An Integrated Framework to Evaluate Resilient

Water Resour Manage https://doi.org/10.1007/s11269-018-1960-2

An Integrated Framework to Evaluate Resilient-Sustainable Urban Drainage Management Plans Using a Combined-adaptive MCDM Technique Yaser Tahmasebi Birgani 1,2

& Farhad Yazdandoost

3

Received: 6 June 2017 / Accepted: 7 March 2018 # Springer Science+Business Media B.V., part of Springer Nature 2018

Abstract Due to the inevitability of urban flood in presence of the rainfalls exceeding design capacity of urban drainage system, resilience approach has been recently considered instead of the conventional urban drainage management. However, acceptance of resilience approach necessitates considering sustainability in the selection of urban drainage projects due to the various aspect of flood impacts. This paper presents a new integrated framework to show how urban drainage plans are resilient and sustainable. The framework consists of several indicators including technical, economic, social, environmental and planning aspects. On the other hand, the selection of suientropy of the probability distribution pi. In fact, entropy reduces the effect of plan among available suggested plans is complicated in presence of multiplicity of the indicators. A new combined-adaptive multi criteria decision making technique including combination of Adaptive analytical hierarchical process, Entropy and TOPSIS is here introduced to facilitate the decision making process as well as dealing with uncertainties due to the subjective experts’ preferences. Moreover, presented framework are applied on a part of urban drainage system of Tehran, Capital City. Four urban drainage plans are designed and suggested to be evaluated along with existing system in terms of their sustainability and resilience. The results shows the presented framework provide comprehensive information regarding the behavior of the urban drainage plans against urban floods as well as their sustainability for urban managers. In addition, presented framework facilitates and accelerate the complicated

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11269-0181960-2) contains supplementary material, which is available to authorized users.

* Yaser Tahmasebi Birgani [email protected]; [email protected]

1

Environmental Technologies Research Center, Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran

2

Department of Environmental Health Engineering, School of Health, Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran

3

Department of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran

Y. Tahmasebi Birgani, F. Yazdandoost

process of decision making. Therefore, it can be employed as comprehensive decision support tool for resilient and sustainable urban drainage management. Keywords Urban drainage management . Urban flood . Resilience . Sustainability . MCDM technique

1 Introduction It is now accepted that full protection of urban drainage systems (UDSs) against urban pluvial flood is impossible due to the rainfall uncertainty. Todays, there is a growing trends to find solutions to enhance resilience against urban floods (Djordjević et al. 2011; Siekmann and Siekmann 2015; Zevenbergen et al. 2008). On the other hand, multifaceted adverse impacts of urban stormwaters and floods on urban infrastructures and life of residents (Karamouz et al. 2010) have recently increased interest in the sustainable drainage systems as the solutions to reach more sustainable urban stormwater management (Roy et al. 2008; Stovin 2010; Zhou 2014). To recognize the effectiveness of these solutions to enhance sustainability and resilience, there is a need to measure these two concepts. However, this task is expressed as a significant challenge in various related literature (Cutter et al. 2008; Milman and Short 2008; Shen et al. 2011b; Zhou et al. 2010). The development and use of indicators is a common suggested way to promote and measure both sustainability and resilience concepts in urban water management (Ares and Serra 2008; Lhomme et al. 2013; Milman and Short 2008). Specifically, several studies have recently attempted to measure resilience via the quantifiable indicators considering the technical-economic (Birgani and Yazdandoost 2014), hydraulic (Mugume et al. 2015) and social-institutional (Birgani and Yazdandoost 2016) behavior of UDSs. Some studies have also been conducted to evaluate sustainability of UDSs considering treatment related (Balkema et al. 2002), service related (Belmeziti et al. 2015) and multi-dimension (Benzerra et al. 2012; Ellis et al. 2004; Martin et al. 2007) aspects of UDSs using set of indicators. Due to the necessity of building resilience in UDSs for promotion of long-term urban sustainability (Mugume et al. 2014) and of unpredictable change consideration for future sustainability (Ahern 2011), there is a need to integrate both sustainability and resilience concepts in urban drainage management. However, there is no study which deals with this issue in the area of urban drainage management yet. Therefore, this paper presents a new framework in urban drainage management using integration of sustainability and resilience indicators. On the other hand, it should be noted that the urban drainage plans range from the conventional UDSs to the best management practices (BMPs) with the aim of mitigating adverse impacts of urban stormwaters. The variety of these practices confront urban planners with a challenge of selecting these practices. This challenge will be further complicated in presence of multiplicity of resilience and sustainability indicators. This is a decision making problem and multi-criteria decision making (MCDM) is a suitable technique to deal with this complex problem (Fernández and Lutz 2010). Several studies have acknowledged that applying MCDM techniques are considerably effective facing with the decision making related challenge in water resources development and planning (Banihabib et al. 2017; Rousta and Araghinejad 2015; Weng et al. 2010). A new combined-adaptive MCDM technique including combination of new Adaptive-AHP (AAHP), Entropy and TOPSIS method is introduced to improve AHP technique in terms of decision making process time, preferences uncertainties and ranking.

An Integrated Framework to Evaluate Resilient-Sustainable Urban Drainage...

The novelty of the study is that several multifaceted sustainability indicators has been introduced and integration of these indicators with the resilience indicators has been evaluated using the new MCDM technique for a UDSs in Iran. The rest of the paper is organized as follows: section 2 gives an overview of the presented framework, section 3 introduces sustainability and resilience criteria for urban drainage management, section 4 presents the new MCDM method for BMP ranking, section 5 discusses the results of the presented framework for a case study and the conclusion is finally drawn in the last section.

2 Framework Overview The first step in this framework is to design different urban drainage alternatives among which the municipality managers may select the final plan. These alternatives may be conventional pipe or channels systems, BMPs, non-structural methods or combination of them. The next step is to simulate designed alternatives using suitable stormwater model under different return period rainfalls. Several stormwater management models, e.g. EPA SWMM, MUSIC, MOUSE and MIKE URBAN (explained in detail in (Elliott and Trowsdale 2007)), can be employed for the design and simulation process. Here, one of the most popular model, EPA SWMM (Rossman 2010) is used due to the simplicity and capability to model the most common BMPs. SWMM as a widely used hydraulichydrologic model is used to estimate flood volume and pollutant load as well. It is a dynamic rainfall-runoff simulation model which can support the computation of runoff quantity and quality associated with single-event and long-term simulations (Gironas et al. 2010; Rossman 2009). SWMM performs dynamic wave routing through solving 1D SaintVenant equations. SWMM is also capable of modelling hydrologic performance of some specific BMPs. Several indicators including qualitative and quantitative ones are then provided to quantify sustainability and resilience concepts considering different aspects. Quantitative indicators are computed by the results obtained from SWMM (flood volume, time of flooding; and pollutant load) and related equations (expected annual damage, etc.); and qualitative indicators are scored by related experts on scale ranging from 0 to 10. The output of this step is a decision matrix (DM) that indicates the values of indicators for designed urban drainage alternatives. Expert’s preferences regarding relative importance of the indicators are then provided for AAHP. The weights from AHP together with DM are then used for Entropy method to extract weights uncertainty. Eventually, DM and Entropy weights are used as inputs for TOPSIS method to prioritize urban drainage alternatives. Fig. 1 shows the hierarchy of the process of presented framework.

3 Sustainability-Resilience Indicators 3.1 Sustainability Indicators Since the late eighties, the concept of sustainable development has been promulgated among managers and planners as a guiding map, organizing principle and operational plan in order to meet human’s future needs while protect natural resources and ecosystems. Despite the different interpretations of sustainability in diverse disciplines, there is a consensus that sustainability must consider social, environmental and economic aspects (Balkema et al.

Y. Tahmasebi Birgani, F. Yazdandoost Urban drainage alternatives (e.g. BMPs, conventional system etc.) design

A AHP Sustainability indicators Decision Matrix

Experts’ opinions

Entropy

Resilience indicators

Stormwater management model (simulation for different rainfall return periods)

TOPSIS MCDM Techniques Selection of the final urban drainage plan

Fig. 1 Schematic of the presented framework

2002; Barbosa et al. 2012; Milman and Short 2008). The use of indicators termed here as Bsustainability indicators^ can effectively facilitate the evaluation of various practices to attain sustainable development in abovementioned aspects (Nation 2007; Shen et al. 2011a). Nevertheless, in the majority of urban drainage projects, the political preferences are the main factors to determine the development trajectory. For example, the construction cost is the highest (or even only) priority in selecting most of urban drainage plans in Iran. A holistic approach should then be adopted by relevant organizations. In this approach, technical and planning aspects should be considered in addition to the abovementioned aspects. This paper presents several indicators in different aspects as follows:

3.1.1 Indicators of Technical Aspects Typically, the UDS performance indicators such as peak flow rate and flood volume are considered to interpret technical aspects of an urban drainage plan. However, several important issues in this context are typically ignored. As an example, urban managers essentially needs to know how simple the old UDS can be connected to the newer UDSs in future planning. The indicator ease of connection (EC) is thus defined to understand whether selected urban drainage plans can be easily connected to the other UDSs. On the other hand, the simplicity of implementation of urban the drainage plans is one of the prime preferences of planners. Obviously, the difficulty of UDSs implementation results in the residents’ discontent and higher costs. Ease of implementation is the indicator to understand this issue. Furthermore, the operation lifetime of projects should be long enough to serve the expected long-term sustainable development objectives and to be cost-effective. It is clear that the long-term operation of UDSs necessitates upgrading and renewing the system. Indeed, the most preferred plans are those that are easy to be upgraded and renewed. This also help to the fast recovery once there is the dysfunctional performance in the UDSs under an extreme event occurrence. Table 1 shows details about the presented indicators.

3.1.2 Indicators of Economic Aspects One of the most important factors to select urban drainage plans such as BMPs is their construction and maintenance costs (Young et al. 2009). Economic considerations are inseparable elements in the decision making regarding projects selection. In Iran, there are many enthusiasts for considering construction cost as the most significant criterion of project assessment so that the plans with environmental justification are often rejected due to their

Environmental

Social

Runoff volume

Warning point

Ability of recovery Resistant point

Graduality Life style Residents’ welfare Beauty of urban landscape Expected annual response

Sustainability

Resilience

Sustainability

Resilience

Expected annual damage

Resistance capacity

Resilience Sustainability

Recovery duration Construction cost Maintenance and Operation cost Land ownership cost

Economic

Sustainability

Ease of implementation Ease of connection Ease of renewing Ease of maintenance Lifetime Multi-functionality

Technical

Categories

Indicators

Criteria How simple to implement UDSs How simple to connect to the other UDSs How simple to update UDSs The time that the UDS works well How simple to maintain UDSs The urban drainage plan has other functionality such as entertainment usage, etc. The flood subsidence time The construction costs of urban drainage plan The maintenance and operation costs of urban drainage plan The costs that urban authority should pay to purchase a land from individuals or other organizations The average of expected flood damage due to different rainfall return periods The maximum rainfall that the UDS system can tolerate without flood damage The rate of increase in damage against rainfall depth Improve residents’ life style To create recreation and entertainment for resident To beautify landscape of the city The average of expected social response due to different return period rainfall The ability of the city to recover from pluvial flood the maximum rainfall at which the the social response in flooded area is equal to zero The rainfall that would result in further disorder in flooded area due to domination of response over the recovery ability. The amount of recovery or response in WP(x) The runoff volume at the urban watershed outlet

Definition

Table 1 Sustainability and resilience indicators for urban drainage management

% mm of the rainfall mm of the rainfall

% CMS

+

+/− –

% (L/M/H) (L/M/H) (L/M/H) % + +

+ + + + –

mm of rainfall

mRials/year

– +

% Rials Rials (L/M/H)

(L/M/H) (L/M/H) (L/M/H) (L/M/H) (L/M/H) (L/M/H)

Unit

+ – – –

+ + + + + +

Type (+/−)

WP(y) RV

WP(x)

AR RSP

G LS RW BUL EARP

RSC

EAD

RD CC MO LC

EI EC ER LT EM MF

Abbreviation


Planning

Criteria

Compliance with managers’ policies Compliance with sustainable development goals Residents’ acceptability Development outlook Simplicity of training

Pollutant loads

Indicators

Table 1 (continued)

Sustainability

Categories

Implementation of plans comply with sustainable development goals The implementation of plans satisfy residents Implementation of plans result in positive outlook How simple to train stakeholders and personnel in various plans

The amount of pollutant loads discharged to the receiving water Implementation of plans comply with managers’ policies

Definition

(L/M/H) (L/M/H) (L/M/H) (L/M/H)

+ + + +

(L/M/H)

Kg

– +

Unit

Type (+/−)

RA DO ST

CSD

CMP

PL

Abbreviation



high cost. BMPs are such urban drainage plans which have high land ownership, construction and maintenance and operation costs. Economic indicators are defined in Table 1.

3.1.3 Indicators of Social Aspects Integrated sustainable approach explores measures to improve social conditions in the face of rainfalls and to maintain social service in an accepted level (Ellis et al. 2004). BMPs may provide potential for enjoying stormwater. The question arises, to what extent BMPs can help to improve individuals’ life style. For example, employing Green roof and detention pond may lead to use stored rainwater for non-drinking activities. This may lead to modify consumption patterns in long time or to create places for residents’ recreation. Finally, aesthetic benefits arise out of implementing BMPs in urban areas. The three social indicators are then given in Table 1 as sustainability indicators.

3.1.4 Indicators of Environmental Aspects Stormwater quality protection and enhancement is an essential objective in drainage planning. However, this has been sacrificed for economic considerations in conventional single objective urban drainage management. Two main water quality objectives are considered in this paper as environmental related criteria: pollutant loads and runoff volume. Pollutant loads emphasizes the amount of different pollutant loads discharged to the receiving water. Runoff volume reduction accentuates pollutant loading and peak flow reduction on one hand and movement towards natural hydraulic regime on the other hand.

3.1.5 Indicators of Planning Aspects For integrated urban drainage management, decision making should be accomplished considering all the stakeholders in urban areas. A factor to be considered in planning for selection of the urban drainage plans is whether implementation of plans complies with managers’ policies or not. In addition, an urban drainage plan should comply with sustainable development policies and goals and it should be useful to achieve these goals. Furthermore, the residents’ acceptability plays a prominent role in planning level of the urban drainage management. This varies depending on cultural context, income, education, etc. in a region. In the planning phase, it is crucial to determine whether a positive outlook can be expected with the implementation of development plans. The indicator Bdevelopment outlook^ is then introduced to qualitatively evaluate plans in this context. Another essential factor for preliminary planning is the amount of knowledge about urban drainage plans among personnel, managers and residents. All the stakeholders and personnel involved in planning and implementing stages should be then trained in the type of urban drainage plans.

3.2 Resilience Indicators Since resilience concept has been first defined by Holling (1973), several studies have attempted to quantify resilience via indicators in numerous disciplines such as sustainability sciences and flood management. However, few studies have investigated indicators


to quantify urban drainage management resilience. Birgani and Yazdandoost (2014) and (2016) introduced a set of indicators to quantify resilience for urban drainage risk management systems considering technical, social, institutional and economic aspects. These indicators and their values has been used in this paper. These indicators focuses on how urban flooded area respond to and recover from pluvial flood due to the extreme rainfalls.

4 Combined-adaptive MCDM 4.1 Adaptive AHP (AAHP) Analytical hierarchical process (AHP) is one of the most common MCDM technique in UDS management (Benzerra et al. 2012; Dong et al. 2008; Young et al. 2011; Young et al. 2009). In AHP process, however, determination of consistent pairwise comparison matrix (PCM) is time-consuming among numerous decision indicators. Lin et al. (2008) proposed AAHP using binary Genetic algorithm (GA). Motivated from Lin et al. (2008)'s work, this paper also proposes AAHP using real GA to facilitate the construction of consistent PCM. Typical AHP is performed by solving the following equation as an eigenvalue problem: ðA−λmax I Þw ¼ 0

ð1Þ

where, A is a PCM based on experts’ judgments, λmax is the largest eigenvalue of matrix A, I is identity matrix and w is the weight vector of criteria. Whilst, an ideal consistent PCM conforms to the following equation: 0 0 ð2Þ A −nI w ¼ 0 in which, A′ is an ideal consistent PCM, n is the size of square PCM, and w′ is the criteria weight vector. Comparing Eq. (1) and (2), it is clear that λmax should equal n for the construction of fully consistent PCM. However, this is not completely achieved due to the inconsistency of experts’ judgments. Therefore, λmax − n can be considered as a measure of inconsistency of PCMs in realistic situations. Obviously, it is highly preferred that this measure approaches to zero in the PCM construction process, although this is time-consuming. This is a minimization optimization problem and real GA is applied to solve the problem automatically and to reduce the time of PCM construction in following steps: Step 1. Coding variable to generate population. Initially, there is a need to generate a set of chromosomes as depicted in Fig. 2. Each chromosome contains a set of genes indicating the elements above the main diagonal of PCM. Obviously, each element of the lower triangular of PCM is the inverse of its corresponding symmetrical element in the upper triangular of PCM. 2 Since the number of elements of upper triangle of n × n -PCM are n 2−n, therefore each chromosome contains n 2−n genes. Step 2. objective function. As mentioned earlier, consistency is one of the key characteristics of PCM. Therefore, objective function should be established in a way that the optimization 2


problem find a consistent matrix as a solution. λmax − n was just interpreted as a suitable measure whether a PCM is consistent or not. However, the consistency is not sufficient alone to find PCM. Because GA only find a consistent PCM generated by random number without consideration of decision maker’s preferences. Therefore there is a need to incorporate the decision makers’ preferences into the optimization process. In doing so, a PCM is constructed by decision makers, regardless of its consistency. Optimization process should then find a consistent matrix which its elements are highly similar to those of the primary matrix constructed by decision makers. This paper proposes the following equation to measure the amounts of similarities between two matrices obtained by the optimization algorithm and the decision makers: f ¼

jjOPCM:=PCM jj þ jjOPCM:=PCM jj rffiffiffiffiffiffiffiffiffiffi 1 n2 −n 2 2

ð3Þ

in which, PCM and OPCM are the pairwise comparison matrices obtained by decision makers and optimization algorithm respectively. For use in eq. (3), PCM and OPCM should be transformed in vector form in conformity with chromosomepattern depicted in Fig. 2. Clearly, if two matrices are exactly similar, f equals zero. Since the goal of the optimization problem here is minimization, therefore objective function are defined as follows: min F ¼ λmax −n þ f ¼

jjPCM :=OPCM jj þ jjOPCM:=PCM jj rffiffiffiffiffiffiffiffiffiffi 1 n2 −n 2 2

ð4Þ

The optimized PCM obtained from optimization is employed in AHP to achieve weight vector of the criteria.

1

⋯ 1

⋮

⋮

1 1

Fig. 2 Chromosome coding pattern to generate population to construct PCM


4.2 Entropy method Entropy is a technique for selection of effective evaluation criteria based on their subjective and objective weights (Malekian and Azarnivand 2016). Entropy in theory of information is considered as a measure of uncertainty of a discrete probability distribution pi described as in eq. (5) (shannon and Weaver 1947): S ðp1 ; p2 ; …; pn Þ ¼ −k:∑nj¼1 p j :ln p j

ð5Þ

where, k is a positive number and S(p) is entropy of the probability distribution pi. In fact, entropy reduces the effect of criteria weights which are not influential in decision making process as following steps: Step 1. given D = [Xij] as decision matrix, the value of j-th criterion is determined as a probability pij using equation below: pij ¼

X ij ; ∀i; j ∑m i¼1 X ij

ð6Þ

in which, Xij is value of j-th criterion for i-th alternative. Step 2. entropy Ej is calculated as a set of values of j-th criterion for m alternatives: E j ¼ −k:∑m i¼1 pij :ln pij ; ∀i; j

ð7Þ

where the constant k (k = 1/ ln m) ensures that Ej remains between 0 and 1. Step 3. diversification degree implying uncertainty is calculated for each j-th criterion as: d j ¼ 1−E j ; ∀ j

ð8Þ

Step 4. the final weight of j-th criterion is calculated based on following equations:

w0 j ¼

L j :w j ; ∀j ∑nj¼1 L j :w j

ð9Þ

dj ; ∀j ∑nj¼1 d j

ð10Þ

wj ¼

where wj is the weight of j-th criterion without consideration of experts’ preferences and Lj is the vector of decision makers’ preferences (here is the weight vector obtained from AAHP).

4.3 TOPSIS method TOPSIS is a technique to prioritize alternatives based on distance to positive ideal solution and maximum distance to negative ideal solution. The following six steps should be employed to prioritize alternatives for a given decision matrix D = [Xij]:


Step 1. the normalized decision matrix (R = [rij]) is constructed to provide dimensionless indicator in order to enable comparing different indicators: X ij rij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ∑m i¼1 X ij

ð11Þ

Step 2. The weighted normalized decision matrix is constructed as follows: V ij ¼ w j rij ; j∈1; …n

ð12Þ

Where wj is the decision makers’ preference vector (here is the weight vector obtained from entropy method). Step 3. Positive ideal solution and negative ideal solution are identified using eq. (13) and (14):

n max 0 min Aþ ¼ v1 þ ; v2 þ ; …; v j þ ; …; vn þ ¼ v j∈ J ji ¼ 1; 2; …; m vij j∈ J ; i ij i

ð13Þ

n min 0 max A− ¼ v1 − ; v2 − ; …; v j − ; …; vn − ¼ v j∈J ji ¼ 1; 2; …; m vij j∈ J ; i ij i

ð14Þ

where the sets J and J′ are associated with benefit and cost criteria respectively. Step 4. the Euclidean distance of each alternatives from positive ideal and negative ideal solution are calculated using eq. (15) and (16) respectively: Siþ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ∑nj¼1 vij −v j þ

; ði ¼ 1; 2; …; mÞ

ð15Þ

Si− ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ∑nj¼1 vij −v j −

; ði ¼ 1; 2; …; mÞ

ð16Þ

Step 5. Relative closeness of alternative Ai to positive ideal solution A+ is calculated as follows: Si− þ ; 0 < c < 1; i ¼ 1; 2; …; m ð17Þ ci þ ¼ i ðS i þ þ S i − Þ Obviously, ci+ approach to 1 for an alternative which is the closer to positive ideal solution and farther from negative ideal solution. Step 6. Alternatives are sorted in a descending order with respect to their ci+. The first alternative in this ranking is selected as a final plan.

5 Applying the Framework for a Case Study 5.1 Study Area This paper applies presented framework to a real case study in 22nd municipality district in the north west of Tehran City in Iran surrounded by Alborz Mountains from the north and Azadi


Stadium and Karaj Highway. This 72-ha study area is located in longitude 35°44′38′′N and latitude 51°15′45′′E. In recent years, this area has been experienced rapid urbanization. Much of the area has been taken up by residential land use (about 70%) and commercial, administrative (18%) and the rest of land use is assigned for green spaces (12%). Since wide part of the area is covered by impervious surface, high amount of runoff and flood are hence expected. A conventional concrete channel network is responsible to transport runoff to the Kan River (Fig. 3).

5.2 Urban Drainage Plans (UDPs) This paper aims at ranking several UDPs suggested by Birgani and Yazdandoost (2014) for the study area. These plans includes conventional channel (CE) enlargement as well as three BMPs including green roof (GF), pervious pavement (PP) and detention pond (DP). In addition, the existing channelized UDS (ES) are considered as a plan to compare with other suggested plans. Later plan implies that no conventional system or BMPs are added to the existing system to improve its performance.

5.3 Quantifying Indicators SWMM was run for 2, 5 10, 20, 50 and 100-year return period rainfalls to calculated corresponding resilience indicators due to the different UDPs. Flood volume and time of flooding in the channel junctions are used to calculate RD. Flood depth are used to calculate

Fig. 3 The location of 22nd municipal District of Tehran and study area


EAD and G. The place of the flooded area and their land use and traffic characteristics are determined using geographic information system fuzzy inference system to calculate EARP, AR, WP(x) and WP(y). Cumulative rainfall depth which UDSs can tolerate without any reaction are then considered to determine RSC and RSP. Sustainability indicators are divided into two groups including quantitative and qualitative. All qualitative indicators are scored on a scale ranging from 0 to 10 by respective experts and data bases. The most effective UDPs in satisfying the respective indicators is scored 10 and zero is assigned to the less effective UDPs. Construction and maintenance and operation (M&O) costs are computed by the relationship given in supplementary data 1 (gathered from (Brown and Schueler 1997; Young 2006) and adapted for present time using following equation: PC ¼ Pð1 þ iÞn

ð18Þ

where, PC is the presents day cost, P is the BMP costs ($) originally reported in the study, i is discount rate and n is difference between present year and the year that project would be constructed. In this paper, total suspended solids (TSS) and runoff volume computed by SWMM are considered as the indicators PL and RV. The values of indicators for suggested UDPs has been given in the supplementary data 2. This table are considered as a decision matrix for presented MCDM technique.

5.4 Computing Weights by AAHP Supplementary data 3 illustrate the hierarchal structure of decision problem. The first level is the selection of sustainable-resilient UDP as a goal. The second level is the four main criteria presented in this paper and the third level is corresponding indicators given in Table 1. Two groups of experts are involved in this study. One tends to consider environmental aspect weights as the first priority while the other tends to consider economic aspect as the most important aspect. The weights of criteria and indicators obtained from AAHP has been given in Table 2. The results show the environmental and social criteria are in higher priority for the group with environmental preferences (0.414 and 0.307), and economic and technical criteria are more significant for the other group (0.43 and 0.29). These results agrees with the experts’ judgment and shows that AAHP works well to take experts’ preferences into account. It should be noted that AAHP calculates the weights in a short time while the weighting process by conventional AHP lasts longer time without guarantee to yield consistent PCMs. As an example, the PCM and OPCM for the indicators of social aspects are given in the supplementary data 4. As shown in supplementary 4, consistency of the OPCM is 0.049 while PCM is inconsistent at all. Minimized f is obtained 1.6 after 1000 iteration of GA algorithm which indicate the acceptable similarity with experts’ preferences.

5.5 Applying Entropy Entropy technique was applied on the decision matrix and the weights of criteria using Eq. (5) to Eq. (10). The weights obtained from Entropy have been given in Table 3. For convenience comparison, the AAHP and Entropy weights have been graphically compared in Fig. 4. As shown in this figure, the values of AAHP weights are changed after applying Entropy technique. These changes are considerable for some indicators. For example, the values of

Y. Tahmasebi Birgani, F. Yazdandoost Table 2 The weights of criteria and indicators obtained from AAHP Criteria and indicators

Weights of criteria and indicators Environmental priority Criteria (second level)

Technical EI EC ER LT EM MF RD Economic RSC EAD G CC MO LC Social RSP EARP AR WP(x) WP(y) RW BUL LS Planning CMP CSP RA DO ST Environmental PL RV

Economic priority Indicators (third level)

0.135

Criteria (second level)

Indicators (third level)

0.29 0.041 0.004 0.005 0.053 0.006 0.007 0.018

0.049

0.088 0.008 0.01 0.115 0.014 0.016 0.038 0.43

0.002 0.021 0.003 0.014 0.004 0.006 0.307

0.014 0.18 0.03 0.122 0.033 0.053 0.15

0.008 0.094 0.114 0.006 0.015 0.023 0.016 0.03 0.094

0.004 0.046 0.056 0.003 0.007 0.011 0.008 0.015 0.04

0.046 0.014 0.008 0.022 0.003 0.414

0.018 0.005 0.003 0.008 0.001 0.09

0.21 0.21

0.045 0.045

indicators PL and RV are equal in AAHP method while these values have changed to 0.37 and 0.046 respectively (Fig. 4(a)). The value of CC obtained from AAHP is 0.014 while it has been increased to 0.165 due to the applying Entropy (Fig. 4(a)). For economic priority, as shown in Fig. 4(b), Entropy technique considerably increases EAD, CC and MO; and decreases most of the other indicators compared with AAHP. This is attributed to the values diversity of these indicators (refer to the supplementary data 2).

5.6 Applying TOPSIS for Ranking TOPSIS techniques has been applied to the decision matrix given in Table 3 and the weights obtained from Entropy technique. The plans ranking are listed in Table 4. For socioenvironmental priority, PP is the first plan which can be used in the study area to satisfy


Table 3 The weights of indicators obtained from Entropy technique

Indicators

Technical EI EC ER LT EM MF RD Economic RSC EAD G CC MO LC Social RSP EARP AR WP(x) WP(y) RW BUL LS Planning CMP CSP RA DO ST Environmental PL RV

Weights Socio-Environmental priority

Economic priority

0.013 0.002 0.002 0.024 0.003 0.01 0.005

0.0102 0.0014 0.0016 0.02 0.003 0.01 0.004

0.0002 0.07 0.0003 0.165 0.027 0.005

0.006 0.23 0.0008 0.54 0.088 0.016

0.003 0.037 0.016 0.0003 0.0001 0.039 0.026 0.043

0.0005 0.007 0.003 0.00006 0.00002 0.007 0.005 0.008

0.031 0.019 0.014 0.022 0.004

0.004 0.003 0.002 0.003 0.0005

0.37 0.046

0.03 0.004

sustainability and resilience indicators. GF, DP, ES and CE are in the next ranks, respectively. On the other hand, CE is the first plan in the economic priority. DP, PP, ES and GF are ranked accordingly. Additionally, for better understanding the effects of Entropy on final decision, AAHP weights are directly used in TOPSIS without consideration of Entropy. As shown in Table 4, the rank of ES have changed to 5 instead of CE for socio-environmental priority. This implies that with consideration of Entropy, there is no justification for implementation of CE from the socio-environmental view point. While CE is preferred to ES once Entropy is ignored. For economic priority, the ranks of most of plans have changed once Entropy is ignored. For example, the ranks of GF and ES are 5 and 4 respectively in presence of Entropy. While ignorance of Entropy results in change in GF and ES ranks. This implies that with consideration of Entropy, GF is not preferred due to its cost. While the rank 4 of GF in AAHPTOPSIS technique indicates that the effect of cost is rather ignored in decision making. It accordingly seems that PP and DP plans have more stable rank orders than the others. Therefore these two plans are suggested to be implemented in our case study based on the presented framework.

Y. Tahmasebi Birgani, F. Yazdandoost 0.4 adaptive AHP

Entropy

0.35 0.3

Weights

0.25 0.2 0.15 0.1 0.05

PL RV

CMP CSP RA DO ST

RSP EARP AR WP(x) WP(y) RW BUL LS

RSC EAD G CC MO LC

EI EC ER LT EM MF RD

0

Indicators

(a) 0.6 Adaptive AHP

Entropy

0.5

Weights

0.4

0.3

0.2

0.1

PL RV

CMP CSP RA DO ST

RSP EARP AR WP(x) WP(y) RW BUL LS

RSC EAD G CC MO LC

EI EC ER LT EM MF RD

0

Indicators

(b) Fig. 4 Comparison AAHP and Entropy weights, (a) Socio-Environmental priority, (b) Economic priority

Table 4 The ranks of UDPs due to applying the presented framework Plans

Rank Socio-Environmental Priority

ES GF PP DP CE

Economic Priority

AAHP-Entropy-TOPSIS

AAHP-TOPSIS

AAHP-Entropy-TOPSIS

AAHP-TOPSIS

4 2 1 3 5

5 2 1 3 4

4 5 3 2 1

5 4 2 3 1


6 Summary and Conclusion Due to the rainfall uncertainties, pluvial urban floods occurrence cannot be absolutely avoided in presence of the rainfall exceeding UDSs design capacity. Resilience approach has been increasingly promulgated among urban planners for urban flood management. On the other hand, multifaceted adverse impact of pluvial urban flood necessitate the implementation of the methods such as BMPs to achieve sustainability. However, quantifying the resilience and sustainability in order to understand to what extent the different UDPs are suitable in resilientsustainable urban drainage management are still challenging. Therefore, this paper presented an indicator and MCDM-based framework to select UDPs with respect to their resilience and sustainability. In addition to the several indicators to quantify resilience and sustainability considering different technical, economic, environmental and social aspects, this paper accentuated the planning aspect with introducing five indicators. These indicators were qualitative and quantitative. Qualitative indicators were scored by experts on scale ranging from 0 to 10 and the quantitative indicators were measured using given equations and software. Furthermore, due to the multiplicity of presented indicators and UDPs, a combined MCDM method were presented including combination of AAHP, Entropy and TOPSIS. GA-based AAHP were developed to accelerate the weighing process based on experts’ preferences considering consistency criterion. Furthermore, Entropy were considered to be connected with AAHP to deal with weights uncertainties via accentuating the role of effective criteria in decision making. Finally, TOPSIS suitably ranked different UDPs based on the obtained weights. Presented framework was then applied on a part of 22nd municipal district of Tehran, Capital of Iran as a case study. Some urban drainage plans were designed and suggested to be added to the existing system. Two separate groups of stakeholder with socio-environmental and technical-economic preferences were asked to involve in decision making process. It was demonstrated that applying the AAHP can impressively reduce the time of PCM construction while it satisfies the consistency criteria. It was also demonstrated that Entropy technique can amplify the role of criteria which their values are significantly different for various UDPs. Although based on stakeholders’ preferences and presented MCDM technique, PP and DP were interpreted as suggested plans for the case study, however the other MCDM techniques may suggest the other UDPs. Furthermore, the nature of multifaceted resilient-sustainable urban drainage management necessitates considering more aspects of sustainability and resilience. It is thus suggested to investigate incorporation of more criteria and indicators, and the presented framework.

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