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

Abstract

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 Niño-Southern Oscillation (ENSO). This is a companion paper to Kyrölä 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.

Trends in the average temperature in Finland, 1847–2013

“…Details of the construction procedure of a DLM model and estimations of model states and parameters can be found in Gamerman (2006) and in Petris et al (2009). We use an efficient adaptive MCMC algorithm by Haario et al (2006) and the Kalman filter likelihood to estimate the four parameters in h. The details of the estimation procedure can be found in Laine et al (2014) who use similar DLM model to study trends in stratospheric ozone concentrations. We also conducted our analyses with dlm-package in R-software (Petris 2010) to verify the computations.…”

“…The first describes a software package dlm for R statistical language that can be used to do the calculations described in this paper. We have used the Matlab software and computer code described in Laine et al (2014). In this work, we use a DLM to explain variability in the temperature time series using components for a smooth varying locally linear mean level, for a seasonal effect, and for noise that is allowed to have autoregressive correlation.…”

Merged SAGE II, Ozone_cci and OMPS ozone profile dataset and evaluation of ozone trends in the stratosphere

“…For this purpose, a multivariate regression has been applied to the merged SAGE-CCI-OMPS data: Kyrölä et al (2013) and Laine et al (2014), the best estimate of the turnaround point is in 1997 for the majority of latitude bands and altitude levels. The sensitivity of regression results to the choice of turnaround point is discussed in Harris et al (2015).…”

“…These data are biased and can induce artificial data drifts. GOMOS IPF V6 data have been combined into the merged SAGE II-GOMOS dataset, which was used for ozone trend analysis Kyrölä et al, 2013;Laine et al, 2014;Tummon et al, 2015;WMO, 2014). The new GOMOS ALGOM2s dataset used for the merged dataset has not only improved data quality in the UTLS, but it is also expected to be more stable in the whole atmosphere due to an advanced screening of unreliable data .…”

Detectability of the impacts of ozone-depleting substances and greenhouse gases upon stratospheric ozone accounting for nonlinearities in historical forcings

“…For analyses spanning both the depletion and ozone recovery periods, purely linear trends are inadequate for capturing the more complex nonlinear evolution of ozone change in certain parts of the stratosphere (as we will J. Bandoro et al: Detectability of the impacts of ozone depleting substances and greenhouse gases show later). Many ozone trend studies address this nonlinear behavior by performing piecewise linear regressions with a break point around 1997 (Bourassa et al, 2014;Chehade et al, 2014;Jones et al, 2009;Kyrölä et al, 2013;Laine et al, 2014). The slopes of the piecewise trends are not constrained by physical and chemical considerations and are typically arbitrarily chosen to enhance the slopes for each of the eras.…”