The behavior of reactive compounds in the atmosphere and their interaction with ecosystems could vary due to differences in the processes of physical transport, deposition on surfaces, biological uptake or release, and chemical transformations. Vegetation and soils can act as a source or a sink for such pollutants, and this behavior can differ near the ground, at the canopy top, or above it. Therefore, estimating the source/sink vertical distribution of air pollutants within and above forested canopies is critical for understanding the fate of these compounds and their effect on vegetation functioning. Since direct measurements of these sources or sinks are difficult to conduct, measured concentration profiles can be used to inversely infer the effective source-sink distribution. In this work, the vertical source-sink profiles of reactive nitrogen and sulfur were examined using multiple inverse modeling methods in a mixed hardwood forest in the southern Appalachian Mountains, which is a region sensitive to deposition of nutrients and acidity. Measurements of the vertical concentration profiles of ammonia (NH₃), nitric acid (HNO₃), sulfur dioxide (SO₂), and ammonium (NH₄⁺), nitrate (NO₃^-), and sulfate (SO₄^2-) in PM_2.5 were measured at the Coweeta Hydrologic Laboratory during five intensive sampling campaigns between May 2015 and August 2016. The mean concentration of NH₃ decreased with height in the upper canopy and increased below the understory toward the forest floor. All other species exhibited patterns of monotonically decreasing concentration from above the canopy to the forest floor.

Using the measured concentration profiles and within-canopy flow fields, we estimated the vertical source-sink flux profiles using three inverse approaches: a Eulerian high-order closure model (EUL), a Lagrangian localized near-field (LNF) model, and a new full Lagrangian stochastic model (LSM). Models predicted positive (upward) NH₃ fluxes near the forest floor, indicating emissions from the litter or soil. The modeled above-canopy flux of NH₃ tended to be negative (downward), indicating that the forest was a net sink of NH₃. The modeled flux profiles of HNO₃ and SO₂ presented a monotonically decreasing trend with most uptake occurring in the upper canopy. Significant differences in the estimated flux profiles can be found between different models and for different timescale inputs. The vertical distributions of fluxes from the inverse models were compared with net canopy-scale, stomatal, cuticular, and soil fluxes estimated from resistance-based big-leaf models. This study provides new insight into atmosphere-biosphere exchange of reactive compounds in forest ecosystems and advances the development of soil-vegetation-atmosphere models capable of partitioning canopy-scale deposition of nitrogen and sulfur to specific ecosystem compartments.