the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Towards Interpretable LSTM-based Modelling of Hydrological Systems
Luis Andres De la Fuente
Mohammad Reza Ehsani
Hoshin Vijai Gupta
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.
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Luis Andres De la Fuente et al.
Status: open (until 19 Dec 2023)
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RC1: 'Comment on hess-2023-252', Anonymous Referee #1, 27 Oct 2023
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hess-2023-252 “Towards Interpretable LSTM-based Modelling of Hydrological Systems” LA.De la Fuente, MR.Ehsani, HV.Gupta, LE.Condon
This re-submission has a done a good job of addressing comments and corrections. Now it reads better and makes definite linkages between AI/ML and traditional hydrologic modelling that do aid in interpretability of LSTM models. Further they confirm the published experience of hydrologic modellers with regard to results in water-limited versus energy-limited catchments, consideration of the most important inputs, and the number and arrangement of “storages” when constructing their models.
Citation: https://doi.org/10.5194/hess-2023-252-RC1 -
AC1: 'Reply on RC1', Luis De La Fuente, 02 Nov 2023
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We are glad to know that we have addressed your comments and concerns.
Citation: https://doi.org/10.5194/hess-2023-252-AC1
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AC1: 'Reply on RC1', Luis De La Fuente, 02 Nov 2023
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RC2: 'Comment on hess-2023-252', Tadd Bindas, 18 Nov 2023
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Thank you for allowing me to review your paper for the second time. I appreciate you including some of my previous suggestions in the submission to clarify your experiments and scientific findings.
I propose that this paper be accepted to HESS subject to technical corrections (see comments below).Best,
Tadd Bindas
Minor Comments:
Line 90: Grammatical fix: “Explore the similarities and differences between LSTM models and the hydrologic reservoir model.”
Table 1: Are the brackets supposed to be facing outward? (ex: o = ]0,1[ ) Assuming this is the case since this was a minor comment from my previous paper comments.
Figure 6/7: Can you change the scatter plot dots to a color other than yellow? The choice of color makes the points hard to identify individually.
Citation: https://doi.org/10.5194/hess-2023-252-RC2 -
AC2: 'Reply on RC2', Luis De La Fuente, 22 Nov 2023
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Hello Tadd,
Thank you for taking the time to review this revised version of the manuscript. We are glad to know that we addressed your comments and concerns.
Luis De la Fuente et al.
Minor Comments:
Line 90: Grammatical fix: “Explore the similarities and differences between LSTM models and the hydrologic reservoir model.”
Response: We will fix this typo in the revised version.
Table 1: Are the brackets supposed to be facing outward? (ex: o = ]0,1[ ) Assuming this is the case since this was a minor comment from my previous paper comments.
Response: We kept the inward brackets because it is mathematically possible that “o” could have a 0 or 1 value. Nonetheless, in Hydrology, such values would not make sense, as they would indicate a bucket that is either full or non-existent. However, the idea of the bracket was to represent the mathematical range of values.
Figure 6/7: Can you change the scatter plot dots to a color other than yellow? The choice of color makes the points hard to identify individually.
Response: We have chosen this color to ensure that individuals with color blindness can read the figure, but we are exploring alternative color schemes to ensure even better representation.
Citation: https://doi.org/10.5194/hess-2023-252-AC2
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AC2: 'Reply on RC2', Luis De La Fuente, 22 Nov 2023
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RC3: 'Comment on hess-2023-252', Anonymous Referee #3, 20 Nov 2023
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The authors have revised all my concerns. I recommend publishing this article.
Citation: https://doi.org/10.5194/hess-2023-252-RC3 -
AC3: 'Reply on RC3', Luis De La Fuente, 22 Nov 2023
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We are glad to know that we have addressed your comments and concerns.
Citation: https://doi.org/10.5194/hess-2023-252-AC3 -
AC4: 'Reply on RC3', Luis De La Fuente, 22 Nov 2023
reply
We are glad to know that we have addressed your comments and concerns.
Citation: https://doi.org/10.5194/hess-2023-252-AC4
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AC3: 'Reply on RC3', Luis De La Fuente, 22 Nov 2023
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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 https://doi.org/10.5065/D6MW2F4D
Model code and software
GitHub repository (Codes folder) Luis De la Fuente https://github.com/ldelafue/Hydro-LSTM
Interactive computing environment
GitHub repository (Notebooks folder) Luis De la Fuente https://github.com/ldelafue/Hydro-LSTM
Luis Andres De la Fuente et al.
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