Validation of the vertical profiles of HCl over the wide range of the stratosphere to the lower thermosphere measured by SMILES

Hydrogen chloride (HCl) is the most abundant (more than 95 %) among inorganic chlorine compounds Cly in the stratosphere. The HCl molecule is observed to obtain long-term quantitative estimations of total budget of the stratospheric anthropogenic chlorine compounds. In this study, we provided HCl vertical profiles at altitudes of 16–100 km using the superconducting submillimeter-wave limb-emission sounder (SMILES) from space. The HCl vertical profile from the upper troposphere to the lower thermosphere is reported for the first time from SMILES observations; the data quality is quantified 5 by comparison with other measurements and via theoretical error analysis. We used the SMILES Level-2 research product version 3.0.0. The period of the SMILES HCl observation was from October 12, 2009 to April 21, 2010, and the latitude coverage was 40◦S–65◦N. The average HCl vertical profile showed an increase with altitude up to the stratopause (∼45 km), approximately constant values between the stratopause and the upper mesosphere (∼80 km), and a decrease from the mesopause to the lower thermosphere (∼100 km). This behavior was observed in the all latitude regions, and reproduced by the Whole 10 Atmosphere Community Climate Model in specified dynamics configuration (SD-WACCM).We compared the SMILES HCl vertical profiles in the stratosphere and lower mesosphere with HCl profiles from Microwave Limb Sounder (MLS) on the Aura satellite, as well as from Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on SCISAT and from TEraheltz and submilimeter LImb Sounder (TELIS) (balloon-borne).The TELIS observations were performed using the superconductive limb emission technique, as used by SMILES. The globally averaged vertical HCl profiles of SMILES agreed 15 well with those of MLS and ACE-FTS within 0.25 and 0.2 ppbv between 20 and 40 km (within 10% between 30 and 40 km, There’s a larger discrepancy below 30km.), respectively. The SMILES HCl concentration was smaller than those of MLS and ACE/FTS as the altitude increased from 40 km, and the difference was approximately 0.4–0.5 ppbv (12 – 15%) at 50–60 km. The difference between SMILES and TELIS HCl observations was about 0.3 ppbv in the polar winter region between 20 and

In this study, we examined HCl vertical profiles from 16-100 km, including the upper mesosphere and lower thermosphere (MLT) region. We used the SMILES NICT Level-2 product version 3.0.0 (v300), which was released in late 2012 (http://smiles.nict.go.jp/pub/data/index.html). HCl vertical profiles from the upper troposphere to the lower thermosphere are reported for the first time. We perform a validation of the SMILES HCl vertical profiles by comparisons with the corresponding 55 global model results of SD-WACCM, satellite observations from MLS and ACE-FTS, balloon-borne observations from TELIS and we provide a SMILES HCl error analysis.
The SMILES HCl observations and retrieval procedure are described in Sect. 2. The HCl vertical profile derived by the SMILES product and comparisons of HCl distribution between 40 • S-60 • N with SD-WACCM are shown in Sect. 3. Results of HCl comparisons between SMILES and other instruments are described in Sect. 4. An estimation of the systematic and random 60 errors is presented in Sect. 5. Section 6 describes our conclusions.

SMILES HCl observations
The SMILES instrument had been attached to the Japanese Experimental Module (JEM) on the ISS, since September 2009. SMILES operational period started on October 12, 2009 and ended on April 21, 2010. The ISS has a non-sun-synchronous circular orbit with an inclination angle of 51.6 • with respect to the equator. The height of the ISS changed slowly over the 65 observational period ranging 340-360 km. We tilted the line-of-sight at a 45 • angle in the direction of the forward movement of the ISS to observe the northern polar region. The SMILES parameters are summarized in Table 1. The details of the SMILES observations are described in Kikuchi et al. (2010) and in an ozone-validation paper by , respectively.
Herein, we briefly describe the SMILES atmospheric observations in terms of the HCl spectra. The SMILES had three frequency bands in the submillimeter-wave regions, Band A (624.32-625.52 GHz), Band B (625.12-626.32 GHz), and Band 70 C (649.12-650.32 GHz). Each single-scan provided a combination of two out of three of the frequency bands: Bands A+B, C+B, or C+A. The combinations changed on a daily basis, as described in Kikuchi et al. (2010). The rotational transitions of two HCl isotopologues were located in Bands B and A for H 35 Cl at 625.9 GHz and H 37 Cl at 624.9 GHz, respectively. Two acousto-optical spectrometers (AOSs) were equipped in the SMILES instrument. The spectral resolution obtained by AOS1 and AOS2 was 0.8 MHz. The band configuration for each HCl isopologues had three patterns as follows:, Band-B was always associated with AOS2. Figure 1 shows the number of observations per day obtained for H 35 Cl (Band-B) and H 37 Cl (Band-A) for 5 • latitude 80 bins during the SMILES observational period. It should be noted that the sampling is not homogeneously distributed for the SMILES observations. The SMILES instrument was sometimes not in operation, for example, when the ISS was boosted up from a low to a high altitude, and the solar panels disturbed the observational line-of-sight. The SMILES observational latitude which happened three times during the 7-month-long observational period. 85 We used the SMILES NICT Level 2 product version 3.0.0 (v300) for this study. The general method of v300 for the HCl retrieval is similar to that of the Level 2 product version 2.1.5 (v215) . The major updates from the v215 product are as follows: 1) An improvement in the spectrum calibration, particularly for the gain non-linearity of the receiver system (Ochiai et al., 2013), 2) An improvement in the accuracy of the tangent height estimation (Ochiai et al., 2013), and 3) An update of the temperature retrieval. The temperature profile used in the SMILES version 3.0.0 retrieval was synthesized, 90 assuming the hydrostatic equilibrium, using the Goddard Earth Observing System, Version 5 (GEOS-5) reanalysis meteorological datasets and the climatology based on the Aura/MLS measurements . The GEOS-5 datasets were used in the upper troposphere and stratosphere, and the Aura/MLS datasets were used in the mesosphere and lower thermosphere, respectively. The temperature profile was also retrieved using the ozone transition in the SMILES version 3.0.0 retrieval process, but it was not applied to the retrieval of atmospheric species including HCl, except for ozone, to avoid systematic error 95 propagation issues (SMILES-NICT, 2014). The level 1b spectrum data version 008 was used for the SMILES NICT Level 2 product v300 (Ochiai et al., 2013). The spectroscopic parameters for the HCl retrieval were based on Cazzoli and Puzzarini  Cazzoli and Puzzarini (2004). b: Baron et al. (2011) (2004) and Laboratory measurement, as summarized in Table.2. We used only the H 35 Cl data because the intensities of the H 37 Cl spectra were weaker than those of H 35 Cl, as shown in Fig. 2. The criteria for the selection of the H 35 Cl profiles used in this study are as follows: (1) χ 2 less than 0.8. χ 2 is defined by y is the observed spectrum, S is the covariance matrix of the measurement noise, x a is the a priori state, S a is the covariance matrix of x a , and F(x) is the forward model depending on the state vector x. We used the U.S.standard atmosphere profiles as the a priori state (x a ) (US-Standard, 1976). They are used separately for polar, equatorial, summer mid-latitude, or winter midlatitude regions.The forward model is essentially the atmospheric radiative transfer and the instrument model. (2) measurement 105 response, MR, between 0.8 and 1.2 for each vertical grid. MR is defined by A is the averaging kernel matrix. A value of MR near unity indicates that most of the information in the retrieval results is provided by observations. A low value of MR indicates that the retrieval results are largely influenced by the a priori state and are forced to be identical to a priori values.

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An example H 35 Cl profile and its averaging kernel are presented in Fig. 3  as shown in Fig. 3. The full width at half maximum (FWHM) of the averaging kernels is approximately 3 -4 km at altitudes of

Vertical and latitudinal distribution of SMILES HCl
In this section, we provide the HCl vertical profiles derived from the SMILES NICT Level 2 product v300. approximately constant values between the stratopause and the upper mesosphere (∼80 km), and a decrease with altitude from the mesopause to the lower thermosphere (∼100 km). In the lower and middle stratosphere, HCl is generated by the reaction of Cl with CH 4 and HO 2 and transported by circulation (e.g. Brewer-Dobson circulation). The HCl abundance is balanced by production (Cl + HO2 → HCl + O 2 ) and loss (HCl + OH → Cl + H 2 O, HCl + hν → H + Cl) in the upper stratosphere and mesosphere. Near the mesopause, the photodissociation becomes the dominant reaction, and the HCl abundance decreases with 125 height (Brasseur and Solomon, 2005).
This behavior was reproduced by the Whole Atmosphere Community Climate Model version 4 (WACCM4) in specified dynamics configuration (SD-WACCM) (Lamarque et al., 2012;Limpasuvan et al., 2016), see the panel (B). In the specified dynamics configuration, the simulated meteorological fields in the troposphere and stratosphere are constrained to the Global Modeling and Assimilation Office Modern-Era Retrospective Analysis for Research and Applications (Rienecker et al., 2011).

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The horizontal resolution of SD-WACCM simulation is 1.9 • and 2.5 • for latitude and longitude, respectively. The vertical grid is from the ground to 150 km with 88 levels, and the time resolution is 3 hours. Differences of HCl abundance between SMILES mechanisms of HCl for the mesosphere/thermosphere (Brasseur and Solomon, 2005).

Comparison of SMILES HCl profile with those obtained using other instruments
We performed a comparison between SMILES HCl products and other datasets obtained using the MLS on the Aura satellite, the ACE-FTS on the SCISAT satellite, and the balloon-borne TELIS instrument. The characteristic of instruments and datasets are summarized in Table 3. The mean absolute difference, ∆ abs , for each altitude between SMILES and the other instrument 145 is defined as where x s,i (z) and x c,i (z) are the HCl volume mixing ratio (VMR) of ith coincidence at an altitude z for SMILES and the other instrument, respectively. N (z) is the number of coincidence at an altitude z. The mean relative difference in percentage, ∆ rel , for each altitude is given by The coincidence criteria between the SMILES observations and those of the other instruments was set to within 2 • for latitude,

Comparison with Aura/MLS
The Aura satellite has a sun-synchronous orbit with an ascending node at 1:45 PM local time (Waters et al., 2006). The 155 measurements cover latitudes from 82 • S to 82 • N and provide approximately 3500 vertical profiles each day. We used version 4.2 of the Aura/MLS HCl profiles for these comparisons. The Aura/MLS team provided two HCl products one from spectral band 13 (HCl-640-B13) and one from band 14 (HCl-640-B14). The HCl-640-B13 product is available for the pressure region between 100 hPa and 0.32 hPa. The single profile precision of HCl-640-B13 is less than 0.8 ppbv (25%) in the stratosphere, and the estimated accuracy is approximately 0.3 ppbv (10%) (Livesey et al., 2018).
160 The vertical and horizontal resolutions are 3-5 km and 200-400 km, respectively. The vertical resolution of MLS is of the same order as that of SMILES. We used the recommended parameters "Status," "Quality," and "Convergence" for screening the Aura/MLS data based on Livesey et al. (2018). The good profiles were selected using (1) Quality < 1.2, (2) Convergence

Comparison with SCISAT/ACE-FTS
The ACE-FTS is an instrument mounted on the Canadian SCISAT satellite. SCISAT moves along an orbit at a 650 km altitude and is inclined at 74 • to the equator (Bernath et al., 2005). The ACE comprises two instruments: the Fourier Transform profiles from the version 4.0 software, which is the latest data version (Boone et al., 2020). The vertical resolution of the ACE-FTS HCl retrieval is 3-4 km, and the values from the retrieval grid are interpolated onto the 1-km grid, using a piecewise 185 quadratic method (Bernath et al., 2005). The vertical resolution of ACE-FTS is of the same order as that of SMILES. In this study, we used the data within ±3 times the median absolute deviation (  and ACE-FTS for each month and confirmed the seasonal variation of the bias. Figure 9 (B) shows a seasonal variation of the difference between the SMILES and ACE-FTS profiles in the northern hemisphere (from 30 • N-65 • N latitude range). The upper panels in Fig. 9 (B) show a mean of the SMILES (blue) and ACE-FTS (green) profiles for each month at three altitude 200 levels. The difference for every month, shown in the lower panels, was represented by the mean for each month at each altitude, and the error-bar showed the 1 σ standard deviation. No significant seasonal dependence of the difference was observed. The difference of HCl value from these measurements was consequently about 0.5 ppbv at 50 km.

Comparison with balloon-borne instrument TELIS
The     (Webster et al., 1993;Wegner et al., 2016). Both the SMILES and TELIS profiles agree well in general, but the TELIS profiles 220 are larger than the SMILES profiles above 32 km (8 hPa). The H 37 Cl line is still rather strong at higher altitudes, and the dominant error source of the TELIS data stems from the non-linearity in the calibration process, which shows that even a small uncertainty may result in significant errors in the retrieval (Xu et al., 2018).

Theoretical error analysis
We have evaluated the total error in the HCl vertical profiles observed by SMILES, and we discussed the cause of the bias 225 observed in the comparison study, see Sect. 4.

Estimation of total error
We employed a perturbation method to estimate the total error of the SMILES HCl profile. The details of the perturbation method of the SMILES error analysis have been described in Kasai et al. (2006) and Sato et al. (2014), , and Sato et al. (2012) for ozone isotopes, ozone, and ClO, respectively. We assumed an averaged HCl profile within the where I is the inversion function, b 0 is the vector of model parameters and ∆b 0 is the uncertainty on model parameters.The 245 y ref is the reference spectrum calculated using the reference profile. The details of the estimation of the total error are described in Sato et al. (2012). The error sources and perturbations for the model parameter used in this study are summarized in Table   5. These parameters and perturbation values are based on Sato et al. (2014). The uncertainties of the spectroscopic parameters of the O 3 transition 625.37 GHz were included to estimate the error due to the interference from the line shape of O 3 spectrum.
The calibration error was not considered in this study because the latest L1b data version 008 was used and Sato et al. (2014) 250 reported that the error due to the spectrum calibration in this L1b data was insignificant. The estimated errors in the SMILES HCl v300 product are presented in Fig. 11. The total model parameter error, labeled as "Param", was calculated by a root-sum-square (RSS) of all model parameter errors. The three spectroscopic parameters, line intensity, air-pressure broadening coefficient (γ air ), and its temperature dependence (n air ) were dominant error sources below 30 km. The γ air was a major error source between 30 and 60 km, which was about 0.09 ppbv (∼ 3%) at 50 km. At 255 altitudes of 60-90 km, the largest error source was the AOS response function, and its peak value reached 0.38 ppbv (∼12%) at 70 km.

Discussion: Cause of the negative bias of the SMILES HCl vertical profile
In Sect. 5.2, we discuss the cause of the negative bias of the SMILES HCl vertical profile, i.e., approximately 10 % less than those of Aura/MLS and ACE-FTS especially at the altitudes between 40 -60 km. Such a large bias could not be explained by 260 the total error estimated by the perturbation method described in Sect. 5.1. We further investigated the cause of this bias by difference of temperature profile used in the retrieval calculation. The temperature profile used for the retrieval procedure of SMILES was lower than those of MLS and ACE-FTS particularly in the upper stratosphere and mesosphere. We estimated the Figure 11. Summary of the errors for a single scan observation. The left and right panels, respectively, show the absolute difference and relative difference, which were estimated using the perturbation method. The green marker indicates an error due to the uncertainty in line intensity ("Intensity"). The red and blue square show errors for the air broadening coefficient ("γair"), and its temperature dependence ( difference of the retrieved HCl vertical profile, ∆x, due to the difference of the temperature profile, ∆T , as follows. The jacobian K T indicates the sensitivity of the spectral brightness temperature (y) with reference to changes of the temperature (T ). Here we synthesized the jacobian with a perturbation of 0.5 K. Figure 12 (A) shows the jacobian as a function of tangent height. Here the minimum value of the column of the K T matrix is plotted. A negative jacobian value means that higher temperatures induce a lower brightness temperature spectrum, thus increasing the HCl abundance in the retrieval to profile of temperature of SMILES is approximately 5 -10 K lower than those of both MLS and ACE-FTS for altitudes between 50 and 60 km. The a priori temperature profile used in the SMILES retrieval procedure is based on the GEOS-5 profile in the stratosphere and MLS retrieved profile in the mesosphere and above.The altitude limit of the MLS temperature profile is 0.001 hPa, with a vertical resolution of 6 -14 km and a precision of 1.2 -3.6 K per profile. MLS used GEOS-5 up to 1 hPa as with 275 SMILES. For pressures smaller than 1 hPa, the COSPAR International Reference Atmosphere (CIRA-86) is used as a priori temperature information (with a loose constraint) in the MLS retrieval procedure (Schwartz et al., 2008). The altitude range and vertical resolution of the CIRA-86 profile are ground to 120 km and 2 km, respectively (Fleming et al., 1990). The MLS temperature profiles in the the stratosphere and above were retrieved primarily from bands near the 118 GHz O2 spectral line (Livesey et al., 2018). The temperature value retrieved by MLS is 10 K lower than the a priori profile on average in some 280 areas for pressure values smaller than 1 hPa (Schwartz et al., 2008), based on earlier version validation studies (Schwartz et al., 2008). The ACE-FTS HCl retrieval procedure uses the temperature profile retrieved from the ACE-FTS measurements between 18-125 km. The ACE-FTS temperature profiles were retrieved from CO 2 VMR using hydrostatic equilibrium (Boone et al., 2020). The vertical resolution of ACE-FTS retrieved temperature is 3 -4 km. The temperature values retrieved by ACE-FTS are less than 10 K larger than the MLS derived temperatures. (Schwartz et al., 2008). These types of difference are also seen in 285 the comparison results performed here. Figure 12 shows the ∆x due to the difference of the temperature profile. This temperature difference caused an increase in SMILES HCl of 0.12 and 0.20 ppbv at 50 -60 km for the MLS and ACE-FTS comparisons, respectively.

Panel (D) in
In the comparison study, see Sect. 4, we confirmed the negative bias in the SMILES HCl vertical profile of 0.4±0.38 and 0.5±0.28 ppbv between 40 -60 km for MLS and ACE-FTS, respectively. We estimated the total error by the perturbation 290 method and investigated the temperature profile used in the retrieval calculation, in order to investigate the cause of this negative bias. The largest error sources were the uncertainties in γ air of the H 35 Cl transition and the temperature profiles used in the retrievals. We assumed a 3 % uncertainty in γ air which could lead to a −0.1 ppbv bias in the 40 -60 km region. In addition to the error due to the γ air coefficients, the effect of temperature differences should be taken into account at altitudes above 50 km. The gradual increase in bias is caused by the difference in altitude at which these two errors become more 295 pronounced. The difference in temperature profiles used in the retrieval between SMILES and ACE-FTS caused a negative bias of about 0.2 ppbv at 50 -60 km. In summary, 0.3 in 0.5 ppbv (60 %) negative bias between SMILES and ACE-FTS can be explained by the uncertainty in γ air and the temperature profiles used in the SMILES retrievals. The effect of γ air error on the negative bias between SMILES and MLS is less than that of SMILES and ACE-FTS, since the SMILES and MLS observed the same H 35 Cl transition lines and the values of the γ air are consistent within approximately 1 % (3.39 MHz/Torr for 300 SMILES and 3.42 MHz/Torr for MLS (Drouin, 2004)

Conclusion
In this study, the HCl vertical profile in a wide range from the upper troposphere to the lower thermosphere was reported for the first time using the SMILES NICT Level 2 data product v300. The HCl distribution shows an increase with altitude with a maximum below the stratopause (∼45 km), approximately constant values between the stratopause and the upper mesosphere (∼80 km), and a decrease with altitude from the mesopause to the lower thermosphere (∼100 km). In the lower and middle 310 stratosphere, HCl is generated by the reaction of Cl with CH 4 and HO 2 and transported by circulation (e.g. Brewer-Dobson circulation The data quality of the SMILES HCl vertical profile was quantified by comparisons versus other measurements, and supported by a theoretical error analysis. We compared the SMILES HCl vertical profiles with well validated data of two satellite instruments, Aura/MLS and ACE-FTS, as well as a balloon-borne instrument, TELIS, at their temporal-spatial coincidences. The SMILES HCl profiles at 20-40 km showed good agreements, within less than 0.25±0.3 (1σ) and 0.20±0.2 (1σ) ppbv, versus MLS and ACE-FTS, respectively. The comparison with the TELIS in the polar winter region at 20-34 km showed similar 320 behavior with differences within 0.3 ppbv, which is the same order of magnitude as the systematic error of the TELIS data. A negative bias (<0.5 ppbv) of the SMILES HCl profiles from 40 to 60 km altitudes was observed in comparisons versus MLS and ACE-FTS HCl profiles.
We estimated the total error for SMILES HCl based on the perturbation method and considering the uncertainties in atmospheric temperature profiles used in the retrievals. The dominant contributions to the systematic errors were from the air 325 broadening parameter (0.09 ppbv) and the AOS response function (0.38 ppbv) at 30 --60 km and 60-100 km altitudes, respectively. The uncertainty in the temperature profile used in the retrieval calculation caused a negative bias of 0.12 to 0.20 ppbv between 50 -60 km, which was 30% and 40% of the HCl abundance difference between SMILES and MLS, and SMILES and ACE-FTS, respectively. The uncertainties of the air broadening parameter and the temperature profile are capable of contributing a total of 40 -50 % of the SMILES HCl negative biases at 50 -60 km. In summary, our theoretical error analysis showed 330 that the HCl profiles had a negative bias of 0.20 -0.25 ppbv at 50 -60 km, which is consistent with the observed differences versus MLS and ACE-FTS profiles within 1 standard deviation. The spectroscopic parameters of the HCl transitions and the temperature profile above the stratopause are key parameters for potential improvements in the SMILES retrieval algorithms.
The observation of HCl abundances in the upper atmosphere is important to investigate the long-term total budget of anthropogenic chlorine in the Earth's atmosphere. Further observations and model studies are needed to better understand the sources 335 and sinks, transport processes, and chemical reactions related to HCl.
Data availability. The SMILES data is available at http://smiles.nict.go.jp/pub/data/index.html.
The MLS data is available at https://disc.gsfc.nasa.gov/datasets?page=1&keywords=AURA%20MLS or see https://mls.jpl.nasa.gov/data/ The ACE-FTS data is available at http://www.ace.uwaterloo.ca/instruments_acefts.php The details on the TELIS 1.8 THz channel and its L1 data processing are shown in https://elib.dlr.de/66749/ "Development and characterization of the balloon borne instrument TELIS (TErahertz and submillimeter LImb Sounder): 1.8 THz receiver Suttiwong, Nopporn (2010)" and/or https://elib.dlr.de/97249/ "Inversion for Limb Infrared Atmospheric Sounding Xu, Jian (2015)" The WACCM data is available at https://www2.acom.ucar.edu/gcm/waccm Author contributions. SN designed the study and performed the analysis. YK designed the study and provided the SMILES data. TOS provided the code for the error analysis and contributed to data analysis and interpretation. TY, TF, and KK contributed to the data analysis