**1. Introduction**

Recent studies have shown that in Central Italy, the occurrence of torrential rainfall, exceeding 100 mm/d, has increased in the last decades [1]. Furthermore, future projections by global and regional climate models indicate an intensification of extreme precipitation events in Italy [2–4]. As a consequence of global warming, sea level rise is also expected in the next years in the Mediterranean region [5,6]. Lambeck et al. [7] have argued that in the central Tyrrhenian Sea, sea level rise will mainly impact the coasts near Rome. Some of these coasts include the southern Latium, with its mainly coastal lakes, the Voltuno littoral, and the Sele River area, with sea level rise ranging from 315 to 1400 mm, depending on the climate scenario considered. Rising sea levels and intensification of extreme precipitation significantly increases the flood risk in such low-lying coastal areas. This has some substantial consequences, as the coastal areas around Rome are densely populated, with extensive and highly developed agriculture along with a large presence of industrial activity.

Within this region, an area particularly vulnerable to flooding is in the Mazzocchio zone, the lowest lying area of the Pontina plain (see Figure 1a). The majority of this zone has a soil surface elevation equal to or lower than the mean sea level. Historically a swamp, this zone was recovered in the years 1926–1937 by a large reclamation work covering an area of 20,000 ha.

**Figure 1.** (**a**) Hydraulic network and basins of the study site. (**b**) Mazzocchio's basin ground elevation.

As seen in Figure 1a, the Mazzocchio zone is enclosed by two rivers: Ufente in the north and Linea Pio in the south. To ensure dry soil, water runoff is intercepted within and outside the zone. To intercept the runoff outside the zone, the two rivers act as barriers, and within the zone, water runoff—caused by rainfall over the zone—is collected by a dense channel network in the Selcella River. Downstream of the Selcella River, there is a pumping station which lifts the water from the Mazzocchio area into the Ufente River, with a maximum capacity of 36 m3/s. Figure 1a shows the water coming from the upstream basins of the Ufente, Linea Pio, and Amaseno Rivers, together with the pumping water from the Mazzocchio area, flowing through the Portatore Channel towards the sea.

On 7 November 2014, a heavy rainfall event (approximately 100 mm/d) caused a serious crisis to the entire channel network, with flooding in the Mazzocchio area and overflowing and subsequent collapse of a large portion of the levees along the Ufente River. Most of the damage occurred along the Ufente River stretch closer to the Mazzocchio pumping station (downstream from the confluence with the Selcella collector). High rainfall amount and sea level rise due to storm surge at the outlet of the Portatore channel were the two main factors which caused the crisis of hydraulic system.

As mentioned before, the expected intensification and increment in frequency of such extreme rainfall events, as well as the sea level rise, causes serious concerns with regard to the capability of the hydraulic infrastructures to cope with similar or more intense events in the future. Therefore, methodological approaches need to be developed to assess the efficiency and reliability of existing hydraulic infrastructures. As a number of authors suggest, such methodologies must evolve to address "change" from climate variability at the global scale to local human impacts [8,9]. Recently, rainfall downscaling models have been constructed to perform projections of rainfall occurrence and amount at the basin level, under different global warming scenarios simulated by global or regional circulation models (GCMs and RCMs) [10,11]. Therefore, such models can be used to provide the hydrological inputs necessary to run hydraulic models to assess the reliability of existing hydraulic infrastructures, and eventually the design of new ones, to manage future flooding risk at the local scale. Preliminary to such assessment, it is, however, necessary to perform an analysis on the capability of the existing infrastructure to manage the risk of flooding due to extreme rainfall and high tidal sea level events. This is very useful to identify the elements of the hydraulic network which are more vulnerable.

In this context, we propose a methodology and related models to assess the reliability of hydraulic infrastructures in control flooding events and apply it for the case of the reclamation region of Mazzocchio. The first question that arises in developing such a methodology is how to assess the reliability and efficiency of existing pumping–hydraulic network systems to mitigate flooding in the Mazzocchio basin under different hydrological inputs. This question arises because different pumping schedules can be hypothesized to manage extreme stream flows. In other words, as a consequence of adopting alternative pumping schedules, for the same set of hydrological inputs, a number of different configurations of hydraulic systems may potentially exist. In order to compare the effects of the different hydrologic inputs on the hydraulic system, we should identify a particular set of pumping schedules. This restricts the analysis to a few arbitrarily chosen cases of pumping schedules. To perform a more general and less restrictive analysis, in order to compare the possible different configurations of a hydraulic system under different hydrological inputs, this paper proposes to use sets of Pareto optimal solutions as calculated by a multiobjective optimization approach, in which the switching on/off levels of the pump system are assumed as decision variables. Given two or more optimality criteria, the Pareto set identifies not a unique optimal solution, but an ensemble of nondominant configurations of the system that belong to the Pareto front. Such a set of non-dominant solutions is chosen as optimal, if no objective can be improved without sacrificing at least one other objective. Therefore, for given hydrological inputs, the set of Pareto optimal solutions is unique. This solution can then be used to compare the possible states of the hydraulic system (as identified by the free surface levels and flow rates along the rivers and channel networks) forced by different hydrological inputs—rainfall amount and sea level rise—and depending on the optimal pumping schedules associated to the solutions lying in the Pareto front. In this paper, the sets of Pareto optimal solutions are calculated by a simulation–optimization model, which combines a multiobjective evolutionary algorithm (the non-dominating sorting genetic algorithm, NSGA2) and a hydraulic model. While a number of optimization methods exist [12], we use a genetic algorithm due to their reliability in solving nonlinear, nonconvex, multimodal, and discrete problems, unlike classical optimization methods [8]. Since genetic algorithms are independent of derivative information, they also allow a less restricted formalization of the objective functions and constraints. Even though a number of genetic algorithms have been proposed in the past, we adhered to NSGA2, since a number of studies have proved the reliability and robustness of such an algorithm [13]. The use of a simulation–optimization model, in which a multiobjective optimization model and hydraulic model are combined, is not novel in the literature. For instance, Cioffi and Gallerano [13], proposed a multiobjective programming model including output from 2D hydraulic simulation for habitat assessment to optimize power production and fish habitat suitability as a Pareto set. In the past, a number of simulation–optimization models specifically aimed to find the optimal schedule of pumping systems have been proposed for urban drainage systems [14–16], irrigation pumping stations [17], water supply systems [18], and water resource management [19]. However, the above-cited studies were mainly focused on the optimal control and operation of such systems. Some researchers have proposed criteria and methodologies that use simulation–optimization models to assess how climate change and global warming affect the hydrologic cycle and its effects on the performance of water resource systems. Most of these studies are addressed to assessing the climate change impacts on hydropower production by reservoirs [20–22]. Direct application of multiobjective optimization to flood risk management under climate change is very rare in the literature [23]. Most of the papers focus on cost–benefit analysis [24]. For instance, Woodward et al. [25] identify a set of Pareto optimal solutions using NSGA2, in which costs and benefits of flood risk intervention strategies are compared, taking into account the uncertainty in the future projected sea level rise. In such studies, flooding simulations by hydraulic models are carried out separately from the optimization process; the output from hydraulic simulations are used to assess the costs and benefits related to the specific flood risk intervention strategy hypothesized. Such approaches, however, seem difficult to apply in the cases in which pumping systems are part of flooding control hydraulic infrastructures. In this paper, the hydraulic simulations are integrated in the multiobjective optimization algorithm and the objective functions are not defined on the basis of economic variables, but directly in terms of flooding surface and pumping power. The main reason of such a choice is due to the uncertainty of the estimation of damage from flooding, since agriculture is the main activity over the basin, and productivity and damage depend on the period of the year, as well as the type and state of growth of crops. To calculate the sets of Pareto optimal solutions, two optimality criteria are defined: (a) to minimize the maximum flooding surface over the Mazzocchio basin; (b) to minimize the pumping power necessary to limit the flooding over the Mazzocchio basin. In formalizing the multiobjective

problem, the state variables are the free surface levels and flow rates along the hydraulic network as well as the surface of the flooding areas, and the decisional variables are the levels switching on and off the pumps in the Mazzocchio station. Temporal and spatial distribution of the rainfall amount and the sea level are the input variables. State and decisional variables range within the constraints imposed by the flow carrying capacity of the channel network downstream from the pumping station. The hydraulic state variables are simulated by a hydraulic model. In order to limit the calculation time, due to the large number of simulations necessary to solve the multiobjective problem by the genetic algorithm, a simplified version of the hydraulic model has been constructed to represent the flow river network and the rainfall–runoff and flooding processes over the river basins. The calculation along the river network is performed numerically solving the 1D de Saint-Venant equations, while the basins are represented by storage areas connected to the river network by linear channels. The paper is organized as follows: In Section 2, a description of the study areas and hydrological data is provided; in Section 2 also, the hydraulic and multiobjective optimization models are described. In Section 3, the procedure of calibration and validation for the hydraulic model, the construction of the design hydrograph, and finally the set of Pareto optimal solutions for the Mazzocchio zone obtained by solving the multiobjective problem are discussed. Comparing the different Pareto sets, the reliability of the existing pumping systems and of the hydraulic channel network is inferred.
