#
Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Acquisition and Processing

^{2}that covers the Water District of Thrace. It is delimited by the boundaries of Greece with Bulgaria and Turkey on the north and east, respectively, by the Thracian Sea on the south, and by the watershed of Nestos River on the west. This area was identified: (a) To have common rainfall erosivity spatiotemporal patterns [3]; (b) to form a region with a distinct monthly temporal distribution of erosivity density [13], a parameter strongly related to seasonal rainfall intensity [10]; and (c) to have similar intra-storm temporal distribution intensity patterns of heavy and, consequently, erosive precipitation [22].

#### 2.2. Rainfall Erosivity Calculations

#### 2.3. Empirical Equations for the Estimation of Erosivity

#### 2.4. Generalized Aditive Models

**X**is the matrix of input variables.

#### 2.5. Validation and Model Performance Criteria

## 3. Results and Discussion

^{−16}and the deviance explained by the model was 86.5% (in the training set). Given the above values, there was strong evidence that both terms explained erosivity adequately.

^{2}was closer to one, and RMSE and MAE had lower values).

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Plots of the smoothing functions of each variable used in generalized additive models (GAMs). Dashed lines give the confidence intervals of the predictions of the fitted smooth curves (solid lines). The number in the parenthesis (Y-axis) gives the estimated degrees of freedom for the model terms.

**Figure 3.**Calculated annual erosivity values coming from pluviograph data, versus predicted values using the three models on the testing set. The black line symbolizes the identity function f(x) = x. Values are in MJ·mm·ha

^{−1}h

^{−1}.

Name | Latitude (°) | Longitude (°) | Elevation (m) | Duration (y) | |
---|---|---|---|---|---|

1 | TOXOTES | 41.09 | 24.79 | 75 | 27 |

2 | M. DEREIO | 41.32 | 26.10 | 116 | 22 |

3 | FERRES | 40.90 | 26.17 | 43 | 31 |

4 | PARANESTI | 41.27 | 24.50 | 122 | 34 |

5 | GRATINI | 41.14 | 25.53 | 120 | 27 |

6 | KECHROS | 41.23 | 25.86 | 700 | 24 |

7 | M. KSIDIA | 41.13 | 25.64 | 70 | 27 |

8 | THERMES | 41.35 | 25.01 | 440 | 26 |

9 | GERAKAS | 41.20 | 24.83 | 308 | 24 |

10 | ORAIO | 41.27 | 24.83 | 656 | 26 |

11 | SEMELH | 41.09 | 24.84 | 65 | 23 |

12 | CHRYSOUPOLI | 40.99 | 24.69 | 15 | 14 |

**Table 2.**Annual time step estimation of the out-of-sample error metrics for the two empirical equations and GAM. R

^{2}values are unitless. Root-mean-squared error (RMSE) and mean absolute error (MAE) values are in MJ·mm·ha

^{−1}h

^{−1}y

^{−1}.

Model | R^{2} | RMSE | MAE |
---|---|---|---|

GAM | 0.88 | 306.43 | 231.20 |

Richardson et al. | 0.77 | 419.64 | 308.50 |

Yu and Rosewell | 0.76 | 431.19 | 309.24 |

**Table 3.**Daily time step estimation of the out-of-sample error metrics for the two empirical equations and GAM. R

^{2}values are unitless. RMSE and MAE values are in MJ·mm·ha

^{−1}h

^{−1}.

Model | R^{2} | RMSE | MAE |
---|---|---|---|

GAM | 0.73 | 89.19 | 53.00 |

Richardson et al. | 0.63 | 104.83 | 61.28 |

Yu and Rosewell | 0.61 | 107.58 | 59.82 |

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**MDPI and ACS Style**

Vantas, K.; Sidiropoulos, E.; Evangelides, C. Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models. *Environ. Sci. Proc.* **2020**, *2*, 21.
https://doi.org/10.3390/environsciproc2020002021

**AMA Style**

Vantas K, Sidiropoulos E, Evangelides C. Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models. *Environmental Sciences Proceedings*. 2020; 2(1):21.
https://doi.org/10.3390/environsciproc2020002021

**Chicago/Turabian Style**

Vantas, Konstantinos, Epaminondas Sidiropoulos, and Chris Evangelides. 2020. "Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models" *Environmental Sciences Proceedings* 2, no. 1: 21.
https://doi.org/10.3390/environsciproc2020002021