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 an 

automated 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 03 . 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 ( NOZ ). The rate of these 

photochemical reactions, as well as the subsequent 

transport and scavenging of 03, depends greatly on 

rneteorological 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 3concentra- 
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 03) by airmass types for a remote area in South 

Dakota; Muller and Jackson (1985), who developed 

an 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 which 

airmass types are defined. Accordingly, a more objective approach such as that recommended by Crutcher 

et al. ( 1986 ) was preferred, in which the meteorological 

data 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 (Kalkstein 

and Corrigan 1986; Kalkstein et al. 1987). More recently, a two-stage clustering approach that utilizes average linkage and convergent k-means techniques has 

been 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-stage 

clustering approach as part of an automated meteorological classification scheme designed to better elucidate the dependence of 0 3on 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 several 

reasons. In addition to having the requisite meteorological and 03data, 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 the 

isolation 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 03concentrations 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 multiple 

regression 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 the 

homogeneous 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 period 

1981-90, 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 magnitudes 

should 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 of 

the air mass ( Barry and Perry 1973). Dewpoint temperature was selected over other moisture indicators 

because 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 3 

monitors and the surface ( Birmingham Municipal Airport) and upper-air data (Centreville) meteorological stations. 

03 , 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 due 

to 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 mixing 

heights ( 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 by 

the 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 03data 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 maximum 

concentrations 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 data 

validation based upon frequent zero, span, and precision checks as well as a rigorous quality assurance program. 

To provide a continuous, regionally representative 

03database, 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 3concentrations 

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 

03concentrations 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 3that 

was 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 pooled 

mean ( 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 99.15 
OCTOSER 1994 E D E R E T A L. 1 185 

all subsequent references to 0 3concentrations 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 matrix 

of the raw meteorological data to develop daily principal component scores. These are then clustered into 

homogeneous meteorological regimes using a two-stage 

approach. Finally, a stepwise regression analysis is applied to each meteorological regime, with the daily 

1-h maximum 03as the dependent variable and a suite 

of 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 order 

to 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 also 

reduces 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 a 

square, 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 the 

units 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, 59 

eigenvector—eigenvalue pairs were derived. The eigenvectors represent the mutually orthogonal linear combinations, while their respective eigenvalues represent 

the 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 the 

Scree 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 and 

the meteorological parameter. While physical interpretation of the principal components is not vital to 

this procedure, it is worth noting that the larger the 

component loading, the more important the meteorological parameter is in interpretation of that component. Principal component 1 loads highly with both 

surface and upper-air temperature and dewpoint temperature, indicating the importance of thermal and 

moisture 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 fourth 

component 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 67.68 
1186 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, each 

day ( 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 with 

the smallest within-cluster variance and the large between-cluster separation. This characteristic, along with 

its 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 2statistics, which indicate the 

level 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 2is 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 tZstatistics, but cannot be used for significance 

testing due to the lack of an underlying distribution 

assumption. A guide for the selection of the final clustering solution is to observe a local maximum in the 

pseudo-F, followed by a local maximum in the pseudot 2as the number of clusters decreases ( denoted by bold 

in Table 3)( Stooksbury and Michaels 1991) . This occurs three tirries, at 12-, 7-, and 5-cluster solutions. The 

largest drop in R zoccurs 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 RZ 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 days 

have 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 values 

converged 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 exhibiting 

similar 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 regression 

In an attempt to objectively define and weight accordingly those meteorological variables most influencing the 03concentrations 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 

[ 031 = 00 + ~ NiXi, 

where [ 03] represents the maximum daily 1-h ozone 

measurements for clusters 1-7, 0 0is 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 compared 

to 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 intravariable 

correlation discussed in section 3, the suite of ineteorological variables used in development of the stepwise 

multiple regression was somewhat different than that 

used 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 Smith 

1981)], 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 and 

twice-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). It 

was 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. An 

example 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. Cluster 

2 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 in 

cool 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 

Solair: 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 with 

C1—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 little 

diurnal 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 

m 1020 1020 

- - 

~ 1015 -- 1015 

m 

a` 1010 1010 

30 

Solar: 233 Wm 2 

30 U 

m 25 26 

~ 20 -------- 20 

E 16 15 

1! 10 10 

01 04 07 10 13 

Hour (LSn 

16 19 22 

1eo 

 Y, 

yo .,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 1020 ----- ----- -- --------- lozo 

~ 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 decreases 

in 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 meteorological 

clusters should exhibit significantly different concentration characteristics. Verification of this hypothesis 

was achieved first qualitatively, through the examination of summary statistics (Figs. 11 and 12, Table 

5) associated with the 03 data as stratified by meteorological cluster. Marked differences are noted in the 

03 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) . . . F7 (x)]. The Kolmogorov—Smirnov 

test 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: Ho : 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°l0 

significance 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 

E 15 --------------- 16 

~ 10 10 

01 04 07 10 13 16 19 22 

Hour (LST) 

~ 

1 6V 16 ~ 

`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 Mixirig Hgt: 385 m 2282 m 

1025 E 

m1020 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 

16b 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 significantly 

different. The number decreases to 15 for a= 1% significance level. 

The characterization of the meteorological clusters 

and subsequent analysis of 0 3concentration 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 3concentration (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 3concentrations 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 3climatology 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 of 

its high frequency of occurrence and requisite meteorology (i.e., clear skies, warm temperatures, and light 

winds resulting in poor lateral and vertical dispersion), 

the 03climatology 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 

v30 30 

m 25 25 

~ 20 ---~ — — _ 20 

E15 15 

m 

~ 10 10 

01 04 07 10 13 16 19 22 

~C Hour (LST) 

1 3 ~ 1 3 ~ 

,020 102a

t2.,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 

03concentrations 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. ~ : 

OCTOBER 1994 EDER ET AL. 

(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 addition 

to providing ideal meteorological conditions, the typical positioning of these transitional anticyclones ( north 

and east of the study region), unlike that of the Bermuda high (typically overhead), allows nearly continuous transport of 03and 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 on 

the 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 

1192 JOURNAL OF APPLIED METEOROLOGY VOLUME 33 

140 

120 

100 

:c 

a 80 

O 60 

N O 

40 

20 

r

c, rc2, ~ rc,~JrcJ, ~ rc,srrc,6~ rc,' ~ 

+r~~ ery~O +~

W3 

4, 

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

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 the 

tendency 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 03concentrations (with 95% 

confidence limits) and relative frequencies of the seven meteorologcal 

clusters. 

were noted during the 10-yr period during the months 

of June, July, or August. Although the limited frequency of C3 prevents it from dominating the 0 3climatology 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 of 

all 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 supported 

in the data, which exhibit nearly identical concentrations during May and September. 

TABLE 5. Summary statistics of the daily 1-h maximum 03(ppb) concentrations associated with each cluster and the overall dataset. 

Cluster n Mean sZ Skewness Number(%) >80 Number (%) >100 Number (%) > 120 

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 03formation. 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 likelihood 

of precipitation. None of these four clusters have resulted in 03concentrations 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 3characteristics exhibited 

by each of the clusters can be gained through an examination of their diurnal patterns, the shape of which 

can provide useful information concerning the formation, scavenging, and transport of ozone within an 

area. In particular, diurnal patterns help ascertain if a 

location is being exposed more to local, photochemically generated 03 or to 03transported 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 range 

of concentrations to which humans, plants, and animals are exposed (Bohm et al. 1991; Wolff et al. 1987). 

The mean hourly 03concentrations ( 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 the 

other clusters ). This pattern is reversed, however, during the nighttime hours. After approximately 2000 and 

prior to 0700 LST, the 0 3concentrations 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 03concentrations 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 3 

concentrations 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 inversion 

layer 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 

03iis dependent upon a number of factors including 

wind speed and cloud cover, which are typically favorable under anticyclonic conditions. Above , this 

nocturnal 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 03(ppb) attributes of the seven clusters. 

Cluster 

03 

Minimum 

(hour LST) 

03 

Maximum 

(hour LST) 03Diurnal range 

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 to 

solar heating, convection progressively mixes this depleted layer with the air above the inversion, so that 

03-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 generally 

stronger 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 3concentrations 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 study 

examining the factors that controlled the diurnal behavior of 03in 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 this 

time are likely attributed to local photochemical reactions. With this in mind, the largest difference between C1 and C5 occurs during this early morning 

period 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 03aloft 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 

"03river" [ Wolff and Lioy ( 1980 )], which flows above 

this nocturnal boundary layer and is able to transport 

03great distances in substantial concentrations without 

extensive 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 0C 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, the 

cold-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 in 

C4 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 3concentrations. 

b. Regression analysis 

1) INDIVIDUAL CLUSTER REGRESSION MODELS 

Having established that the differences between 

mean daily 1-h maximum 0 3concentrations exhibited 

by the seven meteorological clusters are statistically different, investigation into those differences can now be 

facilitated through a determination of which meteorological variables most strongly influence the variability of 03within each cluster. Attributes of the stepwise regression models (which again seek out the optimum set of ineteorological parameters influencing 

the 03concentrations ), developed for each of the seven 

clusters, as well as the overall dataset are presented in 
OcrosER 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 the 

maximum temperature, the higher the daily 1-h maximum 03concentration. 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 3in 

C2. 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 the 

mean 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 coelTicients 

associated 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 R2 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 03variance. 

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 use 

in 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 

03in 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 2of 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 03 , 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 heights 

in 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 03concentrations. This underestimation is observed in most studies using simple 

linear regression and is attributable to the fact that 

03 '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 03concentrations 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 3concentrations 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 better 

modeled. 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. Examination ~

of 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 evident 

in the overall model ( Fig. 14), while not totally alleviated, have been reduced. When compared to the 

overall model, which again had an R Zof 0.53 and an 

TABLE 9. Meteorological variables significantly (a = 0.10) contributing to the 1-h maximum 0 3concentration 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 

Variable One Two Three Four Five Six Seven 

Overall 

model 

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 63.92 565.84 
OCTOBER 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 regression 

models, 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-stage 

clustering approach as part of an automated meteorological classification scheme designed to better elucidate the dependence of 0 3on meteorology. When 

applied to 10 years (1981-90) of ineteorological data 

for Birmingham, Alabama, the classification scheme 

identified seven statistically distinct meteorological regimes. Because of the critical impact meteorological 

conditions have on the formation, transport, and deposition of 03, it was hypothesized and later substantiated through the use of a nonparametric, two-sided 

Kolmogorov-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 the 

largest 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+ RZ = 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 03concentrations 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 3and 

its 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 third 

highest 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 3exhibited 

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 03concentrations 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 

~

100 

& 

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-frontal 

passage: 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 in 

extensive 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 3and reduce its diurnal 

range. 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 3climatology 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 with 

respect 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 to 

its 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 subsequent 

amalgamation of the seven individual regression models into a cluster composite, a better parameterization 

of 03 '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, for 

their 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 names 

or commercial products does not constitute endorsement or recoinmendation for use. 

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