Abstract

Concerns about the concentrations of chlorofluorocarbons (CFCs) in the atmosphere are based on their effects on the ozone layer by catalytically destroying ozone. The recent steady decline in atmospheric concentration of CFC could be a direct result of the Montr\'eal Protocol's ban on CFC products, in effect since 1989. However, CFCs have long atmospheric residence times because of their low chemical reactivity, and as a consequence have already been distributed globally. To study the spatial effects and extent of the decline, we apply the proposed spatial-longitudinal bent-cable model to CFC data observed over a global detection network. The bent cable is a parametric regression model to study data that exhibits a trend change. It comprises two linear segments to describe the incoming and the outgoing phases, joined by a quadratic bend to model the transition period. For spatial longitudinal data, measurements taken over time are nested within spatially dependent locations. Here, it is useful to extend the existing longitudinal bent-cable regression to handle spatial effects. We do so in a hierarchical Bayesian framework by allowing the error terms to be correlated across space. The methodology is illustrated with applications to CFC-11 and 12 data. Our analysis reveals that: (a) there is a strong spatial relationship among all the monitoring locations across the globe; (b) both CFC-11 and CFC-12 increased significantly before entering into a transition zone; (c) after completing the transition, CFC-11 has been decreasing significantly from the atmosphere, but a slow (insignificant) decrease for CFC-12 is observed; and (d) it may take almost 5 times longer to diminish CFC-12 from the atmosphere compared to CFC-11.

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