Mixing of stratospheric and tropospheric air plays an essential role in the stratosphere-troposphere exchange (STE) of chemical species. Although evidence of mixing is frequently observed, quantifying its effect has been a significant challenge. We present an analysis using both observations and modeling tools to address the issues of where mixing occurs and how models can quantify its effect to STE across the extratropical tropopause. The data are from remote and in situ measurements on board the NASA DC-8 during the Subsonic Assessment: Ozone and Nitrogen Oxides Experiment (SONEX). The model simulations use the Chemical Lagrangian Model of the Stratosphere (CLaMS). Our analyses use tracer correlations together with lidar measurements of ozone cross sections to characterize the spatial extent of the observed mixing. The results also serve to identify the air mass that is involved in an irreversible exchange. Results of the CLaMS simulations of lidar and in situ observations for a case observed on 29 October 1997 demonstrate the model's ability to characterize mixing near the tropopause. The results also indicate that using the shear and deformation in large-scale winds, we can reproduce the observed mixing and the overall features of the stratospheric intrusion. An artificial tracer is used to quantify the transport between the stratosphere and troposphere, to track the preferred location and the cumulative effect of mixing. These results demonstrate progress toward modeling mixing and STE using Lagrangian models and show the potential of the CLaMS model in quantifying the effect of mixing on the chemical composition of the upper tropospheric and lower stratospheric region.