,
and they were critical of Ridker's use of 1960 Census Data coupled
with pollution data gathered in 1963 and 1964.
This, they argued,
could result in biased estimates.
Wilson and Minnotte1s study, of soiling caused by stationary
sources of particulate emissions in the Washington,.-D. C., area [74]
uses benefit-cost analysis to make.pollution control recommendations
By combining a diffusion model with Michelson's data on soiling
damages, they calculate a benefit figure, for each control increment.
Costs of control are then subtracted from the calculated benefits,
yielding a net benefit calculation for every control level.
They
conclude that benefit-cost analysis can be used in making emission
control decisions, and with better input data can be used to estab­
lish emission levels for all types of pollutants.
They warn that
their model can be used only for illustrative purposes, as it deals
with only one type, of pollutant and one geographic area.
I
3
Marginal damages refer to an !additional 10 mg/m /day of sus­
pended particulates plus an additional .1 mg SO^/lOO cm2/day 0f
sulfation.
14
Stroup develops a model [60] which is capable of locating optimal
control levels for any number of air pollution sources under the juris­
diction of a control authority.
The model is then used to analyze
various control strategies, detailing the.strengths and weaknesses
of each.
By applying the model to a particular copper smelter, it is
demonstrated that several million dollars in annual damages can b e .
avoided at optimal control strategies-..
Many developments in this paper
are based on Stroup's methodology.
The Literature on Plant Injury by Air Pollutants
Scientific attention was directed to the problem of pollutant
injury to plants as far back as 1871, when Stockhardt [59] wrote
about smoke damage to German forests and whe n .Cameron [9] examined
the damage to vegetation in London.
Research on sulfur dioxide damage
to plants in this country began at the turn of,the century [64],
with Swain [62] reviewing the outstanding periodic developments.
Another good review of the effects of pollution damage to plants, is
Crocker [12] who reviewed much of the early work on sulfur dioxide
and other pollutants by the Boyce Thompson. Institute.
A publication
by the National Research Council of Canada [40] examines much of the
sulfur dioxide research in connection with smelter injury to plants.
Also, an excellent comprehensive review of the.entire problem of air
pollution effects on vegetation is given by Thomas [64] and updated
by him in 1961 [65] .
15
It has been established in the literature [42,66] that sulfur
dioxide injury to vegetation follows the relationship
(C - C0)t = K.
(2-1)
In this equation, C is the concentration of sulfur dioxide
(parts per. million— ppm) which can cause traces of injury to alfalfa
in t hours, and
and K are constants.
Under conditions of maximum-
sensitivity, Cq was found to be 0.33 and K equalled 0.92.
That is,
given a concentration of 1.25 ppm, incipient markings can be found
on alfalfa in one hour.
Notice that a concentration of 0.33 ppm can
be endured indefinitely without causing injury.
Thomas and Hill [67] generalized the preceding equation, calcu­
lating equations for various amounts of leaf destruction at maximum
sensitivity for alfalfa as .follows:
t(C - 0.24) = 0.94
Incipient Injury
t(C - 1.4) = 2.1
50% Leaf Destruction
t(C - 2.6) = 3.2
100%.Leaf Destruction
(2-2)
From these equations, concentration levels of 1.2, 3.5, and 5.8
ppm would, in one hour, destroy traces, half, or all of the leaf ■
area of the crop, respectively.
The different species of plants vary considerably in their
susceptibility to injury by sulfur dioxide.
.0'Gara-worked .out factors
for about 300 species and varieties of plants, giving their sensitivity
16
relative to alfalfa as unity.' These have been published and. some are
listed in Table I [66].
Environmental factors have a significant effect on predisposing
vegetation to SO 9 injury [32,52,66].
Relative humidity is perhaps
the most important' external factor affecting a plant's susceptibility,
High relative humidity favors the opening of the. stomata and this
allows a high absorption rate of the plant.
Soil moisture is another
important environmental factor, causing plants to become extremely
resistant when moisture approaches the wilting point.
VJhen the soil
moisture is very low, the leaf stomata tend to close in order to
guard against excess transpiration losses.
When moisture is adequate
for growth, however, .variations within wide limits do not appreciably
affect susceptibility.
The importance of light intensity and its
relation to the response of a plant has been assessed differently
by various investigators.
Swain [62] considers it to be a major
factor, while Holmes [29] and Setterstrom [52] believe it to be of
minor importance.
Considering atmospheric temperature, Swain [61]
concludes that a plant is more resistant to sulfur dioxide at
temperatures of 5 0C and below, with little,-variation above 5°C,
Wells
[73] agrees with this basic conclusion.
Brisley and Jones [8], Hill and Thomas [28] , Holmes, Franklin,
and Gould [29], National Research Council of Canada [40], and Thomas
and Hendricks [66] found that reduction in.yield is proportional to
17
TABLE I .
RELATIVE-SENSITIVITY OF CULTIVATED AND NATIVE PLANTS TO.
INJURY BY SULFUR DIOXIDE (Determined by O'Gara).
Sensitive________ :_____ Intermediate____ :_____ ■ Resistant
____ ■
________
Cultivated Plants
___ ' -_____
More probable factors based on later experience.
O
I
CO
to
Io-
CO
b/
1.6a
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.9
2.0
2.1
2.1
2.1
2.1
2.1
2.2
2.2
2.2
2.3
LO
a/
Gladiolus(1.1-4. 0)b 2. Ga
Horse-radish
2.6
2.6
Sweet cherry
Canna
2.6
Rose
2 . 8 -4.3
3.0
Potato (Irish)
3.2
Castcrbean
3.3
Maple
3.3
Boxelder
3.3
Wisteria
3.5
Mock orange
3.5
Honeysuckle
3.7
Hibiscus
3.8
Virginia creeper
3.8
Onion
4.0
Lilac
4.0.
Corn
Cucumber
4.2
5.2
Gourd
Chrysanthemum
-7.3
5.8
Snowball
6.4
2.3 .Celery
6.5-6.9'
2.3 •Citrus
2.3 Cantaloupe
7.7
2.3
(muskmelon)
7.8
2.3 Arbor vitae
12.0
2.4 Currant blossom
14.0
2.4 Live oak
15.0
2.4 Privet
2.5 C o m silks and
.2.5
21.0
tassels
25.0
Apple blossoms
87.0
Apple buds
Factors of relative resistance compared with alfalfa as unity.
Alfalfa
I. pa Cauliflower
Barley
1.0 Parsley
1.0 Sugar Beet
Endive
1.0 Sweet William
Cotton
Four o'clock
1.1 Aster
Cosmos
1.1 Tomato (1.3-1. 7)b
Rhubarb
1.1 Eggplant
Sweet pea
1.1 Parsnip
1.2 Apple
Radish
1.2 Catalpa
Verbena
.
1.2 Cabbage
Lettuce
1.2 Hollyhock
Sweet potato
1,2 Peas
Spinach
.
Bean
1.1--1.5 Gooseberry
1.3 Zinnia (1.2)b
Broccoli
Brussels sprouts 1.3 Marigold
1.3 Hydrangea
Pumpkin
1.3 Leek
Table beet
1.3 Begonia.
Oats
Bachelor's-button 1.4 Rye (l.O)b
1.4 Grape
Clover
■
Squash(I.1-1.4)b 1.4 Linden.
1.5 . Peach
Carrot
1.5 Apricot
Swiss chard
1.5. Kale
Turnip
1.5 Nasturtium
Wheat
Elm
Birch
Iris '
Plum
Poplar • •
18
the amount of leaf area destroyed.
The following equation may•then
be used when the constants have been determined.
Y = a - bX
where:
(2-3)
Y = the yield;
X = the percentage leaf area destroyed;
a = a constant approximately 100 percent: and
b = the slopes
The question frequently arises as to how far conclusions drawn
from the results of experimental fumigations under cabinets may be
applied to crop plants growing under natural field conditions in a
smelter zone.
Katz [32,p.2458] found that "the results demonstrated
conclusively that the response of crop plants to sulfur dioxide under
natural conditions is not essentially different from that found in .
fumigation'experiments under cabinets."
The issue at hand is not just one of specifying effects, but
actually determining whether these effects have any economic impor- '
tance.
Regardless of the biochemical mechanisms involved, or the
striking damage appearing on colored photographsthe essence.of the
analysis must be an estimate of the magnitude of losses' suffered by
society.
Chapter III,-presents a methodology and Chapters V and VI
use it to empirically, investigate :the damages■from sulfur dioxide
pollution by a.specific smelter.
,
CHAPTER III
AN ECONOMIC PRESENTATION:
Dirty air is expensive.
sive.
DIAGRAMMATICAL AND MATHEMATICAL
Unfortunately, clean air is also expen­
The resulting trade-off is one between the size of control
costs and the size of pollution damage costs.
These costs are the
focus of the following economic analysis and tneir subsequent measure­
ment the key to sound decisions of control.
The monev and prices used to measure these costs are useful as a
unit of account and a common denominator.
The focus of interest is
not on dollars and prices themselves, but rather their role as a yard­
stick in measuring the problems, opportunities, and choices or people.
The price system in a market economy is a system of social accounting
which (in the absence of externalities) keeps track of all the benefits
and costs of an economic activity.
Diagrammatic
A simplified view of the physical problem is shown in Figure I,
and its resultant economic aspects in Figures 2, 3, and 4.
Pollution (emissions) vented to the atmosphere (transport mechanism)
yield levels of ambient air (air quality) which cause some degree of
economic losses (damages) as shown in Figure I.
Transport Mechanism
Emissions
▼
Figure I.
20
If society wants a certain standard of air quality maintained,
such as point A in Figure 2, control costs of CC^ must be incurred.
Given CC^ of control, quantity
costs.
of emissions would cause DC^ damage
Damage costs can then be thought of as a function of emissions
(or an air quality standard).
By combining the southeast and southwest quadrants of Figure 2,
the damage and control costs of various levels of emissions can be
represented by Figure 3.
Adding damage costs to control costs yields
a total cost curve for varying emission levels pictured in Figure 4.
TC^ and E^ represent minimum total cost at an optimum level of
emissions.
At this point, E^, the marginal costs of control equal the
marginal costs of pollution damage.
Air Quality Standard
Figure 2.
21
Total Costs
Damage Costs + Control Costs
Control
Cos ts
Damage
Costs
Emissions
Figure 3.
Figure 4.
22
Mathematical
Economic analysis indicates that marginal damage costs of pollu­
tion must equal the marginal costs of pollution control in order to
achieve minimum cost quality objectives.
Specifying both as a func­
tion of emissions,
DCi = d (E)
(3-1)
and
CC1 = c. (E)
] . 3
where:
(3-2)
th.
,
DC^ = cost of the i
type of pollution damage, i = I, n
CCj= cost of the
type of control, j = 1, m; and
E = emissions.
The total cost to society, TC, become the sum of equations (3-1) and
(3-2) :
TC = DC
.
1
+ DC
2
+ ... + DC + CC1 .+ CCn + ...
n
I
2
CC ■ =
m
(3-3)
d (E) + d (E) + ... + d (E) + C1 (E) + c„(E) + .. . + Cm (E) ■
I
2
■
n
x. '
2
111
Minimizing TC with respect to emissions produces the minimum cost
to society and the optimum air quality objectives.'The necessary first-order, conditions are '
23
--■^ E) =
(E) + ... + dn (E) + C1 (E)- + .
+ c (E) = O
in
(3-4).
and the sufficient second-order conditions are
2
d TCE
> 0
(3-5)
To satisfy the necessary conditions., the summation of the. marginal
costs of pollution control and damages must equal zero, or likewise,
that the marginal costs of pollution damages equal the marginal costs
of pollution.control. .That is.
Zdi (E) ■
(P)
dE
4
dE
L
±
I
dE^
so that
•I
i
-C (E)
= I — a=—
g
(3-6)
The. foi lowing chapters represent an empirical attempt to combine
the control costs of pollution with pollution damage costs to.enable
decision makers to make marginal evaluations of emission control. ■
CHAPTER IV
STUDY AREA—rEMITTERS
■ Problem Area
The Helena Valley in Montana has an air pollution problem (Table II)
Located between the Big Belt Mountains on the north and east and the
main chain of the continental divide on the west and south, the. valley
houses approximately 30,006 residents .who are subjected to various ■
degrees of pollution.
In particular...the■American Smelting and
Refining Company operates a custom lead smelter, emitting- quantities of
sulfur dioxide ,to the- atmosphererwhich substantially exceed the Airibient.
Air Quality.Standards' set for Montana and are in excess of the most
.lenient air standards set anywhere in the nation [3.8 ,p. 3] .
Government
studies [38] indicate that concentrations of sulftir dioxide in excess
of 15 ppm ,(parts' per million) have been recorded near the plant,
causing considerable damage to commercial .crops and other vegetation..
Basically, sulfur dioxide is a. colorless gas that can.be.tasted
at concentration levels of .3 ppm to I ppm and can.cause pungent, irri­
tating odors at concentration levels above 3 p p m . Once in the
atmosphere, sulfur dioxide is partly converted to sulfur'trioxide or
to sulfuric acid, by photochemical or catalytic processes.. .In the ■■
presence of moisture,'sulfur trioxide is immediately converted to
. ,
sulfuric acid.
-
'
'•
. . .
■ .
.
.
.
-
'
The'rate -at which sulfur dioxide oxidizes in the
atmosphere depends■on factors such as residence time, amount of
.,
'.
TABLE II. EMISSION FROM COMBUSTION M D PROCESS OPERATIONS, HELENA, EAST HELENA, HELENA
VALLEY / M O N T M A (Tons Per Day Averaged Over the Year) .*
Pollutant
Sulfur Dioxide
TotalEmissions
198.03
58.65
Carbon Monoxide
Source and Amount of Emissions
Industrial and Commercial
■Domestic
Fuel
Process
Fuel
Gas Wastes Emissions Oil
Gas Wastes
Coal ' Oil
1.68
.001
.001
.2
.001
.001
.005
0.5
5.26
.07
.001
Neg
.03
Oxides of
Nitrogen (NO3)
5.51
1.40
.001
.30
.06
22.72
290.17
5,70
.03
.09,
Particulate
.TOTAL
.
.010
.001
2.0
.001
.001
.001
Neg
.002
.001
Neg
Unknown
16.0
.02
0.21 ■O.lO
54.0
0.15
.11
4.7
0.35
.38
.22
2.6
0.55
.03
.31
1.8
.30
.26
*Source: Montana State Department of Health', Divisioh of Air Pollution Control and
Industrial Hygience, "A Study of Air Pollution in the Helena-East Helena Area,"
October 1965-October 1968, p. 10.
25
Hydrocarbons
196.0
Vehicular
Diesel
Gas
Fuel
26
.
moisture present, and the intensity and duration of sunlight.
The
presence of catalytic material, hydrocarbons, nitrogen oxides, and
sorptive and alkaline materials also affect the oxidation process [70].
Plane Description
The American Smelting and defining Company's smelter was built in
1885 and has vented to the atmosphere all by-product sulfur dioxide
since that time.
A brief description of the plant's operation is
:
included here.
All incoming shipnenus of lead concentrates are sampled and deter­
mined for sulfur content.
After being mixed with zinc residues, lime­
stone and siliceous ere, the concentrate is pelletized to give a charge
conforming to metallurgical requirements.
After the pelletized charge
is delivered to the sintering plant, it. is mixed with return sinter
and fed to one of four Dv/ight Lloyd's sintering machines where the
sulfur content is reduced through oxidation and the charge is agglom­
erated into a product known as sinter.
The sinter is then screened
for removal of fines, which are in turn crushed and used as return
sinter for blending with more fresh charge coming from the charge
preparation system.
Once delivered to the blast furnace, the gases
from the sinter are conducted through flues to the electrostatic
precipitator plant (ESP) where the dust in gases is. largely removed
and the cleaned gases still containing sulfur dioxides are discharged
up a 400-foot stack.
27
■ Finished sinter .and coke are- then charged in one'of two blast
furnaces where they are melted and reacted to form lead bullion and
slag.
The molten products flow but of the furnace through a patented
tapper and are separated by gravity in a brick-lined settler.
The
slag overflows the settler into slag pots for delivery co Anaconda's
zinc fuming plant while the lead bullion is tapped into other pots
for transfer'to the dressing plant. ,.Dust from the gases of the blast
furnace is filtered through large woolen bags in the baghouse.
Cleaned
gases are then vented to the atmosphere through three baghouse stacks."*
The two sources of air pollution.produced by the American
Smelting and Refining C o m p a n y t h e n , are the effluent gases from the
ESP plant (DSps of total) and the.gases from the baghouse (2% of total) .
The other source of SO^ pollution in the area is the Anaconda
Company's zinc 'fuming plane.
This, slag-treating plant processes the
waste slag of the American Smelting and Refining Company to make a
zinc cxide product.
The process involves charging molten slag to a
fuming furnace where a 2 2 0 0 °E temperature causes the zinc and lead to
I
■
Plant visit to the American Smelting and Refinery Company in
East Helena, Montana on October 15, 1969... Attending .were: Stanley
Lane, Plant Manager; K . W. Nelson,- Director, Department of Environ­
mental Science; Carl Thompson, Public .Relations; Ben Wake, Director,
Division of Air Pollution Control, Montana; members of the National
Air Pollution Control Association.,
28
fume off and form zinc oxide and lead oxide.
Furnace gases are then
cooled before passing into a large radiant cooler.
Zinc oxide and
lead oxide in the cooled gases are then removed by a fabric filter
equipped with Dacron bags before the gases still containing sulfur■
dioxide are discharged into the atmosphere.
The gases from these five
stacks, 100 feet high, account for approximately 2 percent of the SO^
in the area.
CHAPTER VESTIMATING THE DAMAGE COSTS OF POLLUTION
Household Damage Costs
The area surrounding the stack was divided into 540 sectors corre­
sponding to each of the 36 wind directions, each sector I mile deep,
out to 15 miles discant from the polluting stack (15 x 36 .= 540) .
The number of houses in each sector were found by using Highway
Survey maps, which indicate the location of each house, and the'1970
U. S. Census of Population, for locating the number of bouses in
Helena.
I
The additions to sulfation loadings in each sector were calculated
using local weather data (three hourly observations) and a dispersion
equation.
Additions to pollution concentration (sulfation) resulting
from stack emissions were calculated every 3 hours and summed on an
2
annual basis for the years 1965-1969.
The basic dispersion equation"
3
used in the computer model^ follows the form..:
Chi =
cxp[.5 (HZaz)1
2I
(5-1)
■
z
1
Bob Keck,,Highway Planning Survey Superintendent, and his crew of
engineers- deserve.speed al thanks for their efforts.■
2
•Mr. Bruce Turner, Air Pollution Control Office, Durham,.North
Carolina, communicated this equation to. me in a telephone'conversation
November 5, 1970 (see {71,p.38]).
3
See- Appendix A for description of computer model.
30
where: Chi = pollution concentration;.
Q = emissions (2,772 grams at zero control) ;
X = distance from stack in meters;
U = wind speed in meters per second;
o
= vertical dispersion coefficient, a function of downwind
distance and atmospheric stability; and
H = effective stack height in meters.
The computer model's predicted sulfation measurements were tested
by comparing them with lead peroxide candle sulfation measurements
taken by the Federal Government
4
in a study conducted June through
November 1969, in East Helena, Montana.
The lead peroxide candle is a
widely used technique used for determining a sulfation rate.
Although
it provides no indication of short-term fluctuations it can give
reasonable indications of sulfur dioxide concentrations for periods o f '
one month duration [55,p.103].
By comparing the'lead peroxide candles to the computer-model's
predictions, it was found the model underpredicted sulfation concentra­
tions by about. 15 percent (arithmetic mean) from I to 8 . miles distance
from the stack.^
Government-measurements of.sulfation did not.exceed
.8 miles from the polluting stack. .
—-T-—
Title of project:
Helena Valley, Montana ,. Area Environmental
Pollution Study. Principal investigators: ,The National Air Pollution
.Control Administration and the Montana Department, of■Health.
5
See Appendix: C for a discussion of how these values were'deter­
mined.
31
The damage costs of pollution to households were found, then,
using a dispersion model to estimate pollution concentration (sulfation)
in each sector, the relative decreases in property value which people
were willing to pay for increased sulfation as determined by Ridker's
study,
G
where calculated damages to households were found by Ridker
to be directly proportional to pollution concentration, and the number
of houses in each sector. ■Sn. interest rate of 6 percent was used to
convert present value to annual costs.
Damage
costs, then, follow the form:
DC = XiHiRB '
where:
X±
(5-2) ;
the increment of pollution concentration from the large
stack (annual average) in the i*-*1 sector with no control;
. H , = the number of dwellings in the It*1 sector;
i
R = the annual damage■per unit of pollution concentration
per dwelling (Ridker)U and
E = the proportion of generated pollutants which are emitted..
Table III and IV present.the results.
See Chapner II, where it was noted, that Ridker found that peopl|
did pay approximately $245 more for a house for each ;25 mgSO /100 cm /
day (annual, average sulfation) avoided in St. Louis in I960..
/7The use of Ridker's value data is virtually a necessity,as no
other data, comprehensive- in scope of damages and considering SO^ '
specifically, is currently available. .
32
TABIE III.
ANNUAL HOUSEHOLD DAMAGE COSTS.(100% Emissions).
Year
-
Household Damage Cos ts
a■
„ ''b .'
1965
31,922
22,302
1966
30 ,,772
19,929
1967
33,720
24,260
1968
33,570
19,946
1969
.32,600
21,200
■
. .
■
^Calculated costs stemming from a sulfation rate adjusted
to empirical data . Figure C--4 in Appendix C indicates the adjustments.
Ij
Calculated costs stemming from an unadjusted model.
TABIE IV.
AVERAGE ANNUAL HOUSEHOLD DAMAGE COSTS AT 6 DISCRETE LEVELS
OF. CONTROL (100% Emissions).
Control Level
•Percent ■
45
78.
88
90
93
99.4
Household Damage. Costs
Dollars
■
17,220.
4,270
- 3,046
• 2,321
1,347
,
1.86
Calculated, costs stemming from a sulfation rate adjusted to
empirical data. 'Figure Cr-4 in Appendix. C indicates the adjustments.
33
Damage ..Costs to Agriculture
■ The following discussion describes the procedures by which damages
(yield reduction) to alfalfa and barley is calculated. . A: basic oat­
line is included to acquaint the reader with the order of terms which
follow»
Basic Outline
I.
Yield reduction is a function of leaf damage.
A.
Leaf damage is a function 'of the absorption, rate of the
■plant, A; concentration level of pollutant, C; and
duration Lof fumigation, T .
a.
A is a function, of light, intensity,'; soil moisture,
temperature, and relative humidity.
b.
C is calculated using a dispersion equation that
includes, emissions from the .stack: and effective
stack height as constants.
Variables include .
horizontal and vertical dispersion coefficients
■ which depend on stability conditions and downwind
distance from the source; windspeed and a cross-wind .
distance variable y which depends on changes in wind
•• direction.
•c.
T. is a variable time interval over %hlch C- is .
constant.
34
Recalling from Chapter II that reduction in yield is proportional
to the amount of leaf'area destroyed.
YR = f (LD)
(5-3)
where: .
■ YR = yield reduction;
LD = leaf damage.
.
An equation was formulated to predict leaf damage from the work of
Thomas and Hill (67 ,p.299-300) which follows the form:
TCA ~ 610 - 155T
14.0 + 15.4T
where:
(5-4)
LD - leaf damage;
T = time (duration of fumigation);
C = concentration level of pollutant; and
A - absorption rate of the plant.
Procedures to estimate the absorption rate of the plant, the concentra­
tion level of p o l l u t a n t a n d the duration of fumigation are discussed
in turn.
Absorption Rate of the Plant
The absorption rate' of the plant ■depends on a number of environ­
mental factors, including light.intensity, soil moisture, temperature,
and relative humidity.
The model formulated in this study assumed-
damage to plants would only take place in daylight, hours, adequate
35
soil moisture, and. daytime temperatures above 40°F.
When these condi­
tions are favorable for damage, relative humidity becomes the crucial
variable of plant susceptibility to sulfur dioxide.
O 1Gara [42]
recognized the importance of relative humidity by specifying a '
quadratic equation which gave the relative sensitivity of plants at
different air humidifies.
Hendricks and Hill [6 8 ].
TABLE IV.
This equation was confirmed by Thomas,
Table IV gives solutions to the equation.*
RELATIVE SENSITIVITY OF PLANTS TO INJURY BY SULFUR DIOXIDF.
AT DIFFERENT ATMOSPHERIC RELATIVE. HUMIDITIES.*
Relative Hunudity
Percent
Percent
100
100
80
60
50
40
30
89
77
69
54
31
18
13
• 20
10
0
*Source:
..
Relative Sensitivity
■
10
O 1Garaf P. J . , "Relative Sensitivity of Cultivated and •
Native Plants to Injury by Sulfur Dioxide," Magii, et al.
,(Eds.) , Air Pollution Handbook, 1956.. . .
The variable A, then, becomes a measure of the absorptive rate per
unit (dry) weight of the leaves and is mathematically independent of
the duration and intensity of fumigation.
The data collected by..
Thomas and Hill revealed that A ranged from a minimum of 30 to.a
36
maximum of 650 in their different daylight experiments-.
The dimensions.■
of A were so chosen that when duration;of fumigation was expressed in
hours and concentration of SO^ in the air by parts per million by
volume, the absorption was given as parts per million of the dry leaf'
tissue [67,p.302].
Using 100 percent relative humidity as repre­
senting maximum sensitivity of plants' to injury,-' the absorption rate. .
was estimated by multiplying relative'humidity by 650, i.e., a relative humidity of 100 percent' = '1 .0 -
Dcllution Concentration and Fumigation 'Duration*
7
Calculating■pollution concentration (C) and fumigation .duration
(T) for a receptor field in a given wind direction required.a "disper­
sion model Which would reflect varying pollution concentration^ with
changes•in wind direction.
As wind.changed from its initial direction,
the center of'the plume would meve away from the receiving field and
the field would suffer, smaller, concentration levels of.pollution.,
The .
7
dispersion model used was of the form:
C - — ■&.
TTO- O
■ eyp[-.-5(y/c )2]exp;[-.5 (H/a )2]
U
Y
. (5-5)
6
From. U . .S. Department,of Health ,-'Education and Welfare,. Public
Health Service, Workbook'of Atmospheric. Dispersion Estimates,•Pub.
No. 999-AP-26, Revised 1969, p. 7.
37
where:
C = concentration level of pollutant;
Q = emissions;
ir = 3.14159;
a
^
= horizontal dispersion coefficient, a function of downwind
distance and stability;
.#2 = vertical dispersion coefficient, a function of downwind
distance and stability;
U =-: wind speed;
H = effective stack height; and'
y = cross-wind distance (distance.in meters from plume centerline) .
Cross-wind distance, y, reflects the distance of plirme centerline from a receptor field, where increasing, distance results in. a
decreasing pollution concentration. '■By calculating y and relating it
to a time interval, pollution concentration and fumigation duration
could then be estimated.
A computer program was written.(see Appendix B) .which Would esti­
mate cross-wind distance y resulting 'from changes in wind direction.
By using the formula for arc length,
AL -
(5-6)
180
where: AL = arc length in meters;
TT = 3.14159;
r '= distance in meters from pollution emitter to receptor
field; and
38
0 = the difference between original wind direction in degrees
and the new wind direction in degrees..
the arc length (cross-wind distance = y) could be found for a change in
wind direction (6 °).
■
Assume, for example, the receptor field to be I ltdIe from the
polluting stack and in the 90° wind direction.
If the wind blew in
the 90° direction continuously, the given field would receive centerline plume concentrations.
The cross-wind distance variable y in the
dispersion model would, be assigned, the Valua zero and a pollution
concentration would be calculated using the simplified dispersion
model
c =
y z
e^ 1- 5 tozoZ'21
.
<5-7>
If, however, the field was fumigated half the time by a wind in the
95° direction, che field would suffer less than center plume line
concentration levels, and equation (5-6) used in Appendix B would, be ■
used to calculate y for use in dispersion equation (5-5).
■
A Rustrak recorder was used to provide continuous wind direction
data which was collected in Bozeman by the meteorologists, at Montana
State University.
Employing sensitive graph paper moving an inch an .
hour, the recorder indicates .wind direction every 2 seconds'.
Wind
speed in mph.was averaged for each hour so that a constant windspeed was thus assumed for.each of.the 1,800 wind directions for that
39
hour.
Each hour of data was then partitioned using the arbitrary rule
of minutes it takes for the wind to move one-half mile.
Wind direction data of wind speeds equalling 5 miles per hour,
for example, were partitioned into 6 -minuce intervals (the time it
takes for wind moving at that velocity to move one-half mile); 6 miles
per hour into 5-minute intervals; and so on to wind speeds' of 12 miles
per hour into 2.5-minute intervals.
If the wind speed was 5 miles per
hour, the hour's wind direction data were partitioned into 10 intervals
with ISO wind directions in each interval.
averaged for each interval.
Wind .direction was then
8
*
Ar: array of the above averages was then obtained for each wind
speed representing wind direction in degrees.
For example, 280°, 278°,
272° ... for a wind speed of 5 miles per hour indicated a wind direc­
tion of 280° for 6 minutes, 278° for 6 minutes,. 272° for 6 minutes, and
so on for the remainder of the data for that hour.
Using these wind
direction data for each wind speed in a computer program (see Appendix
B) produced estimates of the cross-wind distance, y, for each of the
time intervals -
Pollution concentration was then calculated for that
dWind speed of less than 4 miles per hour and greater than 12
miles per hour were omitted. Basically, wind speeds of less than 4.
miles per hour exhibited such variability that a receptor field wouli
seldom receive fumigation durations sufficient enough to cause plant,
damage. Wind speeds of greater than- 12 miles per hour, on the other
hand, would not produce high-enough levels.of pollution concentration
to cause plant injury. -Exceptions will be discussed .belovj.
40
particular wind speed for each 1 -mile sector from the polluting stack.
This was then repeated for each of three 1-mile segments.
Pollution concentration and fumigation duration was then plotted,
for each of a number of combinations of miles from the polluting
stack, stability conditions, and wind speed.
Figure 5 illustrates
the procedure.
Pollution Concentration
(ppm)
Time (Hours)
Figure 5.
Pollution Concentration Given a Wind Speed of 5 Miles per
Hour, a Downwind Distance of 3 Miles from the Source, and
an Unstable Stability Condition.
-41
Notice first in Figure I that for a wind speed of 5 mph the
distance between any two points represents 6 minutes.
In this
example, 30 points were calculated and plotted, each representing
a pollution concentration of 6 minutes duration and in total a. period
of 3 hours.
Each graph was examined and average pollution concentra­
tions during specific periods of time were estimated visually.
In
this example, a pollution concentration of one ppm was chosen for the
2-hour innerval from .5 to 2.5 hours.
Since research has indicated
that a plant can withstand .3 to .5.ppm indefinitely without sustaining
any leaf.damage,, concentration levels of pollutant between zero and
0.5 hours and between 2.5 and 3 hours were treated as- zero in any
calculations of leaf damage.
■
A minimum of 5 and a maximum of 10 graphs
9
.
were plotted for each
combination of wind speed, distance from the polluting stack, and
stability condition, from which average pollution concentration C for
each T was estimated from each graphi Estimates of pollution concen-
Recall that each pollution concentration C was calculated using
a different cross-wind distance variable y and that each y was the
result of wind direction averaged for a specific interval depending on
wind speed. Wind speeds of 12 mph, for example, required direction
averages for 72 intervals for a 3-hour period, each interval 2.5
minutes duration. Approximately 350 intervals were averaged for each
wind speed, yielding enough.data for.five 3-hour graphs at wind speeds
of 12 mph.and.ten 3-hour graphs for wind speeds of 5 mph. The writer
recognizes the limited data plotted and suggests refinements and
mechanization for future work.
42
tration and fumigation duration ranged from an average pollution con­
centration for the entire 3-hour period to three or four average
pollution concentrations, each with fumigation durations whose total
was 3 hours.
Figure 6 presents another illustration of the discussion.
Pollution Concentration
(ppm)
-1.7
Time (Hours)
Figure 6 . Estimating Pollution Concentration and Fumigation Duration.
This data, for example, was plotted, visually inspected and esti­
mated for pollution concentrations C of 1.2, 0.9, and 1.7 ppm each of
I hour duration.
Combining each C and its T with an absorption rate of
the plant A, leaf damage was calculated for each hour of the 3-hour
period.
Total leaf damage for each graph representing a 3-hour period
was then calculated, and by adding the leaf damages for all calculated
43
under the same conditions and dividing by the number of 3-hour periods,
a mean (average) leaf damage was found and used to calculate yield
reduction for each set of conditions.
Please note that the graphs were
averaged visually and therefore no claim is made for a completely accu­
rate prediction of leaf damage.
If a computer routine had been devised,
slightly different results might have been produced.
Calculating Yield Reduction
The following equations were then used to predict yield reduction
as a percentage of total crop yield by using leaf damages calculated
above.
Since alfalfa does not exhibit a stage of growth effect [28,66],
equation (5-3) becomes, for all stages of growth
Y = 100 - .302X
where:
'
(5-8)
Y = percent of total yield;
X = percentage leaf damage (i.e., 10% = X =
10).
For barley, which does suffer greater damages with increasing ■
growth, the following coefficients were used to estimate, loss in yield
[8 ] .
Y = 100 - .OOX
1 st -
6 th week
Y = 100 - .2 OX
7th -
9th week
Y = 100 - .35X
1 0 th - 14th week
.
(5-9)
44
The average annual yield of alfalfa and barley in each sector,
assuming no pollution, was determined using data supplied by the
Helena Valley Irrigation Project.
Alfalfa was assumed to yield 2 tons
per acre at $23.50 a ton, and barley was assumed to produce 40 bushels
an acre at 85 cents a bushel. Each fumigation, coupled with the right
environmental facnots, would reduce the total yield attributable to that
sector as discussed above.
Table V depicts the average annual damages to alfalfa and barley for
all sectors given emission levels ranging from 100 percent to 50 percent.
TABLE V.
AVERAGE ANNUAL DAMAGE COSTS TO ALFALFA AND BARLEY.FOR'YEARS'
1965-1969.
Emission Level
Percent
100
95
90
80
70
60
50
Alfalfa
Barley
---Dol] ars----
Total■
494
392
273
161
105
59
14
2,500 ■.
2,052
'1,717
1,391
1,139
801
505
2,006 •
1,660
1,444
.1 ,220 .
1,034 .
742
491
.
■ ■
A curve was fitted .to the cost estimates of varying emission levels
using least squares regression analysis which took the form:
ADC = .0203 + ..081E - .105E
where:
2
+ .046SE
3
ADC = agricultural damage costs;
E = emission levels (100% = .E = 1.0) ■
XO
ADC is in millions of dollars.
10
CHAPTER VI
ESTIMATING THE CONTROL COSTS OF POLLUTION.
Attempts have been made to control sulfur oxide emissions for the •
last 150 years [51].
High costs of control as well as the fact that
the costs of not controlling emissions are mainly external to the
emitter have generated little volition on the part of emitters to
purchase control equipment-
When econ'omic conditions or pollution
control regulations do warrant control, sulfur dioxide has been
recovered as sulfuric acid or elemental sulfur.
Recently a cheaper way to convert polluting oxides to elemental
sulfur was' announced by E . Van Dornick, whose process would rid the
■ ■
I
gas of 90 percent of its sulfur content at a cost of $5 per ton. ■ The
process is now being tested and preliminary results are now becoming
available.
In correspondence with Van Dornick, he estimated the .
capital cost of the process plant for the American Smelting and
Refining Company in East Helena to be $11 million and the operating
costs to be $5 to $6 per ton of elemental sulfur product.
Unfortunately
for potential users of this process, the price of elemental sulfur
has fallen from $38 a ton in 1968 to under $10 a ton presently.
2
■A description of the sulfur dioxide pollution reduction process
by E . Van Dornick can be obtained•by writing the Chemical Technology .
Corporation,'9400 Whitmore Street, El Monte, CA .97131.
2
■ Wall Street.Journal, November 9, 1970, p. 18.
46
A planned 60 percent increase in flue gas concentration by ASSR
would reduce the capital costs of the process plant to $7 to $8
million.
3
Assuming, then, a capital cost of $8 million, operating
costs of $5.50 per ton, and the production of 42,000 tons of elemental
sulfur per year. Table VI reveals the market price of sulfur which
would have to be received for a breakeven control cost.
TABLE VI.
Interest
Rate
Pet.
MARKET PRICES OF ELEMENTAL SULFUR NEEDED.TO FORCE CONTROL
COSTS TC ZERO GIVEN THREE RATES OF INTEREST USED TO
CONVERT CAPITAL COSTS TO ANNUAL COSTS.
Capital
Operating
Total
Cost
Cost
Cost
-- Millions of Dollars—
9?
Market Price
Contro]
of Sulfur"
Costs
---- Dollars-- •
.30
.22
1.03
24.52
0.00
6 .
.48
.23
■ .71
16.88
0.00
3
.24
.23
.47
Ili 19
0.00
.10
The process plant is based on a 90+ percent SO^ removal and a 95+
percent elemental sulfur recovery. . Essentially all of the particu­
lates can be conveniently removed either by the process equipment alone
or with nominal auxilliary facilities.
The process is designed speci- .
fically for a 90+ percent SO^ .removal and is a 95+ percent operation.
Van Dornick explains that the process could not be operated at lower
levels of recovery or SO^ removal.3
3
.
This information 'was communicated to me by E . Van Dornick in a
letter dated September "8 , 1970.
47
Minimum cost control- methods of
more conventional design for the
ASKR lead smelter under consideration were furnished by the Environ­
mental Protection Agency.^
Cost data for control of a Dxvight Lloyd
sintering machine were given that would result in the lowest cost
per ton of sulfur removed for the control level specified.
Basic
assumptions used to derive the capital and operating costs for
various levels of control efficiency are explained as follows.
Investment and operating costs were taken from the Systems Study
for Control of Emissions:
Primary Nonferrous Smelting industry, .by.
Arthur G. McKee and Company, June 1969.
5
A 15-year straight-line
depreciation, with interest costs at 10 percent, and administration
costs of 3 percent:, were used for calculating annual capital costs.
A
credit of $5.35 per ton of recovered acid was assigned wherever
applicable. ■ At the 99.4 percent control level,' the smelter's operator
is assumed to purchase reactive.lime for $4 per ton rather than invest
in a lime kiln and produce the material.
This■assumption is valid,
because of the small quantity of lime needed to treat the final I per­
cent of waste sulfur dioxide.
T"~
The cost data are listed in Table VTI.-
■
”
_
Mr. Frank Bunyard,■Environmental Protection Agency, Air Pollution
Control Office, Division of Economic Effects', Research, communicated the
necessary information to me in a letter dated February 11, 1971.
4
^Available from the clearinghouse for Federal Scientific and Tech­
nical Information, U. S , Department of Commerce, Springfield, Virginia.
48
TABLE VII. CQST DATA FOR SULFUR EMISSION CONTROL.*
Control Efficiency
I.
45
■:
78
Percent
: 88
:
93
99.4
Capital Cost ($ million)
a.
.b .
c.
• d.
Limestone grinder
Lime kiln
Scrubber & waste
treatment■
Contact acid plant
Total'Capital Cost
2.
:
:
.7
1 .1
2.9
■' 1.1
1 .8 .
.1.2
a.
b.
c.
1.3 .
8.4 •
3.4
9.7
1 .6 8 ;
1.94
1.37
(.80)
1.60
( .80)
'
.Annual capital costs
Operating. & maintenance
costs
By-product credits
.36':
Total Operating Costs
*Source:
4.1
2.3
Annual Operating Cost
($ million)
8.4 '
1.2
.46
.83
.46
■ .82
■ 1.05.
.82
1.28
1.88
2.25 '
■ 2.75 .
Mr. Frank Bunyard corrarmnicated the information in this
table to me in a letter date February 11, 197i.
49
Least•squares regression was used to fit a curve to the five
data points for the various emission levels which took the form: .
CC = -2.97 + 6.311* e (~E)
where:
C C = control costs;
E = emissions.
A linear fit was suggested by Mr. Bunyard for control efficiencies
between 0 and 45 percent control.
ship took the form:
CC = -2.22E - I.
The fit for this linear relation'
CHAPTER VII
SENSITIVITY OF RESULTS TO PARAMETER CHANGES
• In the search for ways to improve the misallocation [of
resourcesJ resulting from external effects, care must always
be exercised to take into account any additional costs or
penalties associated with the remedy. It is quite .possible,
for example, to set standards designed to reduce external
effects so strict that there will be a loss to national
product rather than a gain [26 ,p.9].
Estimaues of the social costs of pollution and control, although
difficult, must be made for rational control policies.
These esti­
mates are reviewed, here for purposes of analysis, enabling authorities
to.make better decisions because of increased information.
Under the assumption that Ridker's value data do not fully cap- '
ture the disbenefits associated with SO , the average annual household
2
■
i
damage costs of $33,000 listed in Table ill were, doubled.
average annual agricultural damage costs of $2,500
Adding
(Table V), total
^Recall that damages per household were estimated using Ridker's
St. Louis study where people■there paid $245 more for a house for
each .25 mg SO 3 /IOO cm^/day avoided. At 6 percent interest, $245
represents about $1.20 per month per household. Ridker's value data
estimate only household damages. Since damages occur to people
and property, the somewhat arbitrary assumption was made to double
the damages calculated by using Ridker's numbers to capture total
damages.
51
pollution costs were estimated to be $68,500..
Total annual costs,
including control, agriculture, and household, can. then be summarized '
by
TAC. .= -2.22E + 2.22 - .0203 + .C81E - .105E2 + .046SE3 + .066E
where:
TAC = total annual costs;
E = emissions (100% = 1.0);
'
-2.22E + 2.22 = control costs ;
-.0203 + .081E - .105E
2
+ .0468E
■;
3
= agricultural damage costs;
.066E = household damage costsi
All cost figures are in millions of 1971 dollars.
If the socially desirable amounts of pollution control are
assumed to be the least costly combination of means available, the
level of pollution sought,should be the point where the cost of a
further reduction would just exceed the benefits, i Given the damage
costs' estimated in this study and the control possibilities estimated
by the Environmental Protection.Agency, there is no level of
The linear control cost function is included here where an
interest rate of 10 percent was used to convert capital costs to
annual costs. Least squares regression analysis was used to fit a
curve ■to the five "discrete control costs estimated by NAPCA.. taking
the- form C = -2.97 + 6 ..311*Exp(-E) . C represents costs and'E
represents emission levels.
V \
52
control which can presently be justified on efficiency grounds.
Although substantial damages have been estimated, the total cost ...
function i s ■minimized at 100 percent emission levels and a total
cost of $63,500.
Table VIII shows the pollution and control costs
for seven discrete points of control and for changes in the basic
assumptions.
Ar. asterisk (*) indicates the control levels necessary
to minimize costs given various assumptions about the data.
The first line in each set of assumptions indicate a zero level
of control.
by
EPC
Lines 2 through 6 indicate, the control costs estimated
for five discrete control levels.. Line 7 gives the control
cost estimates by E. Van Dornick (EVD) for. the 90 percent control,
level.
The basic assumption, B , indicates a doubling of household damage
costs estimated using Ridker's value data.
Ten, 6 and 3 percent indi­
cate the rate of interest used to convert capital costs to annual costs.
Control cost estimates for E . Van Do m i c k 's 90 percent control
method .are estimated as follows.
The basic capital cost is converted
to annual costs by the appropriate interest rate,
The plant is capable
o f 'producing 42,000 tons of elemental sulfur per year at an operating
cost of $5.50 per ton.. Assuming the market price of sulfur to be.
$9 per ton, $378,000 are then subtracted from the plant's total annual
operating and capital costs to yield the annual control cost estimates.■
Assumptions I, 2, and 3 indicate that total costs would be
minimized at 0 percent control levels■given the basic assumption B
•.
;
■
53
TABLE VIII.
Change in
Assumptions
THE DISCRETE CASE CONTROL COSTS' ESTIMATED BY EPC AND
E. VAN DOBNICK (EVD). (All Costs are in Annual Terms)
Agricultural
Control Control
Damage
Household
Emissions Level
Costs
Costs
Costs
Pet.
— Millions of Dollars-—
I. R- (10%)
0
1.0
.55
.22
45
78
88
93
99.4
90
.12
.07
.006
EVD
2. B
.1
(6 %)
0
1.0
45
78
.55
.22
EVD
3. B
.12
88
.07
.006
93
99.4
90
.1
(3%)
.55
.22
EVD
4. 20B (10%)
-
45'
78
.12
88
.07
.006
.1 .
93
99.4
90
1.0
.55
.22
.12
.07
.006
EVD
0
1.0
.1
0
45
78
88
93
99.4
90
.0025
0.00
1.00
.0002
.0000
1.51
2.29
3.09
3.72
..652
•
.0000
.0000
.0000
.0000
0.00
.0025
.928
1.418
2.126
2.754
3.332
.332
.0002
.0000
.0000
.0 0 0 0 '
.0000
.0000
0.00
.0025
.874
1.349
2.003
2.502
3..041
.092
.0002
.0000
.0000
.0000
0.00
1.00
1.51
2.29
3.09
3.72
.652
'
;
.
ooo'c
.0000
.0025
.0002
.0000
.0000
.0000
.0000
.0000
.0660
.0172
,.0043
.0030
.0013
.0001
.0023.
.0660
.0172
,0043
.0030
.0013
.0001
.0023
Total
Costs
.0685*
1.0172
I.,5143
2.2930 .
3.0913
3.7201
.6543
.0685* ■'
.9452
I, 4223
2.1290
2.7513
3.3321
.3343
.0660 . .0685*.
.0172' .8912
. .0043 1,3533
.0030 2.0060 .
.0013 2.5033
3.0411
.0001
.0943.
.0023
■1.3200
.3440
.0860
.0600
.0260
.0025
.0460
(table■continued)
1.3225
I .3440
1.5960
2.3500
3.1160
.6980*
.54
TABLE VIII.
(continued)
Agricultural.
Change in
Control Control
Damage
Household Total
Assumptions .Emissions Level
Costs
.Costs
Costs
Costs
Pet.
—-- — -Million's of Dollars-----—
5. 20B (6 %)
o
45
78
1.0
.55
.22
.12
•
.07
.006
EVD
,' '
.1
6 . 2OB.. (3%)
1.0
.55
45
78
.1
(7%)
EVD
8 . 7B
(?%)
EVD '
%
9.3
99.4
90
1.0
0
.1
90
i.o
.1
.
88
.07
.006
7. B
93
99.4
SO
0
,22
' .12
EVD
88
■
0
90
0.00
.0025
0.928
I..418
2.126
2.754
3.332
.332
.0002
.0000
.0000
.0000
.0000
.0000
0.00
.0025
0.874
1.349
2.003
2,502
3.041
.0.92
0.00
..413
0.00
.413
9. B .(7%)
EVD
■ '1.0
0
.1
90
0.00
.056
.0002
.0000
.0000
.0000
.0000
•.0000
.0025
.0000
1.3200 1.3200
.3440 1.2180
.0860 1,4350
.0600 2.0630
. .0260 ‘ 2.7800
.0025 ■3.0735
.1380*
.0460
1.3200
.3440
.0860
.0600
.0260
.0025
.0460
.0660
.0023
1.3200
.1.2720
■1.5040
2.1860
2 *5280
. 3.3345
. .378*
.
.0685*
.4153
.0000
.4620
..0161
..4645, ■
.4291*
.0025
.0000
.0660
.0023
.0685
.0583*
.0025
55
and for .interest rates of 10, 6 , and 3 percent.
The market price of
elemental sulfur would have to be $23,00, $15.42, and $9.72 for
assumptions I, 2, and 3, respectively, before EVD would become a
minimum cost solution.
Multiplying household damage costs by 20 (20B) as shown by assump­
tions 4, 5, and 6 , indicates that minimum cost solutions would involve
zero control for the cost figures estimated by EPC.
Excluding Van
Dornick and using the lowest discrete control level,destimated by
EPC, the basic estimate of damage costs would have to be increased by
a factor of 20 before control could be justified on efficiency grounds.
If damages were 203, EVD becomes the minimum cost solution at a control
level of 90 percent.
Assumptions 7 and 8 are included to indicate the viability of
the EVD control process as a minimum cost means of control.
interest rate of 7 percent
4
3
Using an
.
and a market price of elemental sulfur
of $9 , the conclusions are as follows.
Given the basic assumption,^
The money rate of interest was determined by checking the
corporation bond market in the July 23, 1971 Wall Street Journal for
the American Smelting and Re fining Company. Showing a coupon value
(contract rate of interest) of 4 5/8, a $1,000 bond was selling for
$705, maturing in 17 years. By examining the. present value of $1,000
due in 17 years and the present value of annuity of $42.63 received
at, the .end. of each year >■a .money rate of interest of I ■percent was
determined.
^Price of a long ton of elemental sulfur f.o-b-. Alberta, Canada
July 23, 1971.
56
B , no control can be justified as shown in assumption 7.
Assump­
tion 8 indicates that the basic estimate of damages would have to be
increased by a factor of 7 before EVD minimizes costs.
Assumption 9,
indicates the market price of sulfur would have to be approximately
$17.50 before EVD becomes the minimum cost solution.
Comments on Results
Conclusions other than those reported in this study would be
warranted given the following possibilities.■ First, damage costs may
be significantly underestimated.
Second, control methods less costly
.
than those reported may become available.
'■
And finally, the alterna­
tive of plant shutdown as a control alternative is a possible solution.
Imperfect information about the pollutant’s effect on health,
vegetation, and materials, a lack of certainty in the diffusion model,
and the possibility of an increased effect (synergism) by a chemical
recombination once,airborne, could all affect estimates of damage costs.
The damage costs, calculated in this study are probably under­
estimates .
Care was taken to adjust annual sulfation rates by a conserva­
tive factor of 10 percent, and though damages could occur at annual
2
sulfation levels below .49 mg SO^/lOO, cm /day, all damages below this
level were excluded.
' v
•
‘
•
:
57
This was consistent with Ridker's study of using .49 mg as a
background level.
In addition, the harmful effects of intermittent
high level concentrations of sulfur dioxide were not estimated.
Estimated damages to agriculture were also minimum.
Although the
relevant research indicated differences of opinion regarding damages
to alfalfa and barley during night hours, damages were estimated only.
during daylight hours.
Abnormal weather conditions causing heavy con­
centration levels of pollution and/or extended fumigation durations
in relatively small areas could cause significant leaf damages.
Although these conditions probably .inflict greater, damages than those
estimated, the frequency of occurrence was not known and hence not
evaluated.
An indication of the underestimate of crop damages is the
fact that over $14,000 were paid for crop damages in 1967, 1968, and
1969 by AS SR while chis study indicated damages of $7,2 3‘5 for the
comparable 3-year period.
Means of conurol less costly than those estimated by the Environ­
mental Protection Agency (EPC) and E . Van Domick could also alter the
conclusions in this study.
A representative of EPC indicated, however,
that."the one control scheme that would result in the lowest cost per
ton of sulfur removed for the specific control level" was used, and
further, "in a practical sense, a smelter operator
would choose the
least-cost strategy for a given control level similar to the approach
58
I am presenting you ." 5
Concerning the EVD control process, many
engineering evaluations indicate that it is superior in simplicity and
cost compared to other existing methods recovering elemental sulfur
from flue gas.
/
6
Another possibility would be the alternative of plant shutdown.
If the basic assumptions in this study are correct then shutdown would
appear to be socially efficient if expected annual rent losses to
land, labor, and capital were less than $68,500.
An estimate of these
losses would be. difficult and is beyond the scope of this study.
■
‘
Implications of the Results
Damages of $68,500 are certainly not inconsequential, especially
when seven-tenths of these damages occur within I 1/2 miles of the
stack.
If people do have the right to clean, air, equity would require
that they be compensated by the amount they are damaged.
Remuneration,
for example, might include direct payments from AS SR to the receptors.'
A payment schedule appears to be an attractive alternative, both on
equity and incentive grounds.
First, damaged parties are compensated
j^r. Frank Bunyard communicated this•information to me in a
letter dated February 11, 1971.
. ^ ’Scientific Evaluation, Engineering and Technological Appraisal
of the Van Dornick Sulfur Dioxide Reduction Process," Dr. Walter W.
Walker, P.E., F.A.I.C.,729 No. Richey Blvd.,. Tucson, Arizona and
Joseph H.; Herz, Chief Technologist, California Portland Cement Co.,'
Colton, California.
59
according to the costs they incur... And second, the current trend of
dogmatic' insistence.by
polluters that control mechanisms are too
expensive could be reversed by creating an incentive to seek control
methods which would cost less than damages paid.
If the damages to
receptors are known and payments enforced, the plant would continue
to emit only as long as the costs, from additional emissions axe less
than.that which it would have to pay to reduce emissions.
Until cheaper control possibilities- are: discovered or future,
research indicates damages-presently unaccounted for, the gain i n •
efficiency by better social control decisions at this plant appear to
be negligible.
Further research on the significant parameters in
this study as they apply to this plant of the American.Smelting and
Refining Company, [except on the possibility of shutdown) would, not
appear to be warranted.
Given that receptor damages depend in part on factory location
and wind patterns,' it appears that this plant is suitably located.
If tne prevailing winds, for example, were toward the city,of Helena
95 percent of the time, instead of the current 4 to 6 percent, the
model indicated household damages of $4,423,000 and an emission control
level of 90+ percent.
The model was also, applied to the ASSR copper smelter in Tacoma,
Washington;' (emissions only double), where household damage costs
totaled $8 million and the minimum cost-solution called for 90+.percent
60
emission control.
Plant location, then, as well as emissions and .
control costs affect control decisions.
CHAPTER VIII
SUMMARY AND CONCLUSIONS
A 1969 governmental study of the ASSR lead smelter in East
Helena, Montana recommended that a substantial reduction in sulfur
oxj.de
was necessary and. in keeping with the. varying activities and
economic interests of the area.
Empirical guidance for determining
the efficiency of a "substantial reduction" has been lacking due. in
part to the lack of information on pollution costs.
A computer program was written, to refine and extend a methodology
developed by Stroup to estimate household damage costs, while agr
cultural damage costs were estimated.using -a -new methodology for
calculating yi.eld loss due to S0„ fumigations. 'Combining these
pollution costs with control costs estimated by EPC and Van Dornick,
a total cost equation was estimated and minimized to indicate efficient
levels of emission control.
The household damage costs were calculated using local weather ■
data in a computer program written to predict annual sulfation rates,
population and housing data, and the value data from a St. Louis
property value study by Ridker.. Agricultural damage costs were
estimated by combining a dispersion model to predict pollution con­
centration , and a study by Thomas indicating the absorption rate of
the plant, with estimates of fumigation duration using wind direction
data.
62
The basic total cost estimate was minimized at zero control, where
efficiency indicated that even if estimated damages were increased by
a factor of 20 using EPC estimates or a factor of 7 using Van Dornick
estimates, uncontrolled emissions were still optimal.'
Substantial pollution damages were estimated, however, arid if
people do have the right to clean air, remuneration seems equitable.
In summary, the model presented in this paper was an attempt to
give an operational answer to the hard policy questions facing decision
makers.
The model can be adapted to other situations: as it was in
Tacoma, or it can be adjusted for new numbers when new research like
Ridker's becomes available.
Limitations of Study
The lack of empirical research similar to the study by Ridker makes
air pollution control decisions difficult.
Reasons for assuming his
numbers low as applied to Montana would include the increased awareness
of the environment, since his I960 study and the possibility that people
who live in Montana have greater preferences for clean air.
Differing
supply conditions for housing of each environmental quality, between
Helena and St. Louis, also could affect the applicability of Ridker's
figures in Helena.
Any new research made available and yielding new
numbers, however, could easily be incorporated into the model.
63
The methodology developed to estimate agricultural damages is
lengthy and improvements in estimates could be made by refining and
mechanizing it.
In addition, the dispersion model used to estimate
agricultural damages was not empirically tested, although it is widely
published as being a reasonable representation of the real world.
Future Research
Perhaps the most difficult of all control alternatives to evaluate,
and one not considered in this paper, is plant shutdown.
Loss of
rents to the emitter as well as to the employees and suppliers in the
area of the emitter basically comprise the social costs of this strategy
In view of the- conclusions of this study, such an evaluation might be
deemed worthy.
If emission control is considered necessary, further study of the
feasibility of the E . Van Dornick control process would be warranted. .
In this case the price of -elemental sulfur and the costs involved of
increasing the concentration of sulfur dioxide in the flue gas to
reduce capital costs become important determining factors.
Further information on the damage costs of SO^ to people could be ■
acquired by medical studies examining East Helena resident health
costs with comparable residents of nonpolluted areas.
.The damages estimated in this paper could be partially validated
by conducting a survey in the area asking people how. much they would be
(
.
64.
willing to pay to have pollution reduced.
For example, the people in
East Helena could be asked, "would you like pollution to be reduced-by
X percent (excluding cost of living increases) or would you rather
receive a payment of Y percent with present uncontrolled emissions?"
An analysis could be made indicating the importance of plant
location to damage costs and therefore to air pollution control
decisions.
65
APPENDICES
APPENDIX AA NARRATIVE:DESCRIPTION OF THE COMPUTER PROGRAM
v
The following verbal, presentation' of the computer.program .
including a flow chart and a listing of the computer program describes
the information necessary 'to calculate sulfation pollution in each
sector and the damages it causes to households and crops.
The numbers
of the steps that follow are the same as those assigned to corresponding
parts of the'flow'chart and to the card numbers in the computer program.
Please refer to Appendix D 'for definitions of the symbols used.
Steps I
18.— Define the format, dimension, and integer
statements.
Steps 19 - 38.— Read, dimension, integer, store data and
initialize variables.
Steps 39 - 40;— Read the three hourly weather data•cards for the
annum.
Step,41.-— When windspread equals zero, wind direction is.also
zero.
The decision was made to read the next weather data card and.'
double the concentrations in each sector for that wind direction
using a multiplier (MULT).
■ '
:■
■
Steps 42 - 63.— In order to calculate concentration levels of
pollution using the dispersion models discussed in Chapter IV, sta­
bility classifications must be estimated.
Basically, these stability
classifications for each of the eight-'daily WBAN Hourly Surface •
67
Observations are based on the work by Dr. F. Pasquill of the British
Meteorological Office.
Net radiation and wind speed are the primary factors affecting
stability conditions near the ground.
On a cloudless day, incoming
radiation (insolation) is dependent upon solar altitude, which is in
turn a function of time of day and time of year.
course, decreases incoming and outgoing radiation.
Cloud cover,.of
In this system,
insolation is estimated by solar altitude and modified for existing
conditions of total cloud cover and cloud ceiling height.
Night
estimates of outgoing radiation, are made by considering cloud cover.
The stability classes are as follows:
Stability Class
I
2
3
4
5
6
7
. Extremely unstable
Unstable •
■ Slightly unstable
Neutral
Slightly stable
Stable
Extremely stable
Appendix Table A-I gives the stability class as a function of net
radiation and wind speed.
The net radiation index ranges from 4,
highest positive net radiation directed toward the ground, to -2 , the
highest negative net radiation directed away from the earth. , Stable
conditions occur with high negative net radiation and light wind speeds
neutral conditions with cloudy skies or high wind speeds, and unstable
conditions with high positive net radiation and low wind speed.
68
STABILITY CLASS•AS A FUNCTION OF NET RADIATION .
AND WIND SPEED.
4
-' Net -Radiatlon Index
3 ' ' 2 /•
I
O
H
APPENDIX TABLE A-I.
I
I
2
3
4
6
7
2, 3
I
2
2
3
■4
6
7
4, 5
I
2
3
4
4
'5
6
6
2
2
3
4
4
5
6
■ 7
, ■ 2
2
3
4
4
O
Wind Speed
Knots'
.
„1 ■■
4
5
8, 9
2
3■
3
4
4
10
3
•3
4
4
4 '
4
5' .
11
3
3
4
4
4 •
4
>12
3
4 '
4
4
4
4
■
4
'4
"
,
■
-2
' 4
5
69
Stability classes were determined using the following scheme [69]:
1.
If the total cloud cover is 10/10 and the ceiling is less
than 7,000 feet, use net radiation index equal to zero
(whether, day or night) ; .
2.
For nighttime (between sunrise and sunset):
■ a.
If total cloud cover _< 4/10, use. net radiation index
equal to - 2 .
b.
If total cloud cover > 4 / 1 0 , use net radiation index
equal to -I.
.
3.
For daytime-.-steps 1-15 in computer subroutine:
a.
Determine the insolation class number as a function of
solar altitude^ from .Appendix Table A-2.
b.
If total cloud cover <_ 5/10, use the net radiation index
in Appendix Table A-I corresponding to the insolation
class number.
c.
If cloud cover > 5/10, modify the. insolation class number
for the fo lowing conditions:
1)
Ceiling <7,000 feet, subtract,2.
2)
Ceiling >_ 7,000 feet, but < 16,000 feet, subtract I. .
3)
Total cloud dover equal 10/10, subtract.I. .
4)
If modified insolation class number is. less than I,
let it equal I.
5)
Use the net radiation index in Appendix Table A-I
.corresponding to the modified insolation class number.
Step 64.— Converts wind speed given in knots to meters, where wind
speed in knot's times' .514.8 equals wind speed in meters.
•Solar altitude was determined by using the Smithsonian Meteoro­
logical Tables, Sixth revised.'edition, pp. 495-497.
>
70
APPENDIX TABLE A-2.
Solar Altitude (a)
Insolation
Insolation Class Number
60° < a
Strong
4
35° < a _< 60°
Moderate
3
15° < a <_ 35°
Slight
2
a < 15°
Weak
I
71
Step 65.— Determines effective stack height in meters. .Effective
stack height equals actual stack height plus the rise of the plume.
The rise of the plume above the stack was determined using
Hollands equation:
Vd
•
(1.5 + 2.63 x 10
H =
where:
T
- T ■d
— —
p
(A-I)
H = rise of plume above stack;
•V
s
= stack gas exit velocity, m sec
-I
;
d = inside stack diameter (16 feet = 4.876 meters);
U = wind speed, m sec
-I
;
p = atmospheric pressure, mb (26 inches = 881 mbs);
T
= stack gas temperature, °K (130°F.=.328°K);
T
= air temperature, 0K (43°F = 2790K).
V .= VolHne ^ 1 9 M 0 0 _ c f m
s
Area
201
where:
= 4.85'm sec"1'
(A-2)
Area = r^ .=■ 3.14(8^) = 201.
Therefore,
AH = 4 ‘85 (- - - --[1.5 + 2.68 x 10~3 (881) (328 ~R279)4.876)
U
uZO
76.23/U .
(A-3)
Step 6 6 .— Q represents emissions from the polluting stack of 2,772
grams per second at zero control;
Step 67.— Permits examination of a.3-hour period- (DAYS = 1/8) up ■to a year (DAYS - 365).. '
72
Steps 68 - 73.-r-Calculate the pollution concentration Chi and
store this concentration in the appropriate wind direction, K r and
for each of 15 miles distant from the stack, M.
Chi was doubled using
the multiplier if wind speed was zero.
■ Step 74.-— The model assumed agricultural damages to occur only
within 3 miles of the stack.
Step 75.— Unless the stability conditions were calculated to be
either 2 of 3, pollution concentrations were not sufficient to inflict
agricultural damages, and another data card was read.
Step 76.— Agricultural damages only occur from May 25 to August 25
Step 77.— The model assumed agricultural damages to occur only
with wind speeds between 2 and 10 knots.
Step 78.— The model assumed agricultural damages to occur only
when temperature ■was greater than 40°F.
Steps"79 - 80.— The model assumed agricultural damages to occur
only during daylight hours.
Steps 81 - 82.— This step calculates the absorption rate of the
plant.
Since relative humidity was hot punched on the data cards, it
was calculated using the dewpoint vapor pressure divided by the
temperature vapor pressure.
This calculation (relative humidity) was
then multiplied b y 650 to indicate the sensitiveness of the plant
[67,p.302] .
hh-f;;
■
.
■
73
Steps 83 - 9 6 .— These steps are used to estimate the agricultural
damage.costs (yield losses) to alfalfa and barley.
Percent yield loss
was calculated previously and entered as data in this main program.
Each card contains percent yield loss for alfalfa and barley given
an absorption rate of the' plant, a particular wind speed, the relevant
day and month, a particular stability conditions, and the distance of
the field from the stack.
After calculating the absorption rate of the plant, steps 81 - 82,
the absorption rate (11 = 1,7) is partitioned into seven categories,
steps 83 - 90.
If the calculated absorption rate falls between 600
and 650, Il was set equal to I.
Likewise, a rate between 500 and 600
forced Il = 2, between 500 and 550, 1 1 = 3 , and so on to Il = 7, where
the absorption rate falls somewhere between 300 and 350.
An absorption
rate below 300 was not sufficient to generate leaf damages given the,
pollution concentration levels.
Steps 91 - 93.— Set 12 = I if the day and month was•between Iiay 25
and July I; 12 = 2 if the date is between July 2 and July 21.; 12 =■ 3
if the date is between July 21 and August 25.
Damage to alfalfa was
assumed to occur throughout the summer as mentioned in Chapter V.
Barley suffered increasing damages, with no damage the first six
weeks (1 2 = I), increasing damage the next three weeks (12 = 2 ), and
maximum damage (12 = 3).
74
Steps 94 - 96.— -Set T 3 = I if windspeed was between .2 and 5 knots,
13 = 2 if windspeed was between 5 and 8 knots, and 13 = 3 if windspeed
was either g, 9, or 10 knots. .
Step 97.— Set 1.5 = I for fields I mile distant from the stack, 15
= 2 for 2 miles, and 15 = 3 for 3 miles.
Step 98.— Set. 16 .= I if the crop was alfalfa and 16 = 2 if the
crop was barley.
Steps 99 - 102.--Multiplies the potential yield of each crop (16)
in the appropriate sector (wind direction^ K, and distance from stack
15) by the percent yield IoSs given by a 3-'llour fumigation at a certain
absorption rate (Il), windspeed (12), day and month (13), stability
condition (14 = S), miles from stack (15) > and crop (16).
The number of acres of alfalfa and barley in each, sector was deter
mined by interviews in the area,^ data supplied by the Helena. Valley.
3
4
Irrigation Project,■ and aerial photographs.
Barley was assumed to '
produce 40 bushels an acre at 85 cents a bushel.
Alfalfa was assumed
to yield 2 tons per acre at $23.50 a ton.
2
-
Special thanks to Paul Kleffner, long-time farmer-rancher in the
East Helena'area, for his assistance.
■
3
Special thanks to Bob Green, superintendent of the Helena Valley
Irrigation Project, for his assistance. .
4
'
• ‘
U. S . 'Department of Agriculture,.. Agricultural- Stabilization' and
Conservation Service, Invitation. No. ASCS-7-64-dc, item 4.,
8'
75
Steps- 103 - 104.r— Set multiplier equal to I and read another data
card.
Steps 105 - 108.— After all weather data cards are read, these
steps give the format and,read statements for adding the contribution
of small stacks.
Steps 109 - 111.— These steps convert pollution in,g m
_3
given
by the dispersion equation to pollution in parts per-million (ppm) ,
add the contribution of small stack's., adjust the model according to
empirical data, and print the pollution in ppm for each of the 540
sectors;
Steps 112 - 115.— These steps set the pollution concentration in
each sector to zero if annual concentration is less than .017.ppm
2
(.49 mg of SO_/ 100 cm /day) and subtract the marginal contributions
3
of smaller stacks;
,Ridker used this figure as a background level of
which.■anything below i f cannot be included in pollution damages. ■
Steps 116 — 121.— Concentration of pollution in ppm is converted
to,a sulfation rate by using parallel measurements found in the litera­
ture [47,76],' and concurred by the Montana State Department of Health
and the National Air Pollution Control Administration.• Parts per
million.were converted to sulfation rates using the relationship I tag.
2
■ ‘
of SOyzIOO cm /day (sulfation) is equivalent to ,035.ppm SP2 .
'
tion was then printed out for the 540 sectors.
Sulfa­
7.6
Steps 122 - 129.-'-These steps print out the household damages from
pollution for each of the 540 sectors and their total.
the damages to households in the
Step .126 states
wind direction and the j
mile
out equals the amount of sulfation in that sector divided by .25 and
multiplied by $245, where Ridker fdund the decrease in property value
to be $245 for every .25 mg of SO^/lOO cm^/day, multiplied by an
interest rate of '6 percent to convert present value to annual costs, •'
multiplied by the number of houses in that sector, and.multiplied by
the increase in the price level.
Steps 130 -■ 137-.— ^These steps print out ,the damages to alfalfa
and barley for each wind direction and each mile, out, with a total
for each sector, and a final crop damage total for all sectors. .
Steps 138 - 139.— End of program.
109
Cp-
add the c o n trib u tio n o t small stacks.
A d lIist m o d , nd convert grams u f
(K)UutiOi. to p,im
I
^$TA»T^
I 38
I
Re.id.intcyvr, and
dim vnsion data.
In itia lize variablfs
Read Pata
has data
ended?
*
\/rc
Enrl c /IJotJ
I
Convert ppm to sultauon
JIl
46
A
___
t
’ 27-130
Print damages tn housvdolds
in e :ch sector and u ta l
---Tyt-
05
is tvtu l Cl x id
cover less Uv*.
o r equal to 4- *,C?
t
I
S T A B Il ITY
C O N D ITIO N
FQ UALS
n 3 kn ot J
j
5 )
v- cufate p o llu tio n
concentratir r* Ciu Cl
is w nd r.| cd I
than h kn ot:./
J
ta
A
\yf-
"Lr
IZIZl"tZ --A9
is w in d sp«xd less
than o r equal to
10 k n o t
-
_X
stcr* the concentration
m ea-h ar ca in t r •
anr-i,fupr-attf w in d dir- c tio n
k., and
ai fo r each n tie o u t. M
4 -
61
is w ind sr " rX' ess
than 3 knots?
131-137
P rint c ro p d a in t ies i.i
each sector and total
dspci
----J?,T-
.s s ta b ility co n d itio n euusl
to 2 o r I y
- \
14r
is w i d spct J less
than o r ei|ual
to 6 knots?
I__
I
I
\
____ Ak GStifttvulil
He
use stahiMty co nd itio n
subroutine - 2
C
is ceiling height
less than 7,000 ft?
IZiiL S u trv irin e 1-17
is tem pcra’ ure greater
than 40 degrees F ?
- O o Z -T A
I
is it a d ayligh t
hour?
JZ
8-89
determ ine date
S iib rru tiite
use s ta b ility c o n d itio n
S ibrou nnc = 4
*s the w ind speed between
2 and 10 knots?
CMCLiate the absorption
rate o f the plan t
use S tahility co n d itio n
subroutine = 3
___________
ml)
/5
is the date between May
25 and August 2 5 ?
is total cloud
cover less than
o r equal to 5 '1 0
i y
I
--- 1---
1-17
determ ine w in d speed
LzV
L
calculate and store crop
damage in each sector
has the 3CS-duy period
ended yet?
Figure A- L.
'2 6
Cz.’i .u la tc h ot.schoki damag is
I
{
K 9-12 1
P rint sulfntio n rate
in each area
is it a
mght hour?
C
119
E
~ps~
is to ta l clrxid
c o v e = I U IO
iilm g I- Iqht
less m an 7.C j O It?
tl
H i
Subtract c o n trib u tio n o f
sin.nlI stacks t o get concentration
in each a > c a b y th ? I ig stuck
_j
( L os v,
spci
equal
equal izero^
I
I
117113
Set concentration in each area
equal to zvro if p pm < .017
J_
3S
40
®<
H O 111
Print concentration in each
art a (ppm)
Pd)
Generalized Flow Chart for the Computer Program.
C A L C U L A T E A IK P A L L L T T'S. C a m / O rS
3 r SRt'AT !SllO)
.
I:
4 • Fe-^AT(ISIR)
10 F 5 4 A T (fX, 1 2 F 5 » 4 )
F C F v A T ( p y . 12, 14, I 2 , A 2 , I S X , I 2 ; I 2 , I 2 ; 4 X , I 3 , 6 X , A 1 , 2 5 X )
4 SCCC
6 FSRf AT.( 11 ) . .
.5
S l l O F S T v AT ( 'C ' , 1 2, 'C M L F g tE)
6
Si CC FBTrr AT (,I ClAj PARTS' PCP y ILL I 6 \ i / 3 X , 1518)
7
S1 30 F G R v A T (,I S U L F A T I 0 N R A T E r / 3 X j 1518)
5
O
IC
11
12
12
14
15
16
17
IS
15
2C
21
22
22
24
Pr
26
27
22
PS
SC
31
32
33
.3'4
25
36
37
3g
39
40
F U G FSRrAT ( 11
3131
E-'LL AF D a MAOf S
HSLSE^BLCS')
F c R 1'AT (///' T c T A L R M j S E C Ar AGE I, 11 c )
SlSc FSFrAT!!C 'I I2/2X>1EJ8)
81 7Q F S R ivAT ( U ' )
F U O FSRf AT ( / / / ' C R S F C a.N.a CE IN D O L L A R S IN D IR E C T I SN M 2 )
Sl SO F B s f A T ( (TS-Ta l C r SF R A M A G E V S X ' A u F A L F A S A r l EV
1ST A l '/SX s 18 )
LOGICAL NCELHT
C I Mc NS ISN X H E ) ,SIGZ ( 7 , 15),CI A ( 3 6 , 1 5 ) , C S S (26,1.5 ), ADj (36,15 )
INTr-CER C-, M , CRLHT, CLCCV, H S U S E (36-, 15), C R ^ P V (36, 3, 2 ), C R Q P D (2.6, 4,3 )
I, AM T
!,CR' F C T (2.)
■ CAiA CRPrD/43P-*:C/.*C-SPCT/3■wC/
■ R E A L CRC-F(7,3,3,? :3,3,S)
CS i I= 1,36
C C l O = 1 ,1 5
I
C I A ( I , v ) = CCS SC 1= 1, 15
R E A D ( I C E , 3). X < I ) , ( 5 I G Z ( J , I >/0=1,7)
■ 56 C S N T I N L F
CS c 1= 1, 36
2 READ ( I C E , 4 I (hPL'S.E ( I, U ), J = I, 15 )
CS 8 I =),36
READ ( 1 c 5>4.) ( (CRSFV( I.,J,K), v = 1 , 2 ) , K = 1 , 2 )
■ a CPNTINLE
• C S s 11 = 1,7
CS s I E = I , 3 ■
- .
CS S 12 =1 ,3
9 ■ FE AC (IC=J 10) ((! (CROP( II, 12, 13, 14,1-5, 16) ), 15 = 1,3), 1 4 = 2 , 3 ) / I6 = U £ )
R E / C (105, ICC > ( ( A D J ( U J ) , J-=U 15), I = 1,36)
R E A-C (I CF, I CC ) ( (CSS (I, J ), J = 1,15 ), I = I, 3 / )
5
RE A:-.( I CE, PDCC, END = S I O )N VR, N/'SDA Y, N H S ijR » C E l -HT , NDEV.PT, N 1,!IN'DI, NKNDSp,
INTt-' Ft C L C C V
calculate
a
,
I
. fc2
^3
■ 44
-.45
46
47
48
.49
EC
El
: 5c
53
5^
EE
56
57
5?
ES
.6C
. 61
■ 62
63
64
'65
66
67
63
69
7-C
71
.72
"73
74
7E
76
77
78
75
SC
A IR P e L l L T I Q N CA'-'A Cr. 5
- IF ( !a M l SP-*FC.C ) P L L T = PU LT + 1 « I GC T 8 5
N C L i - H - , T R l F.,IF (L F L P T ^L t » 3 H 7.c )NCEl.l-'T=-F A i„ SE.
IF (C L C C v • E C , I h ~ ) N C L C C V = I'C J C f: T 5 7
. C E C " C h (4j 6 j C L C C V LN CL DCV
7 I F ( \ C L C C V . C C , 1 C , A N C , , N E T s N C E L H T ) S « 4 ; 08 TB SCO
IF (N h QLP • E.Cf.C-:. 5R, N H e L R = EG, CE-'IR, NH CU Re E g «20. Q R d N W Q U R «EC «23) 33 .
ITE 5CC
T R ( N C L C C V e L F f E ) CA LL S T A B (E / 2 , N i'N C 5 P A' P 5 C A Y > N H 5 U R ) j GQ T0 SCO
I F ( N C L C C V f C T fE , A N D . . N Q T o N C E L H T ) CA LL S T A E ( 3 ; 3 ^ N N N D S P i N P Q D A Y ^ N H Q U R J
1 1 GP TC SC:
IP' (' C L C C V • CT * E » AND e I'CEL MT ) C A L L S T A B ( S ; M n NCSP^ N>6CAY#.NH8UR ). I
I GE Tb 8GC
S=Ej CG TS PCC
ECO J F (■' C L D C V ,LE, 4 ) Ge TB H O
'■ GB TO 620
* .
61C IF (''NNDcPfLEeS )S = 7 1GC TB SCti IF ('■ N N D £ P « LE « 6 )3 = 6 j G 3 TQ gCO
I F ( M f 1-DSPflFe-IC)S = E j G e TS SCC
IF (I■N t\D g F , GT , IC )S = 4 ; GS T 5 SCC
620 IF (:-N n D c p . LE'. 3 )S = 6 j CS TB SCC
l F ( ' k h C s P . L E , 6 ) S » S ; S e - TB SCC
I f (N v n -'-SP.GT«6 )S = 4;GQ Ta aco
SCO L r N ''NDSf- * ,E14P-
H= Icl• + 76.g3/U
-G = 277 2
DAYS- a 365
DB 3C2 N = U l E
CF I=4« 567b*G/(Si GZ(Sj>PI)*X (P) *U)*EXP(-.5* (H/S.IG.Z (S;>N) )##2)
IF (N1
A IND I«G-T i) 1> ) K= NkINDI -18
IF (: M h D I»lL «13 )■ K= N'klhCl +.12
CHI = CH I M M L I
C-I A(KtP)-= C I a . ( K t N ) + CHI
I F t fMfcT,!) -OF- -TS -gG 2
IF ( ~ • i'E ,2 • a ' c «'P . NE , 3 )G TB 8 CE
IF ('"■^ B D A Y , LT ,-E25 «S R ,NH-QDA.Y» G.T. SEE ) GB TB SCE
IF ('•k-NCsF.l E ,2.GReNVhD$P«GT.10> GB TB 802
IF ( N T E N F . L T . 4 0 Ge TB R C 2
IF ('NHQLR. N E . 8. A N D . N H B U P ,NE, 11. A N D , N H Q U R .NE «14 » A N D ,N H S U R o N E . I? )
IGB TO S-C2
•^3
VD
AIR 'FEiLtTIQK C*"AGrc
A = ((,cCF2kLCLApTm.cCCC7*\CELPTf»2+,CCOCC2*KDEkPT**3)/(,CCc8*
gS:
IKTr'•F- ,CCCCy^NTErF**2-i- »CCCCC2 # KTEKF>»S ).)-* 65C
S3:
Il = I
SA:
IE ( A *L7 »6CC ) 11=2 '■ '
SE:
IF'(-'LT,55C) 11=3
J E (A ,L T ,5005 Il=S
S-6:
£7
I F i A - L T A 5 C ) Il=E
ss:
If (At. I.Tt A CC.) 11=5
SS'J
IF
L I . 35C) 11=7
IE { a ,L i *S Q C ) CO TB 8 c E
so:
si:'
SC3 12 = 1' . .
Es;
lF(i'^ e C A V . CT ,7 C 1 > 12 = 2
S3:
IFu--v S C A V . C l * 721) 12 = 3
SA ;
■ 13=1'
. SE:
Ic (i' V A D f F t G T t E ) 13 = 2
sc:
I F ( 'W NE £ F •G T .£ ) 13 = 3
57;
CS '"'CA T5 =l /3
92:
CS '--CA 16 =1/2
ss:
KR;:"" C R S P V (K , 1 5 / 1 6 ) * C F S F ( 1 1 , 1 2 , 1 3 , S j 15,16)
I Co:
CR'jr;DC-<, I5-, 16 )= CRSPC.(K> -I5, 16)+ KR3P '
I c i : SC A CR3' E(X,I5,2 )* - C R 6 F D (K,I5,3) + KRQp
SCE CSRT INUr .
:
1C2:
: ICS:
r u u r =■ i«'
calculate
*-i:
. ICA.: .
" GQ I? 5 ..
■ Ic 5 : 'Slc KR IT E.( 1C 2, =IOC M l I )', 1 = 1,15)
icc:
CS AlS 1=1,36
IC7 : ICC f S- ' A T ( I E c B r c )
DQ -Ell U = I j t E
Ics: •
1:9:
811 CIa (Ij w) = (CIA(I,J)/(S,*CAYS)*262 + CSS(I,J ))*ADJ(I/J)
lie:
ill:
If(I.EG.19) K R l T E ( I C S j S l C C ) ((N),N =l,15)
',RITE (1C.?, SI 1C) I, { C I A U , W:), J = I, 15)
CS. ~ 12 C = I f l E
■ '
. IiS:
IF (C I ( I, u') «LT «»C l 7 ) C I A ( U j ) =C,
113:
117: I F (ClA (I , v IrKErC,) C I A ( I j U ) « C l A ( I j J ) - C S S ( U U ) W A D U ( I j U )
■ ' . . n s : ' 812 - C f t IR l E '
lie:
'a R IT E ( IC 8 , 2 13 C ) ( ( I ) , 1 = 1,15.)
117:
CS f U 1 = 1,36
' ns:
Ce > 1 3 v = U 15
ns:
813 CI a ( IjJl=CI •' ( I, j) * 2 8 , 6
IF (U £G ,19 ) KR ITE (108,8130 ((N) ,KuUlE )
■ice:
C A L C U L A T E AIR PeLL1-TlCV- CAN-/,CES
814 UR IT E (IC 2 a 2 1 1 C )■ I/ (CIA('I,U),Usl#15)
I? I!
R;I T E (I q ? ^ P 5,4 C )
122
' 123
■ AM- =C,
124
CP K l t I = I v 36
CE' 6 IB
1 ,15
125
HEULE(1,J) = ((C!A(I,J)/.25)*245*«C6 *H6USE(IvJ )4.5)*i»344
' 126
"
127
815 APT = AMT+ HCUoE(IjJ)
. 816
129
U R l T E d C S ' 9131) APT
'
I29
8151 VR I T E U C S /« .170
Isc
:is:
138.
132
1 34
125
136
137
138
139.
DC S 17 P =I.,36
UR I T E (’ I CS' ? I £ C ) K
CS 7 1,7 +=1,3..
CS S 18 -16 = 1,3
818 CRfiPCT( 1 6 ) = CRfiPCT( 1 6 ) +CRfiPO(K j M t 16)
817 U R l T E ( I c P j J i E Q ) M, (CRfiPC (K ' P j> I ) / I = I / 3 )
■ -URI T E d C S j 8 1 9 0 C R S P D T STOP
END ’ 1
COMPUTER SUBROUTINE
• •-.
CALCULATE A:IR. FSLL1^ I3K D-V-1AGCS
'I';.
.2 i
S U 3 ‘;8U.T IKE S T A H < S, N, N|*\CsP, N M s b A Y A 1H S U R )
. IKTliGtR Al (A, A ).« A('+,5'3); A 5 ( 1 4 , 4 ) , T I X E , S
3? ■
.^ I
CATa Al/
'
I^ I^“C = “G 9 / ^ 2 5 /
6
5
IC
U
is
1.4
15
Iqi Sif^
ll;2/2,l,2;3,3,2,3,4,k,i,2,3,3,Q,1.-2,2,0'I'I,I;I,I,1,1., !,1,2,2,
2.1, V I, I,c, I, I, I,C/ I, I^ I, I, I, 2, 2,1,2,3,.3,1, I, 2, 2, c, I, I, I, r/
.
7
2
SE IiSg I»7q I^7 1 3 / 1 2 3 1/ Iqq
■
DAJA AS/
' 13,3*3.,3,4,4,4, 4,4,4,4, t,4,4,2,2,2'2, 3,3, 2, 3, 3,3, 4,4,4,4, I, i,2,2,2,
22,2,2,3,3,3,3,3,4,%,I,I,I,I,i,2,2,2,2,3,3,3,3/
. TIvE =(KHSvR-S)/3 +1
CG IC 1=1,4, .
10 IF('VGDAY.LE.Al(TIh'E,I!) GQ TQ 11
■ I=S
IT S =Ab (K'a KDSF, (A (T IKE, I, N -1))*
• RET1--RK
'
EKD '
OD
to
APPENDIX B
A DESCRIPTION AND LISTING OF PROGRAM TO CALCULATE
CROSS-WIND DISTANCE VARIABLE (y)
As discussed in Chapter V, a change in wind direction for any
receptor field will affect the level of pollution concentration it
suffers, and hence, the damages it sustains.
This program uses the
wind direction data as input to generate changes in cross-wind distance
y, to be used in dispersion equation!(5 -5 ).
The program uses BASIC language, which is gaining, wide acceptance
as a general-purpose computer language, particularly in modern time­
sharing systems..
Each step is numbered, which will facilitate exposi­
tion^
Program to Calculate Cross-Wind Distance Variable for a
Distance of I Miles from Stack
5 DIM M(IOO)
10
DE .= 30
15
MAT READ M(DE)
20
DATA 230,233,245,236,234,235,233,225',. etc.
30
Ml = I
35
N= Ml*2 + I
50
Y =O
51
L — N—2 •
.55
Y= Y +(N-L)*14*(M(N) -M(L)) .
56
N = N-I
•
57
Y = Y+
64
N = N-I
65
IF N > L THEN 56
(N-L) *14* (M.(L)-M(N).)
. ■,
84
70
N + N+l
75
IF N > NE THEN 999
80
PRINT Y
82
N + N+2
85
G0 T0 50
999. ST(Z)P
Step.5 :
This step dimensions the data matrix.
saves 100 spaces for the matrix.
In this case, the computer
Although only.30 entries were read
in as data in this particular problem, the number 100 was chosen to
cover any likely application.
Henceforth, only the; DATA statement
heeds changing.
Step 10;
This step indicates the number of data entries and will be used to
close the run..
Step 15: .
'
This step instructs the computer to read the 30 data entries.
Step 20;
This step enters the 30 wind directions; for a particular 3-hour,
period. ■ 233 represents the 233° win d .direction;, etc.
Step 30:
This step indicates the miles from polluting stack..
85
Steps 35-80:
These steps calculate the cross-wind distance y as follows:
Using the formula.for arc length, equation (5-6) in Chapter V, the
distance center plume line moves away from the receptor field of I mile
can be calculated by estimating the degree (°) change in wind direc­
tion for each period.
Since each wind direction estimate represents
the time it takes for wind to travel one-half mile, the distance of
plume centerline
from a field I mile out depends on wind, direction
at the time the plume left the stack and again at the one-half mile
distance.
Assume a filed, lay in the 240° wind direction and that wind
direction in the previous period was 238°, and the period before that
235°.
How many meters distant would the plume be from the receptor
field?
Using formula (5-6), the first calculation would be:
irr„°
3
^ ~W
(3.14159) (1609)
=
I
s
o
-
5°
140 meters
The half mile calculation would be:
AL
(3.14159)(804.5)
180
42 meters
As the plume left the stack, wind direction was 235°.
Assuming
no directional change, a 5° directional difference (240° - 235°) would
cause the center plume to be 140 meters distant from the field.
However, wind changed directions after moving one-half mile.
Now the
directional change is 3° (235° - 238°), and since the plume is already
86
half the distance to the field— 804 meters, instead of 1,609— 42 meters
must be subtracted from 140 meters to yield a cross-wind distance y
of 98 meters.
For a receptor field I mile distant from the stack., then> crosswind distance y is calculated by. subtracting the differences of wind ■
direction between" a given period and two periods previous, multiplied
by 28, arid algebraically adding this to the difference between wind
direction two periods previous and one period previous, multiplied by
14.
Notice,
^
ap],rollImately 28 ana ^ - I 4^ ) (8 O4 ,5),
is approximately 14.
Each cross-wind distance y represents the distance of plume center
line from a receptor field in a specified wind direction.
Steps 82-85
These steps .increment N , go back to step 50, set y = 0, and begin
the steps necessary to calculate another y . ,
For distances of 2 miles, wind direction is needed ,for four stages
the wind direction when plume leaves.the stack, wind direction at onehalf mile, wind direction at I mile, and wind direction at I 1/2
miles.
The-following-changes were needed in the. program for distances
of 2 miles and for distances of 3 miles..
I
87
For 2 Miles
30
Ml = 2
51
L = N-4
52
Y = Y + (N-L)*14*(M(N)-M(L))
53
N = N-I
54
Y = Y + (N-L)*14*(M(L)-M(N-2))
55 . N = N-I
56
Y = Y + (N-L)*14*(M(N-I)-M(L+2))
57
N = N-I
58
Y = Y + (N-L)*14*(M(L+2)- M (N+2))
60. N = N-I
82
■
N = N+4'
For 3 Miles
30
Ml = 3
51
L = N ^-6
52
Y = Y + (N-L)*14*(M(N)-M(L) )
53
N = N-I
54
Y = Y + (N-L) *14*'(M(L) -M(N-4) )
55 ■N = N-I
56
Y = Y + (N-L)*14*(M(n-3)-M(L+2))
57
N = N-I
58
Y = Y
59
N =' N-l.
60
Y = Y
61
N = N-I
62
Y = Y + (N-L)*14*(M(L+4)-M(N+4))
82
N =■N +6
+ (N-L)*14*(M(L+2)-M(N))
+ (N-L)*14*(M(N+1)-M(L+4) )
APPENDIX C
ADJUSTING POLLUTION CONCENTRATION LEVELS
The Montana State Department of Health, and the National Air
Pollution Control Administration conducted a study beginning in June
through November 1969 of the types, amounts, sources, distribution,
and effects of environmental pollution in the Helena Valley.
In
particular, continous measurements of sulfur dioxide were taken at
five locations, while monthly measurements were taken at approximately
215 locations using Huey sulfation plates.
Sulfation measurements
after November were made.on a three month basis for purposes of
surveillance and obtaining annual sulfation rates.
These figures
were used.for comparison and adjustments of the model used in this
study to predict annual concentrations of sulfur dioxide.
Figure C-I shows the percentage error of actual against predicted
pollution concentrations,
An arithmetic addition of the underpredic­
tions and overpredictions indicates the model underpredicted sulfation
rates by 15 percent.for the combined months of July tilrough November.
Figures C-2 and C-3 were included to show the percentage
differences for two specific months,. July and September.
The model
underpredicted actual measurements by 4 percent in July and by 30
percent in September.,
Using the data from Figure C-I, an iso-error map was drawn
indicating the percentage underestimation and overestimation for all
sectors less than 8 miles distant from the polluting stack.
Depicted
in Figure C-4, this map was used to make the appropriate adjustments
89
to the values estimated.by the model for each sector.
For distances
greater than 8 miles.>. a correction factor of 1.1 was used’ for each
sector, indicating the model to be underpredicting by 10 percent.
A
corrective factor of 10 pergent for all .sector's outside the,.limits of
empirical data would appear to be conservative.
An. R
2
of .74 was calculated before the adjustment., indicating that
74 percent of the variation in observed sulfation levels was explained'■
by variations in.the predicted sulfation level.
calculated after the model was adjusted.
' 2
An R of .99 was-
90
360°
A t -45 “7
0
-30 -14 0
-42\.
3 miles
Figure C-I.
180°
9
= stack
Spatial Distribution of Percentage Differences Between
Actual and Predicted Sulfation Measurements (July November, 1969).
91
360°
3 miles
stack
180°
Figure C-2.
Spatial Distribution of Percentage Differences Between
Actual and Predicted Sulfation Measurements (July 1969).
92
360°
-50 0
-25, -20
+16 0
3 miles
Figure C-3.
stack
Spatial Distribution of Percentage Differences Between
Actual and Predicted Sulfation Measurements (September
1969).
93
I" - 3 miles
(b = stacK
Figure C-4r. An Iso-Error Spatial Distribution of Percentage
Differences Between Actual And Predicted Sulfation
Measurements (July-November, 1969).
APPENDIX D
GLOSSARY OF SYMBOLS USED IN THE PROGRAM •
The symbols used in the program are defined here.
If a symbol
was defined in detail in the program, it will not be defined at
length in this appendix.
A
= absorption rate of the plant
ADJ
= adjustment of pollution concentration in each sector
AMT
= the amount of dollar damages to households resulting from a
3-hour addition to pollution loadings in each sector
CELHT
= ceiling height
CHI
= pollution concentration
CIA
= concentration in each area (sector)
CLDCV
= cloud covei
CROPD
= crop damage in each sector
CROPDT =■ total crop damage
CROPV ■= potential crop value (yield in dollars) in each sector
CSS ■ =: contribution of smaller stacks by the American Smelting and
Refining Company and the Anaconda Company to total pollution
levels in the study area
DAYS
= days (length of study)
EXP
= exponential used in dispersion model
H
= effective stack height
HOUSE. = the number of houses in each sector
11 .
= the absorption rate•of the plant categorized
12
= the date by month and day
95
13
= wind speed in mph
•14
= stability conditions
15
= miles from stack
16
= crop
K
= wind direction
M
= miles from stack
MULT
= multiplier-
If wind speed equals zero', another data card is
read and its contribution to pollution loadings is doubled
for that wind direction
-
NCELHT = ceiling height .
NCLDCV = cloud cover
NDEWPT
NHOUR
= dewpoint
= hour
NMODAY = month and d a y ■
NTEMP • ='temperature .
NWINDI = wind direction
NWNDSP = wind speed ■■
NYR
= year
Q
= emissions.
S
= stability conditions
Sig Z
= vertical dispersion coefficient
STAB
= stability condition subroutine
T
= duration (time) of fumigation
.
"
"
96
wind speeddistance from 'stack, in meters
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