United States
Environmental Protection
Agency
Office Of
The Administrator
(A-101F6)
EPA 101/F-91/047
February 1991
Nitrate Risk Management
Under Uncertainty
#90-2503
Printed on Recycled Paper
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DISCLAIMER
This report was furnished to the U.S. Environmental Protection
Agency by the student identified on the cover page, under a National
Network for Environmental Management Studies fellowship.
The contents are essentially as received from the author. The
opinions, findings, and conclusions expressed are those of the author
and not necessarily those of the U.S. Environmental Protection
Agency. Mention, if any, of company, process, or product names is
not to be considered as an endorsement by the U.S. Environmental
Protection Agency.
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NITRATE RISK MANAGEMENT UNDER UNCERTAINTY
by
Yong W. Lee
Department of Civil Engineering
W 348 Nebraska Hall
University of Nebraska
Lincoln, Nebraska, 68588-0531
This paper describes work performed under the National
Network for Environmental Management studies (NNEMS)
program (contract No. o-913265-oi-o)
U.S. Environmental Protection Agencv
library (PL.
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ABSTRACT
In many areas throughout the U.S., groundwater supplies are
contaminated by nitrates. Nitrate contamination has been a subject
of concern because nitrate salt can induce infant methemoglobinemia
and cancer. Nitrate risk management describes the process of
evaluating nitrate control strategies and selecting the best
management scheme. Available nitrate risk management strategies
(several potential nitrate control methods and possible changes of
health risk level) can be investigated based on the acceptable risk
level and the reasonableness of the nitrate control cost. However,
the objectives of the risk reduction and cost are in conflict, and
each phase of the risk and cost analysis is associated with
uncertainty. In this study, a multicriterion decision-making
methodology is provided to assist decision makers to determine,
under uncertain information, which of the nitrate risk management
strategies "best" satisfies the reduction of both health risk and
cost. A numerical example is illustrated to show how the
methodology can be applied to solve nitrate risk management problem
under uncertainty.
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INTRODUCTION
The purpose of this study is to examine the problem of choosing
the "best" nitrate risk management scheme using a fuzzy composite
programming. Nitrate contamination in groundwater supplies has
been a subject of concern due to the finding that nitrates can
cause infant methemoglobinemia and human cancer. Most nitrates in
groundwater can be traced to the excessive application of
commercial fertilizers. However, some nitrates are contributed by
the fixation of atmospheric nitrogen by plants, industrial wastes,
domestic wastewater, and animal wastes. Generally, nitrate salts
reach groundwater by percolation through the soil.
To reduce nitrate risk from groundwater supplies, several
strategies can be developed based on the acceptable level of human
health risk, the reasonableness of nitrate control cost, and the
technical feasibility of nitrate control methods, where nitrate
control methods include nitrate source control, development of new
water supply, blending two or more water supplies, and direct
treatment of nitrates. High cost strategies may provide a high
degree of human health risk protection, while low cost strategies
may not provide adequate protection. In other words, the objectives
of the risk reduction and cost are in conflict with each other. In
addition, the objectives may be of varying degrees of importance.
Thus, the ultimate goal of the nitrate risk management is to
determine, under the different importance of objectives, which
strategy "best" satisfies the reduction of both human health risk
and nitrate control cost (a risk versus cost trade-off analysis).
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2
In nitrate risk management process, each phase of human health
risk analysis, and possibly nitrate control cost and the technical
feasibility of each control method, is associated with uncertainty.
Sources of uncertainty include exposure assessment, interspecies
conversion, dose-response assessment, and inaccuracy of data used.
The uncertainty in problem variables (risk, cost and technical
feasibility) and its impact on results can be represented with an
application of fuzzy set theory.
The concept of fuzzy set theory is briefly introduced in
Appendix I. The fuzzy set approach, pioneered by Zadeh (1965), has
been widely applied to solve, under uncertainty, decision-making
problems (Watson et al., 1979; Zimmermann, 1985) and, specifically,
multicriterion decision-making problems (Yager, 1977; Bogardi and
Bardossy, I983b; Anandalingam and Westfall, 1988).
In this study, a fuzzy composite programming method is used to
formulate a methodology for solving nitrate risk management
problem. The fuzzy composite programming method has been used as
a useful tool to solve decision-making problems where there are
conflicting objectives; values of problem variables are uncertain;
and the objectives are of varying degrees of importance (Bardossy,
1988; Lee et al., 1990). This is a multi-level multiobjactive
programming method using fuzzy sets.
HEALTH EFFECTS OF NITRATES
Nitrate salts themselves are probably harmless to humans. The
human health hazard of nitrates results from the nitrites formed by
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the bacterial conversion of ingested nitrates. These nitrites
induce methemoglobinemia and possibly cancer.
Infant Methemoglobinemia
Nitrate ion has been known as the causative agent of methemo-
globinemia, which is more commonly called the "blue baby" syndrome.
This disease usually occurs to infants and pregnant women, in
particular infants under 3 months of age are more susceptible (WHO,
1978). Sine the pH of the infant's gastric juice is relatively
high (from 5 to 7) , nitrate-reducing bacteria can live in the
infant's stomach rather than being limited to the intestines as in
older children and adults (Andersen, 1980). As shown in Figure 1,
nitrate is reduced to nitrite by the nitrate-reducing bacteria in
the stomach, and the nitrite is absorbed in blood and converts
hemoglobin (a protein in red blood corpuscles) into methemoglobin,
which can not carry oxygen to the body's tissues.
Nitrate
nitrate-reducing bacteria
Nitrite
Hemoglobin
methemoglobin
methemoglobin-reducing
bacteria
Figure 1. Basic Reaction in the Development of Methemoglobinemia
from Nitrate (Winton et al., 1971).
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The American Public Health Association performed a survey of
infantile nethemoglobinemia cases (Walton, 1951). Results of the
survey are summarized in Table 1. Table 1 also shows results of
the study conducted by Winton et al. (1971). Based on these two
studies, the methemoglobinemia can occur to infants consuming water
which contains nitrates over 10 mg/1 (as N).
Table 1. Nitrate Toxicity Studies
Nitrate-nitrogen
concentration (mg/1)
0-10
11 - 20
20 - 50
51 - 100
> 100
< 1.0
1.0 - 4.9
5.0 - 9.9
10.0 - 15.0
Number of humans
investigated
Of 214 data
available
63
23
20
5
Number with
methemo-
globinemia
0
5
—36
81
92
0
0
0
3(*)
Source
Walton
(1951)
Winton et
al. (1971)
(*) infants with methemoglobin level of 5.9 % higher than normal
level of about 1.6 %. A level greater than 3 % is defined as
methemoglobinemia (U.S. EPA, 1987).
Human Cancer Risk
Nitrites, produced by the reduction of the nitrates, react in
the stomach with amines and amides to form nitrosamines and
nitrosamides, which induce cancer (Mirvish, 1977). There is no
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5
conclusive evidence that nitrates are responsible for human cancer
yet. However, some studies have shown that nitrate ingestion can
be the cause of human cancer (Mirvish, 1977; Lu et al., 1984;
Crespi and Ramazzotti, 1990).
Since there are no data related directly to cancer incidence in
humans, data obtained from animal experiments can be applied to
estimate the human cancer risk caused by nitrates. This
interspecies conversion is performed under the assumption that
nitrosamines are as carcinogenic in humans as they are in animals.
Although the interspecies conversion is a controversial issue, it
may be the "only" method, short of extensive epidemiological
studies, for modelling the relationship between nitrate dose to
humans and its corresponding cancer response.
Lee et al. (1990b) performed a study to estimate human cancer
risk corresponding to a particular dose of nitrate. In this study,
animal data obtained by Terracini et al. (1967) were used for the
interspecies conversion (from animal to human), and a combined
probabilistic/fuzzy set framework is used to represent the un-
certainty in values reguired for the interspecies conversion. Based
on the study, the relationship between human nitrate dose (X,
g/day) and its corresponding cancer response (Y) is as follows:
(1 + expfZ,))'1 <; Y < (l + exp(Z2))-1 (i)
where:
Z, = 3.331 + (1-p) 1.138 - 3.429(logcX) + (1-p)0.881|logftX|
Z2 = 3.331 - (l-p)1.138 - 3.429(logeX) - (1-p) 0.8811 logeX| .
where the response Y is the probability of developing cancer, and
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the value p (0 < p £ 1) is used to define the domain for the
interval value of the response Y. Thus, the response Y is a fuzzy
number (fuzzy probability) that belongs to a given set (interval)
with a degree of membership (p). Figure 2 shows the lower and
upper bound lines for the response Y calculated by using the value
p = 0.5 which is neither optimistic nor pessimistic.
0.0
0.0 0.8 1.6 2.4 3.2 4.0 4.8
HUMAN DOSE OF NITRATE (g/day)
5.6
6.4
Figure 2. Response versus Human Dose of Nitrate When p = 0.5.
NITRATE CONTROL METHODS
Some studies have identified methods for reducing or removing
nitrates from water supplies (Musterman and Bergo, 1980; Sorg,
1980; Dahab, 1987). In this section, the nitrate control methods
are reviewed as follows:
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Nitrate source Control
Contamination of groundwater by nitrate can be decreased by
efficiently managing the agricultural, industrial and urban systems
which generate nitrates. In other words, nitrates can be reduced
by decreasing the use of commercial fertilizer in the agricultural
area and including a nitrification/denitrification process in the
wastewater treatment systems. However, if these methods are
implemented, a very long period of time would be required to
improve the quality of groundwater contaminated by nitrates because
of the large storage capacity for nitrate in the soil and the long
residence time of groundwater. In addition, it seems to be
economically and politically infeasible to enforce stringent enough
fertilizer control actions which would reduce the contamination of
nitrate.
Development of New Water Supply
The method of developing new water supplies can be considered
if nitrate-free water sources exist in the area. First, surface
water can be a source of the new water supply. However, undeveloped
or partially developed surface water supplies can be expensive
because of the expenditure required to remove other contaminants
such as organic materials and suspended solids. Second, new wells
can be constructed to draw water from a nitrate-free aquifer. The
disadvantage of this method is that the quality of water drawn from
the new wells might be changed with pumping and time. The third
alternative is to purchase water from a neighboring community.
However, in this case the community would have no control over its
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8
water supply and would become dependent on the neighboring
community. Finally, bottled water could be used for individual
systems or very small communities.
Blending Two or More Water Supplies
Blending nitrate-contaminated water with uncontaminated water
of different source can be a reasonable approach if a "good" source
of water exists in the area. To implement this approach, a
blending facility and new piping systems should be constructed,
which may require a large expenditure.
Treatment of Existing Water Supply
Techniques for nitrate treatment include ion exchange, reverse
osmosis, biological denitrification, electrodialysis, chemical
reduction, and distillation. Currently, the first three mentioned
above can be considered practical and economical. Those three
techniques are discussed below.
Ion exchange
The nitrate treatment process by ion exchange is accomplished
by contacting nitrate ions in solution with the ion exchange resin
which in turn releases sodium ions into the solution. The nitrate
removal efficiency by this process varies with the quality of the
water. For example, high sulfate water can lower the efficiency of
the process because ion exchange resins generally prefer sulfate
ions over nitrate ions for exchange. Thus, high sulfate water is
more costly to treat than low sulfate water. As a result, if the
water is low in concentration of total dissolved solids, the ion
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9
exchange technique for nitrate removal is practical and economical
(Sorg, 1980). In addition, the cost of the brine disposal should
be considered before the ion exchange process is applied for a
full-scale system. In some situations, disposal of the regenerant
brine may account for a large fraction of the overall cost of the
process. Potential alternatives for the brine disposal include
discharge to the local municipal wastewater treatment plant,
application to the land, transport to the other treatment plant,
and disposal in the ocean.
In the United States, several full-scale ion exchange plants
were operated at the Long Island in New York (Gregg, 1973) and
currently at several locations in California (Lauch and Guter,
1986; Guter and Kartinen, 1989). Each of the plant operates to
treat the part of the influent water and blend the treated water
with the raw water so the blended effluent water has a nitrate
concentration lower than the drinking water standard of 10 mg/1 (as
N).
Reverse osmosis
Reverse osmosis is a process which is used to remove ionic
species (e.g., nitrates) from the water by forcing the water to be
transported across a semipermeable membrane. The nitrate removal
efficiency by this process is dependent on operating pressure and
the type of membrane. This process involves high cost resulting
from the intensive energy requirement. However, the process is
fairly effective for other processes under certain situations.
That is, the use of the reverse osmosis process is warranted when
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10
the water supply is high in total dissolved solids, and/or when
nitrate and other contaminant(s) removal from water supply is
required (Sorg, 1980). There are some full-scale reverse osmosis
plants in the United States such as one in the Greenfield, Iowa
(Laverentz, 1974) and in the City of Cape Coral, Florida (Ashton,
1986). However, none of the plants was specifically designed to
remove nitrate.
Biological denitrification
Biological denitrification process is conducted by contacting
facultive microorganisms with the water supply containing nitrates.
Under this contact, the microorganisms utilize the nitrates as a
terminal electron acceptor in place of the molecular oxygen,
reducing the nitrates to the nitrogen gas which is harmless.
Although this process has a well established history in the realm
of wastewater treatment, full-scale application of the process in
the U.S. has not been introduced to the field of water treatment
due to the potential contamination by organics and microorganisms
of the treated water supply. There are large-scale plants being
operated in Europe (Rogalla et al., 1990).
With laboratory-scale experiments, Dahab and Lee (1988) have
studied the potential of using biological denitrification for
nitrate removal in groundwater supplies. The result of the study
showed that the concentration of nitrates as high as 100 mg/1 (as
N) can reduced to levels below 1.0 mg/1. This high efficiency
(nearly 100 percent) can not be practically achieved by other
processes available for nitrate removal. Furthermore, wastes
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11
(excess biological growth) produced from the process is much easier
and less expensive to dispose of than wastes produced from other
nitrate removal processes (Dahab, 1990). Consequently, the
biological denitrification process can be used as a pretreatment
step in a water purification system because the post treatment
steps are required to remove residual organics and microorganisms.
METHODOLOGY FOR NITRATE RISK MANAGEMENT
In this section, a methodology is provided to assist decision
makers to determine the "best" nitrate risk management strategy,
that is, the one that best satisfies the objectives of problem
variables such as risk, cost and technical feasibility. To
formulate the methodology, fuzzy composite programming method
(Bardossy, 1988; Lee et al., 1990) is employed. Fuzzy composite
programming organizes a problem into the following sequential
format: 1) define management strategies 2) define basic
indicators, 3) group basic indicators into progressively fewer,
more general, groups, 4) evaluate and rank the management
strategies.
Selection of Basic Indicators
To represent both potential benefits and problems of each
nitrate risk management strategy, basic indicators are selected.
These indicators are then used as the input variables to evaluate
each strategy. This example is shown in Table 2. Because the
selection of the basic indicators tends to be case specific, it is
difficult to generalize. In other words, the kind of basic
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12
indicators varies with the nitrate control methods applied, and the
number of basic indicators depends on the level of analysis desired
(preliminary or detailed).
Table 2. Basic indicators and their Definition
Basic indicators
Methemoglobinemia
Human cancer
Adverse impact of
performance
Status of technology
Ease of operation
Cost
Definition
The level of methemoglobinemia risk
associated with nitrate contamination.
The level of human cancer risk related
to nitrate contamination.
Adverse environmental impact that occurs
by performing a process to remove
nitrates from water supplies.
Suitability of the method used to remove
nitrates, and assessment of whether or
not its technology is fully developed.
Evaluation of whether the employed
method or process is easy to operate.
The expenditure required to reduce
health risks and adverse environmental
impact below specified levels.
Composite Procedure
The composite procedure involves a step by step regrouping of
a set of various basic indicators to form a single indicator
(Bogardi and Bardossy, 1983a). Figure 3 shows an example of the
indicator grouping. The set of basic (first-level) indicators is
grouped into a smaller subset of second-level indicators. For
example, the basic indicators such as risks of methemoglobinemia
and human cancer can be grouped into human health risk, an element
of the subset of second-level indicators. The status of technology
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13
and the ease of operation are grouped into the technical feasi-
bility, the other element of the subset of second-level indicators.
Further, second-level indicators such as human health risk and
the adverse impact of performance are grouped into environmental
risk, an element of the subset of third-level indicators.
Similarly, the final indicator (system) can be formed by composing
environmental risk, technical feasibility and cost.
Level 1
Level 2
Level 3
Level 4
Methemoglobinemia
Human cancer
Human health
risk
Adverse impact
of performance
Adverse impact
of performance
Environmental
risk
Status of technology
Ease of operation
Technical
feasibility
Technical
feasibility
Cost
Cost
Cost
Figure 3. Example of Composite Structure.
Trade-off Analysis
The values of the basic indicators for nitrate risk management
process are estimated as fuzzy numbers to characterize their
uncertainty. The fuzzy numbers are values which belong to a given
set (interval) with a degree of membership. In order to evaluate
the various nitrate risk management strategies under uncertainty,
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14
let Zj (x) be a fuzzy value for the i-th basic indicator, and let
its membership function /jfZ,. (x)) be a trapezoid (Figure 4), where
x is one element of the discrete set of nitrate risk management
strategies. Note that if the trapezoid is reduced to a vertical
line, it represents a so-called crisp number. At this time, a
level-cut concept (Dong and Shah, 1987) can be used to define the
interval of each basic indicator at various levels of "confidence".
As shown in Figure 4, Z. h is the interval value of the i-th basic
indicator at level-cut h (i.e., a < Z, h < b) .
i, n
most likely interval
i.o H
h -
0.0
i r
b
largest likely interval
Figure 4. Fuzzy Estimate of the i-th Basic Indicator.
Since the units of basic indicators such as risk and cost are
different and thus difficult to compare directly, the actual value
of each basic indicator (Z, h(x)) should be transformed into an
i ,n
index. As shown in Figure 5, using the best value (BESZ,-) of Z{ and
the worst value (WORZ^) of Z, for the i-th basic indicator, the
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15
actual value Z, h(x) can be transformed into an index value Sf WORZ,, then
1 , Z,jh(x) £ BESZ,
Z, h(x) - WORZ,
BESZ, - WORZi
-, WORZ, < Z,fh(x) < BESZ,.
, Zj>h(x) < WORZ,-
2) If BESZj < WORZ,., then
1 , Zi/h(x) < BESZ,.
Zj>h(x) - WORZ,
BESZj - WORZj
, WORZ, < Zijh(x) < BESZj
, Zi/h(x) >
(2)
(3)
a) BESZj >
1.0 -
d •
S|fh<*>
c •
0.0
b) BESZ,. <
1 f> J
d -
S|fh(*>
c •
0.0
WORZj
^^
^^
^^
WORZ,. a b BESZ, zi,h(x)
WORZ,
""\^
"^^
^^^^
BESZ, a b WORZ,
Figure 5. Transferring the actual value Z, h(x) into an index S.>h(X)
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16
To assign the best and worst values (i.e., BESZ{ and WORZ.) of
the i-th basic indicator, we can use one of two options. The first
option is to assign the best and worst values of the i-th basic
indicator according to the overall best and worst values of the i-
th basic indicator, among the given strategies. The second option
is to assign the best and worst values of the i-th basic indicator
according to the opinion of expert. Since the actual value Z.jh(x)
is an interval with lower bound a and upper bound b (i.e., Zf h(x)
e [a, b]), the index value S? h(x) resulting from Zi h(x) is also an
interval (i.e., S,. h(x) e [c, d]) (Figure 5).
Next. index values, Lih(x), for second-level composite
J »n
indicators can be calculated by using the index values of basic
indicators, or:
nj
Ljrh (x) = C =wi.j (Si,h,j(x»PJ 1<1/V («>
where:
n, = the number of element in the second-level group j,
S,. h - = the index value for the i-th basic indicator in the
second-level group j of basic indicators,
w{ - = the weight reflecting the importance of each of basic
indicators in group j; Z w, j = 1, and
p. = the balancing factor among indicators for group j.
Weights represent the relative importance between indicators in
a group. The greater the importance of an indicator, the greater
should be the weight assigned to it. The balancing factors are
assigned for each group of indicators. The balancing factor p
(p > 1) reflects the importance of the maximal deviations of the
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17
indicators, where maximal deviation means the maximum difference
between an indicator value and the best value for that indicator.
The processes available for determining the weights and balancing
factors are given in detail elsewhere (Lee et al., 1990).
Using the index values for second-level indicators, index
values, Lkh(x), for third-level composite indicators can be defined
as:
nk
LM <*> = t.^J-k (6)
K™~i
where:
Lk.h ~ the i°dex value of the third-level group k in the
final group (system),
wk = the weight representing the importance among elements
in the final group, and
p = the balancing factor for the final group.
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18
Note that the process of computing the index value is applicable
to fewer or more than the four levels used in this study.
Ranking Management strategies
As the first step for determining the ranking of various
nitrate risk management strategies, let L(x) be the fuzzy number
representing the final composite indicator (system) of strategy x.
In other words, the index value, L(x), of the final composite
indicator is given as a fuzzy number. With the help of two index
values L^fx) and I^.gfx) (Equation 6), the membership function,
M(L(x)), of the fuzzy number L(x) can be approximately calculated
from the piecewise linear function (Figure 6):
L(X) - R^
» Rmin * L
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19
by applying a ranking method such as the one developed by Chen
(1985). This method determines the ranking of n fuzzy numbers by
using a maximizing set and a minimizing set (Figure 7).
0.0
L(x)
Rmax ~" ^in
Figure 6. Membership Function of Fuzzy Number L(x)
membership
value
1.0 -
0.0
max ~" min
Figure 7. Ranking Method of Fuzzy Numbers.
O left utility value
right utility value
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20
The maximizing set M is a fuzzy subset with membership function
given as:
*" TI"^' Lmin - L - ^
0 , otherwise.
where for x = 1, ..., n, Lmjn = min [ min L^x)] and Lmax = max
[max L^o (x)].
Then, the right utility value, UR(x), for strategy x is defined as:
UR(X) = max{ min [MM(L), M(L(x))]} (9)
The minimizing set G is a fuzzy subset with membership function MG
given as:
' min — — max
- Lmax (10)
0 , otherwise.
The left utility value, UL(X), for strategy x is defined as:
UL(x) = max{ min [MC(L) , /i(L(x))]} (11)
The total utility or ordering value for strategy x is:
U(x) = (UR(x) + 1 - UL(x))/2 (12)
The strategy that has the highest ordering value in the discrete
set of strategies is then selected as the "best" strategy.
ILLUSTRATIVE EXAMPLE
A community with a nitrate water quality problem is chosen for
the illustrative example. Currently, the community consumes one
million gallon of water per day (MGD) , and the community's only
water source is groundwater that has nitrate level of 20 mg/1 (as
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21
N), sulfate level of 120 mg/1, and total dissolved solids of 800
mg/1.
Table 3 shows five strategies available to the community to
reduce the nitrate level in the community's water supply.
Strategies 1 and 2 treat all of the influent water (1.0 MGD) by
using biological denitrification and ion exchange, respectively.
Strategies 3 and 4 treat 80 percent of the influent water by using
biological denitrification and ion exchange, respectively, and the
treated water (0.8 MGD) is blended with the raw water (0.2 MGD).
These treatment rates are determined to achieve the target level of
nitrate in the finished water (acceptable human health risk level) .
To calculate the treatment rates, it is assumed that the nitrate
removal efficiency is 85 - 95 % for biological denitrification and
60 - 80 % for ion exchange. Strategy 5 is to blend the existing
water with groundwater of different source. The amount of ground-
water which can obtain from the different source is 0.6 MGD, and
the water includes nitrates in the range of 0 to 6 mg/1 (as N).
Table 3. Nitrate Risk Management Strategies for the Example
Community
Strategy
1
2
3
4
5
Nitrate control method
Biological denitrification
Ion exchange
Biological denitrification
Ion exchange
Blending two water supplies
Nitrate in the finished
water, mg/1 (as N)
1-4
4-7
4-7
7-10
8-12
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22
Table 4. Basic indicator values for five different strategies
strategies
1
2
3
4
5
basic
indicators
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
most likely interval
low
1.0
5.5xlO'10
11.4
0.4
0.2
950
0.9
l.lxlO'8
4200
0.6
0.5
570
0.9
l.lxlO'8
9.1
0.4
0.2
760
0.8
6.2xlO"8
3500
0.6
0.5
456
0.2
1.2xlO'7
0.0
0.9
0.8
523
high
1.0
9.2xlO'8
12.6
0.6
0.4
1050
1.0
l.OxlO'6
4640
0.8
0.7
630
1.0
l.OxlO'6
10.1
0.6
0.4
840
0.9
3.5xlO'6
3870
0.8
0.7
504
0.4
5.7xlO'6
0.0
1.0
0.9
578
largest likely interval
low
1.0
l.7xlO"11
9.6
0.3
0.1
800
0.8
3.4xlO"9
3540
0.5
0.4
480
0.8
3.4xlO'9
7.7
0.3
0.1
640
0.6
3.0xlO'8
2950
0.5
0.4
384
0.0
4.9xlO'8
0.0
0.8
0.7
440
high
1.0
3.7xlO'7
14.4
0.7
0.5
1200
1.0
2.0xlO"6
5300
0.9
0.8
720
1.0
2.0xlO"6
11.5
0.7
0.5
960
1.0
5.7xlO'6
4400
0.9
0.8
576
0.5
9.9xlO"6
0.0
1.0
1.0
660
* (1); methemogloblnemia, (2); cancer risk, (3); adverse impact of
performance, (4); status of technology, (5); ease of operation,
(6); the total cost required for capital and O & M (dollar/day).
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23
Table 4 contains data of the basic indicators for each of the
strategies. Data on cancer risk are calculated by using Equation
1, and cost data are obtained from the literatures (Sorg, 1980;
Dahab, 1987; Guter and Kartinen, 1989). The cost data assigned to
strategy 5 are hypothetical. Data on the adverse impact of
performance correspond to the volume (m3/day) of wastes produced
from the process used to remove nitrate. Data on methemo-
globinemia, the status of technology and the ease of operation are
assigned by transferring qualitative definitions into numerical
values. For example, the basic indicator "status of technology" can
be characterized with qualitative definitions such as bad, good,
excellent, and numerical values corresponding to the qualitative
definitions can be obtained using Figure 6.
Numerical
value
1.0 -I
0.5 -
0.0
bad
quite good very
good good
excellent
qualitative
definitions
Figure 6. Transferring qualitative definitions to numerical values.
As shown in Table 4, the value of each basic indicator is
represented by two intervals (i.e., most likely interval and
largest likely interval) to reflect the uncertainty in each basic
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24
indicator. These intervals are used to construct the membership
function (Figure 4) for each basic indicator. Table 5 displays the
best and worst values of the six basic indicators, and the weights
and balancing factors assigned to each indicator are shown in Table
6.
Table 5. Best and Worst Values
Basic Indicators
Methemoglobinemia
Human cancer
Adverse impact
Status of technology
Ease of operation
Cost
Best value
1.0
l.7xlO'11
0
1.0
1.0
384
Worst value
0.0
9.9X10'6
5300
0.3
0.1
1200
Table 6. Weights (w) and Balancing Factors (p)
Basic
indicators
Methemoglobinemia
Human cancer
Adverse impact
of performance
Status of
technology
Ease of
operation
Cost
w
0.6
0.4
1.0
0.5
0.5
1.0
P
1
1
2
1
Second- level
indicators
Human health
risk
Adverse impact
of performance
Technical
feasibility
Cost
w
0.9
0.1
1.0
1.0
P
2
1
1
Third-level
indicators
Environmental
impact
Technical
feasibility
Cost
w
0.4
0.3
0.3
P
2
Final
indicator
System
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25
With the help of Tables 4, 5 and 6, the fuzzy composite
programming software developed by Lee et al. (1990a) was used to
determine which of the five nitrate risk management strategies
"best" satisfies the objectives of basic indicator variables. The
software is microcomputer-based and utilizes the methodology
described in the previous section. Using the software, the
ordering value for each of the five strategies can be calculated as
shown in Table 7.
Table 7. Ranking of Nitrate Risk Management Strategies
Ranking
1
2
3
4
5
Strategies
Strategy 2
Strategy 4
Strategy 5
Strategy 3
Strategy 1
Ordering values
0.548
0.547
0.494
0.362
0.345
The microcomputer-based software provides the trade-off
information in numerical and graphical form. The graphical output
is displayed in the form of a box so it is easily interpreted by
decision makers. Figure 7 shows an example for the boxes formed
between environmental risk and cost for each nitrate risk
management strategy. The risk-cost boxes are produced as the
result of trade-offs between indicators under the third-level
indicators, and the widths of the boxes represent the uncertainty
in trade-offs. With the boxes formed between the risk and cost, we
can identify the status of the trade-off analysis. That is,
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26
Strategy 1 provides the lowest risk, but it requires very large
cost. The strategy 4 provides the lowest cost, but it does so at
a relatively high risk. Based on the widths of the risk-cost
boxes, Strategies 4 and 5 include relatively high uncertainty.
Using Equations 2 and 3, the closer the actual value of the i-th
basic indicator is to the best value, the closer the index value
resulting from the actual value is to 1.0. Thus, the "ideal point"
located at (1,1) in Figure 7 represents the lowest cost and the
largest reduction in environmental risk.
Ideal
Point
O
o
1 .U-
n q.
0.8-
n 7
0 6-
0.5-
0.4-
0.3-
0.2-
0.1 -
n n.
Strategy 4
Strategy 5
2
Strategy 3
W
Strategy 1
0.0 0.1 0.2 0.3
0.4 0.5 0.6
Environmental Risk
0.7 0.8 0.9 1.0
Figure 7. Risk versus Cost Boxes shown at Level-cut h=0.
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27
DISCUSSION AND CONCLUSIONS
In this study, a multicriterion decision-making methodology was
developed to assist decision makers to solve nitrate risk
management problem under uncertainty. In the methodology, the basic
indicator values are transferred into fuzzy numbers to represent
their uncertainty. Using these fuzzy numbers, the uncertainty in
the basic indicator values can be incorporated into the trade-off
analysis.
For the illustrative example, strategy 2 is ranked as the best
of the five strategies because it has the highest ordering value
(Table 7) . Strategy 2 appears to be the most cost effective
alternative. This can be demonstrated by comparing with the "next
best" strategy for the cost. Since the ordering value of strategy
4 is close to the ordering value of strategy 2, it may be
reasonable to consider a combined use of the strategies 2 and 4.
Combining the two strategies means changing nitrate level in the
finished water because both of them use ion exchange process to
remove nitrate in the water supply (Table 3) . Note that the final
result (ranking of the strategies) varies with the weights and
balancing factors assigned to each indicator and group.
Results of this study lead to the following conclusions:
1. The uncertainty in the values of the basic indicators selected
for nitrate risk management can be represented using the fuzzy
set approach.
2. The fuzzy composite programming method can be a useful tool for
solving nitrate risk management problem where there are
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28
conflicting objectives; values of the basic indicator variables
are uncertain; and the objectives are of varying degrees of
importance.
3. This study shows how the fuzzy composite programming method can
be employed to formulate the methodology for nitrate risk
management.
4. Under the situation of the illustrative example, ion exchange
is the most effective nitrate removal method, that is, the
method shows the "best" compromise between environmental risk,
technical feasibility, and nitrate control cost.
ACKNOWLEDGEMENT
Research leading to this paper has been supported by the U.S.
Environmental Protection Agency (contract No. U-913265-01-0). The
author wishes to express his sincere appreciation to Dr. Bogardi
and Dr. Dahab, professors in the Department of Civil Engineering,
University of Nebraska-Lincoln. Their comments and suggestions
were very useful.
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29
APPENDIX I.- CONCEPT OF FUZZY SET
Fuzziness represents situations where membership in sets can
not be defined on a yes/no basis because the boundaries of sets are
vague (Zadeh, 1965). The central concept of fuzzy set theory is
the membership function which represents numerically the degree to
which an element belongs to a set. In a classical set, a sharp or
unambiguous distinction exists between the members and non-members
of the set. In other words, the value of the membership function
of each element in the classical set is either 1 for members (those
that certainly belong into the set) or 0 for non-members (those
that certainly do not) . However, many sets such as the sets of
tall men, beautiful women, highly contaminated water or numbers
much greater than 1.0, do not exhibit this characteristics. That
is, their boundaries are fuzzy.
Since the transition from member to non-member appears gradual
rather than abrupt, the fuzzy set introduces vagueness (with the
aim of reducing complexity) by eliminating the sharp boundary
dividing members of the set from non-members (Klir and Folger,
1988) . Thus, if an element is a member of a fuzzy set to some
degree, the value of its membership function can be between 0 and
1. When the membership function of an element can only have values
0 or 1, the fuzzy set theory reduces to the classical set theory.
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30
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