Uncertainty Estimation with Deep Learning for Rainfall–Runoff Modeling

Quantifying the uncertainty in a model prediction can be a complex, after-the-fact process which attempts to account for input error, model structure and parameter error, error in target streamflow observations and for true randomness in the world – whew! What if we could have our model learn to tell us the uncertainty in its predictions?

This paper compares and benchmarks different approaches to creating probabilistic predictions using deep learning hydrology models. The approach we use, mixture density networks, allows the model to predict a full probability distribution directly based on the model inputs, its current hydrologic states and what it has learned about randomness and uncertainty from large training datasets.

Read the paper here.

Klotz, D., Kratzert, F., Gauch, M., Keefe Sampson, A., Brandstetter, J., Klambauer, G., Hochreiter, S., and Nearing, G.: Uncertainty estimation with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 26, 1673–1693,, 2022.