An incoherent broadband cavity-enhanced absorption spectrometer for simultaneous NO₃ and N₂O₅ measurements, integrated into a NO_y instrument suite: characterization and first field deployment

Reactive nitrogen species (NO_y) are involved in the formation of secondary pollutants, thus following their interconversions is crucial for understanding their impact on air quality. While nitric oxide (NO) and nitrogen dioxide (NO₂) are important contributors to total NO_y, further constituents such as the nitrate radical (NO₃) and dinitrogen pentoxide (N₂O₅), formed from NO₂ oxidation, are key intermediates in nocturnal oxidation processes. Even though NO₃ and N₂O₅ affect the NO_y budget in the following day, their role is poorly constrained in isolated measurements. We present the “NOyBOx”, a new instrumental framework combining measurements of NO, NO₂ and NO_y from commercial analyzers with a custom-built incoherent broadband cavity-enhanced absorption spectrometer (IBBCEAS) that measures NO₃ directly and N₂O₅ via a thermal dissociation inlet (TDI) and channel differencing. We describe the design of the IBBCEAS subsystem, characterize the TDI, cavity optics, transmission losses, and, using a synthetic spectra simulation approach, the bias of ambient NO₂ and water vapor on our concentration retrieval procedure. Under optimal laboratory conditions we find a limit of detection (LOD) of 1.5 and 2.2 pptv (1σ Allan deviation, 15 s) for NO₃ and N₂O₅, respectively. Under field conditions, interference by water vapor and NO₂ worsens these LODs to 3.1 pptv with a total measurement uncertainty (TMU) of 12 % for NO₃, and to 4.4 pptv with a mean TMU of 21 % for N₂O₅. Exemplary results from its first deployment during a field campaign in a temperate forest atop a 40 m tall tower are discussed.

1 Introduction

Reactive nitrogen species, collectively referred to as NO_y, constitute a broad class of atmospheric trace gases involved in the formation of secondary pollutants such as tropospheric ozone (O₃) and particulate matter (Crutzen and Lelieveld, 2001; Kiendler-Scharr et al., 2016), as well as in the regulation of the atmosphere's oxidative capacity (Geyer et al., 2001a; Monks, 2005). Consequently, NO_y species play a crucial role in air quality, human health and climate (Lelieveld et al., 2020; Wild et al., 2016). Even though natural sources of NO_y emissions exist, NO_y is predominantly released into the atmosphere in the form of nitric oxide (NO) through combustion processes, that is readily converted to nitrogen dioxide (NO₂) in the presence of typical ambient O₃ levels (Dutta et al., 2026; Logan, 1983). At the same time, NO₂ is partially photolysed to NO by sunlight during the day. This interconversion between NO and NO₂ is reflected in the use of the term NO_x, which denotes the sum of these two species (Seinfeld and Pandis, 2012). While NO_x can often form the dominant fraction of NO_y in freshly polluted air masses (Pandey Deolal et al., 2012), it is progressively oxidized to a diverse suite of further (often secondary) reactive nitrogen species (NO_z = NO_y − NO_x) including nitric acid (HNO₃), nitrous acid (HONO), organic nitrates (RONO₂ and RO₂NO₂) in both gas and particle phase (pNO₃), the nitrate radical (NO₃), dinitrogen pentoxide (N₂O₅), halogenated nitrogen species (e.g. nitryl chloride, ClNO₂), and others (Finlayson-Pitts and Pitts, 2000). As air masses undergo chemical processing, the contribution of NO_z to the NO_y budget often increases with air mass age (Brown et al., 2017; Parrish et al., 1993; Stratmann et al., 2016). Several NO_z species, notably HNO₃ and organic nitrates, are sufficiently long-lived to be transported over long distances and later re-release NO_x in remote regions, thereby effectively functioning as NO_x reservoirs and further impacting air quality (Ito et al., 2007; Lee et al., 2016; Pye et al., 2015, 2010; Rindelaub et al., 2015).

One particularly important species among reactive nitrogen compounds crucially impacting the formation potential of particulate matter is the above-mentioned NO₃ radical: It is formed from oxidation of NO₂ by O₃ (Reaction R1) and is in thermal equilibrium with NO₂ and N₂O₅ (Reactions R2 and R3) (Wayne et al., 1991). Since NO₃ is readily photolysed by sunlight (Reactions R4a and R4b) or rapidly reacts with NO (Reaction R5), its mixing ratios remain too low to be detected during the day (Brown and Stutz, 2012).

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

$$\begin{array}{}\text{(R4a)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+h\mathit{\nu }\to {\mathrm{NO}}_{\mathrm{2}}+\mathrm{O}{(}^{\mathrm{3}}P)\text{(R4b)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+h\mathit{\nu }\to \mathrm{NO}+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

$$\begin{array}{}\text{(R5)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}}\text{(R6)}& {\displaystyle }\begin{array}{rl}{\mathrm{NO}}_{\mathrm{3}}+\mathrm{VOC}\to & \text{products\hspace{0.17em} }(\text{e.g.\hspace{0.17em} }{\mathrm{HNO}}_{\mathrm{3}},\mathrm{SOA},\\ & \text{ \hspace{0.17em}organic\hspace{0.17em}\hspace{0.17em}nitrates})\end{array}\text{(R7)}& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\text{surface\hspace{0.17em}\hspace{0.17em}(e.g.\hspace{0.17em}\hspace{0.17em}particles)}\to \text{products}\end{array}$$

During the night, in the absence of sunlight and at low NO levels, NO₃ has been shown to be an important oxidant for unsaturated biogenic volatile organic compounds (BVOC) such as isoprene and terpenes (Brown and Stutz, 2012; Dewald et al., 2024; Hu et al., 2023; Liebmann et al., 2019; Mermet et al., 2021; Mogensen et al., 2015; Ng et al., 2017). In urban environments, anthropogenic volatile organic compounds (AVOC), especially phenolic compounds, are also efficiently oxidized by NO₃ (Bolzacchini et al., 2001; Zhang et al., 2025). These reactions between BVOC or AVOC and NO₃ (Reaction R6) can yield high amounts of the NO_x reservoir species detailed above including organic nitrates, nitric acid and secondary organic aerosol, all of which can significantly impact air quality, climate, and human health (Fry et al., 2014; Kumar et al., 2023; Ng et al., 2017; Schueneman et al., 2025; Wennberg et al., 2018). In addition, N₂O₅ (and therefore indirectly NO₃) can be irreversibly removed through heterogeneous hydrolysis on e.g. aerosols (Reaction R7), producing nitrate that can be ultimately lost by wet or dry deposition (Aldener et al., 2006; Brown et al., 2009; Phillips et al., 2016). These processes can be an important sink for NO_x, with NO₃ and N₂O₅ acting as the key intermediates linking nocturnal chemistry to the removal of NO_y and, consequently, to reduced ozone formation on the following day (Finlayson-Pitts and Pitts, 2000; Kane et al., 2001).

The NO₃ radical is highly reactive, so its nocturnal mixing ratios rarely exceed a few parts per trillion by volume (pptv), especially in forests (Liebmann et al., 2018; Mermet et al., 2021; Yáñez-Serrano et al., 2018), and it shows strong spatio-temporal variability (Brown et al., 2007; Vrekoussis et al., 2007). Detecting it therefore requires techniques with both high sensitivity and fast time resolution.

Platt et al. (1980) made the first tropospheric NO₃ measurements using differential optical absorption spectroscopy (DOAS), which determines a gas' concentration by measuring how much light of specific wavelengths it absorbs along a long open-air light path (often several km) between a light source and a distant detector. Because of its exceptional sensitivity at that time, long-path DOAS became one of the most widely used NO₃ methods (Geyer et al., 2001b; McLaren et al., 2004; Platt et al., 1981; Sommariva et al., 2007). However, it only yields a concentration averaged over the whole absorption path, giving it poor spatial resolution, and it cannot operate under snow or fog (Platt and Stutz, 2008).

Since then, several alternative techniques have emerged: laser-induced fluorescence (LIF) (Matsumoto et al., 2005; Wood et al., 2003), cavity ring-down spectroscopy (CRDS) as well as cavity-enhanced absorption spectroscopy (CEAS) (Berden et al., 2000; Brown, 2003; Brown and Stutz, 2012; Lin et al., 2026). Both CRDS and CEAS work by trapping light inside an optical cavity formed by two highly reflective mirrors, so that light is reflected thousands of times before escaping. This effectively folds a path of many kilometers into a compact cell, greatly amplifying the light's interaction with trace gases without requiring a long open-air path.

CRDS has become a particularly powerful tool for measuring atmospheric trace gases, including NO₃, thanks to its spatial resolution, sensitivity, and accuracy (Ball et al., 2001; Bitter et al., 2005; Dubé et al., 2006; Li et al., 2018; Lin et al., 2022; Odame-Ankrah and Osthoff, 2011; Schuster et al., 2009; Sobanski et al., 2016; Türk et al., 2026; Wagner et al., 2011; Wang et al., 2015; Wu et al., 2020). Rather than measuring absorbed light directly as in DOAS, CRDS infers concentration from how quickly light intensity decays (“rings down”) inside the cavity once a pulse (pulsed CRDS) or continuous source (cw-CRDS) is switched off: gases in the cavity absorb light and shorten this decay time, and the change in decay rate gives the concentration. Operating at a narrow wavelength range, CRDS suffers only negligible interference from O₃, H₂O, or NO₂, achieves effective path lengths of tens of kilometers, and reaches, as recently reviewed in Türk et al. (2026), detection limits often below 1 pptv for a few seconds of averaging. It also requires less power and is smaller and lighter than DOAS setups.

Incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS), first proposed by Fiedler et al. (2003), is a variant of these cavity techniques that has gained increasing popularity as a means of detecting NO₃ in field and chamber measurements (Ball et al., 2004; Dorn et al., 2013; Fouqueau et al., 2020; Kennedy et al., 2011; Langridge et al., 2008; Ling et al., 2023; Nam et al., 2022; Suhail et al., 2019; Varma et al., 2009; Venables et al., 2006; Ventrillard-Courtillot et al., 2010; Wang et al., 2017, 2023; Wang and Lu, 2019). Unlike CRDS, which uses a single laser wavelength and needs fast-response detectors to track the decay, IBBCEAS setups consist of simpler and lower-cost components by coupling a broadband (multi-wavelength) light source into the cavity and measuring the resulting absorption spectrum, thereby avoiding the need for fast detection electronics while keeping much of the cavity-enhanced sensitivity. This gives IBBCEAS advantages of both DOAS and CRDS: like DOAS, its broadband source allows simultaneous measurement of multiple trace gases (Ling et al., 2023; Nam et al., 2022), rather than the single-species selectivity of CRDS; like CRDS, its compact optical path makes it easy to combine with other in-situ data for analyzing local atmospheric chemistry and physics. Both CEAS and CRDS are also flexible enough to deploy on ground stations, towers, vehicles, ships, and aircrafts to capture spatio-temporal variations in NO₃ at local scales, and, unlike DOAS, both are largely unaffected by weather conditions.

Finally, quantifying ambient N₂O₅ indirectly requires thermally dissociating it into NO₃ before detection by any of the techniques mentioned above (Dubé et al., 2006; Sobanski et al., 2016; Türk et al., 2026; Wang et al., 2017). Alternatively, a thermal dissociation inlet can be coupled to a chemical-ionization mass spectrometer, allowing N₂O₅ to be detected indirectly through the formation and subsequent detection of e.g. ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Kercher et al., 2009; Slusher et al., 2004).

As detailed in Fuchs et al. (2010), NO_x is commonly measured using optical methods including DOAS, CRDS, CEAS, laser-induced fluorescence (LIF), cavity attenuated phase shift (CAPS) and chemiluminescence detection (CLD). The latter quantifies NO with detection limits in the pptv range based on the detection of chemiluminescent emission of excited NO₂ formed from the reaction of NO with excess O₃ (Clough and Thrush, 1967; Hosaynali Beygi et al., 2011; Tadic et al., 2020). To quantify NO₂, it is first converted to NO, typically by photolysis or catalytic conversion prior to entering the detection cell (Nussbaumer et al., 2021; Reed et al., 2016). A LIF-based NO₂ measurement relies on excitation of NO₂ at wavelengths above 400 nm and fluorescence detection above 600 nm (Day et al., 2002; Javed et al., 2019). DOAS detects ambient NO₂ by exploiting its structured absorption spectrum between 400 and 600 nm, using either broadband light sources over long optical paths or natural sunlight (Leser et al., 2003; Merten et al., 2011). Cavity techniques such as CRDS, CAPS and CEAS rely on NO₂ visible absorption but enhance sensitivity through long effective optical path lengths achieving excellent detection limits below 50 pptv (Fuchs et al., 2010; Gherman et al., 2008; Sobanski et al., 2016; Thieser et al., 2016; Wild et al., 2014). In case of CAPS, NO₂ concentrations are deduced from the phase shift of the modulated light transmitted through the cavity, which is directly related to the optical attenuation caused by the presence of NO₂ (Ge et al., 2013; Kebabian et al., 2005). NO can likewise be quantified through these techniques by first converting it to NO₂ via oxidation with O₃ (Friedrich et al., 2020; Ohara et al., 2024; Wüst et al., 2025).

Early NO_y measurements relied on converting reactive nitrogen species to NO using heated gold or molybdenum converters, followed by chemiluminescence detection (CLD). Gold converters were designed to exclude particulate nitrate, whereas molybdenum converters also responded to particulate nitrate (Fahey et al., 1986; Williams et al., 1998). More recently, thermal dissociation techniques have been adopted, in which NO_z species are thermally decomposed to NO₂ prior to detection by LIF or cavity-enhanced absorption methods (Day et al., 2002; Dewald et al., 2026a; Paul et al., 2009; Wild et al., 2014). Although these approaches provide high sensitivity and speciation capability, elevated temperatures can induce secondary reactions that generate measurement artefacts. These effects can be mitigated by operating at reduced pressure or scavenging reactive radicals, although additional corrections based on laboratory calibration and chemical modelling may still be required (Womack et al., 2017; Wüst et al., 2025).

Figure 1 Schematic diagram of the NOyBOx instrument. The two custom-built IBBCEAS subsystems with separate inlets 1 and 2 is shaded grey. The commercial analyzer subsystem for NO, NO₂, and total gas-phase NO_y is shaded blue and share inlet 3. The gas supply assembly for purging (orange solid lines), background and calibration measurements is marked in orange. The valves are coloured according to the modes (blue: background, brown: calibration, purple: sampling, grey: always open) they are active in. The black dashed lines show how the cavity exhaust flow is coupled to the NO₂ analyser during calibration periods. Note that the NO₃ channel's inlet is equipped with an additional charcoal filter (not shown) when calibrated with NO₂.

Here, we present the NOyBOx, an integrated instrument suite that simultaneously measures NO₃, N₂O₅, NO, NO₂, and NO_y. As outlined in the chemical framework above, NO₃ and N₂O₅ can not only influence NO_x-NO_y partitioning but also remove reactive nitrogen from the atmosphere via heterogeneous loss of N₂O₅, NO₃, and its oxidation products (e.g. organic nitrates, HNO₃). Previous multi-channel instruments have combined NO₃ $/$ N₂O₅ measurements with measurements of selected additional nitrogen species, such as organic nitrates and NO₂ (Kennedy et al., 2011; Sobanski et al., 2016), or measured total NO_y without speciated NO₃ $/$ N₂O₅ measurements (Friedrich et al., 2020; Wild et al., 2014). One exception is a six-channel CRDS instrument as detailed in Brown et al. (2017), which included channels for O₃, N₂O₅, NO, NO₂, and total NO_y, as well as NO₃, although NO₃ measurements were not successfully obtained during that deployment. NOyBOx combines two custom optical cavities for NO₃ $/$ N₂O₅ measurements with commercial analyzers for NO_x species and total NO_y. This configuration provides the combined measurements needed to investigate the role of nocturnal oxidation processes in the reactive nitrogen budget that remains barely accessible with isolated measurements, while potentially reducing instrument complexity and cost compared with an approach based entirely on custom CRDS channels. In the following sections we describe the instrument's design, characterize its NO₃ $/$ N₂O₅ subsystem and present results from its first field deployment during the Atmospheric ChemistRy Of the Suburban foreSt (ACROSS) campaign.

2 Instrument design and methodology

As depicted in Fig. 1, the NOyBOx instrument consists of three commercial analyzers for the measurement of NO, NO₂, and NO_y (blue-shaded), two custom-built IBBCEAS cavities for the quantification of ambient NO₃ and N₂O₅ (grey-shaded), installed in a portable rack (120 cm × 80 cm × 150 cm), and a gas supply assembly (orange-shaded) for zeroing and calibration of both subsystems. The instrument can be operated in three modes: (i) ambient sampling, (ii) background measurements by supplying both subsystems with zero air (ZA) from a synthetic air cylinder (purity ≥ 99.9999 %, Air Liquide, Alphagaz), and (iii) calibration using a standard gas containing a known NO₂ concentration (800 ppbv (parts per billion by volume) in N₂/O₂, Air Liquide). During ambient sampling, air is drawn through three dedicated inlets (Fig. 1, purple): inlet 1 supplies the NO₃ IBBCEAS cavity, inlet 2 supplies the N₂O₅ IBBCEAS cavity, and inlet 3 supplies the commercial analyzers. The NO₃ and N₂O₅ IBBCEAS inlets are equipped with a polytetrafluoroethylene (PTFE) membrane filter (Pall Corporation, R2PJ047) in a PTFE holder (Mace, 930-1244-101) to remove particles with a diameter bigger than 2 µm that would worsen the detection limit through scattering and deposition on mirror surfaces when entering the instrument. The commercial analyzers are equipped with internal filters. During background and calibration, gas flows are regulated by critical orifices (CrO). The mode switching in the commercial analyzer subsystem and the N₂O₅ channel is enabled by $\mathrm{3}/\mathrm{2}$-way solenoid valves consisting of PTFE (Bürkert, type 0121, no. 20063588), while a 2-way solenoid PTFE valve (Bürkert, type 0121, no. 77191) in combination with a Perfluoroalkoxy alkane (PFA) T-piece (Swagelok, PFA-420-3) is used in the NO₃ channel for reasons of hardware availability. Excess gas in the latter is vented via its own sampling inlet, whereas a dedicated overflow outlet (OFL) is used for the former. In both cases, the corresponding vents are equipped with removable charcoal cartridges to prevent the release of calibration gases into the ambient air. A technical scheme detailing the exact gas flows and positions of the components is available in Fig. S1 in the Supplement. Operation of the instrument is fully automated through a custom Python software, which controls the mass flow controllers (MFCs), the heaters, and the valve switching between operating modes. It also executes ambient measurements, background, and calibration sequences, and continuously acquires data from the optical cavities, gas analyzers, and auxiliary sensors (temperature, pressure). Details of the individual instrument components are provided in the following subsections.

2.1 Commercial analyzer subsystem for NO₂, NO and NO_y

Our measurements of NO, NO₂ and NO_y rely on commercial analyzers that have already been thoroughly tested in the past and are widely used by the geoscience community. Their description below is thus limited on a purely technical level and do not require any further characterization. During field operation, they are zeroed with synthetic air using the background mode. Each analyzer is generally calibrated against another commercial CLD (Horiba, APNA-370) by injecting well-defined amounts of NO and/or NO₂ (typically 2–100 ppbv) into the Multiphase Atmospheric Experimental Simulation Chamber (CESAM) prior to field deployment (Wang et al., 2011). Alternatively, the analyzers were calibrated by direct injection of well-defined NO and NO₂ standards using a dilution system, with NO₂ additionally calibrated by gas-phase titration of excess NO with O₃.

2.1.1 NO₂ analyzer

A CAPS instrument (TELEDYNE API, Model T500U) measures NO₂ via absorption of radiation from a light emitting diode (LED, 450 nm center wavelength) inside a cavity equipped with two highly-reflective mirrors and a vacuum photodiode detector. The cavity is thermostated (45 °C) to prevent water condensation on the mirror surfaces and minimize temperature-induced variations in the NO₂ absorption cross section. It features a low zero drift (< 0.1 ppbv d⁻¹) and provides a limit of detection (LOD) of 40 pptv (30 s) with a relative precision of 0.5 %. The analyzer samples with ca. 0.9 standard (STP) litres per minute (SLPM).

2.1.2 NO analyzer

NO was measured using a chemiluminescence-based NO analyzer (ECO PHYSICS CLD 780 TR). Excess O₃ required for NO detection (see above) is supplied by an integrated ozone generator operated under low pressure (ca. 14 mbar) maintained by an external vacuum pump. The instrument's limit of detection is 10 pptv (1 min), with a sample flow rate of 3 SLPM. The ozone generator can be fed with either pure O₂ or dry ambient air (0.3 SLPM); both configurations were used during the ACROSS campaign (Sect. 4). When operating on ambient air, we dried the supply air using a silica gel cartridge that was periodically renewed. Note that maximum sensitivity and accuracy was achieved when supplying the ozone generator with pure O₂.

2.1.3 NO_y analyzer

NO_y are transformed to NO by a gold converter (ECO PHYSICS CON 765) and detected by a second ECO-PHYSICS CLD 780 TR analyzer. This converter operates by reducing all NO_y species through a reaction with CO catalyzed on a gold surface at high temperature (300 °C). The sample flow is set to 3 SLPM and the CO flow is 0.03 SLPM. The NO analyzer was first calibrated alone, with the gold converter disconnected, either using the CESAM chamber or direct injections (see above). The converter was then reconnected and its conversion efficiency determined by generating a known NO₂ concentration and comparing the resulting NO_x signal to that of the Horiba APNA-370 analyzer, yielding a conversion efficiency of 88 %.

Figure 2 Exemplary IBBCEAS spectral retrieval for a representative measurement at the simulation chamber CESAM with the NO₃ channel: (a) Raw spectra I₀ (reference, blue) and I (sample, black) with the corresponding transmission $T=I/I_{\mathrm{0}}$ on the right axis (grey dashed). (b) Measured effective absorption coefficient α (black dots) and best-fit model (blue line); retrieved concentrations are annotated. (c) Reference absorption cross-sections of NO₃ (blue, Orphal et al., 2003) and NO₂ × 10³ (orange, Vandaele et al., 1998) convolved with the instrument spectral response function on the left axis, and the effective H₂O absorption coefficient ${\mathit{\alpha }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ (RH = 33 %, 23 °C) on the right axis (grey). (d) Fit residual (black solid line).

2.2 IBBCEAS subsystem for NO₃ and N₂O₅

The two IBBCEAS channels (Fig. 1, grey-shaded) exploit the extended optical path length achievable within a high-finesse optical cavity in order to attain a sufficiently high sensitivity to detect NO₃ and N₂O₅ at ambient concentration levels. Both channels target the strongest absorption band of NO₃ at 662 nm (Orphal et al., 2003). To enable detection of N₂O₅, the sample air is first passed through a 1 m PFA thermal dissociation inlet (TDI) operated at 80–200 °C (residence times of 0.12–0.16 s), which quantitatively dissociates N₂O₅ into NO₃ and NO₂ (Reaction R3). The resulting stream then enters the N₂O₅ cavity, maintained at 80 °C to suppress the reverse recombination reaction (Reaction R2). The signal in this channel reflects the sum of ambient NO₃ and N₂O₅, from which N₂O₅ is isolated by difference with the NO₃ channel (see below). Although this cavity technically detects the sum of two components, for simplicity we refer to it as the N₂O₅ channel throughout the text. Gas flows through both cavities (7 SLPM for NO₃ and 5 SLPM for N₂O₅ resulting in residence times of 1.31 and 1.53 s, respectively) are regulated by dedicated mass flow controllers (Alicat, MCP-20SLPM) and operated at a fairly stable intracavity pressure (970 mbar, typical value at ground level), before being combined, pumped through a charcoal trap, and vented. All connections and lines upstream the cavity consist of PFA to ensure reduced NO₃ losses.

2.2.1 Light source

In each channel, light is provided by a thermally stabilized red LED (NO₃: Mouser Electronics – Starboard, Luminus SST-10-DR-B130 Deep Red, max. 430 mW; N₂O₅: Thorlabs M660D2) with a near-Gaussian emission profile centered at 657.4 nm (FWHM 18 nm) and 660.4 nm (FWHM 21 nm) for the NO₃ (Fig. 2a, blue line) and N₂O₅ channels, respectively. Precise thermal regulation to ± 0.01 °C (as specified by the manufacturer) via a thermoelectric cooler (Arroyo Instruments, Laser Mount) driven by a laser diode controller (Arroyo Instruments, model 6310), at operating currents of 650 and 1150 mA for the NO₃ and N₂O₅ channels, suppresses wavelength drift and intensity instabilities that would otherwise corrupt the spectral baseline. The different operating currents originate from deploying two different types of LEDs. Under these operating conditions, we observed no statistically relevant long-term drifts in the centre wavelength with values (± 2σ) of (7.3 ± 7.6) pm h⁻¹ (NO₃) and (4.7 ± 3.4) pm h⁻¹ (N₂O₅), which are below the spectrometer's resolution (> 140 pm, see below). The divergent LED emission is collimated and focused to the cavity midpoint by an aspheric condenser lens (Thorlabs ACL2520U, 25.0 mm diameter, f = 20 mm, NA = 0.79), ensuring efficient coupling into the cavity.

2.2.2 Cavity

The core of the instrument is a pair of high-finesse optical cavities, each formed by two high-reflectivity mirrors (Layertec, planar/concave, radius of curvature 1 m, diameter 25 mm, nominal reflectivity (99.98 ± 0.01) % at 630–690 nm) separated by 61.5 cm. At this reflectivity, light undergoes thousands of round trips before exiting, accumulating an extended effective path length that is the origin of the technique's sensitivity. The cavity body is a stainless-steel tube (internal diameter 18.5 mm) coated with PFA and sealed with O-rings at each mirror mount. Since any loss of mirror reflectivity directly degrades measurement sensitivity – as made explicit by Eq. (1) below – each mirror is continuously purged with clean and dry zero air (100 sccm, Fig. 1 orange lines) from the gas cylinder (purity ≥ 99.9999 %), delivered through three $\mathrm{1}/\mathrm{16}$-inch (inner diameter) PFA tubing regulated by critical orifices at an upstream pressure of 1.5 bar, preventing aerosol deposition or condensation of semi-volatile compounds on the mirror surfaces.

2.2.3 Detection

The light transmitted through the cavity carries the spectral imprint of the intracavity absorbers. It is collected by a fiber-coupled collimator (Thorlabs, F810-SMA, f = 35.41 mm, NA = 0.25), guided via an optical fiber (Ocean Optics Vis–NIR, 200 µm slit, 1.5 m) to a dedicated spectrometer (Ocean Optics, QE65000) with a CCD thermoelectrically cooled to −15 °C to minimize dark current, and covering 617–724 nm (107 nm bandwidth) and 639–685 nm (46 nm bandwidth) for the NO₃ and N₂O₅ channels, respectively.

2.2.4 Spectral fitting and calculation of ambient mixing ratios

The wavelength-dependent (λ) absorption coefficient of the intracavity sample, α(λ), is then retrieved from the ratio of the transmitted intensities measured in the absence (I₀, Fig. 2a, blue) and presence (I, Fig. 2a, black) of the absorbing species (Engeln et al., 1998):

$$\begin{array}{}\text{(1)}& \mathit{\alpha }\left(\mathit{\lambda }\right)=\left({\displaystyle \frac{\mathrm{1}-T\left(\mathit{\lambda }\right)}{T\left(\mathit{\lambda }\right)}}\right)\left({\displaystyle \frac{\mathrm{1}-R\left(\mathit{\lambda }\right)}{d_{\text{eff}}}}\right)\end{array}$$

where $T\left(\mathit{\lambda }\right)=I\left(\mathit{\lambda }\right)/I_{\mathrm{0}}\left(\mathit{\lambda }\right)$ (Fig. 2a, grey dashed), R(λ) is the mirror reflectivity, and d_eff is the effective mirror distance. Equation (1) makes explicit that I₀(λ) and R(λ) must be characterized regularly, which is why each is determined, as mentioned above, through a dedicated operating mode: The reference spectrum I₀(λ) is recorded in background mode using zero air. The mirror reflectivity R(λ) is determined in calibration mode by introducing a known concentration of NO₂ from the standard (800 ppbv) into the cells (see Sect. 3.2).

With I₀(λ) and R(λ) established, α(λ) is fully constrained during ambient sampling (Fig. 2b, black), and the concentrations of individual absorbers are retrieved by fitting their known absorption cross-sections using a least-squares (differential evolution) algorithm (Storn and Price, 1997) implemented in a custom Python data processing routine including SciPy (Virtanen et al., 2020):

$$\begin{array}{}\text{(2)}& \mathit{\alpha }\left(\mathit{\lambda }\right)=\sum N_i{\mathit{\sigma }}_i\left(\mathit{\lambda }\right)+p\left(\mathit{\lambda }\right)\end{array}$$

where σ_i(λ) (${\mathrm{cm}}^{\mathrm{2}}\mathrm{molec}{.}^{-\mathrm{1}}$) and N_i ($\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$) are the absorption cross-section and concentration of species i, and p(λ) is a cubic polynomial baseline correction accounting for residual source intensity fluctuations (Venables et al., 2006) and particle extinction within the cell (Varma et al., 2013).

Within the spectral range used to monitor NO₃, absorption features from NO₂, H₂O and O₃ are also present. However, given their atmospheric abundances and cross-section magnitudes (Keller-Rudek et al., 2013), all of these contribute meaningfully to the retrieved absorption. In order to quantify NO₃ accurately, the interference by H₂O and NO₂ must be accounted for by including their absorption cross-sections in the fitting routine. The strictly monotonic behaviour of the O₃ absorption spectrum in the considered spectral region allows its contribution to be accounted for within the polynomial baseline correction p(λ). The NO₃ and NO₂ reference cross-sections used in the spectral fitting are taken from Orphal et al. (2003), with a peak value of (2.13 ± 0.06) × 10⁻¹⁷ ${\mathrm{cm}}^{\mathrm{2}}\mathrm{molec}{.}^{-\mathrm{1}}$ at 298 K and 662.05 nm (Fig. 2c, blue), and Vandaele et al. (1998), respectively (Fig. 2c, orange). Both reference spectra were convolved with the instrument spectral response function.

Since NO₃ absorption cross-sections are temperature-dependent (IUPAC, 2026), a correction was applied when fitting spectra from the heated N₂O₅ cavity (353 K): the convolved cross-section from Orphal et al. (2003) was scaled by the ratio of the 662 nm band peak intensity at 298 and 353 K following Osthoff et al. (2007), yielding a value of (1.70 ± 0.10) × 10⁻¹⁷ ${\mathrm{cm}}^{\mathrm{2}}\mathrm{molec}{.}^{-\mathrm{1}}$ at 353 K. For NO₂, the ambient-temperature reference spectrum (Vandaele et al., 1998) was scaled using the ratio of the cross-sections between 640–650 nm at 298 and 353 K as reported by Davidson et al. (1988).

Water vapor presents a particular challenge, as its absorption bands partly overlap with those of NO₂ and NO₃, and the relative intensities of its rotational lines vary with ambient humidity and temperature (Aliwell and Jones, 1996), precluding the use of a single synthetic reference spectrum. To circumvent this, we use H₂O reference spectra measured in-situ in the absence of NO₃ $/$ N₂O₅ (e.g. clean daytime ambient air, laboratory air or humidified synthetic air from a chamber, Fig. 2c, grey). Since such a reference is an empirical spectrum rather than a literature cross section, it is expressed as an absorption coefficient α as derived from Eq. (1). The H₂O reference in Fig. 2c was obtained by sampling laboratory air shortly before the experiment with its humidity (33 % RH at 23 °C) taken from a laboratory hygrometer reading (C2AI, Comet T7318) at the time of recording. The H₂O amount in a sample spectrum is then retrieved from the fitted scaling factor of this reference; for example, the 31.8 % RH in Fig. 2b is the scaling factor multiplied by the reference RH. This approach is quantitative only if the reference is recorded shortly beforehand under conditions (in particular temperature) similar to those of the sample. Under such conditions, the retrieved RH agrees well with the CESAM chamber hygrometer (Vaisala HMP234), as suggested by a linear regression analysis yielding a slope (± 2σ) close to unity (1.01 ± 0.09, Fig. S2). While CEAS principally allows simultaneous retrieval of multiple species in the general case (Nam et al., 2022), accurate quantification of NO₂ and H₂O can be impeded by potential residual NO₂ in the reference or variability in H₂O relative band intensities in our approach, especially when reference and sample conditions differ. As discussed below with a synthetic spectra analysis (see Sect. 3.5), for accurate NO₃ quantification, what matters is that the NO₂ and H₂O absorption structures are represented in the fit, not the accuracy of the retrieved NO₂ amount: While NO₂ quantification is strongly biased in the presence of water, the NO₃ retrieval accuracy is only marginally impacted. An example fit along with the retrieved concentrations is shown in Fig. 2b (blue line) for a mixture NO₃ $/$ NO₂ $/$ H₂O generated in CESAM simulation chamber (https://www.cesam.cnrs.fr/, last access: 9 November 2026). Note that in this example fit, constraining NO₂ to the CAPS measurement (17.9 ppbv) would alter the retrieved NO₃ amount by less than 0.5 %. To improve fit accuracy, spectral points near the characteristic absorption features of NO₃ (662 nm), NO₂ (642 nm), and H₂O (651.5 nm) were weighted more heavily via a Gaussian boost function centered on each species' band. In this routine, NO₃ is the target species; NO₂ and H₂O are fitted mainly to account for their spectral interference, and their retrieved amounts are subject to larger uncertainty. Following the example of commonly used fitting routines such as DOASIS (Kraus, 2006), spectral shift and squeeze were treated as free fit parameters (shift bounded to ± 0.1 nm, squeeze to ± 1 %), rather than fixed values, leading to very low fit residuals (Fig. 2d).

After the purely spectral concentration retrieval, final correction accounts for the loss of NO₃ on surfaces along the sampling path as thoroughly discussed in earlier publications (Fuchs et al., 2008; Türk et al., 2026). In our NO₃ channel, the fitted concentration ($N_{{\mathrm{NO}}_{\mathrm{3}}}$) must be corrected for the transmission efficiency through the filter (T_Filter) and cavity ($T_{{\mathrm{NO}}_{\mathrm{3}}\mathrm{channel}}$) according to Eq. (3):

$$\begin{array}{}\text{(3)}& \left[{\mathrm{NO}}_{\mathrm{3}}\right]={\displaystyle \frac{N_{{\mathrm{NO}}_{\mathrm{3}}}}{T_{\text{Filter}}\cdot T_{{\mathrm{NO}}_{\mathrm{3}}\mathrm{channel}}}}\end{array}$$

Since NO₃ transmission is not necessarily identical across the two channels, deriving N₂O₅ by channel differencing requires a slightly more general expression similar to that derived by Türk et al. (2026):

$$\begin{array}{}\text{(4)}& \left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]={\displaystyle \frac{N_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}-T_{\text{Filter}}\cdot T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}\cdot \left[{\mathrm{NO}}_{\mathrm{3}}\right]}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}},\end{array}$$

with the fitted NO₃ concentration in the N₂O₅ channel $N_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$, the corrected NO₃ concentration [NO₃] calculated from Eq. (3), and the transmission efficiencies through filter and the combined transmission of TDI and N₂O₅ cavity ($T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}$). Note that NO₃ resulting from N₂O₅ dissociation only resides in the cavity, therefore a slightly higher transmission has to be applied ($T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }$, Türk et al., 2026). As discussed below, heterogeneous N₂O₅ losses within the instrument are not considered. Cavity temperature and pressure, monitored at the outflow of each cavity, are used to convert all retrieved concentrations from $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ to mixing ratios. When the NO₃ cavity temperature strongly differs from ambient temperature, NO₃ levels must be corrected to account for the shift in the highly temperature-dependent NO₂-NO₃-N₂O₅ equilibrium (Reactions R2 and R3) during the residence time in the cavity.

3 Characterization of the IBBCEAS subsystem

The retrieval of NO₃ and N₂O₅ concentrations from IBBCEAS measurements requires accurate determination of the cavity absorption coefficient as described in Sect. 2. According to Eq. (1), the absorption coefficient depends on the effective cavity length (d_eff) and the mirror reflectivity (R). The effective cavity length accounts for the reduction of the geometric cavity length caused by the mirror purge flows and is therefore required to determine the true optical path within the cavity. Once d_eff has been established, R can be determined, enabling calculation of the wavelength-dependent cavity absorption coefficient and, consequently, quantitative retrieval of NO₃ and N₂O₅ concentrations through the spectral fitting procedure according to Eq. (2).

Additional instrument characterizations are required to account for the thermal conversion and sampling efficiencies as shown in Eqs. (3) and (4) of the measurement system: Since N₂O₅ is quantified via thermal dissociation to NO₃, a thermogram is recorded to determine the temperature at which maximum conversion is achieved, ensuring quantitative conversion while avoiding unnecessary heating. Furthermore, transmission losses throughout the sampling and optical path are characterized to determine the fraction of NO₃ reaching the cavity. These characterization steps require to sample stable amounts of NO₃ (and N₂O₅) through the NO₃ $/$ N₂O₅ subsystem. To achieve this, we mixed 10–50 sccm (standard (STP) cubic centimetre per minute) of NO₂ from the calibration bottle (800 ppbv) with O₃ in a Teflon-coated (FEPD-121, Chemours) 0.4 L glass reactor. Ozone was generated by 185 nm photolysis of O₂ in a 60 sccm flow of dry zero air. The resulting ca. 70–110 sccm reactant flow leads to a residence time of ca. 5 min and was diluted in 5 and 7 SLPM dry synthetic air prior to sampling through the NO₃ and N₂O₅ channel, respectively. In this configuration, NO₃ + N₂O₅ mixing ratios of 0.05–1 ppbv were attained.

3.1 The effective cavity length

As indicated above, the presence of a zero air purge flow (100 sccm) to prevent the deposition of particles on the mirror surfaces reduces the geometric cavity path length of 61.5 cm to an effective cavity length d_eff. To estimate it we coupled the NO₃ source to the cavities and took the ratio of the signals from both NO₂ and NO₃ absorption obtained with and without mirror purge flow. Averaging the ratios across both analytes and three separate experiments result in effective cavity lengths (± 2σ) of (59.7 ± 1.1) and (60.3 ± 0.9) cm for the NO₃ and N₂O₅ channel, respectively. Note that both values are, within their associated uncertainties, consistent with the reduction of the geometric cavity length to 60.6 and 60.3 cm, respectively, predicted from the cavity-to-sample-flow ratio (i.e. the pure dilution effect).

3.2 The mirror reflectivity

Equation (1) emphasizes the need of precise knowledge of the wavelength-dependent mirror reflectivity R(λ). The two most common methods to determine R(λ) include: (i) measuring a known concentration of a stable absorbing gas compound (Venables et al., 2006; Ventrillard-Courtillot et al., 2010), and (ii) measuring the ring-down time or the phase shift (Ball et al., 2004; Kennedy et al., 2011; Langridge et al., 2008). In this study we use the first method by purging the cavities with NO₂ taking advantage of its absorption across the entire spectral region of the LED emission, its well-known absorption cross sections ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{2}}}$ (in ${\mathrm{cm}}^{\mathrm{2}}\mathrm{molec}{.}^{-\mathrm{1}}$) as well as its precisely known concentrations injected from the gas cylinder ($N_{{\mathrm{NO}}_{\mathrm{2}}}$ in molecule cm⁻³) thanks to the coupled NO₂ analyzer directly measuring each cell outflow during the calibration process (Fig. 1 dashed black lines). Together with d_eff (Sect. 3.1) and the directly measured transmission T(λ), the reflectivity R(λ) is deduced using Eq. (5):

$$\begin{array}{}\text{(5)}& R\left(\mathit{\lambda }\right)=\mathrm{1}-\left(d_{\text{eff}}{\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{2}}}{N}_{{\mathrm{NO}}_{\mathrm{2}}}{\displaystyle \frac{T\left(\mathit{\lambda }\right)}{\mathrm{1}-T\left(\mathit{\lambda }\right)}}\right)\end{array}$$

To compensate for the weak absorption cross-section of NO₂ in the 660–670 nm spectral range (Fig. 2b, orange), high NO₂ mixing ratios (400–800 ppbv) were used to reduce the uncertainty in the mirror reflectivity determination. Figure 3 shows representative wavelength-dependent reflectivity measurements for both cavities. Between 640 and 670 nm, R(λ) ranged from 99.9866 % to 99.9886 % in the NO₃ cavity (blue points) and from 99.9768 % to 99.9837 % in the N₂O₅ cavity (orange points). Linear regression (solid lines) of the reflectivity yielded (1.18 ± 1.58) × 10⁻⁸ nm⁻¹ × λ + 99.987 % and (4.81 ± 0.75) × 10⁻⁸ nm⁻¹ × λ + 99.949 %. The slope for the NO₃ cavity is not significantly different from zero, indicating no evidence for a systematic wavelength dependence of R over the investigated spectral range. In contrast, the N₂O₅ cavity exhibits a statistically significant positive slope. Given the relatively small magnitude, the scatter of this variation and the greater uncertainty in the NO₂ absorption cross sections at 353 K compared with 298 K, the observed wavelength dependence may partly reflect systematic uncertainties in the reflectivity determination rather than an intrinsic wavelength dependence of R.

Figure 3 Exemplary mirror reflectivity measurements for the NO₃ (blue circles) and N₂O₅ (orange circles) channels along with linear regressions (same coloured solid lines).

At 662 nm, corresponding to the NO₃ maximum absorption, the reflectivity was found to be 99.988 % for the NO₃ channel and 99.984 % for the N₂O₅ channel, in good agreement with the manufacturer's specifications ((99.98 ± 0.01) % at 630–690 nm). The corresponding overall optical path lengths L(λ) were calculated with $d/(\mathrm{1}-R(\mathit{\lambda }\left)\right)$ as 5.1 and 3.8 km, for the NO₃ and N₂O₅ channel, respectively.

Mirror reflectivity was also found to depend strongly on mirror cleanliness. During the ACROSS campaign (the instrument's first field deployment), the reflectivity at 662 nm varied between 99.983 % and 99.988 % for the NO₃ channel, corresponding to changes in L by a factor of 0.7, underlining the necessity of daily (or even more frequent) mirror reflectivity measurements.

Figure 4 NO₃ equivalents detected in the unheated N₂O₅ cavity (black points) resulting from NO₃ and thermally dissociated N₂O₅ provided from the glass reactor as a function of the preheater temperature setpoint (“thermogram”). Model 1 (orange line) shows the theoretically expected thermogram between 300 and 1000 K using IUPAC-recommended reaction rate coefficients for k₂ and k₃ as well as k₈ according to Womack et al. (2017). Model 2 includes a temperature-dependent NO₃ wall loss rate ($k_{\text{Hill}}(T/{\mathrm{s}}^{-\mathrm{1}})=\mathrm{0.1}{\mathrm{s}}^{-\mathrm{1}}+(\mathrm{0.3}\times T^{\mathrm{25}}/({\mathrm{410}}^{\mathrm{25}}+T^{\mathrm{25}})$) and was adjusted to reproduce the observations. The vertical grey dashed line indicates the optimal temperature setpoint of 95 °C.

3.3 The thermal dissociation of N₂O₅

Detection of ambient N₂O₅ requires its thermal dissociation to NO₃ via the TDI mentioned in Sect. 2.2. To determine the TDI heater temperature needed for quantitative N₂O₅ conversion, we coupled our NO₃ source upstream of the TDI and the N₂O₅ cavity, varying the TDI setpoint temperature between 300 and 473 K while recording the signal in the unheated N₂O₅ cavity, which thus served solely to characterize TDI conversion efficiency. The resulting NO₃ signal as a function of TDI temperature (the “thermogram”) is shown in Fig. 4 (black points). N₂O₅ dissociation increases continuously above 300 K, reaching a maximum at 373 K; above this temperature, the signal decreases following a sigmoidal shape before levelling off between 450 and 475 K.

This behaviour prompted us trying to reproduce the observation and to run numerical simulation using FACSIMILE (Curtis and Sweetenham, 1987) based on the residence time in the TDI and cavity (derived from their volumes and the flow rate) together with the relevant reaction rate coefficients, including the NO₃–N₂O₅–NO₂ thermal equilibrium (k₂ and k₃; IUPAC, 2026), NO₃ thermolysis (k₈, Womack et al., 2017) and an NO₃ wall loss reaction (Reaction R9):

$$\begin{array}{}\text{(R8)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+M\to {\mathrm{NO}}_{\mathrm{2}}+\mathrm{O}+M\text{(R9)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\text{surface\hspace{0.17em} }\to \text{ \hspace{0.17em}products}\end{array}$$

In order to verify if our observations are consistent with known gas-phase chemistry, we set k₉ to 0 s⁻¹ in Model 1 (Fig. 4, orange). This model reproduces the N₂O₅ dissociation up to 373 K very well, but predicts a plateau beyond the maximum, since NO₃ thermolysis only becomes significant above 600 K – implying that a heterogeneous process, active only above 373 K, must be responsible for the observed decline. We reproduced the observations empirically with Model 2 by adding a Hill-type, temperature-dependent wall-loss term k₉=k_Hill(T) = $\mathrm{0.1}{\mathrm{s}}^{-\mathrm{1}}+(\mathrm{0.3}\times T^{\mathrm{25}}/({\mathrm{410}}^{\mathrm{25}}+T^{\mathrm{25}}\left)\right)$: an arbitrarily chosen constant background loss (0.1 s⁻¹) between 300 and 373 K, followed by a sigmoidal increase in k₉ to 0.4 s⁻¹ between 373 and 473 K. Such behaviour is consistent with a surface process governed by an activation barrier – for instance, the desorption of a passivating layer once a threshold temperature is exceeded. The background loss of 0.1 s⁻¹ is consistent with the wall loss we estimated for our unheated NO₃ cavity (see below) while the high temperature wall loss of 0.4 s⁻¹ appears plausible considering that previous studies report NO₃wall loss rates that are 3–4 times higher in heated Teflon (or Teflon-coated) tubes than in their unheated equivalents (Sobanski et al., 2016; Türk et al., 2026). We find that 95 °C (grey dashed line) is the optimal TDI temperature, as it guarantees quantitative N₂O₅ conversion and lower NO₃ wall losses.

N₂O₅ detection typically relies on quantitative thermal conversion to NO₃ at a fixed, elevated temperature, with TDI temperature commonly verified by calculating the thermal N₂O₅ lifetime or via thermograms based on NO₂ (Friedrich et al., 2020; Womack et al., 2017), but rarely on NO₃ detection (Dubé et al., 2006; Fuchs et al., 2008). Dubé et al. (2006) determined the conversion efficiency at temperatures up to only 150 °C and saw a marginal decrease above 130 °C. Fuchs et al. (2008) focused on the interplay of sampling flow, TDI temperature and conversion efficiency rather than discussing thermograms at a fixed flowrate. The behaviour observed here underscores the importance of thoroughly verifying the optimal TDI temperature based on NO₃ detection, as done in this study.

Figure 5 (a) Dependency between residence time and measured NO₃ mixing ratios (orange circles) in the NO₃ cavity. The blue dashed line indicates modelled NO₃ mixing ratios accounting for reestablishment of the thermal equilibrium while the solid orange line shows a model run including an NO₃ wall loss rate adjusted to reproduce observations. (b) Dependency between measured NO₃ mixing ratios and the summed residence time in N₂O₅ cavity (maintained at 80 °C) and TDI heated at 80 °C (grey crosses), 95 °C (blue circles) and 200 °C (orange squares). Solid lines in the same colour represent corresponding linear regressions. The slopes ± 2σ are indicated in the legend and correspond to the NO₃ wall loss rate.

3.4 Losses of NO₃ during sampling

NO₃ is a highly reactive radical prone to surface losses during sampling. While inert materials (PFA, FEP, halocarbon wax) and short residence times minimize these losses, they remain a significant artefact in cavity systems (Fuchs et al., 2008). NO₃ (and N₂O₅) can be lost on: (1) PFA inlet tubing, (2) the filter holder, (3) the membrane inlet filter, and (4) the cavity (and TDI, for the N₂O₅ channel). Losses on PFA sampling lines are reported to be negligible and are typically disregarded by keeping residence times short relative to the cavity via minimal tubing length or high bypass flow (Crowley et al., 2011; Kennedy et al., 2011; Türk et al., 2026). The same applies to our filter holder: We observed no alteration in the NO₃ signal whether sampling was performed through it or through a 15 cm 1/4 in. PFA tubing. Losses on the PTFE inlet filter type we deploy (Pall Corporation, R2PJ047) are very common and have been characterized repeatedly during the past 25 years, with reported transmission values reproducibly ranging between 86 % and 98 % (Brown et al., 2002; Crowley et al., 2010; Dubé et al., 2006; Nam et al., 2022; Türk et al., 2026). The most recent estimate from Türk et al. (2026) reports a transmission efficiency of (90 ± 5) % during field operation. By repeatedly switching between sampling NO₃ from CESAM through PFA tubing and through a clean filter, we found a transmission efficiency (± 2σ) of (90 ± 1) %, thereby confirming previous estimates (Fig. S3). We therefore selected this value for our correction factor calculation, i.e. T_Filter is 0.9 in both channels. Direct heterogeneous N₂O₅ losses on Teflon-coated surfaces are negligible relative to NO₃ losses and are therefore commonly excluded from the correction procedure (Fuchs et al., 2008; Kennedy et al., 2011; Türk et al., 2026).

To complete the correction scheme, we estimated the wall loss rate in the NO₃ cavity and the combined wall loss rate of TDI + N₂O₅ cavity. The NO₃ source was coupled to each cavity in turn, and residence time was varied via the cavity flow rate as previously demonstrated (Fuchs et al., 2008; Sobanski et al., 2016; Türk et al., 2026); for the NO₃ cavity, the TDI was positioned between source and cavity to boost NO₃ concentrations. Figure 5a shows the resulting exponential decay in NO₃ with increasing residence time in the NO₃ cavity. Since the NO₃ $/$ NO₂ mixture is not in thermal equilibrium upon entering the cavity, the decay was simulated with our box model from above (including k₂ and k₃ only), adjusting the initial NO₃ value to match the first data point. The dashed blue curve shows the signal decrease expected from equilibration alone, which fails to reproduce the data; varying the NO₃wall loss rate to best-fit the observations (orange line) yields (0.10 ± 0.02) s⁻¹. With our residence time in the NO₃ cavity of 1.53 s, this results in a transmission efficiency $T_{{\mathrm{NO}}_{\mathrm{3}}\mathrm{channel}}$ of (88 ± 2) %.

The same approach was applied to the TDI + N₂O₅ cavity ensemble (latter thermostated at 80 °C), and repeated at three TDI temperatures (Fig. 5b) to qualitatively validate the wall-loss hypothesis underlying the N₂O₅ thermogram (Fig. 4, blue curve). Here, no equilibrium correction is needed, so effective wall loss rates were derived directly from the slopes (± 2σ) of linear regressions: (0.26 ± 0.02), (0.27 ± 0.03), and (0.65 ± 0.11) s⁻¹ at TDI temperatures of 80, 95, and 200 °C, respectively – corresponding to transmission efficiencies $T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}$ of (64 ± 2), (63 ± 3), and (34 ± 6) %. Note that even though the thermogram (Fig. 4) implies incomplete N₂O₅ conversion at 80 °C, numerical simulations suggest quantitative dissociation within the first 0.2 s (from overall residence time 1.31 s) inside the heated cavity, suggesting that the linear regression approach is appropriate even at that temperature. The results in Fig. 5b are consistent with the thermogram: wall loss rates show no significant increase between 353 and 368 K, but increase 2.5-fold at 473 K. Note that we cannot directly implement the measured wall loss rates from Fig. 5b in the box model since the N₂O₅ cavity was unheated when measuring the thermogram. This reinforces the need to carefully select the TDI temperature to avoid unnecessarily large correction factors and the associated increase in measurement uncertainty. Recall that for freshly formed NO₃ in the TDI, k_Wall only applies to the residence time in the cavity leading to slightly higher transmissions $T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }$ of (67 ± 2), (66 ± 3) and (37 ± 6) %, at temperatures of 80, 95, and 200 °C, respectively.

3.5 Performance

The experiments presented above establishes the instrument response and the correction procedures required to account for sampling artifacts, including wall losses. With these effects quantified, the analytical performance of the instrument can now be assessed in terms of detection limits and overall measurement uncertainty.

3.5.1 Allan deviation and detection limits

The intrinsic detection capability of the instrument was estimated using overlapping Allan deviation analysis, which characterizes signal stability as a function of integration (averaging) time τ. For this purpose, both cavities were continuously flushed with dry zero air, and 1778 consecutive spectra with a sampling rate of 1 s were recorded under stable laboratory conditions. After converting the measured transmissions to NO₃ equivalents applying Eq. (1) and fitting with ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{3}}}$, the overlapping Allan deviation was calculated using AllanTools.py (version 2024.4).

The resulting Allan deviation curves for the NO₃ and N₂O₅ channel under typical measurement conditions are shown in Fig. 6. Increasing the integration time initially decreases the Allan deviation in both channels, as expected, with a slope of ca. $\mathrm{1}/\sqrt{\mathit{\tau }}$ because uncorrelated fluctuations in transmission (white noise) are progressively reduced through averaging. At longer integration times, however, slow instrumental drifts – arising from factors such as LED intensity fluctuations, cavity alignment and variations in pressure and temperature – become increasingly important, causing the Allan deviation to rise. The minimum of the Allan deviation therefore defines the optimum integration time reconciling averaging and drift effect and the corresponding noise-limited limit of detection achievable under these controlled conditions. Above 10 s, the two channels diverge: the N₂O₅ channel remains stable up to 100 s, whereas drift degrades the NO₃ channel LOD beyond 30 s. During the data acquisition period, the internal NO₃ cavity temperature increased by 0.6 °C. While the absence of temperature regulation in the NO₃ cavity may lead to temperature-induced misalignment, potentially explaining its lower long-term stability compared to the N₂O₅ cavity, other sources of slow instrumental drift may also contribute to this observation. The long-term oscillations in the N₂O₅ Allan plot likely reflect heating cycles from the temperature controller. Overall, Fig. 6 indicates an optimal compromise integration time of 15 s, yielding noise-limited LODs (LOD_noise) of 1.5 pptv (NO₃) and 2.2 pptv (N₂O₅). This analysis assumes that the mirror reflectivity remains constant. Drift effects, contamination and cleaning can additionally lead to a variability in R, thereby additionally affecting the LOD. For instance, over the entire ACROSS campaign, the standard deviation (1σ) of (1−R) from consecutive reflectivity estimations serving as measure for its variability was 21 % for the NO₃ channel and 27 % for the N₂O₅ channel. Propagating these 1σ variabilities into the Allan deviation analysis gives upper limits for LOD_noise of 1.8 pptv (NO₃) and 2.8 pptv (N₂O₅). The effect of the (1−R) variability on LOD_noise is represented by the shaded areas in Fig. 6.

Figure 6 Overlapping Allan deviation (1σ) in dependence of the NO₃ channel's (blue circles) and N₂O₅ channel's (orange squares) integration time. The grey dashed line marks the $\mathrm{1}/\sqrt{\mathit{\tau }}$ slope. Ther vertical black dashed line marks the optimal integration time of 15 s. The effect of potential variabilities in mirror reflectivity is represented by shaded areas.

Figure 7 Retrieval performance of the NO₃ fitting routine as a function of interfering NO₂ and water vapor, based on Monte Carlo simulations of synthetic spectra for the NO₃ channel (10 noise realisation points average, 600 LHS points): (a, b) Retrieved vs. true NO₃ mixing ratio, with points colored by (a) true NO₂ (ppbv) and (b) relative humidity (RH, % at 23 °C). The dashed line indicates the 1:1 relationship; the dotted red line marks LOD_noise derived from the Allan deviation, and the solid black line marks the effective detection limit LOD_eff, which additionally incorporates the standard deviation (2σ) of the retrieval bias across all simulated spectra. (c, d) Retrieval bias (retrieved – true NO₃) for points NO₃ > LOD_noise plotted against (c) NO₂ and (d) RH, colored by the complementary variable in each case. Black circles show bin-averaged values (± 1σ). Black lines show weighted linear fits to the bin-averaged points.

As described in Sect. 2.2, NO₃ (and N₂O₅) concentrations are estimated by spectral fitting. Due to the spectral interference with NO₂ and H₂O, both of which are usually present alongside NO₃ and N₂O₅ in ambient air, the LOD is likely to be worse under field conditions. Even though it is well known that both NO₂ and water vapour can influence the NO₃ retrieval performance of the fitting routine (Nam et al., 2022; Wang and Lu, 2019), to the best of our knowledge, their combined impact has not yet been systematically assessed. To investigate this effect, we were inspired by a synthetic-spectrum approach used to characterize fitting bias in other spectroscopic retrievals (e.g. Adkins and Hodges, 2022), here applied to IBBCEAS. Synthetic CEAS transmission spectra were generated using a rearranged form of Eq. (1), $T=[\mathrm{1}+\mathit{\alpha }(\mathit{\lambda })\cdot d_{\text{eff}}/(\mathrm{1}-R\left(\mathit{\lambda }\right)){]}^{-\mathrm{1}}$, where α is directly computed from the laboratory reference cross-sections of NO₃ and NO₂ and the measured H₂O reference spectrum via Eq. (2). Gaussian white noise, scaled from the Allan-deviation noise floor (LOD_noise) via the NO₃ reference spectrum, was added to α(λ) to yield an equivalent spectral noise level. Concentration combinations of NO₃ (0–10 pptv), NO₂ (0–50 ppbv), and H₂O (RH = 0.3 %–100 % at 23 °C) were drawn using a Latin Hypercube design (600 unique points, each with 10 independent noise realisations, giving 6000 spectra in total) (McKay et al., 1979) embedded in SciPy, and each synthetic spectrum was subsequently analysed with the same operational retrieval routine used for the ambient measurements.

Retrieved (averaged over the 10 noise realisations) vs. true NO₃ mixing ratios are shown in Fig. 7a and b, coloured by NO₂ and RH, respectively. As expected, the routine underperforms below LOD_noise (red dashed line), tending to overestimate NO₃, with scatter narrowing toward the 1:1 line (black dashed) at higher mixing ratios. This scatter shows no dependence on NO₂ (Fig. 7a) but correlates with RH (Fig. 7b). Plotting retrieval bias against NO₂ and RH (Fig. 7c and d) confirms this pattern: linear regression reveals no significant NO₂ dependence, but a modest negative trend with RH, corresponding to biases of +0.49 to −0.71 pptv, comparable to the retrieval's inherent scatter (± 0.64 pptv, 1σ). This suggests that the presence of H₂O and NO₂ biases the spectral fitting as soon as both are included as fitting parameters, with the bias showing only a marginal dependence on H₂O concentration and no apparent dependence on NO₂ concentration. Hence, instead of indicating an LOD depending on H₂O and NO₂, we prefer adding twice this inherent bias (2σ) across all 600 samples to LOD_noise resulting in an effective LOD of 3.2 pptv (solid black line, Fig. 7a and b), above which the data scatter symmetrically around the 1:1 line – consistent with this threshold representing a meaningful detection limit. The same analysis was carried out for the N₂O₅ channel, using the corresponding reference spectra and LOD_noise to generate a separate set of 6000 spectra; results are shown in Fig. S4. In this case, the bias decreases slightly with NO₂ and increases with RH, though again by a magnitude negligible compared to the fit-induced scatter. Using the standard deviation (2σ) of the mean bias yields an effective LOD of 4.4 pptv for the N₂O₅ channel. Note that this simulation approach only allows deduction of ballpark values as it neglects variability in both R and ${\mathit{\alpha }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\left(T\right)$. For example, using the upper-limit values of LOD_noise, which account for variability in R results in worst-case (recall that R may fluctuate in both senses) effective LODs of 4.0 pptv (NO₃) and 5.8 pptv (N₂O₅).

The synthetic spectra also show an RH-dependent NO₂ bias (Fig. S5), which increases approximately linearly with RH by 0.20 (NO₃ channel) and 0.33 ppbv per % RH (N₂O₅ channel). For NO₃ above the LOD, this NO₂ bias is only weakly correlated with our above-mentioned NO₃ biases (r = −0.36 and +0.32 for the N₂O₅ and NO₃ channel, respectively), thereby confirming the low sensitivity of the NO₃ retrieval accuracy to NO₂ quantification. Nevertheless, taking advantage of the instrument's integrated CAPS analyzer, constraining NO₂ in the fit to measured values may allow reduction of the retrieval bias in both channels – especially under very humid conditions.

3.5.2 Total measurement uncertainty

Alongside the LOD, the total measurement uncertainty (TMU) is another important indicator of instrument performance. As is evident from Eqs. (1)–(3), the TMU of the NO₃ measurement is obtained by propagating, in quadrature (root-sum-square method), the relative uncertainties in: the retrieved $N_{{\mathrm{NO}}_{\mathrm{3}}}$ from the spectral fitting procedure, the mirror reflectivity R, the effective path length d_eff, the NO₃ absorption cross-section ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{3}}}$, and the NO₃ transmission through the filter (T_Filter) and cavity ($T_{{\mathrm{NO}}_{\mathrm{3}}\mathrm{channel}}$). This assumes the individual error sources are independent and uncorrelated.

The uncertainty in $N_{{\mathrm{NO}}_{\mathrm{3}}}$ from the spectral fitting procedure is accessible via the relative bias, the ratio of absolute bias to true NO₃ mixing ratio, derived from the simulated spectra in the previous section. This relative bias for the NO₃ channel is plotted against the true NO₃ mixing ratio in Fig. 8. It decreases exponentially with increasing NO₃ mixing ratio and approaches a constant systematic bias above the effective LOD. We captured this trend by binning the data and fitting a biexponential decay; the y-offset of the fit gives the relative fitting uncertainty, found to be 6.7 %.

Figure 8 Relative bias in retrieved NO₃ ($\mathrm{|}\text{retrieved}-\text{true}\mathrm{|}/\text{true}$) versus true NO₃ concentration from Monte Carlo simulations for the NO₃ channel. Gray points: individual retrievals; black circles: quantile-binned means ± 1σ. Solid line: biexponential fit with parameters (a₁, a₂, b₁, b₂, c), relative bias = $a_{\mathrm{1}}\times \text{exp}(-b_{\mathrm{1}}\times {\mathrm{NO}}_{\mathrm{3}})+a_{\mathrm{2}}\times \text{exp}(-b_{\mathrm{2}}\times {\mathrm{NO}}_{\mathrm{3}})+c$, capturing the noise-dominated divergence at low NO₃ and the systematic interference floor (c=0.067, blue dashed line) at higher NO₃. Orange dotted line: effective LOD.

The relative uncertainty in the mirror reflectivity R is derived from Eq. (5) by propagating the relative uncertainties in d_eff (1.8 %), ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{2}}}$ at 298 K (3 %), $N_{{\mathrm{NO}}_{\mathrm{2}}}$ concentration (0.5 %), and the spectral transmission (6 %, from the Allan deviation analysis), giving 7 %. Propagating this together with the uncertainties in d_eff, ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{3}}}$ (5 % at 298 K), T_Filter (5 %; Türk et al., 2026), and $T_{{\mathrm{NO}}_{\mathrm{3}}\mathrm{channel}}$ (2 %) yields an overall TMU of 12 % for [NO₃].

The same approach applies to the combined NO₃ + N₂O₅ signal $N_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ measured in the N₂O₅ channel. Repeating the Fig. 8 analysis for this channel (Fig. S6) gives a relative fitting uncertainty of 9.9 %.

Propagating this with the uncertainty in R (10 %, itself from 5 % in ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{2}}}$ at 353 K, 1.5 % in d_eff, and 9 % in the spectral transmission) and in ${\mathit{\sigma }}_{{\mathrm{NO}}_{\mathrm{3}}}$ at 353 K (8 %) yields a relative uncertainty of 17 % in the summed signal.

Because N₂O₅ is obtained by channel differencing (Eq. 4), its total uncertainty requires propagating absolute errors (indicated with Δ) and directly measured values, and is given by:

$$\begin{array}{}\text{(6)}& {\mathrm{\Delta }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}=\sqrt{\begin{array}{c}{\left(\frac{{\mathrm{\Delta }}_{N_{{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}}}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}\right)}^{\mathrm{2}}\\ +{\left(\frac{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}\left[{\mathrm{NO}}_{\mathrm{3}}\right]{\mathrm{\Delta }}_{T_{\text{Filter}}}}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}\right)}^{\mathrm{2}}\\ +{\left(\frac{T_{\text{Filter}}{T}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}\mathrm{\Delta }\left[{\mathrm{NO}}_{\mathrm{3}}\right]}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}\right)}^{\mathrm{2}}\\ +{\left(\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]\frac{\mathrm{\Delta }{T}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}\right)}^{\mathrm{2}}\\ +{\left(\frac{T_{\text{Filter}}\left[{\mathrm{NO}}_{\mathrm{3}}\right]\mathrm{\Delta }{T}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}}{T_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\mathrm{channel}}^{\ast }}\right)}^{\mathrm{2}}\end{array}}\end{array}$$

The uncertainty related to [N₂O₅] depends on the NO₃-N₂O₅ ratio. During the ACROSS campaign (see below), an average relative TMU of 21 % for N₂O₅ was found.

Table 1 Comparison of our instrument's performance with those of selected other IBBCEAS setups. Values estimated for our setup are highlighted in bold.

3.5.3 Comparison to other instruments

Table 1 compares the LOD and TMU of this instrument with previous closed-path, field-deployable IBBCEAS setups for NO₃ and N₂O₅.

Direct comparison is complicated by differing averaging times: several instruments report LODs at 1 s (Ling et al., 2023; Nam et al., 2022; Wang et al., 2017) or second-to-few-second integration (Ball et al., 2004; Kennedy et al., 2011; Langridge et al., 2008; Ventrillard-Courtillot et al., 2010), whereas our LOD is reported at 15 s. Since LOD scales approximately with the inverse square root of averaging time, our 1.5 pptv at 15 s corresponds to a higher 1 s-equivalent LOD, indicating that, while not the most sensitive system in this comparison, this instrument's noise-limited performance remains within the established range for closed-path IBB-CEAS instruments. Comparable or lower LODs at shorter integration times, as for example reported by Kennedy et al. (2011) and Nam et al. (2022), often go hand in hand with longer effective path lengths achieved through mirrors with higher reflectivity. However, higher mirror reflectivity reduces the intensity reaching the detector, so that increasing R does not necessarily improve the LOD (Vaughan et al., 2008). Our choice of mirror reflectivity and cavity length represents a compromise between sensitivity, transmitted intensity, mechanical stability and cost.

More directly comparable is the TMU, which varies less sensitively with averaging time. Here, our value of 12 % for NO₃ is in good agreement with Kennedy et al. (2011, 11 %) and Nam et al. (2022, 11 %), and notably lower than Wang et al. (2017, 19 %). For N₂O₅, our mean TMU of 21 % is comparable to the lower end of the range reported by Kennedy et al. (2011, > 14 %) and Wang et al. (2017, 22 %–36 %). This indicates that our systematic uncertainty of our retrieval is competitive with previously reported closed-path IBBCEAS instruments.

Importantly, the effective (field-relevant) LODs reported here, 3.2 pptv for NO₃ and 4.4 pptv for N₂O₅, already account for the fitting-induced bias identified in Sect. 3.5.1, which to our knowledge has not been systematically quantified in prior studies. Kennedy et al. (2011) reported effective LODs deduced from daytime ambient measurements. Other works report only a noise-limited LOD, however the true field detection limit may in practice be similarly elevated. The analysis presented here suggests that noise-limited LODs alone may understate the effective detection threshold achievable under realistic ambient conditions.

4 Field deployment

The NOyBOx instrument was deployed for the first time during the ACROSS campaign (Cantrell and Michoud, 2022), which took place over one month in summer 2022. The instrument was set up atop a 40 m tower amid and above the canopy (16–20 m) of the Rambouillet forest, ca. 50 km from Paris – a site dominated by biogenic emissions but occasionally impacted by urban plumes emanating from Paris. The IBBCEAS subsystem was operated as detailed in Sect. 2.2, but with a 120 s integration time and a TDI temperature of 473 K; R and I₀ were determined every 24 h and 1–1.5 h, respectively, and inlet filters were changed manually every 4–6 h. The N₂O₅ inlet filter was positioned between the TDI and the cavity during that period, which is why Eq. (4) was modified accordingly to retrieve N₂O₅ mixing ratios. A power outage disabled our NO analyzer, so NO was instead measured with another chemiluminescence instrument (T200U, Aerodyne; LOD = 30 pptv) operated by IMT Nord Europe. The NO_y and NO₂ analyzers were operated as described in Sect. 2.1, allowing NO_y to be derived as well. O₃ was monitored by a UV absorption instrument (HORIBA APOA-370, LOD = 2.5 ppbv), and temperature was measured at 5 and 41 m along the tower (Atexis PT1000 and Thermoset PT100) by CNRM (Météo-France).

Figure 9 Nocturnal time series during the ACROSS campaign (16–17 July 2022, 00:00–06:00 LT); yellow shading indicates sunrise (05:30 LT). (a) NO₂ (orange, left axis) and O₃ (blue, right axis). (b) Measured NO₃–N₂O₅–NO₂ relationship $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\right[{\mathrm{NO}}_{\mathrm{2}}\left]\left[{\mathrm{NO}}_{\mathrm{3}}\right]\right)$ (orange), compared with the evaluated, temperature-dependent equilibrium constant from Burkholder et al. (2025) (blue line, shading = uncertainty). (c) NO₃ (blue, left axis) and N₂O₅ (orange, right axis) mixing ratios with the total measurement uncertainty (shading), alongside NO (gray, right axis, provided py IMT Nord Europe); the dashed line marks the NO detection limit (30 pptv). (d) NO_y (blue, left axis) and NO_z (orange, right axis). (e) Ambient temperature at 40 m (blue, left axis) and the temperature difference ΔT between 5 and 41 m (orange, right axis) from CNRM (Météo-France).

Figure 9 shows the time series of a representative night (16–17 July 2022) from this campaign. Note that NO₃ levels were additionally corrected by a factor of 0.94 on average using our box model introduced in Sect. 3.3. This accounts for further NO₃ formed by N₂O₅ dissociation (Reaction R3) during the residence time in the cavity, which was ca. 5 K warmer than ambient air (see Fig. S7). O₃ decreased from 50 to 44 ppbv and NO₂ from 4.7 to 2.6 ppbv over the course of the night (Fig. 9a, right axis, blue); NO (Fig. 9c, right axis, grey) remained below the LOD until sunrise at ca. 05:30 LT. It was a mild summer night, with temperature (Fig. 9e, blue) decreasing from 292 to 289 K. NO₂ peaked at 4.7 ppbv at 00:30 LT, increasing the NO₃ production rate; by 01:00 LT, NO₃ and N₂O₅ reached 6 and 30 pptv, respectively (Fig. 9c). Despite the continued gradual decline in NO₂ and O₃ thereafter, NO₃ and N₂O₅ continued to increase through the night, coinciding with the onset of a temperature inversion (ΔT = T_41 m–T_5 m, Fig. 9e, orange) reaching ca. 3 K, in which air atop the tower was warmer than at ground level. As discussed in detail for this campaign by Dewald et al. (2024) and Andersen et al. (2024), such inversions decouple the tower from below-canopy reactive trace-gas emissions, reducing NO₃ reactivity – consistent with the observed rise in NO₃ $/$ N₂O₅. Peak mixing ratios of 12 pptv NO₃ and 182 pptv N₂O₅ were reached at 05:15 LT, shortly before both fell below the LOD around sunrise (05:30 LT).

Using our simultaneous NO₃, N₂O₅, and NO₂ measurements, we calculated $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\left[{\mathrm{NO}}_{\mathrm{3}}\right]\right[{\mathrm{NO}}_{\mathrm{2}}\left]\right)$ (Fig. 9b, orange) and compared it to the purely temperature-dependent value recommended equilibrium constant K_eq by JPL (Burkholder et al. (2025); blue line). The two agree fairly within uncertainties for most of the night, with only occasional deviations. Following Crowley et al. (2010), the time needed to reach equilibrium, ($k_{\mathrm{2}}/k_{\mathrm{3}}$ × [NO₂])⁻¹, was 6–10 s on this night using IUPAC-recommended rate coefficients, so thermal equilibrium should be established essentially throughout. We attribute the initial disagreement to instrument line and filter passivation from priorly sampled highly reactive air, an effect also reported for other cavity-based setups (Crowley et al., 2011; Türk et al., 2026). The deviations at 04:30 LT can be reconciled with local disturbances of the NO₃–N₂O₅ equilibrium, for instance due to boundary-layer instabilities as reflected in the continuous breakdown of the temperature inversion (Fig. 9e), leading to sudden BVOC entrainment and very local NO₃/N₂O₅ sinks (Brown et al., 2003; Dewald et al., 2020). Indeed, Chen et al. (2022) confirmed systematically with simulations that a purely temperature-derived K_eq is expected to deviate substantially from the ambient $\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]/\left(\left[{\mathrm{NO}}_{\mathrm{3}}\right]\left[{\mathrm{NO}}_{\mathrm{2}}\right]\right)$ ratio when competing NO₃ and N₂O₅ sinks prevent the system from reaching true equilibrium.

NO_y remained stable at ca. 5 ppbv throughout the night (panel d, blue), indicating that deposition of newly formed NO_y species is negligible. NO_z (= NO_y − NO_x; Fig. 9d, orange) fell to zero between 00:00 and 01:00 LT, indicating that NO_x was the only reactive nitrogen species present at that time and pointing to a certain degree of decoupling from below-canopy emissions. With the onset of NO₃ and N₂O₅ formation, 0.5–1 ppbv of NO_z was produced showing that NO₃ and N₂O₅ alone cannot close the NO_y budget. Indeed, these elevated NO₃, N₂O₅, and NO_y mixing ratios coincided with the detection of NO₃ + BVOC oxidation products by CIMS; this will be explored in a forthcoming publication.

This case study illustrates the broader value of combining NO_x, NO_y, and NO₃ $/$ N₂O₅ measurements within a single instrument. By simultaneously constraining NO_z production, we can directly assess how efficiently NO₃ and N₂O₅ are being converted into higher-generation products – as demonstrated here, where the observed NO_z increase accounted for only a fraction of the concurrent NO₃ $/$ N₂O₅ signal, pointing to additional, yet-unquantified oxidation pathways. For example, the NO₃-initiated oxidation of BVOCs can lead to the formation of organic nitrates, which themselves may be hydrolysed to contribute to HNO₃ production.

5 Summary and conclusions

We presented the design and characterization of the NOyBOx instrument, combining NO_x, NO_y, and IBBCEAS-based NO₃ $/$ N₂O₅ measurements within a single framework. The noise-limited and effective detection limits of the NO₃ and N₂O₅ channels were determined via Allan deviation analysis and a synthetic-spectra approach, yielding effective LODs in ambient air conditions of 3.2 and 4.4 pptv, and total measurement uncertainties of 12 % and 21 %, respectively – performance competitive with previously reported closed-path IBBCEAS instruments. Moreover, using synthetic spectra spanning realistic ambient NO₂ and H₂O concentrations, we showed that spectral interference from these species can bias the NO₃ $/$ N₂O₅ retrieval beyond what is predicted by the noise-limited LOD alone. Accounting for this bias is essential to avoid underestimating the true detection threshold under field conditions, and we recommend that future IBBCEAS studies evaluate this effect explicitly rather than relying on noise-limited LODs alone.

A thermogram of N₂O₅ based on NO₃ detection was performed. With the exception of Dubé et al. (2006), which covers only the range between 70 and 150 °C, no NO₃-based thermogram is available in the literature. Our study therefore provides the first complete NO₃-based thermogram of N₂O₅ over the temperature range of 30 to 200 °C, revealing substantially high wall losses at elevated temperatures. This finding underscores the necessity of characterizing the TDI for N₂O₅ dissociation based on NO₃ detection in order to prevent the application of unnecessarily high correction factors.

Finally, the instrument was successfully deployed for the first time during the ACROSS field campaign, thereby demonstrating the value of combining NO_x, NO_y, and NO₃ $/$ N₂O₅ within a single internally consistent framework. As inferred from our case study, NO₃-initiated chemistry formed a significant source of other NO_z species. Such observations, achievable only through co-located NO_x, NO_y, and NO₃ $/$ N₂O₅ measurements, is essential for constraining the fate of reactive nitrogen at night and represents a key advantage of the NOyBOx over instruments measuring these species in isolation.