The SAGE III/ISS instrument was launched to the ISS on 19 February 2017. The instrument scans over the Sun during sunrise and sunset events, measuring the atmospheric extinction along the line of sight (Cisewski et al., 2014). SAGE III/ISS profiles are produced on a 0.5 km grid with an estimated vertical resolution of 0.7 km from 10 to 50 km for NO2 and from 6 to 85 km for O3 (SAGE III Algorithm Theoretical Basis Document, 2002). SAGE III coverage and number of profiles are limited to about 15 sunrise and 15 sunset events per day, with the majority of observations occurring between 60∘ S and 60∘ N. Dubé et al. (2021) reported that the SAGE III/ISS NO2 V5.1 is over 20 % biased high in much of the mid-stratosphere even when accounting for diurnal variability. We also use the “aerosol ozone” (AO3) ozone retrieval, which is similar to the SAGE II retrieval method (Damadeo et al., 2013), as recommended by Wang et al. (2020). Wang et al. (2020) reported that the V5.1 O3 profile has 5 % accuracy between 15 and 55 km and 3 % precision between 20 and 40 km. They also reported a 5 %–8 % sunrise versus sunset bias in the upper stratosphere that they could not explain. However, the Wang et al. (2020) analysis did not account for O3 diurnal variability and attributed the larger bias above 45 km to the O3 diurnal cycle. The difference between V5.2 and V5.1 ozone is less than 0.5 % and resulted from various algorithm improvements, while the NO2 in V5.2 decreased by 5 %, which was caused mainly by the new wavelength map (SAGE III/ISS V5.2 release notes, 2021). Additional changes include better oxygen dimer (O4) corrections and the removal of all vertical smoothing.

The OSIRIS instrument (Llewellyn et al., 2004) is a limb sounder that was launched in February 2001 on board the Odin satellite (Murtagh et al., 2002). OSIRIS provides vertical profiles of ozone, aerosol, and NO2 with approximately 2 km vertical resolution. Variations in SZA along the line of sight can impact retrievals of species with strong diurnal cycles such as NO2 for occultation and limb measurements (Mclinden et al., 2006; Brohede et al., 2007). The reported accuracy of the OSIRIS V6.1 NO2 retrieval is ±10 % when accounting for the diurnal variability in NO2 along the line of sight (Sioris et al., 2017) and 5 % above 21 km for the ozone v5.07 retrieval (Adams et al., 2014).

The ACE-FTS (Bernath et al., 2005; Bernath, 2017) measures trace gas profiles from the SCISAT-1 satellite. ACE-FTS, like SAGE III/ISS, uses solar occultation to take measurements during sunrise and sunset. Consequently, comparisons between ACE-FTS and SAGE III/ISS observations do not require correction for the diurnal cycle as long as sunset is compared with sunset and sunrise with sunrise. The ACE-FTS O3 profile accuracy is within 5 % between 20 and 45 km and exhibits a large bias of 10 %–20 % above 45 km (Sheese et al., 2017). The NO2 accuracy is 20% between 20 and 40 km (Kerzenmacher et al., 2008). We used version 3.6 instead of V4.1 since it was the recommended version for validation studies (Wang et al., 2020). In addition, the positive bias for ozone in the mid-stratosphere is approximately 3 % in version 3.6 but 2 %–9 % in version 4.1 (Sheese et al., 2022).

MLS (Waters et al., 2006) was launched on the Aura satellite (Schoeberl et al., 2006) in July 2004 and provides global observations of trace gases including ozone. MLS O3 observations extend from the upper troposphere to the mesosphere. We use MLS V4.2 O3 observations, since the differences in stratospheric O3 compared to version 5 are small (Livesey et al., 2022). We use MLS data from both early afternoon and nighttime overpasses. The accuracy of MLS O3 measurements varies with altitude, ranging between 5 % and 10 % from 68 to 0.2 hPa (∼18–59 km) (Livesey et al., 2020).

OMPS consists of three instruments designed to measure the ozone layer. OMPS is on board the Suomi National Polar-orbiting Partnership (NPP) satellite (Flynn et al., 2006), which launched in October of 2011. The LP instrument is designed to provide high-vertical-resolution O3 and aerosol profiles from measurements of the scattered solar radiation in the 290–1000 nm spectral range and can provide daily global measurements of O3 and aerosol profiles from the cloud top up to 60 and 40 km, respectively. The V5.2 O3 profiles' accuracy is within 10 % at altitude range 18–42 km, except for the northern high latitudes, which have a larger negative bias between 20 and 32 km and above 43 km (Kramarova et al., 2018).

We use the global three-dimensional Goddard Earth Observing System (GEOS) model (Molod et al., 2015) coupled with the Global Modeling Initiative (GMI) stratospheric and tropospheric chemistry mechanism (Nielsen et al., 2017; Duncan et al., 2007; Strahan et al., 2007) and the Goddard Chemistry Aerosol Radiation and Transport (GOCART) aerosol module (Chin et al., 2002; Colarco et al., 2010) to simulate the distribution and variability of O3, NO2, and other trace gases and aerosols. GMI uses an updated version of Fast-JX (Bian and Prather, 2002) to simulate photolysis. The GOCART aerosols are coupled to the GMI chemistry and impact the photolysis rates as well as the surface area density (SAD) of polar stratospheric clouds for heterogeneous chemistry. A replay method described by Orbe et al. (2017) is used to constrain the model's meteorology to the MERRA-2 reanalysis (Gelaro et al., 2017). We refer to this simulation setup hereafter as GEOS-GMI.

The simulation has 72 vertical levels from the surface to 1 Pa, a horizontal resolution of approximately 100 km, and a chemistry time step of 15 min. Three-dimensional O3 and NO2 concentrations are output every half hour in order to better resolve the diurnal cycle. We simulate the period from January 2017 through December 2020. In addition to trace gas concentrations, the model simulation includes several other diagnostics used in this analysis. These include SZA and the tendency of O3 due to chemistry and the tendency due to dynamics. These tendencies quantify the change in O3 in a given grid box caused by local chemical processes vs. large-scale transport and are diagnosed from the change over a given operator in the model.

We construct diurnal scaling factors from the GEOS-GMI model output by taking the ratio of the O3 and NO2 concentrations at each zenith angle to the concentration at sunrise and sunset. For convenience, we use “signed SZA”, with negative values for afternoon and positive values for morning. We thus define sunrise as SZA = 90∘ and sunset as SZA = -90∘. We interpolate the model output at each latitude/longitude to the SAGE III/ISS geometric altitude levels, which have a grid spacing of 0.5 km.

While model output is available for every day, we use monthly zonal mean values to construct the scaling factors for each latitude, altitude, and SZA. The diurnal variability of O3 is influenced by dynamics as well as chemistry. Sakazaki et al. (2013, 2015) highlight the contribution of tidal winds to the diurnal variability of stratospheric O3. Schanz et al. (2021) report variability in the O3 diurnal cycle due to dynamics in reanalysis fields. We aim to capture the chemistry effects as well as systematic dynamical effects on the diurnal cycle while filtering out the short-term temporal and spatial variability caused by day-to-day variations in transport. Using monthly and zonal means filters out much of this random variability to create a more reliable picture of the diurnal cycle and the relative role of chemical vs. dynamical effects. Examination of the dynamical vs. chemical tendencies from the simulations within the SAGE III/ISS observation range shows that the diurnal cycle in the O3 tendency from dynamics is important between 40 and 50 km, even in the monthly zonal mean. Figure 1 compares the amplitude of the diurnal cycle, defined here as the maximum of the monthly mean diurnal cycle minus the minimum, for the chemical and dynamical tendencies of O3 and NO2 for January 2019. While the chemical tendency of O3 is dominant throughout much of the atmosphere above 30 km, the diurnal amplitude of the dynamical tendency term can equal or exceed the amplitude of the chemical term near 45 km in the tropics. Our calculated scaling factors thus include both chemical and dynamical effects on the diurnal cycle. Our scaling factors for NO2 also include both chemical and dynamical effects, but for NO2, the chemical tendency is dominant throughout the profile (Fig. 1d–f). We note that if the tendencies are normalized by the concentration of the constituent, the chemical tendency of NO2 (% s-1) increases with altitude above 45 km rather than peaking at 40–50 km.

We calculate scaling factors referenced to sunrise and sunset for easy application to SAGE III/ISS data when comparing to observations from different times of day. The factors are provided on an SZA by altitude grid with one file per month for January 2017 through December 2020. The SZA grid is nonlinear to allow finer resolution near the terminator when the values are changing rapidly. In addition to the year-specific scaling factors, we provide a monthly climatology of scaling factors, based on the average of 2017 through 2020, that can be applied to other time periods. We also provide the zonal mean concentrations of O3 and NO2 as functions of SZA, latitude, and altitude, so that users can derive their own scaling factors for arbitrary SZA pairs.

We present the climatological scale factors as a function of latitude, altitude, SZA, and month. Figure 4 shows the climatological sunrise and sunset diurnal scale factors for NO2 as a function of signed solar zenith angle for January and July at 45∘ N at 35 km. The U shape of the scaling factors reflects the high NO2 values at night and low values during the day, with sharp gradients occurring at sunrise (SZA = 90∘) and sunset (SZA = -90∘). The sunrise and sunset factors have a similar shape but are offset in magnitude because the sunrise and sunset values of NO2 differ as described in Sect. 3.1. Gaps in the plot represent SZA values that do not occur in the monthly mean. A larger gap around SZA = 0∘ occurs in January compared to July at 45∘ N, reflecting the lower Sun angle in January. The January scaling factors also reach a larger maximum value at night compared to the July factors at this latitude. While the overall shape of the NO2 scaling factors is similar across the altitude range of the SAGE III/ISS measurements, the magnitude changes dramatically with altitude because of the larger diurnal cycle of NO2 at higher altitudes. Figure S4 uses a nonlinear color scale to show the large amplitude of the diurnal scaling factors at high altitudes.

We next explore the latitudinal variability in scaling factors using the sunrise factor for SZA = 60∘ at 35 km altitude as an example. We show the variations in the scale factor as a function of latitude for 1 month in each season in Fig. 5. There is considerable variability in the factor with both latitude and month. January shows the greatest variability, with values ranging from 0.65 at 69∘ S to 0.95 at 39∘ N. Both January and October show the largest deviation from 1 at the southern end of the range for which SZA = 60∘ is reached, while April and July deviate most strongly from 1 at the northern end.

Since we have created diurnal scale factors from both monthly climatological averages and from individual years, we investigate how much IAV exists in the NO2 diurnal scale factors. Figure 6 shows the IAV in the sunrise NO2 scaling factors for October. All 4 years show a similar shape for the factors as a function of signed SZA at the Equator at 25 km (Fig. 6a), but in 2018 the scale factors are larger than the climatology for SZA < 90∘, while for 2017 and 2019 they are smaller. The situation is reversed at the southern high latitudes, where 2018 and 2020 are smaller than the climatology and 2017 and 2019 are greater (Fig. 6b). Figure 6b shows that the percent difference between the individual years and the climatology is largest near the Equator and south of 60∘ S in October. Considering the difference from climatology for the SZA = 60∘ factor as a function of altitude, we find that, at the Equator, the differences are largest from approximately 15 to 35 km, but deviations from climatology do not exceed 15 % below 50 km (Fig. 6c). Park et al. (2017) found that the quasi-biennial oscillation (QBO) plays a dominant role in the IAV of tropical stratospheric NOx seen in OSIRIS observations. Zawodny and McCormick (1991) found that QBO variability of SAGE II NO2 was related to changes in the vertical transport of NOy and noted that the time of day could affect the relationship of NO2 with the QBO. We find that the yearly anomalies in the NO2 scale factors for the lower stratosphere show a similar vertical structure to the anomalies in the vertical gradient of the zonal wind anomalies at the Equator (Fig. 6f), indicating that variability associated with the QBO is likely responsible for the interannual variability at these altitudes.

At 60∘ S, the differences between individual years and climatology reach values above 20 % near 10–20 km (Fig. 6d). Considering all latitudes and altitudes below 50 km, the maximum difference between an individual year and climatology for the SZA = 60∘ factors is 54 % in October. The largest difference for the SZA = 60∘ factors when all months are considered is 75 %, which occurs in September at 23.5 km. When all SZA values between -90 and 90∘ are considered, the maximum difference reaches 118 % at 13.5 km in September. However, the IAV differs according to the month and latitude considered, so many of the differences average out when an entire year or large latitude range is considered.

We demonstrate the utility of the NO2 diurnal scaling factors by comparing SAGE III/ISS NO2 observations with observations from OSIRIS with and without the application of the diurnal scaling factors. We also include the solar occultation ACE-FTS as a reference since it does not require any diurnal corrections when comparing with SAGE III/ISS. We note that the scale factors are intended to account for the temporal change in concentration between different observation times and not to alter the value of the SAGE III/ISS retrieval itself.

Figure 7 shows the percent difference between SAGE III/ISS sunrise (SR) and sunset (SS) and OSIRIS and ACE-FTS NO2 observations averaged over three latitude bands before and after applying the diurnal scale factors. The coincidence criteria between SAGE III and the reference instrument are defined as same-day measurements that are within 3∘ latitude and 10∘ longitude. For ACE-FTS, we matched SR/SS that met the criteria and were within 3 h of each other. In general, the disagreement between SAGE III and ACE-FTS for both sunrise and sunset measurements (magenta and green lines in Fig. 7) is 20 % or less for most altitudes. The difference between SAGE III and OSIRIS (red and blue solid lines) is large. The difference for sunrise observations exceeds 50 % below 20 km and exceeds 25 % below 35 km north of 20∘ S. Differences are especially large in the tropics below 22 km. Sunset differences exceed 50 % throughout much of the atmosphere below 35 km. NO2 diurnal variability and the mismatch of the measurement times explain much of these differences. The difference between the two instruments is significantly reduced when accounting for the NO2 diurnal cycle (red and blue dashed lines). The difference becomes mostly less than 50 % for both sunrise and sunset and below 25 % above 25 km, except for the sunrise observations between 20∘ S and 20∘ N. Applying the scaling factors improves the agreement between the SAGE and OSIRIS profiles in all latitude bands (Fig. 7) and improves the consistency between the sunrise and sunset comparisons, particularly in the 20–60∘ N and S ranges. The larger difference below 25 km is mostly caused by the diurnal effect error which occurs due to the variation of the SZA along the line of sight in occultation measurement. Like SAGE III, ACE-FTS does not account for the NO2 diurnal variability along the line of sight, and these two versions have a relatively uniform difference for all altitudes. The diurnal effect error is similar to what Brohede et al. (2007) found when comparing SAGE II and III to OSIRIS. In a recent study by Dubé et al. (2021), they attempted to correct for this effect in SAGE III/ISS NO2 measurements, which improved the agreement between SAGE III and OSIRIS below 20 km. However, they also noted that the corrections were not sufficient to account for all the differences at these altitudes.

The scale factors applied in this comparison were derived using individual months/years of the simulation. We found little difference when using monthly climatological scale factors, except for the year 2019 at altitudes between 10 and 20 km in the tropics and Northern Hemisphere (NH) midlatitude, where the difference can reach 2 % in the tropics and 7 % in the NH (not shown). It is therefore our recommendation that it is sufficient to use the global climatology when correcting for the NO2 diurnal variation in validation studies. However, we recommend using the month/year scale factor when merging multiple datasets for trend studies as differences caused by the QBO variability can be as large as 7 % below 20 km. Scale factors for specific years are also valuable when focusing on a specific month and region.