Flood Impacts on a Water Distribution Network

Floods cause damage to people, buildings and infrastructures. Water distribution systems are particularly exposed, since water treatment plants are often located next to the rivers. Failure of the system leads to both direct losses, for instance damage to equipment and pipeworks contamination, and to indirect impact, since it may lead to service disruption and thus affect population far from the event through the functional dependencies of the network. In this work, we present an 5 analysis of direct and indirect damages on a drinking water supply system, considering the hazard of riverine flooding as well as the exposure and vulnerability of active system components. The method is based on interleaving, through a semi-automated GIS procedure, a flood model and an EPANETbased pipe network model with a Pressure-Driven-Demand approach, needed when modelling water distribution networks in highly off-design conditions. Impact measures are defined and estimated so 10 as to quantify service outage and potential pipe contamination. The method is applied to the water supply system of the city of Florence, Italy, serving approximately 380 000 inhabitants. The evaluation of flood impact on the water distribution network is carried out for different events with assigned recurrence intervals. Vulnerable elements exposed to the flood are identified and analysed in order to estimate their residual functionality and to simulate failure scenarios. Results show that in the 15 worst failure scenario (no residual functionality of the lifting station and 500-year flood) 420 km of pipeworks would require disinfection with an estimated cost of 21 Me, which is about 0.5% of the direct flood losses evaluated for buildings and contents. Moreover, if flood impacts on the water distribution network are considered, the population affected by the flood is up to three times the population directly flooded. 20

Vulnerable WSS components are often located in low-lying areas or nearby rivers, with a consequent high exposure to inundations. Flood events affecting water utilities can lead to costly repairs, 60 disruptions of service and public health advisories (U.S. Environmental Protection Agency, 2014).
The management of flood risk entails a combined approach comprising mitigation, preparedness, response and recovery (WHO, 2011). Among the mitigation activities, the identification of hazard and a comprehensive vulnerability analysis are recognized as pre-eminent. Risk assessment is a fundamental support for decision makers because it increases the awareness and fosters the adoption 65 of mitigation strategies (Large et al., 2014).
The implementation of Water Safety Plan promoted by the World Health Organization (WHO) and International Water Association (IWA) (Bartram et al., 2009) aims at harmonising hazard and risk assessment procedures through an appropriate method. It identifies issues on treatment plants and source water quality (Ginandjar et al., 2015) as the main hazards associated with floods. Floods 70 and heavy rainfall are associated with elevated turbidity and dissolved organic matter (Göransson et al., 2013;Murshed et al., 2014), which can affect drinking water purification whose source is a surface water body or storage reservoir. However, if indirect/cascade effects are accounted for, other impacts should be considered such as those related to power outage, which is likely to occur if electric devices, e.g. valves and lifting stations, are affected (Khan et al., 2015). In fact, a short-75 term loss of the electric power may induce pressure fluctuations or intermittent supply, which may lead to ingress of contamination from leakage orifices and air vacuum valves (Ebacher et al., 2010).
Thus, besides the economic costs the contamination may cause, there are repercussions on social and operational domains characterizing urban water systems (Blackmore and Plant, 2008;Hrudey et al., 2006). Hence, a comprehensive flood risk assessment of WSS's should integrate a flood model 80 and a WSS model capable of properly representing the network behavior in low pressure conditions (Seyoum and Tanyimboh, 2016  Shaded boxes represent activities that are not carried out in this work). mand (PDD). Failure scenarios are based on the analysis of exposure and vulnerability of critical network components, e.g. lifting stations. Three metrics for the assessment of flood impact are introduced and the model is tested on a case study.

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The flood risk assessment of a WSS requires a comprehensive approach including several scales of analysis and models in order to capture the dependencies between environmental forcing (i.e. a natural hazard) and WSS components besides the inner dependencies of the WSS. Impacts on the WSS pertain to quantity and quality of the drinking water. Figure 1    hydraulic model for the floodplain consists of several storage areas (cells) connected to the river banks through a set of lateral weirs, whose geometry is extracted from topographic survey. When 140 the inundation starts, the quasi-2D module -governed by continuity and stage-storage relationscalculates water levels from the volume stored in the cell. Flow between adjacent cells is described by a weir equation accounting for backwater effects. The details of the model construct and equations adopted in the HEC-RAS framework (for both 1D and quasi-2D modules) are described in Arrighi et al. (2013). Moreover, the availability of inundation maps from local and national water 145 authorities is growing due to the evolving normative frameworks in flood risk management (EU Parliament, 2007). Thus, official inundation maps can be adopted if accessible and adequate in spatial resolution in the area of interest. Geographic Information Systems (GIS) are unavoidable to identify exposed asset. All the components of the WDN, both active and passive must be geo-referenced to be compared with inundation maps for assigned scenarios.

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Exposure analysis consists of four steps. Firstly, the coordinates of the WSS point components (nodes, reservoirs, lifting stations, etc.) are exported from the WSS model to a layer in the GIS environment, so that a new vector is created whose coordinate reference system is assigned in the shapefile properties. Afterwards, the raster inundation map is imported into the GIS workspace and converted if necessary to a compatible reference system. The raster cell information (i.e. water depth) 155 is then extracted over the point feature and added as attribute using open plugins (e.g. Point Sampling Tool available for QGIS). The point features whose water depth attribute is larger than a threshold are considered exposed and added to the list of exposed asset. The threshold, in this work, is assigned a fixed value of 0.25 m. For each component pertaining to exposed asset and failure-prone, local water depth is compared to a threshold depth which takes into account local geometry and functional properties modified in the WSS model (section 2.2) to reproduce the failed configuration.

Distribution Network Model
The model is based on the freely available EPANET libraries, which calculate time-varying pressures at the nodes given a set of initial tank levels, pump switching criteria, node base demands and demand 165 patterns. In particular, EPANET can be launched by other software through a set of DLL libraries.
One drawback of the standard EPANET implementation is its strict demand-driven approach, which stems from the primary goal of simulating correctly operated networks. In such networks, pressure at each node is sufficient so as to allow withdrawal of required demand from each node, so that demands can be assumed as defined input data. However, when simulating strongly off-design 170 networks, nodes featuring a reduced pressure are possible and quite common, so that a pressuredriven approach is needed (Cheung et al., 2005;Walski et al., 2017). PDD models differ from conventional ones in that demands at nodes are not attributed a priori, but their value depends on the current pressure at the considered node.
In particular, and consistently with practice, the model assumes that each node can be in one of 175 three states: fully served -if H i ≥ H service , the node is able to withdraw its nominal demand; partially served -if H service > H i > 0, the node withdraws a reduced demand proportional which can be expressed as where α is a constant exponent set to 0.5.
non-served -if P = 0, the node is unable to withdraw any water, yielding to null demand.
EPANET allows two types of nodes: nodes are assigned a time-varying, pressure-independent demand, and can be effectively used to model fully served users, whereas emitters, conceived to model fixed cross-section water outlets such as fire hoses and orifices, adequately model the 185 aforementioned behaviour of partially served users. Emitters are defined by a fixed exponent α, equal for all instances, and a flow coefficient which represents the volume flow rate for unitary pressure loss across the orifice. Unfortunately, emitters do not cope well with calculated negative pressures, attributing a negative -i.e. entering -flow rate where such negative pressures occur.
In order to cope with this issue, a MATLAB code has been implemented so as to run transient 190 simulation while correctly using a PDD approach. The code -as shown in Figure 2 -works as follows: three node states are defined: "2" for served nodes, "1" for partially served ones and "0" for non-served ones; type 2 and type 0 nodes are modelled as EPANET nodes with nominal demand  equal to the assigned nominal demand D i and zero respectively, whereas type 1 nodes are modelled as emitters whose flow coefficients are calculated to ensure that 195 For each timestep, a first trial simulation is run with all nodes in state 2 in order to get the expected pressures. Afterwards, each node is checked to assess whether its pressure is in the pressure range corresponding to the current flow regimen and, if this is not the case, its state is accordingly raised or lowered by one unit (namely, it is not possible to jump from state 2 to state 0 and vice versa). After node states have been changed, simulation is repeated till no more node state change is 200 necessary. Calculated flow rates and pressures are considered to represent network operation during the following timestep. In particular, flow rates are used to calculate the time to the next event (tank being filled or emptied), and the first event affecting network topology is considered (e.g. demand change, or pump setting toggle due to time pattern, tank getting empty or full). Tank levels are the updated and simulation proceeds to the next timestep.

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The described procedure allows to calculate pressure and supplied demand at each node for each timestep, therefore fully estimating the network state in each moment.

Model initialisation
The model, featuring non memory-less elements (tanks), needs to be correctly initialised. In normal operation, tank levels undergo a daily pattern of filling and emptying, according to demands and water availability. In order to appropriately initialise tank levels, a warm-up simulation is run by randomly initialising tank levels and checking their value every 24 hours. If the calculated levels with a time difference of 24 hours differ by less than a tolerance parameter, the model is considered to be in long-term steady state and water level for each tank and time value are saved in a matrix, which can be thereafter be used to initialise such values for the forthcoming simulations. Inhabitants are assigned to nodes as follows: an uniform demand per capita is assumed in each area and calculated, and the number of inhabitants for nodes pertaining to that area is estimated accordingly. In particular: where P i is the population assigned to node i belonging to area A and P A is the total population of area A. The global damage parameter Non-Served Population (NSP) is therefore estimated as the sum of population attributed to nodes with reduced or null pressure, i.e.
where H service is the minimum head required to consider a node fully served (5.0 m in the case study).
As a second parameter, network damage due to pipe contamination is evaluated by calculating the total length of pipework to be decontaminated. A pipe is considered to be contaminated if at any point in time the head inside the pipe is lower than the flood water head outside or below zero, i.e.
where J i is the set of pipes with either end connected to node i.  The meter scale DTM used for the hydraulic model is freely available in the regional cartographic repository (dati.toscana.it/dataset/lidar). The hydraulic data (hydrographs and river water profiles) are made available by the catchment authority ("Autorità di Bacino del Fiume Arno"), which is in charge of flood risk management and water resource planning.
For the application of the method described in Section 2, four flood scenarios with given recur-255 rence interval RI are considered: a frequent scenario (i.e. 30-year return period), two medium recurrence intervals (100 and 200 years) and a rare scenario (500 years). Accordingly, four inundation raster maps are generated for during the exposure analysis.

Water distribution network
The studied WSS features one main treatment facility, 17 tanks and the pipework to supply drinking 260 water for domestic and industrial use.
Fresh water supply is ensured by the river Arno, which flows westbound amidst the urban area.
Water is abstracted from the river by three 373-kW pumps in the treatment plant "Anconella", which is located in the left bank and designed to process 4 m 3 /s (Fig. 3).   Anconella, shown in the right-hand side of Figure 3, is flooded with a water depth exceeding 0.85 m.
For these scenarios, issues are expected because of drinking water treatment restrictions, loss of control and power shut-down of the lifting station. The "VCMantigna" tank is still exposed, with water depths as high as 2 m for RI=500.  assumed that the DWTP completely stops providing fresh water to the system. Whereas in scenario 2 some backup system is envisaged to keep one of the three main pumps feeding the network in 295 operation.

Affected areas
The heads at nodes after 120 minutes from the lifting station failures are shown in Figure 4 in failure scenarios 1 (panel a) and 2 (panel b). After 120 minutes from the shutdown in the failure scenario 1 ( Figure 4, panel a), about 50% nodes already experience heads lower that 1 m, where just three zones, 300 one in the westernmost part of the network (due to the lower altitude favouring piezometric head) and two on the northern and southern hills (due to local tanks providing capacity, see Sect. 4.3) feature heads higher than 20 m. After six hours (Fig. 5), the number of served nodes is further reduced, with only the westernmost part of the network and southern hills (low altitude and higher with a great number of tanks respectively) being served.

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For what concerns failure scenario 2 ( Figure 4, panel b), most nodes of the network are operational after 120 minutes from the shutdown, with pressures in the minimum range of residual level of service(1-10 m). A few nodes on the northern hills (about 15%) experience heads lower than 1 m and a significant part of the western city in the right bank experience heads comprised between 10 and 200 m due to their low terrain elevation.

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In both cases the service disruption, due to insufficient pressures, affects also nodes outside the inundated area, thus it can be considered an indirect impact of the flood triggered by the failure of the lifting station due to the physical contact with water.

Calculated metrics
The time evolution of aggregate service metrics are calculated for the two aforementioned failure 315 scenarios. Population Not Served is shown in Figures 5 and 6 as a fraction of total population for the two scenarios.
In failure scenario 1, the complete shutdown of the DTWP pumping station puts almost 50% of the population in a no service condition after 3 hours, consistently with the dynamics shown in 12 Nat. Hazards Earth Syst. Sci. Discuss., https://doi.org/10.5194/nhess-2017-205 Manuscript under review for journal Nat. Hazards Earth Syst. Sci.    In failure scenario 2, total affected population ranges from 62 to 77%. Nevertheless, inhabitant experiencing no service at all are about 15%, rising to less than 30% only after 9 h.
For what concerns evaluation of network damage, Figures 7 and 8 show the length of contaminated pipe as a function of time for the two studied failure scenarios.

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Again, scenario 1 shows a critical situation, where about 25% of the network undergoes contamination risk shortly after the shutdown and 68% of the network is out of service just six hours afterwards. In scenario 2, the contaminated pipe length fraction rises from 9% to 26% in the first 12 hours, thus suggesting a milder impact. Nevertheless, caution must be paid for the risk of backflow towards nodes which lie on the borders of the served areas.

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In principle, contaminated pipe length does depend of the RI considered, since higher floodwater depth leads to higher contamination risk. Nevertheless, results show that in the studied case there is little difference between the 200 and 500-year recurrence intervals.

Tank dynamics
350 Figure 9, shows the water volume stored in the tank system at a given time after the failure. In scenario 1, where no water is provided by the DWTP, the entire demand is met by withdrawing water from the tank system. This is highlighted by the average slope of the curve in the first three hours (about 0.75 m 3 /s, which corresponds to half of the total demand in normal conditions. After about 3 and 5 h, reservoir configuration changes, so that the average slope of the volume of the tanks 355 changes.
Slope changes in both curves are caused both by demand variations and tanks becoming empty.
In particular, the abrupt change for failure scenario 1 after about 5 h corresponds to a tank serving a great number being emptied, thus corresponding in sudden change in served demand (slope). The relationship between served demand and curve slope is not so evident for failure scenario 2, since 360 slope curve only relates to those users not directly served by the DWTP.

Sensitivity to tank levels
In case of power shutdown, the transient behaviour of the system is dictated by the amount of water stored in tanks. In order to better understand the relevance of each storage tank in the system, a sensitivity analysis has been performed. In particular, a sensitivity matrix is calculated by numerically is is estimated that 68 to 100% of the network undergoes backflow risk depending on event duration, whereas the aforementioned improvement reduces length of pipeworks to be flushed by 60%, with a first-estimate saving of about 13 Me. Sensitivity of nodal pressures to tank levels is also studied, thus identifying influence areas of the various storage facilities.

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The implemented methodology uses flood data, WSS topology and characteristics, and water demand data to compute WSS contamination risk maps and service maps at various time moments after the event. The model is automated and lightweight, the analysis being completed in few minutes, and can be effectively used in the strategic planning of disaster recovery procedures or in comparing network strengthening solutions in budget allocation activities.

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Future developments may include studying the effect of first-intervention procedures (e.g. subsectioning of the network prior to the flood to select specific areas to contaminated while preserving functionality in others) and extending of the model to simulate recovery procedures, in order to estimate recovery times and transient network behaviour based on scheduling and available resources.
Data availability 420

Author contribution
First author conceived the impact assessment methodology and was responsible of flood hazard, exposure assessment, GIS operations and mapping. Second author implemented the PDD code, simulated the piping network and evaluated the impact metrics. Third author supervised the network modelling and last author promoted the research and supervised the flood risk aspects.