Abstract
This study explores the application of long short-term memory (LSTM) networks to simulate runoff at the national scale of Denmark using data from 301 catchments. This is the first LSTM application on Danish data. The results were benchmarked against the Danish national water resources model (DK-model), a physically based hydrological model. The median Kling-Gupta Efficiency (KGE), a common metric to assess performance of runoff predictions (optimum of 1), increased from 0.7 (DK-model) to 0.8 (LSTM) when trained against all catchments. Overall, the LSTM outperformed the DK-model in 80% of catchments. Despite the compelling KGE evaluation, the water balance closure was modelled less accurately by the LSTM. The applicability of LSTM networks for modelling ungauged catchments was assessed via a spatial split-sample experiment. A 20% spatial hold-out showed poorer performance of the LSTM with respect to the DK model. However, after pre-training, that is, weight initialisation obtained from training against simulated data from the DK-model, the performance of the LSTM was effectively improved. This formed a convincing argument supporting the knowledge-guided machine learning (ML) paradigm to integrate physically based models and ML to train robust models that generalise well.
Highlights
The runoff at a given point along a river network can be defined as the outflow generated in the upstream contributing area
The long short-term memory (LSTM) was benchmarked against the DK-model (PBM), and the effect of pre-training was investigated
The conclusion was less clear for the water balance closure (Fbal); here, the physically based model (PBM) showed normally distributed under- and over-estimates with a median close to zero
Summary
The runoff at a given point along a river network can be defined as the outflow generated in the upstream contributing area. A multitude of numerical modelling tools, from parsimonious conceptual rainfall-runoff models to complex fully distributed physically based models (PBMs), have been developed. Machine learning (ML) models, in particular, long short-term memory (LSTM) networks, have proved useful for rainfall-runoff modelling. The knowledge-guided ML paradigm aims to increase robustness and generalisability by integrating scientific knowledge into ML models (Nearing et al 2020; Reichstein et al 2019). This can be achieved by building physical constraints, such as the first-principle law of mass conservation (Hoedt et al 2021), into a ML model or using a PBM to augment training data
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