Analysing time-varying trends in stratospheric ozone time series using the state space approach

Abstract. We describe a hierarchical statistical state space model for ozone profile time series. The time series are from satellite measurements by the Stratospheric Aerosol and Gas Experiment (SAGE) II and the Global Ozone Monitoring by Occultation of Stars (GOMOS) instruments spanning the years 1984–2011. Vertical ozone profiles were linearly interpolated on an altitude grid with 1 km resolution covering 20–60 km. Monthly averages were calculated for each altitude level and 10° wide latitude bins between 60° S and 60° N. In the analysis, mean densities are studied separately for the 25–35, 35–45, and 45–55 km layers. Model variables include the ozone mean level, local trend, seasonal oscillations, and proxy variables for solar activity, the Quasi-Biennial Oscillation (QBO), and the El Nino–Southern Oscillation (ENSO). This is a companion paper to Kyrola et al. (2013), where a piecewise linear model was used together with the same proxies as in this work (excluding ENSO). The piecewise linear trend was allowed to change at the beginning of 1997 in all latitudes and altitudes. In the modelling of the present paper such an assumption is not needed as the linear trend is allowed to change continuously at each time step. This freedom is also allowed for the seasonal oscillations whereas other regression coefficients are taken independent of time. According to our analyses, the slowly varying ozone background shows roughly three general development patterns. A continuous decay for the whole period 1984–2011 is evident in the southernmost latitude belt 50–60° S in all altitude regions and in 50–60° N in the lowest altitude region 25–35 km. A second pattern, where a recovery after an initial decay is followed by a further decay, is found at northern latitudes from the equator to 50° N in the lowest altitude region (25–35 km) and between 40° N and 60° N in the 35–45 km altitude region. Further ozone loss occurred after 2007 in these regions. Everywhere else a decay is followed by a recovery. This pattern is shown at all altitudes and latitudes in the Southern Hemisphere (10–50° S) and in the 45–55 km layer in the Northern Hemisphere (from the equator to 40° N). In the 45–55 km range the trend, measured as an average change in 10 years, has mostly turned from negative to positive before the year 2000. In those regions where the "V" type of change of the trend is appropriate, the turning point is around the years 1997–2001. To compare results for the trend changes with the companion paper, we studied the difference in trends between the years from 1984 to 1997 and from 1997 to 2011. Overall, the two methods produce very similar ozone recovery patterns with the maximum trend change of 10% in 35–45 km. The state space method (used in this paper) shows a somewhat faster recovery than the piecewise linear model. For the percent change of the ozone density per decade the difference between the results is below three percentage units.