This study incorporates measurements made at two towers in a mature jack pine (Pinus banksiana) forest. The location of the towers relative to surrounding mines and processing facilities is shown in Fig. 1a. The York Athabasca Jack Pine (YAJP) tower is located at 57.1225∘ N, 111.4264∘ W. The second meteorological tower is operated by the Wood Buffalo Environmental Association (WBEA), a nonprofit environmental group, which monitors pollutants in the AOSR. WBEA identified this tower as “1004”. It is approximately 540 m directly south of the YAJP tower. The forest extends for at least 10 km in all directions. Images of the YAJP and WBEA (1004) towers and surrounding forest are shown in Fig. 1b and c, respectively. The ground beneath the forest is covered in reindeer moss (Cladonia spp.). Undergrowth vegetation in the area is limited to sparsely distributed blueberry bushes. The soil is sandy and well-drained. The forest canopy height is approximated as 19 m tall (with the tallest trees in the area ranging from 16 to 21 m in height). The canopy leaf area index (LAI) density profile measured in the vicinity of the YAJP tower is shown for comparison in Fig. 1d. The total LAI near the YAJP site is 1.17. Details of the LAI measurement technique are given in our companion paper (Zhang et al., 2023).

The village of Fort McKay is approximately 15 km to the NW of the site, and the town of Fort McMurray is 40 km south. The site is surrounded by oil sands production facilities. These include thermal in situ extraction, such as at Husky Sunrise and Suncor Firebag (approximately 23 km NW and 34 km WNW, respectively); open-pit mining, such as at Shell Jackpine (10 km north), Syncrude Aurora (20 km NNW), and Shell Muskeg (15 km NW); and combined mining and upgrading facilities, such as Suncor (13.5 km south), Syncrude (18 km SW), and CNRL (30 km NW). The upgrading facilities produce significant SO2 plumes (see Gordon et al., 2015), which are intermittently brought to the tower sites when the winds are from the south and SW directions (see Sect. 3.2). Additionally, the Hammerstone limestone aggregate quarry is located 10 km NW of the tower.

The 1004 tower measured wind speed and direction at heights of 2, 16, 21, and 29 m and recorded the data as 1 h averages. The YAJP tower measured high-frequency wind data with a 3D sonic anemometer (Type A, Applied Technology Inc.) mounted at a height of 29 m. Between September 2017 and August 2018, a second anemometer (Type V) was mounted within the canopy at a height of 5.5 m. All flux, wind, and temperature measurements from the YAJP tower were calculated in 30 min periods unless stated otherwise.

Between 4 and 8 June 2018, SO2 measurements were made at a height of 2 m at the YAJP tower with a 43i Thermo Scientific analyzer (herein referred to as “43i”). A tethered balloon system made measurements of SO2 using modified ozonesondes up to a height of 300 m between 13 and 15 July 2018. Between 7 and 26 August 2021, SO2 measurements were made at heights of 2 m and 29 m using two 43i instruments sampling though lengths of 1/4′′ Teflon tubing. For the 29 m height, the residence time of the tubing was measured as 14 s (a flow rate of 1.0 Lmin-1). Between 20 July and 31 August 2021 an Envea AF22e gas analyzer (herein “AF22e”) measured SO2 at a height of 2 m. The AF22e was solar-powered when generator power was not available. It was therefore operated for a longer time span than the 19 d of 43i measurements in 2021. All 43i measurements were at a frequency of 0.2 Hz, while AF22e measurements were once per minute. Calibration of the 43i instruments determined a standard deviation of less than 0.07 ppb at 0 ppb and less than 0.43 ppb at 80 ppb. The AF22e was not laboratory-calibrated but was corrected against the co-deployed 43i (sampling from the same inlet) for measurement values ranging from 0 to 60 ppb (R2=0.97).

To investigate the vertical structure of SO2 plumes, a tethered balloon system was used to lift two ozonesondes. Following the technique outlined in Yoon et al. (2022), one ozonesonde sampled through a filter tube coated with KMnO4 solution (which absorbs SO2) so that the difference between the two ozonesonde measurements gives the SO2 mixing ratio. The procedure for ozonesonde preparation and calibration is outlined in Yoon et al. (2022).

Passive samplers were deployed at the YAJP and 1004 towers over eight separate exposure periods between October 2020 and October 2021. The first two deployments were at YAJP, the third was a co-deployment at YAJP and 1004 for the same period, and the remaining five were at 1004. The deployments ranged in duration from 2 to 3 weeks. Samplers were mounted at heights of 2, 4, 8.5, 13.5, 18, and 23 m on the YAJP tower and heights of 4, 8, 13, 17.5, and 22 m on the 1004 tower. The samplers mounted at a height of 2 m on the YAJP tower were only used for two of the three deployments.

The devices used in this work were badge-type passive samplers (Blanchard and Aherne, 2019; Islam et al., 2016; Zbieranowski and Aherne, 2012) that housed a Whatman 40 filter paper pretreated with a KOH solution (Hallberg et al., 1984; Salem et al., 2009). Following field exposure, filters were extracted in 10 mL of 0.3 % hydrogen peroxide solution and the resulting sulfate (SO42-) concentrations were determined via ion chromatography. The mass of SO2 collected (Q [µg]) on the filter paper was calculated following Zbieranowski and Aherne (2012) as 1Q=VMRSf-Sb, where Sf [µg L-1] is the measured SO42- concentration in the extraction solution, Sb is the average field blank SO42- concentration (three per deployment), V [L] is the extraction volume, and MR= 6.67 × 10-4 is the molar conversion from SO42- to SO2. For this study, the average value of Sb was 0.01 mg L-1 SO42- compared to an average Sf of 1.38 mg L-1 SO42-; hence, the uncertainty due to blank subtraction was assumed to be negligible. The atmospheric concentration of SO2 was then calculated from Q as 2C=QRtAt, where C is the concentration of SO2 (µg m-3), A is the sampler cross-sectional surface area (m2), t is the exposure time (s), and Rt is the total badge-sampler resistance (s m-1). A study-specific Rt value was estimated through the co-deployment of passive samplers at five WBEA monitoring stations equipped with continuous SO2 monitors. Refer to Appendix A for further detail regarding Rt determination and WBEA sampling site information.

Samplers were deployed in duplicate or triplicate on the underside of rain shelters. Data variability was assessed by calculating the coefficient of variation (CV) among replicate samplers. To reduce vibration and sway with winds, a rigid mounting system was developed to attach the samplers to a pulley rope (YAJP) or metal cable (1004), as shown in Fig. 2. At the YAJP site, the samplers were attached to a 1.5 m plastic tube that was fixed to the pulley rope at the top and bottom of the tube. Three of the five tubes were guyed to the ground with strings for additional stability. The lowest (2 m height) sampler at the YAJP site (used for two of the three deployments) was fixed to the tower base. At the 1004 site, the pulley system used a metal cable loop. Here the mounting system was fixed to one side of the loop, while the other side of the loop passed though forked stabilizers to eliminate vibration and sway.

The passive samplers co-deployed at the five WBEA continuous monitoring stations allowed the evaluation of sampler performance. Comparison with corresponding continuous measurement data enabled the calculation of passive sampler bias (%), while a Spearman rank-order correlation test was applied to test the level of agreement (α<0.05) between samplers. At the YAJP tower, the AF22e was operational for the duration of the fourth sampler exposure period, and the 43i was operational for the duration of the third sampler co-deployment at both the YAJP and 1004 towers. These comparisons are discussed in Sect. 3.3.

Deposition fluxes were calculated from the passive sampler mixing ratio gradients following the gradient flux method from a procedure outlined in You et al. (2021). The relationship between the SO2 deposition flux (F, positive downward) and the gradient (dC/dz) is 3F=KCdCdz, where the trace gas diffusion coefficient (KC) and vertical concentration gradient (dC/dz) are modeled as constant throughout the height of the canopy, although this assumes that the flux divergence is insignificant in the canopy (equivalent to assuming all deposition is to the surface and not to the canopy elements). This approach has been demonstrated to reproduce deposition velocities by Wu et al. (2016) using gradients at heights of 16.5 and 33 m in a 22 m high mixed-deciduous canopy. This mixed-deciduous forest had an LAI of 4.6 compared to the LAI of 1.17 at our boreal forest site, suggesting that the denser foliage would have a greater effect on the in-canopy gradient at the mixed-deciduous site relative to our boreal site. The approach was also demonstrated by Meredith et al. (2014) using gradients measured at heights of 24 and 28 m in a nearly 24 m high temperate forest with an LAI of approximately 4. Here we determine the concentration gradient using a least-squares fit to the measured five-point profile within and above the canopy. Although some profiles had six points, the lowest measurement is not used in these cases for consistency in the analysis. We also compare this to a two-point concentration gradient determined using the two highest measurement heights. The LAI density distribution in Fig. 1d and Supplement Fig. S1 demonstrates that the two upper measurement heights (18 and 23 m at YAJP or 17.5 and 22 m at 1004) can be considered above-canopy relative to the canopy height of 19 m. Results from both gradient calculation techniques are compared in Sect. 3.3.

While KC was not measured, the momentum diffusion constant (KM,G) can be determined through the momentum flux–gradient relationship as 4u∗2=KM,Gdudz, where u∗ is the friction velocity (measured at a 29 m height) and the wind speed gradient (du/dz′) is approximated as Δu/Δz from the wind velocity difference between heights of 29 and 5.5 m. The uncertainty due to this approximation is investigated below. Since the wind speed gradient was only measured between September 2017 and August 2018, the 2020–2021 measurements require a parameterization of the diffusion constant. Ignoring the effects of the canopy on diffusion, Prandtl's mixing length model is adjusted for stability to give (Garratt, 1994) 5KM,P=κzmu∗ϕ, where κ=0.4 is the von Kármán constant, zm is the flux measurement height, and the stability parameter (ϕ) can be determined from the Obukhov length (L) following Garratt (1994) as 6ϕ=1-16z/L-1/4-5<z/L<01+5z/L0<z/L<1. Between 23 September 2017 and 2 August 2018, two anemometers were functional on the YAJP tower, and a gradient (Δu/Δz) was measured. For this period, we calculated KM,G from the flux–gradient method (Eq. 4) and compared this to the parameterization of KM,P from Eqs. (5) and (6). A least-squares fit to all the 30 min values of KM,P as a function of KM,G over the ∼ 10-month period gave a slope of 2.6 with R2=0.83 (Fig. 3), which supports the use of the Δu/Δz approximation. Hence, the diffusion can be more accurately parameterized as KM,P=κzmu∗/ (2.6ϕ), which is simplified to KM,P=κzm′u∗/ϕ, where zm′=zm/2.6=11 m. We note that the height of zm′=11 m lies between the two measurement heights (5.5 and 29 m), which supports the use of this technique. As demonstrated in Fig. 3, values of KM,G>5 m2 s-1 will be underestimated by this parameterization; however, less than 6 % of the KM,G measurements in the 10-month period are greater than 5 m2 s-1. Other parameterizations (not shown here) that account for the effects of the canopy on mixing and turbulence are described in Stroud et al. (2005), Wu et al. (2016), and Makar et al. (2017). While these parameterizations provide greater accuracy for vertically resolved modeling within the canopy, they do not improve the correlation between KM,P and KM,G for these data. This is likely because we approximate diffusion here with a single value throughout the canopy.

The trace gas diffusion constant can be related to the momentum diffusion constant by the turbulent Schmidt number as 7Sc=KMKC. Schmidt numbers determined in previous studies demonstrate a range of values. Similarly, Flesch et al. (2002) measured values between 0.17 and 1.34, while Gualtieri et al. (2017) report values in experimental and numerical studies between 0.1 and 1.3. You et al. (2021) defined a modified Sc that incorporates the stability parameter (z/L) and found that the value varied between 0.04 and 2.90. The average values (or values determined by least-squares fitting) from Flesch et al. (2002), You et al. (2021), and Gualtieri et al. (2017) are Sc=0.6, 0.74, and 0.99, respectively. Here we use an average of 0.8 and estimate the uncertainty in the calculated values based on the 0.6 to 0.99 range of values.

With these assumptions, Eqs. (3) to (7) are combined to give the deposition flux as 8F=κzm′Scu∗ϕdCdz.

The total resistance to pollutant deposition at height z (rt,z) is modeled as the sum of the aerodynamic (ra), quasi-laminar sub-layer (rb), and bulk surface (rc) resistances. The deposition velocity is the inverse of the total resistance as 9vd,z=1rt,z=1ra+rb+rc=FCz-C0, where Cz and C0 are the concentrations at height z and at a compensation point, respectively. Typically, a zero concentration is assumed at the compensation point (C0=0) either within the soil or the leaf, and the deposition velocity (vd,z) can be related to the flux as vd,z=F/Cz

Our measurements in this study were limited to a height of 23 m and are therefore a calculation of vd,23m. We compared these values to values determined by the GEM-MACH deposition parameterization (described in Sect. 2.5 below), which are also determined at a height of 23 m.

The deposition velocities in Hayden et al. (2021) were initially determined from aircraft measurements at heights > 150 m and then adjusted to a height of 40 m to give vd,40m. This accounts for reduced aerodynamic resistance between 40 and 150 m. Hayden et al. (2021) state that this extrapolation is considered their largest source of uncertainty. For comparison of the deposition velocity calculated form YAJP and 1004 tower measurements, we added the aerodynamic resistance between heights of 23 and 40 m, which can be calculated by integrating Eq. (3) between these two heights with Kc=κzu∗/Scϕ and averaging to give 10ra,23-40m=Scκϕu∗ln⁡4023. This is added to the total resistance to give vd,40m=rt,23m+ra,23-40m-1. The uncertainty associated with the added resistance is discussed below.

The total deposition can be calculated by combining Eqs. (8), (9), and (10). As discussed in Sect. 2.2, the gradient (dC/dz) is determined using either a least-squares fit to five measurement heights (the five-point gradient) or only using the two above-canopy measurement heights (the two-point gradient). Using the two-point gradient means that all uptake resistance (rt,23m) is below the gradient. However, due to uncertainty in the measured value of C using the passive samplers, there is higher uncertainty associated with a two-point gradient measurement. This uncertainty can be reduced by calculating the gradient as a least-squares fit to the five values of C at all measurement heights. However, there are likely sinks in the region over which the five-point gradient is estimated. As Fig. 1d demonstrates, most of the leaf area is closer to the surface, and the mean canopy height (50 % total LAI) is 11.5 m. Hence, the deposition velocity is calculated with the five-point gradient assuming that the error in the calculated gradient due to sinks throughout the canopy is small compared to the uncertainty in a two-point gradient measurement. Both approaches are compared in Sect. 3.3.

The use of long-term passive samplers (2 to 3 weeks in duration) to determine the gradients necessitates time-averaging the equations. If it is assumed that KM (a function of u∗/ϕ), the concentration (C), and the gradient (dC/dz) are all independent variables, this gives 11vd,40m=(κzm′Scu∗ϕ1〈C〉dCdz-1+Scκϕu∗ln⁡4023)-1, where the angle brackets 〈〉 indicate time-averaging over the sampling period. This assumes that there is no correlation between the stability-corrected friction velocity (u∗/ϕ), the concentration (C), and the concentration gradient (dC/dz), since they are averaged separately in the equation. If u∗/ϕ, C, and dC/dz are correlated, the assumption of independent variables will introduce an error in this flux estimation (since 〈u∗/ϕCdC/dz〉≠〈u∗/ϕ〉1/〈C〉〈dC/dz〉). In order to estimate the error associated with the assumption of independent variables, we also calculate the deposition velocity (in Sect. 4.1) using a time series of 30 min average concurrent friction velocity, stability, and concentration measurements (using the high-frequency SO2 gradient measurements made with the two 43i instruments in August 2021), which does not require long-term averaging of these terms.

During some of the long-term averaging periods, due to a lack of sunlight to charge the batteries or instrumentation failure, a complete time series of turbulence measurements (u∗/ϕ) was not available. In these cases, missing values of u∗ were filled using the hourly averaged wind speed (U) at the 1004 tower, which demonstrates a strong correlation (R2>0.8) with u∗ at the YAJP tower. Missing heat flux values (to determine Obukhov length, L) were filled based on a median diurnal pattern determined from the available measurements. The extent of each case of turbulence data replacement is presented in the Results section below, and the uncertainty based on the parameterization is discussed in Sect. 4.1.

The GEM-MACH deposition parameterization used to compare to our measured values is described in Makar et al. (2018). The reader is referred to their Supplement S1 (their Eqs. S.1–S.20) for a detailed description. Very briefly, the parameterization accounts for aerodynamic (ra), quasi-laminar (rb), and bulk surface resistance (rc), which includes resistances associated with soil, canopy, mesophyll, cuticle, and stomatal surfaces as well as resistance to buoyant convection. Here we model the forest as evergreen needleleaf. The parameterization is a function of temperature, relative humidity, atmospheric stability, solar radiation, and CO2 mixing ratio. For these values, we used measurements from the YAJP and 1004 towers, and we calculated deposition velocity (herein vd,GEM) for the time periods coincident with the profile measurements.

As discussed above, the parameterized GEM-MACH deposition velocity values were significantly lower than the observations of Hayden et al. (2021) for the same time periods and locations. Hayden et al. (2021) used a Monte Carlo analysis of the GEM-MACH deposition algorithm to demonstrate that the most likely cause of underestimation was in the standard model assumption that concentrations of hydrogen ions on the mesophyll, cuticle, and exposed surfaces corresponded to a neutral pH (6.68). The oil sands facilities are known sources of significant base cation emissions (the neutralizing impact of the base cations on acidifying deposition was noted in Makar et al., 2018). Hayden et al. (2021) showed that the increase in surface pH associated with deposited base cations could account for the discrepancy between modeled and measured SO2 deposition velocities and fluxes. That is, SO2 deposition close to the sources is likely being enhanced by the co-deposition of base cations.

An analyte detection limit was calculated as the product of standard deviation (five blanks per sampler batch) and the t value for a 99.0 % confidence critical value. The sampler batch detection limits (assigning the shortest exposure length for conservative values) ranged between 0.016 and 0.022 ppb SO2, with a study average of 0.019 ppb SO2. A significant linear correlation (R2=0.95; α < 0.05) was observed between the 14 co-located passive samplers and WBEA continuous SO2 measurements. The estimated sampler bias was low (2.3 %), while replicate sampler variability remained low throughout the study period with a CV = 4.5 %.

A time series of SO2 measurements is shown in Fig. 4. These measurements demonstrate the intermittency of the plumes and range of values. There are also 10 d of data from 2018 not shown here, which demonstrate a similar intermittency. Figure 5 plots all the measurements (including the 2018 measurements) with wind direction. This distribution demonstrates that most of the SO2 is transported from the Suncor (13.5 km at 195∘) and Syncrude (18 km at 225∘) stacks. All the measurements between 1 and 10 ppb (green dots) outside the 160 to 250∘ range are from one day in July with low winds and variable wind direction measured with the AF22e. This is maybe a recirculation event drawing back a Syncrude or Suncor plume from different directions.

Figures 4 and 5 demonstrate how winds bring elevated SO2 levels from the south to southwest. Plumes of SO2 with 5 ppb or higher appear on the majority of days, typically occurring between 09:00 and 18:00 MT (Mountain Time), although the duration of the plume exposure through the day can last from 1 to 8 h. The skewness of the data (i.e., a majority of near-zero values with some strong intermittent pulses of high SO2 levels) has implications for how an average passive sampler value should be interpreted. For example, when comparing passive sampler measurements at two locations, slight differences in wind patterns between the two locations could lead to vastly different average SO2 values.

SO2 measurements were made from a modified ozonesonde on a tethered balloon. These measurements are compared here to ground SO2 measurements (43i) in Fig. 6. The figure demonstrates decoupling and coupling of the different vertical layers of air in the boundary layer above the forest. During the first half of the ascent (elevation shown by black line), the balloon and ground SO2 measurements are nearly equal (red and green lines, respectively), demonstrating a well-mixed boundary layer. At the end of the ascent (∼ 13:10), the sonde samples an SO2 plume, while the ground 43i samples clean air. The plume begins to mix to the ground level near 13:25, and things become well-mixed near 13:40 with nearly equal ground and elevated SO2 values. This demonstrates that plumes are not only intermittent due to horizontal variation in wind direction but can also vary considerably in the vertical direction. Our analysis of deposition using a flux–gradient approach assumes that when these horizontal and vertical variations are averaged over a 2- to 3-week period, a smooth vertical gradient is observed.

The nine passive sampler profiles (from eight time periods) are listed in Table 1. Durations of the sample periods range from just over 12 d to more than 3 weeks. The sampler vertical profiles of SO2 mixing ratio with height are shown in Fig. 7. The gradients (dC/dz) are determined either as a two-point gradient above the canopy (to give vd,23m+) or from a least-squares fit to the five-point gradient (to give vd,23m). The mixing ratio (C) is determined from the highest sampler location. Using the two-point, above-canopy gradients, the deposition velocities calculated with Eq. (8) range from 1.4 to 28.0 cm s-1, with an average of 9.5 cm s-1. Using the five-point gradients, the deposition velocities calculated with Eq. (8) range from 2.9 to 9.4 cm s-1, with an average of 6.9 cm s-1. The R2 values for the least-squares fits are given in Table 1. Although the above-canopy, two-point gradient results in a higher average deposition velocity, there is much higher variation across the nine profile measurements, and the average values from each method (9.5 and 6.9 cm s-1) are not statistically different at a 55 % confidence level (i.e., v‾d± 0.75 σ/√n). Hence, we conservatively focus on the lower deposition velocities calculated with the five-point gradient determined by least-squares fit (vd,23m), but note the high uncertainty associated with these measurements.

Adjusting the deposition velocities (calculated with the five-point gradients) to a height of 40 m (from 23 m) reduces the range to 2.7 to 7.7 cm s-1 with an average value of 5.9 cm s-1. The difference between vd,23m and vd,40m for each profile ranges from 7 % to 18 %. The values measured here are approximately double those of Hayden et al. (2021), which range from 1.2 to 3.4 cm s-1. As was seen in Hayden et al., the values are considerably higher than the GEM-MACH parameterization (Makar et al., 2018) and an inference model used in Hsu et al. (2016) for the AOSR, which range from 0.2 to 0.3 cm s-1.

The AF22e and 43i analyzer measurements are compared to the passive sampler measurements in Fig. 7 for coincident periods during Profiles 3a and 3b (two sampler installations at the same time at the YAJP and 1004 towers) as well as Profile 4 (1004 only). In both cases, measurements near the surface show good agreement with passive samples measurements (accounting for the gradient of mixing ratio with height). During the Profile 4 period, the 43i measurements at a height of 29 m are much lower than the highest passive sampler measurement over the same period. Using the linear fit to the passive sampler gradient and assuming a linear interpolation of the gradient below and above the canopy, the mixing ratio at canopy height (19 m) would be approximately 1.37 ppb from the passive sampler profile versus 0.93 ppb from the 43i profile (a 32 % difference). One potential reason for this discrepancy could be a dependence of the passive sampler resistant (Rt) on wind speed, which could lead to overestimation of the passive-sampler-measured concentration above the canopy (where the wind speed is greater). This potential effect is investigated in greater detail in Sect. 4.2. The deposition velocity calculated with the 43i profile measurements (adjusted for aerodynamic resistance between 29 and 40 m) is 4.4 cm s-1, which is 68 % of the 6.5 cm s-1 deposition velocity determined by the passive sampler gradient over the same period (Profile 4, Table 1). This value is in close agreement with the flux–gradient measurement (4.1 cm s-1) of Hayden et al. (2021).

There is approximately a factor of 2 difference between the range of deposition velocities reported here (vd,40m between 2.7 and 7.7 cm s-1) and the aircraft-based measurements in the region (1.2–3.4 cm s-1, Hayden et al., 2021), but in both cases the measured values are considerably higher than the GEM-MACH parameterized values and the values determined by an inference model for the AOSR of Hsu et al. (2016). For comparison, the range of deposition velocities for different methods and studies is listed in Table 2. We note that the aircraft measurements of the Hayden et al. (2021) study cover a range of different forests and land types, including lakes, wetlands, and surfaces modified by oil sands extraction, waste, and tailings. The estimate made using a flux–gradient approach in Hayden et al. (2021) is from a 3 d period (4.1 cm s-1) at a tower in the town of Fort McKay. This value is closer to our measured values, but still 30 % less than our average value. Below we investigate whether measurement uncertainty based on assumptions in the methodology might be responsible for the observed differences.

As discussed above, the use of the five-point gradient effectively moves the total resistance (including aerodynamic, quasi-laminar sub-layer, and bulk surface resistances) to the ground level, following the “big-leaf” assumption typically used by regional- and global-scale models, as opposed to a vertical distribution of uptake throughout the canopy. While there is uncertainty associated with this assumption which is difficult to quantify, the average deposition velocity calculated with the two-point, above-canopy gradient is greater than the average deposition velocity calculated with the five-point gradient, suggesting that the deposition velocity calculated with the five-point gradient may be a conservative estimate (although the averages are within ± 0.75 standard errors and hence not significantly different).

The deposition velocities (vd,40m) from the nine profiles can be compared to a normal distribution, with 78 % (seven values) within 1 standard deviation (σ) of the mean, one value (Profile 8) 1.3σ higher than the mean, and one value (Profile 5) 2.4σ lower than the mean. The anomalous deposition velocity of 2.9 cm s-1 for Profile 5 is due to a combination of a weak gradient and high mixing ratio relative to the other profiles (Fig. 7). The fit to the profile is moderate (R2=0.72), but not the weakest fit. Meteorological conditions shown in Appendix A (Fig. A1) demonstrate some rainfall (> 25 mm) and some cloudy, humid conditions, but similar conditions are seen in other profile periods (e.g., rain in profile periods 1 and 3, clouds and high humidity in profile periods 6 and 8). Hence, the reason for this anomalous value is unknown.

The two highest deposition velocities (vd,40m=6.9 and 7.7 cm s-1 for Profiles 1 and 8) are from periods when most of the turbulence data were unavailable (61.5 % and 96 % missing, respectively). As discussed in Sect. 2.2, u∗ and the heat flux were parameterized based on measured wind speed and an assumed diurnal profile. Hence, there will be greater uncertainty in these measurements. As an example, recalculating all the deposition velocities with completely parameterized u∗ and heat flux results in a range of vd,40m from 3.2 to 7.8 cm s-1 with an average of 6.3 cm s-1. This suggests that the parameterization of missing turbulence data may lead to an approximate 10 % overestimation of vd.

Equation (5) was used to parameterize KM due to a lack of wind gradient measurements during the passive sampler measurement period. As demonstrated by Fig. 3, this introduces some uncertainty to the measurements. Previous measurements at the site demonstrate deviation from a linear fit for values of KM,G> 5 m2 s-1, which corresponds to values of KM,P>12.5 m2 s-1 or u∗/ϕM>2.8 m s-1. By comparison, the maximum value reached during Profile 3b (for example) is u∗/ϕM=1.4 m s-1 (or KM,P=6.2 m2 s-1), so the effect of this deviation from the linear fit should not be significant. The uncertainty can be approximated from the standard error of the slope, which is 0.017. From Eq. (8), this standard error gives an uncertainty of less than 2 % in the final vd estimate using a 95 % confidence interval.

Since vd is inversely proportional to the Schmidt number, our assumption of a constant value of Sc=0.8 can be assessed against other published average values of Sc=0.6 and 0.99. Using a value of Sc=0.6 would result in an increase of 33 % in vd, while a value of Sc=0.99 would result in a 20 % decrease. You et al. (2021) suggest a Schmidt number which is a function of stability (based on the ratio of the measured momentum diffusivity coefficient to the measured concentration diffusivity coefficient). We use the turbulence data from Profile 3b to investigate the use of this variable Schmidt number. Profile 3b is chosen because of the strong fit of the slope (R2=0.91) and the completeness of the turbulence data over that period (Table 1). For this reanalysis, Sc=0.08+3.13×10-9 exp. ((z/L+19.5)/1.008) for z/L<-0.18 and Sc=0.74 for z/L≥-0.18 (following You et al., 2021). It is noted that we are using a parameterized momentum diffusivity coefficient (KM,P) to estimate the gradient momentum diffusivity coefficient (KM,G) and the parameterization (Eq. 5) includes a correction for stability. Hence, this method includes two stability corrections: one for the assumption of KM,P=KM,G and one for the variability observed in Sc=KM,G/KC. Regardless of this complication, the use of this variable Schmidt number results in a decrease in vd,40m of 50 % (to 2.7 cm s-1) for Profile 3b.

As discussed in Sect. 2.4, the assumption that u∗/ϕ,C, and dC/dz are independent variables will result in an error if they are correlated. We investigate this assumption by calculating the deposition velocity using a continuous time series of 30 min averages of the friction velocity, stability, and SO2 observations (measured with the 43i instruments at 2 and 29 m heights). The use of 30 min averages is long enough to give confidence in the calculated turbulent statistics but should allow for co-variation in u∗/ϕ, C, and dC/dz. This allows for a calculation of vd,40m for each 30 min period. The average of these 30 min vd,40m values can then be compared to an average over the entire period following Eq. (11) (i.e., 〈κzmScu∗ϕ1CdCdz〉 compared to κzmSc〈u∗ϕ〉1〈C〉〈dCdz〉). In order to avoid large numbers caused when C≈0, the analysis is restricted to times when a plume is present using a criterion of C>1 ppb SO2 (see Fig. 4). This gives 73 30 min averages for analysis when SO2 mixing ratio and turbulence data are available (no filling of missing turbulence data is applied here). The average of all 73 30 min deposition velocities is vd,40m=3.3 cm s-1. The deposition velocity calculated using the averages of 〈u∗/ϕ〉, 〈C〉, and 〈dC/dz〉 for the same 73 30 min values is vd,40m=4.4 cm s-1. This indicates that the assumption of independent variables required by long-term averaging could lead to a 30 % overestimation of the deposition velocity. Here we define a corrected deposition velocity (which assumes that the 30 % overestimation applies to all measurements) as vd,40m∗=vd,40m/1.3. Applying this correction to the range of deposition velocities listed in a Table 1 gives a corrected range of 2.1 to 5.9 cm s-1, with an average of 4.6 cm s-1.

Some of the profiles shown in Fig. 7 have mixing ratios near or above the canopy which are much higher than the within-canopy values. Although the within-canopy values demonstrate an increase with height, for many profiles that increase is much more pronounced across the canopy top. For example, Profiles 1 and 4 show a sharp increase in mixing ratio above the canopy, while Profiles 3a and 8 show a sharp increase in the two highest measurement heights (relative to measurements in the sub-canopy). These four profiles (1, 3a, 4, and 8) demonstrate higher-than-average deposition velocities (≥ 6.3 cm s-1). By comparison, Profiles 2 and 3b show the best agreement with the linear least-squares fit (R2=0.99 and 0.91, respectively) and have the lowest deposition velocities (5.3 and 5.4 cm s-1). These results suggest that the greater-than-average increase in mixing ratio at the top of the canopy is associated with higher estimates of vd and a lower correlation of the profile with a linear fit.

Wind speed can affect the sampling rate of badge-type samplers; however, the effect is reduced by the diffusion membrane (Plaisance, 2011) and use of a wind shield (Masey et al., 2017). Hofschreuder et al. (1999) noted that with a proper sampler and draught shield design the influence of wind speed can be reduced to less than 10 %. Although our sampler concentrations were corrected using samplers mounted at WBEA stations coincident with continuous gas analyzers, the wind conditions at these stations might show significant differences compared to the canopy, and the increase in wind speed near the canopy top may have a significant effect on the measured SO2 gradient.

Using the wind speed profiles measured at 1004, the correlation of the above-canopy concentration gradient (dC/dz) between 18 and 23 m can be compared to wind data for each profile period. The values of dC/dz for each period show no correlation (0.001<R2<0.03) with the average wind speed gradient (dU/dz between 16 and 29 m), the average wind speed at 29 m, or the variance in hourly wind speeds at 29 m (all measured over the same time periods as the profiles). If wind speed had a direct effect on the sampler uptake, leading to higher measured SO2 mixing ratios for higher wind speeds, then a stronger correlation would be expected between the upper concentration gradient across the canopy top, where the wind gradient is largest. However, the low correlation between dC/dz and various variables related to wind speed suggests that the vertical gradient of wind speed between the sub-canopy and above the canopy does not have a significant effect on the measured SO2 mixing ratios.

In order to assess passive sampler performance, passive samplers were deployed at five WBEA continuous monitoring sites over five 2-week periods, resulting in 14 comparisons between passive sampler and continuous measurements (the number of deployment sites for the five periods were two, three, four, four, and one, respectively). During these periods, wind speeds at the site (measured at a 10 m height) ranged from an average of 1.3 to 4.0 m s-1. The passive sampler measurement error (the difference between the passive sampler and continuous measurements) ranged from -0.36 to 0.29 ppb. If the passive sampler resistance (Rt) varies with wind speed it would be expected that this error would correlate with the average wind speed for each sampler comparison. However, the correlation between sampler error and average wind speed is R2=0.003. Similarly, the correlation between sampler error and either maximum wind speed or wind speed variance is R2<0.003. Hence, these results do not suggest a strong influence of wind speed on the measured passive sampler concentration.