We perform the first uncertainty quantification analysis of the turn-of-the-century drought in the Western United States using a large perturbed-parameter ensemble of the Community Atmosphere Model version 4.0 (CAM4). We develop several metrics to characterize the aridity bias, spatial extent and tropical forcing of the drought and use statistical models to ascertain that the modeled drought was mainly sensitive to CAM4 parameters related to deep convection and clouds. Deep convection parameters account for over half the variance across the drought metrics. We employ observed estimates of these drought metrics to infer probability distributions of the model parameters that lead to a better agreement with observations, thereby providing guidance on how to improve the simulation of drought in CAM4. We find that in some cases, the suggested parameter values that improve the simulation of one drought characteristic would degrade the simulation of another, suggesting that there is a complex relationship between the model parameters and drought in the Western United States. We also demonstrate reductions in the uncertainty of the drought metrics of up to 30% by constraining with observations of all metrics. Furthermore, we demonstrate for the first time that improvements to the simulation of the spatial extent of the turn-of-the-century drought also lead to improvements in the spatial extent of the Australian Millennium drought, suggesting that physics of drought as encoded by the model parameters may be generalizable.