# Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain)

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Methodology

#### 3.1. Two Dimensional (2D) Model

#### 3.2. One Dimensional (1D) Model

#### 3.3. Finite Volume Model for the 1D Flow Equations

#### 3.4. Reservoir Model

#### 3.5. PID Regulation

- Proportional term: Expresses a proportionality between the required action and the error.
- Integral term: The required action takes into account the time integral of the error over a given period.
- Derivative term: The controller actuation is formulated from the time derivative of the error.

## 4. Model Application

#### 4.1. Discretisation of the Domain

#### 4.2. Performance Analysis of the 1D and 2D Models

#### 4.3. Performance Analysis of the 1D and 1D-0D Models

#### 4.4. Performance Analysis of the 1D and 1D-0D Models Including DAM Regulation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of Spain in Europe (

**a**); location of the Ebro River basin in Spain (

**b**) and location of the computational domain of the study in the basin (

**c**).

**Figure 2.**Representation of the 2D simulation domain of the Ebro River with the most important cities and gauging stations of CHE. The labels correspond to the official names of the gauging stations.

**Figure 3.**Zoom view of an ortophoto with measured extension of the flooded area (blue) in 2018 flood event.

**Figure 4.**Representation of the two different approaches for reservoir representation: 1D distributed discretisation as the rest of the domain (

**a**); or coupling the 1D model of the river with an aggregated 0D model of the reservoir (

**b**).

**Figure 7.**Discharge temporal evolution comparison between 1D model, 2D model and observation at Gelsa (A263) gauging station (

**upper**) and comparison between models and estimations at Mequinenza dam (E003) (

**lower**) for 2015 event.

**Figure 8.**Water level temporal evolution comparison between 1D model, 2D model and observation data at Gelsa (A263) gauging station for the 2015 event.

**Figure 10.**Discharge temporal evolution comparison between the 1D model, the 2D model and the observation at Gelsa (A263) gauging station (

**upper**) and comparison between models and estimations in Mequinenza dam (E003) (

**lower**) for the 2018 event.

**Figure 11.**Water level temporal evolution comparison between the 1D model, the 2D model and the observation in Gelsa (A263) gauging station for the 2018 event.

**Figure 12.**Longitudinal profile of bottom level, z, and water surface elevation (WSE) at different times computed with the 1D model and the coupled 1D-0D model for the 2015 case.

**Figure 13.**Comparison of computed water surface elevation (WSE) at x${}_{L}$=L’ using 1D model and 1D-0D model and computed WSE at x${}_{L}$=L using 1D model.

**Figure 14.**Temporal evolution of the water level and dam crest computed with the fully 1D model and the coupled 1D-0D model for the 2015 case with the control of a PID algorithm.

**Figure 15.**Temporal evolution of the outlet discharge at Mequinenza dam (E003) computed with the 1D model and the coupled 1D-0D model for the 2015 case with the control of a PID algorithm.

Event | Duration | 2D GPU Time | 1D CPU Time |
---|---|---|---|

2015 | 600 h | 47 h | 511 s |

2018 | 430 h | 23.8 h | 364 s |

**Table 2.**Computational times for 2015 flood event simulated in the Ebro River with the 1D-0D model and the pure 1D model.

Event | Duration | Pure 1D | 1D-0D |
---|---|---|---|

2015 | 600 h | 511 s | 196 s |

**Table 3.**Computational times for 2015 flood event simulated in the Ebro River with the 1D-0D model and the pure 1D model, both with the dam regulated with a PID algorithm.

Event | Duration | Pure 1D | 1D-0D |
---|---|---|---|

2015 | 600 h | 484 s | 176 s |

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**MDPI and ACS Style**

Echeverribar, I.; Vallés, P.; Mairal, J.; García-Navarro, P.
Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain). *Water* **2021**, *13*, 3160.
https://doi.org/10.3390/w13223160

**AMA Style**

Echeverribar I, Vallés P, Mairal J, García-Navarro P.
Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain). *Water*. 2021; 13(22):3160.
https://doi.org/10.3390/w13223160

**Chicago/Turabian Style**

Echeverribar, Isabel, Pablo Vallés, Juan Mairal, and Pilar García-Navarro.
2021. "Efficient Reservoir Modelling for Flood Regulation in the Ebro River (Spain)" *Water* 13, no. 22: 3160.
https://doi.org/10.3390/w13223160