Changes in the strength of the transport barrier at the edge of the stratospheric polar vortex can affect the rate at which air descends through the vortex, as well as the chemical composition of the stratosphere. We investigate methods for determining the strength of this barrier in the middle stratosphere using reanalysis data. Firstly, we develop two quantitative measures related to the strength of the barrier, which are based on a recently introduced method known as the function M derived using the path lengths of Lagrangian trajectories [de la Camara et al. 2012], and show that they are both potentially worthwhile at isentropic levels of 600-900 K. The first of these is a measure of vortex strength and permeability and the second is a measure of vortex barrier area. These measures are both calculated using an isentropic Lagrangian trajectory model based on wind velocity data from the MERRA reanalysis. We also investigate the use of satellite data for identifying the location of the polar vortex by dividing measurements of CO and N2O into clusters corresponding to intra- and extra-vortex air in tracer-tracer space using two different clustering schemes. This method is tested in the middle stratosphere at 700-1250 K against a potential-vorticity based method, and also against the CO probability distribution function (PDF) based method detailed in McDonald and Smith [2013]. By using different combinations of chemicals, such as CO/water, this method could be extended into the upper stratosphere, where reanalysis data becomes less reliable but chemical tracer data from satellites such as the Aura- MLS (Microwave Limb Sounder) is readily available. No clear evidence is found that this method identifies vortex air more accurately than the CO PDF-based method. However, it is shown that this method is particularly good at identifying air located outside the vortex.