Chlorine and bromine atoms lead to catalytic depletion of ozone in the stratosphere. Therefore the use and production of ozone-depleting substances (ODSs) containing chlorine and bromine is regulated by the Montreal Protocol to protect the ozone layer. Equivalent effective stratospheric chlorine (EESC) has been adopted as an appropriate metric to describe the combined effects of chlorine and bromine released from halocarbons on stratospheric ozone. Here we revisit the concept of calculating EESC. We derive a refined formulation of EESC based on an advanced concept of ODS propagation into the stratosphere and reactive halogen release. A new transit time distribution is introduced in which the age spectrum for an inert tracer is weighted with the release function for inorganic halogen from the source gases. This distribution is termed the “release time distribution”. We show that a much better agreement with inorganic halogen loading from the chemistry transport model TOMCAT is achieved compared with using the current formulation. The refined formulation shows EESC levels in the year 1980 for the mid-latitude lower stratosphere, which are significantly lower than previously calculated. The year 1980 is commonly used as a benchmark to which EESC must return in order to reach significant progress towards halogen and ozone recovery. Assuming that – under otherwise unchanged conditions – the EESC value must return to the same level in order for ozone to fully recover, we show that it will take more than 10 years longer than estimated in this region of the stratosphere with the current method for calculation of EESC. We also present a range of sensitivity studies to investigate the effect of changes and uncertainties in the fractional release factors and in the assumptions on the shape of the release time distributions. We further discuss the value of EESC as a proxy for future evolution of inorganic halogen loading under changing atmospheric dynamics using simulations from the EMAC model. We show that while the expected changes in stratospheric transport lead to significant differences between EESC and modelled inorganic halogen loading at constant mean age, EESC is a reasonable proxy for modelled inorganic halogen on a constant pressure level.

It is well established that chlorine and bromine atoms in the stratosphere
enhance ozone loss via catalytic reaction chains (Stolarski and Cicerone,
1974; Solomon, 1999; Molina and Rowland, 1974; Wofsy et al., 1975). Ozone
depletion has been observed at mid-latitudes (Pawson and Steinbrecht et al.,
2014) and in particular at high latitudes during winter and springtime
(Farman et al., 1985; Dameris and Godin-Beekmann et al., 2014). The chlorine
and bromine atoms responsible for the ozone depletion are not injected
directly into the stratosphere, but are released from organic halocarbons, so-called ozone-depleting substances (ODSs), which are emitted in the
troposphere. Ozone is thus depleted not by reactions with the chemicals
emitted but by reaction with the inorganic halogen released from these
chemicals. The extent of the catalytic ozone depletion depends on the amount
of inorganic halogen in the stratosphere. In models which include both
chemistry and transport of the stratosphere, the amount of inorganic halogen
can be directly calculated as Cl

The transport into and within the stratosphere is described by the mean age
of air,

For chemically active species, in addition to the transport, the chemical
loss leading to the release of inorganic halogen needs to be considered. This
release of inorganic chlorine and bromine from the halocarbon source gases is
characterized by the fractional release factor

This reference mixing ratio has typically been calculated using Eq. (1), i.e.
assuming that the chemically active gas propagates in the same way as a
chemically inert gas. Plumb et al. (1999) showed that the age spectrum

EESC is influenced by the temporal trends of the source gases, their
FRFs and the transport into the stratosphere. While
all these factors may vary with time, e.g. due to changes in stratospheric
circulation (Douglass et al., 2008; Li et al., 2012b),
FRFs in particular should not depend on the tropospheric trends of
the trace gases (Ostermöller et al., 2017). As in the
case of FRF, EESC is usually calculated as a function of mean age and again
a mean age value of 3 years is adapted for the lower stratosphere of the
middle latitudes and a mean age value of 5.5 years is used for polar winter
conditions in the lower stratosphere (Newman et al.,
2007). The formulation which is currently used to calculate EESC is based on
the concept of fractional release and mean age, using the age spectrum

In this paper we discuss the interaction of chemistry and transport in the propagation of chemically active tracers with tropospheric trends into the stratosphere and suggest an improved method for the calculation of EESC. The paper is organized as follows. In Sect. 2 we present some general thoughts on the propagation of tropospheric trends taking into account chemical loss. In Sect. 3 we derive a new mathematical formulation for EESC, based on the ideas developed in Sect. 2. This new mathematical formulation is applied in Sect. 4 to the scenario of source gas mixing ratios given by Velders and Daniel (2014) and the results are compared to their results for the estimated recovery of EESC to 1980 values. We also present sensitivity studies of the new EESC formulation to different parameters and compare the different formulations of EESC to simulations of inorganic halogen loading from two different comprehensive three-dimensional atmospheric chemistry models. Finally we draw some conclusions and present an outlook in Sect. 5.

Age spectrum

Age spectrum

In addition to transport and temporal trends in the troposphere, the
stratospheric mixing ratio of a species with chemical loss in the
stratosphere depends on the loss processes and on the interplay between
transport, chemical loss and the temporal trend (Volk et al., 1997; Plumb et
al., 1999). The age spectrum

We can now define a second transit time distribution,

For the calculation of

The new mathematical formulation of EESC proposed here is derived based on
the concept of how a trace gas of tropospheric origin with a temporal trend
and chemical loss in the stratosphere propagates into the stratosphere. The
organic source gases of chlorine and bromine are such gases. In order to
derive the amount of inorganic chlorine or bromine that has been released
from such an organic source gas at some point

As

For simplicity, we have assumed here that the source gas releases only one
atom of inorganic halogen. Transport and mixing are described by the transit
time distribution, also known as the age spectrum or Green's function

and the integral over all transit times weighted by their probability is the
mean age of air

We now use the new transit time distribution

As

We can, however, define a new, normalized release time distribution

The integral over

The integral over all transit times weighted by the normalized release time
distribution

The integral in the denominator of Eq. (12) represents the first moment of
the distribution of all FRFs, thus a mean FRF, which is a function of the location

Inserting Eq. (15) into Eq. (12) and solving for

Using the definition of

The term

In contrast to

After multiplying the right-hand side of Eq. (20) by the amount of halogen
atoms released from a halocarbon (

In order to apply this new formulation of EESC, the normalized release time
distribution

The arrival time distribution

In a similar way as for

In a similar way as for the mean release time, a mean arrival time

Multiplying (Eq. 22) with

Replacing

Extracting the transit-time-independent FRFs
(Ostermöller et al., 2017) from the integrals yields

All the integrals in Eq. (27) can be solved as they are the first moments of
the respective distribution functions: mean age

Again we express

Mean arrival time

Mean arrival time

For the calculation of mean release time

The FRFs from the most recent WMO reports are largely
based on observations from the time period 1996 to 2000
(Newman et al., 2007) and were derived using

In this formulation, the age spectrum for an inert tracer is used, which does
not include chemical loss. Solving (31) for

Equation (32) allows us to convert fractional release factors

Estimated temporal evolution of EESC for a mean age of 3 years using
the old (red line) and the new (black line) formulation of EESC. Also shown
is the difference (red dashed line) and the recovery date to 1980 values for
the old and the new formulation. Our new formulation yields a recovery date,
which is more than 10 years later than using the current formulation. This
shift in recovery date is mainly caused by the lower EESC levels calculated
for the increasing phase, i.e. the 1980 reference value. All values given
here are mole fractions given in ppt, which is equivalent to
pmol mol

The FRFs used for the reference calculation presented
in Sect. 4 are those used by Velders and Daniel (2014), modified using
Eq. (32) to be consistent with the new formulation given by Ostermöller
et al. (2017). The mean release time

The new formulation of EESC (Eq. 21) uses a loss-weighted transit time
distribution, the release time distribution and different FRFs from those used in the formulation (Newman et al., 2007). The new
FRFs are based on the formulation suggested by
Ostermöller et al. (2017) and have been derived from available FRFs (see Sect. 3.2). No method to calculate the release time
distribution is available so far. Both the mean release time

As already mentioned, new time-independent FRFs and
the release time distribution are needed for our new formulation of EESC.
The release time distribution is approximated assuming the form of an
inverse Gaussian with a species-specific first moment

The new time-independent FRFs are based on the concept
of arrival time distribution (Plumb et al., 1999). Ostermöller et
al. (2017) showed that using this concept, FRFs can be
calculated, which are independent of time, as long as stratospheric transport
or photochemistry remain unchanged. More specifically, these FRFs are independent of the tropospheric trend of the respective
species. We have recalculated FRFs used in the most
recent ozone assessment report (Harris et al., 2014) to be consistent with
the new formulation of fractional release. The FRFs
commonly used are largely based on observations (Newman et al., 2007), except
for the hydrochlorofluorocarbons HCFC-141b and HCFC-142b (Daniel et al.,
1995) (see Tables 1 and 2). Other observation-based FRFs have been presented by Laube et al. (2013). The uncertainty due to
the use of different FRFs, different emissions and
different lifetimes has been discussed in details by Velders and
Daniel (2014) . Here, we focus on the uncertainties due to the suggested new
formulation for the calculation of EESC. Using these new FRF values and the
mean arrival time

Recovery years for EESC to return to 1980 values and maximum EESC
values using our new formulation and the current formulation (Newman et al.,
2007), as shown in Figs. 3 and 4. In all cases the width

Estimated temporal evolution of EESC for a mean age of 5.5 years
using the old (red line) and the new (black line) formulation of EESC. Also
shown is the difference (red dashed line) and the recovery date to
1980 values for the old and the new formulation. Our new formulation yields a
recovery date to 1980 values, which is about 2 years later than using the
current formulation. The smaller shift in comparison to the calculation for
mean age of 3 years is due to the near complete fractional release of most
halogen source gases for these old air masses. All values given here are mole
fractions given in ppt, which is equivalent to pmol mol

Figures 3 and 4 show the calculation according to Eq. (21) using the new time-independent FRF values for mean ages of 3 and 5.5 years, respectively, and
compare it with the calculation applying formulation Eq. (3) using the FRF
values of the ozone assessment reports (Harris et al., 2014). All values
given here are mole fractions given in ppt, which is equivalent to
pmol mol

For polar winter conditions (mean age of 5.5 years) shown in Fig. 4, the recovery date calculated here is 2077, relative to a value of 2076 derived based on the currently used method using the same scenario (Velders and Daniel, 2014). The reason that only a very minor change is calculated for polar winter conditions is that under these conditions nearly all source gases are converted to their inorganic form and the differences between the age spectrum and the release time distribution become very small.

Influence of new fractional release factors for calculation of EESC
at a mean age of 3 years. In both calculations the new formulation of EESC
has been used, yet both calculations use different fractional release
factors. The calculation using the new fractional release factors (Table 1)
for mean age of 3 years is shown in black, while the calculation using the
original values as used by Velders and Daniel (2014) (VD2014) is shown in
red. As the fractional release factors currently used (Harris et al., 2014;
Velders and Daniel, 2014) are largely based on measurements (Newman et al.,
2007; Schauffler et al., 2003), which were taken during a period of rather
small tropospheric trends for most species, the change due to the new
formulation (Ostermöller et al., 2017) is rather small. For HCFCs 141b
and 142b, uncertainties on observational fractional release factors are large
and the same fractional release factors were used in both calculations, which
are based on the parameterization given by Velders and Daniel (2014). The
difference of the calculation using the VD2014 fractional release factors and
our new time-independent fractional release factors is shown as red dashed
line. The fractional release factors used here are summarized in Table 1. All
values given here are mole fractions given in ppt, which is equivalent to
pmol mol

As mentioned above, we will concentrate on the sensitivity of the new EESC
method on the limited knowledge of the new release time distribution

To evaluate the changes due to the changes in FRFs, we
use our new release time distribution

The new release time distribution

Recovery years for EESC to return to 1980 values and maximum EESC
values using different assumptions on the width of the release time
distribution

Sensitivity of EESC calculation using the new formulation for a mean
age of 3 years on the parameterization of the shape of the release time
distribution. In two cases the general shape was assumed to be an inverse
Gaussian function with different parameterizations of the width

Sensitivity of EESC calculation using the new formulation for a
mean age of 5.5 years on the parameterization of the shape of the release
time distribution. In two cases the general shape was assumed to be an
inverse Gaussian function with different parameterizations of the width

The scenarios with

Recovery years for EESC to return to 1980 values and maximum EESC
values varying the stratospheric lifetimes in the calculations of the mean
arrival time

The overall range of the calculated recovery dates is 2.2 years in the case
of 3-year mean age and 3.8 years in the case of 5.5-year mean age. The
recovery dates and the maximum values of EESC calculated under the different
assumptions are compared in Table 4. This rather small dependence on the
width of the applied transit time distribution even for the assumption of
extreme cases is due to two factors. Firstly, the deviation of tropospheric
trends from linearity in the years prior to the reference year of 1980 and
during the recovery phase after 2030 are rather small, in which case the
propagation values becomes independent of the shape of the distribution (Hall
and Plumb, 1994) and only depend on the first moment, i.e. the mean release
time

Another source of uncertainty is that the stratospheric lifetime of the
individual compounds needs to be known in order to calculate the mean arrival
time

Comparison of EESC using the formulation by Newman et al. (2007)
and the new formulation suggested here to TOMCAT model calculations
(Chipperfield et al., 2017) of ESC for southern hemispheric mid-latitude
conditions (3 years mean age). Fractional release values were calculated from
the model and differ from those shown in Table 1 but are used in order for
EESC and ESC to be consistent. The model simulation used here has fixed
dynamics, using 1980 meteorology. While small differences remain, the new
formulation yields much better agreement between EESC and ESC. All values
given here are mole fractions given in ppt, which is equivalent to
pmol mol

In order to evaluate our new formulation of EESC we have compared the results
of our calculations with the inorganic halogen loading calculated from two
comprehensive three-dimensional atmospheric chemistry models. Due to expected
long-term changes in mean age on a given pressure level associated with the
simulated changes in the Brewer–Dobson circulation (e.g. Butchart, 2014;
Austin and Li, 2006), changes in FRFs on mean age
levels are also observed in free-running model calculations (Douglass et al.,
2008; Li et al., 2012b). We have therefore compared our new formulation of
EESC to model calculations with changing and with annually repeating
(“fixed”) dynamics. To compare the new formulation with the formulation by
Newman et al. (2007), we used a model simulation from the TOMCAT model
(Chipperfield et al., 2017), which was driven by a repeated meteorology, in
this case for the year 1980. Effects due to changing dynamics, which are not
included in the concept of EESC, will thus not impact this calculation,
making it an ideal test bed for comparison of the two formulations. For long-term changes, we have used model results from the EMAC model (Jöckel et
al., 2016), which includes expected changes in stratospheric transport. As in
general the relationship between mean age and Cl

For comparison of the two formulations to model calculations with fixed dynamics, we used a TOMCAT model run (Chipperfield et al., 2017), which was driven by repeated 1980 meteorology. Output from this model run is available from the years 1960–2016. The FRFs derived from the model for the Northern Hemisphere are significantly higher as a function of mean age than the observed fractional release values. Southern hemispheric fractional release values for 3-year mean age showed better agreement with observation-derived FRFs (Newman et al., 2007). For this reason we compared simulated ESC from the Southern Hemisphere with EESC calculated using our new formulation and the formulation by Newman et al. (2007), in both cases using fractional release values derived for the year 2000 model results.

Figure 8 shows the comparison between the modelled ESC and EESC for a mean
age of 3 years calculated as described above, including all bromine and
chlorine species included in the model and also including inorganic chlorine
and bromine entering the stratosphere. As the differences between the two
formulations of EESC are most pronounced for 3-year mean age, we show
this comparison for 3-year mean age only. A much better agreement is
observed when applying the new formulation than using the formulation by
Newman et al. (2007) due to the improved treatment of the combined influence
of transport and mixing on chemical loss. Remaining discrepancies between
model ESC and EESC are most probably due to an imperfect parameterization of
the loss time distribution

Comparison of EESC at 3-year mean age using our new formulation
to model ESC evaluated at the 60 hPa level (corresponding to 3-year mean
age in 2000) and to ESC at 3-year mean age. Model data are from the EMAC
model as described by Jöckel et al. (2016). Fractional release values
were calculated from the model and differ from those shown in Table 1 but
are used in order for EESC and ESC to be consistent. The model simulation
shown here used prescribed trace gas scenarios, sea surface temperatures and
sea ice content. All values given here are mole fractions given in ppt,
which is equivalent to pmol mol

Under changing stratospheric dynamics (e.g. Butchart, 2014), it is expected that FRFs at a given mean age level will change (Douglass et al., 2008; Li et al., 2012b; Ostermöller et al., 2017). Therefore, the inorganic halogen loading as a function of mean age would be expected to change even if all source gases remained constant in time. Under such conditions, EESC is not expected to follow ESC on a given mean age level. To estimate the validity of EESC as a proxy for inorganic halogen loading of the stratosphere, we have compared our new formulation to a free-running chemistry–climate model simulation. We used data from the EMAC model simulation RC2-base-04 from the ESCiMo project for this (Jöckel et al., 2016). This simulation covers the 1950–2100 time frame with simulated sea surface temperatures and sea ice contents. As described above, we again calculated FRFs from the model in order to have results which are internally consistent. Northern hemispheric FRFs for the year 2000 are in good agreement with observation-based FRFs (Newman et al., 2007; Laube et al., 2013) and therefore we used northern hemispheric data for this comparison. In addition to comparing ESC on a fixed mean age level we also compared ESC on a fixed pressure level to our new formulation of EESC. A similar comparison has been presented in Shepherd et al. (2014), who compared model ESC on a fixed pressure level to EESC on a fixed mean age level (using the formulation of Newman et al., 2007), showing good agreement. Figure 9 compares the time evolution of EESC for 3-year mean age with model ESC at the 60 hPa level (corresponding to 3-year mean age in the year 2000) and model ESC at a mean age of 3 years. The year 2000 and the corresponding level of 60 hPa were chosen, as we also evaluated FRFs in the year 2000 of the model run. As expected, ESC at a mean age of 3 years deviates systematically from EESC, especially in the future when fractional release evaluated on a mean age surface changes significantly in the model. The agreement with ESC on a fixed pressure level is however much better. In this comparison EESC at a mean age of 3 years would slightly overestimate ESC on a pressure level in the future and significantly underestimate ESC on a mean age level. The exact magnitude of changes in stratospheric dynamics is highly uncertain but it has been shown that ESC evaluated at pressure levels is a good proxy to describe the influence of halogens on the ozone column (Shepherd et al., 2014; Eyring et al., 2010). Based on the much better agreement of EESC with ESC at pressure levels, we conclude that EESC is a reasonable proxy for the effect of halogen loading on stratospheric ozone, given the overall high uncertainties associated with the future evolution of stratospheric dynamics.

We have shown that for the calculation of the propagation of chlorine and bromine source gases with photochemical loss, different transit time distributions must be used to calculate the amount of organic or inorganic chlorine present at a given mean age level. First, treating the propagation of these tracers with the age spectrum for an inert tracer leads to fractional release values, which show a strong temporal variability in case of large tropospheric trends of the respective gas (Ostermöller et al., 2017). FRFs, which are independent of the tropospheric trends (Ostermöller et al., 2017), must be used to correctly describe the fraction that has been transferred from the organic source gas to the inorganic form and can then influence ozone chemistry. Secondly, changes in tropospheric mixing ratios lead to changes in stratospheric inorganic halogen with a time delay that is longer than the mean age, which describes the propagation of an inert tracer. This can be described by a modified transit time distribution, in which the transit times from the classical age spectrum are weighted with the chemical loss during this transport time. We suggest the term “release time distribution” for this modified tracer-specific transit time distribution.

We developed a new formulation of EESC, which uses the release time
distribution and time-independent FRFs calculated by
the method of Ostermöller et al. (2017). This approach more accurately
represents the amount of Cl

The two changes relative to the currently used formulation for EESC are the
use of new time-independent FRFs and of the release
time distribution. We have shown that the new time-independent FRFs do not differ very much from the FRFs
currently used (Harris et al., 2014; Velders and Daniel, 2014), as they were
derived during a period of rather small tropospheric trends for many species.
Consequently, the projected EESC recovery dates vary by 2 years or less,
depending on which FRFs are used. We have also shown
that the calculation of the recovery date shows some sensitivity to the
assumed width of the release time distribution, with variations of about
2 years for the mid-latitude calculations and 3.5 years for the high-latitude
case. Varying the stratospheric lifetimes assumed for the calculation of the
loss-weighted transit distribution

The work is based on the scenario developed by Velders and Daniel (2014). We have used the scenario “All_parameters_SPARC2013_mostlikely_mc.dat” given in the appendix to the paper by Velders and Danial (2014). For data availability of the EMAC simulation results we refer to Jöckel et al. (2016). The TOMCAT model results are available by emailing Martyn Chipperfield.

AE performed most of the calculations in the paper, wrote the manuscript and developed the ideas presented in the paper together with JO and HB in the frame of many open discussions. JO and HB both participated in the discussion and preparation of the manuscript. JO performed the calculations for the comparison with model data (Sect. 4.3.). SD and MC provided TOMCAT model results. PJ is PI of the ESCiMo project, conducted the EMAC model simulations and provided the corresponding data. All authors were involved in the final revision of the paper.

The authors declare that they have no conflict of interest.

This work was partly supported by DFG Research Unit 1095 (SHARP) under project numbers EM367/9-1 and EN367/9-2. The EMAC simulations have been performed at the German Climate Computing Centre (DKRZ) through support from the Bundesministerium für Bildung und Forschung (BMBF). DKRZ and its scientific steering committee are gratefully acknowledged for providing the HPC and data archiving resources for the consortial project ESCiMo (Earth System Chemistry integrated Modelling). The TOMCAT simulations were performed on the Archer and Leeds ARC supercomputers. We thank Wuhu Feng (NCAS) for help with the model. We thank Tanja Schuck and Joachim Curtius for comments on the manuscript. Edited by: Jan Kaiser Reviewed by: four anonymous referees