Diurnal variability of total column NO2 measured using direct solar and lunar spectra over Table Mountain, California (34.38°N)

A full diurnal measurement of total column NO2 has been made over the Jet Propulsion Laboratory’s Table Mountain Facility (TMF) located in the mountains above Los Angeles, California, USA (2.286 km above mean sea level, 34.38°N, 117.68°W). During a representative week in October 2018, a grating spectrometer measured the telluric NO2 absorptions in 10 direct solar and lunar spectra. The total column NO2 is retrieved using a model-based minimum-amount Langley extrapolation, which enables us to accurately treat the non-constant NO2 diurnal cycle abundance and the effects of pollution near the measurement site. The measured 24-hour cycle of total column NO2 on clean days agrees with a 1-D photochemical model calculation, including the monotonic changes during daytime and nighttime due to the exchange with the N2O5 reservoir and the abrupt changes at sunrise and sunset due to the activation or deactivation of the NO2 photodissociation. The observed 15 daytime NO2 increasing rate is (1.29 ± 0.30) × 10 cm–2 h–1. The total column NO2 in one of the afternoons during the measurement period was much higher than the model simulation, implying the influence of urban pollution from nearby cities. A 24-hour back-trajectory analysis shows that the wind first came from inland in the northeast and reached the southern Los Angeles before it turned northeast and finally arrived TMF, allowing it to pick up pollutants from Riverside County, Orange County, and Downtown Los Angeles. 20


Introduction
Nitrogen dioxide (NO2) plays a dominant role in the ozone (O3)-destroying catalytic cycle (Crutzen, 1970). NO2 column abundance has been measured using ground-based instruments since the mid-1970s (Network for the Detection of Atmospheric Composition Change, http://www.ndacc.org), which serve as the standards for validating satellite measurements. Noxon (1975) and Noxon et al. (1979) retrieved the stratospheric NO2 column by differential optical absorption spectroscopy 25 (DOAS) in the visible spectral range using ratios of scattered sunlight from the sky and direct sun/moonlight at low (noon/midnight) and high (twilight) air mass factors over Fritz Peak, Colorado (39.9°N). Since the optical path of sun/moonlight at dawn or dusk (solar/lunar zenith angle ≈ 90°) is much longer than the optical path of the direct sunlight at noon/midnight, the NO2 absorption in the noon/midnight spectrum can be assumed to be small and the NO2 absorption in the twilight slant column could therefore be isolated effectively by ratioing the scattered twilight spectrum to the scattered noon https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License. spectrum. This DOAS principle also applies to ratios of direct moonlight or sunlight at low and high air mass factors. Noxon et al.'s (1979) measurements revealed sharp changes of the stratospheric NO2 column before and after sunsets and sunrises at mid-latitudes. Similar DOAS measurements at high latitudes in the 1980s focused on the role of NOx in controlling O3 and active halogen species in the polar stratosphere (Fiedler et al., 1993;Flaud et al., 1988;Keys and Johnston, 1986;Solomon, 1999). Johnston and McKenzie (1989) and Johnston et al. (1992) reported a reduction in the southern hemispheric NO2 over 35 Lauder, New Zealand (45.0°S), following the eruptions of El Chichón (in 1982) and Pinatubo (in 1991), respectively.
NO2 column abundance has also been measured using direct solar spectra acquired by Fourier-Transform infrared (FTIR) spectrometers. Advantages of direct solar measurements are the lack of Raman scattering in the spectra, air mass factors determined geometrically rather than through a radiative transfer code, and provision of NO2 column abundances at most times during the day. Sussmann et al. (2005) retrieved the stratospheric NO2 column abundance over Zugspitze, Germany 40 (47°N) using the infrared absorption in the solar spectrum near 3.43 μm. The stratospheric NO2 column abundance was then subtracted from the total column estimated from satellite measurements to obtain the tropospheric column. Wang et al. (2010) demonstrated how high spectral resolution measurements using a Fourier transform spectrometer could perform absolute NO2 column abundance retrievals without the need for a solar reference spectrum. Because of the solar rotation, the Fraunhofer features in the UV spectra acquired simultaneously from the east and west limbs of the solar disk are Doppler shifted while 45 the telluric NO2 absorptions are not shifted (Iwagami et al., 1995). Thus, the telluric NO2 absorptions can be identified by correcting the Doppler shift without the need of an a priori solar spectrum. Other techniques, such as balloon-based in situ measurements (May and Webster, 1990;Moreau et al., 2005), balloon-based solar occultations (Camy-Peyret, 1995) and ground-based multi-axis DOAS (MAX-DOAS; Hönninger et al., 2004;Sanders et al., 1993), have also been employed to further characterize the vertical distributions of NO2. 50 Here we retrieve the total column NO2 over Table Mountain Facility (TMF) in Wrightwood, California, USA (2.286 km above mean sea level, 34.38°N, 117.68°W) using Langley extrapolation to determine the reference spectrum and considering both daytime and night time chemistry. Daytime NO2 concentration remains significant, albeit small relative to the night-time concentration, and varies from morning to afternoon. This daytime variation has traditionally been a source of error in determination of the DOAS reference spectrum using Langley extrapolation. Comprehensive assessment of NO2 must 55 include both daytime and nighttime values. We therefore also retrieve daytime column NO2 by acquiring direct sun spectra throughout the day. We will compare the daytime and nighttime total column NO2 with those simulated in a one-dimensional (1-D) photochemical model. The effect of urban pollution on the measured total column NO2 can be deduced from this comparison.

Instrumentation and measurement technique
The grating spectrometer used for the NO2 spectral measurement is similar to the one used by Chen et al. (2011) and is installed in the same observatory. A heliostat and a telescope are used to direct and launch light into a fibre optic bundle placed at the focal plane of the telescope (Figure 1). The bundle consists of 19 silica fibres, 200 µm in diameter, arranged in a circular configuration (in SMA 905 connectors) on the source end and in a linear pattern on the spectrograph end. Before 65 entering the spectrograph, light is passed through an order sorting filter (Schott GG-400 glass) and a shutter. The imaging spectrograph is a Princeton Instruments SP-2-300i with a 0.3-m focal length used with a 1200 g mm −1 grating blazed at 500 nm. A CCD detector (Princeton Instruments PIXIS 400B) is placed at the focal plane of the spectrograph. The 1340 × 400 imaging array of 20 × 20 µm 2 pixels are vacuum sealed and thermoelectrically cooled to −80 °C.
We acquired direct moon and direct sun spectra for lunar/solar zenith angles less than 80° and 5 to 7 days surrounding 70 the full moon. When direct sunlight was used, two ground glass diffuser plates were inserted into the beam prior to the telescope primary to integrate over the entire solar disk and to attenuate light. Additional attenuation of light to avoid detector saturation was accomplished by placing a 23% open area screen in the beam just after the diffuser plates. The resulting spectrum has a spectral grid spacing on the detector of 0.048 nm from 411 nm to 475 nm with a measured line shape of 0.34-nm FWHM sampled at ~7 pixels. Spectral calibration and line shape measurements were accomplished using a diffuse reflection of an 75 Argon lamp near the fibre end, which gives a nearly linear result between pixel and wavelength with a small second order correction; the second order correction is considered in the calibration and the fitting. The exposure time was 4 s and 0.25 s during the lunar/solar noon observations, respectively. At higher zenith angles, longer exposures were taken to keep the detector counts in the same range. The data were dark corrected and averaged to obtain the desired signal levels; for the sun, this was consistently ~4 minutes; for the moon, the averaging time varied from ~8 minutes during the night of the full moon 80 to 24 minutes on the night 3 days from full moon.

The DOAS retrieval
The DOAS technique is used to retrieve the NO2 slant column (Noxon, 1975;Noxon et al., 1979;Platt et al., 1979;Stutz and Platt, 1996). A spectrum measured by the grating spectrometer at any time of the day is ratioed to a pre-selected reference spectrum. From the ratioed spectrum, we retrieve the differential slant column NO2 relative to the column that is 85 represented by the reference spectrum. The total slant column is then the sum of the differential slant column and the reference column.
Our reference spectrum is a solar spectrum measured at the TMF ground level at local noon (Chen et al., 2011). This solar reference spectrum is used to ratio all other spectra collected, including those during the solar and lunar measurement cycles. In principle, one can retrieve the reference NO2 column from the reference spectrum. However, this requires precise 90 knowledge of the solar spectrum at the top of the atmosphere in order to isolate the NO2 absorption. We will use a variant of https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License. the Langley extrapolation to circumvent the need of the retrieval of the reference column (Lee et al., 1994;Herman et al., 2009); see following section for details.
The differential slant column NO2 is retrieved by fitting the ratioed spectrum between 430 and 468 nm. The spectral fitting is accomplished through the Marquardt-Levenberg minimization using QDOAS retrieval software (http://uv-95 vis.aeronomie.be/software/QDOAS/). The highly spectrally resolved NO2 absorption cross sections at = 215 K, 229 K, 249 K, 273 K, 298 K, and 299 K based on Nizkorodov et al. (2004) are convolved to the instrument resolution using the instrument line shape function and the Voigt line shape prior to its use in QDOAS. The temperature profile for the calculation of the Voigt line shape is determined by the yearly average of the TMF temperature lidar measurements. In addition to NO2, other absorptions by O3, O4 (O2 dimer), and H2O in the same spectral window are simultaneously retrieved. The NO2 100 abundance retrieved from QDOAS is the desired differential slant column NO2 relative to our chosen reference spectrum.

The model-based minimum-amount Langley extrapolation
Let be the differential slant column NO2 along the line-of-sight, the reference column NO2, the stratospheric airmass factor (which is proportional to the geometric secant of the solar zenith angle in the stratosphere for these direct solar and lunar observations), and the total vertical column NO2; is our target quantity. The differential slant column can be 105 approximated as the total vertical column multiplied by the stratospheric airmass factor after the subtraction of the reference column: If were known, then would be simply ( + ). The Langley extrapolation technique for determination of the extraterrestrial reference obtains and − as the slope and the intercept of the linear regression of against , respectively, assuming is temporally constant (i.e. the vertical column does not change during the course of the day). In this formulism, the reference column is an extrapolated value corresponding to hypothetical zero airmass ( = 0).
The Langley extrapolation was first used to measure the solar spectrum at the top of the atmosphere (Langley, 1903) 115 and has also been used to measure atmospheric constituents (e.g., Jeong et al., 2018;Toledano et al., 2018;Barreto et al., 2017;Huber et al., 1995;Bhartia et al., 1995). However, the assumption of a constant is often violated due to diurnal variabilities in the atmospheric constituents driven by, e.g., the incident solar radiation, transmittance, circulation, and human activities. In our case, the afternoon total column NO2 is greater than the morning total column NO2 (see our Figure 3). Several modifications have been proposed to relax the assumption of a constant (e.g., Ångström, 1970;Shaw, 1976;Long and Ackerman, 2000;120 Cachorro et al., 2008;Kreuter et al., 2013;Marenco, 2007). In this work, we combine the modifications used in Lee et al. (1994) and Herman et al. (2009) to account for the effects due to the NO2 diurnal variability and urban pollution. Lee et al. (1994) replaced the constant with an a priori function of , denoted by ( ): https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License.
Eq. (2) is analogous to Eq. (1) except that now is regressed against the product ( ); is the target quantity that will be obtained from the slope of the regression line. serves as an effective scaling factor that adjusts the chemical rates in the model. Eq.
As in Lee et al. (1994), assuming the chemical processes of NO2 are much faster than the dynamical processes so that 130 the NO2 diurnal cycle is at photochemical equilibrium, we obtain ( ) from a 1-D photochemical model (to be described in the next section). The ( ) we use corresponds to a clean atmosphere only. To perform the regression, we plot against the product ( ) (Figure 2, blue open circles). If all NO2 columns are measured on clean days, then they would ideally fall on a straight line. However, if there is a pollution source near a measurement site, then some of the measured NO2 column may be significantly higher than ( ), leading to a vertical spread in the scattered plot. The deviation from ( ) may be 135 highly variable, depending on the source types and the meteorology. When a large number of measured NO2 columns on clean and polluted days are plotted together against ( ), the baseline of the scattered data may be considered as the NO2 diurnal cycle in a clean atmosphere (Herman et al., 2009 To obtain the baseline, we divide the range of ( ) (from ~5 × 10 to 3 × 10 molecules cm -2 during our 140 campaign) into 20 equal bins. Herman et al. (2009)

The photochemical model
Our ( ) is based on the Caltech/JPL 1-D photochemical model (Allen et al., 1984;Allen et al., 1981), shown as the black solid line in Figure 3. This photochemical model includes the stratospheric species that are important for O3, oddnitrogen (NOx = N + NO + NO2 + NO3 + 2N2O5) and odd-hydrogen (HOx = H + OH + HO2) chemistry, including the reactions discussed in Section 3.1. Nitrous oxide (N2O) is the main parent molecule of NO2 in the lower stratosphere. The concentration 150 of N2O at the ground level of the model is fixed at 330 ppb (https://www.esrl.noaa.gov/gmd/hats/combined/N2O.html). The kinetic rate constants are obtained from the 2015 JPL Evaluation (Burkholder et al., 2015).
The sunrise/sunset times and the solar noontime in the model are calculated using the ephemeris time. We use Newcomb parameterizations of the perturbations due to the Sun, Mercury, Venus, Mars, Jupiter, and Saturn (Newcomb, 1898).
We also use Woolard parameterizations for the nutation angle and rate (Woolard, 1953). More modern calculation of the 155 https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License. ephemeris time may be used (e.g., Folkner et al., 2014) but the difference in the resulting ephemeris time is small (less than 0.1 s) and does not significantly impact our model simulation.
We progress the model in time until the diurnal cycle of the stratospheric NO2 becomes stationary. Throughout the progression, the pressure and temperature profiles are fixed and do not vary with time. The model latitude is set at 34.38°N and the model day is set as October 26. The total column NO2 is the vertical integral of the NO2 concentration. The simulation 160 represents the NO2 abundance in a clean atmosphere without tropospheric sources.

Diurnal variation in total column NO2
Figure 3 presents our preliminary observational data (colour dots) obtained during October 23-28, 2018. During the measurements, the skies were mostly clear or only partly cloudy, so we were able to make continuous solar spectral 165 measurements throughout the whole period. During October, the local sunrise and sunset time were around 07:00 PST and 18:00 PST, respectively. At sunrise and sunset, the ambient twilight in the background of the moonlight occultation should be accounted for in the NO2 retrieval, which is beyond the scope of this work. For this work, we exclude lunar total column NO2 data when the ambient scattered twilight, including those from civil sources, is significant, which typically occurs when the lunar elevation angle is less than 6° above the horizon. The solid black line of Figure 3 is the simulated 24-hour cycle of the 170 total column NO2 variability in the 1-D model. The dashed line is a second simulation with a slightly lower temperature (see Section 3.3). Overall, the baseline simulation captures the observed trends during the daytime and the nighttime.
On most days, the total column NO2 over TMF increased from ~2 × 10 molecules cm -2 in the morning to ~3.5 × 10 molecules cm -2 in the evening. There are 3 main sources of NOx contributing to the daytime increase. The ultimate source is the reaction of N2O with excited oxygen O( 1 D) resulting from the photolysis of O3 in the stratosphere between 20-175 60 km, which produces nitric oxide (NO) molecules and eventually NO2 through the NOx cycle aided by O3: NO + O3 → NO2 + O2. 180 Another major source is the photolysis of the reservoir species, nitric acid (HNO3) and dinitrogen pentoxide (N2O5): There is also a small source due to the photolysis of NO3: https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License.
but this source is not significant due to the low NO3 abundance during daytime. NO2 is converted back into NO through the 190 reaction with oxygen atom (O) in the upper stratosphere (above 40 km): or via photolysis below 40 km: 195 But since NO and NO2 are quickly interconverted within the NOx family, Reactions R6 and R7 do not contribute to a net loss of NO2. The ultimate daytime loss of NO2 is the reaction with the hydroxyl radicals (OH) that forms HNO3, which may be 200 transported to the troposphere, followed by rainout: The significant deviation of daytime NO2 from the model simulation on October 27 was likely due to urban pollution (see 205 section 3.4).
At sunset, the photolytic destruction (Reaction R7) in the upper stratosphere terminates while the conversion of NO (Reaction R2) continues in the lower stratosphere. Meanwhile, the production of O is significantly reduced, which also reduces the loss of NO2 via Reaction R6. As a result, the total column NO2 increases by a factor of ~3 at sunset.

215
Most N2O5 stays throughout the night, although there is a small portion that thermally dissociates back to NO2 and NO3. Thus, the net effect is a secular decrease in nighttime NO2.
Finally, at sunrise, photolytic reactions resume, resulting in an abrupt decrease in the total NO2 column by a factor of ~2 due to Reactions R6 and R7.

Vertical profile of NO2 production and loss 220
To better understand the contributing factors of the variability of total column NO2, we show the simulated vertical NO2 profile in Figure 4. The NO2 concentration is dominant between 20 km and 40 km (Figure 4a). At noontime, the model NO2 profile has a peak of ~1.7 × 10 molecules cm -2 at 30 km (Figure 4a, orange line). At mid-night, the NO2 concentration is much higher throughout the stratosphere. The corresponding peak has a larger value of ~2.4 × 10 molecules cm -2 and is shifted slightly upward to 32 km (Figure 4a, green line). Therefore, the total column NO2 is dominated by the variability near 225 30 km.
The diurnal cycles of the NO2 concentration at altitudes between 14 km and 38 km are shown in Figure 4b. These cycles show that the daytime increase and the nighttime decrease occur only in the lower stratosphere between 18 km and 34 km. At other altitudes, the daytime and nighttime NO2 concentrations are relatively constant. The NO2 cycles closely resemble those of N2O5. Figure 5 shows the N2O5 concentrations between 14 km and 34 km. During daytime, N2O5 is photolyzed into 230 NO2 and NO3 through Reaction R4, leading to an increase in the daytime NO2; during nighttime, NO2 is thermally converted into N2O5 through Reactions R9 and R10, leading to a decrease in the nighttime NO2. Figure 5 shows that the conversion between the reservoir and NO2 dominates between 18 km and 34 km, consistent with the NO2 diurnal cycles. Therefore, the secular NO2 changes during daytime and nighttime are dominated by N2O5 conversions.

Daytime NO2 increasing rate 235
Reactions (R1)-(R5) contribute the daytime increase of NO2. Sussmann et al. (2005) first obtained a daytime NO2 increasing rate from ground-based measurements. They reported an annually averaged value of (1.02 ± 0.06) × 10 cm -2 h -1 over Zugspitze, Germany (2.96 km, 47°N). For October alone, they obtained a value of (1.20 ± 0.57) × 10 cm -2 h -1 . For comparison, we calculate the daytime increasing rate using our data between 7 AM and 4 PM. To obtain a rate corresponding to a clean atmosphere, we define a baseline of the diurnal cycle using the 20-percentile in the 15-minute bins from 7 AM to 4 240 PM ( Figure 6). This results in a total of 37 bins, which is roughly the number of points in October shown in Figure 3a of Sussmann et al. (2005). We then apply the linear regression to the baseline and obtain an increasing rate of (1.29 ± 0.30) × 10 cm -2 h -1 in October over TMF (34.4°N). Thus our value is consistent with Sussmann et al.'s (2005) value.

Temperature sensitivity
The chemical kinetic rates in the model are dependent on temperature. The temperature profile that has been used to 245 obtain the baseline diurnal cycle corresponds to a zonal mean temperature profile at the equinox and 30° latitude (Figure 7, solid line). To test the sensitivity of the simulated 24-hour cycle of NO2 column, we reduce the input temperature below 60 km by 5 K (Figure 7, dashed line). Note that the 5 K reduction is much larger than the observed tidal variation in stratospheric temperature below 50° latitude, which is ~0.1 K in the lower stratosphere and ~1 K in the middle stratosphere (Sakazaki et al., 2012). We choose this exaggerated reduction in order to clearly show the temperature effect on the NO2 chemistry. 250 https://doi.org/10.5194/amt-2020-173 Preprint. Discussion started: 23 June 2020 c Author(s) 2020. CC BY 4.0 License. Figure 3 (dash-dotted line) shows the simulated NO2 column using the reduced temperature profile. Because of the reduction in temperature, the nighttime loss due to the reactions with O3 and NO3 through Reactions R9 and R10 is slower. As a result, the simulated nighttime NO2 column is higher than the baseline simulation but it still agrees with the spread of the nighttime observations. In addition, due to the less efficient reaction NO + O3, the simulated daytime NO2 column is slightly lower than the baseline simulation but it still agrees with the daytime observation. Thus, given that the tidal temperature change 255 in the middle atmosphere is much smaller than the change in the sensitivity test, the equinox temperature profile used in the baseline run is sufficient for the simulation of the diurnal cycle of the NO2 column.

Back-trajectories
Since the TMF is located at the top of a mountain in a remote area, high values of column NO2 measured on October 27, 2018, were likely due to atmospheric transport of urban pollutants from nearby cities, especially the Los Angeles megacity. 260 While chemical processes would quantitatively alter the amount of NO2 to be observed over TMF, a back-trajectory study suffices to provide evidence on how the urban pollutants may be transported to TMF.

Summary
We have presented the diurnal measurements of total column NO2 that has been made over the TMF located in 285 Wrightwood,California (2.286 km,34.38°N,117.68°W) from October 23 to October 28, 2018. The instrument measures the differential slant column NO2 relative a reference spectrum at the noontime. To retrieve total column NO2 in the reference spectrum, we applied a variant of the Langley extrapolation. The conventional Langley extrapolation assumes a constant column throughout the day, which does not hold for NO2. To properly consider the time-dependency of column NO2, we combine two methods independently developed by Lee et al. (1994) and Herman et al. (2009). The combined method, called 290 the model-based minimum-amount Langley extrapolation, first obtains a baseline of the observed diurnal cycle, which is assumed to be the diurnal cycle in a clean atmosphere. Then the baseline is fitted against the modelled diurnal cycle in a 1-D photochemical model so that the column NO2 in the reference spectrum is given by the y-intercept of the fitted line.
The measured 24-hour cycle of the TMF total column NO2 on clean days agrees well with a 1-D photochemical model calculation. Our model simulation suggests that the observed monotonic increase of daytime NO2 column is primarily due to 295 the photodissociation of N2O5 in the reservoir. From our measurements, we obtained a daytime NO2 increasing rate of (1.29 ± 0.30) × 10 cm -2 h -1 , which is consistent with the value observed by Sussmann et al. (2005), who reported a daytime NO2 increasing rate of (1.20 ± 0.57) × 10 over Zugspitze, Germany (2.96 km, 47°N). Our model also suggests that during nighttime, the monotonic decrease of NO2 is primarily due to the production of N2O5. Furthermore, the abrupt NO2 decrease and increase at sunrise and subset, respectively, are due to the activation and deactivation of the NO2 photodissociation. 300 The total column NO2 in the afternoon on October 27, 2018 was much higher than the model simulation. We conducted a 24-hour HYSPLIT back-trajectory analysis to study how urban pollutants were transported from the Los Angeles Basin. The back-trajectories in 4 of the 6 days during the measurement period went directly from inland desert areas to the TMF. The back-trajectory in another day came from the southwest coastline, spending less than 6 hours over the Los Angeles Basin before reaching the TMF. Lastly, the 24-hour back-trajectory on October 27, 2018 was characterized by a unique slow 305 wind that came from inland in the northeast and spent more than 18 hours in the Los Angeles Basin, picking up pollutants from Riverside, Orange County, and finally Downtown Los Angeles before reaching TMF.  The blue circles are the observed differential slant columns during our campaign over TMF from October 23 to October 28, 2018. Each observational value is plotted against the total slant column modelled 445 at the same time of the day (e.g. 11:05 AM PST). The green dots are the 20-percentile of 20 uniform bins on the -axis. The red line is a linear regression of the green dots, which is taken as the diurnal cycle in a clean atmosphere. The linear fit is = .