OPTIMIZATION
OF A M B I E N T AIR Q U A L I T Y M O N I T O R I N G NETWORKS
(Part III) P R A S A D M. M O D A K
Environmental Science and Engineering Group, Indian Institute of Technology, Powai, Bombay, 400 076, India and B. N. L O H A N I
Environmental Engg. Division Asian Institute of Technology, P.O. Box 2754, Bangkok, Thailand, 10501
(Received 9 July, 1984) Abstract. The methodologies presented in Parts I and II (refer Modak and Lohani, 1984a and b) are
essentially for deciding the best number and configuration for a single pollutant monitor. In practical situations however, Air Quality Monitoring Networks (AQMN) are expected to measure more than one pollutant and therefore simultaneous consideration of different types of pollutants must be made. In this paper, two new approaches have been developed for the multipollutant AQMN design. The first method makes use of the index theory and the other makes use of the principles of Pareto optimality. As an illustration of these methodologies, an example from Taipei City, Taiwan is considered.
1. Introduction
The methodologies presented in parts I and II (refer Modak and Lohani, 1984a and b) are applicable for deciding the number and configuration of a single pollutant monitor. In practical situations however, Air Quality Monitoring Network (AQMN) are expected to measure more than one pollutant and therefore the optimization procedure warrants simultaneous consideration of different types of pollutants. Normally, the primary or quasi-stable pollutants such as sulfur dioxide, carbon monoxide and suspended particulates are routinely measured in most AQMNs today. Monitoring of reactive pollutants such as ozone, hydrocarbons and the nitrogen oxides is also becoming common at a number of installations. Unfortunately, the problem of multi-pollutant AQMN design has often been considered to be analogous to that of single pollutant design. Surprisingly and oddly enough, recent books on the AQMN design such as Noll and Miller (1977) and Munn (1981), do not discuss methodologies for consideration of multiple pollutants. A few research workers in the past, notably Darby et al. (1974) and Brady (1978) have made some attempt to incorporate more than one pollutant in their design methodologies. In this paper, two new approaches have been developed for multi-pollutant AQMN design. The first makes use of the index theory and the other makes use of the principles of Pareto optimal compromise. To begin with however, it may be appropriate to discuss some basic considerations in the multi-pollutant AQMN design with respect to pollutant specificity and philosophy of common monitoring sites. EnvironmentalMonitoring and Assessment 5 (1985) 39-53. 9 1985 by D. Reidel Publishing Company.
0167-6369/85.15.
40
P. M. MODAK AND B. N. LOHANI
2. Pollutant Specificity and Philosophy of Common Sites In general, it has been observed that every moderate or large scale multi-pollutant A Q M N adheres to a policy of retaining a maximum number of common sites, i.e., sites where a number of pollutants are simultaneously measured. Networks with pollutant specific sites are rare. Economic and assessment considerations appear to be the principal reasons for such a preference to a common site multiple pollutant AQMN design.
3. Economic Considerations Every pollutant has its characteristic variability due to its specific emission sources, rates of diffusion as well as transformations; and therefore it is expected that the number and location of monitors would be specific for each pollutant. Recent studies carried out by Karl (1980), Handscombe and Elsom (1982) and Hanna (1982) also support such a possibility. It is quite logical therefore to expect that the optimum number and configuration are pollutant specific. For instance, pollutant A having a spatial variability more than pollutant B, is expected to require more monitors in order to represent regional patterns. Further, pollutant A and pollutant B may require the same number of monitors, but then it is possible (or likely) that their optimal configurations would be different. It is therefore expected that in a pollutant specific design, the number of sites is expected to be almost equal to the number of monitors installed, i.e., it is unlikely that a site would be common to the best interests of several pollutants. It could therefore be observed that the costs of siting (installation and maintenance) in a pollutant-specific design would be higher than that for a common site design. For a common site network, the costs of installation and maintenance of the monitoring sites are shared amongst the pollutants, and therefore the total cost of the monitoring effort is reduced. The analysis of the AQMN costs, as reported by Hickey et al. (1971) indicates that the more the monitors at a single monitoring site, the more economical the system is to initiate and to maintain. In other words, it is economical to install and operate an A Q M N having many monitors at a site than an AQMN incorporating the same number of monitors at several different sites. The results of Hickey et al. (1971) therefore favour a common site approach to the AQMN design.
4. Assessment Considerations In many instances, a common-site design is prefered due to the following considerations. (1) Exposure assessment is never complete when only one pollutant is measured. It is well known that several pollutants are synergistic and therefore it is mandatory to measure certain pollutants at a common site. A case of sulfur dioxide and that of total suspended particulates could be cited as an example. An increasing practice of reporting
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
41
monitoring station data in terms of an aggregation, such as an Air Quality Index (AQI) also supports the interest of having a maximum number of common monitoring facilities. (2) If more than one pollutant is measured at a common site, then missing value estimation for a pollutant is possible especially when the cross-correlations between the other pollutants are quire high and are already established. Stern (1976) notes that the trend toward monitoring a number of pollutants at a common site is expected to increase in future. This is expected to be particularly true for the assessment of photochemical smog, which depends on nitric oxide, nitrogen dioxide, ozone, and hydrocarbons, etc. The above benefits of maintaining common sites may be impossible to quantify. In recent years therefore, there has been a growing trend to design multi-pollutant monitors which are capable of simultanious measurement of more than one (normally two to five) pollutants. Multi-pollutant monitors for carbon monoxide, hydrocarbons, nitrogen oxides and ozone are particularly popular. One of the typical features of these multipollutant monitors is that their cost is often less than the total costs of purchasing individual monitors. Such a bonus therefore adds to the list of advantages to a common site network design to make it a rather attractive proposition. To conclude therefore, pollutant-specific designs are rarely envisaged and normally a policy of installing a network with a maximum number of common sites is prefered.
5. Multi-Pollutant AQMN Desing Using Air Quality Index A simple approach to the multi-pollutant AQMN design is to aggregate air pollutants in the form of an Air Quality Index (AQI). Once the multi-pollutants are converted in the form of a single variable, methodologies such as the utility and the sequential interactive approach (discussed in Part II, Modak and Lohani, 1984b) could readily be used. A method based on AQI has an implicit assumption that all the monitoring sites are common to multiple pollutants. A number of AQI could be used for such an aggregation (Ott, 1978).
6. Limitation of the Index-Based AQMN Design It is expected that the results of the index approach would heavily depend on the specification of the index structure function. One could obtain different designs of the A Q M N for different index formulations. Secondly, when more than three to four pollutants are involved, it would not be correct to substitute for pollutant specificities by a mere blanket function in the form of an index. Historically, the idea of an AQI has been to represent the interest of the severity of a combination of pollutants. The interest of the AQI has certainly n o t been to represent the spatial variability. This distinction is indeed important in the application of the index theory to AQMN design. To illustrate, an AQI derived for two pollutants such as the sulfur dioxide and the Coefficient of Haze (COH) would represent the severity of two pollutants in combination (though synergistic relationships are often not possible to incorporate) but not the variability of each. The
42
P. M. MODAK AND B. N. LOHANI
variability of the AQI, which would depend upon the choice of the structure function, would certainly be different than the original variables, i.e. pollutants. It is possible therefore that an optimized AQMN based on AQI, for total coverage (Equation (7)), may not provide adequate pattern representation for the pollutants under consideration. In some cases, if the sources and the diffusion characteristics of pollutants are not widely different, then it is possible that an AQI-based design may satisfy a criterion of coverage for all the pollutants. The index approach may not work well however, when pollutants of significantly different variabilities are involved such as primary and secondary or reactive and quasi-stable pollutants. Yet another difficulty with the index approach is that there is no explicit way to indicate pollutants preferences. This is especially important since in some cases the Decision Maker (DM) may be more interested in sulfur dioxide than in COH or vice versa. Lastly, the index approach is attractive only for certain well defined combinations of pollutants for which an index has been defined or routinely reported. The index-oriented approach is then an approximate method to the multi-pollutant design of the AQMN.
7. A Pareto Optimal Approach to Multi-Pollutant Design The principal objective of the Pareto optimal network is to look for something attractive for a group of pollutants as a whole rather than focussing on specific pollutants. The basic idea in such a philosophy is to have maximum opportunity of measured several pollutants at common sites. A design for such a compromise is described herein as the Pareto Optimal Design (POD). This approach differs from the index method because in this case, the specificity of each pollutant is explicitly retained in the optimization procedure both in terms of its severity (violations) as well as in terms of spatial variability. An approach of additive utility to accommodate a global i~terest of various subutilities (all of which are to be maximized) is normally categorised as a method of Pareto optimality. Approaches based on the POD are gaining popularity in the multicriterion decision-making literature. A POD could be defined as follows: If the shape function U(u) is POD, then for any other U(u) either the values of all the objective functions remain the same or at least one of them worsens compared with its value at U(u). A POD can be computed by maximizing or minimizing a single performance index obtained by combining the multiple objectives in a weighted sum, P
U'(u) = ~ ajuj
(1)
P
Z aj = 1 j=l
(2)
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
43
where, aj = the importance associated with pollutant j; u} = the sub-utility for pollutant j at location i; u t = the cumulative utility for P pollutants at location i. In the P O D therefore, the interest of each pollutant is treated as a sub-utility and the optimization of the A Q M N configuration is carried out for a single additive utility function. A POD formulation attains a general quasi-additive form, such as, = N;j(N{j)
(3)
or
u~ = Npj (N{j K') b
(4)
b>0 N~j = the pattern score for pollutant j at location i; N~j = the violation score for pollutant j at location i; K i = the importance associated with population activity at location i. (Refer to Modak and Lohani, 1984a and b; for definitions of pattern and violation
SCOFPS.) 8. Preference in the Pareto Optimal Design A preference to the pollutants in the A Q M N design is a quite practical issue. To site an example, the sulfur dioxide concentrations in Taipei City are fairly low as compared to the concentrations of COH, and therefore it may be desired that the monitoring of sulfur dioxide be reduced. Another case could be that of monitoring of photochemical oxidations. In Taipei City, the photochemical reactions are weak and therefore only a few monitors would need to be installed for monitoring of the photometrical oxidants. There are three ways in which a preference to a pollutant could be indicated in a POD. (1) One approach for expressing a preference is to indicate a high value of importance aj, while computing the cumulative utility function. In case of pollutants A and B for instance, pollutant A could be given an importance of al = 0.75 and a2 = 0.25 (as per Equation (2)). (2) Another possibility is to express the preferences for the pollutants in terms of their respective level of cut-off correlation coefficients. For pollutants A and B, for instance, it may be desired to obtain a solution such that C o (max) forA is 0.95 and for B is 0.90; further, C ~ (rain) for pollutant A could be 0.85 whereas for pollutant B it could be 0.80. This situation clearly favours pollutant A while sharing a common monitoring budget. A specification on the ranges of C o could thus be effectively used to indicate preferences to the pollutants. (3) Yet another way could be to specify different coverage effectivenesses for each pollutant. Pollutant A may be desired to have a total coverage whereas for pollutant B, a coverage effectiveness of say 85~o may be deemed to be sufficient.
44
P. M. MODAK AND B. N. LOHANI
9. Formulation and Computational Algorithm for Pareto Optimal Design The optimization problem could be stated as,
Max
(5) j=li=l
or
j=li=l
for, (Mp~ w Mp2 w . . . M p ) = (M1 w MpZ... ~)MN)
(7)
p - - l , 2. . . . P M;, = the set of candidate locations having cross-correlations higher than C o with location i for pollutant p, such that T < T~
(8)
T O = is the maximum allowable budget for monitoring P pollutants; (Tis a function of number of monitors for each pollutant and number of monitoring sites); m = the number of monitoring sites; P = the number of pollutants. The solution algorithm for the POD is easily derived as an extension of the basic utility approach. The various steps of this algorithm (especially that of the Minimum Spanning Tree (MST)) are similar to that of the algorithm discussed in Part II of this paper (Modak and Lohani, 1984b) except that the utilities are defined on a more comprehensive basis, i.e., in the interest of more than one pollutant (Equation (1)). For the specified limits of cut-off correlation coefficient C O then, an iterative execution of the MST algorithm is carried out to optimize the parameter b (Equation (1)). A description of this algorithm is however omitted to avoid repeatition. Modak (1984) should be referred for the computational details.
10. Application of Index and Pareto Optimal Approaches to Taipei City Taipei City has 11 COH monitoring instruments (tape samplers) and these are co-located with sulphur dioxide samplers (Figure 2 of Modak and Lohani, 1984a). A field of COH was generated from the monitored data based on the interpolation algorithm described by Modak and Lohani (1983). Figure 1 shows typical contours of COH at 9.00 A.M. which is the period of maximum concentration in Taipei City. Since COH and sulfur dioxide were the only two pollutants under consideration, Green's Index (Green, 1966) was considered to be appropriate for purpose of aggre-
45
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS 24 23 22 21 20
23 f
~
22 [-
/[
[ I
I
I
I ~
C~
:&m
= 9
: ns _-- 9___
19 18
17 16 15
17 16 15
I
2 34
I 2 3 4 5 6 7 8 9 I0 II 12131415 16171819 KILOMETERS
5 6 7 8 9 10111213141516171819
KI LOMETERS Note
Fig. 1.
: Numbers
indicate
the order of station selection
9
Sulfur
dioxide monitor
9
COH
m
Number
ns
N u m b e r of monitoring
C~
C u t - off correlation
monitor of monitors stations coefficient
Pollutant specific configurations for SO 2 and Coefficient of Haze (COH) at C O = 0.95.
gation. The structural form of Green's Index could be expressed in terms of the sub-index functions I 1 and 12 by: I I = 84 ( 5 0 2 ) 0"431
(9)
12 = 26.6 ( C O H ) ~
(10)
Index = (11 + 12)/2.0
(11)
(SO2 in ppm and COH in COH units). Green (1966) suggested that the index be interpreted in the way indicated in Table I. A nonlinear segmented weighting function of the form shown in Table II was used to apply the scheme given in Table I. In the case of the POD violation scores for COH were calculated based on a non-linear segmented weighing function (Table III), similar to that used for the sulfur dioxide (Modak and Lohani, 1984b). Equal preferences were specified for both pollutants, i.e. al = a2. For both methods (i.e. the index and the Pareto optimal
46
P . M . MODAK AND B. N. LOHANI TABLE
I
Green's Index and associated air quality (Green, 1966) Index
Air quality
< 25 > 50 > 60 > 68 > 100
Desired level of air quality First alert level Second alert level Third alert level Extreme level
TABLE
II
Non-linear segmented weighting function for Green's Index Index level
Score
25.0 < 68.0 > 6 8 . 0 < 100.0 > 100
0.5 1.5 3.0 5.0
TABLE
III
A non-linear segmented weighting function for Coefficient of H a z e ( C O H )
Concentration COH units
Score
2.0 < 3.0 > 3.0 < 4.0 >4.0
1.0 1.5 3.0 5.0
approach) a budgetory constraint of 1000 000 U S $ was introduced and the maximum and minimum values of C Owere set at 0.95 and 0.85 respectively. Detection of violations and pattern representation were considered as the joint principal objectives of the A Q M N . In addition, estimation of pollution dose to populations (in terms of the population Dosage Product - PDP) was considered as a cursory objective of the monitoring program. Tables IV and V provide a summary of solutions for the index and Pareto optimal approach respectively. The various terminologies used in these tables, such as Percentage Exposure, Percentage Compliance, Percentage Variance, and Percentage Common Sites are defined as follows. Percentage Exposure has been defined as a ratio of the P D P detected by the A Q M N to that of the total P D P calculated on summing over all the candidate locations, for all the pollutants. Percentage Compliance denotes a ratio of the violation score
47
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORINGNETWORKS TABLE IV
Results of index oriented design Objective
Cost 1000 US$
Percentage exposure
Percentage eomplaince
Percentage variance
Percentage coverage SO2
COH
(a) Representation of patterns as sole objective
937.2
18,6
24.5
90.2
92
100
937.2
25.7
25.5
86.5
98
100
(b) Representation of patterns and detection of violations as objectives
TABLE V
Results of pareto optimal design Objective
Cost 1000 US$
Percentage exposure
Percentage complaince
Percentage common sites
Percentage variance
1158.0
24.4
25.5
54.5
90.2
994.6
28.7
28.7
88.9
81.0
(a)
Representation of patterns as sole objective
(b) Representation of Patterns and detection of violations as objectives
detected by the A Q M N to that of the total violation score, calculated by summing over all the candidate locations, for all the pollutants. Percentage Variance is defined as the square of the population correlation coefficient C~ . Percentage Common Sites is defined as the ratio of number of sites where all the pollutants are measured to that of total number of monitoring sites. A comparision between solutions (a) and (b) of Tables IV and V shows how a formul ation of the utility function (Equation (1)) improves the interests of the as sociated objectives by compromising on the reliability of pattern representation. The importance of multi-objective considerations to A Q M N design is therefore obvious. It is to be noted from Table IV that a POD maintains a good percentage (normally more than 50 ~o) of common sites in the monitoring design. Interestingly, the percentage of common sites in the multi-objective design has also been increased from 54.5 to 88.9 Yo. This is attributed to the policity of compromise on C ~ since more common sites are expected at lower C O values.
48
P. M. M O D A K A N D B. N. L O H A N I
Table V shows that the index-oriented design does not necessarily meet a criterion of total coverage for individual pollutants. However, since the sources of sulfur dioxide and C O H in Taipei City are more or less the same, such a deviation is not severe. The results show that Green's index duplicates about 90 to 98 ~o of spatial variance of both sulfur dioxide and the COH. Such situations are however not guaranteed when pollutants from diferent sources are involved.
II. Pollutant Specificity, Index, and Pareto Optimal Approach-Revisited Figure 2 shows the pollutant specific configurations of the A Q M N obtained for sulfur dioxide and COH at C O--- 0.95. Figure 3 shows the multipoUutant configurations obtained based on the index and the Pareto optimal approach. Configurations obtained
index Oriented Configuration
Poreto Optimal Configation 24 23 22 21 2O J9 18 17 J6 15
N i3 ~m o, ll ,~ io 9 8
7 6 5 4 3 2i I I 2 3 4 5 6 7 9 I0 II 12 131415 16171819 KILOMETERS
I 2 3 4 5 6 7 8 9 10111213141516171819 KILOMETERS
Note : Numbers indicate the order of monitor selection
Fig. 2.
9
Sulfur dioxide monitor
9
COH monitor
m
Number of monitors
ns
Number of monitoring stations
C~
C u t - off correlation
coefficient
P a r e t o o p t i m a l a n d index oriented configurations for SO2 and Coefficient of H a z e ( C O H ) at C O = 0.95.
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
49
in Figure 2 and 3 have been obtained with respect to representation of regional patterns as the sole objective. Table VI shows summary statistics for these 4 configurations. The results indicate that the spatial variability of each pollutant is different, i.e. the spatial variability is pollutant specific. It is logical therefore to expect that for the same C o, each pollutant may require different numbers of monitors and their optimal configuration could also be different. In this case, for C O= 0.95, 9 monitors were required for sulfur dioxide, whereas for COH, 8 monitors were required for total coverage. Further, Figure 2 shows how the optimal configurations for these monitors are distinctly different. It is evident that pollutant specificity has a great influence on the percentage of common sites in multipollutant A Q M N design.
TABLE VI Summary statistics to Figures 2 and 3 Type
Number of monitors
Number of monitoring sites
SO 2
COH
Pollutant specific
9
8
13
Index oriented
9
9
Pareto optimal
9
8
Percentage common sites
Percentage coverage CO 2
COH
65
100
100
9
100
88
97
11
77
100
100
Table VI shows the superiority of the Pareto optimal approach. In this case, consideration of joint utility leads to an increase in the number of common sites in the AQMN design. An examination of Table VI shows that the percentage of common sites in the pollutant-specific design is only 65~o whereas in the Pareto optimal approach, this percentage is improved to 77 ~o. In the case of the index approach, all sites are considered to be common for each pollutant, but then a criteria of total coverage is not met. A Pareto optimal approach however assures that the criterion of total coverage is satisfied for all individual pollutants under consideration.
12. Zero-One Allocation in Pareto Optimal Design It should be noted that the Pareto optimality criterion does not imply that all the pollutants would be measured at each of the selected monitoring location. In the selection algorithm, for instance, it is possible that effective gain (refer to Modak and Lohani, 1984a) for a particular pollutant is zero, but the corresponding cumulative
50
P. M. MODAK AND B. N. LOHANI
utility function is maximum. Mathematically, e
Gi = Z apgip >
(12)
0 and Maximum
p=l
but, gp=0
for some p
(13)
P = the number of pollutants under consideration at location i. Such a situation could be reckoned as that of a degeneracy in the POD. Monitor for pollutant p for instance, may not be installed at ith site in the interest of the cumulative utility. A case of degeneracy could be considered as inherent in a multi-pollutant AQMN design, since the variabilities of two pollutants would always be different. To illustrate this situation, Table VII shows pattern and violation scores (hypothetically considered) for pollutants Pl and P2 at 3 candidate location, A, B, and C. TABLE VII An illustration to the zero-one allocation of monitors
Location
Pattern P1
Score P2
Violation P~
Score P2
Cumulative utility (b = 1)
A
5
7
10
4
50 + 28 (78)
B
10
0
14
9
140 + 0
C
7
9
4
8
Xp,
Xp2
1
0
28 + 72
(1oo)
It is to be observed from Table VII that the Pareto optimality criterion would select location B as the best choice as compared to A and C. Further, at location B, it may suffice to install a monitor only for pollutant Pl since the utility of installing monitor P2 is zero. In the computational algorithm of POD, a listing of situations such as those in Equations (11) and (12) is maintained such as P
G i = ~ apg'p > 0 and Maximum p=l
but, gp = 0
for some p
otherwise
then
Xp = 0
(14)
Xp-- 1.
(15)
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
51
The solution to a POD thus attains a typical form of a zero-one allocation problem of identifying an optimal distribution of monitors between the monitoring sites. It is expected that as the number of pollutants increases (or if their variabilities are different), the extent of zero-one allocation would increase. A similar trend may be observed at high C O values. Figure 3 for POD shows such an allocation between sulfur dioxide and COH monitors. In this case, only a sulfur dioxide monitor has been assigned to location number 8. 13. General Features of Pareto Optimal Approach It is to be observed that the Pareto optimal approach is a general approach for multiobjective and multipollutant optimization of AQMN. This method is indeed flexible to account for more than one pollutants and more than one objective with preferences as indicated by the Decision Maker (DM), with explicit consideration of available monitoring resources. This method, in general, requires only the following specifications. (1) Simulated data on pollutants at the candidate locations of interest. If probabilities of occurrence are available of if the frequencies are to be used as case weights, then a probabilistic optimization of AQMN is also possible. (2) Monitoring budget. (3) Weightings for the computation of violation scores of each pollutant (such as in Table III) or population importances (K value in Equation (4)). (4) Preferences to pollutants. (5) Inaccuracy in the simulations in terms of percentage randomness introduced ( f ) for each pollutant. If no random perturbations are desired, then indicate f = 0. (Refer Modak and Lohani, 1984a for the discussion on the implications of f ) . The Pareto optimal method provides, (1) Optimal number of monitors for each pollutant. (2) Optimal number of monitoring locations. (3) AQMN configuration, i.e. locations. (4) Zero-one allocation between monitors. (5) Maximum possible reliability of pattern representation. (6) A best possible compromise with the associated objectives such as detection of violations and/or estimating pollution dose to populations, with respect to all the pollutants under consideration. It is clear therefore the Pareto optimal approach has great potential for practical applications in AQMN design. 14. Summary and Conclusions (1) The issue of multiple pollutants is of practical relevance in AQMN optimization. Pollutant specificity plays a major role in the philosophy of multi-pollutant AQMN
52
P. M. M O D A K
A N D B. N . L O H A N I
design. An AQMN optimized for the interest of one pollutant may not perform satisfactorily in the interest of another. Consequently, only a few common monitoring locations are expected in such pollutant-specific designs. Normally, an AQMN with a maximum number of common sites is prefered since the costs of siting are shared (economic considerations) and concurrent measurement of several pollutants is possible for the interest of total assessment. (2) In this paper, two new approaches have been developed, namely the index-derived approach and the Pareto optimal method. In the case of the index approach, a problem of multiple pollutants is converted to that of a single pollutant by transforming to an Air Quality Index (AQI). An AQI-based AQMN could be solved either using a utility approach or the sequential interactive method (Modak and Lohani, 1984b). One of the limitations of AQI-based designs is that an index could possibility represent the severity of the pollutant combination but not the spatial variability. The spatial variability of an index could be different from that of the individual pollutants. It is not guaranteed therefore that an AQI-based design would ensure representation of the pollution patterns with respect to each pollutant. Besides, the AQI approach is specified to the index structure and does not provide any flexibility to indicate preferences to the pollutants. An AQI-based design is indeed an approximation to the multiple pollutant optimization of the AQMN. (3) The principle of Pareto optimality differs from that of the AQI approach since in this case the specificity of each pollutant is given due consideration and yet an opportunity of measuring common locations to multiple pollutants is maximized. In this case, the pollutant specificity is amalgamated in the form of a comprehensive additive utility function - by extending the utility approach. Unlike the AQI approach, the Pareto optimal method ensures representation of the air quality patterns with respect to each pollutant. In this case, it is not expected that all the pollutants would be measured at all locations - such as in the AQI - and therefore an optimal mix of distribution of pollutant monitors amongst the monitoring locations is identified. In this method, unlike the AQI approach, it is possible to indicate the preferences to the pollutants, by specifying the coefficients in the comprehensive additive utility function - or prescribing a specific range of cut-off correlation coefficient or the criterion of coverage effectiveness. This feature thus adds flexibility to the multi-pollutant design.
Acknowledgements The various contributions made in this paper are basically a part of the doctoral research carried out by the first author, while at Asian Institute of Technology, Bangkok, Thailand. All correspondence regarding this paper should be therefore addressed to the first author. The support of the Government of Japan is gratefully acknowledged for providing financial assistance to complete the above doctoral research.
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
53
References Brady, P. J.: 1978, 'Optimal Sampling and Analysis Using Two Variables and Modelled Cross-Covariance Functions', Journal of Applied Meteorology 17, 12-21. Darby, W. P., Ossenbruggen, P. J., and Gregory, C. J.: 1974, 'Optimization of Urban Air Monitoring Networks', Journal of Environmental Engineering Division, A.S.C.E. 100, EE3, 577-591. Karl, T. R.: 1980, 'A Study of the Spatial Variability of Ozone and other Pollutants at St. Louis, Missouri', Atmospheric Environment 14, 681-693. Green, M. H.: 1966, 'An Air Pollution Index Based on Sulphur Dioxide and the Smoke Shade', Journal of the Air Pollution Control Association 11,703-706. Handscombe, C. M. and Elsom, D. M.: 1982, 'Rationalization of the National Survey of Air Pollution Monitoring Networks Using Spatial Correlation Analysis - A Case Study of the Greater London Area', Atmospheric Environment 16, 1061-1070. Hanna, S. R.: 1982, 'Natural Variability of Observed Sulfur Dioxide and Carbon Monoxide Concentrations in St. Louis', Atmospheric Environment 16, 1061-1070. Hickey, H. R., Rowe, W. D., and Skinner, F.: 1971, 'A Cost Model for the Air Quality Monitoring System', Journal of Air Pollution Control Association 21,689-693. Modak, P. M.: 1984, 'Optimum Siting of Ambient Air Monitors', A dissertation submitted as the partial fulfillment for the degree of Doctor of Engineering, Asian Institute of Technology, Bangkok, Thailand. Modak, P. M. and Lohani, B. N.: 1983, 'Vector Mapping of Ambient Air Quality', submitted to Journal of Air Pollution Control Association, U.S.A. Modak, P. M. and Lohani, B. N.: 1984a, 'Optimization of Ambient Air Quality Monitoring Networks Part I', Environmental Monitoring and Assessment 5, 1-19. Modak, P. M. and Lohani, B. N.: 1984b, 'Optimization of Ambient Air Quality Monitoring Networks Part II', Environmental Monitoring and Assessment 5, 21-38. Munn, R. E.: 1981, Design of Air Quality Monitoring Networks, MacMillan Press Ltd. B asingstoke, Hampshire, U.K. Noll, K. E. and Miller, T. M.: 1977a, Air Monitoring Network Design, Ann Arbour Science, 1977. Ott, W. R.: 1978, Environmental Indices: Theory and Practice, Ann Arbour Science. Stern, A. C.: 1976, 'The Problem Before Us', in M. M. Bennarie (ed.), Key-Note Address, Proceedings in the 12th International Colloquim on Atmospheric Pollution, Elsevier, Amsterdam, pp. 1-10.
OF A M B I E N T AIR Q U A L I T Y M O N I T O R I N G NETWORKS
(Part III) P R A S A D M. M O D A K
Environmental Science and Engineering Group, Indian Institute of Technology, Powai, Bombay, 400 076, India and B. N. L O H A N I
Environmental Engg. Division Asian Institute of Technology, P.O. Box 2754, Bangkok, Thailand, 10501
(Received 9 July, 1984) Abstract. The methodologies presented in Parts I and II (refer Modak and Lohani, 1984a and b) are
essentially for deciding the best number and configuration for a single pollutant monitor. In practical situations however, Air Quality Monitoring Networks (AQMN) are expected to measure more than one pollutant and therefore simultaneous consideration of different types of pollutants must be made. In this paper, two new approaches have been developed for the multipollutant AQMN design. The first method makes use of the index theory and the other makes use of the principles of Pareto optimality. As an illustration of these methodologies, an example from Taipei City, Taiwan is considered.
1. Introduction
The methodologies presented in parts I and II (refer Modak and Lohani, 1984a and b) are applicable for deciding the number and configuration of a single pollutant monitor. In practical situations however, Air Quality Monitoring Network (AQMN) are expected to measure more than one pollutant and therefore the optimization procedure warrants simultaneous consideration of different types of pollutants. Normally, the primary or quasi-stable pollutants such as sulfur dioxide, carbon monoxide and suspended particulates are routinely measured in most AQMNs today. Monitoring of reactive pollutants such as ozone, hydrocarbons and the nitrogen oxides is also becoming common at a number of installations. Unfortunately, the problem of multi-pollutant AQMN design has often been considered to be analogous to that of single pollutant design. Surprisingly and oddly enough, recent books on the AQMN design such as Noll and Miller (1977) and Munn (1981), do not discuss methodologies for consideration of multiple pollutants. A few research workers in the past, notably Darby et al. (1974) and Brady (1978) have made some attempt to incorporate more than one pollutant in their design methodologies. In this paper, two new approaches have been developed for multi-pollutant AQMN design. The first makes use of the index theory and the other makes use of the principles of Pareto optimal compromise. To begin with however, it may be appropriate to discuss some basic considerations in the multi-pollutant AQMN design with respect to pollutant specificity and philosophy of common monitoring sites. EnvironmentalMonitoring and Assessment 5 (1985) 39-53. 9 1985 by D. Reidel Publishing Company.
0167-6369/85.15.
40
P. M. MODAK AND B. N. LOHANI
2. Pollutant Specificity and Philosophy of Common Sites In general, it has been observed that every moderate or large scale multi-pollutant A Q M N adheres to a policy of retaining a maximum number of common sites, i.e., sites where a number of pollutants are simultaneously measured. Networks with pollutant specific sites are rare. Economic and assessment considerations appear to be the principal reasons for such a preference to a common site multiple pollutant AQMN design.
3. Economic Considerations Every pollutant has its characteristic variability due to its specific emission sources, rates of diffusion as well as transformations; and therefore it is expected that the number and location of monitors would be specific for each pollutant. Recent studies carried out by Karl (1980), Handscombe and Elsom (1982) and Hanna (1982) also support such a possibility. It is quite logical therefore to expect that the optimum number and configuration are pollutant specific. For instance, pollutant A having a spatial variability more than pollutant B, is expected to require more monitors in order to represent regional patterns. Further, pollutant A and pollutant B may require the same number of monitors, but then it is possible (or likely) that their optimal configurations would be different. It is therefore expected that in a pollutant specific design, the number of sites is expected to be almost equal to the number of monitors installed, i.e., it is unlikely that a site would be common to the best interests of several pollutants. It could therefore be observed that the costs of siting (installation and maintenance) in a pollutant-specific design would be higher than that for a common site design. For a common site network, the costs of installation and maintenance of the monitoring sites are shared amongst the pollutants, and therefore the total cost of the monitoring effort is reduced. The analysis of the AQMN costs, as reported by Hickey et al. (1971) indicates that the more the monitors at a single monitoring site, the more economical the system is to initiate and to maintain. In other words, it is economical to install and operate an A Q M N having many monitors at a site than an AQMN incorporating the same number of monitors at several different sites. The results of Hickey et al. (1971) therefore favour a common site approach to the AQMN design.
4. Assessment Considerations In many instances, a common-site design is prefered due to the following considerations. (1) Exposure assessment is never complete when only one pollutant is measured. It is well known that several pollutants are synergistic and therefore it is mandatory to measure certain pollutants at a common site. A case of sulfur dioxide and that of total suspended particulates could be cited as an example. An increasing practice of reporting
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
41
monitoring station data in terms of an aggregation, such as an Air Quality Index (AQI) also supports the interest of having a maximum number of common monitoring facilities. (2) If more than one pollutant is measured at a common site, then missing value estimation for a pollutant is possible especially when the cross-correlations between the other pollutants are quire high and are already established. Stern (1976) notes that the trend toward monitoring a number of pollutants at a common site is expected to increase in future. This is expected to be particularly true for the assessment of photochemical smog, which depends on nitric oxide, nitrogen dioxide, ozone, and hydrocarbons, etc. The above benefits of maintaining common sites may be impossible to quantify. In recent years therefore, there has been a growing trend to design multi-pollutant monitors which are capable of simultanious measurement of more than one (normally two to five) pollutants. Multi-pollutant monitors for carbon monoxide, hydrocarbons, nitrogen oxides and ozone are particularly popular. One of the typical features of these multipollutant monitors is that their cost is often less than the total costs of purchasing individual monitors. Such a bonus therefore adds to the list of advantages to a common site network design to make it a rather attractive proposition. To conclude therefore, pollutant-specific designs are rarely envisaged and normally a policy of installing a network with a maximum number of common sites is prefered.
5. Multi-Pollutant AQMN Desing Using Air Quality Index A simple approach to the multi-pollutant AQMN design is to aggregate air pollutants in the form of an Air Quality Index (AQI). Once the multi-pollutants are converted in the form of a single variable, methodologies such as the utility and the sequential interactive approach (discussed in Part II, Modak and Lohani, 1984b) could readily be used. A method based on AQI has an implicit assumption that all the monitoring sites are common to multiple pollutants. A number of AQI could be used for such an aggregation (Ott, 1978).
6. Limitation of the Index-Based AQMN Design It is expected that the results of the index approach would heavily depend on the specification of the index structure function. One could obtain different designs of the A Q M N for different index formulations. Secondly, when more than three to four pollutants are involved, it would not be correct to substitute for pollutant specificities by a mere blanket function in the form of an index. Historically, the idea of an AQI has been to represent the interest of the severity of a combination of pollutants. The interest of the AQI has certainly n o t been to represent the spatial variability. This distinction is indeed important in the application of the index theory to AQMN design. To illustrate, an AQI derived for two pollutants such as the sulfur dioxide and the Coefficient of Haze (COH) would represent the severity of two pollutants in combination (though synergistic relationships are often not possible to incorporate) but not the variability of each. The
42
P. M. MODAK AND B. N. LOHANI
variability of the AQI, which would depend upon the choice of the structure function, would certainly be different than the original variables, i.e. pollutants. It is possible therefore that an optimized AQMN based on AQI, for total coverage (Equation (7)), may not provide adequate pattern representation for the pollutants under consideration. In some cases, if the sources and the diffusion characteristics of pollutants are not widely different, then it is possible that an AQI-based design may satisfy a criterion of coverage for all the pollutants. The index approach may not work well however, when pollutants of significantly different variabilities are involved such as primary and secondary or reactive and quasi-stable pollutants. Yet another difficulty with the index approach is that there is no explicit way to indicate pollutants preferences. This is especially important since in some cases the Decision Maker (DM) may be more interested in sulfur dioxide than in COH or vice versa. Lastly, the index approach is attractive only for certain well defined combinations of pollutants for which an index has been defined or routinely reported. The index-oriented approach is then an approximate method to the multi-pollutant design of the AQMN.
7. A Pareto Optimal Approach to Multi-Pollutant Design The principal objective of the Pareto optimal network is to look for something attractive for a group of pollutants as a whole rather than focussing on specific pollutants. The basic idea in such a philosophy is to have maximum opportunity of measured several pollutants at common sites. A design for such a compromise is described herein as the Pareto Optimal Design (POD). This approach differs from the index method because in this case, the specificity of each pollutant is explicitly retained in the optimization procedure both in terms of its severity (violations) as well as in terms of spatial variability. An approach of additive utility to accommodate a global i~terest of various subutilities (all of which are to be maximized) is normally categorised as a method of Pareto optimality. Approaches based on the POD are gaining popularity in the multicriterion decision-making literature. A POD could be defined as follows: If the shape function U(u) is POD, then for any other U(u) either the values of all the objective functions remain the same or at least one of them worsens compared with its value at U(u). A POD can be computed by maximizing or minimizing a single performance index obtained by combining the multiple objectives in a weighted sum, P
U'(u) = ~ ajuj
(1)
P
Z aj = 1 j=l
(2)
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
43
where, aj = the importance associated with pollutant j; u} = the sub-utility for pollutant j at location i; u t = the cumulative utility for P pollutants at location i. In the P O D therefore, the interest of each pollutant is treated as a sub-utility and the optimization of the A Q M N configuration is carried out for a single additive utility function. A POD formulation attains a general quasi-additive form, such as, = N;j(N{j)
(3)
or
u~ = Npj (N{j K') b
(4)
b>0 N~j = the pattern score for pollutant j at location i; N~j = the violation score for pollutant j at location i; K i = the importance associated with population activity at location i. (Refer to Modak and Lohani, 1984a and b; for definitions of pattern and violation
SCOFPS.) 8. Preference in the Pareto Optimal Design A preference to the pollutants in the A Q M N design is a quite practical issue. To site an example, the sulfur dioxide concentrations in Taipei City are fairly low as compared to the concentrations of COH, and therefore it may be desired that the monitoring of sulfur dioxide be reduced. Another case could be that of monitoring of photochemical oxidations. In Taipei City, the photochemical reactions are weak and therefore only a few monitors would need to be installed for monitoring of the photometrical oxidants. There are three ways in which a preference to a pollutant could be indicated in a POD. (1) One approach for expressing a preference is to indicate a high value of importance aj, while computing the cumulative utility function. In case of pollutants A and B for instance, pollutant A could be given an importance of al = 0.75 and a2 = 0.25 (as per Equation (2)). (2) Another possibility is to express the preferences for the pollutants in terms of their respective level of cut-off correlation coefficients. For pollutants A and B, for instance, it may be desired to obtain a solution such that C o (max) forA is 0.95 and for B is 0.90; further, C ~ (rain) for pollutant A could be 0.85 whereas for pollutant B it could be 0.80. This situation clearly favours pollutant A while sharing a common monitoring budget. A specification on the ranges of C o could thus be effectively used to indicate preferences to the pollutants. (3) Yet another way could be to specify different coverage effectivenesses for each pollutant. Pollutant A may be desired to have a total coverage whereas for pollutant B, a coverage effectiveness of say 85~o may be deemed to be sufficient.
44
P. M. MODAK AND B. N. LOHANI
9. Formulation and Computational Algorithm for Pareto Optimal Design The optimization problem could be stated as,
Max
(5) j=li=l
or
j=li=l
for, (Mp~ w Mp2 w . . . M p ) = (M1 w MpZ... ~)MN)
(7)
p - - l , 2. . . . P M;, = the set of candidate locations having cross-correlations higher than C o with location i for pollutant p, such that T < T~
(8)
T O = is the maximum allowable budget for monitoring P pollutants; (Tis a function of number of monitors for each pollutant and number of monitoring sites); m = the number of monitoring sites; P = the number of pollutants. The solution algorithm for the POD is easily derived as an extension of the basic utility approach. The various steps of this algorithm (especially that of the Minimum Spanning Tree (MST)) are similar to that of the algorithm discussed in Part II of this paper (Modak and Lohani, 1984b) except that the utilities are defined on a more comprehensive basis, i.e., in the interest of more than one pollutant (Equation (1)). For the specified limits of cut-off correlation coefficient C O then, an iterative execution of the MST algorithm is carried out to optimize the parameter b (Equation (1)). A description of this algorithm is however omitted to avoid repeatition. Modak (1984) should be referred for the computational details.
10. Application of Index and Pareto Optimal Approaches to Taipei City Taipei City has 11 COH monitoring instruments (tape samplers) and these are co-located with sulphur dioxide samplers (Figure 2 of Modak and Lohani, 1984a). A field of COH was generated from the monitored data based on the interpolation algorithm described by Modak and Lohani (1983). Figure 1 shows typical contours of COH at 9.00 A.M. which is the period of maximum concentration in Taipei City. Since COH and sulfur dioxide were the only two pollutants under consideration, Green's Index (Green, 1966) was considered to be appropriate for purpose of aggre-
45
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS 24 23 22 21 20
23 f
~
22 [-
/[
[ I
I
I
I ~
C~
:&m
= 9
: ns _-- 9___
19 18
17 16 15
17 16 15
I
2 34
I 2 3 4 5 6 7 8 9 I0 II 12131415 16171819 KILOMETERS
5 6 7 8 9 10111213141516171819
KI LOMETERS Note
Fig. 1.
: Numbers
indicate
the order of station selection
9
Sulfur
dioxide monitor
9
COH
m
Number
ns
N u m b e r of monitoring
C~
C u t - off correlation
monitor of monitors stations coefficient
Pollutant specific configurations for SO 2 and Coefficient of Haze (COH) at C O = 0.95.
gation. The structural form of Green's Index could be expressed in terms of the sub-index functions I 1 and 12 by: I I = 84 ( 5 0 2 ) 0"431
(9)
12 = 26.6 ( C O H ) ~
(10)
Index = (11 + 12)/2.0
(11)
(SO2 in ppm and COH in COH units). Green (1966) suggested that the index be interpreted in the way indicated in Table I. A nonlinear segmented weighting function of the form shown in Table II was used to apply the scheme given in Table I. In the case of the POD violation scores for COH were calculated based on a non-linear segmented weighing function (Table III), similar to that used for the sulfur dioxide (Modak and Lohani, 1984b). Equal preferences were specified for both pollutants, i.e. al = a2. For both methods (i.e. the index and the Pareto optimal
46
P . M . MODAK AND B. N. LOHANI TABLE
I
Green's Index and associated air quality (Green, 1966) Index
Air quality
< 25 > 50 > 60 > 68 > 100
Desired level of air quality First alert level Second alert level Third alert level Extreme level
TABLE
II
Non-linear segmented weighting function for Green's Index Index level
Score
25.0 < 68.0 > 6 8 . 0 < 100.0 > 100
0.5 1.5 3.0 5.0
TABLE
III
A non-linear segmented weighting function for Coefficient of H a z e ( C O H )
Concentration COH units
Score
2.0 < 3.0 > 3.0 < 4.0 >4.0
1.0 1.5 3.0 5.0
approach) a budgetory constraint of 1000 000 U S $ was introduced and the maximum and minimum values of C Owere set at 0.95 and 0.85 respectively. Detection of violations and pattern representation were considered as the joint principal objectives of the A Q M N . In addition, estimation of pollution dose to populations (in terms of the population Dosage Product - PDP) was considered as a cursory objective of the monitoring program. Tables IV and V provide a summary of solutions for the index and Pareto optimal approach respectively. The various terminologies used in these tables, such as Percentage Exposure, Percentage Compliance, Percentage Variance, and Percentage Common Sites are defined as follows. Percentage Exposure has been defined as a ratio of the P D P detected by the A Q M N to that of the total P D P calculated on summing over all the candidate locations, for all the pollutants. Percentage Compliance denotes a ratio of the violation score
47
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORINGNETWORKS TABLE IV
Results of index oriented design Objective
Cost 1000 US$
Percentage exposure
Percentage eomplaince
Percentage variance
Percentage coverage SO2
COH
(a) Representation of patterns as sole objective
937.2
18,6
24.5
90.2
92
100
937.2
25.7
25.5
86.5
98
100
(b) Representation of patterns and detection of violations as objectives
TABLE V
Results of pareto optimal design Objective
Cost 1000 US$
Percentage exposure
Percentage complaince
Percentage common sites
Percentage variance
1158.0
24.4
25.5
54.5
90.2
994.6
28.7
28.7
88.9
81.0
(a)
Representation of patterns as sole objective
(b) Representation of Patterns and detection of violations as objectives
detected by the A Q M N to that of the total violation score, calculated by summing over all the candidate locations, for all the pollutants. Percentage Variance is defined as the square of the population correlation coefficient C~ . Percentage Common Sites is defined as the ratio of number of sites where all the pollutants are measured to that of total number of monitoring sites. A comparision between solutions (a) and (b) of Tables IV and V shows how a formul ation of the utility function (Equation (1)) improves the interests of the as sociated objectives by compromising on the reliability of pattern representation. The importance of multi-objective considerations to A Q M N design is therefore obvious. It is to be noted from Table IV that a POD maintains a good percentage (normally more than 50 ~o) of common sites in the monitoring design. Interestingly, the percentage of common sites in the multi-objective design has also been increased from 54.5 to 88.9 Yo. This is attributed to the policity of compromise on C ~ since more common sites are expected at lower C O values.
48
P. M. M O D A K A N D B. N. L O H A N I
Table V shows that the index-oriented design does not necessarily meet a criterion of total coverage for individual pollutants. However, since the sources of sulfur dioxide and C O H in Taipei City are more or less the same, such a deviation is not severe. The results show that Green's index duplicates about 90 to 98 ~o of spatial variance of both sulfur dioxide and the COH. Such situations are however not guaranteed when pollutants from diferent sources are involved.
II. Pollutant Specificity, Index, and Pareto Optimal Approach-Revisited Figure 2 shows the pollutant specific configurations of the A Q M N obtained for sulfur dioxide and COH at C O--- 0.95. Figure 3 shows the multipoUutant configurations obtained based on the index and the Pareto optimal approach. Configurations obtained
index Oriented Configuration
Poreto Optimal Configation 24 23 22 21 2O J9 18 17 J6 15
N i3 ~m o, ll ,~ io 9 8
7 6 5 4 3 2i I I 2 3 4 5 6 7 9 I0 II 12 131415 16171819 KILOMETERS
I 2 3 4 5 6 7 8 9 10111213141516171819 KILOMETERS
Note : Numbers indicate the order of monitor selection
Fig. 2.
9
Sulfur dioxide monitor
9
COH monitor
m
Number of monitors
ns
Number of monitoring stations
C~
C u t - off correlation
coefficient
P a r e t o o p t i m a l a n d index oriented configurations for SO2 and Coefficient of H a z e ( C O H ) at C O = 0.95.
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
49
in Figure 2 and 3 have been obtained with respect to representation of regional patterns as the sole objective. Table VI shows summary statistics for these 4 configurations. The results indicate that the spatial variability of each pollutant is different, i.e. the spatial variability is pollutant specific. It is logical therefore to expect that for the same C o, each pollutant may require different numbers of monitors and their optimal configuration could also be different. In this case, for C O= 0.95, 9 monitors were required for sulfur dioxide, whereas for COH, 8 monitors were required for total coverage. Further, Figure 2 shows how the optimal configurations for these monitors are distinctly different. It is evident that pollutant specificity has a great influence on the percentage of common sites in multipollutant A Q M N design.
TABLE VI Summary statistics to Figures 2 and 3 Type
Number of monitors
Number of monitoring sites
SO 2
COH
Pollutant specific
9
8
13
Index oriented
9
9
Pareto optimal
9
8
Percentage common sites
Percentage coverage CO 2
COH
65
100
100
9
100
88
97
11
77
100
100
Table VI shows the superiority of the Pareto optimal approach. In this case, consideration of joint utility leads to an increase in the number of common sites in the AQMN design. An examination of Table VI shows that the percentage of common sites in the pollutant-specific design is only 65~o whereas in the Pareto optimal approach, this percentage is improved to 77 ~o. In the case of the index approach, all sites are considered to be common for each pollutant, but then a criteria of total coverage is not met. A Pareto optimal approach however assures that the criterion of total coverage is satisfied for all individual pollutants under consideration.
12. Zero-One Allocation in Pareto Optimal Design It should be noted that the Pareto optimality criterion does not imply that all the pollutants would be measured at each of the selected monitoring location. In the selection algorithm, for instance, it is possible that effective gain (refer to Modak and Lohani, 1984a) for a particular pollutant is zero, but the corresponding cumulative
50
P. M. MODAK AND B. N. LOHANI
utility function is maximum. Mathematically, e
Gi = Z apgip >
(12)
0 and Maximum
p=l
but, gp=0
for some p
(13)
P = the number of pollutants under consideration at location i. Such a situation could be reckoned as that of a degeneracy in the POD. Monitor for pollutant p for instance, may not be installed at ith site in the interest of the cumulative utility. A case of degeneracy could be considered as inherent in a multi-pollutant AQMN design, since the variabilities of two pollutants would always be different. To illustrate this situation, Table VII shows pattern and violation scores (hypothetically considered) for pollutants Pl and P2 at 3 candidate location, A, B, and C. TABLE VII An illustration to the zero-one allocation of monitors
Location
Pattern P1
Score P2
Violation P~
Score P2
Cumulative utility (b = 1)
A
5
7
10
4
50 + 28 (78)
B
10
0
14
9
140 + 0
C
7
9
4
8
Xp,
Xp2
1
0
28 + 72
(1oo)
It is to be observed from Table VII that the Pareto optimality criterion would select location B as the best choice as compared to A and C. Further, at location B, it may suffice to install a monitor only for pollutant Pl since the utility of installing monitor P2 is zero. In the computational algorithm of POD, a listing of situations such as those in Equations (11) and (12) is maintained such as P
G i = ~ apg'p > 0 and Maximum p=l
but, gp = 0
for some p
otherwise
then
Xp = 0
(14)
Xp-- 1.
(15)
OPTIMIZATION OF AMBIENT AIR QUALITY MONITORING NETWORKS
51
The solution to a POD thus attains a typical form of a zero-one allocation problem of identifying an optimal distribution of monitors between the monitoring sites. It is expected that as the number of pollutants increases (or if their variabilities are different), the extent of zero-one allocation would increase. A similar trend may be observed at high C O values. Figure 3 for POD shows such an allocation between sulfur dioxide and COH monitors. In this case, only a sulfur dioxide monitor has been assigned to location number 8. 13. General Features of Pareto Optimal Approach It is to be observed that the Pareto optimal approach is a general approach for multiobjective and multipollutant optimization of AQMN. This method is indeed flexible to account for more than one pollutants and more than one objective with preferences as indicated by the Decision Maker (DM), with explicit consideration of available monitoring resources. This method, in general, requires only the following specifications. (1) Simulated data on pollutants at the candidate locations of interest. If probabilities of occurrence are available of if the frequencies are to be used as case weights, then a probabilistic optimization of AQMN is also possible. (2) Monitoring budget. (3) Weightings for the computation of violation scores of each pollutant (such as in Table III) or population importances (K value in Equation (4)). (4) Preferences to pollutants. (5) Inaccuracy in the simulations in terms of percentage randomness introduced ( f ) for each pollutant. If no random perturbations are desired, then indicate f = 0. (Refer Modak and Lohani, 1984a for the discussion on the implications of f ) . The Pareto optimal method provides, (1) Optimal number of monitors for each pollutant. (2) Optimal number of monitoring locations. (3) AQMN configuration, i.e. locations. (4) Zero-one allocation between monitors. (5) Maximum possible reliability of pattern representation. (6) A best possible compromise with the associated objectives such as detection of violations and/or estimating pollution dose to populations, with respect to all the pollutants under consideration. It is clear therefore the Pareto optimal approach has great potential for practical applications in AQMN design. 14. Summary and Conclusions (1) The issue of multiple pollutants is of practical relevance in AQMN optimization. Pollutant specificity plays a major role in the philosophy of multi-pollutant AQMN
52
P. M. M O D A K
A N D B. N . L O H A N I
design. An AQMN optimized for the interest of one pollutant may not perform satisfactorily in the interest of another. Consequently, only a few common monitoring locations are expected in such pollutant-specific designs. Normally, an AQMN with a maximum number of common sites is prefered since the costs of siting are shared (economic considerations) and concurrent measurement of several pollutants is possible for the interest of total assessment. (2) In this paper, two new approaches have been developed, namely the index-derived approach and the Pareto optimal method. In the case of the index approach, a problem of multiple pollutants is converted to that of a single pollutant by transforming to an Air Quality Index (AQI). An AQI-based AQMN could be solved either using a utility approach or the sequential interactive method (Modak and Lohani, 1984b). One of the limitations of AQI-based designs is that an index could possibility represent the severity of the pollutant combination but not the spatial variability. The spatial variability of an index could be different from that of the individual pollutants. It is not guaranteed therefore that an AQI-based design would ensure representation of the pollution patterns with respect to each pollutant. Besides, the AQI approach is specified to the index structure and does not provide any flexibility to indicate preferences to the pollutants. An AQI-based design is indeed an approximation to the multiple pollutant optimization of the AQMN. (3) The principle of Pareto optimality differs from that of the AQI approach since in this case the specificity of each pollutant is given due consideration and yet an opportunity of measuring common locations to multiple pollutants is maximized. In this case, the pollutant specificity is amalgamated in the form of a comprehensive additive utility function - by extending the utility approach. Unlike the AQI approach, the Pareto optimal method ensures representation of the air quality patterns with respect to each pollutant. In this case, it is not expected that all the pollutants would be measured at all locations - such as in the AQI - and therefore an optimal mix of distribution of pollutant monitors amongst the monitoring locations is identified. In this method, unlike the AQI approach, it is possible to indicate the preferences to the pollutants, by specifying the coefficients in the comprehensive additive utility function - or prescribing a specific range of cut-off correlation coefficient or the criterion of coverage effectiveness. This feature thus adds flexibility to the multi-pollutant design.
Acknowledgements The various contributions made in this paper are basically a part of the doctoral research carried out by the first author, while at Asian Institute of Technology, Bangkok, Thailand. All correspondence regarding this paper should be therefore addressed to the first author. The support of the Government of Japan is gratefully acknowledged for providing financial assistance to complete the above doctoral research.
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References Brady, P. J.: 1978, 'Optimal Sampling and Analysis Using Two Variables and Modelled Cross-Covariance Functions', Journal of Applied Meteorology 17, 12-21. Darby, W. P., Ossenbruggen, P. J., and Gregory, C. J.: 1974, 'Optimization of Urban Air Monitoring Networks', Journal of Environmental Engineering Division, A.S.C.E. 100, EE3, 577-591. Karl, T. R.: 1980, 'A Study of the Spatial Variability of Ozone and other Pollutants at St. Louis, Missouri', Atmospheric Environment 14, 681-693. Green, M. H.: 1966, 'An Air Pollution Index Based on Sulphur Dioxide and the Smoke Shade', Journal of the Air Pollution Control Association 11,703-706. Handscombe, C. M. and Elsom, D. M.: 1982, 'Rationalization of the National Survey of Air Pollution Monitoring Networks Using Spatial Correlation Analysis - A Case Study of the Greater London Area', Atmospheric Environment 16, 1061-1070. Hanna, S. R.: 1982, 'Natural Variability of Observed Sulfur Dioxide and Carbon Monoxide Concentrations in St. Louis', Atmospheric Environment 16, 1061-1070. Hickey, H. R., Rowe, W. D., and Skinner, F.: 1971, 'A Cost Model for the Air Quality Monitoring System', Journal of Air Pollution Control Association 21,689-693. Modak, P. M.: 1984, 'Optimum Siting of Ambient Air Monitors', A dissertation submitted as the partial fulfillment for the degree of Doctor of Engineering, Asian Institute of Technology, Bangkok, Thailand. Modak, P. M. and Lohani, B. N.: 1983, 'Vector Mapping of Ambient Air Quality', submitted to Journal of Air Pollution Control Association, U.S.A. Modak, P. M. and Lohani, B. N.: 1984a, 'Optimization of Ambient Air Quality Monitoring Networks Part I', Environmental Monitoring and Assessment 5, 1-19. Modak, P. M. and Lohani, B. N.: 1984b, 'Optimization of Ambient Air Quality Monitoring Networks Part II', Environmental Monitoring and Assessment 5, 21-38. Munn, R. E.: 1981, Design of Air Quality Monitoring Networks, MacMillan Press Ltd. B asingstoke, Hampshire, U.K. Noll, K. E. and Miller, T. M.: 1977a, Air Monitoring Network Design, Ann Arbour Science, 1977. Ott, W. R.: 1978, Environmental Indices: Theory and Practice, Ann Arbour Science. Stern, A. C.: 1976, 'The Problem Before Us', in M. M. Bennarie (ed.), Key-Note Address, Proceedings in the 12th International Colloquim on Atmospheric Pollution, Elsevier, Amsterdam, pp. 1-10.
