Size-Resolved Particle Fluxes and Vertical Gradients over and in a Sparse Pine Forest

Abstract

Although a number of flux data sets indicate apparent upward fluxes of particles over forests, the causes of such fluxes remain only partially understood. Using data collected during the 2011 BEACHON experiment, it is shown that over one third of fluxes of both sub- and super-30-nm diameter particles over this sparse pine forest are upward. Quadrant analysis, timescale analysis using a particle dynamics model, and frequency power spectra of particle concentrations demonstrate that, in this environment, the morning upward fluxes tend to be associated with downward “sweeps” of particle depleted air during break down of the nocturnal inversion, and it is the most common mechanism resulting in upward fluxes of particle size distributions with diameters above 30 nm. Upward fluxes of particles later in the day are more strongly linked to “ejections” of particle enriched air from the canopy that are attributable to growth of fairly recently nucleated particles by both addition of oxidation products of biogenic volatile organic compounds and coagulation. This mechanism appears to dominate upward fluxes of sub-30-nm particles, although the resulting destabilization of the particle size distribution can result in upward fluxes of larger particles. Vertical gradients of particle size distribution above, through, and below the canopy are also analyzed to investigate the size dependence of canopy uptake of particles and indicate that, in accord with wind tunnel analyses, penetration efficiencies are lower for smaller geometric mean diameters (∼15–20 nm) and increase with diameter up to approx. 80 nm (the largest diameter considered here).

Copyright 2013 American Association for Aerosol Research

1. INTRODUCTION AND OBJECTIVES

Differences between size-resolved particle dry deposition rates over forests from numerical models and field observations remain incompletely understood, and knowledge gaps regarding the functional dependencies of fine particle fluxes confound development of representative fluxes and/or deposition rates (Pryor et al. 2008b). Here, we present data collected from a subproject of the bio-hydro-atmosphere interactions of energy, aerosols, carbon, H₂O, organics, and nitrogen (BEACHON) experiment conducted in summer 2011. The experimental plan for this component of BEACHON was designed to investigate two aspects of particle fluxes over and in forests:

i.	To identify, quantify, and undertake attribution of upward fluxes of ultrafine atmospheric aerosol particles.
ii.	To compare inferred size-resolved canopy capture efficiencies from a sparse forest with canopy penetration efficiencies from wind tunnel experiments.

Although several studies have reported incidences of upward fluxes of total particle number concentrations or particles in specific size ranges above forests (Schmidt and Klemm 2008; Pryor et al. 2008a; Grönholm et al. 2009; Ahlm et al. 2010; Gordon et al. 2011), the causes of observed upward (i.e., apparent emission) fluxes remain uncertain (Pryor et al. 2008a). Previous research has identified a number of processes as potential causes of upward fluxes that result from nonideal experiment sites. These include the presence of local particle emission sources (Buzorius et al. 2000), and deviations from assumptions regarding homogeneous planar flow (i.e., high attack angles on sonic anemometers [>20° from the horizontal]) due to either topographic effects or tower shadow influences (Nakai et al. 2006). However, other phenomena may also be important. During moderate to high turbulence conditions, aerodynamic resistance to uptake becomes a minor component of the processes controlling dry deposition and phenomena within the canopy sublayer and at the leaf surface dominate (Petroff et al. 2008). In general, deposition velocities (v_d ) for aerosol particles generally scale with leaf area index (LAI) (Vesala et al. 2005), but there is evidence that the precise nature of the canopy structure (e.g., vertical distribution) plays a key role in determining size-resolved deposition rates (Katul et al. 2011), and given the majority of forest canopies are not homogeneous, there is evidence that the canopy storage term is not zero, because particles are stored in the canopy space at night and diluted with cleaner air from above during the daytime as the boundary layer grows (Nilsson et al. 2001; Pryor et al. 2008a; Gordon et al. 2011). Even in the absence of these effects, particle flux divergence due to nonstationarity of the particle size distribution (PSD) during the transport process can also act to confound interpretation of flux measurements, when the timescales at which the number concentration in each mode (or size-bin) is evolving as a result of coagulation or growth out of the size class due to condensation of semivolatile compounds (Pryor and Binkowski 2004).

Wind tunnel experiments of ultrafine particle uptake on pine branches found removal efficiency was highest for 20-nm particles and declined as particle diameter approached 100 nm, and that increased branch packing density increased removal efficiency, with a smaller effect of wind speed and no measurable effect from branch orientation (Lin and Khlystov 2012). Thus, in the absence of particle growth within the canopy due to condensation of oxidation products of biogenic volatile organic compounds (BVOC), there is an expectation that even under conditions of a sparse canopy the canopy will be the largest particle sink and thus the vertical gradients of PSD will show a canopy minimum with the minimum being most marked for particles with smallest diameters. This postulate is tested using a gradient measurement approach to obtain canopy penetration efficiencies (computed as the ratio of particle concentrations in a given size range as measured above, within, and below the canopy), which are compared with estimates derived from particle deposition to spruce and pine branches in a wind tunnel experiment (Lin and Khlystov 2012).

2. EXPERIMENTAL DETAILS

One second PSD of sub-0.5-μm aerosol particles were taken using a TSI Fast Mobility Particle Sizer (FMPS; model number 3091) during the BEACHON experiment conducted between 21 July and 11 August 2011, inclusive in the 67 km² Manitou Experimental Forest, CO (38.64°N, 105.11°W, ∼2300 m asl). The Manitou Experimental Forest (MEF) is a 6758 hectare forest dominated by open-canopy ponderosa pine. The forest close to the sampling tower has an LAI ∼ 1.9 (DiGangi et al. 2011). Processing of satellite remote sensing products indicate that trees closest to the tower on which the instrumentation was deployed have an average height of approximately 15 m, whereas the median height for this region of the forest is approximately 17 m. The stem density for trees with a stem diameter >50 cm at an estimated breast height is ∼80 ha⁻¹ in the tower footprint with range 70–112 for individual hectares within approx. 5 km of the tower. The forest is located in the front range of the Colorado Rockies in a topographically complex region, and the wind direction data indicate evidence of thermotopographic flows with upslope flow during the day and nocturnal drainage flows.

The FMPS employs a sampling system wherein particle detection and sizing occurs using multiple, low-noise, electrometers (Tammet et al. 2002), and number concentrations are reported in 32 logarithmically-spaced channels in the size range, 6.04 to 523.3 nm. It should be acknowledged that the PSD derived from FMPS measurements are subject to larger uncertainties than those from scanning mobility particle sizers (or differential mobility particle sizers) due principally to higher measurement uncertainty caused by the unipolar charger and issues with the calibration matrix. However, the high temporal resolution of the FMPS makes it one of the few instruments suitable for direct flux applications for size-resolved fine (i.e., sub-100 nm) particles (Pryor et al. 2009; Gordon et al. 2011).

All PSD presented herein derive from a single FMPS operated within a two-stage experimental design in which from 00 to 30 minutes past each hour air was sampled from a height of 25 m (0.1 m below the base of a sonic anemometer) down a copper tube (length ∼ 52 m, ID ∼ 8.9 mm) at a rate of 27 lpm and sampled by the FMPS (these measurements are referred herein to as flux measurements) (Figure 1). During 31–59 minutes past each hour air was sampled at a flow rate of 17 lpm down conductive tubing (length ∼ 25 m, ID ∼ 8.0 mm, and then on through an equivalent length of copper tubing, ID ∼ 8.9 mm) connected to a winch system that operated to sample air from heights between 3 and 21 m and again sampled by the FMPS at 1 Hz (these measurements are referred herein to as gradient measurements). The flux measurements are thus above the canopy sublayer (which is typically characterized as 1.1 to 1.6 times the canopy height [Katul et al. 2011]), whereas the gradient measurements sample the PSD at different levels above, within, and below the forest canopy. Data from the first 30 minutes in each hour are thus used for the purposes of direct flux determination, whereas those from the second half of each hour are used to characterize and quantify PSD gradients through the canopy.

FIG. 1 Schematic of the experimental design and photographs of the two sampling systems as deployed during BEACHON 2011. (Color figure available online.)

Consistent with long-term measurements at this site (Levin et al. 2012). a number of new particle formation (nucleation) and growth events were observed during the field experiment. In keeping with evidence that MEF is a major source of BVOC that can readily be oxidized to form low volatility products that partition readily into the aerosol particle phase (Kim et al. 2010), a substantial fraction of the ultrafine aerosol particles are characterized by organic compounds (Levin et al. 2012).

3. PARTICLE FLUXES

Particle number fluxes were computed for each of the 32 FMPS size channels, after coordinate rotation of the sonic time series and despiking of all data using the eddy covariance approach (applied as in [Pryor et al. 2009]). Perturbations in the water vapor pressure can cause large errors in particle flux measurements conducted under conditions of strong humidity gradients (Kowalski 2001); however, the fluxes were not corrected for perturbations in the water vapor pressure due to the absence of colocated robust high-frequency water vapor concentration measurements. The majority of the fluxes computed for the individual size channels reported by the FMPS did not exceed the statistical uncertainty (Rannik et al. 2009), thus herein we focus on the number fluxes integrated across size classes. Figure 2 shows histograms of half-hour average particle number fluxes in two particle “modes”; sub-30-nm diameter particles (i.e., 6–30 nm), which is used to describe relatively freshly nucleated particles and super 30-nm particles (i.e., 30–500 nm), which is dominated by the Aitken mode. The mean v_d for sub-30-nm particles computed for all sampling periods is 2.3 × 10⁻³ ms⁻¹, and the mean v_d for super-30 nm particles computed for all sampling periods is 1.7 × 10⁻⁴ ms⁻¹ (i.e., the net flux of both size classes is downward). The mean exchange velocities for the large particles are thus of similar magnitude to those reported for the mixed forest at Borden, Ontario (Gordon et al. 2011). However, in accord with that study and other prior research, the flux results indicated a large fraction of hours (>33%) in which the total number flux, and/or the number fluxes in the two size classes (sub- and super-30-nm diameters) exhibit statistically significant upward fluxes (Figure 2). The largest magnitude fluxes (both up and down) overwhelmingly occur during the daylight hours (Figure 2) due, in part, to higher particle number concentrations but primarily due to the more well-developed turbulence. Upward fluxes of the larger particles occurred most frequently during the early morning hours (the median flux is upward during 09:00 and 10:00 LST), whereas the upward fluxes of sub-30-nm particles typically occurred later in the day (the median flux is upward during 13:00 and 18:00–20:00 LST), leading to the postulate that different processes may be responsible for causing upward fluxes of particles with different diameters. This postulate is explored further below using case studies drawn from two representative days of measurements.

While several periods exhibited upward particle fluxes, 5 August was characterized by two distinct periods of upward fluxes that were speculated to have arisen from different physical mechanisms, and thus this day is used here as an example of times where the sign (i.e., direction) of the total particle number flux and size-resolved fluxes varied markedly. Throughout 5 August 2011, the momentum and sensible heat fluxes exhibited physically consistent behavior, and only a very brief period of light rain was observed (Figure 3a). During much of this day the PSD was trimodal, with a nucleation mode, Aitken mode and a smaller (but observable) mode centered at approx. 200 nm (Figure 3b). For example, a fit to the mean PSD for data collected between 13:00–13:30 LST indicate a trimodal distribution (Figure 4). Early in the morning the total particle number fluxes were of relatively small magnitude, until at about 11:00 LST the PSD indicated initial evidence for the appearance of the nucleation mode that subsequently grew toward a relatively stable Aitken mode centered at a geometric mean diameter ∼50–60 nm (Figure 3b). During 11:00–11:30 and 12:00–12:30 LST, the sub-30-nm mode exhibited large magnitude upward fluxes, followed by a large magnitude net downward flux (−45 × 10⁶ m⁻² s⁻¹) during 13:00–13:30. The super 30-nm particle flux was downward during 10:00–10:30, 11:00–11:30, and 12:00–12:30, but during 13:00–16:30 the Aitken mode exhibited upward fluxes (of between 5–22 × 10⁶ m⁻² s⁻¹) (Figure 3a). As discussed further below, we postulate that the upward fluxes of Aitken mode particles may have been caused partly by growth of the nucleation mode.

FIG. 2 (a) Histograms of the half-hour average particle number fluxes for all 30-min periods that did not experience any precipitation. The fluxes are shown for two diameter classes; Dp sub-30 nm and super-30 nm. (b) and (c) show boxplots of the particle number fluxes in the two size classes by hour of the day. (b) Shows fluxes of particles with diameters <30 nm, whereas (c) shows fluxes of particles with Dp >30 nm. The horizontal line in the box denotes the median value, the box extends from the 25th to 75th percentile values, and outliers are defined as points lying >2.7 standard deviations from the mean. (Color figure available online.)

FIG. 3 (a) Time series of fluxes of momentum and sensible heat (right axis), and the number flux of particles with diameters below 30 nm, and above 30 nm (left axis) during 5 August 2011. The uncertainty bars on the particle number fluxes are computed following Rannik et al. (2009). (b) PSD as measured by the FMPS. The particle concentrations derive from measurements during the flux measurement period of 30 min during each hour, and they have been corrected for tubing losses using an empirical correction. (c) and (e) The fraction of all measurements during the specified hour on 5 August where the “instantaneous” (i.e., 1 second average) deviation of particle number concentration in the (c) Aitken mode or (e) nucleation mode from the mean (i.e., C′) and the deviation of the vertical wind velocity from the mean (w′) fell into each of the quadrants defined from the C′ w′ plane. The four quadrants (listed in the order in which they appear in these frames) are: (Q1) Ejections: upward particle flux (F _up) due to updrafts of relatively particle enriched air (C′ > 0, w′ > 0), (Q2) Sweeps: upward particle flux (F _up) due to downdrafts of relatively particle depleted air (C′ < 0, w′ < 0). (Q3) Outward interactions: downward particle flux (F _down) due to updrafts of relatively particle depleted air (C′ < 0, w′ > 0). (Q4) Inward interactions: downward particle flux (F _down) due to downdrafts of relatively particle enriched air (C′ > 0, w′ < 0). (d) and (f) Relative contribution of each quadrant to the total flux of (d) Aitken mode or (f) nucleation mode particles when a hyperbolic hole of 20 is applied (i.e., only samples where

are included in the analysis). As shown, during 12:00–12:30 when an upward flux of nucleation mode particles was observed (see frame (f)) high magnitude events exhibit a large contribution from ejections (updrafts of relatively particle enriched air). This is also true of the subsequent hour (13:00–13:30) when an upward flux of Aitken mode particles was observed and, as shown in frame (d), the large magnitude events during this half-hour were also characterized by ejections (but this time of Aitken mode particles). (Color figure available online.)

FIG. 4 Mean PSD as measured with the FMPS during (a) 5 August 13:00–13:30 LST and (b) 24 July 16:00–16:30 LST. Also shown are trimodal fits to the data that are used to initialize the UHMA model for the timescale analyses. The observations have been corrected for tubing losses using an experimental tubing penetration correction. The fit shown in (a) has the following properties: mode 1: geometric mean diameter (GMD) = 9.6 nm, standard deviation (σ) = 1.62, and total number concentration (N) = 1.85 × 10³ cm⁻³, mode 2: GMD = 57 nm, σ = 1.65, and N = 2.06 × 10³ cm⁻³; mode 3: GMD = 195 nm, σ = 1.33, and N = 2.26 × 10² cm⁻³. The fit in (b) is mode 1: GMD = 11.3 nm, σ = 1.83, and N = 3.56 × 10³ cm⁻³; mode 2: GMD = 44 nm, σ = 1.38, and N = 2.80 × 10³ cm⁻³; mode 3: GMD = 180 nm, σ = 1.25, and N = 8.98 × 10² cm⁻³. (Color figure available online.)

A quadrant analysis was conducted in which the 1-s values of C′ in the nucleation mode and w′ for each half-hour period are divided into four quadrants in the C′, w′ plane (Shaw et al. 1983; Pryor et al. 2008a);

	(Q1) Ejections: Upward particle flux due to updrafts of relatively particle enriched air (C′ > 0, w′ > 0).
	(Q2) Sweeps: Upward particle flux due to downdrafts of relatively particle depleted air (C′ < 0, w′ < 0).
	(Q3) Outward interactions: Downward particle flux due to updrafts of relatively particle depleted air (C′ < 0, w′ > 0).
	(Q4) Inward interactions: Downward particle flux due to downdrafts of relatively particle enriched air (C′ > 0, w′ < 0).

To examine the relative importance of short-lived events in dictating the flux, we also performed the analysis with a fifth conditionally sampled region in the analysis (a hyperbolic hole), where the size of the hole (Shaw et al. 1983). This analysis is conducted to identify extreme (i.e., high magnitude) flux periods within each half-hour and thus to separate events from relatively quiescent motions. The example presented below is articulated in terms of the contribution of large magnitude events in each quadrant for H = 20.

The quadrant analysis show that the upward flux of nucleation mode particles during 11:00–11:30 and 12:00–12:30 shows a relatively even distribution between the four-quadrants but with the largest fraction of the data in the second quadrant (i.e., Q2: downdrafts of relatively particle depleted air), possibly due to entrainment of air with lower concentrations of nucleation mode particles from the free troposphere during growth of the boundary layer (Figure 3e). When a hyperbolic hole of 20 is applied, during 12:00–12:30 ejections (Q1) become more evident indicating short-lived—but high magnitude—bursts of high particle concentrations were being carried upward passed the sampling system (Figure 3f). The upward fluxes of the nucleation mode that were observed later in the day (e.g., during 18:00–18:30) also exhibited a greater contribution from ejections of relatively particle enriched air (Q1) (Figure 3e). The period of upward fluxes of the Aitken mode (13:00–13:30) also exhibited a large contribution from ejections (Figure 3c), and the importance of ejections is amplified when a hyperbolic hole of 20 is applied (Figure 3d). These analyses are consistent with the postulate that relatively recently nucleated particles were growing to detectable sizes (i.e., Dp > 6 nm) at least partially via condensation of low volatility vapors at or close to the surface (possibly oxidation products from BVOC emitted from the canopy).

The interpretation of particle dynamics influencing the fluxes is also consistent with the particle power spectra for 5 August (Figure 5). Initially, i.e., in the period 10:00–10:30, particles with Dp < 30 nm and total particle concentrations exhibited evidence of a −2/3 inertial dissipation slope (a best-fit line has a slope of −0.7), but in 13:00–13:30 the sub-30-nm particles exhibited high frequency variability and deviated markedly from the expected behavior in the inertial subrange, and subsequently (e.g., 15:00–15:30) power spectra for the super-30-nm particles also exhibited evidence of enhanced variance (seen as a flattening of the inertial subrange in Figure 5d, yielding a slope of −0.1). We postulate that the increase in variance at high frequencies reflects the impact of particle dynamics in generating variability in the number concentrations of particles across the entire measured size spectra and thus a deviation from a −2/3 slope. However, it is acknowledged that (i) at least some fraction of the frequency behavior above frequencies of 0.1–1 s⁻¹ may be due to white noise from the FMPS electrometers (which would be manifest in the power spectra as a +1 slope at high frequencies), (ii) that damping due to tubing may be responsible for the slightly greater than −2/3 slope shown by the Aitken mode in the spectra from 10:00–10:30 and 13:00–13:30 (Figure 5b and c) (Eugster and Senn 1995) and (iii) that the smoothed power spectra are subject to some uncertainties. To address point (iii) we compute the uncertainties in the power spectra (Sørensen and Larsen 2010) invoking the assumption that each Fourier mode from the fast Fourier transform is normally distributed and uncorrelated with the other modes, and thus when the modes are averaged to produce the spectra shown in Figure 5 the relative uncertainty is a function of the sample period and frequency range over which the spectra is averaged.

FIG. 5 Power spectra from 5 August of (a) the vertical wind component (w) for all 30-min periods 10:00–19:30 and sonic virtual temperature (T) during 10:00–10:30, 13:00–13:30, and 15:00–15:30, and of the total number concentration (6–500-nm diameter) and for the super-30-nm particles for three 30-min periods (b) 13:00–13:30, (c) 14:00–14:30, and (d) 15:00–15:30. The dashed line in each panel depicts the −2/3 slope that characterizes the inertial subrange. Also shown in frames (b), (c), and (d) are estimates of the upper and lower bounds of the smoothed spectral estimates computed as described in Sørensen and Larsen (2010). (Color figure available online.)

Flux divergence occurs when the response time of processes leading to a change in the particle number concentration in a given size bin (τ_c) is equal to the response time of physical transfer to or from the surface (τ_d) (Kramm and Dlugi 1994; Pryor and Binkowski 2004). If τ_d/τ_c ≫ 1 or τ_d/τ_c ≪ 1, the constant flux layer is not violated, but where τ_d/τ_c ∼ 1, the aerosol dynamics timescales are of the same order as transport time scales, and hence aerosol dynamics processes can significantly modify the transfer to/from the canopy. Thus, these timescales were computed and compared using the University of Helsinki Multicomponent Aerosol (UHMA) model for each flux period during 5 August and for each of the two modes. The UHMA model contains parameterizations of the dynamics of multicomponent PSDs: nucleation, condensation, coagulation, and dry deposition (Korhonen et al. 2004). A fixed sectional discretization is used to simulate the PSD, which is initialized using the log-normal fits to the data, and run to compute estimates of τ_d and τ_c for two modes that at 13:00–13:30 (LST) as follows:

where: v_d is the mean deposition velocity for that mode (a weighted average by the number concentrations in sections within the mode), z = measurement height (25 m), d = displacement height (estimated to be 2/3 canopy height [Raupach and Thom 1981]).

Using this approximation implicitly assumes that that processes beyond aerodynamic resistance to transport contribute to the deposition timescale as discussed in Section 1.

where N = total particle number concentration in the mode, N_Loss _coag = rate of loss of number concentration due to coagulation, N_Loss _cond = rate of loss of number concentration due to growth of particles out of the mode.

It is important to note that these timescales represent the time it takes for the specified process to remove (add) a randomly selected (average) particle from the mode under consideration. Calculations for each mode as measured during 13:00–13:30 in 5 August indicate τ_c/τ_d ∼ 0.1–0.3 (τ_c and τ_d were ∼ 5 × 10³–5 × 10⁴ s during the periods shown in Figure 5). This is consistent with the observations of nonideal flux behavior, since both modes were evolving as a result of coagulation (i.e., net loss of particle number) and condensation (and thus growth of particles into and out of the mode). We postulate that the smaller of the two modes exhibited higher additional variability of number concentrations (and thus variance in the power spectra as shown in Figure 5) due to continued introduction of newly formed particles produced by nucleation. This speculation is supported by the UHMA simulations that suggest in the absence of nucleation and growth to detectable sizes (i.e., 6 nm) the fine mode number concentration in the subsequent hour (14:00–14:30) would have been approximately 12% lower than was actually observed.

The synthesis of the analyses of data collected on 5 August is thus that the upward fluxes of the nucleation (and Aitken) mode can be ascribed to strong nonstationarity of the PSD and specifically the appearance and growth of a nucleation mode, possibly due to within canopy growth due to condensation of oxidized BVOC. A second period of upward flux of both modes (18:00–18:30 and 19:00–19:30) followed a period of light rain and was associated with relative humidity (RH < 50%), which may also thus reflect nonstationary PSD due to evaporation (Figure 3a).

Conditions during 24 July illustrate two further examples of upward particle fluxes (Figure 6a). This day was initially characterized (prior to approx. 15:00 LST) by a defined Aitken mode (centered at a GMD ∼ 45 nm), a mode centered at approx. 200 nm, and the absence of a nucleation mode (Figure 6c). Thus fluxes for this period were computed for the dominant (Aitken) mode and for the nucleation mode only after the hour in which the mode was well defined (14:00–14:30 LST). The Aitken mode showed downward fluxes for all morning hours except 8:00–8:30 during the hour when the boundary layer was growing rapidly (the first hour of positive sensible heat flux was 07:00–08:00) (Figure 6a), and is thus likely attributable to entrainment of particle free air from above the nocturnal inversion layer (Pryor et al. 2008a; Grönholm et al. 2009). This interpretation is consistent with the results of quadrant analysis for 24 July (Figure 6b), which show that the upward flux of the particles in the Aitken mode that occurred during 08:00–08:30 was associated primarily with downdrafts of particle depleted air (Q2; sweeps) likely due to erosion of the nocturnal inversion and entrainment of relatively clean air from aloft. However, the upward flux during 15:00–15:30 is driven primarily by the ejection (Q1) of relatively particle enriched air from below consistent with the postulate that relatively recently nucleated particles were growing via condensation of low volatility vapors at or close to the surface (possibly oxidation products from BVOC emitted from the canopy). During this period of upward fluxes (16:00–16:30 LST), there was a well-defined nucleation mode and the trimodal distribution. During this period τ_c/τ_d for the nucleation mode was 0.5, while that for Aitken mode was 0.3 thus this period exhibited strong evidence for flux divergence. For comparative purposes, the τ_c/τ_d for the Aitken mode during all half-hour periods 07:00–15:00 on this day was <0.1.

FIG. 6 (a) Time series of fluxes of momentum and sensible heat (right axis), and the number flux of particles in the Aitken and nucleation modes (left axis) during 24 July 2011. The uncertainty bars on the particle number fluxes are computed following Rannik et al. (2009). (b) Quadrant analyses of the Aitken mode particle fluxes. (c) PSD as measured by the FMPS. The particle concentrations derive from measurements during the flux measurement period of 30 minutes during each hour, and they have been corrected for tubing losses using an empirical correction. (Color figure available online.)

The synthesis of these analyses for 24 July is thus that the early period of upward fluxes of the Aitken mode was likely due to entrainment of relatively particle depleted air from above the nocturnal inversion layer, while the later period (like those that occurred on 5 August), appear to be more strongly associated with nonstationarity of the PSD and specifically the appearance and growth of a nucleation mode, possibly due to within canopy growth due to condensation of oxidized BVOC.

4. VERTICAL GRADIENTS OF PSD THROUGH THE CANOPY

The PSD from the gradient measurements are presented herein for 3-h composites to ensure repeated sampling of the entire profile. The following stationarity constraints were applied to conditionally sample data periods for analysis; (i) no rain during the entire 3-h period, (ii) the PSD was relatively stable through time and space (i.e., the GMD for each mode was within 2 nm for each mode fitted at each level), (iii) >500 individual samples were taken within the four sampling increments; 0–5 (representative of conditions below the canopy), 5.1–10.9, 11–16, and above 16 m agl (i.e., above the canopy). Application of these selection criteria means that the samples are dominated by nighttime conditions, and the above canopy wind speeds are typically low (<4 ms⁻¹). Once suitable periods were determined, PSD were then averaged in each height interval and fitted to 3 (or fewer) log-normal modes (see examples of the mode fitting approach given in Figure 4) to reduce the influence of uncertainties in the number concentration in each FMPS size channel. The resulting modal fits were evaluated in terms of the residuals (i.e., difference of the fit to observed data), and where the fits were found to be a good representation of the PSD and to represent a stable data sample at each height (i.e., consistent GMD), these fitted data were then used to compare the mean PSD outside of the canopy (quantified by the above and below canopy measurements) and the mean PSD in each mode within the canopy (determined from the two in canopy measurements), and thus to infer the difference in modal number concentrations (within versus outside the canopy) as a function of modal GMD.

FIG. 7 Box plot of the canopy penetration efficiency expressed as the ratio of the total modal particle concentration within the canopy to that (a) above the canopy, or (b) the average of the above and below canopy concentrations, as a function of modal GMD. The GMD classes shown on the x-axis indicate the mean for a bin. The range around the mean value is ± 3 nm for GMD = 15 nm, for GMD = 43 nm ± 5 nm, and for GMD = 78 nm ± 10 nm. The horizontal bar in the box plot denotes the median value, whereas the large black square shows the mean value. The box extends from the 25th to 75th percentile values, and the whiskers extend to the highest and lowest values of the ratio.

The observationally derived canopy penetration efficiencies are not directly comparable with those from the wind tunnel that are computed as the ratio of the downstream particle concentration to the upstream particle concentration at a given diameter (Lin and Khlystov 2012). Nevertheless, the vertical gradients of PSD indicate a canopy minimum in terms of particle number concentrations, and consistent with the wind tunnel experiments, when conditionally sampled by GMD indicate greatest uptake of particles with diameters below 20 nm (Figure 7). There is also relatively good accord between the implied canopy penetration efficiencies for differing GMD. The canopy penetration estimates from the wind tunnel indicate and average penetration efficiencies for GMD ∼20 nm of approximately 60% (with variations due to wind speed and foliage packing density) (Lin and Khlystov 2012), whereas our in situ data indicate a mean value of 70%. The canopy penetration for GMD ∼50 nm from the wind tunnel are 90%–95% (with variations due to wind speed and foliage packing density), whereas the in situ observation indicate a mean value of 94%. These canopy penetration efficiencies are similar when the denominator is derived from either only the above or only below canopy PSD. However, these estimates must be viewed with caution, since they are based on only 13 sample periods, and as shown in Figure 7, the individual sample periods differ substantially from the mean penetration efficiency for each GMD.

5. CONCLUDING REMARKS

Data collected during the 2011 BEACHON experiment indicate that over one third of fluxes of both sub- and super-30-nm diameter particles over this sparse pine forest are upward. The largest magnitude fluxes (both up and down) occur during the daylight hours. Upward fluxes of particles in the Aitken mode (i.e., with Dp > 30 nm) occurred most frequently during the early morning hours, whereas the upward fluxes of sub-30-nm particles typically occurred later in the day. Quadrant analysis, timescale analysis using a particle dynamics model and frequency power spectra of particle concentrations demonstrate that, in this environment, the morning upward fluxes of particles in the Aitken mode tend to be associated with downward sweeps of particle depleted air during break down of the nocturnal inversion. Upward fluxes of particles in the nucleation mode typically occur later in the day and are more strongly linked to ejections of particle enriched air from the canopy that are attributable to growth of fairly recently nucleated particles by both addition of oxidation products of BVOC and coagulation. It should be acknowledged that the relative importance of sweep versus ejections as a function of particle size may be location specific and that the data set analyzed herein is of relatively short duration. Thus, further analyses are certainly warranted to address the degree of generalizability of these findings.

Vertical gradients of the PSD above, through, and below the canopy as measured during BEACHON imply canopy penetration efficiencies are lower for smaller GMD (∼15–20 nm) and increase with diameter up to approx. 80 nm (the largest diameter considered here). These findings and the relative magnitude of canopy penetration efficiencies, 60%–70% for GMD of 12–18 nm and 90%–95% for GMD of 38–48 nm, are consistent with data from a wind tunnel experiment (Lin and Khlystov 2012). It is important to note that the canopy penetration estimates derived from the measured vertical concentration gradients are based on a relatively small sample size and are thus subject to relatively high uncertainty; however, these analyses emphasize the substantial variability in canopy uptake efficiency with particle diameter.

Acknowledgments

The authors would like to thank funding from the National Science Foundation (Grant no. 1102309). They would also like to thank Steve Scott of IU for technical assistance, Andrew Turnipseed of NCAR for providing the sonic anemometer data, Niall Robinson and Martin Gallagher of the University of Manchester for access to their winch system, and Hannele Korhonen of the University of Kuopio for providing a version of the UHMA model. The clarity of this manuscript was improved by the helpful comments of three reviewers and discussions with L. L. Sørensen of the University of Aarhus and S. Larsen of DTU.