Despite the huge success of Long Short-Term Memory networks, their applications in environmental sciences are scarce. We argue that one reason is the difficulty to interpret the internals of trained networks. In this study, we look at the application of LSTMs for rainfall-runoff forecasting, one of the central tasks in the field of hydrology, in which the river discharge has to be predicted from meteorological observations. LSTMs are particularly well-suited for this problem since memory cells can represent dynamic reservoirs and storages, which are essential components in state-space modelling approaches of the hydrological system. On basis of two different catchments, one with snow influence and one without, we demonstrate how the trained model can be analyzed and interpreted. In the process, we show that the network internally learns to represent patterns that are consistent with our qualitative understanding of the hydrological system.
The use of artificial neural network (ANN) models in water resources applications has grown considerably over the last decade. However, an important step in the ANN modelling methodology that has received little attention is the selection of appropriate model inputs. This article is the first in a two-part series published in this issue and addresses the lack of a suitable input determination methodology for ANN models in water resources applications. The current state of input determination is reviewed and two input determination methodologies are presented. The first method is a model-free approach, which utilises a measure of the mutual information criterion to characterise the dependence between a potential model input and the output variable. To facilitate the calculation of dependence in the case of multiple inputs, a partial measure of the mutual information criterion is used. In the second method, a self-organizing map (SOM) is used to reduce the dimensionality of the input space and obtain independent inputs. To determine which inputs have a significant relationship with the output (dependent) variable, a hybrid genetic algorithm and general regression neural network (GAGRNN) is used. Both input determination techniques are tested on a number of synthetic data sets, where the dependence attributes were known a priori. In the second paper of the series, the input determination methodology is applied to a real-world case study in order to determine suitable model inputs for forecasting salinity in the River Murray, South Australia, 14 days in advance. Abstract. Rainfall–runoff modelling is one of the key challenges in the field of hydrology. Various approaches exist, ranging from physically based over conceptual to fully data-driven models. In this paper, we propose a novel data-driven approach, using the Long Short-Term Memory (LSTM) network, a special type of recurrent neural network. The advantage of the LSTM is its ability to learn long-term dependencies between the provided input and output of the network, which are essential for modelling storage effects in e.g. catchments with snow influence. We use 241 catchments of the freely available CAMELS data set to test our approach and also compare the results to the well-known Sacramento Soil Moisture Accounting Model (SAC-SMA) coupled with the Snow-17 snow routine. We also show the potential of the LSTM as a regional hydrological model in which one model predicts the discharge for a variety of catchments. In our last experiment, we show the possibility to transfer process understanding, learned at regional scale, to individual catchments and thereby increasing model performance when compared to a LSTM trained only on the data of single catchments. Using this approach, we were able to achieve better model performance as the SAC-SMA + Snow-17, which underlines the potential of the LSTM for hydrological modelling applications.