Conventional Probable Maximum Precipitation (PMP) methods face several limitations, including the lack of statistical uncertainty characterization, subjectivity in storm maximization, and the assumption of a stationary climate. To address these limitations, we propose a nonstationary PMP approach that combines the novel stochastic spatiotemporal rainfall generation model StormLab with a nonstationary Generalized Extreme Value (GEV) model. We applied the new approach to the Upper Red River Basin in the south-central United States. StormLab provided 10,000 years of high-resolution (6-hour, 0.03°) precipitation fields from 1901 to 2100, based on 50 ensembles of a global climate model (GCM). A nonstationary GEV model was fitted to the simulated precipitation annual maxima, providing PMP estimates under different climate periods with an associated annual exceedance probability (AEP). The simulated precipitation was then integrated with a hydrologic model to generate annual peak discharge in major tributaries and to estimate the probable maximum flood (PMF). Our approach produces PMP estimates for areas ranging from 10-20,000 mi2 and durations from 6 to 360 hours. Results show a 16-25% increase in PMP with an AEP of 10-4 from 2020 to 2100 at different spatial and temporal scales. Higher increases of 35% and 37% are projected in PMF with the same AEP in two major tributaries. The PMP and PMF results were further compared with previous PMP/PMF estimates. This study demonstrates the value of utilizing stochastic rainfall models and GCM large ensembles to inform PMP and PMF analysis in a changing climate.