Ground-based FTIR retrievals of SF₆ on Reunion Island

SF₆ total columns were successfully retrieved from FTIR (Fourier transform infrared) measurements (Saint Denis and Maïdo) on Reunion Island (21^∘ S, 55^∘ E) between 2004 and 2016 using the SFIT4 algorithm: the retrieval strategy and the error budget were presented. The FTIR SF₆ retrieval has independent information in only one individual layer, covering the whole of the troposphere and the lower stratosphere. The trend in SF₆ was analysed based on the FTIR-retrieved dry-air column-averaged mole fractions ($X_{{\mathrm{SF}}_{\mathrm{6}}}$) on Reunion Island, the in situ measurements at America Samoa (SMO) and the collocated satellite measurements (Michelson Interferometer for Passive Atmospheric Sounding, MIPAS, and Atmospheric Chemistry Experiment Fourier Transform Spectrometer, ACE-FTS) in the southern tropics. The SF₆ annual growth rate from FTIR retrievals is 0.265±0.013 pptv year⁻¹ for 2004–2016, which is slightly weaker than that from the SMO in situ measurements (0.285±0.002 pptv year⁻¹) for the same time period. The SF₆ trend in the troposphere from MIPAS and ACE-FTS observations is also close to the ones from the FTIR retrievals and the SMO in situ measurements.

1 Introduction

Sulfur hexafluoride (SF₆) is very stable in the atmosphere and is well-mixed and one of the most potent greenhouse gases listed in the 1997 Kyoto protocol linked to the United Nations Framework Convention on Climate Change (UNFCCC). It has an extremely long lifetime of 850 years (Ray et al., 2017) with global warming potential for a 100-year time horizon of 23 700 (relative to CO₂) (Kovács et al., 2017). Since SF₆ is a very stable trace gas in the atmosphere and its annual growth rate seems relatively constant during the last two decades (Hall et al., 2011), it is usually applied to calculate the age of air (Patra et al., 1997; Engel, 2002; Patra et al., 2009; Stiller et al., 2012; Haenel et al., 2015).

Figure 1 Time series of historical and projected global SF₆ emissions. Historical data cover 1900–2005 (black), and projections for the 2005–2100 time period correspond to four RCP scenarios with 2.6, 4.5, 6.0 and 8.5 W m⁻² radiative forcing in 2100 relative to pre-industrial values (Moss et al., 2010). The black dot is the annual growth of SF₆ in 2012 according to the WMO report (WMO, 2014).

SF₆ is emitted from anthropogenic sources at the Earth's surface, mainly from the chemical industry, such as in production of electrical insulators and semi-conductors, and magnesium manufacturing. The mole fraction of SF₆ in the atmosphere has increased in recent years and the globally averaged near-surface SF₆ volume mixing ratio (VMR) has reached up to 7.6 pptv (parts per trillion by volume), with an annual increase of 0.3 pptv year⁻¹ in 2012 (WMO, 2014). Figure 1 shows the SF₆ historical global emissions in 1900–2005 (Schultz et al., 2008; Mieville et al., 2010). Emissions of SF₆ started in the 1940s and have been increasing since then. Only during 1990–2000 the emissions almost remain constant. The most likely reason is that SF₆ emissions decreased in developed countries between 1995 and 1998 but then increased again after 1998 (Levin et al., 2010; Rigby et al., 2010). The SF₆ global total emissions in 2005 were 6.341 Gg year⁻¹ (1 Gg=1000 t), which is about 8 times larger than that in 1970 (0.789 Gg year⁻¹). Figure 1 also shows the predictions of SF₆ global emissions for 2005–2100 according to four representative concentration pathway (RCP) scenarios with different radiative forcing values (2.6, 4.5, 6.0 and 8.5 W m⁻²) in 2100 relative to pre-industrial values (Moss et al., 2010). The RCP 6.0 and RCP 8.5 scenarios assume the emissions keep increasing until 2020 and 2100 respectively, while RCP 2.6 and RCP 4.5 scenarios assume that there will be a steep decrease after 2010. The predictions from these four scenarios are very different, so it is very important to monitor the abundance of SF₆ in the atmosphere. The most recent Scientific Assessment of Ozone Depletion report (WMO, 2014) points out that the global emissions have amounted to 8.0 Gg year⁻¹ in 2012, marked by a black dot in Fig. 1.

The Advanced Global Atmospheric Gases Experiment (AGAGE) gas chromatography–mass spectrometry (GC–MS) system has measured the SF₆ concentration since 1973 (Rigby et al., 2010). The Halocarbons and other Atmospheric Trace Species Group (HATS) started SF₆ sampling measurements at eight stations in 1995 and in situ measurements at six fixed sites in 1998 (Hall et al., 2011). The flask and in situ measurements show that the SF₆ abundance in the atmosphere has been increasing since the 1970s (Maiss and Levin, 1994; Geller et al., 1997; Maiss and Brenninkmeijer, 1998; Moss et al., 2010). In recent decades, remote sensing techniques also contribute to monitoring SF₆. Rinsland et al. (1990) used the spectra observed by the Atmospheric Trace Molecule Spectroscopy instrument (ATMOS) aboard the space shuttle, as part of the Spacelab 3 (SL3) payload, to retrieve SF₆ concentrations in the upper troposphere and lower stratosphere. In addition, space-based sensors, such as the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) (Bernath et al., 2005; Bernath, 2017) and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) (Stiller et al., 2008), are applied to obtain an SF₆ global distribution and trend. Zander et al. (1991) succeeded in monitoring the increasing total column of SF₆ using the ground-based Fourier transform infrared spectrometer (FTIR) at Jungfraujoch (46.55^∘ N, 7.98^∘ E, 3.58 $\mathrm{km}\mathrm{a}.\mathrm{s}.\mathrm{l}.$). Later on, Rinsland et al. (2003) and Krieg et al. (2005) obtained the total columns of SF₆ from the FTIR measurements at Kitt Peak (31.9^∘ N, 111.6^∘ W, 2.09 $\mathrm{km}\mathrm{a}.\mathrm{s}.\mathrm{l}.$) and Ny-Ålesund (78.91^∘ N, 11.88^∘ E, 0.02 $\mathrm{km}\mathrm{a}.\mathrm{s}.\mathrm{l}.$). They found that the mixing ratio of SF₆ is continuously increasing and that the mean increases of SF₆ are 0.31±0.08 pptv year⁻¹ at Ny-Ålesund, 0.24±0.01 pptv year⁻¹ at Jungfraujoch and 0.28±0.09 pptv year⁻¹ at Kitt Peak from March 1993 to March 2002. In the latest Scientific Assessment of Ozone Depletion, the trends of SF₆ from in situ measurements are consistent with the trends in the troposphere from remote sensing measurements (ACE-FTS, MIPAS and Jungfraujoch FTIR) (WMO, 2014).

Figure 2 The typical spectrum of SF₆ retrieval microwindows (946.5–949.0 cm⁻¹) at St Denis (a) and Maïdo (b). The bottom panels list the absorption contribution from each species. To clarify the absorption lines, the transmittance is shifted by 0.02 for each species and the solar (sol) line list. The middle panels only show the transmittance between 0.95 and 1.05 and identify the SF₆ absorption line. The top panels show the transmittance residual (observed minus calculated).

The objective of this paper is to investigate the SF₆ retrievals in the southern tropics based on the spectra observed by two FTIR spectrometers on Reunion Island (21^∘ S, 55^∘ E) from 2004 to 2016. In Sect. 2, SF₆ retrievals are carried out with the well-established SFIT4 algorithm, which is upgraded from the radiative transfer and retrieval algorithm SFIT2 (Pougatchev et al., 1995; Hase et al., 2004) and widely used in the Network for the Detection of Atmospheric Composition Change Infrared Working Group (NDACC-IRWG) community. The FTIR SF₆ retrieval strategy and the error budget are discussed in detail. In the following section, the trend in SF₆ is analysed based on the FTIR retrievals, the HATS America Samoa (SMO) in situ measurements (14^∘ S, 170^∘ W, 77 $\mathrm{m}\mathrm{a}.\mathrm{s}.\mathrm{l}.$) and the collocated satellite measurements (MIPAS and ACE-FTS). Finally, conclusions are drawn in Sect. 4.

2 FTIR retrievals on Reunion Island

The Royal Belgian Institute for Space Aeronomy operates at two FTIR sites on Reunion Island. One is at Saint Denis (St Denis), close to the coast (20.90^∘ S, 55.48^∘ E; 85 m  a.s.l.), and the other one is located at the Maïdo mountain site (21.07^∘ S, 55.38^∘ E; 2155 m a.s.l.). At present, both sites are equipped with a Bruker 125HR spectrometer, a precise solar-tracker system and an automatic weather station. The St Denis FTIR is dedicated to the near-infrared spectral region and has contributed to the Total Carbon Column Observing Network (TCCON) since September 2011, whereas the Maïdo FTIR is dedicated to the mid- to thermal infrared spectral region and has become an NDACC-IRWG instrument in March 2013. Before September 2011, a Bruker 120M instrument was operated at St Denis in the NDACC mid- to thermal infrared configuration. For detailed information about the two sites, please refer to Zhou et al. (2016) and the references therein.

The SF₆ retrievals use the spectra in the thermal infrared range. Therefore, we select the spectra from the Bruker 120M at St Denis (2004–2011) and from the Bruker 125HR at Maïdo (2013–2016).

The spectra of 700–1400 cm⁻¹ at St Denis and Maïdo are recorded with the same settings. Two maximum optical path differences (MOPDs) of 82 and 125 cm are operated to gather the interferogram of the direct solar radiation, and then the interferogram is transformed to a spectrum with the spectral resolutions of 0.010975 and 0.0072 cm⁻¹ through a fast Fourier transform (FFT) algorithm. The HgCdTe (MCT) detector collects the spectrum and one specific interference filter is used to narrow the optical band to regions of interest in order to improve the signal-to-noise ratio (SNR).

2.1 Retrieval strategy

We used the SFIT4_v9.4.4 algorithm (Pougatchev et al., 1995) to retrieve information from the spectra: it simulates the spectrum observed by the ground-based FTIR and looks for the optimum state vector (the retrieved state) to minimise the residual between the simulated and the observed spectra. Table 1 lists the retrieval window, interfering gases, spectroscopic database, a priori profile, background parameters and SNR used in the SFIT4 algorithm for the SF₆ retrieval at St Denis and Maïdo, together with the obtained degrees of freedom of signal (DOFS).

2.1.1 Retrieval window

The broad unresolved Q branch of the ν₃ band of SF₆, at 947.9 cm⁻¹ (Varanasi et al., 1992), is always used to retrieve SF₆ by remote sensing techniques. Zander et al. (1991) used 946.9–948.9 cm⁻¹ for the FTIR retrieval at Jungfraujoch and Krieg et al. (2005) used 947.2–948.6 cm⁻¹ for Kitt Peak and Ny-Ålesund FTIR retrievals. We also used the SF₆ absorption line at 947.9 cm⁻¹ and the retrieval window 946.5–949.0 cm⁻¹ to perform the FTIR retrieval at Reunion Island. However, compared with the previous studies, our retrieval window contains an additional weak H₂O absorption line at 946.68 cm⁻¹. Since there is a strong H₂O absorption line at 948.26 cm⁻¹ and a strong CO₂ line at 947.74 cm⁻¹ (see Fig. 2), the SF₆ is inevitably influenced by these two species, especially from H₂O due to its larger variability in the atmosphere. A better fitting of H₂O (with a smaller root mean square (rms) of the fitting residual) is obtained by the larger retrieval window. In addition, to minimise interference from H₂O and CO₂, their profiles are retrieved simultaneously with the SF₆ profile.

2.1.2 Instrument line shape

In order to acquire the instrument line shape (ILS) and to verify the alignment of the instrument, daily HBr cell measurements are carried out automatically at both sites. The LINEFIT14.5 programme (Hase et al., 1999) is applied to obtain the modulation and phase parameters of the ILS, which are used as input to the SFIT4 algorithm. Note that we made a 3-order polynomial fitting from the LINEFIT outputs and then retrieved the polynomial parameters in SFIT4 algorithm for both modulation and phase.

2.1.3 Spectroscopy

The spectroscopy of SF₆ was taken from the pseudo-line lists (http://mark4sun.jpl.nasa.gov/pseudo.html), and the spectroscopy of the other species was obtained from the ATM16 line lists (Toon, 2014). Pseudo-line lists were produced by Geoff Toon (NASA-JPL) by fitting all the laboratory spectra simultaneously, which includes mean intensities and effective lower state energies on a 0.005 cm⁻¹ frequency grid. These artificial lines at arbitrary positions do not represent transitions of molecules. Instead, their line-widths and intensities are fitted to the laboratory spectra such that the pseudo-line lists allow to simulate the measured spectra.

2.1.4 A priori profile

To construct an a priori profile that is close to the true one, we used the US standard atmosphere (1976) SF₆ (National Geophysical Data Center, 1992) as the shape of the a priori profile, and then scaled it with a factor of one to make the concentration of the lowest level equal to the annual mean of SMO measurements in 2009. The H₂O a priori profile was derived from the 6-hourly NCEP reanalysis data. For the a priori profiles of the other interfering species (see Table 1), the mean of the Whole Atmosphere Community Climate Model (WACCM) version 6 monthly profiles between 1980 and 2020 were adopted.

2.1.5 Regularisation matrix

The a priori covariance matrix, together with the measurement noise covariance matrix, determine the weights of a priori knowledge and measurement information (Rodgers, 2000). The SNR were set to 180 and 400 at St Denis and Maïdo, respectively. In order to extract as much information as possible from the measurements and to avoid too many oscillations in the retrieved SF₆ profiles, we used 30 and 14 % as the diagonal elements (the same value for all levels) to create the regularisation matrices at St Denis and Maïdo, respectively. The correlation width was set to 10.0 km. Note that the diagonal value of the regularisation matrix is a key parameter that balances the contribution from the measurement information and the a priori information, but does not represent the real variability of SF₆ in the atmosphere.

2.1.6 Averaging kernel

Figure 3 shows the typical averaging kernel of the SF₆ retrieval at Maïdo. The FTIR retrieval is sensitive to the altitude range from the surface to 20 km (the whole of the troposphere and lower stratosphere). The mean and standard deviations of the DOFS of the SF₆ retrievals are 1.0±0.1 at St Denis and 1.1±0.1 at Maïdo, indicating that the SF₆ retrievals have information content in only one individual layer (mainly 0–20 km) and have no profile information. That means the retrieved profiles are not reliable, and we should focus on the total column. In this study, the SF₆ retrievals at St Denis were combined with Maïdo retrievals to extend the time coverage for the trend in Sect. 3. The DOFS at the two stations are very similar, and there is no observed trend in the time series of the DOFS.

Figure 3 The typical averaging kernel of SF₆ retrieval at Maïdo. The solid lines represent the sensitivities at specific altitudes. The red dashed line is the sum of the rows of averaging kernels scaled by 0.1, indicating the vertical sensitivity.

2.2 Error budget

Based on the optimal estimation method (Rodgers, 2000), the difference between the retrieved state vector $\widehat{\mathit{x}}$ and the true state vector x_t could be expressed as

$$\begin{array}{ll}{\displaystyle }\widehat{\mathit{x}}-{\mathit{x}}_{\mathrm{t}}=& {\displaystyle }(\mathbf{A}-\mathbf{I})({\mathit{x}}_{\mathrm{t}}-{\mathit{x}}_{\mathrm{a}})\\ \text{(1)}& {\displaystyle }& {\displaystyle }+{\mathbf{G}}_y{\mathbf{K}}_b({\mathit{b}}_{\mathrm{t}}-\mathit{b})+{\mathbf{G}}_y\mathrm{\Delta }\mathbf{f}+{\mathbf{G}}_y{\mathit{\epsilon }}_y,\end{array}$$

where x_a is the a priori state vector; A is the averaging kernel matrix, representing the sensitivity of the retrieved state vector to the true state vector; I is a unit matrix; G_y is the contribution matrix, representing the sensitivity of the retrieval to the measurement y; K_b is the weight function, representing the sensitivity of the forward model F(x,b) to the forward model parameters; b is the vector of forward model parameters that are not retrieved; b_t is the vector of true forward model parameters; Δf is the forward model systematic uncertainty; ε_y is the measurement noise covariance matrix. Note that the state vector x, which is the vector of forward model parameters that are retrieved, is a higher-dimensional vector which consists of the target SF₆ profile components, the concentration profiles for the interfering species (H₂O, CO₂) and other retrieval parameters (slope, ILS, etc.).

The error in the target SF₆ profile is obtained by extracting the SF₆ components from the vectorial equation in Eq. (1). The error in the retrieved SF₆ profile $(\widehat{\mathit{x}}-{\mathit{x}}_{\mathrm{t}}{)}_{{\mathrm{SF}}_{\mathrm{6}}}$ then consists of the smoothing error $(\mathbf{A}-\mathbf{I})({\mathit{x}}_{\mathrm{t}}-{\mathit{x}}_{\mathrm{a}})$, model parameter error G_yK_b(b_t−b), forward model error G_yΔf and measurement noise G_yε_y. As the SFIT4 algorithm is well established and only the physics of the absorption is included in the transmission of radiation, the forward model error can be ignored.

Table 1 The retrieval window, interfering gases, spectroscopic database, a priori profile, background parameters (slope and zshift) and SNR used in the SFIT4 algorithm for FTIR SF₆ retrieval at St Denis and Maïdo, together with the achieved DOFS (mean and the standard deviation) of the retrievals.

The smoothing error, except for the uncertainty from SF₆, also includes the uncertainties from the H₂O profile, the CO₂ profile, the C₂H₄ and O₃ scaling factors and some other parameters (see Table 1), and is defined as the retrieval parameter error ε_re. Since the absorption lines of H₂O and CO₂ are very strong in the retrieval window, the ε_re is separated into three components.

$$\begin{array}{ll}\text{(2)}& {\displaystyle }& {\displaystyle }(\mathbf{A}-\mathbf{I})({\mathit{x}}_{\mathrm{t}}-{\mathit{x}}_{\mathrm{a}})=({\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{SF}}_{\mathrm{6}}}-\mathbf{I})({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}})+{\mathit{\epsilon }}_{\text{re}}{\displaystyle }& {\displaystyle }{\mathit{\epsilon }}_{\text{re}}={\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}({\mathit{x}}_{\mathrm{t},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}-{\mathit{x}}_{\mathrm{a},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}})\\ {\displaystyle }& {\displaystyle }+{\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{CO}}_{\mathrm{2}}}({\mathit{x}}_{\mathrm{t},{\mathrm{CO}}_{\mathrm{2}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{CO}}_{\mathrm{2}}})\\ \text{(3)}& {\displaystyle }& {\displaystyle }+{\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},\text{others}}({\mathit{x}}_{\text{t,others}}-{\mathit{x}}_{\text{a,others}}),\end{array}$$

where ${\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{SF}}_{\mathrm{6}}}$, ${\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$, ${\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{CO}}_{\mathrm{2}}}$ and ${\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},\text{others}}$ are the matrices extracted from the full averaging kernel A by selecting the components A_ij where the row index i runs over all SF₆ components in the state vector x and the column index j runs over all SF₆, H₂O, CO₂ and other components in state vector x. ${\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}$ and ${\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}}$, ${\mathit{x}}_{\mathrm{t},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ and ${\mathit{x}}_{\mathrm{a},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$, ${\mathit{x}}_{\mathrm{t},{\mathrm{CO}}_{\mathrm{2}}}$ and ${\mathit{x}}_{\mathrm{a},{\mathrm{CO}}_{\mathrm{2}}}$, x_t,others and x_a,others are the true and a priori values of SF₆, H₂O, CO₂ and other retrieval parameters.

Systematic and random components are considered to characterise the uncertainty of each parameter. For the smoothing error $({\mathbf{A}}_{{\mathrm{SF}}_{\mathrm{6}},{\mathrm{SF}}_{\mathrm{6}}}-\mathbf{I})({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}})$, we assumed that the systematic uncertainty of $\mathit{\epsilon }({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}})$ is 5 % relative to the a priori profile (${\mathit{\sigma }}_{\mathrm{SF}\mathrm{6},\mathrm{a}i}=\mathrm{0.05}{x}_{\mathrm{a}i}$). Then, the diagonal and off-diagonal values of the systematic part of $\mathit{\epsilon }({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}})({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}}{)}^T$ are calculated as (${\mathit{\sigma }}_{\mathrm{SF}\mathrm{6},\mathrm{a}i}^{\mathrm{2}}$) and ${\mathit{\sigma }}_{\mathrm{SF}\mathrm{6},\mathrm{a}i}{\mathit{\sigma }}_{\mathrm{SF}\mathrm{6},\mathrm{a}j}$, respectively (von Clarmann, 2014). The random part of $\mathit{\epsilon }({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}})({\mathit{x}}_{\mathrm{t},{\mathrm{SF}}_{\mathrm{6}}}-{\mathit{x}}_{\mathrm{a},{\mathrm{SF}}_{\mathrm{6}}}{)}^T$ is constructed in the same way as the regularisation matrix but the diagonal elements were set to 30 % for both St Denis and Maïdo. For the measurement error G_yε, there is no systematic uncertainty and the random uncertainty is derived from the SNR.

For the ε_re, we mainly focus on the influence from H₂O and CO₂. The systematic and the random uncertainties of the H₂O profile were derived from the bias and the standard deviation of the differences between the NCEP profiles and the balloon sondes. In general, the systematic uncertainty is about 5 % and the random uncertainty is about 10 % from surface to 10 km. The CO₂ systematic uncertainty is assumed to be 5 % of the average of the WACCM monthly profiles, and the random uncertainty is the standard deviation of the WACCM monthly profiles from 1980 to 2020.

Table 2 The systematic and random uncertainties for the FTIR-retrieved total column (%) at St Denis and Maïdo. σ_b are the relative systematic (random) uncertainties of the non-retrieved parameters (%). The “retrieval parameters” represents the “others” in Eq. (3). The SF₆ spectroscopy uncertainty is from the pseudo-line database. When a relative uncertainty is smaller than 0.1 %, it is considered negligible and represented as “–”.

For the model parameter error G_yK_b(b_t−b), we only show the significant parameters here, i.e. temperature, spectroscopy, solar zenith angle (SZA), ILS and zero level offset (zshift). The systematic and random uncertainties of the temperature profile were derived from the mean and the standard deviation of the differences between the NCEP profiles and the balloon sondes on Reunion Island in 2011. In general, the systematic bias is about 5 K below 10 km, 3 K between 10 and 15 km and 1 K above 15 km. The standard deviation is about 2–4 K in the troposphere and 5–10 K above tropopause height. The SF₆ spectroscopy uncertainty is from the pseudo database: 2 % for the systematic part and zero for the random part. Values of 0.1 and 0.2 % were adopted for the systematic and random uncertainties of SZA according to the Pysolar package (one Python code to calculate the solar position http://pysolar.org/), while 5 and 1 % were adopted for both systematic and random uncertainties of the ILS parameters and zshift, respectively.

Table 2 lists the SF₆ FTIR retrieval systematic and random uncertainties (%) at St Denis and Maïdo. The “retrieval parameters” in Table 2 represents the “others” in Eq. (3). The smoothing error, measurement error, H₂O interference and temperature error at St Denis are much larger than those at Maïdo. In total, the retrieval systematic and random uncertainties (relative to the retrieved SF₆ total column) are 4.6 and 14.0 % at St Denis and 3.7 and 6.7 % at Maïdo, respectively.

3 SF₆ trend analysis

3.1 Data sets

3.1.1 SMO in situ measurements

Since 1998, a four channel gas chromatograph (CATS) system has been measuring the surface SF₆ at the SMO site. Due to the high accuracy and precision, the CATS SF₆ daily data from the NOAA ESRL halocarbon in situ measurement programme are considered to be a reference for comparison with the FTIR retrievals. Note that these are daily median data instead of daily means and are used to filter the higher outliers from local pollution. As there is an improvement in the instrument in June 2000, the standard deviation of 1-day measurements decreased from 0.2 to 0.4 to 0.02–0.04 pptv after the change (Hall et al., 2011).

3.1.2 MIPAS

MIPAS derived the global distributions of profiles of SF₆ from limb observations between 2002 and 2012. MIPAS observed spectra in full spectral resolution (FR) mode (spectral resolution: 0.05 cm⁻¹) and reduced resolution (RR) mode (spectral resolution: 0.121 cm⁻¹) before and after January 2005. In this paper, we used the latest SF₆ product with newly calibrated level 1b spectra (Haenel et al., 2015) to compare it with the FTIR retrievals and to make the SF₆ trend analysis. The SF₆ data used here are versions V5h_SF6_20 for the FR data product and V5r_SF6_222 and V5r_SF6_223 for the RR period. The MIPAS retrievals cover the upper troposphere (down to cloud top, or ∼6 km in cloud-free cases) and the stratosphere only (about 55 km; see Fig. 7). Since MIPAS single SF₆ profiles are very noisy, we used the monthly means in the latitude band of 20–25^∘ S.

3.1.3 ACE-FTS

Global distributions of SF₆ are also monitored by ACE-FTS occultation measurements from 2004 (Boone et al., 2013). We used the ACE-FTS level 2 version 3.5 monthly data (2004–2013) from the ACE/SCISAT database, and only the measurements without any known issues (quality flag = 0) were selected (Sheese et al., 2015). The ACE-FTS data have been validated with MkIV balloon profiles (Velazco et al., 2011). Since ACE-FTS mainly look at the polar area, there are few measurements in the tropical zone. Geller et al. (1997) found that SF₆ is well mixed throughout the Southern Hemisphere; therefore, we enlarged the latitude band for ACE-FTS measurements to 0–40^∘ S to get a robust result. Similar to MIPAS measurements, ACE-FTS collects the spectra in the upper troposphere and stratosphere (about 10–30 km; see Fig. 7).

Figure 4 The locations of the ground-based sites (Reunion Island and SMO) as well as the latitude bands covered by the satellites (MIPAS and ACE-FTS).

Figure 5 Time series of SMO in situ SF₆ daily median (blue), MIPAS SF₆ monthly mean (20–25^∘ S) at 11 km (black), ACE-FTS SF₆ monthly mean (0–40^∘ S) at 12.5 km and FTIR $X_{{\mathrm{SF}}_{\mathrm{6}}}$ monthly mean at St Denis and Maïdo (red). For MIPAS, ACE-FTS and ground-based FTIR measurements, the error bar is the standard deviation within 1 month.

3.1.4 Ground-based FTIR

As the FTIR SF₆ retrievals have only one layer of information, we applied the dry-air column-averaged SF₆ ($X_{{\mathrm{SF}}_{\mathrm{6}}}$) of FTIR measurements to quantitatively compare it with other data sets. $X_{{\mathrm{SF}}_{\mathrm{6}}}$ is obtained by dividing the SF₆ total column by the dry-air total column.

$$\begin{array}{}\text{(4)}& {\displaystyle }& {\displaystyle }{X}_{{\mathrm{SF}}_{\mathrm{6}}}={\displaystyle \frac{{\text{TC}}_{{\mathrm{SF}}_{\mathrm{6}}}}{{\text{TC}}_{\mathrm{air}}^{\mathrm{dry}}}},\text{(5)}& {\displaystyle }& {\displaystyle }{\text{TC}}_{\mathrm{air}}^{\mathrm{dry}}={\displaystyle \frac{P_{\mathrm{s}}}{g{m}_{\text{air}}^{\text{dry}}}}-{\text{TC}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}\left(m_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}/m_{\text{air}}^{\text{dry}}\right),\end{array}$$

where ${\text{TC}}_{{\mathrm{SF}}_{\mathrm{6}}}$ and ${\text{TC}}_{\mathrm{air}}^{\mathrm{dry}}$ are the total columns of SF₆ and dry air; P_s is the surface pressure; g is the acceleration of gravity depending on the latitude and altitude; and $m_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ and $m_{\text{air}}^{\text{dry}}$ are the molecular masses of H₂O and dry air, respectively; ${\text{TC}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ is the total column of H₂O from NCEP re-analysis data. The surface pressure is recorded with a Vaisala PTB210 sensor, with accuracy better than 0.1 hPa. The systematic uncertainty of H₂O in the troposphere is about 5 %, and the ${\text{TC}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ on Reunion Island is about 1–2 % of the TC_air. As a result, the uncertainty of the ${\text{TC}}_{\mathrm{air}}^{\mathrm{dry}}$ is better than 0.1 %.

Note that the SF₆ concentration is almost constant in the troposphere but much lower in the stratosphere. This kind of profile will lead to a systematic bias if we combine the$X_{{\mathrm{SF}}_{\mathrm{6}}}$ in 0–100 km (above St Denis) and $X_{{\mathrm{SF}}_{\mathrm{6}}}$ in 2.155–100 km (above Maïdo) directly. To avoid this systematic bias, we kept the $X_{{\mathrm{SF}}_{\mathrm{6}}}$ at St Denis unchanged and applied a scaling factor of 1.01 to the $X_{{\mathrm{SF}}_{\mathrm{6}}}$ at Maïdo, which is the ratio of $X_{{\mathrm{SF}}_{\mathrm{6}}}$ in 0–100 km to $X_{{\mathrm{SF}}_{\mathrm{6}}}$ in 2.155–100 km based on the FTIR SF₆ a priori profile but scaled with the annual mean of SMO in situ measurements in 2014.

Figure 6 SF₆ annual growths from SMO in situ measurements (2004–2016) (blue bar), ground-based FTIR measurements (2004–2016: combined St Denis and Maïdo)(pink bar), MIPAS measurements (2002–2012) in the latitude band of 20–25^∘ S for different altitudes (9–52 km) (black solid line) and ACE-FTS measurements (2004–2013) in the latitude band of 0–40^∘ S for an altitude range of 10.5–32.5 km (brown solid line). For MIPAS and ACE-FTS measurements, the dotted line of the same colour is the number of monthly means used for trend analysis at each altitude.

Figure 4 shows the locations of the ground-based observations and the latitude bands covered by the satellites. The SF₆ time series of SMO in situ, MIPAS and ACE-FTS measurements and FTIR retrievals at St Denis and Maïdo are presented in Fig. 5. For MIPAS, ACE-FTS and FTIR data, the error bar is the standard deviation of all the measurements in 1 month. Since the FTIR retrieval has the largest sensitivity in the vertical range of 5–15 km (see Fig. 3), we selected 11 km of MIPAS and 12.5 km of ACE-FTS. In general, SF₆ from these data sets are in good agreement, as the difference between each two measurements is within their uncertainties.

3.2 Methodology

A regression model (Weatherhead et al., 1998) is applied to derive the SF₆ linear long-term trend based on the measurements of FTIR daily means, SMO daily medians and satellite (MIPAS and ACE-FTS) monthly means.

$$\begin{array}{ll}{\displaystyle }\mathit{Y}\mathbf{\left(}\mathit{t}\mathbf{\right)}=& {\displaystyle }{A}_{\mathrm{0}}+A_{\mathrm{1}}\cdot \mathit{t}+\sum _{k=\mathrm{1}}^{\mathrm{3}}\left(A_{\mathrm{2}k}\cos \right(\mathrm{2}k\mathit{\pi }\mathit{t})\\ \text{(6)}& {\displaystyle }& {\displaystyle }+A_{\mathrm{2}k+\mathrm{1}}\sin \left(\mathrm{2}k\mathit{\pi }\mathit{t}\right))+\mathit{\epsilon }(\mathit{t}),\end{array}$$

where Y(t) is measurements with the t in fraction of year; A₀ is the intercept; A₁ is the annual growth; A₂ to A₇ are the periodic variations, mainly representing the seasonal cycle; ε(t) is the residual between the measurements and the fitting model. To estimate the trend error σ_c, the autocorrelation of the residual should be taken into account (Santer et al., 2000).

$$\begin{array}{}\text{(7)}& {\displaystyle }{\displaystyle }{\mathit{\sigma }}_c={\mathit{\sigma }}_d{\displaystyle \frac{(n-\mathrm{2})}{\left[n\right(\mathrm{1}-r)/(\mathrm{1}+r)-\mathrm{2}]}},\end{array}$$

where σ_d is the regression error; n is the number of measurements; and r is the lag-1 (1 month) autocorrelation coefficient of the regression residuals.

Figure 7 SF₆ monthly means of volume mixing ratios profiles (a, b) and the number of measurements in each month (c, d) for MIPAS in the latitude band between 20 and 25^∘ S (a, c) and ACE-FTS in the latitude band between 0 and 40^∘ S (b, d).

3.3 Annual change

Figure 6 shows the SF₆ trends from the SMO in situ measurements, the ground-based FTIR retrievals, the MIPAS measurements in the latitude band of 20–25^∘ S for different altitudes (9–52 km), and the ACE-FTS measurements in the latitude band of 0–40^∘ S for altitude range of 10.5–32.5 km. The vertical sensitivity of the FTIR retrieval is between the surface and 20 km (see Fig. 3). For MIPAS and ACE-FTS measurements, Fig. 6 also shows the number of monthly means used for the trend analysis at each altitude (dotted lines). The annual growth of FTIR measurements is 0.265±0.013 pptv year⁻¹ from 2004 to 2016, which is slightly weaker than the trend in the SMO in situ measurements (0.285±0.002 pptv year⁻¹) for the same time period. Waugh et al. (2013) pointed out that the age of near-surface SF₆ at SMO (14^∘ S) is about 0.4 years higher than that on Reunion Island (21^∘ S). In addition, the global surface in situ measurement network (https://www.esrl.noaa.gov/gmd/hats/combined/SF6.html) shows that the growth rate of SF₆ slightly increases with time. Therefore, it is acceptable that the trends from FTIR measurements on Reunion Island are slightly weaker than those from the SMO in situ measurements.

The trend uncertainty from MIPAS data is less than from the ACE-FTS data and the FTIR retrievals because MIPAS has many more data points. The profile of SF₆ trend shows a peak at altitude of 11–13 km from the MIPAS measurements, and a peak at 11.5–16.5 km from the ACE-FTS measurements. As the SF₆ emissions are all at the Earth's surface and there is almost no removal mechanism in the troposphere and stratosphere (Kovács et al., 2017), the SF₆ concentration should be well mixed in the troposphere (the tropopause height above Reunion Island is about 16.5 km) and decreases above the tropopause, which was confirmed by the airborne in situ measurements (Patra et al., 1997). Figure 7 shows the SF₆ monthly means and the number of measurements in each month from MIPAS and ACE-FTS. The numbers of good quality measurements at 9 km for MIPAS and 10.5 km for ACE-FTS are considerably reduced because a large number of measurements are contaminated by clouds. As a consequence, the trends at these altitudes from MIPAS and ACE-FTS were derived from a small number of measurements, leading to larger uncertainties. For example, in October 2004, there are only three ACE-FTS measurements within the latitude band range 0–40^∘ S, and the SF₆ monthly mean at 10.5 km is 7.57 pptv, which is very large compared with the monthly means in November 2004 (4.92) and December(5.80 pptv).

In general, the SF₆ trend from the SMO in situ measurements at surface or from the FTIR retrievals is close to the trends at the troposphere from the MIPAS and ACE-FTS measurements. In the stratosphere, satellite measurements (both MIPAS and ACE-FTS) show that the SF₆ trend decreases with increasing altitude. The change in the SF₆ trends in the stratosphere could be applied to estimate how long it takes for the well-mixed air mass to transport from the surface to the high altitude on a large scale (Waugh, 2002; Stiller et al., 2012).

4 Conclusions

The SF₆ total columns were retrieved with the SFIT4 algorithm from two FTIRs on Reunion Island (21^∘ S, 55^∘ E) in 2004–2016. The FTIR SF₆ retrieval is sensitive to the whole troposphere and lower stratosphere but has only 1 degree of freedom. We used the retrieval window (946.5–949.0 cm⁻¹) for the SF₆ retrieval at St Denis and Maïdo, with the broad unresolved Q branch of the ν₃ band of SF₆, at 947.9 cm⁻¹. Nearby are a strong H₂O absorption line at 948.26 cm⁻¹, a weak H₂O absorption line at 946.68 cm⁻¹ and a strong CO₂ line at 947.74 cm⁻¹. The SF₆ retrieval product is influenced by these two species, especially by H₂O due to its larger variability in the atmosphere. The retrieval window in this study is wider than the previous ones (Zander et al., 1991; Krieg et al., 2005) because for the humid sites, such as St Denis, a better fitting is obtained with the larger window.

To estimate the SF₆ retrieval error, four components (the smoothing error, forward model parameter error, measurement error and other retrieval parameter errors) have been discussed in detail. In total, the systematic and random uncertainties of the FTIR-retrieved SF₆ columns are 4.6 and 14.0 % at St Denis and 3.7 and 6.7 % at Maïdo. Both systematic and random uncertainties at St Denis are larger than those at Maïdo, because of the lower SNR and the higher water vapour abundance at St Denis.

The trend in $X_{{\mathrm{SF}}_{\mathrm{6}}}$ derived from FTIR measurements is 0.265±0.013 pptv year⁻¹ for 2004–2016, which is slightly weaker than the trend from the SMO in situ measurements (0.285±0.002 pptv year⁻¹) for the same time period. The SF₆ trends at 9 km from MIPAS measurements and 10.5 km from ACE-FTS measurements are rather uncertain due to scarceness of data, because the MIPAS and ACE-FTS measurements are contaminated by cumulus clouds at low altitudes and these values are not included for the trend calculation. The SF₆ trends in the troposphere from both MIPAS and ACE-FTS measurements are close to the trends from FTIR retrievals and SMO in situ measurements; the SF₆ trends from MIPAS and ACE-FTS above the tropopause height decrease with increasing altitude.