# A Modified IHACRES Rainfall-Runoff Model for Predicting the Hydrologic Response of a River Basin Connected with a Deep Groundwater Aquifer

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. The Alcantara River Basin

^{2}. The headwater of the river is at 1400 m a.s.l in the Nebrodi Mountains, while the outlet in the Ionian Sea is reached after 50 km. Table 1 lists the main morphometric and hydrologic characteristics of the entire river basin, as well as of its main sub-basin, at Moio Alcantara.

#### 2.2. The Modified IHACRES Model

## 3. Results and Discussion

#### 3.1. Calibration and Validation of the Modified IHACRES Model

^{3}per year, most of which is concentrated above Moio, and that about 32 Mm

^{3}per year are for municipal water use only, while the remaining is mainly for irrigation purpose [5], we have derived a time series for $L\left(t\right)$. In particular, 2/3 of the total extracted volume was equally distributed during the year, and the remaining added to the irrigation season, lasting from May to October. These values are assumed to also include the natural losses from the aquifer.

#### 3.2. Sensitivity Analysis of Modified IHACRES Model Parameters

_{1}. Conversely, the model appears more sensitive to the variation of parameters

**x**, and ${\mathit{\tau}}_{\mathbf{1}}$, representing the share-out parameter of the effective rainfall u(t), and the storage constant of the quick flow conceptual reservoir. This result highlights how it is important to deeply understand the main physical characteristics of the basin under investigation to keep under control the model simulation dynamics and outputs and to reduce the uncertainties in simulations due to model parameters estimation. To this end, parameter estimation could benefit from the availability of other measured data, such as spring discharges, soil moisture, as well as of a separate calibration to reduce model uncertainties.

_{1}## 4. Conclusions

_{1}, and ${\tau}_{1}$, representing respectively the share-out parameter of the effective rainfall u(t), and the storage constant of the quick flow conceptual reservoir.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Moio Alcantara sub-basin (in red) and the Northern Etna groundwater aquifer (in light blue).

**Figure 5.**Observed versus modeled streamflow for the calibration period, by using as model input (

**a**) effective rainfall generated from climate data, or (

**b**) effective rainfall generated from observed streamflow.

**Figure 6.**Observed versus modeled streamflow for the validation period by means of (

**a**) the modified IHACRES model and (

**b**) the original IHACRES model.

**Figure 7.**Uncertainty analysis in the assessment of the total discharge Q(t) based on first-order sensitivity analysis on model parameters.

Characteristic | Alcantara Basin | Moio Alcantara Sub-Basin |
---|---|---|

Area (km^{2}) | 603 | 342 |

Mean elevation (m a.s.l.) | 531 | 1142 |

Max elevation (m a.s.l.) | 3274 | 3274 |

Min elevation (m a.s.l.) | 0 | 510 |

Main river length (km) | 54.67 | 34.66 |

Medium river slope | 0.059 | 0.080 |

Mean annual rainfall (mm) | 880 | 874 |

Mean annual runoff (mm) | 342 | 222 |

Mean annual runoff coefficient | 0.39 | 0.25 |

Permeable area (%) | 43 | 46 |

**Table 2.**Parameter values and performance indicators of the modified IHACRES model for the calibration period (effective rainfall time-series generated from climate by means of the loss module).

Parameters | Value | Performance Indicator | Value |
---|---|---|---|

c [mm] | 576.70 | RB NSE | 0.25 0.60 |

${\tau}_{0}$ | 2 | ||

f [1/°C] | 3.5 | ||

${x}_{1}$ | 0.15 | ||

${\tau}_{1}$ [days] | 0.46 | ||

${y}_{1}$ | 0.75 (if ${G}_{2}\left(t\right)<0$) | ||

1 (if ${G}_{2}\left(t\right)>0$) | |||

${\tau}_{2}$ [days] | 17.63 |

**Table 3.**Parameter values and performance indicators of the modified IHACRES model for the calibration period (effective rainfall time-series generated from streamflow record).

Parameters | Value | Performance Indicator | Value |
---|---|---|---|

${x}_{1}$ | 0.15 | RB NSE RB_s NSE_s | −0.036 0.86 −0.21 0.64 |

${\tau}_{1}$ [days] | 0.45 | ||

${y}_{1}$ | 0.75 (if ${G}_{2}\left(t\right)<0$) | ||

1 (if ${G}_{2}\left(t\right)>0$) | |||

${\tau}_{2}$ [days] | 28.54 |

Performance Indicator | Value |
---|---|

RB | 0.19 |

NSE | 0.81 |

RB_s | 0.14 |

NSE_s | 0.54 |

Performance Indicator | Calibration Value | Validation Value |
---|---|---|

RB | −0.34 | −0.31 |

NSE | 0.81 | 0.77 |

RB_s | −0.65 | −0.56 |

NSE_s | 0.47 | 0.20 |

Sobol Index | Value |
---|---|

${\left[S\right]}_{{\mathit{\tau}}_{\mathbf{1}}}$ | 0.0422314 |

${\left[S\right]}_{{\mathit{\tau}}_{\mathbf{2}}}$ | 0.016778 |

${\left[S\right]}_{\mathit{x}\mathbf{1}}$ | 0.063349 |

${\left[S\right]}_{\mathit{y}\mathbf{1}}$ | 0.03130456 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Borzì, I.; Bonaccorso, B.; Fiori, A. A Modified IHACRES Rainfall-Runoff Model for Predicting the Hydrologic Response of a River Basin Connected with a Deep Groundwater Aquifer. *Water* **2019**, *11*, 2031.
https://doi.org/10.3390/w11102031

**AMA Style**

Borzì I, Bonaccorso B, Fiori A. A Modified IHACRES Rainfall-Runoff Model for Predicting the Hydrologic Response of a River Basin Connected with a Deep Groundwater Aquifer. *Water*. 2019; 11(10):2031.
https://doi.org/10.3390/w11102031

**Chicago/Turabian Style**

Borzì, Iolanda, Brunella Bonaccorso, and Aldo Fiori. 2019. "A Modified IHACRES Rainfall-Runoff Model for Predicting the Hydrologic Response of a River Basin Connected with a Deep Groundwater Aquifer" *Water* 11, no. 10: 2031.
https://doi.org/10.3390/w11102031