Geoscientific Instrumentation Methods and Data Systems Trends in stratospheric ozone profiles using functional mixed models

Abstract

This paper is devoted to the modeling of altitude-dependent patterns of ozone varia-tions over time. Umkher 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 5 appropriate basis. To capture primary modes of ozone variations without losing essen-tial information, a functional principal component analysis is performed as it penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data driven basis functions are obtained. Secondly we estimate the effects of covariates – month, year (trend), quasi biennial oscillation, the Solar cycle, 10 arctic oscillation and the El Niño/Southern Oscillation cycle – on the principal compo-nent scores of ozone profiles over time using generalized additive models. The effects are smooth functions of the covariates, and are represented by knot-based regression cubic splines. Finally we employ generalized additive mixed effects models incorporat-ing a more complex error structure that reflects the observed seasonality in the data. 15 The analysis provides more accurate estimates of influences and trends, together with enhanced uncertainty quantification. 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. The strongly declining trends over 2003–2011 for altitudes of 32–64 hPa show that stratospheric ozone is not yet fully recovering.