2.1 NO₃ reactivity measurements

The NO₃ reactivity instrument was operated in a laboratory located on the third floor of the MOHp station building at the Hohenpeissenberg. Air samples were drawn at a flow rate of 2900 cm³ (STP) min⁻¹ through a 2 µm membrane filter (Pall Teflon) and 4 m of PFA tubing (6.35 mm OD) from the centre of the bypass flow (see above), resulting in a 7.5 s residence time for the transport of air from the sampling point. During night-time (≈ 19:00–03:50 UTC) ambient air samples were drawn through a heated glass flask (35 ^∘C, residence time 20 s) to destroy ambient N₂O₅ and NO₃, which would potentially interfere with the reactivity measurements. Operational details of the instrument were recently described by Liebmann et al. (2017). NO₃ radicals were generated by mixing NO₂ and O₃ at elevated pressure (1.5 bar, ≈5 min reaction time) and passing the mixture through an oven at ≈ 100 ^∘C to convert all N₂O₅ to NO₃ (Reactions R2–R5). The effluent from the oven was mixed with either zero-air or ambient air in a flow tube with the temperature set to 21 ^∘C to yield typical (initial) NO₃ mixing ratios of 40–60 pptv.

After a fixed reaction time, the remaining NO₃ was detected by cavity ring-down spectroscopy (CRDS) at 662 nm. The lower pressure at the top of the Hohenpeissenberg station (903±8 hPa) meant that the reaction time was reduced from 10.5 s as previously reported (Liebmann et al., 2017) to 9.5 s. The measurement cycle was typically 400 s for synthetic air and 1200 s for ambient air, with intermittent signal zeroing (every ≈100 s) by addition of NO. The fractional loss of NO₃ in ambient air compared to zero-air was converted to a reactivity via the numerical simulation of a simple reaction scheme (Liebmann et al., 2017) using measured amounts of NO, NO₂, and O₃. The parameter obtained, $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$, is an NO₃ loss rate constant from which contributions by NO and NO₂ have been removed and thus refers to reactive loss to organic trace gases (OTGs) only. Throughout the paper, NO₃ reactivity and $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ are equivalent terms, with units of s⁻¹. The upper measurement limit to $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was 45 s⁻¹, achieved by automated, dynamic dilution of the air sample. The lower limit was 0.005 s⁻¹, defined by the stability of the NO₃ source. Online calibration of the reactivity using an NO standard was performed every ≈2 h for 10 min. The uncertainty of the measurement was between 0.015 and 0.205 s⁻¹, depending mainly on dilution accuracy, NO levels, and the stability of the NO₃ source as described by Liebmann et al. (2017). Since its first description in Liebmann et al. (2017), the instrument has been extended with a further cavity to measure mixing ratios of NO₂ (see below).

2.2 NO₂, NO, and O₃ measurements

Since its first deployment, the NO₃ reactivity instrument described by Liebmann et al. (2017, 2018) has been extended with a further cavity to measure NO₂. This is described here for the first time and thus in detail. The CRDS measurement of NO₂ uses a 2500 Hz, square-wave-modulated, 40 mW laser diode located in a Thorlabs LDM21 housing and thermally stabilized at 36 ^∘C using a Thorlabs ITC-510 Laser Diode Combi Controller to produce light at 405 nm (0.5 nm full-width at half-maximum). The laser-diode emission is first directed through an optical isolator (Thorlabs IO-3D-405-PBS), focused by a lens (Thorlabs C340TMD-A) into the optical fibre (0.22 NA, 50 µm core, 400–2400 nm), and then collimated (Thorlabs FiberPort collimator PAF-X-7-A) to a beam diameter of about 6 mm before entering the cavity. Part of the laser emission was directed to an Ocean Optics spectrograph to continuously measure the laser emission spectrum.

The NO₂ cavity (Teflon-coated glass; DuPont, FEP, TE 9568, length 70 cm, volume 79 cm³) was operated at 30 ^∘C at a flow rate of 3000 cm³ (STP) min⁻¹, resulting in a residence time of approximately 1 s. To remove particles, air was drawn through a 2 µm membrane filter (Pall Teflon) from the centre of the same high-flow bypass used for the NO₃ reactivity measurements. Light exiting the cavities through the rear mirror was detected by a photomultiplier (Hamamatsu E717-500), which was screened by a 405 nm interference filter. The pre-amplified PMT signal was digitized and averaged with a 10 MHz, 12 bit USB scope (Picoscope 3424), which was triggered at the laser-modulation frequency of 2500 Hz.

The ring-down constant in the absence of NO₂ was obtained by adding zero-air every 30 points of measurement for approximately 15 s. The L ∕ d ratio (the ratio of the distance between the cavity mirrors, L, and the length of the cavity that is filled by absorber, d) was determined as described previously (Schuster et al., 2009; Crowley et al., 2010) and was 1.00±0.03. Inverse decay constants in dry zero-air at 660 Torr were usually between 28 and 31 µs, indicating optical path lengths of ≈8–9 km. The measurement precision (6 s integration) was circa 150 pptv. The cavity was not pressure stabilized, leading to a pressure difference of circa 2.5 Torr when switching from ambient air to zero measurements. The data were corrected for the change in Rayleigh scattering resulting from the pressure difference (typically 120 pptv) and also different relative humidities (typically 60 to 100 pptv) when switching from ambient to zero-air measurement as described by Thieser et al. (2016). The laser spectrum was measured every hour and used to calculate an effective cross section ($\approx \mathrm{6}\times {\mathrm{10}}^{-\mathrm{19}}$ cm² molecule⁻¹) using a literature absorption spectrum (Voigt et al., 2002). The overall uncertainty of the measurement is mainly determined by the uncertainty in the cross section (6 %). Other contributions are from NO₂ formation (from reaction of NO with O₃ in the inlet lines, ≈0.5 %), the correction for humidity and pressure differences (5 %), and uncertainty in the L ∕ d ratio (2 %), giving an estimated uncertainty of 9 %. The detection limit of the instrument can be estimated from the variability in the zeros and was usually around 150 pptv.

NO₂ measurements were made from 20 July to 4 August with breaks from 27 July to 2 August and from 4 to 6 August due to instrumental problems. NO₂ mixing ratios were corrected for its formation (Reaction R1) during transport from the rooftop inlet to the cavity (≈7.5 s).

Two commercially available instruments operated permanently at the site also provided measurements of NO₂ and NO. These were a cavity phase-shift (CAPS) instrument for NO₂ measurement and a chemiluminescence device (CLD) for NO₂ and NO. The CAPS (Aerodyne ambient monitor version 2012) had a detection limit of 315 pptv (3σ in 1 min integration time) and an uncertainty of 10 % (1 min integration time). The uncertainty of the CAPS increased during the period of the campaign due to increased noise, probably caused by an undetected leakage or mechanical instability between the lens and the mirror of the measurement cell.

The CLD (ECO PHYSICS, model AL 770 pptv) uses chemiluminescence from the reaction of NO with ozone in combination with a blue-light converter to convert NO₂ to NO. The instrument was routinely calibrated once a week (10 ppmv ± 5 % NO in N₂; Riessner, Germany). Deviations between two calibrations are typically below 3 %. Detection limits during the intensive were 11 pptv for NO, 16 pptv for NO₂ (3σ in 1 min integration time), and median uncertainties are 27 pptv (7 %) for NO and 70 pptv (10 %) for NO₂ (2σ at 1 ppbv in 1 min integration time). Corrections were applied to take into account NO loss (≈5 %–30 %) and NO₂ formation (≈0 %–12 %, typically ≈2 %) due to further reactions involving ozone in the inlet tubing.

A comparison of the three NO₂ measurement instruments is given in Fig. S1 of the Supplement, which plots the NO₂ mixing ratios (averaged over 60 s) of the CLD and CAPS instruments versus the CRDS. A least-squares fit (considering errors in both parameters) to the plot of NO₂ (CLD) versus NO₂ (CRDS) has a slope of 0.94±0.25 and an intercept of 0.00±0.04. For the plot of NO₂ (CAPS) versus NO₂ (CRDS) comparison we derive a slope of 0.95±0.02 and an intercept of 0.00±0.02. Within combined uncertainty, the NO₂ measurements are thus in agreement. The NO₂ mixing ratios used as input to calculate the NO₃ reactivity were taken from the CRDS instrument, with data gaps filled by CAPS measurements.

Ozone was monitored with a UV absorption instrument (Thermo Environmental Instruments Inc., model TECO 49C), which is calibrated at regular intervals with a transfer standard (TECO 49PS). The uncertainty in the ozone mixing ratio is 1.2 ppbv or 2 % (2σ in 1 h).

2.3 NO₃ measurements

For the measurement of ambient NO₃, a 10 m length of PFA tubing (3∕8 inch outer diameter) was installed on the top of the building circa 10 cm from the VOC inlet. A 2 µm pore PTFE filter (47 mm in diameter, replaced every hour) in a PFA filter holder was located at the end of the inlet. The tubing was connected to a bypass pump operated at 20 dm³ (STP) min⁻¹ to reduce the residence time. The sample flow through the cavity was increased to 8 dm³ (STP) min⁻¹ to reduce the NO₃ residence time within the cavity. NO₃ mixing ratios were recorded every 6 s (3600 ring-downs co-added) with zeroing by titration (NO addition) every 15 data points. The NO₃ transmission through the inlet (67±15 %), filter and filter holder (84±10 %), and cavity (88±10 %) was established post-campaign as described by Schuster et al. (2009) and used to correct the data. The overall uncertainty in the NO₃ measurements, including uncertainty in the absorption cross section, was circa 35 %.

2.4 OH reactivity measurements

OH reactivity measurements were conducted using a chemical ionization mass spectrometer (CIMS) in which OH radicals (generated by the photolysis of H₂O at 184.95 nm) are converted to H₂SO₄ (Berresheim et al., 2000; Schlosser et al., 2009). For the derivation of OH reactivity ($k_{\mathrm{total}}^{\mathrm{OH}}$), relative OH radical concentrations are measured at two fixed reaction times and a decay constant is derived assuming exponential behaviour. After correction for wall losses, as well as NO-induced HO_x recycling in the sample tube, ambient reactivities between 1 and 40 s⁻¹ are measurable. OH reactivity measurements were made every 20 min throughout the measurement period. Measurements were discontinued during periods of precipitation and when the pinhole to the mass spectrometer vacuum system was blocked by insects. The instrument performs best if NO mixing ratios are below 4 ppbv and reactivities do not exceed 15 s⁻¹; for the measurements reported here, the mean uncertainty in the OH reactivity was ±1.2 s⁻¹ (or 46 %). OH reactivity calibration was carried out before and after the measurement period, and the calibration factor was applied to the whole dataset. The determination of the OH wall loss rate from zero reactivity measurement (null measurement) using synthetic air cylinders was not reliable and therefore the zero was estimated using night-time measurements when sampling from above the boundary layer. Details are given in the Supplement.

2.5 VOC measurements

A gas chromatograph (GC-MS/FID model Agilent 6890 with 5975 B inert XL MSD) was used for the detection of C₅–C₁₃ NMHCs and BVOCs (Hoerger et al., 2015). In a custom-made pre-concentration unit, air was sampled at 30 ^∘C on a three-bed adsorption trap and, after a cryo-focussing step, injected onto the GC column (50 m BPX-5). Subsequently, signals were detected with a mass spectrometer (MS) running in parallel with a flame ionization detector (FID). The instrument measured i.a. isoprene and a wide variety of monoterpenes with uncertainties (2σ) from 6 % to 100 % depending on the compound.

For the detection of light NMHCs (C₂–C₈), a GC-FID system (GC-1, Varian 3600 CX, FID detector) described in detail by Plass-Dülmer et al. (2002) was used. In both systems, an ozone scrubber (impregnated filter with Na₂SO₃) was used and water was removed from the sample air either by hydrophobic adsorbents (C₅–C₁₃) or a cold trap (C₂–C₈) prior to the pre-concentration step. VOCs were sampled every hour for either 15 (C₂–C₈) or 20 min (C₅–C₁₃). During the rainy period from 24 July 12:00 UTC to 27 July 12:00 UTC, VOCs were only measured twice daily.

2.6 Particle measurements

The aerosol surface area was calculated using particle number size distributions obtained from a custom-built SMPS described in detail in Wiedensohler et al. (2012) and Birmili et al. (2016). Briefly, the instrument uses a Vienna-type DMA with a condensation particle counter (CPC model 3772, TSI Inc.) to measure particles between 10 and 800 nm. The sheath flow rate is 5 L min⁻¹ at an aerosol flow rate of 1 L min⁻¹; both are actively dried. The typical time resolution for one combined up-scan and down-scan is 5 min.

3.1 NO₃ reactivity

NO₃ reactivity was measured continuously during a 3-week intensive (20 July to 6 August 2017) with the exception of one night (2–3 August) when, using the same instrument, NO₃ mixing ratios were measured instead. The full dataset of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ is reproduced in Fig. S3 of the Supplement together with the corresponding 95 % uncertainty limits, which take into account drifts in the zero signal, the stability of the NO₃ source, uncertainty in the dilution factors, uncertainty of the NO and NO₂ mixing ratios, and the corresponding rate constants.

Figure 2(a) $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (black) and O₃ mixing ratios (red) from 29 to 30 July. From 23:50 UTC until sunrise the measurement site is located in the residual layer and free troposphere. (b) Temperature (T), relative humidity (RH), and wind direction (WD) during the same period.

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As described above, during daytime the short NO₃ lifetime normally results in levels that are under the detection limit of most instruments, precluding the estimation of NO₃ reactivity via stationary-state calculations based on its mixing ratio and production rate. In contrast, our direct measurement enables us to derive the NO₃ reactivity over the full diel cycle. During the intensive, the 10 min averaged values of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ ranged from below the detection limit (<0.005 s⁻¹) to values as high as 0.3 s⁻¹. Campaign-averaged values were low (≈0.01 s⁻¹) during night-time but a factor of 10 larger ≈0.1 s⁻¹ at 14:00 UTC (local 16:00) and more variable during daytime.

This observation is in stark contrast to the high relative night-time–daytime NO₃ reactivities we observed in a boreal forest (Liebmann et al., 2018) and is related to very different meteorological conditions at the two sites. In the boreal forest, the canopy-level NO₃ reactivity was controlled by the rate of emission of biogenic VOCs into a nocturnal boundary layer of varying height and stability. The elevated location of the Hohenpeissenberg observatory, located on a mountaintop above the surrounding countryside, favoured sampling from the residual layer and free troposphere at night-time. In the absence of turbulent exchange, the residual layer and free troposphere may become disconnected from the planetary boundary layer (PBL) and thus from ground-level emissions of reactive trace gases; the layers may thus contain low levels of biogenic trace gases as well as low(er) levels of NO₂ and higher levels of ozone (Aliwell and Jones, 1998; Allan et al., 2002; von Friedeburg et al., 2002; Stutz et al., 2004; Brown et al., 2007a, b; Brown and Stutz, 2012). NO₃ lifetimes as long as 1 h (using stationary-state analyses) have been reported for mountain sites when sampling air from above the nocturnal boundary layer (Brown et al., 2016; Sobanski et al., 2016).

During the Hohenpeissenberg intensive two distinct air mass types were encountered at night, whereby values of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ were either at (or below) the detection limit or well above it (referred to as “type 1” and “type 2”, respectively). Figure 2 displays a time series of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ over a single night (29–30 July) in which a switch from type 2 to type 1 was observed. From early evening until shortly before 12:00 UTC, NO₃ reactivity was variable with values between circa 0.02 and 0.03 s⁻¹. A sharp reduction in $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was then observed with values close to the detection limit until sunrise (04:00 UTC). The reduction in $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was accompanied by a drop in relative humidity (from 70 % to 60 %) and an increase in O₃ (46 to 52 ppbv), both clear indicators of sampling from the residual layer. At the same time, the wind speed increased and the temperature became more variable, indicating that the site was close to the inversion level. At first sunlight, turbulent mixing resulted in gradual connection of the boundary layer and overlying residual layer, leading to an increase in $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$. Upslope winds caused by heating of the mountainside may also have enhanced transport of air masses with high reactivity to the measurement site. Median diel profiles of NO₃ reactivity on type 1 (altogether five) and type 2 nights (altogether 10) are shown in Fig. 3. With the exception of the very low reactivity during type 1 nights, type 1 and type 2 have similar diel shapes and similar maximum reactivities.

Figure 3Median diel profile of the NO₃ reactivity. Type 1 nights (black line) show values around the detection limit during night, and type 2 nights (red line) are above the detection limit.

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3.2 NO₃ reactivity calculated from VOC measurements

In this section we assess the contribution of various VOCs to the observed NO₃ reactivity. The most abundant BVOCs were isoprene, sabinene, α-pinene, and β-pinene with maximum mixing ratios during the warm period around August. The time series of BVOC mixing ratios are displayed in Fig. S4 of the Supplement. $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ is a total loss rate constant for chemical reactions of [NO₃] with all organic trace gases present and can be compared to the summed loss rate constant ($k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$) (also in units of s⁻¹) obtained from the concentrations of individual VOCs in the same air mass, [C_i], and the rate coefficient (k_i):

where [C_i] is the measured BVOC concentration and k_i the corresponding rate constant. Individual values of $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$, calculated using rate constants from the IUPAC evaluation (IUPAC, 2018) or elsewhere in the literature (Shorees et al., 1991), are plotted with interpolated 20 min averages of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ as a time series in Fig. 4a.

The data are also displayed as a pie chart in Fig. 4b in which the contribution of individual biogenic trace gases to the NO₃ reactivity are listed. Of the terpenoids, α-pinene contributed most to the overall NO₃ reactivity (≈16 %) followed by sabinene (≈12 %) with other individual BVOCs contributing less than 10 %. VOCs such as methanol, acetaldehyde, ethanol, acetone, methylethylketone, alkanes, and aromatics were also measured but not included in calculations of $k_{\mathrm{VOC}}^{\mathrm{N}{\mathrm{O}}_{\mathrm{3}}}$ as their summed contribution reached a maximum of $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹ and was on average $\mathrm{5}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹. As $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ show a similar dependence on wind direction (Fig. S2) and because only BVOCs were used for the derivation of $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$, we conclude that the high NO₃ reactivities measured in air masses arriving from the east and north-east are mostly from trace gases of biogenic origin.

Figure 4(a) Measured values of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (black) compared to the loss rate constant attributed to individual VOCs. The term “other” includes terpinolene, β-phellandrene, α-terpinene, γ-terpinene, α-thujene, and camphene. Myrcene and α-phellandrene were also measured but below the detection limit during the whole campaign. The pie chart (panel b) indicates the campaign-averaged contribution of each measured VOC to the NO₃ loss rate as well as reactivity that could not be attributed to measured VOCs (“unassigned reactivity”).

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Type 1 nights were characterized by very low BVOC mixing ratios, sometimes below the detection limit, whereas isoprene was still present. This observation is consistent with a long lifetime for isoprene in the residual layer at night (Brown et al., 2007a) as the OH concentration is too low and the NO₃ reaction too slow to remove it efficiently. Under conditions of very low NO₃ reactivity, the fractional contribution of isoprene to the overall reactivity could increase to ≈100 % (from typically 20 % during the day). During type 2 nights (those with non-zero NO₃ reactivity) isoprene and monoterpenes were always detected and monoterpenes were the dominant reaction partners for NO₃.

The difference between $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (i.e. the NO₃ reactivity not accounted for by measured VOCs) is defined as unassigned reactivity (s⁻¹).

A plot of $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ versus $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (see Fig. S5 of the Supplement) has a slope of 1.55 and an intercept of 0.005. This implies, on average, an unassigned reactivity of ≈34 % when $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}=\mathrm{0.3}$ s⁻¹ and a unassigned reactivity of ≈50 % when $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}=\mathrm{0.03}$ s⁻¹. However, both $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ are associated with uncertainty, which needs to be rigorously assessed to test whether the unassigned reactivity is significant. To do this we propagated uncertainty in each of the terms $\sum k_i^{\mathrm{N}{\mathrm{O}}_{\mathrm{3}}}\left[C_{\mathrm{i}}\right]$ (mainly related to VOC measurements and assuming 15 % uncertainty in the rate coefficients) and derived mean diel profiles of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ for the whole campaign (hour averages). We note that IUPAC-listed uncertainties for each VOC are generally larger than 15 % (especially when only few studies are available) and the use thereof would substantially increase the uncertainty in $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$. The results are shown as a time series and a campaign-averaged diel profile in Fig. 5. For the time series, we plot data points only when values of both $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ were available. The time series illustrates that, within combined uncertainty, the data overlap so that unassigned reactivity is not significantly distinct from zero apart from a few isolated data points. This contrasts with the conclusions of a previous campaign (boreal forest) with this instrument (Liebmann et al., 2018) in which up to 40 %–60 % of the measured reactivity could not be accounted for by measured VOCs.

Figure 5(a) Time series of $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$. The error bars on the $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ measurements are total uncertainty calculated as described by Liebmann et al. (2017). The uncertainty in $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (shaded red area) is dominated by uncertainty in the mixing ratios of the VOCs. Panel (b) is a campaign-averaged diel profile of the same parameters, whereby the uncertainties also include variability.

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The comparison of measured NO₃ reactivity with that calculated from VOC measurements suffers from substantial uncertainties in both parameters. For this campaign, the uncertainty in NO₃ reactivity was larger than previously reported (Liebmann et al., 2018) due to reduced stability of the NO₃ source, which will be improved in future versions of the instrument. A further obstacle to the calculation of unassigned reactivity was the uncertainty in the measurements of biogenic VOCs and the associated rate constants for the NO₃ reaction. The latter could be reduced by more plentiful and more accurate data on NO₃ rate coefficients with some of the more important biogenic species.

3.3 NO₃ measurements and comparison with stationary-state calculations

Although rough estimates of NO₃ concentrations at the Hohenpeissenberg have been made (Handisides et al., 2003; Bartenbach et al., 2007), no direct NO₃ measurement had been previously made. For this reason, on just one night during the intensive (2–3 August), the instrument was modified to enable measurement of ambient NO₃ mixing ratios rather than NO₃ reactivity. The NO₃, O₃, and NO₂ mixing ratios and meteorological data are plotted in Fig. 6.

Figure 6NO₃ mixing ratios measured in the night from 2–3 August as well as NO₂ and O₃ (which define the NO₃ production rate). T: temperature, RH: relative humidity, WD: wind directions, WS: wind speed.

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NO₃ mixing ratios slowly increased in the first half of the night, reaching a maximum of 13 pptv around 21:40 UTC. At this time the O₃ mixing ratios were also the largest and highly variable. After ≈22:30, O₃ was slowly removed, and the NO₃ decreased by a factor of 10 or more, indicating that the instrument was sampling more reactive boundary layer air. This is also evident in the increase in relative humidity and decrease in the temperature until about 01:30.

Given sufficient time, stationary state can be reached for NO₃ at night in which the production and loss terms are approximately balanced (Brown et al., 2003a; Crowley et al., 2010, 2011). In this case NO₃ mixing ratios can be described by the ratio of their production rate and loss rate (Eq. 3).

The production rate is governed by the [NO₂] and [O₃] mixing ratio and the corresponding rate constant k₂. If the loss processes are due to reaction with VOCs only, this expression becomes

During this night $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was not measured so $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was used to account for NO₃ losses.

Figure 7 shows the measured NO₃ mixing ratios (black) compared to those derived from Eq. (4) using the measured VOC concentrations (red curve). Clearly, the predicted stationary-state NO₃ concentrations are too high (by a factor of up to 3–4), implying that other NO₃ loss processes must be considered. As the directly measured reactivity, $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$, agrees rather well with that derived from VOC measurements ($k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$) calculated on other campaign nights, it would seem unlikely that unmeasured VOCs contribute sufficiently to NO₃ losses to explain this large factor. Stationary-state concentrations of NO₃ are influenced not only by VOCs but also by NO (if present at night) and also indirectly via the heterogeneous loss of N₂O₅. Equation (5) can be extended to include these processes (Martinez et al., 2000; Geyer et al., 2001; Brown et al., 2003a, b, 2009; Crowley et al., 2010; Sobanski et al., 2016).

where K₅ is the equilibrium constant for the forward and reverse Reactions (R4) and (R5). The loss frequency due to the heterogeneous uptake of N₂O₅ to particles (f_het) can be calculated by Eq. (6):

which is approximately valid if the particles are less than ≈1 µm in diameter. In this expression, A is the aerosol surface area density (cm² cm⁻³), $\stackrel{\mathrm{‾}}{c}$ is the mean molecular velocity of N₂O₅ (26 233 cm s⁻¹ at 298 K), and γ is the dimensionless uptake coefficient. If we assume a large value for the uptake coefficient of 0.03 as characteristic for aerosol with low organic content (Bertram and Thornton, 2009; Bertram et al., 2009; Crowley et al., 2011; Phillips et al., 2016) and use the aerosol surface area density of 1.25–$\mathrm{1.55}\times {\mathrm{10}}^{-\mathrm{6}}$ cm² cm⁻³ (measured by a scanning mobility particle sizer for 10–890 nm), we obtain values for f_het of 2.4–$\mathrm{2.9}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹. Incorporation of the heterogeneous loss of N₂O₅ reduces the predicted NO₃ by only about 5 pptv as shown in Fig. 7 and cannot reproduce the observed NO₃ mixing ratios. The efficient reaction of NO with NO₃ means that low mixing ratios of NO can contribute to NO₃ reactivity, and we calculate that ≈5 pptv NO would approximately align the calculated NO₃ mixing ratio with that measured for much of the night. This value is, however, below the detection limit of the CLD (11 pptv) used to measure NO and we cannot conclude that NO at such levels was responsible for the reduction in NO₃ levels required to bring observations and steady-state calculations into agreement.

Figure 7Comparison of measured NO₃ mixing ratio (black) with calculated stationary-state mixing ratios using $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ (red), $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}+k_{\mathrm{Het}}$ (blue), and $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$, $+k_{\mathrm{Het}}+k_{\mathrm{NO}}$ (green).

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The discussion above demonstrates that the calculation of NO₃ reactivity from stationary-state calculations can be precarious and subject to large cumulative uncertainty from e.g. measurement uncertainty in NO₃ mixing ratios, uptake coefficients, aerosol surface area, and NO mixing ratios close to instrumental detection limits.

Figure 8(a) Stationary-state NO3 mixing ratios calculated using $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$, [NO]k₃, K₅[NO₂]f_het, and $J_{{\mathrm{NO}}_{\mathrm{3}}}$ for the entire campaign and comparison with the measured NO₃ mixing ratios (3 August). Panel (b) plots the time series of production and loss rates used for the calculation of [NO₃]_ss.

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To assess the NO₃ mixing ratios for the rest of the intensive, Eq. (6) can be augmented by adding the loss rate constant for NO₃ photolysis $J_{{\mathrm{NO}}_{\mathrm{3}}}$ and substituting $k_{\mathrm{VOC}}^{{\mathrm{NO}}_{\mathrm{3}}}$ for $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$.

In the absence of a direct measurement of $J_{{\mathrm{NO}}_{\mathrm{3}}}$, the diel cycle of the relative NO₃-to-NO₂ photolysis rate constant ($J_{{\mathrm{NO}}_{\mathrm{3}}}/J_{{\mathrm{NO}}_{\mathrm{2}}}$) was calculated using the TUV (tropospheric ultraviolet and visible radiation) model (https://www2.acom.ucar.edu/modeling/tropospheric-ultraviolet-and-visible-tuv-radiation-model, last access: March 2018) and then put on an absolute basis using measured $J_{{\mathrm{NO}}_{\mathrm{2}}}$ values.

Figure 8 shows the NO₃ production rate (panel b, black curve) and total loss rate (panel b, red curve) as well as the stationary-state NO₃ mixing ratios for the entire intensive period (Fig. 8a, black curve). During nights on which the reactivity fell below the detection limit of the instrument $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ was set to 0.005 s⁻¹. Calculated NO₃ mixing ratios were in the sub-pptv range during daytime and around 1–15 pptv during night-time. The NO₃ mixing ratios thus derived are comparable to those measured on a single night (Fig. 8, red curve) and are broadly consistent with previous estimates for this site (Handisides et al., 2003; Bartenbach et al., 2007).

3.4 Contribution of NO₃ reactivity to NO_x loss

At night-time, in the absence of NO and sunlight, each NO₃ radical formed in the reaction of NO₂ with O₃ will either be removed indirectly via the uptake of N₂O₅ onto particles or will react with a biogenic hydrocarbon. The latter results in the formation of an organic nitrate at a yield of between 20 and 100 %, depending on the specific VOC (Ng et al., 2017) and hence the removal of NO_x. The large daytime values for $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ obtained in this study suggest that even during sunlight hours (when NO₃ is generally considered to be of little importance owing to its rapid photolysis) significant amounts of NO₃ form organic nitrates rather than reforming NO₂ by reaction with NO or photolysis.

The fraction, f, of NO₃ that will react with organic trace gases is given by

where the denominator sums all loss processes for NO₃. Mixing ratios of NO below the 11 pptv detection limit were set to zero. Figure 9 illustrates this via a diel cycle of the median for f. At night-time, ≈99 % of the NO₃ will be lost to reaction with BVOCs, with indirect heterogeneous losses representing the remaining 1 %. Note that the presence of NO at 5–10 pptv levels during the night would significantly reduce this value (see Sect. 3.3).

Figure 9The fraction, f, of the total NO₃ loss with organic trace gases as a campaign mean diel cycle where $f=k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}/(k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}+J_{{\mathrm{NO}}_{\mathrm{3}}}+[\mathrm{NO}]k_{\mathrm{3}}+K_{\mathrm{5}}[{\mathrm{NO}}_{\mathrm{2}}\left]f_{\mathrm{het}}\right)$. The error bars reflect variability only and do not consider systematic uncertainty.

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Figure 10(a) Time series of $k_{\mathrm{Total}}^{\mathrm{OH}}$ (shaded region is 1σ uncertainty). (b) Time series of $k_{\mathrm{OTG}}^{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{\mathrm{OTG}}^{\mathrm{OH}}$. The data are plotted so that the curves overlap at the peak reactivity (1 August).

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During daytime, at the peak of the actinic flux (max $J_{{\mathrm{NO}}_{\mathrm{3}}}\approx \mathrm{0.2}$ s⁻¹) and correspondingly high levels of NO (k_NO=0.1–0.2 s⁻¹), 20 % of the formed NO₃ was lost due to reaction with organic trace gases, increasing up to 40 % in the late afternoon. This result is comparable with reactivity measurements in a boreal forest in Finland during IBAIRN 2016 in which a very similar diel profile for f was determined (Liebmann et al., 2018). The NO₃ reactivity data from these measurements indicate that the role of NO₃ as a daytime oxidant of biogenic VOCs in forested regions may so far have been underestimated, which in turn has implications for understanding the diel cycle of organic nitrate and secondary organic aerosol formation in such environments.