The Southwest U.S. comprising of the four states-Arizona, New Mexico, Colorado, and Utah-is the hottest and driest region of the United States. Most of the precipitation arrives during the winter season, but the summer precipitation makes a significant contribution to the reliability of water resources and the health of ecology. However, summer precipitation and its extremes, over this region exhibit high degree of spatial and temporal variability. In this study we developed a novel spatial Bayesian hierarchical model to capture the space-time variability of –summer season 3-day maximum precipitation over the southwest U.S. In modeling framework, the data layer the extremes at each station are assumed to be distributed as Generalized Extreme Value (GEV) distribution with non-stationary parameters. In addition, the extremes across space is assumed to be related via a Gaussian Copula. In the process layer, the parameters are modeled as a linear function of large scale climate variables and regional mean precipitation covariates. This is akin to a Generalized Linear Model (GLM). The parameters of the covariates at each station are spatially modeled using spatial Gaussian processes to capture the spatial dependency and enable generating the spatial field of the hydroclimate extremes. The likelihood estimates of the GLM at each station form the initial priors. The posterior distribution of the model parameters and consequently the predictive posterior GEV distribution of the hydroclimate extremes at any arbitrary location, or grid and for any year are obtained. The model is demonstrated by application to extreme summer precipitation at 73 stations from this region. The model validation indicates that return levels and their associated uncertainty have a well-defined spatial structure and furthermore, they capture the historical variability very well. The posterior distribution of the GEV parameters were generated on a 1/8th degree grid, providing maps of various return levels for all the years. Maps of return levels provide information about the spatial and temporal variations of the risk of extreme precipitation in the Southwest U.S. that will be of immense help in management and planning of natural resources and infrastructure.