Reactive nitrogen oxides (NOx) as nitrogen monoxide (NO) and nitrogen dioxide (NO2) play a crucial role in atmospheric photochemistry both in the troposphere and in the stratosphere (Crutzen, 1970). In the tropospheric boundary layer, the NOx origin is mainly anthropogenic from the combustion of fuels and the use of nitrogen-based fertilizers. To a lower extent, biomass burning and biological processes in soils contribute to NOx production (Crutzen, 1979). In the upper troposphere near the tropopause, NOx concentration is mainly controlled by lightning events and air traffic (Grewe et al., 2001). As a precursor to several harmful air pollutants, e.g., ozone (O3) and nitric acid (HNO3), the build-up of NOx in the troposphere directly affects human health (World Health Organization Regional Office for Europe, 2003). In the stratosphere, NOx is produced by the photolysis of nitrous oxide (N2O), which has been transported through the tropopause and is part of the biospheric nitrogen cycle (Johnston, 1992). As an important part of the O3-destroying catalytic cycle, NOx controls the abundance of O3 in the stratosphere (Murphy et al., 1993). Consequently, since the Montreal Protocol was passed in 1987 with the aim to protect the stratospheric O3 layer, the monitoring of both O3 and NOx had become the focus of attention of much research (Tripp, 1987).

The global distributions of atmospheric NO2 and NO have been monitored by satellite missions since 1967 in various operational modes (Godin-Beekmann, 2010; Rusch, 1973): NOx data products are available from nadir-looking instruments like TROPOMI, GOME, and SCIAMACHY (Griffin et al., 2019; Richter and Burrows, 2002; Sierk et al., 2006); limb-viewing instruments like MIPAS and OSIRIS (Funke et al., 2005; Haley et al., 2004); and solar occultation measurements namely ACE-FTS and SAGE III/ISS (Fussen et al., 2005; Cisewski et al., 2014). The validation and correction of these data with ground-based measurements are still an ongoing process which has significantly reduced statistical and systematic errors between different satellite and ground-based measurements in the past few decades (Van Geffen et al., 2022; Verhoelst et al., 2021; Kerzenmacher et al., 2008; Wetzel et al., 2007; Brohede et al., 2007; Heue et al., 2005). However, when comparing data (satellite vs. ground) which are in general recorded during different times of the day, a major problem arises: there is a strong diurnal variation in stratospheric NOx due to a complex photochemistry (Solomon et al., 1986), so biases arise just due to time mismatch.

Facing this mismatch, a common method is the use of correction factors calculated from photochemical models to extrapolate retrieved data to the same time of the day. By now these models have a high accuracy, giving information about NOx concentration that is dependent on altitude, latitude, and the time of the day (Dubé et al., 2020; Strode et al., 2022). However, to the best of the authors' knowledge, a reliable analysis of long-term observations of NOx stratospheric partial columns and their diurnal variations, which could be used for validation of model data, does not exist. This is due to the lack of measurements able to record stratospheric NOx as a function of the time of the day.

For the ground-based observation of NOx, several different measurement techniques are well established, such as microwave radiometers (MRs), zenith sky (ZS) and multi-axis (MAX) differential optical absorption spectroscopy (DOAS), and Fourier-transform infrared (FTIR) spectrometry. The MR technique is sensitive at high altitudes and offers the possibility to obtain NO2 columns independent of night- and daytime (Ricaud et al., 2004). ZS-DOAS or Système d'Analyse par Observations Zénithales (SAOZ) instruments are well established at many stations all over the globe and provide long-term information about trace gas columns (e.g., NO2) in the stratosphere (Platt and Stutz, 2008; Vandaele et al., 2005; Pommereau and Goutail, 1988; Solomon et al., 1987). However, these instruments have good sensitivity especially at high solar zenith angles (SZAs) near sunrise or sunset (Tack et al., 2015). To get information at lower SZAs, MAX-DOAS measurements are performed, providing information about tropospheric trace gas concentrations at different times of the day (Dimitropoulou et al., 2020; Hönninger et al., 2004). However, these measurements do not provide information about trace gas concentrations at the tropopause and in the lower stratosphere.

Accurate information on NO2 and NO columns is accessible via FTIR solar absorption spectrometry, which can cover the whole diurnal variation in NOx (Fischer, 1993). Since the first ground-based FTIR measurements of NO2 (Camy-Peyret et al., 1983) and NO (Hanst et al., 1982), some progress has been made in monitoring seasonal trends and diurnal variation in stratospheric and tropospheric NOx (Zhou et al., 2021; Yin et al., 2019; Virolainen et al., 2014; Hendrick et al., 2012; Flaud et al., 1988; Rinsland et al., 1988). However, the majority of these studies investigated time periods covering only a few days up to several months. An examination of reliable long-term FTIR measurements with regard to stratospheric NO2 columns was done by Hendrick et al. (2012). Even though the NO2 diurnal variation is not discussed, the evaluation of 20 years of measurements above Jungfraujoch depicts a consistent picture of (1) the seasonal variability of stratospheric NO2 columns, which undergo a maximum in summer and a minimum in winter, and (2) a long-term trend which seems to show a slight decrease in stratospheric NO2 of the order of 3.6 % over 20 years from 1990–2010, before the study by Sussmann et al. (2005) had quantified the NO2 diurnal variation from ground-based FTIR measurements at Zugspitze. This study successfully showed that the stratospheric NO2 diurnal variation can be measured at a high-altitude site without the strong influence of tropospheric pollution events (Sussmann et al., 2005). However, due to the comparably short time period analyzed in this earlier study (2.5 years), a seasonal dependency could not be retrieved. A reliable long-term study from Zhou et al. (2021) analyzed NO tropospheric and stratospheric partial columns retrieved from FTIR measurements above Xianghe and Le Maïdo. This study comprises both the seasonal variability of stratospheric NO with a maximum in winter and a minimum in summer and the diurnal variation that is dependent on the local time (Zhou et al., 2021). However, a quantification regarding the seasonal dependence of the diurnal increase was not discussed.

Therefore the goal of this work is (i) to analyze the full Zugspitze and Garmisch FTIR time series covering more than 25 years (1995–2022) and 18 years (2004–2022) of measurements, respectively, in order to derive the slope of the linear fit of NO2 and NO stratospheric columns that depend on the local solar time (LST) – namely the diurnal increase – above our mid-latitude sites while eliminating the impact of tropospheric pollution or tropopause variabilities; (ii) to investigate whether a significant seasonal variation in the NO2 diurnal increase can be inferred; and (iii) to perform a comparison with NO stratospheric columns to further validate the analysis method and the reliability of the obtained data. The measurement data set published along with this paper will be a solid basis for validating current and upcoming photochemistry model simulations and improving satellite validation.

This paper is Part 1 of two companion papers dealing with the experimental description of the diurnal NOx variability above Zugspitze by means of ground-based FTIR measurements. Our paper first discusses the stratospheric NOx photochemistry and the consequences for the diurnal behavior of NO2 and NO in Sect. 2. In Sect. 3 we describe the retrieval strategy for NO2 and NO from solar FTIR measurements at Zugspitze and Garmisch. Section 4 focuses on the retrieval results, the separation of the retrieved columns into stratospheric and tropospheric contributions, and the introduction of a pollution filter for the obtained stratospheric columns. The calculation of NO2 diurnal increasing rates and their seasonal variation is made in Sect. 5 followed by a comparison to NO morning diurnal increasing rates, validating the analysis method in Sect. 6. Section 7 gives the summary and conclusions.

As the background for our FTIR data interpretation later, we present a short overview of the model understanding of NOx stratospheric photochemistry. More details can be found in the literature (Crutzen, 1970; Crutzen, 1979; Coffey et al., 1981; Cariolle, 1983; Jaeglé et al., 1994; Lary, 1997; Cohen and Murphy, 2003; Brasseur and Solomon, 2005).

During daytime the main NO2 source is the photolysis of the reservoir species HNO3 and N2O5, see Reactions (R1) and (R2), resulting in a continuous increase in NO2 during the day. 1HNO3+hν→NO2+OH2N2O5+hν→NO2+NO3 Both reactions take place on a timescale of minutes to hours between sunrise and sunset, and the kinetics depend on solar elevation.

The main NO source is the reaction of nitrous oxide (N2O) with excited oxygen (O(1D)) resulting from the photolysis of O3 given in Reactions (R3) and (R4). This leads to a similar continuous increase in NO during the day as seen for NO2. 3O3+hν→O(1D)+O24N2O+O(1D)→2NO According to the model understanding, the reaction rate of Reactions (R1) to (R4) decreases after noon, leading to a lower NO2 and NO increase in the afternoon than observed in the morning.

Additionally, both NOx species are interconverted into each other on timescales of seconds within the O3-destroying nitrogen catalytic cycle, 5NO+O3→NO2+O2,6NO2+O→NO+O2,7net:O+O3→2O2, and via the photolysis of NO2 (Reaction R8), resulting in an equilibrium during daytime: 8NO2+hν→NO+O. This equilibrium is reached very fast after sunrise and is nearly constant in the morning where the concentration increase in both species follows in a good approximation a linear behavior. In the afternoon, the equilibrium changes due to the strong solar elevation dependency of Reaction (R8) and due to the increasing abundance of O3 with daylight (Wang et al., 2020; Strode et al., 2022). Consequently, after noon, the NO increase slows down, whereas NO2 continues to increase with a similar rate. Between an SZA of 80–90° the trace gas concentrations are still influenced by the thermally driven reactions taking place at night, leading to a strong deviation from a linear behavior during very early morning.

Following the retrieval strategy and the quality control described in Sect. 3, NOx vertical profiles are derived above Zugspitze (NO2 and NO) and above Garmisch (NO2) for each spectrum and are shown in Fig. S3a (Zugspitze) and b (Garmisch) for NO2 and in Fig. S4a and b for NO (red lines). From the remaining 16 023 (Zugspitze, NO2), 14 460 (Garmisch, NO2), and 6213 (NO) spectra, mean DOFSs of 1.38, 1.49, and 2.14, respectively, are derived.

In this section we use the pollution-filtered NO2 stratospheric partial columns measured at Zugspitze and Garmisch to calculate diurnal increasing rates that depend on the month. The latter quantitatively describes the seasonal variation in diurnal stratospheric NO2 concentrations. For validation of the observed behavior and the retrieval method used, we furthermore correlate the NO2 diurnal increasing rates obtained from both observatories (Zugspitze and Garmisch).

In this section we analyze the retrieved NO stratospheric columns above Zugspitze. This analysis is motivated by the question of whether the observed seasonal dependence of the NO2 diurnal increasing rate originates from stratospheric photochemistry and consequently can be seen in the NO data too.

In this study, we analyzed long-term FTIR data recorded within the last 25 years at Zugspitze (47.42° N, 10.98° E; 2964 m a.s.l.) and Garmisch (47.47° N, 11.06° E; 745 m a.s.l.), Germany. We present a retrieval and analysis strategy for the given FTIR data, which provides NO2 and NO stratospheric partial columns (> 16 km altitude) that are only weakly influenced by the tropospheric partial column and by pollution events. The obtained NO2 stratospheric partial columns have a bias of only 2.5 ± 0.2 %, very similar above Zugspitze and Garmisch, reflecting the reliability of the given analysis. The observed diurnal behavior of both the NO2 and the NO stratospheric partial columns that depend on the local solar time (LST) reflects the expected behavior described in the literature via photochemical model simulations: the NO2 stratospheric partial column follows a linear increase from sunrise to sunset, independently of the season. In a similar way, the NO stratospheric partial column increases linearly before local solar noon. In the afternoon, the increase in the NO stratospheric partial column slows down significantly, especially in summertime. Besides these basic observations, we quantified the described diurnal increase in NO2 and NO that depends on the LST by calculating monthly NO2 diurnal increasing rates above Zugspitze and Garmisch with mean values of (0.89 ± 0.07) × 1014 and (0.94 ± 0.07) × 1014 cm-2 h-1, respectively, and monthly NO morning diurnal increasing rates above Zugspitze with a mean value of (1.42 ± 0.06) × 1014 cm-2 h-1. Here, the mean NO2 diurnal increasing rates fit together perfectly with the literature value published by Sussmann et al. (2005). Additionally, for the first time we could experimentally show a significant seasonal variation in both the NO2 diurnal increasing rate and the NO morning diurnal increasing rate with a maximum of (1.13 ± 0.04) × 1014 cm-1 h-1 for NO2 and (1.76 ± 0.25) × 1014 cm-1 h-1 for NO in September and a minimum of (0.71 ± 0.18) × 1014 cm-1 h-1 in December for NO2 and a minimum of (1.18 ± 0.41) × 1014 cm-1 h-1 in November for NO. Although the correlation analysis of both NO2 and NO diurnal increasing rates gives quantitative evidence of their interconnection in the stratospheric photochemistry only within 85 % confidence, both diurnal increasing rates follow the same seasonal cycle.

Part 2 of the companion paper (Nürnberg et al., 2023) will show the generalization of the observed NOx partial columns (> 16 km) by converting them into experiment-based NOx scaling factors describing the NOx diurnal variability that depends on the SZA and will give a first comparison to recently published model-based scaling factors.

The data and analysis method given in this paper (Part 1) can be the first step for a latitude-dependent (multi-station) data set reflecting the diurnal behavior of the stratospheric NOx column that depends on the season. Furthermore, the measurements with its high time resolution can serve as a basis for the validation of future photochemistry models and the improvement of satellite validation.