## Abstract

Statistical models that account for the separate influences on total atmospheric ozone of ozone-depleting substances, anthropogenic greenhouse gases, and natural processes are formulated from the Merged Ozone Data (MOD V8 and V8.6) and used to explore scenarios for ozone’s evolution from 1900 to 2100. The statistical models based on MOD V8 project larger growth in total ozone during the twenty-first century than do coupled chemistry–climate models globally and in the tropics where the chemistry–climate models indicate persistent ozone depletion. The statistical models based on MOD V8.6 suggest, instead, that total ozone everywhere never (or barely) recovers to 1980 levels. Since the decline in ozone-depleting substances and the increase in greenhouse gas concentrations are both expected to increase ozone in the twenty-first century, these results suggest that downward instrumental drifts may be present in MOD V8.6. Instrumental drifts, of opposite sign, may also be present in MOD V8 since it is possible to reduce the projections of the corresponding statistical models to agree with those of the chemistry–climate models by altering the long-term trends of the MOD V8 data within the estimated long-term uncertainty. Alternatively, the chemistry–climate models may project excess tropical ozone depletion by overestimating trends in the upwelling of tropical (ozone poor) air associated with global warming and the resultant decline in mean age of air. This possibility is consistent with independent observations that the age of stratospheric air has not declined during the past three decades, as the globe has warmed 0.3°C, and that model parameterizations of tropical convection may be inadequate.

## 1. Introduction

By regulating ozone-depleting substances (ODSs), the 1987 Montreal Protocol averted the collapse of Earth’s ozone layer and minimized biological impacts of excess solar UV radiation (WMO 2011). Since halogen gases strongly absorb infrared radiation, their regulation also averts future radiative forcing of surface climate additional to that by increasing concentrations of carbon dioxide, methane, and nitrous oxide greenhouse gases. As concentrations of ozone-depleting substances decrease and tropospheric greenhouse gases (GHGs) increase during the twenty-first century, the reliable detection of ozone’s recovery to 1980 levels and its subsequent evolution are primary challenges for atmospheric research. Moreover, climate change in response to growing concentrations of long-lived greenhouse gases is anticipated to have “an increasing influence on stratospheric ozone abundances in the coming decades” (WMO 2011), supplanting halogen gases as the primary source of anthropogenic ozone change.

Increased concentrations of GHGs may accelerate or decelerate ozone changes in different geographical regions and at different altitudes in Earth’s atmosphere (e.g., Rind et al. 1998; Waugh et al. 2009; Eyring et al. 2010). Increased GHGs in the upper stratosphere enhance radiative cooling to space, which increases ozone by, for example, slowing the catalytic chemical destruction cycles that involve ODSs. Increased concentrations of methane and nitrous oxide also affect ozone chemistry, in ways that depend strongly on dynamical and temperature changes (Revell et al. 2012). Increased GHG concentrations are expected to accelerate the global-scale Brewer–Dobson circulation, which decreases tropical ozone and increases midlatitude ozone by more rapid poleward transport from low latitudes (e.g., Eyring et al. 2010).

Since direct space-based observations of ozone exist only since 1970, knowledge of ozone’s evolution in the past and future must be obtained from model calculations. According to an ensemble of chemistry–climate model simulations that take into account the effects of both ODSs and GHGs on the atmosphere and ozone (Eyring et al. 2010; WMO 2011), annually averaged global total ozone is expected to recover to 1980 levels around 2032, some 20 years before stratospheric halogen lodes return to their 1980 levels, and then rise to 10 Dobson units (DU) (3%) above 1980 levels by 2100. The World Meteorological Organization (WMO) anticipates a “super” recovery in ozone at northern midlatitudes, which is more sensitive to greenhouse gas increases than at southern midlatitudes, and a protracted depletion in tropical ozone wherein levels in 2100 are projected to remain lower than in 1980. Internal model variability, limitations of model design and parameters, missing or poorly represented processes, and future emission scenarios all contribute uncertainties to chemistry–climate model simulations; the projection that global total ozone will be 10 DU higher in 2100 than in 1980, for example, has a 1σ uncertainty of at least 3.8 DU (WMO 2011).

The reason why tropical total ozone never recovers to 1980 levels by 2100 in chemistry–climate model simulations is because at low latitudes the increased GHG concentrations decrease lower-stratospheric ozone by more than the reduced ODSs increase upper-stratospheric ozone (e.g., Austin and Wilson 2006; Hegglin and Shepherd 2009). Tropical lower-stratospheric ozone decreases because GHG warming of the surface and lower atmosphere accelerates the upwelling of tropical ozone-poor air in the models. Although this strengthening of the Brewer–Dobson circulation with increased GHGs is a robust feature of chemistry–climate models (e.g., Butchart et al. 2006; Garcia and Randel 2008; Oman et al. 2010) it has, as yet, no direct observational support (Li et al. 2009). On the contrary, various observations suggest that stratospheric circulation has not changed even as GHGs have produced radiative climate forcing of 0.9 W m^{−2}. Some recent measurements indicate that there has been no change (or even an increase) in the mean age of stratospheric air, an indicator of circulation changes (Engel et al. 2009). Furthermore, chemistry–climate model simulations tend to overestimate both the decline in tropical total ozone (WMO 2011) and trends in topical tropospheric temperatures relative to observations in the past three decades (Mitchell et al. 2013). These differences suggest that the climate model parameterizations of the convective processes that facilitate the Brewer–Dobson circulation in chemistry–climate models may be inadequate, possibly compromising their projections of the evolution of ozone in the twenty-first century (Engel et al. 2009).

As an alternative approach to chemistry–climate model projections of twenty-first century ozone changes, statistical models of total atmospheric ozone are formulated directly from three decades of space-based measurements and projected forward using ODS and GHG future scenarios. The statistical models calculate the response of total ozone globally, in three different latitude zones, and regionally on a 5° × 10° latitude–longitude grid, to a linear combination of known drivers, specifically ODSs, GHGs, solar activity, volcanic aerosols, and oscillations, including the quasi-biennial oscillation (QBO) and El Niño–Southern Oscillation (ENSO). Even though multiple interactive and nonlinear processes couple ODS- and GHG-induced ozone changes, and would seem to preclude a linear formulation of ozone variability such as statistical models enact, chemistry–climate model simulations suggest that when vertically integrated, the linear (non) additivity of ozone responses to ODSs and GHGs is relatively small, and comparable to the overall uncertainty of the model projections (Eyring et al. 2010; WMO 2011).

Using the statistical models formulated with time series of ozone observations from the Merged Ozone Data (MOD; McPeters et al. 2007, 2013; McPeters and Labow 2012) and known drivers of ozone variability, the evolution of total atmospheric ozone is projected into the twenty-first century by inputting assumed changes in each of the drivers. Using historical information about the drivers, total atmospheric ozone is also reconstructed since 1900 to provide a past perspective for the present and future. The evolution of total atmospheric ozone in the twenty-first century evaluated using the statistical models with a range of scenarios of future ODSs and GHGs is compared with WMO’s synthesis of chemistry–climate model-based projections, considering uncertainties in both the statistical and chemistry–climate models, including those in the long-term calibration stability of the MOD V8 and V8.6 ozone datasets, and associated with the assumed linearity of the ODS and GHG components of the statistical models.

## 2. Observed and modeled total ozone variability

### a. Total ozone observations

Continuous space-based measurements of total atmospheric ozone have been made since November 1978, when a Total Ozone Mapping Spectrometer (TOMS) was launched on the *Nimbus-7* spacecraft (Balis et al. 2007). There now exist monthly regional climatologies of total ozone over more than three decades, obtained by cross calibrating and combining individual measurements made by the TOMS and Solar Backscatter Ultraviolet (SBUV) instruments (acd-ext.gsfc.nasa.gov/).

The MOD version 8 dataset (Stolarski et al. 2006; McPeters et al. 2007) extends from 1970 to 2011 and includes time series of global and zonal total ozone (toms_sbuv.v8.mod_v3.70–11.za.rev5) as well as total ozone values on a 5° × 10° latitude–longitude grid (toms_sbuv.v8.mod_v3.70–11.5×10.3.rev5). The algorithm used for V8 data processing, including adjustments for long-term sensitivity changes in the instruments, has been validated by comparisons with independent ozone datasets obtained using different algorithms (e.g., McPeters et al. 2008, Kroon et al. 2008) and the dataset itself has been validated against ground-based measurements (e.g., Antón et al. 2010). Instrument drift uncertainties are “slightly greater than 1% decade^{−1}” in the TOMS total ozone observations (Stolarski et al. 2006).

A new MOD version 8.6 ozone dataset (sbuv_v86_mod.int_lyr.70–12.za.r2.txt) has been released recently (McPeters et al. 2013), constructed by combining measurements made by eight SBUV instruments, utilizing the basic V8 algorithm but with new ozone absorption cross sections and new ozone and cloud-height climatologies (Bhartia et al. 2012). In MOD V8.6 the calibration adjustments are determined at the radiance level and do not rely on comparison of retrieved ozone products with other instruments (DeLand et al. 2012). The estimated long-term uncertainty is on the order of 3% for the 34-yr duration of the dataset, and the total column record is estimated to be accurate to within about 1% (McPeters et al. 2013).

Removing total ozone’s dominant seasonal variations by subtracting an average annual cycle (determined for all years) from the observations produces the time series of deseasonalized monthly averaged global (60°S–60°N) ozone anomalies (relative to 1980) shown in Fig. 1a for MOD V8 and Fig. 1f for MOD V8.6. Evident in both these records is a decline from 1979 to 1993, an increase to 2000, and approximately level ozone values for the decade thereafter, from 2000 to 2010. But average global total ozone decreased less from the decade 1980–90 to the decade 2000–10 in MOD V8 (−3.8 DU) than in MOD V8.6 (−4.7 DU). Figures 2a and 2f show the corresponding changes in tropical (25°S–25°N) total ozone in MOD V8 and MOD V8.6, respectively. Both the initial decline and subsequent increase are less pronounced than in global total ozone. Nevertheless, as with the global time series, the average tropical total global ozone decreased less from the decade 1980–90 to the decade 2000–10 in MOD V8 (−0.9 DU) than in MOD V8.6 (−1.6 DU).

### b. Models of total ozone variability

Statistical models formulated using multiple linear regression have been used extensively to interpret the ozone climatological record, with a primary goal of detecting and quantifying the effect of ODSs. Such models often specify a linear trend to represent general ozone depletion by anthropogenic gases and the 10.7-cm flux index to represent the solar influence on ozone (e.g., Reinsel et al. 2005; Randel and Thompson 2011). Halogen gas concentrations are no longer changing linearly; as a result of regulation by the Montreal Protocol they are now decreasing following a four-decade increase. To accommodate this, statistical models have been developed that use the effective equivalent stratospheric chlorine (EESC; Newman et al. 2007) to represent ODSs. Stolarski et al. (2006) used such a statistical model to extract the components of ozone variability in the TOMS observations for comparison with general circulation model simulations of stratospheric ozone from 1975 to 2025.

It is now understood that increasing GHG concentrations may also be affecting ozone, even as its depletion by halogen gases subsides. This has motivated the use of a linear trend (to represent GHGs) and the EESC (to represent ODSs) in statistical models. Dhomse et al. (2006) reported, however, that using either a linear trend or the EESC did not alter the statistical significance of their regression model of Northern Hemisphere ozone changes from 1979 to 2003. But a recent analysis of the relative sources of variability in the southern annular mode found evidence for both a linear trend and a connection with ODSs, represented by the EESC (Roscoe and Haigh 2007).

Statistical separation of the ODS and GHG anthropogenic components of ozone variability requires that the time series of ODS and GHG concentrations differ sufficiently, and are ideally orthogonal. This was not possible prior to the mid-1990s because until then the concentrations of ODSs and GHGs were both increasing with time. But for the past 16 years (since ~1997) ODS concentrations have decreased while GHG concentrations have continued to increase, suggesting that with more than 33 years of continuous ozone observations it may now be feasible to construct statistical models of total ozone variability that account separately for the influences of ODSs and GHGs, each specified by time series of their respective concentrations.

Such statistical models represent the observed total atmospheric ozone TAO_{obs} in terms of a model TAO_{model} that linearly combines the anthropogenic drivers with natural solar and volcanic influences and the internal quasi-biennial and El Niño oscillations and a residual term *R* as

with

where TAO_{0} is a baseline (invariant) ozone amount and the individual variability components are specified at time *t* (months) as

The indices *Q*_{30} and *Q*_{50} represent quasi-biennial oscillations in winds at 30 and 50 hPa, respectively (www.cpc.ncep.noaa.gov/data/indices/), *S* is the solar UV irradiance in a band from 200 to 295 nm, updated from Lean et al. (2005) using the Global Ozone Monitoring Experiment (GOME) Mg index of solar activity (www.iup.uni-bremen.de/gome/gomemgii.html; Skupin et al. 2004), *V* is the atmospheric optical depth at 500 nm, an index of volcanic activity (Sato et al. 1993; data.giss.nasa.gov/modelforce/strataer/), *E* is the MEI index of El Niño–Southern Oscillation (Wolter and Timlin 1998; esrl.noaa.gov/psd/enso/mei/), *O* is a representation of ODSs by the effective equivalent stratospheric chlorine, EESC A1_2010 (Newman et al. 2007; acd-ext.gsfc.nasa.gov/Data_services/automailer/), and *G* is the climate forcing by greenhouse gas concentrations specified by, for example, the representative concentration pathways (RCPs) (Moss et al. 2010; tntcat.iiasa.ac.at:8787/RcpDb/). The annual and semiannual oscillations accommodate imperfect deseasonalization. Inclusion of an ENSO-related component of ozone variability follows the detection of tropical ozone responses to this driver (Marsh and Garcia 2007). The lags *τ*_{Q30}, *τ*_{Q50}, *τ*_{E}, and *τ*_{V} (months) are chosen to maximize the observed variance that the model explains.

The presence of autocorrelation in the residual term, *R*(*t*), decreases the effective degrees of freedom in a regression model and correspondingly increases the uncertainties of the model coefficients. Following, for example, Wilks (1995) and Weatherhead et al. (1998), *R*(*t*) may be estimated from the residuals as a first-order autoregressive process of the form

where *c*_{1} is the autocorrelation of *R*(*t*) at lag *t* = 1 and is a white noise term. The autocorrelation of *R*(*t*) at lag *t* = 1 month provides an estimate of the decay time (to 1/*e*) of the residuals as *τ =* (1 + *c*_{1})/(1 − *c*_{1})/2. Conceptually, a decay time greater than 1 month reduces the effective number of degrees of freedom in the regression model by a factor *2τ* and inflates the uncertainties of the model coefficients by a factor (2*τ*)^{1/2} [J. T. Emmert 2013, personal communication, based on Emmert and Picone (2010, 2011)].

The coefficients TAO_{0} and *a*_{1}–*a*_{11} of the statistical models are determined from multiple linear regression using the observed monthly averaged deseasonalized total atmospheric ozone (MOD V8 from 1979 to 2011 and MOD V8.6 from 1979 to 2012), globally, and in zonal means of midlatitude and tropical latitude bands. Prior to the regression, the driver time series are converted from their native units to time series having zero mean and unit variance. In addition to the statistical models of total ozone globally and in three broad latitude bands, models of total ozone variability are also formulated for the 1296 individual points of the 5° × 10° latitude–longitude grid of MOD V8 observed (deseasonalized) ozone, to elucidate spatial patterns of ozone change and characterize the regional impacts of the individual drivers. (Latitude–longitude maps of MOD V8.6 total ozone are not yet available.)

In the statistical models of global total ozone (60°S–60°N), the ODS [Eq. (7)] is specified by EESC (P. A. Newman 2011, personal communication) with 3-yr mean age of air and a bromine scaling factor of *α* = 40 (denoted EESC 3,40). The EESC for tropical ozone is determined with 2-yr mean age of air and α = 30 (EESC 2,30), and for northern and southern midlatitudes (35°–60°) with 4-yr mean age of air and *α* = 45 (EESC 4,45). The mean age of air values used to evaluate EESC are obtained from an ensemble of measurements [see, e.g., Stiller et al. (2012), their Fig. 4, adapted from Waugh and Hall (2002)]. The observed average zonal mean age of air at 20 km (the approximate altitude of peak ozone concentration) is integrated over the appropriate latitude band of the ozone observations, weighted by zonal mean total ozone (in 1980) and the cosine area factor. The bromine scaling factors used to evaluate EESC are obtained by integrating the scaling factors (Daniel et al. 1999, their Fig. 5) over the respective latitude bands, weighted by zonal mean total ozone (in 1980) and the cosine area factor.

The statistical models of monthly averaged global (60°S–60°N) total ozone formulated from both the MOD V8 and V8.6 observations are shown as the solid black lines in Figs. 1a and 1f. The statistical models closely track the observed changes (symbols) over the entire record, accounting for 83% of the variance (*r* = 0.91) in both datasets. The 1σ standard deviation of the differences between the global total ozone measurements and models in Fig. 1a is 1.8 DU (MOD V8) and in Fig. 1f is 1.7 DU (MOD V8.6). The statistical models of monthly averaged tropical (25°S–25°N) total ozone, shown as the solid black lines in Figs. 2a (MOD V8) and 2f (MOD V8.6), similarly track the observed changes (symbols) over the entire record, accounting for 62% of the variance (*r* = 0.79) in both datasets. The 1σ standard deviation of the differences between the tropical total ozone measurements and model in Fig. 2a is 2.3 DU (MOD V8) and in Fig. 2f is 2.1 DU (MOD V8.6).

Figure 3 shows the time series of the residuals and their histograms and autocorrelation functions obtained using MOD V8 total ozone globally (Fig. 3a), in the tropics (Fig. 3b) and at northern and southern midlatitudes (Figs. 3c,d). The distributions of the residuals are approximately Gaussian and there is significant autocorrelation on times scales of months. For global total ozone (Fig. 3a), for example, the autocorrelation of the residuals at lag *t* = 1 month is *c*_{1} = 0.7 and the corresponding decay time is *τ =* (1 + *c*_{1})/(1 − *c*_{1})/2 = 2.8 months. This reduces the effective number of degrees of freedom by a factor of 5.6 and increases the uncertainties of the model coefficients by a factor of 2.4 relative to those obtained without consideration of the autocorrelation in the residuals.

Table 1 lists the coefficients and uncertainties (for the zero-mean, unit-variance driver time series) of the components of the statistical models of ozone variability, for global total ozone, total ozone in the tropics (25°S–25°N), and at northern (35°–60°N) and southern (35°–60°S) midlatitudes, formulated separately from the MOD V8 and MOD V8.6 datasets. The uncertainties given in Table 1 for the model coefficients are the 1σ uncertainties estimated from the covariance matrix of the residuals modeled as a first-order autoregressive process (following Emmert and Picone 2011). For the ODS and GHG components of the global total ozone model the uncertainties listed in Table 1 are factors of 2.3 and 2.2 larger, respectively, than the uncertainties estimated without accounting for autocorrelation, consistent with the expectation from the autocorrelation of the residuals shown in Fig. 3a.

The coefficients (*a*_{6}) for the ODS components in each of the statistical models formulated from both the MOD V8 and V8.6 datasets are factors of 3–10 larger than their estimated 1σ uncertainties (Table 1), which suggest that the ODS component is more than 99% significant in the statistical models of total ozone globally and in all three latitude zones. The coefficients (*a*_{7}) for the GHG components are at least a factor of 2 larger than their 1σ uncertainties (and therefore at least 95% significant) in the statistical models formulated from both the MOD V8 and V8.6 global total ozone datasets. As well, the coefficients of the GHG components exceed their 1σ uncertainties (and are therefore at least 66% significant) in the statistical models of total ozone in the tropics and at northern midlatitudes for the models formulated from the MOD V8 dataset (but not at southern midlatitudes) and in the tropics and at southern midlatitudes for the models formulated from the MOD V8.6 dataset (but not at northern midlatitudes). This suggests that separation of these two different anthropogenic drivers of total ozone variability is statistically feasible globally and in at least some zonal bands using both the extant 33-yr MOD V8 and 34-yr MOD V8.6 datasets.

To better assess the significance of including both the ODS and GHG drivers, the statistical models were reformulated using only one (instead of two) anthropogenic component (alternatively ODSs or GHGs). For the statistical models formulated from both the MOD V8 and MOD V8.6 datasets the standard deviation of the residuals increases when just the ODS or just the GHG time series is used. And in all cases the ODS times series, alone, explains a larger fraction of the variance in observed total ozone (i.e., the correlation coefficient of is higher) than does the GHG time series, alone. Table 2 summarizes the performances of these altered statistical models formulated from the MOD V8 dataset relative to the models that include both the ODS and GHG drivers.

To quantify the significance of using either the ODS or the GHG time series in the statistical models, an *F* value *F*_{replace} was determined for this index replacement, following Roscoe and Haigh (2007) and von Storch and Zwiers (1999), as

where and are the sum of squares of the statistical model [as defined, e.g., by Wilks (1995, p. 164)] using, respectively, the ODS and GHG drivers, is the sum of squares of the error (residual) of the statistical model and observations, and df is the number of degrees of freedom. For the statistical models formulated from both the MOD V8 and V8.6 datasets the use of the ODS time series instead of the GHG time series is more than 99% significant in all four geographical regimes (global, tropics, and northern and southern midlatitudes). Table 2 lists specific values of *F*_{replace} and the quantities used to evaluate this [Eq. (11)] for the statistical models formulated from the MOD V8 dataset.

To test whether inclusion of the GHG component in addition to the ODS component is warranted in the statistical models, the level of significance of this added index was determined by calculating an *F* value *F*_{add} of the addition, again following Roscoe and Haigh (2007) and von Storch and Zwiers (1999), as

where is the sum of squares of the statistical model using both the ODS and GHG drivers in the model and is the sum of squares of the residual of the statistical model and observations. According to this metric, using the GHG driver in addition to the ODS driver in the statistical models is most significant in the statistical models of global total ozone. Specifically, this addition is 98.1% (99.0%), 85.8% (74.3%), 80.1% (18%), and 55.5% (72.2%) significant in the statistical models of global, tropical, northern midlatitude, and southern midlatitude total ozone time series from the MOD V8 (V8.6) dataset. Table 2 also lists specific values of *F*_{add} and the quantities used to evaluate this [Eq. (12)] for the statistical models formulated from the MOD V8 dataset. Only for the statistical model formulated from the MOD V8.6 total ozone dataset at Northern Hemisphere midlatitudes is inclusion of the additional GHG component not significant with greater than 50% confidence.

The tests summarized in Table 2 substantiate inclusion of both the ODS and GHG terms in the statistical models of total ozone globally and in broad latitudinal bands. Similar statistical models were then developed for total ozone in each of the individual 5° × 10° latitude–longitude grids using the MOD V8 dataset (only, since the MOD V8.6 gridded dataset is not yet available). The close agreement evident in Fig. 4 between the regional distributions of observed and reconstructed total ozone in 1980 (Figs. 4a,b) prior to significant ODS-related depletion, and in 1996 (Figs. 4c,d) near the time of maximum ODS-related depletion, indicates that the statistically modeled total ozone latitude–longitude maps capture the observed regional patterns of total ozone change. In both the observations and the statistical model total ozone decreased from 1980 to 1996 more at midlatitudes than in the tropics.

### c. Variability components

Figures 1b–e and 1g–j compare the changes in global total ozone (relative to 1980) that the statistical models formulated from, respectively, the MOD V8 and MOD V8.6 datasets attribute to individual natural and anthropogenic drivers, converted from their native units to equivalent Dobson units by the coefficients obtained from the multiple linear regression analysis. Global total ozone changes in response to the QBO, ENSO, solar, volcanic, and ODS influences are qualitatively similar in the statistical models formulated from the two different ozone datasets, but differ quantitatively. MOD V8 infers a solar cycle increase of ~4.5 DU from the minimum to maximum of recent solar activity cycles, a decrease of ~4.5 DU as a result of the Pinatubo volcanic eruption, and a decrease of 10 DU in response to increasing ODSs from 1980 to 1996. MOD V8.6 infers a smaller solar cycle increase of ~3.5 DU, a larger Pinatubo-related decrease of ~5.5 DU, and a smaller decrease in global total ozone of 8 DU in response to increasing ODSs from 1980 to 1996. However, global total ozone changes attributed to the GHG influence differ in both magnitude and sign in the statistical models derived from the MOD V8 and V8.6 datasets: whereas MOD V8 has an increase of 3 DU in response to increasing GHGs from 1980 to 2009, MOD V8.6 has a decrease of 2 DU.

The relative strengths of the various drivers for tropical total ozone, shown in Figs. 2b–e and 2g–j for the statistical models formulated from the MOD V8 and MOD V8.6 datasets, respectively, differ somewhat from those of global total ozone but exhibit similar patterns. Compared with MOD V8.6, MOD V8 infers larger changes during the solar cycle and in response to ODSs, and a positive (versus negative) response to GHGs. Similar differences are also present in the statistical models formulated from the MOD V8 and MOD V8.6 total ozone at northern and southern midlatitudes, namely larger changes in response to the solar and ODS influences, and responses of opposite sign to GHGs. Note in particular that the statistical model formulated from the MOD V8.6 dataset does not attribute any variability in midlatitude Northern Hemisphere total ozone to solar irradiance changes [the coefficient *a*_{3} for the solar UV irradiance driver (see Table 1) is zero in this particular statistical model], whereas in the statistical model formulated from the MOD V8 dataset, the magnitude of this coefficient is at least 66% significant.

The natural and anthropogenic drivers of total atmospheric ozone produce characteristic regional patterns that combine at any given time to alter total ozone in different ways depending on geographical location. Figure 5 compares the regional patterns and their corresponding zonal mean profiles determined for each of the natural drivers by evaluating Eq. (1) on the 5° × 10° latitude–longitude grid of the MOD V8 total ozone observations. Figure 6 compares the regional patterns and their corresponding zonal mean profiles determined for the two anthropogenic drivers. The regional patterns integrate to reproduce the individual global components determined independently (i.e., as shown in Figs. 1 and 2). The specific combinations of the individual regional patterns that produce the statistical model of total ozone distribution in 1980 and 1996 are shown in Figs. 4b and 4d, to illustrate that their net effect captures the observed regional distribution in Figs. 4a and 4c.

The statistical model of the MOD V8 gridded ozone data indicates patterns of response to natural influences that are broadly consistent with current physical understanding. The ENSO response (Fig. 5a) is overall anticorrelated with the MEI index and peaks in the tropics (Marsh and Garcia 2007). The QBO influence (Fig. 5b) is strongly concentrated at the equator, volcanic aerosols decrease ozone, especially in the Northern Hemisphere (Fig. 5c) (Randel et al. 1995), and the solar influence (Fig. 5d) is primarily positive with increasing solar UV irradiance and extends broadly across low and midlatitudes (Hood 1997). The patterns of ozone response to anthropogenic influences are more ambiguous. The influence of increasing ODSs (Fig. 6a) is everywhere negative, with minimum depletion at topical latitudes and maximum depletion at mid- to high latitudes, with approximate hemispheric symmetry. This differs somewhat from chemistry–climate model simulations that suggest a stronger response to ODSs at southern midlatitudes and a weaker response at northern midlatitudes (WMO 2011, their Fig. 3-10). Consistent with the chemistry–climate model simulations, the statistical model formulated from the MOD V8 gridded dataset indicates that increasing GHG concentrations increase total atmospheric ozone most at northern mid- to high latitudes (Fig. 6b). But contrary to the chemistry–climate model simulations, the MOD V8 gridded statistical model indicates that total ozone also increases (rather than decreases) throughout the topics. The Southern Hemisphere response in Fig. 6b is, as indicated in Table 1, not significant in the statistical models formulated from the MOD V8 dataset.

## 3. Total ozone changes 1900–2100

Inputting to the statistical models appropriate scenarios for past and future drivers of ozone variability allows the reconstruction of historical total atmospheric ozone prior to observations and the projection of future levels. Solar UV irradiance is reconstructed prior to 1979 using solar indices and a model of the transport of magnetic flux on the sun’s surface (Lean et al. 2005). Solar cycles after 2012 are assumed identical to solar cycle 24. Figure 7 shows the adopted scenarios of anthropogenic climate forcings and ozone-depleting substances from 1900 to 2100.

The four representative concentration pathways (Moss et al. 2010) shown in Fig. 7a provide scenarios for future radiative climate forcings that range from approximately 2.6 to 8.5 W m^{−2} in the year 2100 (relative to preindustrial conditions) and are the core scenarios for climate change simulations in the Intergovernmental Panel on Climate Change Fifth Assessment Report (IPCC AR5; Taylor et al. 2012). RCP6.0, for example, stabilizes radiative climate forcing near 6.0 W m^{−2} in the postindustrial period, which corresponds to 2.35°C global warming from 1980 to 2100, assuming climate sensitivity is 0.56°C (W m^{−2})^{−1} of forcing. For comparison with the RCP scenarios, Fig. 7a also shows scenario A1B of the IPCC Special Report on Emission Scenarios (SRES; Nakicenovic and Swart 2000), used in climate modeling studies for IPCC's Fourth Assessment Report (AR4; Solomon et al. 2007) and WMO’s (2011) chemistry–climate model simulations (Eyring et al. 2010). As implemented in the statistical models, the GHG scenarios are equivalent prior to 2011 and diverge from 2012 to 2100.

The effective equivalent stratospheric chlorine EESC A1_2010 index encapsulates the effect of halogen compounds on ozone (Newman et al. 2007). This ODS index depends strongly on the adopted mean age of air, and to a lesser extent on the age of air spectrum width and bromine scaling factor α. Shown in Fig. 7b are three different EESC time series (normalized to unit amplitude) determined for mean age of air *A* and bromine scaling factor *α* corresponding to the globe (*A* = 3, *α* = 40), tropics (*A* = 2, *α* = 30), and midlatitudes (*A* = 4, *α* = 45). In each case the age of air spectrum width equals half the mean age of air.

Using statistical models to extrapolate total ozone beyond the epoch of direct observations—whether in the past or future—assumes that the relationship of ozone to its drivers remains the same as that defined [by Eq. (2)] for the period of the observations. Because ODSs and GHGs affect ozone through complex interrelated mechanisms, including chemical reactions (e.g., temperature dependent and CH_{4} and N_{2}O chemistry) and dynamical processes (e.g., the effect of GHG enhancements on the Brewer–Dobson large-scale circulation in the stratosphere), the response of ozone to anthropogenic influences is expected to change, relative to the present period, as GHGs increase (Fig. 7a) and ODSs decrease (Fig. 7b) throughout the twenty-first century.

For the vertically integrated ozone column (i.e., the total atmospheric ozone considered here), however, chemistry–climate model investigations suggest that such nonlinearities manifest minimally, if at all. To test linear additivity, Eyring et al. (2010) compared total ozone changes simulated from 1960 to 2100 using time-varying ODSs and GHGs with the sum of the changes simulated with varying ODSs (and fixed GHGs) and varying GHGs (and fixed ODSs). Relative to the ozone change from 1960 to 2100 accruing from simultaneously varying ODSs and GHGs, a linear combination of the separate ODS- and GHG-induced changes underestimates tropical total ozone by 2 DU, overestimates total ozone by 5 DU at northern midlatitudes, and is no different at southern midlatitudes (differences from 1980 to 2100 are comparable or smaller). These nonlinearities are less than the uncertainties in WMO’s synthesis of chemistry–climate model projections of total ozone in 2100 (3.2, 8.2, and 8.5 DU for tropical and midlatitude Northern and Southern Hemisphere total ozone, respectively); they are sufficiently small to encourage use of the statistical models to explore the evolution of total atmospheric ozone in the twenty-first century.

### a. Reconstructions of past total ozone

Shown in Fig. 8a is a reconstruction of global total ozone changes since 1900 (relative to 1980), estimated by the statistical model formulated from the MOD V8 dataset in response to the adopted natural and anthropogenic drivers (GHGs, Fig. 7a; and EESC with mean age of air *A* = 3 years and α = 40 for ODSs, Fig. 7b). Figure 8 also shows the contributions of individual drivers of the total ozone changes; QBO and ENSO (Fig. 8b), solar and volcanic activity (Fig. 8c), and ODSs and GHGs (Fig. 8d). The historical reconstruction is compared in Fig. 8a with MOD V8 global total ozone observations from 1980 to 2011 (the period for which the statistical model was formulated) and with earlier space- and ground-based observations, beyond the epoch for which the statistical model was formulated. The reconstructed global total ozone anomaly in 1970 is 3–4 DU higher than the MOD V8 observations, a difference that encompasses estimated instrument drift uncertainties of “slightly greater than 1% per decade” in the TOMS total ozone observations (Stolarski et al. 2006), equivalent to 3+ DU from 1970 to 1980. The evolution of reconstructed global total ozone from 1926 to 2007 is also broadly consistent with long-term changes in (deseasonalized) total ozone measured at Arosa, Switzerland (Scarnato et al. 2010). These comparisons suggest that the approach of extrapolating historical total ozone by inputting past drivers to the statistical models appears to be plausible. Figure 9 shows the total ozone regional distributions and zonal means corresponding to the global changes in 1960 (Fig. 9a) and 1996 (Fig. 9b), relative to 1980.

For the first half of the twentieth-century reconstructed global total ozone in Fig. 8a exceeds 1980 levels, reaching levels 8 DU higher in 1960 during the peak of solar activity in cycle 19. Table 3 lists numerical values that the statistical models formulated from both the MOD V8 and V8.6 datasets estimate for total ozone changes in 1900, 1960, and 1996 (relative to 1980), globally, in the tropics, and in northern and southern midlatitudes, determined as the net change arising from both natural and anthropogenic drivers. The specific times in Table 3 correspond to the gray vertical bars in Fig. 8. Table 3 also separately lists total ozone changes estimated for the individual (ODS and GHG) and combined anthropogenic influences. Although total ozone’s value in 1980 is widely adopted as a metric for future ozone recovery from anthropogenic influences (e.g., Austin et al. 2010), recent modeling studies (e.g., Fleming et al. 2011), the Arosa observations, and the statistical models (shown in Fig. 8d and listed in Table 3) indicate that by 1980 ODSs may have already caused a total ozone decline comparable in magnitude to the subsequent decline from 1980 to 1996; the statistical model of global total ozone formulated from MOD V8 (V8.6) estimates that total ozone declined 11 (8) DU from 1900 to 1980 and a further 10 (8) DU from 1980 to 1996 in response to increasing ODSs (Table 3).

### b. Projections of future total ozone

Shown also in Fig. 8a are global total ozone changes (relative to 1980) projected to 2100 with the statistical model formulated from the MOD V8 dataset. Estimates of future drivers input to the statistical model have the impacts on ozone shown individually in Figs. 8b–d. The GHG twenty-first-century scenario used for the projections in Fig. 8 is SRES A1B (Fig. 7a), shown in Fig. 8d converted from units of watts per square meter to equivalent DU by the model’s *a*_{7} coefficient [Eq. (8)]. Since WMO’s (2011) ozone projections considered only the ODS and GHG drivers (omitting natural variability scenarios), Fig. 8a also shows the statistical model projections of twenty-first-century total ozone changes arising from just these two anthropogenic drivers.

Table 3 lists numerical values for the net change in total ozone that the statistical models project in response to both natural and anthropogenic drivers in 2025, 2050, 2075, and 2100 (relative to 1980), as shown globally in Fig. 8a, and also in the tropics and in northern and southern midlatitudes (the gray vertical bars identify these times in Fig. 8). Also given in Table 3 are the total ozone changes estimated for the individual ODS, GHG, and combined anthropogenic influences; these latter values allow direct comparisons with WMO’s chemistry–climate model projections, which are listed in Table 3 in parentheses. Figure 9 shows the regional distributions and zonal means corresponding to the global changes in 2025 (Fig. 9c) and 2075 (Fig. 9d), relative to 1980, accordingly to the statistical model of the MOD V8 gridded ozone data.

Estimates of total ozone’s increase in the near term, from 1980 to 2025, due to anthropogenic influences (combined ODSs and GHGs) made with the statistical models formulated from both the MOD V8 and MOD V8.6 datasets agree with the projections of WMO’s chemistry–climate models to within their combined estimated uncertainties. Figure 10 compares these two different projections and their overlapping uncertainties: the uncertainties shown for the statistical models are determined by combining the 1σ uncertainties of the ODS and GHG coefficients (Table 1) while those for the chemistry–climate models are 1σ estimates for combined internal variability and model uncertainties (taken directly from WMO’s Fig. 3-17). Figure 10 and Table 3 nevertheless indicate that, overall, the changes in total ozone from 1980 to 2025 projected by the statistical models formulated from MOD V8 globally (1 ± 2 DU), at northern midlatitudes (4 ± 14 DU), and at southern midlatitudes (−4 ± 9 DU) are numerically closer to the chemistry–climate model projections (−2 ± 4 DU globally, 3 ± 9 DU in northern midlatitudes, and −5 ± 6 DU in southern midlatitudes) than are the MOD V8.6-based statistical model projections (−7 ± 2 DU globally, −9 ± 11 DU in northern midlatitudes, and −14 ± 8 DU in southern midlatitudes).

Beyond 2025, the projections of the two sets of statistical models (formulated from the MOD V8 and MOD V8.6 datasets) diverge from each other, and both diverge from the chemistry–climate model projections. Figure 11 compares these different projections for the SRES A1B GHG scenario (shown as the dashed lines in Fig. 11), as well as for the four RCP GHG scenarios (solid lines in Fig. 11). By 2100 the statistical model formulated from MOD V8 projects (for the SRES A1B GHG scenario) that global total ozone will be 21 ± 6 DU higher than in 1980 whereas the statistical model formulated from MOD V8.6 projects that global total ozone will be 7 ± 5 DU lower. WMO’s projection of a 10 ± 4 DU increase (values taken directly from WMO’s Table 3-3 and Fig. 3-17), shown by the circles in Fig. 11 and listed in parentheses in Table 3, is consistent in sign with that of the MOD V8-based statistical model, but it is a factor of 2 smaller in magnitude. The statistical model formulated from MOD V8 also projects that tropical total ozone will increase throughout the twenty-first century, to 13 ± 6 DU above 1980 levels by 2100. In distinct contrast, the statistical model formulated from MOD V8.6 and the chemistry–climate models both project that tropical total ozone levels in 2100 will be lower than in 1980, by 3 ± 5 DU and 3 ± 3 DU, respectively.

With all four RCP scenarios (with EESC 3-yr mean age of air and α = 40), as well as with the SRES A1B scenario, the statistical models formulated from the MOD V8 (V8.6) dataset project larger (smaller) anthropogenic increases in global total atmospheric ozone throughout the twenty-first century relative to WMO’s chemistry–climate models. These differences are evident in Fig. 11a. The situation is similar in tropical regions (Fig. 11b) where, for all four RCP scenarios (with EESC 2-yr mean age of air and α = 30) and the SRES A1B scenario, the MOD V8-based statistical model projects higher tropical total ozone values throughout the twenty-first century than do the chemistry–climate models, whereas the statistical model formulated from MOD V8.6 projects approximately equivalent tropical total ozone levels.

The uncertainty estimates of the statistical model projections for 2025 shown in Fig. 10 and for 2100 in Fig. 11 are ±1σ estimates, obtained from the statistical uncertainties of the model coefficients, only. For neither the statistical model formulated from MOD V8 nor the statistical model formulated from MOD V8.6 does the 1σ uncertainty in global total ozone projected for 2100 overlap with the 1σ uncertainty given for WMO’s chemistry–climate model projections. This suggests that there is at least a 66% chance that the statistical models, as formulated, disagree with the WMO projections. For the statistical model formulated from MOD V8 the 2σ uncertainty does overlap the WMO values, so the differences are not certain at the 95% level: In IPCC parlance they are “likely” (Mastrandrea 2010). But for the statistical model formulated from MOD V8.6 not even the 2σ uncertainty overlaps the uncertainty of the WMO projections, so in this case the differences in global total ozone are “very likely.” Correspondingly, the differences between the projections of tropical total ozone by the model formulated from the MOD V8 dataset and those of the chemistry–climate models (Fig. 11b) are “likely.”

There are also differences between the statistical and chemistry–climate model projections of total ozone evolution in the twenty-first century at northern midlatitudes that Figs. 11c and 11g illustrate. As with global and tropical total ozone, the statistical model formulated from the MOD V8 dataset projects a larger total ozone increase (with SRES A1B and EESC age of air 4 yr and α = 45) from 1980 to 2100 (52 ± 31 DU) than does WMO (22 ± 8 DU), whereas the statistical model formulated from MOD V8.6 projects a minimal (1 ± 26 DU) increase. These differences are within the combined ±1σ uncertainties of the statistical and chemistry–climate model projections. At southern midlatitudes the projections shown in Fig. 11d of the statistical model formulated from MOD V8 (with SRES A1B and EESC age of air *A* = 4 yr and α = 45) of an increase of 26 ± 21 DU in total ozone from 1980 to 2100 relative to 1980 are relatively consistent with WMO’s (2011) chemistry–climate model projections of an increase of 19 ± 9 DU. However, the projections of the statistical model formulated from MOD V8.6, shown in Fig. 11h, that total ozone at southern midlatitudes will decease 16 ± 20 DU from 1980 to 2100, are not consistent.

### c. Uncertainties in model projections

How meaningful are differences between the statistical and chemistry–climate model projections of twenty-first-century total ozone changes and what might their causes be? Limitations of the statistical model formulation and implementation may contribute additional uncertainties to the projections of total ozone in the twenty-first century not captured by the statistical uncertainties of the model coefficients. This section considers five additional sources of uncertainty and discusses the extent to which each may (or may not) explain the differences between the statistical and chemistry–climate model projections of total ozone in the twenty-first century. Discussed are 1) calibration drifts in the MOD V8 and V8.6 total ozone datasets, 2) the (limited) length of the total ozone datasets, 3) seasonal ODS and GHG dependencies, 4) nonlinearities between the GHG and ODS components, not accommodated in a linear statistical model, and 5) representation of the ODSs by the EESC formulation.

#### 1) Total ozone dataset drifts

It can be assumed that drifts are present in the calibration of one or both of the MOD V8 and V8.6 total ozone datasets, since the total ozone projections made using the statistical models formulated from these two different datasets diverge during the twenty-first century; by 2100 the changes in total ozone relative to 1980 are, respectively, +21 ± 6 and −7 ± 5 DU globally, +13 ± 6 and −3 ± 5 DU in the tropics, +52 ± 31 and +1 ± 26 DU at northern midlatitudes, and 26 ± 21 and −16 ± 20 DU at southern midlatitudes (Table 3d).

The reason for the divergence of the twenty-first-century projections of total ozone made by the statistical models formulated from the MOD V8 and V8.6 datasets is the models’ quite different representations of the GHG component; their ODS-related changes from 1980 to 2100 are equivalent to within 2 DU (Table 3b). Because the temporal structure of the GHG component in the statistical models is approximately linear during the epoch of 1979 to 2012, it is inseparable from long-term calibration drifts in the total ozone observational dataset. The statistical models formulated from the MOD V8 total ozone dataset estimate total ozone growth throughout the twenty-first century globally, in the tropics, and at midlatitudes because of in-phase relationships of total ozone with GHGs, whose concentrations increase in twenty-first-century emission scenarios, augmenting the increase in total ozone from declining ODSs. The opposite is true for the statistical models formulated from the MOD V8.6 total ozone dataset where the projected decline of total ozone in 2100 relative to 1980 in global, tropical, and southern midlatitude total ozone occurs because of out-of-phase relationships of total ozone with (increasing) GHG concentrations, which more than cancel the increase in total ozone from declining ODSs.

Lines fitted directly to the total ozone time series of the MOD V8 and MOD V8.6 datasets quantify the differences in their long-term trends. Table 4 compares the magnitudes of these linear trends. Overall downward trends are present in both the MOD V8 and MOD V8.6 datasets, globally, in the tropics, and at northern midlatitudes, but in MOD V8.6 the trend magnitudes are, respectively, 20%, 142%, and 21% larger than in MOD V8 (MOD V8 and V8.6 trends agree to within 2% at southern midlatitudes). As a result, the net decrease in total ozone over the three decades from 1980 to 2010 is everywhere less in MOD V8 than in MOD V8.6. Figure 12 shows time series of the differences (DU) of these two datasets to illustrate how their relative calibrations evolve from 1979 to 2011. Over this 33-yr period, the MOD V8.6 total ozone values have a net decline relative to the MOD V8 values of 1.68 DU globally, 1.65 DU in the tropics, 1.82 DU at northern midlatitudes, and 0.83 DU at southern midlatitudes.

The largest differences between the MOD V8 and V8.6 datasets occur between 1994 and 1996 (Fig. 12). This time period corresponds to the merging of measurements of total ozone made by SBUV instruments on the *National Oceanic and Atmospheric Administration* (*NOAA*)*-11* and *NOAA-14* spacecraft, each using different calibration techniques (DeLand et al. 2012). As noted earlier (section 2a), and evident in comparisons of Figs. 1a and 1f and Figs. 2a and 2f, the average level of total ozone decreases less from 1980–90 to 2000–10 in the MOD V8 dataset than in the MOD V8.6 dataset. Were the absolute values of the *NOAA-14* SBUV total ozone measurements too low by ~1 DU relative to those of the *NOAA-11* SBUV total ozone measurements, then their merging in the MOD V8.6 composite would manifest as a (spurious) decrease in total ozone after 1996, relative to total ozone prior to 1994, and this decrease would produce an apparent downward trend in the 34-yr record.

To better assess the impact of long-term trends in the MOD V8 and V8.6 total ozone datasets on the statistical model projections, the models were reformulated after artificially altering the long-term trends in the observations to force the statistical models projections of total ozone in 2100 to agree with those of WMO’s chemistry–climate models. Table 4 lists the altered linear trends in the MOD V8 and V8.6 datasets that bring the (reformulated) statistical model projections into agreement with the chemistry–climate model projections of ozone levels in 2100. A resolution between the statistical and chemistry–climate model projections is clearly possible, were the calibration drifts in MOD V8 (V8.6) to have been overcorrected (undercorrected) by amounts less than 1% decade^{−1}, which is within the uncertainty of the long-term trends in the MOD V8 and V8.6 datasets.

As noted above, calibration drift uncertainties in the TOMS total ozone observations are estimated to be “slightly greater than 1% decade^{−1}” (Stolarski et al. 2006). Those in the composite of SBUV total ozone observations that compose the MOD V8.6 dataset are similar, on the order of 3% for the 34 years of the dataset. But in the tropics, in particular, there are long-standing differences between the TOMS total ozone trends and those derived from integration of ozone profiles measured by the Stratospheric and Gas Experiment (SAGE). For example, Randel and Wu (2007) showed that whereas the TOMS total tropical ozone declined ~1 DU from 1979 to 2005 (about 0.14% decade^{−1}), the vertically integrated SAGE tropical ozone declined about 7 DU (about 0.97% decade^{−1}). Ground-based observations support the extant MOD V8 dataset in showing little or no decline in tropical total ozone (e.g., Fioletov et al. 2002).

#### 2) Length of total ozone dataset

How robust are the statistical model projections of ozone evolution throughout the twenty-first century in terms of the statistical model formulations from (just) 33+ years of total ozone observations? To test the stability of the statistical model projections, model coefficients [i.e., the coefficients *a*_{1 }*… a*_{11} in Eqs. (3)–(8)] were derived from shorter epochs of the MOD V8 and V8.6 total ozone datasets. Figure 13 compares projected changes in total ozone from 1980 to 2100 obtained using statistical models formulated (on the left) for five different epochs of observations (each beginning in 1979 and ending sequentially in years 2008–12) and (on the right) for an additional five different epochs of observations (beginning sequentially in years 1980–84 and each ending in 2012).

The statistical model projections for total ozone in 2100 compared in Fig. 13 are essentially invariant with the length of the dataset used to construct the model, providing that the cross correlation of the ODS and GHG time series (shown in the bottom panels in Fig. 13) is less than ~0.6. In particular when using the epoch from 1984 to 2012, this cross correlation is ~0.2 and the 2100 projections made with the corresponding statistical model agree with those made using the model formulated from the full dataset. Thus, reformulating the statistical models from fewer years of the primary 33-yr ozone dataset does not alter the results shown in Figs. 8, 10, and 11 or the overall conclusions that the projections made by the statistical models formulated from MOD V8 (V8.6) of the changes in total ozone from 1980 to 2100 likely overestimate (underestimate) those of WMO’s chemistry–climate models (hatched regions in Fig. 13).

#### 3) Seasonal GHG and ODS dependencies

Can seasonal differences in the statistical model coefficients account for differences from the chemistry–climate model projections? The statistical model formulation [Eq. (2)] does not explicitly allow for seasonal differences of the ozone response to the various drivers. Although the models are formulated using all months of available ozone data (i.e., data from all seasons, each well sampled in the MOD V8 and V8.6 datasets) the resultant seasonally invariant coefficients represent the annually averaged responses. To assess the effect of total ozone’s seasonal sensitivity to ODSs and GHGs, the statistical models were formulated using only the months pertaining to each of the four seasons [i.e., December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON)]. The dashed lines in Figs. 1d and 1j and Figs. 2d and 2j are the corresponding ODS and GHG seasonal components, which bracket and track the annually averaged responses closely. This suggests that seasonal dependencies are unlikely to explain the differences between the statistical and chemistry–climate model projections.

#### 4) Nonlinearities between GHGs and ODSs

Might the statistical model projections misrepresent twenty-first-century ozone changes because of nonlinearities in ozone’s response to combined GHG and ODS influences, for which the statistical models do not account? Linear additivity is estimated to be <1, −2, 5, and 0 DU for the globe, tropics, and northern and southern midlatitudes; these are the amounts by which a linear combination of total ozone’s responses to ODSs and GHGs individually underestimates the simultaneous response, according to chemistry–climate models simulations [Eyring et al. 2010; see their Figs. 4c and 7 and also WMO (2011) Fig. 3-10]. These values are too small to account for the differences between the statistical and chemistry–climate models (Table 3). Furthermore, in the tropics, the overestimate (by up to 2 DU) of the simultaneous response relative to the linearly combined individual ODS and GHG responses actually increases (slightly) the discrepancy between total tropical ozone projection for 2100 using the MOD V8-based statistical model and that of the chemistry–climate models.

Nevertheless, total ozone observations and models integrate complex atmospheric responses to both ODSs and GHGs that are strongly height dependent and that may evolve with time, including in the troposphere (Young et al. 2013). To the extent that the statistical and chemistry–climate models fail to capture these details then their respective determinations of total atmospheric ozone will differ; variations in tropical total atmospheric ozone are particularly sensitive to the balance between the increase in upper-stratospheric concentrations and the decrease in lower-stratospheric concentrations (Eyring et al. 2010).

#### 5) Representation of ODSs

How dependent are the statistical model projections on the representation of ODSs by the EESC, a convenient but imperfect proxy that depends strongly on the mean age of air used for its formulation? The comparisons of the statistical and chemistry–climate model projections shown in Figs. 10 and 11 and discussed above utilize EESC scenarios evaluated with mean age of air values derived from observations and bromine scaling factors estimated by models, weighted by total ozone amount and cosine latitude and integrated over the relevant geographical regions (globe, tropics, midlatitudes). When the EESC is formulated with shorter age of air, its time profile peaks earlier (Fig. 7b). This different temporal structure alters the attribution of ODSs and GHGs in the statistical models. For example, in the statistical models formulated from the MOD V8 dataset the earlier the EESC time profile peaks, the smaller the resultant GHG component and the smaller the corresponding GHG-related ozone growth in the twenty-first century, bringing the statistical model projections into better agreement with WMO’s chemistry–climate model projections.

To assess how a different EESC formulation may alter the future ozone changes that the statistical models project, new statistical models were formulated from the MOD V8 dataset using alternative EESC profiles corresponding to shorter age of air, specifically mean age of air *A* = 2.5 yr and bromine scaling factor α = 40 globally, *A* = 1 yr and α = 30 in the tropics, *A* = 3 yr and α = 40 at northern midlatitudes, and *A* = 3.5 yr and α = 45 at southern midlatitudes. The resultant tropical total ozone increase from 1980 to 2100 is now smaller, in the range of 4–9 DU for the four RCP scenarios, but still larger than, and still of opposite sign to, the chemistry–climate model projection of −3 ± 3 DU. For total ozone globally and in northern midlatitudes, differences between the statistical and chemistry–climate models’ twenty-first-century projections now agree to within their combined 1σ uncertainties.

But although using the altered instead of the default EESC scenarios can bring the statistical model projections into agreement with the chemistry–climate model projections, these replacements can degrade the statistical models’ representations of present-day observed total ozone estimates. Calculating *F*_{replace}, analogously to Eq. (11), as

gives *F*_{replace} = 2 (with df = 68) for global total ozone and *F*_{replace} = 2.5 (with df =70) for tropical total ozone. That these replacements are, respectively, 84% and 88% significant indicates that the default EESC time series give superior statistical model performance relative to the alternative EESC time series. This is consistent with the default EESC scenarios for the globe and tropics being more realistic than the altered EESC scenarios; according to observations, a 3-yr mean age of air is more appropriate for the globe than is the 2.5-yr age of air.

A related issue is that the EESC formulations used to construct the statistical models and their projections have constant mean age of air. According to chemistry–climate models, increasing greenhouse gases are expected to alter the age of air in the range of −0.05 to −0.2 yr decade^{−1} (Waugh 2009), although the recent observations by Engel et al. (2009) were not able to detect such trends. Since a shorter age of air results in smaller EESC and correspondingly larger total ozone, such trends in the future would increase the discrepancy between the statistical and chemistry–climate model projections, rather than help resolve it.

## 4. Discussion: Total ozone recovery and future changes

The lack of agreement of the MOD V8 and V8.6 datasets about total ozone’s long-term changes indicates that spurious instrumental trends are present in one or both of these datasets. Such calibration drifts manifest in the statistical models as equivalent GHG signals, whose changes are also essentially linear over the years from 1979 to 2012 of the MOD total ozone datasets. An overall downward trend that is too small (large) in MOD V8 (V8.6) total ozone relative to ozone’s true changes would therefore produce a corresponding trend in the GHG component of the statistical models that is too large (small), thereby generating spurious changes in 2100 when the GHG component is extrapolated into the future.

The indication by the statistical models formulated from the MOD V8.6 dataset that during the twenty-first century global (and southern midlatitude) total ozone will never recover to 1980 levels, declining to levels in 2100 that are as much as 14 DU lower (Fig. 11), globally, than in 1980, is a physically implausible scenario. According to current understanding of the physical processes that alter total atmospheric ozone, decreasing concentrations of ODSs and increasing concentrations of GHGs are expected to increase global and midlatitude total ozone throughout the twenty-first century. Spurious long-term downward trends in the MOD V8.6 dataset are a likely reason for these physically unlikely projections. The merging of the *NOAA-11* and *NOAA-14* observations around 1995 may be a source of such calibration drifts in the MOD V8.6 dataset. It is at this time that the MOD V8 and V8.6 datasets have their largest discrepancies, and the average values of MOD V8.6 total ozone in the decade 2000–10 (after this merge) are overall lower (relative to the decade 1980–90 before the merge) by ~1 DU than are MOD V8 total ozone levels. And since the time of this merge coincides approximately with the Pinatubo volcanic eruption and the descending phase of solar cycle 23, the resultant uncertainties may account for differences in the solar and volcanic components of the statistical models formulated from the MOD V8 and V8.6 datasets.

To the extent that the MOD V8 dataset affords a more realistic representation than does the MOD V8.6 dataset of true ozone changes in the past 33 years, and if the statistical models formulated from the MOD V8 dataset are plausible, why might the chemistry–climate model projections underestimate the growth of total ozone during the twenty-first century in the tropics?

The reason why the chemistry–climate models project protracted tropical ozone depletion throughout the twenty-first century is because, although increasing greenhouse gas concentrations cool the stratosphere, which increases ozone through changes in chemistry, surface warming accelerates the upwelling of tropical ozone-poor air into the lower stratosphere. The depletion of lower-stratospheric ozone more than counters the growth of upper-stratospheric ozone accruing from both the cooler upper stratosphere and diminished catalytic destruction by declining ODSs. The increased tropical upwelling and associated stratospheric wave drag accelerates the stratosphere’s large-scale Brewer–Dobson circulation with accompanying midlatitude downwelling preferentially in the Northern Hemisphere, which produces total ozone’s “super” recovery at northern midlatitudes. One inference from the twenty-first-century projections of the statistical models formulated from the MOD V8 total ozone dataset is that chemistry–climate models may overestimate tropical upwelling and ozone depletion in response to increasing GHGs. However, were this the case, the chemistry–climate model projections of total ozone at northern midlatitudes would be correspondingly reduced, since in these models a decreased Brewer–Dobson circulation transports less ozone to midlatitudes, which would widen the discrepancy of the statistical and chemistry–climate models at midlatitudes. More generally, hemispheric differences in midlatitude ozone may not depend as strongly on Brewer–Dobson circulation transport as the chemistry–climate models suggest (Garny et al. 2012).

Recent observations that stratospheric mean age of air (an indicator for stratospheric circulation) has not changed noticeably in the past three decades, even as the surface has warmed (Engel et al. 2009), do suggest that chemistry–climate models may overestimate the effect of surface global warming on stratospheric ozone because of exaggerated Brewer–Dobson acceleration. Consistent with this are recent indications that modeled changes in tropical upper-troposphere temperature in recent decades typically exceed the observed changes, except in models with very high-altitude resolution, which better parameterize the convective transport of surface warming to the troposphere. Comparisons of observations and models of the mean age of stratospheric air have already “highlighted certain problems with transport in the models” (Waugh and Hall 2002); at 20 km, for example, the chemistry–climate models appear to systematically underestimate observed mean age of air by a factor of 2, which suggests that they overestimate the current strength of the Brewer–Dobson circulation.

If chemistry–climate models do have a high ozone-depletion bias, then stratospheric-to-tropospheric ozone flux (Hegglin and Shepherd 2009), radiative and dynamical stratospheric forcing of surface climate (WMO 2011), and projections of future surface UV radiation doses (Taalas et al. 2000; WMO 2011) would also need to be reconsidered.

## 5. Summary

Statistical models formulated from the MOD V8 and V8.6 total ozone datasets that account individually for anthropogenic ODSs and GHGs as well as natural influences explain in the range of 46% (at northern midlatitudes) to 83% (globally) of the observed variance in total ozone between 1979 and 2012. Global total atmospheric ozone in 1996 was 11 DU lower than in 1980 (and ~19 DU lower than near its twentieth-century peak in 1960), primarily as a result of increased halogen gas concentrations. Projections made by the statistical models formulated from the MOD V8 dataset suggest global and tropical total ozone may recover to 1980 levels by as soon as 2025 and increase to levels that in 2100 are the highest in two centuries, in the range of 11–29 DU above 1980 levels globally, and 6–18 DU in the tropics (depending on GHG emissions).

The statistical models formulated from the MOD V8.6 dataset suggest the opposite scenario, that global total ozone will not recover to 1980 levels, declining to levels in 2100 as much as 14 DU lower, globally, than in 1980. This latter scenario is deemed implausible because decreasing concentrations of ODSs and increasing concentrations of GHGs are both expected to increase ozone throughout the twenty-first century. Spurious long-term downward trends in the MOD V8.6 dataset are a likely reason for these physically unlikely projections.

The statistical models formulated from the MOD V8 dataset project increases in tropical total ozone in the range 6–18 DU from 1980 to 2100 (depending on GHG emissions) that exceed the projections by WMO’s chemistry–climate models, according to which total tropical ozone will be 3 ± 3 DU lower (not higher) in 2100 than in 1980. It is unlikely that this difference between the statistical and chemistry–climate model projections of twenty-first-century total ozone in the tropics is caused by the statistical model failing to account for nonlinearities between the ODS and GHG-induced processes, since these difference exacerbate (by a few DU) the differences rather than reconcile them. Nor can it be reconciled by altering the EESC profile using a range of plausible mean age of air scenarios.

A possible explanation for the differences between the projections made by the statistical models formulated from the MOD V8 dataset and those of the chemistry–climate models is an overcorrection of long-term drifts in the observations used to construct the MOD V8 dataset, since imposing larger long-term trends on this dataset, within its estimated 1% decade^{−1} uncertainty, brings the statistical model projections into agreement with the chemistry–climate model projections.

It is also possible that chemistry–climate models overestimate the impact of GHG-induced changes in the stratosphere, exaggerating trends in tropical upwelling and overaccelerating the Brewer–Dobson circulation. This scenario is consistent with recent observations that the age of stratospheric air has changed little in the past three decades, even with greenhouse gas forcing of 1 W m^{−2} and net global surface warming of 0.3°C from 1980 to 2011, and that modeled changes in tropical ozone and upper-troposphere temperature in recent decades may overestimate the observed changes. Improvements may therefore be needed in chemistry–climate model transport, for example in the parameterizations of dynamic and convective processes that connect the tropical troposphere and stratosphere.

Statistical models themselves have notable limitations, and further work is needed to improve these models and validate their usefulness as a bridge between observations and physical models. An application of the statistical model formulation to chemistry–climate model simulations in the present, with comparisons of their respective projections in the past and future, is one possible approach. Nevertheless, these comparisons of the statistical models formulated from the two different ozone datasets with each other, and with chemistry–climate model simulations, underscore the challenge of reliable attribution and understanding of the recovery and evolution of total atmospheric ozone in the twenty-first century. Continued ozone observation and reanalysis are crucial to extend and improve the datasets, improve statistical models, and validate chemistry–climate model simulations. Resolving the differences between statistical and chemistry–climate model simulations of ozone responses to natural and anthropogenic drivers will increase confidence in projections of ozone evolution in the twenty-first century.

## Acknowledgments

NASA funded this work. Discussions with Richard Stolarski, Paul Newman, and David Rind are very much appreciated, as are numerous thoughtful and constructive comments by the reviewers, who pointed out, among other things, the discrepancy between the long-term trends in the MOD V8 and MOD V8.6 datasets and between the TOMS and SAGE tropical total ozone observations, and suggested the utility of statistical model formulations of chemistry–climate model simulations. Also acknowledged are extensive discussions with John Emmert and J. Michael Picone about statistical models; especially appreciated is their invaluable help implementing the code to calculate statistical model uncertainties taking into account autocorrelation.

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