A three-dimensional Chemical Tracer Model is used to simulate the distribution of water vapor in the upper troposphere (UT) and lower stratosphere (LS). The simulations include only the large scale advection of water vapor and the restriction that the air be at or below saturation at all times. This simulation is used to help distinguish among those processes that control water vapor in the UT/LS. The exchange of water vapor across the tropopause is analyzed in detail. The simulation qualitatively reproduces the water vapor distribution given by satellite and radiosonde observations on both sides of the tropopause, confirming the importance of the global temperature distribution and advection in controlling the water vapor distribution. Quantitative differences with observations of water vapor are ascribed to input temperature biases. Water vapor enters the stratosphere at all longitudes in the tropics. Details of subgrid-scale dynamic and convective processes are not necessary to explain the entry of water vapor into the stratosphere, but these are found to be important for controlling the water vapor distribution in the upper troposphere.