Enhancing Water Temperature Prediction in Stratified Reservoirs: A Process-Guided Deep Learning Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of the Site
2.2. Field Monitoring and Data Collection
2.3. Process-Based Model (CE-QUAL-W2 (W2))
2.4. Deep Learning Model (Long Short-Term Memory (LSTM))
2.5. Development of the PGDL Model
2.6. Validation of Energy Conservation in the PGDL Model
2.7. Pre-Training of LSTM Using an Uncalibrated W2 (W2-gnr) Model
2.8. Evaluation of Model Performance
3. Results
3.1. Validation of the CE-QUAL-W2 Model
3.2. Prediction Performance of the PGDL Model
3.3. Prediction Performance of the Pre-Trained PGDL Model
3.4. Evaluating the Energy Consistency of the PGDL Model
4. Discussion
4.1. Comparative Analysis of Water Temperature Prediction Errors
4.2. Applicability of the PGDL Model for Water Quality Modeling
4.3. Strengths of the PGDL Model in the Lack of Data
4.4. Limitations of the PGDL Model and Scope for Future Studies
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Variables | Unit | Value |
---|---|---|
Sample size | n | 399 |
Air temperature | °C | 17.5 (8.9) * |
Cloud cover | % | 5.0 (.0) |
Dew point temperature | °C | 12.6 (9.8) |
Long-wave radiation | W m−2 | 356.1 (64.8) |
Precipitation | mm | 4.4 (15.2) |
Relative humidity | % | 73.0 (12.2) |
Solar radiation | W/m−2 | 168.8 (86.8) |
Wind speed | m s−1 | 1.3 (.5) |
Parameters | Units | Description | The Values of Model Parameters | |
---|---|---|---|---|
W2-gnr | W2-calib | |||
AX | m2 s−1 | Horizontal eddy viscosity | 1.0 | 1.0 |
DX | m2 s−1 | Horizontal eddy diffusivity | 1.0 | 1.0 |
WSC | - | Wind sheltering coefficient | 0.85 | 1.0–1.5 |
FRICT | m1/2 s−1 | Chezy coefficient | 70 | 70 |
EXH2O | m−1 | Extinction coefficient for pure water | 0.25 | 0.45 |
BETA | - | Solar radiation absorbed in the surface layer | 0.45 | 0.45 |
CBHE | W m−2 s−1 | Coefficient of bottom heat exchange | 0.3 | 0.45 |
Model | Hyperparameters | Definition | Hyperparameter Range | Defined Hyperparameters |
---|---|---|---|---|
LSTM | Learning rate | Amount of change in weight that is updated during learning. | [0.0001, 0.1] | [0.0001, 0.01] |
Batch size | Group size to divide training data into several groups. | [32, 64] | [32, 64] | |
Epochs | Number of learning iterations. | [1000, 50,000] | [40,000, 50,000] | |
Optimizer | Optimization algorithm used for training. | [SGD, RMSprop, Adam] | Adam | |
Dropout rate | Dropout setting applied to layers. | [0, 1] | [0.1, 0.2] | |
LSTMEC | Learning rate | Amount of change in weight that is updated during learning. | [0.0001, 0.1] | [0.0001, 0.01] |
Batch size | Group size to divide training data into several groups. | [32, 64] | [32, 64] | |
Epochs | Number of learning iterations. | [1000, 50,000] | [40,000, 50,000] | |
Optimizer | Optimization algorithm used for training. | [SGD, RMSprop, Adam] | Adam | |
Dropout rate | Dropout setting applied to layers. | [0, 1] | [0.1, 0.2] | |
LSTMEC,p | Learning rate | Amount of change in weight that is updated during learning. | [0.0001, 0.1] | [0.0001, 0.01] |
Batch size | Group size to divide training data into several groups. | [32, 64] | [32, 64] | |
Epochs | Number of learning iterations. | [1000, 50,000] | [40,000, 50,000] | |
Optimizer | Optimization algorithm used for training. | [SGD, RMSprop, Adam] | Adam | |
Dropout rate | Dropout setting applied to layers. | [0, 1] | [0.1, 0.2] |
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Model | RMSE (°C) | ||||||
---|---|---|---|---|---|---|---|
Proportion of Field Data Used in the Model Training Phase (%) | |||||||
0 | 0.5 | 1 | 2 | 10 | 20 | 100 | |
W2-gnr | - | - | - | - | - | - | 1.930 |
W2-calib | - | - | - | - | - | - | 1.781 |
LSTM | - | 15.978 0.380) | 9.403 0.284) | 2.432 0.257) | 0.289 0.113) | 0.131 0.089) | 0.062 0.010) |
LSTMEC | - | 15.007 0.319) | 8.915 0.256) | 2.229 0.212) | 0.243 0.100) | 0.092 0.033) | 0.042 0.007) |
LSTMEC,p | 7.214 0.327) | 3.007 0.301) | 2.015 0.156) | 1.160 0.115) | 0.230 0.088) | 0.078 0.012) | 0.018 0.001) |
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Kim, S.; Chung, S. Enhancing Water Temperature Prediction in Stratified Reservoirs: A Process-Guided Deep Learning Approach. Water 2023, 15, 3096. https://doi.org/10.3390/w15173096
Kim S, Chung S. Enhancing Water Temperature Prediction in Stratified Reservoirs: A Process-Guided Deep Learning Approach. Water. 2023; 15(17):3096. https://doi.org/10.3390/w15173096
Chicago/Turabian StyleKim, Sungjin, and Sewoong Chung. 2023. "Enhancing Water Temperature Prediction in Stratified Reservoirs: A Process-Guided Deep Learning Approach" Water 15, no. 17: 3096. https://doi.org/10.3390/w15173096