# 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

- Guo, S.; Zhang, H.; Chen, H.; Peng, D.; Liu, P.; Pang, B. A reservoir flood forecasting and control system for China / Un système chinois de prévision et de contrôle de crue en barrage. Hydrol. Sci. J.
**2004**, 49, 959–972. [Google Scholar] [CrossRef] - Bruwier, M.; Erpicum, S.; Pirotton, M.; Archambeau, P.; Dewals, B.J. Assessing the operation rules of a reservoir system based on a detailed modelling chain. Nat. Hazards Earth Syst. Sci.
**2015**, 15, 365–379. [Google Scholar] [CrossRef] [Green Version] - Iveti´c, D.; Milašinovi´c, M.; Stojkovi´c, M.; Šoti´c, A.; Charbonnier, N.; Milivojevi´c, N. Framework for Dynamic Modelling of the Dam and Reservoir System Reduced Functionality in Adverse Operating Conditions. Water
**2022**, 14, 1549. [Google Scholar] [CrossRef] - Tedla, M.G.; Cho, Y.; Jun, K. Flood Mapping from Dam Break Due to Peak Inflow: A Coupled Rainfall–Runoff and Hydraulic Models Approach. Hydrology
**2021**, 8, 89. [Google Scholar] [CrossRef] - Dobson, B.; Wagener, T.; Pianosi, F. An argument-driven classification and comparison of reservoir operation optimization methods. Adv. Water Resour.
**2019**, 128, 74–86. [Google Scholar] [CrossRef] - Gabriel-Martin, I.; Sordo-Ward, A.; Garrote, L.; Granados, I. Hydrological Risk Analysis of Dams: The Influence of Initial Reservoir Level Conditions. Water
**2019**, 11, 461. [Google Scholar] [CrossRef] [Green Version] - Luino, F.; Tosatti, G.; Bonaria, V. Dam Failures in the 20th Century: Nearly 1000 Avoidable Victims in Italy Alone. J. Environ. Sci. Eng.
**2014**, 3, 19–31. Available online: http://www.cnr.it/prodotto/i/285435 (accessed on 15 November 2022). - Bocchiola, B.; Rosso, R. Safety of Italian dams in the face of flood hazard. Adv. Water Resour.
**2014**, 71, 23–31. [Google Scholar] [CrossRef] - Direttiva del Presidente del Consiglio dei Ministri 8 luglio 2014. Indirizzi Operativi Inerenti All’attività di Protezione Civile Nell’ambito dei Bacini in cui Siano Presenti Grandi Dighe. Available online: https://www.dighe.eu/normativa/allegati/2014_Direttiva_PCM_8-07.pdf (accessed on 8 July 2014). (In Italian).
- Koutsoyiannis, D.; Economou, A. Evaluation of the parameterization-simulation-optimization approach for the control of reservoir systems. Water Resour. Res.
**2003**, 39, 1170–1434. [Google Scholar] [CrossRef] [Green Version] - Huang, L.; Xiang, L.; Fang, H.; Yin, D.; Si, Y.; Wei, J.; Liu, J.; Hu, X.; Zhang, L. Balancing social, economic and ecological benefits of reservoir operation during the flood season: A case study of the Three Gorges Project, China. J. Hydrol.
**2019**, 572, 422–434. [Google Scholar] [CrossRef] - Giuliani, M.; Lamontagne, J.R.; Reed, P.M.; Castelletti, A. A State-of-the-Art Review of Optimal Reservoir Control for Managing Conflicting Demands in a Changing World. Water Resour. Res.
**2021**, 57, e2021WR029927. [Google Scholar] [CrossRef] - Papathanasiou, C.; Serbis, D.; Mamassis, N. Flood mitigation at the downstream areas of a transboundary river. Water Utility J.
**2013**, 3, 33–42. [Google Scholar] - Hardesty, S.; Shen, X.; Nikolopoulos, E.; Anagnostou, E. A Numerical Framework for Evaluating Flood Inundation Hazard under Different Dam Operation Scenarios—A Case Study in Naugatuck River. Water
**2018**, 10, 1798. [Google Scholar] [CrossRef] [Green Version] - Zhou, T.; Jin, J. Comparative analysis of routed flood frequency for reservoirs in parallel incorporating bivariate flood frequency and reservoir operation. J. Flood Risk. Manag.
**2021**, 14, e12705. [Google Scholar] [CrossRef] - Shen, G.; Lu, Y.; Zhang, S.; Xiang, Y.; Sheng, J.; Fu, J.; Fu, S.; Liu, M. Risk dynamics modeling of reservoir dam break for safety control in the emergency response process. Water Supply
**2021**, 21, 1356–1371. [Google Scholar] [CrossRef] - Acreman, M.C. A simple stochastic model of hourly rainfall for Farnborough, England. Hydrol. Sci. J.
**1990**, 35, 119–148. [Google Scholar] [CrossRef] [Green Version] - Cameron, D.; Beven, K.; Tawn, J. An evaluation of three stochastic rainfall models. J. Hydrol.
**2000**, 228, 130–149. [Google Scholar] [CrossRef] - Vandenberghe, S.; Verhoest, N.E.C.; Buyse, E.; De Baets, B. A stochastic design rainfall generator based on copulas and mass curves. Hydrol. Earth Syst. Sci.
**2010**, 14, 2429–2442. [Google Scholar] [CrossRef] [Green Version] - Volpi, E.; Fiori, A. Design event selection in bivariate hydrological frequency analysis. Hydrol. Sci. J.
**2012**, 57, 1506–1515. [Google Scholar] [CrossRef] - Brigandì, G.; Aronica, G.T. Generation of Sub-Hourly Rainfall Events through a Point Stochastic Rainfall Model. Geosciences
**2019**, 9, 226. [Google Scholar] [CrossRef] [Green Version] - Salvadori, G.; De Michele, C.; Kottegoda, N.T.; Rosso, R. Extremes in Nature. An Approach Using Copulas; Springer: Dordrecht, The Netherlands, 2007. [Google Scholar]
- Genest, C.; Favre, A.C. Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. ASCE
**2007**, 12, 347–368. [Google Scholar] [CrossRef] - Requena, A.I.; Mediero, L.; Garrote, L. A bivariate return period based on copulas for hydrologic dam design: Accounting for reservoir routing in risk estimation. Hydrol. Earth Syst. Sci.
**2013**, 17, 3023–3038. [Google Scholar] [CrossRef] [Green Version] - Balistrocchi, M.; Orlandini, S.; Ranzi, R.; Bacchi, B. Copula-based modeling of flood control reservoirs. Water Resour. Res.
**2017**, 53, 9883–9900. [Google Scholar] [CrossRef] - Rizwan, M.; Guo, S.; Yin, J.; Xiong, F. Deriving Design Flood Hydrographs Based on Copula Function: A Case Study in Pakistan. Water
**2019**, 11, 1531. [Google Scholar] [CrossRef] [Green Version] - Tan, Q.; Mao, Y.; Wen, X.; Jin, T.; Ding, Z.; Wang, Z. Copula-based modeling of hydraulic structures using a nonlinear reservoir model. Hydrol. Res.
**2021**, 52, 1577. [Google Scholar] [CrossRef] - Klein, B.; Schumann, A.H.; Pahlow, M. Copulas—New Risk Assessment Methodology for Dam Safety. In Flood Risk Assessment and Management; Schumann, A.H., Ed.; Springer: Dordrecht, The Netherlands, 2010; pp. 149–185. [Google Scholar] [CrossRef]
- Huizinga, J.; De Moel, H.; Szewczyk, W. Global Flood Depth-damage Functions. JRC Technical Report. Available online: https://publications.jrc.ec.europa.eu›JRC105688 (accessed on 30 May 2022).
- Candela, A.; Brigandì, G.; Aronica, G.T. Estimation of synthetic flood design hydrographs using a distributed rainfall-runoff model coupled with a copula-based single storm rainfall generator. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 1819–1833. [Google Scholar] [CrossRef] [Green Version] - Kao, S.-C.; Govindaraju, R.S. Probabilistic structure of storm surface runoff considering the dependence between average intensity and storm duration of rainfall events. Water Resour. Res.
**2007**, 43, W06410. [Google Scholar] [CrossRef] - Genest, C.; Rivest, L. Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc.
**1993**, 88, 1034–1043. [Google Scholar] [CrossRef] - Maidment, D.R. Handbook of Hydrology; McGraw-Hill International: New York, NY, USA, 1992. [Google Scholar]
- Kottegoda, N.T.; Rosso, R. Applied Statistics for Civil and Environmental Engineers; Blackwell Publishing Ltd.: Oxford, UK, 2008. [Google Scholar]
- Huff, F. Time Distribution Rainfall in Heavy Storms. Water Resour. Res.
**1967**, 3, 1007–1019. [Google Scholar] [CrossRef] - Wooding, R.A. A hydraulic model for the catchment stream problem: 1.-Kinetic wave theory. J. Hydrol.
**1965**, 3, 254–267. [Google Scholar] [CrossRef] - US Department of Agriculture. Soil Conservation Service, National Engineering Handbook, Hydrology: Sec.4; US Department of Agriculture: Washington, DC, USA, 1986. [Google Scholar]
- Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1998. [Google Scholar]
- Yevjevich, V.M. Analytical integration of the differential equation for water storages. J. Res. Nat. Bureau Stand.-B. Math. Math. Phys.
**1959**, 63, 43–52. Available online: https://nvlpubs.nist.gov/nistpubs/jres/63B/jresv63Bn1p43_A1b.pdf (accessed on 30 May 2022). [CrossRef] [Green Version] - Aronica, G.T.; Tucciarelli, T.; Nasello, C. 2D Multilevel Model for Flood Wave Propagation in Flood-Affected Areas. J. Water Resour. Plan. Manag.-ASCE
**1998**, 124, 210. [Google Scholar] [CrossRef] - Aronica, G.T.; Candela, A. Derivation of flood frequency curves in poorly gauged catchments using a simple stochastic hydrological rainfall-runoff model. J. Hydrol.
**2007**, 347, 132–142. [Google Scholar] [CrossRef] - Candela, A.; Aronica, G.T. Probabilistic Flood Hazard Mapping Using Bivariate Analysis Based on Copulas. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng.
**2017**, 3, A4016002-A1. [Google Scholar] [CrossRef] - Rusmini, M. Pan-European Flood Hazard and Damage Assessment; Evaluation of a New If-SAR Digital Terrain Model for Flood Depth and Flood Extent Calculation. Available online: https://webapps.itc.utwente.nl/librarywww/papers_2009/msc/aes/rusmini.pdf (accessed on 30 May 2022).
- INEA. Il Valore della Terra. Available online: https://rica.crea.gov.it/download.php?id=938 (accessed on 30 May 2022).
- Bonaccorso, B.; Aronica, G.T. Estimating Temporal Changes in Extreme Rainfall in Sicily Region (Italy). Water Resour. Manag.
**2016**, 30, 5651–5670. [Google Scholar] [CrossRef] - Bonaccorso, B.; Brigandì, G.; Aronica, G.T. Regional sub-hourly extreme rainfall estimates in Sicily under a scale invariance framework. Water Resour. Manag.
**2020**, 34, 4363–4380. [Google Scholar] [CrossRef] - Doherty, J. PEST: Model Independent Parameter Estimation; Watermark Numerical Computing: Brisbane, Australia, 2010. Available online: https://www.epa.gov/sites/default/files/documents/PESTMAN.PDF (accessed on 30 May 2022).
- Levenberg, K. A method for the solution of certain non-linear problems in least squares. Q. Appl. Math.
**1944**, 2, 164–168. [Google Scholar] [CrossRef] [Green Version] - Marquardt, D. An algorithm for least-squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math.
**1963**, 11, 431–441. [Google Scholar] [CrossRef] - Ponce, V.; Hawkins, R. Runoff Curve Number: Has It Reached Maturity? J. Hydrol. Eng.
**1996**, 1, 11–19. [Google Scholar] [CrossRef]

**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