Spatiotemporal simulations can provide critical insights to understand the underlying mechanisms of complex geographic phenomena. Therefore, spatiotemporal simulations play a vitally important role in solving the global geographic problems such as habitats loss, climate change, and deforestation. Due to complex mechanisms and big spatial data, computational intensity greatly hinders the application of spatiotemporal simulations at large scale. Cyberinfrastructure has been recognized as a promising tool to tackle computational intensity in spatiotemporal simulations. However, a challenge lies in the accurate estimation of its computing performance, which may prevent an efficient utilization of cyberinfrastructure. This dissertation demonstrates a surrogate-based approach to appropriately estimate the computing performance of parallel spatiotemporal simulations within cyberinfrastructure environments. A generalized computational framework is developed to integrate surrogate-based models, spatiotemporal simulations, and cyberinfrastructure. I applied the computational framework to simulate urban growth in North Carolina as a case study. Results show that surrogate-based approaches accurately estimate the computing performance. Kriging has a better prediction performance than linear regression surrogate-based model in this study. With the support of surrogate-based approaches, the computational framework substantially supports spatiotemporal simulations by efficiently handling computational intensity.