Continuous time series of hourly meteorology and PM2.5 (µg m-3) observations between January 2005 and August 2016 (inclusive) were obtained from four air quality monitoring stations (Chullora, Earlwood, Liverpool and Richmond) in the NSW Office of Environment and Heritage (OEH) network in Sydney (Fig. 1). Monitoring stations are located at varying elevations and in semi-rural, residential and commercial areas (Table 1). These four locations were chosen because they have the longest uninterrupted record of PM2.5 measurements in Sydney. Prior to 2012 PM2.5 was measured using tapered element oscillating microbalance (TEOM) systems. Since 2012 beta attenuation monitors have been used to measure PM2.5. Although there appear to be effects from instrument change, such effects are generally small if compared to the daily or hourly fluctuations in PM2.5 levels.

To compare how PM2.5 concentrations varied over daily and monthly timescales, we also obtained hourly measurements of PM10 (µg m-3), nitrogen dioxide (NO2) (parts per hundred million – pphm) and oxides of nitrogen (NOx) (pphm) from these stations. Meteorological variables included in our analyses were surface wind speed (m s-1), wind direction (∘), surface air temperature (∘C) and relative humidity (%). Hourly global solar radiation (W m-2) data were available at the Chullora station only, but were subsequently omitted as a predictive variable (see Sect. 3.3.1).

Hourly total cloud cover (okta) and mean sea level pressure (MSLP; hPa) were obtained from the Australian Bureau of Meteorology (BoM) Sydney Airport weather station (WMO station number 94767). These are included as covariates in models for the four monitoring sites. The 24 h rainfall totals (mm) were approximated for each OEH station from the BoM weather station that is nearest (Fig. 1).

Given its role in the turbulent transport of air pollutants (Seidel et al., 2010; Pal et al., 2014; Sun et al., 2015; Miao et al., 2015), we included planetary boundary layer height (PBLH) as an explanatory variable. PBLH has previously been derived from observational meteorological data by Du et al. (2013) and Lai (2015), using a method which they found was an effective estimate of the PBLH and its relationship with PM concentrations. Although direct PBLH measurements would be ideal, these are unavailable for the study domain at appropriate spatial and temporal resolutions. Hence, we derived PBLH estimates at the location of each monitoring station from a subset of the meteorological data following the method used by the above authors (Eqs. 1 and 2). PBLH=1216(6-s)t-td+0.169s(ws+0.257)12fln⁡hl,f=2Ωsin⁡θ, where s is a stability class that estimates lateral and vertical dispersion, t is surface air temperature and td is surface dew point temperature (approximated for the location of each station using the method proposed by Lawrence, 2005), ws is wind speed, h is wind speed altitude in m for a given monitoring station, l is the station's estimated surface roughness index, f is the Coriolis parameter in s-1, Ω is the earth's rotational speed (rad s-1) and θ is the station latitude. The stability typing scheme was based on the Pasquill–Gifford (P–G) stability categories (Turner, 1964), via a turbulence-based method using the standard deviation of the azimuth angle of the wind vector and scalar wind speed.

We calculated the 24 h mean for hourly meteorological and PM2.5 measurements, where wind direction was vector-averaged (i.e. averaging the u and v wind components). Log-transformations were applied to PM2.5 and rainfall. Applying transformations to the remaining explanatory variables did not greatly reduce heterogeneity.

Temporal variables trialled for inclusion in analyses included day of the year, weekday, week, month (all representing different seasonal terms) and year (because air quality varies from year to year). A Julian date variable was incorporated to represent the longer-term trend in PM2.5 concentrations.

Historical records of HRBs conducted between January 2005 and August 2016 in NSW were obtained from the NSW Rural Fire Service (RFS), the firefighting agency responsible for the general administration of HRBs. There were a total of 9200 fire polygons in this data set prior to data conditioning (see Sect. 3). HRBs are conducted predominantly in autumn (months of March to May in the Southern Hemisphere) and spring (September to November), and often at weekends, typically, with burns lit in the early morning. Most historical HRBs have occurred to the west and north-west of Sydney (Fig. 2). Additional predictive variables derived from the HRB data (all daily values) were total number of burns, total burn surface area (ha), median burn elevation (m), median fire duration (days) and median fire distance from the geographic centre of the monitoring stations (km).

It is important to note that other potential sources of PM2.5 emissions in Sydney include motor vehicles, soil erosion and occasional dust storms. Use of domestic wood-fired heaters can also make a substantial contribution to PM2.5 concentrations during winter months (June to August), which is when HRBs are generally not conducted. However, between 2011 and 2016, average PM2.5 air quality index (AQI) values were higher on days when either HRBs or wildfires occurred relative to days when there were no fires (Fig. 3).

Generalised additive models (GAMs) (Hastie and Tibshirani, 1990) offer an appropriate approach with respect to air quality research because relationships between covariates are often non-linear, an issue which can be addressed within the GAM framework. In addition to the seasonal pattern of hazard reduction burning, PM2.5 concentrations in Sydney also show daily, monthly, seasonal and annual variation. Adding terms to a GAM to account for these temporal variations fails to deal with residual autocorrelation completely, as is evident in the autocorrelation function (ACF) of the residuals (Fig. S1 in the Supplement). Given the residual autocorrelation and non-independence of the data, we used a generalised additive mixed model (GAMM) approach to take account of the seasonal variation and trends in the data. GAMMs can combine fixed and random effects and enable temporal autocorrelation to be modelled explicitly (Wood, 2006). We assumed a Gaussian distribution and used a log link function. Cubic regression splines were used for all predictors except wind direction and day of year, which used cyclic cubic regression splines, because there should be no discontinuity between values at their end points. Experimenting with alternative smooth classes did not drastically affect model results or diagnostics. Smoothing parameters were chosen via restricted maximum likelihood (REML). We implemented GAMMs with a temporal residual autocorrelation structure of order 1 (AR-1). More complex structures (e.g. autoregressive moving average models; ARMAs) of varying order or moving average parameters produced marginally higher Akaike information criteria (AICs) (e.g. mean = 259.6) than models with AR-1 autocorrelation (mean AIC = 259.02). Omitting a correlation structure entirely produced the largest AICs (mean AIC = 279.5). In all cases, the AR models for the residuals were nested within 1 month (nesting within weeks and years was also trialled, but produced higher AICs). Autocorrelation plots obtained by applying the GAMMs using the AR-1 structure showed that short-term residual autocorrelation in the residuals had been removed relative to using GAMs (Figs. S1–S2).

We first used the GAMM framework to estimate the annual trend in the weekly mean concentrations of PM2.5 for 2005–2015, split by season, with Julian day as the only predictor. Monthly and daily mean PM2.5, PM10, NO2 and NOx concentrations for all years were also compared to assess how concentrations of each pollutant varied with these timescales. The latter analyses were performed using R software for statistical computing (R Development Core Team, 2015) and the “openair” package (Carslaw and Ropkins, 2012). The annual trend and subsequent statistical analyses described below were performed using R software and packages “mgcv” (Wood, 2011) and “nlme” (Pinheiro et al., 2017).

To assess how PM2.5 concentrations vary in relation to the meteorological, burn and temporal variables, the GAMMs were applied to each monitoring site separately and focused on the period January 2011–August 2016. There were comparatively fewer HRBs conducted prior to 2011, hence the choice of this time frame. For each station, we split the data into two subsets: (1) for all days when HRBs were conducted and the PM2.5 concentration was less than the median PM2.5 concentration for the location in question, “low pollution days”; (2) for all HRB days when the PM2.5 concentration was greater than the median value for the location in question, “high pollution days” (the minimum/maximum number of observations in each low/high subset was in the range 179–189). The time series were conditioned in this manner to better characterise the differences in covariate behaviours between burn days when pollution remains low versus burn days and elevated PM2.5. Since our focus is specifically on PM2.5 concentrations during HRBs, days when wildfires had occurred were excluded.

Meteorological covariates relevant to high PM2.5 concentrations were identified via the GAMMs based on criteria of statistical significance at more than one location, or where the influence of covariates on PM2.5 showed a marked distinction between pollution conditions. We then used the hourly meteorological data for these select covariates to compare their mean diurnal variation on burn days with low versus high pollution. The 95 % confidence intervals of these diurnal means were calculated using bootstrap re-sampling with 1000 replicates.

There is an increasing inter-annual trend in weekly mean PM2.5 concentrations in all seasons during 2011 to 2015, especially in summer and winter (Fig. 4). Mean PM2.5 concentrations range from 6 to 10 µg m-3. Mean monthly PM2.5 averaged over all years shows increasing concentrations from early autumn (March), peaking in May, then decreasing towards the end of winter, before increasing again from early spring (Fig. 5a). Notably, mean daily PM2.5 concentrations (averaged over all years) are higher at weekends relative to other pollutants (PM10, NO2 and NOx; Fig. 5b).

Adjusted R2 values for high pollution models were between 0.44 and 0.60, and between 0.29 and 0.39 for the low pollution models (Table 2). PBLH and total cloud cover were the most consistent predictors of elevated PM2.5 during HRBs (Table 2). On high pollution days, PBLH had a statistically significant, negative influence on predicted PM2.5 concentrations at all locations (Fig. 6). This influence was generally more linear on high pollution days, relative to low pollution days. Notably, fitted curves for PM2.5–PBLH were steeper at lower altitudes (< 800 m) in the high pollution condition. Cloud cover had a negative influence on predicted PM2.5 concentrations that was significant in all but one case (Table 2), though fitted curves do not appear to differ noticeably between pollution conditions (Fig. 7). Although temperature and wind speed showed a more variable pattern of statistical significance (Table 2), they exhibited marked differences in behaviour between low and high pollution days. During high pollution, temperature typically had a negative, curvilinear influence on fitted PM2.5 values (Fig. 8). This negative influence flattens or reverses at temperatures > 20 ∘C. In contrast, the PM2.5–temperature relationship was weak and linear during low pollution days. Wind speed had a significant influence on PM2.5 only at Earlwood and Richmond (Table 2). During low pollution days, this association is negative at most locations. During high pollution conditions at Chullora and Earwood, there is a positive influence on PM2.5 at low wind speeds which reverses at speeds above ca. 2 m s-1 (Fig. S7). During HRBs and high pollution, wind direction curves show peaks between approximately 250 and 310∘ at Chullora, Earlwood and Liverpool (south-westerly to north-westerly flows) (Fig. 9). Earlwood frequently experiences north-westerly flows during spring, autumn and winter, whilst south-westerly flows are common during the same seasons at Liverpool (Fig. S4).

The remaining meteorological predictors either did not show marked differences between pollution conditions or were statistically significant in only one instance. Rainfall generally had a negative influence on PM2.5 during HRBs (Fig. S5). MSLP had a positive association with higher PM2.5 concentrations during low and high pollution (Fig. S6), though this association was only significant during high pollution at Richmond (Table 2).

HRB frequency had a significant and positive influence on PM2.5 only for the high pollution condition at Chullora, Earlwood and Liverpool (Table 2 and Fig. 10). The association between burn area and PM2.5 during high pollution was significant at Liverpool and Richmond only. The influence of Julian day on PM2.5 showed significant non-linear, increasing trends in all instances.

Having identified the most informative and consistent meteorological predictors using the GAMMs, we assessed their mean diurnal variation during the occurrence of HRBs and low versus high PM2.5 pollution in the following sections.

PBLH was the most consistent meteorological predictor of PM2.5. It had a significant, negative influence on PM2.5 at all locations during HRBs and “high pollution days”. There was a marked difference in mean diurnal mixed layer heights between low and high pollution conditions in the early morning (00:00–07:00 LT) and from 20:00 to 23:00 LT, with the PBLH being approximately 100–200 m lower at these times during HRBs and high PM2.5. During these two time periods whilst the PBLH is low, mean cloud cover, temperature and wind speeds are also lower relative to their magnitudes at corresponding times during low pollution. Essentially, these early hours of cold, stable conditions with minimal turbulence (i.e. conditions that are conducive to temperature inversions) prevent the dilution of PM2.5. These subdued conditions often coincide with the night time–early morning westerly cold drainage flows and low mixing heights (inhibiting vertical dispersion), leading to the build-up of PM2.5 during mornings (Lu and Turco, 1995; Hart et al., 2006; Jiang et al., 2016b). These pollution-conducive conditions are similar to those identified in Jiang et al. (2016a) as being related to a ridge of high pressure extending across eastern Australia, resulting in light north-westerly winds. These synoptically driven flows, although light, tend to enhance nocturnal drainage flows, inhibit afternoon sea breeze formation and allow the transportation of pollutants across the Sydney basin to the coast. There is also a large difference in mean diurnal temperatures between low and high pollution conditions from late morning to early evening, with temperatures 3–4 ∘C warmer during high pollution. During warmer daytime conditions, PM2.5 can be potentially higher without fire events, for instance, because these conditions tend to be coincident with increased precursor emissions and generation of secondary organic aerosols in the air. Furthermore, the fact that early morning and late evening temperatures tend to be lower during high pollution conditions may indicate the presence of temperature inversions which hinder atmospheric convection, leading to the collection of particulates that cannot be lifted from the surface. Cold morning temperatures can also result in stronger drainage flows into the Sydney basin. Consequently, if HRBs are being conducted during early mornings in the hills and mountains to the west of Sydney, this could result in the dispersion of particles from such sources, possibly into populated areas.

These findings indicate how the timing of HRBs can be altered to reduce their air pollution impacts in Sydney. Conducting HRBs when the PBLH is forecast to be higher ought to help reduce their air quality impacts in Sydney. More specifically, conducting HRBs later in the morning (for example by a matter of hours) is one way of potentially reducing HRB air quality impacts, because the PBLH generally starts increasing rapidly in height from 07:00 until 12:00 LT. Fires conducted early in the morning when the PBLH is at its lowest and temperatures are cool will promote effects such as fire smoke residing near ground level. One constraint concerning later burn times is that wind speed typically increases as the day progresses. However, the maximum mean diurnal wind speed was approximately 3 m s-1 and occurred at 15:00 LT. This is considerably lower than the RFS's upper-limit of 5.56 m s-1 for conducting safe HRBs (Plucinski and Cruz, 2015). An additional caution for conducting burns later in the afternoon is that onshore coastal breezes can develop during afternoons. The optimal timing of burns will also be dependent on other factors such as burn intensity, lighting method, fuel–soil moisture and geographic location.

There was a negative association between cloud cover and PM2.5 levels. It is possible that fire agencies conduct fewer HRBs during cloudy conditions in case of rain. Rainfall (if any) can also scavenge PM pollution out of the air. However, cloudless skies are also associated with high pressure systems, and therefore cool air descending, resulting in a stable calm atmosphere and low PBLH that is not conducive to pollutant dispersion.

Although there were similarities in the influence of covariates between locations, these associations often varied spatially. For example, mean diurnal PBLH and temperature were lower at Richmond in the early morning and at night in comparison to the other locations (Fig. S10). Richmond is further inland than the other monitoring sites and is thus closer to the mountain range to the west of Sydney. The insights gained into the spatial variation in the behaviour of covariates can support efforts to create location-specific particulate pollution forecasts.

The north-westerly signal apparent for three of four locations during HRBs and high pollution may reflect the fact that, overall, the majority of burns are conducted to the west, north and north-west of Sydney (Fig. 2). From a management perspective, comparatively greater attention might be devoted to adapting burn operations in these regions. In the case of Richmond (where wind direction did not have a statistically significant influence), one possible explanation is that the daily vector-averaging applied to the wind data has smoothed out the signal associated with diurnal changes in wind directions (and speeds), e.g. between drainage flow and sea breezes. Thus, to some degree, the signal of wind influence may be suppressed in this case. Another contributing factor could be Richmond's generally closer proximity to local burns. Also, its geographic location is quite different to that of the other monitoring sites; it is further inland than the other sites and is thus closer to the mountain range to the west of Sydney.

Using a different analysis approach, Price et al. (2012) found that the optimum radius of influence of landscape fires on PM2.5 was 100 km for Sydney. We found that whilst close-proximity fires influenced air quality, fires up to approximately 300 km from monitoring stations also potentially influenced PM2.5. Longer-range exposures on regional scales, particularly from multiple HRBs in an air shed can impact communities at considerable distance under certain atmospheric transport conditions (e.g. Liu et al., 2009).

Multiple concurrent burns are more likely to adversely affect air quality in Sydney, as indicated by the significant, positive influence of the number of concurrent HRBs on PM2.5 during high pollution days at all locations except Richmond. In general, greater numbers of concurrent burns within a given air shed are likely to result in greater quantities of particulate emissions. The area of these burns would also determine the amount of particulate emissions generated. HRB total area per day was a statistically significant predictor at two locations (Liverpool and Richmond). There are several possible explanations for the fact that burn daily frequency and area are not significant predictors at all locations. There will be some noise in total PM2.5 concentrations contributed by other emission sources, and this will vary with location. For example, Richmond differs from the other monitoring sites in that it is near agricultural land, and so emission sources like soil erosion and fertiliser use will introduce noise at this location. Investigating the relationships between burnt area and fire-related tracer species to reduce the noise in total concentrations contributed by other sources could be attempted in future work. There are also uncertainties regarding how accurately the area actually burnt was recorded within some polygons representing HRBs. In particular, to date it has been difficult to obtain timely and accurate estimates of the actual area burnt. Moreover, larger burns are often further away from the urban centres chosen, and are less frequent than smaller burns. In contrast, moderate to small burns are more frequent and often scattered along the urban fringes (rather than confined to one location or direction) and thus have a larger effect on the overall air quality within urban centres. Transport of smoke is also determined by interactions between basin topography and local or synoptic wind conditions. However, the interaction between mesoscale geography and meteorological variables is a factor that could not be easily accounted for in the present study (i.e. each site is located in a different location, therefore each has differing topography and land use type).