Secondary organic aerosol (SOA) produced from the oxidation of volatile organic compounds (VOCs) forms an important contribution to aerosol loading . They can affect regional climate and pose health risks to humans . A large fraction of SOA is formed by biogenic volatile organic compounds (BVOCs), which are emitted in large quantities from forested areas, especially during summer . Isoprene and the monoterpenes α-pinene, β-pinene, and limonene are the most abundant of these BVOCs in the southeastern US . Consequently, SOA mass in this region has a high biogenic contribution .

Anthropogenic emissions can alter the oxidation pathways of BVOCs and thereby the formation of SOA from biogenic precursors . Recently, the contribution of isoprene to SOA in the southeastern US has been studied extensively, with a focus on aqueous-phase reactive uptake mechanisms that are modulated by anthropogenic emissions of sulfur dioxide (SO2) . In addition, isoprene SOA can also be produced through the condensation of low-volatility organic compounds (LVOCs) . Both mechanisms are prevalent under low nitrogen monoxide (NO) conditions, which are important at the SOAS site, under which the initial oxidation of isoprene by the hydroxyl radical (OH) leads to the formation of hydroxyhydroperoxides (ISOPOOHs) , whose oxidation product (ISOP(OOH)2) can condense to form ISOPOOH SOA. The major channel of ISOPOOH oxidation, however, forms isoprene epoxydiols (IEPOXs), which produce IEPOX SOA upon reactive uptake on acidic surfaces . IEPOX SOA formation contributed approximately 15 %–30 % to total observed aerosol mass during the SOAS campaign, while ISOPOOH SOA contributed approximately 2.2 % .

Monoterpene SOA (MT SOA) formation has been shown to be important in the southeastern US and depends on anthropogenic nitrogen oxide (NOx) emissions, which influence daytime oxidation pathways and enhance nitrate-radical-initiated (NO3) SOA formation during night-time .

Sesquiterpene oxidation and the resulting SOA are not included due to its small contribution to SOA during SOAS (3 % compared to ∼45 % for monoterpenes and ∼18 % for isoprene) . Sesquiterpenes are very reactive and those contributions could be underestimated. However, without further information that would suggest a larger importance in the SE US, we did not include sesquiterpenes in the current study.

Since SOA concentrations in the southeastern US are driven by both natural and anthropogenic factors, understanding future changes in SOA concentrations requires an understanding of these different factors and their interactions. Previous modelling studies have focused on the effects of future lower anthropogenic emissions of NOx and sulfur oxides (SOx) on the formation of isoprene-derived SOA . These studies found that reductions of anthropogenic emissions of NOx and SOx lead to a net reduction of SOA formation from isoprene.

Here, we study the formation of SOA from biogenic emissions (specifically from daytime sources) and the SOA diurnal evolution in the context of land–atmosphere coupling, including both biogeochemical interactions (VOC emissions) and biogeophysical interactions (sensible and latent heat fluxes) between the land surface and the atmosphere, in a case study for the SOAS campaign. The diurnal SOA evolution is driven by atmospheric boundary layer (ABL) dynamics and the interaction between the ABL and the free troposphere (FT), as well as by emissions, chemical transformations, and subsequent partitioning into the aerosol phase . The ABL dynamics are often a challenge to represent in global and regional chemistry models; hence, in order to encompass the many aforementioned factors affecting the diurnal SOA evolution, an integrated approach is required to accurately represent the diurnal evolution of SOA and BVOC concentrations.

As sources of SOA, we consider isoprene SOA formation through aqueous-phase uptake of IEPOX and through condensation of ISOP(OOH)2 , and speciated monoterpene SOA formation from α-pinene, β-pinene, and limonene. We account for the anthropogenic influence on biogenic SOA formation by including the influence of NOx concentrations on peroxy radical chemistry, in addition to the NOx-induced changing ratios of oxidant concentrations (OH, NO3, ozone (O3)). We do not include night-time SOA formation.

Our aim is twofold: (1) to improve our understanding of SOA formation in the southeastern US from established and recently elucidated pathways and (2) to understand SOA diurnal evolution in a land–atmosphere coupling context. We build on the case study by that was able to accurately reproduce the dynamics and gas-phase photooxidation of isoprene during the SOAS campaign and then do the following.

We couple the dynamics and chemistry of the boundary layer–chemistry model to the land surface and vegetation factors by including interactive formulations for surface BVOC and heat fluxes.

To constrain and evaluate our model, we use data collected during the Southeastern Oxidant and Aerosol Study (SOAS), held over the period of 1 June to 15 July 2013 , and the Southeast Nexus (SENEX) campaign, held in the same time period . Both campaigns were part of the Southeast Atmosphere Studies (SAS), which coordinated comprehensive measurements of trace gas and aerosol compositions, aerosol physics and chemistry, and meteorological dynamics across the southeastern US . All the measurements (and model results) are shown in Central Standard Time (CST).

The case study represents the SOAS main sites near Brent (32∘54′12′′ N, 87∘15′0′′ W) and Marion (32∘41′40′′ N, 87∘14′55′′ W), Alabama; these are the SOAS ground and flux (above-canopy) measurement sites, respectively. A pre-existing Southeastern Research and Characterization (SEARCH) network site served as the main ground site with gas chromatography–mass spectrometry (GC-MS) (including speciated monoterpene mixing ratios) and aerosol mass spectrometry (AMS) measurements . The National Center for Atmospheric Research C-130 flights collected observations of trace gases, isoprene, monoterpenes, photolysis, methyl vinyl ketone (MVK), and methacrolein (MACR) . At the Alabama Aquatic Biodiversity Center (AABC) flux tower (24 km from the Brent ground site and tower) eddy covariance measurements above canopy for surface latent and sensible heat, BVOC fluxes, and shear velocity (u*) measurements were carried out. We use data from both sites to represent a more regional footprint. Flights with the Whole Air Sample Profiler (WASP) and high-resolution proton transfer reaction time-of-flight mass spectrometer (PTR-ToF-MS) measured trace gas concentrations, meteorological data, and isoprene and monoterpene mixing ratios above the AABC tower , though speciated monoterpenes mixing ratios are only obtained through GC-MS at the SEARCH site. Data are also used from the NOAA P-3 flights during the Southeast Nexus (SENEX) campaign, which included vertical profile data near the SOAS site . To reduce uncertainties from day-to-day variations and gain representativity, we average the meteorological data, isoprene and monoterpene emissions and mixing ratios, and trace gas mixing ratio data for 5, 6, 8, and 10–13 June following . The speciated monoterpene data from the GC-MS measurements are averaged from 5–13 June. WASP research flights were not flown on 7 and 9 June , whereas GC-MS had continuous data.

The total organic aerosol (OA) concentrations measured at the SOAS site by the AMS have previously been apportioned by positive matrix factorisation (PMF) to determine the contribution of individual SOA factors (see discussion below). The main SOA factors observed at the SEARCH site were isoprene-epoxydiol-derived SOA (IEPOX SOA), isoprene hydroxyhydroperoxide SOA (ISOPOOH SOA), more oxidised oxygenated OA (MO-OOA), low oxidised oxygenated OA (LO-OOA), and biomass burning OA (BBOA) ; the total observed SOA is the sum of all these factors. For this study, the aerosol data are averaged for 6, 8, and 10–13 June, since data are not available for 5 June and are incomplete for 7 and 9 June .

We use a mixed layer model for the dynamics of the convective boundary layer with a chemistry and SOA formation module (MXLCH-SOA) to analyse a representative (sub-diurnal) case study for the southeastern US. The model version that we use is described in and , and a derivation of its basic equations is given in . The dynamics and boundary conditions can be seen in Table . In this section, we summarise the main characteristics of the model and in the following subsections we describe the specific adaptations that have been made for this study, which include new chemical pathways (Sect. ), SOA formation mechanisms (Sect. ), interactive BVOC emissions (Sect. ), and a coupled land surface model (Sect. ).

MXLCH-SOA approximates ABL mixing under convective conditions by assuming vigorous mixing throughout the daytime ABL, resulting in constant mixing ratios with height. The ABL height growth due to entrainment is driven by sensible and latent heat flux . We consider the atmospheric boundary layer interface with the free troposphere to be an infinitesimal inversion layer with entrainment-driven exchange of scalars and variables between these layers , i.e. a zero-order closure model. Large-scale meteorology is prescribed based on , species segregation is neglected , and we do not account for horizontal advection via long-range transport.

The chemical reaction scheme, which consists of the essential gas-phase reactions of the O3–NOx–VOC–HOx system (see Table ), is based on and . The standard SOA formation scheme in MXLCH-SOA is based on the volatility basis set (VBS) approach .

We use the MXLCH-SOA model to perform a set of numerical experiments to improve our understanding of SOA formation during SOAS in a land–atmosphere coupling context. First, we set up a base case by expanding the case study of guided by the observations of heat and VOC fluxes, ABL dynamics, and VOC and SOA concentrations. We then evaluate the contributions of the different dynamical and chemical processes to the diurnal evolution of the SOA concentration and dissect the SOA budget to show the contributions of the various precursors and chemical pathways to SOA formation.

The dynamical initial and boundary conditions for the base case are shown in Table  and are based on . We apply a lapse rate of 0.002 K m-1 below 1150 m and 0.005 K m-1 above 1150 m to better constrain the boundary layer height (See Fig. ). The lapse rate mimics upper air conditions and counteracts the development of the ABL, and we adjust this value so that the observed evolution of the boundary layer was satisfactorily reproduced by the model (See Fig. ). The initial conditions for the chemical species are based on observations from the SEARCH and AABC sites and (see Table ). Early morning NOx chemistry and subsequent SOA formation is constrained by the initialisation of NO and NO2 mixing ratios at 06:00 CST based on observed mixing ratios (see Fig. ). The initial concentrations of SOA in the boundary layer are based on AMS observations taken at the SEARCH site . Since the model is initialised at sunrise, it does not explicitly account for night-time SOA formation, but the effect of NO3-initiated night-time SOA formation is included in the value of the prescribed bulk SOA concentration.

After establishing the base case, we carry out a series of numerical experiments to assess the impact of SOA concentrations above the ABL on the diurnal SOA evolution to stress the importance of information on early morning residual layer concentrations. We use concentrations measured above the ABL, as we have a few measurements of SOA concentration at 11:00 CST from SENEX flights . In addition to the base case in which SOA in the RL was initiated at 1.5 µg m-3, we also run simulations in which we initiated it at 1 and 1.8 µg m-3, respectively, which encompasses the range of observed SOA concentrations above the ABL. Further, we included a scenario in which SOA concentrations in the ABL and RL were initialised with uniform values. The latter scenario is then used to estimate the contribution of long-range transport versus local formation of MO-OOA.

Finally, we explore the effect of a changing climate on the near-surface SOA concentration. Our main interest is improving our understanding of the net effect on SOA concentrations of several interacting processes that can either reinforce or compensate for each other. The increase in average air temperature under a warmer climate has several effects on the coupled system that may affect SOA concentrations: (1) VOC emissions increase, (2) the partitioning efficiency of SVOCs into the aerosol phase decreases, and (3) the vapour pressure deficit (VPD) decreases, which modulates the heat fluxes and consequently the boundary layer height . We simulate a warming climate of 1 and 2 K. For this purpose, the early morning values of mixed layer temperature, surface temperature, and soil temperature in both layers are all increased (and decreased) by 1 and 2 K. In order to stay consistent with climate warming predictions, the initial relative humidity is kept constant, which is done by calculating the values of the specific moisture at each temperature increment using the Clausius–Clapeyron relation . In this way the sensible heat flux forcing is more consistent with future climate warming. As previous literature has observed the southeastern US to have undergone a cooling trend compared to the rest of the US in the summer months, we add two more runs with a cooling of 1 and 2 K, respectively.

A bulk budget analysis can be used to differentiate the contribution of entrainment and the different SOA factors to the SOA budget. The entrainment budget for background OA is calculated as per : dOABGdt=weΔOABGh, in which the entrainment flux is calculated from the entrainment velocity (we in m s-1), the concentration jump in background OA (ΔOABG in µg m-3) between the RL and BL, and the boundary layer height (h in m).

From Fig. , we can determine the contributions of different processes and chemical species to total SOA. The early morning SOA consists primarily of MT SOA (formed by gas–particle partitioning) as per Fig. . The contribution of entrainment to the total rate of change of the SOA concentration peaks at 09:00, when entrainment contributes more than 86 % to the total SOA tendency. Hence, as the boundary layer height is growing the fastest (Fig. ) and the entrainment velocity is also peaking (0.12 m s-1 at 09:30), the SOA concentration decreases due to the introduction of SOA-poor air from the RL. Just after 10:00 CST, the effect of entrainment is low and hence the SOA tendency becomes positive again, as production picks up from a sum of IEPOX SOA, ISOPOOH SOA, and MT SOA from G–P partitioning. By the late afternoon, IEPOX SOA has the largest contribution to the SOA budget (68 %), while the contribution of MT SOA decreases (to 27 %) at this time, as the contributions of α-pinene, β-pinene, and limonene are lower in the afternoon. The mixing ratios of monoterpenes decrease due to entrainment in the early morning and strong reaction with OH, which peaks around noon, while the emissions, though continuous, are unable to compensate for the increased oxidation and entrainment; therefore, the monoterpene contribution to SOA later in the afternoon is smaller. ISOPOOH SOA has a very small contribution to the SOA budget (end-of-day contribution 3.9 %).

α-Pinene contributes about 18 % of the total SOA, while β-pinene contributes about 10 % in the early morning. The contribution of both rises, and by 08:00 MT SOA is largely from α- and β-pinene (α-pinene and β-pinene are approximately 50 % each). By the end of the day, α-pinene SOA dominates, contributing about 50 % to MT SOA and 12.5 % to the total SOA. Rather surprisingly, the limonene product dominates the SOA contribution in the morning (approximately 60 %). This is surprising as the limonene mixing ratio is much lower than α- and β-pinene (Fig. ). However, as discussed in previous literature , the limonene SOA yield is much higher than the yield of α-pinene and β-pinene. The stoichiometric coefficients for limonene + OH and O3 are also higher than the OH and O3 + α- and β-pinene stoichiometric coefficients. As there is an OH peak in the morning in the shallow boundary layer and the oxidation reactions between limonene and OH and O3 are fast (Table : R44, R45), this results in a large accumulation of limonene SOA product in the morning. As the boundary layer grows, entrainment dilutes this product, causing a fall in the limonene SOA tendency. As the day progresses the contribution of limonene SOA becomes less dominant (6 % by the end of the day) and the α- and β-pinene contributions become more important. The isoprene + O3 and NO3 pathways lead to a negligible amount of SOA formed in our model, even in the early morning. The early morning NOx chemistry and subsequent SOA formation are constrained through the observed NO and NO2 initial mixing ratios. Since the resulting NO3 (and N2O5) mixing ratios are very small, the NO3-initiated SOA formation is negligible. The oxidant + BVOC pathway contribution can be seen in Fig. ; OH oxidation is the most important contributor to aerosol formation.

To test the sensitivity of the coupled land surface–boundary layer–SOA formation system, we carried out numerical experiments on the initial conditions of the model. We evaluated the effect of the initial RL concentration of SOA on the diurnal evolution of SOA in the ABL.

These experiments are guided by measurements of SOA concentration above the boundary layer at 11:00 CST from the SENEX flights (Fig. ). We use the range of these profile measurements as constraints on the numerical experiments. In the previous section, we discussed the entrainment of aged SOA from previous days from the RL into the mixed layer as the boundary layer grows. Figure  shows the sensitivity of diurnal SOA evolution in the boundary layer to the concentration of background SOA in the RL. We constrain SOA concentrations by the vertical profiles from by the SENEX flights (Fig.  and ) and a case in which the concentration of SOA is the same in the ABL and RL at the start of the simulation. We compare the effect of the RL SOA concentration on the modelled SOA against the observed SOA concentrations.

We find that a uniform SOA concentration in the ABL and RL no longer leads to a drop in SOA due to growth of the ABL, but leads to overestimated values compared to the observations during the end of the afternoon. In cases in which the concentration of SOA is less in the RL than the ABL, there is a dilution of SOA as the boundary layer grows, as entrainment mixes air with less SOA from the RL. This is more marked when the concentration difference is larger. This difference is also found by , who discussed the importance of background OA concentration in the RL; if there is a large jump of background OA between the ABL and RL it has a significant effect on diurnal SOA evolution. Tracer concentrations are generally lower in the RL compared to the ABL (which is the case for SOA in Fig. ), and hence entrainment dilutes the concentrations in the ABL . In order to accurately understand diurnal SOA evolution, it is very important to have a good estimate of its RL concentration in the early morning.

This sensitivity analysis also provides an opportunity to allocate the source of SOA. As SOA is relatively long-lived, the amount of aged SOA in the RL can have a large effect on the SOA in the ABL, as it affects the vertical mixing of SOA and SOA availability for G–P partitioning. The drop in measured LO-OOA concentrations (in the morning) indicates a dilution that is driven by entrainment as LO-OOA-poor air is introduced into the BL from the RL. If we consider a uniform concentration in the ABL and RL, most of the MO-OOA is captured by the model (implying the dominance of local production), though there is an overestimation of SOA formation in the early morning and late afternoon (although the model results are within 1 standard deviation of the measurements and within measurement uncertainties). The more oxidised oxygenated organic aerosol (MO-OOA) could result from entrainment from the RL, though the available measurements show that the OA concentration in the RL is between 1 and 1.8 µg m-3 (Fig.  and ), so not all the aged MO-OOA can be explained by this process and some must be horizontally advected. In addition, the rapid formation of MO-OOA via autoxidation reactions or the substantially lower volatility of ambient SOA compared to that assumed in VBS-based models may contribute to explaining the model–measurement differences in MO-OOA when the experimentally constrained RL concentrations are used in the model.

Using our coupled land surface–boundary layer–SOA formation model, we can study the net effect that temperature has on SOA concentration through VOC emissions, G–P partitioning, and feedbacks between the ABL and the land surface that influence entrainment of SOA from the residual layer. In our experiments, in which we varied the early morning temperature by between -2 and +2 K, we find that the total SOA concentration in the daytime ABL is buffered against temperature changes (Fig. ).

Isoprene (Fig. a) and monoterpene emissions (Fig. d) are temperature dependent , and consequently we observe a positive impact of rising temperature on these BVOC fluxes. At higher temperatures, this means there is an accumulation of BVOCs in the ABL, which consequently leads to a depletion of OH (Fig. ). However, as we do not take OH recycling into account in the oxidation of isoprene, this has an effect on OH depletion. The change in the IEPOX gas-phase mixing ratio (Fig. ) is not as large as the isoprene emissions as a consequence of the depletion of OH and slower reaction rates compared to BVOCs. Consequently, the effect of temperature on IEPOX SOA is rather small, with a minuscule increase in IEPOX SOA formed at higher temperatures at the end of the day (around 0.02; Fig. ).

The abundance of BVOCs leads to a build-up of SVOCs in the ABL that are available for partitioning, but since partitioning to the aerosol phase is generally favoured at lower temperatures, rising temperatures reduce the partitioning coefficient . discussed the fact that the partitioning efficiency of SOA had a non-linear response, especially at low temperatures and high background SOA availability. At low OABG concentrations and high temperatures, the partitioning coefficient is small; however, there is a slight increase in SOA concentration.

A rising temperature could, in principle, affect surface heat fluxes and ABL development by increasing the vapour pressure deficit . However, we find that for a temperature increase of 2 K, this effect is of minor importance (Fig. ), and the entrainment of SOA is hardly affected. Overall, a rise in temperature does not have a significant effect on modelled SOA concentration.

However, the southeastern US, in contrast to the rest of the US, has experienced cooling summer temperatures which have been linked to either high aerosol loading or other large-scale synoptic meteorology predominant in that region . Cooler temperatures favour partitioning to the aerosol phase, although BVOC emissions will be lower. If the concentration of aerosol is already high, however, the low temperatures would lead to an increase in aerosol concentration. The regional cooling caused by the high aerosol concentration could further exacerbate this situation. The decrease in temperature by 1 and 2 K shows that SOA concentrations do not change much despite the decrease in available BVOCs. This means that the cooling that has been seen over this region of the US is unlikely to have affected SOA concentrations above the region.

The radiative effect caused by high aerosol loading means that the region is likely to stay cooler than the rest of the US , which should increase aerosol in the regions, though at cooler temperatures the BVOC emissions will be lower, which would limit SOA formation. These radiative effects of aerosol on the surface energy balance are, however, not included in this work.

The coupled land–atmosphere model gives us the ability to explore the sensitivity of SOA formation to different variables that might change in the future due to changing climate regimes. It would be interesting, for instance, to study the effect of drier or wetter climates on SOA diurnal variability.

We studied the diurnal evolution of biogenic secondary organic aerosol formed from daytime sources in the southeastern US by combining the MXLCH-SOA model with observations from the SOAS campaign. By coupling the MXLCH-SOA boundary layer–chemistry model to modules that interactively calculate surface VOC fluxes and heat fluxes, we can study diurnal SOA evolution in the context of a tightly coupled land surface–boundary layer–SOA formation system.

An evaluation with observations shows that our model system reproduces observations of surface fluxes, tracer concentrations, and boundary layer height satisfactorily. Deviations from observed mixing ratios were found for isoprene and monoterpenes measured just above canopy. However, modelled mixing ratios of VOCs agree better with aircraft observations, which are actually more representative for the mixed layer.

We considered several mechanisms for SOA formation from isoprene and monoterpenes, though the model was limited to daytime, and night-time SOA formation was not included. Reactive uptake of IEPOX SOA agreed well with observations, thereby corroborating previous studies, in a case study that is tightly constrained by observations. ISOPOOH SOA formation though condensation is reproduced within the measurement uncertainty, although the observed peak around noon is not captured by the model. The mean isoprene SOA yield is 1.8 %, which is in the lower range of values reported in the literature.

MT SOA dominates over isoprene SOA, contributing 68 % to aerosol mass, with limonene having the largest contribution in the early morning (60 %) and α-pinene and β-pinene during the rest of the day. The mean MT SOA yield is 10.7 %. In contrast to isoprene SOA, there are no observed monoterpene-specific aerosol factors, so both the LO-OOA and the MO-OOA factors may result from MT SOA formation. Our findings suggest that the more oxidised oxygenated organic aerosol (MO-OOA) could result from entrainment from the residual layer in the late morning and fast autoxidation reactions in the late afternoon, although the roles of horizontal advection and/or lower real MT SOA volatility than in the VBS used here may also play a role in the observed differences. VOC oxidation by the nitrate radical contributed negligibly to SOA formation during daytime, while OH-initiated reactions dominated SOA formation. Overall, the relatively flat diurnal cycle of the total observed SOA can be explained by the contrasting effects of local SOA production and entrainment of SOA-depleted air from the residual layer.

In a sensitivity analysis of the coupled land surface–boundary layer–SOA formation system to temperature changes, we find that the effect of increasing BVOC emissions with increasing temperatures is offset by a depletion of OH concentrations and a decrease in the partitioning efficiency of SVOCs into the aerosol phase. This suggests that near-surface SOA concentrations in the southeastern US are buffered against temperature changes in the region. The use of a fully coupled land surface–boundary layer model that enables the interactive calculation of surface heat and entrainment fluxes makes it possible to study how VOC fluxes, heat fluxes, and ultimately SOA concentrations respond to changing forcings.