Quantifying contributions of chlorofluorocarbon banks to emissions and impacts on the ozone layer and climate

Chlorofluorocarbon (CFC) banks from uses such as air conditioners or foams can be emitted after global production stops. Recent reports of unexpected emissions of CFC-11 raise the need to better quantify releases from these banks, and associated impacts on ozone depletion and climate change. Here we develop a Bayesian probabilistic model for CFC-11, 12, and 113 banks and their emissions, incorporating the broadest range of constraints to date. We find that bank sizes of CFC-11 and CFC-12 are larger than recent international scientific assessments suggested, and can account for much of current estimated CFC-11 and 12 emissions (with the exception of increased CFC-11 emissions after 2012). Left unrecovered, these CFC banks could delay Antarctic ozone hole recovery by about six years and contribute 9 billion metric tonnes of equivalent CO2 emission. Derived CFC-113 emissions are subject to uncertainty, but are much larger than expected, raising questions about its sources.


Supplementary Methods 1 Direct Emissions and Release Fraction
We develop joint sample time series for direct emissions (DE), and release fractions (RF) using parameters to represent 1) how production is apportioned across each type of equipment, and 2) the timing of chlorofluorocarbon loss by equipment type for each year. We describe our priors for each of these parameters below, followed by a description of the sampling procedure.
Parameter 1: Proportion of production by equipment type Estimates for the distribution of production across equipment type are constructed using AFEAS production data (https:// unfccc.int). We assume that this AFEAS production data provides a basis for how production is apportioned across equipment type. The equipment type categories for CFC-11, CFC-12, and CFC-113 are shown in Tables S1, S2, and S3. We use annual production data from the years 1930 to 2000. For each year, we construct a prior distribution for each equipment type, k, as we do for total production, described above. That is, if Prod !,!,! is the reported production for equipment type, k, in year, t, then we assume the prior distribution for production follows a lognormal distribution such that Prod !,!~P rod !,!,! × 0.1 * Log 0,0.5 + 0.95 . For each sampled time series, we sample independently from the respective distribution for each equipment type and each year. After AFEAS data ends in 2000, we use that year for the priors in later years. The one exception is for the CFC-11 unexpected emissions scenario. Because we have no knowledge about the type of production for this additional emission scenario, for each sample time series we randomly partition production across equipment type, assuming each type to be equally probable.
Parameter 2: Emission function by equipment type Estimates for the emission function by equipment type are based on values from Ashford (2004). We construct prior distributions for each emission function related to the equipment types as given in Tables S1 -S3. Broadly, for equipment types with a year 1 emission rate equal to half of production, we chose priors with beta distributions and a standard deviation of 20% of year 1's emission rate. For slower release functions, where annual release fractions are a low percentage of the bank, we use a lognormal distribution for the prior with standard deviations of 15%-20% of the release rate. For emissions functions defined using a lifetime, we assume a lognormal distribution around the lifetime with a 20% uncertainty.

Constructing sampled time series
For Bayesian Parameter Estimation, we sample a total of 500,000 time series. For each joint sample of DE and RF, our sampling procedure is as follows: 1. For each year, t, and each equipment type, k, sample a production value Prod !,! from its prior distribution. 2. For each equipment type, k, sample an emission function for year 1's release rate EF !,!", , and for the banks release rate EF !,!"#$ from their prior distributions. We use the term !,!"#$ to refer to the release fraction specific to equipment type and RF to refer to the release fraction of a specific gas, which aggregates across all types of equipment for that gas. EF !,!" is the RF in the year of production, which we term Direct Emissions (DE) when aggregated across all equipment types. 3. For each equipment type, k, use the samples from Step 1 and Step 2 and simulate forward in time to create a sample time series for the bank (Bank !,! ), absolute direct emissions (DirectEmiss !,! ), and the bank's emissions (BankEmiss !,! ), as follows: The initial bank size for 1930 is assumed equal to zero.
4. Estimate total DE and RF by summing each equipment type's bank, absolute direct emissions, and bank emissions as follows: The resulting time series for DE ! and RF ! represents a sample from the prior distribution used in the Bayesian Parameter Estimate simulation model described in the main text. The time series for CFC-11, 12, and 113, are shown in Supplementary Figures 14-16.

Supplementary Note 1 CFC-113 Emissions and Lifetime Uncertainties
Uncertainties in CFC-113 lifetimes are sometimes estimated from observations of annual concentration changes by making assumptions about emissions (e.g., assumed zero emissions after the international global CFC phaseout date, which would clearly be an incorrect approach if additional emissions are actually occurring). Such an approach was taken to derive a very long upper limit to the CFC-113 lifetime uncertainty of around 109 years in the SPARC lifetime assessment. However, our analysis suggests that additional emissions are much more likely (see main text). We therefore estimate uncertainties in total CFC-113 emissions assuming an uncertainty range of +/-15% in the CFC-113 lifetime from the SPARC lifetime uncertainty estimate using tracer-tracer correlations (and adopted a best estimate of 85 years). Supplementary Figure 13 shows the result.
Recently, positive trends in the CFC-113a isomer 1 of 113 have been reported 1 ; those findings cannot account for the non-zero emissions shown below.

Supplementary Tables
Supplementary   Year 1: