First ground-based FTIR observations of HFC-23 at Rikubetsu , Japan , and Syowa Station , Antarctica

We have developed a procedure for retrieving atmospheric abundances of HFC-23 (CHF3) with a ground-based Fourier transform infrared spectrometer (FTIR) and analysed the spectra observed at Rikubetsu, Japan (43.5oN, 143.8oE), and at Syowa Station, Antarctica (69.0oS, 39.6oE). The FTIR retrievals were carried out with the SFIT4 retrieval program, and the two spectral windows of 1138.5–1148.0 cm-1 and 1154.0–1160.0 cm-1 in the overlapping ν2 and ν5 vibrational-rotational transition 20 bands of HFC-23 were used to avoid strong H2O absorption features. We considered O3, N2O, CH4, H2O, HDO, CFC-12 (CCl2F2), HCFC-22 (CHClF2), PAN (CH3C(O)OONO2), HCFC-141b (CH3CCl2F), and HCFC-142b (CH3CClF2) as interfering species. Vertical profiles of H2O, HDO, and CH4 are preliminarily retrieved with other independent spectral windows because these profiles may induce large uncertainties in the HFC-23 retrieval. Each HFC-23 retrieval has only one piece of vertical information with sensitivity to HFC-23 in the troposphere and the lower stratosphere. The retrieval errors mainly arise from 25 the systematic uncertainties of the spectroscopic parameters used to obtain the HFC-23, H2O, HDO, and CH4 abundances. For comparison between FTIR-retrieved HFC-23 total columns and surface dry-air mole fractions provided by AGAGE (Advanced Global Atmospheric Gases Experiment), the FTIR-retrieved HFC-23 dry-air column-averaged mole fractions (XHFC-23) were calculated. The FTIR-retrieved XHFC-23 at Rikubetsu and Syowa Station have negative biases compared to AGAGE datasets. The trend derived from the FTIR-retrieved XHFC-23 data at Rikubetsu for December to February (DJF) data over the 1997– 3

Under the regulations of the "Montreal Protocol on Substances that Deplete the Ozone Layer (Montreal Protocol)" (UNEP, 2000), production and consumption of ozone-destroying chlorofluorocarbons (CFCs) have been completely banned since 2010, whereas production and consumption of hydrochlorofluorocarbons (HCFCs), which have less effect on ozone depletion, have continued. The Montreal Protocol is phasing out the production and consumption of HCFCs for emissive uses by 2020 in 15 developed countries, and by 2030 in developing countries, while use for feedstock (e.g. in production of HFCs and fluoropolymers) is not restricted. Hence, emissions of HCFCs to the earth's atmosphere are expected to continue for quite a while. HCFC-22, one of the major HCFCs with an ozone depletion potential (ODP) of ~0.03 and a 100-year GWP of 1,760 (Harris et al., 2014), has been widely used in air conditioners, refrigerators, foaming agents, or heat insulating materials, and therefore large banks still exist, which also contribute to ongoing emissions. Emission of HCFC-22 has increased since 2004 20 (Montzka et al., 2009), and global emissions in 2010 are estimated to have reached 386 ± 41 Gg yr -1 by an inversion model (Simmonds et al., 2018a). Clearly, HFC-23 emissions have been increasing as a subsequence.
Currently, hydrofluorocarbons (HFCs) are widely used as substitutes of CFCs and HCFCs, because they have essentially no ODP and are therefore not contributing to ozone depletion. However, HFC-23 is not used as a substitute for CFCs or HCFCs, but is used in halon-1301 (CBrF3) production, semiconductor manufacturing, very low temperature refrigeration, and specialty 25 fire extinguisher (Oram et al., 1998;Miller et al., 2010, Simmonds et al., 2018a, which means that emissions from deliberate use of HFC-23 are small. Hence, HFC-23 has mainly been vented from HCFC-22 production plants into the atmosphere (Montzka et al., 2019). Simmonds et al. (2018a) reported that global annual emissions of HFC-23 were estimated to have reaching 14.5 ± 0.6 Gg yr -1 in 2014 (Simmonds et al., 2018a). The annual global average mole fraction of HFC-23 reached 28.9 ppt (parts per trillion) in 2016, which corresponds to a radiative forcing of 5.2 mW m -2 . This is the second largest radiative forcing among all HFCs and fluorinated-gases just after HFC-134a (14.3 mW m -2 ) (Montzka et al., 2019). Miller and Kuijpers (2011) suggested that if no additional abatement measures are implemented to reduce HFC-23, its emission will rise to 24 Gg yr -1 in 2035, and the mole fraction will rise to 50 ppt which corresponds to a radiative forcing of 9 mW m -2 . Furthermore, if 5 the emissions of HFC-23 are not regulated and all UNFCCC CDM project were terminated, the HFC-23 emission growth rate after 2030 would rise to 0.8 Gg yr -2 , which is four times larger than the previous trend (Miller and Kuijpers, 2011). In 2016, the parties to the Montreal Protocol agreed to amend the Montreal Protocol to gradually reduce the production and consumption of HFCs (the 2016 Kigali Amendment), and to control emissions of HFC-23. Unfortunately, Stanley et al. (2020) reported that the global HFC-23 emissions, derived from atmospheric measurements (top-down estimate), reached 15.9 ± 0.9 Gg yr -1 10 in 2018 which was higher than in any year in history. Moreover, their results indicated that the top-down global emission in 2017 was 12.5 ± 0.7 Gg yr -1 higher than the inventory-based emission of 2.4 Gg yr -1 (bottom-up estimate), despite government mandated emission reductions in China and India. This result clearly implies that unreported HFC-23 by-product emissions exist. Therefore, the global observation system of atmospheric HCFC-22 and HFC-23 abundances is important to monitor the efficacy of the phase-down under the Montreal Protocol and to accurately project the impact of emissions of these compounds 15 on ozone depletion and climate change into the future.
A ground-based in-situ measurement of HCFC-22 with a gas chromatography-mass spectrometer (GC-MS) technique was first reported by Rasmussen et al. (1980). Halocarbons and other Atmospheric Trace Species (HATS) group in Global Monitoring Division (GMD) of Earth System Research Laboratory in National Oceanic and Atmospheric Administration (NOAA/ESRL) has been analysing atmospheric minor constituents sampled in flasks at several remote sites since 1977, and 20 the measurement of HCFC-22 by HATS group has started in 1992 (Montzka et al., 1993;Montzka et al., 2009). The Advanced Global Atmospheric Gases Experiment (AGAGE) observation network supported by a consortium of multinational institutions and organizations started HCFC-22 in-situ measurements in 1998 using a GC-MS (ADS systems since 1998 and more advanced "Medusa" systems since the mid-2000s) (Simmonds et al, 1995;Prinn et al., 2000;O'Doherty et al., 2004;Miller et al., 2008). 25 In contrast, the history of in-situ observation of atmospheric HFC-23 is relatively short. Atmospheric HFC-23 abundances were first reported in Oram et al. (1998) based on GC-MS measurements of flask background air samples collected at Cape Grim,Tasmania,Australia (40.7ºS,144.7ºE), from 1978 to 1995. But high frequency in-situ measurement of HFC-23 by the AGAGE network are only available since the late 2000s using the GC-MS-Medusa at AGAGE stations (e.g. Cape Grim; Gosan, Jeju island, South Korea (33.3ºN, 126.2ºE)) (Miller et al., 2010;Kim et al., 2010;Simmonds et al., 2018a). Also, in-situ 30 measurements of HFC-23 with AGAGE-compatible (but not identical) instruments have been operated at two stations of National Institute for Environmental Studies (NIES) in Japan: Hateruma, Okinawa (24.1°N, 123.8°E, since 2004) and Cape Ochiishi, Hokkaido (43.2ºN,145.5ºE, since 2006) (Yokouchi et al, 2006;Fang et al., 2015). In total, there are, however, only Thanks to the evolution of molecular spectroscopy, and increasing atmospheric concentrations, space-borne remote sensing observation of HFCs, in addition to several CFCs and HCFCs, became possible (Nassar et al., 2006). For HFC-23, the first space-borne and balloon-borne remote sensing observations were done by the Atmospheric Chemistry Experiment-Fourier Transport Spectrometer (ACE-FTS) on SCISAT and the JPL MkIV interferometer, using the spectral region (1140-1160 cm -1 ) covering the ν2 and ν5 vibrational-rotational transition bands of HFC-23 (Harrison et al., 2012). Fernando et al. (2019) 5 reported the HFC-23 trend above cloud-top derived from the ACE-FTS measurements for the period of 2004-2017, and indicated that the annual HFC-23 mole fractions retrieved from the ACE-FTS consistently averaged 5% smaller than ones at ground level from the AGAGE annual global mean dataset. However, the ACE-FTS observations do not have sensitivity to the troposphere where all HFC-23 emissions occur.
The Network for the Detection of Atmospheric Composition Change -Infrared Working Group (NDACC-IRWG) has been 10 globally monitoring abundances of various atmospheric trace gases (e.g. O3, HCl, HNO3, CH4, CO) using ground-based Fourier transform infrared spectrometer (FTIR) instruments (De Mazière et al., 2018). At present, the contributing ground-based FTIR instruments to the NDACC-IRWG are located at more than 20 sites around the world, and have yielded long-term consistent high-quality data by adherence to strict measurement and analysis procedures. For CFCs and HCFCs, for example, atmospheric CFC-11, CFC-12, and HCFC-22 have been retrieved from infrared spectra taken by ground-based FTIRs at Reunion island 15 (Zhou et al., 2016). For HFCs, however, there has been no attempt to retrieve their atmospheric abundances. If routine observations of atmospheric HFC-23 using the NDACC's ground-based FTIRs were possible, we could fill spatial and temporal gaps in the existing observations by AGAGE and ACE-FTS, which would allow for monitoring of global atmospheric HFC-23 abundances in greater detail than ever.
This study aims to investigate the retrieval procedure of atmospheric HFC-23 using the overlapping ν2 and ν5 vibrational-20 rotational transition bands of HFC-23. We analyze solar infrared spectra observed by two ground-based FTIRs installed at Rikubetsu, Japan, and Syowa Station, Antarctica. First, the details of the FTIR observations at both sites are described in Section 2. In Section 3, the retrieval strategy of HFC-23 for both sites is described in detail. Section 4 presents the results and characteristics of the HFC-23 retrievals, including the retrieval error budget. In Section 5, the time-series of our FTIR-retrieved HFC-23 are compared to the in-situ measurements from the AGAGE network, and the modelled annual global mean dataset 25 based on the AGAGE measurements. In addition, we discuss the HFC-23 trends derived from each dataset. Finally, conclusions and perspectives are summarized in Section 6.
Sapporo and located in a small town surrounded by forests and pastures. In October 1997, this observatory was relocated to the top of a hill (380 m a.s.l.) in the vicinity of the town. The first instrument, which operated until April 2010, was a Bruker IFS-120M FTIR spectrometer. In 2013, a Bruker IFS-120/5HR, an upgrade of the IFS-120HR, was installed as a second instrument taking over the observations by the IFS-120M, contributing to the Total Carbon Column Observing Network (TCCON) in addition to the NDACC-IRWG. The FTIR instruments at Rikubetsu have taken solar infrared spectra from 500 5 to 7500 cm -1 with a KBr beam splitter, the NDACC recommended optical filters, and two liquid nitrogen-cooled detectors: Indium-Antimonide (InSb) and Mercury-Cadmium-Telluride (HgCdTe, so-called MCT). Typically, measurements with 2 scans were executed to acquire a spectrum with resolution of 0.0035 cm -1 , however, sometimes 4 to 16 scans were co-added in order to improve signal-to-noise ratios (SNR). The spectra, covering long-term periods, have been used for various studies of atmospheric tracers (e.g. O3, CO, C2H6, and HCN) related to stratospheric composition change and biomass burning 10 Zhao et al., 1997;2002;Koike et al., 2006;Nagahama and Suzuki, 2007).
In this study, we used the spectra measured with the NDACC optical filter #6 (covering 500-1400 cm -1 ) and a MCT detector under clear-sky conditions since October 1997. For the observations with the NDACC filter #6 using the IFS-120/5HR from 2013 up to 2018, unfortunately, the SNR values of the spectra are about 20% of those achieved before the replacement of the instrument because smaller apertures were used. Since 2019, the more suitable aperture size of 1.7 mm has been adopted for 15 the measurements using the NDACC optical filter #6. Hence, those observed spectra were additionally used in the retrievals of HFC-23. Also, these spectra are degraded to 0.0070 cm -1 (see Section 3.3).

Antarctic Syowa Station
Since the Japanese Antarctic Syowa Station (69.0ºS, 39.6ºE; 10 m a.s.l.) was established in 1957, various kinds of scientific 20 observations (e.g. meteorology, upper atmospheric physics, cryospheric sciences, biology, geology) have continuously been conducted around the station. Syowa Station has been maintained by members of the Japanese Antarctic Research Expedition (JARE) each year. In 2007, a Bruker IFS-120M FTIR instrument was installed at Syowa Station by NIES and Tohoku University, in cooperation with the 48 th JARE members. Measurements using the FTIR at Syowa Station contributed to research related to stratospheric composition near the edge of the polar vortex during ozone hole evolution, due to its 25 geographical location (Nakajima et al., 2020). As the station is a remote site in Antarctica, it is possible to observe the background atmosphere of the southern hemisphere which it is not influenced by local human activity.
The instrument had two liquid nitrogen-cooled detectors of InSb and MCT, which were the same as those in the FTIR at Rikubetsu. Solar infrared spectra (500-7500 cm -1 ) were recorded using the same measurement settings as used at Rikubetsu, under clear-sky conditions in 2007Rikubetsu, under clear-sky conditions in , 2011Rikubetsu, under clear-sky conditions in and 2016, but not the polar night period. In this study, we used the spectra covering 30 500-1400 cm -1 detected with the MCT detector. Note, that the observed spectra in 2007 were measured with the NDACC filter #6, but since 2011 the observations covering this spectral region were separated into two measurements using the narrower NDACC filter #7 (covering 500-1100 cm -1 ) and #8 (covering 1000-1400 cm -1 ). Similar to observations at Rikubetsu, these https://doi.org/10.5194/amt-2020-505 Preprint. Discussion started: 13 January 2021 c Author(s) 2021. CC BY 4.0 License. measurements were used from 2 to 16 scans with 0.0035 cm -1 resolution. However, we degrade the resolution of these spectra to 0.0070 cm -1 (see Section 3.3).

Retrieval strategy of HFC-23
To derive HFC-23 vertical mole fraction profiles and total column abundances, all spectra taken from the FTIR instruments 5 at Rikubetsu and at Syowa Station were analyzed with the SFIT4 version 0.9.4.4 program (see https://wiki.ucar.edu/display/sfit4/) based on the optimal estimation method (OEM) of Rodgers (Rodgers, 1976;Rodgers, 2000). This program was developed by scientists from the National Center for Atmospheric Research (NCAR), the University of Bremen, and other institutes taking part in the NDACC-IRWG, as an up-grade version of the previous SFIT2 algorithm (Pougatchev et al., 1995). This program includes the procedure which calculates the theoretical absorption spectrum based on 10 prior information (e.g. meteorological profiles, a priori profile of target) and fits the calculated spectrum to the observed one, for selected one or more spectral regions (micro-windows; MWs). Finally, the program derives the most suitable state vector (i.e. the retrieved target profile) that balances information obtained from observation and from the a priori. Hereafter, the details of HFC-23 retrieval are described.

Retrieval method
From the Rodgers's OEM, measured spectrum y can be written using a forward model F with a vector vertical profile of gas x and all non-retrieved parameters (temperature, pressure, etc.) vector b as; where ε is a measurement noise. By taking a Taylor's series expansion around a priori profile xa and best estimated value + 20 of b, and neglecting higher orders, we get the linear expression of equation (1) where ya is a spectrum calculated from a priori, K and Kb are weighting function matrices, which are often so-called Jacobian, for state vector x and model parameter b, respectively. From the inversion of equation (2), we get the best estimated vertical profile of gas mole fraction vector 3 as; 25 where = 3/ is a gain matrix, whose line elements are so-called contribution function, which mean inversion sensitivity.
Combining a profile x taken from an observed spectrum y with a priori profile as described in Rodgers (1976), if there is a linear relationship of = + , the best estimation 3 is defined as following weighted average; where = -89 is a regularization matrix. The second term of Equation (6) is generally called the constraint and it is important for solving stably the state vector x. In the case of Rodgers' OEM, the covariance matrix obtained from a realistic variability of target gas is used as the regularization matrix R, but we use Tikhonov regularization (Tikhonov, 1963) to set up R in this study. The details about selection of the regularization matrix is described at Section 3.5. Finally, the cost function is 15 minimized by the Gauss-Newton iteration method, so the appropriate profile is found by the iteration which is described as; where i = 0, 1, 2, …, is the iteration counter, Ki is the Jacobian diagnosed at xi, and yi = F(xi). If this iterative calculation converges, the best estimate of 3 results. 20 Table 1 summarizes the strategy for the retrieval of HFC-23 executed in this study. For the retrieval of HFC-23 from FTIR spectra, we used the ν2 and ν5 vibrational-rotational transition bands of HFC-23 located at ~1150 cm -1 , which is the same spectral region as the retrieval of ACE-FTS (Harrison et al., 2012). The infrared absorption by HFC-23 contributes typically to only about 1% of the atmospheric transmittance of solar infrared radiation at ground level (see Figure 3). Hence, choice of 25

Retrieval micro-windows
MWs is critically important for the retrieval from the ground-based measurement. To avoid three strong H2O absorption lines we retrieve profiles of these gases in addition to HFC-23. For the other species except for CH4, we fit to an observed spectrum 30 by scaling the a priori profile (column retrieval). In addition, CH3CCl2F (HCFC-141b) and CH3CClF2 (HCFC-142b) exist as https://doi.org/10.5194/amt-2020-505 Preprint. Discussion started: 13 January 2021 c Author(s) 2021. CC BY 4.0 License. minor interfering gases in the MWs, but these gases were not retrieved in this study because the contributions of these gases to the transmittance in the MWs are very small. More detail is described in the following.

Spectral correction and instrumental line shape
As was stated in Section 2, absorption spectra which include HFC-23 retrieval MWs were recorded with the NDACC #6 5 and #8 optical filters in the MCT channel with 0.0035 cm -1 resolution. In order to reduce the spectral random noise, we degraded the spectral resolution from 0.0035 cm -1 to 0.0070 cm -1 . Note that the zero-level of the measured spectra (see Figure   1) are raised (in maximum, about +5% relative to maximum signal intensity) and curved due to the non-linearity of the MCT detector. Therefore, we corrected this zero-level offset in measurement spectrum with second order polynomial fitting using well-known absorption saturated bands sprinkled over the spectral region between 750-1350 cm -1 . 10 On the other hand, the continuum level, which is equal to 100% in transmittance, was fitted by the following, because the shape of the continuum level is caused by the optical characterization of the FTIR instrument, especially the optical bandpass filter. Since the MWs for HFC-23 retrieval are rather wide, the slope and curvature (parabola) of the spectral continuum level over each MWs are retrieved in the SFIT4 program. This correction multiplies the transmission spectrum B by; where α is the curvature, β is the slope factor, w is the wavenumber vector in the MW, and w0 is the starting wavenumber of the MW. As a result, calculated spectrum yc can be written as; where ( ) is a calculated transmission spectrum with absorptions by each gas and solar lines (the Fraunhofer lines), is a transmission spectrum of ( ) convolved with instrumental line shape (ILS) function. 20 Hydrogen bromide (HBr) gas-cell spectra were taken using a mid-infrared internal light source in order to check the alignment of the FTIR instrument and to evaluate the ILS function for both the instruments at Rikubetsu and Syowa Station. At Rikubetsu, the first HBr cell spectrum was taken at 26 March 2002 after the relocation of the instrument in October 1997.
In this study, all observed spectra from October 1997 to April 2010 with the IFS-120M instrument were convolved with the ILS function derived from the HBr cell measurement, but for all observed spectra with the IFS-120/5HR instrument no ILS 25 function was used because the instrument has always been maintained best optical alignment. At Syowa Station, HBr cell spectra were taken from time to time following installation and re-alignment. Therefore, ILS corrections were applied for all the spectra. The modulation efficiency and phase error of the ILS at Rikubetsu and Syowa Station were evaluated with LINEFIT9 and LINEFIT14 programs, respectively (Hase et al., 1999).

Spectroscopic parameters
For the calculation of absorption by each atmospheric chemical species, the HITRAN 2008 line-by-line spectroscopic database (Rothman et al., 2009) was primarily used. For spectroscopic parameters for H2O and its isotopes, the updated ATM18 line-list by one of us (G. C. Toon, NASA/JPL) was used (For detail, see https://mark4sun.jpl.nasa.gov/toon/atm18/atm18.html, last access 8 August 2020). For heavy molecules (such as CFCs, HCFCs, HFCs, and PAN), there are no resolved line-lists 5 available by HITRAN 2008. For our retrieval of CFC-12, HCFC-22, HFC-23, and PAN, we used pseudo-line-list (PLL) developed by G. C. Toon (For detail, see https://mark4sun.jpl.nasa.gov/pseudo.html). In these PLLs, the 296 K line strength and ground-state energy (E") for each pseudo line were empirically reproduced by fitting transmittance laboratory spectra (absorption cross sections) acquired under various temperature and pressure conditions. In Harrison et al. (2012), the PLL of HFC-23 obtained from the cross sections acquired with a resolution of 0.02 cm -1 and a temperature range of 214-300 K and a 10 total pressure range of 0.184-253 Torr by Chung (2005) were used to analyze solar occultation spectra, but there was a large systematic bias of ~30% in the retrieved profiles. This is dominantly caused by the poor quality of the used cross section dataset (e.g. inconsistency between the spectral absorptions and the temperature-pressure-mole fraction conditions). In order to reduce the systematic uncertainty in the HFC-23 PLL, Harrison (2013) reported new absorption cross section measurements with a resolution of 0.015 cm -1 , which cover a wider spectral range of 950-1500 cm -1 and more realistic atmospheric conditions 15 in the troposphere and the stratosphere (i.e. a wider temperature range of 188-294 K and a wider pressure range of 23-762 Torr.) For the current study, a new HFC-23 PLL was used with a wavenumber interval of 0.004 cm -1 over a spectral range of 1105-1425 cm -1 (https://mark4sun.jpl.nasa.gov/data/spec/Pseudo/CHF3_PLL_Update.pdf). In addition to the Chung's laboratory spectra, this pseudo-line parameters were obtained from re-fitting Harrison's 2013 laboratory spectra, three spectra from the 20 Pacific Northwest National Laboratory (PNNL) infrared database (Sharpe et al., 2004), and one spectrum from Gohar et al. (2004). Using this new PLL, which is dominated by the Harrison 2013 data, the bias in MkIV balloon measurements of HFC-23 is eliminated. In the forward model, the absorption line intensities are calculated by assuming the Boltzmann distribution which includes the temperature dependences of rotational/vibrational partition functions and induced emission. For the rotational partition function, its temperature dependence is calculated from (296/T) β , where T is temperature and β is 25 temperature coefficient. For HFC-23, β was set to 1.5, the normal value for non-linear molecules. To calculate the vibrational partition function, we assumed a harmonic oscillator approximation and used the fundamental vibrational frequencies and degeneracies from Ceausu-Velcescu et al. (2003). For solar lines, we used the empirical line-by-line parameters in mid-infrared region (Hase et al. 2006), which is in the SFIT4 program package.

Information of atmospheric state and regularization matrix
We consider 47 atmospheric layers for Rikubetsu, and 48 layers for Syowa Station from ground to 120 km in altitude. The thickness of the layers increases with height. We used Reanalysis-1 daily temperature and pressure data by National Center for Environmental Prediction (NCEP; http://www.ncep.noaa.gov) from the ground to 40 km, and zonal monthly-mean climatological profiles by the COSPAR International Reference Atmosphere 1986 (CIRA-86) from 40 km to 120 km (Rees et 5 al., 1990). For a priori profiles of atmospheric compositions, the averaged profiles in the period of 1980-2020 derived from the monthly-mean profile data computed by the Whole Atmospheric Community Climate Model (WACCM) version 6 (Chang et al., 2008) were basically used.
For HFC-23, the WACCM does not compute its profile and thus a priori profile of HFC-23 was based on globally and annually mean mole fraction profile by two-dimensional chemistry-radiation-transport model by Naik et al. (2000). This a 10 priori profile shows little decrease above the tropopause, reflecting a very long lifetime (228 years) of HFC-23 in the atmosphere (Montzka et al., 2019). For Rikubetsu, the HFC-23 a priori profile was scaled to 16 ppt at ground, which corresponds to the mole fraction of HFC-23 in 2002 in the northern hemisphere. For Syowa Station, the HFC-23 a priori profile was scaled to 24 ppt at ground, which corresponds to the mole fraction of HFC-23 in 2011 in the southern hemisphere.
For CFC-12, HCFC-22, HCFC-141b, and HCFC-142b, the mean profiles for 1995-2010 at Rikubetsu andfor 2007-2016 15 at Syowa Station derived from the WACCM monthly dataset were used, because these species in the atmosphere have dramatically increased since 1980. Note that the mean profiles of HCFC-141b and HCFC-142b were used as fixed profiles in the HFC-23 retrieval.
For H2O, HDO, and CH4, a priori profiles were preliminarily retrieved (pre-retrieved) using other independent MWs, because these profiles may induce large uncertainties in the HFC-23 retrieval. The detailed pre-retrieval procedure is described 20 in Section 3.6.
In retrieval of atmospheric profile, it is crucial to select an optimal regularization matrix as a constraint on the a priori profile, because the regularization matrix affects the vertical resolution and the retrieval error. In the case of the general OEM, the regularization matrix R is the inverse of the a priori covariance matrix Sa which represents the natural variability for the target.
To calculate Sa, the climatological dataset, which is constructed by a large number of independent profiles, should be used. 25 For O3, this is available because there are several high frequency observations (e.g. balloon-borne sondes, satellite measurements). In many cases, however, it is difficult to calculate a realistic natural variability for a priori profile, and our target gas also is one of them. Therefore, Sa is set up by an ad hoc method. In this study, Tikhonov regularization (Tikhonov, 1963)  discrete derivative operator. We used the discrete first-order derivative operator 9 as : The operator respects the vertical shape of the a priori profile and suppresses oscillation of the retrieved profile. We have to properly determine the value of the regularization parameter , which is tuned to balance the constraint on the a priori profile and the residual between the measured and the calculated spectra, so-called the L-curve method (Hansen, 1992). In this study, we were tuning following the alternative method described in Section 4.D of Steck (2002). This method can determine the 5 optimal to minimize the total retrieval error (the smoothing plus the measurement errors; for details, see in Section 4.2). In this study, we used = 100 for all retrievals at Rikubetsu and Syowa Station.
According to Equation (6), we can understand that the measurement noise covariance matrix ; is also a key constraint that balances the observations against the regularization matrix. The real SNR of the measured spectrum is an indicator of the noise level for each spectrum, but for each retrieval the ad hoc SNR is used to determine ; . The ad hoc SNR is defined as the 10 inverse of the root-mean-square (RMS) value of the residuals in a spectral fit (referred to as the fitted residuals). The ad hoc SNR is smaller than the real one since the fitted residuals are caused by various imperfections in forward model parameters (e.g. spectroscopic data, temperature profile, ILS) in addition to simple measurement noise. It is assumed that ; is a diagonal matrix, and we put SNR 8H = ( ] − O ) : ( ] − O )/ in the diagonal elements of ; , where ] and O are the measured and the calculated spectrum, respectively, and N is the number of spectral points. 15

Pre-retrievals for H2O, HDO, and CH4
The vertical gradient and spatial-temporal variability of water vapor in the atmosphere are very large. In many cases with ground-based FTIR observations, it is impossible to choose the retrieval MWs without absorption structures of water vapor and its isotopes, and thus it is important to use accurate water vapor profiles that are coincident with the location and time of 20 each observation. Many previous studies (Vigouroux et al., 2009;Ortega et al., 2019) used the pre-retrieved H2O (and/or HDO) profiles using the dedicated MWs in order to reduce their interference errors. In this study, a priori profiles of H2O and HDO were acquired by pre-retrievals using the different MWs shown in Table 2. H2O profiles were retrieved by using the MW of 824.40-825.90 cm -1 which has been shown in the Atlas (Meier et al., 2004) and the monthly profiles derived from the WACCM version 6 in the period of 1980-2020 as a priori profile for each spectrum. 25 Since an H2O absorption line having E" of 586.48 cm -1 is in the MW, we assume that the uncertainties of the retrieved H2O profiles caused by temperature dependence of line strength are small. The H2O line is relatively weak and is hardly ever saturated, even when the humidity at Rikubetsu is high in summer. For HDO, the profile was pre-retrieved using the MW of 1208.40-1209.10 cm -1 , and the pre-retrieved H2O profile shape was used as a priori profile shapes of HDO and H2O. This for the pre-retrieved total columns of H2O and HDO, which were mainly due to the systematic uncertainties of the spectroscopic parameters based on the HITRAN 2008.
It is important in deriving the HFC-23 retrieval that the interfering CH4 profile is pre-retrieved with the dedicated MW shown in Table 2 because the weak CH4 absorption structure in the retrieval MWs of HFC-23 could disturb estimation of the true condition of HFC-23. Figure 2 shows the time-series of the total columns of HFC-23 and CH4 retrieved from the FTIR 5 infrared spectra observed at Syowa Station in 2007 and their scatter plot. The HFC-23 total column amounts (red-x plots) derived from retrievals of HFC-23 accompanied by column-retrieval (scaling) of CH4 profile, and the scaled CH4 total columns (green-x plots) are presented in Figure 2 (a). There is an anti-correlation between these two time-series. Since the typical seasonal cycle of CH4 shows a minimum in summer due to destruction by the OH radical, the seasonal cycle of the scaled CH4 total columns in the retrievals is inconsistent with the expected cycle. Furthermore, a seasonal cycle in the HFC-23 total 10 columns is observed, but this is not expected since the atmospheric lifetime of HFC-23 is very long and thus its variability due to atmospheric loss is very small. Figure 2 (b) shows that the scatter plot of the total columns of HFC-23 and CH4 in Figure 2 (a). Examination by a two-side hypothesis testing with Student's t-distribution under a null hypothesis in which there is no correlation between these total columns, the anti-correlation between HFC-23 and CH4 is statistically significant with a significance level of 5% (p-value < 0.05). Figure 2 (c) shows the time-series of the independent retrieved CH4 total columns 15 using a spectral region from 1201.820 to 1202.605 cm -1 from Meier et al. (2004) (green dots), and of the HFC-23 total columns from retrievals using the independent retrieved CH4 profiles (CH4-fixed retrievals; red dots). In contrast to the scaled CH4 in Figure 2 (a), the independently retrieved CH4 shows the expected seasonal cycle. As the result, there is no un-realistic cycle in the HFC-23 total columns analyzed by the CH4-fixed retrievals. As can be seen in the scatter plot of Figure 2 (d), there is no correlation between HFC-23 and interfering CH4. Therefore, we decided to pre-retrieve the CH4 profile with the independent 20 window before the retrieval of HFC-23. For pre-retrieving the profile of CH4, we used the mean CH4 profile  derived from the WACCM and the pre-retrieved H2O profiles mentioned above.
In conclusion, the pre-retrieved profiles of H2O, HDO, and CH4 were used as a priori profiles (H2O and HDO) and fixed profile (CH4) in the subsequent retrieval of HFC-23. The mean RMS with 1σ at Syowa Station is 0.43 ± 0.38%. The mean HFC-23 total column with 1σ standard deviation at Rikubetsu increased from (3.23 ± 1.10) × 10 14 molecules cm -2 in the 1997-2010 period to (5.59 ± 0.43) × 10 14 molecules cm -2 in the 2019-2020 period due to the increase of atmospheric HFC-23.
In the following sections, we describe the vertical information and the error estimation of our HFC-23 retrieval. 10

Vertical information
As mentioned in Section 3.1, the vertical information content of the FTIR retrievals is characterized by the averaging kernel matrix , defined by equation (5). Figure 4 shows typical averaging kernels of the HFC-23 retrieval for the same spectrum shown in Figure 3. Each curve coloured according to the right colour-bar in Figure 4 represents the row value of the averaging 15 kernel matrix on the corresponding vertical layer. All the retrievals, including the typical case in Figure 4, are sensitive to troposphere and lower stratosphere, having a sensitivity peak in averaging kernel at ~4 km. The full widths at half maximum of the averaging kernels are ~20 km, and the mean DOFS for both all retrievals at Rikubetsu and Syowa Station is approximately 1.0. We conclude that only one piece of vertical information (the total column) can be extracted in this study.

Error analysis
The retrieval error can be considered as the difference between the retrieved and the true state vector. Subtract the true state vector from Eq. (3) including the systematic forward model error _ , the difference is defined as the following equation: where is an identity matrix; 2 = − + (Rodgers, 1990;2000). The retrieval error consists of four parts: the smoothing error 25 ( − )( − -), the non-retrieved forward model parameter error 2 2 , the forward model error _ and the measurement noise . The smoothing error is caused by the lack of vertical sensitivity combined with uncertainty inand includes the uncertainties from target gas, interfering gases and any other retrieved parameters (e.g. background correction parameters).
The forward model parameter error 2 2 comes from the uncertainties of the parameters (e.g. profiles of temperature and pressure, line lists of target and interfering gases, SZA, etc.) that are used for the forward model calculation. The forward 30 model error is from the uncertainty in the forward model itself relative to true physics. In this study, the forward model error https://doi.org/10.5194/amt-2020-505 Preprint. Discussion started: 13 January 2021 c Author(s) 2021. CC BY 4.0 License. was ignored, because the physical process (radiation transfer, infrared absorption, etc.) in the SFIT4 algorithm has been established well in previous studies.
The smoothing random error from target gas profile retrieval is described by the covariance matrix where b-c is a part of the full averaging kernel matrix where the row and column elements run over all target 5 components; -,b-c is the a priori covariance matrix. In general, -,b-c should represent the natural variability of the target gas, but we don't know well the natural variability of HFC-23 profile due to the lack of vertically measurement data. Therefore, a variability matrix derived from the AGAGE in-situ/sampling measurement dataset was used at each site as a substitute of -,b-c . For Rikubetsu, the variability of 25% against the a priori profile (square of 0.25 -) based on the background air sampling data at Cape Grim in the period of 1995-2009 (Simmonds et al., 2018b) was adopted to the diagonal elements of the 10 variability matrix. For Syowa Station, the variability of 10% against the a priori profile (square of 0.10 -) computed from the non-polluted data of the AGAGE in-situ measurements at Cape Grim (https://agage2.eas.gatech.edu/data_archive/agage/gcms-medusa/complete/tasmania/, last access 12 August 2020) was set to the diagonal elements of the matrix. Note that the systematic uncertainty for the smoothing error was not considered because we assumed that the shape of the HFC-23 a priori profile does not have a large altitudinal gradient as mentioned in Section 3.1.5. The smoothing random errors for the retrieval 15 uncertainties from all interfering species and some other retrieval parameters (background slope and curvature correction, wavenumber shift, solar line shift, solar line strength, and simple phase correction) can be written by: where b-c,wxv is a part of the full averaging kernel matrix where the row elements run over all target components and the column elements run over all interfering species; b-c,yvz is a part of the matrix where the row and column elements run 20 over all target and other parameter components, respectively; v wxv andwxv , v yvz andyvz are the true and a priori state vectors of interfering species and other parameters, respectively. To estimate the retrieval errors from the interfering gases, the variabilities around the a priori profiles for H2O (HDO) were set to 10% and the ones for other species were set to the values calculated from the used WACCM datasets.
In order to estimate the non-retrieved forward model parameter error, the following covariance matrix _ is calculated: 25 where 2 is the model parameter covariance matrix, which is from the uncertainties in the model parameters. For the random and systematic uncertainties of temperature at Rikubetsu and Syowa Station, the uncertainties on the NCEP temperature profiles were assumed. The uncertainty of temperature at Rikubetsu is about 2 K in the troposphere, 2-10 K between the tropopause and 60 km, and 10 K above 60 km. The uncertainty of temperature at Syowa Station is about 2.5 K in the altitude 30 range from the surface to 20 km, 2.5-10 K between 20 and 60 km, and 10 K above 60 km. The SZA random uncertainty was assumed an uncertainty of 0.15º, considering measurement time. For HFC-23, N2O, O3, H2O, and HDO, the uncertainties of the spectroscopic parameters (i.e. line intensity, | ; air-broadening coefficient, -~c ; coefficient of temperature dependence for https://doi.org/10.5194/amt-2020-505 Preprint. Discussion started: 13 January 2021 c Author(s) 2021. CC BY 4.0 License.
-~c , -~c ) were also estimated. For the uncertainties of | , -~c , and -~c of HFC-23, we set 10%, 15%, and 15%, respectively, based on the PLL database (see https://mark4sun.jpl.nasa.gov/data/spec/Pseudo/CHF3_PLL_Update.pdf). With regard to heavy molecules like HFC-23, ground state energy E" values, which are relevant to the temperature dependency of | , is empirically given, and then their uncertainties are larger than light molecules (e.g. H2O, O3). In addition, the E" uncertainty more affects | at a cold site like Syowa Station. We assumed the error of 50 cm -1 for the E" values of the HFC-23 PLL, and 5 estimated the uncertainties of 10% and 15% at Rikubetsu and Syowa Station, respectively, as the effect of the E" error to | .
For N2O, O3, H2O and HDO, the spectroscopic uncertainties were derived from the HITRAN 2008 database. The uncertainties for N2O and O3 were set with 5%, 10%, and 5% for | , -~c , and -~c , respectively. For H2O and HDO, we gave the uncertainty of 10% to each parameter.
The measurement error was calculated by the error covariance matrix x defined as: 10 where ; is the measurement noise covariance matrix. We adopted the square inverse of the ad hoc SNR for the diagonal elements of ; as mentioned in Section 3.5.
Furthermore, we estimated the impact of the interfering CH4 to the HFC-23 retrieval because the retrieved HFC-23 total column is affected by the retrieval uncertainty of the pre-fitted CH4 profile. The uncertainties of the pre-retrieved CH4 total 15 columns are dominantly caused by the systematic uncertainties of its spectroscopic parameters. Considering the spectroscopic parameter uncertainty provided by the HITRAN2008 database, the mean uncertainties of | , -~c , and -~c on the pre-retrieved CH4 total columns were approximately 5%, 4%, and 1%, respectively, at both sites. Since the MW for CH4 pre-retrieval is closed to the HFC-23 MWs, these spectroscopic uncertainties on CH4 are partly cancelled between both MWs. Therefore, we assumed that the uncertainties of | , -~c , and -~c for CH4 are 3%, 3%, and 1%, respectively, in the HFC-23 MWs. The effects 20 of the CH4 systematic uncertainties to the retrieved HFC-23 total column were calculated from Equation (14) using these uncertainties. On the other hand, the effect of the CH4 random uncertainty to the retrieved HFC-23 was derived from the 1σ variability on the pre-retrieved CH4 total columns. The 1σ standard deviations at Rikubetsu and Syowa Station were 4% and 3%, respectively. To quantity this uncertainty, we tested the HFC-23 retrievals by making the pre-retrieved CH4 profiles scaled by ±4% and ±3% at Rikubetsu and Syowa Station, respectively. Then we calculated the percent difference between the HFC-25 23 total column retrieved with the scaled CH4 profile ("Scaled CH4") and the ones retrieved with the no-scaled CH4 profile ("Normal"). The percent difference D is defined as the following equation: where TC HFC-23,Scaled CH 4 and TC HFC-23,Normal are the HFC-23 total columns retrieved with the Scaled CH4 profile and the Normal CH4 profile, respectively. 30 Table 4 lists the mean contributions to the relative total retrieval errors on the retrieved HFC-23 total columns at Rikubetsu for the 1997-2010 period and Syowa Station for the 2007-2016 period. Assuming that each error is independent, the total errors on retrieved total columns are simply calculated from the square root of the square sum of the error components. At Rikubetsu, the random and systematic errors are 15% and 24%, respectively. The random error is dominated by the measurement error of 12%, and the uncertainty of 7.3% on the pre-retrieved CH4 profile. The relative random uncertainty on the CH4 pre-retrieved profile decreases from about 10% to about 5% during the period of 1998-2010. It indicates that the random error has been decreasing with the increasing trend of atmospheric HFC-23. The systematic error is characterized by the E" uncertainty of HFC-23, the | uncertainties of HFC-23 and CH4, and the -~c uncertainties of H2O and HDO. 5 At Syowa Station, the random and systematic errors are 8.6% and 19%, respectively. The random error mostly comes from the measurement uncertainty of 6.8%, and the CH4 pre-retrieved profile uncertainty of 4.4%. The CH4 pre-retrieved profile uncertainty reduces from 5% to 3% during the 2007-2016 period, similar to the result at Rikubetsu. The systematic error is mainly caused by the E" uncertainty of HFC-23 and the | uncertainties of HFC-23 and CH4. In contrast with the retrieval at Rikubetsu, the contributions of the line parameters of H2O and HDO are small. 10 As the result, the mean total error for all the retrieved HFC-23 total columns at Rikubetsu for the 1997-2010 period and Syowa Station are 28% and 21%, respectively. In our HFC-23 retrieval strategy, the retrieval error is dominated by the systematic uncertainty of the line parameters, especially the | uncertainties of HFC-23 and CH4. The contribution of the random error caused mainly by the measurement noise is relatively small. Figure 5 (a) shows the time-series of the FTIR-retrieved HFC-23 total columns with the total random errors at Rikubetsu 15 and Syowa Station. Note that two high total columns at Syowa Station in 2016 come from temporal contamination of HFC-23 refrigerant used for Cryogenic Frost-point Hygrometer (CFH) sonde observation (Vömel et al., 2007) which was executed at the same place and days. We can see the increasing trend of the retrieved HFC-23 total columns, even taking into account the random retrieval errors on the total columns.

Impact of background correction
Since the width of the MWs for our HFC-23 retrieval is 9.5 cm -1 for MW1 and 6.0 cm -1 for MW2, the shape of continuum levels (transmittance of 1.0) in the observed spectra, which result from the characteristic of the optical filters, should be properly corrected (a so-called background correction). In this study, we used a 2nd-order polynomial (slope + curvature) for fitting of the background continuum shape for a wide MW. If a simple linear slope is employed for the background spectra, 25 the HFC-23 total column is systematically biased toward negative. The difference between using a linear slope and of a 2ndorder polynomial was calculated using the same formula as Equation (16). At Rikubetsu, the mean percent difference was about -33% throughout the analysis period. At Syowa Station, the mean percent difference was about -10%, smaller than at Rikubetsu. These relative biases lead underestimation to the trend on the retrieved HFC-23 abundances compared to that from AGAGE in-situ measurements. Therefore, it is very important that the curvature is considered to the background correction. 30

Ground-based FTIR data
In this study, the fitted RMS residuals for most retrievals were less than 0.5% (Table 3, Figure 5 (b), and Figure 6). Figure   5 (b) shows the time-series of the fitted RMS residuals at Rikubetsu and Syowa Station, along with the SZA. In general, the 5 RMS values rise with increasing SZA due to a decrease in the SNR as shown in Figure 6. However, with SZA lower than 50º, there are some observations with fitted RMS values exceeding 0.5% at Rikubetsu before 1999. This is caused by relatively poor optical alignment of the FTIR instrument until April 1999 when a Bruker technician re-aligned the instrument. In the following analysis, we basically use the FTIR-retrieved HFC-23 data filtered with the threshold of the fitted RMS (< 0.5%) in order to make the FTIR-retrieved data as uniform in quality as possible. However, this threshold rejects most retrievals at 10 Syowa Station in winter when ground-based FTIR observations at large SZA generally give large RMS for the spectral fit residuals due to weak solar intensity. Thus, for the retrievals at Syowa Station, we applied two fitted RMS thresholds depending on the value of SZA: the thresholds are < 0.5% for SZA < 85º and < 1.5% for SZA of 85º or greater. Note that the high HFC-23 abundances caused by the water vapor profile observations with a CFH-sonde at Syowa Station in 2016, as mentioned in Section 4.2, are also excluded. 15 Since the HFC-23 retrievals have only one piece of vertical information, as already mentioned in Section 4.1, we consider the dry-air column-averaged mole fractions X HFC-23 as the following formula: where -˜™8H" , šc› , and -‰ y are the FTIR-retrieved HFC-23 total column, the dry-air total column, and the a priori (pre-retrieved) H2O total column, respectively; a is the surface pressure calculated from the NCEP reanalysis; • is 20 Avogadro's constant; is the column-averaged acceleration; šc› and -‰ y are the mean molecular masses of dry-air and H2O, respectively. Finally, we calculated the monthly mean column-averaged X HFC-23 at both sites.

AGAGE in-situ and air archive measurements
The AGAGE instruments are based on gas chromatography coupled with mass spectrometry (GC-MS) and cryogenic sample 25 pre-concentration system, so-called "Medusa" systems. The GC-MS-Medusa systems, with 2-hourly sampling and cooling to ~-180 ºC, are operated at each AGAGE station (Miller et al., 2008;Arnold et al., 2012). For HFC-23, reported in-situ measurements started in 2007, after HFC-23 contamination from the air pump module had been resolved by changing from Viton to Neoprene diaphragms (KNF Neuberger UN05 pumps). The HFC-23 abundances at all AGAGE stations are reported relative to Scripps Institution of Oceanography (SIO), SIO-07 primary calibration scales, in dry-air mole fractions. The absolute 30 accuracies of the HFC-23 measurements were liberally estimated to be -3 to 2% (Simmonds et al., 2018a). For the comparison with the FTIR measurements at Rikubetsu and Syowa Station, we used the AGAGE in-situ measurement HFC-23 data at Trinidad Head, California, USA (THD,41.1ºN,124.2ºW) and Cape Grim, Tasmania, Australia (CGO,40.7ºS,144.7ºE), respectively. We downloaded the high frequency HFC-23 in-situ measurement dataset for THD and CGO and used the embedded pollution flags (P) to remove polluted data (https://agage2.eas.gatech.edu/data_archive/agage/gc-msmedusa/complete/, last access 24 August 2020) and then calculated daily median mole fractions. Note that there are no in-situ 5 measurements at THD and CGO or other AGAGE sites before 2007 due to the HFC-23 pump contamination problems. Therefore, we additionally used annual global mean mole fractions of HFC-23 estimated by the AGAGE 12-box model, a 2dimensional atmospheric chemistry and transport model (Simmonds et al., 2018a), where pre-2007 abundances are only based on HFC-23 dry-air mole fractions measured in the Cape Grim Air Archive (CGAA) samples (Simmonds et al., 2018b). These data were taken from the Simmonds et al. (2018a;2018b) papers. 10 Figure 7 shows the time-series of the monthly mean FTIR-retrieved X HFC-23 at Rikubetsu and Syowa Station, along with the dry-air mole fractions from the AGAGE annual global mean dataset, the CGAA samples, and the in-situ measurements at THD and CGO. The error bar on each monthly mean X HFC-23 is a 1σ standard deviation around the monthly mean. The AGAGE 15 annual global mean data and the CGAA data are plotted with the uncertainties reported by Simmonds et al. (2018aSimmonds et al. ( , 2018b.

Time-series and seasonal variation
The FTIR-retrieved X HFC-23 data at Rikubetsu during the whole period agree well with the AGAGE annual global mean and the CGAA data. However, the FTIR dataset at Rikubetsu has a peak during spring and summer of each year. On the other hand, the time-series at Syowa Station has a systematic underestimation of about 5 ppt (about 25% relative to the CGO in-situ data in 2007) compared to the CGO in-situ data, and almost no significant seasonal cycle. 20 Figure 8 shows monthly mean de-trended X HFC-23 values (in %, relative to the trend for all data) and 1σ standard deviations at Rikubetsu and Syowa Station. At Rikubetsu, the monthly mean de-trended X HFC-23 rises rapidly from March to May, with a large fluctuation (± 15-20%) within each month. On the other hand, the monthly mean X HFC-23 values from December to February are mostly stable with a relatively small standard deviations of about ±10% and a value of 10-15% smaller than the AGAGE in-situ measurements of HFC-23. As mentioned in Section 1, HFC-23 has a very long lifetime of 228 years and there 25 is almost no sink for HFC-23 in the atmosphere, i.e. HFC-23 is chemically inactive in the atmosphere. In addition, the sources of HFC-23 exist in limited places on the ground. For example, there is no HCFC-22 production in Australia and therefore Cape Grim is not impacted by this major source of HFC-23. Consequently, we expect almost no seasonal variation of the HFC-23 dry-air mole fraction at any remote site as seen in the times-series of the THD and CGO measurements. At Syowa Station, the seasonal cycle on the FTIR-retrieved X HFC-23 is almost unrecognized in Figure 8 because the variability is smaller than the 30 retrieval random error of about 10%. As a hypothesis, we suggest that the peaks at Rikubetsu during spring-summer were caused by atmospheric transport from somewhere emitting HFC-23. Several previous studies using FTIR observations of biomass burning-derived gases and a backward trajectory analysis method 2002;Nagahama and Suzuki, https://doi.org/10.5194/amt-2020-505 Preprint. Discussion started: 13 January 2021 c Author(s) 2021. CC BY 4.0 License.

2007)
, showed that the airmasses over northern Japan at 800-300 hPa level during April to November were mostly transported from the Eurasian continent. Furthermore, Koike et al. (2006) investigated the seasonal contribution from various sources of tropospheric carbon monoxide (CO) at Rikubetsu in 2001, using a 3-dimensional global chemistry transport model. Their study showed that, for CO levels at 1 km, the contribution from Asian fossil fuel combustion increases from early spring to summer due to Asian pollutants transported by the weak southwesterly wind in summer. Figure 5  inversion study, but this exceeds the focus of our study.
We also propose that the FTIR observations at Rikubetsu in December, January, and February (DJF) represent the baseline of the atmospheric HFC-23 at the site. Although the observations at Rikubetsu look consistent with the AGAGE measurements as seen in Figure 7, in fact, it is indicated in Figure 8 that the retrievals at Rikubetsu have a negative bias of about 15%. The FTIR-retrieved X HFC-23 data at Rikubetsu in DJF are shown as green open circles in Figure 7. In Section 5.4, we derive the 15 trends for the X HFC-23 data in DJF, together with those for all X HFC-23 data. These trends are compared with the AGAGE measurements and whether the DJF dataset represents the background level of HFC-23 at Rikubetsu or not. For the trend analysis at Syowa Station, all X HFC-23 data are used due to no significant seasonal cycle. The negative biases occurred at both FTIR sites are described in the following section. 20

Negative bias on XHFC-23
The negative bias with respect to the AGAGE surface measurements of the FTIR-retrieved X HFC-23 at Syowa Station (about 25% in 2007) is larger than that at Rikubetsu (about 15% in 2007). The difference of 10% between both sites could be explained by (1) the latitudinal concentration difference and (2) the temperature dependency of the derived HFC-23 pseudo-line parameter. With regard to the latitudinal concentration difference, Figure 1 of Simmonds et al. (2018a) shows that the 25 difference between the in-situ measurements at mid-latitude in the northern and southern hemisphere is about 1 ppt (5% in 2007). For the remaining of 5% of our observed difference, by using the PLL we retrieved the HFC-23 mole fraction values from each spectrum of four laboratory measurement datasets which had been used to create the HFC-23 PLL (see Section 3.4), and then investigated the discrepancies between the retrieved mole fractions and the reported ones in the laboratory datasets.
We here represent the discrepancies by the HFC-23 mole fraction scaling factors (MFSFs). Figure 9 (a) shows the HFC-23 30 MFSFs at the spectral region from 1105-1240 cm -1 plotted versus temperature. In an ideal spectroscopic parameter, the MFSFs in all temperature region would be 1. The red plots in regard to the laboratory spectral dataset of Harrison (2013) in Figure 9 (a) present the curved temperature dependency like a parabola taking a minimum value of ~0.95 at around 240 K. In other words, it means that a retrieved mole fraction from a spectrum measured at 240 K is about 5% smaller than the actual mole fraction. This is consistent with what the ACE-FTS HFC-23 time-series illustrated in Fernando et al. (2019), whose study used the Harrison's laboratory spectra, has a negative difference of average 5% in comparing with the annual global mean data calculated by the AGAGE 12-box model. As the annual mean surface temperature at Syowa Station is about 260 K, it is 5 assumed that this temperature dependency caused the negative bias of 5% at Syowa Station, in addition to the latitudinal concentration contrast. Also, this temperature dependency on the PLL probably has affected the HFC-23 total columns at Rikubetsu. As shown in Figure 9 (a), the MFSFs of the Harrison's laboratory measurements at > 260 K rapidly increase with raising temperature. Therefore, the temperature dependency may cause a part of the seasonal variation of HFC-23 at Rikubetsu because the surface temperature at the site ranged from 260 K to 300 K approximately. For the unrealistic cycle of X HFC-23 , 10 with maximum in summer, caused by the PLL, we estimated an amplitude of about 1 ppt as peak-to-peak value.
Here we assess the large negative bias of 15% on the FTIR-retrieved X HFC-23 at both sites. As mentioned in Section 4.2, our HFC-23 retrieval was mainly affected by the spectroscopic parameter uncertainties of HFC-23, HDO, and CH4. Therefore, it is reasonable to assume that the negative bias mainly comes from the systematic uncertainty on these spectroscopic parameters.
However, it is difficult to quantify the contributions of these parameters to the bias on X HFC-23 . In order to resolve the negative 15 bias, we suggest that new laboratory measurements are needed to improve the spectroscopic parameters of the HFC-23 PLL.
The negative bias of 15% is consistent with the systematic uncertainty of the HFC-23 line intensity which is estimated by the error analysis in Section 4.2. We suggest that the systematic uncertainty is affected by the temperature and pressure conditions in measuring the laboratory spectra of HFC-23. Figure 9 (b) shows the conditions of the HFC-23 laboratory measurements of Harrison et al. (2013). Harrison's laboratory measurements (total 27 measurements) cover the temperature and pressure region 20 corresponding to the altitude from the surface to the stratosphere, but the number of the measurements corresponding to the lower troposphere (below 600 hPa level) is only 3. The typical surface temperatures at Rikubetsu and Syowa Station range from 260 K to 300 K and from 240 K to 280 K, respectively. Hence, at a pressure corresponding to the surface, there is no measurement in the temperature region covering the surface temperature at Rikubetsu, except for summer, and Syowa Station.
This lack of the measurements could result in a significant error in creating the HFC-23 pseudo-line parameters. Therefore, 25 high-accuracy laboratory spectra of HFC-23 are required at various atmospheric conditions of lower troposphere in order to improve the pseudo-line parameters of HFC-23. In addition, this should be done to further understand the reason for the negative bias and the seasonal cycle by intercomparison with the retrievals using the observed spectra at other NDACC-IRWG ground-based FTIR sites around the world.  Table 5 summarizes the HFC-23 annual changes, in ppt year -1 , computed from the monthly X HFC-23 at both FTIR sites and from the AGAGE datasets. The columns of Table 5 represent the trend in the time periods of 1997-2010, 1997-2020, 2007-2016, and 2007-2020. The annual changes were calculated by linear regression, and any seasonal cycles were neglected. The uncertainty on each annual change represents the standard error of the slope estimated by linear regression. The trend regression line for the X HFC-23 data at Rikubetsu in DJF over the 1997-2020 period shown in Figure 7 as green-dashed line is consistently lower than the AGAGE in-situ measurements at THD by about 3 ppt (about 15% relative to the AGAGE in-situ measurements in 2007) as mentioned in Section 5.2. Although the annual change rate for all X HFC-23 at Rikubetsu over the 1997-2010 period 5

Trend analysis
(1.090 ± 0.072 ppt year -1 ) is larger than the AGAGE annual global mean data (0.820 ± 0.011 ppt year -1 ) and the CGAA data (0.805 ± 0.006 ppt year -1 ) over the same period, the annual change rate calculated from only X HFC-23 in DJF (0.817 ± 0.087 ppt year -1 ) is in good agreement with the AGAGE data and the CGAA data within the uncertainties. For the 1997-2020 period, the annual change rate at Rikubetsu in DJF is 0.806 ± 0.044 ppt year -1 , which is consistent with the one derived from the AGAGE annual global mean dataset during 1997 to 2016 (0.843 ± 0.008 ppt year -1 ). For the 2007-2020 period, the annual 10 change rate at Rikubetsu in DJF (0.894 ± 0.099 ppt year -1 ) is slightly smaller than that of the AGAGE in-situ measurements at THD over the 2007-2019 period (0.984 ± 0.002 ppt year -1 ). In contrast, the annual trends for all X HFC-23 at Rikubetsu over the periods of 1997-2020 and 2007-2020 are 0.794 ± 0.043 and 0.528 ± 0.086 ppt year -1 , respectively, and these are smaller than those for other AGAGE datasets because there are many high X HFC-23 at Rikubetsu before 2010. Considering with the above, it is obviously indicated that the FTIR-retrieved X HFC-23 data in DJF represents the baseline of the atmospheric HFC-23 at 15 Rikubetsu.
At Syowa Station, the annual change rate over the 2007-2016 period (0.823 ± 0.075 ppt year -1 ) is consistent with the annual global mean dataset (0.878 ± 0.020 ppt year -1 ) and the AGAGE CGO in-situ measurements (0.874 ± 0.002 ppt year -1 ) over the same period.
Summarizing the above, the trends of the atmospheric HFC-23 retrieved with our strategy basically agree well with the 20 trends derived from the AGAGE datasets used here, except for the absolute values of HFC-23. These results indicated that the ground-based FTIR measurement has a capacity to monitor the long-term trends of HFC-23.

Conclusions
We have developed a procedure for retrieving atmospheric column abundances of HFC-23 with ground-based FTIR, and 25 the first HFC-23 retrievals were carried out using the infrared spectra taken from ground-based FTIRs at Rikubetsu (1997-2020) and Antarctic Syowa Station (2007-2016 with the SFIT4 retrieval software. The two retrieval micro-windows (1138.5- were then simply scaled in the subsequent HFC-23 retrievals. For a priori profiles of CH4, in order to reduce the retrieval error resulting from competition between several weak absorptions of CH4 and the weak HFC-23 absorption, a pre-retrieval with the dedicated MW of 1201.820-1202.605 cm -1 was carried out for each spectrum and then these CH4 profiles were fixed in the subsequent HFC-23 retrievals. Our HFC-23 retrieval was typically sensitive to the atmospheric layer from the surface to the lower stratosphere. However, its DOFS was only 1 and only total column amount can be retrieved. The mean HFC-23 total 5 columns retrieved from the observed spectra at Rikubetsu over the periods of 1997-2010 and 2019-2020 were estimated as (3.23 ± 1.10) × 10 14 and (5.64 ± 0.59) × 10 14 molecules cm -2 , respectively. The mean HFC-23 total column at Syowa Station over the 2007-2016 period was (3.69 ± 1.35) × 10 14 molecules cm -2 .
We estimated the random/systematic retrieval errors for the FTIR-retrieved HFC-23 total columns assuming four error components -the smoothing error, other retrieved parameter error, non-retrieved model parameter error, and measurement 10 noise error. The retrieval random/systematic errors at Rikubetsu and Syowa Station are 15%/24% and 8.6%/19%, respectively.
The random errors at both sites mainly come from measurement noise and CH4 pre-retrieved profile uncertainty. The systematic errors at both sites are dominated by the uncertainty of the spectroscopic parameters, in particular the spectroscopic uncertainties of HFC-23, H2O, HDO, and CH4. The total error for the retrieved HFC-23 total columns at Rikubetsu and Syowa Station are 28% and 21%, respectively. 15 The time-series of the FTIR-retrieved HFC-23 columns at Rikubetsu and Syowa Station show obviously increasing trends.
The FTIR-retrieved X HFC-23 at both sites were compared with four ground-based datasets of the CGAA samples, the AGAGE 12-box model, and the AGAGE in-situ measurements at THD and CGO. The trends of X HFC-23 at Rikubetsu in DJF and Syowa Station are consistent with the trends derived from those datasets, but at Syowa Station there is a negative bias of 5 ppt compared to the AGAGE in-situ measurements at CGO. The time-series of the FTIR-retrieved X HFC-23 at Rikubetsu has a 20 seasonal cycle with a peak during spring to summer, but the X HFC-23 at Syowa Station did not show a significant cycle. We suggest that the seasonal cycle of HFC-23 at Rikubetsu is caused by the transport of HFC-23 emitted from the Eurasia. We found that the minimum of the seasonal cycle occurred from December to February and represented the background concentration of HFC-23 at Rikubetsu at that time. The negative bias at Rikubetsu in DJF was 3 ppt compared to the AGAGE in-situ measurements at THD. We showed that the bias occurred at both sites and were caused mostly by the spectroscopic 25 parameter uncertainties of HFC-23, H2O, HDO, and CH4. Therefore, these molecules mostly affect the HFC-23 retrieval. A solution for this bias problem may be found in new high-resolution laboratory spectra of HFC-23 measured under the atmospheric conditions of lower troposphere leading to an expected improvement of the HFC-23 spectroscopic parameters.
The annual change rate of the X HFC-23 at Rikubetsu in DJF over the periods of 1997-2010 and 1997-2020 were 0.817 ± 0.087 and 0.806 ± 0.044 ppt year -1 , respectively, which are in good agreement with the trend derived from the annual global 30 mean mole fractions by the AGAGE 12-box model over the same periods. The annual change rate at Syowa Station is 0.823 ± 0.075 ppt year -1 over the 2007-2016 period, which is also consistent with the trend from the CGO in-situ measurements over the same period. The trend derived from the X HFC-23 data retrieved with our retrieval strategy agreed with other ground-based measurements.
The present study demonstrates that ground-based FTIR measurements are capable of monitoring the long-term trend of HFC-23. If this FTIR measurement technique were extended to other NDACC ground-based FTIR sites around world, the measurements reported from these sites would complement the global AGAGE observations and may lead to insights about the atmospheric changes of HFC-23 and its role in global warming.  Tables   Table 1. Summary of retrieval settings used for HFC-23 retrievals.  Table 3: Statistic summary of the fitted SNRs, the root-mean-squares (RMSs) of the fitted residuals (observed minus calculated spectrum), the degree of freedom for signals (DOFSs) and the retrieved HFC-23 total columns at Rikubetsu and Syowa Station. The errors of the fitted RMSs, the DOFSs, and the total columns are the one standard deviation (1σ) around the averages. The numbers of the HFC-23 retrievals (N) are divided into two parts of a number of the retrievals used in this analysis (valid) and of total ones including rejected ones (total).      columns (red-x plots) derived from HFC-23 retrievals accompanied by column-retrieval (scaling) of CH4 profile, and the scaled CH4 total columns (green-x plots). (b) The correlation between HFC-23 and CH4 of (a). (c) Independent retrieved CH4 total columns using a spectral region from 1201.820 to 1202.605 cm -1 (green dots), and HFC-23 total columns from retrievals using the independent retrieved CH4 profiles as fixed profiles (red dots). (d) The correlation between HFC-23 and CH4 of 5 (c). Note that these retrieved HFC-23 columns were selected by the threshold of the fitted RMS value depending on the value of solar zenith angle (SZA): the threshold of the fitted RMS are < 0.5% for SZA < 85º and < 1.5% for SZA of 85% or greater.