On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range.

Decline and recovery of total column ozone using a multimodel time series analysis

Simulations of 15 coupled chemistry climate models, for the period 1960–2100, are presented. The models include a detailed stratosphere, as well as including a realistic representation of the tropospheric climate. The simulations assume a consistent set of changing greenhouse gas concentrations, as well as temporally varying chlorofluorocarbon concentrations in accordance with observations for the past and expectations for the future. The ozone results are analyzed using a nonparametric additive statistical model. Comparisons are made with observations for the recent past, and the recovery of ozone, indicated by a return to 1960 and 1980 values, is investigated as a function of latitude. Although chlorine amounts are simulated to return to 1980 values by about 2050, with only weak latitudinal variations, column ozone amounts recover at different rates due to the influence of greenhouse gas changes. In the tropics, simulated peak ozone amounts occur by about 2050 and thereafter total ozone column declines. Consequently, simulated ozone does not recover to values which existed prior to the early 1980s. The results also show a distinct hemispheric asymmetry, with recovery to 1980 values in the Northern Hemisphere extratropics ahead of the chlorine return by about 20 years. In the Southern Hemisphere midlatitudes, ozone is simulated to return to 1980 levels only 10 years ahead of chlorine. In the Antarctic, annually averaged ozone recovers at about the same rate as chlorine in high latitudes and hence does not return to 1960s values until the last decade of the simulations.

Impact of long-range correlations on trend detection in total ozone

Total ozone trends are typically studied using linear regression models that assume a first-order autoregression of the residuals [so-called AR(1) models]. We consider total ozone time series over 60°S–60°N from 1979 to 2005 and show that most latitude bands exhibit long-range correlated (LRC) behavior, meaning that ozone autocorrelation functions decay by a power law rather than exponentially as in AR(1). At such latitudes the uncertainties of total ozone trends are greater than those obtained from AR(1) models and the expected time required to detect ozone recovery correspondingly longer. We find no evidence of LRC behavior in southern middle-and high-subpolar latitudes (45°–60°S), where the long-term ozone decline attributable to anthropogenic chlorine is the greatest. We thus confirm an earlier prediction based on an AR(1) analysis that this region (especially the highest latitudes, and especially the South Atlantic) is the optimal location for the detection of ozone recovery, with a statistically significant ozone increase attributable to chlorine likely to be detectable by the end of the next decade. In northern middle and high latitudes, on the other hand, there is clear evidence of LRC behavior. This increases the uncertainties on the long-term trend attributable to anthropogenic chlorine by about a factor of 1.5 and lengthens the expected time to detect ozone recovery by a similar amount (from ∼2030 to ∼2045). If the long-term changes in ozone are instead fit by a piecewise-linear trend rather than by stratospheric chlorine loading, then the strong decrease of northern middle- and high-latitude ozone during the first half of the 1990s and its subsequent increase in the second half of the 1990s projects more strongly on the trend and makes a smaller contribution to the noise. This both increases the trend and weakens the LRC behavior at these latitudes, to the extent that ozone recovery (according to this model, and in the sense of a statistically significant ozone increase) is already on the verge of being detected. The implications of this rather controversial interpretation are discussed.

Summertime total ozone variations over middle and polar latitudes

The statistical relationship between springtime and summertime ozone over middle and polar latitudes is analyzed using zonally averaged total ozone data. Shortterm variations in springtime midlatitude ozone demonstrate only a modest correlation with springtime polar ozone variations. However by early summer, ozone variations throughout the extratropics are highly correlated. Analysis of correlation functions indicates that springtime midlatitude ozone, not polar ozone, is the best predictor for summertime polar ozone. Long-term total ozone trends at middle and high latitudes are also different for spring and nearly identical for summer. About 39% of the observed southern midlatitude ozone decline in December can be attributed to the polar ozone depletion up to November. In the Northern Hemisphere, the corresponding contribution is about 15%, but the error bars are too large to make an accurate estimate.