The thesis investigates use cases for Bayesian Neural Networks in the domain of time series forecasting in hydrology, more precisely, in the domain of discharge prediction based on forcings. The approach chosen is based on Long short-term memory (LSTM) neural networks and an algorithm named Bayes by Backprop through time that gives the network the ability to predict uncertainty. Experiments are carried with the freely available CAMELS-Dataset which includes forcings and discharge values for 671 catchments across the US, and an additional dataset including hydrological data from Bavaria. I plan to compare the results to state-of-the-art results achieved with standard LSTMs and moreover to evaluate the quality of the predicted uncertainty that results from the Bayesian approach taken.