# Artificial Neural Networks and Multiple Linear Regression for Filling in Missing Daily Rainfall Data

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## Abstract

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## 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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**Figure 3.**Timeline of daily rainfall data availability and gaps in the datasets (red color indicates gaps).

**Figure 4.**Possible combinations of availability of daily rainfall data. Red indicates that the station in question has no recorded rainfall value for the day of recording. Cases occurring in the dataset are shown in bold.

**Figure 5.**Observed values (blue), and model-generated values from the ANNs (orange) and MLR model (red).

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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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Papailiou, 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