Using Data-Driven Prediction of Downstream 1D River Flow to Overcome the Challenges of Hydrologic River Modeling
Abstract
:1. Introduction
2. Materials and Methods
2.1. The SSARR Model
2.2. The Discrete Convolution Approach
2.3. The Linear Programming Model
- Instead of predicting the downstream discharge by identifying the optimal unit hydrograph of a single upstream source, our model simultaneously identifies the optimal unit hydrograph of multiple contributing upstream sources;
- Instead of assuming the unit hydrograph of each upstream source to be static, the model allows the identification of dynamic unit hydrographs;
- Apart from minimizing the error in predicting the downstream flow, the model also maximizes the smoothness of the identified unit hydrographs.
2.4. The Convolutional Neural Network Encoder
2.5. Discharge-Variant Water Travel Time
2.6. Model Validation
2.7. Site Description
2.8. Datasets
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- Detailed mathematical formulation of the LP method
- Sets
- Parameters
- Variables
- Description
- Unit hydrograph and link to water travel time and mass balance indicator
Appendix B
Parameter | Type | Domain | Optimized Value | Note |
---|---|---|---|---|
Number of convolution layers | Discrete | (1, 10) | 5 | |
Number of convolution filters | Discrete | {4, 8, 16, 32, 64} | 16 | |
Kernel size | Discrete | (4, 193) | 24 | Subject to number of convolutions |
Kernel non-negative constraint | Boolean | {True, False} | False | |
Kernel regularizer L2 factor | Continuous | (0, 0.1) | 0.03 | |
Learning rate | Continuous | (0.00001, 0.01) | 0.002 | |
Batch size | Discrete | {64, 128, 256} | 64 |
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Training Time (Seconds) | Hourly Prediction | Daily Minimum-to-Maximum Prediction | |||||||
---|---|---|---|---|---|---|---|---|---|
Model | MAE (m) | MSE (m2) | R2 | Max Error Residual (m) | MAE (m) | MSE (m2) | R2 | Max Error Residual (m) | |
SSARR | - | 0.0411 | 0.0030 | 0.987 | 0.295 | 0.027 | 0.0014 | 0.669 | 0.180 |
LP | 17 | 0.0296 | 0.0020 | 0.991 | 0.210 | 0.016 | 0.00056 | 0.856 | 0.130 |
CNN | 170 | 0.0171 | 0.00056 | 0.998 | 0.145 | 0.015 | 0.00046 | 0.877 | 0.142 |
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Feinstein, J.; Ploussard, Q.; Veselka, T.; Yan, E. Using Data-Driven Prediction of Downstream 1D River Flow to Overcome the Challenges of Hydrologic River Modeling. Water 2023, 15, 3843. https://doi.org/10.3390/w15213843
Feinstein J, Ploussard Q, Veselka T, Yan E. Using Data-Driven Prediction of Downstream 1D River Flow to Overcome the Challenges of Hydrologic River Modeling. Water. 2023; 15(21):3843. https://doi.org/10.3390/w15213843
Chicago/Turabian StyleFeinstein, Jeremy, Quentin Ploussard, Thomas Veselka, and Eugene Yan. 2023. "Using Data-Driven Prediction of Downstream 1D River Flow to Overcome the Challenges of Hydrologic River Modeling" Water 15, no. 21: 3843. https://doi.org/10.3390/w15213843