Trends in stratospheric ozone profiles using functional mixed models

Abstract

Abstract. This paper is devoted to the modeling of altitudedependent patterns of ozone variations over time. Umkehr ozone profiles (quarter of Umkehr layer) from 1978 to 2011 are investigated at two locations: Boulder (USA) and Arosa (Switzerland). The study consists of two statistical stages. First we approximate ozone profiles employing an appropriate basis. To capture primary modes of ozone variations without losing essential information, a functional principal component analysis is performed. It penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data-driven basis functions (empirical basis functions) are obtained. The coefficients (principal component scores) corresponding to the empirical basis functions represent dominant temporal evolution in the shape of ozone profiles. We use those time series coefficients in the second statistical step to reveal the important sources of the patterns and variations in the profiles. We estimate the effects of covariates -month, year (trend), quasibiennial oscillation, the solar cycle, the Arctic oscillation, the El Niño/Southern Oscillation cycle and the Eliassen-Palm flux -on the principal component scores of ozone profiles using additive mixed effects models. The effects are represented as smooth functions and the smooth functions are estimated by penalized regression splines. We also impose a heteroscedastic error structure that reflects the observed seasonality in the errors. The more complex error structure enables us to provide more accurate estimates of influences and trends, together with enhanced uncertainty quantification. Also, we are able to capture fine variations in the time evolution of the profiles, such as the semi-annual oscillation. We conclude by showing the trends by altitude over Boulder and Arosa, as well as for total column ozone. There are great variations in the trends across altitudes, which highlights the benefits of modeling ozone profiles.

Regional trend analysis of surface ozone observations from monitoring networks in eastern North America, Europe and East Asia

“…The GAM is also widely applied to the spatial analysis of regular or irregular data in order to account for geographical variability (Wood and Augustin, 2002;Wood, 2004). The generalized additive mixed model (GAMM) is an extension of GAM and allows for the incorporation of complex autocorrelation, and is therefore flexible for multi-site modeling (Carslaw et al, 2007;Ambrosino and Chandler, 2013;Park et al, 2013).…”

“…The number of knots for each smooth term is chosen so that a further increase of knots would have negligible impact on the result (here K 3 = 80). More details about spline functions in the trend analysis can be found in Park et al (2013) and Wood et al (2016). The estimation is implemented in R package mgcv.…”

Statistical regularization for trend detection: An integrated approach for detecting long-term trends from sparse tropospheric ozone profiles

“…The specification of a trend component is, however, dependent on the goals of the analysis, and it must be flexible enough to represent the underlying structure in the data (e.g. Niu (1996); Augustin et al (2009); Park et al (2013); Wood et al (2015); Chang et al (2017)); the residual noise series is generally assumed to be an autoregressive process in this scenario.…”

“…In order to reduce the estimation uncertainty of a trend on a particular level, methods have been developed that produce an area average from multiple time series in close spatial proximity (Wigley et al, 1984;Chang et al, 2017), or that employ a dimension reduction technique (e.g. principal component analyses) to project multiple layers of data into a reduced set (Ghil et al, 2002;Meiring, 2007;Park et al, 2013).…”

“…CC BY 4.0 License. Verbyla et al, 1999;Shaddick and Zidek, 2015), and it has been widely applied to a variety of spatial pattern and/or temporal trend studies (Dominici et al, 2002;Schlink et al, 2006;Augustin et al, 2009;Park et al, 2013;Wood et al, 2015;Chang et al, 2017). We thus propose a geostatistical approach to fit the vertical profiles jointly as a smooth field for understanding nonlinear interactions and to determine the long-term vertical variability.…”