Model Uncertainty in Deep Learning Simulation of Daily Streamflow with Monte Carlo Dropout

Deep Learning (DL) is becoming an increasingly important tool to produce accurate streamflow prediction across a wide range of spatial and temporal scales. However, classical DL networks do not incorporate uncertainty information but only return a point prediction. Monte-Carlo Dropout (MC-Dropout) approach offers a mathematically grounded framework to reason about DL uncertainty which was used here as random diagonal matrices to introduce randomness to the streamflow prediction process. This study employed Recurrent Neural Networks (RNNs) to simulate daily streamflow records across a coastal plain drainage system, i.e., the Northeast Cape Fear River Basin, North Carolina, USA. We employed MC-Dropout approach with the DL algorithm to make streamflow simulation more robust to potential overfitting by introducing random perturbation during training period. Daily streamflow was calibrated during 2000-2010 and validated during 2010-2014 periods. Our results provide a unique and strong evidence that variational sampling via MC-Dropout acts as a dissimilarity detector. The MC-Dropout method successfully captured the predictive error after tuning a hyperparameter on a representative training dataset. This approach was able to mitigate the problem of representing model uncertainty in DL simulations without sacrificing computational complexity or accuracy metrics and can be used for all kind of DL-based streamflow (time-series) model training with dropout.