Air quality monitoring networks are established to obtain objective, reliable, and comparable information on the air quality of a specific area, and they serve the purposes of supporting measures to reduce impacts on human health and the natural environment, monitoring specific sources, and documenting air quality trends over time. Typically, the site location of an air quality monitoring network may be determined in response to regulations enforced by government-regulated agencies (e.g. EEA, 1997; US-EPA, 2008) and requires at least some a priori knowledge of the expected concentrations and concentration gradients of the pollutants of interest. The latter are highly dependent on the spatial and temporal distribution and magnitude of the emission sources, the physical and chemical properties of the emitted substance, and atmospheric conditions. The extent to which stations are accessible and the availability of electrical power are additional considerations in monitoring network design. However, recommendations regarding the optimum location and number of monitoring stations may also be achieved by the scientific analysis of existing data. For example, statistical methods making use of existing data have been used to recommend the number and location of monitoring stations required in a network (e.g. Lindley, 1956; Rhoades, 1973; Husain and Khan, 1983; Caselton and Zidek, 1984). Analytical tools such as Gaussian and Eulerian deterministic dispersion models may also be used to identify possible site locations (e.g. Bauldauf et al., 2002; Mazzeo and Venegas, 2008; Mofarrah and Husain, 2009; Zheng et al., 2011). More recently, the spatial distribution of measured pollutants combined with geostatistical modelling has been used to analyse station data (e.g. Cocheo et al., 2008; Lozano et al., 2009; Ferradás et al., 2010; Zhuang and Liu, 2011).

Cluster analysis is a good example of an analysis approach which assumes, like many statistical methods, that the data analysed contain a certain degree of redundant information, which in turn may be used to describe degrees of similarity or dissimilarity between data records from those stations. Typically applied to large and complex air quality databases to identify spatial patterns based on a metric describing the degree of (dis)similarity between data time series from different stations, cluster analysis (Everitt, et al., 2011) may be used for source identification and network station density optimization, with a minimum loss of information (Munn, 1981). Hierarchical clustering is a well-established associativity analysis methodology used to determine the inherent or natural groupings of objects and/or to provide a summarization of data into groups (Johnson and Wicherrn, 2007). The theoretical basis of hierarchical clustering has the advantage of making no assumptions regarding the mutual independence of samples and does not require examining all clustering possibilities. The similarity among members is established by a distance metric or function, which is used to create a similarity matrix in which data are cross-compared using the metric. This is followed by operations on the similarity matrix which group data according to their degree of (dis)similarity with respect to that metric. Many studies have aimed to quantify the spatial similarities among monitoring sites in terms of concentration levels and time variation by applying, respectively, the Euclidean distance and correlation coefficient as similarity metrics. Studies such as Lavecchia et al. (1996), Gabusi and Volta (2005), Gramsh et al. (2006), Lu et al. (2006), and Giri et al. (2007) applied these metrics for analysing the spatial and temporal distribution of air contaminants in cities or regions and present possible links between those concentrations with specific sources, topography, or meteorological patterns. The majority of these studies focused on ozone (O3) and particulate matter (PM). Saksena et al. (2003) applied the methodology to nitrogen dioxide (NO2) and sulfur dioxide (SO2), Ionescu et al. (2000) to NO2, Hopke et al. (1976) and McGregor (1996) to SO2, and Ignaccolo et al. (2008) to PM10, NO2, and O3. Cluster analysis has also been suggested for monitoring network optimization, including station redundancy analysis in studies such as Ortuño et al. (2005) for CO, Jaimes et al. (2005) and Ibarra-Berastegi et al. (2010) for SO2, Omar et al. (2005) for aerosol optical properties, Pires et al. (2008) for O3 and PM, and Iizuka et al. (2014) for nitrogen oxides (NOx), photochemical oxidant (Ox), non-methane hydrocarbons (NMHC), and PM. In this past work, cluster analysis is usually applied to a small number of stations (5 to 70) in different locations around the globe. Solazzo and Galmarini (2015) applied cluster analysis data showing that cluster analysis can potentially accommodate different sampling technologies and could be applied for large areas without the need of prior knowledge of the study area. Note that the data were pre-filtered by iterative moving averages (Kolmogorov–Zurbenko (KZ) filtering; Zurbenko, 1986) to assess the similarity of the spectral components of the hourly time series, independent of station location or monitoring technology employed, without a requirement of prior knowledge of the study area. Their analysis investigated the extent to which concentration time series similarities between the air quality monitoring stations were defined by areas with specific chemical regimes and/or predominant air masses versus by country borders and/or monitoring network jurisdiction. The latter were identified as resulting from differences in monitoring methodology, reducing comparability of the data across those borders and jurisdictions.

Monitoring of air quality within and downwind of the oil sands region is a key concern with the provincial and federal governments of Canada. In order to better quantify emissions, downwind chemical transformation, and downwind fate of emitted chemicals from this region, the governments of Canada and Alberta set up the Joint Oil Sands Monitoring (JOSM) Plan to “improve, consolidate and integrate the existing disparate monitoring arrangements into a single, transparent government-led approach with a strong scientific base” (JOSM, 2016). A key part of this overall framework was to develop methodologies to assess the consistency and spatial representativeness of the existing air quality network of the province of Alberta. The assessment presented here is based on the associativity analysis described in the work of Solazzo and Galmarini (2015) and references therein and further expands that methodology to focus on monitoring network optimization. We use the methodology for the first time for observation datasets collected in Alberta, analysing the data using two different similarity metrics, and rank existing observation stations based on relative station redundancy. We then extend the methodology to a new application of gridded air quality model data – showing that time series from a deterministic air quality model (Global Environmental Multiscale – Modelling Air-quality and Chemistry; GEM-MACH) may be used as a surrogate for observations in air quality clustering analysis. Dissimilarity may thus be used to rank stations in terms of potential redundancy; here we define redundancy as the relative dissimilarity level at which a station joins a cluster. Stations with the lowest levels of dissimilarity may hence be considered sufficiently similar to be considered potentially redundant.

In addition, we apply the same methodology to time series from a deterministic air quality forecast model (GEM-MACH) and assess the extent to which the model output can be used as a potential surrogate for observations in clustering analysis. The combined use of the model and clustering analysis is shown to be a potentially powerful tool for network design and/or optimization of existing air quality networks.

We introduce the methodology to assess potential redundancy of monitoring stations (Sect. 2) and describe the observational and model data used to develop the methodology (Sect. 3). In subsequent sections we present the associativity analysis for the continuous monitoring (Sect. 4) and discuss how the methodology can be used to identify different sampling methodologies (Sect. 5). We then show how the same methodology may be used with output from an air quality model. With favourable comparisons to clustering results from air quality monitoring station observations, we show that model output combined with hierarchical clustering provides a new approach for monitoring network design (Sect. 6). We also discuss potential factors impacting the methodology (Sect. 7) and our conclusions are drawn in Sect. 8.

Solazzo and Galmarini (2015) noted that clustering analysis can be used to determine the extent to which the different monitoring methodologies are comparable. Thus if different methodologies do not provide equivalent data, the clusters generated will be split according to methodology rather than being associated with local chemical and meteorological conditions. The combination of monitoring methodologies here thus has two purposes – to assess the relative dissimilarities between station records and to verify that both passive and continuous monitors provide similar data.

The hierarchical clustering methodology was applied to the 5-year bimonthly averaged time series sampled by continuous and passive monitors (we leave out the a priori KZ filtering step as the data in this case are already long-term averages). The dendrograms resulting from the clustering analysis are shown in Fig. S11 for NO2 and Fig. S12 for SO2. The spatial distributions for the station clusters for the 1-R dissimilarity metric will be the focus here.

The spatial distributions of the NO2 clusters at dissimilarity levels of 1-R= 0.55 and 0.5 are shown in Fig. 5a and b, respectively, with the locations of continuous monitors plotted as inverted triangles and passive monitors as circles. At correlation level R= 0.45 (Fig. 5a) there is a clear distinction between passive and continuous monitors; all the continuous monitors belong to cluster 1, independent of their spatial location. A large number of the passive monitors also fall within this cluster; however, when a slight increase in correlation is applied (Fig. 5, R= 0.5), the clustering pattern changes significantly – most of the continuous monitors remain within the same cluster, but the passive monitors form separate clusters. Two WCAS continuous monitors separate and form a separate cluster at dissimilarity level 0.5 (Fig. 5b). Figure 5 also shows several cases of collocated continuous and passive monitors which do not fall within the same cluster for correlation levels of 0.5 or higher. The analysis shows that as higher levels of correlation are required, the continuous and passive monitors for NO2 do not cluster together despite close physical proximity or even collocation. Some of the passive monitor clusters at R= 0.5 (Fig. 5b) appear anomalous; for example, cluster 3 (red) includes stations in LICA and WBEA, despite these airsheds being separated by a distance of several hundred kilometres. As the level of dissimilarity is decreased from 0.55 to 0.5, the biggest difference in clustering patters is seen for WBEA monitors (in the upper right of the panels of Fig. 5) as passive and continuous monitors located closer to the oil sands facilities fall within cluster 1, while some of the passive monitors farther from the oil sands facilities fall within cluster 3. For levels of correlation above 0.5, the clustering between stations monitoring similar source areas is rare, independent of the airsheds (see dendrogram in Fig. S8).

Figure 6 depicts the clustering results for SO2 based on the 1-R metric for dissimilarity levels 0.75 (Fig. 8a) and 0.65 (Fig. 8b). Higher dissimilarity levels were used as examples for the generation of spatial distributions than for NO2 in this figure. The highly variable nature of the SO2 concentrations, as a result of their origin in stack emissions, results in a greater degree of variability inherent in the collected data, as described earlier (at lower dissimilarity levels, the number of clusters increases markedly). Comparing Figs. S9 and 6, most of WBEA passive and continuous monitors in the north-east of the region form a common cluster at R= 0.25 (Fig. 6a, cluster 11, red). However, at this low correlation level, a common cluster connects sites in LICA, FAP, WBEA, and PAZA airsheds, despite these sites being widely separated in space and influenced by different local sources of SO2 (cluster 12, green, Fig. 6a). At the slightly higher correlation level of R= 0.35 (Fig. 6b), the clustering across airsheds has been reduced, though LICA and FAP still share a common cluster (number 4, light blue). Again, the most direct interpretation of the differences between the SO2 and NO2 results for the 1-R metric analysis, when passive and continuous monitors are clustered together, is that the data time series records for SO2 are more highly variable than for NO2. If 1-R similarity is used for assessing potential station redundancies, then there is a lesser overall degree of potential redundancy in the SO2 data due to its greater degree of variability. However, the cause of that variability should also be considered. For example, we note again that some of the collocated passive and continuous monitors for SO2 do not fall within the same cluster at lower 1-R values (these are shown as different colours in overlapping inverted triangles and circles in Fig. 6b). This indicates that at least some of the variability may reside in the measurement methodologies employed.

In their analysis of European ozone monitoring networks, Solazzo and Galmarini (2015) found similar patterns between different European nations, noting that the differences are likely related to different sampling methodologies, instrument sensitivities, and data acquisition protocols not being harmonized between the countries. The same seems to be true for the Alberta passive and continuous monitoring stations, as the 1-R cluster analysis shows that the continuous stations are more similar to each other within and across airsheds than they are to the passive stations within the same airsheds, or located nearby. Collocated continuous and passive stations do not always show high levels of similarity, which would be expected had they reported the same concentrations. We analysed WBEA data alone using the 1-R metric (dendrogram in Fig. S13) and found that most of the continuous monitors formed a separate cluster from the passive monitors at relatively high levels of the 1-R metric, indicating that the two sources of data provide fundamentally different records. Collocated passive and continuous monitors also tended to have high levels of the Euclidean distance (not shown). Thus, at least some of the variability noted with these datasets seems to lie with the overall sampling methodology, and related confounding factors, discussed further in Sect. 7.

There have been several studies comparing passive and continuous analysers in Alberta (WBK, 2007; Hsu et al., 2010; Pippus, 2012; Bari et al., 2015). Bari et al. (2015), the study with the highest number of samples, cautioned that direct comparisons between NO2 and SO2 continuous and passive methods may be hampered by lower field accuracy in the passive methodology. Several studies show that passive samplers overestimate SO2 ambient concentrations and underestimate NO2 relative to continuous monitors. For example, the Bari et al. (2015) study showed that the median values for the absolute difference between the collocated passive and continuous monitors for NO2 is 1.5 and 0.2 ppbv for SO2. The same study assessed the relationship between passive and continuous measurements by regression analysis, concluding that the agreement between the different types of monitors is moderate, with the coefficient of determination being 0.42 and 0.40 for NO2 and SO2, respectively. We note that these previous comparisons were done for urban sites only; in this study we have carried out cluster analysis including passive and continuous monitoring data for rural, urban, and industrial sites outside of urban regions.

Air quality models such as GEM-MACH provide gridded time series concentrations of atmospheric pollutants and related chemicals at a common time interval, as a standard output. These are compared to observations in order to evaluate the model's performance (for traditional evaluations using the model output used herein, cf. Makar et al., 2018; Akingunola et al., 2018; Stroud et al., 2018). We introduce here for the first time the concept of the use of these time series of air quality model output, combined with hierarchical clustering analysis, as a surrogate for station data, for the purposes of monitoring network analysis and design. Two possible approaches can be taken. First, the model output at the model grid squares containing existing monitoring stations may be analysed in order to determine the extent to which the clustering analysis of model output mimics the clustering analysis of the corresponding observational data. Aside from presenting a new means by which the model output can be evaluated, this approach also can highlight possible causes for the observation data clustering results. The second approach is to use the gridded model output as a surrogate for a dense monitoring network (one “station” at every model grid square centre). The outcome of this second approach is a set of gridded maps – similar to the sparsely distributed observation location maps shown in the figures above, these show the clustering of potential stations. However, the cluster maps resulting from the use of the dense “network” of model grid squares define more precisely a set of regions, within each of which a single station may represent that larger region for the value of the dissimilarity metric chosen. We investigate this second approach from the standpoint of monitoring network design. Note that, in the work above, we have attempted to show how hierarchical clustering may be used to analyse existing monitoring networks; here we show how the same techniques, coupled with the output of a long-term simulation of an air quality model, can provide an optimized network design (where we here define “optimized” as “having a common level of dissimilarity for potential station locations, for the dissimilarity metrics chosen”). Equivalently, these optimized networks maximize the dissimilarity, and hence minimize the potential redundancy, in the location of monitoring network stations.

Our first analysis using model output evaluates the extent to which the model is capable of creating similar clusters as the observations. Hourly model output for the 1-year simulation of GEM-MACH was extracted from those model grid squares containing the station locations, and the resulting time series data were submitted to the same hierarchical clustering methodology as described above. Figure 7 shows the spatial distribution for the cluster analysis at the same levels of 1-R, 0.75, 0.65, and 0.55, as was shown using observation data (compare to Sect. 4, Fig. 2). Each airshed is plotted with a different polygon, and colours indicate clusters. The corresponding dendrograms for these model results are shown in Fig. S14. Note that cluster colours and numbers differ between Figs. 2 and 7; stations fall within similar clusters in each figure. For SO2 dissimilarity level 1-R = 0.75 (Fig. 7a), the difference between the results for model and observations is not substantial; the clustering is identical aside from a single station in both WBEA and LICA, as well as AEP and PAS stations not forming separate clusters. The difference between observed and modelled NO2 clustering results is more notable as the level of dissimilarity decreases (Fig. 7b, c): the model tends to create a larger number of clusters than the observations at intermediate levels of dissimilarity (comparing Figs. 2b and 7b: 6 clusters versus 10 clusters; 2c and 7c: 11 clusters versus 13 clusters). The model results also tend to cluster within the same airsheds to a greater degree compared to the observations results. The model dendrograms tend to have clusters forming at higher levels of dissimilarity for some stations such as Steeper (Fig. S14 for Steeper is 1-R = 0.8, while Fig. S1 for Steeper's node is 1-R = 0.7). Some of these differences may be due to inaccuracies in the emissions data driving the model. For example, the major point source emissions data used in the simulations is based on regulatory reporting to the NPRI, wherein the regulatory requirement for reporting is an annual total. These annual totals must be temporally allocated using assumed temporal profiles for each source, and these month-of-year, day-of-week, and hour-of-day temporal profiles may not always match actual hourly emission levels at any given time. We show elsewhere (Akingunola et al., 2018) that hourly continuous emissions monitoring data used as model inputs may result in very different short-term concentration behaviour, with the corollary here that temporal allocation used here may influence the pattern of clusters. However, the model results at level of dissimilarity 0.65 tend to cluster more similarly with the observation results at level of dissimilarity at 0.55, indicating that the clustering analysis for the model results and observations show a similar spatial distribution, though the model shows overall higher correlation values than the observations.

The results for SO2 (dendrograms for the cluster analysis in Fig. S12, compare to Fig. S5) show the model results clustering similarly to the observations for PAMZ, ACCA, and WCAS stations. WBEA stations in the model results (Fig. S15, red station labels) are split into two clusters, while these stations are part of the same cluster in the observation-based analysis (Fig. S5). At 1-R level 0.75, both model and observation cluster analysis results (Fig. 8a, compare to Fig. 4a) already show many clusters composed of one or few stations, with the model showing slightly more clusters than the observations (21 clusters versus 25, respectively). As noted earlier, SO2 in this region is emitted mainly by point sources, and the use of annual emissions data with an assumed temporal allocation, along with the additional inherent difficulties in accurately predicting plume rise (Akingunola et al., 2018), makes the reproduction of the time record of SO2 by the model a challenge. Inaccuracies in both the emissions and the model meteorology may contribute to these differences.

We next show an example of how hierarchical clustering using gridded model output may be used to generate an optimized monitoring network. For this analysis, we focus on a specific subsection of the model grid; namely a 72 × 72 block of model grid squares centred on the Athabasca oil sands. Figure 9 depicts the resulting mapped 1-R cluster analysis in this area, when each model grid cell has been treated as a potential monitoring station location. Figure 9a and c show the values of 1-R for each grid cell at the point in the analysis where that grid square becomes part of a cluster for NO2 and for SO2, respectively. Those grid cells with high values of 1-R thus join clusters at much lower correlation levels than those which have joined clusters at low values of 1-R. As a result, the maps show the extent of dissimilarity for the grid cells; higher values show grid cells which are so unlike others that they remain separate from the clusters throughout much of the analysis. In contrast, Fig. 9c and d show the clusters which exist for a specific level of 1-R. These show how the methodology may be used to design a monitoring network for a given number of stations (i.e. one station within each of the coloured regions will be sufficient to represent that coloured region, to within the value of 1-R used to generate the clusters). Figure 9b and d show the spatial distribution of the clusters generated by dissimilarity levels of 0.65 for NO2 and 0.8 for SO2, respectively (these levels were chosen based on the analysis above, where the model was shown to provide reasonable results). All the panels in Fig. 9 have the areas where the oil and gas extraction sites and processing facilities are located as a visual aid; these areas are contoured in black.

The 1-R metric maps (Fig. 9a and c) have the highest values where main emissions sources are located – these identify the main open-pit mine facilities of the oil sands, within which may be found both area and stack emissions sources. These regions of high variability are thus where the influence of the emissions and the local meteorology on the dispersion of the emissions is the strongest. In the NO2 dissimilarity map “point” (stack), “line” (roads) and “area” sources (mines) can be distinguished; for SO2 the locations of the stacks for processing and flaring are identified. The spatial distribution of the clusters (each cluster is mapped with a different colour in Fig. 9b and d) shows the areas wherein a single measurement station, placed anywhere within a given coloured region, would represent that region to the given level of dissimilarity. Figure 9c thus shows that for NO2 and for a 1-R dissimilarity level of 0.65, 17 monitoring stations, each placed at any location within each of the 14 coloured regions, would constitute an optimized network for NO2. Similarly, Fig. 9d shows that 17 stations would be required to monitor SO2 with a common 1-R dissimilarity of 0.80, and the regions over which those stations could each be placed. The analysis thus identifies regions which are equivalent from the standpoint of the dissimilarity metric used.

We note that in some cases a single cluster can be discontinuous, split into more than one area. An example of this can be seen in Fig. 9c, where a cluster is split into two separate red coloured regions (cluster 3), whereas Fig. 9d does not show the same split. Local knowledge of the emissions sources, as well as analysing Fig. 9a and b, help explain these results. The dark yellow region (cluster 5) in Fig. 9c and the grey region (cluster 8) in Fig. 9d mark the location of a local emissions source, moderate in magnitude relative to the larger sources in the middle of the domain (oil sand facility boundaries marked in these figures). The clustering thus recognizes the local influence of this moderate source of emissions; however, at greater distances from this source, the impact of the larger sources dominates. The red areas (cluster 3) in Fig. 9c and the green area (cluster 4) in Fig. 9d show that the larger sources have both a local and long-range influence, which only locally can be overwhelmed by the moderate source for both SO2 and NO2. We note that we are using 1-R in this application of the methodology with deterministic model output, so the magnitude of the signal of the two chemicals is not being analysed – rather, its time variation is. To satisfy different monitoring objectives, stations are placed by both geographical and physical location, with physical location defined by the concept of spatial scale of representativeness, the area where actual pollutant concentrations are reasonably uniform. We note that each of these coloured subregions in which a single station could be placed has a relatively large geographic extent and, using this metric, do not describe the concentration gradient in the region but could be used as a first guess for areas of representativeness, potentially providing useful input for applications such as data assimilation of air quality and meteorological observations. Combining spatial distribution of the clusters for 1-R metric with the Euclidean distance will provide further information about the concentration gradients in the area of representativeness. Note that maps such as these could be overlaid with other geographic information (e.g. road networks, the local power grid) to further optimize and decide on potential station locations. The similarity maps, combined with these other factors, could be used to aid in the design of air pollution monitoring networks.

The cluster distribution maps show that the areas for potential station location depend on the pollutant – the SO2 map is influenced to a greater degree by the wind directions throughout the year than NO2, likely due to the emissions sources for the former pollutant being driven almost entirely by stack sources in this region. The wind-rose-like pattern around SO2 sources likely stems from plume fumigation events at different times of the year, leading to a high correlation of SO2 concentrations leading downwind from the sources. The NO2 cluster distribution is patchier, reflecting both the impact of the stacks (which account for about 40 % of the total NO emissions in the region) and the off-road mobile mine fleet (other “area” sources, which account for the bulk of the remainder of the NOx emissions). If potential multi-pollutant monitoring station locations are desired, overlapping the optimized maps for each pollutant, for a given number of stations, would be a further way of aiding the monitoring network design process.

We also note that other metrics could be used in order to capture other aspects of concentration spatial and temporal variability, such as concentration gradients, in addition to temporal correlation – here we have demonstrated a “proof of concept”, and other metrics will be analysed in future work.

Factors that can negatively impact the results of hierarchical clustering include data dispersion (large variance between cluster members), outliers, and non-uniform cluster densities (clusters which are non-compact and non-isolated, and thus not properly distinct from one another; cf. Mangiameli et al., 1996; Milligan, 1980). However, we find that the analysis itself may also be used to identify these conditions. We have shown in the results in Sects. 4 and 5 that the analysis has indeed identified stations that are outliers relative to the rest of the dataset – these stations separate from the other stations as single-member clusters at high levels of dissimilarity. In other words, the analysis identifies the records of those stations as being substantially different from all other station records, for the dissimilarity metric used. This was particularly noticeable in the bimonthly data analyses. The methodology also identified cases of data dispersion, for example, the analysis of combined bimonthly passive and continuous monitors showed cases where monitors in close proximity or even collocated did not cluster together. The methodology thus seems capable of isolating outlier records and data dispersion as well as recognizing cases of substantial differences between data collection methodologies. The latter was noted in the case of hourly ozone observations by Solazzo and Galmarini (2015).

The analysis of combined continuous and passive data has identified systematic differences between the two monitoring methodologies as a potential confounding factor on the station ranking of passive stations; the analysis identifies collocated stations with concentration differences and poorly matching concentration time variation, but cannot identify the causes for these differences. These issues should be the subject of follow-up work. Nevertheless, we note that both passive and continuous data may be subject to errors associated with the accuracy and precision of the sampling methodology.

We examined the potential errors associated with the reported detection limit of the monitoring methodology by using the GEM-MACH derived time series at station locations. Random noise was added to the original model time series results, with the maximum magnitude of the noise for each species taken from the detection limit range of each instrument (i.e. random noise in the range ±0.5 ppbv was added to the NO2 time series and ±1 ppbv was added to the SO2 time series). The NO2 cluster results for hourly time series using 1-R as the dissimilarity metric (Fig. S13, compare to Fig. 2) show no significant difference between the original and noise-added time series. However, this changed as timescales were removed from the original datasets by KZ filtering, especially once monthly and all shorter timescales were removed. Random noise was thus shown to be a potential confounding factor in 1-R hierarchical clustering analyses. However, for the corresponding NO2 Euclidean distance metric, both the hourly and monthly filtered data, with and without noise added, resulted in identical clustering (not shown). The SO2 results showed a larger variation between the clusters generated with the original time series and those containing additional random noise. The difference in clustering was particularly noticeable for the 1-R dendrograms, for both hourly and time-filtered data, and slightly less pronounced for Euclidean distances (not shown). The work described above suggests that much of the “signal” for primary emitted or quickly reacting secondary pollutants for correlation analysis resides in the shorter timescales (hourly to daily); the greater influence of random noise on the results of the time-filtered data implies that the latter are dominated by close-to-background concentrations, which are in turn similar in magnitude to the noise levels added here, and hence a greater influence is seen on clustering of the time-filtered data. For species such as SO2, which are dominated by short-duration high-concentration plumes, this effect may extend to the shorter timescales as well.

Besides the detection limit of the instrument, airsheds report the passive observations with a reporting limit of 0.1 ppbv; hence we also tested the accuracy of the instrument or the number of significant figures being reported, again using the model time series at station locations as a surrogate for observation data. The model results were filtered for three or zero significant figures below the decimal, and the resulting analyses were compared. As for the random error test, we found that for both NO2 and SO2 the dendrogram patterns changed, indicating that the use of fewer significant digits in data reporting will result in enough loss of information to change the interpretation of the data.

In the analysis described in Sect. 4, it was noted that as successively larger timescales are filtered from the data used for clustering, the magnitudes of the clustering metrics show an increasingly higher degree of similarity, with monitors clustering both within and across airsheds. However, the filtering of time series to remove successively larger timescales is not equivalent to averaging, in which shorter timescale information may be retained in the average. To specifically examine the effect of time averaging during data collection on clustering results, the clusters for the hourly data were compared to those from daily, weekly, and monthly averages (Fig. 10). With the original hourly data, specific airsheds were identified as unique clusters (as expected, for 1-R hierarchical clustering; stations located close to airshed-specific sources were identified as being more similar). However, with increasing averaging times, this airshed-specific clustering was gradually lost. Most of the information driving the ability of 1-R clustering to link local sources was thus shown to reside in the shorter timescales. Nevertheless, this information was lost as increasing averaging periods were applied (Fig. 10). A fundamental result of this analysis is that measurements that consist of long-term averages may lose the ability to identify the influence of local sources on the basis of time variation, i.e. they will correlate at an equal level with both adjacent monitoring stations and those that are located in distant regions. However, this information is retained in hourly records, and the latter may be used to identify unique source regions on the basis of correlation.

We note here that the results of analyses of this nature are dependent on the time series data used (including its duration). We have used a 5-year dataset to evaluate bimonthly observation data and a 1-year dataset to evaluate hourly data and deterministic model results. Longer time periods may be preferred in future applications to limit the potential impact of year-to-year variability. Nevertheless, if emissions change in the future, the analysis should be repeated in order to determine whether the pattern of clusters has changed in response to the changes in emissions. Similarly, while long time sets are desired from the standpoint of removing the potential impacts of annual variability in meteorological conditions, if changes in emissions happen frequently, it may argue for yearly rather than multi-year analyses.

A methodology for cross-comparing air quality monitoring networks was proposed here, expanding on the work of Solazzo and Galmarini (2015) by including the Euclidean distance as well as 1-R as dissimilarity metrics for hierarchical clustering and by making use of chemical reaction transport model output as a surrogate for observation station data. We adopted the KZ filter in its original low-pass configuration in order to improve the ability of the methodology to distinguish the impact of different timescales of variation on clustering. The Euclidean distance metric allowed cross-comparison of the stations in terms of the magnitude of the concentrations, whereas 1-R evaluated their temporal variation similarity. Both metrics can be used together or separately to evaluate the similarity of the stations and their potential redundancy. The relative level of potential redundancy for existing observation stations was ranked based on each dissimilarity metric, and we recommend evaluating monitoring station redundancy using both metrics where possible. Stations which form clusters at low values of both 1-R and Euclidean distance are the most redundant, while those with high values of either or both of these metrics are the least redundant. Absolute thresholds for redundancy cannot be generated since the relative rankings depend on the available observation data (number of stations and chemical species observed). In addition, other considerations, such as spatial proximity to sensitive receptors, the regulatory purpose of the station(s), and logistics (e.g. accessibility or power supply), may outweigh the recommendations based on similarity alone.

We have shown, through several analyses, that much of the observation signal which may be used to identify common sources of both primary pollutants and secondary products of fast reactions resides in shorter timescales (hourly to daily). When hourly data are available, the methodology is able to identify groups of stations that are influenced by common emissions sources (e.g. stations that are influenced by oil sand emissions as opposed to stations located elsewhere) as well as outliers or station records that are markedly different from all others in a given dataset. The former property is useful for identifying the influence range of specific emission sources. The latter property shows that the methodology is a useful tool for identifying station instrumentation that may be located such that they are subject to unique conditions (e.g. very nearby sources, anomalous long-term variation) or that have anomalous readings. However, for data consisting of longer-term averages, or observations in which the shorter timescales have been removed by filtering, at least some of the information which identifies the influence of common emissions sources is lost. Nonetheless, the methodology, when applied to time-filtered data, is able to single out stations mainly influenced by seasonality.

Clustering was shown to depend on the chemical species analysed, suggesting that optimization of networks using this methodology should be carried out on a “by species” basis rather than a “by station” basis. The two species examined here originate in different types of emissions sources in the region under study and consequently have different dissimilarity rankings for the corresponding stations.

We have corroborated the work of Solazzo and Galmarini (2015) for ozone in that the methodology is capable of identifying monitoring stations making use of different monitoring methodologies (via our 5-year analysis of passive and continuous SO2 and NO2 observations on a common bimonthly averaging interval). Passive and continuous monitors in the same airsheds did not always fall within common clusters (with several examples in which collocated monitors from the two technologies did not correlate). Some of these issues may be the result of averaging time, though data round-off and accuracy (random noise) were also shown to have a negative influence on the clustering results.

We have expanded the use of hierarchical clustering for air pollution to include its use with air quality model output. This presents a new avenue for monitoring network optimization and design in that each high-resolution air quality model grid square can be treated as a potential monitoring station location. Comparisons of the results of the clustering of model and observed time series at monitoring station locations showed clusters generated from model output tended to be more similar within airsheds than was the case for clusters generated from observations. However, the results are quite comparable, albeit at higher correlation levels for the model than the observations, and the match to observations depends on the chemical species. Tests in which gridded model output was treated as potential station locations resulted in the first dissimilarity-analysis-based maps of optimized air pollution monitoring networks. These showed that the methodology is capable of generating subregions within which a single station will represent that entire subregion, to a given level of a dissimilarity metric. Maps of this nature may be combined with other georeferenced data (e.g. road networks, power availability) to assist in monitoring network design.

While hierarchical clustering's pitfalls include data dispersion and outliers, we show here that the methodology is also able to identify differences in sampling methodologies and anomalous stations records. The analysis was shown to be particularly sensitive for monitors sampling air contaminants such as SO2 in areas of low background concentrations and sudden concentration peaks. For SO2, this is a result of the variation inherent in the type of sources that dominate SO2 emissions in our study region, i.e. large stack plumes. We also note that comparing observation-based cluster analysis with those of air quality model output at station locations might help identify possible deficiencies in the emission data used to drive air quality models. Given that short-term variation has been shown here to have a key impact on identifying common sources, the use of annual totals and assumed temporal profiles as the basis for emission inventory reporting should be avoided, and more time specific records, should be used where possible.