Floods are a complex phenomenon that are difficult to predict because of their non-linear and dynamic nature. Therefore, flood prediction has been a key research topic in the field of hydrology. Various researchers have approached this problem using different techniques ranging from physical models to image processing, but the accuracy and time steps are not sufficient for all applications. This study explores deep learning techniques for predicting gauge height and evaluating the associated uncertainty. Gauge height data for the Meramec River in Valley Park, Missouri was used to develop and validate the model. It was found that the deep learning model was more accurate than the physical and statistical models currently in use while providing information in 15 minute increments rather than six hour increments. It was also found that the use of data sub-selection for regularization in deep learning is preferred to dropout. These results make it possible to provide more accurate and timely flood prediction for a wide variety of applications, including transportation systems.