Developing an Algorithm for Urban Flood Management With the Aim of Reducing Damage and Costs Using the Concept of Conditional Value at Risk&amp;nbsp;

<jats:title>Abstract</jats:title>         <jats:p>Flooding in urban area affects the lives of people and could cause huge damages. In this study, a model is proposed for urban flood management with the aim of reducing the total costs. For this purpose, a hybrid model has been developed using SWMM and a quasi-two-dimensional model based on the cellular automata (CA) capable of considering surface flow infiltration. Based on the hybrid model outputs, the best management practices (BMPs) scenarios are proposed. In the next step, a damage estimation model has been developed using depth-damage curves. The amount of damage has been estimated for the scenarios in different rainfall return periods to obtain the damage and cost- probability functions. The conditional value at risk (CVaR) are estimated based on these functions which is the basis of decision making about the scenarios. The proposed model is examined in an urban catchment located in Tehran, Iran. In this study, five scenarios have been designed on the basis of different BMPs. It has been found that the scenario of permeable pavements has the lowest risk. The proposed model enables the decision makers to choose the best scenario with the minimum cost taking into account the risk associated with each scenario.</jats:p>

section_content: Flood, as one of the most important natural disasters, causes a lot of damage to the world communities every year. Due to the population density and consequently various infrastructures and uses, urban areas are more vulnerable to the damage. On the other hand, today with the expansion of cities to the large areas, most of which have low permeability and temporary depression storage, the amount of damage has increased dramatically. Hence, the importance of planning to reduce flood damage has been emphasized throughout the global community. Every year, many methods and tools are created and developed for the flood management purposes. These methods and tools alone or in a combinative form can be used as an effective solution to mitigate the flood damages. Many researches have been conducted in different parts of the world in order to increase the flood management ability, some of which are mentioned in the following. 

The first necessary step in the researches related to the urban floods is to examine the current situation of the city in the face of possible floods. For this purpose, the behavior of the drainage system should be simulated and flood zone must be determined and necessary strategies should be considered in order to improve the performance according to the floods occurred in previous years and related return periods. Usually, modeling the urban flood flows in the urban drainage system and its outflow is conducted in one-dimensional (1D), two-dimensional (2D) or a combination of them, each has its own advantages and limitations. The 1D methods have been widely used for many years to simulate flow in urban drainage systems because they are relatively easy to adjust, calibrate and explain. However, these methods have limitations such as the inability to fully simulate the complex interaction between flow in the surface water harvesting network and runoff outside the network in the urban area (Seyoum et al., 2012). The 2D flow modeling techniques have made it possible to simulate the flood more accurately, determine the implementation site of the flood controlling and damage reducing measures and also to simultaneously model the flow inside the drainage network and corresponding outflow. Due to the complexities of modeling, the use of 2D models requires far higher computational time and costs than the 1D ones. This issue has made the use of 2D models difficult and sometimes unaffordable for large areas. 

Due to the simple adjustment, relatively easy calibration and high simulation speed in 1D models, as well as leading to good simulation results for the urban drainage network, one can use them to model the urban network flow and compensate the weakness in modeling the outflow through combining these models with a two-dimensional one. 

One of the practical open source 1D models of the urban drainage system is the SWMM simulation model. This model is capable of simulating different mechanisms of runoff production for single events or a sequential rainfall event in the urban areas (Zhang and Pan, 2014). The SWMM software uses a 1D flow routing model in an urban drainage network, which is a combination of pipes and open channels. When the hydraulic gradient line is above the ground level, the excess flow overflows and water is discharged from the node to the ground. In this case, the SWMM model is unable to simulate the behavior of the discharged overflow from the node and thus does not consider it in the simulation. This is one of the major limitations of this model. To overcome this limitation, a 2D flow simulation model can be used to model the outflow from the nodes. Due to the large size and complexity of urban topography, the use of conventional hydraulic models such as TRIM2D (Transient Inundation 2-Dimensional) (Casulli, 1990) and TUFLOW (BMT WBM Machinery Group, 2011) is difficult and very complex for simulating the overflow from the network and has its own complexities. (Schmidt et al., 2004). 

In order to overcome these limitations, the present study employs a quasi-2D CA-based model for the 2D hydraulic modeling. The CA approach, as a mathematical modeling tool, has been developed based on the cellular spaces (Chopard and Droz, 2005). Dottori and Todini (2011) developed an urban flood simulation model based on the CA approach and compared the obtained results with analytical solutions as well as some hydraulic models. They indicated the high capability of the proposed CA-based model in simulating the flooded areas in flood events. Liu and Pender (2013) presented a hydrodynamic model using CA approach in order to simulate the flood spreading in Carlisle, England. Their findings showed an agreement between the results of the proposed method and the measured data during flood events. Cirbus and Podhoranyi (2013) employed the CA method to simulate the complex process of water flow at the ground level. They introduced simple rules and conditions that affect the water movement, including the slope, infiltration and roughness as the inputs to the CA model. The obtained results showed that the CA method requires less computational time to model the flow than other ones, which use 2D flow motion equations. Using the CA theory, Jamali et al. (2019) modelled floods in urban areas and compared the results with those via 2D ones. This comparison illustrated that the proposed CA-based model results in higher flood wave speed than the 2D models. It has also been able to predict flooded area and flood depth with acceptable accuracy. 

Most of developed 2D models have only simulated the outflow from the rivers, flood channels or urban drainage network. However, they are not able to consider solutions in order to reduce the volume of flood outflow from the network. In the meantime, few investigations have addressed this issue such as the study conducted by Abbasizadeh et al. (2017). They proposed a quasi-2D model based on the CA theory. Connecting this model to the SWMM software, they were able to detect the nodes from which the water is outflowed, along with the hydrograph of the outflows and simulate those, which flow in two dimensions. This model is able to return the outflow from the node to the network in places where there is excess capacity. Tavakolifar et al. (2021) made some improvements in CA part of the model developed by Abbasizadeh et al. (2017) to improve the solutions stability. 

Among the shortcomings of flow simulation models in the studies conducted by Tavakolifar et al. (2021), Abbasizadeh et al. (2017) and Jamali et al. (2019), one can mention the inability of these models in modeling the effects of permeability of the study area at the flood volume and flow simulation. This makes these models not capable of modeling changes in the flow status and permeability amount of catchment due to the use of BMPs. 

BMPs are modern urban runoff management technologies, which aim to restore the natural conditions of the catchment being destructed through urban development. Perez-Pedini et al. (2005) and Karamouz and Nazif (2013) attempted to control the urban flood using methods based on the permeability. They extracted the optimal location and number of infiltration-based BMPs in order to reduce the maximum amount of flood in the urban catchment area using a hydrological model and genetic algorithm. Using three evolutionary multi-objective algorithms of NSGA-II, NSHS and MOPSO in combination with SWMM software, Yazdi et al. (2015) developed a method for presenting optimal designs in the buried storm water network. 

Various studies have been conducted on the BMP diversity and their influences on the urban runoff (Jia et al., 2013; Walsh et al., 2014; Moura et al., 2016 and Aminjavaheri and Nazif, 2018) all of which point out the ability of BMPs in reducing the flooding. In particular, the infiltration-based BMPs can be considered as an appropriate option for the urban floods due to the economic reasons and high land use density. Therefore, there is a need for a model capable of modeling the infiltrationbased BMPs through considering the effect of infiltration in flood simulation. 

However, due to very high uncertainties in the urban runoff management issues, in order to determine the effectiveness of a policy, the existing uncertainties in the response of the policy should be considered in its evaluation. For this purpose, an attempt has been made to consider these uncertainties and their associate risks in making decisions about the selection of appropriate BMPs. 

For this purpose, CVaR approach is employed here. The concept of CVaR has been examined as a potentially effective tool for combining the possible uncertainties in water resources management. 

This method was first proposed by Artzner et al. (1999) and developed by Anderson and Uryasev (1999) and Rockafellar and Uryasev (1999, 2002). Also, CVaR has been employed to measure and optimize the expected risk from severe damage with lower probabilities (high loss). CVaR metric has been widely used in financial problems (Filippi et al., 2017). However, its applications have so far been limited in the context of flood-related areas. CVaR has been used in reservoir operation issues in order to minimize the environmental damage due to declining water levels (Webby et al., 2007; Yazdi et al., 2015). Compared to the scenario analysis approaches, CVaR has been shown to provide more reasonable cost estimates and better control over high-risk losses in issues associated with the water resource management (Yamout et al., 2007). 

In the current study, in order to develop and improve the drainage system performance, a model is first developed for the simultaneous simulation of the drainage system and surface runoffs which its basis is taken from Tavakolifar et al. (2021). Tavakolifar et al. (2021) have not taken into account the infiltration effect in two dimensions. The present study develops a quasi-2D model capable of simulating the infiltration in the surface flow routing, which allows for the possibility of reducing flood damage through using different infiltration-based BMPs in the study area. In addition to the cost and damage, an important criterion for selecting the best flood management strategy is the amount of the associated risk. For this purpose and to choose the best strategy with the minimum expected risk, the CVaR method has been used. This different approach in selecting BMPs in urban areas, which has been addressed for the first time in the current study, helps decision makers with choosing the best scenario considering the risk of damages caused by different rainfalls.
section_name: Introduction

section_content: As mentioned earlier, a flood management model has been developed in the present research with the aim of reducing damage and costs using the concept of CVaR. The research has been conducted according to the following steps (Figure 1 ):

1. Determining the design rainfall with different return periods and its hyetograph 2. Developing a quasi-2D hybrid model considering the flow permeability in order to simulate the flow in drainage channels and also over the ground surface. This model simulates the flow in the urban drainage system (UDS), which leads to the determination of its flow characteristics and calculation of the hydrographs of the outflows from the manholes in the study area. This model is capable of modeling the network outflow in a quasi-2D manner along with specifying the flooding depth and range, taking the effect of infiltration into account.
section_name: Methodology

section_content: In this section, it is attempted to make a connection between the SWMM and the developed CAbased 2D models in order to develop a quasi-2D model for the urban runoff simulation. In the CA section, the infiltration modeling capability has been also considered. The structures of these models are described in the following.
section_name: 1D-quasi-2D urban flood simulation model considering the infiltration

section_content: Using SWMM model, the amount of runoff produced at the output point of each sub-catchment is calculated and considered as the urban drainage system (UDS) inlet flow. Then, the 1D flow routing is carried out in the UDS and flow characteristics such as flow depth and discharge rate are determined along the channels and pipes in different time steps. During the simulation, when the hydraulic gradient line is above the ground level, the hydrographs associated with the manhole outputs are determined based on the outflow (Seyoum et al., 2012). This excess flow causes flooding in the areas around the manhole, especially the downstream. 

The hydrographs of the manhole outflows, determined by SWMM simulation, are used as input data for the quasi-2D model. The quasi-2D model simulates the overflow of manholes that run through the streets of the catchment. During the flow simulation, when the surface flow reaches a node from which there is no outflow (manhole), part of it enters the system until reaching the full UDS capacity. The inlet flow hydrograph is then determined using the quasi-2D model. In this case, the UDS function is simulated again by means of SWMM. If the re-entry of surface flow into the UDS causes outflowing from the downstream manholes, the quasi-2D model will run again. This process continues until all the effects of these two flows are considered. In this research, the CA theory has been used to develop the quasi-2D model.
section_name: Urban runoff simulation in the 1D-quasi-2D model

section_content: CA is a mathematical model which uses only local rules instead of complex differential equations in order to model the behavior of physical systems. This approach uses simple neighborhood rules in the modeling process even for the complex systems. To simulate the surface flow (flood) behavior using CA, the study area is meshed using a square grid. Then, the water movement in each time step is simulated in the following order: 1) Identifying cells with considerable infiltration because of BMPs implementation and introducing the characteristics of infiltration equation to them. 

2) Determining the flow path in each cell by comparing the water level in the target cells and their neighbors. 

3) Calculating the volume of inflow to and outflow from each cell in both directions. 4) Calculating the amount of infiltration within the implementation area of infiltration-based BMPs and return water to the manhole. 5) Calculating the volume and depth of water in each cell in a time step using continuity equation and the flows obtained in the previous time step. 6) Continuing the process from step 2 to the end of the time steps. 

In this study, the equations proposed by Dottori and Todini (2010) have been used to calculate the flow between cells (Eq. ( 1 )). Since each cell is only affected by four neighboring cells in two directions, the governing equations are separately solved for each direction. In the developed scheme, the current state of the system depends on the previous time step, so the computational approach is explicit. After estimating the flow displacement between cells by Eq. ( 1 ), the change in water volume per cell is obtained from the following relationship

(2

where Vi is the volume of water inside the ith cell (m 3 ) and ∆ stands for the time step (s). 

In order to accurately model infiltration-based BMPs, it is necessary to simulate the amount of infiltrated flow in the surface flow simulations. In order to consider the infiltration in the development of the quasi-2D model, one can determine the amount of infiltration in each time step per cell and subtract from the volume of water inside the cell. Due to the widespread use in similar studies such as McClymont (2007) and Clemmens et al. (2003) and ease of estimating the coefficients, the Kostiakov equation was used here to estimate the infiltration as in Eq. (3).
section_name: Flow modeling process in the quasi-2D model based on CA theory

section_content: (3)

In the above equation, a (dimensionless) and k (m 3 /m/min) are the experimental parameters corresponding to the type of surface material. Since the amount of infiltration is cumulative, in order to obtain the infiltration value in each time step, the derivative of Eq. ( 3 ) must be obtained with respect to time. As a result, the infiltration rate in each time step is achieved as given by Eq. ( 4 ). 

z=k. a. t (a-1) (4)

Using Eq. ( 4 ) in each time step, the amount of infiltration in each cell is calculated and subtracted from the volume of water inside it while correcting the return flow to the manholes. Using Eqs. ( 5 ) and ( 6 ), the water volume and height in the cell are updated in each time step. 

∆ +∆ = ∆. ( ) + ( 2 ) + (5)

Here, ℎ is the water depth in the cell (m), dx and dy denote the mesh dimensions in the x and y directions (m), respectively, z is the water infiltration height in the cell (m) and O(Q 2 ) stands for the amount of water returning from the cell to the manhole.
section_name: 𝑍 = 𝑘𝑡 𝑎

section_content: The infiltration-based BMPs usually do not require free urban space and are less likely to affect the urban land uses. Therefore, they can be widely employed to reduce the effects of flooding and complete the urban drainage network. Another type of BMP which can be established inside the green marginal spaces along highways and does not require land possession is concrete reservoirs that are used as a BMP type. According to the above-mentioned points, in this study, the permeable asphalt, permeable pavement, vegetative Swale and local concrete reservoirs with low capacity have been used.
section_name: Identification of the BMPs used in the modeling

section_content: In general, the flood-induced damages can be divided into direct and indirect categories. The direct damages are caused because of inundation impacts on infrastructures and properties (Karbasi et al., 2019) while indirect damages occur after the direct ones and are considered as the negative effects of them. The flood management is generally performed on the direct damages that are tangible and according to the relationship between the two types of damages, if direct damages are reduced, the indirect ones are also reduced. For this reason, the direct damages have been evaluated in the current research. 

In this study, the corresponding diagrams presented in Joint Research Centre (JRC) technical reports have been used for developing depth-damage curves (Huizinga et al., 2017). In 2017, JRC presented a globally compatible database of flood depth-damage curves. This database includes the damage curves indicating the relative damages (%) as a function of water depth as well as the maximum amount of damage related to the various types of assets and land use classifications. The maximum amount of damage for each country has been specifically estimated according to the conditions of that country. For countries without these statistics, a fixed set of maximum flood damage values has been calculated using statistical regressions with global economic development indicators (Huizinga et al., 2017). For damage estimation, in the first step, the land use map is prepared in the geographic information system (GIS). In the next step, according to the depthdamage curve extracted from JRC technical reports, the amount of damage in each cell is determined corresponding to the type of specified land use and maximum water height. Finally, the damage to the whole area is estimated by aggregating the damages of each cell.
section_name: Damage estimation

section_content: Among the risk-based methods in the field of decision-making VaR and CVaR metrics are wellknown techniques based on measuring the damage to the system. Figure 3 depicts the VaR and CVaR descriptions using probability density function of system loss. VaR is the probable damage amount at 1-α confidence level. In addition, the value of CVaR is equal to the mean of damages greater than VaR at the determined confidence level. Assuming that f(x,y) is the damage function in terms of the decision variable x and random variable y and p(y) is the probability density function of y, the probability that f does not exceed a certain threshold α can be determined from Eq. ( 7 ). It should be noted that this probability for a constant value of x is the same as the distribution of losses (Rockafellar and Uryasev, 1999). 

According to the concept of CVaR, the lower the value of this measure, the lower the risk. In other words, the scenario having the lowest CVaR at the corresponding confidence level meets the most reliable performance and therefore can be selected as the best one.
section_name: Conditional value at risk (CVaR)

section_content: The developed hybrid model has been applied to select the best urban runoff management options in a case study located in Tehran, Iran. Tehran is located at longitude 51º 8ʹ-57º 37ʹ and latitude 35º

34ʹ-35º 50ʹ. The altitude of Tehran varies between 1850 m in the north and 1100 m in the south. 

Tehran is surrounded by Shahriar and Varamin plains from the south and Alborz Mountains from the north (Nazif, 2011). The study zone is located in the northwestern part of Tehran with an area of 1010 ha. This zone includes mountainous and urban areas. The drainage system of this area includes main and secondary channels, most of which are concrete. The common land use types in this area are residential, commercial, pedestrian, industrial, green and office spaces. The location of the study area on the map is shown in Figure 4 together with the drainage system layout. The study area is faced with the flooding problem in the case of heavy rainfall in some locations, which causes traffic slowness or road closures and damage to some urban infrastructure such as electricity network, sewage and telecommunications. The catchment zoning in the mountainous areas has been done according to the digital elevation model (DEM) data. In urban areas, the service sub-catchment of channels has been determined using layers of 1:1000 urban maps and pavements grading (Mahab, G., 2011). The hydrological characteristics of the sub-catchments have been estimated using land use layers and location of the channels in each of them (Mahab, G., 2011). Table 1 presents the specifications of the study area.
section_name: Case Study

section_name: Results and discussion

section_content: In order to evaluate the accuracy of the developed quasi-2D model, the simulation results of a case study conducted by Clemmens et al. (2003) have been used. Clemmens et al. (2003) developed a 2D flow model taking the infiltration into account using shallow unsteady flow equations and Kostiakov infiltration equations. They used field data obtained by Strelkoff et al. (2003) to control the accuracy of their model. The study area was a 2. 9-ha rectangular field with dimensions of 144*202. 5 m and a slope of 0% whose soil type is sandy loam. The water inlet is approximately at the midpoint of the northern edge side (202. 5 m). A road of 80 m length and 6 m wide extends into the ground from the southern edge. 

The water level has been measured at 26 locations within the catchment. The farm plan and measurement stations are exhibited in Figure 5. The field's surface roughness coefficient is equal to 0. 05 and the coefficients of Kostiakov infiltration equation for this field are reported by Clemmens et al. (2003) to be k=39 mm/ha and a=0. 37. The inlet water flow to the farm is also variable and is described in Table 2. According to the above-mentioned specifications, the flow modeling was carried out and the results are presented in Figures 6 and 7. Figure 6 3.
section_name: Validation of the developed quasi-2D model

section_content: In this research, in order to produce the precipitation with different return periods, the duration and hyetograph suggested in comprehensive plan of the surface waters management of Tehran ( 2011 ) has been used. The rainfall duration which causes the maximum flow in this region is the 6-hour precipitation (Mahab, G., 2011). Here, the precipitations with a return period of 5 to 200 years were used to generate the damage-probability function in order to increase the estimation accuracy of the CVaR value. The precipitation hyetographs for various return periods are given in Figure 8.
section_name: Design rainfall with different return periods

section_content: Considering the capabilities of the SWMM model, it is used for the rainfall-runoff simulation in this paper. The snowmelt, evaporation, groundwater, and water quality components are neglected in this study. The Soil Conservation Service (SCS) curve number method is used for estimating precipitation losses as suggested in previous studies in Iran (Moghadamnia et al. 2015). 

Regarding the slope of the study area which is approximately high, and as the conduits are open channel, there is no flow reversal and pressurized flow in the drainage system, so the kinematic wave method is used for flow routing (Rossman 2010). 

Table 2 presents the number of points in which overflowing from the network occurs along with the total outflow volume according to different rainfall return periods extracted from the SWMM model. The location of the outflow from the UDS for 10-and 100-year return periods is depicted in Figure 7. As would be observed, the number of overflowing points in the 100-year return period is more than twice the one corresponding to the 10-year period. In addition, as it can be seen in Table 4, the overflow volume from the total manholes has nearly quadrupled. The points from which the flow overflows are almost uniformly distributed over the study area, which can be seen
section_name: Flow simulation using developed 1D-Quasi-2D model

section_content: Due to the lack of space to implement various BMPs and high price of the land in the vicinity of Tehran, in cases where network performance needs to be improved, BMPs that do not need new space have been identified. In this study, the permeable pavement with permeable concrete surface, permeable asphalt, vegetative swale and small flood concrete reservoirs have been used, the cost of each is listed in Table 5.
section_name: Selecting possible BMPs

section_content: The outputs of the developed flood simulation model are the flooding sites along with the maximum occurred flooding depth. This information has been used to determine the implementation locations of the BMP scenarios and the corresponding area. In the study area, the surface water harvesting network has been designed for 50-year return periods and has been controlled for 100-year and 200-year ones. Therefore, the scenario design is performed based on the modeling results depicted in Figure 10. In the present study, each BMP implementation scenario only considers one type of BMP in order to better evaluate the performance of each BMP in each scenario. Thus, 5 different scenarios were specified, including: 1-Maintaining the current situation, 2-Using permeable asphalt which has a reservoir layer, with an area of 16 ha, 3-Using a permeable concrete layer which has a reservoir layer on pavements with an area of 4 ha, 4vegetative swale with an area of 2. 6 ha, 5-Using 4 concrete reservoirs of 1500 m 3 volume near to the manholes with a large volume of overflowing.
section_name: Implementation scenario of the BMPs

section_content: In order to estimate the damage, first, the urban land use maps are prepared in such a way to comply with the meshing used in the surface flow modelling. In the next step, using damage estimation functions extracted from JRC (2017), the amount of damage is estimated using the maximum flood depth and type of the land use assigned to the cell. The total damage is then estimated by aggregating the damage of all cells. This process has been separately performed in 5 scenarios for different rainfall return periods. The damage amounts are specified in Table 6 for different return periods and scenarios.
section_name: Damage estimation

section_content: To estimate the CVaR associated with each scenario, the amount of damage in each scenario is estimated in different return periods and added to the corresponding implementation cost. Table 6 lists each scenario's implementation cost and damage in each return period. Using information in Table 6, the damage and cost-probability curves are plotted in Figure 11 for different BMP implementation scenario. 

As shown in Figure 11, due to the zero cost in scenario 1, the damage and cost-probability curves meet the lowest total amounts of damage and cost in the 2-and 5-year return periods. However, increasing the return period, the damage increases with a much greater slope compared to other scenarios, so that in the return period of 10 years onwards, the damage and cost meet their maximum values. Due to the large initial implementation cost of scenario 2, its total cost and damage up to the 10-year return period are more than all scenarios. However, after that, the total damage and cost increase with a very small slope due to the high capacity of this scenario in reducing the flood volume which leads to a better performance for floods with larger return periods as a consequence. The other scenarios were found to have a function between scenarios 1 and 2. 

As can be seen, each of the scenarios has advantages in different probabilities of occurrence, so a criterion is needed to select the best scenario while comparing them. been calculated for each scenario. The calculated CVaR value for each scenario is given in Table 7 at the aforementioned confidence levels. As it is clear, scenario 3 has the lowest CVaR at all three confidence levels. To evaluate the overall performance of the scenario, the variation ranges of CVaR values are plotted in Figure 12 for different scenarios and confidence levels. As can be seen, the higher the damage reduction capacity in the scenarios, the smaller the CVaR variation ranges. In this regard, scenarios 2 and 3 had the best performances, respectively. Considering the implementation cost of the scenarios, scenario 3 has the lowest CVaR at the three confidence levels and can be generally selected as the best scenario.
section_name: Damage and cost-precipitation probability curves

section_content: In this research, the aim was to create a desirable flood management model in order to reduce damage and cost. To achieve these goals, the following steps have been taken. First, a 1D-quasi-2D model was developed to simulate the overflow and flow inside the drainage system considering the permeability. Then, according to the selected BMPs and the location and depth of flooding in the 50-year return period, the scenarios and their implementation sites were selected and controlled with 100-and 200-year periods. After this step, with the development of a damage estimation model, the amount of damage was estimated using the flood depth-damage function in different rainfall return periods and for different BMP implementation scenarios. According to the estimated implementation costs and damages associated with the scenarios, the cost and damage-probability functions were plotted for different scenarios. Finally, using cost and damage-probability diagrams, the value of CVaR was estimated at three different confidence levels. The quasi-2D CAbased modeling, in addition to increasing the computational speed, provides the researchers with the location and maximum depth of flooding and also enables them to consider the exact implementation site of the scenarios. It should be mentioned that the scenarios which use infiltration-based BMPs, cannot completely eliminate the damage due to the gradual impact of these BMPs types. However, if the BMPs implementation is properly located and covered, they can effectively reduce the damage. 

Another important aspect of this research is the examination of a new method in analyzing the damage and sustainability of different scenarios in urban floods. Due to the sensitivity of the CVaR concept to all probabilities of damage beyond the defined threshold, it can be considered as a reliable tool to help decision makers in choosing the superior scenario in the face of floods considering the two aspects of cost and damage. This concept plays an important role in choosing the best flood management approach. In this study, the CVaR values for permeable pavement were estimated as 2. 79, 3. 36 and 4. 6 million dollars at three confidence levels of 80, 90 and 95%, respectively. According to the definition of CVaR, the lower the CVaR value, the lower the risk of damage caused by the implementation of that approach. The present findings indicated that the permeable pavement provides the best performance for this region among other strategies.
section_name: Conclusion

section_content: Figure 1 The proposed ood management algorithm with the aim of reducing the damage and cost using the concept of CVaR

The use of von Neumann neighborhood method to connect the cells Figure 3 VaR and CVaR descriptions using damage probability density function (Rockafellar and Uryasev, 1999) Figure 4 Location of the study area and general outline of the surface water harvesting network along with subcatchments in the SWMM program

Layout for 2. 9 ha Field CVaR values at different con dence levels for various scenarios
section_name: Figures

section_content: criterion is needed to select the best scenario in terms of the performance. For this purpose, the 459 CVaR method has been used in this research and three confidence levels of 95, 90 and 80% have