Quantifying new versus old aerosol deposition in forest canopies: throughfall mass balance with fallout radionuclide chronometry

Net throughfall (NTF) measurements of the fallout radionuclides (FRNs) ⁷Be and ²¹⁰Pb confirm that the atmosphere is a strong net source of particulate matter (PM) and trace metals (TMs) to a temperate forest canopy, which retains nearly 60 % of total wet and dry annual atmospheric flux of the FRNs (four trees, three species, two sites; n=159). Estimation of dry deposition using a multiple-regression technique and predictors of precipitation depth and duration of the antecedent dry period agrees well with ecosystem mass balance, with about 25 % of both ⁷Be and ²¹⁰Pb annual flux deposited by dry processes, and total FRN fluxes in reasonable agreement with regional soil inventories. In contrast to the FRNs, other TMs, including Pb and Hg, show large enrichments in throughfall that derive from processes of internal ecosystem recycling such as PM resuspension, leaching from tree metabolic pathways, and physicochemical weathering of non-foliar biological tissues of the tree canopy (collectively “phyllosphere”). To estimate the contributions to net throughfall from these internal pathways, which we term a change in storage (ΔS), a new FRN canopy mass balance is derived based on the different half-lives of ⁷Be and ²¹⁰Pb. Estimated ΔSs for selected elements are SO₄=7 %, ²¹⁰Pb = 29 %, As = 42 %, ⁹Be = 45 %, Cd = 60 %, Hg = 60 %, Pb = 63 %, Fe = 79 %, Al = 79 %, and P = 91 %. The balance of throughfall (1-ΔS) represents new ecosystem input. Change in storage for all elements was strongly correlated with the export of particulate carbon (FPOM) and dissolved organic carbon (DOC) from the canopy, indicating that physicochemical transformation during residence within the canopy facilitates the release of metals from storage. ΔS thus represents an emergent ecosystem property through which metal, carbon, and hydrologic cycles may converge to determine the fate, reactivity, and timing of metal delivery to underlying soils. The forest canopy represents a substantial reservoir of decade-aged PM and cannot be assumed to be at steady state with respect to ongoing atmospheric deposition, especially in the context of changing atmospheric composition, e.g., declining industrial emissions of Pb and Hg.

1 Introduction

Forest vegetation covers over 30 % of the earth's landmass and thus mediates the impacts of particulate matter (PM) deposition on climate, ecosystem function, and human health (Bortolazzi et al., 2021; Emerson et al., 2020; Farmer et al., 2021; Hosker and Lindberg, 1982; IPCC, 2021; Jiskra et al., 2018; Johnson and Siccama, 1983; Lindberg et al., 1982; Lovett and Lindberg, 1984; McDowell et al., 2020; Van Stan and Pypker, 2015; WHO, 2016, 2021). Despite regulating the composition of both the atmosphere and terrestrial ecosystems, the interaction of vegetation with PM and other atmospheric trace metals (TMs) remains poorly understood. Even a basic understanding of mechanisms that regulate PM uptake by vegetation remain elusive (Luo et al., 2019; Shahid et al., 2017; Zhou et al., 2021). As a result, in part, current estimates for PM dry deposition in global chemical transport models vary across orders of magnitude, underpredict direct observations by as much as 200 %, omit fundamental processes such as resuspension, and lack verification by mass balance (Emerson et al., 2020; Farmer et al., 2021; Hicks et al., 2016; Pryor et al., 2017; Saylor et al., 2019). Moreover, long residence times of PM in recirculation at the Earth's surface prolong the impacts of critical pollutants such as Hg and Pb, and their ultimate fate remains unclear (Resongles et al., 2021; Wang et al., 2020). These uncertainties underscore a critical need for an improved understanding of atmosphere–biosphere interactions.

Two approaches are used for measuring PM and TM deposition to forest canopies, each with characteristic advantages and limitations (e.g., Draaijers et al., 1996). Micrometeorological approaches infer rates of deposition based on concentration gradients in air or on covariance of airborne concentrations with turbulence (e.g., eddy flux; Emerson et al., 2018; Laguionie et al., 2014; Obrist et al., 2021). These methods are critical insofar as they estimate deposition over large areas with, in some cases, resolution of PM by size. However, these results are dependent on assumptions regarding micrometeorological physics, do not provide information on PM composition, and ultimately lack verification by mass balance (“where did it go?”). The logistical demands of the micrometeorological methods are challenging to satisfy as well, requiring long-term deployment of instrumentation to dedicated research sites and strong vertical-concentration gradients (in the eddy gradient approach). For the eddy covariance method, the need for fast and selective detectors restricts the chemical species that can be measured (Farmer et al., 2021).

A complementary approach exploits canopy chemical mass balance by comparing precipitation collected under vegetated canopies (throughfall or TF) with paired bulk deposition measurements under open sky (openfall or OF). Positive net throughfall (NTF = TF − OF) results for most elements. The excess is conventionally attributed to some combination of washoff of dry deposition that has accumulated in the canopy during the preceding dry period and leaching/weathering from biological tissues of the canopy itself. No accommodation is made for long-term PM or TM storage in ecosystem components, however, and quantifying the contribution of dry deposition thus requires uncertain assumptions to distinguish between these competing processes (“where did it come from”?; Lovett and Lindberg, 1984; Ulrich, 1983). Distinguishing between these processes is critical for understanding ecosystem trace-metal budgets since they can represent either a novel external source via dry deposition of PM or internal recycling via either resuspended dust or leaching of biological materials (Avila and Rodrigo, 2004; Lindberg et al., 1982).

One critical source of error in throughfall mass balance is the assumption that precipitation is a simple and efficient process of “washoff” that fully removes the dry deposition that has accumulated during dry periods preceding the rain event (Bishop et al., 2020; Gandois et al., 2010; IAEA, 2009; Lovett and Lindberg, 1984; USEPA, 2005). The canopy is thus assumed to be at steady state, and no accommodation is made for accumulation of PM or TMs over time or for any change in storage within the canopy. Support for precipitation as an efficient washoff process derives from the large enrichments of most elements that are observed in throughfall, from experimental dry applications of PM to vegetation that show residence times on the order of just days to weeks (Chamberlain, 1970; Miller and Hoffman, 1983), and from washing of natural vegetation that shows exponential declines in rates of metal extraction (Avila and Rodrigo, 2004; Shanley, 1989). This conceptualization of washoff also aligns with the “lotus effect”, which is the efficient self-cleaning of leaves by raindrops due to their hydrophobic waxy cuticle (Barthlott and Neinhuis, 1997).

On the other hand, it is well documented that a range of atmospheric metals and metalloids accumulate continuously in vegetation during exposure to the atmosphere. These include the natural fallout radionuclides (FRNs) ⁷Be and ²¹⁰Pb (Landis et al., 2014; Sumerling, 1984); anthropogenic fission products including ⁹⁰Sr (Yamagata et al., 1969), ¹³¹I (Yamagata, 1963), ¹³⁷Cs, and others (Kato et al., 2012; Russell et al., 1981); TMs including Al, Pb, and Hg (Landis, 2024a; Rea et al., 2001, 2002; Wyttenbach and Tobler, 1988); and the oxoanions AsO₃, SeO₃, and CrO₄ (Landre et al., 2009). Moreover, this accumulation continues unabated in senescent vegetation, indicating that PM and TM uptake occurs independent of leaf physiology and is thus unambiguously atmospheric in origin. The foliar metal residence times of Hg, ⁷Be, ²¹⁰Pb, and ¹³⁷Cs have been shown by various means to exceed 700 d, which is generally longer than the lifetime of the foliage itself. This demonstrates strong coupling of atmospheric metals to the carbon cycle (Graydon et al., 2009; Kato et al., 2012; Landis et al., 2014).

In the case of Hg, although its occurrence in the atmosphere is regulated by gaseous elemental mercury (GEM) rather than by PM, recent measurements nonetheless show that long-lived non-foliar materials of the forest canopy including bark, lichen, moss, and foliage (collectively “phyllosphere”) collectively retain many times the annual Hg flux on an areal basis (Wang et al., 2020). This shows that GEM becomes particle-bound during its residence in the phyllosphere and also that surfaces other than foliage therefore play a dominant role in canopy and ecosystem mass balances of Hg and other TMs (Obrist et al., 2021). Stable isotopes of both Hg and Pb reveal that legacy anthropogenic emissions continue to dominate contemporary atmospheric deposition, for example, despite large reductions in both emissions and measured rates of deposition (Farmer et al., 2010; Resongles et al., 2021; Taylor et al., 2022; Yang and Appleby, 2016). These legacy TM sources remain enigmatic but might include resuspended dust from surrounding soils and roads or release from storage in living and dead surfaces of the phyllosphere. Resolving multiple processes that regulate accumulation, storage, and re-suspension of diverse TMs in terrestrial ecosystems and resolving their contributions to depositional budgets remain a challenge to biogeochemical research. This is especially important in the context of changing global emissions of, e.g., Hg and Pb, since the forest cannot be assumed to be at steady state with respect to contemporary deposition.

The natural fallout radionuclide (FRN) tracers ⁷Be and ²¹⁰Pb provide a novel and emerging perspective on PM metal cycling. The FRNs have been shown to accumulate in vegetation primarily by wet deposition rather than dry, as widely presumed (Landis, 2024a; Landis et al., 2014). This distinction is important because approximately 90 % of PM removal from the atmosphere occurs by wet processes (in continental climates), and the accumulation of FRNs in forest canopies might thus reflect a quantitative view of PM cycling from the atmosphere. The FRNs ⁷Be and ²¹⁰Pb are secondary aerosols produced in the atmosphere from gaseous precursors by cosmogenic spallation of N₂ and O₂ or by radiogenic decay of ²²²Rn, respectively, with identical PM activity-size distributions (mean aerodynamic diameters) of ca. 0.5 µm (Gründel and Porstendörfer, 2004; Winkler et al., 1998). FRNs are widely exploited as tracers of other PM components of broad interest, including PM_2.5, black carbon, sulfate, and anthropogenic trace metals in long-range transport (Koch et al., 1996; Lamborg et al., 2013; Landis et al., 2021a; Liu et al., 2016).

The FRNs hold special power as PM tracers through two consequences of their radioactive decay. First, their accumulation in the terrestrial environment is limited such that their occurrence can be unambiguously traced directly to an atmospheric origin. Second, their characteristic rates of decay can be exploited to explicitly measure the timescales of their deposition and redistribution. For example, ⁷Be and ²¹⁰Pb are produced in the atmosphere with a typical activity ratio on the order of 10. In vegetation exposed to ongoing atmospheric deposition, both FRNs accumulate with time, but the ⁷Be :²¹⁰Pb ratio decreases due to their differing half-lives. After 1 year of exposure, foliage has ratios of 2–3. With its short half-life of 54 d, ⁷Be records the PM–vegetation interaction over event-based timescales, whereas ²¹⁰Pb records longer-term storage, resuspension, and recycling of PM deposition over subannual to decadal timescales (Landis et al., 2021a, b).

Here, we use FRN chronometry in a throughfall mass balance approach to resolve the processes and timescales that govern the interactions of PM and atmospheric TMs with forest canopies. We first review contemporary approaches to throughfall mass balance and then derive a new expression using FRNs to distinguish the initial absorption of PM during deposition from later release from canopy storage. We confirm that ⁷Be and ²¹⁰Pb are not systematically fractionated and that the ⁷Be :²¹⁰Pb ratio in throughfall is primarily a measure of PM age. We then extend our throughfall mass balance approach to link the FRNs and other major and trace elements (MTEs) to canopy export of dissolved organic carbon (DOC) and fine particulate organic matter (FPOM).

1.1 Throughfall mass balance

The conventional throughfall mass balance includes two pathways by which PM enters and leaves the canopy. Inputs to the canopy by bulk wet deposition (W) or dry deposition (D) must be balanced by exports via wet throughfall (T) and any exchange with the canopy (C) via leaching (+) or absorption (−):

$$\begin{array}{}\text{(1)}& W+D=T\pm C.\end{array}$$

Bulk deposition (W) is measured under open sky adjacent to the forest, where it may also be called openfall (OF). Net throughfall (NTF) is the arithmetic difference between deposition under the canopy and open sky:

$$\begin{array}{}\text{(2)}& \text{NTF}=T-W=D\pm C.\end{array}$$

W and T are easily measured. The challenge in estimating D by mass balance then remains in distinguishing the contributions of C. Two approaches have been proposed. The more common is the “filtering” approach (Staelens et al., 2008; Ulrich, 1983; Yoshida and Ichikuni, 1989), where an index element is used to apportion dry deposition of the target element, D_i. The index element, typically Na or Al, is assumed to have identical rates of dry deposition as the target element (Eq. 3) but no metabolic contribution from the canopy. This assumption implicitly assumes similar PM size distributions and thus sources with respect to secondary or primary emission, insofar as PM size controls rates of dry deposition (Jaenicke, 1980).

$$\begin{array}{}\text{(3)}& {\displaystyle \frac{D_i}{W_i}}={\displaystyle \frac{D_{\mathrm{Na}}}{W_{\mathrm{Na}}}}\end{array}$$

With C_Na≡0, dry deposition of an element of interest can be calculated as follows:

$$\begin{array}{}\text{(4)}& D_i=W_i\cdot {\displaystyle \frac{T_{\mathrm{Na}}-W_{\mathrm{Na}}}{W_{\mathrm{Na}}}}=W_i\cdot \left({\text{EF}}_{\mathrm{Na}}-\mathrm{1}\right).\end{array}$$

Here, EF_Na represents the Na enrichment factor, $T/W$. Following the calculation of D_i by Eq. (4), C_i can be solved from Eq. (2). Using this approach, any EF_i greater than EF_Na yields a positive C_i, which represents leaching from the canopy. Any EF_i less than EF_Na yields negative C_i, which represents a net loss to the canopy by absorption.

A second approach to describing the canopy interaction uses multiple regression of individual storm events to estimate rate constants for specific canopy processes (Lovett and Lindberg, 1984; Rea et al., 2001; Wu et al., 1992):

$$\begin{array}{}\text{(5)}& \text{NTF}=T-W=D+C={\mathit{\beta }}_{\mathrm{1}}A+{\mathit{\beta }}_{\mathrm{2}}P.\end{array}$$

The coefficient β₁ represents the rate of dry deposition to the canopy [Bq m⁻² d⁻¹ or $\mathrm{\mu }\mathrm{g}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{d}}^{-\mathrm{1}}$], and A is the duration of the antecedent dry period preceding the storm event [days]. The coefficient β₂ represents either canopy leaching or absorption [Bq or $\mathrm{\mu }\mathrm{g}{\mathrm{m}}^{-\mathrm{2}}{\mathrm{cm}}^{-\mathrm{1}}$], with P the precipitation total [cm]. Biotic leaching and abiotic exchange (desorption, dissolution) can be distinguished only by a priori assumptions based on elemental chemistry and by the assumption that one must dominate the other, for example, that base cations (K, Ca, Mg, etc.) are strongly cycled through leaf tissue and are thus derived primarily from leaching, whereas trace metals, e.g., Pb, are not appreciably cycled and are thus dominated by canopy absorption (Lovett and Lindberg, 1984).

An important advantage to this approach is that, provided there are sufficient measurements, additional explanators might be added to the multiple regression to understand effects from other environmental factors such as seasonality, tree species, precipitation pH, dissolved organic carbon (DOC), or fine particulate organic matter (FPOM).

1.2 FRN mass balance: change in canopy storage

The observed accumulation of FRNs and TMs in foliage and long-lived tissues of the phyllosphere requires that canopy exchange accommodate a change in storage if previously deposited PM is later susceptible to weathering processes and export from the canopy in subsequent rainfall over some characteristic time frame. We can distinguish this change in storage as a separate term in mass balance based on different characteristic timescales as follows:

$$\begin{array}{}\text{(6)}& T=W+D\pm \left(C+\mathrm{\Delta }S\right).\end{array}$$

Analogous to the use of an index element for dry deposition in the filtering approach, we propose using ⁷Be as an index of canopy storage. Beryllium is highly reactive to natural surfaces but, due to its short half-life, ⁷Be cannot record long-term storage. In contrast, the longer-lived ²¹⁰Pb persists to record PM fate over annual to decadal timescales. The similar occurrence and behaviors of ⁷Be and ²¹⁰Pb but with different half-lives thus allow us to distinguish instantaneous canopy exchange (absorption or leaching) from a subsequent change in storage. Storage is thus defined as occurring over timescales that are long relative to the ⁷Be half-life (54 d). We assume that the ⁷Be :²¹⁰Pb flux ratio is constant through time but acknowledge that short-term variability and long-term decadal trends in ²¹⁰Pb deposition may require future attention (Landis et al., 2021a; Winkler and Rosner, 2000).

We now write two equations to solve for one unknown, ΔS:

$$\begin{array}{}\text{(7)}& {\displaystyle }{T}_{\mathrm{Be}}=W_{\mathrm{Be}}+D_{\mathrm{Be}}\pm C_{\mathrm{Be}}\text{(8)}& {\displaystyle }{T}_{\mathrm{Pb}}=W_{\mathrm{Pb}}+D_{\mathrm{Pb}}\pm \left(C_{\mathrm{Pb}}+\mathrm{\Delta }S\right).\end{array}$$

Equation (7) ignores radioactive decay, with an assumption that the residence time of dry deposition in the canopy is very short (days) relative to the ⁷Be half-life. This assumption is re-evaluated in Sect. 3.4. Based on their congruent interactions with natural vegetation and particulate matter (Landis, 2023; Landis et al., 2014, 2016, 2021b, 2024b), we next assume that ⁷Be and ²¹⁰Pb have similar canopy interactions and that, for both, C is an equivalent fraction of total wet and dry deposition (Eq. 9).

$$\begin{array}{}\text{(9)}& {\displaystyle \frac{C_{\mathrm{Be}}}{W_{\mathrm{Be}}{\text{EF}}_{\mathrm{Na}}}}={\displaystyle \frac{C_{\mathrm{Pb}}}{W_{\mathrm{Pb}}{\text{EF}}_{\mathrm{Na}}}}\end{array}$$

This allows us to combine Eqs. (7) and (8), with both D and C terms canceling. We then solve for ΔS as follows, by which we attribute any throughfall excess in ²¹⁰Pb relative to ⁷Be to a change in storage:

$$\begin{array}{}\text{(10)}& \mathrm{\Delta }S=T_{\mathrm{Pb}}-T_{\mathrm{Be}}\cdot {\displaystyle \frac{W_{\mathrm{Pb}}}{W_{\mathrm{Be}}}}.\end{array}$$

For species with a gaseous phase such as Hg or SO₄, we cannot assume a constant $D/W$ ratio as in Eq. (3). In these cases, we use an alternative mass balance by directly estimating dry deposition via multiple regression (β₁) for both ⁷Be and, e.g., Hg, as follows:

$$\begin{array}{}\text{(11)}& \mathrm{\Delta }{S}_{\mathrm{Hg}}={\text{Hg}}_{\mathrm{NTF}\ast }-{\text{Be}}_{\mathrm{NTF}\ast }\cdot {\displaystyle \frac{W_{\mathrm{Hg}}+D_{\mathrm{Hg}}}{W_{\mathrm{Be}}+D_{\mathrm{Be}}}}.\end{array}$$

The term Hg_NTF∗ represents NTF without a contribution from C, i.e., Hg${}_{\mathrm{NTF}\ast }=T_{\mathrm{Hg}}-W_{\mathrm{Hg}}-D_{\mathrm{Hg}}$.

Finally, calculating a change in storage acknowledges that a process of exchange occurs within the canopy. Some fraction of new wet and dry deposition is retained by the canopy, while some fraction of previous deposition is released from storage. The proposed mass balance thus provides a new perspective on PM and TM deposition, new versus old. ΔS quantifies the old, and the fraction of new follows from the mass balance:

$$\begin{array}{}\text{(12)}& {\text{Hg}}_{\mathrm{new}}=T_{\mathrm{Hg}}-\mathrm{\Delta }{S}_{\mathrm{Hg}}.\end{array}$$

2 Methods

2.1 Site and tree characteristics

We measured 156 samples of throughfall under mature canopies of two tree species at each of two sites. The Beaver Meadow (BM) site in Sharon, Vermont (104 km², population of 1500), sits at an elevation of 502 m in a mixed forest of sugar maple, red oak, American beech, white pine, and poplar, with understory of striped maple and hornbeam. Annual precipitation has averaged 117 cm yr⁻¹ for the past 30 years (PRISM, 2014). The site is underlain by green schists of the Waits River series and thin glacial till, which leads to the development of well-drained soils typically classified as Inceptisols. Throughfall was collected under red oak (Quercus rubra; diameter at breast height (dbh) = 28 cm) and white pine (Pinus strobus; dbh = 59 cm) in the forest interior, and openfall was collected within 50 m in an adjacent forest gap. The Shattuck Observatory (SO) site is located 18 km distant in Hanover, New Hampshire (130 km², population of 8500), in the semi-urban forest of the Dartmouth College Park at an elevation of 165 m. Annual precipitation averages 101 cm yr⁻¹ (PRISM, 2014). The SO site is underlain by mafic volcanics of the Ammonoosuc series, with frequent outcrops along this ridgeline site (Schumacher, 1988). Throughfall was collected under red oak (dbh = 53 cm) and Norway spruce (Picea abies; dbh = 60 cm) at the forest edge, with openfall collected within 50 m in the adjacent clearing where we have previously reported a long-term time series of atmospheric deposition (Landis et al., 2021a, b).

The sampled trees represent a range of foliar ages and characteristics that may influence FRN activities and MTE concentrations. Red oak is deciduous and sheds most leaves annually after ca. 6 months of growth (May–October); however, some remain on branches following abscission through the following winter (a phenomenon called marcescence). White pine retains needles for 1.5–2 years. Norway spruce retains needles for up to 5–8 years (Reich et al., 1996). Leaf area index (LAI) at each throughfall site was estimated over a 30° zenith angle using hemispheric photos and the software package Hemisfer (Schleppi et al., 2007; Thimonier et al., 2010). Measured LAIs are as follows: BM oak (leaf off) = 0.9±0.3, BM oak (leaf on) = 3.1±0.5, BM pine = 2.79±0.14, SO oak (leaf off) 1.13±0.4, SO oak (leaf on) = 5.9±0.6, and SO spruce = 4.52±0.16.

2.2 Sample collection and filtration

Each openfall and throughfall precipitation sampler consisted of four tandem polyethylene open collectors (area = 650 cm² each, depth = 40 cm; cumulative projected area = 0.26 m²) mounted to a PVC post at a height of 1.5 m above ground. Total collector surface area to projected ground area (surface area index) = 5.2 (e.g., Hicks, 1986). At each site, samplers were located at the same aspect relative to the tree stem sampled, under the midpoint of the tree crown to avoid dripline or stem effects. Collectors were deployed prior to and retrieved following individual rain storms and snowstorms. Upon retrieval, an aliquot was immediately removed for measurement of operationally dissolved major and trace elements (MTEs) and DOC. This aliquot (a0) was filtered with a 0.45 µm nylon filter (Fisher Scientific), the first 1 mL discarded, the next 5 mL used to rinse an acid-washed polyethylene vial and discarded, and a final 20 mL retained and acidified to 2 % HCl (optima grade). Sample pH was then measured in the bulk sample using dual ROSS-type electrodes (Thermo Scientific), calibrated daily with fresh, low-ionic-strength buffer. Bulk samples were then passed through a 1 mm polypropylene screen or hand-picked to remove coarse debris and then filtered to tared 0.5 µm quartz fiber filters (QFFs; Advantech QR-100) to remove an insoluble fine particulate organic fraction (FPOM). The filtrate was acidified to 2 % HCl with concentrated acid (trace-metal grade), and the acidified sample in turn was used to rinse and recover metals absorbed to the sample collection train and collector surfaces.

FPOM on QFF filters was extracted sequentially using 2 % HCl and reverse aqua regia (9:3 HNO₃:HCl and 0.2 mL BrCl) to estimate MTE solubility and to distinguish between fluxes of dissolved (d.Pb, etc.), soluble, and total TM deposition. The acid-soluble fraction (s.Pb, etc.) is the sum of the dissolved and 2 % HCl extraction. The total fraction (t.Pb, etc.) is the sum of the dissolved, 2 % HCl, and aqua regia fractions. The acid-soluble fraction is considered environmentally relevant (Lindberg and Harriss, 1981; Mahowald et al., 2018).

From dissolved and FPOM fractions, we calculate the distribution coefficients (K_D) as follows, where V is the total sample volume (mL) and M is FPOM mass (g):

$$\begin{array}{}\text{(13)}& K_D={\displaystyle \frac{d.\mathrm{Pb}/V}{\left(t.\text{Pb}-d.\text{Pb}\right)/M}}.\end{array}$$

Enrichment factors of MTEs with respect to upper continental crust (EF_crustal) were calculated from dissolved fractions in OF collections to maintain comparability with prior works (Duce et al., 1975; Gandois et al., 2010; Taylor and McLennan, 1995):

$$\begin{array}{}\text{(14)}& {\text{EF}}_{\mathrm{crust}}={\left(M_i/\text{Al}\right)}_{\mathrm{OF}}/{\left(M_i/\text{Al}\right)}_{\mathrm{crust}}.\end{array}$$

2.3 Sample analysis

FRNs were measured by gamma spectrometry following preconcentration by MnO₂ co-precipitation, with yields averaging 88±15 % for Be and 88±16 % for Pb (mean ± SD). A workflow schematic is illustrated in Fig. S1 in the Supplement, and details are given elsewhere (Landis et al., 2012, 2021a). MTEs were measured by inductively coupled plasma optical emission spectrometry (ICPOES; Spectro ARCOS) operated in axial view. Low-level trace elements including As, Cd, Co, Cr, Cu, Fe, Pb, and V were measured by ICP triple-quadrupole mass spectrometry (ICPMS-QQQ; Agilent 8900) in the Dartmouth Trace Element Analysis Core Facility (TEA Core). The reference material NIST1643f was used for quality control, with recoveries within 95 %–105 % for all analytes. Total Hg was measured by double-amalgamation purge-and-trap atomic fluorescence (Brooks Rand Merkx-T, Model III), where samples preserved in 2 % HCl were oxidized by reaction with 1 % $v/v$ BrCl at room temperature for 24 h and then reduced to Hg₀ by the addition of SnCl₂ and hydroxylamine immediately prior to analysis. The reference material NIST1641e was used for Hg quality control, with recovery of 10 pg averaging 97±8 % (mean ± SD; n=48). Sample recovery spikes averaged 97±6 % (n=9). Dissolved organic carbon (DOC) was measured by automated combustion of acidified samples (General Electric); see also Hou et al. (2005) and Gandois et al. (2010).

2.4 Statistical analyses

Statistical analyses were performed in JMP Pro 16.0. Data were transformed to achieve normal distributions and equal variances. For NTF, which includes positive and negative values, this required transformation of the form log₁₀(x+n), with n selected to scale all values >0. Our multiple-regression approach is described in more detail elsewhere (Landis et al., 2021a). We observe the Bonferroni correction for describing the significance of multiple-regression parameters, but the p values presented here do not include this correction since the number of explanators are shown for each regression.

2.5 Literature review

Throughfall enrichment factors were compiled from the literature sources (Ali et al., 2011; Atteia and Dambrine, 1993; Avila and Rodrigo, 2004; Böhlke and Michel, 2009; Bringmark et al., 2013; Demers et al., 2007; Eisalou et al., 2013; Forti et al., 2005; Fu et al., 2010; Gandois et al., 2010; Graydon et al., 2008; Grigal et al., 2000; Henderson et al., 1977; Hou et al., 2005; Huang et al., 2011; Iverfeldt, 1991; Karwan et al., 2016, 2018; Kolka et al., 1999; Kopáček et al., 2009; Landre et al., 2009; Larssen et al., 2008; Lawson and Mason, 2001; Lindberg and Harriss, 1981; St. Louis et al., 2001, 2019; Mahendrappa, 1987; Małek and Astel, 2008; Matschullat et al., 2000; Michopoulos et al., 2005, 2018; Oziegbe et al., 2011; Petty and Lindberg, 1990; Rea et al., 2001; Rehmus et al., 2017; Rodrigo et al., 1999; Schwesig and Matzner, 2000; Skrivan et al., 1995; Sohrt et al., 2019; Stachurski and Zimka, 2000; Tan et al., 2019; Ukonmaanaho et al., 2001; Wang et al., 2020; Wilcke et al., 2017; Zhang and Liang, 2012).

Figure 1 Throughfall enrichment factors for FRNs and MTEs. (a) Percentage increase in throughfall flux when including a fraction extracted from fine particulate organic matter (FPOM). (b) Crustal enrichment factors, where EF${}_{\mathrm{crustal}}=(M/\mathrm{Al}{)}_{\mathrm{OF}}/(M/\mathrm{Al}{)}_{\mathrm{crust}}$. (c) Median flux-based throughfall enrichment factors (EFs) for this study are shown as bars. Note log₁₀ scaling. Lines and whiskers show the means and standard deviations compiled from literature sources, with the number of experiments indicated as n (see Sect. 2).

3 Results

3.1 FRN mass balance in the forest canopy

Data produced for this study are reported by Landis (2025). Throughfall enrichment factors and the partitioning of FRNs and MTEs to FPOM are shown in Fig. 1. Throughfall measurements including rainfall interception, FPOM, and DOC concentrations are shown in Fig. S2. The tree canopies studied typically intercept (retain) 20 % of precipitation. DOC and FPOM are greatly increased through the canopy, with TF concentrations in the ranges of 1–10 and 10-100 µg mL⁻¹, respectively. Throughfall mean pH values for the summer through winter seasons were 5.29, 5.36, 4.98, and 4.86, respectively. The effect of the canopy on throughfall pH was variable (Fig. S3). The canopy was a net sink for H⁺ in summer for spruce, pine, and oak [p<0.05]. On an annual basis, oak was a net sink at both sites, but both pine and spruce were net sources of H⁺.

Flux-based throughfall enrichment factors (EFs) for ⁷Be and ²¹⁰Pb were 54.7±0.3 % and 75.9±1 %, respectively (± SE), significantly lower than 1 and thereby demonstrating that the canopy is an unambiguous net sink for FRNs in wet deposition. ⁷Be shows stronger absorption than either H⁺ or H₂O, which demonstrates its strong preferential absorption by the canopy. Only the following showed EFs less than 1: ⁷Be < H${}^{+}{<}^{\mathrm{210}}$Pb < H₂O < As. All other MTEs showed a net gain through the canopy due to some combination of dry deposition during the antecedent dry period, leaching from biological tissues, or weathering from storage in the phyllosphere. Putative reference elements expected to have minor leaching contributions, such as Al, Fe, U and Na, showed moderate gains from the canopy, with EFs in the range of 2–3. The following trace metals showed EFs less than these reference elements, which nominally indicates net sorption to the canopy: Cr, Sb, V, Cu, Cd, Pb, Hg, ⁹Be, Ni, and Zn. Alkaline and nutrient elements showed much larger EFs than reference elements, indicating strong net gains from the canopy: Co, Ba, S, Ca, Sr, Mg, P, C, Mn, and K, as well as DOC and FPOM.

Crustal enrichment factors (EF_crust) in the range of 10²–10³ indicate that TF metals are generally of anthropogenic atmospheric origin, whereas values of ∼1 confirm a terrestrial dust source for Al, Fe, and U (Duce et al., 1975; Fig. 1b). EF_crust does not strictly identify atmospheric PM, however, since values in the range of 10² for alkaline elements can also reflect the high solubility of these elements and their extraction from biological tissues of the phyllosphere during rainfall.

Among tree species, spruce displayed the lowest EFs for ⁷Be and ²¹⁰Pb (highest interception) but higher EFs than either oak or pine for most elements [p<0.05]. Both spruce and oak at the SO site showed higher EFs for ⁹Be, Ni, Sb, V, and Zn, demonstrating a site effect for these elements that could be related to higher pollutant loads near higher population density or, alternatively, to the underlying mafic lithology at this site [p<0.05]. In contrast, there were no species or site effects for the heavily cycled elements Ca, Mg, K, P, or Mn or for metals including Cd, Cu, Hg, Pb, or U [p>0.05]. Tree species were compared only during deciduous leaf-on months.

3.2 Interpreting canopy processes from FRN throughfall concentrations

Throughfall EFs evaluated on the annual basis described above show that the FRNs absorb strongly and that the canopy is therefore a strong sink for secondary aerosol metals. For further insights into the balance of processes acting to retain and release FRNs within the canopy at the event scale, we also evaluated the concentrations of FRNs as a function of precipitation depth for individual storms. Below 2 cm of precipitation, both ⁷Be and ²¹⁰Pb concentrations in TF are generally greater than 100 % of concentrations in OF, and in some cases more than 300 % higher than their concentrations in incident precipitation. This indicates that net release of FRNs is the dominant process at low precipitation totals, which we attribute to the removal of dry-deposited PM, which was deposited during the antecedent dry period (Fig. 2a).

Figure 2 Relative concentrations of ⁷Be or ²¹⁰Pb in throughfall versus openfall (EF = TF $/$ OF). (a) Oak is shown with circles, pine with triangles, and spruce with open triangles. Black lines show a spline best fit. (b) Net throughfall fluxes (NTFs) of ⁷Be and ²¹⁰Pb as a percentage of total annual deposition. (c) Histograms of ⁷Be and ²¹⁰Pb net flux.

Beyond 2 cm of precipitation, the concentrations of both ⁷Be and ²¹⁰Pb are lower than in openfall, indicating that the canopy transitions to a net sink with increasing precipitation depth. This suggests that at some threshold amount of precipitation, susceptible dry-deposited PM is fully removed, and wet-deposited PM continues to be absorbed by the canopy. The unambiguous net sorption of wet-deposited PM is clear when concentrations are converted to fluxes (by multiplication with precipitation depth; Fig. 2b). At the highest precipitation totals >6 cm, there is some suggestion that the sorption capacity of the canopy may be exhausted and FRN yields from the canopy begin to increase, but data are too few for a confident interpretation.

3.3 Throughfall ⁷Be :²¹⁰Pb ratios as a metric of PM age

²¹⁰Pb is systematically biased to higher yields than ⁷Be despite the same patterns in canopy interactions, and as a result, ⁷Be :²¹⁰Pb ratios are significantly lower in throughfall versus in openfall (Figs. 2a, S3). Mean throughfall ⁷Be :²¹⁰Pb ratios across all species averaged 10.3±0.3 versus mean openfall of 14.8±0.5 [mean ± SE]. Throughfall for each tree species was significantly lower than paired openfall measurements [p<0.0001]. There was no correlation between throughfall pH and the ⁷Be :²¹⁰Pb ratio that might indicate discrimination of the FRNs through aqueous chemistry [R²=0.001, p=0.80; Fig. S3b]. We next used multiple regression to identify independent explanators of throughfall ⁷Be :²¹⁰Pb ratios and to quantify their independent effects on ⁷Be :²¹⁰Pb; we report independent effects as the percentage of total variance explained by each variable [in brackets] (Fig. S4). A predictive model for ⁷Be :²¹⁰Pb showed the following significant explanators: species [22 %], season [12 %], and the ⁷Be :²¹⁰Pb ratio of incident precipitation [9 %] [R²=0.42]. Adjusted for season and incident ratio, ⁷Be :²¹⁰Pb ratios among species increased in the following order: spruce (7.9±0.6)^A< pine < (9.5±0.6)^B < oak (11.9±0.5)^C; values not sharing the same letter are significantly different [p<0.05]. Adjusted for both species and incident ratio, seasonal ratios increased in the following order: autumn (7.6)^A < summer (9.9)^B < winter (10.5)^BC< spring (11.3)^C. Both species and seasonal patterns are consistent with the impact of tree phenology on long-term storage of ²¹⁰Pb, with the higher LAI and older foliage of conifers storing larger reservoirs of ²¹⁰Pb, which is exported in small amounts during subsequent storms.

The strongest discrimination between ⁷Be and ²¹⁰Pb appears to be their characteristic half-lives, in the absence of any evidence for impacts of environmental factors. There was no effect on ⁷Be :²¹⁰Pb from the antecedent dry period [R²=0.01, p=0.27], suggesting no discrimination in dry deposition between ⁷Be and ²¹⁰Pb. There was no positive correlation between rainfall depth and ⁷Be :²¹⁰Pb [R²=0.03, p=0.42] in contrast to OF, where a strong positive correlation reflects the washout–rainout transition (Landis et al., 2021a). Importantly, there were no significant effects from factors that might indicate discrimination between Be and Pb aqueous chemistries, including pH [p=0.32]; log₁₀(K_D) for either ⁷Be [p=0.34] or ²¹⁰Pb [p=0.18]; FPOM [p=0.29]; DOC [p=0.47]; or any MTE concentrations, fluxes, net fluxes, or enrichment factors [p>0.05].

Figure 3 Multiple regressions for prediction of net throughfall (NTF) of FRNs. (a) ⁷Be and (b) ²¹⁰Pb. NTF is modeled with explanators including precipitation depth, antecedent dry period (after 5 mm precipitation), season, and tree species. Models are shown without transformation to retain interpretable units on the data, but this does not impact the significance of the explanators. Three outliers omitted in the ²¹⁰Pb regression are indicated with open symbols.

3.4 Multiple-regression mass balance to quantify dry deposition

We used multiple-regression mass balance to quantify the independent influences of wet and dry deposition and canopy interactions that determine net throughfall (NTF) of the FRNs (Eq. 5). Overall model fits for NTF are good for both ⁷Be [R²=0.49, p<0.0001] and ²¹⁰Pb [R²=0.30, p<0.0001] (Fig. 3). Both ⁷Be and ²¹⁰Pb show positive effects from the antecedent dry period (β₁) [p<0.05] and inverse effects from precipitation depth (β₂), apparent in Fig. 2 [p<0.05]. For ⁷Be, the dry-deposition rate (β₁) is equivalent to 213±53 Bq m⁻² yr⁻¹ or 13±4 % of total annual deposition (assuming that all dry deposition is fully removed by subsequent storms). The multiple-regression dry-deposition estimate does not incorporate the ⁷Be decay that occurs during the antecedent period. However, with a decay rate of 1.3 % per day and a median antecedent period of 7 d (mode of 2 d), the underestimation of ⁷Be dry deposition from ignoring radioactive decay is likely <10 % of estimated dry deposition or <20 Bq m⁻² yr⁻¹. For ²¹⁰Pb, β₁ is equivalent to 19±6 Bq m⁻² yr⁻¹ or 15±5 % of total annual deposition.

It is important to observe from Fig. 2 that dry deposition is not fully removed from the canopy by subsequent rainfall since throughfall FRN concentrations may be higher than incident precipitation for up to 2 cm of precipitation. During and following rain events, it is thus likely that a complex exchange is occurring at the leaf surface between wet- and dry-deposited PM, and both components are likely to be absorbed by the leaf, especially at low rainfall totals. In this case, the multiple-regression estimate of dry deposition is underestimated by a factor equal to the efficiency with which dry deposition is absorbed by the canopy. The implications for dry-deposition absorption are discussed below in Sect. 4.1.

Dry deposition to the canopy is likely derived from ambient PM and not from resuspension of dust. The ⁷Be :²¹⁰Pb ratio of dry deposition to the canopy based on multiple-regression coefficients ($=\mathrm{11}\pm \mathrm{4}$), which is comparable to our prior measurements of ambient PM₁₀ ($=\mathrm{10}\pm \mathrm{2}$), is somewhat lower than openfall wet deposition [flux-weighted average = 15.1±0.6; p=0.22] but significantly higher than bulk dry deposition [$=\mathrm{4.2}\pm \mathrm{0.6}$, p<0.0001] (Landis et al., 2021a).

3.5 Importance of DOC and FPOM in MTE multiple regressions

For MTEs, we similarly estimated dry deposition and canopy interactions that contribute to their enrichment in throughfall using multiple regression. All MTEs were found to have positive correlations with both antecedent dry period and rainfall depth (Table S1 in the Supplement). Importantly, both FPOM and DOC contribute significantly to all FRN and MTE models. This suggests that carbon plays a significant role in release of both FRNs and MTEs from the canopy. DOC is the stronger explanator and typically supersedes FPOM in the model (Table S1). Because they have strong predictive power in FRN and MTE models, we also examined FPOM and DOC using multiple regression (Fig. S5). The FPOM model [R²=0.35] has significant explanators including season [19 %], antecedent duration [11 %], and rainfall depth [5 %]. Surprisingly, there was no effect from species [p>0.05]. The strongest effect from antecedent duration uses a 15 mm rather than a 5 mm precipitation threshold. Including DOC as an explanator strengthens the FPOM model [R²=0.58], as DOC becomes the strongest predictor [21 %]. A model for DOC [R²=0.31] shows the same explanators as for FPOM, with season [14 %], antecedent [7 %], and rainfall depth [6 %] each being significant. DOC production is higher relative to FPOM in spring and fall [p<0.05], which is consistent with tree phenology and peak DOC production with both new foliar growth and senescence (Van Stan et al., 2012).

Figure 4 Dependence of throughfall EF on the DOC binding constant, K_DOC. K_DOC was estimated as the increase in metal NTF per unit increase in DOC, normalized to metal concentration. Elements in black have large oxide (K_OH) over oxalate binding constants (K_ox); elements in green have oxalate preference (Takahashi et al., 1999).

3.6 Dissolved organic carbon regulates FRN and MTE net throughfall

The coefficient β_DOC obtained from multiple-regression mass balance quantifies the increase in NTF per increase in DOC (µmol MTE µmol C⁻¹). This provides an empirical metric of FRN or MTE affinity for throughfall DOC (Table S1). It can be expressed as an association constant (K_DOC) by normalizing each multiple-regression coefficient by the average dissolved FRN or MTE concentration (µmol L⁻¹). K_DOC is significantly correlated with EF across all elements, which supports the notion that DOC aids in regulating the export of MTEs from the canopy (Fig. 4; R²=0.32, p=0.003; see also Hou et al., 2005; Gandois et al., 2010). Moreover, there are additional noteworthy associations within the FRNs and MTEs. They are bound at lower EFs by group 1, which consists of ⁷Be, ²¹⁰Pb, Be^T, Pb^T, Hg^T, Al, and Fe [slope $=\mathrm{0.381}\pm \mathrm{0.056}$; R²=0.90, p=0.001]; these are the elements with the strongest oxide over humate preferences and are thus likely to be most weakly solubilized by DOC (Takahashi et al., 1999).

Separation of FRNs from their stable-isotope counterparts within this relationship, with both lower K_DOC and lower EF, suggests that some age dependence of PM regulates the metal–DOC association (Sect. S2, Fig. S8). Within the ⁷Be–Be^T and ²¹⁰Pb–Pb^T pairs, elemental chemistry is conserved, and differences in K_DOC and EF must be attributed to different PM ages/sources. The distinction made here is between secondary aerosol, which characterizes ⁷Be and ²¹⁰Pb, and resuspended dust or aged PM, which more likely influences Be^T and Pb^T (as well as Hg^T, Al, Fe, and U). Elsewhere we have described this as a particle–age effect to describe how PM metals become increasingly and irreversibly particulate bound with increasing PM age (Landis et al., 2021b).

Alkaline and strongly cycled nutrient elements form a second boundary of group 2 elements at high EFs [slope $=\mathrm{0.478}\pm \mathrm{0.133}$, R²=0.72, p=0.0159]. The alkaline elements Ca, Sr, and Ba have the highest preference for humate over oxide ligands (Takahashi et al., 1999). K_DOC alone does not clearly separate groups 1 and 2 due, in part, to the particle–age effect. This suggests that EF distinguishes the metal source, with atmospheric deposition controlling group 1 and leaching controlling group 2. Trace metals in the intermediate group (3) are increasingly likely to have metabolic contributions from canopy leaching with larger EFs.

Figure 5 Multiple regressions for (a) ²¹⁰Pb net throughfall and (b) ²¹⁰Pb change in storage. Both variables are transformed to provide normal distributions.

3.7 PM storage and change in storage (ΔS) in the forest canopy

Our assumptions for the FRN canopy mass balance underlying the derivation of Eq. (10) appear the same as those observed, with no differences detected in ⁷Be and ²¹⁰Pb geochemical behaviors or in rates of dry deposition. Lower ⁷Be :²¹⁰Pb ratios and an excess of ²¹⁰Pb over ⁷Be in TF should thus be interpreted as a change in storage (ΔS) derived from within the non-metabolic materials of the tree canopy. ²¹⁰Pb_ΔS averaged 0.70 Bq m⁻² per storm or 29 % of annual net throughfall flux. In contrast to net throughfall (²¹⁰Pb_NTF), which decreases with total precipitation, ²¹⁰Pb_ΔS increases significantly with total precipitation at a rate of 0.22±0.04 Bq m⁻² cm⁻¹, which is equivalent to 22±4 Bq m⁻² yr⁻¹ [R²=0.19, p<0.0001]. ²¹⁰Pb_ΔS was not influenced by the antecedent dry period [R²=0.009, p=0.25], which lends confidence to our theory that ²¹⁰Pb_ΔS does not simply reflect different depositional dynamics for ⁷Be and ²¹⁰Pb. Multiple regression for ²¹⁰Pb_ΔS yielded a strong model with significant, independent effects of rainfall depth [13 %], species [9 %], season [7 %], and DOC [15 %] [R²=0.46, n=137(8)] (Fig. 5). ²¹⁰Pb_ΔS was highest in autumn and summer and lowest in winter, irrespective of tree species and including the conifer species [p<0.05]. Spruce contributed larger change in storage than either pine or oak [p<0.05]. Linear, positive dependence on precipitation demonstrates that ²¹⁰Pb_ΔS supply is not readily exhausted, as is the case for dry deposition (i.e., as shown in Fig. 2a).

When we compare regressions for ²¹⁰Pb_NTF and ²¹⁰Pb_ΔS, the importance of DOC is replaced by a stronger correlation with FPOM in the ΔS model. In addition, where modeling of ²¹⁰Pb_NTF found no significant relationships with other metals, for the ²¹⁰Pb_ΔS multiple regression, multiple trace metals also provide explanatory power at the expense of season, DOC, and rainfall depth [R²=0.65, n=102(3)]. MTEs with strong explanatory power were Cu_ΔS [26 %], Fe_ΔS [26 %], Al_ΔS [24 %], P_ΔS [22 %], and Hg_ΔS [14 %]. Correlation with Hg also removes autumn seasonality in ²¹⁰Pb_ΔS. These strong correlations among ΔS for multiple metals suggest that they are entrained in a common weathering process from the canopy. It is important to note that ⁷Be_NTF provided no explanatory power in the ²¹⁰Pb_ΔS model [p=0.35], confirming the decoupling of ⁷Be and ²¹⁰Pb_ΔS through the mass balance model.

Among all MTEs, ΔS increases asymptotically with EF (Fig. S6). Sulfur is a notable exception because high EF is attributable to dry deposition of gaseous SO₂ rather than to ΔS. Change in storage was estimated for MTEs as the relative contribution to annual NTF: SO₄=7 %, ²¹⁰Pb = 17 %, Cd = 40 %, ⁹Be = 45 %, As = 58 %, Hg = 60 %, Pb = 63 %, Fe = 79 %, Al = 79 %, and P = 91 % (Table S1).

4 Discussion

4.1 Verifying throughfall multiple-regression mass balances

Throughfall mass balances and the derivation of ΔS can be verified against ecosystem mass balance for the FRNs since, due to their short half-lives, the FRNs measured in vegetation and soil have unambiguous atmospheric sources. For example, long-term ²¹⁰Pb fluxes calculated from regional steady-state soil inventories average 173±24 Bq m⁻² yr⁻¹ (n=8; Landis et al., 2016, 2024a). Long-term bulk deposition measurements average 177±27 (n=12) but have decreased 4 % per year from 2011 to present, and the most recent 4 years have averaged 158±26 (Landis et al., 2021a). The sum of event-based W and D fluxes estimated from multiple regression reported here over 2 years equates to 151 Bq m⁻² yr⁻¹, which is somewhat lower than expected from soil inventories. However, the multiple-regression estimate of D assumes that dry deposition is fully removed by each subsequent precipitation event (Lovett and Lindberg, 1984). Our analysis of throughfall FRN concentrations in storms has already shown that this is not correct (Fig. 2). Therefore, the multiple-regression approach underestimates D and thereby total annual deposition as well. From a whole-tree mass balance approach (Landis, 2024b), an absorption rate of D was estimated to be 49 %, meaning that the multiple regression underestimates D by a factor of about 2. Adoption of this absorption factor hereafter requires a proportionate increase in annual dry deposition, almost doubling the estimate to 65 Bq m⁻² yr⁻¹ and leading to an annual deposition total of 174 Bq m⁻² yr⁻¹. This more robust quantitation of dry deposition stands in better agreement with soil records. The overall conclusion we reach is that both wet and dry deposition are well retained by the forest canopy.

FRNs also provide an opportunity to evaluate the suitability of conventional filtering throughfall mass balance for MTEs. In contrast to the multiple-regression approach, the rate of ²¹⁰Pb dry deposition predicted by the filtering approach (Eq. 4, with Al as the reference) is higher by a factor of 12, and total annual ²¹⁰Pb deposition is higher by a factor of 2 compared to what is observed in local soils (360 Bq m⁻² yr⁻¹). The total ⁷Be flux predicted by filtering is higher than that observed by a factor of 2.6 (4700 Bq m⁻²). The filtering approach thus grossly overestimates secondary aerosol metal deposition, irrespective of whether Na, Al, or U is used as a reference element. These elements must therefore have substantial contributions from canopy leaching or resuspended dust that do not impact FRNs and other secondary aerosol metals. Total rates of deposition for all MTEs estimated by the filtering approach are higher than those from the multiple-regression approach by a factor of 5 on average (Sect. S3).

4.2 PM age and residence time in the phyllosphere

The strongest control on ⁷Be :²¹⁰Pb ratios in throughfall was tree species. We attribute this to an age effect and to the storage of PM in the phyllosphere by conifers with high foliar masses and LAI. Decreasing throughfall ⁷Be :²¹⁰Pb ratios in the order oak > pine > spruce are consistent with the characteristic leaf retention times of each species, about 6 months for oak, 1–2 years for white pine, and up to 5–8 years for spruce. This trend is also consistent with the size of the total ²¹⁰Pb inventories likely to be stored in these trees based on whole-tree mass balance, increasing to 9 times the ²¹⁰Pb annual flux in oak, from 11 times in pine, and from 17 times in spruce (Landis, 2024b). Given these large estimates of ²¹⁰Pb storage in the canopy and assuming that the canopy is at steady state with respect to inputs and export, the mean residence time of ²¹⁰Pb storage in the canopy (S) can be described as follows, with the corresponding analytical solution:

$$\begin{array}{}\text{(15)}& {\displaystyle \frac{\partial S}{\partial t}}=A-kS-\mathit{\lambda }S\text{(16)}& {\displaystyle }S\left(t\right)={\displaystyle \frac{A}{k+\mathit{\lambda }}}\left[\mathrm{1}-e^{-(k+\mathit{\lambda })\cdot t}\right],\end{array}$$

where S is the canopy inventory (Bq m⁻²) and A is the rate of canopy absorption of ²¹⁰Pb (which elsewhere is estimated as the product of wet and dry fluxes with their characteristic sorption coefficients of approximately 50 % each minus litter losses, summing to 57 Bq m⁻² yr⁻¹; Landis, 2024b). Here, λ is the ²¹⁰Pb decay constant, and k is a characteristic physicochemical weathering rate. k can be approximated if we observe a steady-state S=825 Bq m⁻² based on whole-tree measurements, which is an average for the two throughfall trees at the BM site. With these assumptions, the mean residence time of PM metals in the phyllosphere with respect to weathering is 32 years (Fig. S7). Independent age estimates of individual components of an adjacent red oak tree have also been made with ⁷Be :²¹⁰Pb chronometry for leaves (0.5 years), twigs (1.4 years), branches (7 years), moss (28 years), lichen (21 years), live surface (20–52 years), and bark (18 to >70 years). These ages are consistent with the superposition or ordering of, e.g., twig versus branch and canopy crown versus tree base, and overall confirm that canopy storage of metals persists for decades (Landis, 2024b).

4.3 Implications for rates of MTE deposition to forest vegetation

The FRNs stand apart from MTEs in canopy mass balance, having EFs <1 and NTF that scales inversely with rainfall depth. What distinguishes the FRNs from other PM metals is radioactive decay, and the obvious cause of their diverging behaviors is a difference in characteristic ecosystem residence times. While the FRNs are quintessential atmospheric metals and tracers of PM_2.5, other trace-metal cycles are therefore dominated by recycled pathways rather than by novel PM deposition. This is illustrated clearly for the pairs ²¹⁰Pb versus Pb^T and ⁷Be versus ⁹Be. Within each pair, the FRN shows net sorption to the canopy, while the stable isotope shows net release. Within each pair, elemental chemistry must be conserved, and differences must therefore derive from half-life restrictions, which in turn relate to different PM sources. In the absence of these insights from FRN mass balance, for example, large EFs for both ⁹Be and Pb^T in throughfall would be attributed to novel dry deposition rather than to a change in storage from recycled materials and legacy deposition. This has obvious consequences for estimating PM budgets and dry deposition by canopy mass balance, which may otherwise be overestimated by factors ranging from 2 to 10 (Sect. S3).

A critical question thus emerges: from where does a change in storage originate? Possible sources cannot be discerned by our current methods but include resuspension of aged PM, e.g., dust, from the surrounding forest floor, as well as regional sources such as vehicular traffic and road dust; excretion of metabolic products from the flora of the phyllosphere; or weathering of PM from legacy deposition to living and dead surfaces of the phyllosphere. For all MTEs, the strong dependence of both NTF and ΔS on DOC indicates that the immediate metal source is within the phyllosphere. Production of DOC in the phyllosphere in this case appears to act as a weathering mechanism, meaning that PM, metals, and dust are efficiently captured in the canopy and their constituents solubilized over some characteristic time frame that may span years to decades, likely altering their chemical speciation in association with organic carbon and exporting them from the canopy in an operationally dissolved phase by DOC (Gandois et al., 2010; Roulier et al., 2021). Poorly soluble metals such as Fe and Al require solubilization by DOC to generate high throughfall EFs through ΔS (Hou et al., 2005). In conclusion, the strong correlations of ΔS among many TMs suggest that ΔS may be an emergent ecosystem property through which metal, carbon, and hydrologic cycles converge (Van Stan and Stubbins, 2018). The phyllosphere thus plays a critical role in regulating the timing, bioavailability, and reactivity of metals and carbon that are subsequently transferred to underlying soils. Future work should aim to extend the FRN mass balance to additional biomes and climate gradients so that the importance of phyllosphere storage for PM dynamics can be evaluated on a global scale in the context of climate change.

The role of organic particulate matter or FPOM is important in all MTE canopy cycles and warrants greater attention in future throughfall mass balance (Van Stan et al., 2021). Including the FPOM fraction in mass budgets increases the net throughfall of each MTE on average by 26 %, but this number is higher for particle reactive elements including Hg (73 %) or Pb (45 %). Export of FPOM from the canopy mirrors processes that we observe for all MTEs. Its dependence on both precipitation and the antecedent dry period, in turn, obscures the impact of these factors on MTEs, which would otherwise be attributed to either leaching or novel dry deposition, respectively. Canopy FPOM export is highly seasonal, peaking strongly in summer to reflect productivity of the biological engine in the canopies of all tree species measured here (notably, both deciduous and coniferous). The production of FPOM via herbivory likely plays an important role (Frost and Hunter, 2004; Michalzik and Stadler, 2005). FPOM moreover figures directly in predictive models for DOC export and may thus represent a source of soluble carbon. As such, FPOM and DOC together influence trace-metal cycling in the canopy and unite many trace metals in carbon cycling within the phyllosphere.

4.4 Implications of aerosol ΔS for trace-metal throughfall budgets

PM storage in the forest canopy introduces complexity to the metal exchange processes that control throughfall mass balance. Our compilation of literature TM throughfall highlights the widely varying behaviors of individual metals to transit through the forest canopy, ranging from strong net sorption to strong net release (Fig. 1). This variation is unlikely to result from elemental solubility behavior, metabolic cycling, or the vagaries of event-scale interaction between precipitation and the canopy. Instead, we suggest that throughfall export from the canopy reflects the complexity of aerosol sources, how these have changed through time in both source strength and PM characteristics (Cho et al., 2011), and the transformations that occur during PM residence in both the canopy and the underlying forest soil. Thus, time and history are critical determinants in throughfall metal measurements.

With global anthropogenic emissions of many metals reduced in recent decades through emissions controls, the canopy is unlikely to be in a steady state with contemporary atmospheric deposition. Throughfall is thus likely to be a biased metric of deposition if a change in storage from prior deposition cannot be assessed. Future insights into the storage and solubilization of aerosol metals in the phyllosphere will require a combination of approaches to unravel varying sources and timescales of aerosol deposition to the canopy. We suggest that FRN mass balance and micrometeorology methods for, e.g., Hg deposition, are complementary approaches that can combined to verify both PM depositional processes and fluxes (Landis et al., 2024a). Here, we have shown that multiple-regression mass balance coupled with new FRN mass balance and in combination whole-tree measurements (Landis, 2024b) can accurately quantify both new PM and TM deposition and their release from long-term storage. We anticipate that coupling throughfall, whole-tree mass balances, and FRN chronometry with stable-isotope systems of, e.g., Cd, Cu, Pb, and Hg, will yield new insights into metal dynamics in forest canopies and should be a focus of future efforts to understand the fate and redistribution of atmospherically derived metals.