Surveillance Network Design for Air Pollution Control

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SURVEILLANCE NETWORK DESIGN FOR AIR POLLUTION CONTROL Y. Nakamori* and Y. Sawaragi** *Df'partmfTlt uf Applied .\lathematics, KU1UW Cuil 1enit..\'. Kobl'. Japan **Df'partmeTlt of Computer ScinlCf', Kyoto SanlD'o [ 'nil'enit.\', Kyoto, Japml

Abstract. An interactive optimization method for desi~ning an air quality monitoring network in an urban area is proposed. A constrained Hard method clustering is used to determine the number and location of monitoring stations and their representative areas under averaged meteorological condition. Participation of human in the design process is allowed in such a way that one can modify constraints by taking account of economic and physical conditions as well as inaccuracy of simulation models. The goal is to determine the representative area that can be covered by the individual station under every possible atmospheric condition. This can be done approximately by identifying the membership functions for several typical conditions. An application to the NO x monitoring network in Kyoto, Japan is presented.

Keywords.

Air pollution; clustering; environment control; interactive optimization;

monitoring system; simulation model.

INTRODUCTION In most urban air monitoring systems the measurement

data are continuously stored for a wide variety of purposes. Two main objectives are to estimate pollutant concentration distributions from the data at the limited number of stations and to monitor source compliance with regulations. Unfortunately, it seems impracticable at present to develop mathematical urban air pollution models capable of predicting the spatial and temporal concentration distributions of pollutants under highly varying meteorological and source emission conditions.

We begin by considering reasonable siting criteria and possible constraints in the design. Then we

For this reason, the representativeness of the data from both estimation and control view points has become a problem of utmost importance. The development of air quality monitoring network then involves not only selecting the number and location of stations but also identifying the size of the representative area that can be covered by the individual station.

develop an interactive optimization technique for

the design of urban air quality monitoring network in an airshed. Figure 1 shows the outline of interacting process between people and computers.

From the pollution control view point it is also important to identify a covering area of the individual monitoring station under every possible atmospheric condition. This can be done approximately by estimating the degree of membership of each mesh to every station under several typical meteorological conditions. Finally, we present an application to the NO x monitoring network in Kyoto, Japan.

Two types of monitoring sites, proximate and urban level, are generally required to monitor urban air quality. They have been discussed separately by several authors. The proximate site is to be chosen at the point where the highest pollution concentrations are expected to occur.

In addition to these investigations, the systems approach, based on elaborate mathematical models capable of predicting long-term averages of pollutant concentrations, is essential. Background information for mathematical representations of the design problem is source emission rates, historical meteorological data, existing monitoring data, etc. by which we can develop long-term simulation models. But there is no way to reflect all complicated factors in mathematical models. Human ability must extend to represent reality.

The source-

oriented siting procedures developed by Seinfeld (1972) or NolI and co-workers (1977) are applicable for this purpose.

NOTATIONS AND ASSUMPTIONS Let

Urban level sites are also indispensable to estimate concentrations over the entire region. For this purpose each station should provide data representative of a certain area surrounding the station. In the absence of data between existing stations, optimal network design cannot be achieved by the spatial correlation analysis alone as in Goldstein and Landovitz (1977) or Elsom (1978).

Iwc6-1*

x~, x~,

... , xA be the observation points for

a pollutant in a two-dimensional objective area 0 , and 0 ~, 0;, ... , ~ their representative areas. We use a Gaussian model to estimate the annual mean ground level concentration distribution of the pollutant. Denote the solution of the simulation model by c(x) and write ct=c(xt), i=1,2, ... ,M.

3233

3234

J. Nakamori and Y. Sawaragi

HUMAN UNDERSTANDING

BACKGROUND INFORMATION

'SURVEY OF POLLUTION PATTERN 'CONFIGURATION OF SOURCES 'LOCAL TOPOGRAPHY 'ADMINISTRATIVE CONSIDERATION 'SUITABLE NUMBER OF STATIONS ·EXISTING STATION SITES · RELlABILlTY OF DATA

'SOURCE EMISSION RATE 'METEOROLOGICAL DATA

If the goal is to estimate the overall mean concentration, the sample size in each mesh should be determined in proportion to the square root of the variation index defined in (6) (see Nakamori and co-workers, 1979). But in this case, the sample sizes should be proportional to variation indices. Let us approximate c'

by generating N' uniform k k random numbers Sj (j=1,2, .. • ,N. ) in ~ 'k and k putting

(7)

C( C ). J SURVE I LLANCE AREA

Note that S'k is an unbiased estimator of c' k because {s.} are mutually independent and of id en-

JUDGMENT

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tical distribution. by

I S THE NUMBER OF STATIONS ADEQUATE?

The variance of S'k is given

~--~ ~~A +7~N~L~g~~~+ :L~?

~~~--~----~

Fig. 1.

We divide the whole area ~ into m uniform meshes with the same square measure ~ . Each mesh is assumed to be the smallest cell of division of ~ . By S, we denote a division rule:

In order that the accura c y of S'k as an estimator of c'

should be equivalent to that of S'h (k,h), k the relation

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(1)

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where ~i is the interior of ~ i '

Let m denote the i number of meshes belonging to the subarea ~ i' and ~ ik

(8)

The outline of an interacting process.

~i'

(k=1,2, ... ,m ) the meshes contained in i

We introduce the following notations of variables: c: the spatial average concentration in

c =

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is required. Namely, the significant sample sizes are determined by the proportional allotment to variation indices. We carry out a preliminary sampling to obtain the unbiased estimates of d' as follows: Generating k the same number, say n, of random numbers in each mesh, we approximate d'k/~ by 1

(2)

c{x) dx

c : the spatial average concentration in i

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d : the variation index of subarea i

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(i=1,2, . .. ,M) ar e usuall y different. In fact, if we determine the sample size of every mesh so that

2

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(12)

constant,

the variance of S. is described by

~ ik :

~

m.

(6) var,[ Si

We must evaluate s patial averages of ground-level concentrations in uniform meshes by the atmospheric diffusion model. In practice, we select several random points in each mesh and calculate the direct e ff e cts from all source s in t he simulation area and finall y avera ge them to obtain an approximate spatial average of the mesh. How shall we decide an optimal allocation o f the sample points ?

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S m.

(13)

~

Thus the variance of the estimator of subarea mean decreases by the effect of stratified sampling.

Surveillance Network Design for Air Pollution Control DESIGN CRITERIA As a measure of representativeness of monitoring stations, we consider ( c(x) - C~) 2 dx.

(14)

i=1,2, . .. ,M.

1

The sensor allocation problem is then phrased as that of determining M*: an optimal number of stations. s* : an optimal division rule and x~. i=1.2 •...• M*: an optimal set of locations

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i=l

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1

Assume that we can find the locations x~. x~ •. ". x~ such that the second term of the above equation

is negligible. i.e. in each subarea there is at least one point with equal concentrat ion to the spatial average of the subarea. \,e have Theorem. For every M. the following are equivalent: s* minimizes

L

i=l M (b)

L

s* minimizes

i=l M (c)

s* maximizes

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i=l

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2 .(17)

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1.

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= {i

I

Define (20)

sii ;, So }

which is a set of objective meshes for clustering. Eliminate the rows and columns not belonging to r from S to yield a reduced square matrix. Step 2. Normalize the reduced matrix so that the sum of each row and column is 100. to remove the s iz e of the row or column total. This is done by alternatively normalizing the rows and then the columns until the matrix converges to a doubly stochastic matrix ( s ee Deming and Stephan. 1940). Step 3. Transform similarit y coefficients of the doubly stochastic matrix to dissimilarities by subtracting them from the maximal entry. Step 4. Modify the dissimilarit y matrix to obtain a new matrix R=[rijl. i.j c l . satisfying the ultrametric inequality: r

L

If

'jh

M i=l

Decide a standard concentration s o '

sii < s o. then we exclude the i-th mesh from the

r

di •

Proof. We can easily verify the following equations: M

the cross-impact matrix whose entries are interpreted as a set of similarity coefficien ts. We can easily transform S to a dissimilarity matrix of non-negative real numbers. But. unfortunately. neither symmetry nor the triangle inequality holds on this matrix. On referring to Boyd (1980). we modify the cross-impact matrix to obtain a new matrix R satisfying certain additiona l axioms. The modifying procedure can be described in the following steps:

surveil lanc e area.

M (a)

(19)

1 i.j=1.2 ..... m

S = [ Sij

The performance J can be rewritten in the form: M

The design problem formulated above is based only on the long-term mean concentration pattern . But actual air quality levels change with time by the direct influence of local emission fluctuation and also by atmospheric variabilit y . The selection of monitoring sites should then depend on the configuration of significant sources and the local topography. Then we require an additional rule: Each representative area should be connec ted such that every pair of meshes interact each other. With regard to this. information available fromour simulation mod e l is the average cross-impacts between pairs of meshes. We shall introduce another topology among meshes based on this information and use it as a constraint in the clustering. Denote the direct effe c t mean concentration from the i-th mesh to the j -th me sh by Sij' and call the square matrix

so as to minimize

J

3235

M d. 1

+ l!.

L

m i
m. m. (c. - c,) 2 . (18) 1)

1

)

The first term on the ri ght-hand side in (17) and the left-hand side in (18) are co nstants depending only on the mesh division. Hence we obtain the above result. Roughly speaking. to achieve representativeness of data. one of the following conditions is required: (a) Spatia l variability of the long-term average of pollutant concentration is small. (b) Long-term mean concentration at a station is similar to that at every point in its representa-

ij

s max{rik.r } . for all k cl . k

An efficient procedure for calculating R is given in Boyd (1980) . The advantage of this modification is that the tr8nsitive rule holds for ever y cutoff. Namely. for every cutoff a . the s e t of objective meshes is divided into several equivalence classes uniquel y :

U

_ 0.

empty when ') "

- '.,.; '

(i)

r, .

,; ::t .

(ii)

r, .

S ::t

centration.

We use the Ward method clustering to obtain a suboptimal division rule. and then select one or two meshes in each subarea. with concentrations close to the spatial average of the subarea. as suitable meshes for a station site.

_Cl.

such that for every index set three conditions hold:

tive area.

(c) Stations represent different levels of con-

(21)

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i

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3236

J. Nakamori and Y. Sawaragi

On every clustering stage, we place the following constraints: Only adjacent clusters are allowed to unite and two clusters not forming an equivalence class for the assigned cutoff are prohibited from connecting each other. Thus our network design will be carried out by the constrained Ward method clustering. The importance role of cutoff is that the division of the surveillance area is unique for every cutoff, i.e. the number of stations and their representative areas are uniquely determined.

DETERMINE

FOR SI MULA TI ON

CONCENTRATION PATTERN

INTERACTIVE DESIGN The design process is summarized as follows: Step 1. Develop a simulation model for predicting long-term averages of pollutant concentrations in an urban area. Step 2. Evaluate spatial averages of ground-level concentrations in uniform meshes and cross-impacts between pairs of meshes by the model. ~

3. Modify the cross-impact matrix to generate a constraint in the optimization process.

Step 4. Decide a surveillance area and a cutoff which implicitly designate the number of monitoring stations. NO

Step 5. Determine representative areas of stations by the constrained Ward method clustering. Step 6. Select one or two suitable meshes in each representative area for a station site. However, after the above network design has been completed, the problem of locating the individual stations will remain and will necessarily involve the advice of competent air pollution meteorologists. Furthermore, because the simulation model can never completely realize the phenomena, participation of specialists in the design process is indispensable to judge the importance of various factors in the network. The following four flexible points lie in our methodology that human must come into the picture: (a) Determination of an objective area, i.e. the spatial scale for simulation. (b) Determination of a surveillance area, i.e. the objective area for clustering. (c) Selection of the cutoff which is related to the suitable number of monitoring stations. (d) Judgement on quantified results: Is the division compatible with human understanding? Of the above points, the last two are emphasized to proceed as interaction between people and computers. The number of monitoring stations is usually determined by trade-off between the measurement cost and the estimation error evaluated by, for example, the value s of performance J. Compatibility between human understanding and the quantified result is important from the administrative standpoint. The outputs of a computer, i.e. an allocation of monitoring stations and a division of the entire area, must be checked by specialists or decision-makers. Figure 2 shows the flow chart of our methodology for an interactive monitoring net\o. ork design. l

SURVEILLANCE AREA FOR CONTROL

From the pollution control viewpoint, it is important to identif y the covering area of the individual monitoring station under every possible meteorological condition. We mean the covering area for the region where the sources are distributed and contribute to concentrations at the monitoring station in some degree. Therefore, the covering area of each station varies with the meteorological condition.

Fig. 2. The flow chart of an interactive monitoring network design.

Assume that we have already determine the number and allocation of monitoring stations. lie introduce a membership function:

each of which represents the degree of membership of the j-th mesh to the i-th covering area at the meteorological pattern P . For every P , the memk k bership function is given b y

s ..

J1

(23)

where s .. is the direct effect concentration from J1 all sources in the j-th mesh to the i-th monitoring station. We classify the typical meteorological patterns and for each pattern, prepare the membership matrix: (24) In practice, we must judge which pattern is to be used from the real observed data and determine the membership of each mesh. It is possible to prepare a data base of concentration pattern for every typical meteorological condition. Figure 3 shows the concept of the graphic display system. APPLICATION As an example of our methodology we consider the optimal network design for NO x monitoring stations in Kyoto, Japan. Figure 4 shows the objective area for simulation and existing station sites. The region is divided into 550 meshes of I km square. It is expected that more than 80 per cent of the total emission is caused by automobiles in Kyoto. Figure 4 also shows the moving sources which we treat as line sources in the simulation model.

Surveillance Network Design for Air Pollution Control

I BACKGROUND INFORMATION L I SIMULATION MODELS I OFF - LINE

CONCLUSIONS

DATA BASE CONCENTRA TI ON PATTERN FOR EVERY TYPICAL METEOROLOG I CAL CONDITION

if GRAPHIC DISPLAY

MEASUREMENT METEOROLOG I CAL DATA SOURCE COND IT IONS MONITORING DATA

Fig. 3.

REPRESENTATIVE AREA ON-L1 NE

COVER I NG AREA

Graphic display system for the represent ative and covering area of the individual monitoring station.

After optimizing sample sizes in simulation, we calculate mesh averages of long- term mean concentration. But the differences of variation indices among meshes are very large in this example, then we use suboptimal sample sizes by setting the maximal sample size at 500 and the minimal at 5. We determine the total surveillance area by setting s o=0.5 ppb. Figure 5 shows one of the results for the cutoff=22 with an artificial constraint: A boundary is put in between clusters E and G enforcedly, which is done by modifying the corresponding entries of the matrix R to satisfy r

ij

> 22,

3237

This paper proposed an interactive design procedure of air quality monitoring network in an urban area. A constrained I',lard method clustering was used to determine the number and location of stations and also the sizes of representative area of the individual monitoring stations. Participation of human in the design process was allowed in such a way that one can modify constraints by taking account of economic and physical conditions and inaccuracy of simulation models. The interacting process is repeated un til compatibility between human understanding and quantified results is achieved. Also we proposed the concept of the covering areas of monitoring stations and the graphic display system for pollution control. An application to the NO x monitoring network design in Kyoto, Japan was presented. In practice, an urban air quality monitoring network should be designed by considering proximate and urban level sites for all kinds of important pollutants. Our methodology should be extended to cope with multi-objective optimization problems in the future.

ACKNOWLEDGEMENT We wish to thank Professor S. Ikeda of The University of Tsukuba for frequent, stimulating, and helpful discussions . vie are also grate'ful to Professors T. Hasegawa and T. Ibaraki of Kyoto University for making simulation models available for this study.

(25) REFERENCES

where fl and f 2 denote the index sets holding the boundary between . This constraint is necessary because there lies a mountain between the subareas E and G, while our simulation model neglects the existence of the mountain. In Fig. 5, this constraint is shown by a bold line, the names of subareas are denoted by A- O, and the first two suitable meshes for a station site in each subarea are shown by 1-2. From the economic or physical reason, it is usually difficult to move the existing stations. Figure 6 shows the result in which we consider an additional constraint: Every cluster contains at most one existing monitoring station, which is done by setting r . . >

1J

22,

i

" j,

(26)

where f , is the index set of meshes in which the existing monitoring stations are located. There are many possible divisions with nearly equnl performances. In practice, we must proceed with interaction between people and computers to obtain a reasonable monitoring network. The final example is concerned with the covering areas of monitoring stations. Figure 7 shows the covering areas of four existing monitoring stations under the annual mean meteorological condition. Each subarea consists of meshes which contribute more than 0.5 ppb an hour to the monitoring station. In practice we should construct a graphic display system which presents the covering areas of the monitoring stations bv using the continuousl y stored meteorological and concentration data .

Boyd, J . P . (1980). Asymmetric clusters of internal migration regions of France. IEEE Trans. on Systems, Man, and Cybernetics, 10, 101-105 . Deming, W. E., and F. F. Stephan (1940) . On a least squares adjustment of a sampled frequency table when the expected mar g inal totals are known. Annals of Mathematical Statistics, 11, 427-444 . Elsom, D. M. (1978). Spatial correlatio~analysis of air pollution data in an urban area. Atmospheric Environment, ll, 1103-1107. Goldstein, 1. F., and L. Landovitz (1977). Analysis of air pollution patterns in New York City. Atmospheric Environment, !!, 47-57 . Nakamori, Y., S. Ikeda, and Y. Sawaragi (1979). Design of air pollutant monitoring system by spatial sample stratification. Atmospheric Environment, 13, 97 - 103. NolI, K. E., T. L-:-Miller, J. E. Norco, and R. K. Raufer (1977). An objective air monitoring site selection methodology for large point sources . Atmospheric Environment, !!, 10511059. Seinfeld, J. H. (1972) . Optimal location of pollutant monitoring stations in an airshed, Atmospheric Environment, ~, 847-858.

J. Nakamori and Y. Sawaragi

3238

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