Artificial Neural Networks and Multiple Linear Regression for Filling in Missing Daily Rainfall Data
Abstract
:1. Introduction
2. Materials and Methods
2.1. ANN and MLR Creation
2.2. Model Evaluation
2.3. Case Study
2.4. Different Combinations of Stations Missing Data (Cases)
3. Results
3.1. Root Mean Square Error (RMSE)
3.2. Nash–Sutcliffe Efficiency
- If NSE = 1, then there is a complete match between the simulated values given by the model and those observed by the stations;
- If NSE = 0, then the values simulated by the model give the same result as if the average of the observed values of the stations were used as the forecast model for each time point;
- If NSE < 0, then the model is practically unusable, as the values simulated by it give a less accurate result than if the average of the observed values of the stations were used as a predictive model for each time point.
3.3. Coefficient of Correlation (R)
4. Discussions
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Station | Altitude (m) | Number of Data | Start of Data |
---|---|---|---|
Alikianos | 95 | 3044 | 1 September 2012 |
Chania | 137 | 5448 | 1 February 2006 |
Chania (Center) | 7 | 3745 | 1 October 2010 |
Platanias | 12 | 2011 | 1 July 2015 |
Stalos | 93 | 792 | 1 November 2018 |
Case | RMSE [mm] | |
---|---|---|
ANN | MLR | |
Case 2 | 1.76 | 6.43 |
Case 3 | 1.22 | 2.37 |
Case 6 | 1.22 | 2.92 |
Case 11 | 2.30 | 4.99 |
Case 14 | 1.24 | 3.03 |
Case 15 | 1.16 | 2.46 |
Case 22 | 2.19 | 4.47 |
Case 24 | 1.83 | 3.16 |
Case 29 | 2.42 | 4.94 |
Case | Nash–Sutcliffe Efficiency | Simulated Precipitation Value Station(s) | |
---|---|---|---|
ANN | MLR | ||
Case 2 | 0.967 | 0.803 | Alikianos |
Case 3 | 0.975 | 0.937 | Chania |
Case 6 | 0.981 | 0.882 | Stalos |
Case 11 | 0.954 | 0.803 | Alikianos |
0.957 | 0.882 | Stalos | |
Case 14 | 0.976 | 0.908 | Platanias |
0.969 | 0.845 | Stalos | |
Case 15 | 0.989 | 0.968 | Chania (Center) |
0.973 | 0.871 | Stalos | |
Case 22 | 0.934 | 0.802 | Alikianos |
0.957 | 0.908 | Platanias | |
0.927 | 0.844 | Stalos | |
Case 24 | 0.975 | 0.954 | Chania (Center) |
0.957 | 0.869 | Platanias | |
0.943 | 0.781 | Stalos | |
Case 29 | 0.911 | 0.708 | Alikianos |
0.971 | 0.933 | Chania (Center) | |
0.968 | 0.843 | Platanias | |
0.959 | 0.748 | Stalos |
Case | Coefficient of Correlation (R) | |
---|---|---|
ANN | MLR | |
Case 2 | 0.98353 | 0.80337 |
Case 3 | 0.98777 | 0.93740 |
Case 6 | 0.99066 | 0.88198 |
Case 11 | 0.97737 | 0.76844 |
Case 14 | 0.98639 | 0.87493 |
Case 15 | 0.99101 | 0.90800 |
Case 22 | 0.96842 | 0.78287 |
Case 24 | 0.97975 | 0.86749 |
Case 29 | 0.96998 | 0.74782 |
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Papailiou, I.; Spyropoulos, F.; Trichakis, I.; Karatzas, G.P. Artificial Neural Networks and Multiple Linear Regression for Filling in Missing Daily Rainfall Data. Water 2022, 14, 2892. https://doi.org/10.3390/w14182892
Papailiou I, Spyropoulos F, Trichakis I, Karatzas GP. Artificial Neural Networks and Multiple Linear Regression for Filling in Missing Daily Rainfall Data. Water. 2022; 14(18):2892. https://doi.org/10.3390/w14182892
Chicago/Turabian StylePapailiou, Ioannis, Fotios Spyropoulos, Ioannis Trichakis, and George P. Karatzas. 2022. "Artificial Neural Networks and Multiple Linear Regression for Filling in Missing Daily Rainfall Data" Water 14, no. 18: 2892. https://doi.org/10.3390/w14182892