Using AHP-PROMOTHEE for Selection of Best Low-Impact Development Designs for Urban Flood Mitigation

This work first studies the effects of several Low Impact development methods on urban flood control. The Analytic Hierarchy Process-Preference Ranking Organization Method for Enrichment Evaluation (AHP-PROMETHEE) combination method is then used to select the best design. A drainage system in Golestan town of Semnan under a 5-year return period is investigated as the case study. The LID methods are selected based on the region's conditions and facilities. Then Rain Barrel (RB), Permeable Pavement (PP), and Infiltration Trench (IT) were considered as LID methods. The RB, PP, IT, IT-PP, IT-RB, PP-RB, and IT-PP-RB are considered the best LID usage scenarios. Four analytical ranking criteria, implementation cost, hydraulic performance, environmental impact during implementation, and ease of implementation, are chosen for the ranking procedure. Also, the weight of these criteria was obtained using Analytic Hierarchy Process (AHP). Finally, after determining the weight criteria, the LID designs are ranked using the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method. The results of hydraulic studies demonstrate the effectiveness of the PP-RB scenario with an average reduction of 90% of peak discharge and an average reduction of 80% of total flood volume. It is also observed that the weakest performance is related to the IT scenario, with an average decrease of 60% of peak flow and 47% of total flow volume. AHP-PROMETHEE analysis showed that the simultaneous use of RB and IT with a coverage percentage of 5% and a cost of $ 57,710 reduced the total volume by 51.54% and the peak discharge by 48.8% compared to the results of the current system. According to AHP-PROMETHEE, IT-RB-5 is the best project proposed among the 70 projects studied. This study showed that the AHP-PROMETHEE method is a practical method for choosing from several LID schemes for flood control.

characteristics of these methods to make them more effective in controlling floods and peak discharges. The first goal of using LID in urban environments is to prevent floods by reducing possible runoff with a specified return period (Park et al. 2013). Mathematical models can determine the type of LID and its location, especially when there is a limited budget for urban flood management (Prez-Pedini et al. 2005). These models can be more effective in clarification of LID use (Elliott and Trowsdale 2007).
The main idea is to use the LID method to control runoff and reduce pollution on site (Hamel and Tan 2022). LID types include bio-retention cells, rain gardens, green roofs, rain barrels, infiltration trenches, permeable pavements, roof separation, and green swale (Hoang and Fenner 2016). One of the complexities while using LID methods is optimizing the space allocated to them and their implementation costs (Martin-Mikle et al. 2015;Geng and Sharpley 2019). The purpose of implementing the LID-BMPs is to flood reduction to create the natural hydrology of the urban basin as much as possible (Dadrasajirlou 2021). However, the optimization of LIDs will be commensurate with their performance by considering criteria such as effectiveness in reducing the quantity of flood volume, improving the quality of urban runoff, physical constraints of the area, implementation costs, and even social factors. Therefore, prioritizing the implementation of proposed LID designs has certain complexities and requires multi-criteria selection methods to select the best design. However, using multi-criteria selection methods for LID selection are rarely used in a few studies (Chen et al. 2015;Zou et al. 2015;Efta and Chung 2014). For example, safari et al. selected and prioritized the necessary water resources for irrigation of Buin Zahra urban green basin of Qazvin province in Iran using the AHP-PROMETHEE method (safari et al. 2020).

Multi-Criteria Decision Making
Water basin management is essential for managing and controlling water resources in any region (Sriyana et al. 2020). One of the most understandable systems designed for decisionmaking is AHP which can examine different forms of a problem. These processes involve various decision options, making analyzing the sensitivity of criteria and sub-criteria in these methods straightforward (Ahmadi et al. 2020). The AHP method is a structured method developed based on psychology and mathematics. AHP is used to design and interpret criteria that are generally contradictory. Thomas L. Saaty developed this method in the 1970s. AHP is widely used in studying various scientific disciplines worldwide because it covers a broad and diverse range of decision-making conditions (Thungngern et al. 2015). Another study uses the AHP method to select the most suitable place to store water for use in times of drought (Ahmad and Verma 2018).
Several water resources management studies use the AHP-PROMETHEE technique. For instance, in 2019, Karleusa et al. (2019) used the AHP-PROMETHEE technique to rank suitable neighborhoods in Slovakia for agricultural irrigation projects using three environmental, social, and economic criteria. Finally, they introduced five areas with good potential for implementing irrigation projects (Karleusa et al. 2019). Also, in a study conducted by Tscheikner-Gratl et al. in 2017, it was found that the AHP-PROMETHEE method compared to other multi-criteria decision-making methods, showed better results in selecting the location of wells in urban areas (Tscheikner-Gratl et al. 2017). However, reviewing previous studies indicates insufficient research on the quantitative and qualitative management of urban floods using LID-BMPs to control and reduce urban floods. Latifi et al. (2019) used the game theory model to optimize 1 3 urban flood management. They finally used the PROMETHEE method by identifying the Pareto optimal front to find the best-proposed options for LID methods. They concluded that this method allows decision-makers to make decisions with a more realistic approach to urban flood control (Latifi et al. 2019). Using SWMM and the PRO-METHEE method, Babaei et al. prioritized urban sub-basins by considering the peak flood discharge (Babaei et al. 2018). Using the AHP method and considering different selection criteria in their research, Fuamba et al. and Young et al. sought to select the BMP methods by evaluating the performance in several ways. Sometimes consulting with experts to quantify the criteria for decision criteria can be complex (Fuamba et al. 2011;Young et al. 2010). To rank the performance of BMPs, Jia et al. provide a two-tier index that operates by calculating a cumulative number. However, how to weigh the criteria is not clearly stated (Jia et al. 2013). Martin et al. used the ELEC-TRE III method to weigh the requirements for the stakeholders to select LID methods. However, they used the same weights in cases where the importance of policymakers was similar (Martin et al. 2007). Chitsaz and Banihabib used combined weight selection and ranking methods in their study (Chitsaz and Banihabib 2015). They evaluated eight different multi-criteria ways to select the best technique for flood control.
In the majority of previous studies, the ranking was done only by using LIDs individually. Different LID methods' performances suggest that combined LID methods can be more robust than individual LID methods. Therefore, studies on the performance of composite LIDs in flood control will be quite important.
The primary goal of this study is first to model the drainage system of the study area under rainfall with a return period of 5 years in SWMM software. The innovation in this article is that usually the designs related to flood control systems require the selection of many scenarios or multiple criteria, and usually the designs are based on economic criteria. In this research, the hierarchical method and parametric method are combined so that by using these two, the designers can easily understand which criteria should be used to design the drainage system. The proposed method is a practical method that can readily find important criteria through a survey and then use it to determine the weight of these criteria. Also, the use of low-impact development methods in this method has not been done so far, and this research showed that the proposed method can be effective and practical in projects that include low-impact development methods. Figure 1 shows the process of this study.
In short, this research, using low-impact development methods, investigates their effectiveness in flood control in urban areas. But the approach used in this research is completely practical and should be used as a design method in choosing the type of low-impact development methods, their percentage of use, and the criteria considered by the designer.

Materials and Methods
This section introduces the study area, simulation method, Low-Impact Development (LID) methods and how to choose them, rainfall intensity-duration-frequency (IDF) curves, Analytic Hierarchy Process (AHP) method, and preference ranking organization method for enrichment evaluation (PROMETHEE) method.

Study Area
This study's area is part of Golestan town of Semnan city located in Semnan province in Iran. Semnan province is located in the south of the Alborz Mountains, which caused a large part of this province to have a desert nature. Semnan province is between the longitude of 53° 23ʹ to 53°26ʹ east and the latitude of 35°33ʹ to 35°35ʹ north. The Golestan town is located northwest of Semnan city with an area of about 2.86 Km 2 . The maximum and minimum elevations of the area are 1243.73 and 1175 m, respectively.

SWMM
EPA-SWMM software is an open-source dynamic model for rainfall-runoff simulation, known for urban flood management, planning, analysis, and design of surface water collection networks. This model was first introduced in 1971 by the US Environmental Protection Agency. This software has a simple working environment and high power in simulating quantitative and qualitative models. The equations used in SWMM are the mass conservation equation and the momentum equation, which are known as the Saint-Vanant equations (Eqs. (1) and (2)).   In the above relations, A (m 2 ) is the area of the cross-section of the flow, Q (m 3 /s) is the flow rate, y (m) is the water depth, Sf is the energy line slope, So is the slope of the conduit, g (m 2 /s) is the acceleration of gravity, x (m) and t (min) are spatial and temporal variables, respectively.
By solving Eqs. (1) and (2), SWMM simulates three methods of steady flow routing, kinematic wave routing, and dynamic wave routing. Steady flow routing is the simplest type of routing, which assumes uniform and stable hydrograph flow, and transmits the input current to the output.
Steady flow routing can not model waterway storage, water return effects, inlet and outlet losses, reverse flow, and pressure in conduits. Also, it is not sensitive to time steps and is only suitable for initial analysis and long-term continuous flow simulation. The kinematic wave routing solves the mass conservation equation and the momentum equation's simple form. In solving this equation, the slope of the water surface is considered equal to the slope of the conduit floor.
Dynamic wave routing solves one-dimensional Saint-Venant equations completely without any simplification. Unlike the previous two methods, dynamic wave routing simulates the storage of waterways, the amount of water return, the energy losses at the inlet and outlet of the conduit, and the reverse flow. The present study uses the dynamic wave routing method to simulate rainfall runoff at 1-min intervals.
This study uses Horton's equation to model water infiltration in soil. Horton's equation (Eq. (3)) is as follows: where F t : penetration at time t in millimeters per hour, F c : final penetration intensity in millimeters per hour, F 0 : Initial penetration intensity in millimeters per hour, and k is Horton constant, which depends on land use and soil type.

Low-Impact Development
Two critical issues in using these methods are determining the appropriate places for their construction and the area covered by them according to different criteria. The location of these techniques affects the peak flow rate and flow volume, and their structure in inappropriate sites can contribute to the poor performance of the existing flood collection system. Numerous studies tried to develop standards for the optimal selection of LID-BMPs. For example (Clean Water Services 2009; UACDA (University of Arkansas Community Design Center) 2010; County of Los Angeles Department of Public Works 2014; County of Mendocino 2018) suggested that for slopes between 1 to 5 percent, different types of permeable pavement showed good performance. Also, infiltration trenches are suitable in areas with less than 15% slope, while the area's pitch is ineffective in selecting rain barrels. By studying various LIDs, (Caraco and Claytor 1997) stated that the barrel of rain in cold and mountainous areas has very low effectiveness. Also, the distance of groundwater to Using AHP PROMOTHEE for Selection of Best Low Impact Development… -the permeable pavement and infiltration trench should be more than 1 m and between 2 to 4 feet, respectively. California storm water quality association (2003) and South Burlington storm water utility (2009) suggested that using infiltration trenches and permeable pavement in soils with a minimum penetration intensity of 38.1 mm / h showed considerable effects. Based on previous studies on LID selection, the present research selects  Figure 4 shows examples of rain barrels, permeable pavement, and infiltration trench, respectively. Estimating the cost of construction of these scenarios was proposed considering the area, LID volume, and quality included in the model.

Intensity-Duration-Frequency (IDF) Curve
Some studies show that the choice of storm event return period is essential in designing LID dimensions (Guo and Adams 1998;Baek et al. 2015). Figure 5 (http:// www. semna nweat her. ir/) provides the IDF curve of the Semnan synoptic station within a 2 to 100 years return period. This study takes a 5-years return period to simulate the runoff (Baek et al. 2015).  Rainfall intensity for Semnan station with a return period of 5 years is 10.04 mm per hour. Figure 6 represents the cumulative rainfall over the 5-year return period and concentration time of the catchment. Saaty LT (1990) stated the four principles of inversion, homogeneity, dependence, and expectations as the principles of AHP (Neshat and Pradhan 2015). Saaty used numbers 1 to 9 to compare the pairs of criteria. The number 1 indicates the same importance of the criteria, and the number 9 indicates the importance of the criteria under consideration compared to other criteria. For each pairwise comparison matrix, an acceptable degree of incompatibility is defined as the inconsistency rate (Eq. (5)). Saaty presented the number 0.1 as an acceptable limit and believed that if the degree of inconsistency (Eq. (4)) gets greater than 0.1, it is better to reconsider the judgments. The evaluation criteria for ranking in the present study are implementation cost, hydraulic performance, environmental impact during implementation, and ease of implementation, which can be seen in Fig. 7.

AHP
At first, using a questionnaire, the opinions of ten hydraulic and water experts about decision-making criteria were collected. The four final criteria were shown by involving ten experts in completing the pairwise comparison matrix. By using the geometric mean (Eq. (6)), EXPERT CHOICE (EC) software calculated the final weight of each criterion. The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x 1 , x 2 , …, x n , the geometric mean is defined as: where … Table 3 shows the results obtained from the above operation. The final sensitivity analysis in the weighting process should be less than 0.1 to consider the weighting process correct. The sensitivity analysis of the final weights is equal to 0.07, indicating the operation's accuracy.

PROMETHEE
Burns developed the PROMETHEE method as a ranking method in multi-criteria analysis in 1982. Each criterion is examined based on a separate function without relation to other criteria. Using different scales to measure criteria is a strength of this method. However, this technique does not provide a way to assign weights to criteria (Marcharis et al. 2004), which eliminates this weakness with the AHP technique. Therefore, their combined use is a functional complement to overlap each other's weaknesses. Proponents of this approach proposed six preference functions (Table 4) to decision-makers. The correct choice of these functions depends on the decision-makers understanding the relationship between criteria and options (Brans et al. 1998).
After performing pairwise comparisons and selecting one of the appropriate functions for the function, the final ranking of the two options is obtained by adding the priority of all indicators, which is called the total value and is represented by Eq. (7).
In the above relation, w j (j = 1, 2, 3… n) represents the normalized weights of each index. The value of π (a, b) varies between zero and one, and the higher this value, the higher the priority of option a over b will be. Finally, the ranking process is obtained after calculating π (a, b) for each option a ∈ A and considering the other options x ∈ A. Equation (8) calculates the positive rating current or output current. Equation (9) calculates the negative rating current or input current.
Using AHP PROMOTHEE for Selection of Best Low Impact Development… -- where Φ + (a) indicates the strength of option a, and Φ − (a) indicates the weakness of option a. Each current can generate a complete ranking in A. The largest value of Φ + (a) represents the best a, and the largest value of Φ − (a) represents the worst a (Chitsaz and Banihabib 2015). Finally, the best option can be determined by calculating the net current, which is obtained from Eq. (10) (Martin et al. 2007): Now, the options can be compared with each other and the best option can be selected.

Calibration and Validation of SWMM
Since the information was not available for Golestan town, the model was calibrated and validated with the peak flow obtained from the SWMM, compared with the peak flow calculated from the logical relation (Eq. (12)) in each of the sub-catchment. This strategy was adopted from the land use and all sub-catchments area. Considering that each sub-catchment was composed of different land uses, the size of all different parts of each sub-catchment was calculated using AutoCAD software. Table 5 shows the results of these calculations. Table 6 shows the runoff coefficients of each sub-catchment according to the land use of that sub-catchment. Each sub-catchment runoff coefficient was calculated using relative weight averaging (Eq. (11)).
where C i is the value of the runoff coefficient related to the area A i of each sub-catchment. After calculating the value of C for each sub-catchment using the logical formula (Eq. (12)), the peak flow rate in each sub-catchment was calculated: where Q stands for maximum peak discharge (m 3 /s), C is the runoff coefficient, i is rainfall intensity (mm/hr), and A is the area of the catchment (km 2 ). To compare the peak discharge calculated from the logical formula with the peak discharge calculated by SWMM software, the coefficient of determination (R 2 ) (Eq. (13)

LID Scenarios
The seven scenarios include three individual scenarios, three pair scenarios, and one general scenario. A general rule for all scenarios is that each has ten different designs. This difference is in terms of the level of coverage that each LID occupies from each Linear with indifference sub-basin. Table 7 shows how to name the plans. The maximum flood volume and runoff for the outfall point were considered model outputs. Figure 9 is a schematic view of the runoff collection system in Golestan town. The initial modeling results indicate the phenomenon of flooding in one of the nodes. The simulation results of the drainage system before using LID methods in the study area include the total volume of the flow and the Runoff peak. These results showed that the hydraulic outcomes in the outfall node (O 1 ) are 3.446*10 6 L and 0.559 m 3 /s for the total volume of the flow of and Runoff peak, respectively, while the numbers in the flooded node (J 18 ) are 1.281*10 6 L and 0.569 m 3 /s.

Scenarios 1, 2, 3
The simulation results showed that the rain barrel had an excellent ability to reduce the volume of floods and peak discharges which can be seen in Fig. 10a. It also shows that the hydraulic outputs of RB plans are not much different. It is evident in the resultsthat the RB-10 plan reduced peak discharge and flood volume by 74.5% and 79%, while the RB-100 plan reduced the peak discharge and flood volume by 79.5% and 83%.  Paired composition 10 IT-PP-Usage percentage 5 Paired composition 10 IT-RB-Usage percentage* 6 Paired composition 10 PP-RB-Usage percentage 7 Paired composition 10 IT-PP-RB-Usage percentage Fig. 9 Schematic of the runoff collection system To simulate the system performance in scenario 2, AutoCAD calculated that the area of sidewalks in Golestan town has 112,500 square meters. The required values for the Pavement section in SWMM software were selected according to the research study of Teymouri et al. (2020). Figure 10b shows that by increasing the percentage of LID in scenario 2, flood volume gradually reduced. On the other hand, the plans of scenario 2 showed a similar performance in peak flow control. According to Fig. 10c, the IT scenario shows poorer performance than the PP and RB scenarios. Figure 15 compares the output hydrograph in 100% and 10% LID cases in scenarios 1, 2, and 3.

Scenarios 4, 5, 6
This section presents the results of combined LID methods. According to the simulation results, IT-PP scenario showed an appropriate and acceptable performance in controlling runoff which is shown in Fig. 11a. The flood volume reduction in the IT-PP scenario indicates that this combination's effectiveness on urban runoff in the study area overcomes the hydraulic performance of IT and PP individual plans. Simultaneous use of RB and PP also showed acceptable results in flood control. According to Fig. 11b, increasing the percentage  Figure 11c shows the results of PP-RB scenario. Also, PP-RB scenario shows the highest effectiveness in flood mitigation. This means that this scenario is suitable for flood control, but the cost factor in this section is the most effective in choosing the best plan.

Scenario 7
This scenario examines the performance of using all three LIDs in different plans. The results show that this scenario effectively reduces the flood's volume and peak discharge. This effect increases with increasing the coverage percentage of each LID. Figure 12 shows the hydraulic performance of the plans for this scenario. According to Fig. 12, this method performs well in reducing flood volume and discharge peak. But it is important to note that increasing the coverage percentage of LIDs and consequently increasing the costs does not significantly improve the hydraulic performance of the designs. Therefore, in this scenario, the implementation cost significantly impacts choosing the best plan. As shown in Fig. 13a, it can be seen that using 100% LID hydrographs has significantly reduced the output of the drainage system. However, to select the best design, it is necessary to review all procedures in terms of selection criteria. Figure 13b compares hydrographs in the output node while considering each paired scenario's lowest and highest LID coverage. According to Fig. 13b, the PP-RB-50 shows the highest effectiveness in flood mitigation by recording a peak discharge close to zero. The PP-RB-5 plan performs well, with a peak discharge of 0.12 (m 3 /s). These results show that PP-RB scenario manages the whole flood, and almost at the outfall node, we do not see any severe phenomenon in terms of discharge. According to Fig. 13c, by increasing the all LID coverage the flood reduction will increase.

Average Effects of Scenarios
This section examines the effectiveness of each scenario in terms of cost of implementation, flood volume and peak discharge reduction. For this purpose, the arithmetic mean for the performance of the plans of each scenario is calculated. Figure 14a shows the comparison mode between the seven scenarios in peak discharge. It is evident that the PP-RB scenario shows the lowest peak discharge at the output point while RB, IT-RB, and IT-PP-RB scenarios are in the following ranks, respectively. Figure 14b has the same explanation as Fig. 14a, except that this figure represents the total volume of the runoff. Figure 14c, d show the average peak discharge and flood volume reduction percentage in seven scenarios, respectively. According to these two figures, the PP-RB scenario showed the best hydraulic performance by recording an average 90% reduction in peak discharge and 80% in flood volume. At the same time, the weakest results are obtained in the IT scenario, with an average decrease of approximately 60% in peak discharge and 40% in flood volume. Regarding cost criteria, the highest implementation cost is for the RB scenario, which is around $ 600,000.

Selecting Five Best Plans Using AHP-PROMETHEE
The AHP-PROMETHEE conducted the ranking process. After finding the weights from the AHP method, the plans were ranked by visual PROMETHEE according to the introduced criteria. Table 8 shows the required characteristics of each criterion to perform the ranking process. It should be noted that the implementation environmental criteria and ease of implementation are qualitative, and information about them is included using the five-point method in visual PROMETHEE software. Table 9 also shows the statistical parameters of the analyzes performed.   Table 10 shows the top 5 rankings among the proposed designs. According to the results of this table, the IT-RB-5 plan was able to reduce flood volume by 51%, peak discharge by 49% and record a cost of $57,710, being the best option among all proposed projects.
Investigating Figs. 15 and 16, although the following top rankings were able to reduce the flood volume and the peak performance better than the top rank (IT-RB-5), considering the cost, these plans are more expensive than the top ranking.

Conclusion
The aim of the present study was to investigate the performance of low-impact development methods in reducing the runoff of Golestan city, located in Semnan, Iran. This article also investigated the multi-criteria AHP-PROMTHEE rating method in studies related to providing flood mitigation plans. The obtained results evidently indicated that low-impact development methods can reduce the flood volume and also reduce the peak flow of the flood. Also, the proposed method of AHP-PROMTHEE for ranking and selecting the best plan shows the efficiency of this method. Rain Barrel, Permeable Pavement, and Infiltration Trenches are Low Impact Development methods of this study. Permeable Pavement-Rain Barrel scenario showed the best results in terms of flood volume and peak discharge reduction by 80% and 90% reduction respectively. The Infiltration Trench scenario showed the weakest performance among with an average 60% reduction in peak discharge and a 40% reduction in total flood volume. Implementation cost, hydraulic performance, environmental impact during implementation, and ease of implementation were considered ranking criteria. The weights of decision criteria were determined using the Analytic Hierarchy Process method. Sensitivity analysis was performed using EXPERT CHOICE software which was equal to 0.07. Then, plans got raked using the Preference Ranking Organization Method for Enrichment Evaluation method and specifying the preference functions for each criterion, The results show the superiority of the Infiltration Trench-Rain Barrel-5 plan for 57,710 $, the reduction of flood volume by 51.54 percent, and reduction of peak discharge by 48.8 percent.

Conflicts of Interest
The authors declare no conflict of interest.