Climate models robustly project acceleration of the Brewer-Dobson circulation (BDC) in response to climate change. However, the BDC trends derived from comprehensive models do not fully match observations. Additionally, the changing structure of the troposphere and stratosphere has received increasing attention in recent years and to which extent vertical shifts of the circulation are driving the acceleration is under debate. In this study, we present a novel method that enables the attribution of circulation changes to individual kinematic factors. Using this method allows to study the advective BDC trends in unprecedented detail and sheds new light into discrepancies between different datasets (reanalyses and models) at the tropopause and in the lower stratosphere. Our findings provide insights into the reliability of model projections of BDC changes and offer new possibilities for observational constraints.