# Analysis of the Effects of Reservoir Operating Scenarios on Downstream Flood Damage Risk Using an Integrated Monte Carlo Modelling Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study and Data

^{3}, and an impounded lake with an extension of 1.8 km

^{2}.

^{2}. The Digital Terrain Model (DTM) available for this area, extracted from a 20-m resolution DTM covering the whole Sicilian territory derived by an aerial photogrammetric survey, provides for the analysed sub-catchment at a maximum elevation of 1360 m above sea level (a.s.l.) and a minimum elevation of 250 m a.s.l. at Castello dam section. The normal water level of the reservoir is 293.65 m a.s.l., whereas the maximum water level is 296.65 m a.s.l.

#### 2.2. The methodology

#### 2.2.1. Rainfall Generation Model

#### 2.2.2. Flood Hydrographs Generation Model

_{m,n,p}represents the area of generic cell (m, n) characterized by a concentration time ϑ

_{c}(m,n).

_{m,n→,out}[m] is the hydraulic path length between the centroid of the (m, n) cell and the outlet section of the catchment, k

_{m,n→,out}[m

^{1/3}/s] is the Strickler roughness for the same path, s

_{m,n→,out}[m/m] is its slope, and r

_{m,n}[m/s] is the average rainfall intensity for the rainfall event over the (m, n) cell.

#### 2.2.3. Reservoir Routing Model for Discharged Hydrographs Derivation

_{in}(t) is the inflow hydrograph, Q

_{out}[W(t)] is the outflow hydrograph, and W(t) is the reservoir storage. The problems for which this equation is applicable are given by Yevjevich [39]. Equation (7) has been here solved numerically using a fourth-order Runge–Kutta method implemented in a Matlab routine [39]. Particularly, the inflow discharge can be simulated using rainfall-runoff models, and the outflow discharge can be computed using spillway rating curve as follows:

_{d}is the discharge coefficient assumed equal to 0.385, L

_{e}is the effective length of spillway crest, and 𝐻 is the head on the spillway crest. The effective length of the spillway crest can be computed as follows:

_{n}is the net length of the crest, N

_{p}is the number of the piers, K

_{p}is the pier contraction coefficient, and K

_{a}is the abutment contraction coefficient.

#### 2.2.4. Flood Propagation Modelling Downstream Reservoir

#### 2.2.5. Flood Damage Evaluation

^{2}for the same purchasing power parity (PPP).

## 3. Results

_{n}(z) derived from the empirical data.

_{II}value) available for the sub-catchment (Figure 11).

_{II}) (Figure 11b).

_{III}condition), CN values considered to run the model are those relative to totally wet soil condition (CN

_{III}values), derived from the CN

_{II}values as follows [50]:

^{1/3}/s, respectively.

^{3}/s, a RSR index equal to 0.283, and a Nash-Sutcliffe index equal to 0.921, with an error in-peak discharge of 0.94% and in-flood volume of −4.96%.

^{2}downstream, discretized into 25.436 nodes and 49.278 elements. The terrain elevations for the study area were derived starting from a 2-m resolution DTM interpolated from a LIDAR survey available for the floodplain. Manning’s roughness coefficient was the unique calibration parameter involved in the propagation model; particularly, one coefficient for each triangular element can be chosen but, lacking a robust basis for allowing the roughness coefficient to vary, the entire triangular domain was divided into two principal regions—the floodplain area and the river—and for both regions, a calibrated Manning roughness coefficient was considered (0.037 s.m

^{−1/3}for the river and 0.051 s.m

^{−1/3}for the floodplain area). As an example, in Figure 13, the domain DTM (Figure 13a) and the flood inundated area for a given reservoir condition (Figure 13b), corresponding to normal water level in the reservoir, are reported.

^{2}of agricultural land with the same purchasing power of the area where the study area is located, obtaining the damage curves representing the total damage per m

^{2}in function of the water depth for the main agricultural landcover classes of the Magazzolo floodplain (Figure 14).

## 4. Discussion

^{3}/s and 7.92 Mm

^{3}for 50-yrs return time; 824.0 m

^{3}/s and 8.99 Mm

^{3}for 100-yrs return time.

## 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 5.**Depth–damage functions of main agricultural landcover classes for Italy (after [43]).

**Figure 6.**Q-Q plot (nonparametrically estimated K

_{n}(z) versus parametrically estimated K(z)) for: (

**a**) Frank copula; (

**b**) Gumbel–Hougard copula.

**Figure 7.**Comparison between the level curves of the theoretical copulas (thin lines) and the empirical copulas (thick lines) for: (

**a**) Frank copula; (

**b**) Gumbel–Hougaard copula.

**Figure 8.**Goodness of fit assessment of marginal distribution of: (

**a**) rainfall volumes; (

**b**) durations.

**Figure 9.**(

**a**) Dimensionless hyetographs for the selected events (thick red lines for 5% and 95% percentiles); (

**b**) Scatter plot of 1500 values generated by the model and the empirical data.

**Figure 10.**Flood event of 25–26 February 2015: (

**a**) Observed flood hydrograph and rainfall; (

**b**) comparison between observed and modelled hydrographs.

**Figure 11.**Castello dam catchment: (

**a**) Path length map scale in meters); (

**b**) CN

_{II}spatial distribution map.

**Figure 13.**MLFP-2D model implementation: (

**a**) layout of the model domain, including 2-m resolution DTM and the domain boundary (black dotted line); (

**b**) inundated area for a single random generated hydrograph and a given initial water level reservoir condition (IWL1).

**Figure 15.**Total direct damage (in MEuro) for different IWL conditions: (

**a**) 293.65 m a.s.l. water level (IWL1); (

**b**) 290.00 m a.s.l. water level (IWL2).

**Figure 16.**Spatial interpolation for the total direct damage (damage surfaces) for different IWL conditions: (

**a**) 293.65 m a.s.l water level (IWL1); (

**b**) 290.00 m a.s.l. water level (IWL2).

Main Agricultural Surface | Average Values per M^{2} (Euros) |
---|---|

Non irrigable arable land | 0.9403 |

Fruit trees | 1.9614 |

Permanently irrigated land | 3.0224 |

Vineyards | 1.5923 |

Annual and permanent crops | 1.3474 |

Duration (min) | Volume (mm) | I_{avg}(mm/h) | I_{max,30′}(mm/h) | |
---|---|---|---|---|

Length of record (years) | 17 (2003–2020) | |||

Number of events | 52 | |||

Max | 3870 | 163.8 | 26.51 | 84.80 |

Min | 120 | 19.2 | 0.64 | 9.20 |

Mean | 955.58 | 60.84 | 6.12 | 37.76 |

Standard deviation | 743.96 | 34.35 | 5.38 | 20.01 |

Copula | θ |
---|---|

Gumbel–Hougard | 1.2427 |

Frank | 2.1407 |

Return Time | Q_{max}/V_{tot} | IWL1 (293.65 m) | IWL2 (290.00 m) |
---|---|---|---|

50 years | 653.0 m^{3}/s | € 735,738 | € 354,563 |

7.92 Mm^{3} | |||

100 years | 824.0 m^{3}/s | € 811,862 | € 560,765 |

8.99 Mm^{3} |

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**MDPI and ACS Style**

Brigandì, G.; Candela, A.; Aronica, G.T.
Analysis of the Effects of Reservoir Operating Scenarios on Downstream Flood Damage Risk Using an Integrated Monte Carlo Modelling Approach. *Water* **2023**, *15*, 550.
https://doi.org/10.3390/w15030550

**AMA Style**

Brigandì G, Candela A, Aronica GT.
Analysis of the Effects of Reservoir Operating Scenarios on Downstream Flood Damage Risk Using an Integrated Monte Carlo Modelling Approach. *Water*. 2023; 15(3):550.
https://doi.org/10.3390/w15030550

**Chicago/Turabian Style**

Brigandì, Giuseppina, Angela Candela, and Giuseppe Tito Aronica.
2023. "Analysis of the Effects of Reservoir Operating Scenarios on Downstream Flood Damage Risk Using an Integrated Monte Carlo Modelling Approach" *Water* 15, no. 3: 550.
https://doi.org/10.3390/w15030550