Fate of the nitrate radical at the summit of a semi-rural mountain site in Germany assessed with direct reactivity measurements

The reactivity of NO₃ plays an important role in modifying the fate of reactive nitrogen species at nighttime. High reactivity (e.g. towards unsaturated volatile organic compounds – VOCs) can lead to formation of organic nitrates and secondary organic aerosol, whereas low reactivity opens the possibility of heterogeneous NO_x losses via the formation and uptake of N₂O₅ to particles.

We present direct NO₃ reactivity measurements ($k^{{\mathrm{NO}}_{\mathrm{3}}}$) that quantify the VOC-induced losses of NO₃ during the TO2021 campaign at the summit of the Kleiner Feldberg mountain (825 m, Germany) in July 2021. $k^{{\mathrm{NO}}_{\mathrm{3}}}$ was on average ∼0.035 s⁻¹ during the daytime, ∼0.015 s⁻¹ for almost half of the nights and below the detection limit of 0.006 s⁻¹ for the other half, which may be linked to sampling from above the nocturnal surface layer. NO₃ reactivities derived from VOC measurements and the corresponding rate coefficient were in good agreement with $k^{{\mathrm{NO}}_{\mathrm{3}}}$, with monoterpenes representing 84 % of the total reactivity. The fractional contribution F of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ to the overall NO₃ loss rate (which includes an additional reaction of NO₃ with NO and photolysis) were on average ∼16 % during the daytime and ∼50 %–60 % during the nighttime. The relatively low nighttime value of F is related to the presence of several tens of parts per trillion by volume (pptv) of NO on several nights. NO₃ mixing ratios were not measured, but steady-state calculations resulted in nighttime values between <1 and 12 pptv. A comparison of results from TO2021 with direct measurements of NO₃ during previous campaigns between 2008 and 2015 at this site revealed that NO₃ loss rates were remarkably high during TO2021, while NO₃ production rates were low.

We observed NO mixing ratios of up to 80 pptv at night, which has implications for the cycling of reactive nitrogen at this site. With O₃ present at levels of mostly 25 to 60 ppbv (parts per billion by volume), NO is oxidized to NO₂ on a timescale of a few minutes. We find that maintaining NO mixing ratios of, e.g., 40 pptv requires a ground-level NO emission rate of 0.33 pptv s⁻¹ (into a shallow surface layer of 10 m depth). This in turn requires a rapid deposition of NO₂ to the surface (vd${}_{{\mathrm{NO}}_{\mathrm{2}}}\sim \mathrm{0.15}$ cm s⁻¹) to reduce nocturnal NO₂ levels to match the observations.

1 Introduction

Nitric oxide (NO) and nitrogen dioxide (NO₂) are atmospheric pollutants, which exert a great impact on climate and air quality (Pozzer et al., 2012; Lelieveld et al., 2020). Via its dissociation, NO₂ is the direct photochemical precursor of boundary layer ozone (O₃, a phytotoxin and cause of respiratory illness), and understanding the processes that remove NO_x ($=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$) is of great importance (Crutzen and Lelieveld, 2001; Lelieveld et al., 2016; Edwards et al., 2017). The formation of long-lived or soluble organic nitrates during the oxidation of volatile organic compounds (VOCs) provides a mechanism to convert NO_x to NO_z (where NO_z includes both organic and inorganic nitrates in the gas and particle phase), which may be transported away from the source region or removed via dry or wet deposition, respectively (Rollins et al., 2012; Romer Present et al., 2020).

The major initiators of VOC oxidation are hydroxyl (OH) radicals, ozone (O₃), and the nitrate radical (NO₃; Ng et al., 2017; Wennberg et al., 2018), with OH reactions being most important during the daytime (Lelieveld et al., 2008). The NO₃ radical is generally considered to be important only at nighttime (Brown and Stutz, 2012), although, in some environments, it can also contribute substantially to the oxidation of unsaturated VOC during the day (J. Liebmann et al., 2018; J. M. Liebmann et al., 2018). NO₃ is formed almost exclusively in the sequential oxidation of NO by O₃ (Reactions R1 and R2). During the daytime, NO₃ is lost via rapid photolysis (Reactions R5 and R6, with a lifetime of seconds) and an efficient reaction with NO ($k_{\mathrm{7}}=\mathrm{2.6}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹ at 298 K; IUPAC, 2022), which result in low mixing ratios (Wayne et al., 1991). NO₃ also reacts with NO₂ to form dinitrogen pentoxide (N₂O₅), which is in thermal equilibrium with NO₃ and NO₂ (Reactions R3, R4).

$$\begin{array}{}\text{(R1)}& {\displaystyle }\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\text{(R3)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}+M\to {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M\text{(R4)}& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+M\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}+M\text{(R5)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+hv\to \mathrm{NO}+{\mathrm{O}}_{\mathrm{2}}\text{(R6)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+hv\to {\mathrm{NO}}_{\mathrm{2}}+\mathrm{O}\text{(R7)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}}.\end{array}$$

Reactions (R1)–(R4) can result in the permanent loss of NO_x from the gas phase through deposition or uptake to particles of, e.g., NO₃ or N₂O₅ (Reactions R8, R9; Crowley et al., 2011; Phillips et al., 2016).

$$\begin{array}{}\text{(R8)}& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\to \text{particle (or deposition)}\text{(R9)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}\to \text{particle (or deposition)}.\end{array}$$

In forested regions during the night, NO₃ reacts predominantly with unsaturated volatile organic compounds (VOCs), often of biogenic origin such as isoprene or monoterpenes, which results in the formation of alkyl nitrates (RONO₂; Reaction R10; Hallquist et al., 1999; Fry et al., 2014; Wu et al., 2021). Depending on the biogenic VOC (BVOC) involved, the RONO₂ formed may have low volatility and may deposit to surfaces or transfer to the particle phase to form secondary organic aerosols (SOAs; Reaction R11; Place et al., 2022). The reaction between NO₃ and BVOC consequently represents a loss of NO_x from the gas phase and thus has an impact on air quality via suppression of ozone formation and increases in SOA levels (Fry et al., 2011; Romer Present et al., 2020).

$$\begin{array}{}\text{(R10)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{R}=\mathrm{R}(+{\mathrm{O}}_{\mathrm{2}})\to \to {\mathrm{RONO}}_{\mathrm{2}}\text{(R11)}& {\displaystyle }{\mathrm{RONO}}_{\mathrm{2}}\to \text{deposition}/\mathrm{SOA}.\end{array}$$

The nocturnal NO₃ lifetime close to the surface is generally short (typically in the range of minutes) owing to the buildup of the concentration of reactive gases emitted from the biosphere into a shallow nocturnal boundary layer (J. Liebmann et al., 2018; J. M. Liebmann et al., 2018). Longer NO₃ lifetimes (sometimes exceeding 1 h) have been derived from NO₃ measurements in very clean regions (Allan et al., 2000; Martinez et al., 2000), from measurements in the overlying residual layer using towers and aircraft platforms (Stutz et al, 2004; Brown et al., 2007a, b), and at mountain sites where the meteorological situation results in the measurement location being above the nocturnal surface layer (Carslaw et al., 1997; Brown et al., 2016; Sobanski et al., 2016).

The lifetime of NO₃ has often been derived using a stationary-state approximation, which relies on direct measurements of NO₃, NO₂, and O₃ (Heintz et al., 1996; Allan et al., 1999; Geyer et al., 2001; Brown et al., 2004, 2009; Stutz et al., 2010; Sobanski et al., 2016). This method is limited to periods when NO₃ mixing ratios are above the instrumental detection limit, which (depending on instrument performance) may restrict the method to periods when NO₃ production rates are high and NO₃ reactivities (i.e. the inverse of NO₃ lifetimes) are low. This is usually not the case during the daytime or even during the nighttime in areas with high BVOC emissions (J. Liebmann et al., 2018). Direct NO₃ reactivity measurements not only extends the accessibility to daytime reactivities but also, together with measurements of NO, NO₃, photolysis rates ($J_{{\mathrm{NO}}_{\mathrm{3}}}$), and VOCs, enables the determination of the fate of the NO₃ radical throughout the diel cycle. Recent direct NO₃ reactivity measurements and model calculations (Liebmann et al., 2019; Foulds et al., 2021) suggest that NO₃ also contributes to daytime alkyl nitrate formation, which typically occurs through the OH-initiated oxidation of BVOC in the presence of NO (Wennberg et al., 2018). Quantifying the contribution of NO₃+VOC reactions to the NO₃ reactivity is thus central in understanding the role of NO₃, in, e.g., SOA formation and NO_x lifetimes.

In this study, the fate of the NO₃ radical in the semi-rural Kleiner Feldberg (KF) mountain (in the southwest of Germany) in July and August 2021 (TO2021 campaign), during both day- and nighttime, is analysed by direct measurements of NO, photolysis rates ($J_{{\mathrm{NO}}_{\mathrm{3}}}$), and the first-order NO₃ loss constant resulting from reaction with VOCs ($k^{{\mathrm{NO}}_{\mathrm{3}}}$). Measurements of VOCs that are reactive towards NO₃ enable us to calculate their fractional contribution to $k^{{\mathrm{NO}}_{\mathrm{3}}}$. With the help of NO₃, NO₂, NO, and O₃ measurements, we derive NO₃ loss terms via the steady-state assumption ($L_{{\mathrm{NO}}_{\mathrm{3}}}$) for previous campaigns at this site to assess the impact of differing meteorological and chemical conditions.

2 The TO2021 campaign

The TO2021 campaign took place in July and August 2021 at the Taunus Observatory (TO) at the summit of the Kleiner Feldberg mountain (825 m a.s.l. – above sea level). A detailed description of the location has been given elsewhere (Crowley et al., 2010), and only a brief summary is given here. The Kleiner Feldberg is mostly surrounded by coniferous forest, but an area at the summit (∼100 m²) is cleared of trees and hosts the meteorological measurements of the German Meteorological Service (Deutscher Wetterdienst, DWD) and permanent measurement containers of the University of Frankfurt and the Hessian Agency for Nature Conservation, Environment and Geology (Hessisches Landesamt für Naturschutz, Umwelt, und Geologie, HLNUG). The summit itself is covered with bushes and, especially to the north, with blueberry shrubs. The mountaintops of Altkönig (798 m a.s.l.) and Großer Feldberg (878 m a.s.l.) are in the direct vicinity (<3 km). Air arriving from the southwest and southeast is impacted by anthropogenic emissions from the densely populated cities of Frankfurt, Wiesbaden, and Mainz (20–30 km), whereas air from the northwest, north, and northeast is cleaner, with no major cities for 50–70 km.

2.1 Instrumentation

For the duration of the TO2021 campaign, two (stacked) containers, including the instruments operated by the Max Planck Institute for Chemistry (MPIC), were set up on the site. If not stated otherwise, the instruments sampled from a high volume flow stainless-steel tube (10 m³ min⁻¹; 0.2 s residence time) sucking air from ca. 10 m above the ground. Each instrument with measurements used in the analysis is described below.

2.1.1 NO₃ reactivity

The flow tube cavity ring-down spectrometer (FT-CRDS) set-up used to quantify VOC-induced NO₃ reactivity (Liebmann et al., 2017) consists of a Teflon-coated (FEPD 121; Chemours) glass flow tube reactor, in which a flow of ambient air is mixed with 30–60 parts per trillion by volume (pptv) of synthetically generated NO₃.

NO₃ is generated by the sequential oxidation of NO and NO₂ (3.5 standard (STP) cubic centimetres per minute (sccm) of 1 part per million by volume (ppmv) in N₂; Air Liquide) by O₃ (generated by passing synthetic air over a Hg lamp) in an upstream Teflon-coated glass reactor (thermostated to 30 ^∘C at a pressure of 1.3 bar) in 400 sccm synthetic air. The flow exiting the NO₃ source is passed through ca. 15 cm of $\mathrm{1}/\mathrm{4}$ in (0.635 cm) outer diameter (OD) PFA (perfluoroalkoxy) tubing that is heated to 140 ^∘C so that N₂O₅ is quantitatively decomposed to NO₃ and NO₂ (Reaction R4). The flow from the NO₃ source is then mixed with either 2800 sccm synthetic or ambient air and passed through the flow tube reactor where it resides for time t. The synthetic air used to measure zero reactivities was provided by a commercial zero-air generator (CAP 120; Fuhr GmbH) and humidified to ambient level with a permeation tube (Perma Pure LLC; MH-070-24F-4) immersed in deionized water. The ambient air was sampled from the high-flow inlet through $\mathrm{1}/\mathrm{4}$ in. (15 cm; OD) PFA tubing equipped with a Teflon membrane filter (2 µm pore, 47 mm diameter; Pall Corp.).

NO₃ surviving the flow tube was detected by CRDS at 662 nm. The ring-down time in the absence of NO₃ was determined every ca. 5 min by adding an excess of NO (3 sccm of 100 ppmv in N₂). NO₃ reactivities are deduced from the relative change in NO₃ mixing ratio in ambient air compared to synthetic air. Dynamic dilution of the ambient air with synthetic air was used to keep the NO₃ reactivity in a measurable range when sampling highly reactive air masses.

Since the NO₃ mixing ratio is affected by Reactions (R1)–(R4), (R7), and (R9), in addition to the reaction of interest Reaction (R10), a numerical simulation procedure that corrects for the impact of NO and NO₂ is necessary to extract the NO₃ reactivity towards VOCs ($k^{{\mathrm{NO}}_{\mathrm{3}}}$). The validity of this correction procedure was checked by adding a known amount of NO (1–6 sccm of 245 parts per billion by volume (ppbv) NO in N₂; Air Liquide) every 2 h during the zeroing periods throughout the campaign. As shown in Fig. S1a in the Supplement, the model was able to reproduce the observed NO₃ mixing ratios reliably. A further calibration sequence during the campaign, in which five different amounts of NO were added, is displayed in Fig. S1b. The flow tube predominantly used during TO2021 features a residence time of t=9.5 s and an NO₃ wall loss rate of 0.001 s⁻¹. The limit of detection (LOD) is mainly defined by the stability of the NO₃ source and baseline, which were improved by thermostating both the NO₃ source and the flow tube and insulating the cavity from thermal gradients in the container so that a signal-stability related uncertainty of 16 % was achieved. For the numerical simulation procedure, ambient O₃, NO, and NO₂ mixing ratios and rate coefficients for Reactions (R1–R4) and (R7) were deployed. Liebmann et al. (2017) showed, with the help of Monte Carlo simulations, that the uncertainty associated with this simulation is dependent on the ratio between ambient NO₂ and $k^{{\mathrm{NO}}_{\mathrm{3}}}$. Assuming a typical daytime situation for TO2021 ($k^{{\mathrm{NO}}_{\mathrm{3}}}\sim \mathrm{0.04}$ s⁻¹, [NO₂] = 2 ppbv NO₂) the numerical simulation introduces an uncertainty of 15 %, resulting in an overall uncertainty of 22 %. However, if, for example, $k^{{\mathrm{NO}}_{\mathrm{3}}}$ is 0.006 s⁻¹ in the presence of 1 ppbv NO₂ (as occasionally detected during the nighttime), then the uncertainty caused by the simulation increases to ca. 50 %. During TO2021, the instrument's LOD was 0.006 s⁻¹ for this flow tube.

Between 23 and 25 July, a larger flow tube was tested with the intention of extending the LOD to lower reactivities. The residence time (20 s during the day or 32 s during the night according to position of a moveable injector) and wall loss rates were characterized during the campaign, as detailed by Liebmann et al. (2017). The factor ∼3 longer residence time at night, compared to the smaller flow tube, should have extended the LOD to 0.003 s⁻¹. However, the larger flow tube suffered from a greater NO₃ wall loss rate (>0.04 s⁻¹), which effectively worsened the LOD. For this reason, the deployment of this flow tube was stopped after 2 d.

During the nighttime, before being mixed with 30–60 pptv synthetic NO₃, the air was sampled through a 2 L uncoated glass flask (40 s residence time) that was heated to 35 ^∘C. This ensures that ambient NO₃ and N₂O₅ (at mixing ratios up to several tens of pptv, according to previous measurements; see below) does not reach the flow tube to bias the measurement. The NO mixing ratios that were used in the numerical simulations were corrected (typically by a factor of 0.6) for the reaction with ambient O₃ during residence in the flask.

2.1.2 NO₂, NO, O₃, and actinic flux

Owing to the importance of co-located NO₂ measurements for interpretation of the $k^{{\mathrm{NO}}_{\mathrm{3}}}$ data, the FT-CRDS set-up has a second inlet and cavity to measure NO₂ (J. M. Liebmann et al., 2018), with a total measurement uncertainty (defined by noise and baseline stability) of 8 % and a LOD of 168 pptv (4 s). A further CRDS-based measurement of NO₂ was made using a thermal dissociation cavity ring-down spectrometer (TD-CRDS; Friedrich et al., 2020) for measuring NO_x and NO_y. At nighttime, when NO was generally <80 pptv, the NO_x channel of this instrument essentially measures NO₂. The inlet of the ${\mathrm{NO}}_x/{\mathrm{NO}}_y$ instrument was located on the container roof, ∼2 m to the north and 2 m lower than the top of the high-flow inlet.

In addition, NO₂ was measured with a chemiluminescence (CLD) set-up (ECO PHYSICS; CLD 790 SR) equipped with a photolytic converter to convert NO₂ to NO (Tadic et al., 2020; Nussbaumer et al., 2021). This instrument also provided the campaign NO data set. Calibration (using a dynamically diluted, secondary 5 ppm NO standard) was carried out every 2 h, together with the zero measurement using synthetic air (Westfalen). The LODs for NO and NO₂ were derived from the standard deviation (1σ) of consecutive zeros and were 7 and 10 pptv, respectively, and the total measurement uncertainties were 9 % and 19 % for NO and NO₂.

The three sets of NO₂ measurements are compared in the Supplement (Fig. S2). A bivariate linear regression (York, 1966) of the data sets yields offsets below the LOD of the FT-CRDS NO₂ cavity in both cases. An excellent agreement with the TD-CRDS measurement is observed (slope of 0.99), while a fair agreement (slope of 1.09) within the associated uncertainties is achieved for the intercomparison with the CLD measurement. Note that post-campaign quantification of the NO standard with the CLD and the TD-CRDS set-up yielded satisfactorily agreeing values of (4.7 ± 0.3) ppmv and (4.9 ± 0.2) ppmv. O₃ was measured via UV absorption with two identical commercial ozone monitors (2B Technologies; model 205) that were cross-calibrated after the campaign. The instrument background was estimated approximately every 2 d with synthetic air from the zero-air generator. The uncertainty associated with this measurement is 5 %, and the LOD is 2 ppbv.

Actinic flux measurements were made by a spectral radiometer (METCON GmbH) installed on top of the upper container and converted to photolysis frequencies for NO₃ ($J^{{\mathrm{NO}}_{\mathrm{3}}}$), using evaluated absorption cross sections and quantum yields (Burkholder et al., 2016) with an overall uncertainty of ca. 15 % (Friedrich et al., 2021).

2.1.3 VOC measurements

VOCs were measured from 15 to 31 July with a proton transfer reaction time-of-flight mass spectrometer (PTR-ToF-MS; PTR8000; IONICON Analytik GmbH; Jordan et al., 2009; Bekö et al., 2020) with a time resolution of 20 s, operated with hydronium ions (H₃O⁺) at a pressure of 2.2 mbar and an $E/N$ of 137 Td. Mixing ratios of isoprene, monoterpenes, and sesquiterpenes are derived from calibrating to a gas standard containing isoprene, α-pinene, and β-caryophyllene (Apel-Riemer Environmental, Inc., Colorado, USA), respectively. The limit of detection lies in the range of tens of pptv, and the uncertainty is defined to be below 20 %.

A second PTR-ToF-MS (Vocus; TOFWERK AG) provided uncalibrated VOC data for the period between 20 July and 6 August (Krechmer et al., 2018). Fragmentation patterns in the Vocus PTR-MS are not yet completely characterized, and the first results (using the same gas standard as for the IONICON PTR8000) suggest that different monoterpenes fragment differently on several masses in the VOCUS instrument, which impedes calibration of the monoterpene data based on the α-pinene standard. In order to extend the data availability, the VOCUS data for isoprene, monoterpenes, and sesquiterpenes were therefore scaled to that of the PTR8000 data set (which suffered from less fragmentation and is thus associated with less uncertainty) by applying constant factors during the common time period (see Fig. S4b in the Supplement).

Both PTR-ToF-MS were located in a permanent container of the TO, ca. 8 m distance from the MPIC container. Air was sampled from the roof of the container (ca. 8 m) through a heated inlet line equipped with a polytetrafluoroethylene (PTFE) filter.

2.1.4 Temperature and relative humidity profiles

Deployment of a drone (EVO-X12; Multikopter) equipped with a commercial gas sensor (BME680; Bosch Sensortec GmbH) enabled the measurement of vertical profiles of pressure, temperature, and relative humidity (time resolution of 1 s) to a height of 100 m a.g.l. (above ground level).

3 Results and discussion

An overview of the key meteorological and trace gas measurements used in the analysis for the TO2021 campaign period from July to August 2021 is given in Fig. 1. Grey shaded areas mark the nighttime periods; sunrise during the measurement period was at ∼ 03:30 and sunset at ∼ 19:30 UTC. $k^{{\mathrm{NO}}_{\mathrm{3}}}$ shows a distinct daytime to nighttime variability and generally follows the summed mixing ratio of monoterpenes (ΣMTs) which were present at maximum mixing ratios (during the day) typically between 150 and 400 pptv.

Figure 1 Overview of key measurements during the TO2021 campaign with wind direction (WD), temperature (T), sum of monoterpenes (ΣMT, PTR8000 and scaled VOCUS), wind speed (WS), relative humidity (RH), and NO₃ photolysis rate coefficient ($J_{{\mathrm{NO}}_{\mathrm{3}}}$). Meteorological data were provided by the German Meteorological Service (DWD). Nighttime periods are shaded grey. The x-axis ticks are at 00:00 UTC.

Wind speeds were predominantly between 2 and 4 m s⁻¹, with most wind sectors represented, although wind from the east and southeast, originating from the Frankfurt area (SE), was rarely encountered. The local wind directions and speeds during TO2021 are displayed as a wind rose in Fig. S3a in the Supplement.

There were several periods of rain and fog during TO2021, which is reflected by high relative humidities (RHs) mostly between 75 % and 100 % at moderate temperatures between 12 and 20 ^∘C. Ozone mixing ratios varied between 20 and 60 ppbv. The CLD set-up observed NO mixing ratios close to (10 to 20 pptv) or below the LOD of 7 pptv on about half of the nights but also returned values of between 20 to 80 pptv for prolonged periods on some nights. Daytime NO mixing ratios were between 0.5 and 2 ppbv, with maximum values around midday. Spikes in NO mixing ratios caused by vehicles at the site were removed from the dataset. NO₂ mixing ratios (as measured with the FT-CRDS set-up) were generally between 1 and 2 ppbv, with occasional values of up to 6 ppbv. Photolysis rates of NO₃ ($J_{{\mathrm{NO}}_{\mathrm{3}}}$) of ca. 0.15 s⁻¹ were detected at noon. The data gap between 3 and 5 July was caused by a power failure.

3.1 NO₃ reactivity

As is evident from Fig. 1, $k^{{\mathrm{NO}}_{\mathrm{3}}}$ followed the trend in monoterpene mixing ratios and was generally higher during the daytime compared to the night. As illustrated in a wind rose in the Supplement (Fig. S3b), $k^{{\mathrm{NO}}_{\mathrm{3}}}$ displayed no clear dependence on wind direction. A closer examination of the data reveals that the nights can be divided into the following two types: on 15 of the 34 nights, NO₃ reactivities remained well above the instrument's LOD of 0.006 s⁻¹ (from now on defined as Type 1 nights), whereas during 14 nights, $k^{{\mathrm{NO}}_{\mathrm{3}}}$ was predominantly lower than 0.006 s⁻¹ (Type 2). The other 5 nights showed a transitional behaviour between those two types.

An example of a Type 1 night is shown in Fig. 2a. Following a late evening value of $k^{{\mathrm{NO}}_{\mathrm{3}}}\sim \mathrm{0.1}$ s⁻¹, the NO₃ reactivity decreased during darkness from 0.08 s⁻¹ at 20:00 UTC to 0.02 s⁻¹ at 03:00 UTC. During this period, northerly winds with speeds around 4 m s⁻¹ prevailed, and the decrease in reactivity cannot be related to a change in air mass origin. At the same time, we observed a decrease in temperature (∼17 to ∼13 ^∘C) that was accompanied by an increase in the relative humidity (78 % to 98 %) and a quasi-continuous reduction in O₃ mixing ratios from ∼35 to ∼25 ppbv. Note that ca. 20–30 pptv of NO were detected during this night, implying that Reaction (R7) would represent a significant loss process for NO₃. A detailed discussion of this aspect follows in Sect. 3.4.

Figure 2 Time series of directly measured NO₃ reactivity ($k^{{\mathrm{NO}}_{\mathrm{3}}}$), together with auxiliary measurements during Type 1 (a) and Type 2 nights (b). F1 and F2 mark times at which drone-assisted temperature and relative humidity profiles were measured. The grey shaded area represents nighttime. Abbreviations are defined in the caption of Fig. 1. The shaded areas in the colour of the lines denote the corresponding uncertainty of the measured parameter.

Figure 2b shows an example of a Type 2 night with a sharp decrease in $k^{{\mathrm{NO}}_{\mathrm{3}}}$ from ∼0.02 s⁻¹ just before sunset to below the LOD (0.006 s⁻¹) within the first hour after sunset. As for Type 1, there is no significant change in the wind direction. However, in contrast to the Type 1 example, after a slight increase just after sunset, O₃ was roughly constant and significantly higher throughout the night, with NO below the detection limit during the entire night. In addition, the temperature (14 ± 1 ^∘C) and relative humidity (70 % ± 5 %) were roughly constant, with the latter significantly lower than for the Type 1 example.

Low NO₃ reactivities at nighttime (i.e. Type 2 nights) can result from a low rate of emission of biogenic VOCs (e.g. owing to low temperatures) but can also be associated with strong vertical gradients, which effectively decouple ground-level emissions from the air above. For the latter case, we are dealing with a shallow surface layer with its top below the inlet so that the air is sampled from the nocturnal boundary or residual layer (Brown and Stutz, 2012) in which the NO₃ lifetimes can be very long. This phenomenon has been reported for this and other mountain sites (Carslaw et al., 1997; Brown et al., 2016; Sobanski et al., 2016; Liebmann et al., 2017; J. M. Liebmann et al., 2018). Slow exchange between the surface layer and the residual layer can result in strong gradients in trace gases such as O₃, which undergoes dry deposition in the surface layer but is long-lived in, e.g., the residual layer. The situation for NO₂ is more complex as it may be formed from the O₃-induced oxidation of near-surface emissions of NO and also lost via (slow) reaction with O₃ and dry deposition (Brown et al., 2003b, 2007a; Stutz et al., 2004).

Figure 3 displays the campaign-averaged diel cycles of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ (along with O₃, RH, T, NO, and MTs) classified according to Type 1 or Type 2 nights. $k^{{\mathrm{NO}}_{\mathrm{3}}}$ was on average around 0.015 s⁻¹, during Type 1 nights, with a daytime reactivity of 0.04 s⁻¹ (Fig. 3a). The observed orders of magnitude for $k^{{\mathrm{NO}}_{\mathrm{3}}}$ are consistent with the directly measured nighttime NO₃ reactivities ranging between <0.005 and up to 0.06 s⁻¹ during 3 nights in July 2015 (NOTOMO campaign) with the same instrument (Liebmann et al., 2017).

Figure 3 Median diel profiles of (a) directly measured NO₃ reactivities, (b) O₃ mixing ratios, (c) monoterpenes, (d) temperature, (e) relative humidity, and (f) NO mixing ratios classified by night types (Type 1 in black; Type 2 in red). The grey shaded area represents the nighttime period. The shaded areas in line colour represent the 25th and 75th percentiles. The blue lines denote the LODs of the instruments used to measure NO₃ reactivity and NO.

By definition, the median nighttime reactivity for Type 2 nights is at the instrument's LOD, while the median daytime reactivities prior to Type 2 nights are very similar to those observed prior to Type 1 nights. The median diel cycles for O₃ (Fig. 3b) differ significantly for the two types. During Type 1 nights, O₃ decreases continuously (consistent with previous observations at this site; Handisides, 2001), while during Type 2 nights, O₃ mixing ratios remain fairly constant and higher. There are also significant differences in the median NO mixing ratio, with nighttime values (Fig. 3f) mostly below or close (10–12 pptv) to the LOD during Type 2 nights and values of 30–40 pptv during Type 1 nights.

The lower nighttime $k^{{\mathrm{NO}}_{\mathrm{3}}}$ values observed during Type 2 nights compared to Type 1 nights is accompanied by lower (factor ∼2.5) monoterpene mixing ratios (Fig. 3c). The median temperature during Type 2 nights is up to 1 K colder than compared to Type 1 nights (Fig. 3d), which, based on the expression ($E_{\mathrm{MT}}\propto \exp (\mathit{\beta }\left(T-\mathrm{297}\mathrm{K}\right)$) with β=0.1 K⁻¹; Guenther et al., 1993), results in a change of only 10 % and is thus insufficient to explain the differences observed in ΣMT on these nights.

With values of 85 %–95 %, the median relative humidity (Fig. 3e) was higher by around 5 % (and increased continuously) during Type 1 nights than for Type 2, for which a much smaller increase from 82 % to 87 % was observed.

In summary, in addition to very low NO₃ reactivity, Type 2 nights are characterized by (1) larger and constant O₃ mixing ratios, (2) lower but constant RH, and (3) low concentrations of reactive trace gases like NO and monoterpenes. These observations support the presence of a very shallow surface layer with its top located below the tip of the inlet and decoupling of the sampled air from ground-level emissions (i.e. of NO and VOCs). The top of the bush and shrub-like vegetation adjacent to the inlet (within a 20 m radius) was several metres below the top of the inlet. Previous observations of strong gradients in NO₃ mixing ratios and low reactivities have showed that decoupling of the air mass from ground-level emissions can lead to NO₃ lifetimes of up to hours (Allan et al., 2002; Brown et al., 2016; Sobanski et al., 2016). In order to test the hypothesis that low NO₃ reactivities observed during Type 2 nights are the result of sampling from the nocturnal boundary layer (NBL), we mounted temperature and relative humidity sensors on a multi-copter drone to measure gradients in these parameters on the night of 22–23 July, which is the night depicted in Fig. 2b.

The drone was located ∼20 m to the NE of the inlet, and the starting height (ground level) was about 12 m lower than the top of the inlet. The drone flew a vertical profile with the first ascent/descent starting before sunset at 18:30 UTC (blue dotted line; F1 in Fig. 2b) and a second after sunset at 20:20 UTC (red dotted line; F2 in Fig. 2b). The flights were restricted to heights of ∼100 m a.g.l., owing to operational restrictions in the vicinity of Frankfurt airport.

The gradients in potential temperature θ for the two flights are shown in Fig. 4a. At 18:30 UTC (blue curve), the potential temperature increases gradually with altitude (positive stratification) as expected for a well-mixed boundary layer (Stull, 1988; Brown et al., 2007b). In contrast, the potential temperature gradient measured at 20:20 UTC reveals a strong increase in the first 3 m, which represents the nocturnal surface layer. Above this, the potential temperature increases more slowly until ca. 20 m a.g.l. This zone (shaded in red) represents the stable NBL above which the potential temperature is almost independent of height (neutral stratification), which is the typical behaviour of the residual layer (Stull, 1988; Brown et al., 2007b). The gradient in relative humidity (Fig. 4b) after sunset indicates a similar vertical structure, with the top of the NBL characterized by a minimum in the relative humidity (Brown et al., 2007b), also explaining why RH was, on average, lower during Type 2 compared to Type 1 nights (Fig. 3e). The approximate height of our inlet was situated ca. 10 m a.g.l., and the profile of θ implies that the air we sampled was from a NBL decoupled from ground-level emissions and in which vertical mixing is weak (Brown and Stutz, 2012). Under this scenario, NO originating from soil emissions and VOCs from plant emissions are trapped in the surface layer and only inefficiently entrained into the NBL. Unfortunately, owing to delays in obtaining permission to fly the drone, unfavourable weather conditions, and other logistical considerations, these two flights on this 1 night are the only ones in which vertical profiles of temperature and RH were obtained. Nonetheless, these observations provide important clues as to how the meteorological situation can influence NO₃ reactivity and NO levels at inlet height.

Figure 4 Vertical profiles of potential temperature (a) and relative humidity (b) at the summit of the Kleiner Feldberg at 18:30 UTC (blue) and 20:20 UTC (red). The nocturnal boundary layer (NBL) at 20:20 UTC is shaded red. The inlet height is indicated by a black dashed line.

3.2 Contribution of VOCs to $k^{{\mathrm{NO}}_{\mathrm{3}}}$

As described above, $k^{{\mathrm{NO}}_{\mathrm{3}}}$ includes the contribution of VOCs only, and it is thus expected to correlate with the summed first-order loss rates, Σk_i[VOC]_i derived from the concentration [VOC]_i of each VOC and the corresponding rate constant (k_i) for its reaction with NO₃, provided that all VOCs with a significant contribution were measured.

Unsaturated organic compounds (often of biogenic origin such as isoprene or terpenes) are generally the dominant reaction partners for NO₃ in forested environments (Ng et al., 2017). During TO2021, several hundreds of pptv of isoprene, monoterpenes, and sesquiterpenes were detected during the second half of the campaign when VOC measurements became available (see Figs. 1 and S4). Owing to their low rate coefficients (IUPAC, 2022), alkanes, aromatics, and saturated oxygenated species such as acetaldehyde, acetone, and methanol were found to contribute negligibly to $k^{{\mathrm{NO}}_{\mathrm{3}}}$. Consequently, only isoprene and the sum of mono- and sesquiterpenes are relevant for analysis. GC-MS measurements from a previous summer campaign at this site (Sobanski et al., 2017) derived fractional contributions to ΣMT of 50.5 %, 28.9 % and 20.6 % for α-pinene, limonene, and myrcene, respectively. Using an accordingly weighted average of evaluated kinetic data (IUPAC, 2022), we derived an effective rate constant of $k_{\mathrm{MT}}=\mathrm{8.9}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ for NO₃+ monoterpenes reactions at this site. As speciated measurements of sesquiterpenes are not available, in order to calculate NO₃ loss rates resulting from its reaction with all sesquiterpenes, we used the IUPAC-recommended rate coefficient for NO₃+β-caryophyllene. This is often the dominant sesquiterpene measured in air and is also the sesquiterpene used to calibrate the PTR8000. Neglecting the uncertainty associated with the assumption that the MT mixture was the same in both campaigns and that combining the uncertainty in the measured VOC mixing ratios (20 %) and in the effective rate coefficient (25 %) leads to an overall fractional uncertainty of 33 % in each term of Σk_i[VOC]_i.

In Fig. 5a, we present a time series of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ and Σk_i[VOC]_i. Clearly, $k^{{\mathrm{NO}}_{\mathrm{3}}}$ and Σk_i[VOC]_i agree within associated uncertainties most of the time. The poorer agreement observed around the 16 July may have been related to the presence of fog and droplets in the sampling line, and the poor agreement around the 24 July was most probably caused by conditioning effects when switching between flow tubes. As indicated by the area in purple, the NO₃ reactivity was almost entirely determined by the reaction with monoterpenes. Figure 5b focusses on the Type 2 night previously shown in Fig. 2b (but all $k^{{\mathrm{NO}}_{\mathrm{3}}}\mathit{<}$ LOD set to 0.006 s⁻¹) suspected to be impacted by a boundary layer effect. Within associated uncertainties, the VOC measurements confirm that VOC-induced NO₃ reactivities are close to or below 0.006 s⁻¹ for this period. The average contribution of the VOCs to Σk_i[VOC]_i is depicted in Fig. 5c and shows that 84 % of the overall reactivity is caused by monoterpenes, while isoprene and sesquiterpenes contribute 7 % and 9 %, respectively.

Figure 5 (a) Time series of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ and Σk_i[VOC]_i. Dashed blue line marks the LOD of the $k^{{\mathrm{NO}}_{\mathrm{3}}}$ measurement. The purple line, together with the same-coloured shade, represents the contribution of monoterpenes. The red and grey shaded areas represent the uncertainty associated with $k^{{\mathrm{NO}}_{\mathrm{3}}}$ and Σk_i[VOC]_i, respectively. (b) Same as panel (a) but with a detailed view of the night between 22 and 23 July presented in Fig. 2b. (c) Pie chart of fractional contributions of isoprene, monoterpenes, and sesquiterpenes to Σk_i[VOC]_i over this time period.

Figure 6 plots Σk_i[VOC]_i versus $k^{{\mathrm{NO}}_{\mathrm{3}}}$ for which a bivariate regression yields a slope of 1.04 ± 0.03 (2σ; Boggs et al., 1989) and an intercept of (6.6 ± 0.4) $\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹. A slope close to unity suggests near-closure for the NO₃ reactivity budget, while the intercept is the equivalent to the reactivity caused, for example, by 27 pptv of β-caryophyllene or an overestimation of NO by just 18 pptv. We recall, however, that speciated monoterpenes were not measured in TO2021, and the effective rate constant was based on the (non-testable) assumption that the summertime monoterpene composition at this site is the same as in 2011. Seasonal and meteorological variations and changes in vegetation over the years mean that this assumption (and the slope of 1.04) is associated with significant uncertainty. The correlation coefficient of 0.8 indicates a reasonable quality of fit. This is also seen (Fig. S4c in the Supplement) in a time series showing the difference between $k^{{\mathrm{NO}}_{\mathrm{3}}}$ and Σk_i[VOC]_i. The scatter in both plots is likely to be caused by changes in the monoterpene composition or the different location of the instruments' inlets. The true uncertainty associated with the slope is expected to be close to 30 %, suggesting that the very good agreement may be partially fortuitous. Nonetheless, we can conclude that the vast majority of the reactivity measured directly results from NO₃+ monoterpene interactions.

Figure 6 Plot of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ versus Σk_i[VOC]_i. The red solid line represents an orthogonal distance regression (ODR) with a slope of 1.04 and an intercept of $\mathrm{6.6}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹. For the sake of better clarity, error bars were omitted.

3.3 Fractional contribution of VOCs to NO₃ losses throughout the diel cycle

The dominant direct gas-phase loss of NO₃ occurs via photolysis ($J_{{\mathrm{NO}}_{\mathrm{3}}}$), reaction with NO (k₇[NO]), and reaction with VOCs ($k^{{\mathrm{NO}}_{\mathrm{3}}}$ ). Neglecting depositional losses of NO₃, the fractional contribution F of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ to the overall NO₃ loss rate constant, $L_{{\mathrm{NO}}_{\mathrm{3}}}$, is thus given by the following:

$$\begin{array}{}\text{(1)}& F={\displaystyle \frac{k^{{\mathrm{NO}}_{\mathrm{3}}}}{L_{{\mathrm{NO}}_{\mathrm{3}}}}}={\displaystyle \frac{k^{{\mathrm{NO}}_{\mathrm{3}}}}{k^{{\mathrm{NO}}_{\mathrm{3}}}+J_{{\mathrm{NO}}_{\mathrm{3}}}+k_{\mathrm{7}}\left[\mathrm{NO}\right]}}.\end{array}$$

Based on measured $k^{{\mathrm{NO}}_{\mathrm{3}}}$, [NO], and $J_{{\mathrm{NO}}_{\mathrm{3}}}$ (calculated from actinic flux measurements), we calculated the time-dependent values of each loss process throughout the campaign. Losses due to reaction with RO₂ radicals on this site are expected to be insignificant. Taking the average maximum RO_x mixing ratio of 20 pptv, as measured by Handisides (2001), and the corresponding rate coefficient (IUPAC, 2022) results in an NO₃ loss rate of 0.001 s⁻¹, which is insignificant compared to the other loss rates mentioned above. The resulting mean diel cycle of F is depicted in Fig. 7.

Figure 7 Mean fractional contribution (F) of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ (i.e. VOC contribution) to the overall NO₃ loss rate over the diel cycle. The grey shaded area represents the standard deviation (1σ) of the mean values. Orange shaded area indicates daytime. The pie chart shows the mean fractional contribution to the NO₃ loss in the reaction with NO, photolysis, and the reaction with VOCs during the daytime.

During the daytime, photolysis and the reaction with NO were the dominant loss processes for NO₃, as expected. The fractional contribution of VOC-induced losses is low at noon (∼9 %) but increases to ∼30 % in the afternoon at 18:00 UTC due to the decrease in NO levels between 08:00 and 16:00 UTC (Fig. 3f) and decreasing actinic flux and the associated slowing of both NO₃ and NO₂ photolysis to NO beginning at 16:00 UTC. The NO_x levels at this site are such that, between sunrise and sunset, reaction with NO is on average ( ± 1σ) the dominant loss process for NO₃ (53 % ± 20 %), followed by photolysis (31 % ± 19 %) and the reaction with VOCs (16 % ± 15 %). This non-negligible contribution of VOCs to the daytime losses of NO₃ is in broad agreement with field measurements in a boreal forest in Finland and on top of the Hohenpeißenberg mountain, where values of ∼20 % were reported (J. Liebmann et al., 2018; J. M. Liebmann et al., 2018). Assuming noon mixing ratios of 0.1 pptv NO₃ (see Fig. 9), 42 ppbv O₃ (see Fig. 3), and 10⁶ molec. cm⁻³ OH (Lelieveld et al., 2016) and taking evaluated rate coefficients (IUPAC, 2022), the lifetime of limonene towards these three oxidants would be $\mathrm{2.71}\times {\mathrm{10}}^{-\mathrm{5}}$, $\mathrm{2.08}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹ and $\mathrm{1.65}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹. NO₃ would thus contribute ca. 7 % to the daytime oxidation of limonene. This underlines that NO₃, often considered to be important only at night, also contributes to the oxidation of BVOC during the day and thus potentially to the formation of organic nitrates (in competition with OH- and O₃-initiated oxidation) throughout the diel cycle, for example (Liebmann et al., 2019; Foulds et al., 2021).

At nighttime, in the absence of actinic radiation (to convert NO₂ to NO) and less local anthropogenic NO emissions due to reduced traffic, NO levels are generally suppressed by reaction with O₃. Figure 7 reveals that 50 %–60 % of NO₃ was lost via reaction with VOCs at nighttime during TO2021, the remaining fraction reacting with NO (Reaction R7). The contribution of NO to the nighttime NO₃ reactivity is larger than previously observed with the $k^{{\mathrm{NO}}_{\mathrm{3}}}$-FT-CRDS instrument, where reaction with VOCs was identified as the only significant loss process (J. Liebmann et al., 2018; J. M Liebmann et al., 2018). A significant average contribution from NO is readily understood when one considers the large rate coefficient for reaction with NO₃ ($k_{\mathrm{7}}=\mathrm{1.8}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ at 298 K; IUPAC, 2022) and NO mixing ratios well above the detection limit on many nights.

3.4 Effect of nighttime NO on NO_x budget

Figure 8 reveals a large night-to-night variability in the NO mixing ratio, with minimum values close to the detection limit and maxima >80 pptv in the presence of several tens of ppbv of O₃. The presence of NO and O₃ at the mixing ratios observed implies a significant source of NO₂. In the following, we derive the NO emission and NO₂ deposition rates required to explain the observed NO, NO₂, and O₃ mixing ratios. In the absence of local anthropogenic sources, soil emissions constitute the most likely source of NO at this site. Assuming that a reaction with O₃ represents the only NO loss process and that the stationary state as in Eq. (2) is achieved (a valid assumption as the lifetime of NO is only a few minutes in the presence of 20–40 ppbv of O₃), NO emission rates (E_NO) of 0.18 to 0.47 pptv s⁻¹ are necessary to reproduce the observed nighttime NO mixing ratio within a surface layer of 10 m height.

$$\begin{array}{}\text{(2)}& E_{\mathrm{NO}}=\left[\mathrm{NO}\right]\cdot k_{\mathrm{1}}\left[{\mathrm{O}}_{\mathrm{3}}\right].\end{array}$$

In the absence of measurements of NO soil emission fluxes at the site, and recognizing that these are highly dependent on temperature, season, soil humidity, and degree of fertilization (Pilegaard, 2013), we take an annual mean NO emission flux of 1 kg ha⁻¹ yr⁻¹ for temperate, uncultivated grassland (Ludwig et al., 2001) to derive (assuming the same layer height of 10 m) an NO emission rate of 0.27 pptv s⁻¹, which lies within the range quoted above. Note, however, that this estimation assumes a mixed layer. Assuming a linear gradient in NO mixing ratios with height, the NO emission rates at ground level would be a factor of 2 higher (Shepson et al., 1992; Fischer et al., 2019). As the summit of the Kleiner Feldberg is covered with blueberry bushes and surrounded by coniferous forest and that soils impacted from blueberry plants or spruce can support higher NO net fluxes than grass-covered soils (Bargsten et al., 2010), significant NO soil emissions at the summit of the Kleiner Feldberg appear to be plausible. Figure 8 also reveals that the highest levels of NO observed at 10 m height occur when O₃ values are lowest. Anti-correlated NO and O₃ mixing ratios are often observed when plumes of freshly emitted NO is mixed into aged air masses containing O₃ and is a result of Reaction (R1) which converts NO to NO₂. For our observations at 10 m height, chemistry (temperature-dependent kinetics), boundary layer dynamics (extent of mixing/decoupling of surface layer and NBL) and plant physiology (emission rates of NO) may all contribute to the extent to which NO and O₃ react. As the large night-to-night variability in the NO mixing ratios cannot be explained by temperature-dependent changes in the rate coefficient k₁ or in the emission rate of NO, we conclude that boundary layer effects dominate and that the height of the surface layer and the degree to which NO is entrained from the surface layer into the NBL are the main controlling factors. We consider the following two limiting cases: (1) When the top of the nocturnal surface layer is above the inlet, and mixing is sufficient to homogenize the air within the first 10 m a.g.l., NO originating from the soil can react with O₃ via Reaction (R1) (Aneja et al., 2000). This would correspond to observations during Type 1 nights. (2) When the surface layer is less than 10 m deep and is decoupled from the NBL, soil-emitted NO is not sampled by the inlet (ca. 10 m a.g.l.), and the measured NO mixing ratios are at the instrument's LOD. In this case, levels of O₃ in the NBL remain high, as, e.g., observed around 21 July. In reality, trace-gas gradients within the lowest layers will control the extent of mixing, and case (1) will only operate when high wind speeds induce turbulent mixing close to the surface. We conclude that the variability in nighttime NO and the anti-correlation with O₃ (see Fig. S5a) reflect rapid changes in boundary layer dynamics and vertical mixing within the lowest layers. Similarly, high variability in NO₃ mixing ratios has been attributed to a related phenomenon (Crowley et al., 2011). We note that if the timescales over which boundary layer dynamic change is less than the lifetime of NO, our steady-state assumption breaks down. Nonetheless, the presence of up to 80 pptv of NO at nighttime in the presence of 20–40 ppbv of O₃ implies significant production of NO₂.

Figure 8 Nighttime NO mixing ratios (colour-coded by O₃ mixing ratios) during TO2021. The x-axis ticks represent 00:00 UTC.

We examined the nighttime generation of NO₂ using box model calculations (Facsimile/Chemcat; Curtis and Sweetenham, 1987) employing Reactions (R1) to (R4) and (R7) with IUPAC-recommended, temperature-dependent rate coefficients (Table S5 in the Supplement) and constrained by measurements of NO, O₃, ambient temperature, and pressure. Known loss processes for NO₂ at night are the slow reaction with O₃ (to form NO₃) and with NO₃ to form N₂O₅ (Reaction R2–R4) and deposition to surfaces (e.g. foiliage and soil). Note that this simulation considers Reaction (R1) as being the only NO₂ source and that it is only valid if chemistry and transport happen on a similar timescale. Heterogeneous losses of NO₃ and N₂O₅ were not considered since these were found to be insignificant compared to gas-phase losses (of NO₃) during previous campaigns on the KF (see below; Table 1). Furthermore, note that vertical gradients are not considered in this simulation, which aims to provide a ballpark value for the NO₂ loss term needed to explain its mixing ratios in the presence of a known production rate.

Figure 9 plots the measured nighttime NO₂ mixing ratios (black symbols) together with the model output using the NO₂ deposition velocity (vd) ${}_{{\mathrm{NO}}_{\mathrm{2}}}=\mathrm{0.015}$ cm s⁻¹ (which is based on a mean nighttime NO₂ deposition for foliar surfaces; Delaria et al., 2018) and a value that is a factor of 10 larger (vd${}_{{\mathrm{NO}}_{\mathrm{2}}}=\mathrm{0.15}$ cm s⁻¹) in both cases, assuming a surface layer height of 10 m to derive loss rate constants of $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{5}}$ and $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹, respectively. Clearly, the larger deposition velocity is necessary to roughly align measured and simulated NO₂ mixing ratios. Such large NO₂ deposition velocities have previously been evoked in order to bring observed NO₂ levels and NO emission rates into agreement (Jacob and Wofsy, 1990), and our average, nighttime deposition velocity of 0.15 cm s⁻¹ is comparable to values of 0.1–0.57 cm s⁻¹ determined in boreal coniferous forests (Rondon et al., 1993) at night and 0.096 cm s⁻¹ obtained in a temperate coniferous forest (Breuninger et al., 2013).

Figure 9 Time series of measured nighttime NO₂ mixing ratios during TO2021 (black squares) and modelled NO₂ mixing ratios using deposition loss constants of $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ (model 1; red circles) and $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹ (model 2; blue triangles).

The interaction of NO₂ with foliar surfaces, which can serve as both a source and sink of NO₂, is complex (Breuninger et al., 2013; Delaria et al., 2018), and a scenario in which the high (but variable) nighttime NO mixing ratios result from soil emissions while NO₂ is simultaneously deposited on foliar surfaces is conceivable. Given that the stratification of the lowermost atmosphere at TO2021 was only examined on 1 night, and considering the likely variability in NO emission rates and NO₂ deposition velocities (Ludwig et al., 2001; Ganzeveld et al., 2002), our interpretation of the nighttime NO and NO₂ data remains speculative. Considering the lack of correlation between wind direction and abundance of nighttime NO (Fig. S5b), an alternative point source of NO (e.g. an NO bottle, or exhaust line) seems unlikely. Interferences by other trace gases or reasons for bias of the CLD instrument could not be identified as causes for the high nocturnal levels of NO.

3.5 NO₃ mixing ratios

During the TO2021 intensive, ambient NO₃ mixing ratios were not monitored. However, as both the total loss term $L_{{\mathrm{NO}}_{\mathrm{3}}}$ and the production term $\left(P_{{\mathrm{NO}}_{\mathrm{3}}}=k_{\mathrm{2}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\right)$ are known, we can derive NO₃ mixing ratios by assuming that NO₃ is in the steady state, i.e. that loss and production are balanced and that the derivative of the NO₃ mixing ratios is independent of time. Steady-state calculations of NO₃ lifetimes or NO₃ mixing ratios have been carried out in numerous studies (Platt et al., 1984; Geyer and Platt, 2002; Brown et al., 2011; Crowley et al., 2011; J. Liebmann et al., 2018; J. M. Liebmann et al., 2018) and have shown to be valid when NO₃ reactivities are high enough and the chemical equilibrium to N₂O₅ (Reactions R3 and R4) is not perturbed by sudden changes in NO₂ mixing ratios (Brown et al., 2003a; Dewald et al., 2020). Steady-state NO₃ mixing ratios can be calculated with Eq. (3), as follows:

$$\begin{array}{}\text{(3)}& {\left[{\mathrm{NO}}_{\mathrm{3}}\right]}_{\mathrm{ss}}={\displaystyle \frac{P_{{\mathrm{NO}}_{\mathrm{3}}}}{L_{{\mathrm{NO}}_{\mathrm{3}}}}}={\displaystyle \frac{k_{\mathrm{2}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]}{k^{{\mathrm{NO}}_{\mathrm{3}}}+J_{{\mathrm{NO}}_{\mathrm{3}}}+k_{\mathrm{7}}\left[\mathrm{NO}\right]}},\end{array}$$

which neglects both direct and indirect heterogeneous loss of NO₃ (Reactions R8 and R9). Previous estimates of the NO₃ loss by aerosol uptake on the Kleiner Feldberg returned values of ≈ 0.001 s⁻¹ or lower (Crowley et al., 2010; Phillips et al., 2016; Sobanski et al., 2016) and are consequently insignificant compared to the average nighttime overall NO₃ loss rate of ≈ 0.03 s⁻¹.

Figure 10 displays a time series of the calculated overall NO₃ loss constant, production rate, and steady-state mixing ratios for TO2021. Nighttime NO₃ losses vary typically between <0.006 and 0.03 s⁻¹, while the daytime losses were as large as 0.3 s⁻¹. The NO₃ production rate was, on average, close to ∼0.02 pptv s⁻¹ at nighttime, increasing to 0.1 pptv s⁻¹ during the day when NO₂ and/or O₃ mixing ratios were large. NO₃ mixing ratios thus calculated are lower than about 6 pptv for all nights (with one exception of 12 pptv on the 10 July) and well below 2 pptv for most of the nights.

Figure 10 (a) NO₃ production (left) and loss rates (right) during TO2021. (b) Steady-state NO₃ mixing ratios. Ticks represent 00:00 UTC. Grey shaded areas denote nighttime.

3.6 Comparison with previous NO₃ measurements at the Kleiner Feldberg

NO₃ measurements with which to compare the present data set have been recorded at the Kleiner Feldberg during campaigns in 2008, 2011, 2012, and 2015, for which key details (including names and acronyms) are summarized in Table 1.

Table 1 Nighttime NO₃ and NO mixing ratios, median NO₃ production rates, and median nighttime NO₃ loss rates at the top of the Kleiner Feldberg.

Notes: No. of nights is the number of nights with measurements, and the number in parentheses represents the number of nights where either the NO₃ mixing ratio or the directly measured value of $k^{{\mathrm{NO}}_{\mathrm{3}}}$ was below the LOD. Direct (k₈) and indirect (k₉) loss rates of NO₃ by the heterogeneous uptake of NO₃ and N₂O₅ were calculated only for TO2008 and PARADE. ^a is directly measured, ^b is steady-state calculation, ^c is directly measured with VOC contribution only, ^d is directly measured for three nights, where no NO measurements were available (Liebmann et al., 2017). TO2008 is a mini (unnamed) campaign with only NO₃, NO, O₃, and NO₂ measurements. PARADE is for PArticles and RAdicals and refers to Diel observations of the impact of urban and biogenic Emissions. INUIT is the Ice NUclei research UnIT. NOTOMO is the NOcturnal chemistry at the Taunus Observatory, which offers insights into Mechanisms and Oxidation.

The first measurements of NO₃ (and N₂O₅) at the Kleiner Feldberg were performed on 6 nights in May 2008 (Crowley et al., 2010; this data set is referred to as TO2008), on 21 nights in July 2011 (PARADE campaign; Sobanski et al., 2016), and on 16 nights in August 2012 (INUIT campaign) and in September 2015 during the NOTOMO campaign (Liebmann et al., 2017; Sobanski et al., 2017). All previous NO₃ data sets, except for INUIT, have been published. The time series of the NO₃, NO₂, O₃ mixing ratios (and resulting $P_{{\mathrm{NO}}_{\mathrm{3}}}$ and $L_{{\mathrm{NO}}_{\mathrm{3}}}$ according to Eq. 3) from each of the campaigns used for this analysis are reproduced in the Supplement (Figs. S6–S9) together with key features of the instruments used (Table S1).

The presence of nearby industrial centres imparts a strong wind direction dependence on the composition of the air (and especially NO_x) at the Kleiner Feldberg, with densely populated cities (and thus anthropogenic sources of NO_x) located in the SE and SW sectors. An overview of the prevailing wind directions and NO₂ mixing ratios during each campaign are summarized in Fig. 11. The lowest average NO₂ mixing ratios were encountered during TO2008 (air arriving mainly from the east) and TO2021, which had a large contribution of air masses arriving from the north and west but almost none from the Frankfurt area (SE-SSE). TO2021 is the only campaign with a significant contribution of air masses arriving from the clean northern sector, and the generally lower NO_x levels during TO2021 may also have been a result of changes in vehicle usage in the region as a higher fraction of locally employed people worked from home as a result of the COVID-19 pandemic (Reifenberg et al., 2021).

Figure 11 Wind roses indicating the dependence of NO₂ mixing ratio on the wind direction during TO2008, PARADE, INUIT, NOTOMO, and TO2021. Wind directions were provided by HLNUG for TO2008 and NOTOMO, by a weather station for PARADE and INUIT (Drewnick et al., 2012), and by the German Meteorological Service (DWD) for TO2021.

Figure 12 indicates that, in comparison to the previous summer campaigns (PARADE, INUIT, and NOTOMO) the temperatures were lower during TO2021, with the maximum value of 22 ^∘C being ∼10 ^∘C lower than the maximum value during NOTOMO. TO2021 and PARADE had the highest incidence of very humid days, with a median RH of >80 % for TO2021 and >75 % for PARADE, while for TO2008 the median relative humidity (∼51 %) was the lowest.

Figure 12 Distributions of (a) temperature and (b) relative humidity during five campaigns at the Kleiner Feldberg between 2008 and 2021. Boxes represent the range between the first and third quartiles, and whiskers denote the full range of values.

For comparison of the nighttime NO₃ mixing ratios, periods of daytime–nighttime transitions (when NO₃ mixing ratios strongly change at sunrise or sunset) were excluded. The NO₃ mixing ratios (lower panel), loss rates (middle panel), and production rates (upper panel) for each campaign are depicted in Fig. 13 as a box-and-whisker plot. Note that nights on which the NO₃ mixing ratios were >0 but below the instrument's LOD, were taken into account, whereas for the calculation of $L_{{\mathrm{NO}}_{\mathrm{3}}}$ in the campaigns prior to TO2021, reactivities derived from NO₃ mixing ratios below the LOD (i.e. <1.5 pptv) were excluded from the analysis so that $L_{{\mathrm{NO}}_{\mathrm{3}}}$ is not biased by values associated with high uncertainties.

Figure 13 NO₃ production rates (a), loss rates (b), and mixing ratios (c) measured during five campaigns on the summit of Kleiner Feldberg between 2008 and 2021. Boxes represent the range between the first and third quartiles, and whiskers denote the full range of values. The red line represents the median of directly measured $k^{{\mathrm{NO}}_{\mathrm{3}}}$ during TO2021 at nighttime.

Figure 13a shows that, during PARADE, INUIT, and NOTOMO, the nighttime NO₃ production rates were similar in terms of both median values (∼0.05 pptv s⁻¹) and range. Throughout these three campaigns, high production rates (above 0.3 pptv s⁻¹) were occasionally observed, which for PARADE (Sobanski et al., 2016) were linked to winds originating from urban regions. Figure 13a also reveals that the median nighttime NO₃ production rates during PARADE, INUIT, and NOTOMO were higher than during TO2008 and TO2021 (0.033 and 0.025 pptv s⁻¹), which was driven by the lower NO₂ mixing ratios in TO2008 and TO2021 for which air from the cleaner easterly and northerly sectors was encountered more frequently. Campaign-averaged diel cycles of O₃ in the Supplement (Fig. S10) indicate that O₃ during TO2008 and TO2021 was not substantially lower (it was even higher in the case of TO2008) than during PARADE, INUIT, and NOTOMO.

Figure 13b shows clearly that, with a median value of 0.028 s⁻¹, the nighttime NO₃ loss rates ($L_{{\mathrm{NO}}_{\mathrm{3}}}$) during TO2021 were significantly higher than for all other campaigns, which were 0.0075 s⁻¹ for NOTOMO, 0.0045 s⁻¹ for PARADE, 0.0037 s⁻¹ for INUIT, and 0.0022 s⁻¹ for TO2008. A partial explanation for the greater NO₃ loss term during TO2021 is found in the nighttime NO mixing ratios, which were significantly larger than those measured in, e.g., TO2008 or PARADE. The effect of removing the contribution of NO reaction to $L_{{\mathrm{NO}}_{\mathrm{3}}}$ during PARADE (and TO2008) is minimal, as NO was close to or below the LOD (4–10 pptv) on most nights (Crowley et al., 2010; Sobanski et al., 2016), which is confirmed by the corresponding campaign-averaged diel cycles of NO mixing ratios (Fig. S11). In contrast, the subtraction of the contribution to NO₃ reactivity of the high nighttime levels of NO observed during TO2021 would reduce $L_{{\mathrm{NO}}_{\mathrm{3}}}$ to ∼0.011 s⁻¹ (red horizontal line in Fig. 13b), which is more comparable to that observed during, e.g., NOTOMO and PARADE. As shown in Table 1, nighttime NO mixing during TO2008 and PARADE usually did not exceed 30 pptv. Several parameters impact the NO emission rate of soils (Pilegaard, 2013), and since TO2021 was exceptionally wet compared to previous campaigns, a greater soil water content may have favoured high NO emissions in TO2021.

We note that, in general, the comparison of NO₃ loss rates derived via the steady-state method and direct reactivity may be complicated by the fact that the steady-state method only works when NO₃ is above the detection limit (often a result of low reactivity), whereas the direct measurement of NO₃ losses performs best when reactivities are high. However, Σk_i[VOC]_i suggests that $L_{{\mathrm{NO}}_{\mathrm{3}}}$ was never below 0.002 s⁻¹ on Type 2 nights. As shown in the Supplement, setting values of $k^{{\mathrm{NO}}_{\mathrm{3}}}\mathit{<}\mathrm{0.006}$ s⁻¹ to 0.002 s⁻¹ would only occasionally lead to [NO₃]_ss>10 pptv (Fig. S12a), and thus only have a small impact on the distribution of NO₃ mixing ratios (Fig. S12b), so that this bias cannot be fully responsible for the observed difference.

Nonetheless, Fig. 13a and b indicate that TO2021 was exceptional in that $P_{{\mathrm{NO}}_{\mathrm{3}}}$ was the lowest of all campaigns at the Kleiner Feldberg while $L_{{\mathrm{NO}}_{\mathrm{3}}}$ was the highest, which results in a calculated median NO₃ mixing ratio of just 0.7 pptv. This contrasts greatly with median NO₃ mixing ratios of 15, 10, 11, and 4 pptv observed during TO2008, PARADE, INUIT, and NOTOMO (Fig. 13c) on the Kleiner Feldberg.

As alluded to above, this difference is partially caused by unusually high nighttime NO levels but also results from the low NO₃ production rate during TO2021. During PARADE, INUIT, and NOTOMO, NO₃ mixing ratios above 100 pptv were measured and linked to nights with exceptionally long NO₃ lifetimes. For PARADE, this was suggested to be a result of sampling from above the surface layer, where NO₃ lifetimes can be large owing to the decoupling from ground-level emissions (Brown et al., 2003b; Sobanski et al., 2016). While there is evidence for a similar situation for TO2021 on 21 July (Fig. 4), in the absence of vertically resolved meteorological data on the other nights, it is not clear whether purely meteorological effects are responsible for the observed low reactivities on 14 nights or whether reduced emission rates of reactive trace gases additionally play a role. We are presently developing a drone-borne NO₃ instrument to provide vertical gradients in NO₃ (and T and RH) in order to help resolve this issue.

4 Summary and conclusions

The fate of the NO₃ radical at the summit of the Kleiner Feldberg during the TO2021 intensive in July 2021 was assessed with the help of direct NO₃ reactivity and VOC measurements. Directly measured NO₃ reactivities towards VOCs ($k^{{\mathrm{NO}}_{\mathrm{3}}}$) were on average ∼0.011 s⁻¹ at night and as large as ∼0.04 s⁻¹ during the day. NO₃ reactivities derived from VOC measurements showed an excellent agreement with $k^{{\mathrm{NO}}_{\mathrm{3}}}$ throughout the diel cycle, with VOC-induced NO₃ losses by monoterpenes dominating with a contribution of >80 %. Sesquiterpenes and isoprene contributed 9 % ± 5 % and 7 % ± 4 %, respectively.

During the daytime, NO removed on average 53 % ± 20 % of the NO₃, and photolysis and reaction with VOCs contributed ∼31 % ± 19 % and ∼16 % ± 15 %, respectively. The daytime contribution of VOC-induced reactivity was highly variable and ranged from ca. 10 % at noon to 30 % in the afternoon, implying that NO₃ can contribute significantly, e.g. to alkyl nitrate formation during daytime.

$k^{{\mathrm{NO}}_{\mathrm{3}}}$ was mostly below the LOD of 0.006 s⁻¹ on 14 of the 34 nights. On 1 night, for which a vertical temperature and RH gradient were measured, the low NO₃ reactivity was associated with reduced vertical mixing and the decoupling of a shallow surface layer from the layer above in which the trace gas inlet was situated.

In the absence of direct measurements, NO₃ mixing ratios during TO2021 were calculated from the total loss rate constant (VOCs, photolysis, and NO) and the NO₃ production rate to enable comparison with directly measured NO₃ mixing ratios during four previous campaigns between 2008 and 2015 at the Kleiner Feldberg. For TO2021, NO₃ loss rates were about a factor of 3–5 higher than during previous campaigns, while NO₃ production rates were the lowest. Consequently, the calculated steady-state mixing ratios of NO₃ are much lower than those directly measured during TO2008, PARADE, INUIT, and NOTOMO. The exceptionally high nighttime NO₃ loss rates during TO2021 are partially related to the presence of several tens of pptv of NO, so that VOC-induced losses were 50 %–60 % of the overall loss term. This is in stark contrast to previous observations in forested environments, where reactions with VOCs were the only relevant nighttime loss path of NO₃. The observation of NO at levels of 20–80 pptv at nighttime in the presence of 30–40 ppbv of O₃ imply large rates of NO₂ formation. Constrained box model calculations suggest that rapid losses of NO₂ via, e.g., deposition would be necessary in order to reproduce the observed nighttime NO₂ mixing ratios. In order to confirm this hypothesis, measurements of NO emission and NO₂ deposition rates on the Kleiner Feldberg under similar meteorological conditions are necessary.

Overall, the intercomparison of the NO₃ mixing ratios and NO₃ reactivity revealed high variability in the data obtained over a long period on the same site and emphasizes that not only chemical effects but also boundary layer dynamics and plant physiological processes may have a great impact on observations.