A robust feature of climate and chemistry models forced with projected anthropogenic greenhouse gas emissions is an increase in the water vapor concentration of the lower stratosphere. This projection has concerning implications for surface climate and stratospheric chemistry, yet the underlying mechanisms in these models have not been scrutinized. In particular, the coarse resolution of models and the parameterizations of small-scale processes that control water vapor concentrations at entry to the stratosphere may inhibit models from representing lower stratospheric water vapor in a warming climate. These concerns are amplified by the models' spread in the magnitude of their projections and their inability to reproduce historical observations. In this dissertation, I put aside the complexity of global climate models and explore mechanisms that can drive an increase in the water vapor content of the stratosphere following surface warming. I first revisit the Lagrangian trajectory method that has been used to study the dehydration of air parcels ascending to the lower stratosphere. By leveraging the high temporal and spatial resolution of a new reanalysis data product (ERA5), I calculate the biases that are introduced to the trajectories' temperature minima (i.e. the cold point) when they are computed with lower resolution input data. My main finding is that previous Lagrangian trajectory studies have underestimated the role of processes that are secondary to cold point temperatures in setting the water vapor concentration of the lower stratosphere, such as cloud microphysics and mixing. This work also informs future studies on how to select input data for trajectory calculations in accordance with the studies' error tolerance. I then advance my Lagrangian trajectory method to explore how changes to zonal and vertical wind speeds in the tropical upper troposphere and lower stratosphere will impact the dehydration of air parcels ascending to the lower stratosphere. I find that a deceleration of the Walker Circulation, manifest as a fractional decrease in the magnitude of zonal winds in the region of interest, leads to a warmer average cold point temperature for trajectories rising to the lower stratosphere. This would lead to stratospheric moistening according to the Clausius-Clapeyron relationship. I then show that warmer temperatures and slower winds near the cold point allow ice to grow larger and gravitationally settle greater distances prior to sublimation, which decreases but does not eliminate the overall moistening. Given that a slowdown of the Walker Circulation is a robust response of the tropospheric circulation to surface warming according to both models and theory, this constitutes a stratospheric water vapor feedback that does not require temperatures to warm near the tropopause. Finally, I identify a mechanism that will increase the cold point temperature following surface warming, which would have a first-order effect on lower stratospheric water vapor concentrations. Motivated by observations of constant ozone concentrations at the cold point across seasons, which are unexpected given the seasonal fluctuations of the cold point's temperature and height, I construct an ozone budget for air parcels ascending to the cold point. By using Lagrangian trajectories and ozone concentration and production profiles, I show that both the origin of air parcels that reach the cold point and the production that occurs along their paths are important for the ozone concentration at the cold point. As the surface warms, the troposphere will expand, pushing all processes that happen relative to the tropopause into a region of increased ozone production. This will increase the production of ozone for air parcels as they move into the lower stratosphere, and according to the ozone budget, this will increase ozone concentrations relative to the tropopause and result in a warmer cold point.