I have developed a statistical time series analysis tool for use in examining time series of ozone data generated by satellite instruments, ground-based instruments, and model output. The uses the basic underlying model was originally developed for out 1991 ozone trends paper [Stolarski et al., 1991]. Since that time the statistical tool has been modified many times as the analysis time series got longer and the scientific issues moved forward. The present (2018) time series model, written in IDL is described below.
Ozone trends, solar cycle, QBO, ENSO and volcanic aerosol effects are estimated by
regression analysis. The regression model used is
Where μ, α1, α2, β1, β2, β3, γ, δ1, and δ2 are constants to be estimated. The model for the mean, μ, was a constant plus up to 4 seasonal harmonics of 12, 6, 4, and 3 months. The model can have a trend term and/or an EESC term. The EESC (Equivalent Effective Stratospheric Chlorine) term is adopted from Newman et al. [2007] and has 3 adjustable parameters (age of air, bromine efficiency relative to chlorine, and with of the distribution). The QBO is modeled using the two-EOF decomposition first described by Wallace et al. [1993] and subsequently used in this type analysis by Randel et al. [1995]. The solar term is modeled using the 10.7 cm radio flux measured at Ottawa. The El Chichon and Pinatubo terms are modeled by the 2D simulation of these effects to get a time delay from the aerosol perturbations that is consistent with that expected from the atmosphere. The 2D model used is that described by Fleming, et al. [2001], which obtains a reasonable representation of the age of air in the stratosphere and should thus get the time delays approximately correct. All of these terms have seasonal and semi-annual harmonics added to them. The terms for Pinatubo and El Chichon are given separate coefficients because the expected impact of volcanic aerosols is dependent on the background stratospheric chlorine concentration as described by Tie and Brasseur [1995]. The IDL code for the statistical code is here. The proxies are
| Discussion of proxies for time-series analysis | EESC Proxy | Solar Proxy | QBO Proxy | Volcanic Aerosol Proxy | ENSO Proxy | CO2 Proxy |
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Fleming, E.L., C.H. Jackman, D.B. Considine, and R.S. Stolarski (2001), "Sensitivity of tracers and a stratospheric aircraft perturbation to two-dimensional model transport variations", J. Geophys. Res. 106, 14245-14253.
Li, F., R.S. Stolarski, and P.A. Newman (2009), Stratospheric ozone in the post-CFC era, Atmos. Chem. Phys., 9, 2207-2213.
Newman, P.A., J.S. Daniel, D.W. Waugh, and E.R. Nash (2007), "A new formulation of Equivalent effective stratospheric chlorine (EESC)", Atmos. Chem. Phys. 7, 4537-4552.
Randel, W.J., F. Wu, J.M. Russell III, J.W. Waters, and L. Froidevaux (1995), "Ozone and temperature changes in the stratosphere following the eruption of Mount Pinatubo", J. Geophys. Res. 100, 16753-16764.
Stolarski, R.S., P. Bloomfield, R.D. McPeters, and J.R. Herman (1991), "Total ozone trends deduced from Nimbus 7 TOMS data" Geophys. Res. Lett. 18, 1015-1018.
Tie, X. X., and G. Brasseur (1995), The response of stratospheric ozone to volcanic eruptions: Sensitivity to atmospheric chlorine loading, Geophys. Res. Lett., 22(22), 3035-3038.
Wallace, J.M., R.L. Panetta, and J. Estberg (1993), "Representation of the equatorial stratospheric quasi-biennial oscillation in EOF phase space", J. Atmos. Sci. 50, 1751-1762.