First proposed by Businger and Oncley (1990), the REA method measures the vertical flux of atmospheric species by separating air into updraft and downdraft sampling reservoirs based on high-frequency vertical wind velocity measurements. Flux is derived from the difference of average concentrations between the two reservoirs and the bulk weighting of two turbulence statistics that can be stably measured over a sampling interval: 1F=σwβCup-Cdown where Cup andCdown are the average concentrations in updraft and downdraft, σw is the standard deviation of vertical wind speed (w) and β is a dimensionless proportionality coefficient universal for scalars, which can be calculated from sonic anemometer measurements of sensible heat flux β=W′T′σwTup-Tdown. This framework enables stable and controllable flux calculations, with results highly consistent with EC measurements(Karl et al., 2005; Gaman et al., 2004; Lee et al., 2005; Pryor et al., 2007).

We built an REA sampling system for simultaneous sampling of gaseous and particulate inorganic acidic species (Fig. 1). High-frequency (10 Hz) w was measured by a 3D sonic anemometer (CSAT3B, Campbell Scientific Inc., Logan, Utah, USA). Each of three sampling channels (updraft, downdraft, dead-band) was equipped with an annular denuder (URG-2000-30 × 242-3CSS, URG, Chapel Hill, North Carolina, USA) for gaseous HNO₃, HONO, SO₂ and HCl collection and a filter cartridge with a 2 µm PTFE filter (Whatman 7592-104, 46.2 mm, PP ring-supported) installed downstream for particulate NO3-, NO2-, SO42-, and Cl⁻ collection. The three sampling channels shared a single PM_2.5 cyclone inlet (URG-2000-30EH, URG, Chapel Hill, North Carolina, USA), a 1.35 m stainless steel inlet tube and a sampling pump (KNF N026.1ANE, KNF Neuberger GmbH, Freiburg, Germany). Notably, the system features expandable sorbent tube channels for simultaneous VOC flux measurements, but only its performance for inorganic acidic species is reported herein. The sampling flow rate was set to a nominal 10 standard liters per minute with a mass flow controller (MFC, No. 12 in Fig. 1) mounted on the inlet side of the pump. The flow in the inlet tube was in the laminar regime (the Reynolds number ∼ 200), which is essential for the denuders to work properly (i.e., efficient gas-particle separation). The lag time for air to travel from the inlet to the sampling filter membrane was calculated according to total internal volume of air tubing and volumetric flow rate at the onset of each sampling run. For example, it was 3.1 s at ambient temperature 15 °C.

A CR1000X data logger (Campbell Scientific Inc., Logan, Utah, USA) served as the system central controller, responsible for data acquisition, storage, and conditional sampling logic execution. Conditional switching between the sampling channels was checked at 2 Hz to balance high-frequency flux loss and perturbations to the laminar flow in the denuders. Three-minute running mean (w‾) and standard deviation of w (σw) were calculated in real time to trigger the actuation of three solenoid valves (Numatics LS02M6F00B, Emerson Electric Co., St. Louis, Missouri, USA): updraft sampling at w > w‾+ 0.6σw, downdraft sampling at w < w‾- 0.6σw, and dead-band airflow within the w±0.6σw range. Wind speed triggering threshold selection involves a trade-off between the precision of Cup-Cdown measurements and sample representativeness. As an empirical threshold commonly used in REA studies, 0.6σw has been demonstrated to provide reliable flux estimates (Bowling et al., 1998; Desjardins, 1977; Velentini et al., 1997; Businger and Oncley, 1990).

Lag time was taken into account to determine the precise timing of solenoid valve switching. The CSAT3B sonic anemometer had a minimum response time of 0.7 ms, with effectively zero signal latency to the data logger. The total end-to-end system time delay was 17.9 ms, including 10–15 ms for solenoid valve response, 1.4 ms for relay actuation, and 4 ms for real-time calculation and command execution. This short delay time minimized temporal misalignment between wind measurements and the sampling, reducing updraft/downdraft mixing and flux result distortion.

The REA device was mounted on a 4 m high flux tower. The sonic anemometer was installed at the tower top, oriented due north (the prevailing local winter wind direction). The inlet of the PM_2.5 cyclone was vertically aligned with the anemometer, with a horizontal separation of 0.3 m. The sampling enclosure housing the sampling unit and solenoid valves was fixed on the tower 0.7 m below the anemometer to minimize airflow disturbance around the anemometer. A Vaisala Weather Transmitter WXT536 was also installed near the top of tower to provide supporting measurements of air pressure, air temperature, relative humidity, precipitation, wind speed, and wind direction. The pump and other REA components were mounted at the tower base.

The Wuhan Chemical Industrial Park (WCIP) is located northeast to the urban area of Wuhan. The WCIP covers 71.64 km² and hosts petrochemical, fine chemical, and building material industries. Since its full operation in 2013, the WCIP has been identified as a major industrial emission source influencing atmospheric composition in the surrounding region. The flux tower (114.53° E, 30.65° N) was installed at the center of a vegetable cropland within the 7.3 km² Beihu Farm, which is immediately adjacent to the WCIP. The nearest petrochemical emission source lies approximately 1.0 km north of the tower (Fig. S1 in the Supplement). The cropland was cultivated with Raphanus sativus L. var. longipinnatus (white radish), a typical cold-season vegetable in this region. The tower is situated on flat terrain with no obstructing buildings or trees within a 500 m radius of the tower, ensuring undisturbed airflow measurements.

Field sampling was performed from 29 October to 30 December 2025, with 11 valid sampling days in cloudy or sunny rain-free weather. Each sampling day included three 4 h sampling periods (morning: 08:00–12:00; afternoon: 12:30–16:30; early night: 17:00–21:00; all times are UTC+8). The sampling was conducted during the vegetative growth and harvest periods of R. sativus, and no fertilization activities were conducted throughout the sampling period. Flux footprints were calculated using the FFP online tool developed by (Kljun et al., 2015). Input wind and site information for the model included sampling time, measurement height, zero-plane displacement, wind speed, wind direction, Obukhov length, and friction velocity. The cumulative flux footprint over the entire sampling campaign is presented in Fig. S1.

One set of denuders and filter samples, plus field blanks, was collected per one sampling period. The annular denuders were freshly coated with a sorbent layer for inorganic acidic gases collection prior to sampling, in accordance with the U.S. EPA standard protocol (Fitz, 2002). The coating solution 1 % (w/v) sodium carbonate in water and 1 % (v/v) glycerol in a methanol-water mixture (1:1, v/v) was prepared fresh immediately before use. For coating, 10 mL of the solution was injected into the denuder, which was then sealed at both ends, inverted and rotated repeatedly to ensure uniform inner-wall coating, and purged with 99.999 % high-purity nitrogen until complete methanol and water evaporation. Theoretically, the sodium carbonate sorbent layer has an absorption capacity of 6 mg SO₂, even assuming that only 10 % of the sodium carbonate solution was effectively coated onto the inner wall of the annular denuder. The total cumulative ambient air volume sampled by each denuder during a 4 h measurement was 0.6 m³, which would contain a maximum of only 5 µg SO₂ based on the highest ambient SO₂ concentration documented in local air monitoring records. Even when accounting for coexisting acidic gaseous species, the 0.6 m³ sampling volume is still well below the breakthrough volume of the denuder. Coated denuders were sealed with PTFE caps until use.

After each 4 h sampling run, annular denuders and filters were disassembled for subsequent offline chemical composition analysis. The inorganic salts formed by absorbed acidic gases in the denuder sorbent layer were eluted with 10 mL of 0.05 % (v/v) H₂O₂ aqueous solution, which oxidizes sulfite (SO32-, the product of SO₂ absorption) to the more stable SO42-. Particulate-phase inorganic ions collected on the filters were ultrasonically extracted into 10 mL of ultrapure deionized water. Then, the inorganic ions were analyzed with ion chromatography (Dionex, ICS-1100, Thermo Scientific, Massachusetts, USA). Before running analysis, the system was calibrated using standard solutions. Inorganic ions in a sample solution were identified by comparing with the chromatographic peaks of the known standards and quantified using calibration curves after field blank substraction.

High-frequency flux losses may occur from two sources: (1) valve switching frequency below 10 Hz, and (2) laminar flow in the inlet tubing. These two effects combine to cause non-negligible mixing between consecutive air samples. However, the β coefficient was explicitly determined using temperature measurements from the sonic anemometer (No. 14 in Fig. 1), calculated as W′T′σwTup-Tdown, whereTup and Tdown were derived from sonic temperatures sampled under the same switching frequency and 0.6σw dead-band conditions. This empirically derived β calibration approach provided a correction for high-frequency losses (Skov et al. 2006). The β coefficients for 33 4 h sampling periods fell within the typical range of 0.47 to 0.62. While a single β coefficient was used for each 4 h sampling period, β exhibited intra-period variability. We therefore calculated β at 30 min intervals, and used σβ/β within each 4 h period as the relative uncertainty of the corresponding period-averaged β. The relative uncertainties of β for the 33 sampling periods ranged from 2.80 % to 26.14 % (Table S1).

The remaining source of uncertainty in REA flux measurements arises from the potential biases of the concentration difference of target species between updraft and downdraft samples (Cup-Cdown), the core term in Eq. (1). Concentrations are calculated as Cup=MupVup and Cdown=MdownVdown, where M and V denote the collected analyte mass and the total air sample volume, respectively, for each reservoir. Next, we evaluated the uncertainties associated with M and V determination, from which the precisions and detection limits of flux measurement were derived for each species.

The diurnal variations of inorganic acidic gases (HNO₃, HONO, SO₂, HCl) and particulate ions (NO3-, NO2-, SO42-, Cl⁻) in morning, afternoon and early night during the observation campaign are shown in Fig. 2 (top two rows). In this study, diurnal variation is defined as changes occurring during photochemically active daytime and fully dark early nighttime. At the sampling site, the mean concentration of total nitrogen-containing acidic species (gaseous + particulate) was 8.4 ± 8.0 µg m⁻³ (mean ± standard deviation; the same applies hereinafter). This value was higher than that of sulfur-containing (3.1 ± 1.5 µg m⁻³) and chlorine-containing acidic species (2.0 ± 0.8 µg m⁻³), indicating that atmospheric acidic species at the site were dominated by nitrogen species.

Gaseous HNO₃ and HONO showed similar diurnal patterns of higher concentrations in morning and nighttime than at noon. The diurnal pattern is mainly driven by the diurnal evolution of the atmospheric boundary layer (Finlayson-Pitts and Pitts, 1999; Lin et al., 2006). HONO has multiple sources including combustion (Nie et al., 2015) and soil emissions (Su et al., 2011), as well as secondary formation from gas-phase NO + OH reaction and heterogeneous NO₂ reaction on moist surfaces (Villena et al., 2011; Wong et al., 2012; Liu et al., 2014; Baergen and Donaldson, 2016). Its low noontime levels are mainly due to rapid daytime photolytic loss. In contrast, SO₂ and HCl showed slightly higher daytime mean concentrations (SO₂: 2.7 ± 1.3 µg m⁻³; HCl: 2.3 ± 0.7 µg m⁻³) than nighttime (SO₂: 2.1 ± 0.7 µg m⁻³; HCl: 2.0 ± 0.5 µg m⁻³), being likely related to daytime industrial emissions, as both species are mainly emitted from the combustion of sulfur- and chlorine-containing coal and wastes.

Particulate NO3-, SO42- and Cl⁻ showed higher concentrations in the morning (15.5 ± 10.1, 3.6 ± 1.9, 1.8 ± 1.4 µg m⁻³) and nighttime (18.4 ± 11.9, 4.3 ± 1.7, 2.0 ± 0.6 µg m⁻³), and lower levels in afternoon (12.5 ± 8.9, 3.4 ± 1.2, 1.2 ± 0.6 µg m⁻³). This pattern is mainly controlled by their formation pathways and diurnal boundary layer variation, consistent with previous studies (Chang et al., 2011; Trebs et al., 2004; Young et al., 2022). Particulate NO2- had the lowest concentration (0.1–0.2 µg m⁻³) among the four ions, with lower concentrations in the morning (0.13 ± 0.19 µg m⁻³) than afternoon (0.24 ± 0.27 µg m⁻³) and nighttime (0.24 ± 0.32 µg m⁻³).

Bottom two rows of Fig. 2 shows the diurnal variations and horizontal wind speed (WS) dependence of REA-measured fluxes for the eight acidic inorganic species, grouped by three diurnal time intervals. Figure 3a summarizes the flux detection rate (the percentage of flux events above the detection limit relative to the total number of measurements) and the mean ± standard deviation (SD) of flux values above the detection limits for each target species. The flux detection rates of the acidic species, ranked from highest to lowest, were 88 % for HNO₃ and HONO, 82 % for NO3-, 79 % for SO42-, 61 % for SO₂ and Cl⁻, 48 % for HCl, and 36 % for NO2-. All investigated species showed bidirectional flux behavior, which were also observed in nearly all prior REA measurements from remote forest to urban grassland (Fig. 4). If this is not an intrinsic artifact of the REA method, this demonstrates that surfaces across all atmospheric environments and land types in these studies are capable of emitting these inorganic acidic species into the atmosphere, rather than only serving as a deposition sink. The observed apparent fluxes presented here are modulated by deposition, emission, and probably chemical production/loss and the storage change below the 4 m measurement height, therefore cannot be simply regarded as emission flux from the cropland or directly used to derive dry deposition velocity. HNO₃ recorded the highest count of downward flux events (48 % of the measurements) and the largest downward flux values (-7.5 ± 6.7 nmol m⁻² s⁻¹, equivalent to -0.47 ± 0.42 µg m⁻² s⁻¹) across all species, whereas NO2- had the lowest count (9 %) and smallest values of downward flux (-0.87 ± 0.65 nmol m⁻² s⁻¹, equivalent to -0.040 ± 0.030 µg m⁻² s⁻¹). The downward fluxes of HONO (-0.19 ± 0.11 µg m⁻² s⁻¹) and NO3- (-0.29 ± 0.24 µg m⁻² s⁻¹) at our site were 1–2 orders of magnitude higher than all prior measurements at rural/remote forest or grassland sites, while the negative fluxes of HNO₃, SO₂, SO42- are comparable with prior reports (Fig. 4). This points to substantial nitrogen deposition (specifically, HONO and NO3-) at this site, driven by industrial emissions in the surrounding area.

We focus specifically on the upward fluxes showing emissions of atmospheric acidic species from this cropland under the long-term influence of chemical industrial emissions. Key findings are summarized below: (1) HNO₃ and HONO recorded far more upward flux events (39 % and 48 %) and upward flux values (6.4 ± 5.2 and 6.3 ± 5.7 nmol m⁻² s⁻¹, equivalent to 0.40 ± 0.33 and 0.30 ± 0.27 µg m⁻² s⁻¹) than SO₂ and HCl, indicating significant production of both species below the measurement height. Furthermore, their counts of upward flux events and flux values were higher in the morning than in the afternoon and night (Fig. 2). This pattern points to strong nocturnal production pathways for both species: HNO₃ and HONO accumulate in the surface layer overnight under weak turbulent mixing, and result in pronounced upward fluxes in the next morning as turbulence intensifies. (2) In terms of particulate species, NO3- had more upward flux events (36 %) and higher upward flux values (4.2 ± 2.8 nmol m⁻² s⁻¹, equivalent to 0.26 ± 0.17 µg m⁻² s⁻¹) than other three species. The most likely NO3- sources are in-situ formation of ammonium nitrate near the surface layer from ammonia emitted by the cropland or wind-blown particles from agricultural soils. (3) Like downward flux, upward fluxes of HONO (0.30 ± 0.27 µg m⁻² s⁻¹) and NO3- (0.26 ± 0.17 µg m⁻² s⁻¹) are again one or two orders of magnitude higher at our site than all prior measurements, while those of HNO₃, SO₂, SO42- are comparable with prior reports (Fig. 4).

On the windy day of 24 December (highest mean horizontal wind speed 3.8 m s⁻¹ in the campaign), exceptionally high upward fluxes of HNO₃, HONO, NO3-, and SO42- were recorded, exceeding those from all other measurement days by one order of magnitude. After excluding this outlier, net fluxes over the entire observation period were upward for HONO and NO2- (mean daily 2.49 and 0.53 mg m⁻² d⁻¹, respectively), and negative for all other species: HNO₃ (-7.24 mg m⁻² d⁻¹), Cl⁻ (-4.36 mg m⁻² d⁻¹), NO3- (-2.34 mg m⁻² d⁻¹), SO42- (-1.29 mg m⁻² d⁻¹), SO₂ (-0.24 mg m⁻² d⁻¹), and HCl (-0.817 mg m⁻² d⁻¹), which are shown in Fig. 3b as molar units to facilitate direct cross-species comparisons.

Analysis of wind speed (WS), ambient temperature (Ta), relative humidity (RH), and ultraviolet-A radiation (UV-A) meteorological parameters (Fig. S4) identified wind speed as a key regulator of flux magnitude. Under low wind speeds, all target species exhibited predominantly downward or weak upward fluxes (Fig. 2), while pronounced upward fluxes occurred almost exclusively at wind speeds > 2.1 m s⁻¹. Notably, apparent deposition velocity (-F/C) was correlated with friction velocity (u∗) for both upward and downward fluxes (Fig. 5), demonstrating that turbulence intensity directly drives flux magnitude.

The land surface is a well-documented source of HONO, which could originate from direct soil emission, heterogeneous NO₂ reactions on diverse wet surfaces (e.g., bare ground, building exteriors, urban grime, aerosol particles), and the photolysis of nitric acid/nitrate on leaf surfaces (Zhou et al., 2011). Upward HNO₃ emissions have been widely observed over forests and grasslands (Hansen et al., 2015; Myles et al., 2007; Xu et al., 2021; Pryor et al., 2002; Nemitz et al., 2009). For example, Hansen et al. (2015) reported that about 70 % of the total samples showed HNO₃ emission during late summer/autumn in a mixed deciduous forest site in the USA. Xu et al. (2021) showed about 30 % of the total samples showed apparent HNO₃ emissions at a suburban forest site in Japan. HNO₃ is thought to deposit with a zero resistance even over slightly wet surfaces, where it can also be formed via NO2+ H₂O_(surface) → HONO + HNO₃ and N₂O5+ H₂O_(surface) → 2HNO₃. Potential upward HNO₃ fluxes probably arise from decomposition of NH₄NO₃ aerosols near warm surfaces and deposited NH₄NO₃ on the ground or leaf surfaces as water layers evaporate.

The gross upward flux (Fgross) can be calculated from the apparent flux observed at the measurement height (F) and the surface deposition (D) via Fgross=F+D (Schobesberger et al., 2016). Unlike the apparent flux that is confounded by concurrent atmospheric deposition, Fgross reflects more accurately the actual emission from the near-surface layer to the atmosphere. In this study, we estimated Fgross for HNO₃ and HONO, owing to not only the pronounced positive apparent fluxes of these two species (Fig. 3) but also the feasibility of approximating their dry deposition velocities given their relatively high water solubility.

According to Wesely (2007) resistance model, physical deposition velocity of a molecule from the atmosphere to the surface is calculated as Vd=1Ra+Rb+Rc, where Ra, Rb, and Rc are aerodynamic resistance, molecular diffusion resistance and surface resistance, respectively. For highly water-soluble HNO₃, Rc is near zero; for water-soluble HONO, Rc over slight wet surfaces (like vegetable surface in the cropland) is also far smaller than Ra (Harrison et al., 1996). Thus, Vd for both species can be simplified to Vd≈1Ra+Rb. Substituting the standard formulations Ra=lnzz0-ψmk×u∗ and Rb=2×Sc23k×u∗ into the simplified Vd equation yields 3Vd≈k×u∗lnzz0-ψm+2×Sc23 where k is the von Karman constant, u∗ is friction velocity, z is measurement height, z0 is roughness length, which is constant at a winter underlying surface, ψm is the Businger dimensionless momentum stability function, and Sc is the Schmidt number. Our sampling conditions (4 m measurement height, cloudy winter days, 5–20 °C temperature range) resulted in only 3 %–4 % diurnal variation in Sc and ∼ 1.0–1.1 variation in ψm. The corresponding 10 %–14 % relative variation in the denominator of Eq. (3) justifies a linear approximation Vd=a×u∗, where a is an empirical constant. Substituting surface deposition D=Vd×C into the Fgross definition gives 4Fgross=F+a×u∗×C From Eq. (4), a-Fgross/Cu∗ is equal to -F/Cu∗, which is the slopes of the data points in Fig. 5. We calculated the empirical constant a, for HNO₃ and HONO separately, from the maximum slope -F/Cu∗max of the downward-flux data points in Fig. 5, when Fgross= 0 (that is, no upward emission and apparent flux equals deposition). a was then substituted into Eq. (4) to calculate Fgross for all the sampling periods. Please note that according to the mass balance equation (S=P-L+E-D-F), Fgross includes joint contributions from surface emission (E), net chemical production below the measurement height (P-L) and the storage change flux below the measurement height (S, ∫0hδSXZδtδz), which are not distinguishable in our estimation of Fgross 5Fgross=P+E-S Based on the calculation from Eq. (4), the diurnal variations in upward gross fluxes of HNO₃ and HONO, along with their dependence on horizontal wind speed or ambient temperature, are presented in Fig. 6. Overall, HNO₃ gross fluxes (1.1 ± 0.9 µg m⁻² s⁻¹) were higher than those of HONO (0.4 ± 0.4 µg m⁻² s⁻¹). HNO₃ gross fluxes were higher in the morning (1.6 ± 1.4 µg m⁻² s⁻¹) than in the afternoon (0.9 ± 0.4 µg m⁻² s⁻¹) and nighttime (0.7 ± 0.5 µg m⁻² s⁻¹). Fluxes under high wind speeds (WS > 2.1 m s⁻¹, 1.8 ± 1.1 µg m⁻² s⁻¹) were significantly greater than those under low wind speeds (0.6 ± 0.4 µg m⁻² s⁻¹), indicating that upward gross fluxes of HNO₃ below the measurement height were accelerated under elevated wind speed.

Similar to HNO₃, HONO gross fluxes were higher in the morning (0.5 ± 0.5 µg m⁻² s⁻¹) than in the afternoon (0.3 ± 0.3 µg m⁻² s⁻¹) and nighttime (0.3 ± 0.3 µg m⁻² s⁻¹). In contrast to HNO₃, HONO emission fluxes showed no significant correlation with wind speed, solar radiation, or relative humidity (Fig. S5); instead, the fluxes were significantly higher under low temperatures (T_a < 15 °C, 0.4 ± 0.5 µg m⁻² s⁻¹) than under high temperatures (0.1 ± 0.1 µg m⁻² s⁻¹), as further illustrated by the scatter plots of temperature dependence for both HONO and HNO₃ fluxes (Fig. S6). This behavior is likely attributed to the dependence of HONO surface production from aqueous-phase reactions in soil pore water or surface water films (Wu et al., 2019; Ren et al., 2020). High temperatures reduce soil and surface moisture, thereby suppressing HONO production.