Extrapo… what? Predictions beyond the support of the training data

Neural networks belong to the best available methods for numerous hydrological model challenges. However, although they have shown to outperform classical hydrological models in several applications there is still some doubt whether neural networks are, despite their excellent interpolation skills, capable to make predictions beyond the support of the training data. This study addresses this issue and proposes an approach to infer the ability of neural network to predict unusual, extreme system states. We show how we can use the concept of data surprise and model surprise in a complementary manner to assess which unusual events a neural network can predict, which it can predict but only with additionally data and which it cannot predict at all hinting toward the wrong model choice or towards an incomplete description of the data.