Atmospheric abundance and global emissions of perﬂuorocarbons CF 4 , C 2 F 6 and C 3 F 8 since 1800 inferred from ice core, ﬁrn, air archive and in situ measurements

. Perﬂuorocarbons (PFCs) are very potent and long-lived greenhouse gases in the atmosphere, released predominantly during aluminium production and semiconductor manufacture. They have been targeted for emission controls under the United Nations Framework Convention on Climate Change. Here we present the ﬁrst continuous records of the atmospheric abundance of CF 4 (PFC-14), C 2 F 6 (PFC-116) and C 3 F 8 (PFC-218) from 1800 to 2014. The records are derived from high-precision measurements of PFCs in air extracted from polar ﬁrn or ice at six sites (DE08, DE08-2, DSSW20K, EDML, NEEM and South Pole) and air archive tanks and atmospheric air sampled from both hemispheres. We take account of the age characteristics of the ﬁrn and ice core air samples and demonstrate excellent consistency between the ice core, ﬁrn and atmospheric measurements. We present an inversion for global emissions from 1900 to 2014. We also formulate the inversion to directly infer emission factors for PFC emissions due to aluminium production prior to the 1980s. We show that 19th century atmospheric levels, before signiﬁcant anthropogenic inﬂuence, were stable at 34 . 1 ± 0 . 3 ppt for CF 4 and below detection limits of 0.002 and 0.01 ppt for C 2 F 6 and C 3 F


Introduction
Perfluorocarbons (PFCs) are very potent greenhouse gases (about 7000-11 000 times more powerful than CO 2 on a weight-emitted basis over a 100-year timescale; Myhre et al., 2013).They are very long-lived in the atmosphere, making them of particular relevance for achieving climate stabilisation.We will focus here on three PFCs, CF 4 , C 2 F 6 and C 3 F 8 , but there are other PFCs in the atmosphere with lower abundance than CF 4 and C 2 F 6 (e.g.Oram et al., 2012;Laube et al., 2012).
CF 4 (carbon tetrafluoride, PFC-14) is the most abundant perfluorocarbon in the atmosphere (Mühle et al., 2010).It is released predominantly from aluminium production (due to so-called "anode effects", when the feed of aluminum oxide to or within the electrolysis cell is restricted; Holiday and Henry, 1959;Tabereaux, 1994) and during semiconductor manufacture (Tsai et al., 2002;Khalil et al., 2003).There is a small natural source from rocks (fluorites and granites) released by tectonic activity and weathering (Harnisch and Eisenhauer, 1998;Deeds et al., 2008Deeds et al., , 2015;;Mulder et al., 2013;Schmitt et al., 2013).Other very small industrial sources of CF 4 include release during production of SF 6 and HCFC-22 (Institute for Environmental Protection and Research, 2013) and from UV photolysis of trifluoroacetyl fluoride, which is a degradation product of halocarbons such as HFC-134a, HCFC-124 and CFC-114a (Jubb et al., 2015).Another possible source of CF 4 is from the rare earth industry, particularly in China, specifically neodymium oxide electrolysis (Vogel and Friedrich, 2015).However, these other sources of emissions have been negligible to date compared to the CF 4 emissions due to aluminium production and semiconductor manufacture (Harnisch and Eisenhauer, 1998;Jubb et al., 2015;Wong et al., 2015).
C 2 F 6 (perfluoroethane, PFC-116) is released predominantly during aluminium production and semiconductor manufacture (Tsai et al., 2002;Fraser et al., 2013).It is also used in the R-508 refrigerant blend, although emissions are believed to be small compared to the other sources (Kim et al., 2014).C 3 F 8 (perfluoropropane, PFC-218) is the least abundant of these three PFCs and is used as a refrigerant as well as being released during semiconductor manufacture (EDGAR, 2010;Tsai et al., 2002).C 3 F 8 has been detected at low levels in emissions from aluminium smelters (Fraser et al., 2013;Li et al., 2012).The aluminium industry does not currently account for C 3 F 8 emissions (International Aluminium Institute, 2014) or include them in the current IPCC guidelines for bottom up accounting of PFC emissions from aluminium production (IPCC, 2006), but due to the low levels compared to the other PFCs (Fraser et al., 2013;Li et al., 2012) C 3 F 8 is likely to be difficult to detect with the measurement systems used by the aluminium industry.Natural sources of C 2 F 6 and C 3 F 8 have not been identified (Harnisch, 1999).
Sinks of these PFCs are dominated by unintentional thermal destruction during high-temperature combustion at ground level, giving atmospheric lifetimes for CF 4 , C 2 F 6 and C 3 F 8 of about 50 000, 10 000 and 2600 years, respectively (Cicerone, 1979;Morris et al., 1995;Myhre et al., 2013).PFCs have been targeted by both the aluminium and semiconductor industries for emission controls to reduce greenhouse gas emissions.
Atmospheric measurements of greenhouse gases are the only reliable way to verify estimates of global emissions to ensure that we can predict the effect of emissions on radiative forcing and to guide mitigation options.Mühle et al. (2010) gave a summary of previous measurements of CF 4 , C 2 F 6 and C 3 F 8 , then presented new high-precision measurements from 1973 to 2008 on air from (a) the Cape Grim Air Archive (Langenfelds et al., 1996), (b) a suite of tanks with old northern hemispheric air and (c) the Advanced Global Atmospheric Gases Experiment (AGAGE) in situ atmospheric monitoring network.They presented estimates of global trends in PFC abundance and the corresponding emissions from 1973 to 2008.They showed that global emissions peaked in 1980 (CF 4 ) or early-to-mid-2000s (C 2 F 6 and C 3 F 8 ) before decreasing due to mitigation efforts by both the aluminium and semiconductor industries.The emissions estimates based on atmospheric measurements were significantly higher than previous estimates based on inventories.Kim et al. (2014) extended this work using measured C 2 F 6 / CF 4 emission ratios specific to the aluminium and semiconductor industries to partition global emissions to each industry.They suggested that underestimated emissions from the global semiconductor industry during 1990-2010 and China's aluminium industry after 2002 accounted for the discrepancy between PFC emissions based on atmospheric measurements and inventories.Underestimated PFC emissions may also be from previously unaccounted-for emissions from aluminium production due to undetected anode effects (Wong et al., 2015).
Air extracted from firn (the layer of unconsolidated snow overlying an ice sheet) or bubbles in polar ice provides a reliable way to reconstruct atmospheric composition prior to direct atmospheric measurements.Mühle et al. (2010) estimated the pre-industrial, natural background abundances from firn air at the Megadunes site in Antarctica (air with a mean age of about AD 1910) and air from 11 samples of melted glacial ice at Pâkitsoq in Greenland (with ages between 19 000 and 11 360 BP) to be 34.7 ± 0.2 ppt for CF 4 (based on both Megadunes and Pâkitsoq) and 0.1 ± 0.02 ppt for C 2 F 6 (based on Megadunes alone).Worton et al. (2007) used firn measurements from the North Greenland ice core project site (NGRIP) and Berkner Island, Antarctica, to reconstruct CF 4 from the mid-1950s and C 2 F 6 from 1940 to present.However, these previous records from firn and ice are not continuous through from pre-industrial to recent levels.
Here we present measurements of CF 4 , C 2 F 6 and C 3 F 8 in air extracted from four firn sites (DSSW20K, EDML, NEEM 2008 andSouth Pole 2001) and two ice cores (DE08 and DE08-2).We combine these with the air archive and in situ measurements from Mühle et al. (2010), extended to the end of 2014, and use an inversion calculation to estimate global emissions, with uncertainties, and show how these PFCs have varied in the atmosphere from pre-anthropogenic levels in the 19th century to 2014.We also reformulate our inversion to directly infer emission factors for PFC emissions due to aluminium production for the period up to 1980 when aluminium production dominates PFC emissions.

Data -locations, measurement and calibration scales
The firn and ice core measurements used in this work come from ice or firn air collected at the following sites: -DE08 and DE08-2 are located 16 km east of the summit of Law Dome (66.7 • S, 112.8 • E) in East Antarctica (Etheridge et al., 1996(Etheridge et al., , 1998)).They are 300 m apart and have nearly identical site characteristics, including very high snow accumulation rates (1100 kg m −2 yr −1 ).Ice cores were drilled at DE08 and DE08-2 in 1987 and 1993, respectively.
-DSSW20K is 20 km west of the deep DSS (Dome Summit South) drill site near the summit of Law Dome in East Antarctica (Smith et al., 2000;Sturrock et al., 2002;Trudinger et al., 2002).DSSW20K has a short firn column and a moderate snow accumulation rate (150 kg m −2 yr −1 ).Firn air was collected in January 1998.
-NEEM 2008 firn air was extracted from a borehole near the NEEM (North Greenland Eemian Ice Drilling Project) deep ice core drilling site (77.5 • N, 51.1 • W) in northern Greenland (Buizert et al., 2012).NEEM has a moderate snow accumulation rate (199 kg m −2 yr −1 ).We use air from the EU borehole collected in July 2008.
Here we measure only one sample from the South Pole, collected in 2001 from 120 m.
In addition to the firn and ice core measurements, we use archived and in situ measurements from Mühle et al. (2010), extended to the end of 2014 and focused on the high latitudes in each hemisphere.
Measurements were made using two different measurement systems and primary calibration scales.The measurements in Mühle et al. (2010) were made on Medusa systems (Miller et al., 2008) and reported on Scripps Institution of Oceanography (SIO) primary calibration scales (SIO-05 for CF 4 and SIO-07 for C 2 F 6 and C 3 F 8 ).Measurements of firn air from DSSW20K, NEEM 2008 and South Pole 2001 were made at CSIRO (Aspendale) or Cape Grim on the Medusa system and are also reported on SIO calibration scales.Air was extracted from DE08 and DE08-2 ice in ICELAB at CSIRO (Aspendale) using a "cheese grater" dry extraction system (Etheridge et al., 1988).Air from the DE08 and DE08-2 ice cores and the EDML firn was analysed at the University of East Anglia (UEA) using highsensitivity gas chromatograph/trisector mass spectrometer system (Waters/Micromass Autospec) (Worton et al., 2007;Sturges et al., 2001;Mani, 2010).Measurements made at UEA are reported on UEA calibration scales.We derive conversion factors between the two calibration scales in Appendix A and report all measurements on the SIO-05 (CF 4 ) and SIO-07 (C 2 F 6 and C 3 F 8 ) primary calibration scales.Further measurement details are available in Appendix B. The firn, ice core and archive measurements are available in the Supplement.The in situ measurements are available on the CDIAC website (Prinn et al., 2016).

Firn model
To characterise the age of the air in the firn and ice samples, we use a numerical model of the processes that occur in firn and ice (mainly diffusion of air in the firn layer, advection of snow downwards as new snow falls at the surface and gradual trapping of the air into bubbles).These processes mean that air contained in firn or ice corresponds to atmospheric air over a range of times rather than a single age.We use the CSIRO firn model (Trudinger et al., 1997), updated by Trudinger et al. (2013), and the LGGE-GIPSA firn model (Witrant et al., 2012)  age spread.We use the two independent models as a way to incorporate firn model uncertainty.
The depth profile of diffusivity in the firn and other diffusivity-related parameters in the firn models need to be calibrated for each site that we model.To do this we tune the models to fit firn measurements of trace gases for which we know the past atmospheric history.Calibration of the CSIRO firn model for DE08 and DE08-2 (which are modelled as identical sites), as well as DSSW20K, NEEM 2008and South Pole 2001, is described in Trudinger et al. (2013), and for EDML in Appendix C. Calibration of the LGGE-GIPSA model is described in Witrant et al. (2012) for all sites except EDML and DSSW20K, which are described in Appendix C. Note that although only one South Pole sample (from 120 m) was analysed for PFCs in our study, calibration of diffusivity at South Pole in both firn models was based on measurements throughout the entire depth profile.
The diffusion coefficients we use for the PFCs relative to CO 2 (for temperature of 244.25 K and pressure of 745 mb) are 0.823 for PFC-14 (Buizert et al., 2012, based on measurements by Matsunaga et al., 2005) and 0.583 and 0.497 for PFC-116 and PFC-218, respectively (using Le Bas molecular volumes; Fuller et al., 1966).The uncertainty in relative diffusion coefficients based on measurements by Matsunaga et al. (2005) is about 2 % and about 5-10 % from other methods (based on discrepancies between different estimates; Martinerie et al., 2009;Buizert et al., 2012;Trudinger et al., 2013).
As the firn model is linear, and the physical processes in firn are taken as constant in time, we can characterise the firn models using Green's functions (also known as age distributions, age spectra or pulse response functions) that relate the mole fraction of a trace gas at the measurement depths to atmospheric mole fraction of that gas over a range of times (Rommelaere et al., 1997;Trudinger et al., 2002).We denote these Green's functions as G a→i , as they represent the effect of atmospheric mole fraction in each year on mole fraction at a particular depth in ice or firn, with "a" for atmosphere and "i" for ice (or firn).The Green's functions change shape with depth through the firn layer, widening with increasing depth, but their shape does not change with depth for bubbles trapped in ice (assuming stationary conditions associated with relatively stable climate).Green's functions from the firn model, shown for DSSW20K in Fig. 1a, will be used as described in the next section.
In order to incorporate the effect of uncertainty in the firn models into our inversion calculations, we use an ensemble of Green's functions for each site, constructed as follows.When we calibrate the CSIRO firn model, in addition to finding the diffusivity profile that gives the best fit to calibration observations, we also create some alternative diffusivity profiles that approximately represent the 95 % confidence interval of the firn model parameters, as described by Trudinger et al. (2013).In some cases we also include Green's functions generated with the CSIRO model using different for-mulations of model processes (e.g.convective mixing near the surface at DSSW20K is modelled with exponentially decreasing eddy diffusion or with a well-mixed layer).We select between four and seven Green's functions for each site from the CSIRO model, and add one or more Green's functions from the LGGE-GIPSA model obtained from the analytical method presented in Witrant and Martinerie (2013), to represent the variation in the complete ensemble for each firn/ice site.We repeat the inversion calculation with all combinations of Green's functions for each site, giving more than 1300 combinations for the five firn/ice sites considered in this study.We also include Green's functions calculated with the CSIRO model using our best diffusivity profile but with relative diffusion coefficients that are ±5 % (for CF 4 ) or ±10 % (for C 2 F 6 and C 3 F 8 ) of the values given above (with relative diffusion coefficients used consistently across all sites at once).

Inversion calculations
We begin with an inversion of the air archive and in situ PFC measurements at the monthly timescale and semihemispheric spatial scale, to infer emissions of CF 4 and C 2 F 6 from 1978 to 2014 and C 3 F 8 from 1983 to 2014 (the inversion for C 3 F 8 starts later than the other two because the early archive C 3 F 8 measurements are particularly scattered).Initial mole fraction in 1978 (or 1983 for C 3 F 8 ) is also estimated.This inversion will be referred to as the "InvE1" inversion and is very similar to the inversion given in Mühle et al. ( 2010), but with an updated inversion method (Rigby et al., 2011(Rigby et al., , 2014) ) and with observations extended to the end of 2014.The InvE1 inversion uses the 2-D 12-box AGAGE atmospheric transport model (Cunnold et al., 1994;Rigby et al., 2013) to calculate the mole fraction of the PFCs in each semi-hemisphere from emissions.The 12-box model has four boxes north-south by three boxes in the vertical, with boundaries at 30 • N, 0 • and 30 • S in the horizontal and 500 and 200 hPa in the vertical.
We then use an inversion similar to Trudinger et al. (2002) to infer emissions at the annual timescale from the ice core, firn, archive and in situ measurements from 1900 to 2014.This inversion will be referred to as the "InvE2" inversion.InvE1 is the most appropriate inversion for the in situ and archive part of the record, while InvE2 was developed to focus on the issues associated with inverting firn and ice core measurements.InvE2 will be described in detail here; details of InvE1 are given in the references listed above.InvE2 also uses the AGAGE 12-box atmospheric transport model, mainly for consistency with InvE1.
The firn and archive data do not have adequate information content to constrain semi-hemispheric emissions, so InvE2 infers annual global emissions with a fixed north-south distribution (for this we use the estimated north-south distribution from InvE1 for 1990).The AGAGE 12-box model is used to relate annual high-latitude mole fraction in each SH mf to DSSW20K firn 19001920194019601980  G ef → i hemisphere to annual global emissions with the fixed northsouth distribution, creating Green's functions that are denoted G e→a , with "e" for emissions and "a" for atmosphere (Fig. 1b).InvE2 uses Green's functions that relate measured firn or ice core mole fractions to annual global emissions.We create these Green's functions (which will be denoted G e→i , Fig. 1c) by multiplying the G e→a Green's functions with the G a→i Green's functions described earlier.The observations used in InvE2 are firn and ice core measurements plus highlatitude mole fraction in each hemisphere at annual resolution, obtained by fitting a smoothing spline to the archive and in situ measurements and sampling as described in Appendix D. InvE2 starts from equilibrium (pre-anthropogenic) conditions, so the initial mole fractions are set to the preanthropogenic background levels that we estimate from our measurements.
We may expect to see a shift in the north-south distribution of emissions over time in recent decades, when global emissions have gone from being predominantly due to aluminium production to now include semiconductors and as developing nations such as China have increased their fraction of global emissions.InvE1 is capable of estimating such a shift in emissions, although with the caveat that derived emissions at the semi-hemispheric level are known to be sensitive to uncertainties in the model transport parameters.Use of a constant north-south distribution of emissions in InvE2 is the best choice prior to the 1980s when the emissions distribution was probably more stable than in recent decades, and the firn and ice core measurements would not contain adequate information to resolve distribution changes anyway.However, use of the constant emissions distribution does degrade the fit to observations in recent decades.We can use the emissions distribution already estimated by InvE1 to improve InvE2.We do this by subtracting the (modelled) contribution to all mole fraction measurements of the monthly semi-hemispheric emissions after 1980 inferred from InvE1, before inverting for additional emissions with the constant north-south gradient.These additional emissions estimated by InvE2 will mostly be emissions before 1980, although they could include small adjustments (positive or negative) to the emissions after 1980, but the adjustments will have the constant (1990) spatial distribution.In this way, we are combining the strengths of the higher-resolution InvE1 inversion for the monthly in situ measurements with the InvE2 inver-sion for the ice, firn and early archive measurements, to give our best estimate for emissions.
Because primary aluminium production is known much more precisely than emission factor for the PFCs, we also formulate the inversion to directly estimate PFC emission factors (in kilograms per metric tonne, kg t −1 ) from aluminium production before the mid-1980s, assuming that aluminium production is the dominant source for this period.This inversion will be denoted "InvEF".We create new Green's functions that relate measured high-latitude mole fraction to emission factor, G ef→i with ef for emission factor (Fig. 1d), by multiplying the G e→i Green's functions by global primary aluminium production in each year (using estimates from the U.S. Geological Survey (2014) and International Aluminium Institute (2014), shown by the grey line in Fig. 2e).
For the InvEF inversion, we first subtract from the observations the effect of the InvE1 emissions after a selected date (T 1 = 1985 for CF 4 and C 2 F 6 , and 1988 for C 3 F 8 ), then estimate emission factor only up to the date T 1 .We need to do this because emissions in recent decades were not only due to aluminium production, with semiconductor emissions making a significant contribution to global emissions.T 1 is chosen to be 5 years after the beginning of the InvE1 inversion, to avoid the effect of initialisation of mole fraction on the emissions inferred by InvE1 (see Sect. 3.2).The period up to T 1 is most likely dominated by emissions due to aluminium production, but if there is a significant contribution from other sources, this would lead to emission factors that are too high.EDGAR 4.1 (EDGAR, 2010) estimates that aluminium production was responsible for at least 99 % of CF 4 emissions up to 1985, and 90 % of C 2 F 6 emissions in 1985 (down from 99 % in 1972).C 3 F 8 emissions estimates in EDGAR 4.1 for all sources before 1988 are much smaller than the emissions implied by the atmospheric measurements (Mühle et al., 2010), so it is difficult to be sure about the contribution of different C 3 F 8 sources before 1988, but we would expect it to be similar to CF 4 and C 2 F 6 .Our interpretation of the emission factor results needs to keep in mind the possibility of sources other than aluminium production for the entire period up to T 1 , but the EDGAR emissions estimates have suggested particular care with emission factors for C 2 F 6 between 1972 and 1985.

Uncertainties and regularisation in the inversion calculations
There are a number of contributions to the uncertainties in inferred emissions and atmospheric abundance (Trudinger et al., 2002).The most obvious contributions are data error (analytical, calibration scale, sampling uncertainties) and model error.In our case, model error can be due to the firn model (from missing or incorrectly modelled processes and uncertainty in model parameters), as well as the atmospheric model that relates emissions to mole fraction.To capture the firn model uncertainty, we use an ensemble of Green's functions, from two firn models, as mentioned above.We assume that errors in the atmospheric model at the annual timescale for global emissions would be significantly smaller than other contributions to the error.
The contribution to the error that is most difficult to deal with is due to the fact that we are solving an inverse problem that is ill-conditioned, so that the solution is not unique.In our case, the ill-conditioning is partly due to lack of data (mole fraction in the firn is not known at all depths) but also importantly it is a consequence of the smoothing (and therefore lost information) by the firn and bubble trapping processes.As noted by Rommelaere et al. (1997), an atmospheric event of period shorter than the width of the Green's function is unlikely to be resolved in firn or ice core data.Therefore, when we invert a firn depth profile, the information contained in the firn data does not constrain variations in the atmospheric mole fraction at high (e.g.annual) frequencies.Rommelaere et al. (1997) demonstrated for CO 2 that atmospheric histories with wild (and unrealistic) oscillations can be consistent with the firn measurements (as long as high and low events counteract each other and have periods that are short relative to the Green's function width), but our knowledge of the budget of trace gases often excludes such possibilities.This budget knowledge needs to be incorporated into the inversion somehow, or the uncertainty in annual emissions will be unrealistically high and may therefore not be useful.
Regularisation (e.g.minimising the length of the solution; Menke, 1989) was used by Rommelaere et al. (1997) to address the problem of ill-conditioning.The use of prior information on either mole fractions or emissions can also help.Rigby et al. (2011) used prior information on the rate of change of emissions, rather than the absolute magnitude, as often the timing of changes in emissions is known even if the estimated magnitude may be incorrect.Constraints can also help, such as non-negativity constraints on emissions or mole fraction for long-lived gases (Trudinger et al., 2002).However, once constraints like these are used, the inversion, which originally was linear, usually becomes nonlinear.Another method is to smooth the solution and its uncertainties (e.g.running mean), taking into account the strong anticorrelations between uncertainties in adjacent years, then report the smoothed solution and smoothed uncertainties, as done by Trudinger et al. (2002).It would also be possible to infer mole fraction or emissions at lower frequencies (e.g.decadal averages rather than annual values), but we might then miss out on information about trends within decades that is available in the data when we incorporate our understanding of the budget, and we would need to be careful about temporal aggregation error (Thompson et al., 2011).Each of these methods to deal with the uncertainty due to ill-conditioning has different advantages and disadvantages and it is important to understand the consequences of any choices.
In the InvE2 and InvEF inversions, we use regularisation similar to Rommelaere et al. (1997) to avoid unrealistic oscillations by including a term in the cost function to be minimised that is the sum over all years of the change from one year to the next in emissions (or emission factor).This term is weighted in the cost function by a parameter, α.We need to choose α so that it suppresses unrealistic oscillations but does not smooth out too much of the real year-to-year variation in emissions that we are interested in.We also use a constraint that emissions and emission factors must not be negative.
Uncertainties in estimated emissions are calculated by repeating the inversion many times with perturbations to model inputs, including (a) firn model Green's functions, (b) observations perturbed according to their uncertainty, as in bootstrapping (Efron and Tibshirani, 1993), (c) initial mole fraction and (d) the period for which the spatial distribution of emissions is taken from the InvE1 inversion.We calculate the uncertainties due to each contribution separately, only to see the relative contributions.To calculate the total uncertainty we perturb all inputs at once and take the full range of emissions to represent the 95 % confidence interval of emissions and the full range of the corresponding mole fractions to represent the 95 % confidence interval for atmospheric mole fraction.If we were to combine the uncertainties from the individual contributions in quadrature to calculate total uncertainties, we could end up with negative emissions being included in the uncertainty range for part of the time period, which would imply that the uncertainty range was too large.We wish to stay consistent with the constraints provided by the measurements and ensure emissions are not negative.This is likely to give an uncertainty range that is not symmetric about the best solution when the best solution is near zero.Separately we also test the sensitivity of results to leaving out the observations from each site one at a time, as well as the parameter α that gives the weight of the smoothness constraint in the cost function.
Apart from the regularisation term involving the year-toyear changes in emissions (or emission factor), the cost function consists of the squared model-data mismatch weighted by the observation uncertainties.We do not include the prior estimate in the cost function.Previous studies (Mühle et al., 2010;Kim et al., 2014) found that bottom-up estimates of PFC emissions were too low, and we did not want these to bias our results.A prior estimate is, however, used as a starting point for the inversion calculation.The InvE2 and InvEF inversions are implemented in IDL (Exelis Visual Information Solutions, Boulder, Colorado) using the con-strained_min routine.
Prior emissions for the InvE2 inversion after 1980 (or 1983 for C 3 F 8 ) are taken as zero (because we subtract the effect of the InvE1 emissions from the measurements).Prior emissions before 1980 (or 1983) are based on emissions calculated by multiplying estimates for global primary aluminium production by an emission factor (kg PFC/tonne Al produced) determined as follows.For CF 4 , we use a constant emission factor of 1.2 kg t −1 , chosen to match the InvE1 emissions in 1980.We could have increased the emission factor back in time -for example, Oye et al. (1999) suggested an emission factor of 1.5 kg t −1 in 1948 -but as the prior estimate is used only as a starting point for the inversion we chose the simplest option.We take the emission factor for C 2 F 6 to be 0.13 kg t −1 (95 % of InvE1 emissions divided by aluminium production, because EDGAR 4.1 has C 2 F 6 emissions due to aluminium production contributing about 95 % of the total emissions in 1980), also assumed to be constant in time.For C 3 F 8 , we use an emission factor of 0.01 kg t −1 , based on the InvE1 emissions in 1983, assumed constant with time.

Inversion results
Figures 2, 3 and 4 show inputs and results for CF 4 , C 2 F 6 and C 3 F 8 for all three inversion calculations (InvE1, InvE2 and InvEF).In each case, the first panel shows the firn and ice core measurements and the modelled depth profiles that correspond to emissions calculated by the InvE2 inversion (using observations from all sites at once).The second panel shows Green's functions from the CSIRO firn model that relate the mole fraction at the firn and ice core measurement depths to either northern or southern hemispheric highlatitude atmospheric mole fraction (G a→i ).Each line corresponds to one measurement depth and shows the estimated proportion of the measured PFC mole fraction in that firn or ice core sample that comes from the overlying atmosphere in each year.The Green's functions are narrowest at DE08 and DE08-2, second narrowest at DSSW20K, intermediate width at NEEM and widest at the South Pole and EDML.Depths with measured mole fraction that are below detection limits (for C 2 F 6 and C 3 F 8 ) have Green's functions shown with dashed lines.When the measured mole fraction is zero (or below detection), we can assume that the atmospheric mole fraction for the years covered roughly by the Green's function for that depth had zero or very low mole fraction (Trudinger et al., 2002), give or take a few years for uncertainty in the Green's function and how high the atmospheric mole fraction would need to be during the years near the edge of the Green's function to cause detectable mole fraction in the firn.The Green's functions in the second panel provide the link between the first and third panels and show the significant overlap of Green's functions at different depths and sites.
The third panel shows the estimated history of PFC mole fraction in the atmosphere for the high-latitude northern (dashed) and southern (solid) latitudes calculated with the InvE2 inferred emissions.The annual values of atmospheric PFC mole fraction that are used in the inversion are shown by the black circles for the Southern Hemisphere (based on the Cape Grim air archive and in situ data) and the grey circles for the Northern Hemisphere (based on northern hemispheric tanks and Mace Head in situ data).
The fourth panel shows the emissions estimated by the three inversions.The red, inner black and blue lines show our preferred solution for each inversion.The pink shading, outer black lines and blue shading show the estimated 95 % confidence intervals.The InvEF inversion estimates emission factors, and we combine the inferred emission factor with aluminium production to calculate the corresponding emissions that are shown here.For InvE2 and InvEF, the confidence intervals come from the full ensemble of Green's functions plus other components of the uncertainty as described in Sect.2.3.1.The dashed grey lines show the prior emissions The fifth panel shows emission factors inferred by the In-vEF inversion, with 95 % confidence intervals.We also show estimates of recent CF 4 and C 2 F 6 emission factor from the International Aluminium Institute (2014) (orange line, lower right corner) and the CF 4 emission factor estimate for 1948 from Oye et al. (1999).Reconstructed histories of mole fraction, emissions and emission factor are available in the Supplement.
Our inversions simultaneously match almost all firn and ice core measurements very well, showing consistency between the different sites and between the firn, ice core and atmospheric observations.Our inferred emissions between 1975 and 2008 are very much like those in Mühle et al. (2010).They are based on essentially the same data, and the small differences would mainly be due to choices in the different inversion calculations.The peaks in emissions around 1980 (CF 4 ) or early-to-mid-2000s (C 2 F 6 , C 3 F 8 ), followed by decreases in emissions, are prominent features in the records and have already been described in detail by Mühle et al. (2010).The firn and ice core measurements have shown quite stable mole fraction levels in the early 20th century, followed by peaks in CF 4 and C 2 F 6 emissions around 1940, then strong increases in emissions from around 1960 in all three PFCs.The estimated emission factors are quite high in the first few decades of the 20th century.We will discuss these features of the reconstructions in more detail in Sect.4; in the remainder of Sect. 3 we will look in more detail at the inversion calculations.

Comparison of different inversions
The emissions from the InvE2 inversion are very similar to those from the InvE1 inversion.The only notable differences are that the InvE2 inversions for CF 4 and C 3 F 8 give higher emissions in the early 1980s, but this is when the InvE1 inversion is just beginning, and it depends on the oldest samples in the archive records and could be subject to end-effects including potential aliasing of the emissions with the initial conditions.It is due to these differences that we have chosen the start date for the emission factor inversion, T 1 , to be 5 years later than the start of the InvE1 inversion.
The estimated emissions from InvEF are generally quite similar to those from InvE2, but there are significant differences in the temporal variability.It is important to note that in InvE2, regularisation is applied to emissions (minimising the year-to-year variability in emissions along with the modeldata mismatch, as described in Sect.2.3.1),whereas in In-vEF, regularisation is applied to the emission factor.This has implications for the temporal variability in the two different inversions.Temporal variability in aluminium production is directly reflected in the emissions from the InvEF inversion (emissions are the product of the inferred emission factor and aluminium production).Although the variation in estimated CF 4 emission factor through the 1940s is quite smooth (Fig. 2e), the peak in aluminium production in the 1940s is not smooth, and it gives quite a prominent peak in CF 4 emissions from InvEF at this time (Fig. 2d).We would be less likely to see the same structure in the emissions in InvE2 around 1940, firstly because such rapid variation is unlikely to survive smoothing due to the firn processes to be recoverable in such detail from the firn or ice core measurements, but also the regularisation would penalise solutions with rapid variability in emissions like this.The aim of regularisation is to remove any variations that are too rapid to be resolved in the firn or ice, so these two reasons are related.We do, however, see a relatively sharp peak around 1940 in C 2 F 6 emissions in Fig. 3d.There are physical reasons for expecting the emission factor to vary more slowly than emissions -the emission factor is likely to depend on the current technology used to produce aluminium, which presumably will change more slowly than aluminium production itself which needs to respond rapidly to demands.For this reason, we favour the variability in emissions from the InvEF inversion, with emissions reflecting the product of the slower change in emission factor with the more rapid change in aluminium production.
The estimated emission factors are quite high in the first few decades of the 20th century, but this is multiplied by very small aluminium production, leading to small emissions.The uncertainty in emission factor in this period is large and is dominated by the assumed background mole fraction levels.Our estimated CF 4 emission factor of 1.8-2.7 kg t −1 in 1948 is larger than the 1.5 kg t −1 estimated by Oye et al. (1999).Recall that the emission factor for C 2 F 6 after 1970 might be overestimated if there are significant emissions of C 2 F 6 due to semiconductors at this time.Our estimated emission factors were based on the assumption that aluminium production was the only source for these PFCs before the early 1980s.While we know that this was probably not quite true at the end of the period, we believe it to be true before about 1970.We are not aware of sources of PFCs other than aluminium production that are likely to have been significant before 1970.

Sensitivity studies
Figure 5a shows the sensitivity of the inferred CF 4 emissions from InvE2 to excluding each of the measurement sites (including the Cape Grim and northern hemispheric atmospheric measurements).Exclusion of DE08-2 is the only site that makes a difference to the estimated emissions before 1955, and we see a more gradual increase in emissions from 1900 without DE08-2 rather than the increase from 1920 that the DE08-2 measurements imply.DE08-2 is the site with the narrowest age distributions, and the oldest DE08-2 measurement is centred around the 1920s (Fig. 2b).DE08 has age distributions with the same width as DE08-2 but older air and no samples containing air after 1910.The resolution and timing of the DE08-2 ice core measurements are valuable to these calculations.We do not currently have measurements of C 3 F 8 in the DE08 or DE08-2 ice cores.If we did, the extent to which they would improve the temporal resolution of the estimated C 3 F 8 emissions is likely to depend on their uncertainty and the measurement detection limit.
Figure 5b shows CF 4 emissions from InvE2 for different values of the regularisation parameter α.For the low values we see an increase in the variability, while for the high values we see that the emissions peak around 1980 starts to be suppressed.Interestingly, for lower values of α we get a higher peak in the early 1940s, coinciding with the peak in aluminium production.Our choice of α generally seems a reasonable one to suppress unrealistic variation while retaining much of the variation we are interested in, but it is possible that some real features could be suppressed.
The pre-anthropogenic background level assumed in our inversions influences the emissions estimated for the early part of the calculation, and we include uncertainty in the background level in our uncertainty calculation, using conservative ranges of 33.66-34.82ppt for CF 4 , 0.0-0.01ppt for C 2 F 6 and 0.0-0.001ppt for C 3 F 8 .In Fig. 5c, CF 4 emissions are calculated by InvE2 using different values of the background level.For the low background levels, the inversion includes some emissions in the early 1900s, and for the high levels the increase of emissions from zero is around 5 years later than with the other values.The model-data mismatch is lowest for the CF 4 background level of 34.05 ppt (using the UEA to SIO calibration scale conversion equation given in Appendix A).
The results shown by the lines in Figs. 2, 3 and 4 are our preferred solutions calculated with Green's functions from the CSIRO model, and the confidence intervals use the ensemble of Green's functions from both firn models.In Fig. 5d we compare C 2 F 6 emissions calculated with the InvE2 inversion using the preferred Green's functions from the CSIRO firn model (black line) with emissions calculated using the preferred Green's functions from the LGGE-GIPSA firn model (blue dash-dotted line).The difference between emissions inferred with Green's functions from the CSIRO and LGGE-GIPSA firn models is most noticeable for C 2 F 6 but still fairly small for all three PFCs.

Deep firn and ice
Figure 6 shows the mole fraction depth profiles in the deep firn and ice, for the prior and InvE2 and InvEF inversions.They highlight how much the differences in emissions for the three cases make to the mole fraction depth profiles and therefore give an indication of the size of the mismatch in the mole fraction profile that we are interpreting in terms of emissions or emission factor.The mole fraction near the bottom of the firn contains information about the timing and the rate of increase in atmospheric mole fraction from zero, although interpretation is subject to uncertainties in the firn model.DE08 is not shown because all measurements are at pre-anthropogenic background levels.2007), which were not used in our inversions.Lines show modelled depth profiles created by convolving our inferred atmospheric mole fraction time series in the appropriate hemisphere with Green's functions from the LGGE-GIPSA firn model.CF 4 is shown in black (left axis) and C 2 F 6 in grey (right axis).
The difference between the prior and estimated mole fraction depth profiles, relative to the data uncertainty, is most obvious for C 2 F 6 but is quite consistent for all of the firn sites as well as DE08-2.Inversions InvE2 and InvEF both lead to fairly similar depth profiles, indicating that it would not be worth trying to distinguish between the temporal variation of these two solutions (in particular, the timing and magnitude of the peaks in CF 4 and C 2 F 6 emissions around 1940).This also implies that it is not worthwhile to reduce the value of α that scales the year-to-year constraint in the inversion in order to try to extract more information about the shortertimescale variation from the firn data by allowing solutions with greater temporal variability, because the firn data are unlikely to constrain such variation.et al. (2007) measured CF 4 and C 2 F 6 in firn at Berkner Island, Antarctica, and NGRIP, Greenland, and inferred atmospheric histories from 1955 (for CF 4 ) and 1940 (for C 2 F 6 ).We did not use these measurements in our inversions; instead we saved them for validation.In Fig. 7 we compare the Berkner Island and NGRIP measurements with our preferred mole fraction time series inferred by InvE2 convolved with Green's functions from the LGGE-GIPSA firn model.We have converted the Worton et al. (2007) firn measurements from the UEA calibration scale to the SIO calibration scale using the equations in Appendix A. We find very good agreement between our modelled depth profiles and the Berkner Island and NGRIP firn measurements from Worton et al. (2007).

Worton
A particular strength of this work comes from the fact that the inferred histories of emissions give a good match to overlapping atmospheric, firn and ice core measurements from eight different firn and ice core sites with very different cliwww.atmos-chem-phys.net/16/11733/2016/mate and snow accumulation characteristics, collected at different times, with measurements made at two different laboratories and interpreted using two different firn models.This gives us increased confidence that the firn and ice core data provide a consistent and reliable picture of 19th and 20th century greenhouse gas changes.

Pre-anthropogenic levels
Our oldest samples are from DE08 and contain air with CF 4 and C 2 F 6 mean ages of 1841 and 1837, respectively, and Green's functions extending to before 1810.The oldest EDML firn sample also has PFC Green's functions extending back to before 1810.Our early measurements therefore tell us about PFCs from about 1800.The measured mole fractions of C 2 F 6 and C 3 F 8 were below the detection limits of 0.002 and 0.01 ppt, respectively, in the deepest EDML firn samples and several ice core samples (C 2 F 6 only), indicating that 19th century levels of both C 2 F 6 and C 3 F 8 were either zero or extremely small.The oldest samples were all measured at UEA, as all of the samples measured on the Medusa systems contained at least some air from the 1940s or later.Mühle et al. ( 2010) estimated a C 2 F 6 pre-industrial level of 0.1 ± 0.02, based on firn air from the Megadunes site in Antarctica with a mean age of about 1910, but no account was taken of the age distribution of that sample.It is quite likely that it contained some air from the 1940s or later, which explains the non-zero C 2 F 6 measurement.For example, our South Pole firn sample at 120 m has a C 2 F 6 mean age of about 1903 but measured mole fraction of about 0.1 ppt because the age distribution (red curve in Fig. 3b) includes some air from the 1940s and possibly 1950s.This highlights the need to consider the age distribution for interpretation of firn and ice core measurements, rather than characterising the age with a single number.
The DE08 ice core measurements of CF 4 (purple symbols in Fig. 2a) are constant with depth, indicating that CF 4 levels in the 19th century were stable.The low measurement must be an outlier rather than reflecting real atmospheric variations, due to the long lifetime of CF 4 and the fact that the Green's functions of nearby measurements have significant overlap.For CF 4 , our oldest samples come from measurements made at UEA, so the conversion of measurements from the UEA calibration scale to the SIO-05 calibration scale is important for determining the pre-anthropogenic CF 4 level in the SIO-05 calibration scale.Using our best estimate for the factors relating the UEA to SIO-05 calibration scales (Appendix A), we estimate that CF 4 was stable at 34.1 ± 0.3 ppt during the 19th century, before anthropogenic influence became significant (after about 1910).The uncertainty is 1σ and takes into account measurement uncertainty and uncertainty in the UEA vs. SIO calibration scale.This uncertainty does not include the uncertainty in the CF 4 primary calibration scale, which is 1-2 % (Mühle et al., 2010).
Mühle et al. ( 2010) estimated a CF 4 pre-industrial background level of 34.7 ± 0.2, higher than our estimate, based on ice core measurements from Pâkitsoq, Greenland, and a Megadunes firn sample.The Megadunes firn measurement of 34.90±0.04ppt is likely to be higher than the background level because the sample probably contains some air from the 1940s or later (as for C 2 F 6 described above).Pâkitsoq ice samples correspond to air with ages ranging between 19 000 and 11 360 BP, and Mühle et al. ( 2010) reported an average CF 4 mole fraction of 34.66 ± 0.16 ppt for these measurements.However, these samples have not been corrected for the effect of gravitational settling in firn.After correcting for gravitational effects using measured δ 15 N 2 (Schaefer et al., 2009, Jeff Severinghaus andVas Petrenko, personal communication, 2016), the average of the Pâkitsoq ice samples is 33.75 ± 0.2 ppt.This is slightly lower than our estimate of 34.05 ± 0.33 ppt for the 19th century, but the difference is small considering the uncertainties in each estimate.The period from 11 360 to 19 000 covers the last deglaciation and back into the last glacial.It is possible that atmospheric CF 4 may have varied to some extent since then.Schmitt et al. (2013) found variations in CF 4 between about 31 and 35 ppt over the last 800 000 years, with increasing CF 4 mole fraction during interglacials and decreasing CF 4 during glacials, which they attributed to variations in weathering due to climate, although tectonic activity is likely to be important too (Deeds et al., 2015).
The natural CF 4 source (due to rocks) is very small (of order 0.01 Gg yr −1 = 10 t yr −1 to maintain a background level of 34 ppt with an atmospheric lifetime of 50 000 years).The natural source is very much smaller than anthropogenic emissions and unlikely to have caused significant variations in atmospheric CF 4 in the last few hundred years.

Emissions peaks during World War II
Inversions InvE2 and InvEF for CF 4 and C 2 F 6 both show a significant peak in emissions around 1940 (Figs.2d and 3d), most likely associated with increased aluminium production during World War II (Barber and Tabereaux, 2014), for example for construction of aircraft.The peak is more prominent in C 2 F 6 than CF 4 .We expect to see a small peak after 1940 in inversion InvEF, because emissions are calculated as inferred EF multiplied by global aluminium production, and the aluminium production estimates (U.S. Geological Survey, 2014) contain a peak in the 1940s (Fig. 2e).However, the magnitude of the emissions peak from InvEF for both CF 4 and C 2 F 6 is higher than we had expected (based on the prior estimate with constant emission factor) and comes from the high emission factor that the inversion requires to match the measurements.The peaks in InvE2, in contrast, come from the firn and ice core measurements and occur even if we remove the peak from the prior estimate.The peak in CF 4 is spread from about 1930 to 1945, but the peak in C 2 F 6 is more prominent and of shorter duration.The DE08-2 ice core measurements have the narrowest age spread of the sites we consider (and possibly of any other firn or ice core sites that have been sampled to date) and are the ones that contain most information on this peak (Sect.3.4).The peaks are about at the limit of what we can expect to resolve from firn and ice core measurements.We have no ice core measurements of C 3 F 8 , and the mole fraction level around 1940 is so low that if a similar peak existed in C 3 F 8 it may be difficult to detect.

Emissions factors
Emission factors for PFC emissions from aluminium production have decreased markedly since the early 20th century, from around 2.1-4.4 kg t −1 for CF 4 , 0.49-0.72 kg t −1 for C 2 F 6 and 0.004-0.05kg t −1 for C 3 F 8 in 1940 (ranges are 95 % confidence intervals) to about 0.04, 0.003 and 0.0001 kg t −1 in recent years (Fraser et al., 2013).Our high estimates of emission factors in the early 20th century are plausible.In the early days of aluminium production, there was little alumina feeding control (Edwards et al., 1930), which would undoubtedly have resulted in very frequent anode effects and therefore high PFC emission rates.Averaged across more than 10 USA smelters in 1990 there were 3 anode effect minutes per cell per day, obtained by multiplying the anode effect frequency (per cell day) by the anode effect duration (minutes) (personal communication, Alton Tabereaux, Alcoa).Before the 1950s, there could have been 9-15 anode effect mins/cell/day, which is 3-5 times higher than in 1990.If we assume that the average 1990 CF 4 emission factor was 1.2 kg t −1 , then a pre-1950s emission factor could have been 3.6-6.0kg t −1 , which is about what we see in our inversion.After the 1950s, there was more awareness of the extra costs associated with anode effects due to loss in metal production and extra energy consumption.Thus plants developed more sophisticated alumina feed control systems, leading to reduced frequency of anode effects.

Latitudinal distribution of emissions
The InvE1 inversion gives estimates of monthly semihemispheric emissions.Although the estimates of the northsouth distribution of emissions are sensitive to uncertainties in model transport parameters, we can draw some general conclusions about shifts in the distribution over time.Between 1980 and 2010, we see an increase of the proportion of global CF 4 emissions in the 0-30 • N and 0-30 • S boxes, with a corresponding decrease in the proportion of global emissions in the 30-90 • N box (roughly 20 % of the total emissions).Over this period, we also see an increase in the proportion of global C 2 F 6 emissions in 0-30 • N box, along with a decrease in the 30-90 • N box (also about 20 % of the total).There is no clear change in the latitudinal distribution of C 3 F 8 emissions.We note that our inversion using the AGAGE 12-box model is not particularly well suited to this type of conclusion, and analysis with a model that has more accurate atmospheric transport, such as a 3-D atmospheric transport model, would be required to obtain a robust result.However, a general equatorward shift of a proportion of the emissions is consistent with the rapid rise of China into the aluminium market from the 1990s into the 2000s (International Aluminium Institute, 2009, 2014) at a lower latitude on average than previous emissions based in North America and Europe, for example in locations such as Canada and Norway (a map of the location of many aluminium smelters is shown in Wong et al. (2015), with a significant number of Chinese smelters south of 30 • N).The emergence of semiconductor emissions in recent decades, with significant contributions of emissions from Asia, would also have caused an equatorward shift of a proportion of the emissions.

Global financial crisis (GFC)
Our study adds an extra 6 years of measurements compared to Mühle et al. (2010) (Friedlingstein et al., 2010), followed by a rapid recovery (Peters et al., 2012), although the dip was only around 1.4 % and was dominated by emissions in developed countries and offset by increases in emissions in developing countries.Estimates of global primary aluminium production from the International Aluminium Industry show a 6 % reduction in 2009 compared to 2008, dominated by developed countries but with steady levels from China.The price of primary aluminium dropped by more than half from 2008 to 2009 (Barber and Tabereaux, 2014).Kim et al. (2014) (also shown in Wong et al., 2015) showed global top-down and bottom-up emissions estimated to 2010, and they have dips at the time of the GFC in the top-down estimates as well as both the aluminium and semiconductor components of the bottom-up emissions, but they were not specifically discussed nor related to the GFC.The 2009 dip in bottom-up CF 4 emissions given by Kim et al. (2014) is 23 % for both aluminium and semiconductor emissions and 24 and 26 % in bottom-up aluminium and semiconductor C 2 F 6 emissions, respectively.

Recent years
While the initial reduction of PFC emission factors last century was a consequence of measures to reduce electricity consumption during aluminium production, in recent decades there has been a concerted effort by both the aluminium and semiconductor industries to reduce PFC emissions.However, the rate of decrease of emissions appears to have slowed and possibly stopped in recent years.Other than the 2009 dip, CF 4 emissions have been quite steady since about 1998, C 2 F 6 emissions have been steady since about 2010 and the decline in C 3 F 8 emissions appears to have recently stopped.Primary aluminium production has increased year after year and at a greater rate from the year 2000, so steady emissions imply decreasing emission factors.However, due to the very long lifetimes of these gases, PFCs emitted become effectively a permanent part of the atmosphere and therefore make an enduring contribution to radiative forcing.The long lifetimes, together with their exceptionally high global warming potentials, underpin the urgent need for continued reduction of PFC emissions from all PFC generating industries.This should involve further mitigation efforts by the two major emitting industries (aluminium and semiconductors) and better quantification of emissions and (if necessary) mitigation efforts for the other potential sources (e.g.HCFC/fluorochemical production and rare earth industries).

Summary and conclusions
We have reconstructed emissions and atmospheric abundance of CF 4 , C 2 F 6 and C 3 F 8 from 19th century levels (prior to anthropogenic influence) to 2014, using measurements from four firn sites, two ice cores and archived and in situ atmospheric air from both hemispheres.We also inferred emission factors for PFC emissions due to aluminium production prior to the 1980s.These are the first continuous records of PFC mole fraction and emissions from pre-anthropogenic to recent times.They demonstrate how unintended consequences of human actions and deliberate mitigation efforts have affected these important atmospheric constituents over the past century.
The 19th century levels of CF 4 were stable at 34.1±0.3ppt and below detection limits of 0.002 and 0.01 ppt for C 2 F 6 and C 3 F 8 .CF 4 and C 2 F 6 both show peaks in emissions around 1940, presumably due to increased demand for aluminium production during World War II.These peaks are about at the limit of the time resolution recoverable from ice core and firn measurements.We estimate emission factors in 1940 of 2.2-4.8kg t −1 for CF 4 , 0.38-0.53kg t −1 for C 2 F 6 and 0.003-0.04kg t −1 for C 3 F 8 .
At the recent end of the record, we see temporary reductions in CF 4 (and perhaps C 2 F 6 ) emissions in 2009, presumably associated with the impact of the GFC on global alu-minium and semiconductor production.The strong decrease in PFC emissions that we have seen since the peaks in 1980 (CF 4 ) and early-to-mid-2000s (C 2 F 6 and C 3 F 8 ) appears to have slowed and possibly stopped in recent years.Continued effort from all PFC generating industries is urgently needed to reduce the emissions of these potent greenhouse gases, which, once emitted, will stay in the atmosphere essentially permanently (on human timescales) and contribute to radiative forcing.

Data availability
The firn, ice core and archive PFC measurements and the reconstructed histories of mole fraction, emissions and emission factor are available in the Supplement.The in situ measurements are available on the CDIAC website doi:10.3334/CDIAC/atg.db1001.

Appendix A: SIO and UEA calibration scales
The present study combines firn and in situ PFC measurements made on the Medusa system (reported on the SIO calibration scale) with firn and ice core measurements from DE08, DE08-2 and EDML made only at the University of East Anglia (reported on the UEA calibration scale).To combine these data we need to ensure that they are on the same calibration scale, so we convert the UEA measurements to the SIO calibration scale (SIO-05 for CF 4 and SIO-07 for C 2 F 6 and C 3 F 8 ).We have some firn PFC measurements made on the Medusa system and at UEA at common sites and depths; in some cases the samples measured at one laboratory were subsamples of those measured at the other, and in other cases they were separate samples taken from the same firn sites and depths.For CF 4 we have corresponding samples from DSSW20K, DSSW19K and SPO 2001, for C 2 F 6 we have DSSW20K, DSSW19K, SPO 2001 and NEEM 2008 and for C 3 F 8 we have only NEEM 2008.DSSW19K is a firn site about 1 km from DSSW20K on Law Dome that was sampled in October 2004 in 35 L stainless steel tanks that were filled with undried air via the firn air sampling device to pressures of about 4 bar.There was suspected contamination of some of the DSSW19K samples during collection, so they have not been used for the reconstruction of PFCs, but the same samples were measured on both the Medusa and UEA systems, making them valuable for calibration scale comparison over our range of interest.
Figure A1a-c show measurements on the UEA calibration scale plotted against measurements made on the Medusa at the same firn depths.Figure A1d-f show the same data but plotted as the difference in percent vs. the Medusa measurements, to show nonlinear differences in calibration scale if they exist.The Medusa measurements of CF 4 and C 2 F 6 were made at three different times (several years apart) by different people, and these are shown separately, with separate linear least-squares fits.The NEEM 2008 Medusa measurements of C 3 F 8 were only made once, and we show some additional measurements (open circles) made at similar depths (mostly different by about 0.05 m but up to 0.25 m).The difference in percent for CF 4 and C 2 F 6 is quite consistent, except for scatter of C 2 F 6 at low mole fraction (below about 0.4 ppt).The C 3 F 8 measurements show some nonlinearity at very low mole fraction (below about 0.03 ppt), but these are below the detection limit.
The linear least-squares fit to all CF 4 measurements in Fig. A1a  (shown by the red dashed line) which we use to convert the UEA measurements.Some UEA C 2 F 6 measurements with zero mole fraction in the UEA calibration scale would end up negative; these are set to zero.The intercept in the data fits is around the detection limit and of the order of the uncertainty in the measurements.Data uncertainties assigned to the UEA measurements incorporate the spread from the different linear fits, including one through the origin.
We have only one set of measurements for C 3 F 8 , giving [C 3 F 8 ] UEA + 0.001 0.949 .
The measurements at similar depths were not used to determine the fit, just to give more points for comparison.A linear fit to the NEEM 2008 C 3 F 8 passing through the origin is 946 .

Appendix B: Measurement details
Air was extracted from DE08 and DE08-2 ice core sections at CSIRO using a "cheese grater" dry extraction system (Etheridge et al., 1988(Etheridge et al., , 1996;;Rubino et al., 2013).Ice sections were approximately 800 g in weight and grated after evacuation in a cold room at −20 • C with the extraction vessel and ice having been pre-chilled to −80 • C. The air released by grating from the bubbles in the ice were recollected by cryogenically pumping through an ice-ethanol mixture at −100 • C (to remove water vapour) into a stainless steel cold finger held at < 18 K on the cold stage of a helium compressor cryostat.On warming to room temperature these cold fingers acquired an internal pressure of several atmospheres.These were then shipped to UEA for analysis.Several tests were made extracting bubble-free ice (as a blank), and transferring firn air of known PFC content into the cold fingers (with and without bubble-free ice) to determine system blank levels and to ensure that PFC abundance was unaffected by the ice extraction and air transfer and trapping process.
At UEA the PFCs from EDML firn air and air released from the ice cores were analysed using a high-sensitivity gas chromatograph/trisector mass spectrometer system (Waters/Micromass Autospec) according to the procedures detailed in Worton et al. (2007) and Mani (2010).The volumes of firn air measured were limited to 100 cm −3 to avoid breakthrough of the cryogenic preconcentration system, whilst volumes of between ca. 10 and 50 cm −3 were analysed from To obtain annual mole fraction data for the high northern and southern latitudes, we fit smoothing splines to measurements from Cape Grim (air archive and in situ) and Mace Head (in situ) and the suite of old tanks from the Northern Hemisphere.The splines are sampled at 1-year intervals to give mole fraction corresponding to the start of each year.For the period covered by the air archives, where there are not reliable measurements in every year, we only retain annual values when there are air archive measurements around the same time.The splines have 50 % attenuation at periods of 1 year.Figure D1 shows the original measurements and annual mole fraction data.

- 1 Figure 1 .
Figure 1.(a) Green's functions (G a→i ) relating the mole fraction at DSSW20K measurement depths to high-latitude southern hemispheric (SH) atmospheric mole fraction, from the firn models, with different colours for each depth.The dark coloured lines show the preferred Green's functions from the CSIRO model, while the lighter coloured lines show the other members of the ensemble of Green's functions, with the Green's functions from the LGGE-GIPSA firn model shown with the dot-dashed lines.(b) Green's functions (G e→a ) describing the relationship between atmospheric mole fraction in ppt in the high-latitude Northern Hemisphere (NH, dashed line) and high-latitude Southern Hemisphere (solid line) and annual global CF 4 emissions in Gg in preceding years, from the AGAGE 12-box model based on the spatial emissions distribution described in the text.We define mole fractions to correspond to the start of the year and emissions to correspond to the middle of the year.The x axis gives the time of emission relative to the time of atmospheric mole fraction.(c) Green's functions (G e→i ) relating the mole fraction at DSSW20K measurement depths to annual global CF 4 emissions, derived by combining the Green's functions in parts (a) and (b).Line styles and colours are as in (a).(d) Green's functions (G ef→i ) relating the mole fraction at DSSW20K measurement depths to annual global CF 4 emission factor in kg t −1 , derived by combining the Green's functions in part (c) with annual global primary aluminium production up to 1980.Line styles and colours are as in (a).

Figure 2 .
Figure 2. (a) Depth profiles of CF 4 mole fraction in the firn and ice.Lines show model results corresponding to inferred emissions from InvE2; symbols are measurements with 1σ uncertainties.(b) Green's functions from the CSIRO firn model (colours correspond to those in panel a).(c) Time history of mole fraction in the Northern Hemisphere (NH, dashed line) and Southern Hemisphere (SH, solid line) calculated with emissions inferred by InvE2.Symbols show annual values determined from atmospheric measurements in each hemisphere.(d) Emissions inferred from the three inversions, with 95 % confidence intervals.The dotted line shows the prior estimate based on a constant emission factor.(e) Emission factor inferred by the InvEF inversion with 95 % confidence intervals (blue) and constant prior (dotted).Emission factor estimated by Oye et al. (1999) for 1948 (orange circle) and recent estimates by the International Aluminium Institute (2014) (orange line, lower right corner).Primary aluminium production (U.S. Geological Survey, 2014; International Aluminium Institute, 2014) in 10 6 t (million metric tonnes) is shown with the grey line (right axis).

Figure 3 .
Figure 3. Inputs and results for the C 2 F 6 inversions.Panels, line styles and symbols are as in Fig. 2, except that Green's functions in (b) are dashed if the measured mole fraction is zero (or below detection).

Figure 4 .
Figure 4. Inputs and results for the C 3 F 8 inversions.Panels, line styles and symbols are as in Fig. 3.

Figure 5 .
Figure 5. (a) CF 4 emissions estimated by InvE2 with measurements from all sites (black) and with each site excluded one at a time.(b) CF 4 emissions estimated using alternative values of the regularisation parameter α.(c) CF 4 emissions estimated using alternative values of the pre-anthropogenic background level.(d) C 2 F 6 emissions inferred with the preferred Green's functions from the CSIRO (black solid line) and LGGE-GIPSA (blue dashed line) firn models.In all panels, our standard case is indicated in the legend by an asterisk, and the prior emissions are shown by the dotted lines.

Figure 6 .
Figure 6.Mole fraction depth profiles at the bottom of the firn and in the DE08-2 ice for (a) CF 4 , (b) C 2 F 6 and (c) C 3 F 8 .Solid lines show mole fraction depth profiles for the prior, dotted lines are InvE2 emissions and dashed lines are for InvEF emission factor.Symbols show measurements with 1σ uncertainties.

Figure 7 .
Figure 7. CF 4 and C 2 F 6 at Berkner Island and North GRIP.Symbols show measurements from Worton et al. (2007), which were not used in our inversions.Lines show modelled depth profiles created by convolving our inferred atmospheric mole fraction time series in the appropriate hemisphere with Green's functions from the LGGE-GIPSA firn model.CF 4 is shown in black (left axis) and C 2 F 6 in grey (right axis).

Figure 8 .
Figure 8.(a) CF 4 , (b) C 2 F 6 and (c) C 3 F 8 emissions (Gg yr −1 ) from 2000 for the InvE1 inversion in red and the InvE2 inversion in black.Uncertainty ranges shown for both models are 95 % confidence intervals.
is shown by the red dashed line, and we use this to convert the UEA firn measurements to the SIO-05 calibration scale as follows:[CF 4 ] SIO-05 = [CF 4 ] UEA + 0.117 1.0643 .The range given by the four different linear fits shown in Fig.A1a, as well as a linear fit that is forced through the origin [CF 4 ] SIO-05 = [CF 4 ] UEA /1.0621, is incorporated into the data uncertainties for the UEA measurements, to reflect uncertainty in the calibration scale conversion.The fit to all C 2 F 6 measurements gives [C 2 F 6 ] SIO-07 = [C 2 F 6 ] UEA − 0.0270 0.849 , C. M. Trudinger et al.: Perfluorocarbons since 1800 Appendix D: Annual mole fraction data from in situ and archive measurements

Figure
Figure D1.(a) Mace Head and Cape Grim in situ monthly CF 4 are shown by the solid lines.Cape Grim air archive and northern hemispheric air archive measurements are the open circles.Blue and green circles show selected northern hemispheric (NH) and southern hemispheric (SH) annual values from a spline fit to the observations that has 50 % attenuation at periods of 1 year.Error bars show 1σ uncertainties assigned to the annual means and used in the synthesis inversion.(b) Same for C 2 F 6 .(c) Same for C 3 F 8 .
, extending the estimated emissions www.atmos-chem-phys.net/16/11733/2016/Atmos.Chem.Phys., 16, 11733-11754, 2016 to the end of 2014. Figure 8 shows the estimated emissions from both the InvE1 and InvE2 inversions for the three PFCs from 2000.Our best estimates for CF 4 emissions from both inversions varied mostly within the range 11 ± 0.5 Gg yr −1 between 1998 and 2007, before dropping by about 15 % in 2009, presumably due to reduced economic activity associated with the GFC.CF 4 emissions in 2010 recovered some of this drop, then from 2011 to 2014 they varied about a mean level that was slightly higher than the 1998-2007 mean.The prior estimate for emissions growth rate used by the InvE1 inversion for CF 4 was constant (i.e.assumes no emissions growth) from 2008, so the inferred dip must be due to the atmospheric observations.Emissions of C 2 F 6 from the InvE2 inversion also show a dip in 2009, in addition to the already decreasing trend between 1998 and 2007.The InvE1 inversion does not show a clear C 2 F 6 dip.C 2 F 6 emissions in both inversions were fairly steady from 2010.C 3 F 8 emissions peaked about 2002, then decreased until 2012 and have been steady since.They do not seem to show an additional reduction around 2009 above the already decreasing trend, but both inversions have little interannual variability in their inferred emissions.The magnitude of the dip in the inferred emissions will be sensitive to the statistics of each inversion including data uncertainties and regularisation, although we see that the CF 4 dip barely changes with the choice of the regularisation parameter α in Fig. 5b.The growth rate of a trend curve with 650 day smoothing fitted to Mace Head monthly PFC mole fraction shows pronounced dips in 2009 in CF 4 and C 3 F 8 but only a small dip in C 2 F 6 .Global emissions of CO 2 show a dip in 2009 due to the GFC