Combining Synthetic and Observed Data to Enhance Machine Learning Model Performance for Streamflow Prediction
Abstract
:1. Introduction
2. Materials and Methods
2.1. Methodology
- Rainfall and discharge data were collected from the meteorological and streamflow stations, respectively, to set every input and output of the models. This data set was further divided chronologically: 75% for training and 25% for testing (the most recent data).
- The numerical model based on Iber was calibrated, taking into account high events of the training set.
- Synthetic hyetographs with different periods of return were built using the Alternating Block Method (ABM) and intensity-duration-frequency (IDF) equations. They are employed in the calibrated Iber model to obtain synthetic hydrographs with higher streamflow values than those registered in the measured training set.
- Two RERF models were built using only the training data from the stations (RERF1) and a combination of the training set and the synthetic cases (RERF2).
- The testing set was evaluated considering both models, taking into account general errors and metrics focused on the most important values in the context of an imbalanced domain.
2.2. Study Area
2.3. Data
2.4. Iber Model
2.5. Synthetic Cases
2.6. Regression-Enhanced Random Forest (RERF)
- The k-fold cross-validation method with 10-folds is applied using Lasso regression and the training set following Equation (1) to obtain a suitable penalization parameter (λ). After that, the Lasso model is trained considering the determined λ and the entire training set to establish the coefficients of Equation (5):
- 2.
- An RF model is built using the same inputs given in (1) and the error from the Lasso regression (ϵλ) as the output according to (6):
- 3.
- Finally, the RERF model is given by the sum of the Lasso and the RF model (7). In this sense, according to Zhang et al. [24], it is possible to find linear relations between the inputs and the output, making an approximated extrapolation possible.
2.7. General and Focused Errors
2.7.1. Scalar Errors
2.7.2. Graphical-Based Errors
2.7.3. Errors by Event
3. Results and Discussion
3.1. Synthetic Cases
3.2. General Errors
3.3. Focused Errors
3.4. Overall Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
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MAE (m³/s) | RMSE (m³/s) | MAPE (%) | R² | |
---|---|---|---|---|
RERF1 | 0.14 | 1.17 | 11.10 | 0.94 |
RERF2 | 0.13 | 1.01 | 11.05 | 0.94 |
Total Utility | Relative Utility | Recall | Precision | |||||||
---|---|---|---|---|---|---|---|---|---|---|
(m³/s) | (m³/s) | (m³/s) | (%) | (%) | (%) | |||||
RERF1 | 9.22 | 21.19 | 25.97 | −15.2 | −25.9 | −24.8 | 105.25 | 0.53 | 0.69 | 0.73 |
RERF2 | 7.86 | 16.60 | 19.96 | −11.8 | −16.7 | −15.2 | 116.37 | 0.58 | 0.77 | 0.80 |
Percentage Change | −14.78% | −21.63% | −23.15% | −22.37% | −35.52% | −38.71% | 10.56% | 10.56% | 11.39% | 10.09% |
NSE | VE | |||||
---|---|---|---|---|---|---|
Gloria Storm | 2nd Event | 3rd Event | Gloria Storm | 2nd Event | 3rd Event | |
RERF1 | 0.86 | 0.77 | 0.85 | 0.77 | 0.81 | 0.82 |
RERF2 | 0.91 | 0.81 | 0.84 | 0.82 | 0.83 | 0.81 |
Percentage Change | 6.13% | 5.84% | −1.18% | 6.44% | 1.95% | −1.06% |
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López-Chacón, S.R.; Salazar, F.; Bladé, E. Combining Synthetic and Observed Data to Enhance Machine Learning Model Performance for Streamflow Prediction. Water 2023, 15, 2020. https://doi.org/10.3390/w15112020
López-Chacón SR, Salazar F, Bladé E. Combining Synthetic and Observed Data to Enhance Machine Learning Model Performance for Streamflow Prediction. Water. 2023; 15(11):2020. https://doi.org/10.3390/w15112020
Chicago/Turabian StyleLópez-Chacón, Sergio Ricardo, Fernando Salazar, and Ernest Bladé. 2023. "Combining Synthetic and Observed Data to Enhance Machine Learning Model Performance for Streamflow Prediction" Water 15, no. 11: 2020. https://doi.org/10.3390/w15112020