A wide range of inverse problems in atmospheric transport and chemistry can be solved within the Eulerian backtracking framework. Here it is shown how a new and accurate numerical implementation can be used as an alternative to Lagrangian back trajectory methods in a wide class of process studies. As a key example, the question of how the (time-averaged) stratospheric flux of a finite lifetime chemical species depends upon the location(s) of its surface source(s) is addressed. The resulting sensitivity maps are demonstrated to be robust features of the global atmospheric circulation, with relatively low interannual variability. The maps serve as an at-a-glance resource for policymakers wishing to compare the likely impact of proposed emission locations for very short lived halogenated species on the total loading of stratospheric chlorine and bromine.