24 Oct 2023
 | 24 Oct 2023
Status: this preprint is currently under review for the journal HESS.

Towards Interpretable LSTM-based Modelling of Hydrological Systems

Luis Andres De la Fuente, Mohammad Reza Ehsani, Hoshin Vijai Gupta, and Laura Elizabeth Condon

Abstract. Several studies have demonstrated the ability of Long Short-Term Memory (LSTM) machine learning based modeling to outperform traditional spatially-lumped process-based modeling approaches for streamflow prediction. However, due mainly to the structural complexity of the LSTM network (which includes gating operations and sequential processing of the data), difficulties can arise when interpreting the internal processes and weights in the model.

Here, we propose and test a modification of LSTM architecture that is calibrated in a manner that is analogous to a hydrological system. Our architecture, called HydroLSTM, simulates the sequential updating of the Markovian storage while the gating operation has access to historical information. Specifically, we modify how data is fed to the new representation to facilitate simultaneous access to past lagged inputs and consolidated information, which explicitly acknowledges the importance of trends and patterns in the data.

We compare the performance of the HydroLSTM and LSTM architectures using data from 10 hydro-climatically varied catchments. We further examine how the new architecture exploits the information in lagged inputs, for 588 catchments across the USA. The HydroLSTM-based models require fewer cell states to obtain similar performance to their LSTM-based counterparts. Further, the weight patterns associated with lagged input variables are interpretable and consistent with regional hydroclimatic characteristics (snowmelt-dominated, recent rainfall-dominated, and historical rainfall-dominated). These findings illustrate how the hydrological interpretability of LSTM-based models can be enhanced by appropriate architectural modifications that are physically and conceptually consistent with our understanding of the system.

Luis Andres De la Fuente et al.

Status: open (until 19 Dec 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-252', Anonymous Referee #1, 27 Oct 2023 reply
    • AC1: 'Reply on RC1', Luis De La Fuente, 02 Nov 2023 reply
  • RC2: 'Comment on hess-2023-252', Tadd Bindas, 18 Nov 2023 reply
    • AC2: 'Reply on RC2', Luis De La Fuente, 22 Nov 2023 reply
  • RC3: 'Comment on hess-2023-252', Anonymous Referee #3, 20 Nov 2023 reply
    • AC3: 'Reply on RC3', Luis De La Fuente, 22 Nov 2023 reply
    • AC4: 'Reply on RC3', Luis De La Fuente, 22 Nov 2023 reply

Luis Andres De la Fuente et al.

Data sets

CAMELS: Catchment Attributes and MEteorology for Large-sample Studies A. Newman, K. Sampson, M. P. Clark, A. Bock, R. J. Viger, and D. Blodgett

Model code and software

GitHub repository (Codes folder) Luis De la Fuente

Interactive computing environment

GitHub repository (Notebooks folder) Luis De la Fuente

Luis Andres De la Fuente et al.


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Short summary
Long Short-Term Memory (LSTM) is a widely used machine learning model in hydrology. However, it is difficult to extract knowledge from it. We propose HydroLSTM which represents processes like a hydrological reservoir. Models based on HydroLSTM perform similarly to LSTM while requiring fewer cell states. The learned parameters are informative about the dominant hydrology of a catchment.Our results show how parsimony and hydrological knowledge extraction can be achieved by using the new structure.