Ozone and methane are chemically reactive greenhouse gases, whose increases have contributed to global warming and deteriorating global air quality over the 20th century. Both gases have a major role in atmospheric chemistry, altering the oxidation and removal of other greenhouse gases and pollutants by the hydroxyl radical. Increases in methane have reduced tropospheric hydroxyl, while increases in tropospheric ozone tend to increase hydroxyl. How ozone and methane will respond to 21st-century climate change is not well understood. This dissertation targets ozone and methane, presenting a collection of research aimed at quantifying the role of different mechanisms in controlling their tropospheric abundances. The first of three studies led by the doctoral candidate identifies the observed anomalies in the tropospheric column of ozone with tropopause folds bringing ozone-rich, stratospheric air into the troposphere. The global ozone field (1∞◊1∞◊40-layer◊0.5 hr), simulated by the University of California, Irvine chemistry transport model, reproduces, to a large degree, the variations in individual measurements (0.1∞◊0.5∞) observed from the NASA Aura satellite. We thus provide an approach for monitoring tropopause folds from space and the possibility of globally integrating the fold-related stratosphere-to-troposphere flux of ozone. The second study applies this modeling as a transfer standard to compare the four different Aura instruments measuring ozone, using level 2 swath datasets for 2005-2006. Case studies show that the Aura ozone profiles are inadequate to quantify these folds on an instantaneous basis, but monthly averaged profiles may characterize large scale patterns in fold events as demonstrated here by their ability to identify the longitudinal structure related to the Walker circulation. Inconsistencies in the different instruments and deficiencies of the model are uncovered. Study three identifies summertime convection over continents as an important factor in the influx of stratospheric ozone, increasing surface pollution. Additional doctoral research involved collaborations within the department and internationally. Studies covered a wider range of topics related to atmospheric science and global change: climate impacts of traffic emissions, quantifying model uncertainties, better defining the stratosphere-troposphere boundary, and changes in ethane and methane from fossil fuel use.