* Corresponding author. Tel.:#886-2-8787-9037; fax:#886-2-2362-6243.
E-mail address: [email protected] (T.-Y. Yu).
Delineation of air-quality basins utilizing multivariate
statistical methods in Taiwan
Tai-Yi Yu*, Len-Fu W. Chang
Graduate Institute of Environmental Engineering, National Taiwan University, 71, Chou-Shan, Taipei, Taiwan Received 11 May 2000; received in revised form29 October 2000; accepted 7 November 2000
Abstract
This study analyzed time-series data of air pollutants, O and PM, to determine the division of air-quality basins in Taiwan by employing multivariate statistical methods, Varimax rotational method and cluster analysis. The databases of air pollutants, daily maximum 1-h O and daily mean PM concentrations, were obtained fromthe ROC Environ-mental Protection Administration (ROC EPA) for the period from 1 July 1993 to 30 June 1998. The Varimax rotational method allowed us to delineate "ve homogenous PM subregions that cumulatively accounted for 85.6% of the total variance. The time-series analysis of rotated component scores associated with the PM subregions revealed that all divided subregions presented a strong seasonal cycle. Four of "ve subregions had higher component scores and PM concentrations fromNovember to January. One subregion experienced higher values fromMarch to May. The use of Varimax approach and cluster analysis on the O and PM con"rmed that O was more demonstrative of the air-quality basins in Taiwan. Both the Varimax rotational method and the cluster analysis have speci"c advantages for the division of air-quality basins. This study also proposes a delineation of "ve air-quality basins having homogenous O features as an alternative assignment of atmospheric carrying capacity control regions. 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Air-quality basins; Varimax rotational method; Cluster analysis; O; PM
1. Introduction
Air-quality basins are normally determined by me-teorological and geographic conditions as well as politi-cal boundaries. Weather patterns, mountain topography, locations of emission sources, and di!erences in land use also play major roles in the formation and accumulation of secondary air pollutants. O and portions of PM are secondary air pollutants, in which major source regions do not signi"cantly in#uence its spatial behavior in the rural boundary layer (Vukovich and Fishman, 1986). Rather, the path and frequency of anticyclones dominate because of the requisite meteorological conditions (i.e., warmtemperature, clear skies and stagnant conditions).
Scientists have recognized O as a regional (Logan, 1989) and even global phenomenon (Liu et al., 1987). Thus, O and PM could help to identify separated air-qual-ity basins through multivariate statistical analysis of measured data.
The ROC EPA Air Pollution Control Act (ROC EPA, 1999) introduced a programon 20 January 1999 to prevent signi"cant deterioration of air quality, maximum allowable incremental concentrations of air pollutants, and auditing rules for new or updated stationary sources, for the atmospheric carrying capacity control regions. The ROC EPA has the authority to assign atmospheric carrying capacity control regions according to weather and geographic conditions. The delineation of air-quality basins, which exhibit homogenous O or PM concen-trations, is an alternative method for forming atmo-spheric carrying capacity control regions. Many studies have adopted unrotated principal component analysis (UPCA) to examine the spatial patterns of meteorological
1352-2310/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 0 ) 0 0 5 1 7 - 3
measurements (Kidson, 1975; Wallace and Gutzler, 1981; Walsh and Mostek, 1981; Flocchini et al., 1981) and source contribution of air pollution measurements (Gaarenstroomet al., 1977; Gatz, 1978; Alpert and Hopke, 1980, 1981; Pitchford et al., 1981). However, Buell (1975) indicated the shape of the boundary area to which the correlation coe$cients belong often helps to deter-mine the topography of the unrotated principal compo-nents. Therefore, the UPCA is adopted mainly for data reduction and can be somewhat misleading when applied for spatial delineation. Eder (1989) and Eder et al. (1993) applied the Varimax rotational technique to analyze the SO\
concentrations in precipitation and daily 1-h max-imum O concentrations over non-urban areas of the eastern US (the station numbers were 40 and 77) to determine the spatial features of air pollution measure-ments. This application allowed the former investigators to delineate seven and six homogenous subregions, ac-counting for 74.2 and 64.02% of the total variance, re-spectively. Ashbaugh et al. (1984) utilized the Varimax rotational technique to obtain the spatial patterns of 40 inter-site correlations of sulfur concentrations in the western United States. The "rst "ve components were identi"ed with 57.3% of the total variance in the data. The "rst and second components were attributed to copper smelter emissions and episodic incursion of sulfur. Juang et al. (1996) also utilized the Varimax rotational method to analyze the combined data set of "ve air pollutants, SO, PM, CO, O and NOV to delineate seven air basins with the monitoring data of 1994. Yu and Chang (1999) demonstrated the spatial and temporal features of O concentrations and component scores over Taiwan via the UPCA and Varimax rotational approaches. Most importantly, the Varimax rotational technique supplies a statistical, objective, and better physical interpretation that enables PM and O to be divided into homogenous subregions.
The cluster analysis is another e!ective multivariate statistical method that splits a data set into several similar groups. Kalkstein et al. (1987) grouped similar synoptic weather patterns with three varying cluster pro-cedures, while other scientists (Fernau and Samson, 1990a,b) also applied cluster analysis to de"ne speci"c periods with similar meteorological data and precipita-tion chemistry. Before performing the division of air-quality basins, selecting clustering algorithms, specifying the measured distance and choosing adequate grouping numbers are the major features of the objective classi"ca-tion of cluster analysis.
This investigation continues the work of Yu and Chang (1999) by utilizing the Varimax rotational method and the cluster analysis to determine the divided sub-regions that exhibit homogenous O or PM concen-trations. Moreover, it also ascertains the better criteria pollutant and the better multivariate approach for the delineation of air-quality basins. This study also presents
a novel method to separate air-quality basins through two multivariate statistical methods of the spatial and temporal variability of O and PM concentrations found in Taiwan. Results in this study will hopefully stimulate the implementation of an air pollution control programon atmospheric carrying capacity.
2. Method
The air-quality-monitoring network continuously monitors the air quality via its 72 stations spread over Taiwan. The major air pollutants that are monitored include SO, NO, NO, CO, O, PM and NMHC. Fig. 1 illustrates the locations of the monitoring stations and the political boundaries in Taiwan. The historical data of daily maximum 1-h values of O and daily mean values of PM concentrations are compiled into two distinct databases, lasting from1 July 1993 to 30 June 1998. These data sets can be viewed mathematically as a time series of high-dimensional vectors, each of which has 63 O components and 71 PM components (i.e. the number of total observational stations with measured O and PM data).
2.1. The Varimax rotational method
The Varimax rotational method, as developed by Kaiser (1958), increases the segregation between com-ponent loadings and more clearly de"nes a distinct clus-tering of intercorrelated data and ultimately makes spatial interpretation easier. This technique rotates the predetermined principal components while maintaining that the individual components remain orthogonal to each other. Horel (1981) indicated that the UPCA and the Varimax rotational approaches maximize the sum and the variance of squared correlation coe$cients, re-spectively. The front analysis maximizes the "rst moment statistic (the sum) that causes the correlation coe$cients to be poorly distributed (i.e., many loadings with similar magnitudes), resulting in spatial patterns that are di$cult to interpret. Maximizing the second moment (the vari-ance) causes the correlation coe$cients to be widely distributed (i.e., many loadings close to zero) in an easier explanation for spatial patterns.
The analysis is initiated by extracting a square, sym-metrical correlation matrix (63 columns;63 rows for O and 71 columns;71 rows for PM, the original data matrix was 63 stations;1826 days for O and 71 sta-tions;1826 days for PM). The average values of daily maximum 1-h values of O and daily mean values of PM concentrations at respective stations were sub-stituted for the lost data. The normalized value is (1)
ZGI"CGI!GSG , (1)
Fig. 1. Locations of monitoring stations and political boundaries over Taiwan (Taiwan, ROC).
where ZGI denotes the normalized value of the kth obser-vation on the ith stations, CGI represents the kth O or PM concentration of the ith station, G is the mean value of the ith station, and SG denotes the standard deviation of the ith station. A correlation matrix is signif-icantly more appropriate than a covariance matrix for resolving spatial oscillations (Overland and Preisendor-fer, 1982). Moreover, a correlation matrix presents the isopleths of component loadings, which can be regarded as the correlation coe$cients between the rotational component and individual stations. In sum, the Varimax rotational method aims to obtain the maximum T value, which is represented as ¹"n H L G
AGH hG ! H L G AGH hG , (2) hG" H GH, ZGI"L GAGHRHI,where n denotes the number of stations, AGH represents the loading of the ith station on the jth rotated principal component, hG is the communality of the ith station, and
RHI stands for the component score of the kth variable for
the jth rotated principal component. The standardized scores of the rotated components are symbolized by
PHI"RHI/(H, (3)
where H denotes the eigenvalue or variance of the jth rotated component and PHI represents the standardized scores of the kth variable on the jth rotated principal component.
In the division of air-quality basins, features of geo-graphic and emission inventories are two dominant fac-tors. Fig. 2 represents the spatial patterns of these two factors over Taiwan. Yu and Chang (1999) utilized the Varimax rotational technique to divide Taiwan into "ve homogenous O
subregions (Fig. 3) that account for 75.5% of the total variance. The O subregions are termed Midwestern Taiwan (M-W-T), Tainan-Kaohsiung-Pingtung (T-K-P), Taipei-Keelung (T-K), Tao-Yuan (T-Y), and eastern Taiwan (E-T) in decreasing order of explained contribution. This investigation delin-eates "ve homogenous PM subregions that account for 85.6% of the total variation. The in#uence regimes of the "rst "ve PM
rotated components, P1, P2, P3, P4 and P5, are depicted in Fig. 4. The isopleths of component loadings were determined with Kriging approach, a use-ful geostatistical gridding method. Five maps of the "rst
Fig. 2. (a) Topography, (b) NOV emission inventory over Taiwan, (c) NMHC, and (d) PM emission inventory over Taiwan (Source: ROC EPA, 1997).
Fig. 3. Five homogenous O subregions (Yu and Chang, 1999).
"ve components can be incorporated into one "gure by plotting the suitable loading of each station on their respective rotated principal components. Each of the "ve rotated principal components identi"es an in#uence regime that distinguishes a segregated area of study do-main. Accounted variances of the "ve components are 39.2, 29.3, 7.7, 5.3 and 4.1%. The PM subregions, as delineated by the 0.5 or 0.6 component loading isopleths, exhibit insigni"cant overlapping.
2.2. A time-series analysis of the rotated components
Time-series analysis is an e!ective means of character-izing the relationships between air pollutants' con-centrations and the rotated principal components. This approach has been successfully applied in the aerometric data, including SO\
concentrations in precipitation (Eder, 1989), SO ambient air concentrations (Ashbaugh et al., 1984) and O ambient air concentrations (Eder et al., 1993). The temporal variation of each subregion can
be assessed by examining the standardized scores of the rotated principal components: the standardized scores are weighted summed values whose magnitudes depend on the daily mean PM concentrations and the loadings of rotated components. All of the rotated component scores have a mean of zero and a standard deviation of one since the scores are standardized. The positive and negative scores correspond to higher and lower values than average PM concentrations.The daily principal component scores accurately re#ect the temporal variance of each subregion when plotted as a time series (Fig. 5). Such information also provides a valuable reference for scientists to select PM episodes where the highest PM concentrations are observed. According to our results, the optimum period for simulating potential reductions in PM concentra-tions resulting fromvarious emission strategies is to be determined. For example, model designers could deter-mine the optimum simulation period for the P1 sub-region by examining the daily time series of component scores associated with the "rst rotated principal compon-ent. The occurrence rates of standardized principal com-ponent scores greater than 1, 2, 3, 4, 5, 6 and 7 are 37.7, 29.8, 23.0, 17.5, 12.4, 8.9 and 6.0% during 5 yr period. The time series indicates that 53 days in 1994 had standard-ized principal component scores greater than 5. No other year for this subregion recorded more days where the standardized component scores were greater than 5. In addition, 11 of the 53 days occurred within a month, from 1 April to 30 April, representing the most intensive PM episode experienced by the P1 subregion and, sub-sequently, the optimum simulation period.
The seasonal cycles were depicted by the time series of median values of component scores associated with the "ve subregions over a 5-yr period. (Fig. 5f ) 30-day mov-ing average values of the median score were chosen to enhance the characterization of the seasonal variation for each PM subregion. The standardized component scores of subregions P2, P3, P4 and P5 were positive values fromOctober to January. All PM subregions had negative component scores in summer, from June to August. The P1 subregion exhibits positive component scores during spring, fromMarch to May.
The statistics for each PM subregion were sum-marized as the box plots in Fig. 6. The box plots included the 5th, 10th, 25th, 50th, 75th, 90th and 95th percentile values. PM concentrations in the P2 subregion are considerably higher than in the other subregions across all percentiles fromSeptember to March. Correspond-ingly, the percentile of days that concentrations exceeded 100 (35.9%) and 125g m\ (20.3%) are also the greatest in the entire domain (Table 1). The P1 subregion had the highest PM concentrations during summer, while P3 displayed second highest concentrations for the percent-age of days exceeding 100 (30.8%) and 125g m\ (11.4%). The P1, P2, P3 and P4 subregions had the
Fig. 4. (a)}(e) PM component loadings (;100) associated with "ve rotated principal components. (f) Five homogenous PM concentration regions delineated by the maximum component loadings.
highest PM concentrations in April, December, No-vember and NoNo-vember, respectively. Subregions P1, P2, P3 and P4 experienced the minimum PM con-centrations during February, June, June and June, respectively.
2.3. Cluster analysis
The cluster analysis categorizes di!erent groups ac-cording to similarities or distances. Euclidean distance is the chosen scale of similarity for normalized data of air
Fig. 5. (a)}(e) Daily time-series of the standardized principal component scores associated with the "ve homogenous PM subregions. (f) Seasonal time-series as de"ned by the 30-day moving values of median principal component scores for each of the homogenous PM subregions.
Fig. 6. (a)}(e) Boxplots of the monthly PM concentrations associated with the "ve PM subregions. (f) Boxplots of the PM concentrations associated with the "ve subregions.
pollutants as well as the daily maximum 1-h O values and the daily mean PM concentrations. Ward's min-imum variance clustering method, which merges two clusters that result in the smallest increase in the
sum-of-squares, was the clustering approach employed herein. The plots of percentage change in total root-mean-square deviation (TRMSD) against the number of clus-ters provide the criteria for determining the adequate
Fig. 7. The percentage change in TRMSD with the numbers of clusters. Table 1
Summary statistics of daily mean PM (g m\) concentra-tions associated with each PM subregion
PM subregion N Mean %'100 %'125 P1 49,740 55.3 5.85 2.31 P2 34,280 85.6 35.88 20.31 P3 11,807 69.3 30.80 11.42 P4 11,932 61.9 16.17 6.51 P5 8812 41.4 1.09 0.27 Domain 11,6571 65.3 17.91 8.80
number of clusters (Dorling et al., 1992). The TRMSD is recalculated as the sumof root-mean-square deviations of normalized values of air pollutants from its cluster average at every step. The percentage change in TRMSD values, with the number of O and PM clusters is presented in Fig. 7. Dorling et al. (1992) indicated that adequate numbers of clusters could be located as sudden breaks or large percentage changes during the clustering process because the merging of clustered trajectories have signi"cantly di!erent wind directions and wind speeds. As the cluster numbers of O and PM are greater than "ve and four, we can gain limited explained variances through adding the number of clusters. There-fore, four and "ve clusters of O and PM were em-ployed to analyze the spatial features of Taiwan's monitoring station.
The spatial evaluation of four and "ve clusters of O and PM could be an appropriate method to choose the better criteria pollutant for delineating air quality basins via the cluster analysis. The di!erence, as obtained
fromFig. 8a and b, between four and "ve clusters of O is that the later diagramdelineates the northwestern part of Taiwan as two isolated groups. The division of O sub-regions into "ve clusters via the Varimax rotational method has a similar result in Fig. 3, except that stations 23, 24 and the T-K O subregion were classi"ed as the same cluster and stations 44, 45, 46 and the O M-W-T subregion were categorized as the same cluster. Fig. 8c and d illustrate that some stations (46, 3, 64, 34 and 1) within the same political boundary were arranged into distinct groups depending on whether they had four or "ve PM
clusters. The division of PM subregions into "ve clusters via the Varimax rotational method has sim-ilar delineating results, except for the small overlap on the boundaries of the P1, P2, P3 and P4 subregions. The di!erence between four and "ve clusters of PM is that the later graph divides the northwestern and middle part of Taiwan into two diverse groups.
O is a more suitable pollutant than PM for the division of air-quality basins according to both the Varimax method and cluster analysis. The Varimax ro-tational method provides the accounted variances of rotated components, correlation coe$cients between monitoring stations and rotated components, and opti-mum simulation period for di!erent subregions. The cluster analysis provides the quanti"ed criteria for the selection of cluster numbers and the hierarchy of similarities. Thus, both methods have their speci"c advantages.
2.4. The division of air quality basins
Five air-quality basin divisions are proposed for Taiwan based on political boundaries as well as the
Fig. 8. (a) Four; (b) "ve clusters for O; (c) four; and (d) "ve clusters for PM, the same numbers marked on the position of monitoring sites present the same clusters.
Fig. 9. Five proposed air-quality basins over Taiwan.
O subregions separated by the Varimax rotational method and the cluster analysis (Fig. 9). These air-quality basins are termed as T-K, T-Y, M-W-T, T-K-P and E-T. Local governments within the same air-quality basin should devote their e!orts to enhance air quality. Evalu-ating the relationships between the boundary lines of "ve air-quality basins, mountain topography and emission inventory of NOV and NMHC, we gained the following results. First, geographic condition separated Taiwan into eastern and western parts. Secondly, spatial patterns of emission inventory divided western Taiwan into four distinct air-quality basins. On the basis of the delineation of measured ozone data, 10 counties located within M-W-T air-quality basins have the highest priorities to precede emission abatement strategies of air pollutants, with a special focus on O problems.
3. Summary
This study examined the spatial and temporal variabil-ities of O and PM concentrations over Taiwan from July 1993 to June 1998 via the Varimax rotational method and cluster analysis. The Varimax approach identi"ed "ve homogenous PM subregions, ac-counting for 85.6% of the total variation and each
sub-region exhibited unique PM concentrations. Analysis of the rotated principal component scores as well as the actual PM concentrations revealed a strong seasonal cycle in the P1, P2, P3 and P4 subregions. One of "ve PM
subregions presented its higher component scores and PM concentrations during spring. Other four PM subregions showed their highest component scores and PM concentrations fromNovember to January.
The division of air-quality basins should be based on O instead of PM since: some stations within the same political area were attributed to varying PM clusters and subregions, and a small overlap exists among di!er-ent PM subregions created by the Varimax approach. This study divided Taiwan into "ve air-quality basins based on the political boundary lines and the Varimax method and cluster analysis on O. These "ve air-quality basins could provide the EPA with an alternative assess-ment of the atmospheric carrying capacity control re-gions. The counties winthin the same air-quality basins are proposed to devote their e!orts to improve ozone problems.
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