The composite seasonal cycle of radon at Richmond (Fig. 1a) is characterised by low concentrations November through February and higher concentrations March through October (see also Crawford et al., 2013). Ignoring May for a moment, at least ∼ 30 % of the 4.2 Bq m-3 amplitude of mean monthly radon concentrations seen in Fig. 1a is attributable to “non-local” effects. This can be seen by inspection of the mean afternoon (∼ 15:00 EST) radon concentrations in the composite diurnal cycles presented in Fig. 1c (see also Fig. 4a), which exhibit a seasonal range of about 1.5 Bq m-3. Afternoon radon values near the surface tend to be representative of the mean concentration through the depth of the daytime convective boundary layer (CBL), which is typically 1 km or more and changes only slowly from day to day in response to the passage of synoptic scale weather systems. Seasonal migration of the subtropical ridge leads to variations in the recent terrestrial source regions for radon, and frontal systems, deep convection and variations in the depth of the capping inversion affects the degree of dilution of radon within the CBL.

Climatological summaries of the Sydney Basin region (e.g. Crawford et al., 2013; Chambers et al., 2011) show that regional flow for this region in summer is predominantly easterly to southerly, with recent land fetch typically less than half a day. In winter, however, regional flow is often south westerly to westerly, with recent terrestrial fetch over south eastern Australia of the order of 2–3 days. In May, low mean wind speeds often result in longer air mass time-over-land, leading to particularly large nocturnal radon levels (Fig. 1a, b).

The remaining ∼ 70 % of the seasonal variation observed in mean surface radon concentrations at Richmond is attributable to local diurnal effects. The composite diurnal cycle of radon at Richmond (Fig. 1c) is characterised by peak concentrations near sunrise, when the nocturnal boundary layer is at its shallowest, wind speeds tend to be at their lowest and the influence of local sources dominate. Minimum values are found in the mid-afternoon, when the convective boundary layer is at its deepest (maximum dilution), and radon source influences are dominated by the air mass fetch history of the last ∼ 2 weeks (see discussion above). The timing of the diurnal cycle (Fig. 1c) changes according to seasonal variations in the intensity and duration of incident radiation, with morning peak concentrations shifting from 05:00 EST in summer to 07:00 EST in winter, and the duration of the afternoon minimum period contracting from 6 h in summer to 2 h in winter. Typically lower mean wind speeds (Fig. 1b) and colder drier conditions in autumn and winter generate weaker mixing, leading to shallower nocturnal inversions with high radon levels.

Atmospheric stability indices are designed to provide measures of the atmosphere's capacity to support vertical mixing by local turbulence processes. Variations in the observed radon signal due to the “non-local” processes described above, however, are not directly related to atmospheric stability and can be comparable in magnitude to the stability-related variations. The “non-local” radon signal is largest for sites situated near the coast, due to the strong land/ocean contrast in the radon source function, but will be evident to some degree at all sites since the 3.8 day half-life of radon means that fetch regions over the last two weeks or more influence the observed signal. It is therefore important to characterise and remove (or neutralise) the effects of these “non-local” variations prior to application of radon as a quantitative indicator of atmospheric stability.

When vertically resolved radon measurements are available from towers, a two-point radon gradient can be calculated between the lowest and highest intake levels for the purpose of characterising bulk mixing characteristics in the nocturnal boundary layer (Chambers et al., 2011; Williams et al., 2013). This vertical differencing effectively removes contributions to the absolute radon signal on timescales greater than the diurnal. To demonstrate this point, 10 days of radon gradients between 2 and 50 m from another site within the Sydney Basin (Lucas Heights, 50 km SSE of Richmond) are presented in Fig. 2. Described in Chambers et al. (2011) and Williams et al. (2013), this site is located on a broad ridge 18 km from the coast. Topography in the immediate vicinity is moderately complex, with changes in elevation of ∼ 150 m within a 1 km radius. 4-day back trajectories (Fig. 3) using the HYSPLIT model (Draxler and Hess, 1998) indicated that the increase in daily minimum (afternoon) radon concentrations from day 253 to day 255 in Fig. 2a was a result of an increasing land fetch over eastern Australia. On day 257, both detectors indicated an abrupt reduction in radon concentration corresponding to a synoptic change in air mass fetch from terrestrial (south westerly) to oceanic (south easterly). Inspection of the corresponding radon gradient time series (Fig. 2b), however, shows no significant influence from either the slow or the abrupt fetch changes. Instead, the maximum radon gradient values attained each night are primarily a measure of the amount of locally sourced radon trapped within the nocturnal inversion. Assuming a local radon source function that is approximately constant in time and space, the gradient time series is thus predominantly a function of stability.

Unfortunately, few sites are set up to conduct vertical radon gradient observations. However, the particular qualities of radon, together with an understanding of its distribution in the boundary layer, allow us below to construct an approximate vertical radon gradient using only measurements at a single height near the surface, for use as a stability indictor.

In the mid-afternoon (Fig. 1c), the ABL is relatively well-mixed from the surface to the synoptic inversion and radon measurements close to the surface are representative of bulk ABL radon concentrations (e.g. Chambers et al., 2011; Williams et al., 2011; Moses et al., 1960). When the ABL is deep and well-mixed, radon concentrations reflect the collective influence of all sources (decay weighted) over the air mass's recent (∼ 2-week) fetch history. After sunset, however, in the absence of low cloud or high winds, an inversion layer begins to form from the ground up as a result of the growing thermal stratification (the stable nocturnal boundary layer, SNBL) (e.g. Collaud Coen et al., 2014; Sesana et al., 2006; Stull, 1980). The radon concentration in the residual layer (RL), the air residing between the top of the SNBL and the previous day's synoptic inversion, remains similar to that of the previous day's ABL (ignoring radon decay; e.g. Kondo et al., 2014) and can therefore be approximated from the previous afternoon's minimum (well-mixed) radon concentration near the surface. By linearly interpolating minimum radon concentrations from one afternoon to the next, it is therefore possible to produce a radon time series similar to that which might be measured by a radon detector with an intake height within the RL. Below the nocturnal inversion, however, the radon concentration of the SNBL evolves largely independently of the overlying radon concentration. Since wind speeds are typically < 1 m s-1 on stable nights, the radon that accumulates between the surface and the capping inversion of the SNBL (e.g. morning peak of Fig. 1c) is derived primarily from local sources (i.e. within less than a 40 km radius; Chambers et al., 2011). A radon “pseudo-gradient” can thus be formed by computing the difference between the near-surface observations and the constructed time series approximating the radon concentrations in the RL. This pseudo-gradient will be substantially free from variability associated with “non-local” processes and thus mainly influenced by the strength of the local radon source function (approximately constant) and atmospheric stability.

As an example of the above technique, a 5-week subsection of the 5-year Richmond radon time series is presented in Fig. 4a. Periods of oceanic fetch are evident where daily minimum concentrations drop below 0.5 Bq m-3, as well as periods of multi-day terrestrial fetch with daily minimum radon concentrations of 3–4 Bq m-3. Included in this figure is a linear interpolation between afternoon minimum radon concentrations (red line). The routine used to generate this line identified the minimum hourly radon concentrations between 12:00–18:00 EST each day and linearly interpolated between them. On occasion, when there was a large change in fetch (terrestrial to oceanic) or a large nocturnal mixing event, the difference between the observed radon and the interpolated values (the “pseudo-gradient”) sometimes went negative. On such occasions, the routine adjusted the interpolated series by adding additional linear segments (as few as possible) to maintain a non-negative “gradient”. A subsection of the resultant pseudo-gradient time series is shown in Fig. 4b.

A feeling for the relative contributions of the “non-local” and stability-driven contributions to the seasonal cycle of radon at Richmond can be obtained by separately considering their monthly mean values (Fig. 5a). There is a pronounced seasonality in both components. In the case of the “non-local” signal, this is mainly due to changes in air mass fetch, as already discussed. Stability-driven contributions are smallest in November through February, when wind speeds are higher (Fig. 1b) and air masses tend to be more humid (fetch predominantly oceanic) so that nocturnal cloud cover is more common. These factors reduce the strength of the nocturnal thermal stratification near the surface, leading to deeper nocturnal boundary layers and lower near-surface radon concentrations. In March through October, the predominantly terrestrial fetch results in drier conditions and more cloud-free nights. This enables strong thermal inversions to form near the surface when wind speeds drop, resulting in near-surface radon concentrations that sometimes exceed 40 Bq m-3. May exhibits the largest monthly mean pseudo-gradient, corresponding to the smallest wind speeds (Fig. 1b).

A mean hourly diurnal composite plot of the radon gradient is presented in Fig. 5b, with the time axis chosen to emphasise the nocturnal radon build-up, which begins around sunset (18:00) and starts to erode after sunrise (06:00). We define a 12 h “nocturnal stability window” from 20:00–08:00 (Fig. 5b), chosen to capture the full range of radon concentrations on the majority of nights. The mean radon pseudo-gradient within the nocturnal stability window was calculated for each night, and then quartile ranges of the cumulative frequency histogram of this quantity (Fig. 6) were used to define the following four radon-based whole-night stability classes:

While the nocturnal mean radon gradients reported above are specific to the Richmond site, updated values for any measurement site can be determined by preparing a cumulative frequency diagram (Fig. 6) for the site in question, and reading the new quartile ranges off the graph.

After sorting each whole night of the 5-year data set according to this stability classification, we calculated corresponding diurnal composite radon gradient plots (Fig. 7). For nights classified as near-neutral (Q1), there was little nocturnal accumulation of radon and the amplitude of the diurnal cycle was 1.5 Bq m-3. By contrast, nights classified as stable (Q4) showed a rapid radon build-up after sunset, peaking near sunrise, with a mean diurnal amplitude of 22.9 Bq m-3.

Standard climatological observations were available at Richmond during the period of this study. Of these observations, the parameters most easily relatable to measures of stability and/or mixing are: wind speed, standard deviation of wind direction, and temperature. Diurnal composite plots of these parameters, grouped solely by our radon-based stability classification scheme for whole nights, are shown in Fig. 8.

Nocturnal (20:00–06:00) wind speeds were highest for the nights classified as “near neutral” (on average almost 2 m s-1). High wind speeds result in a deep, mechanically mixed nocturnal boundary layer, and these periods also exhibited the smallest diurnal amplitude in wind speed and temperature as well as a comparatively small standard deviation of wind direction. Such characteristics are consistent with overcast conditions and the passage of frontal weather systems. The smallest mean nocturnal wind speeds were observed on nights classified as “stable” by the radon method, usually dropping below 0.5 m s-1. However, even the weakly stable evenings had wind speeds < 1 m s-1, which is consistent with Sesana et al. (2003) who reported no significant nocturnal accumulation for wind speeds above 1.5 m s-1.

The stable nights also exhibited the greatest standard deviation of wind direction, consistent with the presence of meandering mesoscale flows within the shallow SNBL. The amplitude of the diurnal temperature signal in cases identified as stable was greater than for the other categories, as would be expected for predominantly clear-sky conditions. Furthermore, atmospheric pressure (not shown) was 2 hPa greater on average in the “stable” cases, consistent with anti-cyclonic activity and regional subsidence.

In the previous section, it was seen that the radon-based atmospheric stability classification scheme is clearly an effective quantitative tool for delineation between various nocturnal atmospheric mixing states. As a further evaluation, we used the new classification scheme to quantify changes in various urban pollutant concentrations as a function of atmospheric stability. As can be seen in Fig. 9, despite the “whole night” resolution of the radon-based stability classification scheme, it is capable of characterising the influence of nocturnal mixing on primary and secondary gaseous and aerosol pollutants.

In the case of NO, NO2 and PM2.5, the most stable atmospheric conditions (shallow mixing depths) identified by this scheme are associated with dramatically increased near-surface pollutant concentrations. On average, the diurnal range of NO increases from 1.6 ppb under well mixed conditions to 14 ppb under the most stable conditions. The corresponding diurnal range increase for NO2 is 2.8 to 9.4 ppb, and for PM2.5 3.6 to 12 µg m-3. However, increasing atmospheric stability has the opposite effect on near-surface concentrations of ozone and SO2. Since ozone is highly reactive, when trapped in a shallow inversion layer (stable class) surface deposition processes and titration by NO emitted by vehicles rapidly reduce the concentration. Conversely, when near-surface wind speeds are higher (near-neutral class), ozone is mixed downward from the overlying air mass, resulting in higher nocturnal concentrations. Similarly for SO2, when trapped in a shallow inversion layer chemical sink processes rapidly reduce the near-surface concentration of SO2 formerly present in the ABL. Since there are no significant sources of SO2 in the immediate vicinity of Richmond, no accumulation is observed leading up to sunrise.

As was the case for the climatological variables, the diurnal behaviour of each pollutant species in each of the radon-based stability categories was clearly consistent with current knowledge for urban areas (e.g. O3, Avino et al., 2003; Acker et al., 2006; Di Carlo et al., 2007; Zhang et al., 2012, Pitari et al., 2014; SO2, Jenner et al., 2012; PM2.5, Gupta et al., 2007).

While Fig. 9 clearly demonstrates a close correspondence between mean nocturnal radon accumulation near the surface and pollutant concentrations, the pronounced differences in diurnal cycle characteristics between radon (Fig. 7) and urban pollutants (Fig. 9), largely brought about by spatio-temporal differences in their sources and sinks, can result in low, or highly variable, correlations between radon and specific pollutant concentrations.

Pasquill–Gifford (P–G) atmospheric stability typing (Pasquill, 1961; Turner, 1964; Pasquill and Smith, 1983) is usually employed to facilitate estimates of lateral and vertical dispersion parameters in Gaussian plume models. The P–G stability categories employed here were defined according to the turbulence-based variation of Turner's method (Turner, 1964), based on scalar mean wind speed and the standard deviation of wind direction. In all, there are seven P–G stability categories ranging from A through G (Table 1), although for many regulatory applications (and the turbulence-based version of Turner's method) the more strongly stable categories F and G are grouped together. The key used for assigning the P–G turbulence stability categories are provided in Tables 2 and 3 (see also USEPA, 2007).

All hourly data of the 5-year data set was assigned a P–G turbulence stability category according to Tables 2 and 3. To best match the classification performed by the radon-based technique, we then assigned “whole-night” P–G stability classes based on the modal (most common) hourly stability category defined over the 9-hour period 21:00–05:00 EST; a reduced nocturnal window compared to the radon method was used here to avoid the lag known to exist between hourly P–G stability categories and radon-separate concentrations (Duenas et al., 1996). Lastly, we categorised the climatological and pollutant concentration data on a whole-day basis according to the assigned P–G stability class; selected results are shown in Fig. 10.

Using the radon “gradient” data as a benchmark (Fig. 10a cf. Fig. 7), the P–G stability classes D-F appear to fall roughly between the four radon-defined stability classes. For example, peak radon concentrations for the moderately and strongly stable classifications in the radon-based scheme were 13 and 23 Bq m-3, respectively, whereas the peak “very stable” P–G turbulence value was 16 Bq m-3. This indicates that the P–G “very stable” category is less selective of the strongly stable nights than the equivalent category in the radon-based scheme, a fact that is confirmed by a smaller amplitude in the diurnal temperature composite in Fig. 10c (cf. Fig. 8c). Comparing the morning evolution of near-surface temperature between days classified as stable by the two schemes, fewer of the days classified as stable by the P–G turbulence scheme appear to develop into clear-sky convective conditions than is the case for the radon scheme. In fact, mornings of P–G “stable” days are cooler than the P–G “moderately stable” days. Both schemes predict nocturnal wind speeds of around 0.5 m s-1 under the most stable conditions, whereas the P–G scheme attributes a smaller proportion of wind speed events to the neutral category, as evident from the higher mean wind speed and greater variability over the diurnal cycle.

Perhaps most significantly, the fact that the P–G “stable” category is less selective of the strongly stable nights than the radon-based scheme means that the relationship between atmospheric stability and peak nocturnal pollutant concentrations are underestimated by the P–G scheme (Fig. 10e cf. Fig. 9d for SO2; Fig. 10f, cf. Fig. 9e for PM2.5). Such discrepancies (30–50 %) can have significant implications for public exposure records and would influence air quality management.

While the method described here to derive the radon-based stability classification scheme is applicable to most near-surface radon (or radon progeny) time series, the absolute threshold values adopted for the four stability classifications (shown in Fig. 6) will vary according to site-specific changes in the frequency distribution of the nocturnal mean radon gradient (see Sect. 3.4). At sites that experience consistent snow cover or freezing soils, separate stability classifications may needed for the “warm” and “cold” parts of the year to account for changes to the local radon source function. Similarly, at sites where there is a large summer/winter change in daylight hours, separate seasonal stability classification may be required to account for differences in nocturnal accumulation times. Furthermore, for sites located at, or close to (say < 20 km) the coast, it may be necessary to derive varying thresholds for the classification scheme which take into account the fact that part of the nocturnal radon footprint may be over the ocean with effectively zero flux (e.g. onshore vs. offshore flow). It is also important to note that the choice of four stability classes in this study was essentially arbitrary. The number of stability classes used to apportion the nocturnal radon data could be increased if desired, although care needs to taken to ensure that a sufficient number of observations remain within each defined category to provide statistically sound results. Based on the five years of observations used here, results from each of the four stability categories represented in Figs. 8 and 9 were derived from approximately 400 individual observations (for each hour of each curve in the diurnal composites).

Although radon gradients are calculated hourly, stability classifications in this study have been defined on a “whole-night” basis (20:00–08:00). This was done so that a meaningful analysis of “typical” diurnal patterns could be performed. While intermittent events of various natures can seriously disrupt the atmospheric stability regime on a given night, long-term observations in the Sydney Basin reported by Chambers et al. (2011) have indicated that in more than 70 % of cases a night that begins within a broadly defined stability category will usually persist as such. As evident from the daytime values of Figs. 8 and 9, this level of synoptic “persistence” often extends for the whole day; e.g. stable nights are often associated with, warm, clear-sky days. Having said this, there is no strong reason why radon gradients could not be applied on an hourly basis, for example in an operational environment. If “future” values are unavailable, an estimation of the current RL value can be obtained simply by extrapolating the minimum value from the previous afternoon. The uncertainties introduced by this additional approximation have not been estimated in the current study, but are likely to be small in general.

Since it is usually the larger-scale synoptic conditions that drive atmospheric stability conditions at the surface, the stability categories derived from the current approach are often applicable to a broader region than the immediate vicinity of the observations. For example, an atmospheric stability classification scheme based on hourly radon observations from Warrawong (70 km south of the Sydney CBD; Chambers et al., unpublished data), was more successful at categorising hourly measurements of NO, NO2, Ozone and PM2.5 at a site 10 km to its north, than a Pasquill–Gifford scheme calculated from climatological observations made adjacent to the pollution monitoring station. A corollary of this observation is that, while multiple pollution monitoring stations might be required to assess the pollutant levels for a large urban region (Duenas et al., 1996), a single radon monitoring station could be sufficient to assess the nightly stability regime of a region within a radius of 10s of km, large enough to cover a modestly sized urban area. Furthermore, it is important to note that the method of stability classification outlined here is completely independent of any climatological or micro-meteorological observations, making it a simple and economical alternative to conventional approaches to stability classification.

The consistent and effective way in which the radon-based stability classification scheme resolves the diurnal behaviour of gaseous and fine-particle urban emissions is likely to be a valuable tool in the assessment of chemical transport model performance, by providing diurnal composite pollutant concentrations for a range of nocturnal mixing depths which may, or may not, be resolved by a given model. Since this method enables hourly distributions to be calculated for each quantity over the diurnal cycle for a range of stability classifications, it would be an ideal benchmarking tool.

An alternative interpretation of radon measurements in the stable boundary layer is possible with time-resolved measurements. Radon is assumed to be emitted with a constant flux, F; into a well-mixed box. The height of the box can be determined from the near-surface radon concentration, C, if radon emissions are known.

The box-model approach has been used for several studies since the 1970s (including Pitari et al., 2014; Griffiths et al., 2013; Grossi et al., 2012; Di Carlo et al., 2007; Sesana et al., 2006; Galmarini, 2006; Pasini and Ameli, 2003; Kataoka, 1998; Allegrini et al., 1994; Fujinami and Esaka, 1988; Guedalia et al., 1980; Fontan et al., 1979). In the model, the change in radon concentration within the well-mixed layer adjacent to the surface is due to a balance between surface emissions, radioactive decay and, if the layer is growing, dilution. These assumptions lead to the budget equation: dCdt=F/he-λC-D, where λ=2.098×10-6 s-1 is the radon decay constant, D is the dilution term, nonzero when the boundary layer is growing and therefore entraining low concentration air from above, and here the radon flux, F, is assumed to be 20 mBq m-2 s-1, a representative value for New South Wales (Griffiths et al., 2010).

Equation (1) can be solved iteratively to obtain a time-series of the effective mixing depth, he (Griffiths et al., 2013) or can be solved analytically by assuming that D=0. If dilution is assumed to be zero, we call the resultant length-scale the accumulated estimate of the mixing height, hacc, which is given by Fontan et al. (1979) as: hacc=F1-e-λtλC-e-λtC0, where C0 is the concentration at time t=0, the time when radon concentration reaches its minimum. The effect of radioactive decay is included in Eq. (2), although over the course of a single night it only changes the estimated mixing length scale by less than 5 %.

We used the above two methods to calculate the hourly nocturnal mixing depth since sunset, then – based on the 5 h before sunrise each morning – calculated the distributions (10th, 50th, and 90th percentiles) of mixing depths for each stability category (Fig. 11).

Based on these mixing height estimates the pseudo-gradient classification method leads to similar results as either of the box-model approaches (he or hacc), in spite of the different conceptual framework. Stronger agreement is seen with hacc than with he, and this is not surprising since hacc – like the pseudo-gradient – is based on a measured change since the previous afternoon's minimum.

Under the most stable conditions the radon-based mixing length scale is typically 30–35 m, but occasionally drops below 20–25 m. For the near neutral (well mixed) cases, however, the nocturnal boundary layer is typically 400–500 m deep, but occasionally over 1000 m.

As we have a sufficiently long (5-year) data set at Richmond, it is possible to analyse stability effects on pollutant concentrations as a function of season and air mass fetch. Figure 12 compares winter and summer concentrations of PM2.5, SO2 and ozone in very stable (extreme pollution) conditions. At Richmond, there are strongly contrasting urban signatures within the air mass fetch for winter and summer. In winter, as previously mentioned, regional flow is mainly from the west to south west; emissions are typically of a rural or domestic nature. In summer, however, air mass fetch varies from east to south; frequently directly from the Sydney CBD (to the southeast).

In winter, the peak PM2.5 concentrations (occasionally exceeding 15 µg m-3) occur in the morning, when accumulated smoke from domestic heating around Richmond and the foothills dominates. During the days, however, the westerly fetch covers extensive forested regions of the Great Dividing Range, and PM2.5 concentrations are comparatively low. In summer, both the morning and evening traffic plumes are evident in the PM2.5 concentrations, and – despite deeper daytime ABL depths in summer than winter – the daytime PM2.5 concentrations from Sydney are more than double that observed from the west.

Wintertime SO2 concentrations are generally low at Richmond; during the days, when atmospheric mixing is deepest, the slightly elevated SO2 concentrations likely represent advection from distant pollution sources. For example, Cohen et al. (2012) estimated that 30–50 % of sulfate measured in the greater Sydney region during the cooler months of the year was attributable to releases from distant coal-fired power stations. In summer, SO2 concentrations are higher overall, with morning and evening traffic-related peaks evident (although delayed compared to PM2.5). Although derived from near-surface sources, this urban SO2 can mix throughout the ABL en route to Richmond (> 30 km from Sydney). Since stable nocturnal conditions are usually associated with clear-sky days, these represent the peak ozone times for the respective seasons. In summer, when fetch is from the Sydney CBD and solar insolation is much greater, ozone concentrations are seen to occasionally (15–20 % of the time) exceed 60 ppb; almost twice the peak concentrations observed in winter.

For comparison with the distributions reported here (µ ± 1σ) of the most stable atmospheric conditions for this 5-year period, as presented in Fig. 12) the National standards for criteria air pollutants in Australia guidelines (http://www.environment.gov.au/resource/national-standards-criteria-air-pollutants-1-australia) state that: daily mean PM2.5 concentrations should not exceed 25 µg m-3, hourly average SO2 concentrations should not exceed 200  ppb, and hourly averaged ozone concentrations should not exceed 100 ppb.