A multivariate auto-regressive combined-harmonics analysis and its application to ozone time series data

A new statistical approach is used to analyze Dobson Umkehr layer-ozone measurements at Arosa for 1979–1996 and Total Ozone Mapping Spectrometer (TOMS) Version 7 zonal mean ozone for 1979–1993, accounting for stratospheric aerosol optical depth (SAOD), quasi-biennial oscillation (QBO), and solar flux effects. A stepwise regression scheme selects statistically significant periodicities caused by season, SAOD, QBO, and solar variations and filters them out. Auto-regressive (AR) terms are included in ozone residuals and time lags are assumed for the residuals of exogenous variables. Then, the magnitudes of responses of ozone to the SAOD, QBO, and solar index (SI) series are derived from the stationary time series of the residuals. These Multivariate Auto-Regressive Combined Harmonics (MARCH) processes possess the following significant advantages: (1) the ozone trends are estimated more precisely than the previous methods; (2) the influences of the exogenous SAOD, QBO, and solar variations are clearly separated at various time lags; (3) the collinearity of the exogenous variables in the regression is significantly reduced; and (4) the probability of obtaining misleading correlations between ozone and exogenous times series is reduced. The MARCH results indicate that the Umkehr ozone response to SAOD (not a real ozone response but rather an optical interference effect), QBO, and solar effects is driven by combined dynamical radiative-chemical processes. These results are independently confirmed using the revised Standard models that include aerosol and solar forcing mechanisms with all possible time lags but not by the Standard model when restricted to a zero time lag in aerosol and solar ozone forcings. As for Dobson Umkehr ozone measurements at Arosa, the aerosol effects are most significant in layers 8, 7, and 6 with no time lag, as is to be expected due to the optical contamination of Umkehr measurements by SAOD. The QBO and solar UV effects appear in all layers 4-8, and in total ozone. In order to account for annual modulation of the equatorial winds that affects ozone at midlatitudes, a new QBO proxy is selected and applied to the Dobson Umkehr measurements at Arosa. The QBO proxy turns out to be more effective to filter the modulated ozone signals at midlatitudes than the mostly used QBO proxy, the Singapore winds at 30 mb. A statistically significant negative phase relationship is found between solar UV variation and ozone response, especially in layer 4, implying dynamical effects of solar variations on ozone at midlatitudes. Linear negative trends in ozone of −7.8 ± 1.1 and −5.2 ± 1.4 [%/decade ± 2σ] are calculated in layers 7 (∼35 km) and 8 (∼40 km), respectively, for the period of 1979–1996, with smaller trends of −2.2 ± 1.0, 1.8 ± 0.9, and −1.4 ± 1.1 in layers 6 (∼30 km), 5 (∼25 km), and 4 (∼20 km), respectively. A trend in total ozone (layers 1 through 10) of −2.9 ± 1.2 [%/decade ± 2σ] is found over this same period. The aerosol effects obtained from the TOMS zonal means become significant at midlatitudes. QBO ozone contributes to the TOMS zonal means by ±2 to 4% of their means. The negative solar ozone responses are also found at midlatitudes from the TOMS measurements. The most negative trends from TOMS zonal means are about −6.3 ± 0.6%/decade at 40–50°N.