The modeling structure used in this study incorporates the coupling of two 0-D models designed to investigate detailed differences in chemical processing and SOA formation above and below the forest canopy layer. MATLAB computing software (v. R2014a) was used to perform a diel analysis of each environment (above and below the canopy) with output every second. The model uses a variable-order ordinary differential equation solver (MATLAB_ODE solver ode15s) to solve the underlying system of differential equations. One day of model spin-up was used for each analysis (Pratt et al., 2012). The oxidation mechanisms of α-pinene and isoprene were obtained directly from the Master Chemical Mechanism (MCM v3.2, via the website: http://mcm.leeds.ac.uk/MCM; Jenkin et al. (1997); Saunders et al., 2003), as well as the standard gas-phase inorganic reactions included in the MCM, resulting in a system of 2260 chemical reactions with 712 chemical species. These two BVOCs were chosen because of their relatively high emission rates as well as differences in their reactivity and SOA formation potential. For instance, isoprene is known to react predominately with OH, while α-pinene reacts substantially with all three major oxidants within forests (Fuentes et al., 2007). The SOA yields measured during low-NOx OH oxidation of isoprene are generally lower than those from α-pinene; however, their SOA yields from NO3 oxidation are similar (Table 1).

Chemical species within each 0-D box (above and below the canopy) react in the gas phase via mechanisms dictated by the MCM, partition between the gas and aerosol phases if of sufficiently low volatility, undergo dry deposition, and are transported between environments. While the gas-phase chemical mechanism has been briefly introduced above, the remaining model processes are described in the sections below.

Dry deposition of gases and aerosols is included within both the above- and below-canopy boxes. In the above-canopy model, deposition is assumed to occur onto the top of the canopy, and the resistance to deposition is determined using the method of Meyers and Baldocchi (1988). Deposition velocities for each chemical species are calculated based on resistances from the quasi-laminar boundary layer and leaf mesophyll, cuticular surfaces, and stomata. A thorough description of the particular equations used in this method can be found in Bryan et al. (2012). The specific parameter values used in the calculation of deposition velocities are listed in Table S1 in the Supplement. The above-canopy box height was assumed to vary diurnally based on the boundary layer values utilized in Giacopelli et al. (2005) for a previous model of the CABINEX location. As our model does not calculate aerosol sizes, size distribution data obtained from VanReken et al. (2015) were used to calculate a volume-weighted average settling velocity of aerosol particles.

In the below-canopy model, deposition was assumed to occur to the ground and was modeled following the method of Gao et al. (1993). This method assumes that the deposition velocity is based on the combination of aerodynamic resistance near the ground and a species-specific resistance to deposition to the forest floor. The box height was set to 6 m (the assumed bottom of the canopy layer or top of the trunk space) for the entire diurnal period.

Recent modeling studies have revealed that in-canopy vertical mixing substantially influences overall forest chemistry (Bryan et al., 2012). Mixing is often parameterized in one-dimensional (1-D) models using traditional K-theory, which quantifies the transport of chemical species by eddy diffusion at a rate corresponding to the heat exchange coefficient (Wolfe et al., 2011; Bryan et al., 2012). While one of the most accurate turbulence parameterization methods available, such a process is computationally sophisticated and is better suited to 1-D modeling of an environment. In order to simplify the quantification of mixing, we have implemented the concept of in-canopy residence lifetimes to determine mixing rates. Measured and modeled in-canopy residence times vary substantially depending on the forest environment studied. For instance, Fuentes et al. (2007) report average residence times of ∼ 8 min for a parcel emitted near the ground, during the day, in a forest with a 26 m high canopy, while Farmer and Cohen (2008) calculate residence times of 1–7 min for a forest with a canopy height of only 5.7 m. Maximum residence times of up to 50 min have been reported in tall forests (Strong et al., 2004). Transport back into the canopy is an even more complicated process, as coherent structures (i.e., sweeps of air downward), rather than simple turbulence, often produce the majority of scalar fluxes (Steiner et al., 2011).

For our model, a minimum residence time of 10 min in each location is assumed to apply midday, in agreement with previous measurements, and residence times vary diurnally based on the modeled turbulent heat exchange coefficient produced by the CACHE model (Bryan et al., 2012). In addition, we have included a diurnal above-canopy vertical dilution rate based on the average of methanol and acetaldehyde above-canopy vertical loss calculated by the FORCAsT 1-D model for summertime conditions (Ashworth et al., 2016).

The inclusion of a mixing process, vertical dilution, and dry deposition results in relatively good agreement between measured and modeled concentrations of the sum of the isoprene oxidation products methacrolein and methylvinyl ketone (MACR + MVK) (Supplement Fig. S1). These photooxidation products of isoprene are often significantly overestimated in low NOx conditions modeled in forests (Bryan et al., 2012; Ashworth et al., 2015). The validity of the mixing process specifically is supported by the agreement between the measured and modeled differences in MACR + MVK mixing ratios above and below the canopy (Fig. S1c), as this comparison removes the influence of errors in the chemical mechanism that may produce overpredictions or underpredictions of the overall mixing ratios. While the comparison of differences in mixing ratios above and below the canopy indicates that we likely overpredict mixing in the early morning and underpredict mixing in the late evening, this study is primarily focused on daytime conditions, during which the differences are within a few percent. Different minimum transport lifetimes above and below the canopy (from 10 to 30 min) were analyzed to determine whether better agreement between measured and modeled MACR + MVK profiles could be attained; however, this ultimately produced little variation in the overall agreement, and the use of a 10 min lifetime in each location was found to produce minimum error between measured and modeled MACR + MVK mixing ratios (Fig. S1d).

The CABINEX campaign took place in northern Michigan near the University of Michigan Biological Station (UMBS) in August 2009 and utilized the Program on Oxidants: Photochemistry, Emissions, and Transport (PROPHET) tower to perform gas-phase measurements throughout the canopy. A deciduous forest with a canopy height of around 22.5 m surrounds the PROPHET tower and consists of tree species that emit significant quantities of both isoprene (aspen and oak) and monoterpenes (pine and birch). Above-canopy measurements were made at a height of 34 m, while those below the canopy occurred at a height of 6 m (Fig. S2). More detailed descriptions of both the PROPHET tower and the surrounding environment can be found in the literature (Carroll et al., 2001; Ortega et al., 2007; Griffith et al., 2013).

The primary goal of the campaign was to examine the effect of forest succession on atmospheric chemistry. The majority of studies resulting from the CABINEX campaign have focused on improving understanding of the linkage between gas-phase radical and BVOC chemistry through measurements and modeling (Kim et al., 2011; Bryan et al., 2012; Griffith et al., 2013; Hansen et al., 2014), while two have investigated aerosol concentrations at the site (Ashworth et al., 2015; VanReken et al., 2015). Aerosol size and composition vary widely based on ambient wind direction, but show a stronger anthropogenic influence when air masses come from populated areas to the east and south (VanReken et al., 2015). Accurate modeling of diel changes in SOA mass loadings using a 1-D model has thus far proven difficult (Ashworth et al., 2015).

The model was constrained by diel median values of hydrogen oxides (HOx = OH + hydroperoxy radical (HO2)), NO, NO2 O3, α-pinene (monoterpenes), isoprene, formaldehyde (HCHO), and the photolysis rate of NO2. Each of these species was therefore assigned a median measured value at every hour, and values used for each model time step (e.g., 08:03) were determined by linear interpolation between hourly values. The Indiana University Fluorescence by Gas Expansion (IU-FAGE) instrument was used to measure OH and HO2 (Griffith et al., 2013). Interferences involved in the operation of the IU-FAGE instrument caused slight positive artifacts in the measurement of both OH and HO2 concentrations. During below-canopy measurements, laser photolysis of O3 within the IU-FAGE sampling cell resulted in a minor artificial increase in OH concentrations, while both above and below the canopy, a fraction of peroxy radicals (RO2) was converted into HO2 within the sampling cell, as further explained in Sect. 2.7. The resulting influence of OH on BVOC chemistry below the canopy therefore represents an upper limit. Nitrogen oxides were measured using a two-channel chemiluminescense instrument with a blue-light converter for NO2 measurements (Air Quality Design, Inc.), O3 was measured using ultraviolet absorption (Thermo Environmental Instruments Inc. 49c), and isoprene, monoterpenes, and formaldehyde were measured with a proton-transfer reaction mass spectrometer (PTR-MS) (IONICON, Inc.). As the PTR-MS did not distinguish between monoterpene species, all monoterpenes were assumed to be α-pinene for modeling purposes even though its RONO2 and SOA yields are generally smaller than those of other monoterpene species (Fry et al., 2014; Zhao et al., 2015), likely resulting in a low bias. This assumption is justified by noting that gas chromatography–mass spectrometry (GC–MS) measurements taken at a height of 6 m during CABINEX indicate α-pinene accounted for an average of ∼ 77 % of monoterpenes at the site (Wallace, 2013). The photolysis frequency of NO2 was measured with a Scanning Actinic Flux Spectroradiometer (Flynn et al., 2010). Further information regarding the measurement techniques can be found in Griffith et al. (2013).

Above-canopy photolysis frequencies for isoprene and α-pinene oxidation products were obtained directly from the MCM, while photolysis frequencies for other species were taken from the National Center for Atmospheric Research (NCAR) Tropospheric Ultraviolet and Visible (TUV) Model (TUV Model 4.1, via the website: http://cprm.acom.ucar.edu/Models/TUV/Interactive_TUV/). In order to correct for non-clear-sky conditions, above-canopy photolysis frequencies were scaled to represent differences between the measured NO2 photolysis frequency and that predicted by the TUV model. Below-canopy frequencies were then calculated by scaling by the ratio of the below-to-above-canopy NO2 photolysis frequencies measured during CABINEX. This ratio is time-of-day dependent, with a maximum around noon, and varies over the range of 0.05 to 0.17 during daylight hours (Fig. S3d). Model input data are shown in the SI (Fig. S3).

At CABINEX, O3 levels were relatively consistent throughout the day, reaching a maximum in the afternoon (Fig. S3). Median mixing ratios were consistently ∼ 5 to 10 ppbv larger above the canopy than below (∼ 30–35 ppbv above, ∼ 20–30 ppbv below). While NO2 concentrations peaked at night (∼ 1 ppbv), likely due to both O3 oxidation of local NO and transport from non-local air masses, they were larger below the canopy in the early morning. Concentrations of NO were below the detection limit of the instrument (6.7 pptv) for much of the night and were therefore held at 6.7 pptv for modeling purposes during these periods. Maximum daytime NO mixing ratios reached ∼ 0.2 ppbv in the early morning, largely the result of NO2 photolysis (Seok et al., 2013). Monoterpene (-pinene) concentrations were consistent at around 0.3 ppbv, although they exhibited slight diel variability with maxima occurring at night, whereas the isoprene profile displayed strong emission dependence on sunlight and temperature and reached a maximum mixing ratio of ∼ 1.6–1.7 ppbv mid-afternoon.

Without any changes to the MCM, predicted gas-phase RONO2 concentrations (∼ 400 pptv) are much larger than those modeled by Pratt et al. (2012) (∼ 20–70 pptv), implying that gas-phase RONO2 is overpredicted by the MCM. Dry deposition rates of both isoprene and α-pinene nitrates (∼ 1.5–2.5 cm s-1) are similar to the values used in Pratt et al. (2012), and the vertical dilution rate used in our model is comparable to the value used by Giacopelli et al. (2005) for nitrates at UMBS, suggesting that physical processes are not the reason for the modeled difference.

The discrepancy in total RONO2 concentrations therefore likely stems from inappropriately large RONO2 yields or inappropriately small loss rates within the MCM. While monoterpene nitrate concentrations modeled in previous studies are generally less than 50 pptv (Pratt et al., 2012; Fisher et al., 2016), without applying any changes to the chemical mechanism obtained from the MCM, two first-generation α-pinene hydro-hydroxynitrates, produced from NO3 oxidation followed by RO2 + HO2 reaction, have a cumulative concentration of over 100 pptv for the majority of the day (Fig. S4a). Within the MCM, the first-generation RO2 + HO2 reaction that forms these products has a 100 % hydro-hydroxynitrate yield; however, laboratory experiments have indicated that while such a yield may be suitable for small peroxy radicals such as methyl peroxy, larger peroxy radicals are more likely to produce OH or alcohols upon reaction with HO2 (Jenkin et al., 2007; Dillon and Crowley, 2008). Recent modeling by Fisher et al. (2016) using the GEOS-Chem model assumes that the first-generation monoterpene RO2 from NO3 oxidation has only a 10 % probability of nitrate retention upon reaction. In order to account for the laboratory findings and to align our chemical scheme with that of Fisher et al. (2016), we reduced the production rate of the two hydro-hydroxynitrate compounds by a factor of 10. This results in an average nitrate retention probability of 8.5 % above-canopy and 12.8 % below-canopy for α-pinene RO2 from NO3 oxidation. The finalized concentrations, while still larger than those modeled by Pratt et al. (2012), show much better agreement with previous findings.

Second-generation isoprene nitrate concentrations (∼ 100 pptv) also appear to be overpredicted relative to previous observations, which report concentrations of 20–50 pptv (Pratt et al., 2012; Fisher et al., 2016). Similarly to the first-generation α-pinene nitrate concentrations, modeled second-generation isoprene nitrate mixing ratios are dominated by two species, methyl vinyl ketone nitrate (MVKN) and methacrolein nitrate (MACRN). The MCM does not assume these products react with NO3 or O3, as has been recently suggested (Kerdouci et al., 2010), and the reaction rate of each species with OH is 5–10 times larger in the model used by Pratt et al. (2012) than in the MCM. Adding reactions with NO3 and O3 and modifying the reaction rate with OH to match that used in Pratt et al. (2012) improves agreement (Fig. S4); however, the implications of the remaining differences are discussed in Sect. 3.3. Ultimately, as will be discussed, the RONO2 fraction of SOA agrees well with previous measurements, indicating that the possible remaining errors in gas-phase RONO2 concentrations should not unduly influence the conclusions related to SOA mass loadings.

Measured OH and HO2 profiles above the canopy were compared to those predicted by our model when leaving HOx concentrations unconstrained, which gives an indication of the validity of both the modeled oxidation processes and photolysis frequencies, as both have a large effect on HOx chemistry (Fig. S5). The model tends to underpredict nighttime OH concentrations, similarly to previous model comparisons (Carslaw et al., 2001; Ren et al., 2006; Pugh et al., 2010). On average, nighttime (22:00–06:00 local time) modeled OH concentrations are ∼ 2.5 × 105 mol cm-3 below those observed (∼ 60 % difference). As the model only incorporates α-pinene (for all monoterpenes) and isoprene, the absence of OH-producing ozonolysis reactions with other VOCs likely contributes to this nighttime discrepancy. These reactions have been shown to produce up to ∼ 64–72 % of nighttime OH in rural environments (Bey et al., 1997; Geyer et al., 2003b). Daytime concentrations are also generally underpredicted, especially during the late morning, when the measured OH concentration peaks. Despite the observed difference in the two profiles, only two measured points (11:00, 19:00) fail to capture modeled concentrations within their 68 % confidence intervals. A linear regression of measured versus modeled OH concentrations highlights the ability of the model to capture the diel trend of OH concentrations (r2∼ 0.82) (Fig. S6).

While modeling studies have generally found better performance for HO2 than for OH, many models involving HOx cycling in forested environments tend to underestimate HO2 levels (Lelieveld et al., 2008; Pugh et al., 2010; Stavrakou et al., 2010). Interferences involved in the operation of the IU-FAGE instrument can lead to conversion of isoprene-derived peroxy radicals into HO2, resulting in a positive artifact (Fuchs et al., 2011). Tests indicate that ∼ 90 % of isoprene-based hydroxyalkylperoxy radicals are converted into HO2 in the sampling cell through reaction with NO and subsequent decomposition (Griffith et al., 2013). As a result, IU-FAGE measurements represent both ambient HO2 and a fraction of isoprene peroxy radicals chemically converted to HO2 within the instrument itself. Griffith et al. (2013) noted that HO2 concentrations measured during CABINEX are similar to previously reported concentrations of HO2 + RO2 (Mihele and Hastie, 2003). To account for this, simulated isoprene-peroxy radical concentrations were added to simulated HO2 concentrations when performing a regression analysis, and the discussion of the agreement between measurements and model output focuses on simulated HO2 + isoprene RO2 rather than simply HO2.

While the model results successfully represent the overall diel HO2 profile and show good agreement at night, modeled concentrations of HO2 + isoprene RO2 overestimate measured concentrations midday by about 30 %, suggesting either a missing isoprene RO2 loss mechanism, a HO2 loss mechanism, or a combination of both. Nevertheless, good agreement is observed between measured and modeled concentrations with and without the addition of isoprene RO2 (r2= 0.94, slope = 0.68 with RO2, r2= 0.9, slope = 1.2 without). The observation that adding isoprene RO2 improves the coefficient of determination supports the notion of an isoprene-derived interference (Fig. S6). Ultimately, the agreement observed between measured and modeled HOx concentrations relative to previously published atmospheric chemistry models supports the validity of the modeling process.

Air surrounding the PROPHET tower is free from major NOx sources, causing soil emissions and long-range transport to be dominant influences on NOx mixing ratios (Seok et al., 2013). This ultimately leads to low NO2 (< 1 ppbv) (Fig. S3) and correspondingly low predicted NO3 concentrations (< 1 pptv) (Fig. 1a), despite a relatively high ratio of NO2 to NO (median ∼ 12.3). Mixing ratios under 1 pptv agree well with previous results from Mogensen et al. (2015) in a boreal forest setting and Ayres et al. (2015) in rural Alabama. While this concentration is much lower than previous nighttime observations in polluted urban environments (Brown et al., 2011), model results have shown that NO3 can dominate the total nighttime oxidative strength (defined as reactivity multiplied by concentration) of a forest environment, even at concentrations of less than 1 pptv (Mogensen et al., 2015).

The above-canopy ambient NO3 profile also agrees well with modeled NO3 concentrations at the same site for conditions in 2008 (Pratt et al., 2012). The model of Pratt et al. (2012) includes more BVOCs but less detail in terms of subsequent oxidation chemistry, and the results do not extend below the canopy, preventing a comparison. At night, NO3 concentrations are enhanced above the canopy compared to below, largely due to larger NO2 concentrations measured above the canopy during that period. During the day this trend reverses, and mixing ratios are on average 3 times as large below the canopy as above (0.07 pptv below and 0.023 pptv above). As NO2 concentrations were relatively similar in both locations during the day and O3 was elevated above the canopy, this observation points to a substantial difference in NO3 loss rates in the two locations. The effect of NO3 photolysis specifically is highlighted by the observation of a much stronger diel trend in concentrations above the canopy than below.

The rural nature of the UMBS site prevents large NO3 mixing ratios, so in order to test the response of this environment to increased background pollution, we performed a simple sensitivity analysis wherein the diurnal profiles of O3 and NO were scaled from their original values up to factors of 2 and 5, respectively. In addition, the constraints on OH, HO2, and NO2 were removed, in order to allow accurate modeling of both HOx concentrations and the NO-to-NO2 ratio. The most polluted case studied, where O3 mixing ratios are doubled and NO mixing ratios are multiplied by a factor of 5, produces a maximum NOx mixing ratio of ∼ 10 ppb and is meant to represent a hypothetical suburban area ideally suited for NO3 formation (Fig. S7). In this most extreme case, NO3 concentrations increase by factors of 10 to 12 relative to the conditions observed during CABINEX, resulting in a 0.4 pptv difference on average between the above-canopy and below-canopy environments from 11:00 to 15:00 (Fig. 1b). The implications of this increased difference are investigated subsequently.

Production and loss rates of NO3 were analyzed to determine the specific reason(s) for elevated below-canopy concentrations during the day under the CABINEX conditions. From 06:00 to 12:00, the modeled enhancement of NO3 below the canopy is primarily the result of faster production (due to higher NO2 mixing ratios below than above the canopy), as loss rates are similar (Fig. 2). However, from 12:00 to 18:00, production rates are similar in both environments, and loss rates from NO and VOCs are higher below-canopy than above-canopy, indicating that reduced below-canopy NO3 photolysis is the primary contributor to the observation of elevated below-canopy NO3 concentrations during the afternoon.

Numerous studies have investigated NO3 oxidation of BVOCs and highlighted that such oxidation is especially important at night (Golz et al., 2001; Brown et al., 2005, 2011; Stutz et al., 2010; Brown and Stutz, 2012). Certain classes of BVOCs also show appreciable daytime oxidation rates by NO3 (Geyer et al., 2003a; Brown et al., 2005). The prediction of elevated daytime NO3 concentrations below the forest canopy implies an increased rate of BVOC oxidation in that environment. Oxidation rates (and fractional contributions of the total) by each oxidant are determined by oxidation rate(ppbvh-1)=k[oxidant][VOC]. Ambient CABINEX results (Figs. 3 and 4) show that overall rates of α-pinene oxidation above and below the canopy are similar (∼ 0.06–0.1 ppbv h-1), while the fractional plots indicate that, in both cases, O3 is the most consistent oxidant, contributing over 40 % of total oxidation. Hydroxyl radical oxidation reaches maximum contributions of 67 % above the canopy and 62 % below the canopy near midday (Fig. 4). The NO3 oxidation rates largely reflect the NO3 concentration profile, as α-pinene concentrations are relatively consistent throughout the 24 h period, with above-canopy rates displaying more diel variation than those below, due to the substantial effect of NO3 photolysis. Oxidation by NO3 contributes 17 % of the total above the canopy on average and 18 % below. This similarity in averages is due to the fact that daytime NO3 concentrations are elevated below the canopy relative to above, whereas at night the opposite occurs. The most substantial difference between the two environments occurs from around 08:00 to 20:00, as NO3 contributes on average only 4 % of total α-pinene oxidation above the canopy, but as much as 12 % below.

Increasing the concentration of background pollutants to simulate a suburban environment raises the fractional amount of NO3 oxidation to as high as 32 % during the day (08:00–20:00) below the canopy, similar to the model results of Fuentes et al. (2007) for a forest with 40–60 ppbv of O3 and maximum NOx mixing ratios of 6–8 ppbv. Even during midday when NO3 concentrations are minimized, the contribution of NO3 to total α-pinene oxidation below the canopy is ∼ 18 % in this simulated polluted environment (Fig. 5).

Isoprene oxidation is only briefly discussed, as the total rates and fractional oxidant contributions are similar above and below the canopy (Figs. 3 and 4). In both locations, OH dominates isoprene oxidation, especially during the day when oxidation rates are most substantial. Peak below-canopy oxidation rates are generally smaller than those above, as expected, largely due to increased photolytic activity and OH concentrations above the canopy. Even in the highly polluted conditions, NO3 oxidation accounts for only ∼ 3 % of the total near midday (Fig. 5).

The diurnal profile of the sum of isoprene- and α-pinene-derived gas-phase RONO2 is shown in Fig. 6 for both above- and below-canopy environments. Isoprene is the major precursor of total RONO2 (∼ 70–85 %), following from its larger mixing ratios and much faster daytime oxidation rates than α-pinene. This is in agreement with other isoprene-dominated environments (Pratt et al., 2012; Fisher et al., 2016; Romer et al., 2016). First-generation nitrates produced from NO3 oxidation of both BVOCs have much larger concentrations than the comparable second-generation products, which have virtually negligible concentrations, implying that further oxidation tends to remove the nitrate functional group, after which point further reaction with NO or NO3 and regeneration of the nitrate group is unlikely, as suggested by Lee et al. (2014) and Xiong et al. (2016). As a result, despite the fact that OH only contributes around 20 % of nighttime α-pinene oxidation, RONO2 products formed from OH oxidation of α-pinene constitute over half of nighttime α-pinene RONO2 concentrations.

The efficient mixing process parameterized within the model results in very similar overall concentrations above and below the canopy (within 9 %), despite the modeled differences in BVOC oxidation. While this appears to imply that the canopy exerts little influence on RONO2 production, midday (11:00–15:00) above-canopy mixing ratios of NO3-derived RONO2 products formed from α-pinene and isoprene are 15.2 and 33.7 % larger on average than if the mixing process is turned off and the dilution rate is reduced by one-half (to partially account for the lack of oxidation product transport from below the canopy). Therefore, near midday, the below-canopy environment appears to act as a source of NO3-derived nitrates above the canopy, a finding that is further explored subsequently. We use the term “NO3-derived” extensively throughout the remainder of this paper to indicate products formed from initial oxidation of BVOCs by NO3.

Overall RONO2 accounts for ∼ 7–12 % of total NOy in both environments, which, while somewhat smaller than observations in the eastern US by Perring et al. (2009) (∼ 18 %), nevertheless suggests that RONO2 fate is highly relevant to overall NOx cycling within this environment. However, inconsistencies between studies of RONO2 chemistry underscore the need for continued study of the oxidation pathways involved in RONO2 production and agreement between published mechanisms and laboratory results. For instance, despite our changes to the chemical mechanism, our MCM-based model predicts over twice as much total gas-phase RONO2 as the model of Pratt et al. (2012). Furthermore, second-generation products constitute 50–60 % of total RONO2 (predominantly from the OH–NO pathway) in our model, while models based on laboratory yields, such as that of Pratt et al. (2012), predict almost entirely first-generation products. Observations of isoprene nitrates suggest second-generation products comprise somewhere between 20 and 50 % of the total (Fisher et al., 2016).

In a rural area where RONO2 formation is limited, mischaracterizing RONO2 composition may have a negligible effect on predicting subsequent aspects of atmospheric chemistry; however, in more polluted areas both local and regional O3 and SOA formation rates may be significantly affected by such an error, as NOx reservoirs such as RONO2 can limit O3 production, and first- and second-generation RONO2 products are thought to have different deposition velocities, saturation vapor pressures, and tendencies to release NOx upon oxidation (Lee et al., 2014; Fisher et al., 2016).

While modeled RONO2 mixing ratios above and below the canopy are similar due to efficient daytime mixing within the forest canopy, the physical and chemical differences described previously suggest that production and loss rates differ between locations. The diurnal profiles of simulated RONO2 production rates above and below the canopy are shown in Fig. 7. The total midday production rate of RONO2 above the canopy (∼ 100 pptv) and the dominance of isoprene-derived RONO2 production agree with summertime results obtained for the southeastern US in another deciduous forest (Romer et al., 2016).

In both locations, a large increase in production rates occurs around 06:00, corresponding to the rapid increase in OH, NO, and isoprene concentrations. Production of RONO2 through NO3 oxidation is faster below the canopy than above during the day; however, the difference, factors of 2.75 for α-pinene and 1.35 for isoprene, is slightly lower than the difference in oxidation rates. Following initial oxidation by NO3, the produced RO2 must react with HO2 or RO2 in order to form a stable nitrate, both of which have higher concentrations above the canopy than below (production through NO reaction after NO3 oxidation is negligible). As a result, while daytime oxidation by NO3 is much more rapid below the canopy, the differences in mixing ratios of species involved in secondary reactions slightly offset the difference in NO3 concentrations. Overall, NO3 accounts for ∼ 10 % of total RONO2 production above the canopy and 17 % below near midday (11:00–15:00).

In the more polluted environment, the fraction of total daytime RONO2 produced by NO3 oxidation increases to 14 % above the canopy and 20–25 % below the canopy (Fig. 8). Therefore, while NO3 chemistry becomes more relevant during the day under more polluted conditions, the relative difference between above- and below-canopy production through NO3 oxidation (6–11 %) stays relatively constant.

Loss rates of both α-pinene and isoprene RONO2 are shown in Fig. 9. On average, photolysis and gas-phase oxidation, processes that tend to release NOx, account for approximately half of α-pinene RONO2 loss both above and below the canopy (41 % above and 47 % below) and an even higher fraction of isoprene loss (65 % above and 48 % below), with loss due to photolysis displaying a strong difference between above- and below-canopy environments. Depositional losses are relatively consistent above and below the canopy, as a larger box height above the canopy (the boundary layer height) is offset by faster daytime mixing conditions (deposition velocities) above than below the canopy.

Modeled hydrolysis accounts for less than 5 % of total RONO2 loss on average, a much smaller amount than previous estimations (∼ 30–50 %) based on measurements (Romer et al., 2016) and model predictions (Fisher et al., 2016). However, a few important differences between our model and the assumptions of these previous studies contribute to this difference. The observational study by Romer et al. (2016) assumes no loss of RONO2 to photolysis, which the MCM predicts is a substantial loss process for both α-pinene and isoprene nitrates near midday, while the modeling study of Fisher et al. (2016) assumes all isoprene organic nitrate species hydrolyze at the same rate as tertiary nitrates, likely leading to an overprediction of hydrolysis rates for a given fraction of RONO2 within the aerosol phase in their model.

While the difference between our results and previous measurements of Romer et al. (2016) would be reduced somewhat if photolysis were included in their analysis, their measurements nevertheless suggest a large fraction of RONO2 is lost to hydrolysis even in low-light conditions (06:00–07:00), implying an underprediction by our model of the fraction of RONO2 mass in the aerosol phase. Previous studies using the MCM to predict SOA composition have had to reduce gas-particle partitioning coefficients by factors as high as 500 in order to reproduce observed mass loadings (Johnson et al., 2004, 2006a, b). Essentially this reduction accounts for particle-phase reactions (not captured by modeling simple semi-volatile partitioning) and particle viscosity that decrease the probability of repartitioning into the gas phase. Decreasing the vapor pressures of all BVOC oxidation products by a factor of 100 increases hydrolysis rates substantially, causing hydrolysis to account for a minimum of 40–50 % of α-pinene RONO2 loss above-canopy and 60–70 % below-canopy (Fig. S8). The fraction of isoprene RONO2 lost through this mechanism also increases, but only to a maximum of 10–15 % at night, as only tertiary nitrates undergo hydrolysis. The uncertainty with respect to hydrolysis loss rates highlights the importance of more accurately characterizing gas-particle partitioning when quantifying the lifetime and fate of NOx within an environment.

As we are focused primarily on highlighting differences between the above- and below-canopy locations rather than precisely determining production and loss rates, this uncertainty does not affect our major conclusions regarding the increased relevance of NO3 chemistry below the canopy. In addition, we are primarily focused on daytime conditions, when higher temperatures shift partitioning to the gas phase and reduce overall hydrolysis rates. Nevertheless, future versions of this model will look to improve the characterization of hydrolysis by more accurately describing both hydrolysis rates within the aerosol (when more precise data are available) and more accurately partitioning the suite of BVOC oxidation products between the gas and particle phases. In addition, the choice of α-pinene to represent all monoterpenes can impact these findings due to changes in product distribution that would occur if other monoterpenes were considered.

When considering all relevant losses, midday RONO2 loss rates below the canopy are less than one-half of those above the canopy for α-pinene products and are around 66 % of those above the canopy for isoprene products. As daytime production rates of NO3-derived RONO2 below the canopy are larger than those above the canopy, our results suggest possible net transport of NO3-derived products upward from the below-canopy environment. The net transport of both total RONO2 and NO3-derived RONO2 is shown in Fig. 10.

While net transport of total RONO2 is generally from the above-canopy environment to the below-canopy environment (downward), in agreement with previous NOy flux measurements at UMBS (Geddes and Murphy, 2014), the below-canopy environment acts as a substantial source of NO3-derived RONO2 above the canopy during the day (∼ 25 %). The largest contribution from net transport (∼ 30 % of the total) occurs around 07:00. Recent modeling work indicates that the mass loading of particulate RONO2 is maximized around this time in the southeastern US (Pye et al., 2015). As NO3-derived products are known to be major constituents of SOA in monoterpene-rich areas such as the southeastern US, neglecting below-canopy chemistry could therefore lead to an underprediction of RONO2 SOA mass above the canopy during the day (Ayres et al., 2015; Xu et al., 2015).

While decreasing the vapor pressures of all oxidation products by a factor of 100 decreases the fraction of RONO2 loss caused by photolysis and OH oxidation, the total contribution of net transport to above-canopy NO3-derived RONO2 production is still 14.5 % on average from 06:00 to 18:00 (Fig. S9). Under more polluted conditions, the contribution of transport to total production remains substantial (between 7 and 25 % from 11:00 to 15:00), but is highly dependent on the ratio of O3 to NO (Fig. S10). Our assumption of no depositional losses during transport likely leads to an overprediction of the total amount of net transport that occurs; however, our model underpredicts concentrations of MACR + MVK above and below the canopy during the morning when mixing is beginning (Fig. S1), suggesting that losses during transport may be captured in the parameterization of deposition. Such underprediction could also be the result of errors in the chemical mechanism.

Precise determination of the influence of transport on above-canopy NO3-derived RONO2 production requires more accurate characterization of both hydrolysis losses and deposition during transport than our model can currently achieve. However, our results suggest that NO3-derived products and total RONO2 may undergo net transport in opposite directions. Because of the known relevance of NO3-derived products to SOA production, this possibility should be the focus of further investigation.

Figure 11 displays the simulated diurnal SOA mass loadings modeled above and below the canopy at UMBS. As with gas-phase RONO2, efficient daytime mixing results in a relatively small difference in total SOA mass loading between locations, with an average difference of 6 % at night (21:00–06:00) (higher mass loadings below-canopy) and 7 % near midday (11:00–15:00) (higher mass loadings above-canopy). The similarity above and below the canopy agrees with the results of the 1-D FORCAsT model (Ashworth et al., 2015), which predicts little change in aerosol mass loadings within 100 m from the ground.

To our knowledge, the composition of ambient aerosol at UMBS has only been characterized once before. Aerosol mass spectrometer measurements from 2001 indicate that OA mass loadings varied from ∼ 0.5 to 2 µg m-3, with values reaching 3 µg m-3 during peak pollution events (Delia, 2004), in relatively good qualitative agreement with our results. However, more recent data from CABINEX 2009 indicate that water-soluble organic mass loadings were around 4 µg m-3 on average (VanReken et al., 2015). As a result, while our model predicts more aerosol mass than recent results from the FORCAsT model (Ashworth et al., 2015), total SOA mass loadings may still be somewhat underpredicted.

In terms of SOA composition, ELVOCs comprise a consistent majority of total SOA in the model (∼ 77 % above-canopy and ∼ 72 % below-canopy), which follows from the nearly constant rate of O3 oxidation of α-pinene. The dominance of these products agrees with laboratory studies that find that SOA composition is almost entirely composed of ELVOC species at low total SOA mass loadings (Ehn et al., 2014). However, as the molar yield of ELVOCs varies substantially based on monoterpene studied (Jokinen et al., 2015), and as ELVOCs are not included in major chemical mechanisms such as the MCM, the modeled relevance of this type of oxidation product to SOA mass loadings suggests future studies should look to improve characterization of ELVOC formation processes and update published mechanisms.

Similar amounts of SOA are produced by reactive surface uptake of isoprene products (IEPOX, GLYOX, and METHYLGLYOX) and semi-volatile oxidation product partitioning (ROOH and RONO2). The average mass loadings of isoprene epoxydiols (∼ 0 µg m-3), glyoxal (0–0.1 µg m-3), and methylglyoxal (0.1–0.25 µg m-3) are comparable to modeled mass loadings of these products in northern Michigan by Li et al. (2015). The composition of semi-volatile SOA is split between hydroperoxides (ROOH), predominately formed by OH oxidation followed by reaction with HO2, and RONO2. Organic nitrates constitute 6 % of total SOA above the canopy and 7 % below the canopy, in good agreement with results in both the southeastern US (3–8 %) (B. H. Lee et al., 2016) and a Colorado front-range forest (6–20 %) (Fry et al., 2013). Other oxidation products (alcohols, peroxyacetyl nitrates, etc.) contribute a negligible amount of aerosol.

Ultimately, SOA mass loadings above and below the canopy are within 0.5 µg m-3 of each other, and this similarity is caused by efficient mixing and different influences on aerosol production partially offsetting each other. For instance, lower temperatures below the canopy cause increased partitioning of semi-volatile oxidation products (ROOH and RONO2) to the particle phase relative to above the canopy, resulting in nighttime mass loadings as much as 35 % larger below the canopy than above (when temperature differences are maximized). However, as the majority of semi-volatile products with volatilities low enough to partition appreciably to the aerosol phase contain peroxide functional groups, even in the case of RONO2, lower HOx concentrations below the canopy partially offset the effect of temperature. This is highlighted by the fact that if temperatures above and below the canopy are assumed to be the same, more SOA mass is produced above the canopy than below (Fig. S11).

In addition, ELVOC products have vapor pressures low enough that virtually all of their mass exists within the particle phase, causing temperature to have little to no effect on their partitioning between gas and aerosol. Therefore, higher rates of O3 oxidation of α-pinene above the canopy further offset the effect of increased partitioning of semi-volatile products below the canopy. Isoprene epoxide, glyoxal, and methylglyoxal mass loadings are only slightly larger below the canopy than above for the majority of the day (within 5–10 % of each other) because of lower rates of aerosol deposition and similar gas-phase concentrations in each location (due to mixing), despite the fact that gas-phase epoxide production is more rapid above the canopy.

Overall, NO3-derived products contribute little to total RONO2 SOA mass, causing production of RONO2 SOA to be driven primarily by the OH + NO pathway, even at night (Fig. S12). The small mass loading of NO3-derived products is primarily the result of our assumption that all monoterpenes are α-pinene. As NO3 oxidation of α-pinene produces first-generation nitrates, which have relatively high volatilities, almost exclusively (Berkemeier et al., 2016), the SOA mass yield of NO3 oxidation is relatively small (Table 1). However, previous modeling with a variety of monoterpenes suggests as much as 0.2–0.4 µg m-3 of SOA is produced from monoterpene nitrates in northern Michigan (Pye et al., 2015), in agreement with the much higher mass yields of other monoterpenes such as β-pinene and limonene. Adding this mass to the total amount of SOA would suggest RONO2 contribute 16–24 % of total SOA mass, on the upper end of estimates from previous measurements (Fry et al., 2013; B. H. Lee et al., 2016).

Assuming that this amount of monoterpene nitrate SOA mass is present, and assuming that the fraction of RONO2 mass derived from NO3 oxidation is the same as we have modeled for α-pinene (∼ 45–80 %) (Fig. S13), NO3 oxidation could be expected to contribute around 4–12 % of total SOA mass in this environment. This contribution is reasonable, as A. K. Y. Lee et al. (2016) recently found that RONO2 produced from NO3 oxidation contribute around 22–33 % of biogenic SOA in a remote coniferous forest in Canada. The sensitivity of RONO2 SOA and SOA from NO3-derived oxidation products to background pollutant levels is shown in Fig. S14. Both total RONO2 SOA and NO3-derived SOA increase by a factor of 3–4 under increased pollutant loadings. Interestingly, increases in NO3-derived RONO2 SOA mass are almost solely dependent upon increased O3 mixing ratios, implying that NO3 SOA production is essentially O3-limited for the conditions modeled in the sensitivity analysis.

The preceding analysis serves as an indicator of the potential relevance of NO3 to total aerosol mass in this location; however, our model results also suggest the possibility of net transport of NO3-derived RONO2 from the below-canopy environment through the canopy, potentially resulting in more NO3-derived RONO2 SOA mass than would be assumed if transport were neglected. Indeed, similarly to gas-phase RONO2 concentrations, including in-canopy mixing results in a substantial increase in both isoprene and α-pinene NO3-derived OA above the canopy. This is shown in Fig. 12, where positive values indicate increased amounts of SOA mass above the canopy when mixing is included within the model. Ultimately our results suggest a 20–50 % increase in NO3-derived α-pinene RONO2 mass in the afternoon, which can be thought of as a surrogate for monoterpene nitrate mass, and an even larger increase from isoprene products. While we assume no loss of products during transport, which would reduce this effect, these results highlight the potential relevance of the below-canopy environment to above-canopy SOA mass. Because the contribution of NO3-derived RONO2 to total SOA is predicted to be high in areas such as the southeastern US (Ayres et al., 2015), the potential influence of net transport of NO3-derived products and the associated effect on SOA mass warrants further study.