Abstract

Synoptic conditions are known to strongly influence mesoscale flows and hence local ozone levels in the San Francisco Bay Area of California. Sets of individual days sharing certain combinations of synoptic features constitute “static” meteorological patterns (or regimes) that account for much of the variability in regional ozone levels. Upon labeling each day of the core Bay Area ozone season using a small number of synoptic regimes, the resulting daily sequence of static patterns indicates the time evolution of the synoptic system through a series of regimes realized for various durations. Further insight into ozone buildup processes can be gained by examining this sequence of static labels to identify “dynamic” meteorological patterns affecting local ozone levels. Transition probabilities between each pair of synoptic regimes are modeled using binomial statistics to determine transitions that are either energetically favored or disfavored to occur. The persistency of the meteorological regimes is additionally considered to complement the transition probabilities in forming a more complete statistical characterization of the synoptic evolution. The sequencing method allows identification of two scenarios under which exceedance of air quality standards occurs in the Bay Area.

1. Introduction

Air quality models (AQMs; Russell and Dennis 2000) are commonly used to study the formation and accumulation of urban air pollutants such as ozone, thus guiding control strategies that are effective in reducing their tropospheric concentrations. Simulations such as those performed by Sistla et al. (2001), however, require large amounts of resources and are generally restricted to analyzing a relatively small number of days of interest. But, because meteorological conditions between different periods of interest may vary considerably, different AQM scenarios may predict a wide range of ozone sensitivities to similar emissions reductions. Thus, to maximize the efficacy of photochemical modeling for regulatory purposes, comprehensive knowledge of local meteorology is a prerequisite to ensure that simulated conditions are representative and explore major meteorological regimes of influence (Kuebler et al. 2002).

Synoptic climatological analysis (Yarnal et al. 2001) is an approach that can be used to understand the effects of meteorology on air quality over extended observation periods. The most common approach is through the interpretation of weather maps to define and label days among a finite number of recurring synoptic conditions (Cheng 2001). The accuracy of the results from such studies, however, is limited by the degree of skill possessed by the analysis tool, and scrutiny of a large observation period may prove laborious. To overcome such limitations and reduce the subjectivity introduced by the user, quantitative models can discriminate between various meteorological conditions. Because air quality is largely affected by dispersion near the ground level, transport patterns can be used to determine days with similar wind field evolution. Moy et al. (1994) determine various regimes for local ozone production by grouping days exhibiting like airmass trajectories backward in time, while Schichtel and Husar (2001) use forward airmass trajectories to achieve the same goal. Other approaches apply statistical models to upper-atmospheric data. One common approach is the use of empirical orthogonal functions (EOFs; Lorenz 1956) to compare gridded weather map data (such as 850-hPa height) representing different days (Pryor et al. 1995). Cluster analysis (Everitt 1993) is typically applied to arrays of mesoscale meteorological observations to determine regimes for local ozone buildup; however, as demonstrated in Eder et al. (1994), such patterns often correspond to synoptic conditions. Cluster analysis is attractive for large study periods because this unsupervised method requires minimal user interaction and provides a consistent means of determining meteorological patterns.

In this study, we further refine the results of the cluster analysis described in Beaver and Palazoglu (2006) by focusing on dynamics at the synoptic time scale—transitions of the upper atmosphere occurring over multiple days. In this previous study, a novel form of cluster analysis was applied to hourly, ground-level wind field measurements from the San Francisco Bay Area in California (Fig. 1) to identify and label the times of occurrence for surface flow patterns affecting local ozone composition. By grouping days exhibiting similar diurnal cycles for the wind field, four distinct, recurring mesoscale wind patterns affecting regional ozone buildup processes differently were identified. The result of this cluster analysis is summarized in Fig. 2, showing the cluster assignments for each day from 1 June through 30 September 1996–2003.

Fig. 1.

Study region with locations of meteorological and air quality monitors. Contour lines are at 300, 600, and 900 m. Names, elevations, and subregion classifications for the stations are given in the legend. Note that the air quality monitors at Concord and San Martin are located in close proximity to meteorological monitors. These two stations are not shown explicitly but should be referenced under the meteorological stations bearing the same name.

Fig. 1.

Study region with locations of meteorological and air quality monitors. Contour lines are at 300, 600, and 900 m. Names, elevations, and subregion classifications for the stations are given in the legend. Note that the air quality monitors at Concord and San Martin are located in close proximity to meteorological monitors. These two stations are not shown explicitly but should be referenced under the meteorological stations bearing the same name.

Fig. 2.

Cluster membership for 1 Jun–30 Sep 1996–2003. The x axis represents time (discretized as entire days). The y axis position of an asterisk indicates a cluster assignment for that day; (from bottom to top) tick marks at 1–4 correspond to clusters 1–4, respectively. Each vertical line indicates a day exceeding the NAAQS for 8-h ozone for at least one Bay Area monitor.

Fig. 2.

Cluster membership for 1 Jun–30 Sep 1996–2003. The x axis represents time (discretized as entire days). The y axis position of an asterisk indicates a cluster assignment for that day; (from bottom to top) tick marks at 1–4 correspond to clusters 1–4, respectively. Each vertical line indicates a day exceeding the NAAQS for 8-h ozone for at least one Bay Area monitor.

Visual inspection of Fig. 2 indicates that the meteorological patterns persist for multiple consecutive days on each recurrence; such persistence is consistent with the identification of events at the synoptic time scale. Because each cluster pattern can readily be distinguished and explained by 500-hPa conditions averaged among its member days, it was concluded that upper-atmospheric, synoptic systems strongly influence mesoscale meteorology for the Bay Area. Differences in ozone levels between the various identified synoptic regimes are generally greater than variability in ozone levels within the synoptic regimes. Still, it is noted that Bay Area meteorology is complex and that ozone levels are not fully determined by prevailing synoptic conditions. This narrow air basin with intricate topography is influenced by a sea–land breeze cycle caused by the marine layer to the west, often with associated fog and other low-lying clouds; to the east, Central Valley conditions have the potential to block flows from channeling through the Bay Area. Under relatively infrequent conditions in which the synoptic influence is weak, seemingly similar synoptic motions may even result in vastly different local ozone responses. Overall, however, the synoptic influence on Bay Area ozone levels is strong. A description of the synoptic patterns detected by the cluster analysis will be deferred until section 2.

Breaking the entire ozone season into only four synoptic atmospheric regimes is quite coarse; however, the cluster analysis is useful because it reveals the major weather patterns defining the Bay Area’s synoptic ozone climatology. By investigating the physical nature of the clusters, synoptic features influencing Bay Area ozone buildup, which are on the average either present in or absent from the pool of days assigned to a given cluster, can be identified. Clearly, however, Bay Area air quality cannot be characterized fully by considering only the presence (or lack) of a small number of highly generalized synoptic features. To better elucidate the effects of the synoptic state on Bay Area air quality, it is necessary to determine a more specific set of synoptic regimes affecting local ozone levels, each realized for fewer days than the four coarse cluster patterns. This goal is accomplished not through the identification of a larger number of more finely resolved, static (single day) synoptic patterns (i.e., by forcing the clustering algorithm to yield a larger number of clusters), but rather by examining the sequence of cluster labels, which describes the synoptic evolution of the atmospheric system, to characterize dynamic (multiday) events affecting regional ozone levels.

The distinction between static patterns, indicating the presence of a particular synoptic feature on a given day, and dynamic patterns, describing the evolution of such synoptic features over time, is discussed by Comrie (1992), who applies a sequencing technique to labels produced from the manual classification of daily weather maps to explain regional ozone levels. Taking a more quantitative approach, Darby (2005) applies a similar sequencing technique to the output of a clustering algorithm used to identify flow regimes from hourly wind observations in the Houston, Texas, region. This analysis is performed for a sequence of labels describing boundary layer evolution at an hourly sample rate, resulting from the strong mesoscale influence on Houston air quality. Because Bay Area conditions are largely driven by synoptic meteorology, however, this study will consider sequences of daily cluster labels describing dynamics at the synoptic time scale—transitions of the upper atmosphere occurring over multiple days.

Several statistical tools are introduced and applied to the sequence of cluster labels observed in Fig. 2. Transitions between the clusters are taken to indicate dynamic events that are not captured by the static cluster patterns themselves. We provide a battery of statistical tests to determine which transitions are likely or unlikely to result from a given state, allowing for the inference of physical mechanisms driving the evolution from one synoptic atmospheric regime to the next. Several energetically favored transitions, that is, those occurring at relatively high frequencies, indicate the presence of dynamic trends that have important implications for Bay Area ozone levels. Additionally, the transition probability calculations can be used to identify certain sequences of cluster labels suggesting anomalous atmospheric activity; such instances typically denote not the physical presence of an unlikely atmospheric transition, but rather an inconsistency in the sequence of cluster labels, thus indicating a new type of event not captured by the static cluster patterns. The persistence of the synoptic states, as represented by the distribution of run lengths in the cluster labels, complements the transition probability statistics to form a more complete statistical characterization of the synoptic evolution as represented by a sequence of daily cluster labels.

2. Static cluster pattern descriptions

The four mesoscale surface flow types used to label the days as shown in Fig. 2 capture either predominately cyclonic or anticyclonic conditions. Clusters 2 and 3 capture cyclonic motions, while clusters 1 and 4 capture anticyclonic motions. Weather maps at the 500-hPa pressure level are given for a selected day from each cluster in Fig. 3 that exemplifies the cluster pattern.

Fig. 3.

The 500-hPa weather maps at 1800 UTC for a selected day from each cluster: 10 Jul 1999 (cluster 1, onshore high pressure at the onset of a 3-day exceedance period), 25 Jun 1999 (cluster 2, weaker trough), 24 Jul 1999 (cluster 3, deeper trough), and 25 Jun 2003 (cluster 4, offshore high pressure at the onset of a 3-day exceedance period). The Bay Area study region of Fig. 1 is highlighted.

Fig. 3.

The 500-hPa weather maps at 1800 UTC for a selected day from each cluster: 10 Jul 1999 (cluster 1, onshore high pressure at the onset of a 3-day exceedance period), 25 Jun 1999 (cluster 2, weaker trough), 24 Jul 1999 (cluster 3, deeper trough), and 25 Jun 2003 (cluster 4, offshore high pressure at the onset of a 3-day exceedance period). The Bay Area study region of Fig. 1 is highlighted.

Clusters 2 and 3 are associated with troughs positioned along the Pacific coastline and encompassing the Bay Area study region. Both of these clusters correspond to ventilated conditions in which the marine layer penetrates the Bay Area, channels through a gap in the Coast Range at the delta of the San Francisco Bay, and then flows into the Central Valley. The patterns are distinguished by the fact that cluster 3 indicates a deeper trough, producing marine layer penetration well into the Central Valley, whereas the ventilating effect of cluster 2 is more confined to the Bay Area. Both of these clusters have relatively low Bay Area ozone levels and are very unlikely to result in National Ambient Air Quality Standards (NAAQS) exceedance for ozone (days for which the regional, daily maximum 8-h ozone level exceeds 84 ppb).

Clusters 1 and 4 exhibit anticyclonic motions at the 500-hPa pressure level, affecting ground-level transport and dispersion, such that ozone compositions are elevated and highly variable relative to the ventilated clusters. Cluster 1 corresponds to a persistent cell of high pressure forming over the western United States, including California. This cluster exhibits a weakened marine layer flow that enters through the mouth of the bay but does not penetrate through the Bay Area and into the Central Valley, as for the ventilated regimes. Cluster 4 is associated with a passing offshore ridge of high pressure that causes a northerly shift in wind direction and reduced marine flow entering through the mouth of the bay. In addition to reduced marine ventilation relative to the cyclonic regimes, subsidence contributes to the elevated ozone levels observed under the anticyclonic regimes.

There are distinct ozone spatial distributions for both of the anticyclonic regimes resulting from differing sea-breeze cycles observed under the onshore and offshore high pressure conditions. Cluster 1 experiences a light westerly sea breeze for the inland, eastern portion of the study domain. Thus, cluster 1 typically experiences the highest ozone levels and a majority of its NAAQS exceedances in the Livermore Valley and East Bay; exceedance for cluster 1 in the Santa Clara Valley occurs less frequently. Cluster 4, on the other hand, lacks the westerly sea breeze that is present for cluster 1, and instead exhibits a northerly sea breeze into the Santa Clara Valley. Thus, cluster 4 has the most severe ozone levels in the Santa Clara Valley (at San Martin and/or Gilroy), though high-ozone levels can also occur in the Livermore Valley and occasionally in the East Bay. The onshore flow of cool marine air observed under the trough patterns (clusters 2 and 3) tends to inhibit sea-breeze development, limiting transport to the inland Bay Area valleys.

Approximately 13% of the days in either clusters 1 or 4 result in NAAQS exceedance for 8-h ozone. Thus, both of these clusters exhibit an increased potential for producing an NAAQS exceedance, however there still is important variability in ozone levels within each of these meteorological states that is not fully explained by the cluster patterns. Much of this variability within the anticyclonic states can likely be attributed to increased meteorological complexity due to mesoscale influences such as the sea-breeze cycle playing an increased role in the absence of synoptically driven channeling through the region. As will be demonstrated, however, additional synoptic sources of variability exist as well.

3. Transition probabilities and binomial statistics

First, the realization of a cluster is defined. A single realization of a given cluster occurs for each longest possible, continuous set of days bearing the same cluster label, as determined by inspection of the results of Fig. 2. The day immediately preceding some realization of cluster r either bears another cluster label sr, is unlabeled (because a small fraction of the days cannot be assigned to any cluster with reasonable confidence), or falls outside the study period (in the event that the realization includes the date 1 June for any year). Note that in the latter case, in which the realization includes 1 June, it is readily verified that a realization of the cluster has occurred; however, it is not possible to determine the run length associated with that specific realization because the preceding day (31 May) falls outside the observation period for which the cluster analysis is performed. Similarly, the day immediately following the realization of some cluster bears a different (or no) cluster label, unless the realization includes the edge date of 30 September.

A transition is a dynamic event lasting either 2 or 3 days. Moving forward in time (from left to right in Fig. 2), a transition occurs when the cluster label changes from r to s, with no intermediate days bearing a different (or no) label. A 2-day transition occurs when one day is assigned wholly to r and the next day wholly to s, whereas a 3-day transition occurs when there is an intermediate, transitional day doubly assigned to both clusters r and s. Such transitional days share properties of two clusters and are accordingly doubly labeled because they cannot be assigned to any single cluster with high confidence; no day is assigned to more than two clusters. The difference between the 2- and 3-day transitions is highlighted in Fig. 4. Regardless of their duration, transitions from cluster r to cluster s occur in some observable proportion, and it is of interest to characterize the relative frequencies of all such possible transitions. To ensure that the transition probabilities from a given cluster sum to unity, all of the days bearing no cluster label are lumped to form a (k + 1)th “cluster,” which is appended to the original set of k clusters. Note that the cluster run lengths are not considered in the transition probability calculations; for study regions exhibiting persistent meteorological conditions, the pool of cluster realizations, and thus the number of transitions to examine, may become small.

Fig. 4.

Diagram depicting 2- and 3-day transitions for a hypothetical two-cluster solution on a 13-day observation period. Note that day 11 is unlabeled and no transition from r to s occurs between days 10 and 12.

Fig. 4.

Diagram depicting 2- and 3-day transitions for a hypothetical two-cluster solution on a 13-day observation period. Note that day 11 is unlabeled and no transition from r to s occurs between days 10 and 12.

Given that a transition occurs from cluster r to cluster s, with rs, an estimate for the true transition probability prs can be calculated as the proportion of such transitions existing in the sequence of cluster labels. Let nrs be the number of transitions from state r to s, with elements nrr taken as 0 because they imply no transition. Also, Nr = Σsnrs, the total number of transitions occurring from state r to any other state:

 
formula

This definition of the transition probabilities ensures that Σsrs = 1; however, no such claim can be made for Σrrs because a different Nr is used to normalize each row. When viewed as a matrix, one should only consider the rows of rs, but not the columns.

Each transition probability prs can be assumed to follow a binomial distribution, because each transition can be viewed as the outcome of a binary decision: given that a transition occurs from cluster r, the transition is to cluster s with probability prs and to some other cluster with probability (1 − prs). Confidence bounds Crs corresponding to estimates rs can be calculated using the Wald method (Brown et al. 2001), where α represents the level of significance and zα/2 is the upper two-tailed confidence limit for a standard normal distribution using level of significance α:

 
formula

Using Wald statistics, the true value prs can be estimated to lie within the interval rs ± Crs with level of significance α. The Wald statistics are the most commonly used estimates for binomial variables, however they are flawed because of their potential for producing Crs > rs, indicating a negative lower confidence limit for a probability bounded on [0, 1] by definition. This problem becomes common for small rs and/or a small sample size Nr.

The Wilson statistics (Brown et al. 2001) provide an alternative approach to estimating prs. Estimate Wrs and confidence limit CWrs are intended for use with a smaller sample size Nr and are not as prone to producing unrealistic confidence bounds as the Wald statistics:

 
formula
 
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One disadvantage of the Wilson statistics is that ΣsWrs is not guaranteed to equal unity as with the Wald statistics.

Estimates for prs are used to determine transitions that are either favored or disfavored—those that occur more frequently or less frequently than would be expected by chance, respectively. As the null hypothesis, it is assumed that transitions occur independently of the originating state r. Therefore, the null hypotheses transition probability p0rs should be proportional to the total number of realizations of cluster s. Because of the forward nature of the transition statistics, the number of state realizations for each cluster cannot be computed from nrs but must be counted to avoid edge effects when computing the value of p0rs:

 
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The confidence intervals for prs calculated using both the Wald and Wilson statistics are compared to p0rs to determine if the null hypothesis is rejected, indicating that the number of transitions nrs is significantly different than would be expected by chance. Pairs of clusters for which rsCrs > p0rs or WrsCWrs > p0rs indicate transitions that are favored, or occur more frequently than by chance, while pairs of clusters for which p0rs exceeds the upper confidence bound for either the corresponding Wald or Wilson statistic have disfavored transitions. The Wilson statistics tend to be more conservative than the Wald statistics, less often indicating trends of borderline significance.

Assuming that the null hypothesis is true, that state transition probabilities are equal to p0rs, the likelihood of observing nrs can be computed. Here P(nrs|p0rs, Nr) is the binomial probability of observing nrs, given Nr total transitions from state r and that the null hypothesis is true,

 
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Relatively small values for P(nrs|p0rs, Nr) indicate that the null hypothesis is not likely, and that the transition from cluster r to s occurs more or less frequently than would be expected by chance. This third measure is used in conjunction with the formal hypothesis testing using the Wald and Wilson statistics to form a battery of three statistical methods that can determine cluster transitions that are favored or disfavored.

4. Cluster persistency

As stated previously, the transition probability calculations do not consider the run lengths for the cluster realizations, and thus do not completely characterize the sequence of cluster labels or the synoptic-scale dynamics they imply. Cluster persistency is characterized by the distribution of run lengths, in days, for the realizations of a specific cluster. A histogram is used to indicate the number of runs for each cluster persisting for exactly l days, where l is a positive integer.

Persistence can be used to gauge the stability of identified atmospheric states—stable regimes are highly persistent and capable of lasting for long periods of time, while regimes of transient nature are less persistent. The persistency calculations are also useful for determining unusual sequences of cluster labels, which may be taken to indicate inconsistencies in the cluster solution, potentially indicating new types of events not captured in the set of cluster labels themselves. For example, the realization of a very long duration for a typically transient cluster may indicate the occurrence of some new type of weather pattern. No formal hypothesis testing is applied to the persistency calculations; rather, unusual events are detected as cluster realizations falling outside the typical ranges for the tabulated distributions of persistency.

5. Application of methods

The sequence of daily cluster labels shown in Fig. 2 is first examined to determine all realizations for each cluster. There are 65, 57, 66, and 21 realizations appearing as multiday runs for clusters 1 through 4, respectively. Additionally, 22 days cannot be assigned to any cluster with reasonable confidence and remain unlabeled. This set of unlabeled days is considered cluster 5 for the transition probability calculations—there are 16 lone days and 3 pairs of consecutive days, for a total of 19 realizations. Thus, the original sequence of cluster labels for 976 days (122 days for 8 yr) is represented by 228 individual cluster realizations.

Using the above numbers of state realizations, null hypothesis transition probabilities are calculated using Eq. (5). The results are shown in Table 1. For example, there are 57 + 66 + 21 + 19 = 163 realizations of states other than that of cluster 1. Therefore, if the null hypothesis is true, one should expect a fraction 57/163 (or 0.35) of the transitions from the state of cluster 1 to occur to cluster 2.

Table 1.

Null hypothesis transition probabilities p0rs.

Null hypothesis transition probabilities p0rs.
Null hypothesis transition probabilities p0rs.

The observed number of forward transitions between each pair of states is shown in Table 2. Note that because the last day (or two) of the study period, 30 September (and also 29 September for 2001 only), is unlabeled for each of the 8 yr in the study period, and the total numbers of forward transitions for clusters 1 through 4 (i.e., the sums across the rows of Table 2) are equal to their numbers of realizations; this will not, however, be true for the general case in which the last day of the ozone season bears a meaningful cluster label. Based on these numbers of forward transitions, the transition probabilities and corresponding confidence bounds are estimated using α = 0.05. Confidence intervals using Wald statistics (rs ± Crs) are given in Table 3, while those for Wilson statistics (Wrs ± CWrs) are shown in Table 4. Transitions for which p0rs is not contained within the confidence bound for a given statistic are significant (boldfaced). These transitions occur either more or less frequently than would be expected by chance, suggesting the existence of physical mechanisms that drive or inhibit such synoptic transitions from occurring.

Table 2.

Number of forward transitions between each pair of states.

Number of forward transitions between each pair of states.
Number of forward transitions between each pair of states.
Table 3.

Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wald statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.

Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wald statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.
Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wald statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.
Table 4.

Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wilson statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.

Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wilson statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.
Estimates and α = 0.05 confidence limits (in parentheses) for transition probabilities using Wilson statistics. Statistically significant transitions, as determined by comparison with Table 1, are shown in boldface.

Both the Wald and Wilson statistics are in agreement that transitions of cluster 1 → cluster 3 and cluster 4 → cluster 1 are favored, whereas cluster 4 → cluster 2 and cluster 4 → cluster 3 are disfavored. The Wald statistics additionally indicate that transitions of cluster 1 → cluster 4, cluster 2 → cluster 5, and cluster 3 → cluster 4 are disfavored, whereas the Wilson statistics do not (although p0rs values are very close to the Wilson confidence bounds for these transitions). Note that the Wald statistics indicate a negative lower confidence bound for the cluster 2 → cluster 5 transition, which is indicated as disfavored; the Wilson statistics are less prone to this problem and do not indicate this transition as statistically significant.

Next, the likelihoods of observing the proportions of state transitions, given the null hypothesis is true, are calculated using Eq. (6). Results in Table 5 generally corroborate the Wald and Wilson statistics. Relative frequencies for transitions of cluster 1 → cluster 3, cluster 4 → cluster 1, and cluster 4 → cluster 2 are likely to occur by chance at lower than the 0.001 level, while the cluster 4 → cluster 3 transition likelihood is near the 0.01 level. Observed proportions for these state transitions are highly unlikely to occur by chance, in agreement with both the Wald and Wilson statistics. Additionally, the cluster 1 → cluster 4 transition is likely at the 0.02 level, suggesting this transition is disfavored as suggested by the Wald, but not Wilson, statistics. The transitions of cluster 2 → cluster 5 and cluster 3 → cluster 4, which are indicated as disfavored by the Wald statistics only, are moderately likely (0.03 and 0.04, respectively), suggesting that these transitions may be randomly driven and are neither favored nor disfavored.

Table 5.

Likelihood of observing proportions of state transitions given the null hypothesis transition probabilities of Table 1 are true.

Likelihood of observing proportions of state transitions given the null hypothesis transition probabilities of Table 1 are true.
Likelihood of observing proportions of state transitions given the null hypothesis transition probabilities of Table 1 are true.

The persistency calculations are shown in Fig. 5. Cluster 1 represents perhaps the most persistent meteorological regime, usually persisting for 3–9 days and occasionally as long as 2 weeks. Clusters 2 and 3, representing the ventilated regimes, generally persist for 2–6 days, however these clusters are occasionally realized for durations of up to 3 weeks and have much longer “tails” in their distributions than that of cluster 1. Cluster 4 is clearly the least persistent cluster and is usually present for only 3 or 4 days on each realization.

Fig. 5.

Histograms showing distributions of cluster run lengths.

Fig. 5.

Histograms showing distributions of cluster run lengths.

6. Physical interpretation

The transition from clusters 4 to 1 is heavily favored, indicating that some physical mechanism drives this progression of states. While this transition occurs only 14 times in the 8-yr study period, it has important implications for Bay Area air quality. Though days from clusters 1 and 4 experience poorer air quality than the ventilated clusters, days near the cluster 4 → cluster 1 transition points have some of the highest ozone levels in the study period. While only 13% of the days from either cluster 1 or 4 result in NAAQS exceedance for 8-h ozone, half of the 14 cluster 4 → cluster 1 transitions result in such exceedances. All of the cluster 4 → cluster 1 transition exceedances are multiple days in duration, accounting for over one-third of the 20 total multiday exceedances in the study period.

Each occurrence of this transition is of the 3-day type, with an intermediate day assigned to both clusters 1 and 4. Table 6 lists the dates of occurrence for each cluster 4 → cluster 1 transition and indicates whether or not an NAAQS exceedance results; when an exceedance does occur, it is always multiple days in duration. Interestingly, ozone levels at most locations are usually higher on these doubly assigned, transitional days (those listed in Table 6) than their immediately preceding (assigned solely to cluster 4) and following (assigned solely to cluster 1) days. This effect is illustrated in Fig. 6, which shows the changes in daily maximum ozone level at each monitoring station between pairs of consecutive days during the 3-day cluster 4 → cluster 1 transition periods. Between the last day assigned to cluster 4 and the transitional day between clusters 4 and 1, ozone levels increase significantly at nearly all monitoring stations. The increases are largest at San Martin and Livermore, where ozone levels are typically the highest and NAAQS exceedances are most likely to occur. On the next day, ozone levels tend to decrease at most stations (but may still remain above the exceedance threshold) as the synoptic state transitions into conditions typical of cluster 1—a cell of high pressure forming over northern California and other western states. Note, however, that ozone levels at Livermore decrease less than for the other stations (or sometimes even increase) as cluster 1 is fully realized and produces anticyclonic flow in the Central Valley, blocking channeling through the Bay Area and diverting flow of a polluted airmass to the Livermore Valley. Los Gatos also is likely to have increasing ozone levels into the realization of cluster 1 due to carryover effects as transport from the South Bay into the Santa Clara Valley weakens.

Table 6.

Dates of occurrence for 14 cluster 4 → cluster 1 transitions, listed by transitional days in centers of 3-day transition periods. Comment indicates presence of multiday NAAQS exceedance for 8-h ozone during the transition period, otherwise no exceedance occurs. Note that exceedances occur the day following the 3-day transition period for transitions 3 and 9 (which may be difficult to see in Fig. 2); however, no exceedance is experienced during these transition periods. Two transitions denoted as outliers are discussed explicitly in the text.

Dates of occurrence for 14 cluster 4 → cluster 1 transitions, listed by transitional days in centers of 3-day transition periods. Comment indicates presence of multiday NAAQS exceedance for 8-h ozone during the transition period, otherwise no exceedance occurs. Note that exceedances occur the day following the 3-day transition period for transitions 3 and 9 (which may be difficult to see in Fig. 2); however, no exceedance is experienced during these transition periods. Two transitions denoted as outliers are discussed explicitly in the text.
Dates of occurrence for 14 cluster 4 → cluster 1 transitions, listed by transitional days in centers of 3-day transition periods. Comment indicates presence of multiday NAAQS exceedance for 8-h ozone during the transition period, otherwise no exceedance occurs. Note that exceedances occur the day following the 3-day transition period for transitions 3 and 9 (which may be difficult to see in Fig. 2); however, no exceedance is experienced during these transition periods. Two transitions denoted as outliers are discussed explicitly in the text.
Fig. 6.

Box plots showing change in daily maximum ozone composition at 22 monitoring locations. (top) Change in ozone level between last day of cluster 4 and the following transitional day into cluster 1, and (bottom) change between the transitional day and the next day assigned to cluster 1. Horizontal lines on boxes indicate lower quartile, median, and upper quartile, while the whiskers contain the remaining data except for several extreme values plotted individually using circles (6 Sep 1996 only) or plus signs.

Fig. 6.

Box plots showing change in daily maximum ozone composition at 22 monitoring locations. (top) Change in ozone level between last day of cluster 4 and the following transitional day into cluster 1, and (bottom) change between the transitional day and the next day assigned to cluster 1. Horizontal lines on boxes indicate lower quartile, median, and upper quartile, while the whiskers contain the remaining data except for several extreme values plotted individually using circles (6 Sep 1996 only) or plus signs.

In general, the cluster 4 → cluster 1 transition can be described as producing the highest Bay Area ozone levels, typically lasting for several days but peaking on the transitional day, with the location of daily maximum ozone level shifting from the Santa Clara Valley to the Livermore Valley. Not all of the 14 cluster 4 → cluster 1 transitions follow this generalization, however, and a notable outlier is the transition occurring on 6 September 1996. Between 5 September (assigned solely to cluster 4) and 6 September (doubly assigned), ozone levels increase as expected, with especially large increases in the Santa Clara Valley at Gilroy (16 ppb increase) and San Martin (20 ppb increase). Between 6 and 7 September (assigned solely to cluster 1), ozone levels exhibit a dramatic increase at all stations (shown in bottom of Fig. 6), instead of decreasing as would be expected. Despite their massive increases, however, ozone levels remain just below the exceedance threshold at Livermore and Concord, reporting 81 and 82 ppb, respectively. Ozone levels continue to build through the next day, with exceedances occurring not only at Livermore (88 ppb) but also at Los Gatos (89 ppb) on 8 September, and then decrease by a regional average of 30 ppb in a single day to provide improved air quality on 9 September. The atypical synoptic evolution associated with this outlier cluster 4 → cluster 1 transition will be discussed later in this section.

The 14 occurrences of the cluster 4 → cluster 1 transition share similar mesoscale airflows, typically associated with a shift in the surface wind direction from northerly to westerly over the 3-day transition period. Realizations of cluster 4 are typically preceded by a high pressure cell forming over the Pacific Ocean, far west of the continent, during conditions in which a trough is present along the Pacific coastline (i.e., one of the ventilated clusters 2 or 3). The offshore high pressure center migrates toward the continent, displacing the trough inland and possibly pinching off a cell of low pressure over the western United States. Cluster 4 is realized when the Bay Area is caught between these cells and experiences northerly upper-atmospheric flow. Because both the offshore high pressure and onshore low pressure cells are thermodynamically unstable, cluster 4 is the least persistent cluster and represents a transient synoptic state, almost always transitioning to cluster 1 after being realized for only a few days. Cluster 1 represents conditions with weak, westerly marine flow into the Bay Area, and the transitional days listed in Table 6 experience ground-level wind directions that are intermediate of clusters 4 and 1 with low wind speeds.

This shift in wind direction is evidenced in Fig. 7, showing time-averaged wind fields for 1200–1600 Pacific standard time (PST), averaged among the last days fully assigned to cluster 4 (Fig. 7a), the doubly assigned transitional days listed in Table 6 (Fig. 7b), and the following days fully assigned to cluster 1 (Fig. 7c). The precursor response to the shift in the flow direction is illustrated in Fig. 8, showing hourly time series for NO level at two stations for the 14 cluster 4 → cluster 1 three-day transition periods. Increased overnight carryover of NO is observed leading into the transitional day at the South Bay monitors in Fremont and San Jose, perhaps explaining the severe ozone levels observed in the downwind Santa Clara Valley during the afternoon hours of the following day. In fact, most of the NAAQS exceedance days in cluster 4 are actually transitional days assigned to both clusters 4 and 1; while cluster 4 has elevated ozone levels relative to the ventilated states of clusters 2 or 3, ozone levels do not increase beyond the exceedance threshold until near the transition to cluster 1. Thus, days assigned to cluster 4 but preceding the transition to cluster 1 generally have moderate air quality; however, the northerly shift in Bay Area winds associated with cluster 4 gives warning that a prolonged period of severe ozone levels will likely ensue within several days.

Fig. 7.

The 1200–1600 PST time-averaged wind field, averaged among groups of 14 days from the cluster 4 → cluster 1 transition: (a) last days fully assigned to cluster 4, (b) doubly assigned transitional days, and (c) first days fully assigned to cluster 1.

Fig. 7.

The 1200–1600 PST time-averaged wind field, averaged among groups of 14 days from the cluster 4 → cluster 1 transition: (a) last days fully assigned to cluster 4, (b) doubly assigned transitional days, and (c) first days fully assigned to cluster 1.

Fig. 8.

Time series for 1-h [NO] (ppb) at (a) Fremont and (b) San Jose, respectively, for 14 cluster 4 → cluster 1 three-day transition periods and (c) mean trajectories for 1-h [NO] at Fremont (diamonds) and San Jose (circles); each data point is the average among the 14 observations at each hour for each station.

Fig. 8.

Time series for 1-h [NO] (ppb) at (a) Fremont and (b) San Jose, respectively, for 14 cluster 4 → cluster 1 three-day transition periods and (c) mean trajectories for 1-h [NO] at Fremont (diamonds) and San Jose (circles); each data point is the average among the 14 observations at each hour for each station.

The evolution of the synoptic meteorology associated with the cluster 4 → cluster 1 transition is demonstrated in Fig. 9 for the transition occurring on 9 August 2002. [Weather maps are obtained from National Centers for Environmental Prediction (NCEP) reanalysis data provided by the National Oceanic and Atmospheric Administration (NOAA)/Office of Atmospheric Research (OAR)/Earth Systems Research Laboratory (ESRL)/Physical Sciences Division (PSD), Boulder, Colorado; information is available online at http://www.cdc.noaa.gov/.] On 5 August, cluster 2 is realized and a trough is present over the Pacific coast. A large pocket of high pressure is present north of the Hawaiian Islands; however, at this point the trough buffers the Bay Area from its effects. Cluster 4 is first realized on 6 August (not shown), when the offshore high pressure has migrated sufficiently close to the Pacific coast to affect mesoscale conditions in the Bay Area. By 8 August the trough has been displaced inland and a low pressure cell has been pinched off; both the offshore high pressure and onshore low pressure contribute to northerly upper atmospheric flow over the Bay Area associated with cluster 4. The transition to cluster 1 occurs on 9 August (not shown), and by 10 August a typical cluster-1-type high pressure center over the southwestern United States is present, in addition to residual offshore high pressure. The wide, east–west band of high pressure positioned over the Bay Area is typical of cluster 4 → cluster 1 conditions resulting in multiday exceedance periods. By the next day, the offshore high pressure cell has dissipated and onshore high pressure (i.e., cluster 1) persists for over a week until yet another trough prevails.

Fig. 9.

The 500-hPa weather maps depicting a typical cluster 4 → cluster 1 transition occurring on 9 Aug 2002. Weather maps are shown at 1800 UTC (a) 5, (b) 8, and (c) 10 Aug. The Bay Area study region of Fig. 1 is highlighted.

Fig. 9.

The 500-hPa weather maps depicting a typical cluster 4 → cluster 1 transition occurring on 9 Aug 2002. Weather maps are shown at 1800 UTC (a) 5, (b) 8, and (c) 10 Aug. The Bay Area study region of Fig. 1 is highlighted.

There is of course significant variability among the 14 different cluster 4 → cluster 1 transitions occurring in the study period, however the recurring pattern of offshore high pressure displacing a coastal low pressure system holds for all cases. The cluster 4 → cluster 1 transitions resulting in multiday exceedances (as indicated in Table 6) tend to exhibit a wide, east–west band of high pressure linking the onshore and offshore high pressure centers (as with 10 August 2002, shown in Fig. 9). The remaining cluster 4 → cluster 1 transitions do not result in exceedances. In these cases, the offshore high pressure cell dissipates rapidly and is no longer present by the time that the onshore high pressure center has developed.

A slightly different trajectory than the above example is realized for the previously discussed outlier cluster 4 → cluster 1 transition occurring on 6 September 1996, as depicted in Fig. 10. On 3 September, the day before cluster 4 is realized, no cluster label is assigned—a low pressure cell exists along the coast well north of the Bay Area (as opposed to the troughs typical of clusters 2 or 3; hence there is no cluster label). Unlike the typical cluster 4 → cluster 1 transitions involving an offshore high pressure center moving onshore, this outlier cluster 4 → cluster 1 transition involves a third high pressure cell of tropical origin expanding northward, as observed on 6 September (the transitional day). By 8 September the tropical high pressure has formed a slight ridge along the Pacific Coast, triggering an exceedance in Los Gatos, in addition to driving elevated ozone levels in the usual Santa Clara Valley and Livermore Valley locations. The cluster 4 → cluster 1 transition occurring on 21 September 2003 is similar to the 6 September 1996 outlier; the northward expansion of tropical high pressure originating from over Mexico is noted. Again, exceedances result in Los Gatos in addition to Livermore and San Martin. These two outlier cluster 4 → cluster 1 transitions are distinguished by the fact that cluster 4 is not preceded by a ventilated state. For these two outliers, cluster 4 is immediately preceded by an unlabeled day, which is itself preceded by anticyclonic conditions. The 21 September 2003 outlier is additionally distinguished by the persistence of cluster 4, lasting for an unusually long 6 days before transitioning to cluster 1. Thus, these unusual sequences of cluster labels indicate modified cluster 4 → cluster 1 transitions in which a different type of synoptic activity is triggering exceedances at locations including Los Gatos.

Fig. 10.

The 500-hPa weather maps depicting an atypical cluster 4 → cluster 1 transition occurring on 6 Sep 1996. Weather maps are shown for 1800 UTC (a) 3, (b) 6, and (c) 8 Sep. The Bay Area study region of Fig. 1 is highlighted.

Fig. 10.

The 500-hPa weather maps depicting an atypical cluster 4 → cluster 1 transition occurring on 6 Sep 1996. Weather maps are shown for 1800 UTC (a) 3, (b) 6, and (c) 8 Sep. The Bay Area study region of Fig. 1 is highlighted.

Because the cluster 4 → cluster 1 transition is so heavily favored, it is logical that the transition probability statistics indicate cluster 4 → cluster 2 and cluster 4 → cluster 3 as being disfavored. Cluster 4 is realized as offshore high pressure migrates toward California, producing northerly flow that allows temperature and pressure to build over land due to the lack of westerly marine layer intrusion. Thus, cluster-4-type weather systems produce conditions conducive to the formation of cluster-1-type patterns. It is uncommon for a low pressure system (i.e., clusters 2 or 3) of sufficient strength to appear during the short duration in which cluster 4 is present to displace the offshore anticyclonic system and prevent cluster 1 from being realized. Nonetheless, there are three transitions occurring from cluster 4 to a ventilated state during the study period (3 July 1997, 20 September 2000, and 11 June 2002). In each case, a deep polar low expands southward, preventing the cluster-4-type offshore high pressure cell from taking its usual trajectory toward the continent, and it is instead forced to migrate north. Figure 11 provides an example using the 20 September 2000 occurrence. On 19 September (assigned to cluster 4), a typical cluster-4-type offshore high pressure system dominates Bay Area conditions. A deep polar low is present over the Great Lakes in Canada but does not yet affect the Bay Area. By 20 September (assigned to cluster 3), the polar low has moved south, preventing the usual shoreward trajectory of the offshore high. On 21 September (assigned to cluster 3), the offshore high has been forced north toward the Gulf of Alaska as the polar low expands to the south and west. These two features form an unstable trough that only persists for 3 days before being displaced by a cluster-1-type high pressure system. For the other two cases (3 July 1997 and 11 June 2002), the cluster 4 offshore highs are displaced by lows originating from the Gulf of Alaska and moving south along the Pacific coast, forming deep, stable troughs that persist for over a week.

Fig. 11.

The 500-hPa weather maps depicting the transition from cluster 4 to a ventilated state (cluster 3) occurring on 20 Sep 2000. Weather maps are shown at 1800 UTC (a) 19, (b) 20, and (c) 21 Sep. The Bay Area study region of Fig. 1 is highlighted.

Fig. 11.

The 500-hPa weather maps depicting the transition from cluster 4 to a ventilated state (cluster 3) occurring on 20 Sep 2000. Weather maps are shown at 1800 UTC (a) 19, (b) 20, and (c) 21 Sep. The Bay Area study region of Fig. 1 is highlighted.

The statistics also suggest that the cluster 1 → cluster 4 transition may be disfavored, though they are in disagreement for this transition. Taking the conceptual model of cluster 1 being onshore high pressure and cluster 4 being offshore high pressure, the cluster 1 → cluster 4 transition violates the natural west-to-east progression of Pacific weather systems; this sequence would seem to imply a high pressure cell forming over land and moving offshore in an anomalous westward trajectory. The cluster 1 → cluster 4 transition in fact occurs 3 times (26 September 1997, 25 September 1999, and 12 September 2000); however, the above conceptual model, which is essentially the reverse of the cluster 4 → cluster 1 transition, breaks down. Instead, on each occurrence of the cluster 1 → cluster 4 transition an offshore low pressure cell is present to the south of the study domain, as shown in Fig. 12 for the days preceding the transitions. Thus, the cluster 1 → cluster 4 sequence of cluster labels actually captures a new type of weather pattern that is not accounted for in the set of four static cluster patterns describing various ridge and trough conditions, which dominate Bay Area summers. The latter two realizations of cluster 4 upon transition from cluster 1 are more persistent than normal, further evidencing that a new type of event is coded in these sequences of cluster labels. Ozone responses during the cluster 1 → cluster 4 transitions exhibit dramatic variability due to increased mesoscale influence during these periods of weak synoptic forcing. However, ozone levels remain below the exceedance threshold for all cases.

Fig. 12.

The 500-hPa weather maps for days preceding the three occurrences of the cluster 1 → cluster 4 transition. The Bay Area study region of Fig. 1 is highlighted.

Fig. 12.

The 500-hPa weather maps for days preceding the three occurrences of the cluster 1 → cluster 4 transition. The Bay Area study region of Fig. 1 is highlighted.

A final significant transition is the favored cluster 1 → cluster 3 sequence of cluster labels. Because the cluster 1 → cluster 4 transition is rare, the anticyclonic cluster 1 is generally observed to make a transition into one of the ventilated states, clusters 2 or 3. Cluster 3 represents a deeper trough pattern than cluster 2, suggesting that a low pressure system of sufficient strength is required to displace the cluster-1-type high pressure cell once it forms over California’s Central Valley. The fact that the cluster 1 → cluster 3 transition is favored over the cluster 1 → cluster 2 transition explains the persistency of cluster 1.This cluster is very persistent because it is stable until a sufficiently deep trough (cluster 3) moves in along the California coast. Large decreases in ozone levels at all inland regions occur immediately upon the transition from cluster 1 to cluster 3. This transition often provides overnight relief from intensifying episodes of poor air quality. An example is the 3-day exceedance period (occurring from 10 to 12 July 1999), in which regional, daily maximum 8-h ozone levels (obtained at Livermore and/or Concord, with similar levels at each monitor) reach 92, 116, and 122 ppb, respectively, for these 3 days assigned to cluster 1. The next day, 13 July, is fully assigned to cluster 3 and maximum regional ozone level drops sharply to 59 ppb as a polar air mass pushes south to form a coastal trough. Figure 3 provides weather maps for 10 July, at the onset of the 3-day exceedance period, and 24 July, indicating the cluster-3-type trough persisting for over 2 weeks after terminating the episodic conditions.

The Wald statistics alone indicate the cluster 3 → cluster 4 transition as being disfavored; however, the other tests in the statistical battery fail to confirm this. Thus, no significant transitions occur from either clusters 2 or 3. These ventilated states favor the development of no other states, and the trough patterns persist until being displaced by high pressure introduced by developing synoptic conditions in proximal regions of the globe. On several realizations, the ventilated states are noted to persist for over 2 weeks, as noted by the large tails in their run length distributions (Fig. 5). It may be possible that these two clusters could be dissected to form a larger set of more finely resolved cyclonic patterns, thereby providing insight into the synoptic evolution associated with the onset of anticyclonic conditions. Such detailed analysis of the cyclonic regimes has not, however, been considered in this study, which examines only four coarse synoptic features. Traditional meteorological analysis methods may be useful for identifying important transitions from cyclonic to anticyclonic conditions.

7. Conclusions

Transition probabilities are useful for characterizing sequences of cluster labels describing the evolution of the atmospheric system to provide increased understanding of synoptic effects on Bay Area air quality. Three statistical quantities assuming a binomial distribution form a functional battery for determining statistically significant atmospheric transitions. Binomial statistics provide a simple framework for modeling the state transitions; however, treating the various transitions as independent is not technically correct, because in reality all of the transition probabilities are interrelated. Such interdependencies, though, become obvious when interpreting the results of the hypothesis testing. For example, because the transition from offshore high pressure to onshore high pressure is so heavily favored, it is logical that the transitions from offshore high pressure to the cyclonic states are disfavored. Thus, despite the theoretically inexact nature of the binomial statistics, the results of this study clearly demonstrate their utility for modeling the interrelated transitions among a number of synoptic regimes. Because the binomial statistics consider only transitions between different clusters, the persistency calculations provide a natural complement to statistically characterize the sets of consecutive days spent within each cluster.

The sequence analysis indicates two scenarios under which NAAQS exceedances for ozone generally occur in the Bay Area. The first is the presence of a persistent cell of high pressure over California. Such onshore high pressure conditions tend to persist until adequate marine ventilation results from the intrusion of deep cyclonic systems. The onshore high pressure regime only triggers exceedances on 13% of the days on which it is realized. Because of both its high frequency of realization and tendency to persist for long durations, however, the onshore high pressure regime accounts for the bulk of Bay Area ozone exceedances. The second scenario under which Bay Area ozone exceedances occur is the transition from offshore to onshore high pressure. This regime occurs infrequently, typically near the ends of the ozone season; however it has an approximately 50% probability to trigger a multiday exceedance when it does occur. The northerly shift in winds associated with the onset of offshore anticyclonic motions rarely allows ozone levels to increase to the NAAQS exceedance level; such northerly flows, however, provide warning that a severe and persistent ozone episode will likely ensue within several days unless a deep polar low pushes south to displace the offshore high.

While both scenarios favoring NAAQS ozone exceedances involve anticyclonic conditions, it is noted that the trough patterns tend to inhibit ozone buildup processes. These trough patterns do not favor the development of any future synoptic states, and their persistence times are somewhat variable. Thus, while the cyclonic regimes are noted to suppress ozone exceedances, eventually a transition to an anticyclonic regime favoring reduced air quality will occur unless the end of the ozone season is reached first.

Acknowledgments

Funding provided by the California Air Resources Board and the Central California Ozone Study is gratefully acknowledged.

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Footnotes

Corresponding author address: Ahmet Palazoglu, Department of Chemical Engineering and Materials Science, University of California, Davis, One Shields Avenue, Davis, CA 95616. Email: anpalazoglu@ucdavis.edu