Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling
Abstract
:1. Introduction
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- A time series ARIMA model and various ML techniques, including ANN, GRNN, and ANFIS, are built to predict the daily ET0 of Samsun, Türkiye, based on climate parameters.
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- A novel approach combining ARIMA and ML models is developed for ET0 predictions.
2. Background
2.1. Linear Process: Box–Jenkins ARIMA Model
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- Identification of the ARIMA (p, d, q) model structure;
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- Estimate parameters for ARIMA (p, d, q) model;
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- Check residuals to determine model adequacy;
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- Predict future data from existing data.
2.2. Artificial Neural Networks (ANN)
2.3. Generalized Regression Neural Networks (GRNN)
2.4. Adaptive Neuro-Fuzzy Inference System (ANFIS)
3. Methodology
3.1. Study Area and Dataset
3.2. Data Pre-Processing
3.3. Selection of Component Models
3.4. Performance Criteria of Model
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Coefficient | Standard Error | t-Statistic | p-Value |
---|---|---|---|---|
Constant | 0.12072 | 0.00820 | 14.72 | 0.000 |
AR1 | 0.95476 | 0.00671 | 142.37 | 0.000 |
MA1 | 0.46610 | 0.01990 | 23.41 | 0.000 |
Model | Model Structure | Training | Testing | ||||
---|---|---|---|---|---|---|---|
MAE | RMSE | R2 | MAE | RMSE | R2 | ||
ARIMA | (1, 0, 1) | 0.562 | 0.778 | 0.719 | 0.580 | 0.771 | 0.748 |
ANN | (3, 5, 1) | 0.548 | 0.759 | 0.732 | 0.563 | 0.755 | 0.760 |
GRNN | (3, 0.1) | 0.511 | 0.702 | 0.938 | 0.527 | 0.697 | 0.946 |
ANFIS | (3, trimf) | 0.531 | 0.736 | 0.749 | 0.558 | 0.762 | 0.774 |
Model | Model Structure | Training | Testing | ||||
---|---|---|---|---|---|---|---|
MAE | RMSE | R2 | MAE | RMSE | R2 | ||
ARIMA–ANN | (3, 5, 1) | 0.521 | 0.715 | 0.763 | 0.541 | 0.719 | 0.782 |
ARIMA–GRNN | (3, 0.1) | 0.254 | 0.381 | 0.934 | 0.269 | 0.398 | 0.935 |
ARIMA–ANFIS | (3, trimf) | 0.508 | 0.700 | 0.773 | 0.534 | 0.705 | 0.791 |
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Küçüktopcu, E.; Cemek, E.; Cemek, B.; Simsek, H. Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling. Sustainability 2023, 15, 5689. https://doi.org/10.3390/su15075689
Küçüktopcu E, Cemek E, Cemek B, Simsek H. Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling. Sustainability. 2023; 15(7):5689. https://doi.org/10.3390/su15075689
Chicago/Turabian StyleKüçüktopcu, Erdem, Emirhan Cemek, Bilal Cemek, and Halis Simsek. 2023. "Hybrid Statistical and Machine Learning Methods for Daily Evapotranspiration Modeling" Sustainability 15, no. 7: 5689. https://doi.org/10.3390/su15075689