### 1182 JOURNAL OF APPLIED METEOROLOGY VOLUME33



# An Automated Classification Scheme Designed to Better Elucidate the Dependence of Ozone on Meteorology

BRIAN 

### K. EDER * 

### Atmospheric Sciences Modelfng Divisfon, Air Resources Laboratory, National Oceanic and Atmospheric Administratfon, Research Trfangle Park North Carolina

JERRY 

### M. DAvis


### Department of



### Marine, Eanh and Atmospheric Scfences. North Carolina State Univeisfty, Raletgh, North Carolina

PETER BLOOMF7ELD Depanment ofStatistics, North Carolina State Universfty, Raleigh, North Carolfna
(Manuscript received 1 November 1993, in final form 4 March 1994)

ABSTRACT This paper utilizes a two-stage (average linkage then convergent k means) clustering approach as part of anautomated meteorological classification scheme designed to better elucidate the dependence of ozone on meteorology. When applied to 10 years (1981-90) of ineteorological data for Birmingham, Alabama, the classification scheme identified seven statistically distinct meteorological regimes, the majority of which exhibited significantly different daily 1-h maximum ozone concentration distributions. Results from this two-stage clustering approach were then used to develop seven "refined" stepwise regression models designed to I) identify the optimum set of independent meteorological parameters influencing the 03 concentrations within each meteorological cluster, and 2) weigh each independent parameter according to its unique influence within that cluster. Large differences were noted in the number, order, and selection of independent variables found to significantly contribute (a = 0.10) to the variability of 0 3 . When this unique dependence was taken into consideration through the development and subsequent amalgamation of the seven individual regnession modeis, a better parameterization of Oj's dependence on meteorology was achieved. This "composite" model exhibited a significantly larger RZ 

### (0.59) and a smaller rmse (12.80 ppb) when compared to results achieved from an "overall" model (R 2 = 0.53, rmse = 13.85) in which the meteorological data were not clustered.



## 1. Introduction

Ozone (03) 

## is a secondary pollutant, photochemically produced from reactions involving a variety of volatile organic compounds (VOCs), composed mainly of nonmethane hydrocarbons (HC), in the presence of nitrogen oxides (NO, r ) such as nitric oxide ( NO ) and nitrogen dioxide ( NO Z ). The rate of these photochemical reactions, as well as the subsequent transport and scavenging of 03, depends greatly onrneteorological conditions, which are inherently variable. Because of this strong association, an abundance of studies has attempted to elucidate 03's dependence

• On assignment to the Atmospheric Research and Exposure Assessment Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina.



### Correspondfng author address: Brian IC Eder, MD-80, AREAL, Environmental Protection Agency, Research Triangle Park, NC 27711.



## m 1994 American Meteorological Society 

## on meteorology, most utilizing some form of statistical regression or graphical analysis ( Wolff and Lioy 1978;Clark and Karl 1982; Shrefiler and Evans 1982; Robeson and Steyn 1990; Cardelino and Chameides 1990;Feister and Balzer 1991; Cox and Chu 1991). Unfortunately, the complexity of the relationships often results in less than satisfactory levels of explained variance and understanding (Comrie 1990). Attempts designed to facilitate understanding of meteorological impacts on 03 concentrations, while simultaneously reducing the unexplained variance,have been developed through the utilization of classification schemes in which meteorological variables are categorized or stratified into a number of characteristic classes. Examples of such schemes, which have met with varying degrees of success, include Altshuller (1986, 1988 ) and Lindsay and Chameides ( 1988 ), who stratified concentrations in the St. Louis, Missouri, and Atlanta, Georgia, areas, respectively; Pratt et al. ( 1983 ), who examined concentrations in the upper midwest of the United States; and Mukammal et al. (1982 ) and Peake and Fong (1990), who stratified 0 3 concentra-OCroaER 1994 E D E R E T A L. 

### 1 183

tions over sections of Canada ( southern Ontario and southwestern Alberta, respectively). Other investigators have carried this classification approach further, by attempting a more holistic, albeit subjective, stratification based on general circulation patterns or airmass types. Examples of this approach,which are often accomplished through the visible inspection of synoptic weather maps include Kelly et al.( 1982 ), who subjectively stratified air quality data ( including 0 3 ) by airmass types for a remote area in South Dakota; Muller and Jackson (1985), who developedan air quality potential index based on subjective synoptic weather types for Louisiana; Heidorn and Yap ( 1986 ) and Yap et al. ( 1988 ), who subjectively defined air masses in which they stratified 0 3concentrations in southern Ontario; and finally, Yarnel et al. (1991), who evaluated six synoptic classifications schemes, and Comrie (1992), who developed an enhanced (although still subjective ) scheme, both for 0 3data in Pittsburgh, Pennsylvania. While providing additional information conceming the variability of 0 3concentrations, these latter studies are somewhat limited by the subjective nature in whichairmass types are defined. Accordingly, a more objective approach such as that recommended by Crutcher et al. ( 1986 ) was preferred, in which the meteorologicaldata are objectively segregated by a multivariate statistical technique called cluster analysis. Numerous such analyses have been developed utilizing a variety of clustering techniques such as Ward's method and the centroid and average linkage techniques (Kalksteinand Corrigan 1986; Kalkstein et al. 1987). More recently, a two-stage clustering approach that utilizes average linkage and convergent k-means techniques hasbeen developed ( Davis and Kalkstein 1990). This twostage approach has proven superior in terms of cluster cohesiveness and has been used successfully in several studies relating meteorology to air pollution (Davis 1991; Davis and Walker 1992; Davis and Gay 1993); however, it has never been fully utilized in an 0 3study. The purpose of this paper is to utilize this two-stageclustering approach as part of an automated meteorological classification scheme designed to better elucidate the dependence of 0 3 on meteorology. This approach was applied to Birmingham, Alabama, where summer days during the 10-yr period 1981-90 were stratified into one of a finite number of ineteorological clusters that represent the primary and recurring states of the atmosphere. Birmingham was selected for severalreasons. In addition to having the requisite meteorological and 0 3 data, it was found to be regionally representative of a large section of the southern United States, encompassing Kentucky, Tennessee, Georgia, the western Carolinas, and Alabama (Eder et al. 1993).The area is also relatively free of geographic complications and is isolated from other large metropolitan areas, thereby simplifying interpretation of results. Results from this two-stage clustering approach, which reduces meteorological variance through theisolation and identification of the key atmospheric regimes, are then used in the development of refined stepwise regression models. These models are designed to identify those meteorological parameters influencing the 0 3 concentrations within each meteorological cluster and to weigh each parameter according to its influence. The potential applications of this approach are numerous and varied. The meteorological clusters can be used in the identification and characterization of case study periods; in trends analysis; as an aid in the design of field experiments; and in the development of modeling aggregation schemes. The stepwise multipleregression can be used in the development of clusterspecific empirical models that can enhance current 03 

### forecasting skills. When amalgamated into a composite model, these individual, cluster-specific models provide a better parameterization that reduces unexplained variance and facilitates understanding of 0 3 's dependence on meteorology.

2. Data 

### a. Meteorological data The meteorological data used in development of thehomogeneous clusters and regression models were obtained from the National Weather Service (NWS) and included both surface and upper-air measurements. The data encompassed the 5-month ozone season (May—September) recorded over the 10-yr period1981-90, resulting in 1530 days. Parameters were selected based on two important criteria: first, they should represent both the thermodynamic and hydrodynamic properties of an air mass, and second their magnitudesshould vary significantly between air masses while remaining relatively conserved within air masses ( Kalkstein and Corrigan 1986).The surface observations were recorded at Birmingham's Municipal Airport located in the northwest part of the city [33.57 ° N, 86.75°W, elevation 189 m (Fig. 1)]. These included air temperature and dewpoint temperature ( ° C), barometric pressure (mb), cloud cover ( tenths of sky covered ), and the u (east—west) and v (north—south) components of the wind ( m s' ). Air and dewpoint temperature are standard airmass indicators, defining the thermodynamic properties ofthe air mass ( Barry and Perry 1973). Dewpoint temperature was selected over other moisture indicatorsbecause it is conservative, both diurnally and with respect to temperature. Pressure and wind are excellent indicators of airmass hydrodynamic properties, while cloud cover is indicative of moisture aloft. To provide diumal information, the surface observations were taken eight times daily ( O 100, 0400, 0700, 1000, 1300,1600, 1900, and 2200 LST), resulting in 48 daily surface parameters. Because the vertical structure of an air mass has a profound influence on the behavior of

### 1184 JOURNAL OF APPLIED METEOROLOGY VOLUME 33

FIG. 1. Station location map illustrating proximity of the three 0 3monitors and the surface ( Birmingham Municipal Airport) and upper-air data (Centreville) meteorological stations.



### 0 3 , upper-air data from the Centreville, Alabama, rawinsonde station were also incorporated into the analysis. Any spal:ial discrepancies resulting from this station's distant location ( approximately 70 km southsouthwest of Birmingham) should be minimized dueto the uniformity of upper-air patterns. These upperair observations were taken twice daily, at 1200 and 0000 UTC ( 0700 and 1900 LST ), and for this analysis included temperature, dewpoint depression, and the u and v components of the wind recorded at 850 mb. In addition to the 56 daily measured parameters, three derived parameters [total daily solar insolation ( W m -Z ) an(i the morning and afternoon mixingheights ( m) ] were included to enhance the meteorological cluster - development and understanding. Deri- . vation of the solar insolation considered the solar angle ( based on the day of the year, elevation of the site, and its latitude and longitude ) and the cloud cover. The morning mixing height was calculated as the height above the ground at which the dry-adiabatic extension of the morning minimum surface temperature, plus 5 ° C (to allow for early morning heat island effects), intersects the vertical temperature profile observed bythe 1200 UTC sounding ( Holzworth 1972). The afternoon mixing height was calculated in the same manner, except that the afternoon maximum surface temperature is used, instead of the minimum plus 5 ° C (Holzworth 1972). 

### b. Ozone data

The 0 3 data employed in this analysis were obtained form the Environmental Protection Agency's ( EPA ) Aerometric Information Retrieval System (AIRS) and include both the hourly and the daily 1-h maximumconcentrations collected within the Birmingham, Alabama, Metropolitan Statistical Area ( MSA ). The data [ measured in parts per billion ( ppb )] were monitored by the Jefferson County Department of Health using ultraviolet photometers and strict measurement criteria established by the U.S. EPA (1991), which include multipoint calibrations, independent audits, and datavalidation based upon frequent zero, span, and precision checks as well as a rigorous quality assurance program. To provide a continuous, regionally representative 0 3 database, unencumbered by missing data or localscale variability, several selection criteria were utilized. First, to reduce chemical scavenging by NO found within urban areas, only stations classified as rural or suburban were considered. Second, only those stations reporting a daily capture rate ( cr ) of 90.0% or better (each day must contain all 24 hourly observations) over the 10-yr period (1981-90) were considered. These criteria resulted in the selection of three sites (Table 1). Pinson (cr = 93.46%) is classified as rural and is located 25 km northwest of downtown. The two remaining sites, which are classified as suburban, are Fairfield (cr = 97.65%), located approximately 15 km southwest of downtown, and Tarrant City ( cr = 99.15% ), located 10 km northwest of downtown ( Fig. 1). Correlation coefficients of the 0 3 concentrations observed at the three sites were high, ranging from 0.70 ( Fairfield and Pinson ) and 0.81 ( Pinson and Tarrant City ) to 0.87 ( Fairfield and Tarrant City ). Since the intent of this analysis was to characterize 0 3 concentrations over the entire MSA, as opposed to a particular location, the mean value of the three sites was utilized. This provided a single measure of 0 3 thatwas 1) highly representative of the entire region (correlations between the mean and individual stations ranged from 0.90 to 0.96), and 2) continuous, in that at least one station was operating on each of the 1530 days of the study period. Other measurements of central tendency [ i.e., median, median polish, and the pooledmean ( utilized by Comrie and Yarnel 1992 )] were examined but revealed insignificant differences; hence,

TABLE 1. Station attributes

Latitude Longitude Elevation Capture Monitor ld Location (°N) (°W) (m) Land use (%)

010731003442011 Fairfield 33.486 86.915 183 suburban—residential 97.65 010735002442011 Pinson 33.704 86.669 201 rural—residential 93.46 010736002442011 Tarrant City 33.578 86.774 171 suburban—residential 99.15OCTOSER 1994 E D E R E T A L. 

### 1 185

all subsequent references to 0 3 concentrations refer to the mean value of the three sites.

3. Methodology
The meteorological classification and regression scheme comprises a three-step process. First, principal component analysis is applied to a correlation matrixof the raw meteorological data to develop daily principal component scores. These are then clustered into homogeneous meteorological regimes using a two-stageapproach. Finally, a stepwise regression analysis is applied to each meteorological regime, with the daily 1-h maximum 0 3 as the dependent variable and a suiteof ineteorological parameters as the independent variables.



### a. Principal component analysis
The meteorological dataset employed in this classification scheme is both voluminous and replete with intravariable (i.e., temperature at hour 0100, 0400,0700, etc.) and intervariable (temperature and dewpoint temperature ) collinearity. It is important to eliminate, prior to clustering, this collinearity in orderto prevent variables that are highly correlated from exerting a disproportionate amount of influence and thereby contaminating the results (Davis 1991). This is achieved through the application of a multivariate technique called principal component analysis (PCA). In addition to eliminating all collinearity, PCA alsoreduces the size of the dataset through its linear transformation into a hierarchy of orthogonal and thereby independent components that explain successively less and less of the total variance ( Eder 1989). Mathematically, PCA entails the calculation of asquare, symmetrical correlation matrix R(having dimensions of 59 X 59 ) from the original data matrix ( 15 30 days X 59 variables = 90 270 observations). A correlation matrix was used in this study (as opposed to a cross-products or covariance matrix ) because theunits of the meteorological data are different ( e.g., millibars, degrees Celsius, meters per second). By using R and the identity matrix i of the same dimension, 59eigenvector—eigenvalue pairs were derived. The eigenvectors represent the mutually orthogonal linear combinations, while their respective eigenvalues representthe amount of variance explained by each of the eigenvectors. By retaining only the first few eigenvector— eigenvalue pairs, or principal components, a substantial amount of the total variation can be explained. The exact number of components that should be retained was determined graphically through application of theScree test ( Cattell 1966), which suggested a five component solution explaining 67.68°Io of the total variance. The original meteorological dataset, which contained 59 collinear variables, has thus been transformed to one that contains only five orthogonal and thereby independent variables ( principal components ) and yet still explains more than two-thirds of the total variance (Table 2).When the elements of each eigenvector are multiplied by the square root of the associated eigenvalue, one obtains the principal component loading, which represents the correlation between the component andthe meteorological parameter. While physical interpretation of the principal components is not vital to this procedure, it is worth noting that the larger thecomponent loading, the more important the meteorological parameter is in interpretation of that component. Principal component 1 loads highly with bothsurface and upper-air temperature and dewpoint temperature, indicating the importance of thermal andmoisture characteristics in defining meteorological regime. The second component loads highest on pressure and afternoon mixing height. The third component loads highest on cloud cover, morning mixing height and 850-mb v component of the wind. The fourthcomponent loads highest on the surface v wind component, and finally, the fifth component loads highest on the u component of the wind. Finally, principal component scores, which represent the projection of the original meteorological data onto the five principal components are then calculated for each of the 1530 days. This results in a matrix (1530

X 

### 5) whose reduced size and absence of collinearity make it much more suitable for clustering. In addition to being uncorrelated, the five scores are standardized and designed such that days experiencing comparable meteorological conditions will exhibit similar principal component scores.



### b. Two-stage cluster analysis
The second step in this classification procedure involves the delineation of the homogeneous meteorological regimes. This is achieved through the application of a two-stage clustering technique on the five daily principal component scores, using both hierarchical and nonhierarchical techniques. First, 

### average linkage,an hierarchical, agglomerative method is used to determine the initial number of clusters and the mean conditions within each cluster (mean scores). These initial clusters are then modified using the 

### convergent k means, a nonhierarchical iterative method, to produce the final solution. This two-stage approach, first recommended by Milligan (1980), has proven superior

TASLE 2. Statistics for the first five principal components.

PC 1 PC 2 PC 3 PC 4 PC 5

Eigenvalue 15.70 9.43 7.15 4.04 3.61 Explained variance (%) 26.61 15.98 12.12 6.85 6.12 Cumulative explained variance (%) 26.61 42.59 54.71 61.56 67.681186 JOURNAL OF APPLIED METEOROLOGY vOLUME 33



### to a one-stage approach ( using average linkage alone ) in terms of cliuster cohesiveness and has been applied successfully in meteorological applications (Davis and Kalkstein 1990; Stooksbury and Michaels 1991; Davis and Walker 1992). Hierarchical clustering techniques, of which there are many, are ideal for exploratory analysis. First, the Euclidean distance between all observations (based on daily principal component scores ) is calculated; then the two closest observations are merged to form a new cluster. The dlistances are then recalculated, with these steps repeated until all observations are eventually merged into one cluster. The various techniques differ mainly in how the distances are calculated and how the two closest observations are defined ( Stooksbury and Michaels 1991). In an evaluation of three of the most utilized hierarchical clustering procedures (Ward's, average linkage, and centroid), Kalkstein et al. (1987) found that the average linkage technique,developed by Sokal and Michener (1958), was far superior to both the centroid and Ward's methods in producing clusters that produced the most realistic meteorological groupings. With average linkage, eachday ( as represented by the five component scores ) initially starts out as an individual cluster. Similar days are then merged, where cluster similarity is determined by the mean clistance between all objects in the clusters ( weighted by the number of inembers ), until all days are in one clu.ster. This method produces clusters withthe smallest within-cluster variance and the large between-cluster separation. This characteristic, along withits propensity for developing compact, spherical clusters, makes it especially appropriate for meteorological classification applications ( Davis and Kalkstein 1990). Selection of the final average linkage solution is achieved through a variety of statistical tests. Both the pseudo-F and pseudo-t 2 statistics, which indicate thelevel of cluster cohesiveness, as well as changes in explained variance R Z , provide useful diagnostic information. The pseudo-Fis the ratio ofthe between cluster variance and the within cluster variance, while the pseudo-t 2 is tl'ne ratio of the sum of square errors within two clusters and the sum of square errors within one cluster. Both of these statistics are related to the familiar F and t Z statistics, but cannot be used for significance testing due to the lack of an underlying distributionassumption. A guide for the selection of the final clustering solution is to observe a local maximum in thepseudo-F, followed by a local maximum in the pseudot 2 as the number of clusters decreases ( denoted by boldin Table 3)( Stooksbury and Michaels 1991) . This occurs three tirries, at 12-, 7-, and 5-cluster solutions. The largest drop in R z occurs when clustering to less than seven clusters ( from 0.40 to 0.29 ); therefore, a seven cluster solution was indicated. Once the number of clusters was determined and the starting "seed" values known (mean principal component scores for each average linkage cluster), a TASLE 3. Statistical tests for determining number of clusters to retain.

Number of clusters R Z Pseudo-F Pseudo-t 2

15 0.50 100.72 25.98 14 0.49 105.49 27.23 13 0.48 112.09 15.20 12 0.47 118.12 30.16 11 0.44 114.64 90.51 10 0.44 125.31 16.26 9 0.42 131.73 42.57 8 0.42 148.99 9.34 7 0.40 158.63 56.41 6 0.29 118.14 248.36 5 0.27 131.65 72.57 4 0.20 122.98 124.45 3 0.14 117.18 113.66 2 0.11 179.50 62.45 1 0.000 - 179.50



### nonhierarchical technique called convergent k means was applied. This method, developed by MacQueen ( 1967 ), uses an iterative approach that allows for the reclassification of days after they have been grouped into a cluster, thus refining the final cluster solution. Once the seed values are known, days are assigned to the cluster with the nearest seed values. After all dayshave been assigned, the centroid of each cluster is recalculated and then used as the new cluster seed. These steps were repeated until the change in new seed valuesconverged to specified amount (0.001). Upon completion of this second stage, each day of the 1530-day study period can be grouped with other days exhibitingsimilar meteorological conditions. The resulting meteorological regimes can then be characterized by examining the mean values of the meteorological parameters used in the initial analysis.



### c. Stepwise regressionIn an attempt to objectively define and weight accordingly those meteorological variables most influencing the 0 3 concentrations within each of the seven homogeneous clusters, the final step in this procedure involves development of "customized" stepwise linear regression models of the form

p

[ 0 31 = 00 + 

### ~ NiXi,



### where [ 0 3 ] represents the maximum daily 1-h ozone measurements for clusters 1-7, 0 0 is the constant value, ,6 ; 's are the coefficients (determined by the least-squares method ) of the independent variables X ; 's, and p is the number of independent variables in the equation. For comparison, a regression model was also developed for the full dataset. A stepwise regression procedure was utilized because it identifies, sequentially, the "optimum subset" of in-OcrosER 1994 E D E R E T A L. 

### 1 187

dependent meteorological variables ( Walpole and Myers 1978). At each step of the selection procedure, the meteorological variable is chosen that has the largest partial correlation coefficient with the 03 concentration ( after allowing for those variables previously selected ), thus ordering the meteorological variables according to their ability to account for the variability of 03. The F statistic for each of the independent variables entered into the model is calculated and its p value comparedto the entry significance level of 0.15. After entry, stepwise regression examines all previously entered variables and removes any whose F statistic is not significant at the retention significance level of 0.10. The procedure terminates when no remaining variables have an F statistic significant at the entry level, and every variable in the model is significant at the retention level. Because of the significant amount of intravariablecorrelation discussed in section 3, the suite of ineteorological variables used in development of the stepwise multiple regression was somewhat different than thatused in development of the clusters. Rather than considering all eight of the three-hourly surface parameters observed daily for incorporation into the model [which often resulted in variance inflation factors (VIFs) > 2.0, thus indicating collinearity ( Draper and Smith1981)], either the daily maximum (for surface temperature ), the daily mean ( for the u and v wind component, barometric pressure, and dewpoint), or the daylight mean (cloud cover) ofthese observations was utilized ( Table 4). Additionally, wind speeds for the surface (the daily mean) and 850 mb, as calculated from the u and v components, were also incorporated into the regression models.

4. Results and discussion 

### a. Cluster analysis
To characterize the meteorological regimes associated with the seven clusters, mean values for each of the 59 meteorological parameters were calculated. These means are presented in schematic form [panel(a) of Figs. 2-8]. Conventional meteorological notation and units are used to denote the 3-h surface andtwice-a-day upper-air parameters. Additionally, representative surface maps were selected [panel (b) of Figs. 2-8 ] to characterize the synoptic-scale conditions associated with each meteorological regime.

1) CLUSTER CHARACTERIZATION 

### Cluster one (Cl ) is clearly associated with the westward extension of the quasi-permanent 

### Bermuda high pressure cell and is characterized by warm temperatures (second warmest ofall clusters), high pressure (second highest ), relatively clear skies ( high solar insolation ), and the lightest and most variable winds (Fig. 2a). Itwas the most prevalent meteorological cluster, occurTASLE 4. Independent variables used in stepwise regression.

Variable Variable code

Maximum temperature (°C) MXTEMP Daily mean wind speed (m 

### s') MNWDSP Daily mean u component (m 

### s') MNWDUC Daily mean v component (m 

### s') MNWDVC Daily mean pressure (mb) MNPRES Daily mean cloud cover (tenths) MNCCOV Daily mean dewpoint (°C) MNDEWP Total solar insolation (W m -Z ) TOTSOL Morning mixing height (m) AMMXHT Afternoon mixing height (m) PMMXHT 850-mb temperature (1200 UTC) ( ° C) AM850T 850-mb temperature (0000 UTC) ( ° C) PM850T 850-mb dewpoint depression (1200 UTC) ( ° C) AM85DD 850-mb dewpoint depression (0000 UTC) ( ° C) PM85DD 850-mb wind speed (1200 UTC) (m 

### s') AM85WS 850-mb wind speed (0000 UTC) (m 

### s') PM85 WS 850-mb u wind component (1200 UTC) (m 

### s') AM85UC 850-mb v wind component (1200 UTC) (m 

### s') AM85VC 850-mb u wind component (0000 UTC) (m 

### s') PM85UC 850-mb v wind component (0000 UTC) (m 

### s') PM85VC



### ring on 346 or 22.6% of the study period days. Anexample of the large-scale synoptic conditions associated with this cluster, which occurred most frequently during July and August ( see Fig. 9), is depicted for 5 August 1983 (Fig. 2b). The annual frequency (during May through September) of this cluster was highly variable over the 10-yr period, ranging from only 25 days (1985 ) to 46 days (1986 and 1987 )( see Fig. 10). 

### Cluster two (C2) occurred when the Bermuda high was more riormally positioned—over the island of Bermuda ( Fig. 3). This synoptic pattern resulted in a strong 

### southwesterly flow off the Gulf of Mexico, advecting low-level moisture ( surface dewpoints are highest for this cluster), which resulted in extensive cloud cover, low solar insolation, and small diurnal variations in temperature and mixing heights. Cluster2 is one of only two clusters, the other being C6, associated with maritime tropical air masses. Cluster 2 occurred on 173 (11.3%) of the study period days and was most prevalent during the months of May, June, and July. Annually, the frequency of this cluster ranged from 11 days (1983) to 21 days (1986). 

### Cluster three (C3) occurred when 

### migratory anticyclones moved southeastward out of Canada (Fig. 4). This cluster, which occurred on 180 (11.8% ) of the total days, was limited almost exclusively to the months of May and September. Cluster 3 is characterized by northerly winds (surface and at 850 mb), resulting incool temperatures ( coolest of all clusters ), low dewpoint ( lowest ) and cloud cover ( lowest ), and the highest solar insolation and pressure. Diurnal temperature variations and dewpoint depressions at 850 mb are by far the largest of all clusters, and the morning mixing height is the lowest. Annually, the frequency of this cluster ranged from 7 (1986 ) to 30 (1984).1188 JOURNAL OF APPLIED METEOROLOGY VotuME33

(a) Cluster 1 - Bermuda High (22.6%)

0 1025 E Mix6ng Hgt: 439 m 2127 m 1025 

## m 1020 - '

_

~ '— ---'--------- 1020

0 1015 1015

n` 0 . 1010 1010

Solai r: 327 Wm -Z

v 30 30

m 2b 26



## ~ 20 —

_ _ - — 20 m
E 15 16

I! 10 10

01 04 07 10 13 16 19 22

Hour (LST) 

### o- o- (D /

m 11e

17 ~ 6 

### ~ J 18 n 5/ )„J

(b) 1020 1024

1024

lozo
August 5, 1983

~

FIG. 2. (a) Mean 3-h meteorological conditions associated withC1—Bermuda high, including temperature (solid), dewpoint temperature (long dash), and barometric pressure (short dash); cloud cover, wind speeci and direction (surface and 850 mb); and 850-mb temperature and dewpoint depression (as represented by standard station symbols). (b) Daily surface map for 1200 UTC 5 August 1983.



## Cluster four (C4) clearly identifies 

## cold frontal passages ( Fig. 5) . It occurred on 151 ( 9.8% ) of the study period days, rnost often in May, June, and September. This cluster, which occurred most frequently in 1989(21 days) an(i least often in 1987 (7 days), is characterized by a well-defined wind shift, decreasing temperatures (including 850 mb) and dewpoint, and the lowest (though increasing) pressure. Cloud cover, while extensive earl.y, decreases throughout the day. 

## Cluster five (C5), which occurred on 319 (20.8%)of the study period days, exhibits the warmest temperatures (surface and 850 mb), the highest aftemoon mixing height, light northerly winds, clear skies (second clearest), and high solar insolation (Fig. 6). It is most prevalent during the months of June, July, and August and is associated with an anticyclone positioned to the north-northeast ofthe study area. The 2 ° C increase in 850-mb temperature and the decrease in afternoon dewpoint temperatures are indicative of subsidence and 

### a transitional anticyclone ( from cold core to warm core ) . 

### Cluster six (C6), which occurred on 220 days (14.4°/0 ), is associated with a strong anticyclone off the northeast coast that results in a strong, moist, 

### easterly flow off the Atlantic Ocean ( Fig. 7). Dewpoints are increasing, cloud cover is highest, and the 850-mb dewpoint depressions and solar insolation are lowest of all clusters. Temperatures are mild and exhibit littlediurnal variation. The frequency of this cluster increases each month, reaching a maximum in September, and it is highly variable from year-to-year. Cluster 6 occurred most often in 1989 (37 days) and least often in 1984 (9 days).

(a) Cluster 2- Southwesterly flow 111.3%)

a 1025 Mixing Hgt: 943 m 1650 m 1025 E 1020 m 1020

- - -- 1015 ~ 1015 

### m a` 1010 1010

30 Solar: 233 Wm 2 30 

### U

m 26 25



## ~ 20 -------- 20

15 E 16

1! 10 10

01 04 07 10 13

Hour (LSn 16 19 22 1eo

Y, y o .,a 

## ~ a

1 %1;0 1

6 5

(ro) 1024

H 1024 1020 1016 1012 1008 ,004 

### ,008

1020 1012

1016 1016" 1020

1012

L 1008 1024

H


# ~ 1024

1020

1012 MAY 20, 1982
~ 1016

FiG. 3. Same as Fig. 2 except (a) C2—southwesterly flow

and (b) 20 May 1982.OcroBER 1994 E D E R E T A L. 1 189

(a) Cluster 3 - Migratory anticyclona (11.8%)



### ~ 1026 Mixing Hgt: 271 m 1917 m 1025

m 

### lozo 1020 ----- ----- 

### -- ---------



## ~ 1015 1015
aaS 1010 1010

Solar: 363.4 Wm-2 30 30



### v 26 25



## ~ 20 20



### m 16 15

E

f 5 10 10

5 01 04 07 10 13 16 19 22

Hour (LS7)


# a~ ~ 

# dC( d

12~

12 138 9

(b) 1020 1024 1

~ 4 10zo 1016
1028

016

i

1016 SEPTEMBER 5, 1984 1016

F7c. 4. Same as Fig. 2 except (a) 0—migratory anticyclone

and (b) 5 September 1984.



## Cluster seven (C7), which occurred on 141 (9.2%) of the days, is indicative of a 

## warm frontal passage ( Fig. 8). This cluster is characterized by a strong southerly flow off the Gulf, resulting in increasing dewpoints and temperatures. Pressure is relatively low and decreasesin advance of the approaching cold front. The frequency of C7 mirrors that of C4 ( cold front ), as it is highest in May, and then decreases each month until September. The annual frequency varied from a high of 22 days in 1983 to a low of 8 days in 1982.

2) CLUSTER DAILY 1-h MAXIMUM OZONE
CONCENTRATIONS

### Because of the critical impact meteorological conditions have on the formation, transport, and deposition of 03, the seven homogeneous meteorologicalclusters should exhibit significantly different concentration characteristics. Verification of this hypothesis was achieved first qualitatively, through the examination of summary statistics (Figs. 11 and 12, Table5) associated with the 03 data as stratified by meteorological cluster. Marked differences are noted in the03 concentrations associated with each cluster. Quantification of these differences was achieved through the utilization of a nonparametric, two-sided Kolmogorov—Smimov test ( Gibbons 1976), which tests the differences between the cumulative distribution functions (cdf) of the mean concentrations associated with each cluster 

### [F,(x) . . . F

7 (x)]. The Kolmogorov—Smirnovtest was utilized because the assumption of equal variances required by other conventional tests (ANOVA, Vdaller—Duncan K-ratio tests, etc.) is violated. The null hypothesis: 

### H

o : F,(x) = F2(x) for all 

### x, was tested against the alternative hypothesis: 

### H, : F, (x) =A F2(x) for some x. Results from the test indicate that at a 5°l0significance level, 19 of the 21 possible cluster combinations exhibit statistically different 03 distributions.

(a) Cluster 4- Cold frontal passage (9.8%)

E 1025 Mixfing Hgt: 797 m 1337 m 1025

® 1020 1020



### ~ 1015

- -----__

---- - 1015 ® d 1o10 1010

Soler: 226 Wm"a 30 30 

### U



### m 25 25

m 20 20 

# a --------------- 16 E 15

~ 10 10

01 04 07 10 13 16 19 22

Hour (LST)



# ~

1 6 

# V 1 6 ~

` b) 1016 1012 1008 1008 1012

1020 1



# L

024

1 a

10zo r , ,s> 

# ~

1016

SEPTEMBER 8, 1981

.

FiG. 5. Same as Fig. 2 except (a) C4—cold-frontal passage

and (b) 8 September 1981.1190 JOURNAL OF APPLIED METEOROLOGY VoLUME33

(a) Clusteir 5 - Transitional anticyclone (20.8%)

a 1026 Mixir ig Hgt: 38 5 m 2282 m 1025 

### E

m 1020 1020

1016 ---- --'' ___- m 1016

--

~ 1o10 1010

Solar: 385 Wm " z v 30 30

m 26 25



## ~ 20

- ~ _---_-- - - - 20

E 15 15

1! 10 10

01 04 07 10 13 16 19 22 

# d d o rILS

1 

# 6b 1 6 d

ro ,O,z 

## ) ,o,s L

,0,8 

### ,0zo



## H

,0,6

L1 p

,012 (\



# 1012 SEPTEMBER 17.1982 101

FtG. 6. Same as Fig. 2 except (a) CS—transitional anticyclone

and (b) 17 September 1982.



### Only the cumulative distributions associated with the C1, C3 and C6, C7 combinations are not significantlydifferent. The number decreases to 15 for a= 1% significance level. The characterization of the meteorological clusters and subsequent analysis of 0 3 concentration observed within each cluster revealed many intriguing features. Further examination of these features can be facilitated through an inspection of Fig. 12, which plots cluster frequency ( oirdinate ) versus cluster mean 0 3 concentration (abscissa) and allows identification of the meteorological clusters contributing the most to the 0 3 climatology of the area. From this figure one can see that the three clusters associated with anticyclones ( C 1, C3, and C5 ) exhibit the highest ozone concentrations. This supports earlier findings ( King and Vukovich 1982; Vukovich and Fishman 1986), in which it has been reportecl that because of requisite meteorological conditions associated with anticyclones, 0 3 concentrations were highly correlated with their path and frequency. In terms of overall contribution [ defined as the normalized product of the cluster frequency and mean concentration ( Table 6)], however, only C 1 and C5 stand out from the rest of the clusters. Cluster 3's limited impact on the 0 3 climatology of the area is attributable to its relative infrequency ( n= 180, 11.8°Io ) when compared to C 1 

## ( n= 346, 22.6°Io ) and C5 

## ( n = 319, 20.8%). Contributions from clusters C2, C4,C6, and C7 are limited with respect to both their frequencies and concentrations. The magnitude of the contribution of the Bermuda high ( C 1) ( 25.56% ) supports earlier findings ( Eder et al. 1993 ) in which it was hypothesized that because ofits high frequency of occurrence and requisite meteorology (i.e., clear skies, warm temperatures, and light winds resulting in poor lateral and vertical dispersion), the 0 3 climatology of the region was strongly influenced ( especially in July and August ) by the westward ex-

(a) Cluster 6 - Easterly flow (14.4%)

B 1026 Mixing Hgt: 784 m 1465 m 1025 

### E m 1020 1020 `

------ --- - --
~ 1015 1015 

## m a 1010 1010

Solar: 199 Wm 2 

## v 30 30

m 25 25

~ 20 ---

~ — — _ 20

E 15 15

m

~ 10 10

01 04 07 10 13 16 19 22

~ C Hour (LST)

1 

## 3 1 3 ~ ~

,020 102a



# t

2.,19816 H 1 020 

### ro) ,o,s 20

Z4

za



### oz0

101z1

1012 

# SEPTEMBER 6

F7G. 7. Same as Fig. 2 except (a) C6—easterly flow

and (b) 2 September 1986.125

100



## ~
V 75 

# z

~

~ 50

25

50 

### tension of the Bermuda high. The contribution of this cluster to the number of days exceeding 120 ppb ( 4 40 days or 1.2% of all C 1 days ) is, however, unexpectedly

~ 

### low. This tendency, which will be discussed below, is >' 30 reflected in the relatively small skewness (0.40) of the z 

### 0 3concentrations associated with this cluster. The equally large contribution (24.78%) attributable 0 

### 20 to C5—the transitional anticyclone—is intriguing and requires closer examination. In a study of anticyclo- 10 genesis, Zishka and Smith (1980 ) found that North American anticyclones generally form in western Can- 0 , i ;:' ~ ..................;.....

..• ~

.. ; : ~ ~ ;

.

.. :

..,.., ,y ~ ............ .:,.,....
~ ...,. !'.....e.... ~ ...... :,

........................

-..., ,

. '.. : •: ~ • ~ - '. i .

~ , : •:-• ••.,

. ~ 

### , . .`• ,+• •.• i ~ `

..:'al

~ •. i.,

~ i



### . . »......, ~ .:.......

............ ..

. ..... ..,. ~ : t -.~ .,......

. - ~ •'

, ~ `f .

~ >.° i

~ F•.. \

, ..

~ •'• •..

• ' .

. • .:: i.

~ : EDER ET AL. OCTOBER 1994

(a) Cluster 7- Warm frontal passage (9.2%)

Mixing Hgt: 847 m 1731 m a 1025 E 1025

1020 2 1020

'"------"

_ 

## ~ 1015

------------ 1015

a`. 1010 1010

Solar: 237 Wm '2 

# v 30 30

® 26



### ~ 20 25

20

E 15 --- ----------- 15

m +- 10 10

01 04 07 10 13 16 19 22

Hour (LST) 

# '\ I I I T I ~ 

# -\

14

7 16

~ V~~ _) 4

`—) 1012 1016 1020 1020


### H

100

1604

~ ~ 1020

---

,~ ~ 1020

looa 1016

MAY 25, 1990 1012

FtG. 8. Same as Fig. 2 except (a) C7—warm-frontal passage

and (b) 25 May 1990.



### ada. Once formed, these anticyclones typically traverse the northern sections of the United States in response to their proximity to the summer jet stream. During the months of June, July, and August, however, these anticyclones often dissociate with the jet stream, stall,and become vertically coupled with an upper-level anticyclone. Once this coupling occurs, a rapid transition from a cold-core to a warm-core anticyclone begins. .. f . .:

...... ........................ ;

~ ~ ~ 

### _._._._._._. ~ 

### •:%

~ ~

, •. •
~.~ •

. : : • -'
~ • 

### . •. . :....

. ~

.............. .............. ~.~ ................................... •„ • ~.~ ........

~~ ------- ~'~ • . ~ 

### 1191

125

100

75

50

25

0 T -I . ", i 11 * ................. . --T--L 0 MAY JUNE JULY AUG SEPT
(Cl) Bermuda High •-••-••-•• (CS) Transitional Anticyclone •--•°• (C2) SouthwesterlyFlow •-•-•-• (C6) EasterlyFlow ••.••.••••••• (0) Migratory Anticyclone (C7) Wann Frontal Passage - - - - (C4) Cold Frontal Passage

F1G. 9. Monthly cluster frequencies (#) over the 10-yr period.



### Temperatures ( both surface and aloft ) associated with this transitional anticyclone can easily increase by 2°- 3°C per day in response to surface heat and moisture fluxes and continued, strong subsidence aloft (I{ing and Vukovich 1982; Chu and Doll 1991). In additionto providing ideal meteorological conditions, the typical positioning of these transitional anticyclones ( northand east of the study region), unlike that of the Bermuda high (typically overhead), allows nearly continuous transport of 0 3 and its precursors from the numerous industrial complexes and population centers located to the north (Clark 1980). Support of this supposition is provided by Chu and Cox (1992), who in a study of the Gulf Coast states found that the highest ozone episodes often occur onthe front side of anticyclones, where injection of pre50

40

30

20

10

0 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

YEAR (Cl) BermudaHigh •-••-•-•• (CS) TransitionalAnticyclone '-•---- (C2) Southwesterly Flow •—•—•—• (C6) Easterly Flow •••••••••••• (0) Migratory Anticyclone (C7) Warm Frontal Passage - — — — (C4) Cold Frontal Passage

F[G. 10. Annual (May-September) cluster frequencies (#)

over the 10-yr study period.140

120

100

80

60

40

20 

### 25

20

~ 

### u



## ~ 15



## a



# ~ 10 

### 25



### 20

15

10

40 45 50 55 60 65 70 75 80 JOURNAL OF APPLIED METEOROLOGY VOLUME 33 

## 1192

140

120

100

:c
a 80 

# O 60 N 

## O

40

20



### r c , r c

, 2 ~ 

### rc,

~ J 

### r c

, J ~ rc,sr

rc,6~ 

### rc,' ~

+ r ~~ ery

~ O +~ W3 4

, FIG. 11. Box plots of the daily 1-h maximum 0 3 concentrations 

### associated with the seven meteorological clusters. Statistics include lst and 99th percentiles (0), lOth (1) and 90th percentiles (T), 25th ( LJ ) and 75th ( fl ) percentiles, the median (-), and the mean (0).



### cursor emission, when combined with upper-level subsidence and increased temperature, produced the highest concentrations. This additional contribution, attributable to transport, may be responsible for thetendency of C5 to experience exceedingly high concentrations [ the skewness (0.65) is greater than that found in the C 1(0.40)]. Fully one-half of the total observations (14) exceeding 120 ppb occurred in C5 as compared to only 4 in C 1. The contribution of this cluster reach es a peak in June and again in August, after a slight decrease in July (which is dominated byCl).During May and September, the anticyclones mentioned above! in the work of Zishka and Smith (1980 ) migrate rapi.dly across the northern portion of the United States. These migratory anticyclones (12.88%) are well represented in this study by C3. Their influence on the study area decreases rapidly during the summer months, however, as the jet stream retreats farther north into Canada: As a result, virtually no occurrences OZONE (ppb)

1~YG. 12. Mean daily 1-h maximum 0 3 concentrations (with 95% confidence limits) and relative frequencies of the seven meteorologcal clusters.



### were noted during the 10-yr period during the monthsof June, July, or August. Although the limited frequency of C3 prevents it from dominating the 0 3 climatology of the southem United States, its surprisingly high ozone concentrations warrant further comment. Although most characteristics of C3 are conducive to the formation of 03, (i.e., clear skies, high solar insolation), because of its timing (occurring almost exclusively in May and September), the temperatures experienced within this cluster are by far the coolest ofall seven clusters; thus, one would expect low concentrations. It is hypothesized that the higher than expected concentrations, as well as the relatively large number of days exceeding 120 ppb ( 3 days or 1.7°I° of all C3 days; note skewness is 0.79), are attributable to the positioning of the migratory anticyclone and the northerly flow and subsequent advection of precursors from high emissions areas that results. Other potential contributing influences (siich as the intrusion of stratospheric 0 3 , or the increased emission of natural volatile organic compounds associated with bud break) were dismissed because both would contribute almost exclusively during spring, a characteristic not supportedin the data, which exhibit nearly identical concentrations during May and September.

TABLE 5. Summary statistics of the daily 1-h maximum 0 3 (ppb) concentrations associated with each cluster and the overall dataset.

Cluster n Mean s Z Skewness Number (%) > 80 N umber (%) > 1 00 Number (%) > 12 0

1 346 71.32 347.35 0.40 104 (30.0) 24(6.9) 4(1.2) 2 173 46.85 189.37 0.48 4(2.3) 0(0.0) 0(0.0) 3 180 69.11 342.23 0.79 46 (25.6) 11(6.1) 3(1.7) 4 151 50.78 173.11 0.42 4(2.6) 0(0.0) 0(0.0) 5 319 75.01 328.65 0.65 106 (33.2) 35 (11.0) 7(2.2) 6 220 54.07 289.79 0.22 15 (6.8) 2(0.9) 0(0.0) 7 141 55.64 266.54 0.18 11(7.8) 1(0.7) 0(0.0) Overall 1530 63.11 402.00 0.46 290 (18.9) 73(4.8) 14(0.9)70

60

50

40

30

20

10 70

60

50 A 

# a 40


### 0 30
N Q 20

10 TABLE 6. Normalized contribution of the seven clusters to the

ozone concentrations.

Cluster Normalized contribution

CI-Bermuda high 25.56 C2-Southwesterly flow 8.39 C3-Migratory anticyclone 12.88 C4-Cold-frontal passage 7.94 C5-Transitional anticyclone 24.78 C6-Easterly flow 12.32 C7-Warm-frontal passage 8.12 OCTOBER 1994 E D E R E T A L. 

### 1 193

10 13 16 19 22 Hour


### The small contributions attributable to the remaining four clusters are easily explained. Clusters C2 and C6, which are characterized by southwesterly flow(8.39%) and easterly flow (12.32%), advect moistureladen maritime air from the Gulf of Mexico and Atlantic Ocean, respectively. These meteorological regimes result in extensive cloud cover, low solar radiation, and mild temperatures, conditions that generally inhibit 0 3 formation. Transitional clusters C4 and C7 are the cold- and warm-frontal passages ( 7.94% and 8.12%, respectively) and are characterized by extensive cloud cover, low solar insolation, and the likelihoodof precipitation. None of these four clusters have resulted in 0 3 concentrations exceeding 120 ppb and on only 3 days (out of a possible 685 days) have they produced concentrations exceeding 100 ppb. This aversion toward high concentrations is reflected in the low skewness values associated with these four clusters (ranging from 0.18 (0) to 0.48 (C2)].

3) CLUSTER HOURLY OZONE CONCENTRATIONS


### Further insight into the 0 3 characteristics exhibitedby each of the clusters can be gained through an examination of their diurnal patterns, the shape of whichcan provide useful information concerning the formation, scavenging, and transport of ozone within an area. In particular, diurnal patterns help ascertain if alocation is being exposed more to local, photochemically generated 03 

### or to 0 3 transported from long distances-an important distinction for regulatory considerations ( Kelly et al. 1984; Meagher et al. 1987). These patterns can also be used to quantify the rangeof concentrations to which humans, plants, and animals are exposed (Bohm et al. 1991; Wolff et al. 1987). The mean hourly 0 3 concentrations ( Fig. 13 ) experienced under each of the seven meteorological clusters are quite revealing. Consistent with earlier results examining the daily 1-h maximum concentrations, clusters C1, C3, and C5 experience, by far, the highest afternoon concentrations (15-30 ppb greater than theother clusters ). This pattern is reversed, however, during the nighttime hours. After approximately 2000 and prior to 0700 LST, the 0 3 concentrations associated with these three clusters are considerably lower (by 5- (Cl) Bermuda High 

### .......... (CS) Transitional Anticyclone •------ (C2) Southwesterly Flow •-•-•-• (C6) Easterly Flow °°°°°•° (C3) Migratory Anticyclone (C7) Warm Frontal Passage - - - (C4) Cold Frontal Passage
Flo. 13. Mean hourly 0 3 concentrations associated with the seven meteorological clusters.



### 10 ppb ). As a result, the amplitude of the diurnal curve ( diurnal range ) is much larger for clusters C 1, C3, and C5 (58.76-63.37 ppb) than it is for clusters C2, C4, C6, and C7 (28.86-35.89 ppb) (Table 7). The amplitudes of the diurnal curves of hourly 0 3concentrations can be directly attributed to meteorological conditions associated with the seven clusters. The anticyclonic conditions associated with C 1, C3, and C5 are characterized by generally clear and dry conditions allowing for maximum solar insolation and large diurnal ranges in both temperature and mixing heights. Under such conditions, a nocturnal inversionlayer forms in the lowest tens of ineters above the surface in response to radiational cooling. The strength of this nocturnal inversion, which acts to decouple the surface layer and greatly inhibit the vertical mixing of 0 3i is dependent upon a number of factors includingwind speed and cloud cover, which are typically favorable under anticyclonic conditions. Above , thisnocturnal inversion, in the residual layer, concentrations remain similar to those attained during the previous afternoon. Below this inversion, however, concentrations decrease markedly in response to dry deposition and chemical scavenging. By dawn, the stable

TABLE 7. Diurnal 0 3 (ppb) attributes of the seven clusters.

Cluster 0 3

Minimum (hour LST) 0 3

Maximum (hour L ST) 0 3 Diurnal ra nge

C 1 4.96 (0600) 63.71 (1300) 58.76 C2 11.56 (0600) 40.42 (1400) 28.86 C3 5.69 (0600) 65.00 (1500) 59.31 C4 9.53 (0600) 45.42 (1500) 35.89 C5 4.50 (0600) 67.87 (1300) 63.37 C6 14.02 (0600) 47.38 (1400) 33.36 C7 15.61 (0600) 50.17 (1300) 34.56

### 1194 JOURNAL OF APPLIED METEOROLOGY VOLUME 33



### layer may have a depth up to 400 m and concentrations reach a miniimum. After sunrise, and in response tosolar heating, convection progressively mixes this depleted layer with the air above the inversion, so that 0 3 -rich air is entrained into the deepening mixed layer. These conditions all favor the large diurnal amplitudes ( Fig. 13). Under the nonanticyclonic conditions associated with C2, C4, C6, and C7, dewpoints are higher, skies are considera.bly more cloudy, and winds are generallystronger throughout the day and night; therefore, development of nocturnal boundary layers is greatly inhibited. As ai result, nocturnal depletion attributable to dry deposition and chemical scavenging is partially compensated for by t.he entrainment of 0 3 -rich air from aloft. Subsequently, nighttime 0 3 concentrations remain more similar to those found during the day, resulting 

# in corisiderably smaller amplitudes when compared to those associated with anticyclonic conditions. Given the differences between the amplitudes of the concentrations associated with the three anticyclonic and foui nonanticyclonic clusters, let us now examine the more subtle yet equally revealing differences in the timing or shapes of the diurnal patterns. In a studyexamining the factors that controlled the diurnal behavior of 0 3 in rural locations, Kelly et al. ( 1984 ) attributed the rapid increase often found between 0600 and 1000 LST to entrainment of 0 3from aloft and that any additional increase in concentrations after thistime are likely attributed to local photochemical reactions. With this in mind, the largest difference between C1 and C5 occurs during this early morningperiod between 0600 and 1000 LST, where the concentrations associated with C5 increase more rapidly than those of C 1. This difference, which is roughly 5 ppb, likely accounts for the difference in the daily 1-h maximum concentrations found between these two clusters. Although no attempt will be made in this study to distinguish between 0 3 aloft that is transported from anthropogenic sources and that from the stratosphere, it is hypothesized that under C5, a strong nocturnal inversion forms and northerly winds aloft (note 850- mb wind speed and direction ) allow formation of an "0 3 river" [ Wolff and Lioy ( 1980 )], which flows above this nocturnal boundary layer and is able to transport 0 3 great distances in substantial concentrations withoutextensive nocturnal consumption by NO or dry deposition. Under C 1, the Bermuda high, 850-mb winds are generally too light and from the south-southwest where emissions are much less; subsequently, long-range transport is riot likely as important under this cluster. Given this ex:planation, Why then is the diurnal curve of C3 not siinilar to that of C5, considering that the 850-mb winci flow is similar? Here it is thought that any early mcirning increase attributable to long-range transport is offset or diminished by the very cool morning temperatures exhibited by C3, which suppress the photochemical reactions that lead to 03 

### formation. Early morning temperatures average some 5 0 C cooler at 850 mb and roughly 10°C cooler at the surface for C3 than for C5. Another difference between these three diurnal curves is evident in the late afternoon, where unlike C 1 and C5, which start a rapid decrease from their 1300 LST maxima, the diurnal profile associated with C3 continues to increase, reaching a delayed maximum at 1500 LST. Kelly et al. (1984 ) attributed afternoon increases to local photochemical reactions, and it may be that this delay in the maximum concentration is related to the smaller cloud cover experienced by this cluster in the late afternoon, as compared to C 1 and C5. Even though the daily total solar insolation values are comparable (between 327 and 385 W m -Z ), skies tend to be some 20%-30% clearer in C3 than in either C1 or C5 for the period when the discrepancy occurs (1300-1600 LST ) . The relative shapes of the diurnal patterns associated with clusters C2, C4, C6, and C7 also reveal several subtle differences. Ozone concentrations in C4, thecold-frontal passage, increase in the early morning period more rapidly than the other three "flatter profile" clusters, even to the point of crossing the profile of C2. Similar to the differences found between C5 and the other high-amplitude clusters, it is again hypothesized that the additional increase is likely attributable to transport; because of these four clusters, only C4 has northerly winds aloft. Even though the strength of the nocturnal boundary layer is not as great with these four clusters, some separation likely occurs—hence the more rapid morning increase. Another difference can be found in the timing of the maximum concentrations, which is delayed in C4 until 1500 LST. Like C5 above, that delay found inC4 is thought to be attributable to available solar insolation. During the afternoon hours (1300-1900 LST ) cloud cover averages between 78% and 84% for C2,C6, and C7. In C4, however, postfrontal clearing reduces the sky coverage to 65%. The resulting late afternoon increase in available solar insolation may account for the delayed peak in 0 3 concentrations.



### b. Regression analysis

1) INDIVIDUAL CLUSTER REGRESSION MODELS 

### Having established that the differences between mean daily 1-h maximum 0 3 concentrations exhibitedby the seven meteorological clusters are statistically different, investigation into those differences can now befacilitated through a determination of which meteorological variables most strongly influence the variability of 0 3 within each cluster. Attributes of the stepwise regression models (which again seek out the optimum set of ineteorological parameters influencing the 0 3 concentrations ), developed for each of the seven clusters, as well as the overall dataset are presented inOcrosER 1994 E D E R E T A L. 

### 1195

Tables 8 and 9. The parameters ( defined in Table 4) are ranked in order of their contribution as determined by their coefficient of partial correlation r z (Table 9). Of particular note are the differences in both the number and order of independent meteorological variables that were found to significantly contribute ( a= 

### 0.10 ) to the variability of the 0 3concentrations exhibited within each meteorological cluster. Only four variables were significant in C6, while a total of nine were found to contribute in C 1. Also of interest is the variability of the individual models' coefficients of determination R 2 , which indicate the proportion of the total variance of 0 3explained by the models. These range from 0.30 for C2 to 0.58 for C6 and C7. The root-mean-square errors (rmse), which provide a measure of each model's accuracy, are also variable, ranging from 9.97 ( C4 ) to 15.26 ppb ( C 1) , as are the coefficients of variation (CV-defined here as rmse /mean 03), which range from 18.75% ( CS ) to 25.14% (C2). The three independent variables contributing the most across all clusters were maximum temperature (four firsts: C1, C3, C4, C6; two seconds: C5 and C6), mean daily wind speed ( no firsts; three seconds: C 1, C2, C3; one third: C5 ) and mean daily dewpoint (two firsts: C5 and C6; two seconds: C4, C6; three thirds: C1, C2, and C3). With only one exception (that being C1 and C3), the order of importance was different for each cluster, as was the level of contribution of the independent variables.'I'he coefficients associated with maximum temperature were all positive, indicating that the greater themaximum temperature, the higher the daily 1-h maximum 0 3 concentration. Their range was considerable, however, from 0.92 for C 1 to 4.14 for C6, as was their level of contribution. Surprisingly, while generally the most important variable, accounting from between 9% ( C 1) and 34% ( C3 ) of the variability, temperature did not contribute significantly to the variability of 0 3 inC2. It is interesting that the three clusters with the coolest maximum temperatures ( C3, C4, and C6 ) are the most dependent on this parameter ( r 2 = 0.34, 0.32,and 0.29, respectively), perhaps indicating that temperature is the limiting factor for 0 3under these meteorological regimes. Coeflicients associated with themean daily dewpoint, which was the only meteorological variable used in all seven cluster models, were consistently negative, ranging from between -1.01 ( C4 ) to -3.10 (C6), indicating that the greater the dewpoint temperature, the lower the daily 1-h maximum 0 3 concentration. Like temperature, the contribution of dewpoint also varied considerably between clusters, ranging from 3% for C2 to 34% for C7. The coelTicientsassociated with the mean daily wind speed, which contributed in four of the seven clusters, were also negative, ranging from between -2.36 ( C2 ) to -6.73 ( C 1) . In those models where it was significant, mean daily wind TASLE 8. Attributes of the seven cluster, the overall, and composite stepwise regression models.

Model N R 2 rmse (ppb) CV (%)

Cluster 1 346 0.35 15.26 21.39 Cluster 2 173 0.30 11.78 25.14 Cluster 3 180 0.49 13.41 19.41 Cluster 4 151 0.45 9.97 19.64 Cluster 5 319 0.41 14.07 18.75 Cluster 6 220 0.58 11.17 20.66 Cluster 7 141 0.58 10.82 19.44

Overall 1530 0.53 13.85 21.94 Composite 1530 0.59 12.80 20.29



### speed explained between 5% ( C3 ) and 10% ( C5 ) of the total 0 3

variance. The only other variables explaining more than 5%of the variance in any one cluster were afternoon mixing height in C2 ( r 2 = 0.12, ranked first ) and the morning 850-mb v component of the wind for C6 ( r z = 0.11, ranked third). Two variables available for usein the regression analysis, the 1200 UTC 850-mb temperature and the 0000 UTC 850-mb v component of the wind, did not significantly explain the variance of 0 3 in any cluster. Also worthy of note, but not understood at this time, is the change in sign (direction of contribution ) of the 1200 UTC 850-mb v component of the wind from negative ( C6 ) to positive (0), and the negative contribution associated with total daily solar insolation found in C4.

2) "OVERALL" VERSUS "COMPOSITE"
REGRESSION MODELS


### Results for the overall, nonsegregated model, which had an R 2 of 0.53 and rmse of 13.85 ( Table 8) shows that structure of the overall regression model is greatly different than those of the seven individual cluster models. Although a total of 12 independent variables were found to significantly contribute to the variability of 0 3 , only two variables, the afternoon and morning mixing heights ( 26% and 9%, respectively ), accounted for more than 5% of the variance. Neither maximum temperature ( 2% ), mean daily dewpoint ( 4% ), nor mean daily wind speed ( 5% ), which contributed so much in the individual clusters, contributed much to the overall model. The dominance of mixing heightsin the overall model may be attributable to these variables' ability to provide a better characterization of the general state of the atmosphere (i.e., cyclonic versus anticyclonic conditions ), when compared to any other single variable. Once the general state of the atmosphere has been characterized by the cluster analysis, however, their general contribution to the individual cluster models decreases ( Table 9). The scatterplot associated with the overall model ( Fig. 14 ) reveals that the majority of the data are

### 1196 JOURNAL OF APPLIED METEOROLOGY VOLUtvtE33



### contained wilthin 1:1.5 ratio lines. There is, however, considerable scatter as well as a tendency for the overall model to underestimate, starting around 70- 80 ppb, the llighest 0 3 concentrations. This underestimation is observed in most studies using simple linear regression and is attributable to the fact that 0 3 's depend.ence on meteorology is nonlinear (Robeson and Steyn 1990). The errors associated with using a linear regression approach to model this nonlinear reLationship are increased when the entire range Of 0 3 concentrations is considered at once. The two-stage clustering of the meteorological variables has provided homogeneous, "reduced variance" meteorological datasets. It was hypothesized and later shown that the range of 0 3 concentrations within these clusters was also reduced, as compared to the overall dataset. By performing the stepwise regression on the reduced datasets, the unique variance Of 0 3 exhibited within each of the seven clusters was bettermodeled. Also, utilization of this piecewise or segmented regression approach should help minimize the errors associated with using linear regression to model a nonlinear relationship. Therefore, results obtained from the amalgamation of these seven cluster-specific regression models into a"cluster composite" should, when compared to the overall model, exhibit marked improvement. Exa

~ 

### minationof this composite scatterplot ( Fig. 15 ) reveals a considerable reduction of this nonlinearity as well as a marked tightening of data points about the 1:1 ratio line. The underprediction characteristics so evidentin the overall model ( Fig. 14), while not totally alleviated, have been reduced. When compared to the overall model, which again had an R Z of 0.53 and an

TABLE 9. Meteorological variables significantly (a = 0.10) contributing to the 1-h maximum 0 3 concentration for each cluster and the overall model. Number in parentheses is variable rank, followed by the coefficient of partial correlation r 2 , and variable coefficient.

Cluster

V ariab le One Two T h r ee Four Fiv e S ix Seven Overall

m ode l

MXTEMP (1) 0.09 (1) 0.34 (1) 0.32 (2) 0.10 (1) 0.29 (2) 0.17 (6) 0.02 0.92 2.98 2.51 3.50 4.14 2.42 2.85 MNWDSP (2) 0.07 (2) 0.06 (2) 0.05 (3) 0.10 (3) 0.05

-6.73 -2.36 -4.61 -5.23 -4.16 -4.16 

### MNWDUC (7) 0.01 (7) 0.02 (4) 0.02 (7) 0.01

-2.52 -2.20 -1.88 -1.33 MNWDVC (6) 0.01 (12) 0.01 2.06 0.51 MNPRES (6) 0.01 (4) 0.02 (9) 0.01

-1.65 -1.15 -0.53 MNCCOV (7) 0.01 0.10 MNDEWP (3) 0.03 (3) 0.03 (3) 0.05 (2) 0.06 (1) 0.14 (2) 0.18 (1) 0.34 (4) 0.04

-1.47 -1.20 -1.39 -1.01 -2.81 -3.10 -1.93

_ , -1.83 TOTSOL (8) 0.01 (5) 0.01 0.03 -0.02 AMMXHT (5) 0.01 (2) 0.09 -0.01 -0.004 

### PMMXHT (1) 0.12 (6) 0:01 (3) 0.03 (1) 0.26 0.01 0.01 0.01 0.003 AM850T

PM850T (4) 0.02 -2.19
AM85DD (5) 0.02 (5) 0.01 (6) 0.01 (4) 0.02 (5) 0.03 0.47 0.40 0.31 0.73 0.30 PM85DD (9) 0.01

-0.92
AM85WS (4) 0.02 (5) 0.01 (3) 0.04 (8) 0.01

-1.18 -1.05 -0.67 -0.80
PM85WS (6) 0.02 (10) 0.01 -0.74 -0.35 AM85UC (4) 0.01 0.42 AM85VC (4) 0.03 (3) 0.11 0.91 -1.38 PM85UC (5) 0.02 (8) 0.01

-0.92 -0.58 PM85VC Intercept 1699.04 1238.78 7.95 -2.36 26.91 1.63 63.92 565.84OCTOBER 1994 E D E R E T A L. 1 197



### rmse of 13.85, the composite model does indeed have a higher R z (0.59) and a lower rmse (12.80 )( Table 8). To determine if this improvement was statistically significant, the sum of the residual sum of squares ( RSS ) for the seven clusters was compared to that of the overall model using an F test, where

7 

### [ RSS ( overall ) - 2: RSS ( clusters ) ] /

C=1 7 

### [ df ( overall ) - I df ( clusters ) ]

C=1

7 7 

### 2: RSS (clusters)/ 2: df (clusters)

C=1 C=1

F = 6.10 > Fo.01(39,1478) = 1.60 

### The computed F( 6.10 ) was highly significant for v 1 = (1517 - 1478 ) = 39 and v Z = (1530 - 52 ) = 1478 degrees of freedom. This analysis has shown that 0 3 's dependence on meteorology is unique within each of the meteorological clusters. When this unique structure is taken into consideration through development and subsequent amalgamation of individual regressionmodels, a better model specification is achieved, resulting in a reduction of unexplained variance.

S. Summary
The purpose of this paper was to utilize a two-stageclustering approach as part of an automated meteorological classification scheme designed to better elucidate the dependence of 0 3 on meteorology. When applied to 10 years (1981-90) of ineteorological data for Birmingham, Alabama, the classification schemeidentified seven statistically distinct meteorological regimes. Because of the critical impact meteorologicalconditions have on the formation, transport, and deposition of 03, it was hypothesized and later substantiated through the use of a nonparametric, two-sidedKolmogorov-Smimov test that most of the seven homogeneous meteorological clusters exhibited significantly different daily 1-h maximum concentration distributions.Of the seven clusters, the three associated with anticyclones—the transitional anticyclone: C5 ( mean of 75.01 ppb ); the Bermuda high: C 1( 71.32 ); and the migratory anticyclone: C3 (69.11)—exhibited the highest daily 1-h maximum concentrations and thelargest diurnal ranges (63.37, 58.76, and 59.31, respectively). These characteristics were attributed to the generally favorable meteorological conditions ( i.e.,clear skies, large solar insolation, large diumal temperature ranges, and with the exception of C3, warm temperatures ) associated with these clusters. The skewness of the distributions of 0 3observed in C3 (0.79) and C5 (0.65) was larger than that found in C 1 (0.40), indicating a propensity toward exceedingly high concentrations in C3 and C5, which was attributed to + +*',μ ~~$~ +. ¢+ ♦

~ IYR + ~~~S + N +

+ ~~ i j4 :

.., ~

+ ,,,»++ ~ t

~ t ♦

♦ + ~~~~, •+ +

~

. + 2:+ +kCe+ R Z = 0.53

+ RMSE = 73.85

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 MODELED OZONE ()pb)
FtG. 14. Scatterplot of the observed versus modeled daily maximum 1-h 0 3 concentrations associated with overall dataset.



### the typical positioning of these two anticyclones. Unlike C1, which typically positions itself directly over the study region (resulting in a weak, variable wind flow), the typical positions of C3 and C5 are to the north of the study region. The resulting northerly winds ( surface and aloft) allow for a nearly continuous flow of 0 3 andits precursors from the numerous industrial and population centers located to the north. This transport is likely responsible for the higher than expected mean concentrations found in C3, which despite being the coolest (by far) of all seven clusters exhibited the thirdhighest mean concentrations. Of the 14 ( 73 ) days during the study period that observed concentrations exceeded 120 (100 ) ppb, 7( 35 ) occurred in C5, 3(11) occurred in C3, and 4( 24 ) occurred in C I. The mean daily 1-h concentrations of 0 3 exhibited by the four remaining clusters were considerably less as were the amplitudes of their diurnal patterns. Two of these clusters—the southwesterly flow: C2 ( mean of 46.85, diurnal range of 28.86) and the easterly flow:

+ - C, + ,.~ 

### o ' a Q -C2 '. ,0 0 - p + ' °

, 0 _ Cy ,~o+wa+. ~* ~ eo , ~ ° ~ 1 o-CB 9 Y~-C7 pO > O

e R2 = 0.59 0 o RMSE = 12.80 0

0 10 20 30 40 50 80 70 80 9D 100 110 120 130 140
MODflED oZONE (pO) F1G. 15. Scatterplot of the observed versus modeled daily maximum 1-h 0 3 concentrations associated with composite dataset. 

# F= ,40 ,ao 

### ,zo

„o


## ~ ,00

~ go

€3 so o I

OD

so

o 40 30

m
,0

0

,3

, 20

1



### ~ 1 00

&

0

~ 0 4

3

20

t 

### 70

~

~

### 1198 JOURNAL OF APPLIED METEOROLOGY VoLUME 33



### C6 (54.07, 33.36)—advect moisture-laden maritime air from the Gulf of Mexico and the Atlantic ocean, respectively. 'The other two clusters—the cold-frontalpassage: C4 ( 50.78, 35.89) and the warm-frontal passage: C7 ( 55.64, 34.56 )—are transitional in nature. Each of these four meteorological regimes results inextensive clolud cover, low solar radiation, mild temperatures, srnall diurnal ranges of temperatures, and an increased likelihood of precipitation—all conditions that inhibit the formation of 0 3 and reduce its diurnalrange. Contrary to the results associated with the anticyclonic clusters, none of these four clusters experienced concer.itrations exceeding 120 ppb, and in fact on only 3 days ( out of a possible 685 days ) did these clusters record concentrations greater than 100 ppb. In terms oi - their overall contribution to the 0 3 climatology of the area (defined as the normalized product of the cluster frequency and mean concentration ), C 1( 25.56% ) and C5 ( 24.78% ) stand out from the rest of the clusters. The limited impact of C3 (12:88%) is attributable to its relative infrequency 

## ( n= 180 ) when compared to C 1 ( 

## n= 346 ) and C5 

## ( n= 319). Contributions from C2, C4, C6, and C7 are limited withrespect to both their concentrations and their frequencies 

## ( n= 173, 151, 220, and 141, respectively ). Results from this two-stage clustering approach, which reduced .meteorological variance through the identification and characterization of key atmospheric regimes, were then used to develop seven "refined"stepwise regnession models. These models were designed so as l:o 1) identify the optimum set of independent meteorological parameters influencing the 0 3 concentrations within each meteorological cluster and 2) to weigh each independent parameter according toits unique iniluence within that cluster. Large differences were noted in the number, order, and selection of independent variables found to be significant ( a 

### = 0.10 ) in explaining the variability of 0 3concentrations exhibited within each meteorological cluster.When this unique dependence was taken into consideration through the development and subsequentamalgamation of the seven individual regression models into a cluster composite, a better parameterization of 0 3 's dependence on meteorology resulted. This "composite" model exhibited a significantly larger R Z (0.59) and a smaller rmse (12.80 ppb) when compared to results achieved from an "overall" model (R 2 = 0.53, rmse = 13.85) without clustering. 

## Acknowledqments. The authors would like to acknowledge Bi.11 Cox of OAQPS, U.S. EPA, and Phil Gibb, current:ly with Statistical Analysis Systems, fortheir assistance in obtaining and preparing the meteorological dat.asets used in this research. This paper has been reviewed in accordance with the U.S. Enviironmental Protection Agency's policies and approved for publication. Mention of trade namesor commercial products does not constitute endorsement or recoinmendation for use. REFERENCES

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