Contents

• INTRODUCTION
• METHODOLOGY
  • Analysis of Observed Ozone Data
  • Meteorological Dependence/CART Analysis
• VARIABLE DEFINITIONS
  • Upper-Air Meteorological Data
  • Surface Meteorological Data
  • Air Quality Data
• DATA ANALYSIS RESULTS
  • "Typical" Pattern Analysis
  • OTAG Episode Days
• CART RESULTS
  • Classification on Ozone Exceedance Distribution Patterns
  • Classification on OTAG Episode Days
  • Classification on Aggregated Exceedance Concentration Patterns
• SUMMARY OF FINDINGS
• Animation of Subregional Ozone Concentrations back cover

1. INTRODUCTION

This report summarizes an analysis of the meteorological and ozone air quality conditions observed throughout the Eastern U.S. during the period 1985-1995. The primary objectives of this study were to (1) examine the meteorological and air quality characteristics of the Ozone Transport Assessment Group (OTAG) modeling episodes (LADCO, 1995), (2) identify important features of the episode periods, and (3) determine the frequency of occurrence of the associated (spatial and temporal) ozone concentration patterns and meteorological conditions.

An important component of this analysis was the identification of patterns in observed ozone concentrations. This was achieved by defining geographical subregions within the area of interest (the SUPROXA domain) and identifying ozone concentration patterns based on which subregions exhibited high ozone concentrations.

The ozone concentration patterns were analyzed considering various forms of the threshold ozone concentration (what constitutes high ozone within a subregion) and with respect to frequency of occurrence of individual patterns and sequences of patterns. Those patterns corresponding to the OTAG episode days were identified.

Both episode and nonepisode days for the ten-year period 1985-1994 were also categorized according to concentration pattern and other air quality and meteorological parameters using the Classification and Regression Tree (CART) analysis technique. Using CART, the frequency of occurrence of various types of ozone episodes as well as the distribution of the OTAG episode days within the identified categories was examined.

The data analysis methodologies are described in Section 2 of this report. The meteorological and air quality database and the definitions of variables are summarized in Section 3. The data analysis results are presented in Sections 4 and 5.

2 METHODOLOGY

Two approaches were applied to the analysis of the observed surface level ozone data and the classification of the OTAG episodes. The first approach included statistical and pattern analysis of the observed ozone concentration data for the Eastern U.S. for the years 1985 through 1995. The second approach focused on determining the relationships between observed meteorological parameters and the identified ozone distribution patterns. The methodologies employed for each of these approaches are described in this section.

ANALYSIS OF OBSERVED OZONE DATA

The ozone data record for this analysis consisted of hourly ozone concentration data for monitoring sites located throughout the Eastern U.S. and operating during the ten-year period from 1985 to 1994. The complete record of AIRS air quality monitors for this time frame was examined, and those sites that were operational for the entire ten-year period were selected. Data for 315 monitoring stations were used for this analysis. To facilitate analysis of the regional-scale characteristics of the ozone episodes, data from the monitoring stations were aggregated within defined subregions, with the aggregate information then considered representative of the air quality characteristics of that subregion. The details of the methods used to aggregate the data and to define the subregions are given in Section 3.

An examination of regional-scale ozone concentrations required creation of a single statistic or descriptor variable which contained information on observed ozone concentrations within subregions. The generation of this ozone statistic allowed for a number of analyses, primarily addressing (1) the patterns of ozone concentrations distributed among the subregions over the ten-year period, (2) the recurrence rates for particular ozone distributions, and (3) the temporal evolution of the concentration patterns. These three questions were viewed in terms of gathering information about what is "typical" in the Eastern U.S., as well as what specifically occurred during the 1988, 1991, 1993, and 1995 OTAG modeling episodes.

Ozone Concentration Patterns

The observed ozone concentration patterns were analyzed using two sets of subregions, consisting of 20 and 4 subregions as illustrated in Figures 2-1 and 2-2. For any given day, ozone concentrations vary among the different subregions. For a particular day, the exact distribution of subregions with high and low ozone concentrations defines the ozone concentration pattern. For a particular day, the number and location of subregions with high ozone concentrations gives direct information as to the extent and severity of the episode. Note that in the aggregation of the observed data into subregional information, it is important to consider geographical information as well as the distribution of emissions (e.g. urban areas) and monitoring sites.

The number of possible subregional concentration patterns is dependent upon the number of subregions, and can be quite large (effectively infinite for 20 subregions, depending on the exact pattern definition); however, the set of actual patterns will be some subset of all possible ones. The relation of this subset to the set of all possible patterns provides insight into what are "typical" ozone patterns. There may be no typical ozone pattern, or there may be a large number of recurring patterns. Knowledge of which, if any, patterns are typical is essential to establish the representativeness of the selected OTAG episodes.

Pattern Recurrence Rate

The frequency distribution of the observed ozone distribution patterns was also examined. Specifically, the number of times a particular pattern occurred in relation to all of the days studied, as well as in relation to the number of times other patterns occurred, was determined. Of particular interest were those patterns corresponding to the OTAG episode days. For example, as discussed in detail in Section 4, high ozone concentrations were observed in a number of subregions on 7 July 1988. However, historically, this particular distribution occurs with very low frequency. Both of these factors (geographic extent and frequency of occurrence) are important in classifying and deriving information from the episode day. (Note that these two factors are not redundant: while it is true for the extremes in the data record that large geographic extent of high ozone concentrations have low occurrence rate, it is not true in general. That is, geographic extent is not simply inversely proportional to recurrence rate.)

Analysis of pattern recurrence rate has provided useful information regarding (1) possible geographical relationships (i.e., ozone concentrations influenced by similar meteorological conditions or pollutant transport) and (2) episode representativeness. For instance, the fact that a large number of exceedances (as defined by a peak ozone concentration greater than 124.0 ppb at some site within a subregion) are recorded in both the Houston and Dallas subregions is useful information. It is also useful, however, to know that it is much more typical for an exceedance to occur within the Houston subdomain than within the Dallas subdomain (either independent of or in conjunction with an exceedance in Houston). Further, the fact that Dallas has similar numbers of exceedances both alone and in conjunction with Houston (both of which are much smaller than the number of exceedances in Houston alone) indicates a possible relationship between the two.

It is also important to assess how representative a particular ozone distribution pattern is to determine how likely that pattern is to recur. This is particularly important in interpreting modeling results to guide ozone attainment strategy development. For instance, the 1988 episode is composed almost entirely of days with extremely low recurrence rates, while the 1993 episode is composed of days with much higher recurrence rates. Detailed information on which patterns occur, as well as their likely recurrence rates, is given in Section 4.

Evolution of Ozone Concentration Distributions

Besides recurrence rates of particular ozone concentration distributions, it is also of value to know if there are typical evolutionary patterns of ozone concentrations. For example, is it typical for high ozone concentrations in the Houston subregion to be followed by high ozone concentrations in the Dallas subregion, or is the reverse more typical, or is neither typical? This information may be suggestive of possible transport (or lack of transport) between subregions. Some day-to-day patterns occur only once, while others occur multiple times. Typical ozone episodes last only two days. Detailed information on the temporal evolution of observed ozone concentration patterns and on the duration of episodes is presented in Section 4. An animation is provided for each of the four episodes that visually demonstrates the evolution of the subregional ozone concentration patterns over the entire U.S. Diskettes containing the animations and instructions for viewing the animations are attached to the back cover of the report.

METEOROLOGICAL DEPENDENCE/CART ANALYSIS

The analysis outlined above provides information on the characteristics of ozone episodes within the Eastern U.S. However, it does not address why particular ozone distribution patterns occur. This question (for the Eastern U.S.) was addressed in this study through the use of Classification and Regression Tree (CART) analysis, which examines the dependence of ozone concentration patterns on the prevailing meteorological conditions.

In order to determine the meteorological dependence of the ozone distribution pattern, it was necessary to construct a database of air quality and meteorological variables, upon which the daily ozone distribution pattern over the Eastern U.S. was likely to depend. The creation of this database is detailed in Section 3. A description of the CART method, and the various dependent variables considered and used, follows.

Classification and Regression Tree Analysis

The CART analysis technique partitions a data set into discrete subgroups based on the value of a user-defined classification variable. The remaining variables in the database are selected as to whether or not they provide a predictive segregation of the data between different values of the classification variable. This restriction presupposes that there is a causal relationship between the independent variables and the dependent or classification variable. Consequently, it is necessary to construct a database of independent variables upon which the dependent variable is likely to depend.

The CART software segregates the different values of a classification variable through the growth of a binary decision tree, composed of a progression of binary splits on the values of the independent variables. Each split is chosen such that the segregation of different values of the dependent variable is improved. The resulting tree has multiple branches, of various complexity, each of which represents a path to a particular value of the dependent variable. CART analysis is quite different from typical regression analysis. For example, if the dependent variable is an exceedance in the Cincinnati area, and one of the independent variables is maximum surface temperature at a particular site in Ohio, a typical regression technique would derive an equation relating exceedance pattern to some multiple of the maximum surface temperature at this site. While such a result may provide an analytic description for some of the data dependence, it is not likely to give much physical insight or to be appropriate for the entire Eastern U.S. A regression result such as "3 times surface temperature equals ozone pattern" is not physically intuitive; moreover, the relation between temperature and high ozone concentrations in Maine may be better described using another factor. A single regression analysis cannot accommodate or explain both situations.

On the other hand, in one branch of the tree the CART software would establish a binary split on the value of the maximum surface temperature in Ohio, say 32.0 ° C, where now a greater preponderance of the days with high ozone concentrations in Cincinnati would correspond to high temperatures in Ohio, while days with lower ozone concentrations in Cincinnati would correspond to lower temperatures in Ohio. The binary splitting in this branch of the tree would continue on values of other independent variables, or different values of the same independent variable, until values of the dependent variable are optimally segregated. This approach has the advantage of not arbitrarily mixing units (e.g., high ozone concentration in Cincinnati = 3 times wind speed plus 2 times humidity, as an idealized regression equation would suggest), as well as providing physical insight into the processes contributing to high surface average ozone concentrations in the Cincinnati area.

This technique is particularly applicable for a large regional study, because the independent variables are used independently. That is, the exceedance patterns involving Cincinnati and those involving Maine may be segregated from each other early on based on a binary split on, for example, wind direction aloft. The branch of the tree containing patterns corresponding to exceedances in Maine would then be further split on meteorological variables appropriate to Maine, rather than those appropriate to Cincinnati. Therefore, no one single regression equation is imposed on the entire data set.

The above example is instructive in the virtues of the CART analysis. For example, one branch of the decision tree may indicate that for a particular group of exceedance patterns, there is a dependence on low wind speed in a particular area. Coupled with other variables, this may indicate that these exceedance days are typified by local production of ozone. On the other hand, another branch of the tree may show that another group of days with these same exceedance patterns depends on the same variable (wind speed at some location), but that the value of the variable (wind speed) for this group is high. Coupled with the other variables in this branch of the tree, this may indicate that these exceedance days are typified by transport of ozone or precursor pollutants from an adjacent region. A regression analysis on the entire data set would have to average the dependence on this wind speed variable, thereby giving poor correlation with either of the two dependent variables, and possibly limiting the informational content with respect to the physical relationships among the meteorological and air quality variables. The CART technique not only properly segregates these days, but does so in a manner which provides physical insight into the classified episodes.

Because the meteorological conditions are partitioned between days with varying potential for high surface ozone concentrations, it is possible to predict the likely frequency of such conditions, as well as to specify those conditions. In addition, once the exceedances are classified, information is obtained on the likelihood of an ozone exceedance given a particular set of meteorological conditions. This analysis provides a method of determining the likely recurrence rate for a particular ozone episode, as well as providing physical insight into the prevalent conditions during that episode.

Dependent Variables for CART Analysis

The exact nature of the binary decision tree, and the segregation of the daily data, depends very much on the selection of the dependent variable. For a particular classification exercise, only a single dependent variable can be used. However, by changing the dependent variable and performing a new classification, different information can be obtained. A number of dependent variables were used for this study, with different purposes in mind.

Ozone Distribution Exceedance Pattern

In this case, the dependent variable represented the pattern of subregions within which ozone exceedances occurred. This approach required a definition of "exceedance"; the definitions are detailed in Sections 3 and 4. Classification according to the exceedance pattern gives direct information on the meteorological conditions which distinguished this ozone distribution from others, as well as the dependence of particular subregional ozone concentration patterns on particular meteorological conditions. For instance, this approach addresses the question of what the meteorological conditions are during those days that had an exceedance only in the Baltimore/Washington subregion. This can then be contrasted with the results for days which showed an exceedance in both the Baltimore/Washington and the New York/New Jersey subregions. Results from this approach are presented in Section 5.

OTAG Episode Day

The selection of particular days by OTAG for UAM-V modeling is implicitly a surrogate for ozone concentration pattern. Consequently, for each of the three OTAG episodes, a dependent variable was created specifying whether the day was an element of the episode. Classification on, for example, the 1988 episode, then gives direct information on the meteorological conditions prevalent during this episode, which were distinct from conditions during other periods. Results from this analysis are detailed in Section 5.

Aggregated Exceedance Concentration Patterns

Results from the ozone observation data analysis, presented in Section 4, indicate that there were characteristic regions within which ozone exceedance patterns occurred. For instance, it was not characteristic (although it did occur) that exceedances were observed within both the Houston and New Jersey subregions. Consequently, patterns involving Houston typically did not involve New Jersey. This allowed for grouping together of the patterns which did involve Houston as a subset of the observed patterns. A similar grouping for the New Jersey patterns was also made. Four subsets were determined, roughly corresponding to the geographic regions of Texas, the Southeast, the Midwest, and the Ozone Transport Region (OTR). The OTAG UAM-V episodes could then be distinguished based on measured concentrations within these regions. Note that this grouping of exceedance patterns is different than a geographic partitioning of the domain. For instance, a particular subregion such as that containing Birmingham, AL may have high ozone concentrations in conjunction with both the Houston and Atlanta subregions, but not at the same time. Hence this geographic subregion may be included in ozone patterns grouped as Southeast regional exceedances, and as Texas regional exceedances. The aggregation of exceedance patterns grouped the days into subsets which are characterized by a dominant ozone concentration distribution.

Classification on the aggregated concentration patterns directly gives information about the meteorological dependence of ozone distributions on a regional scale. That is, it enables examination of the meteorological conditions associated with regional-scale ozone episodes. This is a larger scale than that addressed by classifying on the subregional patterns. It is also considerably more effective in capturing the realistic physics than classification on a purely geographic regional scale, in that it recognizes that a regional-scale ozone episode may involve portions of Texas, Louisiana, Arkansas, Mississippi and Alabama, while another may affect portions of Georgia, Alabama, Mississippi, and Tennessee. Including Alabama and Mississippi as part of both types of episodes is important, and partitioning this geographic subregion would not be appropriate.

3. VARIABLE DEFINITIONS

For the analysis of the distribution of ozone concentrations in the historical record according to the CART methodology outlined in Section 2, a database was created for the ten-year period from 1985 through 1994. This database comprised data from upper-air meteorological soundings, surface meteorological observation stations, and surface ozone air quality monitoring sites. This section describes the variables derived from these data.

UPPER-AIR METEOROLOGICAL DATA

Upper-air meteorological data were considered to be of primary importance in the regional scale analysis. Data from all of the National Weather Service (NWS) upper-air meteorological monitoring stations which had a complete data record for the ten-year period of interest were included in the database. After preliminary analysis and quality control of the available data, data were compiled for those sites listed in Table 3-1 and displayed in Figure 3-1.

Using data from these sites, a series of meteorological variables were selected for inclusion in the CART analysis. Ideally one would include all available data in any analysis, but practical limitations on the size of the final database made it necessary to include a subset of variables. While these variables might not adequately describe certain relevant smaller-scale features, they are likely to represent the larger-scale phenomena. The complete list of upper-air variables is detailed in Table 3-2. The upper-air data consisted of data taken at two sounding times per day. Determination of the "morning" or "afternoon" designation depended on converting the reported GMT time and date of the data record to local standard time. Each variable was further identified by the upper-air site map identification number from which it was derived. This resulted in 476 upper-air variables per day.

The variables listed in Table 3-2 were uniformly created for data from each monitoring station. This set of variables was expected to be relevant to all geographic regions in the OTAG modeling domain. No tailoring of variables to a specific region or subregion was performed, with the explicit intention of keeping the analysis uniformly applicable over the entire domain. That is, creation of specific variables for particular sites, based on past experience with data from these sites, was avoided.

SURFACE METEOROLOGICAL DATA

Data from surface meteorological observation stations were also included in the database. The selection of surface sites was based on the distribution of upper-air sites. For each upper-air site, a nearby surface site that had a complete ten-year data record was chosen. The selected surface meteorological sites are listed in Table 3-3 and displayed in Figure 3-2.

Data from each site were chosen such that the surface variables neither duplicated nor conflicted with the upper-air variables. Only those surface measurements that could be used to define regional-scale meteorological features were included in the database. Table 3-4 lists the selected surface meteorological variables. Each variable was further identified by the surface site map identification number from which it was derived. This resulted in 136 surface variables per day.

The combination of the surface and upper-air meteorological variables for each day in the ten-year database resulted in over 2.2 million values of the independent variables.

AIR QUALITY DATA

The upper-air and surface meteorological variables were used as independent variables in the classification of ozone episodes. A method of describing a particular ozone concentration distribution for the entire OTAG modeling domain was required for specification of the dependent variable. Considering that the concentrations observed at a site are influenced by the microenvironment of the site, a method of aggregating the data to represent subregional-scale air quality was developed. Therefore, the OTAG domain was partitioned into subregions which were likely to display similar ozone dependence on meteorological variables.

To do this, each major metropolitan area was identified. This list included cities within nonattainment regions and other large urban centers. Preliminary analysis of the meteorological and air quality data, coupled with previous experience as well as general geographic information, indicated that the ozone dependence on meteorological variables differed for many of these urban areas. From each urban area lines were drawn connecting it to each of the other urban areas with distinctly different meteorological and air quality characteristics. That is, these lines indicated which areas should be segregated from one another. A grid was then developed from two guiding principles: the grid should partition the domain into the smallest number of subregions necessary, and the grid should segregate each of the urban areas identified above. In practice, this meant that at least one grid line should cross each of the lines connecting the cities. While no global-optimization argument can be given proving that the final grid choice is optimal, the final grid choice is eminently reasonable.

The selected grid includes 20 subregions (Figure 2-1), as defined in Table 3-5. Other grids with more or fewer subregions were considered. The grids with fewer subregions suffered from not properly capturing the differences between areas known to exhibit different meteorology, while the grids with more subregions either added no additional information, or became too small to capture the regional-scale phenomena. Regular grids with fixed spacing either did not segregate areas with known meteorological and air quality differences, or had many more subregions than Figure 2-1. For comparison, a grid with only four subregions, roughly corresponding to the regions identified for model performance calculations for the OTAG UAM-V modeling, was also considered. This grid system is shown in Figure 2-2, and the definitions of the grid are listed in Table 3-6.

After selecting a grid definition, the creation of a functional derivative of ozone concentration for each subregion was necessary. The data from a network of 315 AIRS ozone monitoring stations that were operational for the entire ten-year period were used. The locations of these sites are indicated in Figures 2-1 and 2-2. In designing the function such that it quantified whether or not the observed ozone concentrations over the entire subregion were high, two functional forms were considered. The first was defined as the supremum of the daily maxima from the individual sites within the subregion (the "sup max" functional form). The second was defined as the average of the daily maxima from the individual sites within the subregion (the "avrg max" functional form), with missing data excluded.

An exceedance for the sup max functional form was defined as a concentration greater than the critical concentration of 124.0 ppb. The sup max functional form had the virtue of allowing easy comparison with the present regulatory ozone concentration standard, but it suffered from a focus on the extremes in the ozone record. As only the highest daily observed ozone concentration is considered for each subregion, the designation of "exceedance" may not adequately represent the ozone concentrations throughout the subregion. While for smaller scale applications a focus on local maxima may be appropriate, the present study was designed to give information on the regional scale. Consequently, the avrg max functional form was considered to be more likely to characterize subregional-scale ozone.

It was less clear what the critical concentration should be for specifying an exceedance with the avrg max functional form. The procedure chosen is detailed in Section 4, but briefly, with 20 subregions, a critical concentration of 90.0 ppb was used to give approximately the same number of exceedances as were observed with the sup max functional form. To assess the stability of the classification scheme under different exceedance definitions, a second critical concentration of 75.0 ppb was examined. A comparison was also performed with the four-subregion grid definition and an avrg max critical concentration of 80.0 ppb.

The final consideration in defining an air-quality classification variable for the entire OTAG domain was to identify a unique means of aggregating the exceedance/nonexceedance classifications of the subregions into one variable which represented an exceedance pattern for the entire domain. To this end, a binary classification variable was constructed. The subregions were numbered, as shown in Figures 2-1 and 2-2, and each number was used to define the bit location in an n-bit binary number, where n is the number of subregions. Thus, for Figure 2-1, the binary classification variable has 20 bits, bit 1 corresponding to subregion 1 and bit 20 corresponding to subregion 20. Each bit was assigned a value of 0 or 1 depending on whether or not that subregion exhibited an exceedance, according to the particular functional form employed. A zero was a nonexceedance, while a 1 was an exceedance.

For example, for the 20-subregion grid and the avrg max functional form with exceedance level of 90.0 ppb, consider the case where subregions 7, 8, and 20 had exceedances, and no other subregions had average maxima above 90.0 ppb. The binary classification variable then takes on the value 10000000000011000000. The integer equivalent of this value (524,480 = 2¹⁹ + 2⁷ + 2⁶) is assigned to the classification variable for this day, uniquely identifying a pattern of exceedances among the 20 subregions.

If every possible pattern distribution occurred, the classification variable would take on an intractably large number of values (2²⁰ - 1). However, in practice, not all pattern distributions are realized due to the statistical representativeness of the database and the physics of ozone formation. The large database used here reasonably ensures that nearly all of the representative ozone patterns occur, but one should note that even under these conditions it is not expected that all patterns would occur. For instance, it is conceivable that subregions 1 and 13 may never have exceedances on the same day. Similarly, it is conceivable that on every day at least one subregion would not show an exceedance. Consequently, the number of patterns which actually occur, and the number of occurrences for each of these patterns, provide useful information in and of themselves. The results of the analysis of this information are presented in the next section.

4. DATA ANALYSIS RESULTS

The creation of the pattern variable described in the previous section allows for a detailed analysis of the ozone distribution patterns in the Eastern U.S. over the eleven-year period from 1985 through 1995. Two primary questions can be addressed by such an analysis: what, if any, are the "typical" ozone patterns, and what information can be obtained regarding the representativeness of the OTAG ozone modeling episode days?

Section 3 describes the three variables on which the exceedance patterns depend. These are the functional form of the test (sup max or avrg max), the number of subregions (20 or 4), and the critical concentration used to determine whether or not a subregion is in exceedance (124.0 or 90.0 ppb). For the sup max functional form, the only critical concentration considered was 124.0 ppb, in accordance with the current primary ozone NAAQS. Choosing a critical concentration for the avrg max functional form was more difficult. Table 4-1 shows the number of days in the ten-year ozone database which would have average maximum concentrations above a particular critical concentration with the avrg max test and 20 subregions. However, the overall number of days classified as "exceedance" is not the only measure of concern, as the geographic distribution of these exceedances is also important. A few of the cases considered are listed in Table 4-2, along with some statistics for each of these cases.

The sup max test with a cutoff of 124.0 ppb and 20 subregions can be considered a baseline comparison case. The number of "exceedance" days for this case is expected to exceed the total number of observed ozone exceedance days, since there are more data extremes than there are high averages in the historical ozone record. In choosing a cutoff concentration for the avrg max test, the statistics from the sup max test were useful. The avrg max cutoff should be set such that the number of days classified as exceedance days is less than that for the sup max test. However, with a different test, the number of distinct patterns changes as well. Once again, it is desirable that the overall number of patterns be less than or equal to that for the sup max test. Satisfying both these criteria helps to ensure that the concentration used in definition of an exceedance with the avrg max test is not overly stringent nor overly lax. Based on this comparison a cutoff concentration of 90.0 ppb was used for those analyses in which the avrg max statistic and 20 subregions were employed.

"TYPICAL" PATTERN ANALYSIS

Using the pattern definition methodology described in Section 2, the spatial and temporal distributions of the observed high ozone concentrations were examined in a variety of ways. The average number of exceedance days which exhibit a particular pattern gives a measure of the number of unique patterns associated with each exceedance test: the lower the number, the greater the number of patterns having few occurrences. To ensure better population statistics while performing the CART analysis, it is desirable that each pattern have multiple occurrences. However, this criterion cannot be imposed, as it may be physically unrealistic that more than a few patterns occur multiple times. Three columns in Table 4-2 give population statistics for only the more highly populated patterns (the patterns which occur three or more times in the ten-year record) for each of the exceedance tests.

A comparison of the total number of patterns with the number of patterns which occur three or more times (column 4 and column 7 of Table 4-2) shows that for the cases with higher resolution (the 20-subregion cases) most patterns occur only once or twice, and only a few occur more often. This indicates that the historical ozone record for the Eastern U.S. exhibits a large number of unique or nearly unique ozone concentration patterns, yet close to 70 percent (column 10 of Table 4-2) of the exceedance days (when the concentration level for an exceedance is reasonably high) are associated with a much smaller number of patterns. Consequently, there are "typical" ozone distribution patterns which account for the majority of the observed exceedance periods.

In addition to the cases with 20 subregions, Table 4-2 also displays information for the 4 subregions of Figure 2-2. The four-subregion case provides information on the larger scale geographic ozone distributions. This subregion definition, while not fine enough to properly capture the differences between areas of known physical distinction, provides some information on gross concentration distributions in the Eastern U. S.

The recurrence rate of the ozone distribution patterns that occur three times or more in the ten-year database provides insight into which areas of the country exhibit typical ozone patterns, and what those typical patterns are. Figure 4-1 shows a histogram of recurrence rate for a particular pattern distribution with the sup max functional form, 20 subregions, and a critical concentration of 124.0 ppb. Figure 4-2 shows the same information for the avrg max functional form with a critical concentration of 90.0 ppb. Finally, Figure 4-3 shows this information for the avrg max functional form with four subregions and a critical concentration of 80.0 ppb. In the first two of these figures, only the patterns that occur three or more times are considered, and in all three figures the number of recurrences are normalized to the number of days meeting each criterion to allow for comparison between the figures.

Use of the sup max functional form with a critical concentration of 124.0 ppb distributes the data such that only 5 of the 44 (11 percent) higher populated patterns include 3 percent or more of the days. The exceedance days are distributed among a large number of patterns, with one pattern (corresponding to an exceedance in the Houston area only) accounting for nearly 40 percent of the days, and the majority of the remaining patterns only sparsely populated. The second most frequently occurring pattern (pattern 17) comprises 9 percent of the exceedance days and corresponds to high observed ozone concentrations in the New York/New Jersey subregion.

Using the avrg max functional form with a critical concentration of 90.0 ppb, 9 of the 41 (22 percent) higher populated patterns include 3 percent or more of the days. Similarly, the case with four subregions shows 38 percent of the patterns with 3 percent or more of the days. Here pattern 4 corresponds to "exceedances" in the Northeast area only and pattern 1 corresponds to the Southwest area only. Thus, a more equitable distribution of exceedance days is achieved with the avrg max functional form. Analysis of the air quality data suggests that this distribution is also more physically meaningful.

Both Figure 4-1 and Figure 4-2 indicate that the most common patterns of exceedances are those where only a single subdomain is in exceedance. In addition, it is also clear from both distributions that the geographic areas which systematically show the highest ozone concentrations are near Texas (subregion 1 and environs) and in the OTR (subregions 12, 17, 20, and environs). To a lesser extent the Southeast (subregions 6, 7, and 8) and the Midwest (subregions 11, 14, and 15) also show multiple high-concentration days. As expected, Figure 4-2 clearly indicates that on a large proportion of the days for which an exceedance was observed in the Northeast, there are multiple subregions which show an exceedance. On the other hand, in the Southwest many exceedance days are characterized by a single subregion with a high concentration of ozone.

The temporal evolution of the observed ozone concentration patterns was also examined. For example, is it the case that an exceedance in subregion 12 is typically followed by exceedances in subregions 12 and 17, or 17 and 20? Such evolutionary patterns would hint at migratory meteorological features or pollutant transport. In order to address this issue, the recurrence rate for multiday patterns was examined. The ten-year database was examined for patterns over periods of two through six days.

There are a large number of day-to-day distributions which recur, but the majority of these consist of days with a particular exceedance pattern followed by days with no subregions showing an exceedance. In addition, due to the high number of exceedances in both Texas and the Northeast, it is occasionally the case that an exceedance in one of these areas was followed by an exceedance in the other area. We assumed this to be a purely statistical correlation (without physical meaning). Of all the temporal patterns available, a surprisingly small number of physically meaningful patterns actually recurred.

Table 4-3a shows multiday patterns which occurred twice or more, were different from day to day, and were physically interesting. The table lists the subregions which were in exceedance, under the avrg max functional form and a critical concentration of 90.0 ppb, for each day of the recurring sequence. The number of times this sequence occurred is also shown, along with the date of the first day of the sequence for each recurrence. Table 4-3b gives similar information, but only for those temporal sequences which were the same from day to day. A notable feature of Table 4-3a and Table 4-3b is the absence of recurring episodes with duration longer than two days. There are only two such cases. Both involve three-day periods with high ozone concentrations in the same subregion (subregions 1 and 17, respectively). Thus, given the subregion definitions, there are no "typical" three-day or longer inter-subregional episodes with geographically extended ozone concentrations greater than 90.0 ppb in the ten-year database. (Note however that this may not be true when considering only a subset of these subregions. That is, if the geographic domain were restricted to just the Northeast, there may be three-day or longer inter-subregional episodes. For instance, an exceedance in the Baltimore/Washington subregion, followed by an exceedance in the New York subregion, may occur multiple times. However, it could be the case when considering the entire OTAG domain, that different occurrences of this sequence may be distinguished by a simultaneous exceedance in, for example, the Dallas subregion. Restricting the overall domain thus changes the statistics of recurring patterns.)

The recurring patterns can be largely segregated into one of two categories: those observed within the OTR (subregions 12, 16, 17, and 20), and those in the Texas area (subregions 1, 2, and 4). These two regions show pronounced subregional ozone evolution, even when there are no other high average ozone concentrations in the remainder of the Eastern U.S. Within the OTR, many of the possible patterns are observed, with no single simplifying feature. This is in contrast to the recurring temporal patterns in the Texas area, where nearly all entail high ozone concentrations in subregion 1 on the first day. This indicates potential transport from the Houston area. Whether or not this is the case requires a more detailed analysis of these days (see below).

Likewise, Table 4-3b shows that these same two geographic areas are most likely to have high ozone concentrations day after day within the same subregions. However, there are also three periods where subregion 8 (which encompasses North Carolina) experienced high ozone concentrations for two consecutive days.

In order to examine the sensitivity of this analysis to the functional form used to define an exceedance, the same information was gathered using the sup max functional form with a critical concentration of 124.0 ppb and 20 subregions. The results of this analysis are given in Table 4-4a for the temporal patterns which are different from day to day, and in Table 4-4b for the patterns which are identical from day to day. Tables 4-4a and b show that once again, the geographic areas with recurring temporal patterns are primarily confined to the OTR and Texas. Of the patterns which change from day to day and recur (Table 4-4a), nearly all are limited to two days. These qualitative features are similar to those observed with the avrg max test. However, the days flagged as recurring under each test are somewhat different. This indicates that a focus on either a high average ozone concentration, or the extreme ozone concentration, shows that the OTR and the Texas area are the only geographic regions with "typical" recurring two-day patterns (when typical is defined in the context of the entire Eastern U.S.). However, focusing on either geographically extended high ozone concentrations (the avrg max test of Table 4-3) or localized peak ozone concentrations (the sup max test of Table 4-4) changes somewhat the days of interest. The days listed in Table 4-4 that also appear in Table 4-3 are flagged in Table 4-4. These days have high peak ozone concentrations, as well as high average subregional ozone concentrations. A fair portion of the days are listed in both Tables 4-3 and 4-4. However, there is a systematic discrepancy between these tables in that the sup max functional form flags many more episodes during 1990 than the avrg max functional form. This may indicate that 1990 was distinctive in the ten-year database in showing numerous repetitive peak exceedances, without the concurring average subregional exceedances. Elucidating the sources of this difference is somewhat outside the scope of the present study, but merits further investigation.

Finally, Tables 4-5a and 4-5b provide similar information to that contained in Tables 4-3 and 4-4, but with an avrg max functional form with a critical concentration of 80.0 ppb, and the four-subregion grid of Figure 2-2. Longer "typical" sequences are observed, with greater variation in the types of sequences, and a greater number of days exhibiting these sequences. However, it is difficult to draw physical inferences based on these results due to the low spatial resolution. Consequently, for the subsequent analysis, only the 20-subregion grid definition will be considered.

OTAG EPISODE DAYS

In addition to the above analysis of "typical" ozone distributions, it is of interest to examine the OTAG UAM-V modeling episode days with respect to these criteria. The three OTAG episode periods during the ten-year data record used here are 1-15 July 1988, 13-21 July 1991, and 20-30 July 1993. (Data for 7-18 July 1995 were not available in time to be included in the full analysis; however, a partial analysis of these data is presented.) The primary questions of interest are: what are the ozone distribution patterns for these episode days, and how typical are these patterns in the ten-year database? Both of these questions are addressed in Table 4-6 for the 1988 episode.

1988 Episode

For each day of the 1988 episode, Table 4-6 indicates which subregions experienced high ozone concentrations, as well as the number of times that this particular ozone distribution occurred in the database. This information is given for three different functional forms of the exceedance classification with 20 subregions: (1) the sup max functional form with a critical concentration of 124.0 ppb, (2) the avrg max functional form with a critical concentration of 90.0 ppb, and (3) the avrg max functional form with a critical concentration of 75.0 ppb. A comparison of the first two shows that for the 1988 episode, the subregions with exceedances are quite similar under the two different tests. This indicates that not only was the 1988 episode characterized by high peak observed ozone concentrations, but that these high concentrations were not localized. Similarly, the recurrence rates of the ozone distribution patterns under these two tests are similar, and low for the majority of the episode days.

The third set of data is included to give a comparison of the episode characterization under the avrg max functional form but with a different critical concentration. Additional subregions are classified as having exceedances with the 75.0 ppb critical concentration, but the number of times each of these patterns occurs does not uniformly increase or decrease. This indicates that the characterization of the 1988 episode as composed of days with largely "unique" ozone distributions is a robust characterization.

Figure 4-4 shows the ozone distribution patterns for each day of the 1988 episode under the avrg max functional form and a critical concentration of 90.0 ppb. It is readily apparent from this figure that the 1988 episode involved nearly the entire northeastern portion of the U.S. The episode began with no subregions in exceedance. By 3 July, there were subregional exceedances in the Midwest, which then expanded on 4 July, with a concurrent exceedance in the OTR. This was followed on 5 July with an aggregation of these exceedances, which continued to expand to the south and southwestern portions of the domain through 9 July. Beginning 10 July, the regional extent of the exceedances dissipated, and by 12 July conditions were once again clean. The OTR again showed high average subregional ozone concentrations on 13 July, which continued through 14 July with a northward expansion, and through 15 July with a westward expansion. The regional extent of subregional exceedances observed during this episode was one of the greatest in the ten-year historical database.

1991 Episode

Similar information for the 1991 episode is provided in Table 4-7. The sup max functional form and the avrg max function form with a critical concentration of 90.0 ppb classify the episode similarly, but with a notable distinction. The classification with sup max indicates that the episode days involve exceedances in the Midwest (subregions 10, 11, and 14), the Northeast (subregions 12, 16, 17, 19, and 20), and Texas (subregion 1). The avrg max functional form with a critical concentration of 90.0 ppb isolates the high ozone concentrations to the OTR, with concurrent high values in the Midwest (subregions 10, 11, and 15). It is interesting that use of the avrg max functional form, compared to the sup max functional form, results in exclusion of the Lake Michigan subregion, but inclusion of the northern Ohio/western Pennsylvania subregion. This indicates that exceedances near Lake Michigan (subregion 14) were likely isolated. On the other hand, the high observed ozone concentrations in the OTR were more regional in nature.

Once again, the frequency of occurrence of the patterns with which the episode days were classified are similar between the two functional forms. This episode, as with the 1988 episode, is made up of days with patterns with low recurrence rates, indicating, as with the 1988 episode, that the ozone distribution patterns exhibited during this episode are somewhat unique in the historical ozone record for the Eastern U.S. The regional extent and evolution of this episode is indicated in Figure 4-5.

Figure 4-5 shows that the 1991 episode began with three low ozone concentration days. High average ozone concentrations were observed over both the OTR and the Midwest on 16 July. This was followed on 17 July by exceedances in the New England area, as well as a concurrent exceedance in the St. Louis subregion (subregion 10). A similar but more connected high ozone concentration pattern was observed on 18 July. Additional subregions to the north were affected on 19 July, while concentrations within the Ohio River valley subsided. The Baltimore/Washington subdomain was added on 20 July. The pattern indicates that only OTR states were affected on 21 July.

Table 4-7 also contains information on the high ozone concentration patterns observed with an avrg max functional form and a critical concentration of 75.0 ppb. The primary differences between this and the other two functional forms are the inclusion of subregions 4 and 5, and a greater extent of the northeastern portion of the U.S. classified as having high ozone concentrations. Once again, the recurrence rates of these days are low, supporting the conclusion that the 1991 episode is composed of somewhat unique ozone distributions.

1993 Episode

The differences in observed patterns with different exceedance tests for the 1993 episode are shown in Table 4-8, while the evolution of the subregional exceedances during the 1993 episode, under an avrg max functional form with a critical concentration of 90.0 ppb, is shown in Figure 4-6. The differences between the classifications with the three different functional forms in this case are somewhat more pronounced. In all cases, the high ozone concentration patterns center on the Southeast (subregions 7 and 8). There are distinct differences between the ozone distributions with the sup max form and the avrg max form with a critical concentration of 90.0 ppb. The avrg max form (90.0 ppb) shows that the episode began with an exceedance in the Atlanta subregion (subregion 7), which extended to the North Carolina subregion (subregion 8), and was followed by exceedances in more northerly subregions. This pattern is then somewhat repeated during the latter portion of the episode. The sup max form showed similar, if less extended, ozone concentrations during the first four days of the episode, but the latter part of the episode was characterized by high ozone concentrations in subregions 10 and 11 (St. Louis and the Ohio River Valley), as well as 9 and 19 (Kansas City and upstate New York). These differences clearly show that exceedances during this episode occurred in a number of subregions, but within each of those subregions the peak values were not representative of the ozone concentrations over the entire subregion. Examining the subregions in exceedance under the avrg max form and critical concentration of 75.0 ppb also confirms that there were somewhat high ozone concentrations over a wide range of subregions during this episode. However, even with this exceedance definition, subregion 10 on 27 July 1993 and subregion 19 on 29 July 1993 still show only a sup max exceedance. Consequently, for the latter portion of the episode, the peak ozone concentrations do not represent the subregional ozone concentrations.

The recurrence rate of the ozone patterns in the 1993 episode are generally higher than those for the other two episodes considered, although this varies from day to day. This indicates that this episode is composed of days which are more representative of typical ozone patterns in the Eastern U.S., than are the days of the 1988 and 1991 episodes. Figure 4-6 illustrates the ozone concentration patterns associated with this episode. While most activity occurs within the Southeast, subregions within the OTR and the Midwest are affected during the middle and later episode days.

1995 Episode

The ozone patterns and their recurrence rates for the 1995 episode under the three different exceedance tests are described in Table 4-9. Note that the recurrence rates for each of these patterns are based on data from the eleven years from 1985 to 1995. Under each of the tests, the episode begins with an exceedance in the Houston subregion, with either subsequent or simultaneous exceedances in the Southeast. The similarities in the exceedance patterns on the more severe days (11-15 July 1995) between the sup max test and the avrg max (90.0 ppb) test illustrate that this episode was composed of numerous high peak ozone concentrations, but these peaks were not isolated. That is, the majority of the subregions exhibiting high peak ozone concentrations also exhibited high average ozone concentrations, indicating that the areal coverage of high ozone concentrations during this episode was high.

Under any of the methods used for classifying an exceedance, the 1995 episode contains largely days that have unique ozone distribution patterns. This is similar to the recurrence rates observed for the ozone patterns during the 1991 episode. However, the number of subregions showing high ozone concentrations during the 1995 episode is considerably larger than for the 1991 episode, and is only rivaled by the 1988 episode.

The evolution of the subregions showing high ozone concentrations under the avrg max (90.0 ppb) test is illustrated in Figure 4-7. For the first few days of the episode, only the Houston subregion shows high ozone concentrations. This is followed on 10 July 1995 with high concentrations throughout the Southeast. The next two days show high concentrations across a broader area. By 13 July 1995, nearly the entire northern portion of the domain shows high ozone concentrations. The western extent of these high concentrations begins to subside on 14 July, and by 16 July all subregions are below the critical concentration. The episode ends with an isolated high ozone concentration in the Baltimore/Washington subregion. Table 4-9 indicates, however, that the average ozone concentrations in the Midwest and along the East Coast during the last three days of the episode were greater than 75.0 ppb.